Shape and functional elements of the bulk silicon microtechnique: a manual of wet-etched silicon structures

J. Frühauf Shape and Functional Elements of the Bulk Silicon Microtechnique Joachim Frühauf Shape and Functional E...

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J. Frühauf Shape and Functional Elements of the Bulk Silicon Microtechnique

Joachim Frühauf

Shape and Functional Elements of the Bulk Silicon Microtechnique A Manual of Wet-Etched Silicon Structures

With 165 Figures and 75 Tables

Author Prof. Joachim Frühauf Technische Universität Chemnitz Fakultät für Elektrotechnik und Informationstechnik Fachgruppe Werkstoffe der Elektrotechnik/Elektronik Reichenhainer Str. 70 09107 Chemnitz Germany

ISBN 3-540-22109-3 Springer Berlin Heidelberg New York Library of Congress Control Number: 2004112723 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable to prosecution under German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2005

Printed in Germany

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data conversion by the authors. Final processing by PTP-Berlin Protago-TEX-Production GmbH, Germany Cover-Design: design & production GmbH, Heidelberg Printed on acid-free paper 62/3020Yu - 5 4 3 2 1 0

Preface

The idea for this manual was created by the author and Birgit Hannemann (now Professor at the University of Applied Sciences, Bremen, Germany) as an internal catalogue of results of several years of investigations at the Chemnitz University of Technology, Germany. At this base supplying investigations and the elaboration of the manuscript were supported by the Stiftung Industrieforschung, Bonn, Germany. In the course of this the coworkers of the author Eva Gärtner, Steffi Krönert and Cornelia Kowol were directly involved. All the SEM pictures result from preparations performed at the Centre of Microtechnologies at the Chemnitz University of Technology (Head: Prof. Thomas Gessner). The author and his coworkers wish to express their thanks to Wolfgang Bräuer (mask design), Norbert Zichner (processes), Iris Höbelt (SEM pictures) and the student Karin Preißler (manuscript layout support). In particular thanks are due to the Stiftung Industrieforschung for the financial support and to the Springer Verlag for the edition of this manual. Chemnitz, June 2004

Joachim Frühauf

Table of Contents

Symbols................................................................................................................ XI 1 Introduction.........................................................................................................1 2 Technological Basis of Bulk-Silicon-Microtechnique ......................................5 2.1 The silicon wafer as a basis material of microtechnique..............................5 2.2 Technological processes...............................................................................6 2.2.1 The basic conception of the bulk-silicon-microtechnique ....................6 2.2.2 Deposition and structuring of passivation layers ..................................7 2.2.3 Wet and dry etching of silicon ..............................................................8 2.2.4 Metallization.......................................................................................10 2.2.5 Wafer bonding ....................................................................................11 2.2.6 Plastic reshaping of silicon microstructures .......................................13 3 Orientation Dependent Etching of Silicon ......................................................17 3.1 Fundamental principles of the generation of shapes ..................................17 3.1.1 Atomic scale features of silicon etching .............................................17 3.1.2 The formation of shapes by etching masked wafers ...........................20 3.1.3 The importance of different oriented Si-wafers in the microtechnique: {100}, {110}, {112} and {111} ..................................................................30 3.1.4 Detection of the correct orientation between wafer and mask ............33 3.2 Chemistry and techniques of wet silicon etching .......................................37 3.2.1 Chemical reactions and dependence on temperature ..........................37 3.2.2 Influence of composition ....................................................................39 3.2.3 Influence of doping.............................................................................41 3.2.4 Equipment and etching technology.....................................................43 3.2.5 Isotropic etching .................................................................................44 3.3 Etch mask design and simulation of silicon etching...................................46 3.3.1 Calculation of the etch mask...............................................................46 3.3.2 Addition of compensation masks....................................................... 49 3.3.3 Simulation and design tools................................................................50 3.4 Basic processes of the bulk-silicon-microtechnique ..................................52 3.4.1 Shape definition by variation of etch steps .........................................52 3.4.2 Changing of the mask between two etch steps ...................................55 3.4.3 Examples of the most important basic processes and process interfaces......................................................................................................57

VIII

Table of Contents

4 General Overview of the Shape- and Functional Elements and the Procedure of their Design....................................................................................71 4.1 Survey and methodical procedure ..............................................................71 4.2 Guide for the design procedure ..................................................................73 4.3 Legend of the sketches ...............................................................................73 5 Simple Shape Elements ....................................................................................75 5.1 Definitions of shapes by the combination of sidewalls ..............................75 5.1.1 Types of sidewalls arising from one-step etch processes....................75 5.1.2 Types of sidewalls arising from two-step etch processes ...................78 5.1.3 Combinations of sidewalls..................................................................85 5.2 Qualities of etch ground and sidewall-faces and of the edges between them .................................................................................................................86 5.2.1 Quality of the etch ground ..................................................................87 5.2.2 Quality of sidewalls ............................................................................91 5.2.3 Quality of edges..................................................................................93 5.3 Shape elements made by one-step etch processes......................................94 5.3.1 Hollows (Deepenings) ........................................................................94 5.3.2 Mesas (Elevations) ...........................................................................101 5.3.3 Grooves (Trenches) ..........................................................................106 5.3.4 Walls.................................................................................................109 5.3.5 Front-back combinations ..................................................................113 5.4 Shape elements made by two-step etch processes....................................114 5.4.1 General remarks................................................................................114 5.4.2 Alteration of the etch mask...............................................................115 5.4.2 Change of the type of orientation dependent etchant........................119 5.4.3 Change between orientation dependent and isotropic etchants.........122 6 Elements for Mechanical Applications .........................................................127 6.1 Spring elements........................................................................................127 6.1.1 Overview and used crystal faces.......................................................127 6.1.2 Bending springs ................................................................................128 6.1.3 Torsion-bar springs...........................................................................130 6.2 Levers / Spring hinges..............................................................................143 6.2.1 Overview ..........................................................................................143 6.2.2 Levers / Hinges for out-of-plane movements ...................................144 6.2.3 Levers / Hinges for in-plane movements ..........................................144 6.3 Sliding guides...........................................................................................146 6.3.1 Overview ..........................................................................................146 6.3.2 Four-wafer-guide ..............................................................................147 6.3.3 Two-wafer-guide ..............................................................................147 6.3.4 Three-wafer-guide ............................................................................147 6.3.5 Sliding guide with plastically deformed elements ............................147 6.4 Bearings ...................................................................................................149 6.4.1 Overview ..........................................................................................149 6.4.2 Edge bearings ...................................................................................150 6.4.3 Tip bearings ......................................................................................150

X

Table of Contents

8.6 Infrared Prisms .........................................................................................193 8.6.1 General remarks................................................................................193 8.6.2 The prism edge lies inside the wafer plane.......................................193 8.6.3 The prism edge lies perpendicular to the wafer plane ......................193 Appendix.............................................................................................................199 Physical Properties of Silicon ........................................................................201 Survey and comparison with properties of other materials........................201 Mechanical properties................................................................................206 Thermal and caloric properties ..................................................................211 Optical properties ......................................................................................213 Index ...................................................................................................................217

Table of Contents

IX

7 Elements for Fluidic Applications .................................................................159 7.1 Channels...................................................................................................159 7.2 Alterations of cross section of channels ...................................................162 7.2.1 General remarks................................................................................162 7.2.2 Abrupt alterations of the cross section..............................................163 7.2.3 Gradual alterations of the cross section ............................................163 7.3 Elbows......................................................................................................163 7.3.1 General remarks................................................................................163 7.3.2 Elbows out-of-plane..........................................................................164 7.3.3 Elbows in-plane ................................................................................164 7.4 Branchings (Mixers).................................................................................166 7.4.1 General remarks................................................................................166 7.4.2 Branching out-of-plane .....................................................................166 7.4.3 Branching in-plane............................................................................167 7.5 Caverns (Cavities) ....................................................................................169 7.6 Nozzles.....................................................................................................171 8 Elements for Optical Applications................................................................177 8.1 Grooves for fibre positioning ...................................................................177 8.1.1 General remarks................................................................................177 8.1.2 Grooves in an angle of 0 or 90° to the flat ........................................179 8.1.3 Grooves with an angle of 45° to the flat ...........................................179 8.1.4 Grooves in a direction range of ∆α around the 0° or 90° directions to the flat........................................................................................................179 8.1.5 Grooves in any direction to the flat...................................................180 8.1.6 Grooves with inclined direction to the wafer plane ..........................180 8.2 Micro mirrors ...........................................................................................180 8.2.1 Useable mirror faces on the {100}-wafer .........................................180 8.2.2 Reflection at the {100}-wafer surface or {100}-etch ground ...........181 8.2.3 Reflection at sidewall faces out of the {100}-wafer plane ...............181 8.2.4 Reflection at sidewall faces inside the {100}-wafer plane ...............182 8.2.5 Useable mirrors on the {110}-wafer.................................................184 8.3 Beam Splitters ..........................................................................................185 8.3.1 Principles of beam splitting and suitable crystal faces......................186 8.3.2 Beam splitting at a membrane built by the etch ground and the wafer back side ....................................................................................................186 8.3.3 Beam splitting out of the wafer plane ...............................................186 8.3.4 Beam splitting inside the wafer plane...............................................187 8.4 Concave Micro Mirrors............................................................................188 8.4.1 Introduction ......................................................................................188 8.4.2 Parabolic concave mirrors ................................................................188 8.4.3 Spherical concave mirrors ................................................................188 8.5 Gratings ....................................................................................................189

Symbols

a b b d D dLE dT du dUE dU dW EA K k´ l l1 l2 lf p PV R rA Ra Rc Riso T t v v* viso vT vTF vU w W į ∆α

mask extensions for the compensation of underetching of convex corners mask extensions for the compensation of underetching of convex corners width of the window etch distance fibre diameter distance of opposite lower edges (trench)

depth displacement of the upper edge of the sidewall distance of opposite upper edges (trench) distance of underetching wafer thickness energy of activation by ARRHENIUS pre-exponential constant proportionality constant mask extensions for the compensation of underetching of convex corners mask extensions for the compensation of underetching of convex corners mask extensions for the compensation of underetching of convex corners guiding length of the fibre projected width of the sidewall maximum peak to valley of a profile universal gas constant aspect ratio roughness radius of curvature radius of spheres (absolute) temperature etch time etch rate certain etch rate isotropic etch rate etch rate in the depth rate of the face at the top of the sidewall rate of underetching width of the mask window width of the groove inclination angle rotation angle

XII

α α* γ γ*(α) γI γTF λ

Symbols

angle between mask edge and flat certain angle inclination of the sidewall face characteristic angle of inclination inclination of the face i angle of inclination of the top face of the sidewall relative to the wafer plane wavelength

1 Introduction

The manual is written for producers of sensors and microtechnical components but also for producers of components of precision engineering and optical applications. The intention is to support the extension of the application of silicon structures not only in the microtechnique but also in unconventional fields, this means a transfer of the advanced material base and technologies of the microtechnique into the precision engineering. The monocrystalline silicon is a very suitable material for a number of components because of its stable thermomechanical properties. The principles of microstructuring can be applied also for the production of relative large structures having the high precision which must be presupposed for microstructures. The manual gives a summary about the present technical level of the field of shaping in the bulk-silicon-technology. With it the structures are worked out from the volume of silicon wafers by etch processes, which are developed earlier for the technology of Si-microelectronics. So the dimensions of the structures are limited by - the minimal values, which can be mastered technologically (appr. 1 µm), - the thickness of the silicon wafer (appr. 100 to 1000 µm) and - the diameter of the silicon wafer (75 to 200 mm, in future 300 mm, too). An integration with structures of microelectronics or surface-microtechnique and also of nanotechnique is principially possible but not described in this manual. Regarding to their importance and plurality the manual contains mainly elements which can be produced from the {100}-silicon wafer by anisotropical (orientation dependent) wet chemical etching. Also shapes needing wafers with special orientations for their realization are considered (e.g.{110}). However, shapes which are made by doping selective etch processes are not described in detail (etch stop at pn-transitions, p+ - etch stop). Mostly very thin membranes are created with these methods. In comparison with traditional components of precision engineering the microtechnical ones have particular shapes and properties owed to the material silicon, to its cristallography and to the processes of microtechnique. A number of typical shapes and elements has been developed for micromechanical, microfluidical and microoptical applications during the last about 20 years in the bulk-siliconmicrotechnique. The aim of the manual consists in a systematic description of these elements to promote their use in products. The demonstrated elements build in principle the basis for further developments. Other dimensions, modifications

2

1 Introduction

and more shapes can be made, of course. But a briefing of technological possibilities should be done. An introductional chapter describes the technological basis of the bulk-siliconmicrotechnique. The silicon wafer is the main material for it just as for the microelectronics. The characteristical wafer parameters and specials which are important for the microtechnique are shortly described in a first section. A section about the technological conception of the production of microstructures on and in Siwafers follows. Facts about compatible layers are summarized because microtechnical components do not only consist of the material silicon but other materials can be necessary as layers. Therefore the relation of these layers to the Si etch process is of importance. The working of microtechnical components is normally reached by mounting the shape- and functional elements into a chip-sandwich. The packaging has some special features which are noted in the last section of this chapter. The mentioned themes are not described completely in this catalogue. The study of special literature is necessary at these points. For the understanding of typical shapes of the bulk-silicon-microtechnique the basics of formation of shapes by etching will be explained in detail in the third chapter. The comprehension of this process can be difficult because of the strong crystallographical relations. It follows a summary of the chemical reactions and the etching equipment. Finally the course and the problems of the design of bulksilicon-microstructures are discussed: the design of the etch mask suitable for the production of a target structure and the design of the sequence of technological process steps (basic processes). Chapter 4 gives a guide for the design of a target structure and a short survey of the shape- and functional elements of the bulk-silicon-microtechnique as a introduction to the four following chapters, which contain systematic descriptions about -

simple shape elements (chapter 5), elements for mechanical functions (chapter 6), elements for fluidical functions (chapter 7) and elements for optical functions (chapter 8)

together with graphics, photos and references. The physical properties of silicon are summarized in an appendix. They are necessary for the design of microtechnical silicon components and give initial ideas about the application of the material silicon in a new unusual matter. The referenced publications result from a systematical review of related journals (Sensors and Actuators, Journal of Applied Physics, Microsystem Technologies, Journal of Micromachining and Microengineering, Journal of Electrochemical Society) and technical digests of conferences (Transducers, Micro System Technologies). With these references a quick access to basic information and typical examples of application are supported. For further information about materials, technologies and the design of microtechnical components some books and papers can be regarded [Bütt91, Elw98, Ger97, Heu91, Kov98, Menz93, Scha91].

1 Introduction

3

References [Bütt91] [Elw98] [Ger97] [Heu91] [Kov98] [Menz93] [Scha91]

Büttgenbach S (1991) Mikromechanik. B G Teubner, Stuttgart Elwenspoek M, Jansen H (1998) Silicon Micromachining. Cambridge University Press, Cambridge Gerlach G, Dötzel W (1997) Grundlagen der Mikrosystemtechnik. Hanser Verlag, München Wien Heuberger A (1991) Mikromechanik. Springer Verlag, Berlin Heidelberg New York Kovacs GTA, Maluf NI, Petersen KE (1998) Bulk Micromachining of Silicon. Proc of the IEEE, 86, 8: 1536–1551 Menz W, Bley P (1993) Mikrosystemtechnik für Ingenieure. VCH-Verlag, Weinheim Schade K (1991) Mikroelektroniktechnologie. Verlag Technik, Berlin

2 Technological Basis of Bulk-SiliconMicrotechnique

2.1 The silicon wafer as a basis material of microtechnique The silicon wafer is a nearly circular cut slice of a cylindrical silicon monocrystal. Excellent parallelism and flatness of front and back sides are achieved by lapping. The following chemical-mechanical polishing process minimizes the surface roughness extremely. In this condition, the wafers are used as a starting material for the production of microelectronic circuits and for micro electro mechanical systems (MEMS). In table 2.1 typical values are given for the geometric features of commercial wafers. Further, in microtechnique, wafers with different specifications related to the crystallographic orientation ({100} and others), the surface quality (doublesided polished) and the thickness (100 up to 1000 µm) are applied. SOI-wafers (Si-SiO2-Si-sandwich) are used, too [Ger97]. As a monocrystalline material, the wafer exhibits properties which are anisotropic relative to the crystallographic symmetry of silicon (cubic, diamond lattice). Employing the wafers there must be paid attention to this. For this reason, an direction is marked at the circumference of the wafer by a notch or by a flat (also called primary flat, orientation flat or long flat which is perpendicular to ). In connection with the silicon wafers of microtechnique the most important crystallographic planes and directions of the cubic lattice are illustrated in figure 2.1. Table 2.1. Typical geometric features of silicon wafers with orientations {100} or {111} a Property Diameter Thickness Marking of orientation

mm 100 µm 525 Flat

125 625 Flat

150 675 Flat, Notch Total thickness variation µm 5 5 5 Bow / Warp µm < 30 < 30 < 30 Local flatness (20 x 20 mm²) µm < 1 700 °C

Principle r e s h a p in g o f a s in g le e le m e n t F

F

s ta m p

fu rn a c e re s t

b a tc h p ro c e s s F g u id e

Induced by laser irradiaton

s ta m p re s t

la s e r h e a tin g

14

2 Technological Basis of Bulk-Silicon-Microtechnique

The laser bending is possible without any additional tools. The reshaping takes place as a result of the internal stresses that are created inside the microstructural element due to the irradiation. The bending region is determined by the local heating of the laser. Different bending angles can be adjusted by changing the laser parameters. A high accuracy is supported by a turn-off-criteria. The bending by laser offers a good alternative to the process inside the furnace for elements which are not allowed to be heated completely. The reshaping is performed after the etching of the structures and the following removal of the masks. A further etch step after the reshaping to change the shape of the bent element is difficult because of the development of dislocation etch pits. During the plastic deformation dislocations are generated and multiplied in the monocrystalline and original nearly dislocation free material which can change the mechanical and physical properties. Therefore the application of the deformed structures is not possible in all cases. The bending fracture strength of the deformed structures is not made worse by the plastic deformation [Jän00]. Possible applications of the reshaped microstructures are components with a changed slope of definite crystal planes (see section 8.2) and components in positioning and clip systems (see section 6.3) [Gärt2-01].

