Semiconductors and Semimetals. Volume 11: Solar Cells

Semiconductors and Semimetals A Treatise

Edited by R . K . WILLARDSON ELECTRIC MATERIALS DIVISION COMINCO AMERICAN INCORPORATED SPOKANE, WASHINGTON

Volume

ALBERT C . BEER BATTELLE MEMORIAL INSTITUTE COLUMBUS LABORATORIES COLUMBUS, OHIO

1 Physics of III-V Compounds

Volume 2 Physics of III-V Compounds Volume 3 Optical Properties of III-V Compounds Volume 4 Physics of III-V Compounds Volume 5 Infrared Detectors Volume 6 Injection Phenomena Volume 7

Applications and Devices (in two parts)

Volume

Transport and Optical Phenomena

8

Volume 9 Modulation Techniques Volume 10 Transport Phenomena Volume 1 1

Solar Cells

SEMICONDUCTORS AND SEMIMETALS VOLUME 11

Solar Cells Harold J . Hovel THOMAS J. WATSON RESEARCH CENTER IBM CORPORATION YORKTOWN HEIGHTS, NEW YORK

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 OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE 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 Cataloging in Publication Data Willardson, Robert K ed. Semiconductors and semimetals. Bibliographical footnotes. v. Physics of 111-V compounds.-v. 3. Infrared Optical properties of 111-V compounds.-v. 5. detectors. [etc.] I. Semiconductors. 2. Semimetals. I. Beer, 11. Title. Albert C.,joint ed.

CONTENTS:

QC612S4W5 537.6'22 ISBN 0-12-752111-9 (v. 11)

PRINTED IN THE UNITED STATES O F AMERICA

65-26048

Foreword

This book represents a departure from the usual format of Semiconductors and Semimetals in that the entire volume is devoted to a single article. Because of the importance of solar energy and the increasing amounts of research being done on solar cells, we feel that a detailed review is useful and timely. It is especially fortunate that Dr. Hovel, who has made numerous original contributions in this field, has been able to devote the time necessary to provide this valuable addition to our series. The editors and author agreed to the use of cold type composition in order to reduce the production time to a minimum for this particular volume. R. K. Willardson Albert C. Beer

xi

Preface

The importance of energy i n our s o c i e t y has become a l l too apparent i n recent years. Of t h e various energy a l t e r n a t i v e s , s o l a r energy has t h e very d e s i r a b l e property of being e s s e n t i a l l y l i m i t l e s s and without t h e problems of p o l l u t i o n o r physical danger. Solar c e l l s a r e devices which convert sunlight d i r e c t l y i n t o d i r e c t c u r r e n t e l e c t r i c i t y , and they have been an important p a r t of t h e space program f o r over a decade. Solar c e l l s are a l s o capable of making a s i g n i f i c a n t impact on terrestrial energy needs. I t seems s u r p r i s i n g then that t h e r e have been no books and very few review a r t i c l e s written about these devices, and it w a s t h i s lack plus t h e author's i n t e r e s t i n t h e s u b j e c t t h a t prompted t h e present volume t o be written. The book i s intended as a background and general reference source, primarily f o r t h e nonexpert i n t h e f i e l d of photovoltaics and those i n t e r e s t e d i n entering t h e f i e l d . Solar c e l l experts may a l s o f i n d it u s e f u l , especially i n i t s discussions of heterojunction and Schottky b a r r i e r c e l l s , t h i n film devices, and p o l y c r y s t a l l i n e devices. The book should be e a s i l y understandable f o r anyone who has had a t least an introductory course i n s o l i d s t a t e electronics. Chapter 1 is an introduction t o s o l a r cells and t o t h e material and device parameters most important t o these devices. The performance of a s o l a r c e l l i s equally dependent on i t s a b i l i t y t o generate photocurrent and i t s behavior i n t h e dark. Chapter 2 describes t h e process of photocurrent generation and t h e s p e c t r a l response, while Chapter 3 describes t h e elect r i c a l behavior i n t h e dark. The e f f i c i e n c i e s of S i , GaAs, and CdS s o l a r cells under various conditions a r e discussed i n Chapter 4. Since it would be impossible t o describe t h e behavior of s o l a r cells under a l l p o s s i b l e conditions, t h e trends i n behavior caused by changes i n junction depth, doping l e v e l s ,

xiii

xiv

PREFACE

base and top region l i f e t i m e s , surface recombination velocit i e s , presence o r absence of aiding e l e c t r i c f i e l d s , e t c . a r e shown instead. The e f f e c t s of thickness on s o l a r c e l l behavior a r e discussed i n Chapter 5 , together with t h e e f f e c t s of grain boundaries i n polycrystalline films. In Chapter 6, an i n t r o duction i s given t o Schottky b a r r i e r , heterojunction, v e r t i c a l multijunction, and grating s o l a r c e l l s . Radiation e f f e c t s on c e l l s exposed t o t h e space environment are discussed i n Chapter 7, and device behavior under various temperature and i n t e n s i t y environments i s described i n Chapter 8 . Chapter 9 serves a s an introduction t o s o l a r c e l l technology, including c r y s t a l growth, d i f f u s i o n , ion implantation, a n t i r e f l e c t i v e coatings, and Ohmic contacts. I would l i k e t o express my appreciation f o r t h e many helpful comments and reviews of t h e manuscript by my colleagues, A. Onton, C. Lanza, R. Keyes, W. Dumke, W. Howard, B. Crowder, P. Melz, and p a r t i c u l a r l y J. Woodall. I am g r a t e f u l t o t h e IBM Corporation f o r t h e encouragement and support given t o me during t h e undertaking. Most of a l l , I appreciate t h e patience and understanding of my family during t h i s seemingly endless task.

Definitions

Air Mass AM0

AM1 AM2

Back Surface Field Base Dead Layer

Fill Factor

Inherent Efficiency open Circuit Voltage Photocurrent

Secant of the sun's angle relative to the zenith, measured at sea level. Solar spectrum in outer space. Solar spectrum at earth's surface for optimum conditions at sea level, sun at zenith. Solar spectrum at earth's surface for average weather conditions (technically, the spectrum received at earth's surface for 2 path traversals through the atmosphere). Adiffused or grown electrical contact to the base which blocks minority carriers but transmits majority carriers. The bulk region of the solar cell lying beneath the thin top region and the depletion region. A thin region adjacent to the front surface with very short lifetime. The dead layer is a result of the diffusion process, and extends over about a third of the top region. The fraction of the product of the short circuit current and open circuit voltage which is available as power output. The power conversion efficiency of a solar cell without accounting for series resistance, shunt resistance, or reflection losses. Light-created voltage output for infinite load resistance. The current generated by light.

DEFINITIONS Short Circuit Current Spectral Response, Absolute Spectral Response, Relative Spectral Response, External Spectral Response, Internal Top Region

The current for zero-net bias voltage across the device. It can differ from the photocurrent if a large series resistance is present. The actual number of carriers collected per incident photon at each wavelength. Same as the quantum efficiency. Includes reflection from the surface. The number of carriers collected per incident photon at.each wavelength, with the curve normalized to unity at the wavelength of peak response. The spectral response as it would be measured, including reflection of incident light. May be relative or absolute. The response of the solar cell without accounting for reflection from the front surface. May be relative or absolute. The thin, heavily doped region of the cell adjacent to the surface (i.e., the P region in a P/N cell or the N region in an N/P cell, etc.)

.

List of Symbols

A

Aa A0

At A*

A*

*

B CO Dn

*e FF G H H'

Im I0

diode perfection factor (in exp(qV/AkT) ) active area diode perfection factor in single exponential approximation total area Richardson constant for the dark current in Schottky barriers A* modified by scattering, tunneling, and quantum mechanical effects argument in the exponential relationship for tunneling currents surface concentration diffusion coefficient of electron in p-type material diffusion coefficient of holes in n-type material thickness of antireflective coating electric field conduction band edge energy Fermi level energy bandgap energy intrinsic F e d level energy normalized electric field in p-type material normalized electric field in n-type material valence band edge energy energy level of recombination center average energy of all photons in the source spectrum incident photon density per second per unit bandwidth at wavelength X F e d probability that a recombination center is occupied by a majority carrier fill factor carrier generation rate due to incident light total cell thickness (semiconductor regions only) cell thickness minus the junction depth and depletion width current at maximum power point dark current preexponential tern xvii

xviii I0 0

Is, J Jinj Jn(h) JO Jp(h)

JPh Jrg JSC

Jtun

KL K1

K1 rK2 k L,

L,

Lp LpP

"p "ph (Eg)

LIST OF SYMBOLS

dark current preexponential term in single exponential approximation short circuit current current density photocurrent density per unit bandwidth at wavelength h due to collection from the depletion region injected current density photocurrent density per unit bandwidth at wavelength 1 due to electron collection from the p-side of the junction dark current density preexponential term photocurrent density per unit bandwidth at wavelength X due to hole collection from the n-side of the junction photocurrent density (same as short circuit current density for negligible series resistance) space charge layer recombination current density in dark short circuit current density tunneling dark current radiation damage coefficient preexponential constant in tunneling current fractions of the barrier heights on the two sides of a heterojunction Boltzmann constant electron diffusion length in p-type material effective diffusion length for electrons in p-type material when drift field is present hole diffusion length in n-type material effective diffusion length for holes in n-type material when drift field is present acceptor density conduction band density of states donor density density of recombination centers total number of photons/cm2sec in the source spectrum doping levels on the two sides of a heterojunction valence band density of states perfection factor in dark current of Schottky barrier electron concentration refractive index intrinsic carrier density electron density in n-type material electron density in equilibrium electron density in p-type material total number of photons/cm2 sec with energies greater than the bandgap

LIST OF SYMBOL&

Pin PR

Pn

FnO

Pp

Ppo

R

Rs

%h %ck Sfront Sn sP T T vd vj "In

voc Vth W n' wP WP WP+

ES

A

X

XiX

input power density number of recombination centers produced by each radiative particle hole density in n-type material hole density in equilibrium hole density in p-type material hole density in equilibrium reflectance series resistance shunt resistance surface recombination velocity at back surface surface recombination velocity at front surface surface recombination velocity for electrons surface recombination velocity for holes transmission of light through metal film temperature built-in voltage voltage across junction depletion region voltage at maximm power point open circuit voltage thermal velocity depletion width width of the n-region of a VMJ cell width of the p-region of a VMJ cell width of the lowly doped region in the base of a back surface field cell width of the highly doped region at the back of a back surface field cell junction depth (width of the top region) absorption coefficient conduction band energy discontinuity valence band energy discontinuity image potential in Schottky barriers dynamic dielectric constant static dielectric constant wavelength wavelength for minimum reflection radiation fluence barrier height in Schottky barriers low-high junction barrier height sheet resistivity capture cross section lifetime electron mobility in p-type material hole mobility in n-type material phase thickness of optical coating electron affinity

Semiconductors and Semimetals Volume 1 Physics of III-V Chmpo& C. H i l s u m , Some Key Features of 111-V Compounds Franco Bassani, Methods of Band Calculations Applicable to 111-V Compounds E . 0. Kane, The k - p Method V. L. Bonch-Bruevich, Effect of Heavy Doping on the Semiconductor Band Structure Donald Long, Energy Band Structures of Mixed Crystals of IIIV Compounds Laura M. Roth and Petros N . Argyres, Magnetic Quantum Effects S . M. P u r i and T . H . Geballe, Thennomagnetic Effects in the Quantum Region W . M . Becker, Band Characteristics near Principal Minima from Magnetoresistance E . H. P u t l e y , Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H. Weiss, Magnetoresistance B e t s y Ancker-Johnson, Plasmas in Semiconductors and Semimetals Volume 2 Physics of III-V Chmpoands M . G . Holland, Thennal Conductivity S . I. Novikova, Thermal Expansion U. Piesbergen, Heat Capacity and Debye Temperatures G. Giesecke, Lattice Constants

J. R. Drabble, Elastic Properties A . U. MacRae and G . W . G o b e l i , L o w Energy Electron Diffraction

Studies

R o b e r t Lee Mieher, Nuclear Magnetic Resonance Bernard G o l d s t e i n , Electron Paramagnetic Resonance T . S. Moss, Photoconduction in 111-V Compounds E . Antoncik and J. Tauc, Quantum Efficiency of the Internal

Photoelectric Effect in InSb G. W . G o b e l i and F . G . A l l e n , Photoelectric Threshold and Work Function P . S . Pershdm, Nonlinear Optics in 111-V Compounds M . Gershenzon, Radiative Recombination in the 111-V Compounds Frank S t e r n , Stimulated Emission in Semiconductors

xxi

xxii

CONTENTS OF PREVIOUS VOLUMES

Volume 3 Optical Properties of III-V Compounds

Marvin Hass, Lattice Reflection William G. Spitzer, Multiphonon Lattice Absorption D. L. Stierwalt and R. F. Potter, Emittance Studies H . R. Philipp and H . Ehrenreich, Ultraviolet Optical Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Earnest J. Johnson, Absorption near the Fundamental Edge John 0. Dimmock, Introduction to the Theory of Exciton States in Semiconductors B. Lax and J. G. Mavroides, Interband Magnetooptical Effects H. Y. Fan, Effects of Free Carriers on the Optical Properties Edward D. Palik and George B. Wright, Free-Carrier Magnetooptical Effects Richard H . Bube, Photoelectric Analysis B. 0. Seraphin and H. E. Bennett, Optical Constants Volume 4 Physics of III-V Compounds

N. A. Goryunova, A. S . Borschevskii, and D. N. Tretiakov, Hardness N. N. Sirota, Heats of Formation and Temperatures and Heats of Fusion of Compounds AII1 Bv Don L. Kendall, Diffusion A. G. Chynoweth, Charge Multiplication Phenomena Robert W. Keyes, The Effects of Hydrostatic Pressure on the 111-V Semiconductors L. W. Aukermdn, Radiation Effects N. A. Goryunova, F. P. Kesamanly, and D. N. Nasledov, Phenomena in Solid Solutions R. T. Bate, Electrical Properties of Nonuniform Crystals Volume 5

Infrared Detectors

Henry Levinstein, Characterization of Infrared Detectors

Paul W. Kruse, Indium Antimonide Photoconductive and Photoelectromagnetic Detectors M. B. Prince, Narrowband Self-Filtering Detectors Ivars Melngailis and T. C. Harman, Single-Crystal Lead-Tin Chalcogenides Donald Long and Joseph L. Schmit, Mercury-Cadmium Telluride and Closely Related Alloys E . H. Putley, The Pyroelectric Detector Norman B. Stevens, Radiation Thermopiles

CONTENTS OF PREVIOUS VOLUMES

xxiii

R . J . K e y e s a n d T . M. Q u i s t , Low Level Coherent and Incoherent

Detection in the Infrared M. C. T e i c h , Coherent Detection in the Infrared F. R. A r a m s , E. W. S a r d , B. J. P e y t o n , a n d F. P. P a c e , Infrared Heterodyne Detection with Gigahertz IF Response H. S. Sormners, Jr., Microwave-Biased Photoconductive Detector R o b e r t S e h r a n d R a i n e r Z u l e e g , Imaging and Display Volume6

Injection Phenomena

Murray A . Lampert a n d Ronald B . S c h i l l i n g , Current Injection in Solids: The Regional Approximation Method R i c h a r d W i l l i a m s , Injection by Internal Photoemission A l l e n M. B a r n e t t , Current Filament Formation R. B a r o n a n d J . W. M a y e r , Double Injection in Semiconductors W. R u p p e l , The Photoconductor-Metal Contact Volume 7

ApphtiOn and D e h Part A

John A . C o p e l a n d a n d Stephen K n i g h t , Applications Utilizing

Bulk Negative Resistance F . A . P a d o v a n i , The Voltage-Current Characteristic

of MetalSemiconductor Contacts P. L. Hower, W. W. Hooper, B . R . C a i r n s , R. D . Fairman, a n d D. A . T r e m e r e , The GaAs Field-Effect Transistor Marvin H . W h i t e , MOS Transistors G . R. Antell, Gallium Arsenide Transistors T . L. T a n s l e y , Heterojunction Properties Volume7

Application and Devices: Part B

T . M i s a w a , W A T T Diodes H. C. O k e a n , Tunnel Diodes Robert B . Campbell and H u n g - C h i C h a n g , Silicon Carbide Junction Devices R . E . E n S t r O m , H . Kressel, a n d L . K r a s s n e r , High-Temperature Power Rectifiers of GaAsl-xPx

Volume 8 Transport and Optical Phenomena R i c h a r d J. S t i r n , Band Structure and Galvanomagnetic Effects in 111-V Compounds with Indirect Band Gaps

xxiv

CONTENTS OF PREVIOUS VOLUMES'

Roland W . Ure, J r . , Thermoelectric Effects in 111-V Compounds Herbert P i l l e r , Faraday Rotation H . Barry Bebb and E . W . W i l l i a m s , Photoluminescence I: Theory E. W . W i l l i a m s and H . Barry Bebb, Photoluminescence 11: Gal-

lium Arsenide Volume 9 Modulation TeebdquW B . 0 . Seraphin, Electroreflectance R . L . Aggarwal, Modulated Interband Magnetooptics Daniel F. B l o s s e y and Paul Handler, Electroabsorption Bruno B a t z , Thermal and Wavelength Modulation Spectroscopy Ivar BalSleV, Piezooptical Effects D . E. Aspnes and N . B o t t k a , Electric-Field Effects on the

Dielectric Function of Semiconductors and Insulators Volume 10 Transport Phenomena R . L . Rode, Low-Field Electron Transport J. D . W i l e y , Mobility of Holes in 111-V Compounds C. E l . Wolfe and G . 8. S t i l l m a n , Apparent Mobility Enhancement

in Inhomogeneous Crystals Robert L . Peterson, The Magnetophonon Effect

CHAPTER 1

Introduction

A.

Background

A s o l a r c e l l i s a photovoltaic device designed t o convert sunlight i n t o e l e c t r i c a l power and t o deliver t h i s power i n t o a s u i t a b l e load i n an e f f i c i e n t manner. The most important application f o r s o l a r c e l l s i n the p a s t has been i n t h e space program. There are over 500 s a t e l l i t e s of various types i n o r b i t around t h e e a r t h , powered t o a very l a r g e degree by s i l i c o n s o l a r c e l l s , and it i s s a f e t o say t h a t without these c e l l s , we would not have t h e sophisticated weather, conrmunicat i o n s , m i l i t a r y , and s c i e n t i f i c s a t e l l i t e c a p a b i l i t i e s we have today. The advantages of s o l a r c e l l s l i e i n t h e i r a b i l i t y t o provide nearly permanent, uninterrupted power a t no operating c o s t with only heat as a waste product, and t h e i r conversion of l i g h t d i r e c t l y i n t o e l e c t r i c i t y r a t h e r than some intermed i a t e form of energy. They a l s o have a high power/weight r a t i o compared t o o t h e r power sources. Their chief disadvantages l i e i n t h e low power/unit area of sunlight ( t h a t necess i t a t e s l a r g e area a r r a y s ) , t h e i r r e l a t i v e l y low efficiency, and the degradation t h a t takes place i n h o s t i l e high energy p a r t i c l e environments. As useful a s s o l a r c e l l s have been i n t h e space program, t h e i r p o t e n t i a l importance f o r large-scale power generation t o meet e a r t h ' s energy needs i s even g r e a t e r . A few years ago, very few people would have seriously proposed s o l a r energy as a major power source; f o s s i l - f u e l burning, steam-powered generation plants were cheap and f u e l supplies seemed inexhausti b l e . Today, however, t h e r i s i n g p r i c e of f u e l , t h e r e a l i z a t i o n t h a t o i l and gas supplies can only l a s t a r e l a t i v e l y few decades, and the freedom of s o l a r energy from pollution, have a l l led to closer looks a t s o l a r energy a s an a l t e r n a t i v e t o present day f o s s i l - f u e l systems.

1

2

1.

INTRODUCTION

One of the e a r l y schemes f o r large-scale power generation w a s the Arthur D. L i t t l e Company proposal t o p l a c e l a r g e s o l a r c e l l panels t o t a l l i n g about 100 Ian2 i n area i n t o synchronous o r b i t about 36,000 km above t h e earth [1,2]. These panels would be capable of generating up t o 15,000 MW of power, equal t o 4 1/2% of the e l e c t r i c power used i n t h e United S t a t e s as of 1973. The panels would use r e a d i l y a v a i l a b l e S i s o l a r c e l l s , which are about 11-12% e f f i c i e n t and highly r a d i a t i o n " t o l e r a n t . 'I Other schemes f o r power generation v i a s o l a r c e l l s include l a r g e a r r a y s of t h i n f i l m CdS devices, which have received much a t t e n t i o n i n t h e p a s t , and t h e use of either s i n g l e c r y s t a l s i l i c o n "ribbons" o r t h i n films of polyc r y s t a l l i n e s i l i c o n , which are j u s t beginning t o receive a t t e n t i o n now. The d i f f i c u l t y w i t h a l l t h e s e schemes i s t h e i r c o s t ; i f s o l a r c e l l s a r e t o be competitive w i t h o t h e r methods of power generation f o r terrestrial use, their c o s t must be reduced by a f a c t o r of s e v e r a l hundred. The prospects f o r s i g n i f i c a n t cost reduction seem very good, p a r t i c u l a r l y with t h e ribbon o r p o l y c r y s t a l l i n e S i schemes. The high c o s t of today's S i c e l l s i s i n l a r g e p a r t a r e s u l t of s t r i n g e n t r a d i a t i o n t o l e r ance and s t a r t i n g e f f i c i e n c y requirements, as w e l l as t h e absence of mass production methods f o r making the cells. The requirements f o r ribbon or p o l y c r y s t a l l i n e S i devices operating on t h e e a r t h ' s surface, on t h e o t h e r hand, would be g r e a t l y relaxed, and they should be r e a d i l y adaptable t o mass product i o n with a'minimum of problems. CdS s o l a r cells are already made by low-cost techniques and are highly promising f o r use on earth, provided that c e r t a i n degradation problems can be overcome ( s i g n i f i c a n t progress has been made on t h e s e problems i n t h e last few y e a r s ) . V i r t u a l l y a l l s o l a r cells now i n use c o n s i s t of a si s i n g l e c r y s t a l "wafer" 12-18 m i l t h i c k having a very t h i n (0.2-0.5 pm) diffused region a t t h e s u r f a c e t o form a p-n junction (this s u r f a c e region could a l s o be produced by vapor growth). Electrical contact is made t o t h e diffused region i n such a way as t o allow a maximum amount of l i g h t t o f a l l on t h e S i ; Ohmic contact is a l s o made t o t h e back of t h e wafer. A sputtered o r evaporated a n t i r e f l e c t i o n coating is applied t o reduce t h e amount of l i g h t l o s t by r e f l e c t i o n from t h e surface. F i n a l l y , a "cover g l a s s " of quartz, sapphire, o r s p e c i a l l y t r e a t e d g l a s s , w i t h a d d i t i o n a l a n t i r e f l e c t i o n and u l t r a v i o l e t r e j e c t i o n f i l t e r s , is bonded t o t h e c e l l with transparent adhesive w i t h the purpose of preventing high energy r a d i a t i v e particles from reaching arid degrading t h e device. The completed solar c e l l is shown i n Fig. 1. The heavily doped s i d e of t h e junction, produced by d i f f u s i o n o r vapor

A.

BACKGROUND

3

CONTACT BAR

REGION

\

CONTACT

F I G . 1 . Cross s e c t i o n of the Common form of S i solar c e l l used i n the space program i n the p a s t . Thicknesses are not

to s c a l e .

growth, i s c a l l e d t h e top region of t h e s o l a r c e l l . The other s i d e of t h e junction, consisting of the remainder of t h e subs t r a t e except f o r t h e depletion region, is c a l l e d t h e base. The question w a s r a i s e d i n the l a t e 1950's as t o what t h e optimum material i s f o r s o l a r c e l l fabrication. Theory indicated t h a t t h e optimum i n terms of efficiency was a semiconductor with a bandgap of around 1.5 eV, although materials with bandgaps from 1.1 t o 2 . 0 eV should be nearly as good. The chief candidates were S i , InP, GaAs, CdSe, and CdTe. S i l icon quickly showed i t s e l f t o be superior t o any of t h e others experimentally. Of a l l t h e available semiconductors, S i i s t h e most abundant, t h e least expensive, and t h e most technol o g i c a l l y advanced. No material has y e t proven t o be superior t o S i i n converting outer space sunlight, although G a A s c e l l s have come q u i t e close. GaAs is f a r more expensive than S i and not nearly as technologically developed. However, GaAs s o l a r c e l l s are able t o operate a t higher temperatures and have g r e a t e r radiation tolerance, making them a t t r a c t i v e f o r some s p e c i a l applications. The S i s o l a r cell m o s t widely used i n the space program i n t h e p a s t has consisted of a 10 ohm-cm boron-doped wafer, diffused on one s i d e t o a depth of 0.2-0.5 pm with phosphorus, contacted with Ti-Pd-Ag or Ti-Ag-solder, and covered with 800 of SiO. These "N on PI' devices can convert 11.5% of AM0 (outerspace) sunlight and 14% of AM1 (sea l e v e l a t noon ( A i r mass i s a on t h e equator) sunlight i n t o uaeful power. t e r m which describes how sunlight is modified by passage through t h e atmosphere.) This s o l a r c e l l design is a compromise between AM0 efficiency and radiation tolerance; cells made from lower r e s i s t i v i t y boron-doped s u b s t r a t e s yield higher s t a r t i n g e f f i c i e n c i e s but degrade under high energy p a r t i c l e radiation a t a f a s t e r r a t e than t h e 10 ohm-cm devices.

4

1.

INTRODUCTION

several s u b s t a n t i a l breakthroughs i n S i c e l l s have occurred i n recent years. The f i r s t of t h e s e was t h e discovery by Wysocki and co-workers [3] t h a t P on N S i c e l l s doped with L i i n t h e base e x h i b i t g r e a t l y improved r a d i a t i o n tolerance compared t o other c e l l s because of t h e i r a b i l i t y t o "recover" a f t e r t h e damage has occurred. Since t h i s discovery, Li-doped c e l l s have been made with AM0 e f f i c i e n c i e s of 13.8%. The second w a s t h e development by Lindmayer and Allison 141 a t Comsat Laboratories of a d i f f u s i o n technology which eliminates the heavily damaged (low l i f e t i m e , low mobility) so-called "dead region" a t t h e S i surface often caused by normal diffusion techniques. As a r e s u l t of t h e i r work, c e l l s with enhanced response a t blue and u l t r a v i o l e t wavelengths have been produced with AM0 e f f i c i e n c i e s of 15.5%; t h e same c e l l s a l s o e x h i b i t improved r a d i a t i o n tolerance compared t o t h e conventional S i cells. The t h i r d s i g n i f i c a n t development was the discovery [5] that d i f f u s i n g a heavily doped region a t t h e back contact t o t h e c e l l raises t h e output voltage of t h i n (3X10l8 2x1018 1x1019 1x1018 5X10l8 2x1018 1x1019 1x1017 1x1018 2x1018 5X101 2x1017

? ?

0.35 0.092 0.63 >O. 65 0.217 0.057 5.88 5.73 1.50 0.67 0.49 0.40

Zn (LPE) a Zn (LPE) zn (Boat) Zn (Boat) Ge W E ) Ge (WE) Ge (LPE) Ge (LPE) Ge ,Sn Ge,Sn Sn Ge (Si ?)

0.071 -

a LPE = liquid-phase epitaxy.

Ln

6-6.3 1.9-3.3 6 6- 7 4 1.6 23 18 10.5 5.5 7.5 6

2 -

n

Ref.

T

P

0.79 0.77 0.36 1.9

2.2 1.9 1.2

-

3.1-3.5

25 25 26 27 28 29 30 30 31 31 32 32 32 32 33

m

B.

PHOTOCURRENT DERIVATION FOR MONOCHROMATIC LIGHT

15

Surface recombination a t t h e f r o n t i s even more important f o r d i r e c t bandgap materials l i k e GaAs, where most c a r r i e r s a r e generated c l o s e t o t h e surface, than f o r i n d i r e c t ones l i k e S i where many c a r r i e r s a r e generated deep i n the material due t o t h e low absorption c o e f f i c i e n t a t long wavelengths (Fig. 4 ) . On the o t h e r hand, recombination a t the back surface i s more important f o r t h e i n d i r e c t gap, long l i f e t i m e materials such a s S i than f o r d i r e c t gap, low l i f e t i m e mater i a l s l i k e G a s . The recombination velocity a t t h e f r o n t of most S i and G a s s o l a r c e l l s i s i n t h e range 105-106 cm/sec, although etching t h e surfaces of bulk S i c r y s t a l s has been known t o reduce S t o around l o 2 cm/sec i n some cases. For polycrystalline devices, such as t h i n f i l m S i and G a A s s o l a r c e l l s , t h e recombination velocity a t t h e g r a i n boundaries is important, and if t h e grain s i z e i s much less than t h e diffusion length i n a s i n g l e c r y s t a l of t h e same doping l e v e l , the e f f e c t i v e l i f e t i m e and diffusion length i n t h e polycrystalline film are g r e a t l y reduced below t h e i r s i n g l e c r y s t a l values.

B.

Derivation of the Photocurrent f o r Monochromatic Light

The use of a n a l y t i c a l t o o l s t o p r e d i c t the behavior of s o l a r c e l l s , and i n p a r t i c u l a r t o p r e d i c t t h e e f f e c t of variables such as doping l e v e l and junction depth, has proven t o be very valuable i n t h e p a s t , even though t h e assumptions needed t o obtain a n a l y t i c a l expressions a r e violated t o a degree i n a c t u a l devices. The l i f e t i m e , mobility, and doping l e v e l i n t h e base of most s o l a r c e l l s are reasonably constant, b u t a r e functions of position i n t h e top region i f t h i s region i s produced by diffusion. Numerical analyses can be made which take these v a r i a t i o n s i n t o account provided t h a t these functions a r e known. However, a n a l y t i c a l expressions obtained by assuming average, constant values f o r these parameters and by assuming constant e l e c t r i c f i e l d s serve as useful f i r s t approximations i n predicting t h e expected behavior, and a r e f a r l e s s time consuming t o obtain and i n t e r p r e t than the numerical r e s u l t s . Numerical methods w i l l be p a r t i c u l a r l y valuable when very strong v a r i a t i o n s i n device parameters as a function of position are expected and when sunlight concent r a t i o n by a f a c t o r of 2 0 o r more i s used so t h a t "low inject i o n level" conditions no longer apply.

16

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

When l i g h t of wavelength X is incident on t h e surface of a semiconductor, t h e generation r a t e of hole-electron p a i r s as a function of distance x from t h e surface is G ( h ) = a(X)F(X) [ l - R ( X ) ]

exp(-U(A)X) r

(5)

where F ( X ) is t h e number of incident photons per cm2 per sec per u n i t bandwidth and R i s t h e number r e f l e c t e d from t h e surface. The photocurrent that these c a r r i e r s produce and t h e s p e c t r a l response ( t h e number of c a r r i e r s collected per incident photon a t each wavelength) can be determined f o r low i n j e c t i o n l e v e l conditions using t h e minority c a r r i e r continuity equations

f o r holes i n n-type material, and

for electrons i n p-type material. currents a r e

The hole and electron

respectively, where E is t h e e l e c t r i c f i e l d , pn and np a r e the photogenerated minority c a r r i e r d e n s i t i e s , and Prior npo a r e t h e minority c a r r i e r d e n s i t i e s i n e q u i l i b r i u m i n t h e dark. P/N junction s o l a r c e l l s can be represented by one of several d i f f e r e n t physical models, depending on how they a r e made. I n t h e simplest model, both s i d e s of t h e junction are taken t o be uniform i n doping, mobility, and l i f e t i m e ; t h i s can be used t o describe devices with grown top regions and as a f i r s t approximation t o devices with diffused t o p regions. I n t h e second model, electric f i e l d s e x i s t i n t h e base and/or top region a s a r e s u l t of doping nonuniformities, but t h e mobility and l i f e t i m e a r e s t i l l taken as constant i n order t o obtain an a n a l y t i c a l r e s u l t . I f t h e mobility and l i f e t i m e a r e allowed t o vary, numerical methods can be used t o obtain t h e s p e c t r a l response and s h o r t c i r c u i t current. I n t h e t h i r d model, t h e base is divided i n t o two s e c t i o n s w i t h d i s t i n c t l y d i f f e r e n t p r o p e r t i e s . This a p p l i e s , f o r example, t o t h e "back surface f i e l d " c e l l [5] where a p+ region i s d i f fused i n t o t h e back of t h e p-type base t o enhance both t h e s h o r t c i r c u i t current and open c i r c u i t voltage of t h e c e l l .

B.

PHOTOCURRENT DERIVATION FOR MONOCHROMATIC LIGHT

17

I n t h o s e i n s t a n c e s where a ”dead l a y e r ” i s believed t o e x i s t a d j a c e n t t o t h e s u r f a c e of t h e device due t o stress introduced by t h e junction d i f f u s i o n , t h e n-type d i f f u s e d t o p region of t h e c e l l can a l s o be divided i n t o two s e c t i o n s with d i f f e r e n t l i f e t i m e s and m o b i l i t i e s . I n each of t h e s e models, Eqs. ( 5 ) - ( 9 ) can be a p p l i e d t o t h e a p p r o p r i a t e regions and proper boundary conditions can be used t o o b t a i n t h e s p e c t r a l response and t h e photocurrent. 1.

UNIFORM N/P JUNCTIONS

I f t h e two s i d e s of t h e j u n c t i o n are uniform i n doping, then t h e r e are no e l e c t r i c f i e l d s o u t s i d e of t h e d e p l e t i o n region. This model a p p l i e s t o an e p i t a x i a l l y grown j u n c t i o n o r as a f i r s t approximation t o a d i f f u s e d junction. For t h e case of an N/P device, where t h e base i s p-type and t h e t o p s i d e i s n-type, Eqs. (6) and (8) can be combined t o y i e l d d2 (pn-Pno) Dp

dx2

+aF (1-R)

exp ( - a x )

-

( Pn-Pn 0 1

f o r t h e t o p s i d e of t h e junction. t h i s is

5 0

(10)

T

P The general s o l u t i o n t o

aF (1-R)T p (pn-pno) = A

exp (-ax) I

(11)

where $ i s t h e d i f f u s i o n l e n g t h , $ = ( D p ~ p ) 1/2. For a s i n g l e c r y s t a l device, t h e r e are two boundary c o n d i t i o n s ; a t t h e s u r f a c e , recombination t a k e s place: d (Pn-Pn n

a

P h y s i c a l l y , a t o p region with a narrow dead s e c t i o n near t h e s u r f a c e and a wider s e c t i o n of higher l i f e t i m e near t h e junct i o n edge is e s s e n t i a l l y equivalent t o a uniform t o p region with a high recombination v e l o c i t y at its s u r f a c e . Therefore, a “dead l a y e r ” i n t h i s book is modeled as a uniform t o p region with a 3 nsec l i f e t i m e and a s u r f a c e recombination v e l o c i t y of l o 6 cm/sec o r higher.

18

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

w h i l e a t t h e junction edge, t h e excess carrier density i s reduced t o zero by t h e electric f i e l d i n t h e depletion region

[x = x.1. 3

pn-pno = 0

(13)

Using these boundary conditions i n (111, t h e hole density i s found t o be (pn-pno) = [aF(l-R) ~ d ( a ~ % - l ) ] xj-x

sinh-

X

+cosh-

LP xj Y P sinh -+cosh -

-

DP

Lp

LP (14)

and the r e s u l t i n g hole photocurrent density per u n i t bandwidth a t the junction edge i s

.=[

qF (1-R) aLp

(a2L;-1)

]

-exp (-ax,)

(F

cosh j + s i n h

xj spLp sinh -+cosh Lp DP

LP xj -

LP

2) Lp

1

-aLp exp (-axj )

This is t h e photocurrent t h a t would be c o l l e c t e d from t h e top s i d e of a N/P junction s o l a r c e l l a t a given wavelength, assuming t h i s region t o be uniform i n l i f e t i m e , mobility, and doping l e v e l . To find t h e electron current c o l l e c t e d from t h e base of t h e c e l l , (7) and (9) are used, making t h e same approximation as before t h a t t h e base i s uniform i n i t s e l e c t r i c a l propert i e s . The boundary conditions are:

B.

PHOMCURReNT DERIVATION FOR MONOCHROMATIC LIGHT

(np-npo) = 0

[x =

19

(16)

Xj+WI,

Sn (nP-n PO) = -Dn[d(np-npo)/dx1

[x = HI,

(17)

where W is t h e width of t h e d e p l e t i o n region and H is t h e width of t h e e n t i r e cell. Equation (16) states t h a t t h e excess minority c a r r i e r d e n s i t y i s reduced t o zero a t t h e edge of t h e d e p l e t i o n region, while (17) states t h a t s u r f a c e recomb i n a t i o n t a k e s p l a c e a t t h e back of t h e c e l l . ( I f t h e back is covered with an O h m i c c o n t a c t , a p e r f e c t "sink" f o r t h e minority carriers e x i s t s and Sn can be taken a s i n f i n i t e . ) Using t h e s e boundary conditions, t h e e l e c t r o n d i s t r i b u t i o n i n a uniform p-type base is

aF (1-R) Tn (np-npO) =

[):r

-

( a2Li-l

1

I

H'

cosh --exp (-aH I ) +sinh Ln ( SnLJDn)

[

exp[-a(xj+W) 3 cosh

x-xj-w

-exp [-a(x-x j-W)

Ln

H'

-+aLn exp (-aH

I

Ln

sinh

s i n h (H ' /Ln) +cOSh (H /Ln)

I

x-xj-w

1

Ln (18) and t h e photocurrent p e r u n i t bandwidth due t o e l e c t r o n s c o l l e c t e d a t t h e junction edge is

H'

H'

SnL, Dn

H'

sinh- k o s h -

L n L ,

where H' i s t h e t o t a l c e l l thickness minus t h e junction depth and d e p l e t i o n width, H I = H-(x.+W). J Some photocurrent c o l l e c t i o n t a k e s p l a c e from t h e deplet i o n region as w e l l . The e l e c t r i c f i e l d i n t h i s region can be considered high enough t h a t photogenerated c a r r i e r s are a c c e l e r a t e d o u t of t h e d e p l e t i o n region before they can recombine, so that t h e photocurrent per u n i t bandwidth i s equal simply t o t h e number of photons absorbed

20

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOMCURRENT

Jdr = qF(1-R) exp(-axj) [l-exp(-aW) I .

(20)

The t o t a l s h o r t c i r c u i t photocurrent a t a given wavelength i s then t h e sum of (151, (191, and ( 2 0 ) , * and t h e s p e c t r a l response i s equal t o t h i s sum d i v i d e d by qF(1-R) ( i n t e r n a l response) o r qF ( e x t e r n a l l y observed response). A l l of these equations from (12) t o (19) can be t r a n s formed from t h e i r p r e s e n t form f o r N/P c e l l s t o e q u i v a l e n t s f o r P/N c e l l s by interchanging 41, Dn, ‘ c ~ ,and Sn with Lp, D T and S respectively. P’ P’ P’ 2.

CONSTANT ELECTRIC FIELDS

Losses due t o s u r f a c e and bulk recombination can be reduced by decreasing t h e j u n c t i o n depth and s u r f a c e recombination v e l o c i t y and by i n c r e a s i n g t h e minority carrier d i f f u s i o n l e n g t h , p a r t i c u l a r l y i n t h e base. Another way t h a t l o s s e s can be reduced is t o provide electric f i e l d s i n one o r both regions of t h e c e l l t o aid i n moving photogenerated carriers toward t h e junction. ( I n t h e o r y , d i f f u s i o n processes provide electric f i e l d s a u t o m a t i c a l l y by e s t a b l i s h i n g concent r a t i o n g r a d i e n t s of donors o r a c c e p t o r s . I n r e a l i t y , t h e dependence of t h e d i f f u s i o n c o e f f i c i e n t on t h e impurity conc e n t r a t i o n can almost e l i m i n a t e t h e g r a d i e n t and t h e hoped-for d r i f t f i e l d (34-361.) When such a f i e l d i s p r e s e n t , t h e energy band edges a r e sloped, r a t h e r than f l a t as i n Fig. 3, and t h e f i e l d a t any p o i n t is given by t h e s l o p e

E = ( l / q ) (dEc/dx) = (l/q) (dEv/dx) = WP)( 1 / N ) (dN/dx)

(21)

where N i s t h e i o n i z e d impurity c o n c e n t r a t i o n . The f i e l d i n t h e d i f f u s e d region is largest a t the edge of t h e j u n c t i o n and smallest a t t h e s u r f a c e of t h e device; it would b e b e t t e r f o r t h e purposes of overcoming s u r f a c e recombination i f it were t h e o t h e r way around. Using (6) and (81, t h e c o n t i n u i t y equation f o r h o l e s i n t h e d i f f u s e d n-type region becomes

bThese equations are v a l i d f o r all. wavelengths except t h e special case where aL = 1, and they have t h e c o r r e c t l i m i t as aL 1. For d i s c u s s i o n s and d e r i v a t i o n s of t h i s special case, r e f e r e n c e i s made t o Wolf [341. -f

B. PHOTOCURRENT DERIVATION FOR MONOCHROMATIC LIGHT

21

with the boundary conditions

Wolf [341, Ellis and Moss [37], and others have solved these relationships for the special case where the electric field, mobility, and lifetime are taken to be constant across the diffused region. The photocurrent from the diffused region is then [34] qF (1-R) *Lpp

Jp =

(a+Epp)'gP-l

[

(Fpp$$

(a+Epp)Lpp exp (Eppx,1 -exp (xj/Lpp)exp (-axj1 sinh2osh-

LPP (-+EppLpJ 4.

(FP)

(exp (Eppxj1-exp (xj/Lpp)exp (-ax, X

1

-exp(-axj) [ (a+EPP)LPP-q is the normalized electric field in the n-type Epp = qE/2kT

and $p

is an effective diffusion length

When the electric field, lifetime, and mobility cannot be approximated as constant throughout the diffused region, the continuity Eq. (22) becomes far more complex and an analytical solution cannot be obtained. Numerical methods must then be used as has been done by Tsaur et al. [38] for GaAs solar cells, or Fossom 1391 for Si solar cells. The equations above are valid provided that the carriers accelerated by the field do not reach their saturation drift velocity, which occurs at junction depths of around 1000 f l .

22

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

In addition to a drift field in the top region, it is possible to obtain an electric field in the base as well by providing a concentration gradient there, with the lowest doping concentration at the junction edge and increasingly higher concentrations toward the back contact. This electric field aids the collection of carriers generated at low photon energies and is capable of improving the resistance of the cell to radiation degradation [34,37,40-421. The photocurrent in the p-type base can be calculated from (7) and (9)

(np-npo) = 0

[x = xj+Wl

,

Dn(dnp/dx)+v n E = -Sn(n -n ) n P P PO

(29) [X = HI

which are analogous to (16) and (17). If the approximations are made that the field, lifetime, and mobility are constant in the base, the photocurrent at a given wavelength derived from these relationships is [341

(31) where Wolf's [34] equation has been modified slightly to account for the finite width of the depletion region, and En, and hnare defined in the same way as (26) and (27). Without the assumptions of constant material parameters as a function of position in the base, an analytical result for the photocurrent cannot be obtained, and numerical computations must be used [40-421. None of the numerical calculations made so far have been completely satisfactory, since all of them involve approximations and assumptions of various types. The most rigorous calculation to date has been that

B.

PHOMCURRENT DERIVATION FOR MONOCHROMATIC LIGHT

Diagram o f a solar cell i n which the b a s e can be d i v i d e d i n t o two r e g i o n s w i t h d i f f e r e n t doping levels, m o b i l i t i e s , l i f e times, and electric f i e l d s . FIG. 6 .

Region 1

Diffused Region

23

Region 2

Back Contract

of Van Overstraeten and Nuyts 1421. They divide t h e base i n t o a f i r s t region near t h e junction where t h e f i e l d , l i f e t i m e , and mobility a r e a l l variables, and a second region extending t o t h e back O h m i c contact i n which t h e l i f e t i m e and mobility a r e constant and the f i e l d i s zero (Fig. 6). Using numerical i n t e g r a t i o n , they calculated t h e photocurrent t h a t would be obtained under various conditions i n S i devices and showed t h a t t h e photocurrent is most strongly affected by t h e f i r s t 1 0 or 20 pm of t h e base adjacent t o t h e junction edge; t h e impurity concentration should be small and t h e mobility, l i f e time, and e l e c t r i c f i e l d should be high i n t h i s f i r s t 2 0 pm t o obtain t h e highest c o l l e c t i o n efficiency. 3.

