Advances in Electronics and Electron Physics, Volume 37

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 37 CONTRIBUTORS TO THISVOLUME K. M. Adams E. F. A. Deprettere Br...

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 37

CONTRIBUTORS TO THISVOLUME K. M. Adams E. F. A. Deprettere Bruce D. McCombe Kohzoh Masuda Susumu Namba J. 0. Voorman Robert J. Wagner P. K. Weimer

Advances in

Electronics and Electron Physics EDITEDBY L. MARTON Smithsonian Institution, Washington, D.C. Assistant Editor CLAIRE MARTON

EDITORIAL BOARD E. R. Piore T. E. Allibone M. Ponte H. B. G. Casimir W. G. Dow A. Rose L. P. Smith A. 0. C. Nier F. K. Willenbrock

VOLUME 37

1975

ACADEMIC PRESS

New York San Francisco London

A Subsidiary of Harcourt Brace Jovanovich, Publishers

COPYRIGHT 0 1975, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART O F THIS PUBLICATION MAY B E REPRODUCED OR TRANSMITTED I N ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION I N WRITING FROM T H E PUBLISHER.

ACADEMIC PRESS, INC.

111 Fifth Avenue, New York, New York 10003

United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road. London N W l

LIBRARY OF CONGRESS CATALOG CARD NUMBER:49-7504 ISBN 0-1 2-014537 -5 PRINTED I N T H E UNITED STATES OF AMERICA

CONTENTS CONTRIBUTORS TO VOLUME37 .

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vii

FOREWORD.

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ix

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Intraband Magneto-Optical Studies of Semiconductors in the Far Infrared. I I. I1. I11. IV .

BRUCED. MCCOMBE AND Introduction . . . . . . . Theoretical Background . . . . Experimental Techniques . . . Free Carrier Resonances . . . . . . . . . . References

ROBERT J . WAGNER . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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i 2 17 28 75

The Gyrator in Electronic Systems K . M . ADAMS. E . F. A . DEPRETTERE, A N D J . 0. VOORMAN I . Introduction . . . . . . . . . . I1 . Reciprocity in Physical Systems . . . . I11. The Gyrator as Network Element . . . . IV . Filters . . . . . . . . . . . . V. Principles of Realization of the Gyrator . . VI . Basic Electronic Design . . . . . . . VII . Basic Gyrator Measurements . . . . . VIII . Trends in Gyrator Design and Applications . IX . Conclusion . . . . . . . . . . . . . . . . . . . . References

. . . . . . . . . .

. . . . . . 80 . . . . . . 80 . . . . . . 86 . . . . . . 94 . . . . . . 109 . . . . . . 128 . . . . . . 145 . . . . . . 170 . . . . . . 176 . . . . . . 177

Image Sensors for Solid State Cameras P. K . WEIMER I. I1 . 111. IV . V. VI . VII . VIII . IX . X. XI . XI1 .

Introduction . . . . . . . . . . . . . . Photoelements for Self-scanned Sensors . . . . . . Principles of Multiplexed Scanning in Image Sensors . . Early XY Image Sensors . . . . . . . . . . Multiplexed Photodiode Arrays . . . . . . . . Principles of Scanning by Charge Transfer . . . . . Charge-Transfer Sensors Employing Bucket Brigade Registers Characteristics of Charge-Coupled Devices (CCDs) . . . Experimental Charge-Coupled Image Sensors . . . . Performance Limitations of Charge-Coupled Sensors . . Charge-Transfer Sensors as Analog Signal Processors . . Self-scanned Sensors for Color Cameras . . . . . .

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182 183 187 193 198 202 208 213 225 . 236 . 247 . 251

vi

CONTENTS

XI11 . Peripheral Circuits for Solid State Sensors . . . . . . . . 253 XIV . Conclusions . . . . . . . . . . . . . . . . . 257 References . . . . . . . . . . . . . . . . . 259 Ion Implantation in Semiconductors

SUSUMU NAMBA A N D KOHZOHMASLDA I. I1. I11. I V. V. VI .

Introduction . . . . . . . . Concentration Profiles of Implanted Ions Enhanced Diffusion . . . . . . Annealing and Electrical Properties . Measurement Technique . . . . Devices . . . . . . . . . . . . . . . . . References

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and Defects . . . .

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264 271

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2x9 299 . 310 . 325 . 328

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ALTHOR

INDEX .

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331

SC RJtCT

INDEX

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339

CONTRIBUTORS TO VOLUME 37 Numbers in parentheses indicate the pages on which the authors’ contributions begin

K. M. ADAMS(79), Department of Electrical Engineering, Delft University of Technology, Delft, Netherlands E. F. A. DEPRETTERE (79), Department of Electrical Engineering, Delft University of Technology, Delft, Netherlands BRUCED. MCCOMBE (11 Naval Research Laboratory, Washington, D.C.

KOHZOHMASUDA(263), Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan SUSUMUNAMBA(263), Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan J. 0.VOORMAN(79), Philips Research Laboratories, N. V. Philips’ Gloeilampenfabrieken, Eindhoven, Netherlands

ROBERTJ. WAGNER(1), Naval Research Laboratory, Washington, D.C. P. K. WEIMER (181), RCA Laboratories, Princeton, New Jersey

vii

This Page Intentionally Left Blank

FOREWORD

Our present volume starts with the first part of a review by B. D. McCombe and R. J. Wagner on “Intraband Magneto-Optical Studies of Semiconductors in the Far Infrared.” In a much broader survey of farinfrared radiation, Professor L. C. Robinson* confines magneto-optical effects in semiconductors necessarily to barely three pages. In their review, McCombe and Wagner offer an in-depth treatment of this important subject leading to a better knowledge of intraband transitions. A potentially very important device is discussed by K. M. Adams, E. F. A. Deprettere, and J. 0. Voorman in their review of “The Gyrator in Electronics Systems.” They point out that the electronic gyrator, as it now exists, is limited in industrial applications for several reasons. Nevertheless the subject is important enough for a thorough treatment and the reviewers’ presentation will, no doubt, stimulate thinking toward improved solutions. An entirely new trend in image pick-up and reproduction is the subject of P. K. Weimer’s review. Under the title “Image Sensors for Solid State Cameras,” he discusses the new devices more from a research viewpoint “with much greater emphasis on principles of operation, than on details of construction.” The five-year-old discovery of charge coupling has produced a tremendous growth of new devices, which shall be covered soon in a separate monograph presented as a supplement to this series. Weimer’s review is a detailed treatment of one aspect of this growing field. The technology of “doping” semiconductors has progressed considerably since the early days. A very interesting technique, permitting rather precise introduction of impurities, is discussed by S. Namba and K. Masuda in their article on “Ion Implantation in Semiconductors.” The method, which started as a laboratory operation, developed into an important industrial one, allowing large-scale production of semiconductor devices. Many important and interesting reviews are scheduled to appear in future volumes. The list on the next page indicates the contents of the volumes to come.

* L. C. Robinson, “Physical Principles of Far-Infrared Radiation,” Meth. Exp. Phys. (L. Marton and C. Marton, eds.), Vol. 10. Academic Press, New York, 1973. ix

x

FOREWORD

lntraband Magneto-Optical Studies of Semiconductors in the Far Infrared. 11 The Future Possibilities for Neural Control Charged Pigment Xerography The Impact o f Solid Statc Microwave Devices: A Preliminary Technology Assessment Signal and Noise Parameters of Microwave FET Advances in Molecular Beam Lasers Interpretation of Electron Microscope linagcs of Defects in Crystals Development of Charge Control Concept Energy Distribution of Electrons Emitted by a Thermionic Cathode Time Measurements on Radiation Detector Signals The Excitation and Ionization of Ions by Electron Impact Nonlinear Electron Acoustic Waves. 11 The Photovoltaic Effect Semiconductor Micro8ar.e Power Devices. 1 and IT Experimental Studies of Acoustic Waves in Plasmas Auger Electron Spectroscopy 11) S i r i r Electron Microscopy of Thin Films Afterglow Phenomena in Rare Gas Plasmas Between 0 and 300 K Physics and Tcchnologies of Polycrystaliine Si i n Semiconductor Devices Charged Particles as a Tool for Surface Research Electron Micrograph Analysis by Optical Transforms Electron Beam Microanalysis Electron Polarization in Solids X - R a j Imagc Intensifiers Eiectron Bombardment Semiconductor De\ ices Thermistors High Power Electronic Devices Atomic Photoelectron Spectroscopy Electron Spectroscopy for Chemical Analysis Laboratory Isotope Separators and Their Applications Recent Advances in Electron Bcam Addressed Memories Supplementary Volume: Charge Transfer De\ ices

B. D. McCombe and R. J. Wagner K . Pi-ank and F. T. Hanibrccht F. W. Schmidlin and M. E. Scharfe J . Frey and R. Bowers R. A. Haus, R. Pucel, and H. Statz D. C. Lame M. J. Whelan J. te Winkel W. Franzen and J . Porter S. Cova John W. Hoopcr and R. K. Fecney

R. G. Fowler Joseph J. Loferski S. Teszner and J. L. Teszner J. L. Hirschfield and J. M. Buzzi N. C. MacDonald and P. W. Palmberg A. Barna. P. B. Barna. J . P. Pbcia, and I. Pozsgai J. F. Delpech J. Kobayashi J . Vennik G. Donelli and L. Paoletti D. R. Beaman M. Canipagna, D. T. Pierce. K. Sattler, and H. C. Siegmann J. Houston D. .I.Bates G. H. Jonker G. Karady S. T. Manson D. Berenyi S. B. Karmohapatro J. Kelly C. H. Sequin and M. F. Tompsett

Throughout the years we have enjoyed the wholehearted cooperation of many friends. O u r warmest thanks go to them for the help they gave us. We would like to invite, as in the past. comments on the published volumes and suggestions for future ones. L. MAKTON CLAIRE MARTON

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 37


Intraband Magneto-Optical Studies of Semiconductors in the Far Infrared. I BRUCE D. McCOMBE

AND

ROBERT J. WAGNER

N a d Research Luhorutory, Washingrun, D.C.

I. Introduction.. ........................................................................................... 11. Theoretical Background.. ............................................................................ A. Optical Properties ....................... ............... B. Quantum Theory of Free Electrons in a Magnetic Field .............................. C. Electron in a Periodic Pote : The Effective Mass Approximation ............... 111. Experimental Techniques ..... ................................................................ A. Sources and Spectrometers ..................................................................... B. Methods of Detection ........................................................................... IV. Free Carrier Resonances ........................................................................... A. Electron Cyclotron Resonance ..... ..................... ................ B. Spin-Flip Resonances ........................................................................... C. Hole Cyclotron Resonance ..................................................................... References.. ..............................................................................................

1 2 3 6 11

17 17 25

28 28 42 55 15

I. INTRODUCTION The experimental and theoretical determination of the electronic structure of semiconductors has been of considerable interest for a number of years. Optical and magneto-optical studies have proved extremely valuable in such investigations. The optical experiments divide naturally into two categories according to whether the transitions involve quantum states in only a single energy band, intraband transitions, or states in two bands, interband transitions. Due to the nature of the energy bands, effective masses, etc. and available magnetic fields, this natural division also carries over to the spectral region in which the two types of transitions are observed; interband transitions occur in the near infrared through the ultraviolet while intraband transitions occur typically in the far infrared (FIR) or microwave region. Although interband optical and magneto-optical measurements have provided a great deal of useful information (I, Z), intraband magneto-optical studies provide more detailed and precise information concerning effective masses and g-factors of both electrons and holes, impurity I

2

BRUCE D. MCCOMBE A N D ROBERT J. W A G N E R

states, and interactions among the single particle states and collective excitations such as phonons and plasmons. In recent years significant advances in FIR instrumentation have made possible the detailed investigation of a wealth of intraband phenomena with an attendant increase in information and understanding of the quantum electron (or hole) states and their interactions. This rapid evolution and expansion in knowledge indicates the need for an up-to-date in-depth review of this field.* On the one hand, it is important to understand what has been accomplished and what remains poorly understood; on the other hand, the rapid proliferation of experimental data has led to the publication of some misleading and/or erroneous results. In this article we present a review of the recent developments in intraband magneto-optics of semiconductors with emphasis on the above points. In order to achieve these aims it is necessary to ignore for the most part other useful experimental approaches and also similar studies of other material types, e.g. metals and insulators. In addition, we have made a number of subjective judgments concerning the material to be included and the method of presentation. For example, classical magnetoplasma effects are not discussed since these studies have been extensively reviewed by Palik and Furdyna (5). Finally, although the title delineates a rather precise spectral region (the FIR is usually defined to be between 50 and 1000 pm), in the interest of clarity and cohesiveness we have overstepped these spectral boundaries in several instances. The rationale for these judgments will be apparent in the discussion of experimental results. This review will be divided into two parts. The first part, presented here, treats both theoretical and experimental investigations of free carrier magneto-optical transitions in semiconductors. In addition, a brief section on experimental techniques is included in this part. Part 11, to be published in the next issue of this series, will discuss bound carrier magneto-optical studies and the interactions of both bound and free carriers with collective excitations, e.g. phonons and plasmons.

BACKGROUND 11. THEORETICAL In order to obtain information about the electronic states of semiconductors, one must be able to relate the macroscopic information provided by experiments, e.g. the sample transmission or reflection versus magnetic field, to the microscopic states and optical transition probabilities of the charged particles under investigation. In this section we present a brief description of * F o r a review of early, primarily microwave, intraband studies, the reader is relerred to Lax and Mavroides ( 3 ) . A recent review of magneto-optical experiments in general by Mavroides ( 4 ) has some information concerning the subject of this present work.

INTRABAND MAGNETO-OPTICAL STUDIES OF SEMICONDUCTORS. I

3

the macroscopic optical properties of solids, proceeding from Maxwell’s equations, and we then show how these are related to the microscopic energy levels, wavefunctions, and transition probabilities. We also present a quantum mechanical discussion of the motion of a nonrelativistic electron in the presence of a uniform external magnetic field. This discussion is initially confined to free electrons, and then the necessary generalization to include the effects of the periodic array of ions in a crystalline solid is sketched. The nature of the energy levels and the selection rules for electromagnetic (EM) transitions (cyclotron resonance and spin resonance) are discussed in some detail. This provides a sound basis for the examination of the various experiments and the extensions of theory necessary to include the effects of impurities, more complicated energy bands, and the interactions of electrons (or holes) with other elementary excitations (e.g. phonons and plasmons) in semiconduct ors. A . Optical Properties

For a continuous isotropic medium characterized by a real conductivity, and a real dielectric constant, c R ,the following wave equation is obtained from Maxwell’s equations in unrationalized Gaussian units :

(T,

Here E‘ is the electric field vector of the EM radiation, c is the velocity of light in free space, and the magnetic permeability has been set equal to unity since only nonmagnetic or weakly magnetic materials are considered. In an anisotropic medium or in the presence of a magnetic field the tensor character of (T or cR serves to couple the different vector field components. However, for the purposes of exposition and in the interest of simpler notation it is sufficient to consider the isotropic case where (T and cR may be viewed as scalars. The equations are easily generalized when the tensor character must be made manifest. For propagation in the z-direction a solution of Eq. (1) for transverse waves is given by E’ = Eb exp i(mt - K z ) where

Here K is the complex propagation wavevector, o is the angular frequency, and u is the phase velocity of the wave in the medium.

4

BRUCE D. MCCOMBE A N D ROBERT J. WAGNER

A complex refractive index may be defined by ti

- iti' = cKJcu,

(3)

where K2

-

2 1 ~= ~ '471010.

/('2 -F ~ :

It is frequently desirable to describe the optical properties in terms of a complex dielectric function, E = eR + iE, defined by I-: = (ti

-

(4)

iK')2

with

c,

=

(5)

21t-h-'.

With these relationships the electric field of the wave may be written

E' = Eb exp ( - W K ' Z / C ) exp iw(t - t i z / c ) ; hence the amplitude of the wave is attenuated exponentially with an attenuation constant o t i ' / c . Experimentally the quantity of interest is the attenuation of power or intensity rather than amplitude. The ratio of the intensity, 1, at a distance z to the initial intensity 1, is I/l,

=

exp ( - 2 w t i ' z / c )

=

exp ( - q,z).

(6)

The absorption coefficient, M , , has the significance that the intensity falls to lie of its initial value in a distance l/xn. The single surface power reflectivity, R, between the medium and vacuum for normal incidence may be written in terms of the real and imaginary parts of the index of refraction

A=

(ti - 1 ) 2

(ti

+

1)2-+

+ tif2 KZ

'

(7)

and the transmission through a thickness d of the medium assuming ti'
1 and hence that a clear resonance absorption can be distinguished. With the availability of far infrared lasers and high magnetic fields, one can contemplate studying low mobility materials with relatively short scattering lifetimes.

40


TABLE I1

EFFECTIVF MASES FROM FIR CYCL O T R O ~RESOZANCI. Mnteii‘il

T ( K)

InSb

10

0.0139 f 0.0001

InAs

15

0.0230 t_ 0.0003

Johnson and Dickey (42) Litton a at.

I nP

9

0.0803 f 0.0003

Chamberlain

CaAs

4.2

0.0665 f 0.0001

CdTe

4.2

0.0965 i 0.0005

Fetterman er ti/. ( 5 2 ) Waldman Y r d.( 5 5 )

rn*lm,

Reference

(49) (’1

(50)

Few experiments of this type have been reported, but the work of Button

er 01. (58) on SnO, is a good example of the utility of the technique. While previous estimates of electron mass in SnO, varied from 0.1 m, to 0.4 i n o , these workers, using a far infrared laser and high magnetic field solenoids, found a single anisotropic electron band with m* (Bllc) = (0.234 f 0.002) m, and m* (B I e ) = 0.299 4 0.002) m, . The SnO, sample was of quite high quality with a mobility at 97°K of z 9000 cm2/V-sec. In fact, the experiment could have been done using material of much lower mobility. This experiment suggests that useful characterization measurements may be performed on material previously classed as “unsuitable for cyclotron resonance studies. Obviously many large gap, heavy mass semiconductors fall into this category. However in these materials, an additional dilemma frequently arises. In order to obtain the longest scattering time 5, the experimental temperature is frequently less than 100’K. A t these temperatures, large gap semiconductors have very few free carriers. Thus, special detection and (or) carrier generation techniques are required to observe the resonance. In this regard, the microwave work of Hodby ( 3 4 ) on electron cyclotron resonance in the alkali halides is particularly suggestive. Although this optical pumping/photocapacitance approach may not be directly applicable to the FIR, adaptations of this technique seem to be possible. ”

3. Lirie Shape Studies In addition to measurements of peak positions to determine transition energies, the advent of high resolution methods in FIR spectroscopy has made possible detailed studies of cyclotron resonance line shapes. Since the


41

linewidth depends sensitively on the scattering mechanism (or mechanisms), such measurements provide an opportunity to obtain selective information concerning the detailed nature of these mechanisms. Thus far, however, very little experimental linewidth data has been obtained in the FIR. In addition there are only a few theoretical calculations [see, e.g., Kawabata (59), and Shin et al. (60)] that have considered the most important scattering mechanism for pure semiconductors (ionized impurity scattering) under the experimental conditions appropriate to FIR cyclotron resonance. A recent calculation by Shin et al. (60) has emphasized the importance of screening of the ionized impurities. For a screened Coulomb scattering potential these authors find that when the magnetic length, 1 = 1/ p = (hc/eB)1/2,is somewhat less than the screening length, a, of the ionized impurities, the cyclotron resonance linewidth in the quantum limit (all electrons in the lowest Landau level) should increase with increasing magnetic field. This is in disagreement with earlier results of Kawabata (59) obtained for an unscreened Coulomb potential. However, the latter calculation is for nonadiabatic (inter-Landau level) scattering; whereas the results of Shin et al. (60) are valid when “adiabatic” (intra-Landau level) scattering predominates. The question of the relative importance of the two types of scattering as a function of magnetic field is an important one. Shin et al. have shown that for l/a < 1 (high magnetic field) “adiabatic” scattering should predominate. The case for l/a B 1 is still not settled theoretically, but *‘ nonadiabatic scattering should certainly be more important in this regime. Experimental results bearing on these calculations are rather limited at this time. The experiments of Ape1 et al. (61) showed a linewidth that narrowed as the magnetic field was increased from 4 to 20 kG. However, this data may be misleading for several reasons: (1) The sample was not of the highest quality, as evidenced by the inagrritude of the linewidths; (2) it was several absorption lengths thick which made precise linewidth measurements difficult due to the exponential nature of the absorption; (3) only three useful data points were obtained; (4) the lowest frequency data were complicated by an impurity absorption line that overlapped the free carrier cyclotron resonance. More recently, Kaplan et a ] . (62) have obtained cyclotron resonance data on thin samples of higher quality InSb. These data converted to scattering times T = ~ / A W ~where ,~, is the equivalent angular frequency h~rlfwidth at half-maximum absorption, is shown in Fig. 12. These data are compared with the calculation of Shin et al. and Kawabata discussed above. The experimental data show a peak in scattering time near l/a = 0.5; i.e., for fields below this maximum in z, the linewidth decreases with increasing field, while at fields above the maximum the width increases with increasing field. “

”

”

42

BRUCE D. MCCOMBE AND ROBERT J. WAGNER

This appears to demonstrate the critical importance of the parameter Ela in determining the field dependence of the linewidth. However, recent measurements on InP (50)show a decrease in linewidth as a function of field over a region where l/a is apparently less than 1, in contrast to the above results.

1008 06 0 5

0.:

04

0.80.7 -

-c m

0

0.60.50.4-

0.3-

/

0

0

5

10

MAGNETIC

15

20

25

FIELD (kOe)

F I G . 12. Cyclotron resonance linewidth expressed as a relaxation time (as defined in the text) as a function of magnetic field for InSb. The solid lines represent the calculations of Kawabata (59) (NONADIABATIC) and Shin er al. (60)(ADIABATIC). An error in the l/a scale and in the ADIABATIC theoretical curve due to neglect of the background dielectric constant has been corrected. [After Kaplan et al. (62).]

It thus appears that additional work, both experimental and theoretical, is required to explain these puzzling results before the full potential of the FIR techniques in elucidating scattering mechanisms can be realized. B. Spin- Flip Resonances

As mentioned in Section I1 the spin-orbit interaction can have a large effect on the energy levels and allowed transitions in a magnetic field. In addition to modifications of the g-factor due to interband coupling of orbital angular momentum into the spin states, the simple selection rules for EM transitions are changed. In general, transitions which change both the '' spin " and Landau quantum numbers become weakly allowed. These tran-

I N T R A B A N D MAGNETO-OPTICAL STUDIES OF SEMICONDUCTORS. 1

43

sitions can be excited by either the electric or magnetic components of the incident radiation. = eEd1, is typically much larger The electric-dipole interaction, P,,, than the magnetic dipole interaction, &?,,,.d. = g*ehBb/rno c. (For n-InSb in a field of 50 k G I x c . d . l2 = 4 x 10’ I i%fm.d. 12. ) Consequently, in most practical situations it is necessary to consider only transitions excited by electricdipole interaction. Thus in the remainder of this section only electric-dipole spin-flip transitions are discussed, keeping in mind that magnetic-dipole transitions, although allowed, are typically orders of magnitude weaker. The precise nature of the coupling which allows electric-dipole spin-flip transitions via the spin-orbit interaction depends upon band structure details of the particular material considered. For the conduction band of zinc blende semiconductors it has been shown theoretically that electric-dipole spin-flip transitions can arise from two possible sources: (1) the lack of inversion symmetry (63); and (2) a small fundamental energy gap (64,65). For valence bands of diamond and zinc blende semiconductors the application of uniaxial stress removes the degeneracy of the upper valence bands and greatly reduces the complicated mixing of the magnetic energy states. In this case electric-dipole spin-flip transitions can also be identified (66). Additional theoretical calculations for other materials include those for the conduction band of Ge and Si (67), Bi (68), and a-Sn type semiconductors having the inverted zone center band structure (69). While experimental studies of spin-flip resonance have been somewhat limited due to the weak nature of the transitions, in several instances the mechanisms causing the transitions have been unambiguously identified. In addition, studies of these resonances can yield precise and useful band parameters, particularly effective g-factors, and hence provide information complementary to that obtained from the usual cyclotron resonance measurements. “

”

1. Conduction Band of Zinc Blende Structure Semiconductors

Since the most extensive and detailed experimental data exist for the conduction band of zinc blende semiconductors, it is useful to discuss briefly the wavefunctions and matrix elements for this situation. Experimental studies on InSb (70) have shown that the small gap mechanism (64,65) dominates the inversion-asymmetry mechanism (63) for this small gap semiconductor. Transitions due to the latter mechanism have never been conclusively identified experimentally (71) ; hence inversion-asymmetry effects are not included in the following discussion. The conduction band wavefunctions derived from the BY model (see Section IV,A) have been given explicitly by Zawadzki (72):

44



45

As a result of the admixture of valence band states, the wavefunction for is composed of both a given Landau quantum number n and “spin” spin-up (I) and spin-down (1)states as well as harmonic oscillator states of quantum numbers n and n _+ 1. Thus it is clear that matrix elements of P (electric-dipole transitions) are now allowed in which the “spin state changes (from + to - ”), or in which both the “spin” and orbital states change (by -t 1). As mentioned previously, the matrix element may be expressed as a sum of “interband” and “intraband” terms analogous to those of Eq. (50). However, due to the strong admixture of cell periodic and envelope functions in Eqs. (62) and ( 6 3 ) the predominant contribution to the matrix element for the intraband spin-flip transitions comes from the so-called “interband” terms (72), i.e. terms like (S I ? . p I X f iY). The first type of transition (pure spin-flip) arises from the first term of Y + and the fifth term of Y - (and vice versa), and the second type (both spin and orbital states change by f 1) is due to the first term of Y + and the sixth term of Y (and vice versa). The pure spin-flip resonance is excited in this case by the electric component of the radiation field. This transition, termed electric-dipole excited electron spin resonance (EDE-ESR), absorbs radiation in the CRI polarization at the energy En, - En,+ = hvs(n). The momentum matrix element (for E,,, 4 Eg)is given by ”

“

”

“

~

~

The combined resonance involves a change in both spin and Landau quantum numbers and occurs for the radiation electric field polarized parallel to the dc magnetic field (E’JjB)at an energy E,,+l,- - En.+ = hv,,,(n). The matrix element is

These are the results obtained by Sheka (65)who used a canonical transformation to eliminate interband terms and obtained an effective electron velocity operator. As is evident from Eqs. ( 6 6 ) and (67) the spin-flip matrix elements are quite similar in form. They differ in their dependence on electron wave vector; the EDE-ESR matrix element depends on k, (the wave vector parallel to the magnetic field) while the combined resonance matrix element is

46


proportional to d1’2 x B”’. On the other hand, the prefactors are identical in both cases; hence both matrix elements depend strongly on the inverse energy gap. Since the absorption coefficient is proportional to the matrix element squared, the possibility of observing such transitions decreases extremely rapidly with increasing energy gap. In practice, electric-dipole spin-flip transitions of this type have been observed only in quite narrow gap semiconductors. Indium antimonide ( E , = 0.235 eV) is the largest gap material in which these spin-flip resonances have been positively identified. The initial observation of combined resonance was made by McCombe et al. (73). In these experiments the transmission of n-type InSb was studied as a function of magnetic field using a conventional infrared monochromator, linear polarizers, and high magnetic field provided by Bitter-type solenoids. These high field measurements took advantage of the magnetic field dependence of the matrix element [Eq. (67)]. From these studies, the E’/JBselection rule was clearly established. Subsequently, detailed comparison of the calculated and observed magnetic field, carrier concentration, polarization, and orientation dependence of this transition (70) demonstrated conclusively that the small energy gap mechanism discussed above, and not the inversion-asymmetry mechanism, was responsible for the observed resonance in InSb. The EDE-ESR was not observed in these studies. The latter resonance was first reported by Bell (74) who utilized microwave techniques; however, no comparison with theory was presented in this work. McCombe et al. (75)have observed the EDE-ESR in the FIR using a pulsed gas laser spectrometer. The material investigated was the alloy semiconductor Cd,Hg, -,Te (x = 0.193). At this composition Cd,Hg, _,Te has the ‘‘ normal” zinc blende zone center band structure depicted in Fig. 5 with an energy gap of less than 60 meV. Figure 13 shows the results of a polarization study at two laser wavelengths. Again the polarization selection rules discussed above are clearly obeyed. From measurements of EDE-ESR, combined resonance and cyclotron resonance accurate band parameters for materials such as Cd,Hg, -,Te may be obtained. McCombe and Wagner (76) have studied these transitions in an alloy with x = 0.193 and fit their energy versus magnetic field dependence to that calculated from the BY model [Eq. (%)I. The results are shown in Fig. 14 with the indicated values of the parameters used for the calculated curves. These band parameters are in quite reasonable agreement with recent interband measurements (77);however it should be emphasized once again that care must be exercised when comparing band parameters obtained from two different models. It is worth mentioning here that intraband magneto-optical studies utilizing both cyclotron resonance and spin-flip resonances can provide a more accurate set of band parameters for a given


47

model, since both the separation between Landau levels and the separation between “spin” states are measured. Subsequent to the EDE-ESR measurements in Cd,Hg, -,Te this resonance was observed in InSb (78). Due to its larger energy gap the total

FIG. 13. Magnetic field dependence of the transmission of circularly polarized radiation through a sample o f Cd,Hg, _,Te ( Y = 0.193). The laser wavelengths are indicated in the figure. [From McCombe (79).]

I 20c

1oc C

FIG. 14. Transition frequencies versus magnetic field for several intraband transitions in Cd,Hg,_,Te (x = 0.193) with n = 3 x l o L 5c r K 3 and T = 4.5”K: combined resonance (0); cyclotron resonance ( 0 ) ;and EDE-ESR (A). The solid lines are derived from the Bowers and Yafet model with E , = 0.058 eV and E , = 19.1 eV. [From McCombe and Wagner (76).]

intensity is more than 200 times weaker in InSb for the same carrier density. The observed lines are also much narrower in TnSb, and the widths are strongly dependent on carrier concentration and temperature (76). At present, the theoretical explanation for the linewidths is in an unsatisfactory

48

BRUCE D. MCCOMBE AND ROBERT J . WAGNER

state. The observed lines in InSb are more than a factor of ten narrower than would be expected simply from broadening due to the nonparabolicity combined with the kH dependence of the transition matrix element [Eq. (66)] in the absence of scattering (79). Recent theories (80-82) which can be interpreted physically in terms of dynamical or "motional " narrowing, and which have been used to explain the linewidths of spontaneous spin-flip Raman scattering, give qualitatively reasonable results for the EDE-ESR linewidths in some cases. However, they do not correctly describe the observed temperature dependence in higher concentration samples. It is clear that further experimental and theoretical work is required to attain a quantitative understanding of the line shapes.

I " " " " '

00

Fic,. 15. Electron ~/-\alucsversus magnetic field for InSb. Experimental points werc obtained a t 4.3 K with Bi'[1 1 I]. The calculation of Pidgeon PI t i / . (83) (solid line) is for B [ l 1 I]. while that of Johnson and Dickey ( 4 2 ) (dashed line) is for BIl[1101. [From McCombe and Wagner (78).]

Nonetheless, in the quantum limit at low temperature the position of the EDE-ESR line yields a precise determination of the energy separation between the two spin states of the lowest Landau level and hence the y-value of this level. Such precise measurements can be used to test the quality of energy band models and parameters obtained for these models by other experimental methods. As an example of this the y-values for the lowest Landau level in InSb obtained from EDE-ESR measurements (78) are compared with values calculated from fits to two different band models in Fig. 15. Both models include effects of remote band interactions. Here the y-value is defined by y(n) = hvs(r7)/pBB. In the PMB model parameters were

49

I N T R A B A N D MAGNETO-OPTICAL STUDIES OF SEMICONDUCTORS. 1

obtained from interband measurements, while in the J D model parameters were obtained from intraband measurements. The experimental points deviate from both calculated curves. The deviation from the Johnson and Dickey calculation is not quite as large as it appears, due to an anisotropy in the g-factor. On the other hand, the disagreement with the interband results (solid curve) is greater than 8% between 30 and 80 kG. This is well outside the combined experimental errors, and it is of the same order as the discrepancy between the calculated zero field g-factor and that measured by standard microwave ESR (84) (indicated by the triangle in Fig. 1s).Similar discrepancies between inter- and intraband measurements have been noted in the band edge electron and hole effective masses of several small gap semiconductors (85). At present, these discrepancies are not well understood.

2. Valence Bands of Zinc Blende and Diamond Structure Semiconductors under Uniaxial Stress

As mentioned above, the r-point valence bands of diamond structure or zinc blende structure materials under uniaxial stress also provide a system in which electric-dipole spin-flip resonance can be identified. For zero stress, the valence bands are degenerate in zero field (see Fig. 5). In the presence of a magnetic field the resulting energy levels may be grouped into four sets (see the following Section IV,C,l), which can be labeled for large quantum numbers as ‘‘ light holes ( + ) a and b or heavy holes ( - ) a and b, according to the separation between neighboring levels in a set. If the effects of the inversion-asymmetry of the zinc blende lattice are neglected, this discussion applies equally well for Ge or InSb. As shown in the following section, under certain approximations the wavefunctions for the degenerate Ts(J = 3/2) valence band (15,66) can be written: ”

“

Y : ( u ) = aF(n)@n-lI3/2, - 3 / 2 )

‘Y’(b)

=

b: (n)mn-

”

+ L Z ; ( ~ ) @ , , +1312, ~

-

1/2),

I 3/2, 1/2) + b: (.)a,,+ 1 3/2, - 3/2).

(68)

(69)

The correspondence between the band edge functions in the angular momentum notation and the notation used in the BY model is given in Table I. The energy levels are shown schematically in Fig. 20. The various a’s and b’s are approximately the same size for small n; hence, no unique “spin” state can be identified for a given level (i.e. rn, is not a good quantum number). In general, transitions between the two sets (a set s b set) as well as transitions between different states of a given set are allowed.

50

BRUCE D. MCCOMBE AND ROBERT 3. WAGNER

In zero field the presence of uniaxial stress lowers the cubic symmetry and removes the degeneracy of the f 3 / 2 and k t/2 valence bands. The bands are split into two pairs of Kramer doublets, m, = k 1/2 and ~n= , 3/2, which are separated by a small “energy gap” proportional to the magnitude of the stress. Under compressive stress the splitting is such that the M , = ~ f 1/2 states lie at higher energy than the m, = f 3 / 2 states, i.e. the i ~ i , = , &fstates (upper band) remain populated at large values of stress

v

c.b.

7-

n=-1

n= ____-----1-

2-

3-

1-

I

2-

4-

3-

2%

4-

‘&’ A

m, = -112

.112 (n-1)

n’= (n.1)

312

a-set

n.1

-

2-

3-

5.0.

b-set

n = -1

1-

2-

4-

m

- 412

(n-1)

- 312 (n.1)

t - 1 ~ 16. . Schematic energy-momentum relationship for the relevant bands of a zinc blende (neplecting inversion asymmetry) or diamond structure semiconductor in the presence o f uniaxial compressive stress (left). The first feu energy levels at k, = 0 in the presence of uniaxial stress and an applied magnetic field (right).

(see Fig. 16). For sufficiently large stress the strong admixture of wavefunctions is removed, and with the magnetic field and stress both along the (001) axis the wavefunctions for the upper band can be written

YY,(b)=d,,~,,-,(3/2,-3/2)+~,,+,/3/2,1/2),

M =

1,2.3. (71)


51

Here d,, is the ratio of the energy of the nth level to the stress splitting of the valence bands. For n = - 1 and 0, d, = 0 and for n 2 1, d, 6 1 in the above approximation. Thus Yn-( a )is predominantly composed of effective “ spin projection m, = - 1/2 with a small admixture of m, = + 312; and ’Y,-(b) is predominantly m, = 1/2 with a small admixture of in, = -312. Clearly for this situation m, is a “good” quantum number, and “spin”-flip transitions can be meaningfully discussed. The corresponding energies for these states at k , = 0 referred to the top of the upper band in the presence of stress are

”

+

Ed. f

= fio,(iz’

* +glPlg B,

+ 4)

(72)

where n’ = 0, 1, 2, . . . (see Fig. 16) ho, = ( y l - y2)z2wco,and y1 = 2 ~Here . w,, is the free electron cyclotron frequency, and yl, y 2 , and K are the Luttinger effective mass and effective g-value parameters discussed in the next section. Similar expressions are obtained for the tn, = & 312 levels. In order to calculate the momentum matrix elements for the “spin”-flip transitions in such degenerate bands, it is first necessary to determine the momentum operator appropriate to this situation. From the general expression pop = (m,/fi) d#/dk the proper momentum operator for this specific case has been determined (66,86). In the limit of large stress the combined resonance matrix element (An’ = + 1, AntJ = - 1) for E / \ B(86) is given by ,

(81)

where I J , m J ) are the LK cell periodic functions for the p3,2 and p1 states and a,,(n,) are numerical coefficients. The symmetric gauge is used to specify the Landau functions $I,, n h , k H ; hence the wavefunctions are described by the two “harmonic oscillator” quantum numbers 17, and nb ( I T , is equivalent to the Landau quantum number, II, and nb is equivalent to I I - i n1 of Section 11). By substituting the wavefunction [Eq. (Sl)] into the effective mass equation &Tflh. k f f = EYI,,. k H , a secular matrix for the um,,(na)is generated. This infinite matrix is solved numerically by truncat111

* Fujiyasu r f a!. (Y8) have also reported microwave studies of cyclotron resonance of holes Ge under uniaxial stress.