a) 4 bent short cantilevers

b) 1 bent long cantilever

c) bowed membrane

Fig. 2.3. Silicon structures deformed in a furnace (900 °C) with tools

a) simply bent cantilever Fig. 2.4. Silicon structures deformed by laser

b) multiply bent cantilever

2.2 Technological processes

15

References [Bhar95]

[Bütt91] [Chung00] [Cra01]

[Elw98] [Esa94] [Früh1-99]

[Früh2-99] [Früh1-00]

[Gärt1-01] [Gärt2-01]

[Ger97] [Geß95] [Gös99] [Gu198] [Heu91] [Jän00] [Kass96] [Kwon98]

[Lärm94]

Bhardwaj JK, Ashraf H (1995) Advanced silicon etching using high density plasma. SPIE: Proc of Micromach and Microfab Process Technology 2639: 224233 Büttgenbach S (1991) Mikromechanik. B G Teubner, Stuttgart Chung CK, Lu HC, Jaw TH (2000) High aspect ration silicon trench fabrication by inductively coupled plasma. Microsystem Technologies 6: 106–108 Craciun G et al. (2001) Aspect ratio and crystallographic orientation dependence in deep dry silicon etching at cryogenic temperatures. Transducers ´01: Proc of the 11th Int Conf on Solid-State Sensors and Actuators, USA, Japan, Switzerland: 612–615 Elwenspoek M, Jansen H (1998) Silicon Micromachining. Cambridge University Press, Cambridge Esashi M (1994) Encaspsulated micromechanical sensors. Microsystem Technologies 1: 2–9 Frühauf J, Gärtner E, Jänsch E (1999) New aspects of the plastic deformation of silicon – prereqisites for the reshaping of silicon microelements. J Applied Physics A 68: 673–679 Frühauf J, Gärtner E, Jänsch E (1999) Silicon as a plastic material. J Micromech Microeng 9: 305–312 Frühauf J, Gärtner E, Jänsch E (2000) Plastic reshaping of silicon microstructures: process, characterization and application. MicroMat 2000: Proc of the 3rd Int Conf and Poster Exhibition Micromaterials, Germany: 1164–1167 Gärtner E et al. (2001) Laser bending of etched silicon microstructures. Microsystem Technologies 7/1: 23–26 Gärtner E, Frühauf J, Jänsch E (2001) Mounting of Si-chips with plastically bent cantilevers. Transducers ´01: Proc of the 11th Int Conf on Solid-State Sensors and Actuators, Germany: 206–209 Gerlach G, Dötzel W (1997) Grundlagen der Mikrosystemtechnik. Hanser Verlag, München Wien Geßner T, Wiemer M, Hiller K (1997) High precision acceleration sensor in Silicon. Proc of Conf Sensor, Germany: 409–414 Gösele U et al. (1999) Wafer bonding for microsystems technologies. Sensors and Actuators A 74: 161–168 Gui C et al. (1998) Fabrication of multi-layer substrates for high aspect ratio single crystalline microstructures. Sensors and Actuators A 70: 61–66 Heuberger A (1991) Mikromechanik. Springer Verlag, Berlin, Heidelberg, New York Jänsch E, Frühauf J, Gärtner E (2000) Biegebruchfestigkeiten von geätzten und verformten Mikrostrukturen. Freiberger Forschungshefte B321: 238–253 Kassing R, Ranglow W (1996) Etching processes for high aspect ratio micro system technology. Microsystem Technologies 3: 20–27 Kwon K, Park S (1998) A bulk-micromachined three-axis accelerometer using silicon direct bonding technology and polysilicon layer. Sensors and Actuators A 66: 250–255 Lärmer F, Schilp A (1994) Method of anisotropically etching silicon. US Patent #5501893, German Patent DE4241045

16

2 Technological Basis of Bulk-Silicon-Microtechnique

[Lee03]

[McN00] [Rich02]

[Scha91] [Seid86] [Wiem98]

[Will98]

Lee KL et al. (2003) Low temperature three-axisaccelerometer for high temperature environments with temperature control of SOI piezoresistors. Sensors and Actuators A 104: 53–60 McNie M et al. (2000) High aspect ratio micromaching (HARM) technologies for microinertial devices. Microsystem Technologies 6: 184–188 Richard A, Köhler J, Jonsson K (2002) Weibull fracture probability for characterisation of the anodic bond process. Sensors and Actuators A 99: 304–311 Schade K (1991) Mikroelektroniktechnologie. Verlag Technik, Berlin Seidel H (1986) Der Mechanismus des Siliziumätzens in alkalischen Lösungen. Dissertation Thesis, Freie Universität Berlin Wiemer M, Herziger K (1998) Silizium-Waferbonden: Montageprozesse für Silizium- und Glasmaterialien in der Mikromechanik. DVS Verlag, Düsseldorf Williams KR (1998) Silicon chemical plasma and reactive ion (RIE) etch rates. In: Hull R (ed) Properties of silicon. University Virginia, INSPEC (No. 4): pp 832–842

3 Orientation Dependent Etching of Silicon

3.1 Fundamental principles of the generation of shapes 3.1.1 Atomic scale features of silicon etching The etching as a process of micromachining silicon wafers strives for an even removing of material from the surface which will be displaced parallel to itself as a consequence. The distance d between the original and the etched surface describes the thinning of the wafer or the depth of an etched deepening. A characteristic parameter of the etching process is the etch rate v as the ratio of the etch distance d to the etching time t: d v= . (3.1) t The features of an etched surface are well defined by the mechanisms of removing of atoms during the chemical reaction: - transport of reactants from the etching solution (“etchant”) to the crystal surface, - adsorption at the crystal surface, - chemical surface reaction, - desorption of reaction products, - transport of the reaction products from the crystal surface into the volume of the etchant. With regard to the time necessary for these processes it can be distinguished between two types of etching processes depending on which process dominates the total etching time: - transport controlled etch processes: Transport processes are defined by the liquid etchant resulting in a more isotropic etching but influenced by convection → isotropic etching, - reaction controlled etch processes: Adsorption, reaction and desorption strongly depend on the configuration of atoms and bonds at the crystal surface producing an anisotropy related to the crystallographic surface orientation → orientation dependent etching.

18

3 Orientation Dependent Etching of Silicon (0 0 1 )

[0 0 1 ] [0 1 0 ] [1 0 0 ]

(1 1 0 )

(1 1 1 )

Fig. 3.1. Cut of the silicon lattice; the atoms are located in the centres of the tetrahedral bond configurations

Any surface structure of the silicon crystal can be considered as a section of the diamond structure, figure 3.1, producing more or less free bonds resulting in a certain surface energy [Hesk93]. The separation of an atom from the surface requires the cutting of the back bonds. - {111}-surface: A section between two {111}-double planes produces two surfaces with atoms which only have one free bond resulting in a low surface energy. They are bound by three back bonds resulting in a high activation energy for the separation of atoms. - {100}-surface: The separation of atoms from an {100}-surface requires the cutting of two bonds per atom resulting in a lower activation energy. - {110}-surface: A single atom of the {110}-surface can be separated by cutting three bonds but thereafter its neighbour only has one back bond resulting in two bonds which are to be cut per atom. If the reaction requires a thermal activation for the separation of an atom from the surface the etch process will proceed the slower the higher the activation energy is. Consequently the etching of an {111}-surface is very much slower than the etching of {100}- or {110}-surfaces. Moreover the etch rate of any surface element depends on its crystallographic orientation (hkl): v(hkl), figure 3.2. The reaction of aqueous solutions of alcaline hydroxides with silicon is the most important example (see section 3.2). Additional components in the etchant which do not participate in the chemical reaction can have an influence on the etch rates if their molecules are adsorbed more or less frequently at the silicon surfaces of different orientation. Used additions are alcohols (e.g. isopropyl alcohol = IPA) [Merl93, Price73] or tensides [Seki1-99]. In the case of a chemical reaction which requires little external energy for cutting the Si bonds this process is very quick so far as reactive ions arrive at the surface. A transport controlled etch process results in an isotropic proceeding. The coupled oxidation of surface atoms and dissolving of oxide in HNO3-HF-H2Oetchants is the most important example.

3.1 Fundamental principles of the generation of shapes

[0 0 1 ]

19

[0 0 1 ]

Body of dissolution rates

(1 1 1 )

(1 0 0 )

Body of dissolution rates

(1 1 0 ) 0 .3 (1 1 1 ) 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 0 .9 (1 0 0 ) 0 .8 0 .7 0 .6

(1 1 0 ) 2 .2 2 .0 1 .8 1 .6 1 .4 1 .2

Stereographic projection into (001) (rates in µm/min) a) KOH 30%, T = 80 °C: v{110} > v{100}

Stereographic projection into (001) (rates in µm/min) b) KOH-IPA 27%, T=70 °C: v{110}< v{100}

Fig. 3.2. Examples of etch (dissolution) rates v(hkl) for silicon [Ziel95]

An additional feature related to the surface quality can be derived from these considerations. An atom of the {100}-surface has no bonds to other atoms inside this surface plane. Its separation does not require the separation of a neighboured atom. Atoms of the atomic layer underneath which have lost their neighbours at the surface can be separated as easily as the surface atoms resulting in an atomic rough surface structure with lots of kinks (K-face). The atoms of an {111}-surface have three bonds to neighbours inside their double plane (so called “periodic bond chains” – PBC). Therefore the separation of an atom from the {111}-surface requires the separation of the neighbours. So, at first the whole atomic layer will be removed before the separation of an atom underneath occurs resulting in an atomic flat surface structure (F-face). An intermediate situation characterizes the {110}surface: PBCs exist in a row of atoms which can be separated easily producing a

20


a) Atomic flat face: the {111}-etch ground (on the right) (large deviations from {111} produce macroscopic steps on the left)

b) Atomic rough face: the {100}-etch ground (the resulting wavyness produces only little contrast)

c) Terraced faces: the {110}-etch ground (approximately composed of {144}-faces)

Fig. 3.3. Types of surfaces in KOH-etched deepenings in silicon

step resulting in an atomic stepped surface structure (S-face). The K- and S-faces tend to build rough and wavy surfaces, whereas F-faces tend to build large atomic flat surface regions with steps in between with a height of one ore more atomic distances. Surfaces with any crystallographic orientation can be K-, S- or F-faces or combined of these types. Such combinations occur if the kind and the density of atomic kinks or steps produce a large surface energy which can be lowered by the degeneration of the surface in microscopic steps of low energy faces: “terraced faces”. The terracing can be found in submicroscopic scale but very coarse and irregularly bizarre, too. Real etched silicon surfaces of these types are shown in figure 3.3. A more detailed survey about surface structures and rates of the orientation dependent etching process is given in [Elw98]. The experimental determination of etch rates and surface qualities for faces of all orientations can be realized by etching spherical crystal bodies [Sato98] or concave hemispheres [Koide91]. A method which is better adapted to the micro technological processes uses a special test structure on the {100}-Si-wafer [Yang00, Ziel95]. 3.1.2 The formation of shapes by etching masked wafers The shape of silicon microstructures produced by the orientation dependent wet etching of wafers is determined by - the windows of the used mask and - the relative etch rates of faces of all orientations in the used etchant. Presupposing the mask and the necessary rates are well known the question which shape results is a trivial one only in very simple cases. To describe the development of the shape of a crystal during its growth or dissolution Wulff and Jaccodine have introduced a graphic construction. Applying this construction to the etching of a masked Si-wafer the development of structures can be clearly illustrated. This will be explained in detail below on the basis of the {100}-wafer orientation as an example.


21

The construction of Wulff and Jaccodine [001]-zone: planes ήή [001])

v

(0 1 0 )

2

v

(1 1 0 ) 4 5 °

(1 1 0 )

3 3 ° 1 8 °

1 c e n tre + c y lin d e r a x is [0 0 1 ]

(1 0 0 ) 0 ° 1 8 °

v

(1 0 0 )

c e n tre + c y lin d e r a x is [0 0 1 ]

0 ° (1 0 0 )

3 3 ° 4 5 ° (1 1 0 )

Original shape: Convex cylinder

Etch rates of planes of the [001]-zone

Original shape: Concave cylinder

Fig. 3.4. The use of the construction of Wulff and Jaccodine to illustrate the development of etched shapes from a convex or a concave cylindrical original shape: the sketch shows the fastest etching faces (direction 18°, 45°) bounding the convex body and the slowest etching faces (direction 0°, 33°) bounding the concave body.

In general the resulting shape can be predetermined with good approximation by the so called Wulff-Jaccodine-Construction (WJC) [Jacc62, Weir75]. This method uses a geometrical model idealizing all crystal faces as mathematical planes and neglecting real surface structures. The starting shape of a crystalline body is considered to be composed by plane surface elements (with finite dimensions) or/and by curved surface elements (with infinitesimal dimensions). At the edges or corners all possible tangential surface elements with zero extension must be taken into account. A certain etch rate v{hkl} can be assigned to each surface element related to its crystallographic orientation {hkl}. Then the mathematical plane of each surface element will be displaced by its normal vector of the length v{hkl}·t (the etch distance after an etching time t) which is directed into the interior of the crystalline material. Finally the shape of the etched crystal is composed of such sections of the intersecting planes which have the shortest distances to the centre of curvature, see figure 3.4. Using the WJC the following rules are generally observed during the generation of shapes by orientation dependent etching: - The surface of convex regions of an etched crystal is increasingly formed by faces with high etch rates. The part of faces with low etch rates is decreased. - The surface of concave regions of an etched crystal is increasingly formed by faces with low etch rates. The part of faces with high etch rates is decreased.

The development of deepenings in masked wafers ({100}-wafer as example) The etching of masked wafers produces deepenings in the windows which have concave sidewalls at the mask edge. This is also correct in the case of a masked is-

22


land which develops a shape with a mixed convex-concave curvature. Consequently, the shape of a sidewall can be estimated as a concave one by the WJC. So they are formed by slowly etching faces shown in figure 3.5.

v

(0 0 1 )

2 .5 2

v

1 .5

s u rfa c e b e fo re e tc h in g {1 1 1 } s id e w a ll m a s k

(1 1 1 )

1 0 .5 0

v

(1 1 0 )

Rates of faces of the -Zone

v

e tc h g r o u n d

Sidewall along mask edge

(0 0 1 ) 2 .5

v

2

(1 0 1 )

m a s k

d is ta n c e o f u n d e r e tc h in g

s u rfa c e b e fo re e tc h in g

1 .5

{ 1 0 0 } - n e a r s id e w a ll 1

0 .5 0

v

(1 0 0 )


v

e tc h g ro u n d


(0 0 1 )

2 .5 2

m a s k

1 .5


s u rfa c e b e fo re e tc h in g u p p e r s id e w a ll fa c e

1 0 .5 0

d is ta n c e o f u n d e r e tc h in g

v

lo w e r s id e w a ll fa c e

(1 3 0 )

e tc h g r o u n d


Fig. 3.5. The use of the WJC illustrates the development of concave sidewalls along mask edges of different directions: , , ({100}-Wafer, KOH-type etchant)


23

Underetching of edges and convex corners of the mask ({100}-wafer as example) With the rate vTF of the face at the top of the sidewall (direct under the mask) a more or less large “underetching” of the mask occurs and a rate of underetching can be defined: v vU = TF (3.2a) sin γ TF

(γTF is the angle of inclination of the top face of the sidewall relative to the wafer plane). The rate of underetching corresponds to the displacement du of the upper edge of the sidewall lying directly under the mask (distance of underetching, figure 3.5) which can be observed and measured easily after the etching time t. du (3.2b) t Because of the fact that the sidewall is parallel to the edge of the mask window (all sidewall faces belong to the “crystallographic zone” – faces with a common axis – parallel to the mask edge), the underetching and the corresponding rate must depend on the direction of this mask edge characterized by the angle α relative to the primary flat (figure 2.1) as a direction of reference: vU =

vU = vU (α )

(3.3)

At different mask edges along directions with different angles α, the rates vU (α) have different values. Consequently the dependence of the rates of underetching on the angle α reflects the crystallographic symmetry of the wafer plane, figure 3.6a. This diagram can be experimentally illustrated by etching the so-called wagon-wheel structure: a series of narrow and long windows rotated by a small angle to each other and crossing in the centre, figure 3.6b. Sharp triangular mask regions result which will be underetched corresponding to the directions of their edges. This leads to an increasing shortening of the triangles with increasing underetching, figure 3.6c. 2

< 1 1 0 > = 1

2 1

1 µ m /m in 1

2

< 1 1 0 > d ir e c tio n o f fla t = = 0 °

2

a) Diagram of the rates of underetching on the {100}wafer (KOH-type etchant)

b) Wagon-wheel structure: principle of the mask (∆α = 15°)

Fig. 3.6. Rates of underetching ({100}-Si-wafer)

c) Wagon-wheel structure etched in TMAH (∆α = 3°)