BACK SURFACE FIELD, HIGH-IIIW JUNCTION

A dramatic improvement i n t h e output voltage of S i s o l a r c e l l s has been noted i n t h e l a s t few years with t h e advent of In t h i s device, t h e "back surface f i e l d " (BSF) c e l l [5,43,441. t h e f r o n t (junction) p a r t of t h e c e l l i s made i n t h e normal way, but t h e back of t h e c e l l , instead of containing j u s t a metallic Ohmic contact t o t h e moderately high r e s i s t i v i t y base, has a very heavily doped region adjacent t o t h e contact. In Fig. 6 f o r example, base region 1 represents the normal 1 t o 10 ohm-cm portion while region 2 represents t h e more heavily doped layer adjacent t o t h e contact. Region 2 i s t y p i c a l l y only a micron o r two wide i f made by diffusion o r alloying, but i n some schemes region 1 i s made narrow (10 pm) and region 2, wide by growing a l i g h t l y doped e p i t a x i a l layer on a heavily doped substrate. The advantages of t h e e x t r a region can be seen with t h e help of t h e band diagram of Fig. 7. The p o t e n t i a l energy b a r r i e r $p between t h e two base regions tends t o "confine" minority c a r r i e r s i n t h e more l i g h t l y doped region, away from t h e Ohmic contact a t t h e back with i t s i n f i n i t e surface recombination velocity. I f Wp i s comparable t o o r less than t h e

24

2.

FIG. 7.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

Energy band diagram of a BSF (blocking back c o n t a c t )

device.

diffusion length Ln i n region 1, then some of t h e electrons t h a t would have been l o s t a t t h e back surface cross t h e p-n junction boundary instead, enhancing t h e s h o r t c i r c u i t current. To a f i r s t approximation, t h e BSF c e l l can be modelled as a normal c e l l of width (x.+W+W ) having a very small recombinaJ P t i o n velocity a t t h e back [Eqs. (19) or (31) with Sn = 01 provided Wp >> W + P -. The open c i r c u i t voltage of N on P BSF c e l l s with 10 ohmcm base r e s i s t i v i t y is around 10%higher than conventional c e l l s of t h e same type (0.6 V compared t o 0.55 V) , probably due t o a combination of t h r e e f a c t o r s : t h e increased s h o r t c i r c u i t current [see Eq. ( l ),] a decrease i n 10 ( t h e diode "leakage" current) due t o reduced recombhation a t t h e back surface of electrons i n j e c t e d from t h e n+ top region i n t o t h e base, and a modulation of t h e b a r r i e r $Jpby t h e change i n minority c a r r i e r d e n s i t i e s a t t h e high-low junction edge, i . e . , when the c e l l i s open c i r c u i t e d , a portion of t h e b a r r i e r $Jp might appear a t t h e output terminals i n addition t o t h e voltage from the p-n junction. C.

Spectral Response

The photocurrent collected B t each wavelength r e l a t i v e t o the number of photons incident on t h e surface a t t h a t wavelength determines t h e s p e c t r a l response of t h e device (sometimes known a s t h e quantum e f f i c i e n c y or c o l l e c t i o n efficiency a t each wavelength). The "internal" s p e c t r a l response i s defined a s t h e number of electron-hole p a i r s collected under short c i r c u i t conditions r e l a t i v e t o t h e number of photons e n t e r i n g t h e material

C.

1.0

SPECTRAL RESPONSE

3.0 4.0 Photon Energy, eV

2.0

25

5.0

F I G . 8 . Computed i n t e r n a l s p e c t r a l r e s p o n s e s o f S i N / P c e l l s w i t h uniformly doped r e g i o n s . The s o l i d l i n e s a r e f o r 1 0 , 1 , and 0 . 1 ohm-em b a s e resistivities and S f r o n t = l o 5 cm/sec. The d o t t e d l i n e s a r e f o r 1 ohm-em b a s e s w i t h v a r y i n g S f r o n t . O t h e r parameters, H = 450 Pm, x j = 0 . 5 Pm, Shack = Q). No d r i f t f i e 1d .

while the "external" response i s j u s t t h e i n t e r n a l one modif i e d by r e f l e c t i o n of l i g h t from the surface of t h e device SR(X)ext

= SR(X) [l-R(X) 1 .

(33)

The r e f l e c t i o n of l i g h t from the surface as a function of wavelength e n t e r s i n t o t h e experimentally observed s p e c t r a l response', but i n general the technology of a n t i r e f l e c t i v e coatings on s o l a r c e l l s has been developed t o such a high degree t h a t t h e r e f l e c t i o n and i t s v a r i a t i o n with wavelength can be ignored t o a f i r s t approximation when comparing measured s p e c t r a l response curves t o predicted ones. 1.

CALCULATED RESPONSES

The i n t e r n a l s p e c t r a l responses of S i N/P c e l l s f o r t h e simplest case of uniformly doped top and base regions a r e shown i n Fig. 8 , as calculated from (15), (19) , (20), and (32) using t h e device parameters l i s t e d i n Table 4. The s o l i d l i n e s demonstrate t h e e f f e c t of varying t h e r e s i s t i v i t y

TABLE 4

N QI

Solar C e l l Parameters for Si, 300°K

10 1 0.1

1.25~10~ 1.5X10l6 5x1017

1390 1040 420

P on N c e l l s . PBase

Nd

(n-cm)

(cm-3)

10 1 0.1

4. 5x1Ol4 5 . 1 ~ 1 0 ~ ~ 8. 5X10l6

PP (cm2/v. sec) 580 500 350

36 27 10.9

Na = 5

~

15x10' 10x10-6 2. 5x10-6

0.93 0.28 0.05

0.867 0.930 1.022

1 Dn 0 =~ 2.15, ~ ~ T~ = 1.1x10-6

DP (cm2/sec) 15 13 9

232 164 52.2

T

P

(SeC)

15x107.5~10-~ 1.5~10'~

LP (10-4 c m ) 150 98.5 36.9

W (0 b i a s )

d'

(10'~ cm)

(V)

1.5 0.47 0.12

0.814 0.877 0.950

.

C.

SPECTRAL RESPONSE

27

-

1.2

2.0 2.8 3.6 Photon Energy, eV

4.4

F I G . 9 . Computed i n t e r n a l s p e c t r a l response o f a S i N/P cell showing t h e i n d i v i d u a l w n t r i b u t i o n s f r o m each o f t h e t h r e e regions.

of t h e base while keeping t h e surface recombination velocity and junction depth constant. Raising t h e doping l e v e l i n t h e base lowers t h e l i f e t i m e and diffusion length i n t h e base, increasing t h e l o s s of c a r r i e r s generated deep i n the material and degrading the low energy response. The dashed l i n e s show what happens t o t h e high energy response a t various surface recombination v e l o c i t i e s f o r constant base parameters. A t high photon energies, a l l t h e c a r r i e r s a r e generated near t h e surface because of t h e high absorption c o e f f i c i e n t s a t these energies, and losses due t o high S o r poor l i f e t i m e i n t h e diffused N-type region become c r i t i c a l . Above 3.5 eV where t h e s p e c t r a l response derives e n t i r e l y from t h e N surface region, t h e response (32) s a t u r a t e s a t a value given by

e

Since t h e S i absorption c o e f f i c i e n t a is r e l a t i v e l y constant a t 1 - 2 X 1 O 6 cm'l from 3.5 t o 4.0 e V (Fig. 41, t h i s r e l a t i o n s h i p could be used t o estimate S from a measured s p e c t r a l response P i f t h e value of Dp i s known i n t h e diffused N region. For low values of surface recombination velocity the response remains high and r e l a t i v e l y f l a t over t h e whole s p e c t r a l region. This i s t h e type of response t h a t should be obtained f o r " v i o l e t c e l l s , " Schottky b a r r i e r c e l l s , and c e r t a i n types of heterojunctions with t h i n , high bandgap transparent semiconductor layers on S i o r G a s substrates.

28

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

TABLE 5 Solar C e l l Parameters f o r GaAs, 300OK.

Top Region N, = 2x1019 cm-3 Dn = 32.4 cm2/sec T~ = 1x10-9 sec

L, = 1.8 p

P on N

Base Region Q = 2x1017 cm-3

D~ = 5.7 cm2/sec T~ = 1 . 5 8 ~ 1 0 - sec ~ Lp = 3.0 pm

w = 0.09 p vd = 1 - 4 0 v n i = 1 . 1 ~ 1 0 7cm-3 I n Fig. 9, t h e s p e c t r a l response of t h e 1 ohm-cm N/P Si c e l l with Sp = l o 4 cm/sec a s shown i n Fig. 8 i s divided i n t o i t s t h r e e components, t h e base, t h e diffused top region, and t h e depletion region contributions. A t low energies, most of the carriers are generated i n t h e base because of t h e low absorption c o e f f i c i e n t s , but as t h e photon energy increases above 2.4 e V , the diffused s i d e of t h e junction takes over. I f the junction depth i s made smaller than t h e 0.5 pm shown here, t h e contribution from t h e base increases s l i g h t l y and t h e crossover moves t o s l i g h t l y higher energies, but more importantly, t h e contribution from t h e diffused s i d e a t high energies i s enhanced because of reduced l o s s e s due t o surface and bulk recombination. Most N/P cells made today have junction depths i n t h e 0.3-0.5 range, while t h e " v i o l e t c e l l " has a junction depth of only 0.1-0.2

pm.

The contribution from t h e depletion region is considerable i n the 2.0 t o 2.9 eV range f o r t h e 1 ohm-cm device shown i n Fig. 9. The depletion region contribution becomes g r e a t e r a t higher base r e s i s t i v i t i e s and narrower junction depths , and less f o r lower r e s i s t i v i t i e s and l a r g e r depths, but it never becomes a s l a r g e as t h e diffused region component under any p r a c t i c a l conditions because of t h e very high value of u above 3.2 eV (Fig. 4 1 , which causes almost a l l t h e l i g h t a t high energies t o be absorbed i n t h e f i r s t 1000 o r so. The calculated i n t e r n a l s p e c t r a l responses of N/P G a A s c e l l s with uniformly doped regions f o r s e v e r a l surface recombination v e l o c i t i e s are shown i n Fig. 10, using t h e device parameters of Table 5. GaAs is a d i r e c t bandgap material with a steep absorption edge. V i r t u a l l y a l l t h e carriers generated by sunlight above 1.4 e V a r e generated i n t h e f i r s t 3 pm from t h e surface, and 50%of a l l t h e c a r r i e r s a r e generated within t h e f i r s t 1/2 p. This makes t h e p r o p e r t i e s of t h e top s i d e

C.

SPECTRAL RESPONSE

29

1.o gl

a

0.8

0.6

!i

v)

Om4 0.2

- 0

1.5

2.0 2.5 3.0 3.5 Photon Energy, eV

4.0

F I G . 1 0 . Computed i n t e r n a l s p e c t r a l responses of GaAs P / N solar cells w i t h uniformly doped t o p and base regions for various f r o n t s u r f a c e recombination velocities. H = 300 m, x j = 0 . 5 p m , s b c k -- w. Device parameters of Table 5 .

of t h e junction much more important than i n s i l i c o n , and t h e base of t h e c e l l correspondingly less important. High values of f r o n t s u r f a c e recombination v e l o c i t y and low values of l i f e t i m e and d i f f u s i o n length i n t h e t o p region cause a s t r o n g decrease i n t h e s p e c t r a l response with i n c r e a s i n g photon energy as c a r r i e r s are generated c l o s e r and c l o s e r t o t h e surface. These high s u r f a c e l o s s e s can be p a r t l y overcome by making t h e junction depth small, a s i n S i cells, o r by e s t a b l i s h i n g an a i d i n g electric f i e l d a t t h e surface. To demonstrate the value t h a t a i d i n g electric f i e l d s can have i n improving t h e carrier c o l l e c t i o n e f f i c i e n c y , t h e spect r a l response of an N/P S i c e l l w a s c a l c u l a t e d from ( 2 0 ) , (25), and (31) both with and without electric f i e l d s ; t h e r e s u l t s are seen i n Fig. 11. To i l l u s t r a t e t h e e f f e c t of t h e f i e l d s more s t r i k i n g l y , r e l a t i v e l y poor c e l l conditions were adopted f o r t h e c a l c u l a t i o n s . The l i f e t i m e i n t h e d i f f u s e d t o p region has been assumed t o be low, corresponding t o measured l i f e t i m e s i n S i c e l l s , and t h e s u r f a c e recombination v e l o c i t y has been assumed high. (For t h e uniform doping (zero f i e l d ) c a s e , t h e base r e s i s t i v i t y has been taken a s 1 ohm-cm. For t h e calculat i o n including electric f i e l d s , t h e base i s assumed t o have a a t t h e junction edge doping l e v e l of a few times 1014 with an i n c r e a s e t o a few t i m e s lo1’ s e v e r a l hundred microns The f i e l d i n away, r e s u l t i n g i n an average f i e l d of 10 V/cm. t h e d i f f u s e d N - t y p e region i s taken a s 4400 V/cm.) The electric f i e l d i n t h e base region enhances t h e response a t low energies by d r i f t i n g c a r r i e r s toward t h e junction t h a t (The c o n t r i b u t i o n might o r d i n a r i l y be l o s t deep i n s i d e t h e S i .

30

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

-

1.2

2.0

2.8

3.6

4.4

Photon Energy, eV

FIG. 11. Computed i n t e r n a l s p e c t r a l responses of S i N/P cells both with ( s o l i d ) and w i t h o u t (dashed) electric f i e l d s . (The c o n t r i b u t i o n from the d e p l e t i o n r e g i o n is not shown individually, b u t is included i n t h e total.) Sfront = l o 5 cm/sec, T = 5x10’9 sec, H = 450 p m , x j = 0.5 um, S h c k = 00. P from t h e base i n t h e f i e l d c a s e f o r e n e r g i e s above 1.6 e V can a c t u a l l y be a b i t less t h a n f o r uniform doping, however, because t h e d e p l e t i o n region width i s greater f o r t h e lower doping a t t h e junction edge i n t h e f i e l d c a s e compared t o t h e zero f i e l d case, and some of t h e carriers t h a t would have been c o l l e c t e d from t h e base i n t h e uniformly doped c e l l are generated and c o l l e c t e d i n t h e d e p l e t i o n region i n s t e a d i n t h e d r i f t f i e l d cell. The sum of t h e c o n t r i b u t i o n s frcun t h e base and t h e d e p l e t i o n region is higher when the base d r i f t f i e l d e x i s t s than for uniform doping.) The most dramatic improvement due to electric f i e l d s i s seen i n t h e response from t h e d i f f u s e d t o p region. The combin a t i o n of poor l i f e t i m e and high recombination v e l o c i t y a t t h e f r o n t s u r f a c e causes a s t r o n g decrease i n t h e response with i n c r e a s i n g photon energy when no f i e l d i s p r e s e n t ; t h e response is considerably b e t t e r i f an a i d i n g electric f i e l d is p r e s e n t i n t h e t o p region. The same improvement i n s p e c t r a l response can be seen i n Fig. 12 f o r a GaAs P/N c e l l with a f i e l d of 1280 V/cm i n t h e 0.5 wide d i f f u s e d t o p region. The recombination v e l o c i t i e s on GaAs s u r f a c e s tend t o l i e i n t h e 106-107 range, an orderof-magnitude or more g r e a t e r t h a n t h e v a l u e s found on S i s u r faces. Incorporating a n a i d i n g d r i f t f i e l d and/or reducing t h e junction depth can be very b e n e f i c i a l i n overcoming t h e high carrier l o s s e s experienced i n t h e d i f f u s e d t o p region.

SPECTRAL RESPONSE

C.

P

VJ

1

0.2 0.0

No Field

-

-

''

I

1.5

I

I

I

I

2.0 2.5 3.0 3.5 Photon Energy, eV

31

I

4.0

F I G . 1 2 . Computed i n t e r n a l s p e c t r a l r e s p o n s e s o f GdAs P/N c e l l s , showing t h e improvement o b t a i n e d e i t h e r b y i n c l u d i n g a d r i f t f i e l d i n the t o p r e g i o n or b y reducing t h e j u n c t i o n d e p t h . ( x j = 0 . 5 vm u n l e s s o t h e r w i s e n o t e d . No f i e l d i n the b a s e . Device parameters o f T a b l e 5 . S = l o 6 cm/sec.

Shack

=

*.)

Another method f o r overcoming t h e e f f e c t s of surface recombination and reducing losses due t o bulk recombination i n t h e diffused region i s t o grow a heavily doped, high bandgap semiconductive layer on t h e surface of the diffused region, choosing a material which closely matches t h e l a t t i c e propert i e s of t h e c e l l material. This method has been used with considerable success f o r G a A s s o l a r c e l l s [8,9,36,45], where Gal,xA1xAs i s grown by liquid-phase epitaxy onto G a A s subs t r a t e s . A schematic of t h e s t r u c t u r e and t h e energy band l a y e r is transdiagram a r e shown i n Fig. 13. The Gal,&,+ parent t o most sunlight, and eliminates t h e surface s t a t e s

n GoAs

FIG. 1 3 . Gal,fil&-GaAs (b) energy band diagram.

solar c e l l :

(a) structure,

32

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

Y

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Photon Energy, eV

F I G . 1 4 . Computed i n t e r n a l s p e c t r a l r e s p o n s e s of pGal-xAlxAsgGaAs-nGaAs c e l l s a s a function of the G a l , g l , $ s thickness ( i n m i c r o n s ) . Aluminum w m s i t i o n is 0 . 8 6 . Na = 2X1019 Nd = 2x1017 cm-3, Stop = 10 c m / s e c , Sinterface = 104 c m / s e c . L t o p = 0.27 urn, L * a s = 1.8 m, L d a s = 3.0 urn, X j = 0.5 um, H = 300 m, shack = 00.

!?

and o t h e r imperfections on t h e G a A s P/N j u n c t i o n s u r f a c e t h a t would o r d i n a r i l y r e s u l t i n a high recombination v e l o c i t y . The p-type l a y e r also forms an Ohmic c o n t a c t t o t h e p G a A s region and allows t h i s region t o be m o r e l i g h t l y doped, which improves t h e l i f e t i m e and lowers t h e bulk recombination b u t without c r e a t i n g series resistance problems. Photogenerated e l e c t r o n s i n t h e pGaAs r e g i o n are prevented from e n t e r i n g t h e G a l - x A l x A s l a y e r by t h e energy d i s c o n t i n u i t y AEc i n t h e conduction band t h a t arises from t h e d i f f e r e n c e i n e l e c t r o n a f f i n i t i e s o f t h e two materials. Figure 14 shows t h e computed spectral response of a Gal,xAlxAs-GaAs s o l a r c e l l as a f u n c t i o n of t h e t h i c k n e s s of t h e Gal-xAlxAs l a y e r . The recombination v e l o c i t y of l o 6 cm/sec a t t h e s u r f a c e o f t h e d e v i c e would o r d i n a r i l y r e s u l t i n a dec r e a s i n g response a t i n c r e a s i n g photon e n e r g i e s , as shown i n Fig. 1 0 , b u t t h e low recombination v e l o c i t y a t t h e i n t e r f a c e i n t h e Gal,fil,$s d e v i c e e l i m i n a t e s t h e u s u a l s u r f a c e loss. Light below 2.4 e V passes through t h e semitransparent Gal,xA1xAs l a y e r and i s absorbed i n t h e underlying G a s j u n c t i o n , which has a recombination v e l o c i t y a t its "surface" ( t h e i n t e r f a c e ) of lo4 cm/sec or less. Above 2 . 4 e V , t h e response begins t o A s the c u t o f f due t o a b s o r p t i o n of l i g h t i n t h e Gal-xA1xAs. Gal-xA1&s i s made t h i n n e r , however, it absorbs less and t h e c u t off is moved t o higher e n e r g i e s . I f t h e t h i c k n e s s is

C. 1.o

I

I

I

SPECTRAL RESPONSE I

33

-

I

1.0

1.2

1.4 1.6 1.8 Photon Energy, eV

2.0

F I G . 1 5 . Computed internal spectral responses of N / P S i c e l l s ( 1 ohm-cm, 4 m i l ) with e i t h e r a BSF &back = 10) or an O h m i c back contact ( s h c k = a). Parameters o f Table 4 . No d r i f t f i e l d i n base.

reduced s t i l l f u r t h e r , so t h a t it becomes comparable t o t h e electron diffusion length, some of the c a r r i e r s generated i n t h e Gal,&l&s w i l l d i f f u s e t o t h e i n t e r f a c e and add t o t h e c o l l e c t i o n from the pGaAs, f u r t h e r increasing t h e response a t high energies. The low energy response from the base of S i c e l l s can be improved by t h e addition of a back surface f i e l d (Fig. 7) as well as by a d r i f t f i e l d close to the junction. The back surface f i e l d (BSF) configuration with a back region Wp+ much thinner than t h e main region Wp is equivalent i n f i r s t approximation t o a normal device with a very low recombination veloci t y a t the back surface [431. The e f f e c t i v e low recombination velocity reduces t h e l o s s of photogenerated c a r r i e r s t h a t would o r d i n a r i l y occur a t the back contact, enhancing t h e s p e c t r a l response a t low photon energies as seen i n Fig. 15 f o r a 4 - m i l t h i c k S i c e l l . The improvement i n t h e low energy s p e c t r a l response by addition of t h e p+ region i s g r e a t e r f o r t h i n cells than for thick ones; the influence of t h e back contact becomes s m a l l i f the thickness of t h e base i s much more than a diffusion length. 2.

MEASURED RESPONSES

The calculated s p e c t r a l responses of solar c e l l s are i n reasonable agreement with measured ones, even though many of t h e assumptions used i n order t o obtain a n a l y t i c a l expressions

34

2.

CARRIER COLLECTION , SPECTRAL RESPONSE PHOMCURRENT 1.O

t 0.8 6

n -

0.6

0

& 0.4 0

0 Q

* 0.2 "

1.o

2.0

3.0

4.0

Photon Energy, eV

FIG. 16. Relative spectral responses (measured) of N/P Si s o l a r cells. (1) Low lifetime (dead l a y e r ) , high s u r f a c e recombination velocity device, with X j = 0 . 3 - 0 . 4 ~ u n/461. ( 2 ) No dead l a y e r , x j = 0.1-0.2 urn, " v i o l e t cell" [ 4 ] .

a r e not accurate i n describing r e a l devices. Certainly t h e q u a l i t a t i v e behavioral trends of measured devices having d i f f e r e n t l i f e t i m e s , d i f f u s i o n lengths, e l e c t r i c f i e l d s , e t c . , a r e predicted very w e l l by t h e a n a l y t i c a l expressions, and comparing measured s p e c t r a l responses of devices with ones predicted by theory is a very good method f o r studying s o l a r cells and t h e e f f e c t s of changes i n design, f a b r i c a t i o n processes, material parameters, and t h e l i k e , on t h e device behavior. The wavelength dependence o f t h e a n t i r e f l e c t i o n coating can e a s i l y be taken i n t o account, o r even ignored t o a f i r s t approximation. Spectral responses are measured using a monochromatic source of l i g h t , a d e t e c t o r , and a recording instrument. The l i g h t source can be a well-calibrated g r a t i n g o r prism spectrometer o r a s e t of narrow bandpass f i l t e r s , together with a high color temperature bulb. The d e t e c t o r i s used t o meas u r e e i t h e r t h e p o w e r of t h e monochromatic beam a t each wavelength or t o measure t h e number of photons i n t h e beam d i r e c t l y ; "black" d e t e c t o r s which need no correction f o r wavelength a r e t h e most convenient but any detector with a known wavelength response can be used. A recording must be made of both t h e detector output and t e s t c e l l output a t each wavelength t o obtain t h e response of t h e c e l l . Low frequency beam-chopping and loc-in amplification are o f t e n used t o obtain b e t t e r signal-to-noise r a t i o s a t low i n t e n s i t i e s . It has proven convenient i n s o l a r c e l l s t u d i e s t o normali z e t h e measured s p e c t r a l response to unity a t t h e wavelength of maximum response; t h e r e s u l t is c a l l e d t h e r e l a t i v e s p e c t r a l

C.

SPECTRAL RESPONSE

35

Photon Energy, eV

F I G . 1 7 . R e l a t i v e spectral responses (measured) of a d i f f u s e d P/N GaAs solar cell and of a G a l - f l l g s - G a A s solar cell ( G a l , p l f l s thickness = 0 . 7 pm, x = 0 . 8 5 ) .

response. Then, i f t h e absolute response (quantum efficiency) i s measured a t any one wavelength, as with a l a s e r , t h e absol u t e response a t a l l wavelengths i s obtained. @en response curves a r e published, it i s usually t h e r e l a t i v e ones t h a t a r e given. Figure 16 shows t h e r e l a t i v e s p e c t r a l response as a funct i o n of photon energy of a standard type of 10 ohm-cm, diffused S i N/P c e l l . The response begins a t the bandgap energy, reaches a peak a t around 1.5 e V , and decreases with increasing energy due t o a combination of very s h o r t l i f e t i m e (perhaps less than 1 nsec) i n t h e diffused region and a high surface recombination velocity. An e l e c t r i c f i e l d may e x i s t over a t l e a s t a portion of t h e diffused n-region, but it is apparently i n s u f f i c i e n t t o overcome t h e high losses. The s p e c t r a l response of a "viol e t c e l l " as developed by Lindmayer and Allison [41 a t Comsat Laboratories i s a l s o shown i n Fig. 16. In t h i s c e l l t h e heavi l y damaged, nanosecond l i f e t i m e "dead layer" i n t h e diffused region has been largely eliminated by reducing t h e concentrat i o n of t h e phosphorus and by making t h e junction depth much smaller than usual. The combination of higher l i f e t i m e near t h e surface and narrower junction g r e a t l y improves t h e response a t high energies. Evidence of t h e s a t u r a t i o n predicted by the t h e o r e t i c a l r e s u l t s (Fig. 8) can be seen. Experimental r e s u l t s f o r G a A s and Gal,xA1fis-covered GaAs P/N junctions are shown i n Fig. 17. The GaAs device shows the c h a r a c t e r i s t i c triangular-shaped response due t o

36

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT 1.o

0.8

8

f 0.6

Q

0.2 0

1.0

1.4

1.8

2.2

Photon Energy, eV

2.6

3.0

F I G . 1 8 . R e l a t i v e s p e c t r a l responses (measured) o f Cu2S-CdS t h i n f i l m solar cells f o r i n c r e a s i n g C u p t h i c k n e s s ( t h e numbers refer to i n c r e a s i n g t h i c k n e s s ) . Light i n c i d e n t on Cu2S s u r f a c e ( a f t e r Mytton [471, w i t h permission from The I n s t i t u t e of Physics and the Physical S o c i e t y r London).

a high s u r f a c e recombination v e l o c i t y and a l a r g e junction depth t o d i f f u s i o n l e n g t h r a t i o . The Gal,xAlxAs l a y e r e l i m i n a t e s t h e s u r f a c e losses b u t a t t e n u a t e s some of t h e high energy l i g h t due t o a b s o r p t i o n i n the l a y e r . The spectral responses for f r o n t i l l u m i n a t i o n of t h i n f i l m p o l y c r y s t a l l i n e CdS s o l a r cells as presented by Mytton (471 are shown i n Fig. 18. These devices are made by evapor a t i n g a t h i n CdS f i l m o n t o a conducting substrate, p l a t i n g a l a y e r of copper onto t h e CdS s u r f a c e , converting a t h i n region o f t h e CdS t o CuxS, and providing O h m i c c o n t a c t s i n g r i d form t o t h e CuxS. The CuxS l a y e r ( u s u a l l y 1000 t o 3000 A t h i c k ) has a bandgap of about 1.1 e V , and provides most o r a l l of t h e response below t h e bandgap of t h e CdS (2.4 eV), while t h e CdS l a y e r c o n t r i b u t e s most of t h e response above 2 . 4 eV. The f o u r curves i n Fig. 18 show t h e e f f e c t of i n c r e a s i n g t h e CuxS thickness by varying t h e p l a t i n g t i m e s . I f t h e CuxS i s very t h i n , i t s transparency is too high and no l o w energy response i s p r e s e n t (curves 1 and 2 ) . I f it is t o o t h i c k (compared t o a d i f f u s i o n l e n g t h ) , then carriers generated close t o t h e CuxS s u r f a c e may be lost, which decreases t h e response below 2.4 e V , while a t t h e same time less response i s obtained from t h e CdS above 2.4 e V because less l i g h t penet r a t e s through t o it (curve 4 ) . The optimum CuxS t h i c k n e s s is around 2000 fi (curve 3 ) , which r e s u l t s i n some response from both t h e CuxS and C d s .

SHORT CIRCUIT CURRENT

D. I

I

5-

1

37

I

4 -

3X

e 2-

3 0

.c

0

100.2

0.4

0.6

0.8

1.0

1.2

Wavelength, microns

FIG. 19. Solar i r r a d i a n c e i n photons p e r cm2 p e r second i n a 100 bandwidth for o u t e r s p a c e (AMO) c o n d i t i o n s and for average weather c o n d i t i o n s on e a r t h (RM2). Higher responses between 1.1 and 2.4 e V are obtained when t h e Cu,S l a y e r s are of higher q u a l i t y i n terms of d i f f u s i o n length. Higher responses are a l s o obtained i n t h i s range of wavelengths f o r 'back-wall" cells where t h e device is constructed i n such a way t h a t it can be illuminated through t h e CdS, b u t t h e response abwe 2.4 e V i s reduced i n t h e s e cells because of a t t e n u a t i o n by t h e CdS i t s e l f . D.

S h o r t C i r c u i t Current

1.

CALCULATED PHOTOCURRENT

I n ' a d d i t i o n t o i t s value as a t o o l i n studying s o l a r c e l l s , t h e spectral response can b e used t o compute t h e expected s h o r t c i r c u i t photocurrent f o r any given spectral input. Since t h e spectral response r e p r e s e n t s t h e number of carriers c o l l e c t e d p e r i n c i d e n t photon, t h e photocurrent d e n s i t y per u n i t bandwidth a t a given wavelength is given by

where t h e e x t e r n a l response, Fq. ( 3 3 ) , which includes t h e ref l e c t i o n of l i g h t from t h e s u r f a c e , is used. The t o t a l photoc u r r e n t d e n s i t y obtained when s u n l i g h t ( o r any o t h e r l i g h t source) with a spectral d i s t r i b u t i o n F(A) is i n c i d e n t on t h e c e l l i s found by i n t e g r a t i n g (35)

38

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

Bandgap, eV

F I G . 20.

I d e a l i z e d short c i r c u i t c u r r e n t d e n s i t i e s a s a

f u n c t i o n of s e m i w n d u c t o r bandgap for u n i t y s p e c t r a l response.

T h i s r e l a t i o n s h i p is applicable as long as t h e excess minority carrier density generated by t h e l i g h t is s m a l l compared t o t h e majority carrier density i n t h e device, so t h a t t h e d i f f e r e n t i a l equations involved i n t h e s p e c t r a l response remain l i n e a r 1481. (IGW i n j e c t i o n l e v e l conditions apply up t o a t least 10-20 s o l a r i n t e n s i t i e s i n 10 ohm-cm S i c e l l s and 100 i n G a s devices; t h e higher t h e base doping l e v e l is, t h e greater w i l l be t h e input i n t e n s i t y f o r which low i n j e c t i o n l e v e l calculations a r e s t i l l v a l i d . ) The s o l a r irradiance i n terms of t h e number of photons contained i n a 100 bandwidth located a t a wavelength A , f o r wavelengths from 0 . 2 t o 1.2 urn, is shown i n Fig. 19. The higher curve represents sunlight outside t h e e a r t h ' s atmosphere, the lower one represents t h e l i g h t received a t t h e e a r t h ' s surface on an average, nearly cloudless day. The degree t o which t h e atmosphere a f f e c t s t h e sunlight received a t t h e surface is defined q u a n t i t a t i v e l y by t h e " a i r mass. I' Technically, the a i r mass i s equal t o t h e secant of t h e angle of t h e sun t o t h e zenith, measured a t sea l e v e l , o r i n o t h e r words t h e path length t h a t a ray of sunlight must t r a v e r s e compared t o t h e s h o r t e s t path it could take. This d e f i n i t i o n is inadequate t o describe t h e real s i t u a t i o n on any given day, s i n c e it does not take i n t o account t h e prevailing weather conditions on t h a t day, but it serves at least as a q u a n t i t a t i v e estimate of what might be expected on t h e average a t a given point a t a given time of t h e year.

D.

321

0

I

I

0.2

'

I

0.4

'

SHORT CIRCUIT CURRENT

I

0.6

I

I

0.8

I

39

I

1.0

Junction Depth, microns

FIG. 21. Calculated AM0 s h o r t circuit photocurrents a s a function of junction depth both with (solid) and without (dashed) an electric f i e l d i n the top region. Poor conditions (dead layer) have been assumed for the top region. No f i e l d i n the base. Shack = 00. N/P S i cell: 1 ohm-cm, 1 8 m i l .

The a i r m a s s 0 (AMO) spectrum i n Fig. 19 represents t h e most accurate present estimate by NASA [49,501 f o r sunlight outside t h e e a r t h ' s atmosphere, with a t o t a l incident power integrated over a l l wavelengths of 135.3 mW/cm2 a t t h e e a r t h ' s distance from t h e sun. The AM2 spectrum [511 represents t h e sunlight a t t h e e a r t h ' s surface when t h e sun i s a t an an l e of 6 0 ° , leading t o a t o t a l incident power of 72-75 mW/cm3; it a l s o approximates t h e spectrum obtained f o r average, s l i g h t l y hazy weather conditions and smaller sun angles. The AM1 spectrum represents the sunlight a t t h e e a r t h ' s surface f o r optimum weather conditions with t h e sun a t t h e zenith, leading t o a t o t a l incident power of s l i g h t l y over 100 mW/cm2, with a curve t h a t l i e s between t h e curve f o r AM0 and t h a t f o r AM2 i n Fig. 19. The major differences between sunlight i n space and t h e l i g h t received a t t h e e a r t h ' s surface are i n t h e u l t r a v i o l e t and i n f r a r e d contents. Ultraviolet l i g h t i s f i l t e r e d out by ozone i n t h e upper layers of t h e atmosphere, and i n f r a r e d i s removed from the spectrum by water vapor and C02. Aerosol p a r t i c l e s s c a t t e r l i g h t of s h o r t wavelengths more than long wavelengths. The greater the number of atmospheric constituents t h e r e a r e , t h e more sunlight tends t o be "channeled" i n wavelength i n t o t h e v i s i b l e region, and t h e more t h e amplitude is attenuated a t any wavelength. The d i f f u s e component of l i g h t ( l i g h t reaching t h e surface from a l l p a r t s of t h e sky) is a l s o increased r e l a t i v e t o t h e d i r e c t component as t h e a i r mass increases.

40

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

24L 23

0

0.2 0.4 0.6 0.8 Junction Depth, microns

1.0

FIG. 2 2 . C a l c u l a t e d AM2 short c i r c u i t p h o t o c u r r e n t s a s a f u n c t i o n of j u n c t i o n d e p t h both w i t h ( s o l i d ) and w i t h o u t (dashed) an electric f i e l d i n t h e t o p r e g i o n . Same c o n d i t i o n s as F i g . 2 1 . Materials with high bandgaps y i e l d h i g h e r open c i r c u i t v o l t a g e s than materials with l o w e r bandgaps, b u t they a l s o y i e l d lower photocurrents because t h e s u n l i g h t a t low e n e r g i e s (long wavelengths) is n o t absorbed. F i g u r e 20 shows t h e highest c u r r e n t t h a t could b e obtained as a f u n c t i o n of t h e bandgap, i . e . , t h e i d e a l i z e d photocurrent t h a t would be obtained i f t h e a b s o l u t e spectral response were equal t o u n i t y f o r a l l photon e n e r g i e s above t h e bandgap and zero f o r a l l e n e r g i e s below it. A t AM0 t h e c u r r e n t d e c r e a s e s w i t h bandgap from about 54 mA/cm2 . f o r S i t o about 39 mA/cm2 f o r GaAs and 1 4 mA/cm2 f o r GaP. A t AM2 t h e c u r r e n t s are 34, 2 5 , and 6 . 5 mA/cm2 f o r S i , GaAs, and Gap, r e s p e c t i v e l y . The A M 1 p h o t o c u r r e n t s are roughly halfway between t h e v a l u e s c a l c u l a t e d a t AM0 and AM2. The s h o r t c i r c u i t c u r r e n t i s .always less t h a n t h e ideali z e d values i n F i g . 20 i n a real s i t u a t i o n because of l o s s e s due t o bulk and s u r f a c e recombination. Reducing t h e s u r f a c e recombination v e l o c i t i e s a t t h e f r o n t and back, and improving t h e d i f f u s i o n l e n g t h s i n both t h e top region and t h e base would reduce t h e s e losses and b r i n g measured p h o t o c u r r e n t s c l o s e r t o t h e i d e a l i z e d v a l u e s given above, b u t t h i s i s easier s a i d than done; t h e s e parameters are l a r g e l y determined by t h e p r o p e r t i e s of t h e material and by t h e procedures used t o fabricate t h e device, and are u s u a l l y not as good as one would l i k e them t o be.

D.

48

r

32i

I

I

I

I

I

SHORT CIRCUIT CURRENT I

.... 0:2

I

014

0:s

I

I

'

Oh

41

I

I

1;.

Junction Depth, microns

FIG. 23. Calculated AM0 s h o r t c i r c u i t photocurrents a s a function of base r e s i s t i v i t y and junction depth. Solid l i n e s : 10 ohm-em bases; dashed l i n e s : 1 ohm-em bases; dotted l i n e s : 0.1 ohm-em bases. No dead l a y e r , no d r i f t f i e l d s . Parameters o f Table 4 . Shack = a. N/P Si cell: 18 m i l . Two ways t o minimize these recombination losses and i m prove t h e photocurrent a r e t o decrease the junction depth and t o provide e l e c t r i c d r i f t f i e l d s , as has already been discussed f o r t h e s p e c t r a l response. Figures 2 1 and 22 show t h e calcul a t e d photocurrent obtained a t AM0 and AM2, respectively, f o r S i N/P c e l l s with a 1 ohm-cm base r e s i s t i v i t y using t h e mater i a l parameters of Table 4 (except f o r t h e hole l i f e t i m e and diffusion length i n t h e top region, which were taken as 3 nsec and 0 . 6 2 urn t o correspond t o t h e low values (dead layer) commonly measured i n phosphorus-diffused devices). The photocurrent is considerably improved by making the junction narrow, and f u r t h e r improved by t h e e l e c t r i c f i e l d (which i s assumed t o be equal t o the difference i n Fermi l e v e l s , %-EF, a t the surface and a t the junction edge divided by t h e junction depth). High surface recombination v e l o c i t i e s and low l i f e t i m e s i n t h e top region become l e s s important a s t h e junction depth i s decreased, p a r t i a l l y because of reduced losses and p a r t i a l l y because of t h e g r e a t e r percentage of the photocurrent contributed by the base and depletion regions compared t o t h e top region. The photocurrents are l a r g e r f o r high base r e s i s t i v i t i e s , where diffusion lengths and l i f e t i m e s a r e l a r g e r , than f o r low base r e s i s t i v i t i e s where t h e diffusion lengths and l i f e t i m e s are reduced by the ionized impurity s c a t t e r i n g . Figure 23

42

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRE"

Junction Depth, microns

F I G . 2 4 . GaAs P / N . Calculated AM0 s h o r t c i r c u i t photocurrents a s a f u n c t i o n of j u n c t i o n depth and s u r f a c e recombination veloci t y b o t h w i t h ( s o l i d ) and without (dashed) an electric f i e l d i n t h e t o p r e g i o n . Parameters o f Table 5 . Device thicknesses of 2 5 pm or mre. No f i e l d i n the b a s e . Shack = w.

shows t h e currents calculated f o r 10, 1, and 0.1 ohm-cm N/P S i c e l l s as a function of junction depth using t h e parameters of Table 4 but without any d r i f t f i e l d s . Photocurrent calcul a t i o n s f o r P/N devices f a l l below those of Fig. 23 by several milliamperes per an2 because of t h e smaller hole diffusion length i n t h e base of P/N c e l l s f o r an equivalent doping l e v e l compared t o the electron d i f f u s i o n length i n t h e base of an N / P device. Note t h a t t h e predicted photocurrent is independent of junction depth when t h e dead l a y e r i s absent and when t h e surface recombination velocity is low. Under these conditions, the junction depth could be made l a r g e ( 5 inn) as i n e p i t a x i a l growth of t h e top region without s e r i o u s l y a f f e c t i n g the photocurrent. The photocurrents obtained a t AM0 and AM2 f o r GaAs P/N s o l a r c e l l s both with and without e l e c t r i c f i e l d s i n t h e top region, using t h e parameters l i s t e d i n T a b l e 5, are presented i n Figs. 24 and 25. The same curves a r e obtained f o r o v e r a l l device thicknesses from 1 5 pm t o i n f i n i t y , and f o r back surface recombination v e l o c i t i e s from zero t o i n f i n i t y , s i n c e a l l t h e c a r r i e r s are created within t h e f i r s t 3 t o 4 pm from t h e surface and s i n c e hole d i f f u s i o n lengths are a t b e s t around 2.53 pm f o r common base doping l e v e l s . Reducing t h e junction depth and providing an electric f i e l d i n t h e top region a r e even more important f o r GaAs s o l a r c e l l s than f o r S i cells

SHORT CIRCUIT CURRENT

D.

N

E 24

a E

r’

5

20

43

-

t

3c. 16 -

.-a

.tl 0

5

v)

12

-

84

0

0.2

0.4

0.6

0.8

1.0

Junction Depth, microns

FIG. 25. GaAs P/N. Calculated AM2 s h o r t circuit photocurrents a s a function of junction depth both with (solid) and w i t h o u t (dashed) an electric f i e l d i n t h e top region. Same conditions a s i n Fig. 24.

because of t h e l a r g e r percentage of c a r r i e r s generated close t o t h e surface i n G a A s where the high recombination velocity and low l i f e t i m e usually r e s u l t i n severe losses. The photocurrents obtained a t AM0 and AM2 f o r Gal-xAlxAsG a A s s o l a r c e l l s as a function of junction depth and Gal-xAlxAs thickness a r e shown i n Figs. 26 and 27. The underlying G a ~ s p-n junction i s assumed t o have t h e same parameters as i n Table 5; t h e Gal-xA1xAs i s assumed t o have a recombination velocity of l o 6 cm/sec a t i t s surface, and t h e recombination velocity a t t h e i n t e r f a c e i s taken a s l o 4 cm/sec (same condit i o n s , except f o r junction depth, as i n Fig. 1 4 ) . The e f f e c t of t h e junction depth i s l e s s than f o r normal G a A s c e l l s because surface recombination losses a r e e f f e c t i v e l y absent. The s l i g h t increase i n photocurrent t h a t does occur with decreasing junction depths ( b u t above 0.4 um) is a r e s u l t of reduced bulk losses i n the pGaAs region; t h e decrease i n photocurrent f o r junction depths below 0.4 pm i s caused by t h e l o s s of a few c a r r i e r s generated a t long wavelengths a t distances of 3 t o 4 um from t h e surface. The strongest e f f e c t on t h e photocurrent i s obtained when t h e Gal-xAlxAs thickness is decreased, s i n c e more l i g h t reaches t h e G a A s p-n junction under these conditions (and since some of t h e carriers generated i n t h e Gal,,@,+ can be c o l l e c t e d ) . The b e n e f i t of having t h e Gal-xAlxAs layer on t h e G a A s surface compared t o t h e r e s u l t s obtained without t h i s layer can be seen by comparing Figs. 26

44

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOTOCURRENT

- 0 2

0.2 0.6 1.0 1.4 Junction Depth, microns

F I G . 2 6 . Gal-&llxAs-GaAs. C a l c u l a t e d AM0 short c i r c u i t photoc u r r e n t s as a f u n c t i o n o f j u n c t i o n d e p t h and G a l - f i l g s t h i c k ness. N o d r i f t f i e l d s . Same c o n d i t i o n s as Fig. 1 4 .

and 27 with 24 and 25; t h e photocurrents obtained from Gal,xA1xAs devices f o r thicknesses of 2.5 Irm or less a r e higher than those obtained from G a A s devices with t h e same surface recombination velocity (106 cm/sec).

2.

EXPERIMENTAL PHOTOCURRENT Almost a l l of t h e data a v a i l a b l e on s h o r t c i r c u i t currents

are f o r AM0 s u n l i g h t , due t o t h e much higher i n t e r e s t i n space applications compared t o t e r r e s t r i a l uses up t o a few years ago. The standard 10 ohm-cm N/P S i c e l l found on most s a t e l lites y i e l d s [52J about 35 mA/cm2, which becomes 38 mA/cm2 a f t e r correction f o r the portion of t h e c e l l masked by t h e

contacts and 4 1 mA/cm2 a f t e r correcting f o r r e f l e c t i o n , i n good agreement with Fig. 21. N / P devices with 1 ohm-cm bases y i e l d around 35-37 mA/cm2 a f t e r both corrections (30-32 mA/cmP before any c o r r e c t i o n s ) . P/N S i c e l l s with t h e same r e s i s t i v i t i e s y i e l d comparable but j u s t s l i g h t l y smaller c u r r e n t s ; t h e smaller minority carrier d i f f u s i o n length i n t h e base of a P/N c e l l compared t o an N/P device with t h e same base resist i v i t y (see Table 4 ) is p a r t l y compensated f o r by t h e l a r g e r diffusion length expected i n the top region of t h e P/N device. The " v i o l e t c e l l , " with i t s improved s p e c t r a l response a t s h o r t wavelengths compared t o conventional c e l l s , y i e l d s [ 4 , 531 around 4 0 mA/cxn2 uncorrected, o r 46.5 mA/cm2 a f t e r both

D.