61

y 2 , y 3 , q, ing to an 80 x 80 matrix. An arbitrary selection of values for the K , and strain (deformation potential) parameters allows the matrix to be diagonalized, energy levels determined, and the anticipated spectra computed. However, with this approach it would be impossible to match theory uniquely with experiment. The large number of lines, their potential k,-dependence, and broadening effects would make it impossible to determine the constants unambiguously. In order to surmount part of the problem HS made use of the fact, previously noted, that the application of uniaxial compressive stress results in a considerable simplification of the degenerate bands and thus of the experimental results. Figure 21 is illustrative of this simplification. First, the light hole transitions below 1 kOe disappear as the stress is increased to 1900 kg/cm2; second, the large number of heavy hole transitions in the region 2-8 kOe are “reduced ” to a series of about 5 lines near 8 kOe; finally, and most importantly, the line (0, - 1/2) + (1, - 1/2) moves only slightly as stress is increased from 490 to 1900 kg/cm2. This is one of thefundamental transitions. These developments can be qualitatively understood from a consideration of the hole wavefunctions and energy levels as described previously. The compressive stress splits the k = 0 valence band degeneracy. This has the effect of reducing the hole population and cyclotron resonance strength for the lower band. In addition, the stress reduces the admixture of band edge wavefunctions. With magnetic field applied, four series of levels develop; two associated with the m, = f 1/2 states and two with the m, = & 312 states as shown in Fig. 16. In the high stress limit these ladders become equally spaced, and the cyclotron resonance series approach ellipsoidal low and high mass values. The lowest transitions, (0, -3/2) --t (1, -3/2) and (0, - 1/2) (1, - 1/2), are virtually independent of stress and simply related to the parameters y l , y 2 , and y 3 . These relationships are shown in Table IV for two high symmetry directions. The reason for the stress independence of these lines in lowest order is easily seen by examining the zero stress wavefunctions in the spherical approximation. For example, as mentioned above, both \ r l l ( u )and ‘ Y i ( a ) are proportional only to /3/2, - 1/2) and have no contribution from 13/2, +3/2). Hence, since the predominant effect of the stress is to “decouple” m, = - 312 from m, = + 1/2 and m, = 3/2 from m, = -- 112 states, the stress has no effect on the 0 1 transition in this approximation. By studying the stress dependence of the many cyclotron resonance lines which were observed, HS were able to identify the two fundamental transitions. They found that these lines were extremely sharp and, as a result, they were able to make the following very precise determinations of the Luttinger .--f

+

.--f

62

BRUCE D. MCCOMBE AND ROBERT J . WAGNER

m o

i

d

un

d

0

0

I

I

MAGF(ETK: FIELD IN OERSTEDS

FIG. 21. Valence band cyclotron resonance spectra in Ge showing the effects of iiniaxial siress. The data were obtained at 1.2' K and 52.9 GHz with B~~[111]1! stress. Hole resonances at

zero stress are designated by their effective mass values. For finite stress the transitions are labeled by the (17~. +ni,,) notation abbreviated to n'+ (all transitions shown are r n , = i 1,2). [From Hensel and Suzuki (95).]

parameters: =

13.38 f 0.02;

;'2

=

4.24 +_ 0.03;

;a3

=

5.69 & 0.02.

Hensel and Suzuki also noted that while the transition (0, -312) + (1, - 3 i 2 ) was stress independent to the limits of their experimental resolution, the transition (0, - 1/2) + (1, - li2) showed an extremely weak ( 1 '!()), but clearly observable. stress-dependence. From this dependence they were able to determine values for the valence band spin-dependent uniaxial deformation potentials.


63

The spin-flip transitions which occur for E’IIB allowed a determination of the K and q parameters as discussed in the previous section. Using all of the Luttinger parameters determined in this manner HS proceeded to calculate the stress-free cyclotron resonance spectrum of holes in Ge on the basis of

TABLE IV EFFECTIVE MASS TENSORCOMPOKENTS FOR LOWESTTRANSITIONS I N EACH LADDERIN HIGH STRESSLIMIT".^ Stress

rn, =

1’2

m,

=

THE THE

i312

The parallel axes of the tensors are along the stress direction. After Hensel and Suzuki (Y5).

the theoretical model previously described. Assuming each component line to have Lorentzian shape with z = 2.7 x 10- l o sec, they calculated the integrated intensity of each line as a function of crystal momentum in the direction of the field, k,, and were thus able to synthesize the zero stress spectra. From this calculation they found that the dominant contribution to many of the cyclotron resonance lines did not come from transitions at k, = 0. As a result the lines were broadened and actually shifted from their k, = 0 positions. In view of this it is clear why early attempts to understand the spectra with the k , = 0 assumption were unsuccessful. In earlier FIR work, Button rt al. observed “Luttinger” effects in the hole cyclotron resonance spectra in InSb (99) and Ge (100) using an HCN laser. However, these experiments did not make use of uniaxial stress to clarify the data and lines were identified only on the basis of the spherical Luttinger model with k, = 0. At this writing a FIR magneto-optical study

64


comparable to the microwave work of HS has not been published. A detailed comparison of the techniques and experimental conditions for the two types of experiments is illuminating in this regard. Ranvaud's recent uniaxial stress measurements on hole cyclotron resonance in Ge and InSb using a FIR HCN laser (87) allow a direct comparison of the two methods. In the microwave work, the high purity sample is maintained at a temperature of 1.2"K while holes (and electrons) are optically excited with near infrared radiation. A high Q cavity is used in conjunction with a microwave bridge to increase sensitivity. Adequate cyclotron resonance signals can be detected with hole densities of only 108-10'ocm-3 in a thin layer only a few microns thick. In the FIR, a single pass transmission method is generally '

TABLE V COMPARISON OF THFRMAL A N I I PHOTONE \ ~ K G I EFSO R THE MICROWAVEA N D FIR LASER EXPFRIMENTS

DISCUSSED ic THE TEXT

Microwave

0.2 19

0.103 ( T = 1.2"K)

2.126

Laser

3.618

1.124 (T = 20'K)

2.133

used. This requires a significantly larger number of carriers in order to obtain an observable cyclotron resonance signal. Thus Ranvaud utilized samples 2-3 mm thick which were intentionally doped with 10'4-1016 acceptor impurities per cubic centimeter. Free carriers were thermally excited at temperatures 2 20°K. The two techniques are compared in Table V. Note that the condition ho > k , T is equivalently satisfied in both, even though the FIR frequency is 17 times the microwave frequency. In addition the necessity of using rather highly doped material to obtain sufficient carriers for the FIR experiments serves to degrade the carrier scattering time, 5, and to broaden the cyclotron resonance lines. In fact, where HS observed a dozen lines, Ranvaud (87) was able to resolve only four. O n the other hand, for materials such as InSb, where the inherent purity is significantly worse than that of Ge, the advantages of the microwave technique are lost and the necessary condition for sharp resonances, w c s >> 1, is better satisfied in the FIR. For the case of Ge Ranvaud was able to achieve a good fit to his uniaxial stress data using Luttinger parameters that agree well with those of HS.


65

However in InSb Ranvaud found a qualitatively unexplained stress dependence for one of the fundamental transitions. In the absence of a suitable explanation for the stress dependence of this crucial transition, it is difficult to obtain a reliable set of Luttinger parameters from these measurements. As in the case of electron cyclotron resonance, FIR laser sources can be extremely useful for the measurement of classical hole cyclotron resonance when material quality is poor, i.e. when w,z < 1 in the microwave region. With sufficiently high magnetic fields wCoccurs in the FIR and the condition w, z > 1 can often be achieved. This is the approach recently used by Bradley et al. (101) in their measurement of the “classical” light and heavy hole masses in Gap, a typical zinc blende structure semiconductor. Using pulsed magnetic fields up to 200 kG these authors were able to resolve the cyclotron resonances for carriers with effective masses of 0.16 mo and 0.54 m, . This application o f F I R laser techniques promises to be extremely fruitful in the characterization of semiconductors with heavy mass valence bands; to date very few such materials have been investigated in any detail. “

”

2. 1nl;erted Band Ordering: HgTe

As discussed previously HgTe and alloys of Cd,Hg, -,Te with x 5 0.16 possess the “inverted” zone center band structure (Fig. 10). Due to the relatively small energy gap ( E , = 0.3 eV) and the degeneracy of the T, conduction and valence bands, a more general treatment than either the BY model or the Luttinger model for degenerate bands is necessary to properly account for both the nonparabolicity of the conduction band at higher energies and the “Luttinger” effects (similar to those just discussed for Ge) at lower energies. Groves et al. (16) have provided such a generalization based on the earlier work of Pidgeon and Brown (35) for InSb. In this treatment states at k = 0 are divided into two groups. One group (A) consists of the strongly interacting (closely bunched) states of interest, Ts,T8,and r, ; the other group (B) includes all the other states. Interactions of the k * p type between a given state in A and the states in B are removed to second order in k by the LK approach. The resulting renormalized interaction among the states in A gives an 8 x 8 interaction Hamiltonian which is diagonalized exactly by computer for k , = 0. Groves et al. have used this approach to fit their interband magnetoreflection data for both r6+ T8 and T8-+ Ts transitions in HgTe and to obtain an appropriate set of band parameters. Leung and Liu (102) have generalized the theoretical approach of Groves et al. (16) to include the effects of k, # 0. Experimental studies of interband (r, valence + T, conduction) and intraband (T, conduction) magnetoabsorption in HgTe in the spectral region between 2 mm and 100 pm have been reported by Tuchendler et al. “

”

66

BRUCE D . MCCOMBE A N D ROBERT J. WAGNER

(103). In addition transitions which did not extrapolate to zero energy at zero magnetic field were observed. The latter lines were attributed to transitions involving “resonant acceptor impurity states which are degenerate with the r; band continuum in zero field. Both carcinotron and FIR laser sources were used in these experiments. Examples of some of these data are shown in Fig. 22. Experiments were performed in both the Faraday (longitudinal) and Voigt (transverse) geometries. In the Voigt geometry, due to the ”

FARADAY CONFIGURATION

c

c

2’

e w

a

CR

I

0

I

10

20

1

I

I

30

40

50

B(kG) FIG. 22. Transmission versus magnetic field for a thin sample ( 5 10 pm) of HgTe. The trace at 775 pm was obtained with a carcinotron source while the other two traces were obtained with HCN (311 pm) and H,O (1 18.6 pm) laser sources. The line labeled CR is cyclotron resonance and that labeled S is “spin” resonance. [After Tuchendler er a / . (103).]

significant number of free carriers, the cyclotron resonance at lower frequencies was found to be “plasma-shifted” to lower fields as compared to the position of the cyclotron resonance in the Faraday geometry. At higher photon energies the positions of these lines coincided. The position of the plasma-shifted cyclotron resonance is usually given by = 47~Ne~/&,m* is the plasma frequency, N is where wpcr= [ m i + the carrier concentration, and E~ is generally taken to be the low frequency dielectric constant, independent of frequency. However, in a zero gap semiconductor such as HgTe the ri --+ ri interband transitions contribute a frequency dependent term to the dielectric function which can extend to zero frequency. Only by taking this contribution into account were these authors able to obtain agreement between the calculated and observed positions of the plasma-shifted cyclotron resonance.


67

Tuchendler et a/. also identified an electric-dipole “spin resonance for ”

E IB (labeled “ S ” in Fig. 22) and a “combined” resonance for E’IIB (not shown). The spherical Luttinger model was used to provide a theoretical framework for the interpretation of these low energy transitions. As discussed in Section IV,B “spin” is not a good quantum number in these degenerate bands for the lowest levels; thus spin-flip transitions are not well defined. The “spin” transition is presumably a transition from state (1, - 1/2) in the a-set to state (1, -3/2) in the b-set. Again states are specified by ( H ’ , mJ).By reference to the discussion of Section IV,B it is easily seen that the total wavefunctions for these states are Y t ( a ) = (Dl I3/2.

-

1/2)

and

Y’,+(b) = (D, I3/2, -3/2),

respectively. It is not clear, however, why a transition matrix element between these states should be non-zero, since both initial and final states have odd parity. It is possible that inversion asymmetry (which has been neglected) may allow this transition by relaxing the parity selection rule. From a fit to the various observed transitions Tuchendler et a/. have obtained a set of Luttinger parameters which adequately describe their results as well as the interband rz + rC, results of Guldner et a/. (104). In the latter work low energy transitions ( h ~ - oE, < ~ 30~meV) ~ were ~ ~fit using ~ the spherical Luttinger model, while higher energy transitions were fit with the BY model. There is some justification for the use of the spherical approximation, since from the work of Groves et al. the anisotropy is not large (yz - y3)/yz = 0.12. However, the parameters obtained from these experiments, which are mutually consistent, are in some disagreement with the results of Groves et aI. except for the low temperature energy gap. The parameters are compared in Table VI. As can be seen from the table the largest discrepancy is in y1 (35%). The reasons for the discrepancy are not clear. Certainly the theoretical approach of Groves et a/. is more rigorous than the “marriage” of two models used by Guldner et a/. and Tuchendler et a/.; on the other hand, the experimental work of the latter authors is more extensive and detailed (especially since it includes intraband measurements for the r: band). It is possible that k, effects which were found to be very important in Ge by Hensel and Suzuki could account for this discrepancy since such effects were neglected in the interpretation of the experimental data by both groups. However, Guldner et a/. have calculated the k,-dependence of the r energy levels for high symmetry directions. These effects appear to be unimportant for the Ts band levels, and by intrainterband transitions as well as the implication for the P6+ band transitions. In view ofthis it seems that additional work is required for a complete understanding of the degenerate valence-conduction bands of HgTe.

68

BRUCE D. MCCOMBE A N D ROBERT J . WAGNER

TABLE VI

BAND PARAMETERS FOR HgTe"

0.3025 0.3025

- 12.8

- 10.5

8.4 -9.9

~

- 16.98

- 11.29

(103. 104) (16, 105)

" Luttinger parameters are calculated from the higher band parameters of Groves et a/. (16)as follows: 7, = j,2

=

~, , -

=

with E ,

=

?!b.

-

= - 16.98

;.;.b. .,hb.

-

=

~

&b

Ep/3E, Ep/6E, EP/6E, - E,/6E,

10.49 9.32 - 11.29 ~

= -

=

18.1 eV.

3. Tellurium n. Theoretical background. Recently, a large number of FIR magnetooptic experiments have been performed on tellurium. This is in part due to its relatively unique and interesting energy band structure, and in part due to the availability of high quality single crystal material. The crystal structure consists of atoms arranged in spiral chains with three atoms per spiral and spirals situated in a hexagonal arrangement. The Brillouin zone is a hexagonal prism with the crystal c-axis perpendicular to the prism face. In contrast to the diamond or zinc blende zonecentered valence bands, the valence band maxima of tellurium are located at the H-points, corners of hexagonal faces of the Brillouin zone. H u h (106) has suggested a description of the valence bands using a k * p perturbation approach. When the effects of spin-orbit interaction are included, two possible energy band schemes can occur as shown in Fig. 23. These two cases simply reflect different choices of the parameters in the energy-momentum relations (hole energies are measured positive downward with the energy zero taken to be the position of the valence bands at H in the absence of spin):

E E

= 3 , 4=

+ Bok: [ S : k ; + 4Af]1'2 - A 2 . Ak2L + B OkZ, f [S\kt + a2k:]' + A2 , Akt

(82)

where k: = k: + k : . In Fig: 23 and Eqs. (82) we have used a slightly modified version of the notation of Doi et al. (107) who have presented a rigorous calculation using the k p formulation. A comparison between these parameters and those used by other workers is given in Table VII. In Eqs. (82) the z-direction is

-


69

,

taken parallel to the c-axis, and El, E,, and E3, correspond to the H,, H , , and H, states, respectively. The parameters A , B o , S1, and S , represent momentum matrix elements between the valence bands and higher bands, and A 1 and A2 are proportional to the spin-orbit splittings of the valence bands. As is apparent from Eqs. (82) the curvature of H, in the z-direction

H

kz

+kZ

(a 1

(b)

FIG. 23. Schematic E versus k , relationship showing the valence band structure of tellurium in the neighborhood of the H-point of the Brillouin zone (this point is also designated M by some workers (108, 1 2 I ) ) with spin-orbit interaction included. In (a) ( I S : / B , I > 4 1 A , I ) the uppermost valence band exhibits the “camelback” structure. I n (b) ( I S : / B , I < 4 I A 1 I ) it has a single maximum at the H-point. The H, and H, bands are nondegenerate as are the H, bands (except at k , = 0) since their Kramers conjugate states occur at the nonequivalent point H’ due to the lack of inversion symmetry of the tellurium structure.

depends critically on the size of I S:/Bo I relative to 4 I A l I . With I S:/Bo I > 4 1 A 1 1 , the “camelback” of Fig. 23a results. If I S:/Bo 1 .< 4 1 A1 1 , a single maximum at the H-point occurs as in Fig. 23b. In the case of Fig. 23a, 1 kzO1, the magnitude of kZ at the maximum, is [Sf - 16Bg A:]”*/2 1 Bo S1 1 and the energy difference E(k,o) - E ( 0 ) 5 6

=

S:( 1

-

4Bo I A 1 I /S:)/4

I Bo I.

TABLE VII A

NOTATION FOR TELLURIUM BAND PARA METERS^

COMPARISON OF THE

Doi er a/. (107)

Betbeder-Matibet and H u h ( I 1I )

Weiler (108)

In order to avoid confusion with the magnetic induction, B, has been used instead of B in Doi er al. (107).

70


Unlike the rather dramatic changes in shape of the H, band, the shape of

H, and H, remain relatively insensitive to changes in the parameters. Thus since the H, band lies highest and is easily populated with free holes, it provides an ideal situation for intraband magneto-optical studies to determine the band parameters. Rather than outline the detailed calculations of the upper valence band structure of tellurium in the presence of a magnetic field (108-210), we present here a simplified description of the upper (H4) band which is due to Betbeder-Matibet and H u h (111). This simple approach provides a good deal of physical insight into the energy levels and selection rules, while it avoids the mathematical complexities of the more rigorous treatments. Two cases can be distinguished: (a) BJIc,and (b) B Ic. For case (a) the energy in the z-direction is not modified by the presence of the magnetic field. Since the energy in the transverse direction is a quadratic function of k , the transverse motion goes over directly to the Landau quantization as in Section 11, i.e. Ak: + ( a l/;?)ho,. , where ha),, = -2AeB/h. In this somewhat simplified model the separation between adjacent Landau levels is a constant independent of either 11 or k , . However, when higher order terms in the E-k relationship are taken into account, this no longer holds true. The effects of including the higher order terms will be discussed later. For case (b) (B Ic) one must distinguish between the two possibilities shown in Fig. 23. The choice of parameters leading to Fig. 23b would not yield any qualitatively different effects in the presence of an applied magnetic field. O n the other hand the “camelback of Fig. 23a demands special attention. Betbeder-Matibet and H u h (111) have shown that for an electron in the “camelback” band with Bilk, one can obtain an effective onedimensional Schrodinger equation by making the following substitutions in the expression for E , [Eq. (82)]:

+

”

k,

---f

(AIB,)’ 4(eB/H)112X, k,

+

(B,/A)”4(eB/”)’ 2(d/dX)

and E

+ (AB,)’

2(eB/h)c

+ ,412;.

The resulting one-dimensional equation, which yields a good approximation to the energy levels. is d2Y -

dX2

+ V ( X ) Y = EY,

with V ( X )= x 2 - (A;

+ 4(2X2)’/2 + A,

INTRABAND MAGNETO-OPTICAL STUDIES OF SEMICOKDUCTORS. 1

7I

and

A,

=

2(AB,)- ' / 2 ( e B / h ) -'/,Al,

A,

=

( A l l , ) - "'(eB/h)- 1/2A2,

t2 = (Bo/A)"2(eB/h)-'(S,/2Bo). It should be noted that V ( X ) remains unchanged under inversion; X + - X ; hence parity is a good quantum number. For small values of B, V ( X )appears as two separated, harmonic oscillator-like potential wells with minima at

X

=

iX,,

where

X,

=

(Bo/A)'~4(~B/h)-''2k,o.

In the low field limit the iiiterwell barrier is 8 = ( A & - '/'(eB/h)- '6. In this case there is only a slight coupling between potentials. As a result, the two sets of Landau levels are nearly degenerate with E,,t

=

E n = ( n + +)(heB/m.c)

(84)

and the wavefunction can be written Y,,

= 2- 1'2[Qn(X

-

X,) i @),(X + X,)],

(85)

where Qn is a harmonic oscillator function. As B is increased, the separation 2 X , and barrier height 8 of the two wells decreases. This results in increased coupling of the two sets of Landau levels and a splitting of the previously degenerate n' states into n+ and y1-. It is clear that if the camelback condition prevails in tellurium, it will be apparent in the splitting of cyclotron resonance transitions at high fields. Electric dipole selection rules require n' + ( n + 1)-, i.e. allowed transitions are those between states of odd parity with respect to X . The inclusion of higher order terms in k, as done in the more rigorous treatments (108, 110) relaxes this rule somewhat. b. Esperimental results. The availability of high quality p-type tellurium has resulted in very detailed investigations of the valence band structure described above. From early low magnetic field sub-millimeter work (I12), it was concluded that the band was anisotropic with m* (Bilc) = 0.11 m, and m* (B Ic) = 0.26 mo . However, oscillatory magnetoresistance (Shubnikovde Haas) measurements suggested the presence of the camelback condition (113, 114) as did later microwave cyclotron resonance (115). Couder (116), using carcinotron sources from 405-1080 pm (740-278 GHz) and fields to 55 kG, first observed the splitting which is expected from the "camelback" condition. As shown in Fig. 24 for B Ic the primary cyclotron absorption F, observed at 278 and 308 GHz splits into F, and F, at 353 GHz. In addition to these free carrier resonances other lines S,, S, ,and I observed by Couder were attributed to transitions involving impurity states.

72

BRUCE D. MCCOMBE A K D ROBERT J . WAGNER

Following Couder's early work, a number of authors have employed submillimeter lasers (I 17,118) and FIR nionochromators ( I 19) to study the higher energy/magnetic field region of the E versus B plot. The data obtained prior to 1971 have been compiled by Nakao et al. (110) and these data are shown in Fig. 25. The calculation of Nakao et a/. for the transition

I

20

1

BkG)

55

FIG.24. Experimental traces o f transmitted power versus magnetic lield for Te with B i c at the indicated frequencies. The primary low frequency absorption line, F,, splits into two lines, F F z , at higher frequencies. Additional lines. S S,, and I, were attributed t o impurity state transitions. [After Couder (116).]

,,

,,

CY CLOIRON RESONANCE ( H i c)

MAGNETIC FIELD (kOe)

FIC;.25. Transition energies of cyclotron resonance in Te for the case of H I c'. The solid 0,x . and 0 and dashed curves are the calculations of Nakao et a/. (110).The symbols 0, represent the experimental data of Yoshizaki and Tanaka (119) Dreybrodt era[.(118), Couder (116), and Radoff and Dexter (115), respectively. The solid lines correspond to allowed transitions and the dashed lines correspond to forbidden transitions. [From Nakao et irl. (110).]

INTRABAND MAGKETO-OPTICAL STUDIES OF SEMICONDUCTORS. I

73

energies is indicated by the solid (allowed) and dashed (forbidden) lines. Their choice of parameters yielded an energy of 2.54 meV for the height of the camelback ” maximum above the H-point energy. The forbidden transitions O + -+ I + and 0- + 1- have also been observed. These transitions were first identified by Dreybrodt et al. (118). When warping terms of the form k,(k: - 3k:) are included in the k p Hamiltonian, these forbidden transitions become allowed for B I/ bisectrix (B parallel to the hexagonal face of the Brillouin zone and perpendicular to the side of the prism); they remain unallowed for B 1 binary axis (108) (B parallel to the hexagonal face and parallel to the prism side). Experimental results have shown these forbidden transitions in both orientations. The reason for their appearance with B /I binary is not yet understood. Recent work by Couder et al. (120) has clarified the region of 1-2 meV and 10-40 kG. These measurements have confirmed the assignments shown in Fig. 25. Couder et al. also explored the dependence of cyclotron resonance on the angle between B and the c-axis for frequencies both above and below the splitting region. They were able to describe all aspects of their results satisfactorily with the simple camelback model. In the light of the above discussion, it is somewhat surprising that the B/lc orientation seems to have been a greater source of interpretational difficulty than B Ic. Although Couder observed a single absorption line as might be anticipated for low concentration samples, Yoshizaki and Tanaka (119) have reported a much more complicated spectrum for their samples with p z 10’4-1016cm-3. They argued that, although some of the observed spectral features were due to impurity transitions, two of the lines were free hole cyclotron resonance lines, one arising from transitions at the H-point and one from transitions at the valence band maxima, k k,, . It should be reiterated that for the simplified model described above there is no dependence of ho,,Il on k,; thus with this model there could be only one cyclotron resonance line irrespective of where the transitions originate. In the more sophisticated models (108, 110) higher order terms (k: and k t k : ) enter, and these terms give rise to a dependence of hw,, lI on k , as well as on n. At low energies (e.g., the work of Couder et a/.) these terms are unimportant. Bangert and Dreybrodt (121) have calculated the absorption coefficient for cyclotron resonance for the B/lc geometry. Using the model and band parameters of Nakao et al. (110), they found that if a weak broadening mechanism exists, the density of states singularity at the H-point is washed out, and the dominant contribution to the absorption coefficient comes from transitions near the peaks of the “camelback” ( k k , , ) rather than the H-point. This conclusion is in agreement with calculations by von Ortenberg et al. (122). On the basis of these calculations and the other experimental results, it must be concluded that the additional line observed “

-

“

”

74


by Yoshizaki and Tanaka was not an H-point cyclotron resonance transition. As discussed below, in less pure samples interference” effects can give rise to additional structure near cyclotron resonance, and this may be the explanation for the additional line. Bangert and Dreybrodt also noted that a significant line shift should occur on heating from 4.2” to 77°K. von Ortenberg et al. (122) have studied the line position for both BI/c and B Ic as a function of temperature up to 120°K. In order to avoid complications due to interference and (or) impurity effects, they were careful to use the highest purity samples available ( p “v 4 x cmp3). They attempted to fit the experimental results with three different models (108, 110, 123) each based on Doi’s zero field k * p formulation. They found that even qualitative agreement required the introduction of a temperature-dependent broadening factor. von Ortenberg et al. concluded that the model of Weiler (108) provided the best fit to their data. Although all experimental workers have reported some evidence of impurity lines, the results are frequently inconsistent with each other as well as with shallow acceptor results in other materials. Probably the most reliable information has been obtained by Couder et at. (120) using material with p z 1013 ~ m - From ~ . the field dependence of three impurity lines, they concluded that an impurity bound state exists with ionization energy of 1.24 meV. As in the case of shallow acceptors in most Groups IV or IIILV semiconductors, they find the intensity of the inpurity lines weakens with increased temperature. Similarly, Dreybrodt et ul. (118) have studied the temperature dependence of a number of lines, both cyclotron resonance transitions and impurity transitions. They found a dramatic difference in the temperature dependences of these two types of lines and made use of this to identify the impurity transitions. However, the impurity binding energy deduced from these measurements was 0.4 meV. In contrast to the above work, Yoshizaki and Tanaka (119,124). using more heavily doped material, found that the lines that they attributed to impurities increased in intensity with increasing temperature. Yoshizaki and Tanaka (119) and von Ortenberg et al. (122) both found that increased impurity concentration increased the intensity of the subsidiary (impurity) structure relative to the cyclotron resonance lines. It seems more likely that this is indicative of the presence of “interference” effects similar to those described by Cronburg and Lax (125), and not representative of impurity effects in the higher concentration samples. “Interference effects can arise when the index of refraction, K , of the material under investigation varies with respect to photon energy or magnetic field in the neighborhood of a strong absorption line. This change of index can manifest itself in at least two distinctly different ways. On the one hand, the effective sample “

”


75

thickness, ~ dcan , change with an attendant constructive or destructive interference when A(icd) is some multiple of a quarter wavelength. However, this effect requires a sample with parallel faces, a condition usually purposely avoided in the experiments. O n the other hand, “Faraday” rotation of the light polarization by the sample (which results from the difference between K ~ and ~ K, , - ~ ~can ) cause marked effects when light pipe techniques are used. If the radiation is asymmetrically distributed across the cross section of the light pipe, it is possible for the walls of the pipe between the sample and detector to act as an analyzer of Faraday-rotated light. This can also give rise to oscillations in the apparent sample transmission which resemble weaker absorption lines on the shoulder of the main line. It is clear that further work is required to clarify the situation concerning acceptor impurity transitions in Te. Some information about the conduction band at the H-point has been obtained from interband magneto-optical measurements. For this work, Doi et al. (126) have performed a k p calculation for the conduction band. In fitting their data, they obtain m* (B//c)= 0.05 m, and m” (B i c ) = 0.145 i n , . In the only apparent observation of electron cyclotron resonance Button et al. (117) found m* (B Ic ) = 0.135 m, at 200”K, in fair agreement with the interband results.

-

ACKNOWLEDGMENTS We have benefited from helpful discussions with S. Teitler, J. C. Hensel, R. Kaplan, R. Ranvaud, K. L. Ngai, and W. Dreybrodt during the course of this work. J. C. Hensel and R. Ranvaud kindly provided figures and manuscripts prior to publication. Wc would like to express our gratitude to Mrs. L. Graham, Mrs. G. Garrett, Mrs. L. Blohm, Mrs. C. Hepler, and Miss I. Lajko for their efforts in typing various drafts of the manuscript. One of us (B.D.M.) would like to thank the Max-Planck-lnstitut fur Festkorperforschung, Stuttgart for hospitality extended during a sabbatical year while part of the manuscript was prepared.

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12, 413 (1973). 102. W. Leung and L. Liu, Phya. Rer. B 8. 381 I (1973). 103. J . Tuchendler, M. Grynberg. Y. Couder, H. Thome. and R. LeToullec. Ph!..\. Rr~i..B 8, 3884 (1973). 104. Y. Guldner, C. Rigaux. M. Grynberg, and A. Mycielski. Phj,s. Rec. B 8, 3875 (1973). 1 0 5 . C. R. Pidgeon and S. H. Groves. iri ”11-VI Semiconducting Compounds; 1967 International Conference” (D. G . Thomas. ed.). p. 1080. Benjamin. New York. 1967. 106. M. Hulin, J . Phys. Chem. Solids 27, 441 (1966). 107. T. Doi, K. Nakao. and H. Kamimura, J . P h y . SOL..Jtrp. 28, 36 (1970). 108. M. H. Weiler. Solid Sture Cor~nzurz.8, 1017 (1970). 109. M. S. Bresler and D. V. Mashovets. Phys. Sfatus Solidi 39. 421 (1970). 11(J. K. Nakao, T. Doi, and H. Kamimura. J . Phys. Soc. J u p . 30. 1400 (1971). 1 1 1 0. Betbeder-Matibet and M. Hulin. P/iy.\. Sicitu.< Solid; 36. 573 (1969). 112. J. C. Picard and D. L. Carter, J . PI1j.s. Soc. Jup. 21, Suppl., 202 (1966). 113. E. Braun and G. Landwehr, J . P h n . Soc. Jup. 21, Suppl., 380 (1966). 114 C . Guthmann and J. M. Thuillier. Soiitl State Corm7irn. 6. 835 (1968). 115. P. L. Radoff and R. N. Dexter. Pkrs. Srrriir.s Solid; 35. 261 (1969). 116 Y. Couder, Phy,$. Rec. Leu. 22, X90 (1969). 117. K. J. Button, G . Landwehr, C. C. Bradley, R. Grossc, and B. Lax. Phys. Rec. Lerr. 23. 14 ( 1969). 118 W. Dreybrodt, K. J. Button, and B. Lax, Solid Srure ~ O ~ J l i J i8,i ~ 1021 ~ . (1970). 1 1Y. R. Yoshizaki and S. Tanaka. .I. Phjx SOP.Jap. 30, 1389 (1971). 1-70. Y. Couder, M. H u h , and H. Thome. Phys. Reo. B 7, 4373 (1973). 121. E. Bangert and W. Dreybrodt, Solid Srare Corn~nurz.10, 623 (1972).

122.

M. von Ortenberg, K. J. Button. G. Landwehr, and D. Fischer, Phjx Rc’c. B 6. 2100 (1972).

123

W. Dreybrodt. M. H. Weiler. K. J . Button. R. Lax. and G. Landwehr. P r o c I u / . C’orif P / J ~ . .Sernicomi.. s. IOtk, Cumbrirlye. !2.luz.\cicliir.sert\, p. 347. USAEC. Div. of Tech. Info.. Oak Ridge. Tenn.. 1970. 1-74. R . Yoshizaki and S. Tanaka, Solid Srure Curnnnrri. 8. 17x9 (1970). 125. T. L. Cronburg and B. Lax, Plzr.s. Lett. A 37, 135 (1971). 126. T Doi. H. Kamimura, H . Shinno. R. Yoshizaki, and S. Tanaka. Prot.. 1 i i r . C O ~ JPhi.\. /. Se!nicoiid., I 1 f l i . Warsuw, 1972. p. 761. PWN-Polish Sci. Publ., Warsaw. 1972.

The Gyrator in Electronic Systems K . M . ADAMS

AND

E . F. A . DEPRETTERE

Depirrtnient of’ Elecrrictrl Engginerring Dert Unioersity of’Technology. Del$. Netherlands

.

AND

J . 0. VOORMAN Philips Research Laboratories. N .V . Philips’ Gloeilanipvilfubrieken. Eindhouen. Netherlands

I . Introduction .......... ....... .......... I1 . Reciprocity in Physic s ...... .......... A. Some Historical Background ..................................... B. Nonreciprocity ................................................................................. C . The Origin of Antireciprocity .............................................................. D . Further Generalizations ..................................................................... ......... 111. The Gyrator as Network Element ......... A . Historical Introduction .................................... B. Basic Properties of the Gyrator ............................................................ IV . Filters ................................................................................................... A . Introduction ............ B. Basic Configuration ........................... C . The Scattering Matrix ........................................................................ D . Ladder Filters .................................................................................... E . Resonance in Filters ........................................................................... F. Sensitivity ....................................................................................... G . The Gyrator in Filters .............. ..................................................... V . Principles of Realization of the Gyrator ........................ A . Physical Effects ...... ................................. B. Active Circuits .................................................. C . Ideal Active Network Elements .......................................... D. The Nullor ....................................................................................... E. Gyrators Constructed from Nullors and Resistors .................................... VI . Basic Electronic Design ........................................................................... A . Realization Based on Two Resistors in the Signal Path .............................. B. Realizations Based o n Four Resistors in the Signal Path ........................... C . Noise ............................................................................................. VI1 . Basic Gyrator Measurements ..................................................................... A. Introduction .................................................................................... B. The Gyrator as n-Port ........................................................................ C . The Gyrator in Its Applications ............................................................ 79

80 80 80 82 83 85 86 86 88 94 94 94 96 99 101 107 109 109 109 111

113 113 116 128 129 141 143 145 145 146 155

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K. M. ADAMS. E. F. A. DEPRETTERE A N D J. 0. VOORMAN

VIII. Trends in Gyrator Design and Applications ................................................ A. Introduction ..................................... ......................................... B. Gyrators for Application in Consumer Pro s ...................................... C. Gyrators for Professional Use .............................................................. IX. Conclusion.. ..................................................................... References ............................................................................................

170 170 170

171 177

I. INTRODUCTION Recent developments in electronic technology combined with increasing insight into the theoretical basis of physical systems have led to a growing interest in the gyrator and its applications. On the one hand, theoretical results which have been known for more than twenty years are beginning to be applied in earnest to real systems. O n the other hand, the new technology which has made these applications possible has stimulated a reexamination of the theory and has led to new and interesting results, which in their turn can stimulate further developments in technology itself. In this survey article we report and comment on some of these developments. Our approach will be based on an attempt to extract unifying principles from the mass of data now available rather than to give an encyclopedic account of the state of the art. By so doing we cannot fail to adopt a somewhat subjective point of view, approving of some developments, disapproving of others, and being noncommittal on some questions which we d o not yet feel capable of resolving but which certainly deserve attention. We hope that by stating our premises and reasoning clearly, interest in this fascinating field will be further stimulated. Our survey will touch on historical matters, go into various theoretical questions, as well as be concerned with thoroughly practical matters such as system specification and actual hardware. The following sections are so arranged that they can be read largely independently of one another. We would emphasize, however, that for the reader who wishes to be able to apply the existing technology intelligently to his own particular system, a thorough grounding in the theory is essential. 11. RECIPROCITYI N PHYSICAL SYSTEMS

A . Some Historical Background

During the eighteenth and nineteenth centuries, mechanical systems were studied in great detail and in various degrees of generality. It was noticed that in nearly all these systems a reciprocity relation held which

THE GYRATOR IN ELECTRONIC SYSTEMS

81

manifested itself in certain symmetry relations in the coefficients of the constitutive equations of the system, and which ultimately depended on Newton’s third law of motion: the action of a particle A on a particle B is equal and is oppositely directed to the reaction of particle B on particle A.” This reciprocity relationship can be expressed in various forms such as: Let an infinitesimal external force F , acting on a system at a location P, give rise to an infinitesimal displacement x2 at a location P, when no other external force acts on the system. If now the same force F , acts externally on the system at P2 and no other external force is present, then the displacement occurring at P, is equal to x 2 . When it is possible to derive the forcedisplacement relationships from a potential energy function, then the reciprocity follows automatically as a consequence of the commutativity of the operations of partial differentiation with respect to different coordinates. Another example from classical mechanics is the reciprocity between impulsive forces and velocities, which follows from the existence of a kinetic energy function. A corresponding electrical analogue is the reciprocity relation between currents and flux linkages in a linear network of magnetically coupled coils, which follows from the existence of a magnetic energy function. As a result of relations of this type many people erroneously came to regard reciprocity as essentially connected to the concept of energy. From this point it was not difficult to infer (also erroneously) an apparently essential connection between passivity and reciprocity. This idea that passivity and reciprocity are somehow related has played an important role in the evolution of the concepts relating to reciprocity between force and velocity, but has also led to considerable harm. Thus when one comes to consider the reciprocity between voltages and currents in an electrical network, a new difficulty arises. There is no a priori reason for expecting the existence of a function which plays the same role as the energy functions already mentioned. It is true that in the case of a particular type of linear system the situation could be saved by the introduction of a dissipation function (Rayleigh, 1894). However, this step really involved begging the question, since the dissipation function could only be deduced knowing that the system (expressed in network theoretical terms) consisted of linear resistances and ideal transformers; from network theory it is known that such a system is reciprocal since it consists of reciprocal elements. In the case of nonlinear networks, for which either a content or a cocontent function exists (Millar, 1951), we find a similar reciprocity relation between the deviations of the voltages and the currents from a particular distribution of voltages and currents in the network. But again the existence of the content function can only be a priori guaranteed for a network of ideal transformers and one-port resistors with characteristics representing a “

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K. M. ADAMS, E. F. A. DEPRETTERE A N D J . 0. VOORMAN

single-valued mapping of the currents on the voltages or of the voltages on the currents. Another development which has taken place is based on completely different considerations resulting from the study of reversibility in thermodynamic systems. Since 1931 attempts have been made to deduce symmetry relations on the basis of microscopic reversibility (de Groot and Mazur, 1962) in which the reversibility of time in the microscopic equations of a thermodynamic system is supposed to hold. However, in order to make the theory work, terms depending on a magnetic field strength have to be reversed when the time is reversed, and there are grave difficulties in deciding which variables should be regarded as thermodynamic forces and which as affinities. Further, the question of whether time should have a preferred direction of flow or be reversible and why this should be so, as well as the relation to the concepts of order and disorder (Prigogine et al., 1972), has not been satisfactorily resolved. The whole matter has been trenchantly criticized (Truesdell, 1969) as being devoid of a logical structure based on a set of sound and physically acceptable axioms. Even so it is not impossible that new studies of thermodynamics will shed light on this whole question. B. Nonreciprocit)) The physical evidence available to date indicates that there is no a priori reason for expecting any form of symmetry in the equations of general physical systems. If a symmetry does exist, then it is a result of the form of the constitutive equations of the system under investigation and not of any general physical principle. Thus the reciprocity principle as commonly understood is not a principle at all but a property of certain special classes of systems. As we have already seen in the previous section, there is a close relation between reciprocity and energy when certain other very restrictive conditions apply. There are two very simple physical situations where reciprocity does not apply. The first occurs in a mechanical context and concerns the relation between the velocities and the corresponding torques arising in the motion of a gyrostat about mutually orthogonal axes perpendicular to the spin axis. Here, as has been known since the eighteenth century, the matrix expressing this relation for an idealized gyrostat is antisymmetric (Pars, 1965), instead of symmetric as in the case of a mechanical system consisting for example of particles, rods, and dashpots, and which possesses the reciprocity property. In spite of the reality of such gyroscopic systems, many theorists persisted in ignoring their existence in their single-minded search for symmetry, or else quietly excluded gyroscopic terms from the equations of motion as an inconvenient detail.