24


< 1 1 0 >

The underetching of a mask window or of a masked island is determined by the etching behaviour of all upper sidewall faces. The positions of the upper edges of these faces can be principally calculated from the etching time and the rates of underetching. The resulting contour of underetching is the envelope of these edges in the plane of the mask on the wafer. This contour can be found using the WJC, too, demonstrated by the underetching of a rectangular convex corner of a mask shown as example in figure 3.7. It can be seen that sidewalls along certain directions α* assert themselves if their rates of underetching v* have a relative high value (v* must not necessarily be the maximum rate of underetching). A two-faced sidewall is typical for several etchants. Mostly the upper face of the underetching sidewalls is clearly revealed. By its angles α* and γTF it can be assigned to a certain crystallographic plane depending on the used etchant, table 3.1. The upper face is followed by a coarse and irregularly terraced lower sidewall face (“mountain side”, nearly {144}). In most cases such sidewalls are not suitable surface regions in a micro electro mechanical system and should be avoided if possible. Beside of the etch rate in the depth vT the values of α* and v* are characteristical parameters of an etchant. Consequently the etch mask design must take into account the expected underetching of edges and convex corners of the mask as well as all changes of the structure of the sidewalls and other free surface regions of the wafer. A special task is the design of mask extensions for the compensation of the underetching at convex corners (compensation masks), section 3.3.2. The calculation of their dimensions is possible including only faces with special rates v* and directions α* created at the convex corners. From this explanation it can be followed that any masked island will be completely underetched if the etching time is long enough. The underetching of any mask window is discussed below. The result of the etching process can be characterized by the etch depth at which the etch ground is positioned, by the underetching of the mask as well as by the generated sidewalls. The underetching corresponds to the upper edges of the sidewalls. The etch ground is limited by the lower edges of the sidewalls.

m a s k e d r e g io n o n {1 0 0 }-s u rfa c e

= *

u n m a s k e d r e g io n

< 1 1 0 >

a) Illustration by the WJC

b) SEM-picture: KOH

Fig. 3.7. Underetching of convex corners of the mask

c) SEM-picture: KOH-IPA


25

Table 3.1. Fast etching faces at convex -mask corners on {100}-Si wafers α* [°] 30.96

γTF [°] 76.37

{hkl} {411}

Etchant KOH

26.57 17–20 26.57

72.45

{311}

46.51

{313}

18.43

48.19

{212}

KOH TMAH KOH-NPA (NormalPropanol), KOH-IPA, EDP EDA, EDP, KOH-NPA, KOH-IPA TMAH

19–21

Reference [Kamp95, May90, Trieu97] [Puers90, Shik1-01, Trieu97] [Bean78, Bary95, Bäck92] [Abu84, Puers90, Wu87] [Trieu97]

Geometrical etch stop ({100}-wafer as example) The extreme minimum of the {111}-rates corresponding to rates of underetching if {111}-sidewalls are generated leads to final shapes and contours of underetching which are tangentially dominated by the {111}-sidewalls if the etching time is long enough, figure 3.8. In the case of the {100}-wafer the resulting deepening of any window approaches a concave pyramidal or rooflike shape having a rectangular contour of underetching orientated parallel to the -directions (0° or 90° relative to the flat). Because of the minimal etch rate of the {111}-faces no additional sidewalls are generated in the concave angles. In the case of a narrow window with the width b the etch ground is completely removed if the depth dT exceeds the amount b dT = . (3.4) 2 b C d

s to p

z (1 1 1 )

a y

5 4 ,7 4 ° a 2 2

a) Underetching at different times (dotted: etch ground)

b) Final shape

x

c) Geometrical etch stop

Fig. 3.8. Development of the deepening under any mask window (bold line)

26


The width of the etch ground decreases with increasing depth and completely disappears at last. The opposite {111}-faces meet in the depth. Continuing the etch process no noticeable alteration results. This state is called “geometrical etch stop”, figure 3.8c. Trenches with V-shaped cross sections (V-grooves) are received. Inside of small square mask windows “stopping” reverse pyramids are formed.

Joining of deepenings and partitioning of islands ({100}-wafer as example) The underetching of neighboured windows can produce regions of meeting sidewalls. The deepenings are joined. Analogous a convex island can be partitioned. These situations are illustrated in figures 3.9 and 3.10. Events of joining and partioning yield a considerable estrangement of the resulting structure from the mask.

a) Mask

b) Underetching

c) Joining

d) Etching of convex edges

Fig. 3.9. Joining of two deepenings

a) Mask (with corner compensation)

b) Underetching

c) Partitioning of the island

Fig. 3.10. Partitioning of an island

Etching of free convex edges ({100}-wafer as example) The removing of the mask of an wafer with an etched deepening leaves convex edges between the upper sidewall faces and the wafer surface. If the etching process will be continued thereafter new fast etching faces are created at these edges corresponding to the direction α of the edge which represents the zone axis.


27

Analogous to figure 3.5 these faces can be found by the WJC or by experimental measurements, figure 3.11. Also in this case these faces must not be plane or low index faces. In practice they can be described approximately by a characteristic angle of inclination γ*(α) having the rate v(γ*), table 3.2. A similar situation results after a complete perforation of the wafer by etching with two congruent windows at the front and back side, figure 3.12. If the etch grounds meet in the middle of the wafer convex edges are generated at which fast etching faces develop. In this case faces near vertical {110} occur blunting the convex edges in a first stage and producing concave edges after that [Zav94]. Continuing the etch process the vertical faces disappear and a geometrical etch stop follows, see above. Finally, free edges or corners are created after the complete underetching of convex regions of the mask or by joining of two deepenings, figure 3.9. Such edges are attacked by fast etching faces. Consequently the height of such protrusions is quickly lowered but traces never disappear completely. This is the consequence from the concave angle between the etch ground and the fast etching faces analogous to the situation illustrated in figure 3.5b. Inside this angle faces with a week curvature “{FWC}” develop if the etch rate minimum is week. p r o file b e fo r e 2 n d e tc h s te p

p r o file b e fo r e 2 n d e tc h s te p

t o p s u r f a c e

C *

fa s t e tc h in g fa c e { 1 1 1 } - s id e w a ll

to p s u rfa c e

C 2

C 1

fa s t e tc h in g fa c e s

e tc h g ro u n d

a) Sidewall along -direction

e tc h g ro u n d

b) Sidewall along -direction

Fig. 3.11. Etching of sidewalls with free convex edges fr o n t s id e o f th e w a fe r

{ 1 1 1 } -s id e w a ll

e n d p o s itio n o f th e v e r tic a l {1 1 0 }-fa c e

ta n g e n tia l s ta r tin g p o in t o f th e { 1 1 0 } - fa c e (2 {1 4 4 }-fa c e tte s ) { 1 1 1 } -s id e w a ll

{ 1 1 1 } - s id e w a lls in th e o th e r d ir e c tio n g e o m e tr ic a l e tc h s to p

b a c k s id e o f th e w a fe r

a) Schematic presentation of the blunting of {111}-face

b) SEM-picture: blunted {111}-face

Fig. 3.12. Blunting of {111}-faces after perforation of the wafer

28


Table 3.2. Fast etching faces on free convex edges on the {100}-silicon wafer (c curved) Sidewalls along -direction Etchant Measured γ* [°] KOH 30% 80 °C

21.95

KOH 25–60% 40–60 °C KOH 35% 80 °C TMAH 25% 80 °C

25.56 24±2 31.7

TMAH 25% 80 °C KOH-IPA 27–33% 70 °C

24±2 c 21–25

KOH-IPA 35% 80 °C TMAH-IPA 25% 80 °C

24±2 24±2

Sidewalls along -direction KOH 30% 80 °C γ1* = 17.6 γ2* = 73.5 KOH 40% 50 °C γ1* = 17.6 TMAH 25% 80 °C γ1* = 17.4 γ2* = 73.7 KOH-IPA 27–33% 70 °C γ* = 21.4– 24.5

Near low index plane {hkl} γ* [°] 19.47 {114} 25.24 {113} 25.24 {113} 25.24 {113} 25.24 {113} 35.26 {112} 25.24 {113} 19.47 {114} 25.24 {113} 25.24 {113} 25.24 {113}

Rate [µm/min]

Reference

1.89

Own values

1.07 0.98

[Li96] [Resnik] Own values

1.02 0.38

[Resnik] [Resnik]

18.43

{103}

1.94

Own values

21.80 18.43

{205} {103}

1.0

[Li99] Own values

18.43 26.56

{103} {102}

1.0–1.3

Own values

0.53 [Resnik] 0.94–1.11 Own values

Isotropic etching Acid etchants on the base of HF-HNO3-CH3COOH-H2O react with silicon in a transport controlled manner. Consequently, a predominantly isotropic removing of silicon is obeyed. The resulting shapes can be principally explained by the WJC implementing infinite sets of faces in all directions of space. Approximately a finite set of faces can be used which incrementally differ by a small angle. Another method to construct the isotropically changing shape is the elementary wave method known from optics as the Principle of Huygens [Kern81]. So the eikonal equation is suitable to solve the problem analytically [Zöb77]. Graphically spheres have to be put with its centre on the surface. The radius of the spheres is equal to the etch depth

Riso = viso ⋅ t

(3.5)

with viso as the isotropic etch rate and t as the etch time. The new shape is built by the envelope of all spheres. Figure 3.13 illustrates the following facts: - concave edges or points are rounded, - convex edges remain sharp.


Isotropically etched groove; the region of etch ground in projection of the mask window remains flat a) Profiles

Convex corner; mask edge in 90° direction to the flat

29

Rounding of concave etches, conservation of convex edges by the increasingly steep sidewalls, under the mask a sharping of edges occurs

Convex corner; mask edge in 45° direction to the flat

Concave corner; mask edge in 90° direction to the flat

Concave corner; mask edge in 45° direction to the flat

b) Top view Fig. 3.13. Effect of isotropic etching on silicon microstructures

The reverse situation results if a film is isotropically grown on a surface. Consequently, sharp edges cannot be truncated by isotropic etching but by isotropic overgrowth of a thick film. The isotropy of the etching process is an idealized conception. Really the propagation of the etch front is influenced by the diffusion of reactants and the convection of the solution. Both effects depend on the etched shape itself, on the geometry of the vessel and on the agitation. Especially a large etch depth cannot be reached homogenously over the whole wafer. However a short isotropic etch step can produce rounded concave edges in a given surface relief. Not at least because of differences of the reaction kinetics on different crystal faces a week dependence on crystallographic orientation is obeyed, too [Schwes96].

30


Because of the solubility of SiO2 in HF-solutions the usefulness of an oxide mask is strongly limited. Here silicon nitride is the better suitable mask material. 3.1.3 The importance of different oriented Si-wafers in the microtechnique: {100}, {110}, {112} and {111}

For the three dimensional structuring or shaping of masked silicon wafers in the microtechnique the importance of the orientation dependent etching can be attributed to the strong minimum of the etch rate of {111}-faces (a few 0.01 µm/min or less) relative to the rates of other faces (about 0.2 to 2 µm/min). This fact causes only a minimum underetching of mask edges with {111}-sidewalls. Moreover, these faces are atomic flat in the ideal case. Consequently, using a mask layout with edges suitable for the development of {111}-sidewalls very exact and lithographically defined shapes can be produced up to large vertical dimensions. For this the most important silicon wafer orientation is the {100}-one. For special applications {110}-wafers and exceptionally {112}- and {111}-wafers are also used.

Etching of {100}-wafers The {100}-wafer is the most used basis material of the silicon microtechnique. Here two -directions perpendicular to each other exist in the wafer plane, figure 2.1. Along mask edges which are parallel to these -directions {111}sidewalls inclined by

γ = 54.74° = arctan 2

(3.6)

are formed during the etch process (see figure 3.8c). Consequently the underetch rate is very low along such edges of the mask (up to less than a hundredth of the rate in depth) [Bean78]. Other directions with low indices are two -directions which are also perpendicular to one another. With the primary flat respective with the directions they include an angle of 45°. The formation of sidewalls along edges of a mask is in control of the etch rates of faces belonging to the crystallographic -zone, figure 3.5. Here, the minimum rates can belong to the {100}or {110}-faces. Depending on which of the minima is the lower one, either the vertical {100}-sidewalls (inclination to the wafer plane γ = 90°; underetch rate equal to the rate in depth) or the {110}-sidewalls (inclination to the wafer plane γ = 45°; underetch rate equal to 2 times the {110}-rate) are generated. The most important etchant representing the first type is the aqueous KOH-solution. This kind of etchants should be called “KOH-type”. Etchants on the base of aqueous solutions of Ethylene-Diamine-Pyrocatechol produce γ = 45° inclined sidewalls along -edges of a mask. Such a kind of etchant is called “EDP-type”. The addition of alcohol to KOH-type etchants can change this type into the EDP-type. Several etchants produce sidewalls which are combined by a vertical {100}-part under the mask followed by a 45° inclined {110}-part at the etch ground.

3.1 Fundamental principles of the generation of shapes {100}-Si KOH-type etchant

mask II

mask II

{100}-Si EDP-type etchant

mask II

mask II

31

{110}-Si KOH-type etchant

mask II mask II

Fig. 3.14. The same shape of a mask window (bold) results in different shapes of the etched deepening depending on the direction of the layout, on the etchant and on the wafer orientation

Along the edges of a mask with an angle between 0° and 45° to the directions the generated faces of sidewalls are not of a low index type which can be more or less terraced. Depending on the used etchant the produced sidewalls consist of one or two partial faces, see chapter 5. The diversity of etched hollows is illustrated by simulated shapes in figure 3.14. Using the same shape of the mask but with a different orientation on the wafer (45° rotated as an example) respectively placed on a wafer with another orientation ({110} as an example) quite different deepenings are etched.

Etching of {110}-wafers {110}-oriented wafers are of special interest for the microtechnique [Kend85, Bean78]. Two {111}-faces exist which are perpendicular to this wafer plane. They are generated as sidewalls along mask edges which include an angle of 35.26° relative to the primary flat (-direction: 54.74° to ), figure 2.1, because of their absolute minimum of etch rates of the -zone. These {111}-sidewalls show an extremely low underetching of the mask suitable to produce deep trenches with an extreme aspect ratio (ratio depth to width). The rates of underetching related to the -direction which is perpendicular to the flat reflect the symmetry of the -normal direction of the {110}-wafer, figure 3.15. Along mask edges in an angle of 90° relative to the primary flat (parallel to ) {111}-sidewalls are generated (absolute minimum of etch rates of the -zone), which are inclined by 35.26° to the wafer plane in this case. Grooves along this direction can result in a geometrical etch stop. Along mask edges which are parallel to the flat (perpendicular to respective parallel to ) the generation of sidewalls is controlled by the rates of the -zone. Here, the minimum rates belong to the vertical {110}-faces respective to the {100}-faces inclined by γ = 45° relative to the wafer plane. The dominant minimum of rates controlling the sidewall generation depends on the used type of etchant.

32


< 1 1 0 > 2

= = 3 5 ,2 6 ° < 1 1 2 > 1 = 2

1

< 1 0 0 >

µ m /m in d ir e c tio n o f fla t

Fig. 3.15. Rates of underetching on the {110}-Wafer (KOH-type etchant)

The {111}-sidewalls along the -directions of the mask edge are not completely vertical but have a narrow second facette at the bottom ({113}-face) in the case of KOH-etchants. This facette does not occur in TMAH-etchants [Sato99]. A problem using {110}-wafers is the very rough etch ground. The etched {110}-face tends to build microscopic terraces of symmetrically inclined faces of the type {144} or {155} [Sato99] resulting in furrows along . Consequently, applications which need a smooth etch ground have to be ruled out.

Etching of {112}-wafers The {112}-face belongs to the -zone similar to the {100}- and the {110}faces including the angles of 35.26° respective 54.74° with these faces. Considering a groove with mask edges along on the {112}-wafer the developing cross section will be defined by the etch rates of the -zone which must be rotated by 35.26° until the {112}-rate is directed in the depth of the wafer: vT = v{112}. The quality of the {112}-etch ground varies strongly depending on the etchant. The resulting opposite {111}-sidewalls have different inclinations: one sidewall is vertical, the other is inclined by 19.48°. z _ _ [1 1 1 ]

(1 1 1 ) (1 1 0 )

1 9 ,4 8 °

cross section along

(1 1 2 )

9 0 °

3 5 ,2 6 ° (0 0 1 )

_

(1 1 1 ) _ x [1 1 0 ]

cross section along

Fig. 3.16. Sidewalls arising in the etch process of an {112}-wafe{110}-faces.


33

Grooves along -direction can result in a geometrical etch stop having a cross section like a saw tooth. The sidewalls of a groove in -direction (90° to ) are symmetrical, figure 3.16.

Etching of {111}-wafers z

_ (1 1 1 )

_

[0 1 1 ]

(1 1 1 )

e tc h g ro u n d _

_ (1 1 1 )

[1 1 0 ]

_ (1 1 1 )

y

7 0 ,5 °

x

z

y

x _

[1 0 1 ]

a) Top: first step DRIE, b) Crystallographic relations bottom: second step ori- of the {111}-faces entation dependent etching

w in d o w o n (1 1 1 )

c) The resulting shape is limited by opposite {111}-faces (geometrical etch stop)

Fig. 3.17. Etching of an {111}-wafer: a cylindrical dry etched deepening is orientation dependently etched in a second step

{111}-oriented wafers are not useable for orientation dependent etching without additional process steps because of the extremely low {111}-etch rate. No useful depth can be etched and large underetching occurs. But the {111}-wafer can be of interest if a non orientation dependent etch process is performed before the orientation dependent one. In this way a first etch step by DRIE [Hu01] produces deepenings with nearly vertical sidewalls which are attacked by KOH in a second etch step resulting in caves bordered by {111}-facettes. The {111}-sidewall faces are inclined by 70.5°. Similarly by laser assisted etching [Alav92] the crystal is damaged in a region with vertical extension resulting in a strongly increased etch rate in the vertical -direction. The final shape corresponds to a geometrical etch stop. 3.1.4 Detection of the correct orientation between wafer and mask

The quality of the etched shape depends strongly on the correct alignment of the mask relative to the crystallographic orientation of the wafer. If the mask alignment is incorrect steeply increased underetching occurs, figures 3.6 and 3.15. Further the quality of sidewalls is changed respective decreased in the case of the important {111}-sidewalls which are broken by steps. Consequently, the misorientation between the crystal and the mask must be minimized. Three reasons are responsible for the misorientation:

34


- the difference between a crystallographic axis (, , ) and the normal of the wafer surface, - the difference between a crystallographic direction (standard ) and the wafer flat, - the difference between the wafer flat and the layout direction of the mask. Table 3.3. Structures for detection and alignment of misorientation (simulation corresponding to KOH 30 % 80 °C) Mask for {100}-wafer

Simulated contour of underetching 1 Series of grooves rotated by ∆α to each other

Criterion

Groove correctly aligned to : width of groove is minimum and width of neighbouring walls is maximum, see figure 3.18.