SHORT CIRCUIT CURRENT

45

24

. 2

N

E

0

22

+-

e

20

? I

.-c3

0

r

i ’* fn

16

0.6 1.0 1.4 Junction Depth, microns

0.2

F I G . 2 7 . Gal,,+ll@s-GaAs. Calculated AM2 short circuit photoc u r r e n t s a s a f u n c t i o n of j u n c t i o n depth and Gal,,+ll$s t h i c k ness. Same c o n d i t i o n s a s Fig. 2 6 .

corrections, which i s higher than i n conventional 10 ohm-cm N/P devices even though the base i n the v i o l e t c e l l i s usually more heavily doped (2 ohm-cm) [531. Very few measurements have been reported f o r G a s p-n junctions. Gobat and co-workers 161 measured devices with f a i r l y deep junctions (1 pm o r over) i n 1962 and obtained a s h o r t c i r c u i t current of 17.5 mA/cm2 f o r AM1 a f t e r correcting f o r contact area (but not f o r r e f l e c t i o n ) ; t h i s should transl a t e t o about 20 mA/cm2 a t AMO. Improvements i n G a A s technology and t h e incorporation of d r i f t f i e l d s i n the top region t o a i d photogenerated c a r r i e r collection should readily increase t h i s t o 25 mA/cm2 a t AMO. Gal-xA1xAs-GaAs devices have been measured both i n simul a t e d and a c t u a l sunlight, and photocurrents (corrected f o r contact area) of 22.5 mA/cm2 a t AM0 191, 21.3 mA/cm2 a t A M 1 [a], and 19.5 mA/cm2 [8] a t AM2 were reported. The photocurr e n t s i n these devices were limited by attenuation i n t h e Gal-xAlxAs l a y e r , and higher currents w i l l very l i k e l y be reported as t h e layer i s made thinner and i t s A 1 content i s increased. The uncorrected s h o r t c i r c u i t currents of laboratory Cu2S-CdS s o l a r cells l i e i n t h e range of 25-30 mA/cm2 a t AM0 [54] and around 20-25 mA/cm2 a t AM1. The measured s p e c t r a l responses of these devices were not given but must have been considerably b e t t e r than those of Fig. 18 to y i e l d such high currents. Production l i n e devices have photocurrents around 2/3 to 3/4 of these values, and s p e c t r a l responses more

46

2.

CARRIER COLLECTION, SPECTRAL RESPONSE, PHOMCURRENT

comparable t o Fig. 18. The photocurrents are due mostly t o c o l l e c t i o n from t h e Cu2S with i t s 1.1 e V bandgap, and t o a l e s s e r degree, t o c o l l e c t i o n from t h e CdS with i t s 2 . 4 eV bandgap.

E.

Summary

Two of t h e most important parameters i n a s o l a r c e l l a r e the minority c a r r i e r l i f e t i m e and t h e minority c a r r i e r d i f f u sion length. In t h e base of t h e c e l l , t h e l i f e t i m e and diffusion length depend on t h e method of growing t h e c r y s t a l , t h e procedures used t o prepare t h e s u b s t r a t e , t h e s u b s t r a t e resist i v i t y , t h e presence of undesirable impurities such as oxygen and copper, and t h e annealing temperatures and t i m e s ( i f any). I n t h e very t h i n top region, which i s usually prepared by d i f fusion, t h e l i f e t i m e and d i f f u s i o n length depend on t h e type of dopant and i t s surface concentration and t h e surface treatment p r i o r t o t h e diffusion. High surface concentrations and t h e i r associated stress, d i s l o c a t i o n s , and perturbations of t h e band s t r u c t u r e can lead t o a "dead" layer of extremely low l i f e t i m e over a f r a c t i o n of t h e diffused top region adjacent t o t h e surface. The a b i l i t y of a s o l a r c e l l t o generate photocurrent a t a given wavelength of incident l i g h t i s measured q u a n t i t a t i v e l y by i t s " s p e c t r a l response," and t h e t o t a l s h o r t c i r c u i t photocurrent obtained from t h e c e l l i s t h e product of t h e s p e c t r a l response and t h e number of photons i n t h e incident l i g h t spectrum, integrated over a l l wavelengths. Solar c e l l s p e c t r a l responses and photocurrents have been computed f o r t h r e e device models, including uniformly doped base and top regions, cons t a n t electric f i e l d s i n both regions, and a back surface f i e l d (blocking back c o n t a c t ) . The response a t long wavelengths depends mostly on t h e base l i f e t i m e and d i f f u s i o n length. I f t h e d i f f u s i o n length i s l o w , t h e response can be improved by t h e presence of an e l e c t r i c f i e l d i n t h e base adjacent t o the depletion region, but i f the d i f f u s i o n length is high a base f i e l d w i l l have small e f f e c t . A blocking back contact can improve t h e response by minimizing t h e number of photocarriers t h a t would o r d i n a r i l y recombine a t an Ohmic back contact. The back contact conditions a r e only important i f t h e device thickness i s l e s s than several base diffusion lengths. The response a t s h o r t wavelengths depends mostly on t h e f r o n t surface recombination velocity and t h e l i f e t i m e i n t h e top region. "Dead" l a y e r s and high recombination v e l o c i t i e s g r e a t l y lower t h e response, while reducing t h e junction depth

E.

SUMMARY

47

and providing an e l e c t r i c f i e l d i n t h e top region a r e beneficial i n overcoming these problems. Eliminating t h e dead l a y e r e n t i r e l y by optimizing t h e diffusion conditions and lowering t h e recombination velocity by surface passivation or other techniques a r e important i n obtaining high s h o r t c i r c u i t currents. A l l s o l a r c e l l s a r e affected by t h e conditions i n both t h e top region and the base. Solar c e l l s made from i n d i r e c t gap materials such as S i r however, a r e more dependent upon t h e conditions i n t h e base, while devices made from d i r e c t gap materials such as GaAs a r e governed more by t h e conditions of t h e top region. Maximum t h e o r e t i c a l s h o r t c i r c u i t currents of 54 and 39 mA/cm2 a t AM0 and 34 and 2 5 mA/cm2 a t AM2 a r e predicted f o r S i and GaAs s o l a r c e l l s , respectively, but a c t u a l photocurrents are usually about 2/3 of these values due t o t h e recombination losses and r e f l e c t i o n of l i g h t and contact area losses. The measured photocurrents of Cu2S-CdS c e l l s at AM0 have reached 2 5 mA/cm2; most of t h i s current i s due t o collect i o n from the Cu2S layer.

CHAPTER 3

Solar Cell Electrical Characteristics

A.

Current Mechanisms

The voltage-current behavior of a s o l a r c e l l i n t h e dark i s equally a s important as t h e photocurrent i n determining t h e output o f t h e c e l l , s i n c e t h e j u n c t i o n c h a r a c t e r i s t i c s determine how much of t h e e l e c t r i c a l energy developed by t h e c e l l with l i g h t i n c i d e n t on it w i l l b e a v a i l a b l e a t t h e output terminals and how much w i l l be lost as h e a t . When p o w e r is being taken from t h e c e l l , a v o l t a g e exists a c r o s s i t s t e r m i n a l s i n t h e forward b i a s p o l a r i t y , and a j u n c t i o n "dark c u r r e n t " e x i s t s which is o p p o s i t e i n d i r e c t i o n t o t h e photocurrent. The curr e n t being supplied t o t h e load i s t h e photocurrent minus t h i s dark c u r r e n t , and it i s important t o have a s low a dark c u r r e n t as possible a t t h e o p e r a t i n g v o l t a g e t o o b t a i n t h e h i g h e s t efficiency. I n a l l p-n j u n c t i o n s , s e v e r a l c u r r e n t t r a n s p o r t mechanisms ( t r a n s p o r t of h o l e s and e l e c t r o n s across t h e d e p l e t i o n region) can be p r e s e n t a t t h e same time, and t h e magnitude o f each one i s determined by t h e doping l e v e l s on t h e t w o s i d e s o f t h e junction and by t h e presence of any added energy b a r r i e r s as i n heterojunctions. Such t r a n s p o r t mechanisms i n t h e forward b i a s d i r e c t i o n i n c l u d e i n j e c t i o n of carriers over t h e junction b a r r i e r , recombination of holes and e l e c t r o n s w i t h i n t h e deplet i o n region, and i n j e c t i o n of carriers up a p o r t i o n of t h e b a r r i e r followed by tunneling i n t o energy s t a t e s w i t h i n t h e bandgap (tunneling may t a k e p l a c e through a series of s t e p s with recombination i n between, as i n t h e "excess" c u r r e n t i n t u n n e l d i o d e s ) . These c u r r e n t s are shown d i a g r a m a t i c a l l y i n Fig. 2 8 ; t h e r e may be o t h e r p o s s i b i l i t i e s i n s p e c i a l cases. I n t h e absence of shunt or series r e s i s t a n c e e f f e c t s , t h e dark I-V c h a r a c t e r i s t i c s of a s o l a r c e l l a r e given by t h e sum of t h e c u r r e n t mechanisms t h a t a r e p r e s e n t . I n a normal S i p-n j u n c t i o n device with 1 or 1 0 ohm-cm base m a t e r i a l , t h e tunneling c u r r e n t i s n o t l i k e l y t o be of importance compared

A.

CURRENT MECHANISMS

49

FIG. 28. T h r e e c u r r e n t transport mechanisms i n forward biased p-n junctions: ( 1 ) i n j e c t i o n ; (2) recombination within t h e depletion region; and (3) multistep tunneling via energy s t a t e s caused b y defects. t o t h e other two, but i n S i devices made with 0.01 ohm-cm bases, t h e tunneling component w i l l probably dominate. For 0.1 ohm-cm devices (a few t i m e s 1017 ~ m - ~t h) e tunneling curr e n t should be n e g l i g i b l e f o r devices with high junction perf e c t i o n b u t both t h e tunneling and depletion region recombinat i o n mechanisms w i l l be increasingly important as t h e number of d e f e c t s (and hence energy s t a t e s ) within /the depletion region increases. These d e f e c t s can be caused by impurities, d i s l o c a t i o n s r e s u l t i n g from stress caused by t h e junction d i f f u s i o n , and o t h e r problems introduced during t h e device fabrication. (Heterojunctions and Schottky b a r r i e r devices tend t o be subj e c t t o tunneling currents more than p-n homojunctions a r e . Tunneling has been suggested by Fahrenbruch and B u b e [551 and by B6er and P h i l l i p s 1561 as one of t h e two major dark c u r r e n t components i n Cu2S-CdS cells. 1 I n t h i s s e c t i o n , each of t h e s e t h r e e dark c u r r e n t components w i l l be described i n turn. The i n j e c t e d c u r r e n t w i l l be described f o r each of t h r e e device models: uniformly doped regions, constant e l e c t r i c f i e l d s , and a back surface f i e l d . The space charge l a y e r recombination c u r r e n t and t h e tunneling component are l a r g e l y independent of t h e model assumed; they depend mostly on t h e doping l e v e l s a t t h e edges of space charge region. 1.

INJECTED CURRENTS

The dark current-voltage r e l a t i o n s h i p s i n p-n junctions are derived from equations very similar t o (6) and ( 7 ) . The i n j e c t e d c u r r e n t component (1 i n Fig. 28) c o n s i s t s of electrons

50

3.

SOLAR CELL ELECTRICAL CHARACTERISTICS

injected from t h e n-side over t h e p o t e n t i a l b a r r i e r i n t o t h e p-side, where they d i f f u s e and d r i f t ( i f t h e r e i s an e l e c t r i c f i e l d ) away from the junction and eventually recombine e i t h e r i n the bulk o r a t a surface. The current component a l s o consists of an analogous current due t o holes i n j e c t e d from the p-side i n t o the n-side. The behavior of these minority carriers i s governed by the continuity equations ( l / q ) (d/dx) Jn- [ (%-%0)/?~1

= 0

(l/q) (d/dx) Jp+[ (pn-pno)/'rpl = 0 and by t h e current equations

(electrons on p-side) (holes on n-side)

,

, (37) (38).

In order t o obtain an a n a l y t i c a l r e s u l t , it is necessary to assume a l l t h e parameters ( p , ? , E , D ) t o be constant; i f these assumptions cannot be used even as a f i r s t approximation, numerical methods can be used [391, which are more accurate but f a r less expedient. The boundary conditions necessary f o r t h e solution of (37)-(40) i n an N/P c e l l a r e

where x = 0 is t h e f r o n t of t h e c e l l and x = H is t h e back. Equations (41) and (42) are t h e Boltzmann r e l a t i o n s h i p s f o r carriers on t h e t w o sides of t h e junction when t h e voltage across t h e junction is V,, i.e., V . is t h e voltage introduced across t h e junction e i t h e r by l i g h t o r by some o t h e r means such as a b a t t e r y . The maximum value t h a t t h e photovoltage can t h e o r e t i c a l l y have i s t h e "built-in" p o t e n t i a l Vd, which i s r e l a t e d t o t h e bandgap by

A.

CURRENT MECHANISMS

51

The c l o s e r t h e Fenni l e v e l s l i e t o t h e i r respective band edges on t h e two sides, the higher t h e p o t e n t i a l vd w i l l be; f o r degenerate conditions vd can even exceed t h e bandgap. (The a c t u a l open c i r c u i t voltage Voc i s always l e s s than vd; Voc i s equal t o t h e voltage a t which t h e photocurrent i s exactly opposed by t h e t o t a l dark current, and if the dark current components are l a r g e a t a given voltage, then Voc w i l l be correspondingly small.) The injected current component, which i s by f a r t h e large s t i n normal S i s o l a r c e l l s , can now be found by solving (37) through (44) under various conditions. The solutions w i l l be obtained f o r N/P c e l l s , b u t analogous expressions apply f o r P/N devices. a.

U n i f o r m Doping

I f the doping l e v e l s on t h e two s i d e s a r e constant, then t h e e l e c t r i c f i e l d s outside t h e depletion region a r e n e g l i g i b l e and t h e solution takes a simple form. One form of t h e solution t o (37)-(40) can be written as

+A2 sinh [(X-(Xj+W)

/%]

(X,+W

5 x 5 H)

and using t h e boundary conditions (41)- (441, t h e injected current becomes

(48)

52

b.

3.

SOLAR CELL ELECTRICAL CHARACTERISTICS

Uniform Electric F i e l d s

When doping g r a d i e n t s e x i s t , electric f i e l d s w i l l be p r e s e n t o u t s i d e t h e d e p l e t i o n region. I f t h e s e f i e l d s are assumed t o be constant a c r o s s t h e device, then t h e preexpon e n t i a l Jo i n Eq. (49) f o r an N/P c e l l becomes (Xj/Lpp) + ( (SpLpp/Dp)+EppLpp) cash (Xj/Lpp) +EppLpp) sinh (xj/Lpp)+cosh

(X j/Lpp)

as presented by E l l i s and Moss 1371.

The terms Epp, Lpp, Erin, and were defined i n Eqs. (26) and (27). The f i r s t term r e p r e s e n t s c u r r e n t i n j e c t e d from t h e d i f f u s e d n-region i n t o the base and t h e second term r e p r e s e n t s c u r r e n t i n j e c t e d from t h e base i n t h e o p p o s i t e d i r e c t i o n . An i n f i n i t e s u r f a c e recomb i n a t i o n v e l o c i t y ( a s f o r a metallic O h m i c c o n t a c t ) was assumed a t t h e back of t h e c e l l 1371. c.

Back Surface F i e l d

I n Godlewski's e t a l . [43] treatment of t h e c u r r e n t flow when a back s u r f a c e f i e l d (p+-region) i s p r e s e n t (Fig. 71, t h e t h r e e n e u t r a l regions of t h e device are uniform i n doping l e v e l , l i f e t i m e , and mobility (no d r i f t f i e l d s ) and t h e dark c u r r e n t component from t h e base i s then given by [43] Dn n: PSLn/Dn) cosh (WI?/L,) +sinh (W

J o ( b a s e ) = q--

/

I.1 )

(52)

where

and Na, 41, L, are t h e properties of t h e p-base region, while are t h o s e of t h e p+-region. Wp and W$ are t h e NB, D h , widths of t h e l i g h t l y and h e a v i l y doped base regions, respect i v e l y (Fig. 7 ) . The base c u r r e n t (52) is of t h e same form as t h e second term i n (SO), except t h a t t h e recombination

A.

CURRENT MECHANISMS

53

v e l o c i t y "seen" by t h e electrons i n t h e p-region i s S instead of Sn, and S can be much less than Sn, p a r t i c u l a r l y i f t h e doping level N: is much g r e a t e r than Na ( t h e e f f e c t of t h e BSF is l a r g e s t f o r high p-region r e s i s t i v i t i e s and f o r narrow widths Wp r e l a t i v e t o t h e d i f f u s i o n length h). This tendency of t h e BSF t o "confine" t h e minority carriers i n t h e p-region and away from t h e back contact can lower t h e dark c u r r e n t through t h e device considerably and consequently improve t h e open c i r c u i t voltage and' f i l l f a c t o r . The contribution t o t h e dark c u r r e n t from t h e n'diffused f r o n t region of a BSF c e l l i s t h e same as given by t h e f i r s t t e r m of ( 5 0 ) o r t h e f i r s t term of (51). 2.

SPACE CHARGE LAYER RECOMBINATION CURRENT

When a p-n junction i s forward biased, electrons from t h e n-side and holes from t h e p-side a r e i n j e c t e d across t h e junct i o n depletion region i n t o t h e p- and n-sides, respectively, b u t a t t h e sane t i m e some of t h e s e carriers recombine i n s i d e t h e depletion region, r e s u l t i n g i n an increase i n t h e dark c u r r e n t through t h e device. This "space charge l a y e r recombination current" was f i r s t discussed by S a h et a l . 1571 i n 1957, and was l a t e r extended by Choo [58]. I n t h e Sah-NoyceShockley (S-N-S) theory, t h e doping l e v e l s w e r e assumed t o be t h e same on t h e two s i d e s of t h e junction and a s i n g l e recombination c e n t e r located i n t h e v i c i n i t y of t h e c e n t e r of t h e gap w a s assumed a l s o . The dark c u r r e n t component under forward b i a s was derived as

where vd is t h e b u i l t - i n voltage, W i s t h e depletion region thickness, and a r e t h e minority carrier l i f e t i m e s on t h e two sides of t h e junction. The f a c t o r f ( b ) i s a complicated expression involving t h e t r a p l e v e l Et and t h e two l i f e times m

f (b) =

1

dx (55)

x2+2bx+l

b = [exp(-qVj/2kT) 1 cosh[(Et-Ei)/kT+(1/2) where Ei is t h e i n t r i n s i c Fermi l e v e l .

!h(TpO/TnO)

1,

The function f ( b ) has

54

3.

SOLAR CELL ELECTRICAL CHARACTERISTICS

a maximum value of n/2, which occurs a t small values of b (forward biases > 2kT/q); f ( b ) decreases as b increases.

Choo l a t e r extended t h e S-N-S theory t o t h e more general case where the doping l e v e l s are not t h e same on t h e two s i d e s , where t h e l e v e l Et can be away from t h e gap c e n t e r , and where the two l i f e t i m e s TnO, 'c 0 can be orders-of-magnitude apart. P H e derived an equation v i r t u a l l y i d e n t i c a l t o (54) except t h a t t h e function f ( b ) is smaller than i n t h e S-N-S case, i.e., the e f f e c t of junction assymetries i s t o lower t h e recombinat i o n current below t h e value predicted by t h e S-N-S derivation. Equation (54) with f ( b ) = r/2 is t h e r e f o r e t h e l a r g e s t value t h a t t h e recombination current i s expected t o take, provided t h a t t h e t h e o r i e s adequately describe t h e r e a l s i t u a t i o n 1591. 3.

TUNNELING CURRENT

A t h i r d type of dark current component t h a t can exist under some s i t u a t i o n s is a tunneling current caused by elect r o n s o r holes tunneling from t h e conduction o r valence band i n t o energy states within t h e bandgap, followed by e i t h e r tunneling t h e remainder of t h e way i n t o t h e opposite band o r by a tunneling-recombination mechanism ( t h e current marked 3 i n Fig. 2 8 ) . Tunneling is not l i k e l y t o be important i n 10 and 1 ohm-cm S i c e l l s , but i n 0.01 ohm-cm S i devices, heterojunct i o n s such a s Cu2S-CdS, and Schottky b a r r i e r s , tunneling can be a major contributor t o t h e dark current. Heterojunctions o f f e r a p a r t i c u l a r l y graphic method f o r studying tunneling currents because they are very o f t e n dominated by tunneling, a r e s u l t of t h e many energy states t h a t can be introduced within t h e bandgaps by t h e l a t t i c e and thermal expansion mismatches and by t h e cross-doping of one material i n t o t h e other. These tunneling currents take t h e form 1601

where K1 i s a constant containing t h e e f f e c t i v e mass, b u i l t - i n b a r r i e r , doping l e v e l , d i e l e c t r i c constant, and Planck's cons t a n t , Nt i s t h e density of energy s t a t e s a v a i l a b l e f o r an electron o r hole t o tunnel i n t o , and B i s a constant containing t h e doping l e v e l , d i e l e c t r i c constant, and t h e e f f e c t i v e mass, B = (4/3ii) (m*E/WIa) li2. This tunneling dark c u r r e n t (57) v a r i e s exponentially with voltage j u s t as J i n j and Jrg do, and can easily be mistaken f o r one of these. The value of B ( t h e slope of an J versus V) o f t e n l i e s i n t h e range of 20 to 30 [611; i f t h i s slope w a s mistakenly assumed t o be qVj/AkT, values f o r A of 1.3-2 would be deduced a t room temperature. The only

A.

CURRENT MECHANISMS

55

method f o r d i f f e r e n t i a t i n g tunneling currents from thermal ones such as J i n j and J i s by temperature measurements; tunneling rg currents a r e very i n s e n s i t i v e t o temperature, while t h e oppos i t e i s t r u e f o r thermal currents. 4.

TOTAL CURRENT

I-V

When more than one dark current component is present, t h e c h a r a c t e r i s t i c s a r e given by the sum of them

In m o s t S i , G a s , and Gal,xA1fis-GaAs s o l a r c e l l s , only t h e f i r s t two w i l l be important, but f o r CU~S-C~S, other types of heterojunctions, Schottky b a r r i e r s , and very heavily doped p-n junctions, t h e tunneling current may a l s o be important. The major differences between t h e space charge layer recombination current and t h e i n j e c t e d current l i e i n t h e i r voltage, temperature, and bandgap dependences. For 1 t o 1 0 ohm-cm S i devices, the value of Jin extrapolated t o zero b i a s i s around A/cm2, while t h e value of J r g is around A/cm2. A t the same t i m e , J i n j varies as ew(qVj/kT) while J r g v a r i e s as exp(qVj/2kT), so t h a t t h e recombination current dominates a t low forward biases and t h e i n j e c t e d current dominates a t higher biases, with a crossover a t around to A/cm2. Jinj has a bandgap dependence of exp(-Eg/kT), while J varies rg as exp(-Eg/2kT); therefore, J r g becomes increasingly unportant r e l a t i v e t o J i n j f o r high bandgap materials and a t low temperatures. The i n j e c t i o n and recombination currents f o r a S i s o l a r c e l l with a 1 ohm-cm base r e s i s t i v i t y and f o r t w o values of l i f e t i m e i n t h e diffused n-region a r e shown i n Fig. 29. The doping l e v e l i s so much higher i n the diffused region than i n t h e base t h a t the i n j e c t i o n current is determined by electrons i n j e c t e d i n t o t h e base alone t o a l l p r a c t i c a l purposes, and is independent of t h e top surface recombination velocity and t h e l i f e t i m e i n t h e top region. This top region l i f e t i m e does have a s i g n i f i c a n t e f f e c t on t h e recombination current, however, because of i t s appearance i n t h e square-root r a d i c a l of Eq. (54). If i s high, such as t h e s a t u r a t i o n value of 0.4 psec suggested by Ross and Madigan 1181, J r g i s much smaller than J i n j a t t h e operating voltage (0.4-0.5 V ) and has l i t t l e e f f e c t on the device behavior. I f ~~0 i s very low however, as is often measured i n conventional c e l l s a f t e r t h e phosphorus d i f fusion, then t h e recombination current is considerably l a r g e r ; Jrg becomes comparable t o o r even l a r g e r than J i n j a t the

56

3.

SOLAR CELL ELECTRICAL CHARACTERISTICS lo-'

I

I

I

N

I

1

Q

Forward Volts

F I G . 2 9 . C a l c u l a t e d i n j e c t i o n and recombination c u r r e n t s i n a S i N / P s o l a r cell f o r the twu c a s e s of h i g h and l o w lifetimes i n t h e t o p r e g i o n . Parameters o f T a b l e 4 . N o d r i f t f i e l d s . C o n d i t i o n s : 1 oh-cm, 450 pm t h i c k , x j = 0 . 3 w. shack

maximum p o w e r p o i n t (Fig. 2 ) and reduces both t h e open c i r c u i t voltage and f i l l f a c t o r . (Whenever t h e d e f e c t d e n s i t y i s high i n t h e d e p l e t i o n region, and hence t h e l i f e t i m e i s low t h e r e , J r g can be expected t o be unusually high. This could p a r t i c u l a r l y be a problem i n ribbon S i devices and p o l y c r y s t a l l i n e t h i n f i l m c e l l s , as suggested by S t i r n 1621 .) F e recombination c u r r e n t i n GaAs i s much l a r g e r r e l a t i v e t o t h e ' + i n j e c t i o n c u r r e n t t h a n it i s i n S i , a s can be seen by comparing Fig. 30 with Fig. 29. The i n j e c t i o n c u r r e n t i n GaAs c e l l s i s s t i l l determined mostly by t h e base region due t o t h e much lower doping level t h e r e . The high value of t h e recombination c u r r e n t i n GaAs dev i c e s is l a r g e l y a r e s u l t of t h e very low l i f e t i m e s i n t h e two regions. J r g i s o f t e n much lower i n LPE-grown devices, where sec on both s i d e s of t h e carrier l i f e t i m e s can be around t h e j u n c t i o n , than i n bulk or vapor grown material where t h e l i f e t i m e s a r e u s u a l l y smaller.

B.

Equivalent C i r c u i t

The simplest equivalent c i r c u i t o f a solar c e l l i n t h e o p e r a t i n g mode i s shown i n Fig. 31. The photocurrent i s represented by a c u r r e n t generator I@,and i s opposite i n d i r e c t i o n t o t h e forward bias c u r r e n t of t h e diode I i n j + I r g . Shunt res i s t a n c e p a t h s are represented by %h; they can be caused by s u r f a c e leakage along t h e edges of t h e c e l l , by d i f f u s i o n

B.

EQUIVALENT CIRCUIT

57

Forward Volts

F I G . 30. C a l c u l a t e d i n j e c t i o n and recombination c u r r e n t s i n GaAs P/N cells f o r b o t h l o w losses ( S f r o n t = l o 4 cm/sec, Tn lXlO-’ sec, T~ = 1.6X10-8 sec; s o l i d l i n e s ) and h i g h losses (Sfront = l o 6 cm/sec, Tn = l X l O - ’ sec, Tp = 2XlO-’ sec; dashed l i n e s ) . No d r i f t f i e l d s . s h c k = CQ. C o n d i t i o n s : 0.01 ohm-cm; H = 20 Vm-ac; x j = 0 . 5 Vm.

spikes along d i s l o c a t i o n s o r g r a i n boundaries, o r possibly by f i n e metallic bridges along microcracks, g r a i n boundaries, o r c r y s t a l d e f e c t s such as stacking f a u l t s a f t e r t h e contact m e t a l l i z a t i o n has been applied. Series r e s i s t a n c e , represented by Rs, can arise from c o n t a c t r e s i s t a n c e s t o t h e f r o n t and back ( p a r t i c u l a r l y f o r high r e s i s t i v i t y bases, 1 t o 10 ohm-cm), t h e r e s i s t a n c e of t h e base region i t s e l f , and t h e s h e e t r e s i s t a n c e of t h e t h i n diffused o r grown s u r f a c e layer. More complicated equivalent c i r c u i t s can be formulated t o account more accur a t e l y f o r t h e d i s t r i b u t e d n a t u r e of both t h e series r e s i s t a n c e and t h e c u r r e n t generator 1631. The dark c u r r e n t s Iin and Irg are equal t o t h e c u r r e n t d e n s i t i e s Jin, and J r g m u d i p l i e d by t h e total device area A t . The photocurrent i s equal t o t h e photocurrent d e n s i t y multip l i e d by t h e a c t i v e device area A,, i.e., t h e t o t a l area minus t h e area masked by t h e f r o n t contacts. The equivalent c i r c u i t and t h e r e s u l t i n g r e l a t i o n s h i p s must be w r i t t e n i n terms of c u r r e n t s , n o t c u r r e n t densities. The d i f f e r e n c e between t h e t o t a l area and t h e a c t i v e area should be kept i n mind, although the d i f f e r e n c e i s usually only 6-8% and i s o f t e n neglected t o a f i r s t approximation. From t h e equivalent c i r c u i t of Fig. 31, a r e l a t i o n can be w r i t t e n between c u r r e n t output Iout and voltage output Vout. Assuming t h e dark c u r r e n t t o be I i n j + I r g as given by (49) and (54) multiplied by t h e t o t a l area, t h i s r e l a t i o n i s

58

3.

SOLAR CELL ELECTRICAL CHARACTERISTICS

FIG. 31. Equivalent c i r c u i t of a solar cell, including series and shunt r e s i s t a n c e s .

1.

RELATIONSHIPS FOR NEGLIGIBLE

%, Rsh LOSSES

I n order t o use t h e equivalent c i r c u i t t o p r e d i c t s o l a r c e l l output and efficiency and t o make t h e r e l a t i o n s h i p s anal y t i c a l l y manageable, t h e approximations a r e often made t h a t s e r i e s and shunt r e s i s t a n c e e f f e c t s are n e g l i g i b l e and t h a t the dark current can be w r i t t e n as

where the "junction perfection f a c t o r " A0 and t h e new value of t h e preexponential f a c t o r 1 0 0 have been used t o approximate the sum of Iin, and I r g by a s i n g l e term (a glance a t Fig. 2 9 w i l l show t h a t such an approximation i s j u s t i f i e d i f t h e minori t y carrier l i f e t i m e s a r e high but not i f they a r e low). The advantage of these approximations i s t h a t (59) takes a very simple form Iout = Iph-100 [exP(qVout/A~kT)-ll

-

A p l o t of

(61)

(61) has already been shown i n Fig. 2 f o r A0 = 1; the e f f e c t of higher values of A. i s t o round out t h e "knee" i n t h e curve near t h e maximum p o w e r point. The s h o r t c i r c u i t current i s given simply by 'SC

= 'ph

and the open c i r c u i t voltage by (1)

B.

EQUIVALENT CIRCUIT

59

voc

0.5 0.6 0.7 0.8 0.9 1.0

1.00

\

I

l

l

1

1

-

-

-

0.60

I

0

5

l

1

10 15

I

20

I

I

25 30 35

NOC1AOK-I-

FIG. 32. The r a t i o o f the maximum power p o i n t v o l t a g e t o t h e open c i r c u i t v o l t a g e a s a f u n c t i o n o f the normalized open circ u i t v o l t a g e (unmarked curve), v a l i d for a l l Voc, A O , and T . Also shown a r e f o u r curves for A0 = 1-2.5 and 298OK; t h e abs c i s s a for t h e s e c u r v e s is a t the t o p .

(It might be thought from (1) that high values of A. would be desirable in obtaining high open circuit voltages, but this is actually not the case, since high A. also requires high 100 to approximate the two currents Iinj and Irg by the one term (60);Voc for p-n junctions is always higher for low values of A. than the opposite [641. I Since the power output is VoutxIoUt, the maximum power output can be found by differentiating the product and setting the result equal to zero 164,651

60

3.

SOLAR CELL ELECTRICAL CHARACTERISTICS "0 c 0.5 0.6 0.7 0.8 0.9 1.0

1-00

iI

0.70 0.75 0.65' 0

'

5

'

10

I

!

'

'

15 20

,

'

25

,

'

30

'

35

Wo,lA,KT

F I G . 3 3 . The r a t i o of the maximum power p o i n t c u r r e n t t o the s h o r t c i r c u i t c u r r e n t a s a f u n c t i o n o f the normalized open c i r c u i t v o l t a g e , v a l i d f o r a l l Voc, Ao, and T . Also shown a r e f o u r c u r v e s f o r A. = 1- 2. 5 a t 298OK.

is the current output at maximum power and

= ( (JscAa/Jo($it) +1)

(6%)

allows the voltage at maximum power output to be calculated. The f i l l factor (FF), which is V m I ~ I s c V o c , measures the "squareness" of the I-V curve, and is found to be [661

B.

EQUIVALENT CIRCUIT

61

voc, Volts

FIG. 34. F i l l f a c t o r a s a function of normalized

open c i r c u i t voltage, valid for a l l Voc, A g , and T. Also shown a r e four curves for A0 = 1-2.5 a t 298OK. The relationships contained i n (64) t o (66) a r e shown i n Figs. 32-34, assuming t h a t t h e t o t a l and a c t i v e areas are equal. (It should be kept i n mind t h a t these relationships are only useful i n the idealized case where t h e r e a r e no s e r i e s o r shunt r e s i s t a n c e e f f e c t s and where t h e current can be represented by t h e s i n g l e exponential of Eq. (60).) The two r a t i o s Vm/Voc and I&IScand t h e FF a l l improve with increasing values of Voc and with decreasing values of A0 and T. Higher bandgap materials y i e l d higher r a t i o s and f i l l f a c t o r s because of t h e i r higher open c i r c u i t voltages (provided s e r i e s and shunt resistances are not a problem). The nearer t h e value of A. i s t o unity, t h e b e t t e r t h e device performance i s , other things being equal. In S i , f o r example, with a Voc of around 0.58 V , FF is equal t o 0.82 f o r A. = 1 but only 0.72 i f A0 = 2. For GaAs with Voc = 0.9 V , FF decreases from a p o t e n t i a l value of 0.87 f o r A0 = 1 t o 0.79 i f A. = 2. 2.

EFFECTS OF Rsh AND Rs

When s e r i e s and shunt resistance problems become important, t h e relationships of (64)-(66) no longer apply; the two r a t i o s VnJvoc and Im/Iscand t h e FF are a l l reduced below the values shown i n Figs. 32-34. The r e l a t i o n s h i p i n (59) between V o u t and Iout becomes almost impossible t o solve a n a l y t i c a l l y , a l though a numerical solution can be r e a d i l y obtained. The e f f e c t s of s e r i e s and shunt resistances on s o l a r c e l l behaviot

SOLAR CELL ELECTRICAL CHARACTERISTICS

3.

62

0

0.1

0.2 0.3 0.4 Volts

0.5

FIG. 35. The effects resistance on measured cell curves. Tungsten 100 mw/cm2. Cell area

of series Si solar light, = 2 an2.

can be seen easily by placing various resistors alternately in series and in parallel with an otherwise normal solar cell. Figure 35 shows the effect of series resistance on the output of a comnercial Si cell illuminated with tungsten light at 100 mW/cm2 intensity. The open circuit voltage is not changed but the fill factor is seriously reduced. There can also be a reduction in the short circuit current below the value of the photocurrent due to the forward bias across the diode caused by the voltage drop across the series resistance (even though the total output voltage is zero) which results in appreciable dark current in opposition to the photocurrent. Even small values of series resistance, in the 0.5 to 1.0 ohm range for 2 cm2 cells, are enough to cause serious effects. Figure 36 shows the effect of shunt resistances in parallel with the solar cell (same device as in Fig. 35); in this case the short circuit current is not affected, but the fill factor and open circuit voltage are reduced as the shunt resistance decreases. In practical devices, the shunt resistance is usually large enough to have a negligible effect at 1 solar intensity or above. At low intensities however, and to some degree at low temperatures, the shunt resistance takes on increasing importance [23]. On the other hand, the series resistance becomes increasingly important at high intensities and temperatures. The need to minimize the series resistance suggests high doping levels and deep junctions which are just the opposite of the necessary conditions for high current collection efficiency. The compromise has been reached to make the diffused region thin but very highly doped, and at the same time, to optimize the design of the Ohmic contact grid pattern [67, 681 for the lowest sheet resistance consistent with covering only 5-10% of the surface. With the comPnonly found six-finger

C.

EXPERIMENTAL CURRENT-VOLTAGE BEHAVIOR

63

60

50

P ci

5 30

5

020 F I G . 36. The e f f e c t s of shunt r e s i s t a n c e on measured Si solar cell curves. Same conditions a s F i g . 35.

10 0

0

0.1

0.2

0.3 0.4

Volts

0.5

g r i d p a t t e r n used so much i n t h e p a s t , t h e series resistance can be a s much as 0.5 ohm f o r a 2 cm2 Si c e l l ; a t the operating current of 60 t o 65 mA, 30 t o 33 mV can be l o s t across t h i s resistance. Increasing the number of fingers while decreasing t h e f i n g e r width and the distance between fingers lowers the series r e s i s t a n c e and t h e voltage l o s s 141. This has become p a r t i c u l a r l y important f o r devices such a s t h e " v i o l e t c e l l " t h a t have 1000-2000 f( junction depths and lower doping l e v e l s i n t h e diffused region. Violet c e l l s a r e designed with 30 fingers/cm [41, with a f i n a l contact area equal t o 6-7% of the t o t a l . The r e s u l t i n g series resistance i s around 0.05 ohm f o r a 4 cm2 device, considerably l e s s than t h e 0.2-0.25 ohm of more conventional S i devices, i n s p i t e of t h e higher sheet r e s i s t i v i t y and narrower width of t h e diffused region. C.

Experimental Current-Voltage Behavior

Measured S i devices almost always show t h e e f f e c t s of both series and shunt resistances and have higher recombination curr e n t s than predicted by theory [23,69]. Figure 37 shows t h e dark I-V measurement of a 10 ohm-cm N/P S i s o l a r c e l l . The current a t low voltages (less than 0.1 V) i s due t o shunt r e s i s tance (around lo5 ohms). Two exponential regions can be seen s t a r t i n g a t 0.2 V , with slopes of qV/2.lkT and qV/l.lkT, respect i v e l y . The decreasing slope of t h e current around 3 mA/cm2 i s a r e s u l t of t h e s e r i e s r e s i s t a n c e of the device, around 1 ohm. A t t h e short c i r c u i t current value of 30 mA/cm2, 30 mV a r e l o s t across t h i s resistance. Nearly a l l large-area S i c e l l s show some shunt resistance e f f e c t s , a f a c t which i s d i f f i c u l t t o explain from ordinary theories. Edge leakage i s one source of low shunt resistances.

64

3.

SOLAR

CELL ELECTRICAL CHARACTERISTICS

N

I

0.1

l

I

I

I

0.5 Fomard Voltage

0.3

1

0.7

FIG. 3 7 . Dark I - V c h a r a c t e r i s t i c s o f a c o m e r c i a l S i Solar c e l l ( a t 3OO0K), showing t h e t m exponential regions and the e f f e c t o f series r e s i s t a n c e . (The dashed l i n e i s t h e charact e r i s t i c a f t e r correcting f o r t h e s e r i e s r e s i s t a n c e . ) I t i s d i f f i c u l t t o etch t h e edges of a large-area S i device and f i n i s h off t h e etching by a technique t h a t r e s u l t s i n a low density of surface states a t t h e device edges; contaminat i o n from t h e chemicals used and water vapor included i n t h e oxide t h a t forms on t h e edges can both r e s u l t i n leakage. With proper passivation, though, edge leakage can be minimized. S t i r n has pointed out [ 2 3 ] t h a t shunt r e s i s t a n c e problems can a r i s e from small scratches and imperfections on t h e device surface which become p a r t i a l l y o r t o t a l l y covered by t h e cont a c t metallurgy during t h e device f a b r i c a t i o n ; "sintering" t h e contact s t r i p e s t o minimize contact r e s i s t a n c e can cause small metal p a r t i c l e s t o enter t h e s c r a t c h and r e s u l t i n leakage across the p-n junction. Since t h e scratches (and possibly other imperfections such a s stacking f a u l t s ) a r e random along the surface, c e r t a i n areas of t h e device should be b e t t e r i n e l e c t r i c a l p r o p e r t i e s than others. S t i r n [ 2 3 ] has demonstrated t h i s by comparing t h e I - V c h a r a c t e r i s t i c s of a 2x2 cm commerc i a l c e l l with t h e c h a r a c t e r i s t i c s of small mesas etched on the same device (Fig. 38); m o s t small mesas show almost neglig i b l e shunting compared t o t h e f u l l device, while some mesas e x h i b i t much higher leakage than t h e average. The leakage current of t h e f u l l c e l l i s sometimes increased by up t o a hundredfold a f t e r contact s i n t e r i n g compared t o before s i n t e r ing, f u r t h e r establishing t h e r o l e of t h e metallization i n causing shunt r e s i s t a n c e problems.

C.

EXPERIMENTAL CURRENT-VOLTAGE BEHAVIOR

65

M

0.2

0.3

0.4

I

0.5

I

l ’ ,

0.6

1

0.7

I

I

0.8

VOLTAGE, volts

F I G . 3 8 . Dark I - V characteristics o f S i solar c e l l s ( 2 ohm-cm N/P, 192OK), showing the high leakage current measured i n complete ( 4 cm2) c e l l s compared t o mesas etched on the same c e l l s . The A refers t o the slope, from qV/AkT. (After S t i r n 1231; courtesy of the I E E E . )

Most S i and GaAs s o l a r c e l l s e x h i b i t several exponential regions i n t h e dark forward I - V c h a r a c t e r i s t i c s , as seen i n Fig. 37 f o r a S i device and Fig. 39 f o r a GaAs device; t h i s strongly suggests t h e presence of several current components such as J i n j and Jrg- Very seldom do t h e slopes of these expon e n t i a l s ( t h e value of A i n qV/AkT) equal 1 o r 2. For good S i devices, values close t o unity a r e observed (1.1-1.3) a t high voltages and close t o 2 (1.6-1.8) a t lower voltages, with t h e smallest values corresponding t o t h e b e s t devices. For poor devices A values of 3 o r even 4 a r e observed. Values of t h e saturation current J O O(Eqs. (60)(61)) a r e around to A/Cm2 when t h e high current (low A) p a r t of the I - V curve i s estrapolated t o zero v o l t s , and to A/cm2 f o r t h e A 2 portion. According t o theory, these should be around to A/cm2 f o r J i n j and A/cm2 f o r Jrg, f o r 10 ohm-cm cells. Values of A close t o 1 are almost c e r t a i n l y due t o a dominance of t h e injected current J i n . (of a l l the possible current components, t h i s seems t o be $he only one capable of Q ,

66

3.

SOLAR CELL ELECTRICAL CHARACTERISTICS

mE

10

€

1

3 s

4d

'is

si 0.1

P

E

t 3 0.01

0.OolI

0.6

1

0.7

1

0.8

.

1

I

0.9 1.0 Forward Voltage

F I G . 3 9 . Dark I-V c h a r a c t e r i s t i c s o f GaAs solar c e l l s (P/N, 3OOOK). (1) Device w i t h l o w lifetimes and d i f f u s i o n l e n g t h s ; ( 2 ) d e v i c e w i t h high lifetimes and d i f f u s i o n l e n g t h s . Both curves have been c o r r e c t e d for series r e s i s t a n c e .

y i e l d i n g a value of 1). A t high i n ' e c t i o n l e v e l s , amperes p e r an2 r a t h e r than milliamperes per cm3, A approaches 2 , even f o r t h e i n j e c t e d component, b u t t h i s c u r r e n t l e v e l i s not reached i n solar cells u n l e s s they a r e operated a t s e v e r a l hundred solar i n t e n s i t i e s . Values of A close t o 2 a t l o w i n j e c t i o n l e v e l s are most l i k e l y due t o space charge region recombination Jrg o r t o recombination a t t h e edges of t h e device within t h e space charge region 1701; both of t h e s e mechanisms can e x h i b i t Sah A ' s i n t h e range o f 1 t o 2 under c e r t a i n c o n d i t i o n s [70]. [70] has measured t h e I-V c h a r a c t e r i s t i c s of a number of d i f fused S i j u n c t i o n s with small areas and found t h r e e well-defined regions when series r e s i s t a n c e is absent; a t low v o l t a g e s A values of 1.2-1.4 are observed and a t t r i b u t e d t o t h e presence of both Jin, and Jrg. A t m e d i u m v o l t a g e s (0.3-0.5 V i n Sah's devices) t h e i n j e c t e d c u r r e n t becomes dominant and A f a l l s t o around 1. A t high v o l t a g e s (0.7-0.8 V i n Sah's devices) high i n j e c t i o n l e v e l s are reached and A rises t o 2. The higher t h e doping l e v e l i s i n t h e base, t h e h i g h e r t h e v o l t a g e "threshold" is a t which high i n j e c t i o n level e f f e c t s begin t o t a k e p l a c e . High values of A ( > 2 ) are n o t p r e d i c t e d by t h e S-N-S theory [57], b u t could be due i n p a r t t o shunt r e s i s t a n c e e f f e c t s 1231 ( s i n c e a l o w value of shunt r e s i s t a n c e causes a shallow s l o p e i n t h e I - V curve which can be mistaken f o r a recombination curr e n t with a high v a l u e of A) and i n p a r t t o modifications i n t h e S-N-S theory which account f o r nonuniformities i n t h e d i s t r i b u t i o n of recombination c e n t e r s [70,71]. Shockley and

C.