83

The second example concerns the Lorentz force experienced by a charged particle moving in a uniform magnetic field. Here again the relation between the components of the forces and velocities along orthogonal axes in a plane normal to the direction of the magnetic field is given by an antisymmetric matrix.

C. T h e Origin of Antireciprocity If one has been brought up on the premise that symmetry and reversibility should always be present in some form in general physical systems, then it is rather startling to be confronted by an antireciprocal system. The natural reaction is to try to preserve the symmetry or reciprocity at all costs. In the more general form of the reciprocity relation (Rayleigh, 1894), one considers two different “states of the system, corresponding to two different sets of variables satisfying the system equations. Further one distinguishes various types of variables from one another, such as forces from displacements, velocities, and accelerations, or voltages and flux linkages from charges and currents. Denoting the states by A and B and the two types of external system variables by the vectors u and i respectively, the reciprocity relation becomes ”

Now in the case of the gyrostat we can satisfy this relation by taking for state B any member of the set of possible states A transformed by time reversal. (Here u and i represent the torque and velocity vectors respectively.) Then the spin direction is automatically reversed in state B as compared to state A. We can also regard state B as being a member of the set of possible states A but now referring to a d g t r e n t gyrostat, namely with the spin direction reversed, but with otherwise identical characteristics. The important distinction between the t w o approaches lies in the difference between what one regards as the state. In the first case the state refers to all relevant parameters, both internal and externally observable, and thus includes the spin vector of the gyrostat, which, however, is assumed constant. In the second case, only the “external” variables which enter explicitly in (1) are considered. Similar relations hold for a charged particle moving in a magnetic field, provided we reverse the direction of the magnetic field in state B. Of course one can argue that the magnetic field itself is caused by current flow, either macroscopic or microscopic, and if the time is reversed the current flow and thus the magnetic field will be reversed.

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K. M. ADAMS, E. F. A. DEPRETTERE A N D J. 0. VOORMAN

It is tempting to speculate as to what is the basic cause of the antireciprocity in systems of this type.* Two important facts emerge which are evidently closely connected with antireciprocity and with the skew-symmetry of the system matrix. First of all we note that the basic equations in both systems include a vector product which is anticommuting. Thus for the gyrostat we have the equation of motion T

= Cnr

+ Ar

x r,

(2)

where T is the torque vector, r is a unit vector along the spin axis, A and C are principal moments of inertia, and n is the spin velocity. If the spin velocity is sufficiently large, we can neglect the last term and write

T = Cni.

(3)

The projection of the total angular velocity vector on the plane normal to the spin axis is Q=rxr. (4) The total power absorbed by the gyrostat as a result of the action of the external torques is T * Q= 0, (51 by virtue of ( 3 ) and (4). This is an example of what is known as a ??oneneryic 1927). We also note from (3) and (4), that the component of angular velocity which is proportional to a given component of torque is perpendicular to that torque component. These two properties are sufficient to guarantee antireciprocity of the system and lead automatically to an antisymmetric system matrix. In the same way, we have for the charged particle, moving in a uniform magnetic field and in the absence of an electric field, the equation of motion: system (Birkhoff,

F

= ev x

B,

(6)

where F is the force, e the charge, v the velocity, and B the magnetic flux density. Then the power absorbed by the particle as a result of the force is

F - v = 0. (7) Again the system is nonenergic and the force components are perpendicular to the velocity components to which they are proportional. We thus can see the intimate connection between antireciprocity, nonen* Antireciprocity is a special case of nonreciprocity. I f the normal reciprocity relation can be restored by a simple change of sign in some of the describing equations, then we refer to the system as antireciprocal.


85

ergicness, and the properties of three-dimensional Euclidean space, as exhibited by the properties of the vector product. D . Further Generalizations The concepts embodied in Eq. (1) can be applied to far more general systems than those so far mentioned. For example, if one considers linear time-invariant systems in which all the system variables are functions of time and of the form A iexp ( p t ) , with A iindependent of time and p a constant for all the system variables, then the reciprocity relation applies to a large class of such systems (Rayleigh, 1894). An example is a linear n-port network consisting of resistors, capacitors, inductors, and transformers. When the reciprocity concept is applied to three-dimensional field problems, the summation in Eq. (1) is replaced by a spatial integral and a relation between a volume integral and an integral over the bounding surface results. Such relations form the basis of the solution of integral equations by means of Green’s functions and are applicable to a wide class of problems (de Hoop, 1966). Other developments have been concerned with the application of relations like Eq. (1) to two specially related systems which are termed interreciprocal or adjoint (Penfield et d., 1970). The resulting equations lead to useful results for deducing general properties, for network computations, or for the numerical solution of integral equations. All of these developments, however, are special cases of the properties of linear operators and their adjoints in the theory of abstract spaces (Dunford and Schwartz, 1958). For example, in the theory of Hilbert spaces one has the relation

where T denotes a linear operator mapping a Hilbert space $ into itself, T* is the corresponding adjoint operator, x and y are elements of 9, and the symbol (, ) denotes the inner product in 5. Because of the importance of concepts like power and energy in physical systems, the Hilbert space concept with its inner product is especially relevant. Depending on the definition of the inner product that is chosen, a wide variety of reciprocity results of which (1) is the prototype can be obtained. These can refer to variables in the time domain, frequency domain, or spatial domains. The operator T and the space 9 form the abstract representation of the system equations; corresponding to the adjoint operator one can either construct a real system or postulate a fictitious one. As a result of (8) various terms can be made to disappear in the describing equations. It is precisely

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K . M. ADAMS, E. F. A. DEPRETTERE A N D J . 0. VOORMAN

the desirability for the disappearance of such terms and the resulting simplications that have led many physicists to attach such importance to symmetry. Symmetry, however, is only one way to get rid of unwanted terms and corresponds to self-adjoint operators. The really important point to note, however, is that there is no reason to expect the existence of some universal physical principle that guarantees self-adjointness and that the correct use of the adjoint operator will usually allow one to achieve what is desired without having to impose the symmetry condition.

111. THEGYRATOR AS NETWORK ELEMENT A . Historical Introduction In view of Section lI,C, there is no fundamental objection to postulating the existence of an electrical two-port device described by the equations

where u1 and il are the input voltage and current and u2 and i, are the output voltage and current. Such a device is called the ideal gyrutor and is represented by the symbol shown in Fig. 1. The gyrator was introduced as a

FIG. 1. The ideal gyrator.

postulated electrical network element (Tellegen, 1948a) representing the simplest linear, passive nonreciprocal system, before it was clear whether such an element could be a reasonable approximation to some physically real, purely electrical system. I t is true that at about this time, the idea of an antireciprocal passive device was becoming quite clear to several people. Thus an antireciprocal two-port, electromechanical system and its cascade connection with a reciprocal magnetomechanical two-port was considered. The resulting two-port is an antireciprocal electrical two-port (Jefferson, 1945; McMillan. 1946). Indeed gyrator devices based on this principle were built and marketed in the 1960’s, but have not enjoyed much popularity. The ideal gyrostat was


87

also proposed as a mechanical element (Bloch, 1944), and several of its important properties when used in conjunction with other mechanical elements were deduced. Bloch came very close to formulating the electrical gyrator concept, especially in his considerations of the analysis of mechanical networks. However, it was Tellegen who first clearly recognized the fundamental importance of the gyrator as an element, deduced its most important properties, and showed how to employ it in the synthesis of electrical networks (Tellegen, 1948b, 1949; Tellegen and Klauss, 1950, 1951). As a result, electrical network theory and especially network synthesis gained enormously in breadth. In fact as a recent text (Belevitch, 1968) shows, electrical network theory today without the gyrator would be inconceivable. Tellegen, however, not only developed the theory of the gyrator, but also considered possible realizations. This work led him to consider a hypothetical medium in which the electrical polarization can be influenced by the magnetic field strength and the magnetic polarization can be influenced by the electric field strength (Tellegen, 1948a). Such a medium was later found to exist physically (Astrov, 1960, 1961). He also considered the gyromagnetic effect in ferromagnetic materials as a basis for a possible realization. Further calculations by Polder (1949) and experimental work by Hogan led to the first practical gyrator device, operating at microwave frequencies (Hogan, 1952). In spite of all these and many recent developments, the gyrator has not been readily accepted by the electrical engineering and physics communities. Even among network theorists, with a few notable exceptions, there was considerable hesitation in accepting the element and doing theoretical work with it until about 1960. And today one can still find teachers of electrical engineering who prefer their students to remain in complete ignorance of the gyrator concept. We suggest that a major cause of such phenomena is the widespread and deeply-rooted misconception of the true nature of reciprocity. Amongst the designers and users of electronic apparatus, the erroneous notion that a nonreciprocal system cannot be passive is still persistent. It has arisen because all the devices these people came in contact with were either passive and reciprocal or active and nonreciprocal even though by a suitable combination of such devices, passive and nonreciprocal systems could be constructed, at least in principle. Matters have not been helped by references to the reciprocity theorem.” When formulated with any degree of rigor, this “theorem ” either reduces to the tautologous statement that reciprocal systems are reciprocal or to the deduction that a certain specific system constructed from components with certain specified constitutive equations possesses the reciprocity property. The authors of too many books and “

88


papers give the impression that they are appealing to some very general physical principle when they cite the reciprocity theorem or reciprocity principle.” “

”

“

B. Basic Properties of’the Gyrator 1. Siyri Concentions

Figure 2 shows the symbol for the gyrator with various reference voltagepolarity and current-direction signs. These signs and their interpretation as stated here now have fairly general usage. The interpretation is that a quantity such as u , ( t ) is representated by a positive number if the potential of terminal 1 is higher than the potential of terminal 1’ at the instant of time t.

FIG.

2. S i p conventions

Similarly a quantity such as il(t) is represented by a positive number if the current of port 1 flows in the direction indicated by the arrow at time f. In the opposite case the quantity is represented by a negative number. The functions u ( . ) and i(. ) are then the sets of these numbers ordered on the continuous set {t). We are free to choose these reference polarities and directions as we please. Once chosen, however, these references determine the signs to be attached to the algebraic symbols in the describing equations.

2. Noneneryicness The gyrator is an example of what is known as a norieneryic sjxstern (Birkhoff, 1927). That is to say, the instantaneous power absorbed by the element is always zero. Thus from the defining equations (91 we have u l ( t ) i l ( t )+ u 2 ( t ) i 2 ( t= ) 0, The ideal transformer, with defining equations

Vr.

(10)


89

in conjunction with the reference polarities and current directions of Fig. 3, is also nonenergic. The only other nonenergic, linear, time-invariant twoports are two-port combinations of the nonenergic one-ports : the short circuit and the open branch. The proof of this result is a simple exercise in linear algebra.

FIG.3. The ideal transformer with its sign convention in relation to thedefining equations: u I = n u 2 , i2 = - n i l .

The concept of nonenergicness has important uses in much more general contexts (Adams, 1974), but for our present purposes, it is not necessary to go into these details. It is clearly a special case of passivity.

3. Isolation and Power Transmission Consider the two-port networks shown in Fig. 4. If the gyrator is defined by Eq. (9), then the two-port resistance matrix of two-port a is

With the sign conventions of Fig. 2, this means that the power absorbed by port 1 is u,i, = Ri: 2 O

(13) if R > 0. On the other hand, the power absorbed by port 2 can be either positive or negative, depending on the ratio i l / i 2 . Since the resistor is passive, this means that power can be transmitted only in one direction through the two-port. Thus port 2 can deliver power to its surroundings but port 1 will always absorb power. In the same way we find for two-port b that the two-port conductance matrix is

[

G -2G

G O1

(G

=

1/R)

and that the same conclusions regarding power transfer apply. It is as a

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K. M. ADAMS. E. F. A. DEPRETTERE AND J.

0. VOORMAN

result of this property that the arrow associated with the gyrational resistance R in Fig. 2 is employed. This arrow can now be interpreted in two ways. Either we can agree that R is always positive, in which case the arrow denotes the actual direction of power flow in the gyrator-resistor two-port and Eq. (9) applies with R always positive, or we can regard the arrow as a reference direction which corresponds to the direction of power flow when R is positive, or is opposite to this direction when R is negative. If we then agree to introduce the reference voltage polarities and current directions of

=====P

FIG.4. The isolator and power flow

the ports in such a way that the arrow is directed between the terminals associated with plus signs of the two ports, and further choose the current references such that ui is positive when the port absorbs power, then the equations of the gyrator are given by (9). The use of the arrow alone thus enables us to write down the equations with the correct signs and to adopt a consistent reference for voltage polarities and current directions. If for any reason we wish to change any of these references then the corresponding equations can be obtained by replacing the appropriate voltages or currents by their negatives.


91

The gyrator-resistor combination discussed here is known as an isolator and has important applications in microwave technology (Beljers, 1956). 4. Antireciprocity If, as in Section II,C, we consider two states denoted by A and B, then we find that the defining equations yield

This relation can be obtained from Eq. (1) by converting a single minus sign to a plus sign, and thus corresponds to an antireciprocal system. When the impedance or the admittance matrix of an n-port exists, then the matrix is skew-symmetric if the n-port is antireciprocal. Antireciprocity is the simplest form of nonreciprocity. No other nonreciprocal element than the gyrator is required to characterize linear, time-invariant, nonreciprocal n-ports. It is one of the basic results of network synthesis that any passive n-port, which is characterized by linear ordinary differential equations with constant coefficients in the port voltages and currents, can be synthetized from the elements: resistor, capacitor. inductor, ideal transformer, and gyrator (Oono and Yasu-ura, 1954; Belevitch, 1968). As we shall see in the following sections, the ideal transformer and inductor can be deleted from this list. 5. Ideal Transformers A cascade connection of two gyrators is equivalent to an ideal transformer (Fig. 5). Conversely, any ideal transformer can be synthetized by a network of two gyrators with suitably chosen gyrational resistances.

hd t FIG.5. Ideal transformer synrhetized from two gyrators

6. Iininittance Inversion

Perhaps the most important property for engineering applications is the inversion of an impedance or admittance, as shown in Fig. 6. In particular, a capacitance with impedance llpC is converted by a gyrator into an impedance pR2C, corresponding to a self-inductance L = R 2 C . Especially this

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K . M. ADAMS, E. F. A. DEPRETTERE A N D J. 0. VOORMAN

property has led to increased interest in applying the gyrator concept to integrated circuits. More generally, any one-port network N is equivalent to a one-port formed by the cascade connection of a gyrator and a network N’, which has the structure of the dual network of N (if it exists) and with element values proportional to those of the dual network. Another generalization is the two-port equivalence shown in Fig. 7.

-Jj-=j

JY=;;.

FIG.6. Demonstrating the immittance inversion property

7. Iiiterclzange

of’ Variables and Duality

A generalization of the foregoing applies to n-ports. Let IZ gyrators, with gyrational resistors of 1 Q, be connected to the ports of an n-port network N as shown in Fig. 8. There results an 17-portnetwork N’, which is described by 1R

3-c 3-c

n-port

IQ

FIG. 8. Interchange of port variables

93


equations obtained from those of N by interchanging the port voltages and the corresponding port currents. If the equations are expressed in terms of other electrical quantities, then these quantities are interchanged according to their relation to voltages and currents. Thus, for example, charges and fluxes are interchanged. Then network N ’ is equivalent in the n-port sense to the dual of N (when it exists). Thus we can use the gyrator as a dualizing converter in design or analysis. A simple application of this principle is shown in Fig. 9.

FIG.9. A special case of dualizing.

When the gyrator can be used freely, the distinction between current and voltage as ‘‘ through and “across variables disappears, since the topological structures inherent in these concepts and their duals are freely interchangeable. This is one of the reasons for the difficulties in attempts to lay the foundations of nonequilibrium thermodynamics in the conventional manner (de Groot and Mazur, 1962). ”

”

8. Reactioe Power Although the gyrator is nonenergic, this does not mean that the complex power absorbed by the gyrator is zero, but only that the real part of the complex power is zero. The imaginary part, or the reactive power, is given by Qc,

=

f Im ( U ,IT +

U 2IT) = Im ( R I , IT).

(16)

This is not surprising when we consider the relation of reactive power to stored energy, Thus the reactive power absorbed by an inductor is QL = -$ Im (jwLII*) = &wLI Z I z

=

20W, > 0

(w

> 0),

(17)

where W, is the mean stored magnetic energy. For a capacitor we find that Q c = -‘C 2 a (U12 = -2wW, > 0

(0>

O),

(18)

where We is the mean stored electric energy. Since reactive power is conserved in networks (Tellegen, 1952; Penfield et al., 1970), if an inductor is simulated by a gyrator terminated in a capacitor, the difference of the reactive powers absorbed by the capacitor and the simulated inductor must be equal to the reactive power absorbed by the

94


gyrator. It is readily verified from Eqs. (16)-( 18) that QL

= QC

+QG~ 7

when account is taken of the sign convention for currents and voltages and of the interconnection of the elements. This property of storing reactive power is in sharp contrast to the properties of the ideal transformer, for which both the absorbed active and reactive powers are zero. Once the gyrator has been introduced, the distinction between total stored electric energy and total stored magnetic energy of a system disappears. The total stored energy, electric and magnetic, is still relevant but the difference between the two types of energy disappears. In the Lagrangian formulation of networks, this disappearance is compensated by the appearance of linear terms in the Lagrangian function to account for the presence of gyrators (Adams, 1968).

IV. FILTERS A . Introduction

A filter is an apparatus that, when presented with a mixture of certain “things,” allows some of these “things” to pass through it in a specified manner and prevents the passage of the other “things.” In electrical engineering the “things” are usually signals which can be regarded as consisting of various components, some of which are desirable and are to be retained as far as is possible, and others which are undesirable and are to be rejected. Historically, the first filters consisted of linear, time-invariant networks, and were designed for separating the signal components in various frequency bands from one another. Today, the word filter has come to mean almost any signal-processing apparatus or algorithm or program that is remotely connected with the idea of separation of desirable from undesirable quantities. In many of these generalizations from the original simple filter networks, concepts such as reciprocity and antireciprocity apply. The gyrator concept then automatically appears and plays an important role (see, e.g., Fettweis, 1971). In this section we shall concentrate on the classical network filter from which these other more recent developments have evolved. B. Basic Configuration

The classical filter-network configuration consists of a signal source which is capable of delivering a certain maximum quantity of signal power, a passive transmission two-port network which is the actual filter, and a load

95


where the filtered signal is further processed and its accompanying electrical power is finally dissipated into thermal power (Fig. 10). The signal (energy) source can be represented by an ideal voltage source in series with an impedance (Thevenin circuit), or equivalently, an ideal current source in parallel with an admittance (Norton circuit). We shall restrict our discussion to the simplest but very important practical case in which both the source and the load impedances are pure resistances. We shall further restrict ourselves to the case where the signal source strength varies sinusoidally with time.

n a ,

Source

-

Load

Source

Filter I

Load

I I

FIG. LO. Basic filter configuration

Then one of the very important parameters for judging the performance of the filter is the ratio of the power received by the load to the maximum available power of the energy source as a function of frequency (Geffe, 1963; Saal, 1963; Skwirzynski, 1965).* The quality of such a filter is then often judged by such parameters as the closeness with which this ratio approaches unity in certain frequency bands (the passbands), the smallness of the ratio in certain other bands (the stopbands) and the narrowness of the frequency intervals in the remaining portions of the spectrum (the transition bands). These terms are illustrated in Fig. 11. T w o other points should be noted at this stage. The first is that intuitively we should expect the most efficient transmission in the passband, when the filter proper is lossless. At these frequencies the filter is ideally transparent to signals. Secondly, filtering is often connected with such matters as improving the signal-to-noise ratio. This is a power ratio and the noise power of a source is a maximum available noise power, so that, provided the filter itself does not generate any noise, the transmission parameter shown in Fig. I I is most appropriate.

* A filter theory based on this power ratio as primary characteristic is often referred to as the insertion-loss theory. Unfortunately, not all authors mean the same thing by this term, which is the reason why we prefer not to use it in this article.

96


FIG. 1 I . A typical filter characteristic. o is the ratio of the power dissipated in the load to the maximum available power of the source, A and E are the stop bands, C is a passband. and B and D are transition bands.

C. The Scattering Matri.u When analyzing and synthetizing transmission ti-ports, the scattering matrix S is frequently the most suitable tool to use. Amongst its advantages are the fact that it always exists if the n-port is passive, in contrast to most of the other network matrices (Carlin rf id., 19591, and that it is directly related to power transfer and thus to the specification of filter characteristics (Belevitch, 1968). The n-port equations are written in the form

b

=

Sa,

(20)

Here U and 1 are the (complex) port voltages and currents while R is a diagonal matrix with positive diagonal elements, and R'12 is also a diagonal matrix with positive diagonal elements which are equal to the square root of the corresponding elements of R. Then it is clear that

The network relations between the various quantities are illustrated in Fig. 12. The elements of a and b are called wave variables; a is the incident and b is the reflected wave vector. In ordinary (lumped-element) networks this terminology is rat her artificial, but in transmission lines and waveguides these quantities correspond to actual waves. The elements of R are called the

97


normalizing resistances or preferably the reference resistances of the ports. They are real and positive. The diagonal elements S j j of S are called the reflection factors ; the other elements are the transmission factors. If the n-port is lossless, and the signals are sinusoidal, then S is unitary:

STS*

=

(251

1, ,

where 1, denotes the unit matrix of order n. In the more general case of exponential signals, S is para-unitary, i.e. STS* =

1,

(26)

where S, denotes S( - p ) . R.

h,

R2

FIG. 12. Scattering variables of a two-port. u1 = 4R;' ' D o , - Ri ' 1 , .

=

$R;' ' ( U ,

+ R , I,).

=

1. The Canonical Forin In the important special case of a lossless two-port constructed of a finite number of real, lumped, passive elements, S can be written in the form (Belevitch, 1968)

where g, h, f are polynomials in the complex frequency p ; f , , h , denote = & 1. In the case of sinusoidal signals, p = j w and h, = h*. From the defining equations, we see that the zeros of g are the natural frequencies of the network of Fig. 12 when the source intensities are zero, i.e. the original two-port network with the ports terminated in the reference resistances. This terminated network is evidently passive, so that the zeros of g must lie in the left-half of the complex plane, i.e. 9 is a Hurwitz polynomial. The para-unitary condition can now be expressed in the particularly simple form (Belevitch, 1968)

f(-p), h( - p ) , and

98


If now we choose U,, = 0 in Fig. 12, then a, = 0 and we have the basic filter configuration of Fig. 10. Then

U,

=

R;”(U, -I-b,)

=

R:”b,.

(29)

In the case of sinusoidal signals, the (average) power absorbed by the load is

5 I U2 I2/R2 = 4I b, 1.’

(30)

The maximum available (average) power from the source is

I uoi I2/8R, = 4I 12, a1

(31)

so that the fraction of the available power transmitted is

by (27). The fraction of the available power which is not transmitted is “reflected” back into the source. This is (33) by (25) and (28). A filter characteristic is often specified by the so-called characteristic function ) I defined by

I? * = j ,

(34)

which exhibits explicitly the zeros of the reflection and of the transmission factors. As a result of (28) and the fact that y is a Hurwitz polynomial, g is determinable once 1 $ I is known and the procedures of network synthesis then guarantee that a realization can be found (Belevitch, 1968; Youla, 1971).

2. The Circulator The gyrator as a lossless two-port has a particularly simple form of S-matrix if we choose the reference resistances equal to the gyrational resistance. We find

where q

=

+ I . From the gyrator we can construct a certain three-port in


99

either of the ways shown in Fig. 13. This three-port has an S-matrix

where y = 1 for network (a) and y = - 1 for network (b). In both cases the three-port is known as a circulator and has important uses especially in microwave engineering (Bosma, 1964). R

36 30

d

3

b

(cl

FIG. 13. The circulator: (a) the admittance matrix exists, (b) the impedance matrix exists, (c) symbol for the circulator.

D. Ladder Filters Most high-performance filters are realized in the form of an LC ladder network if this is at all possible. It has been found through long years of experience that ladder filters are relatively easy to build and to adjust so as to conform to the filter specification. The theoretical basis for this effect was

100


not fully realized until quite recently (Orchard, 1966). It was brought into focus through the difficulties arising from attempts to construct high performance active RC filters. There are two reasons for the favorable properties of the LC ladder network (see Fig. 14). First, the zeros of transmission are separately determined by the resonance frequencies of the arms of the ladder. Thus at such a transmission zero

FIG. 14. A ladder network. According to popular usage the arms labeled with Z ‘ s are termed the “series” arms and the arms labeled with Y’s are termed the “shunt“ arms.

(or attenuation pole) either one of the “series” arms of the ladder has an infinite reactance or one of the “shunt” arms has a zero reactance. The transmission zeros can thus be accurately adjusted by tuning the arms of the ladder. Since the frequency of the source can be accurately set, it is a simple matter to tune the appropriate ladder arm by adjusting the capacitor or inductor so as to produce a minimum in the output. In practice, because of the particular construction of ferrite pot cores, this tuning is easily carried out by a simple adjustment of the air gap of the core. Thus the zeros offare then accurately determined and we find that the stopband characteristic conforms very closely to the specification. The adjustment of the transmission zero(s) closest to the passband is especially important, since these zeros substantially determine the transition region(s). The second reason is that in the passband the first-order sensitivity of 1 S2 1’ to element-value variations at a zero of S1 is zero. It is very easy to see how this arises as a consequence of the losslessness property. Thus if the element values vary for any reason from their nominal values, the network still remains lossless (we suppose for the moment that the filter is constructed of ideal inductors and capacitors) so that Eq. (25) is still valid. In particular.

,

Is11

l2 +

IS21

l2 = 1

(37)

and a first-order variation yields

,

,

If 1 S , I = 0, then 6( I S,, I ) = 0, since 1 S z 1I and I S, I cannot simultaneously be zero. Further since S,, I 5 1, 16 I S , 1 I 5 1 and is thus finite.

I


101

Thus in the neighborhood of a reflection zero, the transmission characteristic varies little with variations in the element values. Furthermore, in the passband, the reflection factor will not normally differ much from zero if the filter is well designed, so that even at a maximum value of the modulus of the reflection factor, the variation in 1 S,, I will be small. Experience shows that the most sensitive region is near the passband edge, and is closely related to the resonance effect (Section IV,E). It is important to note that (37) and (38) remain valid if the terminating resistors deviate from their nominal values, so that the conclusions regarding the sensitivity also apply here. In practice one finds that very high quality filters can be built with components with 1 tolerance and that for many purposes a tolerance of up to 5 % is good enough. The ladder filter thus en-joysa remarkable property which is not known to hold for any other configuration except those which simulate the ladder exactly or which in some sense combine the properties of losslessness and the ability to set the attenuation poles very accurately (see, e.g., Bruton, 1973). If the reactive components have parasitic losses, then the performance and the sensitivity of the filter deteriorate (Neirynck and Thiran, 1967). It is thus important to reduce the losses as much as possible; the sharper the discrimination between the pass and stop bands, the higher needs to be the quality factor of the components. As a result of these considerations it would seem very attractive to consider replacing the inductances in a ladder filter by a gyrator-capacitor combination. Particularly since it is now possible to simulate inductances in this manner with extremely high and relatively stable Q's in the range 100010,000, this technique would seem to have much to recommend it. There are, however, some grave difficulties in practice which we shall discuss in the following sections. However, the same difficulties appear in many other proposals for filter circuits. E . Resonance in Filters

As already mentioned in Section IV,C, the natural frequencies of the free oscillations of the filter are the zeros of the polynomial g, i.e. the poles of S1 S,, , S, , Szl.If such a network is excited at a frequency which is close to one of the natural frequencies, resonance will occur and large voltages and currents will appear in the various components. Using Eq. (28), we can readily see qualitatively in what region this effect will be most pronounced. Thus for sinusoidal signals ( p = ,jw), Eq. (28) becomes

,

+ Ifl'=

(39) At a point on the j-axis of the complex plane near a zero of g, I g I is small 1912>

yo.

102


and thus I h I and I f 1 are small. Thus this point on thej-axis must be close to zeros of h and$ The only possibility which allows this to occur is for the resonance frequency to lie near the edge of the passband or in the transition band, between a reflection zero and a transmission zero (see Fig. 15). It

1

O

IS2,l-

IS,l-

1

x

+4

i

0

1

IW

Oh xf

t t

-a

FIG. 15. Relation between poles and zeros and the filter characteristic

follows that the narrower the transition band, other parameters being equal, the more pronounced will be this effect. We can give a simple quantitative relation for this effect (Dicke, 1948; Kishi and Nakazawa, 1963; Carlin, 1967; Kishi and Kida, 1967, 1970) based on Tellegen’s theorem (Tellegen, 1952; Penfield ef al., 1970), which is valid for any lossless two-port terminated in the reference resistances. We employ Tellegen’s theorem in the form

1 (U,* A l x + 1: AU,) = 0, a

where a is taken over all branches of a complete network, ( U , } and [I,) refer to a possible network distribution of voltages and currents obeying Kirchhoff’s laws, and (AU,) and (AI,} refer to a variation of voltages and currents about that distribution, also obeying Kirchhoff’s laws. We consider next the situation that port 1 of the lossless network is excited by an energy source while port 2 is terminated in the reference resistance. This results in a certain { U,, la}distribution. For the variational state we allow all the reactances to undergo a small variation but keep the other elements constant. From (40) we find after some calculation, correct to the first order of small quantities,

103


where 8, = -arg (S,) (i,j = I, 2), T is taken over all reactances, P is the available input power, and suffix 1 refers to the fact that port 1 is excited by the source. If the variations of U , and I , result from a variation of the frequency, then we obtain from (41)

where W is the average total stored energy, or in derivative form,

In the same way, if port 2 is excited by a source and port 1 is terminated in its reference resistance, we have

From (43) and (44) we obtain, using (25),

where 5 is referred to as the total transmission time (group delay) from port 1 to port 2 and back to port 1. But

0 1 2+ 8,,

=

-arg (S12S21) = -arg

(F),

so that T =

d 2 d o arg (y) ~

( p = J'LU).

(47)

( j w - .io, + xs),

(48)

We can factorize g as Y =

I
i, , then i, - i, is amplified by T, and causes an extra current to flow in T, (working as a diode) and R,. The potential of the bases of T, and T, rises, so i, increases, thus reducing il - i, . A third point to note is that in every nullor circuit, the bases of the transistors must be supplied with current. There is always at least one base which must be supplied externally to the nullor circuitry. If no provision is made for this in the current sources, then an equal current will flow in the nullor ports, i.e. offset current is generated. This effect can be reduced to a very low level by ensuring that il and i 3 differ by an amount equal to the total external leakage (base) currents of the nullor circuit. We must also

140


include the base currents of T, and T, in this total when several current sources are controlled by the same control network. If we require i, - i, = ni,/P, then we can effect this by increasing the voltage across R 2 and the emitter current ofT2 by ni,/P,but keeping i2 unchanged. This can be effected by the circuit of Fig. 39, whereby the super$ combination is used both for

,+= 11

/$\ 12

Nullor

u-

FIG. 38. Current-source control circuit

FIG. 39. Base-current compensation circuit

base-current compensation and for impedance enhancement of the current source. All of these design principles have been successfully implemented (Voorman and Biesheuvel, 1972). 4. ‘‘ Latch-up ’’

In electronic circuitry one is frequently confronted with the situation where a circuit “locks” in some parasitic equilibrium state and fails to work according to its specifications. What happens is that some or all of the transistors do not receive their correct bias currents so that they are either


141

cut off or bottomed. This situation is known as “latch-up.” The reason for the occurrence of this situation is that the complete set of nonlinear equations which describes the dc behavior of the complete circuit have more than one solution, any one of which represents an attainable (and sometimes stable) current and voltage distribution in the network. Unfortunately, the theoretical studies on this subject are not yet sufficiently well developed to aid the designer in correctly predicting the occurrence of this phenomenon and in adopting corrective measures. The only alternative is a laborious analysis of each circuit on the basis that a transistor either conducts normally, or bottoms, or is cut off. If more than one stable state is detected, then extra diodes can sometimes be introduced, which conduct heavily when an undesirable state is obtained but which do not conduct in the normal situation and thus do not influence the normal working of the circuit. The augmented circuit then has to be checked that only one stable state is possible. B. Realization Based on Four Resistors in the Signal Path

As already mentioned in Section V, there are two configurations of two nullors and four resistors which can serve as the bases for practical realizations. They lead to a well-known circuit due to Riordan (1967) and a more recent circuit due to Trimmel and Heinlein (1971) (Fig. 40). All of these configurations have the limitation that the ports are not galvanically separated. Until now, such circuits have only been used for simulating inductances and not as gyrator two-ports. Also to date, the nullors in these circuits have been realized only by operational amplifiers. It would seem worthwhile investigating the possibilities of using the artificial transistors discussed in Section VT,A in this type of configuration; to our knowledge this has not been done. The circuits of this type have been limited by the requirement that the operational amplifiers have a grounded output and that one port be grounded (Antoniou, 1969; Orchard and Sheahan, 1970). However, the more recent circuit of Trimmel and Heinlein (1971) is free of these restrictions since the amplifiers are fed through current sources. Although the complete performance of this type of circuit is dependent on the particular form of electronic circuitry used to realize the operational amplifiers, there are certain global conclusions which apply. As these circuits have been analyzed in some detail in the literature mentioned above, we shall only quote the results and comment on them. First, there are several ways of combining nullators and norators to form nullors, and secondly the polarity of the gain of each operational amplifier which approximates a nullor can be chosen in two ways. Only a few of the resulting circuits are stable (Antoniou, 1969).

142


In the Riordan circuit, voltage-controlled voltage sources have been employed. Provided the voltage gain is greater than 1000, the input and output impedances of the amplifiers are not important and the selfinductance simulated is approximately L = R , R3R4(C/R2)(1 4/A1) where A , is the gain of the first amplifier at low frequencies. The maximum Q attainable at low frequencies is approximately half the gain of amplifier 2.

+

1

Ri

1'0

f (b)

FIG.40. Two-nullor realizations: ( a ) Riordan circuit; (b) Trimmel and Heinlein circuit.

At higher frequencies, the same tendency for Q to become negative as in the case of the four-nullor, two-resistor configuration occurs. The time constant of amplifier 1 is largely responsible for this effect. Although it is possible to compensate this effect by adding suitable capacitances, the result is difficult to control properly, since it depends on the difference between the time constant of amplifier 1 divided by its gain, and a time constant determined by passive components. The circuit is subject to conditional stability and latch-up unless countermeasures are taken in the electronic design. The circuit of Trimmel and Heinlein employs voltage controlled current sources with high gain as.operationa1 amplifiers. The self-inductance simulated is approximately L = R , R 3 R,(C/R,)(I + 6 ! y I R ) , where y 1 is the transconductance of amplifier 1 and R is the mean value of the resistances when they are nearly equal. The Q at low frequencies is proportional to g 2 ,


143

and inversely proportional to the difference of two resistance ratios. With equal resistors and gains, the Q becomes negative when the time constant is taken into account. Compensation is possible as in the case of all gyrator circuits (Miiller, 1971; van Looij and Adams, 1968) but only in the form of subtracting two nearly equal quantities, which are subject to tolerances or different temperature coefficients. In filter applications, a negative or variable Q is acceptable, provided it is numerically large. The terminating resistors of the filter provide the necessary damping of any inherent low-frequency oscillations.