2 Pairs of rectangular windows rotated by ∆α to each other according to [Chang98] Misorientated grooves are widened by underetching. Finding two pairs of touching grooves: -m∆α and n∆α . The correctly oriented pair is rotated by (-m+n) ∆α/2 (angle of misorientation). 3 Structure according to [Pot85] {111}-sidewalls developing at the outer concave corners mark the correct -direction. The mask contains no edge near which can confuse. 4 Test structure according to [Steck91] {111}-sidewalls developing at the outer concave corners mark the correct -direction. The misorientation is the angle early stage of etching between the length direction of the mask and the final groove which is always correctly oriented. final V-groove


35

Etching of circular windows produces square deepenings (pyramids) dislocated by ∆x. The -directed diameter is signed by the square having minimum values ∆x to its neighbours. , x

arranged on diameters of a circular arc, see figure 3.19 6 Alignment „forks“ according to [Vang1-96] Symmetry of tapered ridges or etch grounds: the symmetric structure is correctly aligned to . The principle is similar to the wagon-wheel structure.

series of “forks” rotated by ∆α to each other Mask for {110}-wafer Simulated contour of underetching

Criterion Correctly aligned grooves have minimum ∆x.

, x

series of pairs of narrow grooves rotated by ∆α to each other

The misorientations between the crystal and the shape of the wafer are supposed to have tiny amounts (< 0.5°) in agreement with the producer of the wafers (see section 2.1.1). The detection of these misorientations can be done by x-ray

36


methods or by optical goniometry of inclinations of etched {111}-facettes relative to the wafer surface. Only the summarized misorientation of the second and third difference can be influenced by the lithographical process, assumed that they are known. For their detection a number of sensitive structures are proposed, table 3.3. These misorientation test structures use three principles: - the minimum underetching of a groove if it is correctly aligned in direction, - the development of correctly -directed edges of {111}-sidewalls independent on the edges of a mask window, - the symmetry of underetching of a series of mask windows rotated to each other by a small angle. The aim is a high sensitivity of the underetching relative to the misorientation after a short etching step. This requires small and accurate dimensions. The finding of the correct orientation should be done quickly and the standard equipment (optical microscope or profiling instrument) should be suitable for detection. F la t

n , =

Fig. 3.18. SEM-picture of test structure 1

Fig. 3.19. Two opposite series of structures are arranged on a circular arc marking a series of diameters with an angular pitch of ∆α, any following mask can be adjusted to this diameter

Figure 3.18 shows a SEM picture of test structure 1. Some of the structures allow to correct the adjustment of the mask in a following lithography process of the real structure, figure 3.19.

3.2 Chemistry and techniques of wet silicon etching

37


3.2.1 Chemical reactions and dependence on temperature

Aqueous alkaline solutions are the commonly used etchants for the anisotropic structuring of silicon: - inorganic solutions (KOH – potassium hydroxide, NaOH, CsOH, ammonia: NH3, hydrazine: N2H4), - organic solutions (TMAH – tetramethylammoniumhydroxide: N(CH3)4OH, EDP – ethylenediamine-pyrocatechol: C2H8N2-C6H6O2). The anisotropic etching reaction is a redox reaction with an electronic transition from the crystal to the etchant at the interface. The hydroxide ions as well as the water molecules affect the etching process. The different cations have an indirect influence (e.g. different hydration influences the activity of the water molecules) [Früh1-97]. The simplified process described by Seidel et al. [Seid86] is shown in the following equations: Si + 2 OH–

à

Si(OH)22+ + 4 e–

(3.7)

4 H2O + 4 e–

à

4 H2O–

(3.8)

4 H2O–

à

4 OH– + 2 H2

(3.9)

Si(OH)22+ + 4 OH–

à

Si(OH)62–

(3.10)

à

SiO2(OH)22– + 2 H2O

(3.11)

à

SiO2(OH)22– + 2 H2

(3.12)

respectively Si(OH)22+ + 4 OH– The summarized equation is: Si + 2 OH– + 2 H2O

In the first step the hydroxide ions react with the silicon. Electrons will be removed and injected into the conductivity band of the silicon lattice. Because of its positive charge the resulting Si(OH)22+-ion is still adsorbed at the silicon surface. During the reaction course the electrons leave the crystal and are absorbed by the water molecules in the solution. These molecules decompose into new hydroxide ions and molecular hydrogen. The OH--ions react with the Si(OH)22+-ions and form a Si(OH)62–-_respectively a SiO2(OH)22–-complex. Another description is given by Allongue et al. [All93] in which the silicon does not directly react with the hydroxide ions but with the water molecule. The hydroxide ions only serve as a catalyst and complexing agent. The chemical reaction consists of several parts which are presented in equations (3.13)–(3.16). An isotropic etch step using HF is preceded to each anisotropic etching process.

38


Thereby a hydrogen terminated surface is produced. The formed Si-H bond is weekly polarized as the hydrogen is slightly more electronegative than the silicon. This bond is hydrolyzed releasing molecular hydrogen. Because of the negative polarization of the hydrogen a substitution is only possible with strong nucleophiles, that means the reaction is catalyzed by OH–-ions. Repulsive forces between neighbouring Si-H bonds favour the chemical hydrolization at dihydrides, for instance at the (100)-surface.

S i

H

S

(-) i( + )

S i

H

+

(-)

O H

H

S i

O H -

O H 5 E(+

S i

(-)

(-)

)

(3.13)

H +

H

H

Because of its higher electronegativity the hydroxyl group polarizes the Si back bonds. The attack of the water molecule is now preferred. The hydroxyle group is attached to the positively polarized and the hydrogen to the negatively polarized Si atom. The Si-Si back bond is ruptured. (-)

S i

S i (-)

(-)

O H S i + H O (+ )

H

S i H

O H S i O H H S i

+ H O

S i H S i

O H

O H S i O H

H

(3.14)

H

The second back bond of the Si atom to the crystal ruptures in the same way. The strong alkaline medium keeps the Si as complex in solution. (3.15) HSi(OH)3 + H2O + 2OH– àSi(OH)62– + H2 Si(OH)62–

à

SiO2(OH)22– + 2H2O

(3.16)

It results the summarized equation as described by [Seid86] (see 3.12). The etch rate corresponds to the rate of the chemical reaction and depends on the temperature T. This temperature dependence of etch rates can be described by an ARRHENIUS-equation

v = K ⋅e

−

EA R⋅T

(3.17)

with K – pre-exponential constant, R – universal gas constant, EA – energy of activation by ARRHENIUS, T – absolute temperature. Figure 3.20 shows the experimentally determined values of etch rates in dependence on temperature (own values). The graph of the function

æ1ö ln v = f ⋅ ç ÷ èT ø

(3.18)

results in straight lines. That means the ARRHENIUS-equation is valid and EA and K can be determined. The values of EA and K depend on the used etchant as well as on the etched crystal surface. EA is constant at small temperature differences. Therefore a determined etch rate v1 at a temperature T1 can be converted into an etch rate v2 at a temperature T2:


v 2 = v1 ⋅ e

é EA æ 1 1 ê ⋅çç − ëê R è T1 T2

öù ÷ú ÷ ø ûú

39

(3.19)

If the activation energies of etch reactions are equal, then the selectivity does not change with the etch temperature. In this case the selectivity corresponds to the ratio of the pre-exponential constant K. T [° C ] 8 0

7 0

6 0

d e p th e tc h r a te [µ m /m in ]

1 0 .0

1 .0

2 .8

2 ,9

v {1 1 0 } K O H

3 0 %

v {1 1 0 } K O H

4 0 %

v {1 0 0 } K O H

3 0 %

v {1 0 0 } K O H

4 0 %

3 ,0

1 /T 1 0 3 [K -1 ]

Fig. 3.20. (100)-Si depth etch rate in dependence on the etch temperature (ARRHENIUS representation) [Früh2-93]

The etching characteristics of {100}- and {110}-Si at ultra-high temperature ranges near the boiling point of KOH-solutions were investigated by [Tana03]. The etch rates for KOH-concentrations of more than 32 wt% are 4–20 times higher than those at 80 °C. The received etch surfaces are very smooth. 3.2.2 Influence of composition

The kind of the components as well as their concentration essentially determine the etch rate and the character of an etchant. Figure 3.21a shows the dependence of the etch rate of (100)-silicon on the concentration of an used KOH-solution [Seid90]. The course of the graph can be described by the following equation

[

]

1

vT = k '⋅ H 2 O ⋅ [KOH ] 4 4

(3.20)


< 1 0 0 > - e tc h r a te [µ m /m in ]

40

1 .5

1 .1

0 .7

1 .4

1 .0

0 .6

0 .9

0 .5

1 .3 1 .2

v

. d

~ [H 2

O ] [K O H ] 4

1 /4

1 .1

0 .8

1 .0

0 .7

0 .9

0 .6

0 .8 0 .7

0 .5 1 0

2 0

3 0

4 0

K O H - c o n c e n tr a tio n [% ]

a) by [Seid1-90]

5 0

0 .4 0 .3 0 .2 0 .1

1 0

2 0

3 0

4 0

K O H - c o n c e n tr a tio n [% ] a t th e K O H -IP A e tc h a n t

b) by [Pri73]

5 0

0 5

1 0

1 5

2 0

2 5

T M A H - c o n c e n tr a tio n [% ]

c) by [Schna91]

Fig. 3.21. (100)-Si depth etch rate in dependence on the concentration of the etch solution

with k´ – proportionality constant. The etch rate is limited by the quantity of water in the case of highly and the quantity of OH--ions in the case of lowly concentrated solutions. The silicon etch rate increases for several times using microwaves with the frequency f = 2.54 Hz. Investigations were carried out in aqueous KOH-solutions by [Dziu00]. The depth etch rate of KOH-solutions and their dependence on the concentration essentially changes when isopropylalcohol (IPA) is added until saturation, figure 3.21b [Pri73]. Such a solution corresponds to the EDP-type mentioned in section 3.1.2. The selectivity of orientation is strongly changed, too: - The etch rates are decreased compared with KOH-solutions without IPA at the same concentration. - The {111}-etch rate stays minimally. - The {100}-etch rate decreases nearly by fifty per cent. - The {110}-etch rate becomes smaller than the {100}-etch rate. Etching with TMAH-solutions is described in detail by [Schnak91]. The {100}etch rate at 80 °C has a maximum at 2 % TMAH, figure 3.21c. The etch rate decreases linearly with an increase of the concentration, however the surface quality increases. Diluted solutions easily form hillocks [Choi98]. The etching characteristics also change by adding IPA as a surfactant to the aqueous TMAH solutions [Merl93]. The TMAH-IPA system is an etchant of the EDP-type. The etch rates of (100)-Si crystal planes decrease linearly with decreasing IPA concentration and are lower than those for KOH-IPA solutions. The addition of IPA to TMAH solutions reduces the undercutting and leads to smoother sidewall surfaces. Because of the chemical etch reaction and the interaction with the atmosphere the use of an etchant always changes its chemical composition during the etch process. That means components of the etching solution are used, silicon is enriched, carbonate is formed with the CO2 of the air and high-volatile components escape. Reproducible etching results can be reached at a controlled composition of the etchant that should be corrected if necessary.


41

The silicon content of aqueous KOH solutions has an influence on the etching behaviour of single crystalline Si [Dor97]. The etch rate of the {100}-planes is not much influenced, but the undercutting of convex corners is more pronounced with increasing silicon content. Furthermore, metallic impurities dissolved in KOH solutions show various effects on the anisotropic etching of silicon [Hein97]. These are changes of the anisotropy, the surface roughness of the {100}- and {111}faces and the shape of convex corners. 3.2.3 Influence of doping

The etch rate of anisotropic solutions can be influenced by the doping level of the Si. High concentrations of phosphorus and germanium strange atoms lead to a small reduction only, but concentrations of boron higher than 5∗1019 cm-3 lead to a tremendous reduction of the etch rate. Figure 3.22 shows such doping dependence using KOH-etching solutions [Seid2-90]. An explanation for this effect exists at the interface between the highly doped p-silicon (p - positive through lack of electrons) and the electrolyte. For p-doping higher than 2.2*1019 cm-3 the Fermi-level, which is in the forbidden band for a non-degenerate semiconductor, goes down into the valency band. The semiconductor shows a quasi-metallic character. The region of space charge being expanded in the lower doped region contracts to a few layers of atoms and disappears. The electrons, which are injected into the crystal during the oxidation (eq. (3.8)) have a very low shelf life. Immediately they recombine with the holes being available in a high concentration. Thus there are not enough electrons for the following reduction step. According to the law of mass action the electron concentration of semiconductors is reversely proportional to the concentration of holes. That means, if four electrons are necessary, the etch rate decreases reverse proportionally to the fourth potency of the boron doping. Using EDP-solutions instead of KOH-solutions the etch rate is considerably stronger influenced by the p-doping. The effect is used to produce etch stop layers realizing mainly cantilevers or membranes which can be etched by this method, see also chapter 6 [e.g. Ios02, Lap98]. This etch stop is called intrinsic or p+-etch stop. A schematical example is shown in figure 3.23. Limited temperature loading after the boron doping and high inner mechanical stresses of the layers are disadvantages of this process. A high dosed implantation of nitrogen is a possibility to reduce the stresses of the layers. An electrochemical stop is another possibility to stop the etch reaction [Pal82, Pal85]. The etch process ends by applying a positive voltage to the silicon which is about 0.7–1.0 V higher than the potential of the open circuit. If the positive prevoltage of the silicon is high enough then electrons injected in the crystal can not reach the lattice surface. The reduction step (see eq. (3.8)) cannot be executed. An electrochemical etch stop can also be performed with a pn-transition layer in Si [Seid86]. A positive voltage is applied to the Si wafer, a negative one to the counter electrode. In dependence on which side of the transition is exposed to the etchant, a voltage drop occurs at the pn-transition. Thereby a positive voltage between wafer and electrolyte is prevented and the etch process starts. Reaching the

42


transition layer during the etching, the voltage drop disappears and the tunnelling back of the electrons from the crystal to the electrolyte is no longer possible and the etch process stops. A simple etch cell with a three electrode configuration is schematically presented in figure 3.24 [Bey96]. 1 0 2

4 2

e tc h ra te [µ m /h ]

1 0

1

8 6 4 2

1 0

0

8 6

1 0 2 4 4 2 5 7 4 2

1 0 8 6 4

% %

% %

K O K O K O K O

H H

H H

-1

2 1 0

-2

1 0

2

1 7

4

6 8 1 0

1 8

2

4

6 8 1 0

1 9

4 2

c o n c e n tr a tio n o f b o r o n [c m

-3

1 0

2 0

]

Fig. 3.22. Dependence of the (100)-Si etch rate on the concentration of B in Si [Seid2-90]

p o te n tio s ta t

S iO 2

S i h ig h ly d o p e d S i a s p + - e tc h s to p la y e r

n -S i

e tc h a n t

p -S i

r e fe r e n c e e le c tr o d e

Fig. 3.23. Thin silicon membrane produced by p+-etch stop technique

c o u n te r e le c tr o d e

Fig. 3.24. Etch cell – three electrode configuration [Bey96]


43

Advantages of this etch stop technology are: - no inner stresses, - good reproducibility, - possibility of producing membrane structures with low variation of thickness and low inhomogeneity. Examples are presented in [Lap98, Kühl94, Ace94]. The necessity of an electric field and with it the necessity of an etch cell is disadvantageous. Only the etching of a single wafer is possible. A new contactless electrochemical etch-stop is described by [Ash98]. The new technique is based on a gold-silicon-TMAH galvanic cell. 3.2.4 Equipment and etching technology

In principle an etch apparatus consists of following pieces: - heat insolated vessel for the etching solution, - heater with temperature control, - cooling for condensation and restitution of vaporized components of the etching solution, - equipment for a constant movement of the etch medium. All parts which are in contact with the solution have to be of an alkaline resistant material, for instance PTFE (polytetrafluoroethylene) or PFA (perfluoroalkoxylalkan). Quartz glass can be used alternatively although it is not completely resistant to alkaline. For the laboratory a beaker (preferably with double walls) with thermometer, temperature controlled heating and magnetic stirrer could be sufficient. Etching can be improved by using commercial reflux cooling, by overflow circulation and better agitation (e.g. N2-bubbling). Compact etch apparatus for larger etch volumes are available. The most important advantages are: - a higher throughput of wafers, - a better realization of an optimal circulation resulting in a better homogeneity and a higher quality of the etch ground, - constant values of volume, temperature and concentration resulting in a constant etch rate over a long period and a better reproducibility. A disadvantage can be the low flexibility when changing the composition or even the etchant. A schematic sketch of an example is shown in figure 3.25. For the generation and the control of the etch solution as well as for the etching process itself only pure chemicals and deionised water should be used. Working under clean room conditions is recommended. The etching process has to be prepared as follows: first the etchant is heated to the etch temperature. In the meantime the Si-wafer must be pre-treated:

44


c o o lin g w a te r c o o lin g c o v e r e tc h a n t N 2

- b u b b lin g

te m p e ra tu re s e n s o r c a r r ie r w ith s ilic o n w a fe rs in n e r b a s in w ith o v e r flo w o u te r b a s in te flo n p la te w ith h o le s h e a te r c ir c u la tin g p u m p c a s e w ith c o n tr o l u n it

Fig. 3.25. Schematical sketch of an etch apparatus

- Because of an easier handling the wafer is put into a special carrier. - To receive a homogeneous etch ground the native oxide layer has to be removed. Therefore an etching in 4 % HF (so called HF-dip) is carried out for about one minute. Then the wafer is rinsed in deionized water. - The wafer is warmed up in a water bath to etch temperature. Thus the etch reaction can start immediately after putting the wafer into the etch solution without any delay. Now the wafer together with the carrier is placed into the tempered etch medium. After passing the required etch time the wafer is removed from the etchant and put into a 2 % acetic acid solution for about two minutes. A chemical neutralization takes place. The etch reaction interrupts suddenly. Afterwards the wafer is rinsed in deionised water about 20 minutes. The wafer is dried in a heater or in a nitrogen stream. After the etching process the achieved etch depth and the quality of the etch ground can be determined. As mentioned in 3.2.2 a permanent analytical control of the composition of the etch solution is necessary. The alkaline and carbonate contents can be analyzed by neutralization titration. The content of dissolved silicon can be easily estimated by the determination of the weight of the Si wafer before and after the etching. The silicon contents can be exactly determined photometrically or colorimetrically [Früh2-93]. 3.2.5 Isotropic etching

The isotropic etching is known as a process which is independent on the crystal orientation of silicon. It forms round structures with any angle to the crystal direction. An isotropic etch solution consists of an oxidizing and an oxide removing


45

component. A common etchant is the system of HF-HNO3-solutions. Additionally water or acetic acid are used as diluents. The chemical reaction can be described as follows: The HNO3 serves as the oxidizing agent. Si will be oxidized to SiO2. After that the hydrofluoric acid removes the formed oxide: à

SiO2 + 6 HF

SiF62- + 2 H2O + 2 H+

(3.21)

The etching solution contains traces of HNO2 which is a stronger oxidizing agent than the nitric acid. The HNO2 enriches autocatalytically by reaction with the formed NO respectively HNO3. Therefore it is difficult to control and reproduce the etching process. 1 0 0

1 0 0

9 0 8 0

O H N

8 1 0

w t.-%

H F (4 9 % )

H F (4 9 % ) 1 0 0

7 0

6 0

5 0

H

4 0 2

3 0

2 0

1 6 0

4 0

7 5 5 5 4 2 3 7 2 5 1 6 7 ,5

3 0

2 0

1 0 1 0 0

O

0

1 0 0

w t.-%

) % i (7 0

1 0 0

4 7 0

5 0

5 6 4 4 3 8 2 5 1 5 7 ,5

2 0

3

3 0

6 0

% ) (7 0

1 8 7 7 5

4 0

7 0

3

0 5 0

6 0 5 0

O H N

8 0 7 0

9 0

7 0

6 0

5 0

4 0

H C 2

3 0

H 3

O

2 0

1 0 0

2

O H N 3

H F (4 9 % )

% ) (7 0

H 2

O

s h a rp e d g e s , ro u g h s u rfa c e

H C 2

H 3

O 2

s h a rp e d g e s , ro u g h s u rfa c e

s h a rp e d g e s , m e t s u rfa c e

s h a rp e d g e s , s m o o th to ro u g h s u rfa c e

ro u n d e d e d g e s , s m o o th s u rfa c e

ro u n d e d e d g e s , s m o o th s u rfa c e

Fig. 3.26. Etch rate [µm/min] and quality of etched Si surfaces in the system HFHNO3-H20

Fig. 3.27. Etch rate [µm/min] and quality of etched Si surfaces in the system HFHNO3-CH3COOH

46


Depending on this fact and of course on the constitution and temperature of the etching solution the etch rates vary in a wide range [Schwes96, Seid91]. Figures 3.26 and 3.27 show the dependence of the etch rate on the constitution of the etching systems HF-HNO3-H2O respectively HF-HNO3-CH3COOH at 25 °C [Robb59, Robb60]. Smooth surfaces are only obtained at concentrations of HNO3 between 30 and 90% and of H2O < 10% respective CH3COOH < 20% [Robb76]. Further, at certain etchant constitutions a considerable influence of the doping level of silicon is obeyed [Seid91].

3.3 Etch mask design and simulation of silicon etching

3.3.1 Calculation of the etch mask

The design work consists of the definition of two dimensional shapes of mask windows and in the calculation of their dimensions and relative positions. The etching process starts at the surface inside the windows producing deepenings which are characterized by their depth, the shape of sidewalls and the underetching. The depth can arrive the back side of the wafer or the etch ground of a deepening coming from the back side resulting in a perforation or a void. By underetching two or more neighboured deepenings can grow together (joining, see figure 3.9). The orientation dependence of the etch process makes it difficult to conclude from the system of mask windows to the resulting three dimensional structure and more than ever to conclude from a wished shape to the necessary mask (which is a non trivial and ambiguous problem). The usual proceeding consists in at least two steps: calculation of the geometric parameters of the mask and checking the result by simulation of the etching process. The calculation of the etch mask can be divided in three steps, figure 3.28: 1. the calculation of the dimensions and positions of the basic shapes of the mask (windows, islands, rectangular or similarly simple), eventually on both wafer sides in view of the wished depths/heights, shapes of sidewalls, residual thicknesses, perforated regions, 2. the merging of the basic shapes to a geometric complex mask, 3. the addition of mask extensions for the compensation of underetching at convex corners (compensation masks).

Calculation of basic shapes The ground plan of the objective structure should be splitted into series of simple rectangles of windows or islands with equal depth respective height. Each series of these basic structures can be collected to construct a mask producing or increasing a certain etch depth, figure 3.28, step 1.


47

For the calculation of the mask of the basic shapes it is useful to take into account the knowledge of the underetching and the inclination γ of the sidewalls resulting in a polygon of the upper edge (contour of the deepening at the mask level) and a polygon of the lower edge in the depth d (contour of the deepening at the etch ground). With regard to a straight edge of the mask the upper edge belonging to it is displaced by the distance of underetching dU whereas the lower edge moves with increasing depth along the inclined sidewall resulting in a projected distance relative to the mask edge (projected width p of sidewall). Having a rectangular mask window of the width w the distances of the opposite upper respective lower edges of the resulting trench can be calculated: d UE = w + 2 ⋅ dU

(3.22)

d LE = w + 2dU − 2 p

(3.23)

respective

Of course, the reverse calculation of the width w of a window necessary for a wished width of a deepening is possible in this simple case. Analogous relations can be formulated for a wall resulting from a masked island of the width w. The relations related on - or -directions are given in table 3.4. Table 3.4. Dimensions of trenches or walls resulting from a mask window resp. island on the {100}-wafer Direction of edge Type of etchant

along KOH- or EDP-type

along KOH-type

along EDP-type

Underetching dU

dU « d

dU = d

dU < d

Sidewall face

{111}

{100}

{110}

Sidewall inclination γ

γ = arctan 2 = 54.74°

γ = 90°

γ = 45°

Projected width of sidewall p

p=d/ 2

p=0

p=d

Trench: distance dUE of opposite upper edges

dUE = w + 2dU

dUE = w + 2d

dUE = w + 2dU

Trench: distance dLE of opposite lower edges

dLE = w + 2dU – 2d / 2

dLE = w + 2d

dLE = w + 2dU – 2d

Wall: distance dUE of opposite upper edges

dUE = w – 2dU

dUE = w – 2d

dUE = w – 2dU

Wall: distance dLE of opposite lower edges

dLE = w – 2dU + 2d / 2

dLE = w – 2d

dLE = w – 2dU + 2d

48


Merging of basic structures 1. Mask definition by rectangular basic shapes 1 window 1 island (mass)

1 window 1 island (mass) 4 islands (springs)

1 window 1 island (square)

4 windows (trapezoidal)

2. Merging of basic shapes

3. Addition of compensation masks: quadrates are used 1 window 1 island (polygonal)

4 windows (trapezoidal)

4. Simulated silicon structure (SIMODE)

Fig. 3.28. Steps of the mask design for an elastic spring-mass-system to be etched in KOH; left: front side (depth 425 µm); right: back side (depth: 100 µm); the lower edges of the windows and the mass islands should be congruent; the width of springs is defined by the lower edges of the spring islands

After the calculation of the dimensions of all windows or islands of a series the relative positions must be stated corresponding with the ground plan using an unique system of coordinates for all masks of both sides of the wafer. For this the calculation of the coordinates of the corners of all windows and islands of a series


49

and, in the case of overlapping of windows or islands, the coordinates of intersection points (“merging”) must be done. The result is a set of series of pairs of coordinates. Each set describes a polygon surrounding a more or less complex window or island, figure 3.28, step 2.

3.3.2 Addition of compensation masks Table 3.5. Mask extensions for the compensation of underetching of convex corners Shape

Calculation

Square

a= a

Rectangle

d ⋅v* vT (sin α * + cos α *)

v* − b ⋅ cos α * vT sin α *

d⋅ a

a= b

b: preset -beam

d⋅ l

b

l=

b: preset

T-L-shape

b

l1

v* 1 − b ⋅ cos α * 2 vT sin α *

d⋅

l2

l1 =

h

v* 3 − b ⋅ cos α * 2 vT −h− 1 b 2 sin α * h and b: preset

-beam

l

b

b = 2d l ≥ 3d

50


The convex corners of islands and merged polygons will suffer a heavy underetching which can not be accepted in the most cases. The extension of the mask in the surrounding of a corner (compensation mask) provides remedy: the front of underetching of the compensation mask must contract to the corner until the moment of achieving the etch depth. The most important cases are convex corners built by perpendicular mask edges of -type, figure 3.6. Because of the small underetching of these mask edges the contraction point differs from the point of the mask corner. The underetching of convex corners will be dominated by sidewalls with a high rate of underetching (near but not equal the maximum) characterized by a certain rate v* and a certain angle α* relative to the -direction (or {100}-wafer flat). The starting position of these sidewalls must have the distance d⋅v*/vT from the contracting point. Beside of the compensation of the underetching of the mask the shape of the sidewalls at the corner must be considered. Sidewalls coming towards the constriction point replace the pyramidal {111}-corner, sidewalls coming sideways leave the pyramidal {111}-corner. For the design of compensation masks a simple rule should be obeyed: a slightly attacked corner can be rather accepted than a residual structure. Consequently, the compensation mask should be a little smaller than calculated. Typical simple mask extensions for corner compensation are summarized in table 3.5 together with the formulas for its design [Abu84, Off92, Puers90, Zhang96]. An example of application shows figure 3.28, step 3. In special cases combined shapes can be used [May90]. The region at the etch ground underneath the compensation mask can have uneven ridges (in the order of 1 µm) left by the front of underetching sidewalls [Kamp95]. This should be the consequence of a weak minimum of the {100}-etch rate. Using the {110}-wafer the underetching of convex corners built by directions can be compensated by rhombic mask extensions [Kim98]. 3.3.3 Simulation and design tools

To check the mask layout, a simulation tool can be advantageously used especially in the case of more complicated situations concerning the interaction of underetchings at all windows or islands of a complex mask structure. An etch simulator can be based on two different models: - the generation of etched shapes by the construction of Wulff-Jaccodine, - the generation of etched shapes by an atomistically modelled removing of volume units.

The Wulff-Jaccodine-based model At the edges and corners of the two dimensional contours of the mask a lot of infinitesimally extended mathematical planes are tangentially positioned. Then these planes are displaced by their normal vector of the length ∆t·v{hkl} into the crystal


51

volume. From the lines of intersection of the displaced planes the etched surface can be calculated considering the concave or convex character of the contour. Because of the possibility of overlapping of shapes resulting from different mask windows the etch time must be divided into short steps for finding such situations in which new tangential planes must be included before the next time step. A difficult problem consists in the occurence of saddle points with a mixed concaveconvex shape. To overcome this problem the simulation can be carried out in a first step with a two dimensional statement: planes are substituted by lines as upper and lower edges of the sidewalls. These lines are displaced by ∆t·vu(α) respective ∆t·vl(α) (vl – rates of the lower edges) and the resulting contours of underetching respective of the etch ground are determined. From these the calculation of the faces of sidewalls follows resulting in a relief etched in a thick silicon plate (relief mode) [Früh1-93, Ziel95]. Alternatively the two dimensional cross section of an etched body can be simulated analogous to figure 3.1.3 (cross section mode). The most used Wulff-Jaccodine based simulator is SIMODE (relief mode) respective Qsimode (cross section mode) (trade marks of GEMAC Chemnitz and AMTEC Chemnitz, Germany). Preferences are the extensive possibility for fitting the database to real etching processes [Ziel01], the non complicated graphic interfaces to the software of mask design systems and FEM simulators [Ziel01] and the relative low demands on the computer.

The atomistically based model An obvious basis for the simulation of etching processes can be the modelling of the separation of a surface atom related to the bonds to its neighbours, see section 3.1. Because of the very large number of atoms belonging to a silicon microstructure the atoms are substituted by volume cells having analogous properties: maximum four bonds to neighbours in tetrahedral configuration (“cellular automata”) [Than94]. Cells on the surface have less bonds and can be attacked by the etchant. The cells can be in one of two states: present or absent. The crystal to be etched will be divided into a number of cells and the surface region attacked by the etchant must be defined. Then the cells in this region are checked with regard to the state of their neighboured cells followed by the decision about their own state. The basis for the decision is a set of rules related to the number and the kind of bonds and affected with a probability for the removing of a cell during a time step derived from the experimentally determined rates of the low index faces: v{111}, v{110}, v{100}. After the etching time a certain number of cells are removed (transferred into the state “absent”) resulting in a crystal shape described by discrete present cells. The simulator based on this model is named AnisE (trade mark of IntelliSense, Santa Clara CA, USA) [Mar98]. The preference of this model is that it has no problems with saddle points because of the unambiguous neighbourhood of each cell. But the complete adaptation to the etch rates of any face {hkl} produces complicated rules. An additional expense is necessary to calculate the geometric representation of the etched shape suitable as an interface for FEM calculations [Steff00].

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Etch mask design tool In practice the shape to be produced by etching is defined by its function. The task is the computer aided generation of the suitable etch mask for the target shape. In view of the ambiguous character of the relation between the etched shape and the suitable mask an iterative way must be used: - the mask design with regard to the target shape and characteristic features of the etching process according to the previous sections, - the check of the mask using an etch simulator, - the redesign of the mask with necessary corrections, - a new check with the etch simulator. For shortening the time necessary for the first design and the following corrections suitable design tools are desirable. Such a tool named EMaDe (trade mark of Amtec Chemnitz, Germany), as an example, is based on the considerations described in ections 3.3.1 and 3.3.2 and corresponds to the simulator SIMODE in view of the file formats for the mask and for the etchant. This tool is focused on the {100}-Si-wafer and permits to design the etch mask starting with dominant dimensions of the target shape. The addition of mask extensions for the compensation of underetching of convex corners is also supported.

3.4 Basic processes of the bulk-silicon-microtechnique

3.4.1 Shape definition by variation of etch steps

The shape of an etched silicon microstructure is substantially defined by the windows in the used etch mask. The layout of these windows must be matched to the used etchant and to the etching time. The most simple etching process needs one mask at one side of the wafer with a passivated back side and one etch step in a definite solution. A certain shape will be produced. Using the same mask but another type of etchant some features of the shape come out differently. In addition it is possible to modify the structure by a sequential use of different types of etchant. Also a second mask can be activated after a certain etching time resuming the etch process in the same etchant or in another type of etchant. A sequence of etching steps using different masks and different types of etchant is conceivable, too. As well the etching process can act sequentially or simultaneously on both wafer sides. In this manner a large number of series of process steps (“Basic Processes”) can be formulated in principle by the combination of different masks and etchants resulting in a lot of different types of structures. Further the isotropic etching and the anisotropic dry etching can be implemented in this concept of basic processes as additional “types of etchant”. In view of the very large number of combinations the considerations must be restricted to practical cases.