EXPERIMENTAL CURRENT-VOLTAGE BEHAVIOR

67

1o3

102

N

kc! a

10

E

U -I

1

lo-’ L

0.5 0.7 Forward Bias Volts

0.3

0.9

Dark I - V c h a r a c t e r i s t i c s of a t h i n f i l m Cu2S-CdS The c o n s t a n t s l o p e and small change i n magnitude w i t h temperature i m p l y t u n n e l i n g . ( A f t e r Martinuzzi e t a l . [771; c o u r t e s y of the I E E E . )

FIG. 40.

solar cell a s a f u n c t i o n o f temperature.

co-workers 171,721 attributed high values of A in their Si junctions to a reduced density of recombination centers at the middle of the space charge region compared to points away from the middle. Nakamura and co-workers 1731 have found that redistribution of heavy metal impurities (gettering) can take place during device processing with strong increases of impurity densities near the surface; this would tend to increase measured recombination currents and measured values of A above values predicted by theory. Sah has postulated that high A values can arise in planar p-n junction devices due to surface channels caused by surface states. In solar cells these channels would lie along the device edges and extend into the base. G a s solar cells tend to be dominated by recombination currents and most devices exhibit a qV/2kT dependence over much of their current range. The dominance of the recombination component is most likely due to low values of lifetime and diffusion lengths; if lifetimes corresponding to 4 pm diffusion lengths are used in E q s . (50) and ( 5 4 ) , theory predicts that Jrg will dominate at low voltage (c0.8 V) and Jinj will dominate at higher values. Figure 39 shows the dark I-V curves of two GaAs p-n junction solar cells (pGal,xA1fis-pGaAs-nGaAs devices)

68

3.

SOLAR C E U ELECTRICAL CHARACTERISTICS

FIG. 4 1 . Dark I - V characteristics of a s i n g l e - c r y s t a l Cu2SCdS s o l a r cell a f t e r normal heat t r e a t m e n t , 1 min a t 25OOC. ( A f t e r G i l l and Bube [74]; c o u r t e s y of t h e American I n s t i t u t e of P h y s i c s . ) produced by liquid-phase epitaxy. Device #1 is known t o have d i f f u s i o n l e n g t h s of around 1 pm and e x h i b i t s a qV/2kT v a r i a t i o n over t h e e n t i r e range of measured c u r r e n t s . Device #2 i s estimated from s p e c t r a l response measurements t o have d i f f u sion l e n g t h s of 3 pm o r more; it e x h i b i t s recombination c u r r e n t with A = 1.9 a t v o l t a g e s less than 0.9 V and i n j e c t i o n c u r r e n t with A = 1.17 a t h i g h e r v o l t a g e s . Device #1 i s t y p i c a l of vapor d i f f u s e d GaAs cells and device #2 is t y p i c a l o f good LPEproduced u n i t s . The dark current-voltage c h a r a c t e r i s t i c s of h e t e r o j u n c t i o n devices a r e n e a r l y always dominated by tunneling. Many experimenters have observed tunneling c u r r e n t s i n Cu2S-CdS s o l a r c e l l s i n both t h e forward and reverse-biased d i r e c t i o n s [55,74-781. Figures 40 and 41 show dark forward I-V c h a r a c t e r i s t i c s of such c e l l s a s a f u n c t i o n of temperature; t h e independence of t h e slope of t h e Iln J versus V and t h e s m a l l change i n t h e c u r r e n t magnitude w i t h temperature are c h a r a c t e r i s t i c o f tunnelingl i m i t e d c u r r e n t s . The I-V c h a r a c t e r i s t i c s are a f f e c t e d s t r o n g l y by the h e a t treatment normally employed during t h e device processing; t h e c u r r e n t a f t e r h e a t treatment measured a t room temperature and below is decreased by s e v e r a l orders-of-magnitude below i t s preheated value. G i l l and B u b e [741 have sugg e s t e d t h a t deep acceptor imperfections (probably Cu i o n s ) have d i f f u s e d f o r a s h o r t d i s t a n c e i n t o t h e normally n-type CdS during t h e h e a t t r e a t m e n t , widening t h e d e p l e t i o n l a y e r and lowering t h e t u n n e l i n g p r o b a b i l i t y . I n l a t e r papers, Fahrenbruch, Lindquist, and B u b e [55,75,76,781 suggest t h a t t h e dark c u r r e n t a f t e r h e a t treatment c o n s i s t s of both a thermal i n j e c t i o n component and a t u n n e l i n g component. The i n j e c t i o n c u r r e n t

D.

SUMMARY

69

becomes dominant above 320°K and i s due t o t h e i n j e c t i o n of electrons from t h e CdS i n t o t h e Cu2S conduction band; the a c t i vation energy of 1 . 2 eV f o r t h i s current corresponds t o t h e b a r r i e r height between t h e two conduction bands. The tunneling current i s dominant below 320°K (as shown by Fig. 41) and i s assumed t o be caused by t h e tunneling of electrons from t h e CdS i n t o i n t e r f a c e s t a t e s where they recombine with holes which have tunneled t h e r e from t h e Cu2S. The observed a c t i v a t i o n energy of 0.45 e V f o r t h e tunneling i s due t o t h e need f o r t h e electrons t o thermally surmount a portion of t h e energy b a r r i e r before the remainder of the depletion region i n t h e CdS becomes t h i n enough f o r appreciable tunneling t o occur. The current i n t h i s tunneling regime can be described by [55,76,78] J

= J o exp(BV)

(67)

where t h e Jo term is highly dependent on processing because of the v a r i a b i l i t y of defect s t a t e s ( N t i n Eq. (57)) while t h e exponent B i s dependent on t h e doping l e v e l s , d i e l e c t r i c cons t a n t s , and number of intermediate tunneling steps. The cons t a n t B i s not strongly affected by processing as is Jo [78]; t y p i c a l values f o r B f o r non-heat-treated devices ( f o r voltages above 0.35 V) range from 24 t o 30, while J o varies from A/cm2 t o a h s t l o m 6 A/cm2 [761. For heat-treated u n i t s (seve r a l minutes t o several hours a t 10O-25O0C), B i s again about 24 t o 30, while J O has decreased by 2 t o a s much a s 5 ordersof-magnitude 1741. The thermal component with 1 . 2 e V a c t i v a t i o n energy which i s present i n heat t r e a t e d devices above 320°K i s not observed i n non-heat-treated units 1741 due t o t h e much higher tunneling current i n these u n i t s t h a t e s s e n t i a l l y “swamps out” any i n j e c t i o n current t h a t might be present.

The current-voltage behavior of a s o l a r c e l l i n t h e dark is j u s t as important as i t s behavior i n t h e l i g h t , since t h e dark behavior l a r g e l y determines t h e voltage output and f i l l f a c t o r . The dark I-V c h a r a c t e r i s t i c s a r e determined by t h e combined e f f e c t s of t h e current transport mechanisms which may be present and any s e r i e s and shunt r e s i s t a n c e problems t h a t may arise. The two current components of most importance a r e t h e i n j e c t e d component due t o the i n j e c t i o n of minority carriers from t h e top region i n t o t h e base, and t h e depletion region recombination current due t o t h e recombination of part i a l l y injected holes and electrons within t h e depletion region.

70

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i n both t h e base In cases of high doping l e v e l s and top regions, a t h i r d component due t o tunneling may be present. The i n j e c t e d c u r r e n t is determined mostly by conditions i n t h e base, and has been calculated f o r t h e three models of uniform base doping, constant electric f i e l d i n t h e base, and a back surface f i e l d . The depletion region recombination curr e n t and t h e tunneling current a r e determined by conditions within t h e depletion region, and depend strongly on t h e width of t h i s region, t h e l i f e t i m e within i t , and t h e number of def e c t states a v a i l a b l e f o r tunneling. Experimental I-V measurements i n d i c a t e t h a t t h e depletion region recombination current i s considerably higher i n S i and GaAs s o l a r cells than expected from theory. This might be a t t r i b u t e d t o a poor l i f e t i m e i n the depletion region due t o unwanted impurities introduced during t h e d i f f u s i o n , or it might i n d i c a t e t h a t t h e present theory of depletion region recombination requires revision t o bring it c l o s e r t o t h e experimental r e s u l t s . Shunt r e s i s t a n c e problems can add t o t h e d i f f i c u l t y of i n t e r p r e t i n g I-V d a t a , but t h e s e problems can be minimized with proper c a r e during contact s i n t e r i n g and with care i n preventing scratches and other d e f e c t s from being introduced during processing. The equivalent c i r c u i t of a s o l a r c e l l c o n s i s t s of a photocurrent generator i n p a r a l l e l with a diode and a shunt r e s i s t a n c e , and a series r e s i s t a n c e leading t o t h e output terminals. From t h i s equivalent c i r c u i t , t h e power output from t h e c e l l can be calculated under various conditions. The series r e s i s t a n c e lowers t h e s h o r t c i r c u i t current without a f f e c t i n g t h e open c i r c u i t voltage, while t h e shunt r e s i s t a n c e does j u s t t h e opposite. Both r e s i s t a n c e s degrade t h e f i l l factor. Analytical expressions can be derived for t h e f i l l f a c t o r and f o r t h e voltage and current operating points i f t h e s e r i e s and shunt r e s i s t a n c e e f f e c t s can be ignored and i f t h e I - V c h a r a c t e r i s t i c can be represented by a s i n g l e exponential instead of t h e sum of several exponentials. F i l l f a c t o r s of 0.75 t o 0.82 f o r S i c e l l s and 0.79 t o 0.85 f o r GaAs c e l l s are predicted t h i s way. Usually series r e s i s t a n c e (and sometimes shunt r e s i s t a n c e ) e f f e c t s cannot be ignored, and several curr e n t mechanisms a r e present. This leads t o s l i g h t l y lower f i l l f a c t o r s and operating voltages, i n agreement with experimental r e s u l t s .

CHAPTER 4

Efficiency

The efficiency of a s o l a r c e l l i n converting sunlight i n t o useful e l e c t r i c a l energy i s t h e s i n g l e most important number defining t h e q u a l i t y of the c e l l . Unfortunately, t h e r e has been no clear-cut standardization of s o l a r c e l l efficiency measurements over the years, and d i f f e r e n t numbers have been reported f o r t h e same type of c e l l without c l e a r l y s t a t i n g t h e s p e c t r a l conditions during t h e measurement. A problem a r i s e s due t o t h e nonuniform s p e c t r a l responses of s o l a r cells; they convert l i g h t of some wavelengths b e t t e r than they do other wavelengths. Since t h e s o l a r spectrum outside the e a r t h ' s atmosphere i s d i f f e r e n t from t h e spectrum received on t h e e a r t h on a c l e a r day, and both of these d i f f e r from t h e spectrum on a hazy day, t h e e f f i c i e n c i e s measured under each of these cond i t i o n s a r e d i f f e r e n t . In t h e early days of s o l a r c e l l s t h e s p e c t r a l conditions f o r outdoor measurements were often not even mentioned, and t h e r e was undoubtedly some e r r o r i n many of t h e reported values. In some instances e f f i c i e n c i e s were reported f o r tungsten bulb (indoor) incident l i g h t , which has a r e l a t i v e l y low color temperature compared t o sunlight. Today, very good simulation of outer space (AM01 sunlight has been developed, consisting of a xenon l i g h t source with c e r t a i n types of absorbing f i l t e r s t o remove c e r t a i n peaks i n t h e xenon l i n e spectrum. A good simulator f o r e a r t h sunlight a t AM1 o r AM2 has y e t t o be developed, but a reasonable simulation can be obtained with a quartz-halogen bulb and a 2-3 m water f i l t e r . Another source of confusion i n s o l a r c e l l measurements a r i s e s from the tendency of some experimenters t o report values corrected f o r the contact area l o s s and o t h e r s t o report uncorrected values. Uncorrected e f f i c i e n c i e s a r e reported on t h e philosophy t h a t these describe what the c e l l can a c t u a l l y d e l i v e r , while efficiency values corrected f o r t h e contact area a r e reported on the b a s i s t h a t these a r e t h e inherent e f f i c i e n c i e s of t h e devices without t h e human f a c t o r s of contact design and process technology. Actually, it seems reasonable t h a t

71

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EFFICIENCY

both values should be reported a t t h e same time, which would eliminate ambiguity. High photocurrents, open c i r c u i t voltages, and f i l l fact o r s n a t u r a l l y lead t o high e f f i c i e n c i e s i n s o l a r c e l l s . A wide, f l a t s p e c t r a l response i n t h e v i s i b l e and near-infrared s p e c t r a l regions and a peak quantum efficiency c l o s e t o unity lead t o high photocurrents, while low forward dark currents and high shunt r e s i s t a n c e s lead t o high open c i r c u i t voltages. Good f i l l f a c t o r s can be obtained i f t h e forward dark currents a r e low, t h e value of A. ( t h e diode I-V "perfection f a c t o r " ) is low, t h e s e r i e s r e s i s t a n c e i s low (less than 1 ohm f o r a 1 cm2 area) , and t h e shunt r e s i s t a n c e i s high ( g r e a t e r than lo4 ohms). Materials with high bandgaps t h e o r e t i c a l l y have higher open c i r c u i t voltages and f i l l f a c t o r s while lower bandgap materials y i e l d higher photocurrents, leading t o a maximum i n t h e efficiency versus bandgap a t about 1.5 eV. In t h i s chapter, t h e e f f i c i e n c i e s a t AMO, AM1, and AM2 w i l l be described f o r s e v e r a l device models and f o r various device parameters, a s has been done f o r t h e s h o r t c i r c u i t curr e n t and d a r k current i n t h e previous two chapters. Dead l a y e r s , high surface recombination v e l o c i t i e s , poor l i f e t i m e s , and high s e r i e s or shunt r e s i s t a n c e l o s s e s r e s u l t i n low e f f i ciencies. Reducing t h e junction depth, incorporating aiding e l e c t r i c f i e l d s , improving t h e l i f e t i m e s , and preventing resistance losses are a l l b e n e f i c i a l i n improving t h e e f f i c i e n c i e s . A.

Calculated E f f i c i e n c i e s

The efficiency of a s o l a r cell i n converting l i g h t of any a r b i t r a r y s p e c t r a l d i s t r i b u t i o n i n t o useful power i s given by

where ,V 1, a r e t h e voltage and current a t t h e maximum power point (Fig. 2 ) . The input power i s 53

Pin

= At

I

F(X) (hc/h) dX

(69)

0

where At is t h e t o t a l device area, F ( h ) i s t h e number of photons per cm2 per sec per u n i t bandwidth incident on t h e device a t wavelength X and hc/A i s t h e energy c a r r i e d by each photon. For s u n l i g h t , t h e spectrum F(X) was shown i n Fig. 19 a t AM0 and AM2. The power output is given by Pout = VmIm

FF VocIsc.

(70)

A.

CALCULATED EFFICIENCIES

73

These equations have been w r i t t e n i n terms of c u r r e n t r a t h e r than c u r r e n t d e n s i t y t o t a k e account of t h e small d i f f e r e n c e between t h e t o t a l and a c t i v e device areas At and A,. I t is p o s s i b l e t o f i n d a n a l y t i c a l expressions f o r t h e e f f i c i e n c y under c e r t a i n i d e a l i z e d c o n d i t i o n s , namely, t h o s e f o r which t h e series and shunt r e s i s t a n c e l o s s e s are ignored. I n t h i s case, assuming t h e dark forward I - V c h a r a c t e r i s t i c can be approximated by t h e s i n g l e exponential i n Eq. ( 6 0 ) , t h e e f f i c i e n c y can be w r i t t e n as

where FF i s given by (661, Voc by (11, and Is, by (36) multip l i e d by t h e a c t i v e area. H i s t o r i c a l l y , a second type of a n a l y t i c a l expression has been derived [64,651 under t h e same i d e a l i z e d assumptions which places t h e e f f i c i e n c y i n terms of t h e average number of c a r r i e r s c o l l e c t e d and t h e average energy of t h e photon i n t h e spectrum

where Nph i s t h e t o t a l number of photons per cm2 per sec i n t h e source Spectrum, Ea, i s t h e i r average energy, nph(Eg) i s t h e number of photons p e r c m 2 per sec with energy g r e a t e r t h a n t h e bandgap, R i s t h e average r e f l e c t i v i t y , and Q i s t h e average " c o l l e c t i o n e f f i c i e n c y , " t h e r a t i o of t h e number of carriers c o l l e c t e d t o nph(Eg), t h e number capable of being c o l l e c t e d . The c o l l e c t i o n e f f i c i e n c y i s r e l a t e d t o t h e s p e c t r a l response by m

and i n t h e event t h a t monochromatic l i g h t is i n c i d e n t , t h e s p e c t r a l response and t h e c o l l e c t i o n e f f i c i e n c y are i d e n t i c a l . (The two ways of expressing t h e e f f i c i e n c y are, of course, equivalent, b u t t h e second method involves a number of averages and i s more d i f f i c u l t t o work with.) The e f f i c i e n c y is a f u n c t i o n of t h e bandgap through t h e i n f l u e n c e s of Voc, FF, and Isc. I t w a s conjectured i n t h e e a r l y s o l a r c e l l days t h a t a maximum would e x i s t a t some bandgap between 1.0 and 2.0 eV. I n order t o e s t a b l i s h what t h i s optimum bandgap might be, a q u a n t i t y known as t h e " l i m i t

74

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conversion efficiency" w a s calculated by making t h e i d e a l assumptions of 100%absorption of a l l photons with energies g r e a t e r than t h e bandgap, 100%c o l l e c t i o n of a l l generated c a r r i e r s , and ideal junction c h a r a c t e r i s t i c s (along with the assumptions of n e g l i g i b l e series and shunt r e s i s t a n c e e f f e c t s , n e g l i g i b l e contact area, and n e g l i g i b l e l i g h t r e f l e c t i o n ) . Under these conditions, t h e efficiency can be w r i t t e n as

where A, and A t a r e equal. The i d e a l s h o r t c i r c u i t current density, q%h(Eg), has already been shown i n Fig. 20 and t h e l i m i t conversion e f f i c i e n c i e s a t AM0 and AM2 calculated from (74) a r e shown i n Fig. 42. The maximum occurs a t around 1.5 eV a t 22.5% for AM0 and around 1.4 e V a t 26% f o r AM2. The shape of t h e AM2 curve and t h e higher e f f i c i e n c i e s a t AM2 a r e due t o the removal of most of t h e u l t r a v i o l e t and portions of t h e i n f r a r e d l i g h t by t h e atmosphere, channeling t h e sun's energy more and more toward t h e v i s i b l e region where t h e s p e c t r a l response i s high as t h e a i r mass increases. I t is important t o regard c a l c u l a t i o n s such as those of Fig. 42 i n a q u a l i t a t i v e sense only. In order to obtain t h i s curve, which demonstrates t h e e f f e c t of bandgap alone, it i s necessary t o assume t h a t material parameters such as mobilities, l i f e t i m e s , doping l e v e l s , and d e n s i t i e s of states a r e t h e same f o r a l l materials over t h e applicable bandgap range. For Fig. 42 t h e parameters of 1 ohm-cm S i have been used, but i f t h e values applicable t o 0.1 ohm-cm S i were used and 100%collect i o n s t i l l assumed, both of t h e curves i n Fig. 42 would be s h i f t e d upward. Different d i f f u s i o n lengths and l i f e t i m e s , d e n s i t i e s of s t a t e s , doping l e v e l s , recombination v e l o c i t i e s , and t h e d i r e c t n e s s o r indirectness of t h e energy bandgap, a l l have strong e f f e c t s on t h e expected e f f i c i e n c i e s of r e a l devices, and individual real materials such a s GaAs, G a p , InP, e t c . , may f a l l e i t h e r above o r below such an i d e a l i z e d curve. The most accurate way t o c a l c u l a t e t h e a c t u a l e f f i c i e n c i e s expected under various conditions i s t o use numerical methods as outlined by Fossom [391. The continuity and current equat i o n s together with Poisson's equation are solved exactly, taking i n t o account t h e v a r i a t i o n of l i f e t i m e , mobility, elect r i c f i e l d , and majority and minority c a r r i e r d e n s i t i e s as a function of doping l e v e l and position. Fossom's type of analysis is p a r t i c u l a r l y valuable when used t o c a l c u l a t e high inject i o n l e v e l behavior, where t h e generated minority carrier

A.

CALCULATED EFFICIENCIES

75

24

ae

20

4 t

0

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Band Gap Energy, eV

F I G . 4 2 . L i m i t conversion e f f i c i e n c i e s a s a f u n c t i o n o f energy gap a t AM0 ( i n p u t power d e n s i t y = 135.3 nW/cm2) and a t AM2 ( i n p u t power d e n s i t y 4 7 4 mW/cm2).

d e n s i t i e s become comparable t o t h e majority c a r r i e r d e n s i t i e s (several hundred s o l a r i n t e n s i t i e s i n G a s , 50 t o 100 i n S i ) . It is much easier, however, t o use a n a l y t i c a l t o o l s than it i s t o use numerical methods. A reasonably accurate method of calculating expected e f f i c i e n c i e s f o r a wide range of cond i t i o n s c o n s i s t s of the use of (36) t o compute t h e photocurrent and (58) t o compute t h e dark current as a function of voltage. Equation (59) yields t h e r e l a t i o n s h i p between Ioutand Vout f o r a r b i t r a r y s e r i e s and shunt r e s i s t a n c e s , and t h e efficiency is j u s t t h e maximum i n V o u t ' Iout divided by t h e s o l a r input. Reflection of incident l i g h t from t h e surface as a function of wavelength and losses due t o contact area can a l s o be included as desired. I f s e r i e s and shunt r e s i s t a n c e e f f e c t s can be ignored, t h e output current is given simply by (Iph'Idark), and t h e power output i s j u s t Vj(Iph-Idark). Since t h e Series and shunt r e s i s t a n c e s and t h e contact area l o s s are determined l a r g e l y by technology ( s e r i e s resistance and contact l o s s can be minimized by optimizing t h e g r i d design and shunt r e s i s t a n c e can be maximized by edge passivation and by preventing metal-semiconductor i n t e r d i f f u s i o n during contact s i n t e r i n g ) , and s i n c e r e f l e c t i o n of the incident l i g h t can be made small by proper a n t i r e f l e c t i o n coatings, it has proven useful t o c a l c u l a t e the somewhat idealized e f f i c i e n c i e s obtained by neglecting these technology-oriented losses. The r e s u l t w i l l be an "inherent" device efficiency demonstrating t h e e f f e c t s of dead layers, depletion region recombination currents, surface recombination,

76

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J

Resistivity, fi - cm

F I G . 4 3 . Calculated inherent e f f i c i e n c i e s o f S i N/P ( s o l i d ) and P / N (dashed) s o l a r c e l l s v e r s u s base r e s i s t i v i t y under o p t i m i s t i c c o n d i t i o n s . The efficiencies f o r GaAs P / N cells under optimum c o n d i t i o n s a r e a l s o shown. T = 300°K, S f r o n t = S h C k = lo2 cm/sec, d r i f t f i e l d s p r e s e n t .

junction depth, e l e c t r i c f i e l d s , and l i f e t i m e . It i s assumed t h a t l i g h t makes only one pass through t h e device, and e x i t s a t t h e back surface r a t h e r than being r e f l e c t e d back i n t o t h e c e l l ; such multiple passes of l i g h t would r a i s e t h e predicted e f f i c i e n c i e s s l i g h t l y , and can become important f o r t h i n s o l a r c e l l s where t h e absorption of long wavelength l i g h t i n a s i n g l e pass can be low. 1.

SILICON

In t h i s section t h e "inherent" e f f i c i e n c i e s of S i s o l a r c e l l s calculated by t h e method j u s t outlined w i l l be shown. The e f f i c i e n c i e s of S i N/P and P/N s o l a r c e l l s under t h e most o p t i m i s t i c conditions a r e shown i n Fig. 4 3 f o r AMO, AM1, and AM2. These a r e t h e counterparts t o t h e " l i m i t conversion e f f i c i e n c i e s , " i . e . , they a r e computed using t h e highest l i f e times found i n the l i t e r a t u r e f o r S i r those of Kendall [791. AM0 e f f i c i e n c i e s of 18 t o 21% could conceivably be obtained i f these very high l i f e t i m e s of t h e b e s t bulk S i could a l s o be obtained i n finished devices (T = 200, 50, 20, 500, 200, and 50 psecs €or minority c a r r i e r s i n 10, 1, and 0.1 ohm-cm p-type and n-type S i r r e s p e c t i v e l y ) . The l i f e t i m e s measured i n a c t u a l S i devices have generally been about an order-of-magnitude l e s s than these o p t i m i s t i c values, and t h e expected e f f i c i e n c i e s of a c t u a l devices a r e correspondingly less. Some of t h e expected material parameters f o r good S i devices were shown i n Table 4 , and t h e e f f i c i e n c i e s

A.

10 102

CALCULATED EFFICIENCIES

lo3 104 lo5 106 Surface Rec. Vet., cm/sec

77

lo7

F I G . 4 4 . C a l c u l a t e d i n h e r e n t e f f i c i e n c i e s a t AM0 o f N/P ( s o l i d ) and P/N (dashed) Si s o l a r c e l l s f o r X j = 0 . 4 pm and t h e parameters o f Table 4 . The numbers refer t o t h e b a s e r e s i s t i v i t y i n ohm-cm. No d r i f t f i e l d s , no dead l a y e r . Shack = 00. C o n d i t i o n s : high r n r r p ; 18 m i l .

f o r AM0 of 10, 1, and 0.1 ohm-cm N/P and P/N devices c a l c u l a t e d using t h e s e parameters a r e shown i n Fig. 44 as a function of t h e f r o n t s u r f a c e recombination v e l o c i t y . The l i f e t i m e i n t h e t o p region has been taken a t a high value as given by Ross and Madigan 1181 (rPo = 0 . 4 pSeC, 'no = 1.1 p s e c ) , i . e . , t h e r e i s no "dead l a y e r " p r e s e n t . For t h e b e s t c a s e under t h e s e condit i o n s , t h a t of a 0.1 ohm-cm N/P device, t h e h i g h e s t c a l c u l a t e d e f f i c i e n c y i s c l o s e t o 18% (values f o r 0.01 ohm-cm devices have not been computed because of t h e u n c e r t a i n t y i n t h e e f f e c t of t h e t u n n e l i n g c u r r e n t Jtun a t high doping l e v e l s i n S i ) . The f i l l f a c t o r and open c i r c u i t v o l t a g e improve while t h e photoc u r r e n t decreases with i n c r e a s i n g doping l e v e l i n t h e base; t h e n e t r e s u l t of t h e s e c o n f l i c t i n g f a c t o r s is t h a t t h e e f f i ciency improves somewhat with decreasing base r e s i s t i v i t y . The e f f i c i e n c i e s of N/P devices are s l i g h t l y higher than t h o s e of P/N c e l l s f o r equal r e s i s t i v i t i e s , due t o t h e higher doping l e v e l f o r p-type material compared t o n-type and due t o t h e l a r g e r l i f e t i m e s and d i f f u s i o n l e n g t h s f o r e l e c t r o n s compared t o holes f o r equal r e s i s t i v i t i e s . So f a r , t h e e f f i c i e n c i e s of s o l a r c e l l s under r a t h e r good conditions have been discussed. I t i s a l s o important t o d i s cuss t h e d i f f i c u l t i e s t h a t can arise and what can be done about them. There are two s e r i o u s loss mechanisms t h a t may b e p r e s e n t i n t h e t o p region: s u r f a c e recombination, and bulk recombinat i o n i n a "dead l a y e r " of very low l i f e t i m e . The e f f e c t of t h e s e two l o s s e s on t h e spectral response and dark c u r r e n t behavior of S i devices has a l r e a d y been discussed i n Chapters 2

78

4. EFFICIENCY

and 3, and t h e e f f e c t of one of them (surface recombination) f o r c e l l s with the parameters of T a b l e 4 has been included i n Fig. 44. Surface recombination i s caused by surface s t a t e s which r e s u l t from u n s a t i s f i e d bonds and from impurities present a t t h e surface; recombination v e l o c i t i e s can be as high as lo5l o 6 cm/sec on S i , and 106-107 cm/sec on GaAs. A "dead layer" i n the top region i s a region near t h e surface with nanosecond o r even subnanosecond l i f e t i m e , caused by t h e s t r a i n , dislocat i o n s , and unwanted impurities sometimes introduced during t h e diffusion o r during o t h e r processing s t e p s . Such dead layers have been described p a r t i c u l a r l y f o r phosphorus-diffused devices [ 4 ] , and t h e success of t h e " v i o l e t c e l l " has been a t t r i b uted t o t h e elimination of t h e dead l a y e r 141 by lowering t h e 'surface concentration of t h e d i f f u s i o n and reducing t h e junction depth. These recombination l o s s e s i n t h e top region can be reduced by decreasing t h e junction depth and by incorporating an aiding d r i f t f i e l d i n t h e top region; both of these s t e p s improve t h e photocurrent and t h e efficiency. Decreasing t h e junction depth minimizes t h e number of c a r r i e r s generated i n t h e top region and moves t h e edge of t h e depletion region (a p e r f e c t "sink" f o r minority c a r r i e r s ) c l o s e r to t h e surface, so t h a t generated carriers have a higher p r o b a b i l i t y of reaching it r a t h e r than recombining. An aiding e l e c t r i c f i e l d improves t h e c o l l e c t i o n efficiency by adding a d r i f t force on t h e photogenerated carriers, moving them toward t h e junction. The b e n e f i c i a l e f f e c t s of a reduced junction depth and an aiding d r i f t f i e l d i n t h e top region can be seen i n Fig. 45. These e f f i c i e n c i e s have been calculated f o r a 1 ohm-cm N/P dev i c e with a dead l a y e r present; t h e average l i f e t i m e i n t h e top region has been taken as 3 nsec. The combined e f f e c t s of surface recombination and t h e dead layer can lower t h e efficiency s u b s t a n t i a l l y f o r l a r g e junction depths, but lowering t h e depth (which a l s o increases t h e magnitude of t h e e l e c t r i c f i e l d ) brings t h e efficiency nearly t o as high a value (17%, Fig. 44) as can be obtained f o r low values of Sp and without a dead l a y e r present. The highest predicted AM0 e f f i c i e n c i e s are obtained f o r 0.1 ohm-cm p-type bases (see Fig. 44) when t h e r e i s no dead l a y e r present and when t h e junction depth i s low and t h e d r i f t f i e l d high t o overcome surface recombination. Values of nearly 18%can be obtained f o r the parameters of T a b l e 4 even with r e l a t i v e l y high values of Sp (but no dead l a y e r ) , as shown i n Fig. 46 ( s o l i d l i n e s ) , and over 17%can be obtained even with a velocity of lo6 cm/sec. The e f f i c i e n c i e s could be even higher i f t h e base l i f e t i m e were l a r g e r , s i n c e i n s u f f i c i e n t c o l l e c t i o n of photogenerated carriers i n t h e base i s a serious l o s s a t

A.

CALCULATED EFFICIENCIES

79

0.2 0.4 0.6 0.8 Junction Depth, micron F I G . 45. C a l c u l a t e d i n h e r e n t e f f i c i e n c i e s o f a 1 ohm-cm S i N / P s o l a r cell a t AM0 w i t h a dead l a y e r p r e s e n t i n the t o p ~ 3~10-' sec). Solid lines-with d r i f t f i e l d present region ( T =

i n t o p r e g i o n ; dashed l i n e s - - w i t h o u t 'back = O0-

a drift field.

H = 18 m i l .

these high doping levels. The computed e f f i c i e n c i e s f o r 0.1 ohm-cm devices with t h e parameters of T a b l e 4 except f o r t h e base l i f e t i m e and diffusion length a r e shown i n Fig. 46 as dashed l i n e s ( l i f e t i m e = 10 psec, diffusion length = 104 pm). Efficiencies of nearly 20% are predicted under t h e b e s t condit i o n s , and almost 19%even f o r a high value of Sp. (The presence of a dead layer i n t h e top region would lower these calculated values by about l%, i . e . , from 20 t o 19%.) The higher base l i f e t i m e improves t h e s h o r t c i r c u i t current, but it i m proves t h e open c i r c u i t voltage even more by reducing t h e dark current. Theoretically, t h e improvement shown f o r t h e high base l i f e t i m e can a l s o be obtained by incorporating a d r i f t f i e l d i n t h e base. Quantitatively, however, it i s not clear how b e n e f i c i a l a base d r i f t f i e l d might be on t h e efficiency, since t h e increasing doping l e v e l i n t h e base as a function of posit i o n , necessary t o obtain t h e d r i f t f i e l d , a l s o r e s u l t s i n a decreasing l i f e t i m e and mobility as a function of position i n t h e base. I t seems l i k e l y t h a t base d r i f t f i e l d s could r e s u l t i n improved e f f i c i e n c i e s , a t l e a s t f o r low and moderate base l i f e t i m e s , but t h e d i f f i c u l t y and c o s t of diffusing over distances of tens of microns might outweigh t h e b e n e f i t s obtained. I t should be noted t h a t s l i g h t l y higher e f f i c i e n c i e s could be predicted f o r 0.01 ohm-cm r e s i s t i v i t i e s than f o r higher base r e s i s t i v i t i e s i f the tunneling component is ignored, but the v a l i d i t y of ignoring t h i s current i s doubtful a t t h e 1019 doping l e v e l s present a t t h i s r e s i s t i v i t y .

80

4.

EFFICIENCY

m 19

16

15

0

0.2

0.4

0.6

0.8

Junction Depth, microns

1.0

F I G . 4 6 . C a l c u l a t e d inherent e f f i c i e n c i e s o f a 0 . 1 ohm-cm Si N/P s o l a r cell a t AM0 w i t h o u t a dead l a y e r p r e s e n t and w i t h an electric f i e l d i n the t o p r e g i o n . S o l i d l i n e s - e x p e c t e d good b a s e l i f e t i m e of 2 . 5 wee; dashed l i n e s - - v e r y h i g h b a s e l i f e t i m e o f 10 Psec. N = 18 m i l . ShCk = 00.

Figure 46 a l s o shows t h a t t h e e f f i c i e n c y i s c o n s t a n t as a f u n c t i o n of j u n c t i o n depth when t h e s u r f a c e recombination v e l o c i t y i s low and t h e bulk l i f e t i m e i n t h e t o p region i s high. The e f f i c i e n c y continues t o be c o n s t a n t f o r j u n c t i o n depths up t o about 7-8 urn, a f t e r which t h e bulk recombination becomes s i g n i f i c a n t . T t should b e possible t h e r e f o r e t o f a b r i cate e f f i c i e n t S i solar cells by epitaxial growth of t h e t o p region r a t h e r than by d i f f u s i o n , as long as t h e t h i c k n e s s of t h e e p i t a x i a l l a y e r i s no more t h a n about 2/3 of t h e v a l u e of t h e d i f f u s i o n l e n g t h i n t h e t o p region. The e f f e c t of t h e "back s u r f a c e f i e l d " as f a r as t h e e f f i ciency i s concerned f o r t h e s e 450-urn t h i c k d e v i c e s is p r a c t i c a l l y (but not t o t a l l y ) n e g l i g i b l e . The back s u r f a c e f i e l d concept becomes p a r t i c u l a r l y v a l u a b l e when t h e t h i c k n e s s i s reduced, as d i s c u s s e d i n Chapter 5.

2.

GALLIUM ARSENIDE

The i n h e r e n t AMO, AM1, and AM2 e f f i c i e n c i e s of GaAs P/N c e l l s under o p t i m i s t i c c o n d i t i o n s are shown i n Fig. 43. There are two sets of numbers shown; the f i r s t ( X ' s ) r e p r e s e n t v a l u e s obtained i f n i , t h e i n t r i n s i c carrier d e n s i t y , i s equal t o lx107 cm-3 as i s commonly assumed f o r GaAs [80]. The second s e t of values (circles) r e p r e s e n t numbers computed i f n i = 1 . 8 X 1 O 6 cm-3 as measured by S e l l and Casey [81]. E f f i c i e n c i e s of 22-25% are p r e d i c t e d a t AMO, 25-28% a t AM1, and 26-29% a t

0

0.2

A.

CALCULATED EFFICIENCIES

0.4

0.6

0.8

81

1.0

Junction Depth, p

F I G . 4 7 . C a l c u l a t e d inherent e f f i c i e n c i e s of 0.01 ohm-cm GaAs solar cells a t AM0 ( s o l i d ) and AM2 (dashed) for t h e parameters o f Table 5 . N o d r i f t f i e l d s . Shack = 00. H = 12 m i l .

AM2 under idealized conditions. The l i f e t i m e s used i n these ~ for calculations were 2 . 1 ~ 1 0 - sec ~ f o r t h e base and 4 ~ 1 0 -sec t h e top region, with S a t t h e f r o n t surface equal t o l o 3 cm/sec or less and an aiding d r i f t f i e l d present ( t h e recombination velocity a t t h e back surface has no e f f e c t on t h e calculations a t these device thicknesses). The l i f e t i m e s measured i n good finished devices made from high q u a l i t y s t a r t i n g material a r e almost as high as those assumed i n t h e optimistic calculation of Fig. 43 (see Table 3 ) . The surface recombination velocityJ on the other hand, i s gene r a l l y much worse than lo3 cm/sec, often about 106-107 crn/sec f o r finished devices. This high surface l o s s is much more d r a s t i c f o r GaAs and o t h e r d i r e c t bandgap s o l a r c e l l s than i t i s f o r S i because l i g h t i s absorbed and c a r r i e r s created much c l o s e r t o t h e surface. The high recombination velocity reduces t h e short c i r c u i t current by lowering t h e c o l l e c t i o n e i f i c i e n c y , and can even lower the open c i r c u i t voltage and f i l l f a c t o r by increasing t h e forward dark current (the portion of t h e forward dark current a r i s i n g i n t h e top becomes s i g n i f i c a n t i f the r a t i o of t h e doping l e v e l i n t h e top region t o t h e doping l e v e l i n t h e base becomes l e s s than 1 0 ) . The e f f i c i e n c i e s calculated a t AM0 and AM2 of GaAs P/N c e l l s with various surface recombination v e l o c i t i e s and junct i o n depths (but no d r i f t f i e l d s ) a r e shown i n Fig. 47 f o r ~ l i f e t i m e s of l X l O - ’ sec i n the top region and 1 . 5 8 ~ 1 0 -sec i n t h e base (Table 5 ) . A decrease i n recombination velocity from lo7 t o l o 5 cm/sec increases t h e efficiency by a f a c t o r of 2 1 / 2 a t l a r g e junction depths (7-17.5% a t AMO) and a f u r t h e r decrease t o l o 4 cm/sec would r a i s e t h e efficiency by a

82

4.

EFFICIENCY

4

u

0

0.2

0.4

0.6

0.8

1.0

Junction Depth, 1.1

F I G . 4 8 . Calculated inherent efficiencies of 0.01 ohm-cm GaAs P/N solar cells at AMO, both with (solid) and without

(dashed) an electric field in the t o p region. Parameters of Table 5. Shck = 00. H = 12 mil.

factor o f almost 3 (7-20%). Reducing the junction depth helps considerably; the AM0 efficiency can reach 16% for S = lo7 cm/sec and 19% for S = lo6 cm/sec at 0.1 pm junction depths even without aiding fields. (The lifetime and mobility in the base become increasingly important as the junction depth is reduced, however. For example, if the diffusion length in the base is small, 1 vm or less, long wavelength-generated carriers will be lost as the junction depth is reduced and decreasing the depth will only give small improvement in the overall photocurrent. If the base diffusion length is large, 2 pm or more, decreasing the depth will not have much effect on the long wavelength collection but will strongly improve the response to short wavelengths, giving a large improvement to the overall photocurrent.) Since the surface losses are so drastic in GaAs, it stands to reason that aiding drift fields in the top region could be of considerable benefit in improving the device behavior, even more than in Si devices. This was first pointed out by Ellis and Moss (371 in 1970, who predicted 20-21% AM0 efficiencies for N/P cells with narrow junctions. The same improvement can be obtained for P/N devices with aiding drift fields, as shown in Fig. 48. The electric field nearly doubles the efficiency of cells with deep junctions and recombination velocities of lo7 cm/sec, and cells with narrow junctions can reach AM0 efficiencies of nearly 20% even though the recombination velocity is this high. The field helps considerably in improving the efficiencies of GaAs P/N or N/P devices with other values of surface recombination velocity also.

A. CALCULATED EFFICIENCIES

83

There are two other features of G a s solar cells which should be mentioned before going on. The first is that the problem of a "dead layer" is probably not as important as in Si solar cells, where the lifetime in the top region is sometimes several orders-of-magnitude less than it ought to be at the doping level which is present. In GaAs devices, the lifetime is already so low to begin with that it takes a relatively great deal of lattice damage to lower it much further, and in any case, diffusions (and vapor growth) of GaAs are carried out at lower temperatures than for Si, and the lattice damage introduced should be correspondingly lower. Very good G a s solar cells can be made with electron lifetimes of 0.5 to 1 nsec in the top region (as in Table 5 and Figs. 47 and 481, and fairly good devices can theoretically be made with electron lifetimes as low as several hundred picoseconds, provided the hole lifetime in the base is 5 to 10 nsec. The second feature is the change in the optimum design from n-type bases to p-type when the junction depth is reduced to less than 0.1 pm. This is due to the larger electron diffusion length compared to the hole diffusion length at a given doping level. When the junction depth is made very small, 50.1 pm, the base region becomes more important than the top region and it is better (i.e., higher efficiencies are obtained) if electrons are the minority carriers in the base. If the junction depth is larger than around 0.1 pm, though, the very small diffusion length for holes (0.1 pm) at the high doping levels found in the diffused top region of N/P devices will result in a high loss of short wavelength carriers (unless a large drift field is present), and P/N cells are more efficient than the N/P variety. Figure 48 shows that the efficiency is fairly constant as a function of junction depth when the surface losses are low. Under these conditions highly efficient GaAs solar cells can be made by epitaxial growth of the top region as well as by diffusion; the epitaxial layer can be several microns thick as long as the electron diffusion length in this layer is 3 pm or higher. Such a condition is difficult (but not impossible, see Table 3) to achieve in GaAs. 3.

Gal,@l$s-GaAs

Reducing the junction depth and incorporating a drift field in the aiffused region have proven to be difficult for GaAs. An alternative method for overcoming the surface recombination problem is to grow a thin, transparent alloy layer of Gal,xA1xAs on the surface of the GaAs junction. The Gal,xA1xAs matches

84

4.

EFFICIENCY

.11 18 c w

16

14 12

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Junction Depth, microns

F I G . 49. Calculated inherent efficiencies o f pGal-xAlxAspGaAs-nGaAs solar cells f o r 2 G a l , & , A s thicknesses ( D ) . I n each set of curves, t h e bottom represents AMO, t h e middle -1, and the t o p AM2. Same conditions a s i n F i g . 1 4 , Table 5 . No f i e l d s , Sba,-k = 03. = 10 Urn; --D = 0.1 pm.

the l a t t i c e of G a A s very c l o s e l y , so t h a t t h e i n t e r f a c e between the two (which is now t h e "surface" of t h e GaAs p-n junction) has very few e l e c t r o n i c s t a t e s and a correspondingly low recombination velocity. A t t h e same t i m e , t h e bandgap of t h e Gal-xA1xAs i s high enough ( 2 . 1 i n d i r e c t , 2.6 d i r e c t ) t o allow most (260%) of t h e l i g h t t o g e t through t o t h e underlying GaAs, and the doping l e v e l of t h e a l l o y l a y e r i s high enough t o help i n reducing t h e s e r i e s r e s i s t a n c e , allowing t h e p-region of the G a A s t o be doped more l i g h t l y f o r a higher l i f e t i m e and b e t t e r c o l l e c t i o n efficiency. Excellent open c i r c u i t voltages and f i l l f a c t o r s have been obtained i n pGal,xA1xAs-pGaAs-nGaAs devices with Gal-XAlxAs thicknesses of 2-10 um [9], but t h e s h o r t c i r c u i t currents have been only 20-22 mA/cm2 f o r AMO. Analyses of t h e s p e c t r a l responses of devices which have such thick G a l - x A l x A s layers show t h a t surface recombination l o s s e s are not t h e cause of t h e low Isc's i n these devices; i n f a c t t h e measurements indic a t e t h a t surface recombination l o s s e s have been eliminated (Sinterface 5 lo4 cm/sec) For these Gal-xAlxAs thicknesses , t h e s h o r t c i r c u i t c u r r e n t and efficiency a r e limited by t h e absorption of high energy l i g h t i n t h e Gal,xA1xAs, which prevents t h e l i g h t from reaching t h e G a A s where c a r r i e r s can be generated and collected. To maximize t h e e f f i c i e n c y , t h e thickness of the Gal-xA1xAs must be reduced and t h e A 1 content increased ( t o r a i s e t h e d i r e c t bandgap v a l u e ) , both of which allow more l i g h t t o penetrate t o t h e G a A s .