C. Noise The principal sources of noise in electronic gyrator circuits are the resistors and the current sources required for supplying the nullors. The nullors themselves, if they are well designed, contribute little to the total noise

(a)

(b)

FIG.41. Noise source representations of the nullor and its associated resistor: (a) thermal and shot noise; (b) flicker (llf) noise. (un, u,) = 2kT(2Rbb+ r,)df, ( i n , in) = 4(1/bre)kTdJ (i,,, in,) = 4kTdJR.

with the exception of the ljfnoise. In the ideal case, since the norator voltage and current are determined in the first instance by the external circuitry and not by the nullor circuitry, it is clear that any internally generated noise does not appear at the nor port. At the null port, there is a base-emitter diode which carries a bias current I,. This results in a shot-noise voltage in series with the port given by (unS, unS) = 2kTr, dJ where re is the diode resistance kT/qZ,. Since in the case of the artificial transistors, I, is very low, this shot-noise voltage can be rather high. There is also a thermal-noise contribution to the total noise voltage, (u,, u,) = 4kTRbbdJ due to the base resistance. A noise-current source across the emitter-base diode can usually be neglected (Fig. 41a; Blom and Voorman, 1971).There remains the llfnoise, which also produces a voltage in series with the null port (Fig. 41b; van der Ziel, 1970). Provided we choose the gyration resistors sufficiently large, the

144


total noise voltage in series with the null port will be primarily the thermal noise of the gyration resistor and the llf’noise. The result is that in the two-resistor four- (or three-) nullor realization, each resistor produces a noise current ( i n , in) = 4kTGdf which, as a result of the nullors, appears in parallel with the gyrator ports, together with the llf noise which contributes ( i s [ , i s l ) ( r e / R ) 2to the port current. The current sources produce similar effects, which appear as currents between the gyrator terminals and the ground (Fig. 42).

I

FIG.42. Noise-current sources due to the supply-current sources.

Since the thermal noise current of these sources is inversely proportional to Re + r e , where re is the emitter-base diode resistance and Re is the external emitter resistance, it is advisable not to make Re too small. On the other hand, a large Re is wasteful of supply power. The ratio of this noise current to that produced by the gyrational resistance is denoted by the noise factor F,. A reasonable practical value of F , for discrete circuits is 4 or 5 (Blom and Voorman, 1971), but F , can be ten times higher in the case of integrated circuits. In the case of the four-resistor, two-nullor realization similar conclusions apply, except that the contribution of the resistors to the noise current at the ports is twice as large in the case of equal resistors (Orchard and Sheahan, 1970). However, depending on the electronic realization one can save on the number of current sources required. When filters are constructed from capacitors and inductors simulated by gyrator circuits and capacitors, the spot noise power observed at the output of the terminated filter, due to the thermal noise of the gyrational resistances, is intimately connected with the average “magnetic energy” stored in the circuit at a given frequency, and is thus dependent only on the scattering matrix of the filter and not on the particular LC realization adopted. This noise power is given approximately by (Voorman and Blom, 1971):


145

where we employ the notation of Section IV,E. The noise is most pronounced near the band edge where -5 = d02,‘dw is a maximum (cf. Section IV,E). In the case of a reciprocal two-port, z = 2.2 [cf. Eq. (45)] and the maximum spot noise is approximately k T d f o z . This occurs at the same frequency where the resonance effect and the sensitivity are highest. From these results we can determine a lower limit to the minimum necessary dynamic range for a given signal-to-noise ratio in the output. This in turn determines the necessary power supply. It is important to note that if the dynamic range is fixed, the permissible input signal level is proportional to l / o z while the output noise is proportional to oz. The S/N ratio at the output is thus proportional to l/(wz)2. VII. BASICGYRATOR MEASUREMENTS A. Introduction

Any theoretical considerations and design philosophy must be supported by measurements on actual circuits. In this section we consider the basic description of a gyrator circuit as an object for measurement. Although in theory a gyrator is a two-port, an electronic gyrator circuit is in practice a

f FIG.43. The gyrator as a grounded four-port

grounded four-port (Fig. 43). In the ideal case the short-circuit admittance matrix Y is Y=

0 0

0 0

+G -G

-G +G

We can either measure the elements of this admittance matrix or of the scattering matrix directly, or we can measure some properties of the gyrator in one or more specific applications, e.g. with two capacitors as resonant circuit. Then it depends on the designer’s philosophy whether we must measure all parasitic effects in detail or only their order of magnitude. The circuit can

146

K. M. ADAMS. E. F. A. DEPRETTERE A N D 3. 0. VOORMAN

be designed such that for its main application all parasitic effects (or almost all of them) are so small that they can be neglected. In this case they may be strongly nonlinear or temperature dependent but because they are so small this is of no importance. For these parasitic effects, only rough measurements, preferably in the context of the main application(s), are necessary. On the other hand, if the parasitic effects are not so small and they must be taken into account or compensated, accurate measurements are required. Quantities which can be measured are accuracy, behavior at higher frequencies, intermodulation, signal-handling capability, noise, dc offset, etc. B. The Gyrator as n-Port Before considering measuring techniques, we must have an adequate description of the gyrator circuit as the object to be measured. We can consider the gyrator most accurately as a grounded four-port and further, depending on the circumstances, as a three-port, two-port, or one-port when one port is terminated by a n impedance. 1. The Gyrator as a Grounded Four-Port

The short-circuit admittance matrix of the ideal gyrator is in this case

0 0

0 0

Y=

+G -G

-G +G

The impedance matrix does not exist and the scattering matrix is not very suitable for describing the grounded four-port. Thus the scattering matrix normalized to G is

S

=+

I -

4

1

2

-2 2

2

1 4

-:I1 1

This is not a very suitable form to take as the basis from which deviations in ideal behavior can be measured. The best description here is the admittance matrix and it seems to be natural t o measure its elements directly. The admittance matrix Y can be written as the sum of its Hermitian and skew Hermitian part

Y

= f(Y

+ Y*') + +(Y

where T denotes the transpose and

-

Y*'),

(108)

* the complex conjugate of the matrix.

147


The admittance matrix of a lossless network is skew Hermitian. The Hermitian part gives a measure of the losses or of the activity of the network. The grounded four-port description is the most complete description of the physical gyrator. The elements of the four-port admittance matrix are not always different in value. Suppose we have a symmetrical voltage-controlled current source

( b)

(a)

FIG.44. Two identical symmetrical stages connected antiparallel, forming a gyrator.

(Fig. 44a) with a grounded four-port admittance matrix Y. Then, owing to the symmetry we have '21

= '34

7

3 '1

= '24

9

'41

'=

y14

9

y32

y33 =

= '23

y,,,

> y42

= y13

= '12,

y43

3

Y44 = Yll.

(109)

A second identical voltage-controlled current source connected to the former one as indicated in Fig. 44b has the following grounded four-port admittance matrix: y' =

'33

'31

'34

'32

'13

yll

y14

'12

For the complete circuit, a well-known gyrator type, we must add the admittance matrices Y and Y and we obtain a matrix with four different element values only. The structure of this grounded four-port gyrator admittance matrix is

where yl

yll

+ '22

>

y 2 = y]2

+

'24

9

3'

= '13

+

'21,

y4

= '14

+

y23

.

(112) If terminal 4 is grounded, then in the resulting semifloating gyrator the four different elements Yl, Y, , Y3, Y4 are still present.

148

K . M.

ADAMS,

E. F. A. DEPRETTERE A N D J. 0. VOORMAN

2. Grounded and Semzjloatiny Gyrators The description of the gyrator as a grounded two-port is applicable if both ports of the gyrator are grounded. Then. in fact. only a part of the fourport admittance matrix is used. For an ideal gyrator we have

The two-port scattering matrix normalized to the gyration conductance G,

0

-1

s = [+l

013

also gives a good description here.

I

FIG.45. Inductance simulation with a semItloating gyrator and a capacitor

Note that for the grounded gyrator the impedance matrix exists too. For the ideal gyrator we have

where R = 1/G is the gyration resistance. A semifloating gyrator (one port grounded, the other floating) can best be described by a grounded three-port admittance matrix. Note that we use each time a grounded-port matrix description because its parameters can be measured easily and accurately, as will be shown in Section VII,B,3. With floating ports this is much more difficult. Once the matrix elements of the grounded-network matrix have been measured, all properties of the circuit can be calculated. For example, if the grounded three-port matrix of a semifloating gyrator (Fig. 45) is

Y=

[I

-G+y21 +GJ'y y31

+G

+

4'12

-G

+

2)13

Y22

y23]

Y32

Y33

9

(116)

where generally / y k , 6 G, we can calculate the behavior of a floating inductor simulated between terminals 2 and 3 when port 1 is terminated by a

149


capacitor C. With I ,

=

-pCU1, we obtain

(1 17)

Because the simulation of an inductance between terminals 2 and 3 must be considered, it is better to introduce as new variables the port voltage Up = U2 - U , and the mean port current I , = (I2 - 13)/2.In addition, we can take for the third and fourth variable the common-mode voltage U,, = ( U , + U 3 ) / 2and the common-mode current I , , = I, l3(the current to the ground, see Fig. 46). In terms of these variables we get

+

I,,

=

[-

(h+ Y 3 & ! L + A PC + Y 1 1

+ 4’22 + y23 + y,, + J’33

1 u,,

(a)

FIG. 46. (a) The port voltage Up = U , - U , and the common-mode voltage U , , = $ ( U , + U 3 ) , where U , and li, are the terminal voltages. (b) The mean port current I , = + ( I 2 - I , ) and the common-mode current I , , = I, I , .

+

150


The coefficient of Up is the inductance term expressed in terms of the measured elements of the grounded three-port admittance matrix. We also see that the inductance value and particularly its quality factor depend on the common-mode signal voltage.

3. Admittance Measurements All input admittances of the short-circuit admittance matrix can be measured accurately with the standard bridge methods (e.g., Stout, 1960). For the transfer-admittance measurements, bridge methods can also be used. For example, the transformerless double bridge of Fig. 47 can be used.

FIG. 47. A transformerless double bridge circuit for accurate transfer-admittance measurements.

The conditions for balance give

Often y , can be taken to be zero. The usual rules for accurate bridge measurements apply here also. The substitution method can also be applied. For higher frequencies it can be very advantageous to use a Wagner earth connection. In fact, point E (Fig. 47) must be connected to earth and automatically the Wagner earth connection is implemented. 4. Measurement of Scattering Purmneters

In the microwave region the scattering parameters, which are related directly to forward and backward traveling waves, can be measured by comparing amplitudes and phases of the waves. In the low-frequency region we are obliged to use voltages and currents. Consequently, we shall translate the scattering parameters into quotients of voltages or currents.

151


First, let us consider a reflection factor Sll.We have: J K a , + ( U , R , I , ) , f i b , = f ( U , - R , I , ) . Hence

=

+

FIG.48. A reflection coefficient S , , expressed as a quotient of two voltages: S ,

=

U,/U3

FIG. 49. A transmission coefficient S , , expressed as a quotient of two voltages: S, = 2JRT*2 ( U 2 / U , ) .

,

In this way a direct measurement of the reflection coefficient is possible. It is also possible to measure the input impedance Zi = Ul/Il, followed by a calculation of the reflection factor from - R, s,, =-.Zi Zi + R ,

Measurement of a transmission factor Szl is even more simple (Fig. 49). With K a , = i ( U , + R , I , ) = i U o , &b2 = * ( U , - R , I , ) = U , , we obtain

Again a quotient of two voltages is to be measured, which can be done for example with a bridge method.

152

K. M. ADAMS, E. F. A . DEPRETTERE A N D J. 0. VOORMAN

5. Offset An electronic gyrator can d o its work properly only if it is biased. The bias voltages and currents should be balanced as well as possible, and in such a way that they are not observable at the ports as components of the port voltages and currents. In practice, perfect balance is not achieved. Unbalance and different dc levels are manifestations of offset. Small offset currents and voltages cannot be distinguished from signal currents and voltages. If is is the signal current vector and iff, is the offset current vector then the vector i of the total currents is i = i, + i,,,,, and similarly for the voltages u = U, + uoff,.Thus

i

=

Gu

-

Gsrr. + iff. ,

(124)

where G is the port conductance matrix. Small offsets, which fall within the signal-handling capacity, cannot be distinguished from signals. We can transform these voltage offsets u,&. into current offsets Cff, by

but generally not vice versa (when G - ' does not exist). Symbolically, we can always write (also if ~ ~ u o fexceeds f . ~ ~ the signal handling capacity) - GUoff.

Ioff. = i f f .

>

giving, with (124), i

=

Gu

+ Ioff,.

(126)

These equivalent offset currents I,,,,, determine the offset behavior of the circuit completely. Measurement of the offset current vector Ioff.can be carried out as shown in Fig. 50. The ports are adjusted to proper dc levels (ul. 2 , u 3 . 4) and the i.

A

FIG.50. Measurement of the offset current vector I,,, .

153


currents i , , i,, i 3 , i, are measured. If the gyrator is ideal, we have from (126)

0 -G +G

0

+G

-G

fG

u3.4

-G

u3.4

(127) As an example we shall calculate the offset of a parallel resonant circuit (Fig. 51), using the offset current vector and assuming that the conductance

FIG. 51. Offset calculation from the offset current vector Iocf,.

matrix G is the matrix of an ideal gyrator. We have i, u2 = u4 = 0, and consequently from (126)

=

i3

=

0,

u.3 = - R I l . f r . ,

' 4 = '3off.

+ '4oTf.

'

In a filter with cascaded gyrator sections which are dc coupled, the offset of one gyrator can decrease the signal handling capability of the others. 6. Noise For a linear noisy n-port, the noise can be completely described by y1 noise sources at the ports (Bosma, 1967). These sources can be wave sources but also voltage or current sources. For a floating port of a gyrator, dc sources supply the bias currents to the floating parts of the gyrator circuit. Noise currents are superimposed on the direct currents. Hence, it is natural to describe the noise behavior by a set of (noise) current sources (Fig. 52). The noise currents can be characterized by their mean squared values per hertz: G,, = (in,, i n k ) and their correlation can be characterized by the functions G,, = (in,, i,,), as observed through an ideal narrow-band filter and expressed in A2/Hz. All functions can be put together in a symmetric

154

K. M. ADAMS, E. F. A. DEPRETTERE AND J . 0. VOORMAN

noise matrix G, such that G,, = G,, = ( i n k , in,). Thus G can be formed by taking the mean value of each element of in iz. Using the Schmidt orthogonalization procedure (Gantmacher, 1959),we can transform in by the relation in = Aj, to an equivalent noise current vector j,, whereby A is so chosen that j, f = l , , where 1, is the fourth-order

A

FIG. 52. Complete noise description of the gyrator.

unit matrix. This transformation of noise currents results in a set of independent currents which can be treated separately. The matrix elements Gkl can be measured with standard methods using a correlator (Bittel and Storm, 1972). Let us consider a specific example (Fig. 53) derived from physical con-

FIG. 53. Noise model for a symmetrical electronic gyrator: inc is the noise current from the gyration conductances G, i n is the noise current from the electronic circuitry, F , are the noise factors. (in

in,>.

(129)

Usually this noise is partly llpnoise, shot-noise, and thermal noise, and the noise factor F behaves as a function of frequency (Voorman and Biesheuvel,


155

1972), e.g., as

F

=

+ 50/f

50

( f i n kHz).

For this example, Fig. 53 gives a representation where all noise currents are uncorrelated. Its noise matrix (see Fig. 52) can be directly calculated. It is l+F -1

0 0 l + F -1 -1 l + F

-1 1 + F 0 0

(130)

C. The Gyrator in Its Applications In Section VII,B the gyrator has been considered as an n-port. Its representation and measurements have been discussed without paying much attention to applications of the device. In this subsection we shall discuss those measurements which are of special interest for the gyrator in its applications, e.g. as an isolator, circulator, transformer, or as an inductance simulator in filters. Performance criteria are measured for these particular applications.

1. Isolator. Circulator, and lransformer Because the gyrator is antireciprocal (Penfield et al., 1970),it can be used most satisfactorily to realize an isolator. The arrow of the gyrator indicates the direction of transmission (Fig. 54a) or isolation (Fig. 54b). The source is matched to the two-port. An ideal isolator is best described by its scattering matrix S: =

[;:]

The accuracy of the isolator can best be estimated by measuring its scattering matrix (Section Vll,B,4). Let us consider the noise factor F of an isolator, in the same way as one considers the noise factor of an amplifier (see Fig. 55). For the gyrator we take the noise model of Fig. 53. Hence (Fig. 5 5 ) the mean square values per hertz are < i n , , inl) = < i n z ,inz)

=

(I

+ FG)4kTG,

(132)

where F , is the noise factor of the electronic circuitry of the gyrator. The thermal noise voltages per hertz of the conductances G are given by 0. In this way a supply current is formed which always fulfills the conditions Z ( t ) > I il(t) 1 and Z ( t ) > I iz(t)I. Moreover, this control mechanism works instantaneously and can be integrated completely. If the resonant circuit is damped, it has a low quality factor and there can be complex signals at the gyrator ports, which means that also the supply current can vary rapidly. If we have a high quality factor, this is not permissible, as a little intermodulation of the supply current with the signal current can influence the quality factor strongly. To study this we shall use a narrowband approximation. Let il(t) = u ( t )sin [coot

+ 4(t)],

(168)

where coo = G/C is the resonance frequency of the circuit and u ( t )and 4(t) are relatively slowly varying functions. With iz(t) = -RCdi,(t)/dt, we obtain for the controlled supply current.

+ w1o d t cos’ (coot + 4) + ... I@

174


If the quality factor is high, both a ( t ) and +(t)are slowly varying functions and the supply current consists of a slowly varying term on which are superimposed small rapidly varying terms.

3. Conjunctors? Generally the gyration resistors of a gyrator cannot be integrated for reasons of accuracy. This means that the I.C. for a fully floating gyrator requires at least 11 terminals (4 port terminals, 4 terminals to insert the gyration resistors, plus and minus, and a terminal to connect a resistor for dc current adjustment). For an adaptive gyrator the last terminal can be omitted but the remaining high number of terminals (a coil has only two) results in high expense and is a potential source of unreliability. Suppose we integrate the gyrator-resistors R , and R 2 . If they were meant to be 10 kR, in practice resistors of 8 kR to 12 kR could result, depending on the diffusion depth and concentration. Their absolute value is not correct but the relative accuracy of R , and R , can be made very high, depending on the circuit integration process. An electronic multiplication of R , as well as R 2 by the quotient ReIR,, where R, is also a monolithic resistor and Re is an accurate external resistor, gives as overall resistances R, R J R , and ReRJR,, which have substantially the same accuracy as R e . In this way, we can relate all monolithic resistors to a single external resistor R e . With this single external resistor we can tune not only the gyrator but also a complete filter. Moreover, this saves us 3 I.C. terminals. What is left is to show how the multiplication of a resistance by a quotient of two resistances can be implemented electronically. First, let us make two currents of a given ratio. To this end we allow a current I , to flow in a resistor R , (Fig. 71a), and in the nor-port of the nullor we find a current

Rm

Re

Rm

-

I

FIG. 71. To multiply the monolythic resistor R by the quotient R J R , , we first make a current ratio IJI,,, equal to R J R , (a) and multiply the current Ir by it (b).


175

I, such that I J I , = R,/R,. Multiplication by a resistance ratio is reduced to multiplication by a current ratio. As multiplication is a nonlinear operation it cannot be performed by a (linear) resistor-nullor network alone. Therefore, we shall introduce ideal diodes defined by the equation U = (kT/q)In ( I / I o ) ,where l ois the saturation current which is assumed to be equal for all diodes. Note that a transistor can be modeled by a nullor and diodes, depending on the degree of idealization. Addition or subtraction of the diode voltages corresponds to multiplication or division of their currents. In Fig. 71b a loop of diode voltages is formed, giving the relation I,,, = IeIr/lm.The VCCS gives I , = Ui,/R. Hence,

giving the correct transfer admittance. In an analogous way we can control all monolithic resistors with R e . The circuit we have designed for reduction of the number of I.C. terminals can also be seen as a controlled gyrator, which is an essential ingredient of the conjunctor, a nonlinear three-port introduced by Duinker (1962). 4. Future Applications

It is felt not only that gyrator design as described in the previous sections can and will be improved but also that integration into telecommunication systems has to be studied thoroughly. It is not only that we have to use the same supply voltages and impedance levels but the gyrators must also fit into the system philosophy. The application of gyrators is more than merely replacing coils by gyrators and capacitors. It is the use of all extra gyrator features to obtain simpler and better solutions. Let us mention one of these new features. With a symmetrical parallel resonant gyrator-capacitor circuit, an oscillator can be made by applying a feedback which keeps the quality factor infinite. If the gyrator is a controllable one, as described in the former section, we can vary the gyration resistance R, = R,(t). Now, we have the equations du2 , dt

u1 = R,(t)C--

u2

= -R,(t)C-

du dt

Put u = u , +.ju2 and the equations can be combined. The solution is: u1 = a cos 4(t) and u2 = a sin 4 ( t ) , where a is a constant and d4/dt =

l/R,(t)C. Hence, the instantaneous frequency d$/dt of the oscillator can be controlled by R,(t) without any transients. This is an ideal FM/FSK oscilla-

176


tor, and is an example of a new device which is obtained by the introduction of the gyrator. The central part of all these devices-the adaptive gyrator or conjunctor, the ideal FM/FSK oscillator-has been monolithically integrated for experimental purposes (about 200 transistors) in the Philips Research Laboratories. For each application a breadboard control circuit (about 40 transistors) is added. The adaptation as well as the controllability (e.g. a factor of over 25 in R, with a deviation from linearity of about 2 % at the extremities) show very promising results. The FM/FSK oscillator is surprisingly good. All of these results will be presented in the near future. In this field of signal processing with gyrators, conjunctors, and probably also traditors (Duinker, 1959; Deprettere, 1973) it is felt that many new developments can be expected, which will be of great practical importance to future systems for professional use.

IX. CONCLUSION In this survey we have emphasized some important principles that are relevant to the design and application of gyrators to electronics and communications. A great deal of material dealing with the detailed electronic design of the complete circuit has had to be excluded for lack of space. We have not gone into a detailed comparison with RC-active circuits. There are, however, two recent developments which deserve a short comment. A development of the “leap-frog’’ circuit (Szentirmai, 1973) is a filter with the same favorable sensitivity properties as the terminated LC ladder. However, for a given degree of the filter, the circuit requires more nullors and supply circuitry than the corresponding gyrator-C filter. It also contains many more resistors, so that both the dissipation and the noise for a given dynamic range can be expected to be considerably worse than in the case of the g y r a t o r 4 filter. Another development is a second-order circuit due to Soderstrand and Mitra (1973). The authors claim zero sensitivity, but to achieve this requires an amplification equal to 16Q2, presumably without phase shift. The spread of element values can be impractical. If, for example, a Q of 500 is required (which is easily attainable with gyrator circuits), then one requires a resistance of 2 GR in parallel with a capacitance of 35 pF. If the 2 GR resistor is replaced by an open circuit, then the low sensitivity of the circuit vanishes. We can conclude that the gyrator as a concept and a device is fully established. To exploit the possibilities fully, a new theory will be needed. Further development of the synthesis theory of nonreciprocal networks, linear time-variable networks, nonlinear networks, and their application to communications is called for. Experience has shown that the technology of


177

integrated circuits has a tremendous potential to meet the demands of current and future system specifications arising from theoretical considerations.

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Image Sensors for Solid State Cameras P. K . WEIMER R C A Luborururies. Princeton. Nett J e m )

I . Introduction .......................................................................................... I1 . Photoelements for Self-scanned Sensors ...................................................... 111. Principles of Multiplexed Scanning in Image Sensors .................................... A . Single-Line Sensors ........................................................................... B. Multiplexed Scanning of X Y Sensors ...................................................... IV. Early XY Image Sensors ................................................. A . Photoconductive Arrays ..................................................................... B. Phototransistor Arrays .................................................................. V . Multiplexed Photodiode Sensors ............. ..... ..... A . Single-Line Photodiode Sensors .......... B. X Y Addressed Photodiode Sensors ......................................................... .................................. V1 . Principles of Scanning by Charge Transfer ........ A . Single-Line Charge-Transfer Sensors ............................... B. Two-Dimensional Charge-Transfer Sensors ........ .................................... VII . Charge-Transfer Sensors Employing Bucket Brigade Registers ........................ A. .4 32 x 44 Element Bucket Brigade Camera ............................................. B. Experimental Tests of C harge-Transfer Readout of an MOS-Photodiode Array VIII . Characteristics of Charge-Coupled Devices (CCDs) ....................................... A . General Description of CCDs ............................................................... B. Transfer Losses in CCD’s ..................................................................... C . Noise Characteristics of C C D s ............................................................ IX . Experimental Charge-Coupled Image Sensors ................... A . Single-Line CCD Sensors ........................................ B. Two-Dimensional Area-Type Charge-Coupled Sensors .............................. X . Performance Limitations of Charge-Coupled Sensors .................................... A . Resolution ........... .......................................................... ;

vity .......................................................................... XI . Charge-Transfer Sensors as Analog Signal Processors .................................... A . Charge-Transfer Delay Lines ............................................................... B . Video Signal Processing within the Camera by Recycling of Signals through the Sensor Itself ....................................................................................... XI1. Self-scanned Sensors for Color Cameras ...................................................... XI11. Peripheral Circuits for Solid State Sensors ................................................... A . Input Circuit Design ........................................................................... B. Output Circuit Design ........................................................................ XIV . Conclusions ..................................................................... References .............................................................................................

181

182 183 187 188 190 193 194 197 198 198 199 202 202 205 208 209 211 213 213 216 220

229 236 231 239 247 247 249 251 253 253 254 259

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P. K. WEIMER

I. INTRODUCTION More than twenty-five years have passed since the invention of the transistor, but television camera and display equipment still depend almost entirely upon special beam-scanned tubes for picking up and reproducing the image. Even though television tubes have now reached a high level of performance the well-known advantages of solid state devices in reliability, compactness, and cost would be welcome in both the camera and receiver. In spite of major advances in solid state technology, it has proved to be extremely difficult to design solid state scanning systems which could match the elegant simplicity of the electron beam. Progress is being made, however, and an increasing number of self-scanned sensors have appeared on the market in the last few years. Single-line sensors are already finding application in page readers, in character recognition equipment, and in satellite cameras. These devices perform a unique function not always suitable for tubes, and are far easier to build than self-scanned area sensors. More recently, two-dimensional area sensors having limited resolution have also appeared on the market. These devices are intended for surveillance or identification and control purposes. They will be useful in applications requiring a very compact camera, with extreme durability and low power consumption. Although costs are still high and general performance falls short of camera tubes, the present rate of development of solid state sensors is very rapid. Many research laboratories, with support from the governmental agencies are now actively involved in work on image sensors (1). Industrial laboratories which have participated in this development over the past ten years include Bell Laboratories, General Electric Co., Fairchild Camera and Instrument Corporation, RCA Corporation, and Westinghouse. A continuing program on sensors has also been carried out at Stanford University where the specific objective has been to develop a reader for the blind (2). From the research point of view, work on image sensors has been both challenging and technically rewarding. T o achieve resolution comparable to camera tubes, sensors will require several hundred thousand picture elements. The development of a suitable scanning technique must be accompanied by a feasible fabrication technology. At RCA Laboratories, work o n sensors was started before silicon integrated circuits showed promise for devices of such complexity. Evaporated thin-film circuits (3),employing an early type of thin-film MOS transistor known as the TFT, were used to scan experimental sensors having up to 5 12 x 512 photoconductive elements. However, by 1970, the silicon technology had been refined and was so widely established that it clearly represented the more powerful technology for image sensors. The first solid state sensors utilized intersecting XY address strips (3)

IMAGE SENSORS FOR SOLID STATE CAMERAS

183

connected to each picture element for scanning. By application of progressive scanning pulses to the address strips, the response at each picture element was measured in sequence yielding a time-varying video output signal. Although valid in principle, the XY address system was subject to difficulties in uniformity and in signal-to-noise ratio. In 1969 and 1970, two discoveries were made which permitted an entirely new approach to solid state scanning. These were the bucket brigade register by Sangster and Teer ( 4 ) and the charge-coupled device by Boyle and Smith (5).These registers, which are easily fabricated in silicon, permit the transfer of analog signals through many stages with very small losses. By means of such registers, the sensor can be scanned by transferring the picture charges in sequence from the array to an amplifier located at the edge of the sensor. Significant improvement in signal-to-noise ratio and in uniformity over earlier XY systems become possible. Charge-coupled devices (or CCDs), because of their lower transfer losses and higher packing density. now appear to be superior to bucket brigades for most applications. Their greater promise for semiconductor memories and signal processing devices has also contributed to the more extensive research effort which they have received. A 128 x 106 element chargecoupled image sensor was incorporated into a camera at Bell Laboratories (6) in 1972. Still larger CCD arrays are being investigated elsewhere. Cameras employing CCD sensors having up to ten thousand elements are now available on the market. Although the impact of the CCD development on solid state sensors has been truly revolutionary it cannot be concluded that charge-coupled sensors will necessarily be best for all types of applications. Advances continue to be made in both CCD and X Y addressed sensors. Many problems remain, however, and their solution will affect performance and relative cost. It is clear that an entire television camera, including sensor and all drive circuits, will eventually be formed on one or two chips of silicon. If this can be done at low cost, many new applications for television should soon follow. The present review discusses solid state sensors from the research point of view, with much greater emphasis on principles of operation than on details of construction. New types of sensors are described and projected performance is compared with existing camera tubes. The extension of solid state scanning techniques to other types of imaging devices and signal processors is considered. FOR SELF-SCANNED SENSORS 11. PHOTOELEMENTS

The function of an image sensor is to generate a time-varying video signal corresponding to the spatial variations in the incident optical image. One of the earliest lessons learned in the development of camera tubes (7)

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P. K. WEIMER

was that high sensitivity operation would require the sensor to integrate the total light flux falling on each element throughout the whole scanning period. How this was accomplished in the vidicon ( 8 )is illustrated in Fig. 1. The vidicon was the first camera tube with a solid state target, and it provided the starting point for the earliest self-scanned image sensors.

PHOTOCONDUCTIVE rTARGET

+ SIGNAL VIDEO

OUT

ELECTRON G U N 7

V (a)

COMMUTATOR SWITCH N 250,000 FOR TV

-

FIG.1 . A cross-sectional drawing of a vidicon photoconductive camera tube ( a ) and the equivalent circuit of its tarset and scanning beam (b).

The continuous photoconductive layer in a vidicon target can be represented as an array of isolated photoconductive elements each shunted by a capacitor. Light integration is attained by choice of a high resistivity photoconductor whose RC time constant exceeds the scanning period of the electron beam. Light flux is integrated in the form of charges collected on each element at the surface of the photoconductor. The elemental charges are neutralized in sequence by the scanning beam, causing a video signal to appear in the lead connected to the transparent electrode on which the photoconductor is deposited. Only a limited number of high resistivity photoconductive materials have been used successfully in the vidicon. These include Sb,S, , PbO, CdSe, and amorphous selenium. A major advance in image sensing occurred with the development of the silicon diode array target ( 9 )for the vidicon. Although the volume resistivity


185

of undoped silicon is too low to serve for charge integration, the depleted region under a reverse-biased photodiode element can be made to meet the requirement adequately for most purposes. As shown in Fig. 2, one form of silicon vidicon target consists of an array of approximately lo6 photodiode elements diffused into a thin wafer of silicon which is illuminated from the side opposite the diodes. The beam contacts the beam landing pads which connect to the diodes and serve to shield the insulating oxide regions between the diodes from the beam. The video signal is derived from the silicon substrate which serves the same function as the transparent conducting coating in the photoconductive vidicons. The silicon vidicon offers the advantages of dependable, long life even when exposed to direct sunlight,

FIG.2. Cross section of a typical silicon photodiode target for a vidicon camera tube

and its target has increased responsivity for visible and near infrared illumination. Its infrared response is useful for low-light-level surveillance applications but has to be filtered o u t when proper color rendition is required. Its complete freedom from photoconductive lag was also an advantage over the early evaporated targets. The development of silicon processing techniques for the vidicon target proved to be highly useful in the subsequent use of silicon in self-scanned sensors. An equally important development in silicon technology which enhanced the attractiveness of silicon for image sensors was the MOS transistor (10). The high ratio of on-to-off conductance of these insulated-gate field effect transistors has allowed them to replace the electron beam as the commutator in self-scanned charge storage sensors. Their simplicity of fabrication and their superb capability for large scale integrated circuits appears ideal for image sensors. Figure 3 shows how an MOS transistor can be

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P. K . WEIMER

combined with a photodiode to serve as a charge-integrating sensor element ( 2 2 ) . The diffused photodiode functions also as the source of the discharge transistor. Its potential variations throughout the scanning period are the same as the charge-discharge cycle of the scanned surface of the vidicon. The photogenerated holes which are collected at the photodiode while the transistor is biased off are discharged through the external circuit at the instant of scan.

i

SCAN PULSE

STRUCTURE

O% T! CURRENT

EOUIVALENT CIRCUIT

1

I\ OPERATING CYCLE

FIG.3 . The structure, equivalent circuit, and operating cycle of an MOS-photodiode imagc sensor element.

The recent development of charge-transfer scanning ( 4 , 5 ) has further advanced the capability of silicon as a detector. The CCD sensors have utilized the fact that an MOS capacitor, produced by covering a silicon semiconductor with an insulating layer and a metal gate, can also serve as an integrating photoelement similar to a diffused photodiode. The photosensitive region is formed by biasing the metal gate so as to deplete the semiconductor surface. Illumination of this region causes the minority carriers to collect at the semiconductor-insulator interface. The accumulated charges can be removed laterally by charge transfer (6) to an adjacent electrode or by charge injection (22, 12a, 13) back into the body of the silicon. The MOScapacitor photoelements should preferably be located on a thin slab of silicon and illuminated through the silicon to avoid light absorption in the conducting gate. However, fairly good sensitivity has been obtained in CCD sensors with top illumination by depending entirely on light which enters the silicon around the edges of opaque metal gates. Transparent polycrystalline silicon


187

gates are also feasible but optical interference effects tend to introduce maxima and minima in the spectral response curves. For all of the above reasons, silicon is currently theoverwhelming favorite as the detector for image sensors operating over a wavelength range from 400 up to 1000 nm. It is not the ideal sensor, however, even for visible light. A wider bandgap material such as PbO, CdSe, or Sb,S, could have lower dark current at room temperature and would not require filtering to remove the unwanted infrared sensitivity. For far-infrared applications a narrower bandgap material than silicon would be preferred. Since the prospects are somewhat remote for achieving electronic properties in these materials equal to single-crystal silicon, their use in self-scanned structures will probably require a hybrid structure. That is, the detector would be used in combination with silicon scanning circuits. However, the low impedance of most infrared detectors makes them difficult to combine with solid state scanning. Fortunately, the number of infrared photons in many scenes of interest is so great that passive imaging is feasible without requiring full photon integration in the image sensor. It will become apparent in the discussion of sensor signal-to-noise ratio in Section X that a detector element which yields more than one carrier per incident photon could be superior in image sensor applications to a silicon photodiode whose quantum yield is always less than unity. Examples of such high gain detectors are the photoconductors CdS, CdSe, and PbS and silicon avalanche diodes. The uniformity of gain from one element to the next would have to be excellent for such detectors to be useful in imaging devices. High gain CdS-CdSe has been used successfully in the thin-film arrays (14) described in Section IV,A. In these devices the internal gain mechanism in the photonconductor (up to lo6 electrons per photon) was used to obtain photon integration without requiring charge storage. The effect of the light was to produce a cumulative increase in the conductivity of the sensor element. Under ideal conditions, this type of “excitation storage” could approach the efficiency of charge storage without seriously compromising the response time of the device. 111. PRINCIPLES OF MULTIPLEXED SCANNING IN IMAGE SENSORS Multiplexed scanning of solid state arrays is directly analogous to electron beam scanning in camera tubes. In each case the picture charge at the element is discharged through a local switch into a common electrode connected to the output amplifier. Prior to the development of charge-transfer scanning all experimental sensors operated in this manner. Multiplexed scanning will be discussed first in terms of single-line sensors, and then for two-dimensional XY arrays.

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P. K. WEIMER

A . Single-Line Sensors Figure 4a illustrates multiplexed scanning of a single-line sensor (I 1 ) in which each element consists of a photodiode in series with an MOS transistor as in Fig. 3. The scan generator is a parallel-output digital shift register with each stage connected to the gate of the elemental transistor. As the negative pulse progresses down the register each transistor is turned on in sequence, discharging the accumulated picture charge into the output bus and resetting the elemental capacitor for the next integration period. The resulting video signal current in the output bus is fed into an amplifier preferably located on the same silicon chip with the sensor and multiplexer.

VIDEO OUT

rl

SCAN GENERATOR

I

la)

SCAN GENERATOR

1

(b)

FIG.4. Multiplexed scanning of a slngle-line image sensor in which the elements comprise (a) MOS-photodetectors and (b) charge-injection capacitor-photodiodes.

The elemental capacitor shunting each diode should be large compared to the stray capacitance shunting the transistor. The elemental capacitor may consist largely of the depletion layer capacitance between photodiode and the substrate or it may be formed of the oxide capacitance to an overlying electrode. As explained in the preceding section, the diffused photodiode

may actually be eliminated completely and the photogenerated carriers collected at the silicon insulator interface. In this case the transistor behaves like a single-stage charge-coupled device. Each picture element in a multiplexed system must contain a light detector and a switch. The switch could be a diode as well as a transistor. In the


189

example illustrated in Fig. 4b the photodiode itself serves alternately as a reverse-biased photodetector during charge integration and as a forwardbiased discharge switch at the instant of scan (13). Sensors employing the discharge of the photogenerated carriers by injection into the substrate will be discussed in Section V,B,2. In case the RC conditions for charge storage are not met in the sensor it is still possible to operate using multiplexed scanning. Although sensitivity would be reduced without charge storage, this mode of operation might be necessary for sensor elements having very low impedance. A serious disadvantage of multiplexed scanning is that the video signals from successive elements are combined on an extended output bus whose total capacitance to ground may exceed the capacitance of each element by several orders of magnitude. The equivalent amplifier noise current would be increased by the square root of this factor beyond its value if it were connected to a single element. The low light threshold of the device as determined by noise would accordingly be raised by the same square root factor. The noise becomes even worse in a two-dimensional array having the added capacitance of XY address strips. A less fundamental disadvantage of multiplexed scanning is the tendency for spurious signals to be introduced into the output signal by variations in size of successive scan pulses. The fact that these pulses tend to be picked up capacitatively in the output bus through the multiplexer switches would not be particularly serious if the pulses were uniform from element to element. However. successive pulses and successive multiplexer switches are not identical so that low frequency variations are introduced which cannot be filtered out. The pictures produced by most of the early sensors contained vertical striations arising from this effect in the horizontal multiplexer. Such striations can be minimized by use of signal integration, double sampling, and sample-and-hold techniques in the output amplifier (see Section XII1,B). However, as the scanning frequencies are increased to accommodate larger arrays it becomes steadily more difficult to suppress the nonuniform switching transients picked u p during the rise and fall of successive pulses. The scan generator for the multiplexer can assume a variety of forms. The most common is a digital shift register or ring counter located adjacent to a single row of sensors or at the edge of the two-dimensional array. Such generators require from three to eight MOS transistors per picture element. The rate of progression of the scan pulse is accurately determined by the clock voltages. Figure 5 shows the circuit for a typical MOS scan generator. If a large two-dimensional array is being scanned, an additional driver stage may be required at each output to drive all the gates along a given row or column. Other types of analog scan generators have also been used. These include bucket brigade registers, which require only a single transistor per

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P. K. WEIMER

B

START

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OUTPUT 1

OUTPUT

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I A CLOCK DRIVE

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b . 1 ~ .5. A typical digital scan generator circuit (complementary MOS transislors are shown).

stage (see Section VII), and resistive-gated generators (15, 15a) in which the outputs are activated in sequence by a linear voltage ramp. Another type of scan generator utilizes an acoustic surface wave (15b) to contact successive elements. This type of system has the disadvantage that the scanning velocity is determined by the material properties of the medium and cannot be adjusted to match the preferred size of array.