53

Table 3.6. Si-etch steps: etching only at one wafer side (description of an etch step ne with n – number of acting mask and e – etchant) Mask No. 1 1 1, 2 1, 2 1, 2

Used etchants e1 e1, e2 e1 e1, e2 e1, e2

Number of etch steps 1 2 2 2 3

Mask-No. / Etchant Step 1 Step 2 Step 3 Step 4 1e1 1e1 1e2 1e1 2e1 1e1 2e2 1e1 2e1 2e2 1e1 1e2 2e2 1e1 1e2 2e1 1, 2, 3 e1 3 1e1 2e1 3e1 1, 2, 3 e1, e2 3 1e1 2e1 3e2 2e2 3e2 1e1 1e1 2e2 3e1 1, 2, 3 e1, e2 4 1e1 2e1 3e1 3e2 1e1 2e1 2e2 3e2 1e1 2e1 2e2 3e1 1e1 2e1 3e2 3e1 1e1 1e2 2e2 3e2 1e1 1e2 2e2 3e1 1e1 1e2 2e1 3e1 1e1 1e2 2e1 3e2 1e1 2e2 3e2 3e1 1e1 2e2 2e1 3e1 1e1 2e2 2e1 3e2 1e1 2e2 3e1 3e2 three masks: 1, 2, 3; two types of etchant: e1, e2 (KOH, EDP, ISO, DRY)

Description of combination 1e1 1e1/1e2 1e1/2e1 1e1/2e2 1e1/2e1/e2 1e1/1e2/2e2 1e1/1e2/2e1 1e1/2e1/3e1 1e1/2e1/3e2 1e1/2e2/3e2 1e1/2e2/3e1 1e1/2e1/3e1/3e2 1e1/2e1/2e2/3e2 1e1/2e1/2e2/3e1 1e1/2e1/3e2/3e1 1e1/1e2/2e2/3e2 1e1/1e2/2e2/3e1 1e1/1e2/2e1/3e1 1e1/1e2/2e1/3e2 1e1/2e2/3e2/3e1 1e1/2e2/2e1/3e1 1e1/2e2/2e1/3e2 1e1/2e2/3e1/3e2

As an example table 3.6. shows the combinations resulting by use of 3 masks and 2 different types of etchants which act only at one side of the wafer. In the case the wafer should be structured on both sides it has to be differentiated between processes acting at each side separately and those acting on both sides simultaneously. In the first case the description according to table 3.6 can be used separately for each side. Examples are dry etching processes or processes in which both sides are exclusively etched in different etchants with passivation of the alternative side. In the second case the current etchant acts on both sides simultaneously in all opened windows of the front and back side masks. The different etch steps on both sides must be compatibly interlinked taking into account the respective etched depths. The resulting basic process can be completed by combining compatible steps. The following facts are to consider: - The arbitrary names e1, e2 of the etchants should be put in concrete terms, for example: K (KOH), E (EDP), I (ISO), D (DRY). - The problem of incompatible steps on one side must be solved by passivation of the alternative side. - The total etch depth in a window can be realized by etching in two or more steps.

54


If the etch grounds of windows at the front side and at the back side meet the wafer is perforated. The etching process can be continued in the last etchant modifying the shape of the silicon structure. This step is described by adding only the symbol of the etchant indicating the previous perforation, for example: 1.1K/2.2K/K. Table 3.7. Combinations of Si-etch steps: etching at both wafer sides (examples) (description of a single etch step: f.be with f resp. b – number of the active mask at the front or back side p – passivated (no window), e – echant Mask Used Mask-No. / Etchant Description of process steps: No. etchants step 1 step 2 step 3 step 4 step 5 f.b etchant conditions One side processes to be combined: 1 front side step, 1 back side step, 1 etchant only f: 1 e1 1e1 1e1 e1 1e1 1e1 b: 1 Two possible combinations (e.g. KOH-etchant): f: 1 K 1K 1.1K d(f1)=d(b1) b: 1 K 1K f: 1 K 1K 1K 1.pK/1.1K d(f1)>d(b1) b: 1 K 1K One side processes to be combined: 2 front side steps, 2 back side steps, 1 etchant only f: 1, 2 e1 1e1 2 e1 1e1/2e1 e1 1e1 2 e1 1e1/2e1 b: 1, 2 Examples of combinations (e.g. KOH-etchant): f: 1, 2 K 1K 2K 1.1K/2.2K d(f1)=d(b1); b: 1, 2 K 1K 2K d(f2)=d(b2) f: 1, 2 K 1K 1K 2K 1.pK/1.1K/ d(f1)>d(b1); b: 1, 2 K 1K 2K 2.2K d(f2)=d(b2) f: 1, 2 K 1K 2K 2K 1.pK/2.1K/ d(f1)>d(b1); b: 1, 2 K 1K 2K 2.2K d(f2)=d(b1)+ d(b2)>d(b2) One side processes to be combined: 3 front side steps, 2 back side steps, 2 etchants f: 1, 2, 3 e1, e2 1e1 2e1 3e2 1e1/2e1/3e2 1e1 2e2 3e2 1e1/2e1/3e2 1e1 2e2 3e1 1e1/2e2/3e1 b: 1, 2 e1 1e1 2e1 1e1/2e1 Examples of combinations (etchant e1: KOH; etchant e2: EDP): f: 1, 2, 3 K, E 1K 2K 2K 3E 1.pK/2.1K/ d(f2)= b: 1, 2 K, E 1K 2K p 2.2K/3.pE d(b1)+d(b2) f: 1, 2, 3 K, E 1K 1K 2E 3E p.1K/1.2K/ d(f1)>d(b2) b: 1, 2 K, E 1K 2K p 1.pK/2.pE/ and d(f1) 3.pE (b1)+d(b2) f: 1, 2, 3 K, E 1K 2E 3K 3K 1.pK/2.pE/ d(f3)= b: 1, 2 K, E 1K 2K 3.1K/3.2K d(b1)+d(b2) f: front, b: back, p: passivated, K: KOH, E: EDP, I: ISO, D: DRY, d: depth


55

Table 3.7 explains the development of such basic etch processes. In this way processes for the production of a lot of different shapes can be created. Generally the following must be taken into account: the technological possibility to realize a process depends in principle on the properties of the used mask materials and on the methods of performing of deposition, structuring and removing of the layers. 3.4.2 Changing of the mask between two etch steps

The deposition of a passivation layer is conceivable in principle after each process step. But its lithographical structuring is impossible after a deep silicon etching. The acceptable depth for a further lithographical transfer of a structure into a profiled passivation layer depends on the available feasibilities and the demanded precision. As a rule: after etching a depth smaller than about 10 µm with a mask in a first Si-etch step this mask can be completely removed and the following process steps can be performed treating the wafer as a new one. In the case that all Si-etch steps produce large depths the complete system of masks acting in succession must be realized as a stack of different, lithographically structured passivation layers before a Si-etch step can be started. The order of deposition and lithographical structuring of the masks must not be the order of their acting. The successive opening of windows by selective removing of layers and Si-etch steps in between produces a series of deepenings with cumulative depths: each opened window acts during all of the following Si-etch steps (with exception of the later discussed interim oxidation). In the case that windows overlap a deepening of a previously opened window an extension of this follows. The edges of this mask are set back and a free convex edge of silicon is etched during the following Si-etch steps (see section 5.1). In principle a different layer material for each mask is conceivable. Practically at least two selectively removable passivation materials A and B are necessary (A: thermal or CVD-Si-oxide and B: Si-nitride as the most important examples). For the successive opening of windows corresponding with N masks and resulting in N different depths (of practical interest in the most cases is: N 3) the following principles can be used: - Buried mask (a previous mask is buried by the following layer): The passivation layers A and B are deposited alternately and are lithographically structured in between. In this process the previous mask windows are buried by the following layer. The windows of each last mask must be opened up to the silicon surface. In this manner the last mask acts at first during the first Si-etch step. By selective removing of each upper passivation layer the buried mask windows are additionally activated after the Si-etch steps in between, table 3.8a. The number L of necessary layers is equal to the number of masks N: L = N. - Prevented mask (the following mask is prevented by the underlying layer): The passivation layers A and B are deposited alternately resulting in the complete stack. The number of necessary pairs of layers P depends on the number N of different masks: P = N – 1 (the first two masks need only one layer per mask,

56


each of the following masks needs one pair of layers). Thereafter the windows of the masks must be transferred lithographically into the stack up to the different layers (without influence of the order): the first acting mask up to the silicon surface (resulting in the largest depth), the next mask up to the lowest oxide layer, the third mask up to the lowest nitride layer, each of the following masks has to be transferred up to one pair higher than the previous mask. Then the first Si-etch step can be carried out followed by a removing of oxide, second Sietch step, removing of nitride, third Si-etch step, removing of oxide and nitride, 4th Si-etch step and so on, table 3.8b. In this process the stack is stripped down and the layers preventing the Si-etching are removed activating the windows of the masks in succession. - Interim oxidation: By an interim oxidation an used mask system can be modified. The free silicon surface etched during previous Si-etch steps is passivated by a selective thermal oxidation. In the case a new window is opened by removing the nitride layer the following etch steps have no influence on the formerly etched deepenings so long as no removing of an oxide layer is necessary (additional possibilities result from different thicknesses of the used oxide layers), table 3.9a. Table 3.8. Changing the acting mask transferred into a stack of oxide and nitride layers a) Buried masks

b) Prevented masks

the complete mask system: 3 masks / 3 layers masks 3 and 2 are buried by the overlaying layers

the complete mask system: 3 masks / 2 pairs of layers masks 2 and 3 are prevented by the underlaying layers

first Si-etch step in the windows of mask 1

first Si-etch step in the windows of mask 1

activation of mask 2 by removing the topmost layer second Si-etch step in the windows of masks 1 and 2

activation of mask 2 by removing oxide second Si-etch step in the windows of masks 1 and 2

activation of mask 1 by removing the top- activation of mask 3 by removing the topmost layer most layer third Si-etch step in the windows of masks third Si-etch step in the windows of masks 1, 2 and 3 1, 2 and 3


57

Table 3.9. Interim oxidation techniques a) Passivation of etched deepenings

b) Mask inversion along {111}-sidewalls

first Si-etch step

first Si-etch step

selective thermal oxidation

selective thermal oxidation

nitride etching

nitride etching

second Si-etch step

second Si-etch step

- Inversion masked-unmasked: Using silicon nitride as the only passivation layer the surface etched in the windows during a first step can be selectively oxidized. Together with a following removing of nitride an inversion of the mask is realized. A second silicon etch step produces deepenings in the regions formerly masked by nitride. The new mask edges are the lines along the upper edges of the sidwalls etched during the first step, table 3.9b. In the two Si etch steps the same or different etch depths are realizable. 3.4.3 Examples of the most important basic processes and process interfaces

The production of a silicon structure by etching processes at first needs a specificated wafer: orientation, diameter, thickness, polished sides, resistivity and tolerances. Next a series of process steps must be established: - steps for growth or deposition of passivation layers as etch masks, lithographical structuring of mask layers and partial removing of mask material in the windows, - steps of etching processes according to the shape to be produced corresponding to tables 3.6 and 3.7, - steps for drying and cleaning. In detail these steps must be settled together with the personal of process control (for example: thickness and kind of passivation layers, regime of deposition of layers, cleaning steps). For an effective process development it is useful to start with a raw formulation of a series of process steps, the so called “Basic Processes” consisting in the series of etch steps and steps of masking (deposition, lithography, removing) corresponding to tables 3.8 and 3.9. Mostly further steps are necessary which are of functional importance but not related to the emergence of the shape. Examples

58


functional importance but not related to the emergence of the shape. Examples are processes for the production of microelectronic components, for the realization of metallic electrodes or magnets or the packaging on wafer level. Microelectronic components should be processed before a three dimensional shape is etched: “Postprocessing” of three dimensional shapes. For other processes unrelated to the etching “Process Interfaces” between two steps can be marked. The most important basic etch processes on {100}-wafers are described below together with illustrations of the resulting passivation layers, etch windows and etched shapes. By the name of a basic process corresponding to tables 3.8–3.21 it is possible to identify the process leading to any structure pictured in the chapters 5 to 8. The following abbreviations are used: O wet etching – orientation dependent wet etching (KOH-type or EDP-type), f – front side, b – back side, 0°, 45° – angle between mask edge and wafer flat (representative also for equivalent angles). Table 3.10. Basic processes 1.pK or 1.pE (back side passivated) No. Process steps 1 2 3 4 5 6 7

Stage of completion after step with * 0°: 1.pK/1.pE 45°: 1.pK 45°: 1.pE

Thermal oxidation Resist Photolithography, f1 Wet etching of Si oxide Stripping of resist * O wet etching of Si, f1 Wet etching of Si oxide *

Table 3.11. Basic processes 1.pK/1.pE or 1.pE/1.pK (back side passivated) No. Process steps

1 2 3 4 5 6

Thermal oxidation Resist Photolithography, f1 Wet etching of Si oxide Stripping of resist * K/E wet etching of Si, f1 *

7 E/K wet etching of Si, f1 8 Wet etching of Si oxide *

Stage of completion after step with * 0°: 1.pK/1.pE or 45°: 1.pK/1.pE 45°: 1.pE/1.pK 1.pE/1.pK


59

Table 3.12. Basic processes 1.pK/2.pK or 1.pE/2.pE (back side passivated) No.

1 2 3 4 5 6 7 8 9 10 11

Process steps

Stage of completion after step with * 0°: 1.pK/2.pK or 45°: 1.pK/2.pK 45°: 1.pE/2.pE 1.pE/2.pE

Thermal oxidation Resist Photolithography, f1 Wet etching of Si oxide Stripping of resist * CVD Si nitride Resist Photolithography, f2 Wet etching of Si nitride Stripping of resist * O wet etching of Si, f1 *

12 Wet etching of Si nitride 13 O wet etching of Si, f2 * 14 Wet etching of Si oxide *

Table 3.13. Basic processes 1.pD/1.pK or 1.pD/1.pE (back side passivated) No.

1 2 3 4 5 6

Process steps

Thermal oxidation Resist Photolithography, f1 Wet etching of Si oxide Stripping of resist * Dry etching of Si, f1 *

7 O wet etching of Si 8 Wet etching of Si oxide *

Stage of completion after step with * 0°: 1.pD/1.pK or 45°: 1.pD/1.pK 45°: 1.pD/1.pE 1.pD/1.pE

60


Table 3.14. Basic processes 1.1K or 1.1E No. Process steps 1 2 3 4 5 6 7

Stage of completion after step with * 0°: 1.1K or 1.1E 45°: 1.1K 45°: 1.1E

Thermal oxidation Resist Photolithography, f1+b1 Wet etching of Si oxide Stripping of resist * O wet etching of Si, f1+b1 Wet etching of Si oxide *

Table 3.15. Basic processes 1.pK/1.1K or 1.pE/1.1E No. Process steps

Stage of completion after step with * 0°: 1.pK/1.1K or 1.pE/1.1E

1 2 3 4 5 6 7 8 9 10 11 12

Thermal oxidation Resist Photolithography, b1 Wet etching of Si oxide Stripping of resist * CVD Si nitride Resist Photolithography, f1 Etching of Si nitride Wet etching of Si oxide Stripping of resist * O wet etching of Si, f1 *

13 Wet etching of Si nitride 14 O wet etching of Si, f1+b1 * 15 Wet etching of Si oxide *

45°: 1.pK/1.1K

45°: 1.pE/1.1E


61

Table 3.16. Basic processes 1.pK/p.1D or 1.pE/p.1D No. Process steps

Stage of completion after step with * 0°: 1.pK/p.1D or 1.pE/p.1D

1 2 3 4 5 6 7 8 9 10 11 12

45°: 1.pK/p.1D

45°: 1.pE/p.1D

Thermal oxidation Resist Photolithography, b1 Wet etching of Si oxide Stripping of resist * CVD Si nitride Resist Photolithography, f1 Etching of Si nitride Wet etching of Si oxide Stripping of resist * O wet etching of Si, f1 *

13 Wet etching of Si nitride 14 Dry etching of Si, b1* 15 Wet etching of Si oxide *

Table 3.17. Basic processes 1.1K/2.2K or 1.1E/2.2E No. Process steps

Stage of completion after step with * 0°: 1.1K/2.2K or 1.1E/2.2E

1 2 3 4 5 6 7 8 9 10 11 12

Thermal oxidation Resist Photolithography, f2+b2 Wet etching of Si oxide Stripping of resist * CVD Si nitride Resist Photolithography, f1+b1 Etching of Si nitride Wet etching of Si oxide Stripping of resist * O wet etching of Si, f1+b1*

13 Etching of Si nitride 14 O wet etching of Si, f1+f2+b1+b2 * 15 Wet etching of Si oxide *

45°: 1.1K/2.2K

45°: 1.1E/2.2E

62


Table 3.18. Basic processes 1.1K/2.1K (mask windows only in 0°-direction) No.