.

A.

24 8 22

CALCULATED EFFICIENCIES

85

7

>: 2 20 .-0) u 18 w

16

14

0.1 0.2 0.5 1 2 5 10 Ga,-,AI,As Thickness, microns

F I G . 50. Calculated inherent e f f i c i e n c i e s o f pGal,filfispGaAs-nGaAs s o l a r cells a s a f u n c t i o n o f Gal-xAlxAs t h i c k n e s s . Same c o n d i t i o n s a s F i g s . 1 4 , 4 9 , and T a b l e 5 . No f i e l d s , Shack = a, X j = 0 . 4 v.

The AMO, AM1, and A M 2 e f f i c i e n c i e s of pGal-xA1&s-pGaAsnGaAs s o l a r c e l l s are shown i n Fig. 49 as a function of j u n c t i o n depth (width of t h e pGaAs region) f o r two d i f f e r e n t G a l - x A l x A s t h i c k n e s s e s . The recombination v e l o c i t i e s are taken as lo6 cm/ s e c a t t h e device s u r f a c e and lo4 cm/sec a t t h e i n t e r f a c e , while t h e P/N G a A s p o r t i o n of t h e c e l l is assumed t o have t h e parameters of Table 5. For Gal,xA1xAs l a y e r s of a few thousand angstroms t h i c k n e s s , t h e e f f i c i e n c i e s a r e over 20, 23, and 24% f o r AMO, AM1, and AM2, r e s p e c t i v e l y . I t would b e very d i f f i c u l t t o reach t h e s e e f f i c i e n c i e s without t h e Gal-xA1xAs l a y e r ; comparable AM0 values i n s t r a i g h t G a s devices with recombination v e l o c i t i e s of lo6 cm/sec can only be reached with very narrow j u n c t i o n s and with a i d i n g d r i f t f i e l d s , as shown i n Fig. 48. The e f f e c t of t h e G a l - x A l X A s t h i c k n e s s on t h e e f f i c i e n c y is seen more c l e a r l y i n Fig. 50, f o r devices with 0 . 4 vm junct i o n depths and t h e parameters of Table 5. The i n c r e a s e of e f f i c i e n c y with decreasing t h i c k n e s s can be a t t r i b u t e d i n p a r t t o t h e g r e a t e r p e n e t r a t i o n of l i g h t t o t h e G a A s as mentioned above, and i n p a r t , t o t h e c o l l e c t i o n of some of t h e carriers generated i n t h e G a l - X A l x A s [45]. The G a l - x A l x A s t h i c k n e s s could t h e o r e t i c a l l y b e reduced t o as low a s 100 8; t h e energy b a r r i e r i n t h e conduction band (Fig. 13) w i l l continue t o prevent photogenerated e l e c t r o n s from e n t e r i n g t h e a l l o y l a y e r . (Below t h i s t h i c k n e s s e l e c t r o n s w i l l begin t o recombine a t t h e s u r f a c e a f t e r tunneling through t h e Gal-xA1xAs, and t h e e f f i ciency w i l l drop.) However, t h e b e n e f i t s of reducing t h e

86

4.

EFFICIENCY

thickness t o l e s s than a few thousand angstroms a r e r e l a t i v e l y small, and it w i l l probably be b e t t e r t o keep t h e layer around 3000-5000 A t h i c k t o minimize series resistance. 4.

SERIES AND SHUNT RESISTANCE MSSES

The a c t u a l e f f i c i e n c i e s of p r a c t i c a l devices are less than t h e calculated values i n Figs. 43 t o 50 due t o t h e r e f l e c t i o n of incident l i g h t , t h e portion of t h e surface masked by t h e metallic contacts, and t h e l o s s of p o w e r i n t h e s e r i e s and shunt resistances. The r e f l e c t i o n of l i g h t i s minimized by applying one o r two layer a n t i r e f l e c t i v e coatings; t h e r e f l e c t i o n averages around 9% over t h e v i s i b l e spectrum f o r a one-layer coating and 2-3% f o r a two-layer coating. The r e f l e c t i o n v a r i e s strongly with wavelength f o r a s i n g l e l a y e r coating, and t h e thickness of the coating i s adjusted t o obtain a minimum a t around 55006000 where t h e peak i n t h e sun's power occurs (see Fig. 19). The contact g r i d is an important p a r t of t h e c e l l ; f o r a given sheet r e s i s t i v i t y of t h e diffused region, t h e contact g r i d design plays a l a r g e p a r t i n determining t h e series resistance. The more t h e surface i s covered with m e t a l l i c contacts, however, t h e l e s s t h e a w u n t of l i g h t i s t h a t can g e t through t o be converted i n t o e l e c t r i c p o w e r , so t h a t a t r a d e off e x i s t s between minimizing t h e series r e s i s t a n c e by adding many contact "fingers" (Fig. 1) and minimizing t h e amount of surface area covered by t h e Ohmic contact. I n mst devices today, about 57.5% of t h e surface is masked by t h e contacts; t h i s can probably be reduced t o 3-4%, but not much less than t h i s . The contact l o s s can be included i n t h e efficiency c a l c u l a t i o n s through t h e a c t i v e and t o t a l device areas & and A t . N o s o l a r c e l l can be made without having some nonzero value of s e r i e s resistance. The r e s i s t a n c e of t h e d i f f u s e d and base regions and t h e contact r e s i s t a n c e s t o both those regions a l l add t o %, but t h e l a r g e s t f a c t o r by f a r i n good devices is t h e sheet r e s i s t a n c e of t h e t h i n , diffused layer. The e f f e c t s of s e r i e s r e s i s t a n c e on t h e AM0 e f f i c i e n c i e s of 1 ohm-cm N/P S i devices and 0.01 ohm-cm P/N GaAs devices are demonstrated i n Fig. 51, where the devices are assumed t o have a 1 c m 2 area. A r e s i s t a n c e of 1 ohm f o r a 1 c m 2 device drops t h e efficiency by 1% f o r S i (15%down t o 14%) and 0.6% f o r GaAs (19.4% t o 18.8%);t h e e f f e c t of s e r i e s r e s i s t a n c e i s s l i g h t l y l e s s on GaAs devices than on S i because t h e photocurrent i s l e s s f p r GaAs. The efficiency drops very rapidly f o r r e s i s t a n c e s of several ohms o r more. Figure 51 can be used f o r 2, 4 , 8 , e t c . , cm2 area devices by dividing t h e abscissa by t h e area i n an2; f o r instance, t h e

A.

CALCULATED EFFICIENCIES

87

5 11 w

Series Resistance, ohms

F I G . 5 1 . The e f f e c t o f series resistance on the AM0 efficiencies of S i and GaAs s o l a r c e l l s . S i N/P c e l l , 1 ohm-cm, parameters o f Table 4 , xj = 0 . 4 Um. GaAs P / N c e l l , 0.01 ohm-cm, parameters o f Table 5 w i t h X j = 0 . 5 urn. S t o p = lo5 cm/sec, shack = m. Rsh = a . N o d r i f t f i e l d s .

drop of 1% i n efficiency due t o Rs occurs f o r 1 ohm f o r a 1 cm2 sample, 0.5 ohm f o r a 2 cm2 sample, 0.25 ohm f o r a 4 cm2 sample, and so f o r t h . The e f f e c t s of shunt r e s i s t a n c e on t h e AM0 e f f i c i e n c i e s of S i and GaAs s o l a r c e l l s a r e demonstrated i n Fig. 52. I d e a l l y , t h e shunt resistance should be as l a r g e as possible, but a varie t y of problems can lead t o low values of R&, including edge leakage and t h e e f f e c t s of contact s i n t e r i n g (which can allow metal "bridges" t o form i n t h e v i c i n i t y of cracks and scratches i n t h e device [ 2 3 1 ) . Shunt r e s i s t a n c e e f f e c t s are not very s i g n i f i c a n t unless t h e value of t h e r e s i s t a n c e becomes l e s s than 1000 ohm f o r a GaAs device o r 500 ohm f o r a S i device, both of 1 cm2 area. The e f f e c t of Rsh i s stronger i n GaAs devices than i n S i ones ( j u s t t h e opposite of t h e series resistance e f f e c t s ) due t o t h e higher output voltage of G a s . A given value of shunt resistance has less e f f e c t on l a r g e devices than s m a l l ones, since t h e output voltage i s independent of device area (the current l o s s equals t h e output voltage d i vided by t h e shunt r e s i s t a n c e ) . For a 4 cm2 device, f o r example, t h e shunt r e s i s t a n c e could be roughly t h r e e t i m e s smaller than t h e values mentioned above f o r a 1 cm2 device before t h e same drop i n efficiency takes place. (Of course, increasing t h e device area increases t h e amount of edge leakage and the proba b i l i t y of metal bridges being formed, so t h a t the shunt r e s i s tance may be lowered, instead of remaining constant, when t h e area is increased.) In general, surface passivation and careful preparation of devices prevents s i g n i f i c a n t shunt r e s i s t a n c e problems, and

88

4.

EFFICIENCY

-

-

10

100

lo3

Shunt Resistance, ohms

lo4

F I G . 5 2 . The e f f e c t of shunt r e s i s t a n c e on the AM0 e f f i c i e n c i e s of S i and GaAs solar c e l l s . Rs = 0 . Same conditions a s F i g . 52. d

they can o f t e n be ignored. On t h e other hand, s e r i e s r e s i s t a n c e problems a r e almst always s i g n i f i c a n t and o f t e n reduce t h e output by 1 t o 1.5 mW per square centimeter of device area. B.

Measured E f f i c i e n c i e s

If t h e measured e f f i c i e n c i e s of 1 and 1 0 ohm-cm S i s o l a r c e l l s a r e corrected f o r r e f l e c t i o n , contact l o s s , and s e r i e s r e s i s t a n c e l o s s , t h e r e s u l t is i n good agreement with t h e "inherent" e f f i c i e n c i e s of S i devices a s described on previous pages, taking i n t o account t h e dead layers, high surface recombination v e l o c i t i e s , and lower-than-expected base l i f e t i m e s t h a t a r e often found i n a c t u a l devices. For S i r t h e most common type of s o l a r c e l l i s t h e 10 ohm-cm N/P v a r i e t y , which has a n AM0 efficiency of about 11.5% (12.8% a f t e r correction f o r contact a r e a ) . These devices have uncorrected e f f i c i e n c i e s of 1 4 % a t A M 1 and 16%a t AM2. A few 1 and 2 ohm-cm devices have been made with s l i g h t l y higher values (as predicted by theory), while devices made with 0.1 ohm-cm bases have not been as good, p a r t l y because t h e base l i f e t i m e and d i f f u s i o n length have not been a s high as they should be. The open c i r c u i t voltages of devices with 0.1 ohm-cm base r e s i s t i v i t i e s have been considerably lower than expected. Both excess tunneling c u r r e n t s (possibly due t o unexpectedly high defect d e n s i t i e s i n t h e v i c i n i t y of the depletion region) and e f f e c t s due t o high doping l e v e l s have been suggested a s possible causes of t h e discrepancy. High defect d e n s i t i e s could lead t o high depletion region recombinat i o n currents as well as t o excess tunneling currents. Application of t h e back surface f i e l d concept t o 1 and 10 ohm-cm devices of 8 t o 10 mil thickness should r e s u l t i n improvements by a s much as one percent ( i . e . , 11 t o 1 2 % uncorrected) over devices without t h e BSF.

B.

MEASURED EFFICIENCIES

89

The v i o l e t c e l l , with i t s very good short wavelength response due t o the elimination of t h e dead l a y e r , i s generally made with 2 ohm-cm p-type base material [531, and has reached AM0 e f f i c i e n c i e s of 14-14.5% uncorrected and 15-15.5% a f t e r contact area correction 141. A t A M 1 these devices have been up t o 18%e f f i c i e n t a f t e r correction. I t should be only a matter of t i m e before a v i o l e t c e l l of 8-10 m i l thickness with a BSF is made; these w i l l probably be another percent higher than t h e v i o l e t c e l l s made i n t h e past. Most P/N S i c e l l s have been lower i n efficiency than N/P devices, i n agreement with Fig. 44. The Li-doped P/N c e l l s developed recently, however, a r e an exception, because the hole l i f e t i m e s and diffusion lengths i n Li-doped n-type S i a r e comparable t o t h e electron l i f e t i m e s and diffusion lengths i n boron-doped p-type S i . The measured AM0 e f f i c i e n c i e s of L i doped P/N c e l l s have achieved 11.9-12.8% [82,83], which becomes 12.9-13.8% a f t e r contact area correction. These high e f f i c i e n c i e s , combined with the enhanced radiation tolerance of the Li-doped c e l l s , make them strong contenders t o replace t h e standard N/P c e l l s i n s a t e l l i t e applications. Experimental GaAs s o l a r c e l l s I i n s p i t e of t h e i r high predicted e f f i c i e n c i e s , have always been lower than t h e i r expected c a p a b i l i t y by nearly a f a c t o r of 2 , almost surely due t o much lower l i f e t i m e s and diffusion lengths than expected from bulk measurements. Measured e f f i c i e n c i e s a t AM0 have been a f t e r correction f o r conabout 10%before correction and 11% t a c t area [38]. A t AM1, t h e corrected e f f i c i e n c i e s have reached 13% [6]. The experimental devices made so f a r have had f a i r l y deep junctions (20.5 pm) and r e l a t i v e l y poor lifetimes i n both regions; the use of high q u a l i t y s t a r t i n g material and of methods t o obtain shallower junctions w i l l probably bring higher measured e f f i c i e n c i e s i n t h e near future. pGal-.&,As-pGaAs-nGaAs devices have proven t o have s i g n i f i cantly b e t t e r e f f i c i e n c i e s than conventional GaAs c e l l s , with AM0 values of 13-13.5% [9,841 a f t e r contact area correction (12-12.5% before c o r r e c t i o n ) . These devices have corrected A M 1 e f f i c i e n c i e s of 16-17% and corrected AM2 e f f i c i e n c i e s of 20-21% 181. The change i n efficiency with a i r mass value i s l a r g e r f o r these devices than f o r S i or conventional G a A s c e l l s because of the cutoff i n response a t around 2.5 eV i n the Gal-xAlxAs devices made so f a r . Thinner Gal,xA1xAs layers should increase the efficiency and decrease t h e dependence on atmospheric cond i t i o n s because of t h e b e t t e r s p e c t r a l response a t high photon energies. The t h e o r e t i c a l e f f i c i e n c i e s of t h i n film Cu2S-CdS s o l a r c e l l s have not been calculated here because t h e r e i s no complete

90

EFFICIENCY

4.

Voc

TABLE 6 and FF ( c a l c u l a t e d ) .

S i l i c o n N/P

Silicon P/N

P

voc

FF

10

.545 .60 .70

.81 .82 -84

1

0.1

G a A s P/N

'front

voc

(cm/sec)

(V)

107

-92 .935 -95

106 105

300°K

P

10 1 0.1

voc

FF

.525 -575 -63

.80 .82 .83

Gal-xA1xAs-GaAs,

FF

.820 .822 -825

D

voc

(urn)

(V)

2.5 0.25

.945 .95

P/P/N

FF

.82 .825

q u a n t i t a t i v e model as y e t which can p r e d i c t a l l t h e phenomena going on i n t h e s e devices, p a r t i c u l a r l y t h e events t a k i n g place a t t h e h e t e r o j u n c t i o n i n t e r f a c e . Considerable progress has been made i n understanding t h e s e d e v i c e s , however, due p r i n c i p a l l y t o t h e work of Lindquist, Fahrenbruch, B u b e , B 6 e r , P h i l l i p s , and o t h e r s , and it should only be a matter of t i m e before a s a t i s f a c t o r y model i s developed. The h i g h e s t measured AM0 e f f i c i e n c y f o r t h i n f i l m devices made i n t h e l a b o r a t o r y i s 8.1%, and AM0 e f f i c i e n c i e s of 5.5% are achieved r o u t i n e l y on product i o n l i n e t h i n f i l m c e l l s [85]. Cu2S-CdS c e l l s made from s i n g l e c r y s t a l CdS y i e l d about t h e same values. Typical open c i r c u i t v o l t a g e s and f i l l f a c t o r s c a l c u l a t e d f o r S i , G a A s , and Gal-xA1xAs-GaAs devices are given i n T a b l e 6. These are median v a l u e s ; d i f f e r e n c e s i n j u n c t i o n depths, s u r f a c e recombination v e l o c i t i e s ( a t t h e f r o n t and b a c k ) , and l i f e t i m e s r e s u l t i n v a r i a t i o n s around them. The c a l c u l a t e d space charge region recombination c u r r e n t s are n e g l i g i b l e f o r S i c e l l s i f t h e parameters of T a b l e 4 are used t o g e t h e r with t h e S-N-S theory, b u t t h e recombination c u r r e n t s can become s i g n i f i c a n t i f t h e l i f e t i m e w i t h i n t h e d e p l e t i o n region i s lower than expected.

c.

SUMMARY

91

Measured open c i r c u i t voltages i n S i 1 and 10 ohm-cm cells are close t o t h e calculated ones i n Table 6, but measured voltages i n 0.1 ohm-cm levices a r e considerably lower than t h e 0.7 V predicted by theory, a s mentioned above. The f i l l f a c t o r s i n S i devices a r e usually 0.75-0.78, s l i g h t l y lower than the predicted values, due mainly t o t h e s e r i e s resistance and perhaps s l i g h t l y t o shunt resistances and space charge l a y e r recombination currents. Measured open c i r c u i t voltages and f i l l f a c t o r s i n G a s devices have generally been lower than t h e computed values of Table 6, with V0c from 0.90 t o 0.94 V and ET from 0.76 t o 0.79. Both t h e computed and measured space charge layer recombination currents are proportionally much higher f o r G a A s devices than for S i c e l l s I591, and along with s e r i e s resistance, these currents a r e t h e probable cause of t h e low f i l l factors. The measured open c i r c u i t voltages and f i l l f a c t o r s of Gal-xA1,+s-GaAs devices have ranged from 0.94 t o 1.0 V and 0.77 t o 0.81, respectively, i n good agreement with t h e calcul a t e d values of Table 6. The higher measured Voc's compared t o Table 6 might i n d i c a t e t h a t n i f o r GaAs i s indeed s l i g h t l y smaller than 1x10' ~ m - ~a ,s suggested by S e l l and Casey [ a l l . The s l i g h t l y lower measured f i l l f a c t o r s compared t o t h e calc u l a t e d values a r e probably the r e s u l t of s e r i e s resistance. Typical open c i r c u i t voltages and f i l l f a c t o r s measured f o r f r e s h t h i n film CuZS-CdS devices are around 0.45-0.50 V and 0.60-0.65, respectively, although these vary somewhat f o r d i f f e r e n t preparation conditions and a s t h e device ages.

c.

summary

In the p a s t , the most important f i g u r e of m e r i t f o r a s o l a r c e l l has been t h e efficiency a t AMO, i . e . , i n outer space. The prospects of t h e wide scale use of s o l a r c e l l s f o r t e r r e s t r i a l use make the efficiency a t AM1 ( e a r t h ' s surface) equally important. The e f f i c i e n c i e s a t AMO, AM1, and AM2 have been calculated f o r a w i d e range of material parameters and f o r t h e t h r e e models of uniform doping, constant e l e c t r i c f i e l d s , and a back surface f i e l d . In each case t h e photocurrents a r e found by t h e methods of Chapter 2 and the t o t a l dark current by the equations of Chapter 3. The dark current is subtracted from the photocurr e n t and the maximum value of the voltage-net current producti s determined. The r e s u l t i s the "inherent" efficiency of the device, which does not include t h e losses due t o contact area masking, r e f l e c t i o n of l i g h t from t h e surface, and series and shunt resistances.

92

4.

EFFICIENCY

The inherent e f f i c i e n c i e s of S i s o l a r c e l l s a t AM0 under optimum conditions range from 18% f o r 10 ohm-cm base material t o 21% f o r 0.1 ohm-cm material. A t AM1, t h e corresponding values a r e 20-22%. GaAs inherent e f f i c i e n c i e s exceed 23% a t AM0 and 25% a t AM1. The predicted e f f i c i e n c i e s a r e considerably below these values when dead l a y e r s , high surface recombination v e l o c i t i e s , low base l i f e t i m e s , o r poor l i f e t i m e s within the depletion region a r e p r e s e n t , leading t o 14-15% predicted e f f i ciencies f o r S i and 11-12% f o r G a A s a t AMO, and 16-17% f o r S i and 13-14% f o r G a A s a t AM1. Reductions i n junction depth and the incorporation of e l e c t r i c f i e l d s help t o overcome these losses, but t h e b e s t r e s u l t s are obtained i f t h e base l i f e t i m e and diffusion length can be improved and t h e dead layer can be eliminated. The a c t u a l e f f i c i e n c i e s of S i and GaAs s o l a r c e l l s a r e 10-20% l e s s than t h e inherent e f f i c i e n c i e s due t o r e f l e c t i o n , contact area loss, and series and shunt r e s i s t a n c e s . The ref l e c t i o n loss amounts t o 6-9% f o r a s i n g l e a n t i r e f l e c t i o n coating. The upper Ohmic contact g r i d masks about 5-8% of the surface, reducing t h e s h o r t c i r c u i t current accordingly. Series and shunt r e s i s t a n c e l o s s e s account f o r t h e remainder. The series r e s i s t a n c e should be less than 0.5 ohms f o r a 1 cm2 device (0.25 ohm f o r a 2 cm2 c e l l , e t c . ) , and t h e shunt r e s i s tance should be g r e a t e r than 1000 ohm f o r a 1 c m 2 device (2000 ohm f o r a 2 cm2 c e l l , e t c . ) t o reduce t h e r e s i s t a n c e losses t o acceptably low values. The present measured e f f i c i e n c i e s of S i s o l a r c e l l s a r e 15%AMO, 18%AM1 f o r t h e " v i o l e t " c e l l , and 13.8% A M O , 16% AM1 f o r Li-doped c e l l s . G a A s c e l l s with Gal,xA1xAs l a y e r s a r e 14% e f f i c i e n t a t AM0 and 18%a t AM1. Cu2S-CdS devices a r e 8% e f f i c i e n t a t AM0 and 10%a t AM1.

CHAPTER 5

Thickness

Up t o a few years ago, t h e thickness of a s o l a r c e l l w a s not a very important consideration. The short c i r c u i t current of a S i device was known [861 t o decrease as t h e base thickness was reduced, and most of t h e early devices were therefore made with 16-18 m i l (400-450 run) widths t o obtain t h e highest collect i o n efficiency. On t h e other hand, t h e power-to-weight r a t i o and t h e radiation tolerance t o high energy p a r t i c l e s both i m proved with decreasing base thickness , so attempts were made t o develop thinner c e l l s with acceptable c h a r a c t e r i s t i c s , and eventually 10-12 m i l (250-300 pm) c e l l s became common. In recent years, t h e device thickness has taken on increasing importance. One reason i s t h e advent of the "back surface f i e l d " concept and i t s influence on device behavior. Another i s t h e p o s s i b i l i t y t h a t t h i n s o l a r c e l l s can be made cheap enough t o have a s i g n i f i c a n t impact on large-scale power gene r a t i o n on earth. These a r e added t o the benefits of high power-to-weight r a t i o s and high radiation tolerance a s mentioned above. When a beam of monochromatic l i g h t i s incident on a s o l a r c e l l , some of it i s r e f l e c t e d from the f r o n t surface, some i s absorbed i n the bulk of the c e l l , and some i s l o s t by complete transmission through t h e device. I f t h e absorption c o e f f i c i e n t i s high, as i t i s f o r short wavelengths, nearly a l l t h e l i g h t is absorbed near t h e f r o n t surface and t h e transmission l o s s i s negligible. For long wavelengths where a is low, a high percentage of t h e l i g h t may be l o s t . The back contact may ref l e c t a portion of t h i s back i n t o t h e device, but f o r planar back contacts made i n the conventional manner t h i s portion i s

small.

When t h e thickness of a s o l a r c e l l i s reduced, t h e behavior is affected i n two ways. F i r s t , t h e l o s s due t o transmitted l i g h t increases ( t h e l o s s i s g r e a t e r f o r i n d i r e c t gap materials than f o r d i r e c t gap ones); second, t h e influence of the back contact becomes greater. The c o l l e c t i o n efficiency may be 93

94

5.

THICKNESS

50

u,

7

20

10 0.1 0.2 0.5 1

2

5 10 20

50 100

500

Total Thickness, I(

F I G . 5 3 . Idealized short circuit current densities for 100% collection efficiency a s a function o f the solar cell thickness.

reduced and t h e dark c u r r e n t increased due t o excess recombinat i o n of photogenerated and dark i n j e c t e d carriers a t t h e back surface. This i n f l u e n c e only becomes important when t h e minority carrier d i f f u s i o n l e n g t h i n t h e base is comparable t o o r l a r g e r

than t h e device t h i c k n e s s [5,43,44,871. Both t h e ribbon Si technology and t h e t h i n f i l m p o l y c r y s t a l l i n e S i technology are aimed a t i n f l u e n c i n g t h e terrestrial use of solar c e l l s t o economically provide l a r g e amounts of electrical power. The ribbon technology involves t h e growth of t h i n (4-8 m i l ) S i s i n g l e crystal ribbons an inch o r so wide and a r b i t r a r i l y long; i d e a l l y , t h e ribbons are produced i n a manner s u i t a b l e f o r f u r t h e r processing ( d i f f u s i o n , c o n t a c t i n g , etc.) without c u t t i n g , lapping, o r polishing. E f f i c i e n c i e s of 10% a t A M 1 have already been demonstrated by Mlavsky and co-workers a t Tycho 1881. S o l a r cells made f r o m t h i n S i films (about 1 0 ptm) grown on cheap metallic or g l a s s substrates hold t h e promise of being u l t i m a t e l y cheaper than S i ribbon devices i f g r a i n boundary effects can be minimized, b u t a t t h e p r e s e n t t i m e only 1-2% e f f i c i e n t devices have been made [891. I n t h i s c h a p t e r t h e e f f e c t of t h i c k n e s s on t h e s h o r t circ u i t c u r r e n t , open c i r c u i t v o l t a g e , f i l l f a c t o r , and i n h e r e n t e f f i c i e n c y of s i n g l e c r y s t a l S i and GaAs p-n j u n c t i o n solar c e l l s f o r s i n g l e l i g h t passes w i l l be d i s c u s s e d , including t h e i n f l u ence of an O h m i c back c o n t a c t or back s u r f a c e f i e l d on t h e device c h a r a c t e r i s t i c s ( t h e width Wp+ of t h e BSF region is assumed t o

A. 50

b

IIIII~ I

IIIIIIII

I

SINGLE CRYSTAL

95

irrmP

40

5

N

E 30

-

20 1

10 100 Thickness H,p

lo00

F I G . 5 4 . Calculated short c i r c u i t c u r r e n t d e n s i t i e s of 10 ohm-cm S i N / P s o l a r c e l l s , f o r both an O h m i c back c o n t a c t and a BSF back c o n t a c t . Parameters of Table 4 , w i t h S f r o n t = l o 5 cm/sec, X j = 0 . 2 w. D r i f t f i e l d p r e s e n t i n t o p r e g i o n .

be n e g l i g i b l e ) . The chapter ends with some speculation about t h e r o l e of grain boundaries i n l i m i t i n g device e f f i c i e n c i e s and some words on t h e e f f e c t of thickness on CdS devices. A.

Single Crystal

1.

SILICON

When sunlight i s incident on t h e surface of a s o l a r c e l l , t h e long wavelength portions of the spectrum may be progressively l o s t as t h e device i s made thinner. I n d i r e c t gap materials such as S i with t h e i r low absorption constants over much of t h e spectrum s u f f e r much more from t h e e f f e c t s of thickness than d i r e c t gap materials such as GaAs, where m o s t of t h e carriers are generated c l o s e t o t h e surface. I f it i s assumed t h a t l i g h t makes a s i n g l e pass through t h e device and t h a t every photon absorbed c r e a t e s a hole-electron p a i r which i s collected, then an idealized s h o r t c i r c u i t current can be calculated as shown i n Fig. 53. Silicon devices begin t o l o s e current when t h e thickness becomes less than 500 pm, and GaAs devices when t h e thickness becomes l e s s than 3 pm. In r e a l cases where normal bulk and surface recombination l o s s e s take place, both the magnitude of the photocurrent and i t s thickness dependence a r e reduced. The thickness dependence does not become appreciable u n t i l t h e thickness becomes less t h a t about 2 base diffusion lengths (232, 164, and 52 wn f o r 10, 1, and 0.1 ohm-cm S i , . r e s p e c t i v e l y ) . Figure 54 shows t h e

96

5.

THICKNESS

0.60

2 -

-::0.52

n

nl

0.84 2

8

0

>"

0.44

0.36

-/I I IIIIIII

1

I

10

I Illllll

100 Thickness H, p

I

I

I

0.80 0.76

U 0.72 lo00

FIG. 5 5 . C a l c u l a t e d open c i r c u i t v o l t a g e s and f i l l f a c t o r s of 10 ohm-cm S i solar c e l l s , for same c o n d i t i o n s as Fig. 5 4 .

Jsc as a function of thickness f o r 10 ohm-cm N/P devices using the parameters of Table 4 and t h e equations of Chapter 2. When t h e back surface i s covered by an Ohmic contact (Sn = a), the current density decreases as H is reduced below 400 pm. The back surface f i e l d (Sn = 0) however, with i t s c a r r i e r confinement and reduced recombination loss, maintains t h e current density a t a r e l a t i v e l y constant l e v e l f o r thicknesses over 100 The b e n e f i t s of a BSF were f i r s t noted experimentally through t h e higher open c i r c u i t voltages obtained from such devices compared t o conventional devices of t h e same r e s i s t i v i t y . Figure 55 shows t h e open c i r c u i t voltage and f i l l f a c t o r calcul a t e d f o r t h e 10 ohm-cm device of Fig. 54. The m o s t s t r i k i n g b e n e f i t of t h e BSF i s i n t h e Voc. For 100 pm devices, a s i n S i ribbon c e l l s , more than 50 mV are gained by a BSF compared t o an Ohmic back contact, and t h e gain becomes g r e a t e r as t h e thickness is reduced f u r t h e r . A b e n e f i c i a l e f f e c t of t h e BSF is a l s o obtained on the f i l l f a c t o r . Actually, t h e e f f e c t s of thickness on t h e Voc should be separated from t h e e f f e c t s of t h e back contact. As t h e thickness of the base i s reduced, t h e amount of b u l k recombination t h a t can take place i s reduced proportionally, which tends t o Ohmic contact a c t s as a p e r f e c t sink f o r minority c a r r i e r s and a p e r f e c t source f o r majority c a r r i e r s . A BSF contact a c t s as a p e r f e c t source f o r majority carriers but blocks minority carriers.

A.

SINGLE CRYSTAL

97

40

N

E 30

Y

a. E

4 20 i. n -

1

10 100 Thickness H, p

lo00

FIG. 56. Calculated short circuit current densities of 0.1 ohm-cm Si solar c e l l s , for both an Ohmic back contact (Shack = a) and a BSF back Contact (Shack = 0 and l o 4 cm/sec).

D r i f t f i e l d present i n top region. Parameters o f Table 4 , w i t h Sfront = l o 5 cm/sec, xi = 0.2 pm.

lower t h e dark current and r a i s e Voc. I f an Ohmic back contact i s present, however, then a surface of i n f i n i t e recombination velocity i s brought closer and c l o s e r t o t h e junction as t h e base thickness is reduced. The r e s u l t i n g increased surface recombination outweighs t h e reduced bulk recombination, r a i s e s t h e dark current, and lowers Voc. On t h e other hand, i f a BSF is present a t the back instead of an Ohmic contact, then back surface recombination i s unimportant and the b e n e f i t s of reduced bulk recombination on lowering the dark current and r a i s i n g the V,, can be obtained. b The e f f e c t of thickness on 1 and 0.1 ohm-cm devices i s q u a l i t a t i v e l y similar t o t h e e f f e c t on 10 ohm-cm devices, but t h e thickness dependence does not become important u n t i l lower thicknesses a r e reached because of t h e smaller diffusion lengths. Figure 56 shows the currents obtained f o r various thicknesses and back surface conditions f o r a 0.1 ohm-cm N/P device. A zero recombination velocity a t t h e back would r e s u l t i n some enhancement of t h e current compared t o an Ohmic contact. The BSF may not y i e l d a zero SRV a t t h e back f o r t h i s r e s i s t i v i t y , however, because of the-reduced value of $p; calculations f o r a recombinat i o n velocity of l o 4 cm/sec a r e shown i n Fig. 56 therefore t o has been suggested t h a t p a r t of the added Voc might be due t o t h e small b u i l t - i n b a r r i e r $p (Fig. 7 ) and t h e f a c t t h a t some of t h i s b a r r i e r voltage might appear i n t h e output C901.

98

5.

THICKNESS

0.72

?

0.88

0.64

0.04

0

>"

b U

0.80

0.56

0.76 0.48

1

10

100

lo00

Thickness H, p

F I G . 57. C a l c u l a t e d o p e n c i r c u i t v o l t a g e s and FF of 0.1 ohm-cm S i N / P solar c e l l s , for same c o n d i t i o n s a s F i g . 56.

simulate a p a r t i a l c a r r i e r confinement. Figure 57 shows t h e open c i r c u i t voltage and f i l l f a c t o r f o r t h e device of Fig. 56. The improvements i n these two q u a n t i t i e s due t o a low SRV a t the back a r e not a s l a r g e as i n t h e 10 ohm-cm device, but a r e noticeable nonetheless. Figures 58 and 59 show t h e e f f i c i e n c i e s calculated f o r 1 0 , 1, and 0 . 1 ohm-cm N/P devices a t AM0 and AM1 as a function of device thickness f o r both zero surface recombination velocity (BSF) a t the back and f o r an Ohmic back contact. When the BSF condition e x i s t s , t h e efficiency peaks a t thicknesses between 2 and 4 m i l . Ribbon S i devices with thicknesses of around 4 m i l o r so would be near t h e optimum, with e f f i c i e n c i e s of almost 18%a t AM0 and 20% a t A M 1 (20.6% a t AM2). Even 10 pm thick s i n g l e c r y s t a l c e l l s a r e capable of high e f f i c i e n c i e s , 16%a t AM0 and 18%a t AM1. A zero surface recombination veloci t y a t t h e back i s b e n e f i c i a l over t h e e n t i r e thickness range from 1 pm up t o about twice t h e base diffusion length, as seen i n Figs. 58 and 59. I f an Ohmic back contact has been made a t t h e back surface r a t h e r than a BSF, t h e e f f i c i e n c i e s a r e 5 t o 6% lower ( i . e . , 1 2 % instead of 1 8 % ) . Much of t h e recent experimental work on t h i n S i s o l a r c e l l s has centered around t h e BSF e f f e c t . Mandelkorn and Lamneck [5] reported considerably higher V o c ' s (0.58 V ) f o r 4 m i l 10 ohm-cm BSF c e l l s than f o r 4 m i l conventional 10 ohm-cm devices (Voc = 0.50 V ) , and improvements i n short c i r c u i t curr e n t and f i l l f a c t o r were seen as well. The AM0 e f f i c i e n c i e s of BSF c e l l s changed very l i t t l e with decreasing thicknesses compared t o conventional devices, i n agreement with Fig. 58; dropped from 1 2 t o 11.3% going from 1 2 t o 4 m i l thicknesses,

A.

S I N G L E CRYSTAL

99

18 16 814

.-$12 5 $10 w

8 6 4

1

10 100 Thickness H, p

1000

F I G . 5 8 . Inherent AM0 e f f i c i e n c i e s of S i N / P d e v i c e s f o r d i f f e r e n t b a s e r e s i s t i v i t i e s and t h i c k n e s s e s . Parameters o f Table 4 , w i t h Sfront = l o 5 cm/sec, X j = 0 . 2 p m . D r i f t f i e l d p r e s e n t i n t o p r e g i o n . O h m i c back c o n t a c t and BSF-type c o n t a c t .

while conventional c e l l s dropped from 11 t o 8.3% f o r t h e same t h i c k n e s s change. More r e c e n t l y , V o c ' s of up t o 0.6 V have been r e p o r t e d f o r 10 ohm-cm BSF c e l l s 143,901. Godlewski e t a l . [43] have pointed o u t t h a t t h e experiment a l open c i r c u i t v o l t a g e s of BSF c e l l s made so f a r have tended t o be c o n s t a n t as a function of t h i c k n e s s , while t h e assumption of a zero s u r f a c e recombination v e l o c i t y a t t h e back p r e d i c t s an i n c r e a s i n g Voc with decreasing t h i c k n e s s . The explanation f o r t h i s discrepancy might be t h a t t h e e f f e c t i v e SRV a t t h e back i s not zero b u t an intermediate value such a s 103-104 cm/sec [ t h e value of S i n Eqs. (52) and ( 5 3 ) ] , implying t h a t some degree of minority carrier leakage a c r o s s t h e b a r r i e r $P (Fig. 7) takes p l a c e . I n t h i s case a c o n s t a n t value of Voc as a f u n c t i o n of t h i c k n e s s can be p r e d i c t e d . The higher t h e b a r r i e r h e i g h t $p and t h e more d e f e c t - f r e e t h e back d i f f u s i o n i s , t h e lower t h e e f f e c t i v e s u r f a c e recombination v e l o c i t y i s l i k e l y t o be. Another p o s s i b l e explanation involves t h e component added t o Voc by $,; t h i s component should be l a r g e l y independent of thickness. Iles and Zennnrich [871 have described experimental t h i n devices (10-2 m i l ) i n c o r p o r a t i n g both a t h i n d i f f u s e d t o p region as i n t h e v i o l e t c e l l and a back s u r f a c e f i e l d t o prevent recomb i n a t i o n a t t h e back c o n t a c t . E f f i c i e n c i e s of 13.75, 13.4, and 10.7% a t AM0 f o r 10, 4 , and 2 m i l t h i c k n e s s e s were measured (contact area uncorrected). These very encouraging r e s u l t s l e a d t o high expectations f0.r t h i n , s i n g l e c r y s t a l ribbon S i devices. Exploration has j u s t begun on devices made from S i t h i n f i l m s (10 pm) on metal, g l a s s , o r o t h e r foreign substrates;.

100

22 20 18

z

16

5.

THICKNESS

; 14

!..- 12 V

5 lo

8 6

-1

A

10

100 Thickness H. g

lo00

FIG. 59. h e r e n t AM1 e f f i c i e n c i e s of S i N/P d e v i c e s for d i f f e r e n t base resistivities and t h i c k n e s s e s . Same conditions a s F i g . 58.

Chu 1891 has r e p o r t e d 1.5% e f f i c i e n c i e s a t AM1 f o r t h i n , polyc r y s t a l l i n e S i f i l m s on g r a p h i t e , and e x p e c t a t i o n s are t h a t t h i s can be brought t o 5% i n a few y e a r s . Redfield [91] has described t h e e f f e c t of m u l t i p l e l i g h t passes through S i t h i n f i l m s on t h e s h o r t c i r c u i t c u r r e n t of t h i n S i solar c e l l s , and h a s suggested t h a t 2 pm t h i c k f i l m s could have high c o l l e c t i o n e f f i c i e n c i e s f o r 10 l i g h t passes o r more. The m u l t i p l e l i g h t passes would be obtained by a r e f l e c t i v e back s u r f a c e and t o t a l i n t e r n a l r e f l e c t i o n a t t h e f r o n t . N o mention w a s made of what t h e dark c u r r e n t might b e i n such t h i n S i d e v i c e s , however, and t h i s would have t o be taken i n t o account b e f o r e t h e e f f i c i e n c y of t h i n f i l m m u l t i p l e pass devices could be estimated. 2.

GALLIUM ARSENIDE

The i d e a l i z e d s h o r t c i r c u i t c u r r e n t s of G a A s s o l a r c e l l s as a f u n c t i o n of device t h i c k n e s s f o r a s i n g l e l i g h t pass were shown i n Fig. 53. The d e c r e a s e i n c u r r e n t with t h i c k n e s s i s very s l i g h t f o r t h i c k n e s s e s down t o 2-3 pm due t o t h e high abs o r p t i o n c o e f f i c i e n t over t h e e n t i r e s o l a r spectrum above 1.4 eV. Even 1 ~.lmt h i c k devices could i d e a l l y r e t a i n a photoc u r r e n t of over 35 mA/cm2 a t AM0 and over 2 8 mA/cm2 a t AMl. For a c t u a l devices t h e s u r f a c e recombination loss can reduce t h e c u r r e n t c o n s i d e r a b l y , b u t t h e s u r f a c e recombination problem can be minimized by making t h e j u n c t i o n depth small (as i n t h e S i " v i o l e t c e l l " ) o r by reducing t h e recombination device). v e l o c i t y a t t h e f r o n t (as i n the Gal-&,As-GaAs Figure 60 shows t h e s h o r t c i r c u i t c u r r e n t , open c i r c u i t v o l t a g e , and e f f i c i e n c y a t AM0 f o r G a A s P/N s o l a r c e l l s . The b e n e f i t s

A.

SINGLE CRYSTAL

101

22 20 0

P 1.o

-

AM0 I Illlll

1

1 I I llllll

I

I I111111

10

0.9

I

100

Thickness H, p

FIG. 6 0 . Inherent AM0 e f f i c i e n c i e s , short circuit current d e n s i t i e s , and open c i r c u i t v o l t a g e s of 0.01 ohm-cm GaAs P/N s o l a r cells a s a f u n c t i o n o f t h i c k n e s s . The f i l l f a c t o r i s 0.82-0.83. Parameters of Table 5 , w i t h Sfroqt = l o 6 cm/sec, x j = 0 . 2 wn. D r i f t f i e l d p r e s e n t i n t o p region. O h m i c back c o n t a c t and BSF-type c o n t a c t . of a low recombination velocity a t t h e back can be c l e a r l y seen f o r a l l t h r e e parameters, and t h e efficiency peaks f o r a device thickness between 2 and 3 w. Even f o r c e l l s only 1 pm t h i c k , an open c i r c u i t voltage of 0.97 V, a photocurrent of 34 mA/cm2, and an efficiency of 19.5% are predicted under optimum conditions. The short c i r c u i t currents and e f f i c i e n c i e s f o r t h e same conditions a s i n Fig. 60 but a t AM1 and AM2 a r e shown i n Fig. 61. Except f o r t h e higher e f f i c i e n c i e s and lower photocurrents, t h e behavior f o r these s o l a r spectra is q u a l i t a t i v e l y the same as a t AMO. The parameters used f o r t h e calculations of Figs. 54-61 a r e c h a r a c t e r i s t i c of r e l a t i v e l y good bulk material (Tables 4 and 5 ) . Such good q u a l i t y material i s not often obtained i n t h i n films, p a r t i c u l a r l y i f the t h i n films a r e grown upon foreign substrates. To demonstrate what might be expected from poor q u a l i t y material (but s t i l l s i n g l e c r y s t a l ) , the inherent e f f i c i e n c i e s a t AMO, AM1, and AM2 have been calculated f o r poor conditions and a r e shown i n Fig. 62. (Silicon: T t o p = 3 ~ 1 0 -Sec, ~ Ltop = 0.44 pl, Tbase = 0 . 5 pSeCl Lbase = 16.5 pm, Sfront = l o 6 Ltop = 0 . 5 7 pm, cm/sec, Shack = m. G ~ A S :T t o p = 0 . 2 ~ 1 0 - 9 s e c , 'base = 3x10'9 sec, Lbase = 0.95 pm, Sfront = lo7 cm/sec, = a,) The e f f i c i e n c i e s a r e considerably lower than i n Figs. 59 and 6 1 , a s expected from the lower l i f e t i m e s and

Shack

102

5.