B. Multiplexed Scanning of XY Sensors Although a single-line sensor duplicated N times would serve as a twodimensional array this approach is not usually suitable. Two-dimensional sensors which are to be scanned by multiplexing employ two perpendicular

19 1


sets of X and Y address strips which connect to each element in the array. Figure 6 shows the elemental circuit for some of the XY sensors which have been built. Each element includes the basic components of a photodetector plus one or more switches connected to the address strips. These include: (a) A thin-film CdS photoconductive array (13)which has been scanned in sizes up to 512 x 512 elements. The switching diode was obtained by use of dissimilar contacts to the photoconductor. This array was operated by excitation storage rather than by charge storage (see Section IV,A). (b) A silicon phototransistor array (16) which was scanned in sizes up to 400 x 500

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FIG. 6. Sensor elements which have been used in XY image sensor arrays: (a) Photoconductor-diode array. (b) Phototransistor array (isolated collector rows). (c) Phototransistor array with an MOS switch. (d) Photodiode array with two MOS switches in series. ( e ) Photodiode array with an MOS amplifier at each element. ( f ) Photodiode array with a single MOS switch. (g) Photodiode array with cascaded MOS switches. (h) Photodiode array which operates by charge injection in the substrate.

elements. Charge storage occurred in the capacitance shunting the collectorbase junction while the emitter-base diode served as the switch (see Section IV,B). (c) A silicon phototransistor (17) array having a common substrate collector and an MOS switch at each element (100 x 100). (d) A silicon photodiode array (18) with common cathodes in the substrate and two MOS switches coupling the photodiodes to a common video output bus. (e)A proposed silicon photodiode array ( 1 9 ) similar to (d) but with an additional amplifying transistor T, at each element. ( f ) A silicon photodiode array (20) having a single MOS transistor at each element. This simple structure can be used with charge-transfer readout. (g) A silicon photodiode array (21) similar to a two-transistor random access memory array (50 x 50 sensor commercially available 1973). (h) A silicon photodiode array which operates by charge injection (12,13) into the substrate. Although most of the

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P. K. WEIMER

photodiode structures listed above were built with a diffused photodiode at each element, an equivalent MOS-capacitor array could be constructed for each as described in the preceding section. This step has already been taken with the charge-injection sensors described by Michon and Burke (12). (See Section V,B,2.) XY arrays are normally operated in conjunction with external multiplexers and scan generators located on the periphery of the array. The physical separation of the photodetectors and the scanning circuits is a potential advantage in permitting hybrid technologies for sensing and scanning. Three common systems of multiplexed scanning of XY arrays are illustrated in Fig. 7. The derivation of signals from the column buses as in (b)

FIG. 7. Three systems of multiplexed scanning of a n X Y image sensor. (a) Video signal from the rows. (b) Video signal from the columns. (c) Video signal from a common electrode such as substrate.

has the advantage that the signals from a whole row can be transferred in parallel to the output multiplexer, with a whole line time available for addressing each element of that row. In a sensor having no storage capacitors at each element, method (b) will give an increase of the total signal over method (a) by the ratio of the line time to the element time. The column bus capacitors required for line storage operation can be added externally, or the internal crossover capacitance of the address strips can be utilized. In sensors having a common substrate or a common video output bus to each element (such as Figs. 6c, 6d, 6e, 6f, 6g, and 6h) no external multiplexer is required. However, the total capacitance of the output electrode will be considerably higher than that of the output bus of the external multiplexer. Since the output electrode capacitance increases directly with the total number of elements the use of a common output electrode will give a degraded signal-to-noise ratio in large high resolution sensors. In small area sensors a common output bus can be used satisfactorily with sufficient illumination.


193

With an external multiplexer the total capacitance shunting the input of the video amplifier is composed of the capacitance of the multiplexer output bus plus the capacitance of one column bus (or row bus) plus the capacitance of the element being scanned. Each bus contains many (off) switches whose gate capacitance adds to the capacitance of the bus itself. It is apparent that even with multiplexed scanning the XY array will suffer a degraded signal-to-noise ratio compared to the signal-to-noise ratio of a single element connected directly to the amplifier. In general, the rms noise contributed by this capacitance will vary directly as the square root of the total capacitance. The noise increase could be as large as 1&30 times for a 500 x 500 element array. Since the multiplex method of scanning of XY arrays yields a poor signal-to-noise ratio at low light levels it would be desirable to provide some means of increasing the signal level prior to scanning. The addition of an MOS amplifier stage at each element (such as shown in Fig. 6e) would improve signal-to-noise ratio but introduces other problems of complexity and nonuniformity. The use of an image intensifier stage prior to the array would be another method of increasing the final signal-to-noise ratio. In addition to problems of random noise, the multiplexed readout of the early XY arrays was subject to fixed pattern noise introduced by spatial variations in the address strips, in the multiplexer switches, and in the scan pulses received from the scan generators. The horizontal scan generator was more critical than the vertical because of its higher clock rate. Variations which fall within the video passband cannot be removed by filtering. They are repeated from line to line and appear as fixed vertical striations in the transmitted picture. In spite of their poor reputation, XY addressed arrays offer a degree of versatility and simplicity of construction not found in some of the more recent COD sensors. Recent advances in signal processing and integrated circuit technology would undoubtedly yield improved results over that obtained several years ago with this approach. The application of chargetransfer techniques to the scanning of XY photodiode arrays (Section VI,B,2) could provide an improved sensitivity which would be adequate for most applications. However, the capacitance of the address strips will always introduce noise which will limit the performance at very low light levels. IV. EARLYXY IMAGE SENSORS During the 1960s, the three principal approaches to solid state sensors employed photoconductive, phototransistor, or photodiode sensor elements. The first two systems appeared particularly attractive at that time because the internal gain in the element itself yielded higher signal levels than could

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P. K . WEIMER

be easily obtained with photodiodes. Recent advances in MOS technology and in small signal processing have favored the photodiode systems which will be discussed in the next section. The photoconductor and phototransistor devices are of more than historical interest, however, since they illustrate scanning systems which may yet profit from future advances in technology. A . Photoconductive Arrays The thin-film photoconductive approach to image sensors (14) was started in the early 1960s, before the silicon integrated circuit technology had become established. This project therefore represented the development +V

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FIG.8. Circuit for the 256 x 256 element thin-film photoconductor sensor including an integrated TFT transistor decoder and multiplexer for horizontal scanning and a Shottky diode decoder for vertical scanning.

195


T 3 cm 1

FIG.9. Photograph of the 256 x 256 element integrated thin-film image sensor deposited on two glass substrates mounted on a printed circuit board.

of a new thin-film technology (3)as well as a study of image sensors. As early as 1965, 180-stage integrated shift registers (22) employing thin-film transistors (TFT's) were produced for scanning of arrays. Figures 8 and 9 show the circuit and integrated thin-film embodiment of a 256 x 256 element photoconductor-diode sensor (13) which was fabricated at RCA Laboratories in 1968. The sensitive area of the sensor was one-half inch square with

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P. K. WEIMER

the picture elements spaced on 50p centers. Each element of the array consisted of an evaporated CdS-CdSe photoconductor in series with a Schottky diode as illustrated in Fig. 6a. The diode action was obtained by use of one blocking contact (Te) and one ohmic contact (In) to the photoconductor element. The entire array including sensor and thin-film scanning decoders were deposited by evaporation onto two glass substrates which were interconnected by thin-film conductors. The scanning decoders employed TFTs, diodes, and resistors interconnected so that the 256 sequential scan pulses could be generated by two external 16-stage shift registers. The output signal was derived from an external multiplexer connected to the column buses so that a large signal increase due to line storage was obtained. The entire 256 x 256 array was scanned in 1/60 sec using a 4.8 MHz horizontal clock rate. The resolution obtained was consistent with the number of picture elements but the transmitted picture contained vertical striations arising from nonuniformities in the scan generators and defective elements in the sensor or decoder. Figure 10 shows pictures transmitted by a 256 x 256 photoconductive sensor. The uniformity was

FIG. 10. Pictures transmitted by the 256 x 256 element thin-film sensor shown i n k-igs. X and 9.

comparable to that obtained with other XY sensors of this period, but much inferior to recent CCD sensors. Pictures were transmitted at normal room illumination but the photoconductive lag was objectionable with moving scenes, particularly at lower illumination levels. Photoconductive arrays with integrated scanning decoders deposited on the same glass substrate were produced in sizes up to 512 x 512 elements (23). Integrated thin-film shift registers having up to 264 driver stages were also produced using complementary cadmium selenide and tellurium TFT's. The thin-film approach for image sensors was eventually discontinued in favor of the silicon technology using charge-transfer scanning.

197


B. Phototransistor Arrays The combination of charge integration and signal gain obtainable from phototransistors (24) made this approach a favorite of several laboratories during the 1960's. Bipolar transistor technology was somewhat more advanced than MOS technology at that time so that large arrays were attempted. A 400 x 500 phototransistor array shown in Fig. 11 was fabricated

T

4 0 0

f

7

MILS

k p - 5 0 0

ELEMENTS

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FIG.1 1 . Layout for a 400 x 500 element phototransistor array of the type shown in Fig. 6b [Strull cr a / . (16), courtesy of Westinghouse Electric Corp.].

by Westinghouse and incorporated into a camera (25). The equivalent circuit for each element of the array is shown in Fig. 6b. The collector rows were formed in the silicon substrate by an isolation diffusion process so that each collector was separated from all other collectors by back-to-back p-n junctions. Individual base and emitter regions were diffused into each collector at regular intervals, and the emitters along each column were connected to common column buses. The row and column address strips were each terminated in bonding pads, through which connections were made to external scanning circuits. Other types of phototransistor arrays were also built in which all elements had a common substrate collector. One method of accomplishing this was by use of a series MOS transistor (17) at each element, as shown in Fig. 6c. Another method was by driving the bases capacitively through the row bus as discussed in Weimer et al. (26). Although the phototransistor arrays have proved to be useful in relatively small sizes, such as a reading aid for the blind (2),they d o not presently appear promising for television applications. The major disadvantage was

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P. K. WEIMER

the random variations in transistor gain and low level threshold caused by emitter offset. Transistor gains could vary as much as 2 to 1, far exceeding the nonuniformities observed in photodiode and photoconductor arrays. In addition, the sensitivity improvement expected from phototransistors was not obtained in practice. The nonlinear characteristic of the emitter base junction resulted in a threshold at low light levels. Advances in the ability to read out small signals from photodiode and CCD arrays has lessened the interest in sensor elements such as phototransistors and photoconductors which provide gain at each element.

V. MULTIPLEXED PHOTODIODE ARRAYS A . Single-Line Photodiode Sensors

The earliest photodiode arrays were single-line sensors in which each element consisted of an MOS transistor in series with the photodiode (11, 17). These were operated in the charge storage mode as discussed in Section 11. The elemental capacitance could be made sufficiently large to give ample stored signal in spite of the unity gain of the photoelement. Single-line sensors having several hundred elements in a row spaced on 2.5 mil centers were scanned by means of externally connected shift registers in 1966. Basically the same system is used in the single-line photodiode arrays which are now available on the market (27). The principal difference is that the digital scan generator is incorporated on the same silicon chip, and the total number of elements and the number of elements per unit length has been increased. Recently a photodiode sensor containing 1024 elements formed on a silicon chip more than an inch long has been announced (28). Its maximum video rate is 40 MHz and the sensor can be used to scan a 8.5 x 11 in. page in a fraction of a second. Applications for single-line sensors include pattern recognition equipment, in-process measurement or inspection of assembly lines, and mapping of the earth’s surface from a moving satellite (29). Motion of a single-line camera relative to the scene permits a two-dimensional picture to be reproduced. For high definition pictures a sequence of silicon chips has been joined to obtain several thousand photodiodes in a row. A critical requirement in the use of linear arrays for picture reproduction is that of uniformity of background from one element to the next. For example, any variation in dark current from adjacent photodiodes will produce streaks in the picture. Such a fixed pattern background can be subtracted out with subsequent signal processing circuits, if necessary, but this added complication would not ordinarily be justified.


199

The presently available photodiode line sensors will soon be forced to compete with CCD line sensors. The characteristics in which they may have difficulty in matching CCD sensors are in resolution, sensitivity, signal-tonoise ratio, uniformity, and fixed pattern noise. The photodiode arrays currently available will operate at higher video frequencies than CCD sensors but this is probably only a temporary advantage. It is too early to predict a cost advantage for either. However, the photodiode sensor can be produced with standard silicon gate technology, which could offer a cost advantage for smaller arrays.

B. X Y

Addimsed Photodiode Sensors

1. MOS-Photodiodr Sensors

Photodiode area-type sensors were slow in being developed, probably because of the rather small picture signals which could be stored on the small elemental capacitors. A possible method for increasing the signal level is to include a voltage-sampling MOS current amplifier at each element (19). (See Fig. 6e.) This structure is too complex to be practical in high resolution arrays. However, 10 x 10 element photodiode arrays (19) with scan generators integrated on the same silicon chip were built in 1968. Larger photodiode arrays (50 x 50) having two MOS transistors at each element as shown in Fig. 6d were built in Japan (18). At the present writing, seif-scanned photodiode arrays in sizes up to 50 x 50 and 64 x 64 are available in solid state cameras. In each case the vertical and horizontal scan generators are included on the same chip with the array. The elemental circuit for the 50 x 50 array (28) is illustrated in Fig. 6g. Although a common video output bus is used which connects to all elements on the chip, the sensitivity is relatively high. An exposure of 2 x fc-sec of tungsten illumination (2870°K) is sufficient to cause saturation. At 400 frames per second dynamic ranges better than 100 to 1 have been measured. 2. ‘‘ Chal-ye-1njection”Sensor.s

In all of the experimental structures described so far the photoelectrons accumulated on the photodiode were returned to the substrate through one or more MOS switches, just as in the linear arrays. Concurrently with this work another type of photodiode array ( 1 3 ) was investigated in which the picture charge was removed by injection of the charge directly into the silicon substrate. As shown in Fig. 6h, each photodiode was coupled capacitively to the row and column address strips intersecting at this point.

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P. K. WEIMER

Figure12 illustrates the potential excursions of the photodiode during one frame period as the scan pulses are applied to the two address strips. It will be noted that both vertical and horizontal scan pulses have such a polarity as to forward-bias the diode, but that the diode is not actually discharged into the substrate until the coincidence of both pulses occurs at the instant of scanning. Between scans the photodiode remains reverse-biased so that it can collect minority carriers produced by the light. The accumulated charge is returned to the substrate by the coincidence of scan pulses. The video signal can be derived from the substrate or from the address strips.

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POTENTIAL 0AT P REL. -VTO SUBSTRATE DARK'

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RESET PULSES

FIG.12. Operating characteristics for an early type of charge injection sensor [Weimer ef o/. ( 1 3 ) ] . Line (3) shows the potential variations of the photodiode during the chargeedischarge cycle. Line (6) shows an improved method of suppressing scanning transients used by Michon and Burke (12).

In the early work on charge-injection sensors two problems were noted: ( 1 ) The failure of the injected carriers (30) to recombine within the duration of the scan pulse could prevent the diode from being completely discharged in one scan. This caused signals to be carried over into subsequent frames giving lag. (2) The video signals tended to be masked by switching transients from the horizontal scan generator. A modified version of this sensor in which the diodes were replaced by a grounded base transistor was found (31) to be useful in reducing the switching transients in the output signal. Operation of arrays employing charge injection has recently been


20 1

reported ( 1 2 . 1 2 ~ indicating ) that good performance can be achieved with this mode of operation. A 32 x 32 element photodiode sensor having a specially designed amplifier connected to the substrate was found to give excellent suppression of the capacitively-coupled switching transients. The signal to the substrate was first integrated to recover the initial scan pulses and then voltage sampled to obtain the video signal from the net injected charge. The transmitted pictures appeared to be entirely free of low frequency striations arising from variations in the scan pulses from either the horizontal or vertical scan generator. Line (6) of Fig. 12 illustrates the operation of the improved circuit. A significant difference in construction of the 32 x 32 element charge injection sensor from earlier sensors of this type is shown in Fig. 13. In the

lo1

c

I

(b) FIG. 13. A comparison of two forms of charge injection sensors. (a) Photodiode-capacitor sensor elements [Weimer et ul. ( 1 3 ) ] .(b) MOS capacitor sensor elements [Michon and Burke (141.

earlier designs most of the minority carriers released by light absorbed in the depletion region of the silicon were collected on the diffused diode prior to injection into the substrate. In the recent charge injection sensors most of the carriers are collected under the gate electrodes at the silicon-silicon dioxide interface just as in a CCD sensor. The small diode connecting the two gate regions provides easy coupling between the two gate regions so that minority carriers can flow back and forth between adjacent gates without being injected into the substrate until both gates are driven into accumulation. The coupling diode could be omitted entirely provided the pair of gates at each element were sufficiently close spaced to permit charge transfer to occur. An improved 100 x 100 element charge injection sensor has recently been described ( 1 2 ~ )A. thin epitaxial layer of ti-type silicon on top of a p-type substrate has been found to give higher efficiency of injection of holes as compared to the homogeneous n-type substrates shown in Fig. 13. The time lag resulting from failure of injected carriers to recombine within the period of the scan pulse is thereby reduced.

202

P. K. WEIMER

Although the derivation of video signal from the substrate permits a simplification of the scan generators and peripheral circuits the relatively large capacitance of the output to ground will degrade the signal-to-noise ratio at low light levels. Since the total capacitance increases directly as the number of elements this source of random noise will become increasingly objectionable for higher resolution sensors. A substantial reduction in output capacitance of an XY array can be obtained by taking the signal from each row or column separately, using an external multiplexer as shown in Fig. 7a or 7b.

VI. PRINCIPLES OF SCANNING BY CHARGE TRANSFER A . Single-Line Churge- Transfer. Sensors

An entirely new system of solid state scanning has resulted from the development of integrated charge-transfer registers. The construction of an MOS bucket brigade (32) and a charge-coupled register (5) is illustrated in

SUBSTRATE (0)

(C)

FIG. 14. Structural cornparisoil of a bucket brigade MOS photodiode sensor and ii three-phase charge-coupled sensor. (a) Circuit for MOS bucket brigade line sensor. (b) MOS bucket brigade line sensor cross section. (c) Charge-coupled line sensor cross section.


203

Fig.14. These devices differ from the earlier digital shift registers in that an utzalog signal introduced at the input will be transferred through the register as a spatial sequence of modulated charge packets. The application of clock voltages to the overlying electrodes causes all charge packets to be transferred along the surface of the semiconductor from one location to the next with relatively small losses per transfer. Although the clock waveforms may have two, three, or four phases, at any instant all packets will be located under the same phase electrode of each group. The present discussion will examine the various ways that charge-transfer registers can be used for scanning of arrays. The detailed operation of CCDs and bucket brigades will be considered later. Clearly, a spatially-varying charge pattern which has been introduced serially into a charge-transfer register can be reconverted into a time-varying (although delayed) signal by simply collecting the charges emerging from the end of the register. Similarly. if the spatial charge pattern is introduced optically to all elements of the register, operation of the register will yield a video signal equivalent to that obtained earlier by multiplexed scanning. The charge-transfer method of scanning offers two potential advantages over multiplexed scanning: 1. Signal-to-noise ratio. The input capacitance of an output amplifier placed on the same chip with the register need be no larger than the capacitance of a single element in the register. The signal-to-noise degradation previously introduced by the large capacitance of the long video bus of the multiplexer is eliminated. The signal-to-noise ratio of a scanned device can now approach that of a single element provided the noise introduced by transfer can be kept small. 2. Uniformity. Since the single discharge switch at the end of the register serves for the entire array the variations previously introduced by multiple switches and nonidentical scan pulses are eliminated. Successive elements are discharged by the recurring pulses from the clock drive, thus removing the need for digital scan generators. In general, all clock signals have at least twice the frequency of the video passband so that they can be readily removed from the video signal by low pass filters. Obviously, these advantages cannot be realized in practical devices unless the transfer losses and the noise introduced by transfer is very low. In the construction of charge-transfer sensors two methods may be used for introducing the photogenerated charge pattern into the register: 1. The register may be illuminated directly while the clocks are stopped for a light integration period (Figs. 14 and 15a). Minority carriers released within the silicon by the light will then be collected at the surface under those electrodes whose voltage forms the deepest potential well. The video

204

P. K. WEIMER

signal will be generated at the output electrode during the scanning period when the clocks are started again. 2. Separate photocells are provided for accumulation of the photocarriers during the integration period (Fig. 15b). The registers are shielded from the light so that they need not be stopped except momentarily when the charges are transferred from the photocells. The use of two parallel registers, as shown in Fig. 15b, reduces the total number of transfers and allows the sensor elements to be more closely spaced.

I ~-l-i--i-t--A-~--i-t--i i b4---- -c---__ A ---__ L ---__ L_____ 4

tltl

4, 4

(bl

FIG. 15. Two forms of charge-transfer single-linc sensors. (a) Illuminated-register sensor. (b) Separate photoelements with two nonilluminated registers.

The illuminated-register sensor, although simple to build, imposes certain limitations on the relative proportion of the time allotted for scanning and for light integration. Unless the optical image is masked off during the scan period the light falling on the register during the scanning period will superimpose a smeared signal over the charge pattern which had developed during the integration period. Although some types of pictures can be reproduced fairly well with a scanning period about equal to the integration time, the scanning period normally should be no more than a few percent of the total time to avoid significant degradation of the image. Sensors with separate photocells offer an additional advantage over illuminated-register sensors in that hybrid technologies can be used for the photodetectors and the scanning circuits. This may be of particular importance for infrared pickup at wavelengths beyond that normally suitable for silicon (33).


205

B. Two-Dimensional Charge- Transfer Sensors 1. Sensors with Internal Registers for Each Row or Coluinn

The simplicity of charge-transfer registers of the bucket brigade or CCD type has made it feasible to build two-dimensional sensors using a register for each row or each column of the sensor. With a suitable scanning organization it is possible to transfer the charge from every element to a lowcapacitance output amplifier located on the same chip without the charge having to pass through any stage whose capacitance is larger than that of a picture element. Figure 16 shows schematically two scanning systems which

O UT P UT

SENSOR AREA

OUTPUT REGISTER O U T P U T RE:GIST[

FIG. 16. Two systems of scanning two-dimensional charge-transfer sensors having illuminated registers. (a) Horizontal transfer along successive rows into a continuously running output register. (b) Vertical frame transfer along columns in parallel through a temporary store into the output register.

have been used for arrays in which the registers in the image area are illuminated directly by the light from the scene. In the horizontal transfer system (20),shown in 16a, the clock voltages for each row are cut off most of the time to allow the charge pattern to accumulate for approximately 1/60 sec. When a given line is to be scanned its gates are activated by the horizontal clocks causing all charges to be transferred into the output register. The output register, which operates continuously at the horizontal clock

206

P. K. WEIMER

rate, transfers the charges to the output amplifier located in the upper right-hand corner of the device. A vertical scan generator which can be either a digital or analog shift register provides the necessary pulses for gating the horizontal clock supply to the proper line. The horizontal transfer system was demonstrated with the 32 x 44 element bucket brigade sensor described in Section VII. The same system could be used with CCD registers and with sensors having interleaved photocells. Since only one line time is used for moving the charge pattern out of the illuminated area the resulting image smear is very small. The vertical frame-transfer sensor (6) shown in Fig. 16b requires a separate silicon area for frame storage when operated with continuous illumination of the sensor area. The clock voltages in the sensor area are stopped during the normal field-scanning period to allow charge integration to occur. The resulting charge pattern is then transferred in parallel to the storage area during the vertical retrace period. The stored charge is then scanned during the following field period by transferring the charges in parallel a line at a time into the horizontal output register. Simultaneously during this field a new picture is being integrated in the sensor area. No scan generators or clock supply gates are required within the array, but the clock voltages applied to the storage area need to operate at two different rates. The horizontal output register runs continuously except during the horizontal retrace period when a new row of charges is transferred in parallel from the vertical registers to the output register. Although the vertical frame transfer format requires additional space on the silicon chip for the storage area, a compensating feature is that the charge in the sensor area can be integrated under different electrodes in successive fields (34) to provide an increase in effective vertical resolution. When one set of sensor gates is held on during the integration period while the other gates are off, the charges collect under the “ o n ” gate. By keeping different gates on during successive fields the effective center of the picture element is displaced, giving increased resolution when successive fields are viewed with interlaced scan. The resolution capability of a single field is unaffected by this process since it can be no greater than the total number of complete stages in the sensor register. Both the horizontal and vertical transfer systems could be built with two, three, or four-phase CCD registers, but the vertical system is somewhat easier topologically to lay out when multiphase clock registers are required. The frame transfer system was used in the three-phase 128 x 106 (interlaced) C C D array built by Bell Laboratories. (See Section IX,B.) The vertical and horizontal transfer systems can also be built with interleaved photocells and nonilluminated registers. The use of separate photocells is particularly advantageous with the vertical transfer system ( 3 5 )


207

because the separate storage area can be eliminated as shown in Fig. 17a. Integration of charge by light incident on the photoelements occurs simultaneously with the readout of the charges from the unilluminated register. The newly developed charge pattern from the photocells is then transferred to the empty registers during the vertical retrace period. As before, the vertical registers shift the entire pattern down one line during each horizontal retrace period, at which time the horizontal output register is loaded with the line to be scanned.

FIG. 17. Two systems of scanning two-dimensional sensor arrays with nonilluminated charge-transfer registers. (a) Shielded registers interleaved with sensor elements. (b) External charge-transfer registers connected to XY address strips.

The use of nonilluminated registers in the vertical transfer format permits the total number of transfers and the total number of clock supplies to be reduced to the same as for the horizontal system of Fig. 16a. An additional feature of the vertical transfer system with interleaved photocells is that an input register can be used for introduction of bias charge and for recycling of signals back into the array for signal processing within the sensor itself (36).Although an input register can be included in the vertical frame transfer system of Fig. 16b, it cannot be used during the normal scanning period since the sensor clocks are stopped at this time.

2. Charge-Transfer Readout o f X Y Sensors In applications not requiring the lowest possible scanning noise a hybrid type of sensor, shown in Fig. 17b, could be useful. This system (20) combines the simplicity and versatility of an XY array with the improved uniformity and noise reduction of charge-transfer scanning in the horizontal direction. As described in Section VII,B, this method of scanning has been tested with

208

P. K. WEIMER

a silicon MOS-photodiode array but it would also be advantageous when nonsilicon detectors are to be used with silicon scanning. The construction of an array with infrared detectors may be simpler in XY form than with interleaved silicon registers. The noise level in the signal from an XY array cannot be less than the fluctuation noise associated with the capacitance of each vertical address strip in the array. Reference to Eq. (2) in the discussion of CCD noise sources in Section VII1,C indicates that a single strip capacitance of 10 pF would yield a noise fluctuation of approximately 1200 electrons. The resulting threshold sensitivity of a silicon XY sensor would be comparable to that of a silicon vidicon which is considered a relatively sensitive tube. In applications where the shot noise in the signal exceeds 1200 electrons this mode of scanning would be comparable in performance to a charge-coupled sensor with internal registers. For very low signal levels, however, where the shot noise in the signal is very much less than this, a CCD sensor having a much lower noise background would be superior.

VII. CHARGE-TRANSFER SENSORS EMPLOYING BUCKETBRIGADE REGISTERS The bucket brigade analog delay line described by Sangster and Teer ( 4 ) in 1969, and by Sangster (32) in 1970, provided a basis for building experimental charge-transfer sensors. A 16 x 16 element bucket brigade sensor (37,38)was built in 1970, and this was followed by a 32 x 44 element sensor (20) which was incorporated into a miniature camera (39). Although the bucket brigade register may be replaced by charge-coupled devices (40,41) for image sensors having internal registers, it offers certain features which may be useful in future devices. A structural comparison of the integrated MOS bucket brigade with the three-phase charge-coupled device was shown in Fig. 14. The principal difference was the presence of the diffused islands which permitted the bucket brigade to be constructed as a series of MOS transistors with all gates slightly offset in the direction of charge transfer. The fact that the bucket brigade device could be represented by such a simple circuit tended to obscure its significant advance over earlier forms of analog shift registers ( 4 2 ) .The MOS transistors do not function as simple switches connecting the capacitors but as active source-followers which cut themselves off when the charge packet has been transferred to the next capacitor. The loss of charge per transfer (43)can be relatively small ( - 10- per transfer) but not usually as small as can be achieved with CCD’s. The diffused islands tend to limit ultimate packing density in sensor arrays employing internal registers but are advantageous in applications where larger dimensions are required.


209 0 OUT

FIG 18 Circuit didgram for a 32 x 44 element bucket brigade sensor The photodiodes formed by sources and drains of transistois are not shown in the diagram

A . A 32 x 44 Element Bucket Brigade Camera Figures 18 and 19 show the circuit and a photomicrograph of a 32 x 44 element bucket brigade sensor. The scanning organization for the sensor was the horizontal line-by-line system illustrated in Fig. 16a of the preceding VERTICAL SCAN GENERATOR -TRANSMISSION GATES OUTPUT AMPLI FIER-,

,'

4

OUTPUT REGISTER'

X 44 ELEMENT BUCKET BRIGADE PHOTOSENSITIYE ARRAY FIG. 19. Photomicrograph of the 32 x 44 element bucket brigade sensor. The elements

were spaced on 3 mil (0.0076cm) centers.

2 10

P. K. WEIMER

section. Each row consisted of a 44-stage bucket brigade register having 88 diffused sources and drains which also served as photodiodes. Alternate diodes were connected capacitively to the overlying metal gates which were activated by the horizontal clock voltages when a given line was to be scanned. During most of the 1/60 sec interval between scans the clock drive for each line was stopped to allow a picture charge pattern to accumulate on the photodiodes. When the charges on a given line were to be transferred to the output register the horizontal clock drive for that line was gated on by the vertical scan generator located on the left side of the drawing. The continuously running output register transported the charge up the right side of the array to the MOS output amplifier located on the same chip. The signal-to-noise ratio could be extremely good because the capacitance at the input to the amplifier was not appreciably larger than that of an individual picture element. The increasing delay introduced by the output register for the lines nearer the bottom of the array was compensated by gradually advancing the phase of the vertical scan pulse which controlled the gating of the horizontal clocks to the rows. For this purpose the vertical clock frequency in the camera was made slightly larger than the normal line frequency of the output signal. The problem of image smear expected from continued illumination of the internal registers during transfer was not visible in uniformly illuminated scenes. Such smearing should be even less significant with sensors having a full 500 lines since the ratio of smeared signal to integrated picture signal would be decreased to 1 part in 500. A lighting situation under which the illuminated registers could yield objectionable streaks occurred when local areas were illuminated at a light level which would overfill the picture element capacitors by one or more orders of magnitude. The excess charges at the illuminated element would then spill over into adjacent elements along the same row giving a bright streak instead of an enlarged round spot as in the silicon vidicon. The picture uniformity was excellent compared to early X Y sensors in spite of a sprinkling of dark current spots such as noted in early silicon vidicons. One feature of the bucket brigade sensor which would be useful for other scanning applications is the bucket brigade scan generator used for vertical scanning. An MOS bucket brigade circuit operated in the manner shown in Fig.20a will serve as a digital scan generator (38) having only one transistor per stage. A typical MOS shift register as shown in Fig. 5 would require six transistors for the same function. Operation in the scan generator mode requires a constant high level input current interrupted only by the “start pulse. The spurious background pulses are of no consequence for vertical scanning but would require some smoothing if used to drive a horizontal output multiplexer. An alternative scan generator mode is shown in Fig. 20b. ”

21 1

IMAGE SENSORS FOR SOLID STATE CAMERAS BUCKET BRIGADE SCAN GENERATOR

I

5 psldiv DOUBLE CLOCK

1

I

PMOS

5ps/div SINGLE CLOCK

FIG.20. Measured voltage waveforms from a P-MOS bucket brigade delay line operated in two modes as a digital scan generator.

B. Experiinental Tests of Cliaiye- Transfer- Readout of at? MOS-Photodiode Array

Bucket brigade registers are more versatile than CCD registers in applications requiring large center-to-center spacing of successive stages. In charge-transfer readout of XY arrays each vertical bus of the array can serve as one stage of a short register coupling the individual elements to the horizontal output register. Figure 21 shows a circuit for scanning an MOSphotodiode array by charge transfer, using the system outlined in Fig. 17b. This circuit was tested with an 8 x 8 element array constructed entirely of discrete components (20, 44). The accumulated charges for all elements along a given row were transferred in parallel via the columns to the row of

2 12

P. K. WEIMER

-V VIDEO OUT

FIG. 21. Circuit used MOS-photodiode array.

for

demonstrating

charge-transfer

readout

of

an

XY

peripheral capacitors C, . Although the high capacitance of the column buses will slow this transfer, a whole line time is available for completing the transfer. If desired, the transconductance of the transistors T, can be made extra large to minimize any carryover of signal into the next line. A transfer loss as large as lo-’ would be tolerable for the vertical transfer stages since so few stages are involved. It is noted that conservation of charge requires that the signal voltage swing on the high capacitance columns will always be less than on the elements and on the C, capacitors. A bucket brigade stage of the “tetrode” type ( 4 5 ) would be particularly suitable in coping with the capacitance of the columns. The charges held temporarily on the CTcapacitors are transferred to the output register during the horizontal retrace period. The output register could be a bucket brigade as shown, or it could be a CCD register. The single-gate MOS sensor illustrated in Fig. 21 is relatively simple to construct with or without diffused photodiodes at each element. However, the above method of parallel readout of an entire row in one line time could be applied with advantage to other types of XY arrays such as charge injection sensors (12). In the latter case this mode of operation would extend the time for recombination of injected carriers from one element time to one line time.


213

VIII. CHARACTERISTICS OF CHARGE-COUPLED DEVICES (CCDs) A . General Description of CCD's

The original proposal of Boyle and Smith ( 5 ) was to store minority carriers in potential wells at the surface of a semiconductor and to transport these charges along the surface by moving the potential wells. In its simplest form a charge-coupled register can be made by depositing a series of closely spaced metal electrodes on top of a thin oxide layer ( - 1500 8, thick) covering a uniformly doped semiconductor. In operation, the metal electrodes are driven by clock voltages but are reverse biased so that the entire surface region of the semiconductor remains depleted of majority carriers. Although the applied voltage is large enough to invert the surface the insulating properties of the depletion region are sufficiently high that several seconds would be required for thermally generated minority carriers reaching the surface to reestablish equilibrium. In CCD operation, minority carriers are introduced into the semiconductor surface by electrical or optical means and transferred along the surface as an analog signal. A condition of quasi-stable equilibrium is established at the surface so that any contribution of thermally generated minority carriers from the body of the semiconductor is constantly swept toward the output electrode along with the signal carriers. The charge-transfer process can be readily explained in terms of the three-phase register illustrated in Fig. 22. The semiconductor in this case is

(CI

FIG.22. Operation of a three-phase charge-coupled shift register. (a) Cross section of the structure. (b) Surface potential profile for d 1 = - V , d, = 0, and d3 = 0, forming a potential well under the phase-1 electrode. (c) Transfer of charge from phase-1 electrode to phase-2 electrode illustrated at times shown in (d). (d) Voltage waveforms of the applied clock voltages.

214

P. I(. WElMER

n-type and the minority carriers to be moved along the surface are holes. The clock voltages shown at the right of the figure are applied to each of the three sets of electrodes. At the time t = t , all holes are initially located in the potential energy wells under the +1 electrodes which at this moment are at the most negative voltage relative to the grounded substrate. The crosshatched region represents the holes whose presence increases the surface potential energy and causes the well to become partially filled like a fluid in a container. At the time t , the 6, electrodes have also reached the maximum negative voltage creating a second well into which the holes under 41 begin to move. The transfer of holes to 42is aided at time t , by the rising voltage on which removes the well under 41. The barrier under electrode d 3 , which is the least negative electrode at this time, prevents any charges from moving back to the left. The transfer is complete at time t, and the original charge is now located entirely under the 4, electrode. Continued application of the clock voltages causes all charge packets to be transferred toward the right with relatively small losses from their original values. The achievement of sufficiently low transfer losses is a major problem which will be discussed in the next section. Charge-coupled registers are constructed so that the carriers are confined to a channel whose width is usually of the order of 10-100 pm. The confining barriers along the sides of the channel can be produced by any of the following methods: (1) Strips of thick field oxide ( - 12 pm thick) between the gate and substrate. (2) Diffused PI+ or p + channel stops of the same type as the substrate. (3) Conducting shields with a fixed bias located between the gate electrodes and the substrate, but insulated from the substrate. Efficient transfer of charge from one well to the next can occur in the three-phase register only if the electrodes are very closely spaced (approximately two microns or less). Too large a spacing permits a barrier to form between electrodes, and the exposed oxide is subject to surface charges which may cause instabilities. Another form of register shown in Fig. 23 employs overlapped aluminum and polycrystalline silicon gates (46,47.470). This structure can be operated with two or four phases. The overlapped construction protects the gaps from ambient effects and the close spacing provides a high uniform field between electrodes. An advantage of this structure is that it can be fabricated with small cell dimensions using standard silicon gate technology without requiring as precise control of the metal spacing as in the earlier three-phase metal gate structures. A two-phase CCD register would be preferred over three-phase structures because of the reduced number of drive voltages and the possibility of having simpler construction. The latter advantage is not always achieved in practice. In order to provide directionality of charge flow in a two-phase

215


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D- I INUM

7 CHANNEL WIDTH = 5 5

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FIG.23. Cross-sectional view and labeled photograph of a 128-stage two-phase silicon gate CCD.

structure an asymmetry must be incorporated into each potential well which may actually increase the complexity of fabrication. Barriers to prevent back-flow can be obtained in one of the following ways: (1) The use of a thicker channel oxide under the rear portion of each gate (48). (2) The use of two gates for each phase with a dc offset voltage under the rear gate (46). (3) The use of an ion-implanted barrier in the silicon under the back part of each gate (49). (4) The use of two levels of fixed charge in the channel oxide over each gate (SO). The silicon gate structure shown in Fig. 23 can be operated with twophase clocks in either of two modes: (1) The silicon gate and aluminum gate for each phase can be tied directly together while depending on the thicker oxide under the aluminum to provide the barrier to prevent back-flow of charge. This mode of operation is more suitable for devices made on low resistivity substrates. (2) Adjacent silicon and aluminum gates can be driven with the same two-phase clocks but with an offset voltage applied to the aluminum gates to enhance their barrier action. Alternatively, all four gates can be driven independently with four-phase clocks.