Process steps

Stage of completion after step with * 0°: 1.1K/2.1K or 1.1E/2.1E

1 2 3 4 5 6 7 8 9 10 11 12

Thermal oxidation Resist Photolithography, f2 Wet etching of Si oxide Stripping of resist * CVD Si nitride Resist Photolithography, f1+b1 Etching of Si nitride Wet etching of Si oxide Stripping of resist * K/E wet etching of Si, f1+b1 *

13 Etching of Si nitride 14 K/E wet etching of Si, f1+f2+b1 * 15 Wet etching of Si oxide *

Table 3.19. Basic processes 1.pK/1.1K/2.1K (mask windows only in 0°-direction, profile 1 and 2 show different mask windows inside the same chip) No. Process steps

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Thermal oxidation Resist Photolithography, f2+b1 Wet etching of Si oxide Stripping of resist * CVD Si nitride Resist Photolithography, f1 Wet etching of Si nitride Wet etching of Si oxide Stripping of resist * K/E wet etching of Si, f1 Dry etching of Si nitride, b * K/E wet etching of Si, f1+b1 Dry etching of Si nitride, f * K/E wet etching of Si, f1+f2+b1 17 Wet etching of Si oxide *

Stage of completion after step with * 0°: 1.pK/1.1K/2.1K profile 1 profile 2


63

Table 3.20. Basic processes 1.pK/2.1K/2.2K (mask windows only in 0°-direction, profile 1 and 2 show different mask windows inside the same chip) No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Process steps

Thermal oxidation Resist Photolithography, b2 Wet etching of Si oxide Stripping of resist * CVD Si nitride Resist Photolithography, f2+b1 Etching of Si nitride Wet etching of Si oxide Stripping of resist * CVD Si oxide CVD Si nitride Resist Photolithography, f1 Etching of Si nitride Etching of Si oxide Etching of Si nitride Etching of Si oxide Stripping of resist * K/E wet etching of Si, f1 Etching of Si nitride Wet etching of Si oxide * K/E wet etching of Si, f1+f2+b1 25 Wet etching of Si nitride * 26 K/E wet etching of Si, f1+f2+b1+b2 27 Wet etching of Si oxide *

Stage of completion after step with * 0°: 1.pK/2.1K/2.2K profile 1 profile 2

64


Table 3.21. Basic processes 1.1K/2.2K/3.3K (mask windows only in 0°-direction, profile 1 and 2 show different mask windows inside the same chip) No. Process steps

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Thermal oxidation Resist Photolithography, f3+b3 Wet etching of Si oxide Stripping of resist * CVD Si nitride Resist Photolithography, f2+b2 Wet etching of Si nitride Stripping of resist Wet etching of Si oxide * CVD Si oxide CVD Si nitride Resist Photolithography, f1+b1 Wet etching Si nitride Wet etching Si oxide Stripping of resist * K wet etching of Si, f1+b1 *

20 21 22 23 24 25

Wet etching of Si nitride Wet etching of Si oxide K wet etching of Si, f2+b2 * Wet etching of Si nitride K wet etching of Si, f3+b3 * Wet etching of Si oxide *

Stage of completion after step with * 0°: 1.1K/2.2K/3.3K profile 1 profile 2


65

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[Kühl94]

[Lap98] [Li96] [Li99]

Frühauf J, Hannemann B, Gerber M (1997) Ätzraten und Oberflächenqualitäten beim Silizium-Ätzen in der Mikrotechnik. Internal Report SMWKProjektförderung 0380/509, Technische Universität Chemnitz Gerlach G (1990) A novel mask compensation pattern for etched microstructures with several convex corners. Micro System Technologies ’90: Proc of the 1st Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 545–550 Hah D, Yoon E, Hong S (2000) An optomechanical pressure sensor using multimode interference couplers with polymer waveguides on a thin p+-Si membrane. Sensors and Actuators 79: 204–210 Hein A, Dorsch O, Obermeier E (1997) Effects of metallic impurities on anisotropic etching of silicon in aqueous KOH-solutions. Transducers ‘97: Proc of the 9th Int Conf on Solid-State Sensors and Actuators, USA: 687–690 Hesketh PJ et al. (1993) Surface free energy model of silicon anisotropic etching. J Electrochem Soc 140, 4: 1080–1085 Hu H (2001) The diagnostic micromachined beams on (111) substrate. Sensors and Actuators A 93: 258–265 Iosub R, Moldovan C, Modreanu M (2002) Silicon membranes fabrication by wet anisotropic etching. Sensors and Actuators A 99: 104–111 Jaccodine RJ (1962) Use of modified free energy theorems to predict equilibrium growing and etching shapes. J Appl Phys 8: 2643–2647 van Kampen RP, Wolfenbuttel RF (1995) Effects of -oriented corner compensation structures on membrane quality and convex corner integrity in (100)-silicon using aqueous KOH. J Micromech Microeng 5: 91–94 Don Kendall L, de Guel GR (1985) Orientation of the third kind: the coming of age of (110) silicon. In: Fung CD et al. (eds) Micromachining and Micropackaging of Transducers. Elsevier Science Publishers BV Amsterdam, pp 107–124 Kern DP, Zarowin CB (1986) Computersimulation of etch front propagation. Proc of the Symposium on Plasma Etching and Deposition, Electrochem Soc, USA: 86–111 Kim B, Cho DD (1998) Aqueous KOH-etching of silicon (110): Etch characteristics and compensation methods for convex corners. J Electrochem Soc 145, 7: 2499–2508 Koide A, Sato K, Tanaka S (1991) Simulation of two-dimensional etch profile of silicon during orientation dependent etching. Proc of the Int IEEE Micro Electro Mechanical Systems (MEMS) Workshop, Japan: 216–220 Kühl K et al. (1994) Bulk micromachining using doping and voltage dependent pn junction etch stop. Micro System Technologies ‘94: Proc of the 4th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 323–330 Lapadatu D et al. (1998) A model for the etch-stop location on reverse-biased pn junctions. Sensors and Actuators A 66: 259–267 Li X, Bao M, Shen S (1996) Maskless etching of three-dimensional silicon structures in KOH. Sensors and Actuators A 57: 47–52 Li X et al. (1999) masked-maskless etch technology for compositebeam structure. Transducers ’99: Proc of the 10th Int Conf on Solid-State Sensors and Actuators, Japan: 556–559

3.4 Basic processes of the bulk-silicon-microtechnique [Mar98]

67

Marchetti J et al. (1998) Efficient process development for bulk silicon etching using cellular automata simulation techniques. SPIE’s Symposium on Micromachining and Microfabrication, Micromachined Devices and Components, USA [May90] Mayer GK et al. (1990) Fabrication of non-underetched convex corners in anisotropic etching of (100)-silicon in aqueous KOH with respect to novel micromechanic elements. J Electrochem Soc 137, 12: 3947–3951 [Merl93] Merlos A et al. (1993) TMAH-IPA anisotropic etching characteristics. Sensors and Actuators A 37–38: 737–743 [Off92] Offereins HL et al. (1992) Compensating corner undercutting of (100) silicon in KOH. Sensors and Materials 3, 3: 127–144 [Pal82] Palik ED et al. (1982) Study of the etch stop mechanism in silicon. J Electrochem Soc 129: 2051–2059 [Pal85] Palik ED, Bermudez VM, Glembocki OJ (1985) Ellipsometric study of the etch stop mechanism in heavily doped silicon. J Electrochem Soc 132: 132– 135 [Pot85] Poteat TL (1985) Submicron accuracies in anisotropic etched silicon piece parts – A case study. In: Fung CD et al. (eds) Micromachining and Micropackaging of Transducers. Elsevier Science Publishers BV, Amsterdam, pp 151–158 [Price73] Price JB (1973) Anisotropic etching of silicon with KOH-H2O-isopropyl alcohol. In: Huff HR, Burges RR (eds) Semiconductor Silicon. The Electrochemical Society, Princeton, New Jersey, USA, pp 339–353 [Puers90] Puers B, Sansen W (1990) Compensation structures for convex corner micromachining in silicon. Sensors and Actuators A 21–23: 1036–1041 [Robb59] Robbins H, Schwartz B (1959) Chemical etching of silicon I. J Electrochem Soc 106: 505–508 [Robb60] Robbins H, Schwartz B (1960) Chemical etching of silicon II. J Electrochem Soc 107: 108–111 [Robb76] Schwartz B, Robbins H (1976) Chemical etching of silicon IV. J Electrochem Soc 123: 1903–1909 [Sato98] Sato K (1998) Characterization of orientation-dependent etching properties of single-crystal silicon: effects of KOH-concentration. Sensors and Actuators A 64: 87–93 [Sato99] Sato K et al. (1999) Anisotropic etching rates of single crystal silicon for TMAH water solution as a function of crystallographic orientation. Sensors and Actuators 73: 131–137 [Schna91] Schnakenberg U, Benecke W, Lange P (1991) TMAHW etchants for silicon micromachining. Transducers ‘91: Proc of the 6th Int Conf on Solid-State Sensors and Actuators, USA, Japan, Switzerland: 815–818 [Schröd92] Schröder H, Dorsch O, Obermeier W (1992) An improved method to align etch masks to the crystal orientation. Micro System Technologies ’96: 5th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 651–655 [Schwes96] Schwesinger N (1996) The anisotropic etching behaviour of so called isotropic etchants. Micro System Technologies ’96: 5th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 481– 486

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[Seid1-90]

Seidel H et al. (1990) Anisotropic etching of crystalline silicon in alkaline solutions. I. Orientation dependence and behaviour of passivation layers. J Electrochem Soc 137: 3612–3626 [Seid2-90] Seidel H et al. (1990) Anisotropic eching of crystalline silicon in alkaline solutions. II. Influence of dopants. J Electrochem Soc 137: 3626–3632 [Seid86] Seidel H (1986) Der Mechanismus des Siliziumätzens in alkalischen Lösungen. Dissertation Thesis, Freie Universität Berlin [Seid91] Seidel H (1991) Isotrope Ätzverfahren. In: Heuberger A (ed) Mikromechanik. Springer, Heidelberg, pp 162–169 [Seki1-99] Sekimura M (1999) Anisotropic etching of surfactant added TMAH solution. Proc of the 12th IEEE Int Micro Electro Mechanical Systems Conference (MEMS’99), USA: 650–655 [Shik1-01] Shikida M et al. (2001) A new explanation of mask-corner undercut in anisotropic silicon etching: saddle point in etching rate diagram. Transducers ’01: Proc of the 11th Int Conf on Solid-State Sensors and Actuators, Germany: 648–651 [Steck91] Steckenborn A et al. (1991) High precision wafer orientation for micromachining. Micro System Technologies ’91: Proc of the 2nd Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 467–471 [Steff00] Steffensen L, Than O, Büttgenbach S (2000) BICEPS: a modular environment for the design of micromachined silicon devices. Sensors and Actuators A 79: 76–81 [Tana03] Tanaka H et al. (2003) Fast wet anisotropic etching of Si {100} and {110} with a smooth surface in ultra-high temperature KOH solutions. Transducers ‘03: Proc of the 12th Int Conf on Solid-State Sensors and Actuators, USA: 1675–1678 [Than94] Than O, Büttgenbach S (1994) Simulation of anisotropic chemical etching of crystalline silicon using a cellular automata modell. Sensors and Actuators A 45: 85–89 [Trieu97] Trieu HK, Mokwa W (1997) A generalized model describing corner undercutting by the experimental analysis of TMAH-IPA. Proc of the 8th Int Conf on Micro Mechanics Europe MME ’97, UK: 51–54 [Vang1-96] Vangbo M, Bäcklund Y (1996) Precise mask alignment to the crystallographic orientation of silicon wafers using wet anisotropic etching. J Micromech Microeng 6: 279–284 [Weir75] Weirauch DF (1975) Correlation of the anisotropic etching of single-crystal silicon spheres and wafers. J Appl Phys 4: 1478–1483 [Wu87] Wu XP, Ko WH (1987) A study on compensating corner undercutting in anisotropic etching of (100) silicon. Transducers ’87: Proc of the 4th Int Conf on Solid–State Sensors and Actuators, Tokyo: 126–129 [Yang00] Yang H et al. (2000) A novel technique for measuring etch rate distribution of Si. Sensors and Actuators A 79: 136–140 [Zav94] Zavratsky PM et al. (1994) Fabrication of vertical sidewalls by anisotropic etching of silicon (100)–Wafers. J Electrochem Soc 141, 11: 3182–3188 [Zhang96] Zhang Q, Liu L, Li Z (1996) A new approach to convex corner compensation for anisotropic etching. Sensors and Actuators A 56: 251–254

3.4 Basic processes of the bulk-silicon-microtechnique [Ziel01]

[Ziel95] [Ziel97]

[Zöb77]

69

Zielke D, Lieske R, Will J Automatic transfer from bulk–silicon technology simulation into the FEM–environment. Transducers ’01: Proc of the 11th Int Conf on Solid–State Sensors and Actuators, Germany: 272–275 Zielke D, Frühauf J (1995) Determination of rates for orientation dependent etching. Sensors and Actuators A 48: 151–156 Zielke D, Frühauf J (1997) Complete simulation support for orientation dependent etched MEMS. In: Adey RA, Renaud P (eds) MICROSIM II Simulation and Design of Microsystems and Microstructures. Computational Mechanics Publications, Lausanne, Switzerland, pp 261–270 Zöbisch J (1977) Geometrie und Abtragungsfronten bei chemigrafischen Prozessen in der elektronischen und mikroelektronischen Industrie. Feingeräte– technik 26, 11: 493–493

4 General Overview of the Shape- and Functional Elements and the Procedure of their Design

4.1 Survey and methodical procedure The orientation dependent etching is a form building process and is used for the preparation of different functional elements. The elements described in this manual are assigned to their application possibilities and shall demonstrate the use and the results of the etch process with examples. The fabrication of a special target shape is the first problem to be solved. Functional elements are applications respectively combinations of shape elements. The shape of a functional element should be optimally related to its application. The possibilities of the etch technique for the development of suitable shapes is described in principle (chapter 3 and 5) and illustrated with examples (chapter 6 to 8). Microtechnical components are normally built by the addition of several functional elements which are realized in different wafers by mounting (gluing, soldering, bonding). Two examples shall be mentioned here: 1. -

A capacitive acceleration sensor, 3 chip levels minimally: a lower tight electrode (simultaneously the ground plate) a movable electrode with a seismic mass (spring-mass-system) an upper tight electrode (simultaneously the cover-plate)

2. -

An electrostatic ventile, 3 chip levels minimally: chip with in- and outlet channel (simultaneously the cover-plate) a spring with stopper and movable electrode (spring-mass-system) a tight electrode (simultaneously the ground plate).

In some cases glass wafers, ceramic substrates or circuit boards are used for similar levels. A general overview of the functional elements of the bulk-siliconmicrotechnique is given in table 4.1, which can be produced by wet chemical etching and have been described in the applications, preparations or designs. Many variants serve an optimal adaptation to the function which is to fulfil.

72

4 General Overview of the Shape- and Functional Elements

Table 4.1. Elements of the bulk-silicon-microtechnique producible by anisotropic chemical wet etching Field of application

Working function

Variants

Examples

Simple shape elements

hollows

one depth, different depths

pits, holes, deepenings, grooves, cracks

rises

one height, different heights

rises (mesas), columns, walls

springs

in-plane, out-of-plane

bent springs, polygon springs, torsion-bar springs

Mechanical elements

membranes levers

unstiffened, stiffened in-plane, out-of-plane

sliding guides in-plane

Fluidic elements

1-side straight levers, 2-side straight levers, angled levers dove tail, rectangular cross section, trapezium cross section, triangular cross section

bearings

perpendicular to the wp

edge bearings, tip bearings

channels

in-plane out-of-plane

cross section: trapezium, rectangle, hexagonal

cross section alteration

in-plane

gradually, abruptly

nozzles

in-plane out-of-plane in-plane out-of-plane in-plane out-of-plane

pyramids, funnels, bowls

caverns

3-dim

elbows branchings

single-pyramid stump, doublepyramid stump, rectangular solid

4.3 Legend of the sketches

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Table 4.1: Continuation

Optical elements

grooves for positioning of in-plane optical fibres in-plane, vertically to the wp, mirrors tilted to the wp

all directions in the plane, tilted to the wafer plane single reflection mirrors, multiple reflection mirrors

beam splitters

in-plane, out-of-plane

edge of two mirror faces, semipermeable membrane

concave mirrors

axis perpendicular to the wp

spherical, parabolic

gratings

in-plane

symmetrical V-groove profile, unsymmetrical V-groove profile

IR-prisms

in-plane vertically to the wp

30°-prism, 60°-prism, 54.74°-prism, 45°-prism

wp wafer plane

4.2 Guide for the design procedure Using this manuel the target structures made from silicon wafers by wet etching can be designed in the following way: - Search a similar structure from the photographs in figures 5.x …..8.x referring to tables 5.x …..8.x with the systematics of the structures. If there is no corresponding photograph search a structure directly in these tables. - Now the design work is splitted into the process design and the etch mask design: Process design Follow the reference to the basic processes (section 3.4) and specify the technological process step sequence in view of additional processes (metallization, mounting…)

Etch mask design Specify the dimensions and design the etch maks following the sequence described in section 3.3. Using simulation tools the functional design can be checked.

4.3 Legend of the sketches Description of the chip cross-section The cross section shapes are drawn in principle. They are not results of simulation.

74 1

a c e .g 2 nd a c e .g S ilic o s t

4 General Overview of the Shape- and Functional Elements tiv e e . S i- N tiv e e . S i- O n

tc h m a s k itr id e tc h m a s k x id e

c o m m o n e d g e s o f fa c e s

Fig. 4.1. Scheme used for the description of shape elements (sidewall types)

s ilic o n - b o d y

B B

Fig. 4.2. Scheme used for the description of shape- and functional elements

Description of directions s tr a ig h t

la te r a lly c u r v e d

d ir e c te d u p w a rd

tilt d o w n w a rd tilt u p w a rd

d ir e c te d d o w n w a rd d ir e c te d u p o r d o w n w a rd

Fig. 4.3. Description of the directions of moving or beaming

Description of the top view These descriptions are created by SIMODE and relate qualitatively to the typical forms. le v e l o f th e o r ig in a l w a fe r s u rfa c e ( m a s k le v e l) B d e e p e tc h e d S i- s u r fa c e (e tc h g ro u n d )

in c lin e d fa c e s o f S i- b o d y ( s id e w a lls )

b a c k g ro u n d ( in s tr u c tu r e s w ith p e r fo r a tio n o f th e w a fe r o n ly )

Fig. 4.4. Description of the top view: height of levels and inclined faces

B

5 Simple Shape Elements

5.1 Definitions of shapes by the combination of sidewalls

5.1.1 Types of sidewalls arising from one-step etch processes According to the facts discussed in section 3.3 a deepening or hollow etched using a mask can be characterized by: - the etch ground at the level of the etch depth, - the underetching as the upper contour of the hollow, - the sidewalls reaching from the mask level to the etch ground. The upper edges of the sidewalls represent the underetching. The lower edges limit the etch ground. Consequently the shape of a body produced by etching is essentially defined by the shapes of the occurring sidewalls and the relations between their positions. Moreover, it was pointed out that the shape of a sidewall depends on the direction of the mask edge and the etch rates of all crystallographic faces situated parallel to the mask edge. Consequently, a special direction of a mask edge together with the application of a special etchant produces a special type of sidewall. Characteristics of this type are the number i of the occurring faces, their inclinations γi and the direction α of the mask edge in the wafer plane. In good approximation the types of sidewalls created by one-step etch processes are independent on the etch time or the etch depth.