THICKNESS 26 24

22

14 12

1

10 Thickness H, p

100

F I G . 6 1 . Inherent efficiencies and short circuit current densities a t AM1 and AM2 of 0.01 ohm-cm GaAs P/N solar c e l l s as a function of thickness. Same conditions as F i g . 6 0 .

diffusion lengths and higher recombination v e l o c i t i e s a t t h e f r o n t surface. Nevertheless, t h e e f f i c i e n c i e s a r e high enough t o be adequate f o r t e r r e s t r i a l use, and t h e 10%A M 1 efficiency f o r 10 wn t h i c k S i devices and t h e 9% AM1 efficiency f o r 1 rn thick GaAs devices o f f e r e x c i t i n g prospects f o r t h e large-scale use of t h i n f i l m s o l a r cells. (It should be emphasized t h a t these calculations a r e f o r s i n g l e c r y s t a l devices.)

14 12

'0 $

.-

8

0)

3 6 r

w

4

2

0 0.5 1

2

5 10

100

lo00

Thickness H, p

FIG. 6 2 . Inherent efficiencies o f 0.1 ohm-cm si N / P solar cells and 0.01 ohm-cm P / N GaAs solar c e l l s f o r poor q u a l i t y single crystal material. N o d r i f t f i e l d s . $back = a; x j =0.3 vm.

B.

POLYCRYSTALLINE DEVICES

v \

103

Minority Carriers

Ec

Maiority Carriers

EV

F I G . 6 3 . Energy band diagram around g r a i n boundaries. The boundaries a c t a s " s i n k s " for m i n o r i t y c a r r i e r s and barriers t o t h e movement of majority c a r r i e r s .

B.

Polycrystalline Devices

Single crystal Si, G a s , or CdS devices can be thinned down to about 1 mil by a combination of lapping and etching (lapping, though, introduces lattice damage which lowers the lifetime and the mobility), and ribbon Si devices can be grown with an initial thickness of 1-2 mil. For the most part, however, when thin solar cells are desired (el mil), they are fabricated by evaporating, sputtering, or vapor growing a thin film of material onto a suitable substrate. Under some circumstances the grown films can be single crystal, but they are m r e often polycrystalline. Therefore, it becomes important to understand what the effect of grain boundaries might be on the internal physics of solar cells. A thorough analysis of grain boundary effects on both the photocurrent and dark current in thin solar cells has never been carried out. A complete analysis of this problem entails a three-dimensional solution to the diffusion equation with eight or more boundary conditions. Shockley I921 has given a partial solution for the simpler case of uniform generation of minority carriers throughout the volume of a rectangular filament, and used his analysis to define a "filament lifetime" made up partly of the bulk lifetime in the filament and partly of surface recombination terms. When the filament dimensions are small and the surface recombination velocities are high, the recombination in the filament is dominated by the surface terms and the "filament lifetime" is much smaller than the bulk lifetime. Similar considerations apply to polycrystalline films, which can be thought of as many filaments connected in parallel (and sometimes in series). Experimentally, it appears that grain boundaries act as minority carrier sinks (surfaces of high recombination velocity) and majority carrier barriers [93], the worst possible combination (Fig. 63); they reduce the

104

5.

FIG. 6 4 .

"HICKMESS

Po2ycrystalline f i l m w i t h random grain o r i e n t a t i o n .

photocurrent, i n c r e a s e t h e dark c u r r e n t , decrease t h e shunt resistance, and i n c r e a s e t h e series r e s i s t a n c e . I f t h e g r a i n s are randomly o r i e n t e d , as p i c t u r e d i n Fig. 64, then only t h e topmost g r a i n or t w o (e.g., A i n Fig. 64) w i l l be able t o cont r i b u t e to t h e o u t p u t ; t h e g r a i n s below (e.q., B i n Fig. 64) are e f f e c t i v e l y i s o l a t e d from t h e j u n c t i o n by t h e g r a i n boundaries above them. This is t h e "series" combination of g r a i n boundaries; t h e e f f e c t i v e lifetime i n t h e f i l m w i l l be very l o w and t h e device w i l l behave poorly. I f t h e t h i n f i l m i s f i b r o u s e p i t a x i a l , however, as i n Fig. 65, then minority carriers within each "filament" can c r o s s t h e j u n c t i o n boundary and t h e whole l a y e r thickness can c o n t r i b u t e t o t h e output. For t h i s c a s e , t h e o v e r a l l solar c e l l can be thought of as a p a r a l l e l combinat i o n of filamentary solar c e l l s , each of which act i n a normal manner except t h a t minority carrier recombination can t a k e p l a c e on t h e "sides" of t h e filaments as w e l l a s a t t h e f r o n t s u r f a c e and back c o n t a c t . This type of f i l m can make a f a i r l y e f f i c i e n t device under some circumstances, while t h e randomly o r i e n t e d f i l m s probably cannot (unless t h e g r a i n s i z e happens t o be of t h e order of a d i f f u s i o n l e n g t h o r more).

FIG. 65.

P o l y c r y s t a l l i n e film w i t h fibrous o r i e n t a t i o n .

B.

POLYCRYSTALLINE DEVICES

105

ia 16

-3

14

0

>

12

0

0

>

0.7 0.6

4

0.5

2

0

0.1

1.o

10

100

Grain Size, p

F I G . 6 6 . AM1 inherent e f f i c i e n c i e s , current d e n s i t i e s , and open c i r c u i t voltages o f 10 pm t h i c k p o l y c r y s t a l l i n e 0.1 ohm-cm si N/P solar c e l l s . Sfront = 10’ m/sec, xj = 0 . 2 p m . S t a r t i n g b a s e d i f f u s i o n l e n g t h ( l a r g e g r a i n sizes) same a s i n Table 4 . D r i f t f i e l d present i n top region.

Even though the three-dimensional equations for thin film polycrystalline devices have not been solved, it would be beneficial to have an estimate of what the behavior of such devices might be. Such an estimate can be made by constructing a logical argument for the effect of the fibrously oriented grain boundaries on the minority carrier distribution. Consider a solar cell with a thickness H and a grain size of 5 H (e.g., 10 pm thick Si films with a 50 pm grain size). Then most of the minority carriers generated inside a given grain on the base side of the junction will have at least 2 1/2 times as far to travel to a grain boundary as to the junction edge (65% of the carriers are generated within the first 2.5 Pm from the surface in a 10 pm thick device). The photogenerated carriers will then have a high probability of being collected, and the device will behave very much as a single crystal solar cell. As the grains become smaller, a loss of photocurrent and an increase of dark current due to recombination at the grain boundaries will begin to occur (the effective diffusion length and the effective lifetime for minority carriers in the base begin to decrease). By the time the grain size is down to the device thickness, minority carriers in the base have at most an equal probability of recombining or of being collected, and the effective diffusion length in the base is then at best about equal to the grain size. For grain sizes less than the

106

5.

THICKNESS 24

-c v)

0

w

22

8

>

1.o

20

14

15

12

lo

10 0.1

0.9 I I lllllll

I 1 lllllll

1.o 10 Grain Size, p

I 1 I

100

FIG. 6 7 . AM1 inherent e f f i c i e n c i e s , c u r r e n t d e n s i t i e s , and open c i r c u i t v o l t a g e s o f 1 m thick p o l y c r y s t a l l i n e 0.01 ohm-ern G ~ A SP/N s o l a r c e l l s . sfTont = 106 cnr/sec, x j = 0.2 w. S t a r t i n g base and t o p r e g i o n d J f f u s i o n l e n g t h s ( l a r g e g r a i n sizes) same a s i n T a b l e 5 . D r i f t f i e l d p r e s e n t i n t o p r e g i o n . O h m i c back contact and BSF-type c o n t a c t .

device thickness, the diffusion length in the base is less than or equal to the grain size, and the effective lifetime is reduced according to the normal relation L =.The philosophy for the effect of grain boundaries on recombination in the top region and depletion region is the same; the grain boundaries may not be important (for fibrous orientation) until the grain size becomes less than about 5-10 times the thickness of these regions. For a 2000 junction depth, grain sizes down to around 2 pm should have little effect on the collection from the top region. Grain sizes down to a halfmicron or so should have little effect on the collection or carrier recombination within the 500 8 wide depletion region (0.1 ohm-cm base material). There is some experimental justification for assuming the minority carrier diffusion length equal to the defect size for thin semiconductor layers. Ettenberg 1941 studied the effect of dislocation density on the diffusion lengths in GaAs layers grown on GaAs and GaP substrates, and concluded that for high dislocation densities (such that subgrains form in the epitaxial layer) the diffusion length became roughly equal to the average spacing between defects (i.e., the grain size in our model). using these optimistic arguments for the effect of grain boundaries on diffusion lengths and lifetimes, the short circuit currents, open circuit voltages, and efficiencies have

B

.

POLYCRYSTALLINE DI%VICES

107

0.5 1

2

5 10

100

Grain Size, microns

F I G . 6 8 . Inherent efficiencies of S i and G a s solar cells for t h e same c o n d i t i o n s as i n F i g s . 66 and 67 e x c e p t t h a t the d i f f u s i o n l e n g t h s and lifetimes a r e determined b y t h e SoclofI l e s a n a l y s i s [ 9 5 ] . O h m i c back c o n t a c t .

~

been calculated a t AM1 f o r 10 pm t h i c k S i devices and 1 pm t h i c k GaAs devices a s a function of grain s i z e f o r fibrously oriented grains, as shown i n Figs. 66 and 67. The S i c e l l loses efficiency very slowly down t o a grain s i z e of 10 pm and more rapidly t h e r e a f t e r . An efficiency of 10%can t h e o r e t i c a l l y be obtained with grain s i z e s a s low as 3 m, and 5% f o r 0.7 pm grains. The e f f e c t of a low recombination velocity a t t h e back i s c l e a r l y seen f o r l a r g e grains, but becomes negligible f o r grain s i z e s below about 2 urn (since f o r small diffusion lengths, n e i t h e r t h e photogenerated nor dark minority c a r r i e r s "see" t h e back of the c e l l ) . The GaAs c e l l s of Fig. 67 have higher e f f i c i e n c i e s than t h e S i devices of Fig. 66, and a r e b e t t e r than S i i n sustaining t h e i r e f f i c i e n c i e s with decreasing grain s i z e . The steep absorption c o e f f i c i e n t and r e l a t i v e l y small diffusion lengths i n GaAs make grain boundaries l e s s important than i n S i , particul a r l y f o r very t h i n (-1 pm) GaAs devices, and r e l a t i v e l y good e f f i c i e n c i e s a r e predicted under optimum conditions even f o r 1 pm grains, provided the grains are fibrously oriented. Even random grain polycrystalline GaAs films may s t i l l y i e l d acceptable device behavior i f the grain s i z e s are 0.5 pm o r more. The calculations of Figs. 66 and 67 represent optimistic estimates f o r t h e e f f e c t of grain boundaries on device behavior. Soclof and Iles [951 have made s i g n i f i c a n t l y lower estimates of device efficiency as a function of grain s i z e , using a twodimensional analysis with fibrously oriented grains. Their

108

5.

THICKNESS

a n a l y s i s i n essence assumes t h a t t h e e f f e c t i v e d i f f u s i o n lengths i n t h e base and t o p regions are reduced t o about o n e - f i f t h of t h e g r a i n s i z e by t h e g r a i n boundary recombination r e g a r d l e s s of t h e t h i c k n e s s of t h e s e regions. C a l c u l a t i o n s of t h e i n h e r e n t AMO, AM1, and AM2 e f f i c i e n c i e s of 1 0 pm t h i c k S i c e l l s (0.1 ohm-cm N/P) and 1 pm t h i c k GaAs cells (0.01 ohm-cm P/N) a r e shown i n Fig. 68, using t h e s t a r t i n g parameters of T a b l e s 4 and 5 b u t allowing t h e d i f f u s i o n l e n g t h s and l i f e t i m e s t o decrease with g r a i n s i z e according t o t h e S o c l o f - I l e s a n a l y s i s . The e f f i c i e n cies p r e d i c t e d by t h i s a n a l y s i s are s u b s t a n t i a l l y lower than those p r e d i c t e d i n Figs. 66 and 67, p a r t i c u l a r l y f o r g r a i n sizes less than 1 0 pm. It i s possible t h a t e f f i c i e n c i e s somewhere between t h e o p t i m i s t i c v a l u e s of Figs. 66 and 67 and t h e less o p t i m i s t i c v a l u e s of Fig. 68 might be obtained someday, b u t f o r t h e moment a t l e a s t , while t h e q u a l i t y of such t h i n f i l m s remains poor (as i n Fig. 62) i n a d d i t i o n t o t h e g r a i n boundary problem, e f f i c i e n c i e s c l o s e r t o t h o s e of Fig. 68 w i l l more l i k e l y be obtained. It hardly needs t o be mentioned t h a t t h e r e a r e severe p r a c t i c a l problems t o f a b r i c a t i n g s o l a r c e l l s from p o l y c r y s t a l l i n e l a y e r s , c h i e f of which is t h e j u n c t i o n formation. Diffus i o n t e n d s t o proceed f a s t e r along g r a i n boundaries and d i s l o c a t i o n s than i n t h e bulk, and low values of shunt r e s i s t a n c e can r e s u l t i f t h e d i f f u s i o n along g r a i n boundaries p e n e t r a t e s through o r almost through t o t h e s u b s t r a t e . I t i s probably better t o u s e Schottky barriers or h e t e r o j u n c t i o n s t o f a b r i c a t e c e l l s on p o l y c r y s t a l l i n e l a y e r s , t o g e t h e r w i t h some method of reducing recombination a t g r a i n boundaries (see below). One of t h e e a r l i e s t experimental p o l y c r y s t a l l i n e S i devices w a s t h a t of Heaps et al. [961 i n 1961, who grew 1-2 m i l t h i c k r a n d o d y o r i e n t e d poly f i l m s on S i s u b s t r a t e s and obtained 0.60.9% e f f i c i e n c i e s f o r "photoflood lamp" l i g h t . Since t h e i r junction depth w a s 2.5 wn and t h e random g r a i n o r i e n t a t i o n l i m i t e d t h e a c t i v e device t h i c k n e s s t o 3-4 pm, e f f i c i e n c i e s higher than t h i s would n o t be expected. The high i n t e r e s t i n t h i n S i solar c e l l s f o r t e r r e s t r i a l u s e s has lead t o some more r e c e n t work on t h i n p o l y c r y s t a l l i n e f i l m s . Chu [891 has deposited 1-2 mil S i f i l m s onto g r a p h i t e s u b s t r a t e s a t around 1000°C and obtained 1.5% e f f i c i e n c y a t AM1. Chu, Fang, and o t h e r s [89,96-981 are attempting t o d e p o s i t 10 ~.lmp o l y c r y s t a l l i n e f i l m s on steel and A 1 s u b s t r a t e s because of t h e low c o s t of t h e s e substrates. Iles [99] has suggested doping the g r a i n boundaries inore h e a v i l y than t h e bulk, which would r e v e r s e t h e "cusp" i n t h e energy bands a t t h e boundary (Fig. 63) and l o w e r t h e recombination t h e r e . (This w i l l work provided t h e d i f f u s i o n does n o t p e n e t r a t e t h e e n t i r e l a y e r and g i v e high leakage.) No reports of e f f i c i e n c i e s from devices

C.

Cu2S-CdS

109

made i n t h e s e ways have appeared as y e t , b u t experiments are p r e s e n t l y under way and w i l l undoubtedly b e reported on soon. Even less work has been done on GaAs t h i n f i l m devices t h a n on S i ones. Vohl et al. [lo01 have described t h e charact e r i s t i c s of 15-50 pm t h i c k G a A s f i l m s deposited by vapor growth on Mo o r A 1 substrates. Solar c e l l s of 4.3-4.6% e f f i c i e n c y f o r tungsten l i g h t were made using e i t h e r evaporated P t Schottky b a r r i e r s o r a CulaBSe l a y e r t o form a heterojunction. Attempted p-n j u n c t i o n s i n t h e s e f i l m s were less s u c c e s s f u l because of r a p i d d i f f u s i o n of Zn along t h e g r a i n boundaries and a r e s u l t i n g low shunt r e s i s t a n c e .

c. cu2s-cds The behavior of t h i n f i l m CdS s o l a r c e l l s as a f u n c t i o n of t h i c k n e s s i s somewhat more involved than f o r S i and G a s devices. The CdS c e l l s are made by evaporating a CdS f i l m about 1 m i l t h i c k onto a t r a n s p a r e n t p l a s t i c s u b s t r a t e , immersing i n a Cu i o n p l a t i n g s o l u t i o n t o form a t h i n Cu2S l a y e r , d e p o s i t i n g a c o n t a c t g r i d , and encapsulating i n a second t r a n s p a r e n t p l a s t i c s h e e t . Depending on t h e manner i n which t h e back c o n t a c t i s made, l i g h t can be i n c i d e n t on t h e c e l l from e i t h e r t h e Cu2S s i d e o r t h e CdS s i d e . CdS i s a d i r e c t bandgap material with high d e n s i t i e s of states i n t h e conduction and valence bands. The absorption c o e f f i c i e n t t h e r e f o r e rises t o very high values (lo5 c m - l ) f o r photon e n e r g i e s even s l i g h t l y higher than t h e baqdgap 11011 (2.4 e V ) . For t h i s reason t h e a c t i v e region on t h e CdS s i d e of t h e h e t e r o j u n c t i o n i s only a micron o r so wide. For a device with l i g h t i n c i d e n t on t h e CdS s i d e , reducing t h e t h i c k n e s s of t h e CdS l a y e r w i l l have e s s e n t i a l l y no e f f e c t a t a l l (from a t h e o r e t i c a l viewpoint) u n t i l t h e CdS thickness becomes less than 2-3 pm. A t t h a t p o i n t more l i g h t would b e able t o reach t h e a c t i v e regions of t h e device ( t h e d e p l e t i o n region width p l u s up t o about 1 d i f f u s i o n l e n g t h i n both the CdS and Cu2S), and t h e e f f i c i e n c y would t h e o r e t i c a l l y i n c r e a s e with decreasing CdS thickness. When t h e t h i c k n e s s became less than a d i f f u s i o n l e n g t h , however, t h e e f f i c i e n c y would decrease because of l o s t carriers t h a t would otherwise be c o l l e c t e d . When l i g h t i s i n c i d e n t on t h e Cu2S s i d e , reducing t h e CdS thickness would again have no appreciable e f f e c t u n t i l t h e t h i c k n e s s became comparable t o o r less than a d i f f u s i o n length; f o r t h i n n e r CdS l a y e r s , carriers a r e l o s t t h a t might otherwise b e c o l l e c t e d and t h e e f f i c i e n c y decreases. This simple reasoning argues t h a t t h e CdS l a y e r i n a Cu2S-CdS s o l a r c e l l can be reduced t o t h e o r d e r of a micron

110

5.

THICKNESS

without harmful e f f e c t , and i n a s i n g l e c r y s t a l device t h i s would be t r u e , b u t f o r a t h i n f i l m c e l l t h e s i t u a t i o n is a b i t mre complicated. The CdS l a y e r is p o l y c r y s t a l l i n e , and t h e g r a i n s i z e i s probably a f u n c t i o n of d i s t a n c e from t h e CdSsubstrate i n t e r f a c e . I f t h e CdS i s made t h i n n e r , t h e number of d e f e c t s i n t h e a c t i v e region w i l l probably i n c r e a s e and t h e c o l l e c t i o n e f f i c i e n c y w i l l d e t e r i o r a t e . I n a d d i t i o n , t h e Cu ions migrate down t h e g r a i n boundaries d u r i n g t h e Cu p l a t i n g and subsequent h e a t i n g s t e p s , and i f t h e p o l y c r y s t a l l i n e CdS is too t h i n , they may migrate t o t h e back c o n t a c t and cause high leakage. The CdS l a y e r is u s u a l l y made 2 0 vm t h i c k o r so t o prevent such problems from a r i s i n g . Some of t h e e f f e c t s o f t h e CuzS t h i c k n e s s have already been discussed i n Chapter 2. This l a y e r i s r e s p o n s i b l e f o r a l l t h e response between 1.1 and 2 . 4 eV. I f l i g h t i s i n c i d e n t on t h e Cu2S a i d e , then t h e r e is an optimum t h i c k n e s s of t h e Cup of around 2000 8. I f t h e Cu2S is t h i n n e r than t h i s , t h e long wavelength response is lost and t h e series r e s i s t a n c e i n c r e a s e s ; i f it is appreciably t h i c k e r , then carriers are generated t o o f a r from t h e i n t e r f a c e and t h e s h o r t wavelength response s u f f e r s . I f l i g h t is i n c i d e n t on t h e CdS side, then t h e Cu2S t h i c k ness i s less important, and it should be made t h i c k e r than u s u a l for lower series r e s i s t a n c e and higher long wavelength response, provided t h a t t h e longer p l a t i n g t i m e s needed f o r t h i c k e r l a y e r s do n o t r e s u l t i n Cu i o n migration along g r a i n boundaries and subsequent l o w shunt r e s i s t a n c e s .

As t h e t h i c k n e s s of a solar c e l l is reduced, l o s s e s may begin t o appear due t o complete transmission of longer wavelength l i g h t through t h e device ( p o s s i b l y modified by r e f l e c t i o n a t t h e back surface) and due t o increased recombination a t t h e back Ohmic contact. By comparison w i t h i t s v a l u e a t l a r g e thicknesses, t h e maximum possible s h o r t c i r c u i t c u r r e n t i n S i i s reduced t o 92, 70, and 25% f o r 100, 10, and 1 pm devices, r e s p e c t i v e l y . I n GaAs t h e drop i n c u r r e n t is n o t appreciable u n t i l t h e t h i c k ness is reduced below 2 vm. The l a r g e s t e f f e c t of t h i c k n e s s on s o l a r c e l l behavior i s due t o t h e back electrical c o n t a c t . An Ohmic back c o n t a c t reduces t h e photocurrent and i n c r e a s e s t h e dark c u r r e n t by a c t i n g as a s u r f a c e of high recombination v e l o c i t y . A blocking back c o n t a c t (such as a BSF) enhances t h e photocurrent and lowers t h e dark c u r r e n t by preventing recombination a t t h e back s u r f a c e . Neither e f f e c t becomes n o t iceable, however, u n l e s s t h e device t h i c k n e s s is less than about 2 d i f f u s i o n l e n g t h s i n t h e base.

D.

SUMMARY

111

The inherent AM1 e f f i c i e n c i e s of 100 pm t h i c k s i n g l e c r y s t a l S i devices f o r r e l a t i v e l y good q u a l i t y material range from 15% (10 ohm-cm) t o 19% (0.1 ohm-cm) f o r Ohmic back cont a c t s and 17% (10 ohm-cm) t o 20% (0.1 ohm-cm) f o r blocking back contacts. 10 um t h i c k s i n g l e c r y s t a l devices have optimum AM^ e f f i c i e n c i e s of 8 % (10 ohm-cm) t o 12% (0.1 ohm-cm) f o r ohmic back contacts and 15% (10 ohm-cm) t o 18% (0.1 ohm-cm) f o r blocking back contacts. The behavior of GaAs devices changes much l e s s with thickness compared t o S i c e l l s because of t h e much smaller diffusion lengths i n GaAs. The inherent A M 1 e f f i c i e n c i e s of 1 pm thick GaAs devices f o r r e l a t i v e l y good q u a l i t y material range from 19%f o r an Ohmic back contact t o 21.5% f o r a blocking back contact. The e f f i c i e n c i e s of both S i and GaAs s i n g l e cryst a l c e l l s a r e reduced strongly i f t h e l i f e t i m e i n t h e material i s poor and t h e f r o n t surface recombination velocity i s high. In polycrystalline s o l a r c e l l s , grain boundaries present t h e biggest problem because of t h e severe l o s s of minority c a r r i e r s t h a t can occur a t t h e boundaries. The e f f e c t of t h e g r a i n s becomes important i n 10 m thick S i devices when the g r a i n s i z e becomes less than 50 w, and i n 1 pm GaAs devices when t h e grain s i z e becomes l e s s than 3 pm. Reasonably good AM1 e f f i c i e n c i e s (7% o r more) are predicted f o r 10 thick S i and t h e grains are devices i f t h e grain sizes exceed 10 fibrously oriented. A M 1 e f f i c i e n c i e s of 10%o r higher are pred i c t e d f o r 1 pm thick GaAs devices f o r grain s i z e s of 1 urn o r more. The e f f e c t of thickness on t h i n f i l m Cup-CdS s o l a r cells is very small. The CdS thickness could t h e o r e t i c a l l y be reduced t o several microns before any appreciable change took place. In p r a c t i c e , however, t h e q u a l i t y of t h e Cu2S and CdS are probably a function of the CdS thickness, and t h i s might r e s u l t i n poor behavior i f t h e CdS thickness were reduced t o less than 5 m.

CHAPTER 6

Other Solar Cell Devices

Although t h e g r e a t majority of s o l a r c e l l s are made with p-n j u n c t i o n s , there are s e v e r a l o t h e r t y p e s t h a t could e x h i b i t unique advantages of one kind o r a n o t h e r , i n c l u d i n g Schottky b a r r i e r s , h e t e r o j u n c t i o n s , v e r t i c a l m u l t i j u n c t i o n devices , and g r a t i n g cells. The Schottky barrier c e l l i s very simple and economical t o f a b r i c a t e , and has improved s p e c t r a l response a t s h o r t wavelengths, b u t the expected e f f i c i e n c i e s may b e somewhat lower than conventional c e l l s because o f lower open c i r c u i t v o l t a g e s . Heterojunction s o l a r c e l l s can a l s o have enhanced s h o r t wavelength response, and are p o t e n t i a l l y as e f f i c i e n t as conventional cells under optimum c o n d i t i o n s . Heterojunction and Schottky b a r r i e r c e l l s could b e very important f o r terrest r i a l a p p l i c a t i o n s because of p o t e n t i a l l y low cost and because they do not n e c e s s a r i l y e n t a i l d i f f u s i o n p r o c e s s e s , which can be d e t r i m e n t a l t o p o l y c r y s t a l l i n e d e v i c e s . Vertical m u l t i junction solar c e l l s are p o t e n t i a l l y high i n e f f i c i e n c y and r a d i a t i o n t o l e r a n c e , and they could become important f o r high i n t e n s i t y a p p l i c a t i o n s . Grating c e l l s could t h e o r e t i c a l l y have both higher s h o r t c i r c u i t c u r r e n t s and higher open c i r c u i t v o l t a g e s t h a n conventional d e v i c e s , and are r e l a t i v e l y simple t o make. Each of t h e s e types of s o l a r c e l l s w i l l b e discussed i n turn. A.

Schottky Barrier C e l l s

If a metal i s brought i n t o c o n t a c t with a c l e a n s u r f a c e of a semiconductor material, a readjustment of charge t a k e s p l a c e i n o r d e r t o e s t a b l i s h thermal equilibrium and under most c o n d i t i o n s an energy band bending occurs a t t h e i n t e r f a c e much as i n a p-n junction. If t h e metal is t h i n enough t o b e part i a l l y t r a n s p a r e n t to l i g h t (while s t i l l maintaining an acceptably l o w s h e e t r e s i s t i v i t y ) , then some of t h e i n c i d e n t l i g h t can p e n e t r a t e t o t h e semiconductor and a photocurrent w i l l

112

A.

SCHOTTKY BARRIER CELLS

113

1

A

t

3

"$0

FIG. 69. Energy band,diagram of a Schottky barrier on an n-type semiconductor.

-0

EV

3

r e s u l t . Figure 69 shows t h e most simple form of an n-type Schottky b a r r i e r device and d e f i n e s some of i t s important parameters: t h e d e p l e t i o n width Wo, t h e b a r r i e r h e i g h t Obo, and t h e d i f f u s i o n v o l t a g e VdO. There are t h r e e p h o t o e f f e c t s t h a t can t a k e place. Light can be absorbed i n t h e metal and e x c i t e e l e c t r o n s over t h e b a r r i e r i n t o t h e semiconductor (1 i n Fig. 6 9 ) ; t h i s e f f e c t is commonly used t o measure t h e barrier h e i g h t ObO. Long wavelength l i g h t is u s u a l l y absorbed deep i n t h e semiconductor, c r e a t i n g hole-electron pairs j u s t as i n a p-n junction; t h e h o l e s must then d i f f u s e t o t h e junct i o n edge t o be c o l l e c t e d ( 3 i n Fig. 6 9 ) . S h o r t e r wavelength l i g h t e n t e r i n g t h e semiconductor is absorbed p a r t l y i n t h e bulk and p a r t l y i n t h e d e p l e t i o n region (2 i n Fig. 6 9 ) , and very s h o r t wavelength l i g h t i s absorbed e n t i r e l y i n t h e deplet i o n region. The high e l e c t r i c f i e l d i n t h i s d e p l e t i o n region "sweeps" t h e photogenerated carriers away b e f o r e they can recombine a t i n t e r f a c e states, r e s u l t i n g i n good c o l l e c t i o n of t h e s e c a r r i e r s , i n c o n t r a s t t o a p-n junction where a low l i f e t i m e i n t h e t o p region and a high s u r f a c e recombination v e l o c i t y can s e r i o u s l y lower t h e response a t s h o r t wavelengths. The e x c i t a t i o n of c a r r i e r s from t h e metal i n t o t h e semiconductor is a much smaller e f f e c t [lo21 (by a f a c t o r of 100 o r more) than t h e band-to-band e x c i t a t i o n mechanisms ( 2 and 3 i n Fig. 6 9 ) , and can be neglected compared t o t h e s e f o r sunl i g h t a p p l i c a t i o n s . As far as t h e photocurrent generation and c o l l e c t i o n are concerned t h e r e f o r e , t h e Schottky b a r r i e r s o l a r c e l l can be thought of as a, p-n j u n c t i o n with a zero junction depth but with an a t t e n u a t i n g metal c o a t i n g a t i t s s u r f a c e . The high f i e l d i n t h e d e p l e t i o n region of t h e Schottky c e l l serves t h e same function as t h e d r i f t f i e l d i n t h e d i f f u s e d region of a normal p-n c e l l i n overcoming s u r f a c e l o s s e s . I n a Schottky b a r r i e r s o l a r c e l l , j u s t as i n a p-n junct i o n c e l l , t h e photocurrent passing through a load causes t h e device t o be forward b i a s e d , and a dark c u r r e n t flows i n t h e

114

6.

OTHERSOLARCELLDEVICES

opposite d i r e c t i o n t o t h e photocurrent. A V-I c h a r a c t e r i s t i c is obtained under illumination which appears q u a l i t a t i v e l y t h e same as i n Fig. 2 , although t h e d a r k current i n t h e Schottky b a r r i e r i s very d i f f e r e n t i n nature from t h e dark current i n a p-n junction. 1.

SPECTRAL RESPONSE AND PH(yp0CuRRENT

The t w o major contributions t o t h e s p e c t r a l response and t o t h e photocurrent come from t h e depletion region and from t h e bulk (the "base" of t h e Schottky b a r r i e r s o l a r c e l l ) . The c o l l e c t i o n from t h e depletion region is q u a l i t a t i v e l y t h e same as i n a p-n junction. I t i s assumed that t h e high f i e l d i n t h e depletion region sweeps carriers out before they can recombine, leading t o a current f o r monochromatic l i g h t equal t o

where T ( h ) is t h e transmission of t h e m e t a l f i l m i n t o t h e underlying semiconductor, F(X) i s t h e incident photon f l u x , a is t h e absorption c o e f f i c i e n t , and W i s t h e width of t h e depletion region, given by [lo31

where es i s t h e s t a t i c d i e l e c t r i c constant. (The kT/q term i s due t o t h e small density of w b i l e carriers within t h e space charge region.) The r e f l e c t i o n of l i g h t from t h e metal surface i s accounted f o r i n T(A). The photocurrent expressed by (75) i s similar t o t h a t expressed by (20) except t h a t t h e transmission of l i g h t through t h e m e t a l [T(X)l replaces t h e transmission (exp(-ax,)) of l i g h t through t h e top region of t h e p-n junction and t h e r e f l e c t i o n of l i g h t from t h e surface of t h e p-n device. The c o l l e c t i o n from t h e base of t h e Schottky b a r r i e r c e l l is q u a l i t a t i v e l y t h e same as from t h e base of a p-n junction c e l l , and t h e equations and derivations of Chapter 2 apply with only t h e transmission f a c t o r as a modification. The photocurrent due t o holes c o l l e c t e d from t h e n-type base region i s then

equation continues

A.

SCHOTTKY BARRIER CELLS

115

where S i s t h e recombination v e l o c i t y a t t h e back contact and H ' i s t h e thickness of t h e device minus t h e width of t h e deplet i o n region: H' = H-W. I f t h e back contact i s Ohmic, ( 7 7 ) s i m p l i f i e s t o Jp =

sFaLp (a2Lg-1)

[

cosh(H'/$)-exp(-aH')

T exp(-aW) a%-

sinh (H'/Lp)

]

(78)

and if t h e device thickness i s much g r e a t e r than t h e d i f f u s i o n length H ' >> $, ( 7 7 ) s i m p l i f i e s t o Jp = [qFa$/(a$+l))

T exp(-aW).

(79)

The t o t a l photocurrent i s found by adding ( 7 5 ) t o ( 7 7 ) , ( 7 8 ) , or ( 7 9 ) as t h e c m d i t i o n s warrant. ( I f a d r i f t f i e l d is present i n t h e base, (31) can be used, s e t t i n g x, = 0, multiplying by T ( h ) , and changing t h e s u b s c r i p t s from n t o p.) I t should be noted t h a t Eqs. ( 7 5 ) and ( 7 7 ) f o r t h e photoc u r r e n t do not e x p l i c i t l y take i n t o account t h e nature of t h e barrier. The derivations are based on t h e assumption of a high f i e l d i n t h e depletion region which sweeps photocarriers o u t of t h i s region regardless of i n t e r f a c e states and which reduces t h e excess minority carrier density a t t h e depletion region edge t o a n e g l i g i b l e value f o r s h o r t c i r c u i t conditions. If i n t e r f a c e e f f e c t s become important, t h e photocurrent may be reduced. I n p a r t i c u l a r , the photocurrent may be reduced if t h e r e i s an i n t e r f a c i a l l a y e r I1041 such as an oxide or another i n s u l a t o r more than 30 o r 40 A t h i c k between t h e metal and t h e semiconductor. For thinner oxide l a y e r s than t h i s , tunneling can t a k e place r e a d i l y and t h e photocurrent w i l l not be s e r i o u s l y affected by t h e oxide layer. For somewhat t h i c k e r oxide l a y e r s , t h e photocurrent may s t i l l not be s e r i o u s l y a f fected i f t h e l a y e r is conducting r a t h e r than insulating. It has been suggested [lo51 t h a t an inversion l a y e r adjacent t o t h e i n t e r f a c e can lower t h e response t o s h o r t wavelengths by causing electrons generated very near t h e surface t o d i f f u s e toward t h e surface along with t h e d r i f t of photogenerated holes, even though t h e d r i f t f i e l d would o r d i n a r i l y cause electrons t o be accelerated away from t h e surface. This theory, however, only a p p l i e s f o r very low l i g h t l e v e l s DO51 (An,Ap 15 >15 1 1

JAM0

JAMl

( m ~ / c m ~ ) (a/cm2)

BSF 00

0-00 0-00 m

0

44.6 42.7 45.2 39.8

35.4 33.9 35.9 31.5

38.2 36.2 30.1 35.0

30.7 29.0 23.1 27.9

semiconductor materials, provided t h e o p t i c a l c o n s t a n t s f o r t h e metal f i l m s are known. Schneider 11061 has derived express i o n s f o r t h e transmission of l i g h t through a m e t a l f i l m i n t o a dielectric mterial when an a n t i r e f l e c t i v e c o a t i n g has been a p p l i e d t o t h e s u r f a c e o f t h e metal. The i n t e r n a l spectral response of 1.0 and 0.1 ohm-cm , ecn-type S i Schottky b a r r i e r s ( 5 ~ 1 and 0 ~ 8~ . 5 ~ 1 0~ ~m ~- ~res t i v e l y ) and of 0.5 and 0.035 ohm-cm (2x1015 and 5X10l6 c m , r e s p e c t i v e l y ) G a s Schottky b a r r i e r s are shown i n Figs. 72 and 73, where t h e transmission T(A) through t h e metal f i l m is assumed t o be unity. These responses were c a l c u l a t e d from (751, (771, and (801, assuming a s u r f a c e recombination v e l o c i t y a t t h e i n t e r f a c e of l o 7 cm/sec and no d r i f t f i e l d s o u t s i d e t h e d e p l e t i o n region. The high energy ( s h o r t wavelength) response i s seen t o approach u n i t y , as a consequence of absorption and c a r r i e r generation i n s i d e t h e d e p l e t i o n region where t h e high f i e l d sweeps carriers o u t w i t h minimum l o s s . The low energy response is determined by t h e c o n d i t i o n s i n t h e base. A BSF enhances t h e response ( j u s t as it does i n a p-n j u n c t i o n ) provided t h e device thickness does n o t exceed about twice t h e d i f f u s i o n length. The e x t e r n a l spectral responses of these same devices with various metals and a n t i r e f l e c t i v e c o a t i n g s on t h e s u r f a c e are found by multiplying t h e i n t e r n a l response of Figs. 72 o r 73 by t h e metal transmission f a c t o r T(A) The s h o r t c i r c u i t photocurrents of t h e s e c e l l s , as calcul a t e d from (81) f o r v a r i o u s c o n d i t i o n s , are given i n T a b l e 7.

-3

.

120

6.

OTHER SOLAR CELL DEVICES

If the transmission f a c t o r i s high, as it would be f o r t h i n metal films with a n t i r e f l e c t i v e coatings, then t h e photocurrent is higher f o r t h e Schottky c e l l than it would be i n a p-n junction c e l l of t h e same material with t h e same device thickness, base r e s i s t i v i t i e s , and f r o n t and back recombination v e l o c i t i e s . The presence of t h e depletion region r i g h t a t t h e semiconductor surface i n t h e Schottky c e l l does indeed go a long way i n overcoming low l i f e t i m e s and high recombination v e l o c i t i e s near t h e surface. On the o t h e r hand, p-n junction c e l l s under t h e b e s t of conditions (no dead l a y e r , d r i f t f i e l d present, small junction depth) have about t h e same calculated photocurrents as t h e b e s t Schottky c e l l s , and t h e photocurrents f o r t h e Schottky devices i n p r a c t i c e w i l l be reduced t o some degree by the presence of the metal film. 2.

ELECTRICAL BEHAVIOR AND EFFICIENCY

Although t h e s p e c t r a l response and photocurrent do not depend very strongly on t h e b a r r i e r height, t h e dark current depends very much on t h i s height. Figure 69 showed an idealized version of a metal-semiconductor contact without an image p o t e n t i a l o r an i n t e r f a c i a l layer. The b a r r i e r height $y,O i n t h e absence of i n t e r f a c e states would be determined by t h e difference between t h e m e t a l work function and t h e semiconduct o r electron a f f i n i t y , but f o r most semiconductors, including S i and GaAs, a l a r g e density of i n t e r f a c e s t a t e s can effect i v e l y "pin" the Fermi l e v e l i n t h e semiconductor near t h e valence band, making t h e b a r r i e r height roughly 2/3 of t h e bandgap f o r n-type Schottky b a r r i e r s and (1/3)Eg f o r p-type b a r r i e r s . Measured b a r r i e r heights f o r various metals on S i and GaAs a r e given i n T a b l e 8. The b a r r i e r heights f o r t h e two metals Au and P t a r e nearly t h e same i n S i as i n GaAs, but otherwise t h e heights are l a r g e r f o r GaAs devices as expected from t h e l a r g e r bandgap. The i n t e r f a c e s t a t e d e n s i t i e s i n Schottky b a r r i e r s and consequently t h e b a r r i e r heights appear t o be strongly i n f l u enced by t h e nature of t h e semiconductor surface I1031 ; $bO tends t o be l a r g e r on cleaved surfaces than on chemically etched ones [ l o g ] , and depends on t h e c r y s t a l l i n e o r i e n t a t i o n as well f o r p o l a r semiconductors such as GaAs [1091. Differences i n surface preparation are usually responsible f o r t h e range of values reported by d i f f e r e n t workers f o r b a r r i e r heights of a given m e t a l on a given semiconductor. In part i c u l a r , b a r r i e r heights tend t o be higher when an i n t e r f a c i a l layer such as an oxide i s present. The a c t u a l b a r r i e r p r o f i l e i n a metal-semiconductor

A.

SCHOTTKY BARRIER CELLS

121

TABLE 8

Barrier Heights t o S i and Metal

Metal S i (p-type)

S i (n-type) Au Ag A1 Cr Ni

Mo Pt PtSi W

0.80 0.56-0.79 0.50-0.77 0.58 0.67-0.70 0.58 0.90 0.85 0.66

.

AU

Ag

A1

cu Ni Pb

0.35 0.55 0.58 0.46 0.51 0.56

G a A s (n-type)

Au As A1 Be

0.90 0.88 0.80 0.81

cu Pt W

0.82 0.86 0.80

'After Milnes and Feucht [601; Sze [1031; and Smith and Rhoderick [112]. c o n t a c t d i f f e r s from t h e i d e a l v e r s i o n of Fig. 69 due t o an i n t e r f a c i a l l a y e r , an image p o t e n t i a l , o r both. The i n t e r f a c i a l l a y e r is t h e r e s u l t of o x i d a t i o n o r o t h e r contamination of t h e material s u r f a c e p r i o r t o d e p o s i t i n g t h e metal. I f c a r e i s taken, t h i s layer w i l l not be over a few t e n s of angstroms i n thickness, and it can be eliminated e n t i r e l y by e i t h e r cleaning t h e s u r f a c e j u s t before d e p o s i t i o n (e.g. , s p u t t e r etching) o r by f i r i n g t h e b a r r i e r metal i n t o t h e mater i a l (as i n P t S i ) . The image p o t e n t i a l on t h e o t h e r hand is a fundamental phenomenon t h a t can be changed i n magnitude b u t not eliminated. I t i s t h e r e s u l t of t h e a t t r a c t i v e f o r c e experienced by a charge carrier i n t h e v i c i n i t y of a metal surf a c e due t o an "image charge" of o p p o s i t e s i g n induced i n t h e metal. This a t t r a c t i v e f o r c e reduces t h e barrier h e i g h t by an amount known as t h e image p o t e n t i a l A$:

122

6. OTHER SOLAR CELL DEVICES

I

Metal

Semiconductor

n - t y p e semiconductor i n c l u d i n g t h e image p o t e n t i a l A 4 .

where Ed is t h e high frequency d i e l e c t r i c c o n s t a n t and cS t h e low frequency d i e l e c t r i c c o n s t a n t (Ed E~ f o r S i and GaAs). I n t h i s equation, vdo is t h e d i f f u s i o n v o l t a g e t h a t would e x i s t i f t h e r e w e r e no image p o t e n t i a l p r e s e n t (Fig. 69). The barrier h e i g h t and d i f f u s i o n v o l t a g e are reduced by t h e image p o t e n t i a l according t o

The image p o t e n t i a l i n c r e a s e s w i t h i n c r e a s i n g doping l e v e l and decreases with i n c r e a s i n g forward bias, and it r e s u l t s i n a rounding of t h e barrier p o t e n t i a l p r o f i l e near t h e i n t e r f a c e , as shown i n Fig. 74. The barrier has a maximum v a l u e a s h o r t d i s t a n c e % away from t h e i n t e r f a c e ; t h i s d i s t a n c e i s about 50 fl f o r 1015 cm-3 doped material and decreases t o about 1 5 f o r 1017 cm-3 m a t e r i a l . The dark c u r r e n t i n t h e forward bias d i r e c t i o n of a Schottky b a r r i e r i s determined mostly by thermionic emission of majority c a r r i e r s from t h e semiconductor i n t o t h e m e t a l 11031, f o r doping levels less t h a n lo1' ~ m - ~ .The Schottky b a r r i e r c u r r e n t can be w r i t t e n a s [lo31 J = A**TZ exp (-qt$b/kT) [exp (qVj/kT)-11

(85)

where A * * is t h e Richardson c o n s t a n t A* modified by o p t i c a l phonon s c a t t e r i n g , quantum mechanical r e f l e c t i o n , and tunneli n g o f carriers a t t h e metal-semiconductor i n t e r f a c e . A* i s given by A* = 4aqm*k2/h3

(86)

where m* is t h e e f f e c t i v e m a s s t e n s o r f o r t h e r e l e v a n t energy bands i n t h e semiconductor and h i s Planck's constant. The dark c u r r e n t (85) i s fundamentally d i f f e r e n t from t h e forward b i a s dark c u r r e n t i n a p-n junction. I n t h e j u n c t i o n device,

A.