216

P. K. WEIMER

A disadvantage of the silicon gate technology for large area devices is that the lateral resistance of the polycrystalline silicon gates (- 50 I2 per square) may lead to an RC delay of clock voltages along the register (47). Another form of sealed-channel CCD has been described consisting of four overlapping aluminum clock lines (51) which are separated by anodized aluminum. The high conductivity of the aluminum should allow better operation at high frequencies, but the opacity of the aluminum gates would be objectionable in image sensor applications if the register were to be illuminated from the gate side. Three-phase CCD sensor arrays with overlapping silicon gates have been described recently ( 5 1 ~ ) . Continuous operation of a CCD register requires means for introducing and removing the minority carriers which transport the signal. In image sensors the initial charge pattern can be provided by direct illumination of the depletion region during a period when the clocks are stopped. In delay lines the carriers are introduced electrically by means of a reverse-biased input diode such as S-1 as shown in Fig. 23. In either case the carriers are removed by means of a second more strongly biased diode D-1 which acts as a drain. The entire C C D register thus resembles an MOS transistor with a multiplicity of gates between source and drain. The added gates near the source and drain assist in controlling the input and output signals. The auxiliary output transistor (S-2, D-2) located on the same silicon chip has its gate connected to a diffused diode touching the channel region near the end of the register. This diode fluctuates in potential in proportion to the size of the charge packet passing along the channel. The signal amplification produced by this voltage-sampling transistor permits smaller charges to be detected with less interference from clock transients and output circuit noise than would be obtained from the drain D-1.

B. Trunsjer Losses in C C D s The most serious losses in CCD’s are caused by failure to transfer the entire signal packet from one stage to the next during a single clock cycle. A short signal pulse would accordingly be attenuated and shifted in phase as the residual charges are transferred during later clock cycles. A longer input pulse could reach full amplitude but with poor frequency response and excessive delay. In image sensors where thousands of transfers must occur the fractional loss per transfer should not exceed at 10 MHz clock if normal TV resolution is to be attained. Surface channel devices of the type discussed so far have difficulty in achieving such low losses at this clock frequency. Buried-channel C C D s which are capable of lower losses at high frequencies will be discussed separately below.

-


217

1. Surjuce-Channel CCD’s

Carriers can fail to transfer to the next electrode within the proper clock cycle for two reasons: they may become trapped in fast interface states, or they may be limited by the dynamics of free charge motion. Three mechanisms control the free charge transfer (52):self-induced drift, thermal diffusion, and fringing field drift. Self-induced drift caused by mutual repulsion of charge is effective only for larger charge densities at the beginning of transfer and has little effect on the final transfer efficiency obtained. Thermal diffusion (53) results in an exponential decay of charge under the electrode with a time constant 12

where L is the center-to-center electrode spacing in microns and D is the diffusion constant. Equation (1) indicates the importance of keeping the electrode dimensions small and the diffusion constant and mobility high for operation at high clock rates. The transfer process can be speeded up by the fringing field ( 5 2 )between electrodes which has a major component in the direction of charge propagation. Its magnitude at the silicon-silicon dioxide interface increases with increasing oxide thickness and gate voltage, and decreases with increasing gate length and doping density. Carnes and Kosonocky (54)have calculated that a p-channel CCD should have losses no more than lop4 at a clock frequency of 10 MHz with a gate length of 7 pm and a substrate doping of 10’ cm- This assumes negligible trapping of carriers. In surface-channel devices the trapping of charge carriers in fast interface states ( 5 5 ) in the channel can cause additional transfer losses. These states can fill very rapidly at a rate determined by the number of free carriers, but their rate of emptying depends only on the energy level of the trapping state. Charges not released within the same clock cycle in which they were captured will be released later resulting in transfer loss and poor frequency response. It has been found that interface state losses can be minimized by introducing a constant background signal or “fat-zero” into the register. The effect of the background charge is to keep the slowest states filled (i.e. those states farthest from the band edge) so that they do not have to be filled and emptied by the signal charge. The background charge can be introduced electrically at the input diode of the register or optically by means of a uniform bias light in the case of an image sensor. Although the background signal causes some inconvenience and reduces the useful dynamic range of the register, it usually does not need to be larger than 10-30% of the full well

’.

218

P. K. WEIMER

16‘

I

I

I

I

0

,&tA //’

/

s

12-

//

I

0

OZ n. Y v)

v)

0 A

-3< 10 =

P

!+to to = 0.85 nsec -

/

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-

LL

16‘

bL pe - 7t I o

I

105103

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I 105

106

r = 64nsec

CCD6-5-8

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108

capacity. Figure 24 shows the measured loss per transfer (47)as a function of clock frequency for a 64-stage two-phase silicon gate register of the type shown in Fig. 23. This register was fabricated on a 1.0 0-cm n-type substrate having (100) orientation. Branch A of the curve was measured without “fatzero current and provided data from which the fast interface state density was estimated. [Nss = 2.9 x 10” (cm’ - eV)-l.] Branch B of the curve showed the reduction in transfer loss observed when a 50% “fat-zero” current was added. The dotted curve on the right represents the calculated transfer loss for free charge transfer for 0.4 mil long gates assuming that self-induced drift dominates transfer for the first 99% of the charge with a characteristic time to = 0.85 nsec, and thermal diffusion dominates thereafter with a time constant of 64 nsec appropriate for L = 0.4 mil. The fringe field has little effect on transfer losses in this case because of the low resistivity of the substrate. Although the background charge is effective in reducing the effect of trapping in the regions directly under the transfer electrodes, a full charge packet spreads out further under the edges of the electrodes (56).The interface states over this additional area can also trap signal charge which will be reemitted when the charge moves on. The edge effect thus contributes to transfer losses regardless of background charge. A more sophisticated ”


219

method of avoiding trapping in interface states is to replace the surface channel by a buried channel as described in the next section. The above discussion on transfer losses has not included the gain or loss of minority carriers from the channel to the substrate which might arise from dark current leakage in the depletion layer or from charge pumping” caused by improper clock voltages. The effect of dark current will be considered in the discussion of fixed pattern noise in C C D sensors in Section VIII,C,2. “

2. Buried-Channel CCDs Experience with the surface-channel CCD’s described above has shown that transfer losses caused by charge trapping in interface states can not be completely eliminated by the introduction of background “ fat-zero current. As will be discussed in the next section the presence of such states will also introduce noise into the transfer process as well as transfer loss. A modified CCD structure has been proposed in which the charges do not flow along the surface but are confined to a channel which lies beneath the surface (57). The number of traps in the bulk silicon are so much less than at the surface that a background current should be unnecessary to maintain low transfer losses. More efficient transfer at high frequencies can be obtained with buried channels because the fringing fields can be made higher and the carriers are at a greater distance from the electrodes. The larger mobility in the bulk silicon will also enhance the speed. The construction of the buried-channel CCD differs from an equivalent surface-channel device in that a thin layer of silicon having opposite conductivity type to that of the bulk is formed immediately under the insulator layer. This layer can be produced by ion implanation at the surface of a homogeneous silicon substrate or by use of an epitaxial surface layer or both. Figure 25 compares the energy level diagrams for a buried n-channel CCD with a surface n-channel device. The n-type surface layer is biased sufficiently positively with respect to the p-type substrate (by means of the n + output diode) that all electrons associated with the n doping are swept out. The clock gate electrodes are then biased so that a potential minimum is formed within the n-type layer rather than at the semiconductor surface. The charges are transferred along the buried channel by application of two, three, or four-phase clock voltages to the gate electrodes. However, the detailed effects of the gaps between electrodes and the barriers introduced by stepped oxide gates are somewhat different in the buried channel device. If too large a charge is introduced into a buried-channel register the channel becomes filled to the point that the carriers can interact with the traps at the surface, degrading the performance (58). For a larger storage ”

220

P. K. WEIMER

I

I~NS

SURFACE-CHANNEL

[ELECTRONS

------i P-TYPE SILICON

CTRONS

!I%

P-TYPE SILICON

(bl FIG. 25. Energy level diagrams [or two types of CCD registers. (a) Surface-channel CCD. (b) Buried-channel CCD.

capability it would be desirable to have a thin gate oxide and a buried channel which lies close to the surface. On the other hand, a deep channel is preferred for higher speed operation. Esser ( 5 9 ) has shown that a graded doping concentration of the surface layer, with highest concentration at the surface, will permit a large storage capacitance with high speed operation. In this case the main part of the charge packet which is closer to the surface is transferred by self-induced fields while the last fraction which determines the effective loss is driven further into the layer where much higher drift fields exist. per transfer at more than 100 MHz Transfer losses as low as 7 x have been reported for the so-called “peristaltic form of buried channel CCD described by Esser (59). In this device the surface layer consisted of a homogeneously doped epitaxial n-type layer of 4.5 pm thickness. Background “fat-zero’’ current had no influence on the losses. ”

C. Noise Clzaructeristics of’CCD’s I. Stntisticul Noise In applications such as image sensors, the noise properties of the chargecoupled registers are crucial in determining device performance. Fortunately, the noise introduced by charge transfer is small enough that many

TABLE I NOISE SOURCES I N

Category Electrical input circuit

Source of noise

CCD’S“

N

(derived)

Charge fluctiations set into first well

N,,= 400(C,,)1’2

Transfer losses

N,,= [2zN,(N,

Trapping losses

m,,= [1.4kTN,, N,A,]“Z

N (typical values)

N, = 40 for C,,

= 0.01 (electrical “fat -zero ”)

Charge-coupled register Transfer processes

Storage processes

External amplifier

m,,> 200 for i.N, = 0.2 N , = 950 for 2000 transfers (N,, = 10’o/cm2/eV)

aw

N, = 56 for N ,

= 3120 where I , = 10 nA/cmZ

Shot noise in thermally generated dark current Shot noise in op tically-generated background signal

Output circuit

+ NrZ)]l’Z

N, = NkL. where N,,

N, = 316 for N,, = l o 5 =

1/10 full well

(optical ‘‘fat-zero ”)

m, = 1300 for C,, N, = 130 for C,,

=

10 p F pF

= 0.1

C,, = capacitance of each potential well in picofarads; E = fractional transfer loss per gate; N , = number of gates or transfers; N , = number of signal carriers per charge packet; NFz= number of background carriers (“fat-zero”) per charge packet; A , = area of a single gate: p = number of phases; Nd = number of carriers per packet from thermally generated dark current. The values of N, given here apply for one scanning period ( T = 1/60 sec).

N

L 2

222

P. K. WEIMER

transfers can be tolerated. Very small signal levels are feasible provided the input and output circuits are carefully designed. In the following discussion, the various CCD noise sources will be considered along the lines outlined by Carnes and Kosonocky (60),but quantitative conclusions are tentative, subject to revision as more detailed studies become available. Experimental results reported to date (96) are in fairly good agreement with the predictions. As shown in Table I, noise generated in a CCD register can arise in three separate areas: (1) the input circuit, (2) the register itself, and (3) the output circuit. It is convenient to represent the signal in terms of the total number of carriers (N,) per charge packet and the magnitude of each noise source N, as the equivalent rms fluctuation in N , . For an example, a typical full well can hold lo6 carriers and the shot noise associated with this signal would be N,”’ or lo3.The other noise components can be added as the square root of the sum of the squares to obtain the resultant signal-to-noise ratio in the output circuit. An MOS-gated input circuit such as illustrated in Fig. 23 can be used for introducing a “ fat-zero” background or an electrical signal to be delayed. The inherent uncertainty in setting the charge into the first well is shown in Carnes and Kosonocky (60) to be given by

-

where C,, is the capacitance of the well in picofarads. As shown in Section XIII, the input circuit must be operated properly to achieve a background noise level as low as that given by relation (2). Unless such precautions are taken the background noise introduced electrically could equal or exceed the shot noise value = N;L2. The noise sources within the register can be separated into two groups: transfer process noise and storage process noise. Thornber and Tompsett (61) have shown that the correlation resulting when charges lost by one packet are gained by the succeeding packet results in a suppression of the low frequency portion of noise generated during the transfer process. The frequency spectrum for transfer noise is thus shifted toward higher frequen. cies regardless of whether losses are incurred by trapping or by free charge dynamics. As shown by Table I, interface trapping (55) represents the major source of transfer noise for a surface channel device. However, the suppressed low frequency content of this noise may tend to reduce its visibility in television applications.

m,


223

No such correlation effect occurs in the storage process noise introduced into the register by dark current leakage or by illumination. The shot noise associated with these charges will have a flat energy spectrum over the useful bandwidth of the device from zero frequency up to the Nyquist limit,f,/2. The equivalent rms fluctuation in carriers resulting from dark current leakage in the register is given by

where 1, is the dark current leakage per unit area ( - 10 nA/cm2), A , the area of each gate ( - lop6cm), p the number of phases (3), and T is the total integration time of a charge packet (1/60 sec). For a simple delay line, T represents the total transit time of a charge packet through the register, but in image sensor applications, where the clocks are stopped to allow photocarriers to be accumulated at each picture element, T comprises the entire frame time. Assuming a uniform dark current of 10 nA/cm2 and other conditions as stated following Eq. (3), the total charge accumulated in each packet in 1/60 sec is N , = 3125 electrons with a shot noise of I?, = 56. (For line storage operation with T = 63.5 p e c , N , and N, would be 9 and 3 electrons, respectively.) The dark current leakage is obviously a function of temperature and the semiconductor processing. When the register is illuminated the optically generated signal N , will also be accumulated during the period T and have the shot noise N,”’ associated with it. In addition to their rms noise components both N , and N , may contain even larger “fixednoise” variations which may dominate the performance of the device (see next section). Two methods commonly used for extracting the signal from a chargecoupled register are: (1) connect the input of an external amplifier directly to the output diode, or (2) connect the external amplifier to an on-chip MOS transistor whose gate is driven by a floating diffusion located near the end of the register as in Fig. 23. In each of the above modes the potential of the output diode or floating diffusion will be reset once each clock period. Thus, no resistor need be connected to the diode, and the output noise will be determined by the error in resetting the floating diode. The reset noise is given by the same expression used for calculating the input noise N, = 400 C;i2. However, the capacitance is very much greater in case (1) above when the capacitance of the lead connecting to an external amplifier must be reset. The resulting value of N, = 1300 is comparable to the amplifier noise limitation in a conventional vidicon camera. In case (2) the

224

P. K. WEIMER

much smaller capacitance of the on-chip MOS gate connected to the floating diffusion yields an equivalent noise which is 0.1 that of a vidicon amplifier. Output circuits having still lower equivalent noise are currently being investigated (62). The relative importance of the various noise sources is determined by the level of signal which is to be transferred. As long as the rms sum of all noise sources is small compared to the shot noise associated with the signal these sources are obviously of small consequence. As will be seen later this situation is actually true for CCD sensors operating under rather dim illumination such as a living room at night. However, under lower light levels such as a landscape illuminated by a full moon the factors listed above could limit the performance. For operation at still lower illumination such as by starlight all of the noise sources listed will have to be reduced. (See Section X on low-light level performance of CCD’s.) The use of buried-channel registers is expected to provide a major reduction in interface state noise and in transfer noise. The dark current noise may be the most difficult to suppress, since cooling of the silicon will be required. Even more serious than the dark current noise is the fixed pattern signal associated with the spatial variations in dark current, discussed in the next section.

2. Fixed Pattern Noise Dark current which varies from one element to the next can produce a nonuniform background of charge whose mean deviation from the average far exceeds the rms noise fluctuations in dark current at each element. This factor can have a major effect in determining the useful sensitivity of an image sensor. It can also affect the operation of series-parallel-series delay lines (see Section XII) where the charge packets are held in parallel registers for relatively long periods. Whenever the signal is passed through parallel channels and then recombined, repetitive patterns will appear in the output signal if the parallel channels are not identical. Such fixed pattern noise is not a problem in a simple serial delay line since every charge packet is equally exposed to the same series of wells. Other types of fixed pattern noise in image sensors can arise from variations in sensitivity from one element to the next and from geometric irregularities in clock lines or in channel stop diffusions. The pickup of clock voltages in the output signal can also mask the useful signal. Fortunately, the clock supply has twice the frequency of the upper limit of the signal passband so that the signals can be separated by filtering. Low frequency interference within the video passband is less likely to occur than with the early forms of scanning by means of digital multiplexers.


225

IX. EXPERIMENTAL CHARGECOUPLED IMAGESENSORS A . Single-Line CCD Sensors

1. Line Sensors with Illuminuted Registers The operation of a CCD register as a line sensor was first reported by Tompsett et al. (63) of Bell Telephone Laboratories in August of 1970. A simple optical image was projected on an eight-bit three-phase register while the clock voltages were stopped so that a charge pattern could form. The clocks were then started again and the accumulated pattern was transferred along the register to an output diode where the charge packets could be collected in sequence. The output signals were used to produce a twodimensional picture by mechanically moving the optical pattern across the row of sensors for successive lines. Since 1970, single-line illuminated-register sensors having up to 500 elements have been produced in various laboratories. These have been made with both three-phase and two-phase registers, and they normally include an input diode for introduction of background current or electrical signals to be delayed. (See,for example, Fig. 23.) Most single-line silicon CCD registers can be operated as a line sensor provided the clock voltages are stopped for a suitable integration period to allow a charge pattern to form. The two-phase silicon gate registers were also operated as line sensors, although light absorption in the silicon gate reduced the sensitivity relative to that obtained with three-phase aluminum gate registers having gaps between the electrodes.

2. Line Sensors with Noniltuminated Registers In most applications of line sensors it is not convenient to have to interrupt the scanning in order to expose the sensor. All problems of image smear resulting from simultaneous exposure and scanning can be eliminated by employing a separate row of photocells with the transfer register shielded from the light. The longest single-chip CCD line sensor of this type reported to date is a 1500 element CCD page reader (64). This device was constructed as illustrated in Fig. 15b using a single row of 1500 photocells coupled to two 750-stage shielded CCD registers located one on each side of the sensor row. With this arrangement exposure of the photocells and readout of the signals could be carried on simultaneously. MOS gates, not shown in Fig. 15b, were located between each sensor element and its adjacent register stage. All gates were normally kept closed,

226

P. K. WEIMER

FIG. 26. Photomicrograph of a buried-channel charge-coupled single-line image sensor having 500 photoelements [Kim and Dyck (65), courtesy of Fairchild Camera and Instrument Corp.].


227

but were opened simultaneously when a new line of information was to be transferred to the registers. The signals from the parallel registers were recombined in the output so that all elements were read in proper sequence. Advantages of the parallel register format were that the total number of transfers and the transfer frequencies were reduced by a factor of two. Also, the sensor elements could be spaced more closely than would be possible if a single output register were used. The transfer losses of the two surface per gate) that good resoluchannel registers were sufficientlylow ( < 5 x tion was achieved over the entire sensor. A 500-element buried-channel line sensor having a useful dynamic range of over lo00 to 1 has recently been reported (65).The scanning organization of this device, shown in Fig. 26, is similar to the 1500-element sensor described above, with two 250-stage three-phase registers located along the sides of the sensor row. All gates were of doped polysilicon with the undoped polysilicon between the gates forming a resistive sheet which minimized charging of the oxide. A final layer of aluminum was deposited over the registers as a light shield to prevent image smearing during transfer. The optically generated carriers in the sensor area were collected on the silicon surface under the central polysilicon photogate electrode. This area was subdivided by means of channel-stop diffusions into 500 separate elements with a center-to-center spacing of 1.2 mils. A short three-phase output register was used to recombine the signals from the two main registers and to transfer the signal to an on-chip gated-charge MOS amplifier similar to that illustrated in Fig. 23, The dynamic range of this sensor was enhanced by the use of buriedchannel registers, which avoid the interface state noise of surface-channel devices and require no " fat-zero" background current. Figure 27 shows three pictures transmitted by the sensor with an integration time of 500 psec and an output clock frequency of 1 MHz (0.5 MHz for the main registers). The illumination level for the top picture (30 fc of tungsten light at 2800°K) approached 90% of saturation in the bright areas. Pictures b and c were reduced 100 x and 1000 x , respectively. Picture b showed no degradation but picture c showed random noise which arose in the output circuit. The large dynamic range obtained with the 500 x 1 buried-channel sensor played a significant role in suggesting the potential capabilities of charge-transfer sensors for low-light-level television. However, it was recognized that the requirements of uniformity in dark current would be far more severe in an area sensor than in a line sensor. For example, the relatively short light integration period in the above tests (500 psec) reduced the dark current contribution in the output signal by a factor of 33 times compared to what it would have been if the usual 1/60 sec integration time had been used.

228

P. K. WEIMER

FIG. 27. Pictures taken with a 500-element linear imagmg device at three d~fferent illumination levels. The highlight signal level in the region around the boy‘s shoulder in (a) is approximately 90s; of saturation. The light levels in (b) and (c) are reduced by 100 x and 1 0 0 0 ~from (a). The operating frequency was 1 MHz [Kim and Dyck (65). courtesy of Fairchild Camera and Instrument Corp.].


229

B. Two-Dimensional Area- Type Charge-Coupled Sensors 1. Sensors with Illuminated Registers

The feasibility of imaging with two-dimensional charge-coupled sensors was demonstrated by Bell Telephone Laboratories (66) in 1971. Figure 28 shows the general layout for a three-phase surface-channel sensor (6) having 64 x 106 imaging cells. This sensor is of the vertical frame transfer type having illuminated registers in the sensor area, and a separate storage area for handling the signal during readout. The 106 vertical registers in the sensor portion each had 64 stages and the storage area was of equal size. The horizontal output register contained 106 stages, with an output diode for collecting the signal. In operation, the charge pattern which has accumulated in the illuminated sensor area during the first field period is transferred to the storage area during the following vertical blanking interval. The pattern continues to advance toward the output register during the next field period and each row of charges is transferred in parallel to the output register during horizontal blanking. The video signal appears at the output diode as the charges are transferred in succession along the fast output register. Meanwhile, during the second field period, a new image pattern has formed in the sensor area so that continuous output signals are obtained. The input register shown in Fig. 28 does not play a useful role in this mode of operation but was included so that the device could also be used as an analog delay line (see Section XII). A total of nine different clock voltages are required for driving the three sets of gates in the sensor, in the storage area, and in the output registers. In addition, other separately addressable gates were provided to allow independent operation of various portions of the device. The 64 x 106 sensor was fabricated on 20-40 Q-cm p-type silicon. An n-type phosphorus diffusion provided input and output diodes as well as the cross-unders required for driving the three-phase registers. A p-type boron diffusion served as channel stops to define the edges of the 106 vertical transfer channels and the two horizontal channels. After removing the masking oxides used for the diffusions, a layer of 1300-1400 8, of dry HCl gate oxide was thermally grown. Typical values for oxide charge and interface state density were 5 x 10" cm-' and 1 x 10'ocm-2, respectively. The coplanar gates were formed by depositing a single layer of tungsten, 1500 8, thick, which was subdivided into gates by etching. All gate electrodes were 9 pm wide in the direction of charge transfer, and were separated by 2 pm gaps, giving a total cell length of 33 pm. The active area of the device was 4 x 5mm.

230

P. K. WEIMER

INPUT GATE

-

l [.

T

. ... I

1

T 1

- .

1 . I 1 7 . 1

p2 OP3

0

!.. 1... 1. 1. 7.: .:I.: I: 1.: I: INPUT

REGISTER DIODE

CHANNEL BOUNDARY DIFFUSION IMAGING AREA

BOTTOM GATE

-

OUTPUT REGISTER PI

0

p20

ELECTRODES

. ...I.. ..I ..I.. ,1..:

r

'r

:.-. :.. r 1

:

1 - 1 1 - 1 1 1

1

' C O U T P U T GATE

P3O

FIG.28. A schematic diagram of the three-phase charge-coupled image sensor built by Bell Laboratories [Sequin et a/. (6)]. Frame transfer sensor with illuminated registers in sensor area.


23 1

The sensor was mounted in the camera so that the optical image entered the silicon through the gaps in the metal electrodes. Figure 29a shows a picture transmitted by the sensor operating in the frame transfer mode just described. The element readout rate was 1 MHz and the field rate was 120 frames/sec. In another mode of operation the image was projected on the entire 106 x 128 element array for 1/30 sec, and was then read out by shifting ail rows downward a line at a time unfil they had all reached the output register. A recognizable picture was obtained, as shown in Fig. 29b, even when the integration period was equal to the readout period but the vertical image smear caused by illumination during readout was objectionable.

FIG.29. Television pictures transmitted by the three-phase charge-coupled image sensor shown in Fig. 28. (a) Operation in the frame transfer mode with 64 x 106 elements, (b) Operation with image projected on entire array of 128 x 106 elements with integration time equal to the readout time [Sequin et al. (6)].

The question arose as to how a vertical frame transfer sensor could conveniently provide a vertically interlaced signal such as required for most television systems. Sequin (34) has described a method of operation which not only achieves interlace but effectively doubles the number of vertical lines in a given sensor. In the normal frame transfer mode described above, the photocarriers were collected under the same phase electrode in each frame. The gate which was held most positive during the integration period would have a deeper potential well than its neighbors and would therefore collect the photoelectrons generated in its neighborhood. For interlaced operation, it was sufficient to collect the carriers under different electrodes in successive fields: e.g. under the phase 1 electrodes in the odd fields and the phase 2 + 3 electrodes in the even fields. Although the vertical resolution in either field could not exceed the 64 stages in the sensor registers, the effective

232

P. K. WEIMER

midpoint of each element would be shifted one-half an element up or down on successive fields. The total number of sampling points in the vertical direction was accordingly increased by a factor of two when considered over two fields. This improvement was clearly visible in the transmitted picture when viewed on an interlaced monitor. Figure 30 shows a comparison 'of interlaced and noninterlaced scanning on a small 45 x 60 element (noninterlaced) frame transfer sensor made at RCA Laboratories (36). The interlaced mode of operation can cause the spots resulting from high dark current in the sensor to be more conspicuous since different sets of defects will be visible in each field and they will flicker at a 30 Hz rate.

FIG.30. Operation of a 45 x 60 element three-phase CCD sensor under two conditions of operation. (a) Normal 1/60 sec integration time with interlace to give 90 x 60 elements. (b) Short integration time without interlace. (Dark current spots were more conspicuous in (a) because the integration time was much longer and because interlace exposes more defects.)

It should be noted that each element of a frame transfer sensor operating in the interlaced mode will have only half the integration time of an interlaced sensor whose vertical elements do not overlap in successive fields. The interlaced frame transfer sensor is analogous to a camera tube whose beam width is twice the center-to-center spacing of the scanning lines. Although the integration time in each case is only 1/60 sec instead of 1/30 sec, no charge is lost. The vertical resolution, however, of the interlaced frame transfer sensor appears to be fully equivalent to that of a noninterlaced sensor having twice as many scanning lines (67). The sensitivity and resolution of CCD sensors will be discussed in more detail in Section X. Although the 128 x 106 element (interlaced) sensor had far fewer elements than the early XY addressed sensors its sensitivity and overall uniformity was considerably better than the earlier XY sensors.


233

Several investigations have been started at various laboratories to develop CCD sensors having full TV resolution. In spite of the extra silicon area required for storage, the frame transfer sensor with illuminated registers is a good candidate for extension to larger sizes. The simplicity of construction of the three-phase register permits element sizes to be as small as one square mil. However, a serious problem in fabrication is to avoid shorts or connecting bridges between electrodes spaced 2-2.5 pm apart. A 128 x 160 element sensor (256 x 160 elements interlaced) was built (68) at RCA Laboratories having aluminum electrodes with 2.5 pm spacing and a total gap length of approximately 12 ft. Very high quality masks are required to produce sensors of this size free of defects. Nevertheless, many experimental devices of this type were built and operated. An even larger experimental sensor (69) of the same type has been produced in the Electro-Optics Department of the RCA Electronic Components Division. The television pictures shown in Fig. 31 were taken with the

FIG.31. Television pictures transmitted by a 256 x 320 element C C D sensor made at the RCA Electronic Components Division [Rodgers (69)].

solid state camera, shown in Fig. 32. The sensor used in this camera (Fig. 33) contained 256 x 320 elements (512 x 320 interlaced). Such a sensor requires a silicon chip approximately 500 x 750 mils and has an active area of 250,000 square mils. This sensor has an important advantage over earlier CCD sensors in that it can be operated at standard TV scan rates and the picture displayed on a regular television monitor. The problem of avoiding blemishes or spots in the output signal can be expected to become more severe as larger area devices are built. Too many defects on the average will reduce the yield and increase the costs beyond what the market will bear. For this reason it is most important that the optimum design of sensor require as few steps in fabrication as possible. Although the frame transfer sensors described above are relatively simple in

234

P. K . WEIMER

FIG.32. Solid state camera incorporating the 256 x 320 element CCD sensor

construction, it may ultimately become necessary to increase their complexity in order to control the overload characteristic known as blooming.” This effect occurs when a brightly lit object in the scene produces excess charge in the sensor which spreads to adjacent elements along the register producing objectionable streaks in the transmitted picture. Blooming can be controlled (71, 72) by introducing diffused diode buses between the registers to draw off the excess charge. If such blooming buses prove to be necessary they can be added most readily to the relatively simple structure of the illuminated register sensors. Most of the large experimental frame transfer sensors made to date have been of the three-phase surface-channel type with the light entering the silicon through the gaps between the electrodes. Two-phase registers require simpler clock voltages and fewer crossovers in the sensor. The sealedchannel silicon-gate registers described in Section VIII could be used in illuminated register sensors, but a fraction of the light in the blue end of the spectrum may be absorbed in the silicon gates, if illuminated from the gate side. Illumination from the substrate side will require thinning of the silicon as in the silicon vidicon. Illuminated register sensors using buried channels have not been reported to date. “


235

FIG.33. A comparison of the size of the developmental 256 x 320 element CCD sensor with a 213 in. silicon vidicon tube which is mounted in its focus and deflection coil assembly.

2. Sensors with Nonilluminated Registers and Interleaved Photocells A charge-transfer sensor having separate photocells and its registers shielded from light avoids all image smearing caused by illumination during transfer. A vertical transfer sensor of the type shown in Fig. 17a has been fabricated ( 7 3 ) in a 100 x 100 element size by the Fairchild Camera and Instrument Corporation. This sensor, which is currently being incorporated in cameras for special applications such as surveillance, represents the first area-type CCD sensor to reach the commercial market. The transport registers are of the two-phase buried-channel type with two levels of polysilicon gates. An overlying layer of aluminum forms electrical connections and shields the registers from light. An advantage of the nonilluminated register sensor is that the need for a separate storage area is eliminated. However, 30-50% of the light incident from the gate side is lost, and the elemental structure is more complex than required for sensors with illuminated registers. Figure 34 shows the potentials under the electrodes of the elemental cell (35)of the 100 x 100 sensor during (1) charge integration and scanning and (2) transfer of charge from the photocell to the register. During integration, electrons are collected in

236

P. K. WEIMER

the potential well under the positively charged transparent photogate electrode. When charges are to be transferred to the registers during the vertical blanking interval the photogate is made much less positive than the adjacent register gate. The scanning gates must be designed to provide a barrier

yrrL

VERTICAL S C A I 6ATE

INTEGRATION OF CHARGE

TRANSFER TO REGISTER

34. Operation of the 100 x 100 element area sensor showing potentials during integration and transfer of charge from photoelements to the registers [Amelio (35),courtesy of Fairchild Camera and instrument Corp.]. Yiti.

which prevents charge from spilling back into the sensor element while the register is running. Interlacing capability is achieved by shifting the evennumbered sensor elements into phase 1 electrodes in field one and the oddnumbered sensor elements into the phase 2 electrodes in field two. The resolution for the 100 x 100 sensor was reported (73) to be 75 lines in both the vertical and horizontal direction. A differential gated charge amplifier was included on the 100 x 100 sensor chip. Dynamic ranges of > 1000 to 1 have been measured at an output frequency of 500 kHz. Random noise set the limit of detection at approximately 400 signal electrons.

X. PERFORMANCE LIMITATIONS OF CHARGE-COUPLED SENSORS Sensitivity and resolution are the two most basic qualities of sensor performance. Other characteristics such as uniformity, the number of picture elements, freedom from spurious signals, reliability, and ease of manufacture are gradually being solved by advances in technology. However, it is the fundamental limitations on sensitivity and resolution which will determine whether CCD sensors will be able to satisfy the more demanding applications now being served by camera tubes. Since representative data on perfor-


237

mance of experimental sensors is not readily available, the present discussion will be based largely on analytical predictions of ultimate limitations.

A . Resolution

A solid state sensor capable of meeting normal broadcast standards should have approximately 5 12 x 680 elements (interlaced) for balanced resolution. Although sensors this large will considerably exceed the size of existing CCD sensors their fabrication appears to be within the foreseeable capabilities of silicon technology. However, single-chip sensors which could match the limiting resolution of special camera tubes such as the return beam vidicon (67) (-4000 lines) are well beyond the present state of the art. In practice, it was soon apparent that the observed resolution in a CCD sensor could fall far below the maximum resolution set by the number of elements. Sampling effects, lateral diffusion of charge within the silicon, nonuniform dark current, clock transients, and illumination during transfer can all contribute to a loss in resolution. The charge loss per transfer, however, introduces the most fundamental limitation on the maximum resolution which can be achieved in a charge-coupled sensor. Transfer losses are normally expressed in terms of the nE product, where n is the total number of transfers and I is the fractional inefficiency (or loss) per transfer. The inefficiency product should be low for both the vertical and horizontal registers in order to maintain the expected spatial resolution. The effect of transfer losses on resolution has been calculated (74, 75), and the results are plotted in Fig. 35. The ordinate shows the degradation in the modulation transfer function (MTF) for various values of nE as a function of the normalized spatial frequency. The curves are terminated at a spatial frequency equal to one-half fo , the geometrical element frequency, since according to Nyquist’s sampling theorem, frequencies greater than this cannot be resolved. (Expressed another way, the useful video passband extends up to one-half the clock sampling frequency.) The block diagram at the right side of Fig. 35 shows the spreading and delay of a single charge packet for different values of the transfer inefficiency product. It is noted that the center of the degraded pulse is delayed independently of signal frequency by a number of stages approximately equal to the nE product. The MTF curves apply for a charge pattern which originates either optically at each element or which is introduced electrically at the input of the register. With optical input, of course, the n& product will become progressively larger for signals originating farther from the output terminal of the register. If the value of nE is larger than a few tenths in any portion of the sensor the picture detail in these areas will be smeared out and delayed either vertically or horizontally.

238

P. K. WEIMER >

0

z

%

w

DEGRADATION OF A SINGLE PACKEl

0

nE = 2.0

. 1 1 1 . -

01

0.2

0.3

0.4

0.5

INPUT FREQUENCY RELATIVE TO ELEMENT FREQUENCY f o

FIG. 35. Degradation in Modulation Transfer Efficiency (MTF) for various values of ~ i as c a function of the normalized spatial frequency. The block diagram at the right shows the delay and spreading of a single packet for different values of the inefficiency product (75), courtesy of Bell Laboratories.]

iw;.

[Tompsett

The ne product in the 64 x 106 element sensor made at Bell Laboratories (Section IX) was measured to be approximately 0.3 for both the vertical and horizontal registers. This value of ns produces a degradation in vertical and horizontal M T F of up to 55% in the most distant corner. The maximum drop in MTF which can be tolerated will depend upon the application and the requirements of the user. If we assume a maximum tolerable ne product of 0.1, we find that the loss per transfer in a 512 x 680 element interlaced three-phase frame transfer sensor should not exceed E = 2.8 x The maximum number of transfers in this example was 3576. A two-phase interlaced sensor with interleaved photoelements could tolerate larger transfer losses per transfer because fewer transfers would be required for the same number of elements. Table I1 shows the maximum tolerable loss per transfer calculated for


239

TABLE I1

MAXIMUM TOLERABLE TRANSFER INEFFICIENCY E FOR VARIOUS SIZESAND TYPES OF CHARGE-TRANSFER SENSORS No elements

Type of sensor‘

45 x 60 (90 x 60 interlaced)

A

450

2.2 x 10-4

6.6 x

100 x 100

B

400

2.5

7.5 x 10-4

64 x 106 (128 x 106 interlaced)

A

702

1.4 x

128 x 160 (256 x 160 interlaced)

A

1248

8 x 10-5

2.4 x 10-4

256 x 320 (512 x 320 interlaced)

A

2496

4 x 10-5

1.2 x 10-4

256 x 680 (512 x 680 interlaced)

A B, C

3576 1872

2.8 x 5.3 x 10-5

8.4 x 10-5 1.6 x 10-4

4500 x 6000 (interlaced)

A B, C

31500 16500

3.2 x lo-‘ 6.1 x

9.5 x 10-6 1.8 x 10-5

max n

-

- _ _

for nE = 0 1 (MTF = 82%)

10-4

&

-__ for ne = 0 3 (MTF = 55%)

4.2 x 10-4

A-Three-phase illuminated register, vertical frame transfer. B-Twophase interleaved photoelements, vertical or horizontal transfer. C-Two-phase, illuminated register, horizontal transfer.

two assumed values of ne and for several different sizes and types of CCD sensors.

B. Low Light Sensitivity In a classic paper entitled “Television Pickup Tubes and the Problem of Vision,” Rose (76) has shown that the resolution of an ideal sensor at threshold illumination is limited by the fluctuations in the photons impinging on the light-sensitive area. Actual devices usually fall short of ideal performance

240

P. K. WEIMER

because of additional noise introduced by the scanning process and because of a low yield of photoelectrons in the primary photoprocess. After fifty years of research and development, camera tubes can now be produced in which scanning noise is negligible. This result has been accomplished in such combination tubes as the I-SIT or the I-isocon by the technique of providing electron image intensification (77) prior to scanning. Improvement of the scanning process alone (as in the isocon without intensification) has not been sufficient to reach photon-limited performance at all light levels. A nonintensified solid state image sensor such as the CCD sensors described above has no gain mechanism prior to scanning. Its only chance for ideal performance lies in attaining substantially noise-free scanning. Although the noise and spurious signals introduced by charge-transfer scanning are fairly low, they can still be large enough to limit the actual low-light performance. A partially compensating advantage of a silicon sensor over the photoemissive cathodes used in the most sensitive tubes is the higher responsivity of silicon and its extended spectral response into the near infrared. Table 111 (seep. 244) compares the measured responsivity of an S-20 multialkali photocathode (such as used in the I-SIT)with that ofa filtered and unfiltered silicon vidicon tube using a standard white light tungsten source at 2856°K. (Responsivity measured with such a standard source is normally expressed in mA/W-2856”K and should not be confused with the unit of responsivity at a single wavelength, A/W. The unit (W-2856 K ) is used to designate the total radiated power in watts, integrated over all wavelengths from a tungsten filament lamp operated at a color temperature of 2856°K. It can be converted directly into lumens by the relationship 1 W-2856°K = 20 lm.) In some of the analysis which follows, it will be convenient to express the measured responsivity of sensors in terms of an average quantum yield, 8, derived from the calculated responsivity of an “ideal” detector having a 100% quantum efficiency over the normal silicon range of 400-1 100 nm. The responsivity of such a detector (78) is taken to be 238 mA/W-2856”K. The measured responsivity of silicon devices usually fall far below this value because of the failure of quanta to be absorbed or because of other losses in the sensor. The Rose analysis (76), which gives the resolution of an ideal sensor as a function of illumination, has been used for many years for evaluating the performance of camera tubes at low light levels ( 7 ) . Similar calculations for C C D sensors have been carried out by Carnes and Kosonocky ( 7 9 ) and more recently by Campana (80). Although the method of analysis for each was essentially the same as the earlier model, the conclusions in the second paper regarding the tolerable C C D noise to match the sensitivity of the I-SIT tube were more stringent. Most of the differences lie in the assumptions regarding responsivity, contrast, threshold signal-to-noise ratio. and ”


24 1

integration time. The derivation is simple and will be reproduced here using radiometric units as in the paper by Campana (80). The number of carriers accumulated at each element during the integration period is given by

N = HSA, t 4 '

(4)

where H is the image irradiance (Watts/m2-2856"K),S the effective responsivity A/W-2856"K), A , the geometric area of each element (m'), t the integration period (sec), and q is the electronic charge (coulombs). The responsivity S includes all light losses due to structure and internal reflection as well as the detector quantum yield 8. Defining the contrast in the charge image as C = A N / N , , the number of signal charges per element will be

ANs = CHSA,t/q,

(5)

while the shot noise associated with N , is given by

Combining N i l 2 with the effective rms noise N arising from all other CCD noise sources (60) (see Section VIII) yields the total rms noise per picture element :

At very low light levels where the observed resolution will be limited by noise the geometric element size (L, = must be replaced by a somewhat larger observable picture element whose side is L. The criterion for calculating the limiting resolution versus irradiance curve is that the ratio of the number of picture charges per observable picture element to the total rms fluctuations per observable picture element must exceed a minimum observable signal-to-noise ratio, k . That is,

6)

A N , . (L2/L2) - k. N,(L/Lif Relation (8) can be expressed in terms of resolution (in TV lines per picture height or line pairs per mm):

242

P. K. WEIMER

where R is the observable limiting resolution and R, is the geometrical resolution. Substituting (5) and (7) in (9) gives:

R

R k

CHSA,t/q (HSA,t/q + N2)1/2

= 3 .-

~

~

Expression (10) has been used to calculate limiting resolution versus irradiance for various assumed values of S, k, t, and fi. The results are plotted in Fig. 36. The irradiance level H , at which R = Rg is obtained by

-aE E

a W

a (0

a:

2

I,,,,,

I

I , , , , , ,

I

I,,,,,,

I

,,

I

I,,,

, , I1

I,,,

FIG. 36. Predicted resolution of silicon image sensors as a function of irradiance of tungsten light for various values of scanning noise and responsivity S . R was calculated from Eq. (10) assuming R , = 20 line pairs per mm (sensor with 1 mil pitch), C = 1, r = 0.2 sec. k = 1. 8, the average quantum yield for all incident photons between 400 and 1100 nm, is related to responsivity S as shown in Table 111: ( @ = 1 corresponds to S = 0.238 A,W-2856 K : 6 = 0.37 corresponds to S = 0.087 AiW-2856"K; 6 = 0.019 corresponds to S = 0.0048 Am-2856-K.) Curves (1)-(3) are for "ideal" sensors having zero scanning noise N = 0. Curves (4)-(8) are calculated for actual sensors with increasing scanning noise I < %< lo4. The dotted curves (9) and (10) are the measured resolution for the I-SIT and SIT camera tubes. (The I-SIT tube meahurcd had S = 0.0048 A W - B W K . ) representa the total scanning noise for the assumed integration period I = 0.2 sec.

m

m

solving (10) for H : H,

=

-

4

[k2

~-

2SA, t C 2

+ k ( k 2 + 4C2N2)"2].

(11)

Relation (11) is useful in assessing the effect of varying the values of the parameters used in calculating Eq. (10).


243

The maximum geometrical resolution R, is assumed in each case to be 20 line pairs per millimeter corresponding to a CCD element spacing of 1.0 mil center-to-center. ( A , = 6.45 x lo-'' m'.) All effects of modulation transfer function and the Kell factor o n resolution are ignored in the present discussion. The contrast C has been taken to be unity in each curve. It is noted from (11) that decreasing C would shift the curves to the right in proportion to C2 if N is zero but in proportion to C if N is large. Relation (11) also shows that the value assumed for k, the minimum detectable signal-to-noise ratio, plays a sensitive role in predicting the irradiance threshold at whch resolution begins to deteriorate. Carnes and Kosonocky (79) used k = 5 as recommended by Rose for detecting small isolated objects. Campana (80) used k = 1, based on experimental tests of detecting bar patterns with an I-SIT camera system. Such a low value of k is reasonable here since the eye is able to sense the cooperative effect of the large number of picture elements that go into making the bar pattern, even though the signal-to-noise ratio of a single observable element is unity. A value of k = 1 was therefore taken for all curves plotted in Fig. 35. The curves would be shifted laterally as the square of k when N = 0 but only as the first power of k when N is large. Curves (l), (2), and (3) in Fig, 36 represent "ideal" sensors in which no noise is introduced in the scanning process, i.e. N = 0. The total noise in this case is shot noise in the signal current. In curve (1) S is assumed to be 238 mA/W-2856"K, corresponding to a theoretically perfect silicon detector having 0 = 1 over the wavelength range 400-1100 nm. In curves (2) and (4)-(8), S = 87 mA/W-2856"K, or 0 = 0.37, the same as an unfiltered silicon vidicon. (See Table 111.) Although this value is approximately three times larger than measured to date in top-illuminated CCD sensors, this value would be a reasonable expectation in a thinned CCD sensor illuminated from the substrate side (81). In all curves the integration time t has been assumed to be 0.2 sec corresponding to the integration time of the eye of the viewer rather than the frame time of the scanning system. It is well-known that the eye will integrate signal and noise in a television picture giving a visual improvement comparable to that of a camera photographing the television screen with an exposure time of 0.2 sec. The exact value of both S and t will have only a first power effect on the irradiance required. Curves (4b(8)show the effect of increasing the total rms scanning noise from 1 to 10,000 electrons per integration period. These curves are applicable for other types of silicon self-scanned image sensors, including the XY addressed photodiode arrays discussed in Section VI. The dotted curves in Fig. 36 are for camera tubes having a modified S-20 photocathode. Curve (3) was calculated for an ideal tube having S = 4.8 mA/W-2856"K, while curves (9) and (10) are the measured values of resolution versus irradiance for an

TABLE 111

RELATIONSHIP BETWEEN R E s P o w s i v r r Y S

AN11

AVERAGE QUANTUM YIELD 0

FOR FOUR TYPES OF

DETECTOR

ELEMENTS

Sensor

Responsivity (pA/lm)

Responsivity (mA/W-2856'K)

Average quantum yield 6 (400-1 100 nm 2856'K) ~~~~

Trialkali photocathode (S-20)

I60

Silicon vidicon with 1R absorbing filter

910

Silicon vidicon unfiltered Type V response

4350

Ideal silicon detector with loo"/, response over wavelengths (400-1 100 n m )

1 1.900

3.2

0.013

Quantum yield at peak raponsivity. 6' ~~

0.20 (at 420 n m )

18.2

0.076

87

0.37

0.83 (at 500 nm)

238

I .o

a 7:

245


I-SIT tube (77a)and a SIT tube (77b).(The SIT tube contains a silicon vidicon target on which high energy electrons from an S-20 photocathode are imaged, producing an electron gain of several thousand prior to integration and scanning.) In the I-SIT tube, the photocathode of a SIT tube is coupled by means of fiber optics to the screen of a separate image intensifier tube, which also uses an S-20 photocathode. The horizontal scale in Fig. 36 shows the equivalent illuminance on the sensor in lumens per square foot (foot candles) using the conversion factor 1 lm/ft2 = 0.5 W-2856”K/mZ. The highlight illuminance on the sensor is approximately one-tenth that on the scene. A scene illuminance of 10- lm/sq ft is typical of starlight illumination on an overcast night. Comparison of the predicted CCD performance with ideal sensors and with the existing SIT and I-SIT tubes show that the scanning noise N must be kept to less than 10 electrons per element (80)per integration period if the CCD is to match the I-SIT under the assumed test conditions. Although a somewhat larger value of N might be tolerated if comparisons were made under conditions of lower contrast and higher signal-to-noise ratio [as in Carnes and Kosonocky (79)] it is clear that N should be kept as small as possible. Since the numerical values of N,, given in Table I were calculated for a single scanning period of 1/60 sec, those values should be increased by a factor of (0.2/0.016)1’2for proper comparison with the curves of Fig. 36 which assume an integration time of 0.2 sec. Although the various noise contributions arise in different ways, they will each be increased in proportion to the square root of the total number of scans in one integration period. arc listed below, and the prospects for reducing The modified values of N,, each are summarized as follows: 1. Shot noise in the electrically introduced “fat-zero’’ current (N= 138). This source of noise can be eliminated by use of registers which do not require a “fat-zero’’ background current (e.g. buried channel registers). 2. Transfer losses (N> 690). Various authors are in disagreement as to the existence and magnitude of this source. According to Carnes and Kosonocky (60) this type of noise would decrease as the transfer loss is reduced. == 3290). This noise source would be most serious 3. Trapping losses in surface-channel devices. It should be substantially smaller with buriedchannel registers. 4. Shot noise in the dark current (N= 194). The thermally induced dark current noise can be reduced by cooling the sensor. (Ndrops by $for each 10°C drop in temperature.) 5. Shot noise in optically generated background current = 1095) for N,, = 0.1 full well.) This source is an alternative to (1). Elimination of the need for “fat-zero’’ current would remove this source.

(m

(m

246

P. K. WEIMER

6. Output amplifier on chip (I7= 416). A method of reducing this noise now being explored is to voltage-sample successive output nodes to produce a distributed parallel-channel output amplifier. Floating-gate amplifiers (62) used singly or as distributed amplifiers may also reduce this noise factor significantly. The total rms noise introduced by the scanning process is obtained by taking the square root of the sum of the squares of each component. The total value of for all of the above components (assuming all were present) would be 3575 for 0.2 sec integration period. This method of summing does not take into account the fact that different noise sources may have a different frequency spectrum and hence may differ in their relative visibility. As stated in Section VIII, fixed pattern noise in practical devices may actually exceed the fluctuation noise discussed above, and can restrict the range of useful operation to higher light levels than predicted in Fig. 36. A major source of fixed pattern noise in experimental sensors is caused by local variations in dark current which will produce a mottled background in the transmitted picture. In this case, the fixed noise background will vary directly as N , and not as the square root. Although improvements in silicon processing would be expected to reduce this problem, operation at very low light levels would require a reduction in dark current variations by several orders of magnitude below that tolerable in a silicon vidicon. Cooling of the device to reduce dark current noise should reduce fixed-pattern noise as well. Spurious signals which remain fixed can also be removed by subsequent signal processing of the video signal. A method of background subtraction which is particularly appropriate for C C D s is to recycle the fixed pattern signal through the sensor itself (36). (See next section.) Another type of fixed pattern noise may arise from variations in clock voltage. The complete removal of all clock voltages from the signal is particularly difficult at very low signal levels. A major research effort is currently being carried out in a number of laboratories ( I ) to develop a simple low cost C C D sensor suitable for use at very low light levels. If it should prove too difficult to reduce sufficiently either the noise associated with scanning or the fixed pattern noise in the sensor, a possible solution would be to introduce image intensification prior to scanning as has been done with tubes. Many combinations of image intensification with C C D arrays are conceptually possible. While vacuum tube intensifiers are quite highly developed, the resulting combination would risk loss of the compact, low cost advantages anticipated for CCDs. Solid state intensifiers (82) combined with C C D sensors might be attractive but they present even more formidable problems in resolution and uniformity. For normal scene illuminations ranging from that of a full moon up to bright sunlight a back-illuminated C C D sensor with a scanning noise back-


247

ground as large as 3000 electrons could still yield a good quality picture. Its operating sensitivity would be comparable to that of a silicon vidicon which is normally considered a sensitive tube, If its cost can be kept low a CCD sensor with an adequate number of elements would be a very attractive device indeed.

XI. CHARGE-TRANSFER SENSORS AS ANALOGSIGNALPROCESSORS The earliest video signal processors requiring delay utilized beamscanned storage tubes (83) operating similarly to camera tubes. More recently, storage tubes have been supplemented by acoustic delay lines, magnetic tape, and video disks. The development of charge-transfer scanning has reemphasized the connection between image sensors and analog signal processing. The sensor itself can be used as a highly versatile delay line, or it can be used simultaneously as a sensor and as a delay line for processing its own signal. Other types of analog signal processors such as transversal filters (84), correlators (85), and time division analog multiplexers (86) can be produced by modified forms of registers. The present section will consider only such video processing that can be carried out by a charge-transfer sensor having an input register. The equally important application of such devices for digital memories is beyond the scope of this paper. A . Charge-Transfer Delay Lines

Significant advantages of a charge-transfer register over an acoustic delay line are: (1) The delay time is electronically variable. (2) Continuous video delay of up to 1/30sec or more will be feasible. (3) The device is compact and easily integrated with other components. Delay time is calculated by dividing the total number of storage elements by the clock frequency. The time axis of the signal can be modified continuously over a wide range by varying the frequency. Sangster (84) has discussed the use of a bucket brigade register for correcting for variations in tape speed of an audio or video tape. Television pictures were shifted and stretched horizontally by changing the clocking frequency of a bipolar bucket brigade from 9 MHz read-in to 3 MHz readout. Video signals were passed through integrated bipolar registers having a total of up to 864 half-stages with negligible deterioration. (Charge amplifiers were included within each integrated register.) Continuous delay of a normal resolution television picture for 1/30 sec in a single serial register would require several hundred thousand transfers. Reference to Fig. 35 shows that the transfer inefficiency E per stage should not exceed lop6per stage to keep the total degradation in MTF to less than 50%. A charge-transfer register known as the series-parallel-series type (87),

248

P. K. WEIMER

n CI

n

5

c, ; FIG.37. Transfer sequence and clock voltages for a series-parallel-series delay line.

illustrated in Fig. 37, would require only 1100 transfers for the same storage capacity. In this case a value of E = 0.3 x l o p 4 would suffice for the same loss in MTF. Tompsett and Zimany (88) have operated the 106 x 128 element CCD sensor as a series-parallel-series delay line. The results are shown in Fig, 38. The right half of the picture was undelayed while the left half of USE OF A 106 x128 ELEMENT CCD TO DELAY HALF A PICTUREPHONE@FIELD

I

DELAYED

DIRECT

I

I DELAYED

DIRECT

FIG. 38. Signals delayed by transmission through a 106 x 128 element three-phase CCD array operating as a series-parallel-series delay line. The left half of each display was delayed one field period (16.7 mhec in the Picturephone system) while the right half was undelayed [Tompsett and Zimany (88),courtesy of Bell Laboratories].


249

the picture was delayed by 16.7 nisec, one field period of the system being used. Only a slight difference is noted in the resolution of the two pictures. Another type of parallel-channel delay line has been proposed having multiplexed gates ( 4 ) rather than clock-driven gates. The multiplexed gate devices allow greater packing density of charges and require still fewer transfers for the same total number of storage elements (89). Parallelchannel delay lines d o not possess the advantage of inherently good uniformity found in a single-channel serial register. In the latter a high dark current spot in one element would add equally to the background signal of a11 charges passing this point. In a parallel-channel register a single spot in one element would be much more noticeable since its effect would appear only in those charge packets which passed through that particular channel. However, the visibility of a localized high dark current spot in a seriesparallel-series delay line could still be less conspicuous than in an image sensor where each current source is reproduced in the transmitted picture as a spot and not averaged over a whole column.

B. Video Signal Processing within the Camera by Recycling of Signals through the Sensor Itself Three signal processing operations which could utilize delay of the video signal for one or more fields are: (1) Multiple readout of the same charge pattern without discharging it. (2) Subtraction of a fixed background signal generated within the sensor. (3) Detection of a moving object in the presence of a stationary scene background. Frame delay in a charge-transfer camera can be carried out in either of two ways: (1) Include within the camera a second charge-transfer sensor which is operated in parallel with the first sensor as a series-parallel-series delay line. (2) Recycle the video signal through the sensor itself (36, 36a) so that it can serve for both sensing and delay. Method (2) is simpler and would be more effective for background subtraction since no new spurious signals are introduced by the delay device. Although an input register could be used with any type of sensor it is particularly convenient with the vertical transfer sensors shown in Figs. 16b and 17a. Figure 39 illustrates the timing sequences for video recycling in a sensor having interleaved photocells and nonilluminated registers. In multiple readout the signal is fed back in either polarity to the input at the same time it is being read out. At the end of one frame each elemental charge (or a constant minus the charge) will again be found at the same site in the vertical register. The horizontal blanking interval allows several additional horizontal clock cycles to be added to each line, if necessary to compensate for any delay in the feedback loop. The process can be repeated for as many fields as required

250

P. K. WEIMER

4

1 -SIGNAL

OUT

FIG. 39. Operation of a charge-transfer sensor with video recycling for multiple nondestructive readout, background subtraction, and as a motion detector. The sensor has nonilluminated registers and interleaved photocells.

until the MTF has become degraded by the nt: product becoming too large. The recycling of signals can also be used with short linear registers to measure E more accurately (90). In background subtraction the fixed pattern signal to be eliminated is normally caused by local variations in dark current. In the subtraction system illustrated in Fig. 39 the optical image is masked off by means of a shutter every other frame in order to allow the background signal to be regenerated. Figure 40 shows how the delayed and inverted background signal is added to the total signal in the next field. This process requires good linearity and dynamic range throughout the entire system.

I

' / I * I1

OR LINE

I1

U'

WHERE I,, ~I,,=I,,,etC. I,, AND I, ARE CONSTANT

FIG. 40. Signal level components for fixed pattern background subtraction in a sensor having nonilluminated registers shown in Fig. 39.


25 1

In spite of the loss of signal by shuttering on alternate fields the subtraction process should permit operation at lower light levels in sensors whose threshold is limited by a fixed pattern background rather than by statistical noise. The requirement for cooling of the sensor to remove the background pattern could be mitigated by subtraction. Statistical noise is of course not removed by the subtraction process but is increased by a factor of the square root of two. A further reduction in signal-to-noise ratio results from the shuttering of every other field. Background removal by recycling is also possible with a vertical-transfer illuminated-register sensor but the signal loss due to shuttering would be three times instead of twice as in the above case. Various methods can be used to reduce the shuttering loss. Motion detection is obtained by recycling and subtracting alternate fields to remove the stationary portions of the image. The difference signal obtained in alternate fields identifies objects in motion. A continuous difference signal could be produced by use of a separate delay register with an external adder. Although the use of recycled signals for each of the above functions has been demonstrated (36),a complete evaluation of their effectiveness has not yet been made. Video signals can also be recycled through the output register alone in order to repeat a line or to apply vertical aperture correction,

XII. SELF-SCANNED SENSORS FOR COLOR CAMERAS Color cameras most widely used in broadcasting (91) employ a separate tube for each color channel, and have special optics for splitting the image into three components. Single-tube cameras having striped color filters in the image plane depend on structure in the target (92)or on various encoding systems (93) to produce a standard NTSC type of color signal. For special applications, single-tube field sequential cameras (94)have been constructed with rotating filter changers in front of the tube. It is apparent that each of these cameras could in principle be converted to solid state by substitution of an equivalent sensor for each camera tube. The relative advantage of such a conversion would depend on the system. For best results the color camera should be completely redesigned to take advantage of the particular properties of image sensors. The present discussion will be limited to a brief assessment of sensor characteristics as they relate to color pickup. 1. Compact design of a sensor. This feature would be particularly valuable in a three-sensor camera. An experimental version of such a camera (95) has already been built using the Bell 106 x 128 element sensor. Figure 41 shows the reduction in size of a typical three-tube camera if the tubes were

252

P. K. WEIMER

replaced with sensors. However, a three-sensor camera would still require special optics and would be more bulky than a single-sensor camera with elemental color filters.

FIG.41. Reduction in size of a three-tube color camera if self-scanned image sensors were substituted for the three camera tubes and focusing coils.

2. Accuracy of scan. This feature would reduce the registry problem in a multiple sensor camera to one of optics alone. In a single-sensor color camera the constant elemental frequency would permit color encoding by phase and amplitude modulation of a suitable reference subcarrier without requiring an accompanying index signal. The feasible systems for efficient color extraction from a single-sensor camera exceed that of a single-tube camera where variations in scanning speed and beam focus limit the choice of encoding system which can be used. However, transfer losses in the sensor must not be sufficiently high to allow color mixing to occur. 3. Low-light-level capability of a sensor. The higher signal-to-noise ratio obtainable in a solid state sensor is highly advantageous for color camerasparticularly for single-sensor cameras in which elemental filters are used. Such filters are more wasteful of light than the color reflective optics used in a multiple sensor camera. Although threshold scene illumination is not required for color transmission the sensors should be designed for high responsivity and low noise to approach the color discrimination of the eye under similar illumination. The responsivity of silicon is excellent for red


253

and green light but may prove to be somewhat deficient for blue light if the sensor is illuminated through polysilicon gates. The infrared response of silicon requires this component of the light to be filtered out for proper color balance. Care has to be taken in sensor design to avoid sensitivity loss at particular wavelengths due to interference effects within the sensor structure itself. 4. Other operating characteristics. Additional characteristics of sensors valuable for color pickup include mechanical and electrical stability, low power consumption, instant turn-on, and freedom from time lag in moving scenes. Clearly, the development of a suitable color sensor will expand the applications of color television. A simple, reliable camera used in conjunction with low cost recording equipment could replace home movies as a new and more versatile form of electronic photography.

CIRCUITS FOR SOLIDSTATESENSORS XIII. PERIPHERAL In addition to the sensor a solid state camera should include inputoutput circuits, clock drives, timing generators, power supplies, and means for interfacing the signal with associated equipment. For maximum reduction in cost and size of camera the peripheral circuits should be integrated, either on the same silicon chip with the sensor or on a small number of associated chips. The equivalent number of components required is less than for the sensor itself and their functional design can be based on standard design rules. Only the input-output circuits will be discussed here since they are the most intimately connected with the operation of the sensor itself.

A . Input Circuit Design

An electrical input circuit can be used with some types of sensors for introducing either a constant background current (Section Vlll,B,l) or a modulated signal in case the sensor structure is to be used for analog delay (Section XI). Although background current can also be injected optically into a sensor, the bias light will yield shot noise fluctuation ( N = NA’’) which would limit performance at very low light levels. As indicated in Section VTII, an electrical input consisting of a diode and several control gates (such as shown in Fig. 23) is capable of a lower noise level, given by N, = 4 0 0 6 . The reduced noise level will be achieved, however, only if the circuit is operated so that the charge set into the first capacitor (Cpf)has reached complete equilibrium with the input signal during each clock cycle.

254

P. K. WEIMER

If, instead, charge were leaked into the first capacitor via a partially pinchedoff gate the rms fluctuations in the final charge would contain full shot noise. Noise fluctuations several times larger than shot noise have even been noted under certain conditions (96). The circuit requirements for a low noise input have been recognized independently by different workers (96, 97, 98) who have arrived at similar methods of operation. In a typical system ( 9 6 ) the first potential well is initially overfilled and then the excess charge is allowed to return to the source. The final input charge is established by the height of the potential barrier under the first gate. This system has the added advantage that the charge introduced is a linear function of the input voltage. B. Output Circuit Design The design of the circuit coupling the sensor to the video amplifier plays an important role in determining sensitivity and freedom from spurious signals. The major requirements on the output circuit are that it provide amplification with negligible introduction of noise, while suppressing all switching transients and fixed pattern noise arising from the horizontal clocks. Since the design considerations for an amplifier to be used with a charge-transfer sensor are somewhat different than for an XY-addressed sensor these cases will be discussed separately.

1. Output Circuits for Charge-Trumfer Sensors The small signals generated by a charge-transfer sensor at low illumination require very low noise levels in the output circuit to avoid further signal degradation. Spurious signals from the horizontal clocks are not a major problem with charge-transfer sensors since these signals are confined to frequencies of more than twice the video passband and can be removed by filtering. However, care must be taken in design of the clock supplies to obtain drive signals having the proper waveforms and containing minimum voltage fluctuations. The output amplifier should be located as close as possible to the output register to reduce clock pickup and to avoid unnecessary capacitive loading on the output lead. A common low-noise output circuit for charge-transfer devices has employed an MOS transistor with its gate connected directly to a diffused diode located in the channel of the output register. This arrangement was illustrated previously in Fig. 23 and is represented in Fig. 42a by the dotted lines. In operation, the potential of the floating diode must be reset once during each clock cycle to a fixed dark level by the transistor T, whose gate is connected to the clock. Noise fluctuations arising from the error in setting

255


CLAMP

VIDEO OUT (0)

(b)

(C)

FIG. 42. Three types of low-noise output circuits suitable for use with charge-transfer sensors at low light levels. (a) Gated-diode output with correlated double-sampling circuit [White er a/. (US)]. (b) Distributed charge amplifiers connected to successive nodes of the output register [Weimer er a[. ( I O I ) ] . (c) Floating-gate amplifier which may also be used as a distributed amplifier [Wen and Salsbury ( 6 2 ) ] .

the dark level of the floating diode are estimated to be N, = 4 0 0 G . White et nl. (99) has found that this source of noise can be reduced by means of a correlated double-sampling process shown schematically by the solid lines in Fig. 42a. The video output from the sample-and-hold processor is obtained by taking the difference between the previously clamped reset level and the same reset level plus the signal increment introduced by the charge packet from the output register. The correlated double-sampling process removes switching transients as well as subtracting out the dark signal component which contains the reset noise. A related double sampling technique (100) was developed earlier for suppression of switching transients in multiplexed scanning of XY arrays. This system will be described in the next section. A different approach to the reduction of reset noise and clock transients makes use of the fact that the voltage change associated with a given charge packet can be sampled at successive nodes (62, 101) in the output register. A distributed amplifier of this type showing four parallel MOS amplifiers at successive nodes of a bucket brigade register (101)is illustrated in Fig. 42b. Auxiliary registers are used to compensate for the time spread as a given charge packet moves down the output register. The total amplifier noise would be expected to decrease in proportion to the square root of the number of parallel stages. Two MOS amplifiers connected to successive nodes of an output bucket brigade register (20) (e.g. see Fig. 21) have been

256

P. K. WEIMER

used with various sizes of two-dimensional charge-coupled sensors (36, 68, 69). The double-output system provides more effective elimination of the clock pulses from the signal as well as a modest improvement in signal-tonoise ratio. Another type of output amplifier shown in Fig. 42c makes use of one or more floating gates (62) in the output register in place of a floating diffusion for driving the MOS amplifier. The floating gate does not require resetting on each clock cycle, and has been proposed for use in distributed amplifiers (62). However, in the single-gate version reported to date the stage following the floating gate amplifier used a gated charge integrator which was reset at clock frequency. Calculations indicated that for a bandwidth of 1 MHz 50- 100 electrons could be detected at room temperature using a single stage floating gate amplifier. Still lower noise levels should be possible in a distributed amplifier of this type. 2. Output Circuits for X Y-Addressed Sensors

In the three common methods of extracting signal from an XY array (see Fig. 7) the output lead is already shunted by a capacitance to ground which may be several orders of magnitude larger than the elemental capacitance of a charge-transfer register. The performance at low light levels will therefore be limited by the fluctuations in the number of carriers required for charging this capacitance (N,= 4 0 0 a ) unless the output circuit can be designed to minimize this source of noise. An equally troublesome source of fixed pattern noise arises from the spatial variations in the multiplex switches and in the successive scan pulses. The resulting signal variations cannot be removed by low pass filters since their frequency falls within the video passband. Two general types of circuits which have been used for suppressing switching noise in multiplexed scanning systems are illustrated in Fig. 43. These include (a) a double sampling technique similar to that discussed in the preceding section, and (b) a differential amplifier scheme. In each case the fixed pattern noise is suppressed by being subtracted from itself. The double-sampled system having an integrating amplifier illustrated in Fig. 43a was described by Brugler (100) in 1968. The integration process provides a means of discriminating between the picture signal (which is dc) and the capacitive feed-through signal from the scan generator (which is ac). Integration of the output signal over the period of the scan pulse cancels out the unwanted capacitive signals but leaves the dc picture charge which is then detected by the second sample. The double sampled charge integration scheme was used by Plummer and Meindl (102)and later by Michon and Burke (12) for scanning XY photodiode arrays (see Fig. 12). Although the


+”

257

P

+V

(b)

(0)

FIG.43. Two types of output circuits which have been used for reduction of switching transients in XY sensors. (a) Double-sampled integrating amplifier (Brugler (loo)]. (b) Differential amplifier with dual input [Weimer er a / . ( 1 3 ) ] .

charge integration technique should be as effective as the sample-and-hold technique described in the previous section for removal of switching transients it would probably not be as effective as that system for suppressing the fluctuation noise associated with the high capacitance of the output bus. All double-sampling schemes become progressively more difficult to implement as the scanning frequencies are increased. The application of a differential amplifier for suppression of switching transients in a single-line photodiode sensor is illustrated in Fig. 43b. This system (103) was found to be useful in scanning the 256 x 256 element photoconductive array shown in Fig. 8. When each elemental capacitor is discharged by the closing of the multiplexer switch the signal currents flowing in the two output leads V, and V, are of opposite polarity. However, the switching transients induced in each lead by the scan generator are approximately equal and will have the same phase. It is therefore possible to subtract one output signal Srom the other to obtain a larger output signal with smaller switching transients than were present in either output alone. The differential amplifier system does not require the auxiliary channel to contain picture signal to be effective. Various other structures have been used to provide a separate transient signal which could then be subtracted from the total picture signal plus transient signal contained in the other channel. As the clock frequencies are increased the achievement of a satisfactory cancellation of transient signals becomes increasingly difficult. XIV. CONCLUSIONS The replacement of beam-scanned camera tubes by solid state sensors, if it occurs, will be a most impressive achievement, surpassed only by the successful development of a solid state display panel suitable for television.

258

P. K. WEIMER

The sophisticated objectives of television pickup have required more than fifty years of continuous research and development on camera tubes. The resulting tubes, in specialized forms, have approached ideal performance in sensitivity, resolution, and freedom from spurious signals and they are fairly low in cost when picture defects can be tolerated. However, camera tubes are often bulky, power consuming, critical to operate, short-lived, or unresponsive to the desired wavelengths, and they are far too costly if high performance is demanded. Recent advances in implementation of the powerful new concept of scanning by charge transfer now indicate the technical feasibility of building solid state sensors which approach the performance of camera tubes in most respects within five or ten years. Whether this can be done at sufficiently low cost to undersell the comparable tube will depend upon the size of the market and on the continuation of an extensive research and development program on sensors. In specialized applications, where the desirable features of solid state devices are required, a higher cost for image sensors may be tolerable for some time to come. Solid state sensors will be capable of more compact cameras, lower power consumption, a more rugged construction, higher responsivity, and longer life than ordinarily obtained with tubes. However, these features may be accompanied by other disadvantages such as a requirement for cooling, or the spreading of the signal around brightly illuminated objects. Fortunately, the fabrication of solid state sensors is based upon a silicon integrated circuit technology in which the cost per component on the chip has decreased at a fantastic rate within recent years. However, high resolution sensors will require active areas of silicon at least ten times larger than the largest present-day LST circuits. The prospects for cost reduction in sensors are fairly good but further advances in technology will be required. Solid state sensors have already found their first market applications in single-line sensors and limited-resolution area arrays. If low cost arrays can be built having a sufficient number of elements to be compatible with standard display equipment, many new industrial and consumer applications for sensors will unfold. The use of sensors with a low-cost TV recording system could provide a form of electronic photography which could rival home movie cameras. Economical and trouble-free operation appears to be the key to the expanded use of sensors in the home, business, school, and industry. Clearly, solid state sensors could coexist with camera tubes for many years with each serving its own market. ACKNOWLEDGMENTS The author wishes to thank G. F. Anielio. J . E. Carnes. R. H . Dyck, W. F. Kosonocky. R. L. Rodgers, 111. C. H. Sequin. G. Strull. M . F. Tompsetl. and their co-authors for permission to reprint figures which first appeared i n their papers.


259

REFERENCES 1. D. F. Barbe and S. B. Campana, Electro-Opt, Conf;. Suss. Low Light Level Trlec. Syst., New York. 1973. 2. J. S. Brugler, J. D. Meindl, J. I>. Plummer. P. J. Salsbury, and W. T. Young, I E E E J . Solid-State Circuits 4, 304 (1960). 3. P. K. Weimer, H. Borkan. G. Sadasiv, L. Meray-Horvath, and F. V. Shallcross, Proc. I E E E 52, 1479 (1964). 4. F. L. J. Sangster and K. Teer. I E E E J . Solid-Srote Circuit5 4, 131 (1969). 5. W. S. Boyle and G. E. Smith, Be“ Syst. Tech. J . 49, 587 (1970). 6. C. H. Sequin, D. A. Sealer. W. J. Bertram. Jr.. M. F. Tompsett. R. R. Buckley. T. A. Shankoff. and W. J. McNamara, I E E E Trans. Electron Derices 20. 244 (1973). 7 . P. K . Weimer, Adcan. Elecrrorl. Ekectrori Piiys. 13, 387 (1960). 8. P. K. Weimer, S. V. Forgue. and R. R. Goodrich, Electronics 23, 70 (1950). 9. M. H. Crowell. T. M. Buck. E. F. Labuda. J. V. Dalton, and E. J. Walsh, Bell Syst. Tech. J . 46, 491 (1967). 10. S. R. Hofstein and F. P. Heiman, Proc. I E E E 51, I190 (1963). 11. G. P. Weckler, I E E E J . Solid-Stare Circuits 2, 65 (1967). 12. G. J. Michon and H. K. Burke, I E E E I n t . Solid-State Circuits Coi& Dig. Tech. Pap.? Philotlrlpliiu p. I38 (1973). 12u. G. J. hlichon and H. K. Burke. I E E E Sulid-Sttr/e Circuits Conf:, Diy. Tech. Pup., Pliiladelpliia. p. 26 (1974). 1 3 , P. K. Weimer, W. S. Pike, G. Sadasiv, F. V. Shallcross, and L. Meray-Horvath, I E E E Spectrum 6, 52 (1969). 14. P. K. Weimer, G. Sadasiv. J. E. Meyer, Jr.. L. Meray-Horvath. and W. S. Pike, Proc. I E E E 55, 1591 (1967). 15. J. W. Horton, R. V. Mazza, and H. Dym. P m . I E E E 52, 1513 (1964). 150. M. V. Whelan and L. A. Daverveld, I E E E I n r . Electron Devices Meet., I E D M Tech. Dig., Wtrshiiiyron, D.C., p. 416 (1973). l 5 h . 1. Kaufman and J. W. Foltz, Pvoc. I E E E 57, 2081 (1969). 16. G. Strull, W. F. List, E. L. Erwin, and D. Farnsworth, Apyl. Opr. 11, 1032 (1972). 1 7 . R. H. Dyck and G . P. Weckler, I E E E Trans. Elecrron Deuices 15, 196 (1968). 18. T. Ando et a/., J . Inst. Telec. h g . J a p . pp. 33-46 (1972). 19. P. J. W. Noble, I E E E Trans. Electron Devices 15, 202 (1968). 20. M. G. Kovac, W. S. Pike. F. V. Shallcross. and P. K. Weimer. Electronics 45, 72 (1972). 2 I . E. H. Snow, I E E E In/ercon Tech. Pap., N e w Y o l k Sess. 37, Pap. 37-2 (1973). 22. P. K. Weimer, G. Sadasiv. L. Meray-Horvath. and W. S. Homa, Proc. I E E E 54,354 (1966). 23. P. K . Weimer, R C A Rer. 32, 251 (1971). 24. R. A. Anders, D. E. Callahan, W. F. List, D. H. McCann, and M. A. Schuster, I E E E Trai7s. Electron Devices 15, 191, 1968. 25. M. A. Schuster and G. Strull, I E E E T r m y . Ekectrou Deriws 13, 906 (1966). 26. P. K. Weimer, F. V. Shallcross. and V. L. Frantz, I E E E J . Solid-Sttrte Circuits 6. 135 (1971). 27. C . P. Weckler, I E E E Intercon Tech. Pap. New f’ork. Sess. 1 , Paper 1;2 (1973). 28. Reticon Corporation, Mountain View, California. 29. See “Advanced Scanners and Imaging Systems for Earth Observations,” Ch. 4. N A S A Spec. Puhl. SP-335 (1973). 30. G. Sadasiv, Solitl-State Sensor Symp., Cur$ Re(,.. Minneupolis, Miriri. p. 13 (1970) (IEEE Catalog No. 70C25-SENSOR). 31. E. Arnold, M. H. Crowell. R. D. Geyer, and D. P. Mathur. I E E E Trirns. Electron Dei,ices 18. 1003 (1971).