SCHOTTKY BARRIER CELLS

123

Forward Volts

FIG. 7 5 . D a r k c u r r e n t d e n s i t i e s of A u - S i and P t - S i S c h o t t k y barriers f o r 1 ohm-cm S i , and of Au-GaAs devices f o r t w o d o p i n g l e v e l s . A u - S i : Js = 5~10'~ A / c m 2 ; P t - S i : A** = 110 A / c ~ ~ ( o K A) U~- ;G ~ A S : A** = 4 . 4 A / c & ( o K ) ~ .

t h e current i s determined by t h e rate a t which minority carr i e r s can d i f f u s e and d r i f t away from t h e junction edge a f t e r being injected from t h e opposite s i d e ; a BSF reduces t h e dark current by reducing t h e r a t e of t h i s c a r r i e r removal. In t h e Schottky b a r r i e r , t h e dark current is determined by t h e r a t e s a t which c a r r i e r s are emitted from t h e semiconductor i n t o t h e metal, and it is a majority c a r r i e r current t h a t is not affected by a BSF on t h e semiconductor. This fundamental difference between t h e two current mechanisms shows up i n a very important way; i n a p-n junction device, t h e d a r k current a t a given voltage d e c r e a s e s strongly with i n c r e a s i n g doping l e v e l i n t h e base, but i n the Schottky barrier, t h e dark current increases ( s l i g h t l y ) o r remains about t h e same f o r increasing doping l e v e l s up t o around 1017 ~ r n - ~ , and increases very strongly (because of tunneling) above 1017 Therefore, t h e open c i r c u i t voltage i s smaller f o r high doping l e v e l s than f o r low doping l e v e l s under otherwise equal conditions. The s l i g h t v a r i a t i o n s i n dark current with doping l e v e l a r i s e from t h e image p o t e n t i a l , which a f f e c t s $b i n Eq. (85), and from t h e o p t i c a l phonon s c a t t e r i n g and quantum mechanical r e f l e c t i o n , which a f f e c t A** [103]. Andrews and Lepselter Ill01 have shown t h a t the value of A** f o r moderately doped S i varies somewhat with e l e c t r i c f i e l d but has an average value of around 110 A/cm2(oK)2 f o r n-type S i and 32 A/cm2(oK)2 f o r

124

6.

OTHER SOLAR CELL DEVICES

TABLE 9 Dark Current Parameters, Au-Si,

1x1015 5x1Ol5 1x1016 5X10l6

5x10-’ 4. 5 ~ 1 0 - ~ 4.5~10-~ 5.5x10

3OO0e

1.0 1.0 1.005 1.015

a A f t e r Chang and Sze [108]. For n-type GaAs, A** i s around 4 . 4 A/crn2(OKl2 f o r p-type. f o r moderate doping l e v e l s 11111. The c a l c u l a t e d forward bias dark c u r r e n t s for Au-Si, P t - S i , and Au-GaAs devices without i n t e r f a c i a l l a y e r s are shown i n Fig. 75 f o r 1 ohm-cm n-type S i and f o r two G a A s doping l e v e l s . The d i f f e r e n c e i n t h e two S i curves arises from t h e d i f f e r e n c e i n barrier h e i g h t s between Au-Si and Pt-Si (Table 8 ) ; t h e b a r r i e r height e n t e r s exponentially i n t o t h e dark c u r r e n t determination, as given i n Q. (85). The d i f f e r ence i n t h e t w o GaAs curves arises from t h e d i f f e r e n c e i n image p o t e n t i a l a t t h e t w o doping l e v e l s (17 mV a t 2x101’ ~ r n - ~ and 39 mV a t 5X10l6 The Schottky b a r r i e r dark c u r r e n t i s o f t e n w r i t t e n as ill31 J = Js [exp (qV/nkT) -11

(87)

where n is t h e s l o p e of t h e Iln J-V c u r v e

F o r mst S i and G a A s Schottky barriers made with c a r e f u l l y cleaned s u r f a c e s , n i s i n t h e range of 1.01-1.03 due t o t h e v a r i a t i o n o f A# and A** w i t h v o l t a g e and doping level. Table 9 lists t h e v a l u e s o f 3, and n f o r Au-Si devices as computed by Chang and Sze 11131; t h e values of n are very l o w f o r t h e moderate doping levels used for Schottky solar cells. On t h e o t h e r hand, minority carrier c u r r e n t s ( h o l e i n j e c t i o n from t h e metal and space charge l a y e r recombination), t u n n e l i n g c u r r e n t s , and i n t e r f a c i a l l a y e r s can r e s u l t i n considerably higher values of n [104,109,111,113], w i t h v a l u e s of 2 o r more observed i n soine cases [1141.

A.

SCHOTTKY BARRIER CELLS

125

TABLE 1 0 Performance o f S i and G a A s Schottky Barriers, 300°K, n = 1-1.02

Au-Si Pt-Si Au-Si Pt-Si Au-Si Pt-Si

300 300 100 100 100 100

BSF BSF

>15

0-00

>15 1

0-m

00 00

m m

0.30 0.38 0,.30 0.38 0.30 0.38

0.72 0.76 0.72 0.75 0.72 0.76

7.2 9.6 6.9 9.1 7.2 9.7

7.8 10.5 7.4 10.0 7.8 10.6

0.47 0.47 0.46 0.46

0.79 0.79 0.79 0.79

10.3 9.9 8.1 9.6

11.6 11.1 8.7 10.6

Nd Au-GaAs

Au-Gas Au-GaAs Au-GaAs

2x1015 5x10 5x10I6 5X10l6

1

00

0

The open c i r c u i t v o l t a g e s , f i l l f a c t o r s , and e f f i c i e n c i e s f o r t h e Schottky barrier cells of T a b l e 7 are listed i n T a b l e 1 0 , assuming 100%metal t r a n s m i s s i o n , no series o r s h u n t r e s i s t a n c e l o s s e s , and s i n g l e crystal material w i t h bulk l i f e t i m e s ( t h e series r e s i s t a n c e o f m o s t m e t a l f i l m s g r e a t e r t h a n 50 thick can be made a c c e p t a b l y low by u s i n g a f i n e p a t t e r n c o n t a c t g r i d as i n t h e v i o l e t c e l l ) . Pt-Si d e v i c e s are more e f f i c i e n t t h a n Au-Si because of t h e l a r g e r barrier h e i g h t s . G a A s devices are o n l y s l i g h t l y more e f f i c i e n t t h a n S i devices because t h e barrier h e i g h t s are o n l y s l i g h t l y h i g h e r on G a A s t h a n t h e y are on Si (Table 8 ) . The c a l c u l a t e d e f f i c i e n c i e s f o r Schottky barrier solar cells on S i and GaAs are lower t h a n f o r p-n j u n c t i o n s of t h e s e materials a t t h e same doping l e v e l s because of t h e low open c i r c u i t v o l t a g e s o b t a i n e d from t h e Schottky barrier cells. The low V o c ' s i n t u r n are a r e s u l t of t h e d a r k c u r r e n t mechanism (85) i n Schottky b a r r i e r s and t h e r e l a t i v e l y l o w values o f 4b; if barrier h e i g h t s equal t o t h e bandgap could be obt a i n e d , t h e " l i m i t conversion e f f i c i e n c i e s " o f Schottky b a r r i e r cells would be about t h e same as f o r p-n j u n c t i o n c e l l s [1151, i . e., about 22% f o r S i and 25% f o r G a A s . As long as t h e barrier h e i g h t s remain l o w , however, as i n T a b l e 8 (measured on S i and G a A s with c a r e f u l l y cleaned s u r f a c e s ) [1031, t h e o u t p u t v o l t a g e s w i l l b e low. The p r e s e n c e of an i n t e r f a c i a l l a y e r

126

6.

OTHER SOLAR C E U DEVICES

can apparently r e s u l t i n i n c r e a s e d barrier h e i g h t s [104,1091 , which would l e a d t o l o w e r dark c u r r e n t s and higher V o c ' s , b u t t h e i n t e r f a c i a l l a y e r may also reduce t h e photocurrent by addi n g an e x t r a energy barrier t h a t photogenerated carriers must tunnel through. It has been suggested [107,114] t h a t high values of n i n Eq. (87) can a l s o l e a d t o l o w dark c u r r e n t s , even without l a r g e b a r r i e r h e i g h t s , because t h e f u n c t i o n exp (qV/nkT) i n c r e a s e s more slowly with i n c r e a s i n g V when n is high. Anderson et al. (1161 have used a value of n = 2 t o p r e d i c t open c i r c u i t voltages of 0.53 V and e f f i c i e n c i e s of 12-16% a t AM1 f o r C r Schottky barriers on p-type S i , assuming t h a t Js i n (87) i s unchanged by t h e high n-value. However, i f t h e higher v a l u e s of n are due t o excess dark c u r r e n t s , it is obvious they cannot l e a d t o higher open c i r c u i t v o l t a g e s ; t h e value of Js w i l l be increased i n t h i s case and lower V o c ' s w i l l b e obtained. If t h e higher values of n are due t o i n t e r f a c i a l oxides, on t h e o t h e r hand, then t h e barrier h e i g h t is increased, t h e v a l u e of Js is decreased, and higher Voc's w i l l be obtained. A trade-off could e x i s t between t h e higher open c i r c u i t v o l t a g e and t h e lower s h o r t c i r c u i t c u r r e n t as a r e s u l t of t h e i n t e r f a c i a l oxide l a y e r . Experimentally, t h e gain i n Voc seems t o outweigh any decrease i n Jph and improved e f f i c i e n c i e s are obtained by adding a t h i n i n t e r f a c i a l l a y e r . The measured e f f i c i e n c i e s o f Schottky b a r r i e r s o l a r cells have been less t h a n 10%. Anderson et a l . [114,1161 have obt a i n e d e f f i c i e n c i e s under AM1-AM2 s u n l i g h t of 8.1-9.5% using C r Schottky b a r r i e r s on 2 ohm-cm p-type S i r with open c i r c u i t v o l t a g e s o f 0.5-0.53 V and s h o r t c i r c u i t c u r r e n t s of 26 mA/cm2. S t i r n and Y e h 11071 have measured open c i r c u i t v o l t a g e s of 0.53 and 1.0 V for Au-GaAs and Au-GaAs0.6P0.4 devices, respect i v e l y , and obtained a s h o r t c i r c u i t c u r r e n t d e n s i t y o f over 18 mA/cm2 under AM0 i l l u m i n a t i o n (with no a n t i r e f l e c t i v e coating) f o r Au-GaAs Schottky barriers, l e a d i n g t o expected AM0 e f f i c i e n c i e s of 10% a f t e r AR c o a t i n g a p p l i c a t i o n . The s p e c t r a l response of t h e Au-GaAs device w a s high a t s h o r t wavelengths, confirming t h e o r i g i n a l premise o f improved collection of c a r riers generated very near t h e semiconductor s u r f a c e . Schottky b a r r i e r solar cells could be highly u s e f u l f o r t e r r e s t r i a l a p p l i c a t i o n s where a s l i g h t l y lower p r e d i c t e d e f f i c i e n c y compared t o p-n j u n c t i o n cells would be f a r outweighed by t h e i r i n h e r e n t s i m p l i c i t y and expected lower cost. They could be p a r t i c u l a r l y applicable t o p o l y c r y s t a l l i n e S i and GaAs s o l a r c e l l s where normalp-n j u n c t i o n d i f f u s i o n processes may be d i f f i c u l t because of t h e presence o f g r a i n boundaries.

B.

HETEROJUNCTIONS

127

F I G . 7 6 . Energy band diagram of a t y p i c a l N / P h e t e r o j u n c t i o n i n thermal e q u i l i b r i u m . (When v o l t a g e i s a p p l i e d , t h e b a r r i e r s become vd2-vj2 i n m a t e r i a l 2 and vdl-vjl i n m a t e r i a l 1 .)

B.

Heterojunctions

Heterojunction s o l a r c e l l s have many s i m i l a r i t i e s and a few differences t o Schottky b a r r i e r c e l l s . The most important s i m i l a r i t y i s t h a t short wavelength photons can be absorbed within or very near t h e depletion region of t h e device under most circumstances, leading t o good high photon energy response. The most important difference i s t h a t t h e open c i r c u i t voltage can be q u i t e high as i n a p-n junction, without t h e need f o r c a r e f u l l y controlled i n t e r f a c i a l layers. The energy band diagram of a t y p i c a l heterojunction between two s i n g l e c r y s t a l materials is shown i n Fig. 76. Light of energy l e s s than E 1 but g r e a t e r than Eg2 w i l l pass through t h e f i r s t material (wzich a c t s a s a "window") and become absorbed by t h e second material, and carriers created within t h e depletion region and within a diffusion length of t h e junction edge w i l l be collected exactly a s i n a p-n homojunction c e l l . Light of energy g r e a t e r than Egl w i l l be absorbed i n material 1, and c a r r i e r s generated within a diffusion length of the junct i o n edge o r within the depletion region of t h i s material w i l l a l s o be collected. The advantage t h a t t h e heterojunction can have over most normal p-n junctions i s i n t h e s h o r t wavelength response; i f E g l i s large, high energy photons w i l l be absorbed inside t h e depletion region of material 2 where t h e c a r r i e r c o l l e c t i o n should be very e f f i c i e n t . I f material 1 i s a l s o thick i n addition t o being high i n bandgap, the device should have lower s e r i e s r e s i s t a n c e and higher radiation tolerance than a p-n junction made e n t i r e l y of material 2.

128 1.

6.

OTHER SOLAR CELL DEVICES

SPECTRAL RESPONSE AND PHOTOCURRENT

The major c o n t r i b u t i o n t o t h e s p e c t r a l response and photoc u r r e n t comes from t h e base material, with a smaller contribut i o n from t h e t o p m a t e r i a l and from t h e two d e p l e t i o n regions. I f a N/P h e t e r o j u n c t i o n i s assumed, with a n e u t r a l base region (no d r i f t f i e l d ) , then t h e photocurrent from t h e base can be found from (7), (91, (161, and (17) a f t e r t a k i n g i n t o account t h e a t t e n u a t i o n by t h e t o p l a y e r

H'

H'

1

+sinh-+apLn2

SnLn 2

H'

Dn2

Ln2

-s i n h

H'

+coshLn2

i

exp(-as')

(90)

1

where Sn i s t h e recombination v e l o c i t y a t t h e back s u r f a c e , F(X) is t h e i n t e n s i t y of monochromatic l i g h t i n c i d e n t on t h e s u r f a c e of t h e t o p l a y e r , a l and a 2 are t h e absorption c o e f f i c i e n t s of t h e two materials, W1 and Wp are t h e d e p l e t i o n widths on each s i d e of t h e i n t e r f a c e , and HI i s t h e width of t h e neut r a l base region, H ' = H-(x.+Wl+W2). The r e f l e c t i o n of l i g h t from t h e i n t e r f a c e due t o t h e d i f f e r e n c e i n r e f r a c t i v e i n d i c e s has been ignored, s i n c e t h i s w i l l g e n e r a l l y be from 3 t o 4% o r less. This r e f l e c t i o n can be included i n (90) by r e p l a c i n g F(X) exp[-al (xj+Wl)I exp(-a~W2)(1-R) by t h e more involved transmission f a c t o r a s done by Milnes and Feucht [60]. The d e p l e t i o n widths are determined by t h e r e l a t i v e doping l e v e l s c o n s t a n t s of t h e two materials

The photocurrent a t a given wavelength from t h e t o p l a y e r can be found from (6), ( 8 ) , ( 1 2 1 , and (13)

equation continues

B . HETEROJUNCTIONS

)

lLpl -exp (-a,xj 1

129

-cosh -+sinh

X

sPLp 1 DP1 -a 1%

1

1 exp (-a 1xj 1

Sinh-+cosh $1

$1

(93)

where S i s t h e s u r f a c e recombination v e l o c i t y a t t h e s u r f a c e P of m a t e r i a l 1. The photocurrents from t h e depletion regions are given by

where r e f l e c t i o n from t h e i n t e r f a c e has again been ignored i n (95). I n order t o o b t a i n t h e s e expressions, i t has been assumed t h a t t h e excess minority c a r r i e r d e n s i t i e s a t t h e edges of t h e d e p l e t i o n region a r e reduced t o zero by t h e e l e c t r i c f i e l d i n t h e d e p l e t i o n region [boundary conditions (13) and (16) I . This i s a reasonable assumption provided t h a t t h e conduction band d i s c o n t i n u i t y AEc i s small ( 2kT/qr where

[

Dn2 n i 2 (SnLn2/Dn2)cosh (H'/Ln2) +sinh (H'/Ln2)

Jo = q$

-Ln2

N2 (SnLn2/Dn2)s i n h (H'/Ln2) +cosh (H'/Ln2)

(100)

I

-

(101)

XT is t h e quantum mechanical transmission f a c t o r a t t h e i n t e r -

f a c e (analogous t o t h e quantum mechanical e f f e c t s i n Schottky b a r r i e r s contained i n A**). Since % i s less than 1, t h e dark c u r r e n t i n t h e heterojunction due t o e l e c t r o n i n j e c t i o n i n t o m a t e r i a l 2 would t h e o r e t i c a l l y b e smaller than i n a homojunct i o n of material 2 alone f o r t h e same doping l e v e l i n t h e base. For t h e special c a s e shown i n Fig. 78c, AE, i s l a r g e r t h a n t h e b a r r i e r h e i g h t vdZ'vj2 i n material 2 , where

I n t h i s case (Fig. 78c), only t h e f r a c t i o n of the v o l t a g e dropped a c r o s s material 1 changes t h e e l e c t r o n d i s t r i b u t i o n , and t h e i n j e c t e d e l e c t r o n c u r r e n t i s then JA = J o exp(qKIV,/kT)

(103)

and is equivalent t o Jn except f o r t h e d i f f e r e n t exponential f a c t o r . A t high enough forward biases, (Vd2-vj2) w i l l become less than AEc even f o r t h e c o n f i g u r a t i o n s of Fig. 78a and b , and Jn w i l l switch over t o JA w i t h a change i n s l o p e (an J versus V) from 1 kT/q t o (l/Kl)kT/q.

134

6.

OTHER SOLAR CELL DEVICES

I n a homojunction, t h e second p o r t i o n of t h e i n j e c t e d dark c u r r e n t , due t o minority carriers i n j e c t e d from t h e base i n t o t h e t o p l a y e r , is usually n e g l i g i b l e because of t h e much lower doping l e v e l i n t h e base than i n t h e top layer. I n a heterojunction, t h i s p o r t i o n may be reduced even f u r t h e r by t h e appropriate energy d i s c o n t i n u i t y i n t h e valence o r conduct i o n band (AE,, i n a N/P c e l l and AEc i n a P/N device). I n t h e N/P devices of Fig. 78, f o r example, t h e energy barrier A% l a r g e l y impedes holes from being i n j e c t e d i n t o material 1, and t h e dark c u r r e n t due t o h o l e i n j e c t i o n becomes

2

and can usually be neglected because of t h e low value of n i l (due t o t h e wide bandgap) and because of t h e high value of N1 (due t o t h e high doping l e v e l ) . The second dark c u r r e n t mechanism, due t o recombination within t h e space charge region, is given q u a l i t a t i v e l y by an expression of t h e form of ( 5 4 ) , although it i s not very clear what q u a n t i t a t i v e e f f e c t s t h e energy d i s c o n t i n u i t i e s and t h e i n t e r f a c e states w i l l have on t h i s c u r r e n t . For example, f o r N/F devices l i k e t h o s e i n Fig. 7 8 , hole i n j e c t i o n from t h e small gap s i d e t o t h e l a r g e gap is prevented by 4%, so a l l t h e recombination e f f e c t i v e l y occurs on t h e small gap s i d e of t h e i n t e r f a c e . Also, i f t h e i n t e r f a c e s t a t e d e n s i t y i s high, t h e i n t e r f a c e recombination v e l o c i t y i s probably also high, and t h e recombination r a t e within t h e d e p l e t i o n region w i l l be much greater than i n a p-n homojunction. To calculate t h e depletion region recombination c u r r e n t comparable t o (541, t h e s e t w o f a c t o r s i n heterojunctions would have t o be taken i n t o account. The t h i r d c u r r e n t mechanism, tunneling, has proven t o be t h e dominant one i n v i r t u a l l y a l l heterojunctions except those with very small l a t t i c e mismatch. Tunneling i n p-n homojunct i o n s has already been discussed i n Chapter 3, where t h e curr e n t w a s of t h e form

where K1 is a constant containing t h e e f f e c t i v e mass, b u i l t - i n voltage Vd, doping l e v e l , dielectric constant, and Planck's constant, Nt i s t h e density of a v a i l a b l e empty states, and N i s t h e doping l e v e l i n t h e base. I n a heterojunction, t h e density of a v a i l a b l e empty states is much l a r g e r because of i n t e r f a c e states and because of energy states within t h e

B.

HETEROJUNCTIONS

135

bandgap as a r e s u l t of c r o s s doping, l a t t i c e mismatch, and thermal expansion mismatch. The tunneling c u r r e n t i s a l s o modified i n a heterojunction by quantum mechanical r e f l e c t i o n a t t h e i n t e r f a c e and by t h e f a c t t h a t only a p o r t i o n of t h e t o t a l barrier (Vd-Vj) i s normally involved i n t h e tunneling. For t h e N/P devices of Fig. 78c o r d , f o r example, tunneling i n t o i n t e r f a c e states i n m a t e r i a l 1 i s given by [611

where N I S is t h e d e n s i t y of a v a i l a b l e i n t e r f a c e s t a t e s . For t h e configurations of Fig. 78a and b , tunneling d i r e c t l y i n t o i n t e r f a c e s t a t e s does not occur, b u t tunneling i n t o o t h e r a v a i l a b l e energy states can t a k e place. When m u l t i p l e step tunneling i s important, i . e . , when t h e d e n s i t y of energy s t a t e s i n t h e forbidden region i s so l a r g e t h a t carriers can cross t h e d e p l e t i o n region by a series o f tunneling-recombination s t e p s , then t h e c u r r e n t due t o tunneling i n material 1 t a k e s t h e form 161,1171

where R i s t h e number of s t e p s involved. These tunneling c u r r e n t s a r e very weak functions of temperature, i n c o n t r a s t t o t h e thermal ( i n j e c t e d and space charge recombination) c u r r e n t s which are strong functions of temperature. There are o t h e r types of tunneling c u r r e n t s t h a t have temperature dependences midway between (106) o r (107) and t h e thermal components; f o r example, e l e c t r o n s may t u n n e l from a p o i n t p a r t way up t h e b a r r i e r , adding a Boltzmann-type exp(qV/AkT) term t o t h e preexponential f a c t o r K1. A l l of t h e s e p o s s i b i l i t i e s f o r tunneling c u r r e n t s make it very d i f f i c u l t t o p r e d i c t what t h e dark c u r r e n t w i l l be f o r a given heterojunction. I t i s s a f e t o say, however, t h a t t h e more p e r f e c t t h e junction is ( t h e c l o s e r t h e l a t t i c e and thermal matches and t h e less t h e chance f o r c r o s s doping), t h e smaller t h e tunneling dark c u r r e n t w i l l be and t h e more e f f i c i e n t t h e device w i l l be. Low doping l e v e l s i n both regions ( p a r t i c u l a r l y Np < lo1’ ~ m ’i n~ t h e base) w i l l a l s o reduce t h e chance of tunneling by widening t h e d e p l e t i o n regions ( b u t , of course, a low doping l e v e l i n t h e t o p l a y e r might l e a d t o high series resistance). The I-V c h a r a c t e r i s t i c s of a Cu2S-CdS heterojunctiori device have already been shown i n Figs. 40 and 41. The n e a r l y c o n s t a n t slope of t h e RnJ-V c h a r a c t e r i s t i c and t h e s m a l l change i n magnitude with temperature a r e t y p i c a l of devices dominated by tunneling. The great majority of h e t e r o j u n c t i o n s

136

6.

OTHER SOLAR CELL DEVICES

10-1

d

10-2

Q

510-~ C

2 L

3 10-4 10-~ 10-6

0.4

0.8

1.2

1.6

Forward Volts

FIG. 79. Current-voltage c h a r a c t e r i s t i c s of pGal-fil+-nGaAs heterojunctions a t : (1) 77OK; (2) 18O0K; (3) 298OK; (4) 371*K; (5) 433OK; (6) 531OK. ( A f t e r A l f e r o v et a l . [121]; courtesy of the American I n s t i t u t e of Physics.) have characteristics very similar t o t h e s e 1611; t h e r e are several exceptions, however, including ZnSe-Ge and G a A s - G e N/P h e t e r o j u n c t i o n s , which have s m a l l AE,'s, and Gal,&l&s-GaAs devices, which have small A q ' s . A l l three of t h e s e devices have good l a t t i c e and t h e r m a l m a t c h e s , and a l l t h r e e have demonstrated t r a n s i s t o r behavior [118-1201, showing t h a t i n j e c t i o n can b e t h e dominant forward bias c u r r e n t mechanism i n some i n s t a n c e s . F i g u r e 79 shows t h e I - V c h a r a c t e r i s t i c of a i n the pGal,&l&s-nGaAs h e t e r o j u n c t i o n w i t h Nd = 2X1017 base and Na = 5x101* i n t h e G a l - x A l x A s ( a f t e r Alferov et a l . (1211). The change i n slope and magnitude of t h e I-V charact e r i s t i c is t y p i c a l of h e t e r o j u n c t i o n s where thermal i n j e c t i o n dcminates

.

b.

Efficiency

A comprehensive c a l c u l a t i o n o f t h e e f f i c i e n c i e s o f heteroj u n c t i o n s o l a r cells, i n c l u d i n g t h e e f f e c t s of t u n n e l i n g curr e n t s , recombination a t i n t e r f a c e states, quantum mechanical e f f e c t s a t t h e i n t e r f a c e , etc., has never been carried out. Several c a l c u l a t i o n s under more i d e a l i z e d c o n d i t i o n s have been made, however. Sreedhar et a l . [1221 have computed a t y p e of

B.

HETEROJUNCTIONS

137

TABLE 11 L i m i t Conversion Behavior, AMOa

Heteroj unction

voc ( V )

rl(%)

Gap-Si, N/P GaP-InP, N/P Gap-GaAs, N/P G a s - I n P , N/P

0.67 0.82 0.87

24 25 21 27

GaP-Si, P/N GaP-InP, P/N Gap-GaAs, P/N GaAs-InP, P/N

0.69 0.94 1.05 0.93

25 30 28 30

0.81

aAfter Sreedhar et a l . [122].

" l i m i t conversion e f f i c i e n c y " f o r various h e t e r o j u n c t i o n s , where t u n n e l i n g and space charge l a y e r recombination are negl e c t e d , t h e base i s taken as i n f i n i t e l y wide, and 100%c o l l e c t i o n e f f i c i e n c y is assumed f o r a l l photon energies greater than Eg2. Their computed open c i r c u i t voltages and conversion e f f i c i e n c i e s are given i n Table 11. The p r e d i c t e d e f f i c i e n c i e s are very high, but bear l i t t l e r e l a t i o n t o what might be a t tained i n a c t u a l f a c t . A more r e a l i s t i c c a l c u l a t i o n has been performed by Sahai and Milnes 11233, who took space charge l a y e r recombination c u r r e n t s and r e f l e c t i o n of l i g h t from t h e s u r f a c e i n t o account and who used equations equivalent t o (90)-(95) t o compute t h e photocurrent. The c a l c u l a t e d open c i r c u i t voltages and e f f i c i e n c i e s f o r Gap-Si and ZnSe-GaAs h e t e r o j u n c t i o n s are given i n Table 12. The authors made no attempt t o optimize t h e mater i a l parameters used i n t h e i r c a l c u l a t i o n s , and t h e e f f i c i e n c i e s apply f o r very p a r t i c u l a r doping levels, l i f e t i m e s , and l a y e r TABLE 1 2 Calculated E f f i c i e n c i e s f o r Heterojunctions with Close L a t t i c e Match, AMOa

Gap-Si, N/P ZnSe-GaAs, N/P

0.65 0.925

aAfter Sahai and Milnes [123].

14.3 15.6

138

6.

OTHER SOLAR CELL DEVICES

20

ae

18

14 12 0

0.2

0.4

0.6

0.8

1.0

Junction Depth, p

FIG. 8 0 . Inherent efficiencies a t AM0 ( s o l i d ) and AM1 (dashed) of pGal-gl&-pGaAs-nGaAs s o l a r c e l l s a s a f u n c t i o n of j u n c t i o n d e p t h , for s e v e r a l base (nGaAsJ d i f f u s i o n l e n g t h s . D = 1 urn,

shack

00.

NO

fields.

thicknesses, but even so respectable e f f i c i e n c i e s a r e predicted, and b e t t e r e f f i c i e n c i e s would be predicted i f a l l parameters w e r e optimized. The m o s t successful experimental heterojunction device i n terms of efficiency i s t h e pGal-xAlxAs-nGaAs device of Alferov et a l . 171, where 10 um t h i c k layers of Ga0.4A10.6As were grown by LPE on lX1017 ~ r n -G~a A s s u b s t r a t e s . AM0 e f f i ciencies of 10-11% were measured, with open c i r c u i t voltages of 0.95 V and s h o r t c i r c u i t currents of 15-20 mA/cmP. The pGal-xAlxAs-nGaAs solar c e l l is not q u i t e a s e f f i c i e n t a s t h e pGal-xAlxAs-pGaAs-nGaAs s t r u c t u r e because t h e l a t t e r c o l l e c t s photogenerated c a r r i e r s over a l a r g e r distance compared t o t h e pure heterojunction [36]. Figure 80 shows t h e efficiency expected a t AM0 and AM1 f o r pGaAlAs-pGaAs-nGaAs devices a s a function of t h e pGaAs width. The e f f i c i e n c i e s can be over 2% higher (15.3% compared t o 13%) when t h e pGaAs region is present compared t o t h e heterojunction case where it i s absent, i f t h e base d i f f u s i o n length i s short. When t h e base d i f f u s i o n length is l a r g e , t h e pGaAs region has less e f f e c t and t h e heterojunct i o n c e l l is nearly as e f f i c i e n t as t h e t h r e e layer device. Several other heterojunction s o l a r c e l l s have been reported a l s o , including Gap-GaAs [124,125], CdS-Si [1261, and CdTe-Cu2Te [126a,1271. The e f f i c i e n c i e s of t h e P/N GaP-GaAs devices were around 8% ( f o r unstated conditions), and around 7% for t h e N/P GaP-GaAs c e l l s under "white l i g h t " conditions.

C.

VERTICAL MULTIJUNCTION CELLS

139

CdS-Si devices, made by evaporation of CdS onto 0.2-3.0 ohm-cm p-type S i wafers, exhibited about 5% e f f i c i e n c i e s f o r AMl-AM2 sunlight. CdTe-Cu2Te polycrystalline cells had e f f i c i e n c i e s of 6% under AM2 sunlight, while the same c e l l using s i n g l e This c e l l i s very c r y s t a l CdTe substrates exhibited 7-1/2%. s i m i l a r t o t h e Cu2S-CdS s o l a r c e l l , which has already been described a t some length i n previous chapters. Fahrenbruch et a l . [127a] have reported t h e experimental and t h e o r e t i c a l e f f i c i e n c i e s of several 11-VI compound heterojunctions with r e l a t i v e l y poor l a t t i c e match. The most promi s i n g devices were made by vapor growth of p-type CdTe onto n-type CdS ( l a t t i c e mismatch l o % ) , yielding an efficiency i n California sunlight of 4% ( t h e o r e t i c a l efficiency 1 7 % ) . The low experimental e f f i c i e n c i e s were a t t r i b u t e d t o t h e much l a r g e r dark currents i n t h e finished cells compared t o t h e t h e o r e t i c a l dark currents. Wagner et a l . [127b,127cl have investigated nCdS/pCuInSep and nCdS/pInP s o l a r c e l l s . The CuInSe2 devices had a broad s p e c t r a l response from 5000 fl t o 1.3 m, and e f f i c i e n c i e s of around 12%. The response of the InP devices w a s high (70% absol u t e ) from 5000 d t o about 9500 A , and AM3 (53 mW/cm2 input) e f f i c i e n c i e s of 12.5% were obtained. These l a t t e r devices had open c i r c u i t voltages of 0.63 V, s h o r t c i r c u i t currents of 1 5 mA/cm2, and FF of 0.71. C.

Vertical Multijunction Cells

The v e r t i c a l multijunction s o l a r c e l l is an i n t e r e s t i n g device concept where l i g h t is incident i n a d i r e c t i o n p a r a l l e l t o t h e junction r a t h e r than perpendicular t o it as i n a conventional s o l a r c e l l . This has some important consequences, chief of which i s t h a t t h e s p e c t r a l response ( i n t h e i d e a l case) becomes very high a t a l l wavelengths, leading t o a high p o t e n t i a l efficiency. The main features of t h e v e r t i c a l multijunction s o l a r , c e l l can be understood with t h e a i d of Figs. 81 and 82. In Fig. 81a, a conventional N/P s o l a r c e l l i s shown. Light i n c i dent on the surface c r e a t e s hole-electron p a i r s a t a depth which depends on t h e absorption c o e f f i c i e n t ; long wavelength photons c r e a t e minority c a r r i e r s deep i n t h e material which must d i f f u s e t o t h e junction edge t o be collected. The longer t h e wavelength is, the greater the distance t h e generated carrier must t r a v e l and t h e greater the chance of i t s loss. The s p e c t r a l response then increases with decreasing wavelength, reaches a maximum, and decreases a t shorter wavelengths when most of the c a r r i e r s a r e generated i n t h e low l i f e t i m e N+ region.

140

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OTHER SOLAR CELL DEVICES

FIG. 81. Conventional , hybrid, and mu1 t i j u n c t i o n solar cell configurations. (C)

In Fig. 81b, v e r t i c a l N regions have been added t o t h e conventional s t r u c t u r e . Carriers generated deep i n t h e mater i a l now have a much s h o r t e r distance t o t r a v e l t o reach a junction edge, and i f t h e width between t h e v e r t i c a l N regions is l e s s than t h e d i f f u s i o n length, t h e p r o b a b i l i t y of collect i o n i s high. The long wavelength s p e c t r a l response of t h e s t r u c t u r e i n Fig. 81b w i l l be high, while t h e s h o r t wavelength response i s t h e same a s before due t o t h e losses i n t h e surface Ni region. In Fig. 81c, t h e N+ sheet covering t h e surface has been eliminated. Now c a r r i e r s generated anywhere between the vert i c a l N+ regions have an equal p r o b a b i l i t y of reaching t h e junction edge (provided surface recombination i s negligible) and t h e s p e c t r a l response i s uniformly high over t h e e n t i r e wavelength range. The individual junctions i n Fig. 81b and c a r e connected i n p a r a l l e l by t h e nature of t h e way t h e devices a r e made (the N+ regions i n Fig. 81c are connected together a t one end of t h e wafer). I f t h e v e r t i c a l N+ regions extend a l l t h e way through t h e device, then t h e junctions can be connected e i t h e r i n p a r a l l e l o r i n s e r i e s a s desired. Figure 82 shows several proposed schemes f o r v e r t i c a l multijunction devices as proposed by & h i l l y , Stella and GOvEr, Chadda and Wolf, and others [1281341. In Fig. 82a, t h e junctions are connected i n p a r a l l e l ; t h e photocurrent w i l l be high while t h e voltage output w i l l be l e s s than o r equal t o t h a t of a s i n g l e junction. In Fig. 82b and c , t h e junctions are connected i n series; t h e photocurrent w i l l be low but t h e voltage output w i l l be high, equal i n princ i p l e t o t h e sum of t h e voltages of each junction [133].

C.

VERTICAL MULTIJUNCTION CELLS

N P N P N P N P N P N P

141

t H

N P N P N P N P N P N P

N P N P N P h P 1\P N P

FIG. 8 2 . schemes.

fC)

Vertical m u l t i junction solar c e l l interconnection

Regardless of whether a series or p a r a l l e l interconnect i o n method i s used, a l l t h e v e r t i c a l multijunction devices have t h e p o t e n t i a l of high s p e c t r a l response over a wide spect r a l region, provided the surface recombination v e l o c i t i e s a r e low. Figure 83 shows t h e s p e c t r a l response of VMJ devices Fig. 82) compared t o a convenof several c e l l widths (Wp+Wn, t i o n a l device f o r surface recombination v e l o c i t i e s of l o 3 cm/ sec, as calculated by Chadda and Wolf [132]. The enhanced response a t long wavelengths i s c l e a r l y seen, a s i s the improved response a t decreasing wavelength. (The conventional c e l l i n Fig. 83 i s a p a r t i c u l a r l y good one; i f a dead l a y e r were present i n the conventional device, t h e short wavelength response would be low and the advantage of the VMJ device a t s h o r t wavelengths would be more s t r i k i n g . ) The surface recombination velocity plays a much more important r o l e for the VMJ device than i n conventional s o l a r c e l l s [128,131,132,134]. I f t h e u n i t c e l l width (Wn+Wp) i s l a r g e , c a r r i e r s generated close t o t h e f r o n t surface a r e strongly influenced by t h e surface, and recombination velocit i e s exceeding l o 3 cm/sec have a very detrimental e f f e c t on t h e short wavelength response and t h e photocurrent [131-1321. BY way of c o n t r a s t , recombination v e l o c i t i e s of 1 0 3 cm/sec have no appreciable e f f e c t on a conventional c e l l . The recombination velocity a t the back surface of a VMJ c e l l is much l e s s important t o t h e photocurrent 11311 than the recombination velocity a t t h e f r o n t surface (as long a s t h e device thickness i s g r e a t e r than 50 pm), since most c a r r i e r s a r e created closer t o t h e f r o n t surface. Reducing the u n i t c e l l width can p a r t i a l l y

142

6.

OTHER SOLAR CELL DEVICES

1.o

0.2

0.4

0.6

0.8

1.0

1.1

Wavelength Alp)

F I G . 8 3 . Internal s p e c t r a l responses of S i v e r t i c a l m u l t i junction s o l a r cells for various u n i t cell widths (W = Wn+Wp) and of a conventional S i s o l a r c e l l . Dashed l i n e s : conventional c e l l ; SF = l o 3 c m / s e c - l . S o l i d l i n e s : v e r t i c a l junct i o n c e l l ; SF = SB = l o 3 cm/sec. ( A f t e r Chadda and W o l f f1321; c o u r t e s y of t h e IEEE.)

overcome t h e e f f e c t of f r o n t s u r f a c e recombination by p l a c i n g generated carriers closer t o a j u n c t i o n edge. Reducing t h e u n i t c e l l width h e l p s t o reduce t h e bulk recombination l o s s as w e l l as t h e s u r f a c e loss? and t h e bulk recombination l o s s i s e s s e n t i a l l y n e g l i g i b l e as long a s L i 1 3Wi where W i i s t h e width of t h e i region (N o r P) and L i i s t h e minority carrier d i f f u s i o n l e n g t h i n t h a t region. As long as t h i s condition is f u l f i l l e d , t h e r e s i s t i v i t i e s o f t h e N and P regions can be reduced (to o b t a i n better Voc's) without a f f e c t i n g t h e s p e c t r a l response ( i n a conventional c e l l reducing t h e r e s i s t i v i t y lowers t h e long wavelength response and hence t h e photocurrent). Lowering t h e u n i t c e l l width is n o t without i t s disadvant a g e s , however, s i n c e t h e number of j u n c t i o n s required t o make a 1 cm long device i s i n v e r s e l y p r o p o r t i o n a l t o (Wn+Wp>, and t h e dark c u r r e n t i s p r o p o r t i o n a l t o t h e number of j u n c t i o n s . The number of j u n c t i o n s p e r cm i s t h e r e f o r e one of t h e import a n t design parameters of t h e o v e r a l l device. R a h i l l y [128] has c a l c u l a t e d t h e performance of p a r a l l e l VMJ s o l a r c e l l s a s a f u n c t i o n of t h e number of j u n c t i o n s N, and shown t h a t t h e o v e r a l l e f f i c i e n c y s a t u r a t e s w i t h i n c r e a s i n g N, due t o t h e opposing i n f l u e n c e s of i n c r e a s i n g dark c u r r e n t and i n c r e a s i n g photocurrent. The AM0 e f f i c i e n c i e s c a l c u l a t e d w e r e 16% €or N j 1 1000 using 1 ohw-cm p-type s t a r t i n g material and 13% f o r

VERTICAL MULTIJUNCTION CELLS

C. 0.18

?i

I

I

I

143

1

0.16

.-00 E 0.14 w

I-

//

w=rooum

-I

I

0 0.10

I


6OoC) in air; (3) at high temperatures when illuminated; (4) when the load voltage exceeds 0.33 V; or (5) after temperature cycling (-150°C to +6OoC) for a number of times. Water vapor causes a decrease in Is, to occur, but leaves Vo, and FF largely unchanged 12261. Moisture is capable of penetrating the plastic lamination and becoming absorbed into the underlying Cu+-CdS structure, resulting in electronic traps which lower the collection efficiency. The initial Is, can be recovered by heating the cell at 180°C in vacuum for several hours. A second, irreversible degradation can occur if the plastic or adhesive absorbs the moisture; Mylar sheets with epoxy adhesive are superior to Kapton with Capran adhesive in this regard L2261. Careful, thorough encapsulation with nonporous materials should largely eliminate the humidity problem. Heating a cell in vacuum in the dark to temperatures as high as 2OOOC has no appreciable effect on it, but if a device is taken much above 6OoC in air, irreversible decreases in Is, can occur [227,2281, which are attributed to oxygen and moisture attack of the CuxS and its conversion to mixtures of CuO and Cu20. As with the humidity problem, more thorough encapsulation should

C.

CADMIUM SULFIDE SOLAR CELLS

197

be capable of minimizing t h e amount of a i r reaching t h e CuxS layer. A second degradation of Is, can take place a t temperat u r e s above 6OoC when t h e device is illuminated, even i f no a i r is present. This degradation is apparently caused by a light-activated phase change i n the CuxS, i . e . , Cu2S goes t o lower forms of CuxS [54,228,2291. Experimentally, it appears t h a t even s l i g h t deviations of the CuxS from p e r f e c t s t o i c h i ometry (x = 2) lowers t h e efficiency considerably. Bogus and Mattes I541 have g r e a t l y improved t h e high temperature s t a b i l i t y of CdS cells by evaporating a 100 layer of Cu onto t h e CuxS surface and driving it i n by subsequent heat treatment, ensuring t h a t t h e CuxS remains nearly stoichiometric Cu2S. This Cu evaporation s t e p a l s o helps t o mask against t h e oxygen a t t a c k mentioned above, retarding the conversion of C u s t o cufl. I f a CdS c e l l with l i g h t incident i s operated a t a load voltage greater than 0.33-0.35 V, degradation i n both t h e Voc and FF can take place, while Isc remains l a r g e l y unchanged 154,228-2303. This behavior is accompanied by t h e appearance , l a y e r and near t h e i n t e r f a c e . of metallic copper within t h e CuS Bernatowicz and Brandhorst 12291 , Mathieu et al. [2311 , and others have shown t h a t a light-activated electrochemical react i o n takes place a t a threshold of 0.35 V, a t which Cu2S conv e r t s i n t o CuS and Cu. The released Cu ions form f i n e filaments t h a t a c t as shunt paths across t h e junction, degrading t h e e l e c t r i c a l performance. This voltage-induced degradation can be minimized by ensuring that t h e load voltage never exceeds 0.33 V , but more importantly, it appears t h a t it can be eliminated altogether by doping t h e CdS t o 5 ohm-cm o r below [232], which seems t o i n h i b i t t h e movement and p r e c i p i t a t i o n of Cu across the CuxS-CdS i n t e r f a c e . The transport of Cu across t h i s i n t e r f a c e appears t o be t h e s i n g l e m o s t damaging cause of degradation i n these devices [ l o ] , r e s u l t i n g i n both a decrease i n t h e s h o r t c i r c u i t current under some conditions [55,781 and a reduction i n voltage output and FF when filaments a r e formed. The prevention of these problems by doping t h e CdS i s a major breakthrough i n solving t h e i n s t a b i l i t y problems of CdS s o l a r cells. F i n a l l y , thermal cycling and t h e r e s u l t i n g s t r e s s e s within t h e c e l l due t o t h e difference i n expansion c o e f f i c i e n t s between t h e p l a s t i c and t h e two semiconductors can cause delamination of t h e p l a s t i c encapsulation and a l i f t i n g of t h e s t r i p e cont a c t s t o t h e CuxS, with consequent l o s s of Isc and increased series resistance [226,229]. This problem is not severe f o r devices operated a t t h e e a r t h ' s surface, since t h e temperature range on e a r t h i s not very l a r g e , but devices i n space, where temperatures can r i s e t o 8OoC or higher i n sunlight and drop

198

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t o -15OOC o r lower i n t h e dark, are l i k e l y t o f a i l a f t e r a long enough period of time. Electroplated Au contact s t r i p e s i n place of t h e pressure-applied Cu g r i d s can reduce t h e problem considerably, and it would seem t h a t o t h e r types of plast i c s and adhesives could be found t h a t would be b e t t e r from t h e thermal expansion p o i n t of view. Overall, then, it would seem t h a t considerable progress has been made i n understanding and overcoming t h e i n s t a b i l i t y problems of CuxS-CdS s o l a r cells [232a], and i f they can be made r e l i a b l e enough i n a p r a c t i c a l s t r u c t u r e , they could have a major impact on t e r r e s t r i a l energy needs. Experimental CdS s o l a r c e l l panels have already been placed on houses and have performed w e l l f o r several years 1111, using a dry N2 atmosphere t o prevent water vapor and O2 from reaching t h e c e l l s , and cooling t h e back of t h e devices with an a i r flow t o keep t h e temperature below 6OoC [10,111 ( t h e devices a v a i l a b l e a t t h e beginning of t h i s experiment d i d not have a l l t h e i n s t a b i l i t y correcting f e a t u r e s ) . Using accelerated l i f e - t e s t s t u d i e s , estimates of 20 y r o r more f o r t h e useful l i f e of c a r e f u l l y protected CdS s o l a r c e l l s have been made [10,111, and estimates of t h e c o s t of producing l a r g e amounts of e l e c t r i c a l p o w e r using these c e l l s have ranged from less than $lOO/av k W [233,2341 t o about $500/av k W 1113, about t h e same a s t h e present c o s t of a conventional f o s s i l f u e l power p l a n t . ( E s t i m a t e s of t h e c o s t of generating e l e c t r i c i t y using ribbon o r t h i n f i l m S i o r t h i n f i l m GaAs f a l l i n t h e same b a l l park.) Jordan [234] has described an i n t r i g u i n g method of massproducing CdS s o l a r c e l l s on a large-scale, continuous b a s i s . The method makes use of t h e e x i s t i n g g l a s s sheet technology. Large g l a s s sheets are produced i n continuous fashion using t h e f l o a t - g l a s s process [234], where r a w materials are fed i n one end of a furnace and molten g l a s s i s poured o u t t h e o t h e r end onto a bed of molten t i n . Thin f i l m s of t h e transparent conductor SnO, a r e sprayed onto t h e g l a s s s u r f a c e , followed by deposition of 2-5 vm t h i c k CdS f i l m s , a l s o by spraying. Other chemicals are sprayed onto t h e CdS s u r f a c e t o produce t h e Cu2S l a y e r a f t e r t h e glass-Sn0,-CdS s h e e t s have cooled below 15OOC. The device i s f i n i s h e d by c u t t i n g the s h e e t s t o t h e d e s i r e d size and evaporating t h e t o p electrodes. These c e l l s are illuminated through t h e back, and t h e transparent SnO, acts as t h e back electrode. The whole process can e a s i l y be automated, and c o s t p r o j e c t i o n s are very low ($52/peak kW, $250/av k W f o r t h e e n t i r e p o w e r generating p l a n t ) . P r e l i m i nary devices have already been made by a prototype process 12341, but l i t t l e d a t a on t h e process o r t h e r e s u l t i n g devices are a v a i l a b l e as yet.