260

P. K. WEIMER

3-7. F. L. J. Sangster, I E E E Irzt. Solid-Strife Circuits Conf:. Dig. Twh. Pap., 13. 74 (1970). 33. A. J. Steckl and T. Koehler, C C D A p p l . Con$ Proc., Nur.. Electron. Lab., Smi D i q o , CaliJ

TD-274, p. 247 (1973). C. H. Skquin, I E E E Truns. Electron Decices 20, 535 (1973). G. Amelio, I E E E intercon Tech. Pup., New York Pap. Ii3 (1973). P. K. Weimer, W. S. Pike, M . G. Kovac, and F. V. Shallcross. I E E E I n r . Solid-Srute Circuits Cot$, Dig. Tech. Pup., Philudelphiu p. 132 (1973): also in Data Comniiiii. Design 2, No. 3. 21 (1973). 360 P. K. Weimer. W. S. Pike, F. V. Shallcross, and M. G. Kovac, RCA R r r . 35 No. 3, 341 (1974). 3 7. M. G. Kovac, P. K. Weimer, F. V. Shallcross, and W. S. Pike, f E E E Int. E k f r o i i Detices Meer., Absri., Wnshington, D.C. p. 106 (1970). 38. P. K. Weimer, M. G. Kovac, F. V. Shallcross, and W. S. Pike, I E E E Trtrris. Electron Devices 18, 996 (1971). 3Y. W. S. Pike, M. G. Kovac, F. V. Shallcross, and P. K. Weimer, RCA Reo. 33. 483 (1972). 40. G. F. Amelio, W. J. Bertram, Jr., and M. F. Tompsett, I E E E Trans. Electron Devices 18, 986 (1971). 41. M. F. Tompsett. G. F. Amelio, W. J. Bertram, Jr., R. R. Buckley, W. J. McNamara. J. C . Mikkelsen, Jr., and D. A. Sealer, I E E E Trans. Elecfron Devices 18, 992 (1971). 42. W. J. Hannan, J. F. Schanne, and D. J. Woywood, I E E E Trans. Mil.Elecfroii. 9. 246 (1965). 43. C. N. Berglund and H. J . Boll, I E E E Trans. Electron Devices 19, 852 (1972). 44. M. G. Kovac, F. V. Shallcross, W. S. Pike, and P. K. Weimer, I E E E Electroii Derice.5 Meer., Abbrr., p. 74 (1971). 45. L. Boonstra and F. L. J. Sangster, Elecrroriics 45, 64 (1972). 46. W. F. Kosonocky and J. E. Carnes, I E E E I t i r . Solid-State Circuit5 Con$. Dig. Tech. PUIJ., p. 162 (1971). 4 7. W. F. Kosonocky and J. E. Carnes, R C A Rev. 34, 164 (1973). 4 7tr W. F. Kosonocky and J. E. Carnes. I E E E Inr. Elecrron Devices Meet., I E D M Tech. Dig., Washington, D.C. p. 123 (1973). 48. W. S. Boyle and G. E. Smith, I E E E Specrrurn 8, 18 (1971). 49. R. H. Krambeck. R. H. Walden, and K. R. Pickar, Bell Sysr. Tech. J . 51. 1849 (1972). 50. W. F. Kosonocky, private communication (1973). 51. D. R. Collins. S. R. Shortes, W. R. McMahon, R. C. Bracken. and T. C. Penn. J . Elecrrochern. Soc. 120, 521 (1973). 5 1( I C. H. SCquin, D. A. Sealer, W. J . Bertram, R. R. Buckley. F. J . Morris, T. A. ShankolT. and M. F. Tompsett, I E E E Solid-Srufe Circuits Corif: Dig. Tech. Pup., Philutfelphiu. p. 24 (1974). 52. J. E. Carnes, W. F. Kosonocky, and E. G. Ramberg, I E E E Truns. Electron Derices 19. 798 ( 1 972). .. i?C. K . Kim and M. Lendinger. .I. , ~ / J / I / . f'lij,\. 42, 3586 (1971). 54. J. E. Carnes and W. F. Kosonocky, R C A Eng. 18, 7 8 (1973). 5 5 . J. E. Carnes and W. F. Kosonocky, A p p l . Phys. Lett. 20, 261 (1972). 56. M. F. Tompsett, I E E E Trans. Electroi7 Devices 20, 45 (1973). 5 7 . R. H. Walden, R. H. Krambeck, R. J . Strain, J. McKenna, N. L. Schryer, and G. E. Smith, Bell Syst. Tech. J . 51, 1635 (1972). 58. K. C. Gunsagar. C. K. Kim, and J . D. Phillips, I E E E Int. Electron Deaices Meet.. I E D M Tech. Dig., Washiiiyton, D.C. p. 21 (1973). 5Y. L. J. M. Esser, CCD Appl. Con/; Proc.. NuL.. Electron. Lab., Sari Diego, Cul$ TD-274. p. 269 (19731. 60. J . E. Carnes and W. F. Kosonocky, RCA Rev. 33, 327 (1972). 34. 35. 36.


26 1

61. J. K. Thornber and M. F. Tompsett, I E E E Trans. Electron Decicrs 20, 456 (1973). 62. D. D. Wen and P. J. Salsbury, I E E E Solid-State Circuits Conf, Dig. Tech. Pap., Philadelphia p. 154 (1973). 63. M. F. Tompsett, G. F. Amelio, and G. E. Smith, Appl. Phys. Lett. 17, 111 (1970). 64. M. F. Tompsett, D. A. Sealer, C. H. Sequin, and T. A. Shankoff, I E E E Intercon Tech. Pap., New York Sess. 1, Pap. 1/4 (1973). 65, C. K. Kim and R. H. Dyck, l’roc. I E E E 61, 1146 (1973). 66. W. J. Bertram, Jr., D. A. Sealer, C. H. Sequin, M. F. Tompsett, and R. R. Buckley, I E E E Intercon Dig. p. 292 (1972). 67. 0. H . Schade, Sr., R C A Rec. 31, 60 (1970). 68. M. G. Kovac, F. V. Shallcross, W. S. Pike, and P. K. Weimer, C C D Appl. Co$ Proc., Nac. Electron. Lab., Sun Diego, Calif TD-274, p. 37 (1973). 69. R. L. Rodgers, 111, I E E E 1tire.rcon Tech. Pap.. Sess. 2, Pap. 2,;3 (1974). 70. S. B. Campana, Electro-Opt. Syst. Design June. p. 22 (1971). 71. C. H. Sequin, Bell S ! s . Tech. J . 51, 1923 (1972). 72. W. F. Kosonocky. J. E. Carnes, M . G. Kovac. P. Levine. F. V. Shallcross. and R. L. Rodgers. 111. RC-1 Ref.. 35. No. 1 . 3 (1974). 73. L. Walsh and R. H. Dyck, C C D Appl. ConJ Proc., NUV. Elrcrron. Lab., Sun Diego. CuliJ TD-274, p. 21 (1973). 74. W. B. Joyce and W. J. Bertram, Bell S j r t . Tech. J . SO, No. 6, 1741 (1971). 75. M. F. Tompsett, J . Vac. Sci. Technol. 9, 1166 (1972). 76. A. Rose. Aduan. Electron. 1, 131 (1948). 77. R. W. Engstrom and G. A. Robinson, Electro-Opt. Syst. Design ST-4693 (1971). 77a. 4849 I-SIT Camera Tube. R

This is for a well channeled particle. There is another effect for secondary channeled particles which enter a group of channeled particles from the group of randomly directed particles. Secondary channeled particles produce some contribution to enhanced diffusion which will be described in Section 111. 111. ENHANCED DIFFUSION

A . Introduction

The approximate shape of the depth distribution of implanted atoms is gaussian. LSS suggested some deviation of the depth distribution from a single gaussian distribution. In the case of the existence of a large deviation

290

SUSUMU NAMBA AND KOHZOH M A S U D A

from the gaussian distribution the calculation of the higher moments is important for the determination of the shape. Furukawa calculated the third moment for the heavy ion implantation and obtained a small deviation from a gaussian distribution with the assumption of a particular potential. Since the experimental data show some deviation from a gaussian distribution, this calculation of the higher moments gives a better fit between calculated and experimental values. Gibbons made similar comments on the possibility of explaining the skew of the distribution based on the third moment of the straggling of the range. But the accuracy of the activation analysis, backscattering analysis, and the analysis by nuclear reaction is not good enough to check the agreement between the calculated and experimental values when the deviation is small. Recently a measurement of the backscattered atoms from the implanted surface was made to detect the amount of gaussian distribution which is outside the sample surface. This method may possibly give detailed information of the skew of the straggling of the distribution (21). All experimental results of the profiles on amorphous solids are in good agreement with the theoretical calculation by LSS except for the small skewness of the profile. This minor disagreement between theory and experiment due to the small skewness will probably be solved by a calculation of the higher moment of the profile. The basic assumption of the theoretical calculation is that the length of the target in the direction of the ion beam is infinite. Strictly speaking, this assumption is not true. Backscattered ions across the surface of the target escape without scattering. A detailed comparison between the theoretical calculation and the experimental value in the backscattered ions outside the surface of the target is very difficult because of the existence of the assumption of abrupt discontinuity which is unfortunately extremely difficult to include. In contrast to the amorphous target, considerable enhancement of the penetration beyond the maximum peak is observed in the case of a single crystal target. A tail of the profile beyond the maximum of the peak is normally observed in the profile of the implanted ions in a single crystal. This tail shows a deeper penetration in a single crystal than in an amorphous target. The profiles of ions implanted in the channeling direction show a longer range than those calculated for an amorphous target. Therefore the reason for the appearance of the longer range is often assumed to be a channeling effect. However the enhancement of the penetration is observed to be independent of the direction of the incident beam relative to the crystal orientation. In other words, the enhancement of the penetration is observed even in the case of implantation in a nonchanneled direction. Thus the reason for the enhancement of the penetration is very complicated.

ION IMPLASTATION IN SEMICONDUCTORS

29 1

Even in the case of a well channeled beam a difference of the tail beyond the peak of the channeled particles is found. This phenomenon suggests the existence of some mechanisms other than channeling, even if they are very small. Profiles of this case are shown in Fig. 15 (17).

DEPTH ( p n l

FIG. 15. Different tails of the profiles of channeled particles.

The mechanisms to be considered for the enhancement of the profile in the tail are diffusion assisted by vacancies produced by the high energy radiation, diffusion of the interstitial foreign atoms which have a lower activation energy than substitutional foreign atoms, and secondary channeling. The enhanced diffusion is observed in the case of hot implantation. But it is also observed during the thermal annealing after implantation. B. Diffusion Assisted by Vacancies Produced by High Energy Radiation

The diffusion of atoms in the crystal depends upon the number of vacancies in the crystal and the activation energy of the migration of the atoms. The diffusion constant is written by Di = a2WoN(V'), (26) where a is the distance between neighboring atoms, W, the probability of jumping from one site to the nearest neighbor site, and N ( V ) is the number of vacancies at the nearest neighbor site. The distance between neighboring atoms is automatically determined when the sample is chosen as Si or GaAs, etc. The probability of jumping from one site to the nearest neighbor site is strongly dependent upon the potential barrier height between the two sites. This is normally approximated by the Boltzmann formula and expressed as

292

S U S U M U NAMBA A N D KOHZOH MASUDA

where E l is an activation energy for hopping. The hopping probability depends upon the temperature T, of the sample. V, is the frequency for the hopping. Hopping of the atom to the neighboring substitutional site does not occur when the neighboring sites are occupied by either host or foreign atoms. The probability of finding an empty nearest neighbor site is equal to that of finding a vacancy at the same site. This probability is proportional to the density of the vacancies. It is understandable that the diffusion constant of the foreign atoms depends upon the activation energy for the hopping, the temperature of the sample, and the density of vacancies because the distance between the neighboring atoms is a constant. Ions penetrating into the target produce many damage centers which are vacancies, host atom interstitials, and some lattice irregularities. Among these damage centers vacancies are most useful for the enhanced diffusion of foreign atoms. The fundamental ideas for the calculation of the number of displaced atoms had been given by Seitz and Kohler (22). The fundamental formula to calculate the total number of displaced atoms N , is

where T is the number of displaced atoms produced for each primary displacement, n the number of primary displacements per incident particle, and Y is the total number of incident particles. The assumption that the threshold energy E , is isotropic is often used for the calculation of N , . The number of primary atoms displaced by an incident particle in traversing a distance dx through a target is given by

where no is the number of atoms per unit volume and

E is the energy of the ion and

where M I , Z, are the mass and charge of the incident particle, M , , Z , the mass and charge of the target particle, uo the Bohr radius of the hydrogen atom, and R , is the Rydberg energy for hydrogen. The number of displaced atoms produced by subsequent displacements by a primary knock-on atom is very complicated to calculate. Calculations of each v(E)have been given by Chadderton (23). There are other difficulties such as the estimation of E d . The value for E ,

29 3

ION IMPLANTATION IN SEMICONDUCTORS

was assumed to be 25 eV by Seitz and Kohler. This value might depend on the material and also the crystal axis and the temperature. Experimental values of Ed are shown in Table 11. TABLE I1 SOMEEXPERIMENTAL VALUESOF Ed

Material Copper Copper Copper Silver Gold Nickel Iron Germanium ("-type) Germanium Silicon Graphite a

Property measured

Threshold energy (eV)

Temperature

Electrical resistivity Electrical resistivity Electrical resistivity Electrical resistivity Electrical resistivity Electrical resistivity Electrical resistivity Electrical conductivity

25 22" 19 28" 40" 34.5 24" 31

78 10 4.2 4.2 4.2 4.2 4.2 78

Minority carrier lifetime Minority carrier lifetime Electrical resistivity

14.5 12.9 25

(W

300 300 300

Denotes effective threshold displacement energies

Changes in the physical properties of materials are only observed when an energy greater than Ed is transferred to the atom. The electrical resistivity, Hall constant, minority carrier lifetime, ESR, and backscattering measurements can be used to detect the threshold energy for the occurrence of defect production. The number of displaced atoms Nd is calculated using Eqs. (28) and (29). We can assume that the number of vacancies is equal to or proportional to the number of displaced atoms. Then the amount of enhancement of the diffusion by the vacancies is estimated from N,. The number of the Frenkel pair n at thermal equilibrium is calculated from the condition to minimize the free energy as follows : n =(NN~)I/~~-~/Z~TS

(30)

where N, N,are the number of atoms at the lattice site and the number of interstitial sites and w is the formation energy of the vacancy interstitial pair. The diffusion constant is determined by the larger value of either the density of the vacancies at thermal equilibrium or the density of the vacancies produced by bombardment. In the latter case enhancement of the diffusion constant is expected.

294

S U S U M U NAMBA A N D KOHZOH MASUDA

The change in the diffusion constant below about 1000°Cfor a dose rate of 7.2 x 10'Z/cmZ is shown in Fig. 16 (24). The diffusion constant is determined by the density of the vacancies in the thermal equilibrium state over 1000°C and by the density of the vacancies produced by the bombardment below 1000°C.In the latter case, the diffusion constant is independent of temperature when the dose rate of the implantation is constant. If the dose rate is increased, the diffusion constant is increased because of the increase in the density of vacancies during the bombardment. TEMPERATURE

800

1

600 500

\

lo""' 06

a

0.6

' 1.b

' l.i '

(lOoO/T'K)

FIG. 16. Diffusion constant for various temperature of 0 1.2 x 10'2/cm2.sec; A 7.2 x 10'2/cm'. sec; normal diffusion.

hot

implantation.

The substrate temperature is effective in changing the diffusion constant in some cases. When the enhanced diffusion is controlled by the number of vacancies produced by bombardment, the vacancy yield and the lifetime of the vacancy are very important for determining the enhanced diffusion constant. Even at room temperature some of the vacancies produced by bombardment vanish by the thermal annealing effect. At an elevated temperature more intense annealing of the vacancies is expected. Much experimental evidence shows a considerable difference between hot and room temperature implantation. In the case of hot implantation, increases of W, and N ( v ) occur simultaneously so that enhanced diffusion is observed. But in the case of room temperature implantation, only enhancement of N ( u ) will be observed.

295


But because of the short lifetime of the vacancies, only part of the total number of radiation induced vacancies is effective. Therefore little enhancement of the diffusion is observed in the case of room temperature implantation. The diffusion coefficient in the region between room temperature and 800°C was measured. The relation between the implanted ions N ( x , To)and the diffusion coefficient D is expressed as

-

5 ' 20

[erfc(4DT0 ~

x2 - erfc20,~)

+

-~

where To is the duration of ion implantation, I , is the dose rate per unit area, and o,,is the standard deviation of the projected range. Equivalent diffusion coefficients calculated from Eq. (31) are shown in Fig. 16. In the higher temperature region the diffusion coefficient is controlled by the thermal diffusion equation. But in the temperature range between 800" and 500°C the effective diffusion coefficients are the same. In this region the diffusion coefficient is fixed by the number of radiation induced vacancies. When the flux density of the incident ion beam is increased the effective diffusion coefficient is increased because of the increase in the density of the radiation induced vacancies. At around room temperature this effect of the enhancement of diffusion coefficients is no longer observed. A certain energy is necessary to release the impurity atoms from the original site to the other site where the atom is able to migrate with the assistance of the adjacent vacancy. This energy is greater than the thermal energy of the lattice at about 300"K, so that the diffusion coefficient will drop towards the value of the normal thermal diffusion coefficients. C. Interstitial Difftision Mechanism for Enhanced Diffusion

Another mechanism for the enhanced diffusion with hot implantation is that of interstitial diffusion. The following evidence points to this conclusion. 1. Exponential Tail

Profiles for these cases show the exponential tail after the major gaussian peak. This exponential tail is calculated as follows.

296

SUSUMU NAMBA AND KOHZOH MASUDA

The one-dimensional diffusion equation can be written:

where K , is a unimolecular rate constant for trapping and D is the diffusion constant for the interstitial motion. Setting a N ( x ) / ? t = 0, we see that the equilibrium distribution has an exponential form (25)

N,,(x)

=

N,,(O) exp [ - (K,/D)"' . x],

(33)

so that the exponential tail can be explained by the interstitial migration with uniformly distributed trapping centers. 2. Foreign Aton? Locution in the Lattice Measurements of the lattice location show that most of the atoms are located neither at the exact substitutional site nor at the exact interstitial sites in the region of extra tail (26) in the case of Ga and In implantation in silicon. If the impurity atoms diffuse by exchange between their sites and adjacent vacancies, the final positions of the atoms should be at the substitutional sites. But in the case of another mechanism such as interstitial migration, the final sites of the impurity atoms will be some irregular positions because a trapped interstitial atom can easily shift its position due to the stress field around the trap or the irregularity of the surrounding potential field. The results of the He beam channeling experiments show that the enhanced tail is not caused by vacancy assisted diffusion but by interstitial migration. 3. Dependence on Eiierqj, oj the Iiiczileizt Particle

The ranges of the channeled particle are proportional to the square root of the incident energy. As shown In Fig. 17 the enhanced tail is not dependent upon acceleration voltage. In this case, channeling is not the major mechanism for producing enhanced diffusion. 4. Teniperatuw Dependence of the Projles

The enhanced tail increased at 500'C implantation more than that at room temperature implantation. This tendency suggests that the enhancement is a thermally assisted process such as diffusion or migration of impurity atoms and strongly rejects the possibility of channeling ( 2 4 ) .


297

FIG. 17. Energy dependence of ion profiles of implanted As in Si at room temperature. 0 35 kV, 5 x 10i3/cm2; A 45 kV, 5 x 10'3/cm2: A 60 kV, 2.5 x 10'J/cm2; 0 130 kV, 2 1 0 ~ ~ 1 ~ ~ 2 .

D. Radiation Enlzanced DijJusion The radiation enhanced diffusion (referred to as R.E.D.) means the bombardment of light ions in order to change the profile of impurity ions drastically. This is an excellent technique for device fabrication. R.E.D. was tried by several groups. One of the examples is shown in the following. Silicon slices containing a thermally diffused junction are irradiated at temperatures between 600' and 1200°C with protons of 0.2 1.0 MeV energy. The penetration depth of the protons is less than the original junction depth. In the portion of the sample immediately beneath the irradiated region, a significant increase in junction depth occurs, as can be seen in Fig. 18 (27). In this case, it is suggested that the vacancies produced by proton beam irradiation migrate into the deeper region which make the diffusion coefficient of impurities extremely high. The behavior of impurities and vacancies is similar to that in hot implantation. Glotin discovered the enhanced diffusion of phosphorus and boron in

-

298

SUSUMU NAMBA AND KOHZOH M A S U D A

6~ n - T Y P E Si

IRRADIATED REGION

7$-

MOVEMENT OF

FIG. 18. Schematic representation of the movement of a p-!I junction following proton irradiation at elevated temperature.

silicon by the measurements of radiotracer technique (28). First, he implanted 32Pat room temperature to a dose of 1014ions/cm2; he then increased the substrate temperature up to 700°C and implanted again the stable isotope 31Pto a dose of 3 x lOI5/cm2. He found that this second implantation caused an increase in the depth of the first implantation. The effective diffusion coefficient in this case was 2.7 x cm2/sec. Since the distribution profile in this case was gaussian the vacancy assisted diffusion mentioned previously will be a good explanation of this enhancement. Abe performed the experiment on a Sb enhanced diffusion in silicon layer using a 100 keV proton beam. The effective enhanced diffusion coefficient in the region of the epitaxial growth region was 1 x 10- cm’/sec. Profiles in this epitaxial layer are shown in Fig. 19. In the profile of impurities which were redistributed by enhanced diffusion there was not a single gaussian so he suggested that there was a nonuniform distribution of diffusion coefficients (29).

’

DEPTH (pm)

(r

=

FIG. 19. Shift of the boundary of the epitaxial layer. 0.33 p . 40 min; -- u = 0.5 p, 40 min.

---

u

=

0.25 p, 40 min;

--

299


In A1 implantation in silicon at room temperature an enhanced diffusion of A1 has been observed after annealing. Figure 20 shows the effects of surface layer removal on the enhanced diffusion of Al. Prior to annealling at 800°C for 20 min, steps were formed in the as-implanted wafer by means of anodic oxidation and HF stripping. The removal of the first layer of 160 8, does not cause any change in junction depth, but the second layer removal (total 320 A) caused a remarkable AMORPHOUS REGION \ (-16OA)

,\

(Ad (

JUNCTION n-Si

- 6 0 07 A -1200A

i

L FIG.20. Decrease in junction depth depend on removal of surface layers.

A)

decrease in junction depth. The third layer removal (total 480 also caused a considerable decrease, but the region deeper than 480 8, does not contribute to a detectable decrease in junction depth. From this it can be seen that the region which does contribute to the enhanced diffusion is not the amorphous layer but the isolated disordered region (30).

IV. ANNEALINGAND ELECTRICAL PROPERTIES A . Introduction In the case of implantation, normally annealing is necessary to obtain good electrical properties. Thermal annealing changes nonsubstitutional atoms into substitutional atoms which are effective in obtaining an electrically active center (31).A large fraction of the penetrating atoms just at the end of their path in the solid occupy nonsubstitutional positions because there is more space than for substitutional positions. The annealing temperature at which the conversion from nonsubstitutional to substitutional sites occurs is relatively lower than that for the occurrence of normal thermal diffusion. But in some cases thermal treatment for annealing is not effective in obtaining good electrical properties even in the case of high temperature annealing. In this case hot implantation is expected to be effective. Imperfections produced during ion implantation are also annealed by

300

SUSUMU NAMBA A N D KOHZOH MASUDA

heat treatment. The production efficiencies of the defects in both hot implantation and room temperature implantation are different. This is probably due to the interaction between the defects because of the high total dose of the implanted ions. Backscattering, ESR, and electron microscopy are useful methods for measuring the physical properties of the defects. Radiation induced defects decrease the electrical carrier mobility because of the action of trapping centers and decrease the efficiency of luminescence. B. Silicon The concentration of charge carriers is obtained by the Hall effect measurements in order to determine the effect of thermal annealing on Sb implanted Si. An abrupt increase in the number of charge carriers is observed at around 600°C as shown in Fig. 21a (20). Substitutional Sb can be a donor + Substitutional ,,,

0.8 R.T. Implant

r

Hot substrap 1rnphnt:Sb

0.4

0.4

;

;charge ; Carriers

C

200

LOO

600 800

Anneal Temperature

('c)

(a)

FIG. 21. (a ) Annealing effect of Sb implanted Si (room temperature implantation). (b) Annealing effect of Sb implanted Si (hot implantation).

center. But if the donor center is compensated, this donor center can not act as donor. It is very important to know what percentage of atoms are in the substitutional sites. Channeling experiments give the exact answer to this question. The ratio of the substitutional components to the total number of implanted atoms is measured in one sample. The growth of the substitutional component is exactly the same as for the generation of charge carriers in room temperature implanted Sb in Si, as mentioned earlier. In the case of hot implantation at 35OoC,as shown in Fig. 21b, the substitutional component constitutes almost 90% of all implanted atoms even at the low annealing temperature of 400°C. However the density of charge carriers is very low even though a high substitutional component is obtained. After annealing at 800 C, agreement between substitutional components and the density of the charge carrier is obtained. Between the annealing temperatures of 400" and


30 1

80O0C, some defects which compensate the donor carriers are generated from the substitutional Sb atoms. There exist two mechanisms which contribute to thermal annealing. One is the conversion from the nonsubstitutional site to the substitutional site. The other is the recovery of crystal defects. Defects produced by implantation are much more complicated than in the case of low dose irradiation of neutron beams or electron beams, which have already been reviewed in other books (32). The efficiency of production of defects by ion beams is much greater than by fast neutron beams so that the range ofdensities of the defects is widely spread. In the low density range, each defect is isolated from the others. The interaction between defects increases with increasing defect density and finally the amorphous phase is produced at the heaviest implantation dose. Thus we must study the behavior of the isolated defect, compound defects, and the amorphous phase in the solids. Figure 22 illustrates W

2 + V

a 1.0 -\ LL

400K

V

\\

W

\ \

W

0.1

“SATURATION”-!

-

8 8

x\

\

b 0

P” 200KeV 112HR 5W’C ANNEAL

10’~

10”

10”

1d6

DOSE-NO IONS crr-’

FIG22 Fraction of dose electrically active agalnst implantation at 1 W K ( x), 200 K(O), 300 K(O), 350 K(O), and 400’K(A).

the relations between doping efficiency and total dose for each implantation temperature. When the 3 ’ P ions were implanted in Si with 200 keV and post annealing at 55OoC, doping efficiency is dependent upon implantation temperature and total dose. The doping efficiency is almost 100% below the dose of 10’3/cn12which means that the number ofcarriers is almost equal to that of implanted ions. On increasing the dose, the doping efficiency first decreases gradually then increases gradually after a minimum point and again reaches 100%.The dose at which the doping efficiency reaches 100%is called the critical dose which is equal to that at which the amorphous phase occurs. At an extremely high dose, the concentration of the implanted ions

302


exceeds the solubility limit of the ions. Therefore the doping efficiency decreases in this region as shown by the dashed line indicated by “saturation” in Fig. 22 (33). The critical dose increases in the high temperature region because of the annealing effect of defects produced during the implantation. The doping efficiency does not reach 100% at 400°C implantation because of the large annealing effect during implantation. It is reasonably well understood that the easy recovery of the carriers in the low dose region is due to the fact that the defects can be annealed at low temperature. There are no clear explanations of why the carrier recovery is easier when the amorphous layer is formed compared to when there are only isolated amorphous islands. But the appearance of the amorphous layer has an important role in the annealing behavior of the implanted layer. This amorphous phase gives an isotropic ESR signal of g = 2.006. Therefore it can be one of the criteria of existence of the amorphous phase (34,35).

1200-

\

K‘SPECTRP RANDOM

1000-

B 9

0 3 0

I

I

I

I' I

1

I

6 O

102 L 1o2

0 o

,w 0.2

0.4

I

0.6 DEPTH ( prn)

a8

I

FIG.24. Carrier concentration profile of P implantation

304


high density beam of neon was used to create extra damage in a boron preimplanted layer. Preimplantation of B was done with 10" atoms/cm2 at an acceleration voltage of 50 keV. Post bombardments of Ne were done with and 1014atoms/cm2 and zero. The results are shown in Fig. 25. 1

I

I

1

I

1

FIG.25. Neon dose dependence of annealing of boron implanted Si. B: SO keV . 10" cm'. Ne: 125 keV. R(Ne)/R(B)= 1.2. 0 1 0 ' h ~ c m zA ; 10'5/cmZ; 0 10"!cm2; 0 bithout Ne. Anneal time 10 min.

At the relatively low level of implantation damage of 10" atoms/cm2 reverse annealing was observed. The degree of the reverse annealing decreases with an increasing dose of Ne. Finally no reverse annealing effect was observed at a dose of 1OI6 atoms/cm2 which is a region of formation of a continuous amorphous phase (38). The dose dependence of the degree of reverse annealing was also done at 1.5 x lo", 7 x 1014,and 1 x 1014 atoms/cm2 of B at a substrate temperature of 80"K, as shown in Fig. 26. We see no reverse annealing effect at the

u Anneal Ternp.?C)

FIG.26. Dose dependence of annealing of boron implanted silicon for 50 keV at 80 K.


/

6 3 Ole

305

I 1000

Anneal temp. ("c)

FIG.27. The change of a fraction of the substitutional component of the implanted atoms at various annealing temperatures.

high dose of 1.5 x 10" atoms/cm2, but reverse annealing was observed at the dose of 1 x 1014 atoms/cm2. Reverse annealing was also observed in the behavior of the substitutional B concentration as shown in Fig. 27. The reverse annealing effect changes not only the carrier concentration but also the atom locations in the lattice. C. GaAs

Research on ion implantation in GaAs was delayed relative to Si because of the complexity of compound materials. In the case of Si, even though reverse annealing or interstitial migration occurs which creates some complexity in annealing phenomena, there is no stoichiometry problem. On the

306

S U S U M U NAMBA A N D KOHZOH M A S U D A

other hand, in GaAs, shifts from chemical stoichiometry easily happen when annealing at a high temperature because either Ga or As migrates faster, depending upon the environmental condition. Furthermore, hot implantation is often considered to be a better method of obtaining good electrical characteristics. When the substrate is hot, the difference between the speeds of migration of Ga and As in GaAs produces some complexity in the compositions and also electrical characteristics. Deviation from chemical stoichiometry also happens in the fabrication of p-n junctions. Mayer et al. (39) implanted Zn and Te into n and p type GaAs to get p and n type GaAs respectively. But a p-n junction was not obtained by implantation with 20 kV at 400°C and post annealing at 600°C. This conclusion was drawn from measurements of the V-I characteristics of the diode. The hole mobility of 50 cm2/V sec for Zn implantation was obtained, but the electron mobility was not obtained in the case of Te implantation because the diode characteristics were not abrupt. Hunsperger et ul. (40)also obtained a very broad junction width which is more likely a p-i-n junction rather than a p-n junction with 70 kV implantation at 400°C and annealing at 500°C. The depth distribution of implanted ions expected from this p-i-n structure is much deeper than that expected from LSS theory. The widths of the i region were 0.18 pm and 2.7 pm for the substrate dopant density of 1.8 x 10l8 atoms/cm3 and 1 x 10l6atoms/cm3, respectively. He showed that the changes in the mobilities and carrier concentrations depend upon the post-annealing temperature so as to stress the importance of the post-annealing effects. Roughan implanted Zn into GaAs at room temperature with 80 k V and annealed at 650°C. In this implantation, he found that it is possible to make a p-n junction at a dose of 10l6atoms/cm2 and a p-i-M junction was obtained at a dose of 1015atoms/cm3. This fact suggests that the interactions between implanted atoms and defects produced during implantation are important factors in determining whether a p-n junction is formed or not. Defects produced around the junction may suppress the migration of each component. Foyt et al. (41) reported that they obtained an abrupt junction by implantation with 70 kV at 500°C and post annealing at 800°C. Hunsperger and Marsh (42) tried to check in detail how the change of the i structure depends on the temperature of annealing. The width of the i layer increases with increasing temperature for implantation with 20 kV at 400°C in both cases of Cd and Zn implantation. But after properly prepared post annealing the i layer almost completely vanished. The dependence of the i layer on the annealing temperature is shown in Fig. 28. Under these circumstances the migration of As from the junction region was assumed, but some direct proof of the escape of the As is needed. Itoh


307

did a preimplantation of As which was expected to escape from the junction region. After this preimplantation of As, the same amount of Cd was implanted into the GaAs with 20 kV at 500°C and post annealing at 650°C. He obtained a p-n junction as was expected. Measurements were done by the C-V method and V-I characteristics. Without preimplantation of As, it was not possible to obtain a p-n junction. We can conclude that there are two successful methods. One is to suppress the escape of As by having the sample at low temperature. Another is to compensate for the As escape by preim-

:5 -

w

z 40 Y

?

32-

a

-

I -

O t

500

600 ANNEAL

700

800 TEMPERTURE ('C)

I 900

-

FIG. 28. Dependence of the i layer thickness on anneal temperature. - - - - - Substrate impurity concentration was 1 x 10'0/cm3. Implant conditions: dose 8 x 1015/cm2, 20 k V Cd' ions, substrate at room temperature, 10 rnin anneal period. -~~ Substrate 5 x 1015/cm3. Implant conditions: dose 1 x 1016/cm2, impurity concentration was 20 k V Zn' ions, substrate at room temperature, 10 min anneal period.

-

plantation. One of the advantages of the ion implantation over the thermal diffusion method was that it can be performed at relatively low temperature. This requirement for low temperature processing is more important in the case of GaAs than in the case of Si. But if one performs an ion implantation at low temperature, such as at room temperature, a high temperature annealing is necessary to obtain good electrical properties and this high temperature annealing produces many unexpected problems. A typically hot implantation with a substrate temperature of about 400°C is proposed to obtain good electrical properties. What is the operative mechanism of hot implantation in this case? Channeling experiments were carried out by Gamo et al. to clarify this situation. They observed that if the Te atoms were implanted at low temperatures, such as at room temperature, even after considerable high temperature annealing the lattice location of Te is not a substitutional site. This fact

308


was proved by the implantation of Te with 70 kV at room temperature and 500T with post annealing at 800°C and 900°C (43). The small fraction of substitutional components which appear at 400°C annealing is shown in Fig. 29. But even at an annealing temperature of

ANNEAL TEMPERATURE ( O C )

FIG.29. Dependence of the Tc amni location in the lattice on annealing temperature.

800 C , this fraction of the components is around 50% and there is no tenatoms/cm2 dency to increase this for both implantation doses of 1 x and 2 x 1016 atoms/cm2. O n the other hand, the fraction of the substitutional components of implanted atoms is 90% for hot implantation at 550-C. This result suggests that the thermal energy and the kinetic energy are necessary to place the Te ions at the substitutional sites at the end of the collision cascade. During post annealing the implanted atom has only thermal energy. Thus when the sample is set at the same temperature for both post annealing and hot implantation the conditions of the surroundings are quite different. This difference gives the advantage of lattice location for the case of hot implantation of GaAs. Moreover, the charge state of the defect during ion implantation is different from that during post annealing, causing the migration energies for the different charge state defects to be considerably different. For example, in the case of silicon the neutral vacancy has an activation energy of 0.33 eV whereas the negative vacancy has an activation energy of 0.18 eV. Group V atoms easily occupy substitutional sites even at room temperature implantation and post annealing. Implantations of P into GaAs were done successfully to obtain p-rz junctions (44-47). Fabrication of an insulating layer on the conductive GaAs wafer is also performed by proton beam irradiation. In this case a minimum carrier density of 10" carriers/cm3 (48) was obtained. This value is small enough to make an isolation pattern in an integrated circuit of GaAs. The optimum dose to obtain the most resistive layer was also found.

309


>

.

nonchanneled

Y

I

I

T

0

- lam

Ol

87'k implant

.t c

.,

v,

300Ok anneal

-

-800

296'k implant

-600

-

-400

unimplanted

-200 I

I

I

Energy ( keV

1

FIG.30. Shift of the damaged peak of ( I 1 I ) direction spectrum

As mentioned earlier, defects in GaAs easily migrate and some of them can migrate even at room temperature. Vook measured the backscattering of GaAs and found abnormal enhanced diffusion during the low temperature implantation of oxygen at over 275°K (49). The proof of this enhanced diffusion is the shift of the damaged peak of the 11 1) direction as shown in Fig. 30. A similar enhanced diffusion of defects is reported by Namba et a/. (50). They performed an experiment on photoluminescence intensity as a function of implanted dose and found a considerable decrease in the photoluminescence intensity which depended on the migration of the defects. For the abnormal enhanced diffusion, Stein suggested the charge state change mechanism for defects during both implantation and post annealing ( 5 2 ) . The pattern of the migration of defects in the implanted sample is not very well understood. One of the reasons for the complexity in the mechanism of defect migration is the complexity of the structure of the defect itself. As already mentioned the density of the defects is very large in the case of ion implantation. Overlap of defects creates multivacancies and stress between

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