D. D.

HETEROJUNCTIONS AND SCHOTTKY BARRIERS

199

Heterojunctions and Schottky Barriers

The most promising heterojunction p a i r s from t h e l a t t i c e match, electron a f f i n i t y , and expected efficiency points of view a r e Gal-xA1&s-GaAs, ZnSe-GaAs, Gap-Si, and ZnS-Si. The pGal-xAlxAs-nGaAs device i s s i m i l a r t o t h e three-layer s t r u c t u r e already mentioned (Section B4) except f o r t h e absence of a pGaAs region. Solar c e l l s of t h i s type have been made by LPE [71, but vapor growth should a l s o be r e a d i l y adaptable 12171. I f a t r u e heterojunction i s desired, care must be taken t o prevent the formation of a pGaAs region while the Gal,xAl.& l a y e r i s being grown. I f Zn i s used as t h e acce t o r species, t h e nGaAs s u b s t r a t e must be doped above 10l8 cm- t o i n h i b i t t h e pGaAs layer from forming. The use of Ge t o dope t h e Gal-$l,$s should obviate t h e problem because of the low d i f f u sion c o e f f i c i e n t of G e i n G a A s a t 900°C and below. nZnSe-pGaAs heterojunctions have been grown by both LPE 12353 of G a s on ZnSe from Sn solution a t 520-560°C and by vapor growth 1236,2373 of ZnSe on G a A s s u b s t r a t e s a t 490-610OC. 12351 The conversion efficiency of t h e LPE device was low (1%) because of t h e very high doping l e v e l i n t h e G a A s cme3) and because of high s e r i e s r e s i s t a n c e due t o t h e high resist i v i t y of t h e ZnSe (>1 ohm-cm), but t h e good s p e c t r a l response a t high photon energies v e r i f i e d t h e theory that t h e i n t e r f a c e recombination velocity should be low i n t h i s heterojunction. N o e l e c t r i c a l - o p t i c a l measurements were reported on t h e vapor grown devices, but i f t h e d i f f i c u l t i e s of obtaining low r e s i s t i v i t y ZnSe can be overcome, it should be possible t o make highly e f f i c i e n t s o l a r c e l l s between ZnSe and GaAs. Epitaxial ZnS-Si and GaP-Si heterojunctions have been grown by a number of methods. Single-crystal ZnS has been grown on S i 12381 by H2 transport a t temperatures of 450-600°C, with growth r a t e s of 1300 A/hr o r less. The t h i n oxide which i s invariably present on S i surfaces was removed j u s t before growth by a vapor etch i n H2 a t 125OOC followed by etching i n HC1 a t t h e same temperature. GaP-Si devices have been made by evaporation [239], vapor transport with HC1 12401, vapor synthesis using organometallic compounds 12411, and LPE 12421. In a l l cases, steps such a s those mentioned were taken t o eliminate t h e unwanted oxide from t h e S i surface j u s t before growth. Temperatures of 750-1150OC were used, but s i n g l e c r y s t a l layers were obtained only above 900°C. A t temperatures above 1000°C, very high growth r a t e s could be achieved, a s much as a micron per minute. The major problem encountered w a s cracking of t h e GaP layers when t h e devices were cooled from t h e growth temperature; t h e cracking i s due t o t h e s t r e s s caused by t h e thermal expansion difference between GaP and S i

5

200

9.

SOLAR CELL TECHNOLCGY

Thickness,

A

F I G . 106. Sheet r e s i s t a n c e s of t h i n metal films. ( A f t e r S t i r n and Yeh 11071; courtesy of t h e I E E E . )

(the l a t t i c e match of t h i s p a i r i s good). Slower cooling rates and thinner Gal? epitaxial l a y e r s w e r e h e l p f u l i n reducing t h e cracking problem. No s o l a r c e l l s have been reported using Gap-Si heterojunctions as y e t . Schottky b a r r i e r s o l a r c e l l s are probably t h e simplest of a l l types t o f a b r i c a t e , requiring only an Ohmic contact a t t h e back and a semitransparent metal a t t h e f r o n t , along with t h e usual contact g r i d p a t t e r n t o lower t h e series r e s i s t a n c e . The transparent metal f i l m i s normally evaporated onto t h e c a r e f u l l y p r e ared semiconductor surface [103,107] , and films of about 100 thickness y i e l d transmissions of around 60% with sheet r e s i s t i v i t i e s of 5-50 ohms/square. Figures 70 and 71 showed t h e transmission through t h i n gold films as a funct i o n of thickness and wavelength, r e s p e c t i v e l y , and showed t h a t t h e addition of a proper a n t i r e f l e c t i o n coating can reduce t h e o p t i c a l l o s s due t o t h e metal f i l m down t o a few percent 11061. Figure 106 shows t h e sheet r e s i s t a n c e s of various m e t a l films as a function of thickness, as presented by S t i r n and Yeh [1071. Gold and s i l v e r appear t o be good prospects f o r Schottky b a r r i e r s o l a r c e l l s i n terms of low sheet r e s i s t a n c e , good b a r r i e r heights (Table a), and high transparency. P l a t i num i s probably even b e t t e r , but i n t h e p a s t has been more c o s t l y and more d i f f i c u l t t o work with.

!i

HETEROJUNCTIONS AND SCHO'N'KY BARRIERS

D.

201

100

80

20

1.5

2.0

2.5

3.0

3.5

4.0

Photon Energy, eV

F I G . 107. Transmission of l i g h t through t r a n s p a r e n t conducti n g l a y e r s on s a p p h i r e s u b s t r a t e s : ( 1 ) In203/Sn02; ( 2 ) Sn02/ A1203 w a f e r . ( R e f l e c t i o n accounts for most of t h e loss a t l o w e n e r g i e s .)

One of t h e p o t e n t i a l l y most v a l u a b l e types of heterojunct i o n o r Schottky b a r r i e r s o l a r cells has received very l i t t l e a t t e n t i o n i n t h e p a s t . There i s a c l a s s of materials known as t r a n s p a r e n t conducting g l a s s e s , c o n s i s t i n g of In203, SnO,, ZnO, and t h e l i k e , which have bandgaps of 3 eV o r above and r e s i s t i v i t i e s o f 0.0005 ohm-cm o r less under some conditions. Such materials could p o s s i b l y b e used t o make h e t e r o j u n c t i o n devices with p-type semiconductors o r Schottky b a r r i e r s with n-type semiconductors. The transparency of t h e s e conductors i s high (Fig. 1071, u s u a l l y above 90% f o r l a y e r s s e v e r a l thousand angstroms t o a micron i n t h i c k n e s s , and t h e i r s h e e t resist i v i t i e s can be as low as several ohms per square 12431. They can be evaporated 12441 , sprayed 1234,2451 , o r s p u t t e r e d [ 2 4 3 , 2461 o n t o a s u i t a b l e s u b s t r a t e , and are p o t e n t i a l l y economical i n both c o s t and energy consumption. Several solar c e l l dev i c e s of both t h e Schottky b a r r i e r type 12471 and heterojunct i o n type [248] have been made using Sn02 on S i and GaAs substrates, b u t t h e e f f i c i e n c i e s were low ( Q l % ) , probably due t o t h e poor q u a l i t y of t h e Sn02 f i l m s o r t o d e t r i m e n t a l energy b a r r i e r s a t t h e i n t e r f a c e . E f f i c i e n c i e s i n excess of 10% should be o b t a i n a b l e with very low r e s i s t i v i t y t r a n s p a r e n t c o a t i n g s on S i and GaAs.

202

E.

9.

SOLAR CELL TECHNOLOGY

Ion Implantation

Ion implantation t h e o r e t i c a l l y o f f e r s s e v e r a l advantages over d i f f u s i o n as a means of f a b r i c a t i n g junctions. One advantage i s t h a t very shallow junctions (go%) o p t i c a l transparency. Transparent conducting materials such as In203 could be useful f o r both heterojunction and Schottky barrier cells. Ion implantation as a s o l a r c e l l fabrication technique has t h e advantage t h a t shallow junctions with high surface concentrations can e a s i l y be obtained, and the doping p r o f i l e i n t h e top region can be t a i l o r e d t o produce an aiding d r i f t f i e l d . The disadvantage i s t h a t t h e l a t t i c e damage produced by t h e implantation i s d i f f i c u l t t o anneal, and low open c i r c u i t voltages a r e therefore usually obtained. Antireflective coatings are important i n reducing t h e l a r g e f r a c t i o n of the incident l i g h t r e f l e c t e d from a bare S i or G a A s surface. Single layer AR coatings can reduce t h e average r e f l e c t i o n from about 40% (bare material) t o around l o % , and double layer coatings can f u r t h e r reduce t h e reflect i o n t o around 3%. For s i n g l e l a y e r coatings, a material should be used which has low o p t i c a l absorption and which has an index of r e f r a c t i o n equal t o o r s l i g h t l y l a r g e r than t h e square root of t h e r e f r a c t i v e index of t h e semiconductor substrate.

224

9.

SOLAR CELL TECHNOLOGY

A wide v a r i e t y of metals and a l l o y s can be used as Ohmic contacts t o S i and GaAs, with high e l e c t r i c a l conductivity along t h e s t r i p e s , low contact r e s i s t a n c e t o t h e semiconductor, and t i g h t adherence t o t h e semiconductor a s t h e important c r i t e r i a . Contact s i n t e r i n g is necessary t o produce low cont a c t r e s i s t a n c e b u t must be done c a r e f u l l y t o prevent shunt r e s i s t a n c e problems. The contact g r i d p a t t e r n should be designed c a r e f u l l y ; the s e r i e s r e s i s t a n c e decreases as the square of the number of g r i d l i n e s . The conductance of the metal g r i d i t s e l f becomes a s i g n i f i c a n t problem a t high i n t e n s i t i e s . Organic s o l a r c e l l s have been low i n conversion efficiency because of poor c a r r i e r c o l l e c t i o n . The key t o improving these devices l i e s i n reducing t h e trap density, lowering t h e r e s i s t i v i t y , and providing good Ohmic contacts.

ADDENDUM

Recent Results

During t h e early summer of 1975, while the main portion of t h i s book was being p r i n t e d , several important conferences i n s o l a r energy took place, and a number of new and i n t e r e s t ing r e s u l t s were presented. The most important of these symposiums from t h e photovoltaics point of view was t h e 11th IEEE Photovoltaics S p e c i a l i s t s Conference held i n Scottsdale i n May. A Workshop on CdS s o l a r c e l l s w a s held i n Delaware, and a symposium on materials and processes f o r s o l a r energy conversion was held as p a r t of t h e Electrochemical Society spring meeting i n Toronto. Other conferences sponsored by t h e American Vacuum Society were held i n Yorktown Heights and Boston. Most of these conferences w i l l publish proceedings o r extended a b s t r a c t s , and a few of the important d e t a i l s presented a t these meetings w i l l be discussed b r i e f l y here. Some of t h e most important recent r e s u l t s were centered around t h e new S i s o l a r c e l l produced with a s e r r a t e d surface (Chapter 10, Section F); t h i s c e l l i s now designated a s t h e CNR c e l l f o r Comsat NonReflecting. The main features of t h i s device are shown i n Fiqs. 118 and 119. The concept i s a r a t h e r r a d i c a l departure from t h e very f l a t , polished surfaces used i n t h e p a s t . The pyramidal surfaces can be produced on oriented wafers by p r e f e r e n t i a l etching techniques (a hydrazine-hydrate etch f o r 10-30 min was discussed by NASA-Lewis). The b e n e f i t s obtained a r e reduced r e f l e c t i v i t y , l e s s dependence on t h e a n t i r e f l e c t i o n coating, and increased c o l l e c t i o n efficiency due t o c a r r i e r generation c l o s e r t o t h e junction. Figure 119 i l l u s t r a t e s these points i n one dimension. Light incident on t h e side of a pyramid can be r e f l e c t e d onto another pyramid instead of being l o s t , provided t h a t t h e pyramid base angle i s around 45O o r more. The r e f l e c t i v i t y of bare S i is reduced from 35 t o 45% f o r f l a t surfaces t o around 20% f o r the serrated surface, and the addition of an a n t i r e f l e c t i o n coating reduces t h e o v e r a l l r e f l e c t i o n t o a few percent.

225

226

ADDENDUM

FIG. 118. Serrated surface of a nonreflecting CNR cell. The increased c o l l e c t i o n efficiency i s a r e s u l t of t h e refract i o n of t h e l i g h t entering t h e Si. C a r r i e r s are generated on t h e average c l o s e r t o a c o l l e c t i n g junction boundary, which makes t h e c e l l less dependent on t h e base d i f f u s i o n length than a planar c e l l and gives it high r a d i a t i o n tolerance. Some degree of t o t a l i n t e r n a l r e f l e c t i o n may take place a t t h e back of t h e c e l l , which improves t h e long wavelength response. CNR c e l l s with very narrow junctions (as i n t h e " v i o l e t c e l l " ) and with pyramidal heights and spacings of 10 and 5-10 pm, respectively, have yielded photocurrents of 45 rnA/cm2 (180 aA f o r a 4 a n 2 device) compared t o 38-40 mA/cm2 f o r planar c e l l s . The dark I-V c h a r a c t e r i s t i c s a r e reported t o be excell e n t , and AM0 e f f i c i e n c i e s of over 15%have been obtained so f a r . Work on these cells is being done a t Comsat Laboratories and NASA-Lewis and w i l l probably be s t a r t e d i n many o t h e r laboratories shortly. High doping l e v e l e f f e c t s i n S i s o l a r c e l l s w a s another subject of considerable i n t e r e s t . Conventional t h e o r i e s pred i c t t h a t t h e voltage output and power conversion efficiency w i l l increase with decreasing base r e s i s t i v i t y down t o about 0.1 ohm-cm; they a l s o p r e d i c t t h a t t h e doping level i n t h e diffused region w i l l have l i t t l e e f f e c t on t h e M l t a g e output, since t h e dark current contributed by t h e base region of an abrupt junction device w i l l be much l a r g e r than t h e dark curr e n t contributed by t h e top region. Experimentally, a l l t h i s seems t o be t r u e down t o about 1 ohm-cm bases f o r v i o l e t c e l l s , but unexplained behavior occurs f o r more heavily doped bases and f o r heavily doped diffused regions; t h e open c i r c u i t voltage and e f f i c i e n c y s a t u r a t e o r even decrease with base r e s i s Several papers w e r e presented t i v i t i e s of less than 1 ohm-cm. i n which t h i s was a t t r i b u t e d t o a combination of bandgap shrinkage [290], extremely low l i f e t i m e s i n the diffused region, and the l i n e a r l y graded nature of t h e junction. The bandgap shrinkage i s due t o t h e very high surface concentration of impurities i n t h e diffused region, 5X1O2O1021 atoms/cm3 i n nonviolet c e l l s , which can r e s u l t i n an energy band configuration ( e l e c t r i c f i e l d ) which forces carriers toward t h e surface r a t h e r than toward t h e junction. The smaller bandgap would a l s o cause higher absorption and

RECENT RESULTS

INCIOENT

I

F I G . 119. R e f l e c t i o n and refraction of l i g h t incident on a s e r r a t e d s u r f a c e .

/

227

INCIDENT

I

SURFACE

c a r r i e r generation near t h e surface, where surface recombination and poor l i f e t @ e s would reduce t h e i r collection probability. The s h o r t l i f e t i m e i n t h e diffused region i s t h e familiar "dead layer" problem t h a t has been largely solved by t h e low doping l e v e l , narrow junction p r i n c i p l e s of the v i o l e t c e l l , but which is present i n conventional c e l l s . For high doping l e v e l s t h e l i f e t i m e may decrease by as much as N i 2 due t o t h e s t r a i n , dislocations, point defects, and unwanted impurities introduced by t h e diffusion process. Very low l i f e t i m e s would have t h e e f f e c t of lowering t h e photocurrent and lowering t h e open c i r c u i t voltage by increasing t h e dark current. The l i n e a r l y graded junction model i s a l s o important i n explaining t h e e f f e c t s of high doping on t h e dark current. In an abrupt junction t h e current due t o minority carriers injected from t h e base i n t o t h e diffused region would be neglig i b l e , but i n the graded junction t h e current injected from t h e base would be comparable t o and perhaps even l a r g e r than t h e current injected i n t o t h e base. Increasing t h e b a s e doping l e v e l , according t o t h e theory, increases t h i s dark current due t o i n j e c t i o n from the base i n t o the diffused region, lowering t h e open c i r c u i t voltage. Increasing t h e doping l e v e l i n t h e d i f f u s e d region a l s o increases t h e dark curreM because of t h e bandgap shrinkage and t h e very low l i f e t i m e s (I00 p s e c ) , and again t h e open c i r c u i t voltage i s reduced. There are a l s o other possible explanations f o r high doping l e v e l e f f e c t s on voltage outputs from s o l a r c e l l s including tunneling, excess space charge recombination, Auger recombinat i o n , and possibly f i e l d and mobility gradient e f f e c t s . Which of these is most important is s t i l l open t o question a t t h i s point. Experimentally, the open c i r c u i t voltage i n N/P S i c e l l s s a t u r a t e s a t 0.625-0.635 V f o r around 0.1 ohm-cm base material, instead of reaching t h e 0.70 V predicted by convent i o n a l theories (Table 6). The efficiency peaks a t a base r e s i s t i v i t y between 0.1 and 1 ohm-cm f o r conventionally d i f fused c e l l s , but probably c l o s e r t o 0.1 ohm-cm i n v i o l e t c e l l s . Contributions i n t h e understanding of high doping e f f e c t s were made by t h e University of Florida, t h e University of

228

ADDENDUM

I l l i n o i s , North Carolina S t a t e University, Optical Coating Laboratory, AEG-Telefunken, NASA-Lewis, and Wayne S t a t e University. A s i g n i f i c a n t advance i n t h e understanding of t h e back surface f i e l d (BSF) mechanism has been made a t NASA-Lewis. s o l a r c e l l s w e r e made from 1, 10, and 100 ohm-cm p-type subs t r a t e s , including back surface f i e l d s . Conventional Voc and 1 measurements were made under AM0 conditions. The f r o n t nz-p junction w a s then etched o f f , leaving only t h e p-p+ junct i o n a t t h e back. Ohmic contact w a s made t o t h e f r o n t , and s o l a r c e l l measurements were made once again. A 100 mV Voc was obtained with 100 ohm-an material, and a 1 0 mV Voc w a s obtained with 10 ohm-cm material, e s t a b l i s h i n g t h a t some of t h e increased output (but not a l l ) obtained from BSF c e l l s is In a due t o voltage generation a t t h e high-low junction. 10 ohm-cm c e l l , t h e open c i r c u i t voltage i s increased from 0.55 V to 0.6 V ; 0.01 V i s t h e r e f o r e due to a voltage generat i o n a t t h e back, and 0.04 V i s due t o t h e b e n e f i t s of t h e carrier confinement i n reducing t h e o v e r a l l dark current. C e l l s made from 100 ohm-cm material with a BSF had t h e same 0.6 V output as 10 ohm-cm BSF cells. C e l l s with 1 ohm-cm bases apparently have no appreciable voltage generated a t t h e highlow junction, but may s t i l l b e n e f i t somewhat from confinement provided t h e base d i f f u s i o n length exceeds t h e c e l l thickness. Advances i n S i materials technology and i n nonconventional S i devices w e r e reported also. Solar c e l l s made from EFG ribbon w e r e reported by Mobil-Tyco, and c e l l s made from dend r i t i c web w e r e described by Westinghouse. E f f i c i e n c i e s of 10%a t AM1 have been achieved with t h e ribbon and 11-12% with t h e web S i . One of t h e problems here seems t o be t h a t a r r a y s of p a r a l l e l s l i p bands o r tw in s o r other l i n e defects are sometimes present i n t h e s e materials and act as zones of high recombination, decreasing t h e s h o r t c i r c u i t current. When such p a r a l l e l l i n e defects are absent, considerably b e t t e r short c i r c u i t currents are obtained [290al. Experiments i n processing metallurgical-grade S i i n t o s o l a r c e l l s w e r e described by Dow Corning. Czochralski ingots w e r e pulled from r e l a t i v e l y crude metallurgical S i r a t h e r than high p u r i t y semiconductor grade, r e l y i n g on t h e l o w segregat i o n c o e f f i c i e n t s of most elements i n S i t o self-purify t h e S i ingot as it w a s grown. " F i r s t " ingots had impurity contents around 100 times less than t h e s t a r t i n g material. When selected areas of these w e r e remelted and a second ingot grown, higher p u r i t i e s were obtained and t h e material could be used t o f a b r i c a t e reasonably good s o l a r c e l l s . In another technique, chlorine and oxygen w e r e passed over t h e surface of t h e molten S i , and t h e impurity content of t h e m e l t was reduced by the formation of

RJ3CENT RESULTS

229

v o l a t i l e chlorides, oxides, and other compounds. The r e s u l t i n g S i could then be gradient frozen t o obtain f u r t h e r p u r i f i c a t i o n by segregation. Thin film solar c e l l s made on carbon and metallurgical grade S i substrates were described by Southern Methodist Univ e r s i t y . It w a s discovered t h a t " r e c r y s t a l l i z a t i o n " 12911 , annealing of t h e grown S i layer near o r even above t h e melting p o i n t , could r e s u l t i n much l a r g e r grain s i z e s (100 um) than obtained i n t h e i n i t i a l S i layer (5-10 m). AM0 e f f i c i e n c i e s of 2.5% were obtained from c e l l s made from p o l y c r y s t a l l i n e layers grown on metallurgical si substrates. The efficiency w a s probably limited by remaining small grains within the l a r g e grains. A review of p o t e n t i a l l y low-cost processing methods f o r S i photovoltaics was presented by M. Wolf of t h e University of Pennsylvania. Such methods include t h e ribbon and d e n d r i t i c w e b c r y s t a l techniques, hot r o l l i n g and extrusion t o form S i sheets, continuous S i production from sand and carbon using SiF2 transport, sheet casting, and even solution growth. Many of these f a s t sheet production methods w i l l l i k e l y r e s u l t i n polycrystalline material, so t h a t r e c r y s t a l l i z a t i o n techniques t o obtain s u f f i c i e n t l y l a r g e grains are important. There i s much room f o r i n t e r e s t i n g materials work here; p a s t processes have optimized material q u a l i t y a t t h e expense of c o s t , energy used, and speed, while f u t u r e processes w i l l have t o optimize speed per u n i t cost per u n i t energy f o r a s u f f i c i e n t l y pure s o l a r grade q u a l i t y capable of making a 10%e f f i c i e n t c e l l . Continuous, flowthrough processing f o r both materials preparat i o n and device fabrication w i l l have t o be emphasized i f low-cost c e l l s are t o be made. Devices used i n concentrated sunlight schemes, however, could s t i l l be produced by e f f i c i e n t batch processing techniques. With well-designed, continuous processing, t h e energy payback t i m e (the time needed f o r a device t o generate as much energy as used t o f a b r i c a t e it) w i l l be about 1/2 year. With concentrated sunlight schemes, t h e payback time could be considerably l e s s . Recent r e s u l t s on r a d i a t i o n damage t o s o l a r c e l l s i n t h e space environment were presented, including neutron, electron, and W i r r a d i a t i o n tests. The CNR c e l l s were reported t o be more r e s i s t a n t t o radiation degradation than t h e conventional planar v i o l e t c e l l , which i s already a r a d i a t i o n t o l e r a n t device. Vertical multijunction (VMJ) c e l l s were described which consist of separate p a r a l l e l v e r t i c a l slabs (not f i l l e d i n between as i n Fig. 8 1 ~ 1 ,combining t h e CNR nonreflecting surface concept with t h e inherent high radiation tolerance of VMJ devices. A s i n g l e paper w a s presented on Li-doped S i

230

ADDENDUM

c e l l s . There seems t o be a de-emphasis l a t e l y on Li-doped devices; t h e speculation i s that t h e s e devices a r e only s l i g h t l y b e t t e r than v i o l e t c e l l s and cannot j u s t i f y t h e i r added c o s t and f a b r i c a t i o n complexity. In t h e "New Approaches" session r e s u l t s on Schottky barrier c e l l s , high-efficiency GaAs c e l l s , induced junction dev i c e s , heterojunctions, and p-i-n s t r u c t u r e s were reported. In Schottky cells t h e evidence continues t o grow t h a t a t h i n i n t e r f a c i a l l a y e r can improve t h e performance s i g n i f i c a n t l y . Several t h e o r e t i c a l p i c t u r e s were presented, including one t h a t a t t r i b u t e s t h e higher output voltages t o t h e presence of surface states, fixed charge, and t r a p s within t h e i n t e r f a c i a l layer i n a c e r t a i n configuration. Data were presented by S t i r n of JPL on Au-GaAs Schottky barrier cells; improvements of Voc from 0.45 t o 0.70 V could be achieved by heat t r e a t i n g t h e GaAs substrate p r i o r t o depositing t h e semitransparent metal layer. E f f i c i e n c i e s of 15%i n t e r r e s t r i a l sunlight were seen i n some small area c e l l s . Apparently t h i s increase i n VoF: can be obtained without adversely a f f e c t i n g t h e s h o r t c i r c u i t current or f i l l f a c t o r , a t least f o r oxides of t h e order of 50 A t h i c k o r less. Similar improvements i n device behavior by i n t e r f a c i a l oxides have been seen i n S i devices a s w e l l [292,2931. Contributions i n t h e Schottky c e l l area came from t h e University of B r i t i s h Columbia, Pennsylvania State Univers i t y , t h e J o i n t Center f o r Graduate Study, and t h e Jet Propulsion Laboratory. Heterojunction and Schottky barrier s o l a r c e l l s made with In203 o r Sn02 on n- and p-type S i w e r e described by a j o i n t Innotech Corporation-Syracuse University group. E f f i c i e n c i e s a t A M 1 of 6%w e r e seen on In203-pSi devices, with open c i r c u i t voltages of 0.30 V and s h o r t c i r c u i t currents of 35 mA/cm2. The electron a f f i n i t y of In203 w a s estimated t o be about 4.34 eV; t h i s l i m i t s t h e Voc's and n's t h a t can be obtained from InpOg heterojunctions on p-type S i t o about 0.4 V and 11%, respect i v e l y , and e f f e c t i v e l y rules o u t t h e p o s s i b i l i t y of good Schottky barrier cells (nIn203-nSi heterojunctions) due t o a maximum Voc of about 0.15 V. The electron a f f i n i t y of Sn02, however, is much higher (4.75 eV) , and t h e r e f o r e , good Schottky b a r r i e r c e l l s (nSn02-nSi) are p o s s i b l e , but good heterojunct i o n s (nSn02-pSi) are probably not. V o c t s of up t o 0.35 V and JSc's of up t o 25 mA/cm2 were seen on nSn02-nSi devices (about 1 ohm-cm S i r e s i s t i v i t y ) . The f i l l f a c t o r s w e r e lower i n t h e s e cells (0.4) than i n In203-pSi c e l l s (0.6) f o r reasons which are not c l e a r a t t h i s time. The transparent conductor f a b r i c a t i o n techniques have been applied successfully t o a v a r i e t y of S i s u b s t r a t e s . In203 films on p-type S i have r e s u l t e d i n : Voc = 0.33 V , Jsc =

RECENT RESULTS

231

30 mA/cm2 for 1.4 ohm-cm Czochralski wafers; Voc = 0.30 V, ,J = 36 mA/cm2 on 9 ohm-cm TYCO ribbon; vOc = 0.31 V, J , = 30 mA/cm2 on 1 ohm-cm polycrystalline wafers (large grain sizes); and Voc = 0.085 V, Jsc = 10 mA/cm2 on 0.05 ohm-cm metallurgical grade Si wafers. All these were at AM1 conditions , 100 mW/cm2 input. GaAs solar cells received some attention also. J. Ewan of Hughes Research Laboratories described a liquid-phase epitaxy s stem for making large numbers (30-40) of large area (22 cm ) Gal-xA1xAs-GaAs cells on a semicontinuous basis, while J. Hutchby of NASA Langley and K. Takahashi of Tokyo Institute of Technology described theoretical predictions for a graded bandgap Gal-++-GaAs device. An IBM Research group described a technique for making good GaAs cells (18% AMO) out of poor quality substrates by a combination of leaching in Ga to r m v e recombination centers and fabricating cells with deep (1-1.5 pm) instead of shallow (0.3-0.5 pm) junctions. Measured efficiencies of 14.7% at AM0 and 19% at AM1 have been obtained in this way. The devices also behave well at high temperatures; the measured AM0 efficiency drops to 9% at 250°C and 6% at 300°C. A group from Varian Associates described their results on high sunlight concentrations on Gal,xA1xAs-GaAs cells [294]. Efficiencies of 19% have been obtained for devices operating at 1735 solar intensities, and 23% efficiencies have been measured at AM1.4 at low concentrations (10). The output at 1735x amounted to 240 kW/m2 of cell area. Operation of Gal-fi1fis-G-s cells at up to 5000 suns has been reported [295]. The importance of this work lies in its terrestrial implications. Optical concentrators are much less expensive than solar cells, and calculations indicate that solar power generation can be made.economically viable even using the highly expensive, high-performance GaAs solar cells if concentrations greater than 1000 suns can be incorporated. Silicon systems can be made viable (even at today's Si prices) for concentrations of 100 suns or more. At the two American Vacuum Society Conferences in Yorktown Heights and Boston, the outlooks for low-cost thin film GaAs photovoltaics were described by the IBM Research group. Evaluations indicate that it may be possible to fabricate 10% efficient (AM1) devices using polycrystalline films of 1 Um thickness with 1-2 pm grain sizes. Even thin film single crystal devices are feasible; single crystal films of GaAs have been grown on tungsten substrates in the past. The final session of the photovoltaics conference was devoted to CdS solar cells. A major workshop on CdS and related solar cell structures was held in Delaware during early May 1975. Advances were made in understanding the physics

s

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ADDENDUM

of these devices, in new fabrication and testing techniques, and in solving the stability problems. CdS/Cu2S cells stable under open circuit conditions, and at 100°C with light incident were reported by the French group at CNES. A technique of preparing the cells in which the Cu2S would lie below rather than on top of the CdS was discussed; in this way the effect of moisture and oxygen on the cells would be greatly lessened. Recent results on low-cost preparation techniques using spraying of SnOp, Cups, and CdS were described. Contributions in these areas came from the University of Stuttgart, the Universite des Science et Technique du Languedoc, the University of Delaware, CNES, and the D. H. Baldwin Company. Methods of preparing Cu,S and CuInSe2 on various substrates were reported by Brown University, and descriptions of nCdS/pCdTe and nCdS/ nCdTe/pCu2Te heterojunction cells of 4-5% efficiencies were given by Stanford University. Heterojunctions based on CdS/ InP systems were reported by Bell Laboratories; these devices are about 12% efficient at AM2 and could potentially be as simple to fabricate and as low in cost as CdS/CupS cells.

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Index

Absorption coefficient, 6, 8, 10, 15, 211f parameters affecting, 8 Abundance of materials, 217f Air mass, 2, 38-39 irradiance at different, 38 power input as function of, 39 Annealing, 10-12, 156, 160, 202 effect on lifetime, 10-12 ion implantation, 202 recovery from radiation degradation, 156, 160 Antireflection, 25, 86, 117f, 203f, 207, 225 p-n junctions, 203f Schottky barriers, 117f velvet cell, 207, 225f Back surface field diffused, 209 effects on dark current, 52f, 97 efficiency, 80, 88 photocurrent, 96 radiation tolerance, 163 spectral response, 16, 2324, 33 Voc, 4, 24, 96, 99, 228 high-low barrier height, 97 vapor grown, 186 Bandgap effect on efficiency, 3 effect on Isc, Voc, 6

reduction, 11, 226 Barrier height BSF devices, 24, 97, 99 heterojunctions, 131, 133 p-n junctions, 5 Schottky barriers, 113, 120, 122 Base region collection from, 18-19, 22 Base resistivity effects on efficiency, 77f photocurrent, 42 radiation tolerance, 153, 187 VOC, 227 lifetime affected by, 11 Bridgman crystal growth, 191 Broken knee effect, 178 "Built-in" voltage , 50, see also Barrier height Cadmium sulfide cells, 2-4, 181 , 195f dark current, 68-69, 135 efficiency, 89 fabrication, 4, 109, 196, 198, 232 generation capability, 219 'ohmic contacts, 210 radiation tolerance, 164 short circuit current, 45 spectral response, 36 stability, 4, 196f, 232 thickness of CdS, 109 thickness of CuxS, 36, 109

249

250

INDEX

V O C l 91 Collection efficiency, 73, see also Spectral response Concentration, 180, 210, 221, 231,see also Intensity cost CdS cells, 2, 195f concentration, 166 ribbon, 2 Si cells, 2, 185, 229 terrestrial applications, 2, 217f, 229 Cover glass, 2, 161f adhesive, 162 as antireflection system, 203, 206 integral, 162 Critical fluence, 151 Crucible, 182, 185 Crystal growth CdS, 196, 198 GaAlAs, 195 GaAs, 191f Si, 181f CuInSep, 139, 218, 232 Czochralski G a s , 191 lifetime of, 10, 183 Si, 181f

Dark current, 5, 48, 51f depletion region recombination, 48, 66-67, 134 effect of doping, 48 equivalent circuit, 57 injected, 48, 65, 133f organic cells, 214 temperature, 168, 174 tunneling, 48, 68, 134f Dead layer, 17 effect on efficiency, 77f, 83 effect on photocurrent, 41f lifetime in, 11 violet cell affecting, 4 Depletion region, 6, 19-20, 28 heterojunctions, 128

Schottky barriers, 113 Diffused region, 2, 17-18, 21, 189 in GaAs, 193f in Si, 188f Diffusion length, 12 base, 95 effect on photocurrent, 41 polycrystalline films, 15 Diode perfection factor, 5, 72 p-n junctions, 58, 63-67 Schottky barriers, 124, 126 Direct bandgap absorption, 8 effect on efficiency, 81 effect on spectral response, 28 lifetime, 12 radiation tolerance, 163 surface recombination velocity, 15 thickness, 95 Discontinuity effect on barrier height, 131 effect on dark current, 134 heterojunctions, 32, 129f Distribution coefficient, 182, 192 Dopants effect on lifetime, 12 effect on radiation tolerance, 153-154 GaAs, 192f Si, 182, 186f Doping level effect on lifetime, 27 high doping effects, 88, 226f Efficiency, 71f effect of bandgap, 73-74 effect of contact area, 71 effect of solar spectrum, 71, 74 method of calculating, 75 of CdS cells, 89 of GaAs cells, 4, 80f, 83€, 89, 231

INDEX

251

of Li cells, 4, 89 effect on shunt resistance, of organic cells, 216 57 of poor quality cells, 101 effect on Voc, 107 of ribbon cells, 185 effective diffusion length, of Si cells, 76, 88, 99, 185 105-106 of violet cells, 4, 89 junction formation, 108 of VMJ cells, 142-143 orientation, 104 parameters affecting, 72 recombination at, 15, 103 Electric drift fields, 6 Grating solar cells, 112, 145f effects on dark current, 52 dead layer, 29-30 Heterojunctions, 127f efficiency, 78f, 82 advantages, 112, 132 radiation tolerance, 163 dark current, 68, 133 spectral response, 16, 20 effect of BSF, 130, 148 Energy balance, 217, 229 efficiency, 136f, 201, 230 Energy band diagram energy band diagrams, 127, heterojunctions,126,132. 132 p-n junctions: 8-9 fabrication, 199 Schottky barriers, 113, 122 interface states, 129 Equivalent circuit, 56f lattice mismatch, 129, 135137, 199 Fill factor, 5-6, 60-61, 72, short circuit current, 130, 91 132, 230 parameters affecting, 6 spectral response, 128, 130 typical values, 91 temperature, 174 Float-zone Voc, 127, 137 Li-doped cells, 157 lifetime, 10, 183 Image potential, 121f Si growth, 182f Indirect bandgap absorption, 8 GaAs solar cells, 3-4, 35, 80 lifetime, 12 back surface field, 101 thickness, 95 dark current, 65, 67 Injected dark current dead layer, 83 p-n junctions, 51f efficiency, 80f, 87-88, 102 temperature, 55 fabrication, 191f InP, 139, 218, 220 generation capability, 219f Intensity, 174f Ohmic contacts, 210 effects on efficiency, 176radiation tolerance, 164 177 short circuit current, 42-45 fill factor, 174, 176, 178 spectral response, 29, 31Isc, 174-175, 178 33, 35 Voc, 174, 176, 178 series resistance, 62, 174, voc, 90-91 177 GaAlAS-GaAS, 4, 31-33, 35, shunt resistance, 62, 175, a3f, 138 178 Grain boundaries, 103ff effect on Isc, 107 terrestrial applications, 166f

252

INDEX

VMJ cells, 145 Interfacial layer, 115, 120121, 126 Inversion layer, 115 Ion implantation, 202f

equivalent circuit, 59 high doping effects, 226f parameters affecting, 5-6 typical values, 90f Organic solar cells, 211f Oxygen, 12, 157 effect on lifetime, Si, 12 Li cells, 157

Junction depth effect on efficiency, 78, 80, 82f effect on short circuit cur- Polarity, output, 8 rent, 39-46 Polycrystalline cells, 2, 103f effect on spectral response, CdS, 109f 28-30 G a s , 109f Junction perfection factor, Si, 108f, 186 see Diode perfection factor Power generation capability, 219f Li-doped cells, 4, 157f, 190, 229 Quality of material, 101 gradient, 158, 190 oxygen rich, lean, 157 Radiation damage coefficient, recovery, 157, 188 5-6, 151, 153f Lifetime, 6, 9-13, 183 Radiation degradation effect on dark current, 55 cover glass, 2, 161f filament, 103 effect of doping level, high doping effects, 226f dopat, 3-4, 153 in dead regions, 11, 83, 189f electron-induced, 151, 153f in GaAs caiculations, 28, 81 float zone versus Czochralin Si calculations, 13, 26, ski, 154f 76 lattice damage, 149, 156 Limit conversion efficiency, Li cells, 157f 74, 76, 125, 137 of CdS cells, 164 Liquid-phase epitaxy, 12, 31, of CNR (velvet) cells, 229 192, 195, 231 of GaAs cells, 164 effect on dark current, 56 of Si cells, 153f, 229 of violet cells, 4, 156, 160 Maximum power current, 5, 59 of VMJ cells, 143f Maximum power voltage, 5, 60 photon-induced, 156 Metallurgical-grade Si, 228 proton-induced, 156 Multiple light passes, 100 Recombination current, 53-56 effect of temperature, 55 Ohmic contact, 2-3, 207f, see Refractive index, 203f also Back surface field Resources, 218f back, 96-98, 179 Ribbon material, 2, 94, 183grid pattern, 62-63, 86, 177, 185, 191 208 advantages, 94, 184 Open circuit voltage, 5-6, 59 dendritic web, 184, 228 effect on efficiency, 72 efficiency, 94, 228

INDEX EFG, 184, 228 lifetime, 185 power generation capacity, 219 thickness, 94, 98

253

227 efficiency, 76-80, 87-89 fabrication, 181f fill factor, 61 generation capability, 219221 Schottky barrier cells, ll2f Ohmic contacts, 208-210 advantages, 112, 126 radiation tolerance, 151-160 barrier heights, 120 short circuit current, 39-41, dark current, 112f 44 effect of BSF, 119, 123 spectral response, 25-30, efficiencies, 125-126, 230 33-35 energy band diagram, 113, 122 voc, 90-91 fabrication, 200 Solar irradiance, 38-39 interfacial layer, 115, 230, Solar satellite power staspectral response, 116, 119 tion, 2 temperature, 174 Spectral response, 6, 24f transmission through metal BSF cells, 33 film, 117 CdS cells, 36 Voc, 125, 230 drift field cells, 29-30 Series resistance, 6, 57f, GaAlAs cells, 31-33, 35 177, 208 GaAs cells, 36 causes, 57, 75 grating cells, 146 effect on dark current, 63 heterojunction cells, 128, effect on efficiency, 86f 130 effect on I-V curve, 62 organic cells, 213f equivalent circuit, 57 Schottky barrier cells, 116, Serrated surface, 207, 225f 119 Sheet resistivity, 188, 200 Si cells, 35 Short circuit current, 5, 37f theory, 24f effect of drift field, 41-42 violet cells, 4, 35 effect of GaAlAs layer, 43 VMJ cells, 139f effect of junction depth, Stability 41-42 CdS cells, 196f idealized, 40 Li cells, 157 parameters affecting, 6, Surface concentration, 189, 194 37f, 40 Surface recombination velocity, Shunt resistance, 6, 62, 75, 6, 9, see also Back surface 175, 178 field causes, 56-57, 64, 75 at back, 13 effect on efficiency, 87 direct gap materials, 15 effect on I-V curve, 62 effect on efficiency, 77f equivalent circuit, 56 effect on spectral response, Silicon solar cells 27f crystal growth, 181f G a s , 15, .31f dark current, 63, 65 grating cells, 146 dead layer, 77f, 187, 189f, indirect gap materials, 15

254

INDEX

parameters affecting, 13 Si, 15 VMJ cells, 141

Uniformly doped regions collection from, 16f efficiency in cells of, 77, 81

Temperature, 166f effects on CdS, 174 Van Allen belt, 149 dark current, 168 Vapor growth, 2, 12, 186, 191 diffusion length, 167f Velvet cell, 207, 225-226 efficiency, 173 Vertical multijunction cells, fill factor, 168, 173 139f GaAs, 174 advantages, 112 heterojunction cells, 174 BSF effect on, 148 lifetime, 167 current output, 140, 145 mobility, 167 efficiency, 142-143 Schottky cells, 174 fabrication, 186 short circuit current, 167high intensities, 145 168 number of junctions, 142 Si, 173 radiation tolerance, 143f Voc, 166, 168 spectral response, 139-141 Terrestrial applications, 1-2, surface recombination 181, 190, 195, 217f velocity, 141 Thickness, 93f thickness, 143 effects on absorption, 93, voltage output, 140, 145 100 Violet cell dark current, 94 efficiency, 4, 78, 89 efficiency, 99 radiation tolerance, 156, short circuit current, 96, 160 100 series resistance, 63, 208 Vocr 96, 98 short circuit current, 44 Thin film cells spectral response, 34 CdS, 2, 109f GaAs, 15, 100f, 107, 109, 231 power generation capacity, 219f Si, 2, 15, 94f, 98-99, 108, 185, 229 Transmission, 116, 200 Traps, 213f Tunneling CdS cells, 49, 68-69 effect of temperature, 55, 168, 174 effect on efficiency, 77, 79 heterojunctions, 49, 68 p-n junctions, 54, 227 Schottky barrier cells, 49

8 c D E

6 7 B 9

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