{100}-wafer The types of sidewalls occurring in the {100}-wafer are shown in table 5.1. Along an -edge of the mask (parallel or perpendicular to the flat: 0°- or 90°-direction) the sidewalls are very slowly etching {111}-faces with an inclination of 54.74° relative to the wafer plane. Along an -edge of the mask (α = 45° relative to the flat) the developing type of sidewall depends on the used etchant. According to the considerations of

76


section 3.1.3, the KOH-type etchants produce vertical {100}-sidewalls (inclination γ = 90° relative to the wafer plane) whereas EDP-type etchants develop {110}-sidewalls with an inclination of γ = 45°. Corresponding to the region from α = 0° to α = 45° of a mask edge the sidewalls differ as shown in table 5.1. With exception of the border values α = 0° and 45° the sidewalls contain steps and consist partially of two or more faces. For the most applications they have insufficient surface qualities. In some cases sidewalls deviating slightly from α = 0° can be used to produce an inclined Vgroove, see section 8.1. Along curved mask edges deviating slightly from α = 45° vertical sidewalls curved in the wafer plane are produced in KOH-type etchants [Hanf02]. Table 5.1. Sidewall shapes in {100}-wafers for one-step etch processes α

Etchant: KOH-type C = 5 4 .7 4 ° {1 1 1 }

0 °

Etchant: EDP-type C = 5 4 .7 4 ° {1 1 1 }

5 °

1 0 °

1 5 °

2 0 °

2 5 °

3 0 °

3 5 °

4 0 °

C = 9 0 ° {1 0 0 }

4 5 °

C = 4 5 ° {1 1 0 }

α : angle between mask edge and flat; γ : inclination of the sidewall face.


77

{111}-Sidewalls along Preferably, the microtechnique uses the {111}-sidewalls which develop along 0°- or 90°-edges of the mask and permit a rectangular design pattern. These sidewalls arise in all orientation dependent etchants. They have a minimal underetching and an excellent precision. Sidewalls along In the case of mask edges in an angle of 45° relative to the wafer flat the resulting sidewalls depend on the used etchant. In principle etchants of KOH- or EDPtype must be distinguished which produce vertical {100}- or 45°-inclined {110}sidewalls respectively, table 5.1 (see also section 3.1.3). Both sidewall faces have relatively large etch rates resulting in a considerable underetching. The following conditions decide which of the two kinds arises [Früh3-97]: - {100}-sidewalls if v{110} 2 v{100}, - {110}-sidewalls if v{110} < 1/ 2 v{100}. In the intermediate cases a two-face sidewall occurs combining a vertical {100}-face at the top with an inclined {110}-face at the bottom. Often only narrow facets at the top or at the bottom appear. {100}-sidewalls are crystallographic equivalent to the etch ground having the same etch rate and smooth surface. Really they are not exactly of {100}-type deviating slightly from the vertical slope and having a weak curvature, see section 5.2.2. {110}-sidewalls have furrows reaching from top to bottom as the result of the stepwise composed face, see section 5.2.1. Consequently, the surface is rough. The best quality can be achieved by using EDP- or TMAH-NCW-solutions, see section 5.2.2.

{110}-Wafer The {110}-wafer is mostly used because of the occurrence of vertical {111}sidewalls. The extremely low etch rate allows the production of very deep trenches having a high aspect ratio depth to width. Unfortunately a rectangular design pattern is impossible because the mask edge must be along which is in an angle of 35.26° relative to the primary flat, see section 3.1.1. Two other sidewalls have a limited importance, see table 5.2. Using mask edges along (perpendicular to the flat) also {111}-sidewalls develop inclined by 35.26° relative to the wafer surface. The type of sidewalls arising along (parallel to the flat) depends on the used etchant analogous to the case of an {100}-wafer. KOH-type etchants develop 45°-inclined sidewalls of {100}type with a smooth surface. EDP-type etchants develop vertical {110}-sidewalls with a furrowed surface.

78


Table 5.2. Important sidewall shapes in {110}-wafers for one-step etch processes Etchant: KOH-type

Angle α between mask edge and flat

Etchant: EDP-type

0° γ = 45° {100}

γ = 90° {110}

90° γ = 35.26° {111}

γ = 35.26° {111}

35.26° γ = 90° {111}

γ = 90° {111}

{112}-Wafer The {112}-wafer is only used in very rare cases because of the left-right difference of the {111}-sidewalls along the mask edges. This asymmetry can be seen assuming a rotation of the wafer surface from the {001}-situation by 35.26° about the -direction into the {112}-situation. The pair of opposite {111}-sidewalls moves into an asymmetric configuration: one {111}-sidewall is vertical, the other is inclined by 19.48°, figure 3.16. Sidewalls at mask edges perpendicular to the -direction are parallel to the -direction. Consequently, they must consist of faces of the zone. Because of the mirror symmetry of the cubic silicon lattice (see figure 3.1) the sidewalls must be symmetric. In KOH-type etchants a steep sidewall with considerable underetching results. 5.1.2 Types of sidewalls arising from two-step etch processes By two-step etch processes the sidewalls arisen in the first step are modified facilitating new shapes. Between the both steps of two-step etch processes an alteration of the etch mask, a change of the etchant or of the etching procedure as well as combinations of them are conceivable [Früh3-97]. The partial removing of the etch mask known as “maskless” etching [Li96] is also a two-step process with alteration of the mask producing new sidewalls. This technique is applied to the etching of {100}-wafers but no information exists about the applications with {110}- or other wafer orientations.


79

In the case of processes combining dry etching with wet etching it must be distinguished between complete independent process steps and processes modifying the sidewalls. Only the last ones are of interest especially for etching the {111}-wafer which is discussed in section 3.1.3. Consequently, the following considerations are related only to the etching of {100}-wafers.

Alteration of the etch mask An alteration of the etch mask is the expansion of a window. Thereby, both the firstly active (the smaller) window and the secondly active (the larger) window can be implemented into a stack of two selectively removable passivation layers (SiO2 and Si3N4) before the silicon etch process is started. After the first etch step, the free surface region of the layer with the smaller window will be removed by a selective reaction acting on this layer material. Consequently, the layer with the larger window works as the mask during the second step of the silicon etch process. This procedure corresponds to a "putting back of the mask edges". Along the new mask edge new sidewalls and a new etch ground are generated during the second etch step analogous to the first etch step. The upper convex edges of the sidewalls produced during the first etch step are no longer protected by masking material. Here, new fast etching faces develop consuming the new etch ground and the slowly etching faces of the old sidewalls until the complete removal of these faces, see section 3.1.2. At this time the fast etching faces meet other faces of the old or new sidewalls forming concave edges. From this situation new slowly etching faces can be created. Commonly faces with a weak curvature (FWC) are observed in the case of a weak anisotropy of the etch rates around the concave edge. In all a complex sequence of a number i of sidewall faces are generated which can be characterized by the crystallographic type (respective inclination γi relative to the wafer plane and direction α relative to the primary flat), the order and relations of magnitude of the occurring faces. Consequently, the plurality of the types of sidewalls which can be produced by etch processes is extended essentially. In figure 5.1 series of sidewall types are shown which can develop along -parallel mask edges. In this case the shapes are qualitatively independent on the type of etchant. Along -edges of the mask the conditions are different if different etchants are used as shown in figures 5.2 and 5.3. A more difficult task is the realization of an etch mask in regions of the silicon surface which are unprotected during the first etch step. This supposes the control of lithography on an etched wafer surface and should not be under consideration here. On the other hand by the techniques of interim oxidation and mask inversion (section 3.4.2) the sidewalls produced during the first etch step are protected and remain unchanged while the sidewalls arising during the second step are independent on the first step.

80


0 0 1

1 1 1

s ta r tin g p o in t o f a fa s t e tc h in g fa c e

0 0 1

1 .1 0 0 1

1 .2

a b 1 1 1

0 0 1 1 1 l

1 .1 1

0 0 1

a 1 1 l 1 1 1

1 .1 1

1 .4

0 0 1

b a

1 1 l

0 0 1

1 .6

0 0 1 1 1 l F W C

1 .1 3

b a

0 0 1

b a

1 1 1

1 1 1

1 .7

b

0 0 1

0 0 1

1 .1 3

0 0 1

a

s ta r tin g p o in t o f a s lo w ly e tc h in g fa c e

0 0 1

1 1 l

1 1 1

1 1 1

1 .5

0 0 1

1 .1 2

0 0 1

1 .1 2

1 1 1

1 .3

b

0 0 1

1 1 1

0 0 1

1 1 l F W C

1 .8

0 0 1

a

0 0 1 F W C

1 .1 4

b

a

0 0 1

b

0 0 1

1 1 1

1 .9

F W C

1 .1 4

0 0 1

a

0 0 1

b

1 1 1

1 .1 0 0 0 1

a b

Fig. 5.1. Sidewall shapes for putting back an -directed mask edge. Series 1 is valid for KOH and EDP in principle. a-type: without; b-type: with flat etch ground; γ : inclination angle between sidewall face and wafer plane. The upper {001}-face will go down to the level marked with a broken line if the mask is removed completely after the first etch step. Then the notation of the type is the lower one. It means: 111: {111} crystallographic face, γ = 54,74 ° 001: {001} crystallographic face, γ=0° 11l: fast etching face, γ ≈ 23 ° FWC: face of a weak curvature γ : 0 ° ... some deg.

5.1 Definitions of shapes by the combination of sidewalls s ta r tin g p o in t o f tw o fa s t e tc h in g fa c e s

0 0 1 1 0 0

2 .1

0 0 1 1 0 0

2 .2 2 .1 1

0 0 1

1 0 l l0 1 0 0 1 0 0 1 1 0 0 0 0 1

0 0 1 1 0 0

2 .3

1 0 l

l0 1

1 0 0

2 .1 1

0 0 1

2 .6

1 0 0

l0 1

0 0 1

0 0 1

1 0 0

1 0 l

l0 1

0 0 1

0 0 1

1 0 l l0 1

2 .1 2

0 0 1

2 .1 2

0 0 1

2 .5 1 0 0

1 0 0

2 .4

0 0 1

2 .7

1 0 0

1 0 l

0 0 1

2 .1 3

0 0 1

0 0 1

0 0 1

2 .8

81

1 0 0 l0 1

2 .9 0 0 1

2 .1 3

0 0 1

2 .1 0

1 0 0

1 0 l

0 0 1

1 0 0 0 0 1

Fig. 5.2. Sidewall shapes for putting back an -directed mask edge with an etchant of KOH-type (series 2). The upper {001}-face will go down to the level marked with a broken line if the mask is removed completely after the first etch step. Then the notation of the type is the lower one. It means (γ: inclination angle between sidewall face and wafer plane): 010: {010} crystallographic face, γ = 90 ° 001: {001} crystallographic face, γ=0° 10l: {10l} crystallographic face, γ = 17 ° l01: {l01} crystallographic face, γ = 73 ° The faces of weak curvature are neglected in this series.

82

5 Simple Shape Elements 0 0 1 s ta r tin g p o in t o f a fa s t e tc h in g fa c e

1 0 1

0 0 1

3 .1

a

0 0 1 1 0 1

3 .2

b

0 0 1 1 0 l 0 0 1

1 0 1

3 .7

a b

0 0 1

3 .3

3 .7

0 0 1 1 0 1

1 0 1

3 .4

1 0 l 1 0 1

0 0 1

a

0 0 1

1 0 l

0 0 1

3 .8 0 0 1

b a

b

1 0 1

3 .5

1 0 l

0 0 1

3 .8 a

b

0 0 1

3 .6

1 0 1

a

0 0 1

b

Fig. 5.3. Sidewall shapes for putting back an -directed mask edge with an etchant of EDP-type (series 3). The upper {001}-face will go down to the level marked with a broken line if the mask is removed completely after the first etch step. Then the notation of the type is the lower one. It means (γ : inclination angle between sidewall face and wafer plane): 001: {001} crystallographic face, γ=0° 101: {101} crystallographic face, γ = 45 ° (weak corrugated) 10l: {10l} crystallographic face, γ = 23 ° The faces of weak curvature are neglected in this series.


83

Change of etchant or change of etching procedure Combinations of the following etchants or etching procedures can be considered: -

orientation dependent etchants of KOH-type, orientation dependent etchants of EDP-type, isotropically acting etchants, anisotropically acting dry etching processes.

Following only changes between anisotropically acting etchants of different types should be discussed. Along the -edges of the mask the change of etchant type has no effect. Here, always {111}-sidewalls are produced. In the case of mask edges along (45° relative to the wafer flat) the sidewalls produced by KOH-type etchants are different from the sidewalls produced by EDP-type etchants. Complex sidewalls can be formed by changing the type of etchant. A very interesting shape can be realized by the application of a KOH-type etchant in a first step developing vertical {100}-sidewalls followed by a second step using an EDP-type etchant. Thereby the now slowly etching {110}-faces are generated at the upper edge (directly under the mask) and at the lower one at the etch ground an undercut sidewall is formed as shown in figure 5.4 [Früh2-00].

84


a) 1

s t

2

e tc h s te p K O H -ty p e

n d

e tc h s te p E D P -ty p e

0 0 1

0 0 1 1 0 1 1 0 0 1 0 1

1 0 0

0 0 1

0 0 1

4 .2

4 .1

0 0 1

0 0 1 1 0 1

1 0 1 1 0 1 1 0 1

0 0 1

4 .3

4 .4

b) s h a p e a fte r th e 1

s t

e tc h s te p E D P -ty p e

0 0 1 1 1 0

0 0 1

5 .1 a 2

0 0 1

n d

e tc h s te p K O H -ty p e

1 0 0 1 1 0

5 .2

b 0 0 1 1 0 0

0 0 1

0 0 1

5 .3

Fig. 5.4. Sidewall shapes for two-step etch processes with alteration of the type of etchant; a) first etch step: KOH-type; second etch step: EDP-type (series 4); b) first etch step: EDP-type; second etch step: KOH-type (series 5) It means (γ : inclination angle between sidewall face and wafer plane): 001: {001} crystallographic face, γ = 0 ° (etch ground) 100: {100} crystallographic face, γ = 90 ° (perpendicular to the wafer plane) 110: {110} crystallographic face, γ = 45 ° 1 10 : {110} crystallographic face, γ = 135 ° (undercut) The faces of weak curvature are neglected in this series.


85

5.1.3 Combinations of sidewalls The design of shape elements can be realized on the base of combinations of sidewalls. Considering only one side of the wafer a sequence of sidewalls which run parallel to each other or enclose an angle builds the shape element. In the case of two side etch processes sidewalls at the front side can be combined with sidewalls at the back side in a twofold manner: sidewalls in congruent position or in displaced position. Table 5.3. Types of combinations of sidewalls forming different shapes One wafer side Type of combination Combination of concave angles

Shape element

Shape of mask

hollow; hole (depth wafer thickness)

window

Combination of convex angles

mesa; column; tip (completely underetched)

island; island inside a window

Mixed combination of convex and concave angles resulting in convex or concave bulges Left-right combination as a window region

peninsulas (tongues); bays

peninsulas or bays inside a window

Left-right combination as a masked region Front-back combination with etch ground at the same side of the sidewalls Front-back combination with etch ground at different sides of the sidewalls

groove; trench; narrow window; slit (depth > wafer neighboring isthickness) lands; opposite peninsulas wall; narrow island inknife side a window; (completely neighboring underetched) windows

Schematic representation

86


Apart from complete underetching of masked regions the upper edges of all sidewalls run at the level of the mask. The lower edges run at the level of the etch ground with exception of the geometric etch stop. This is also valid for twostep etch processes with change of the etchant modifying the sidewalls. Two-step etch processes with change of the mask additionally generate different etch ground levels. In view of the design of shape elements the principles of sidewall combination can be analogously used. Simple schematic variants of combinations are shown in table 5.3. Any etched shape can be constructed by such combinations. Further, concerning the layout of mask edges the following points of view must be principally considered: - Combination of concave angles in the wafer plane: new slowly etching sidewalls can be developed in the concave corners. - Combination of convex angles in the wafer plane: new fast etching sidewalls can be developed at the convex corners. - Left-right combination as a wall: a free convex edge is developed below the mask level in the case of a complete underetching of the mask region which is common to both sidewalls. Here new fast etching faces are generated resulting in a new type of sidewall which is a characteristic of two-step etch processes with removing of the mask (see figures 3.9 and 3.10). - Front-back combination with congruent etch ground: when the etch grounds from the front and the backside of the wafer meet (equivalent to the perforation of the wafer) free convex edges are produced, too. The faces which are generated here modify the type of sidewall (see figure 3.12). The interaction of different sidewalls at concave or convex corners and sidewalls which additionally develop at these places are illustrated in sections 5.3 and 5.4 using hollows or mesas as representative examples.

5.2 Qualities of etch ground and sidewall-faces and of the edges between them According to section 3.1 the etched faces can have very different surface qualities depending on the crystallographic orientation, the etchant and the etching conditions. On the other hand, any application makes demands at least of faces having functional importance. Consequently, the choice of the wafer orientation, the etching conditions and the mask design must consider the quality of the resulting faces. Certainly, the parameters of quality are influenced on one hand by the etched depth and by the width of the etch ground and on the other hand by the measurement itself (tactile: tip radius, profile length; optical: evaluated area). At this time it is impossible to find values measured under standardized conditions and suitable for comparison. So, the values in the following tables are guidelines.

5.2 Qualities of etch ground and sidewall-faces and of the edges between them

87

5.2.1 Quality of the etch ground The quality of an etch ground can be characterized by the roughness, deviations from the flatness PV (maximum peak to valley of a profile) and by defects (pyramids on the etch ground, etch pits, steps).

{100}-wafer The {100}-etch ground can deviate from a flat face parallel to the wafer plane in a fourfold manner: “Notching” effect Along {111}-sidewalls a larger depth is reached as in the middle of a deepening. This deviation is called “notching effect”. It is assumed to be the consequence of concentration differences between the centre of a deepening and the region near the {111}-sidewall which is very slowly etched [Find92, Kwa95]. The notching effect depends on the etchant, the etching conditions and the wafer material and increases with increasing depth, figure 5.5a [Früh03]. It is possible to produce a relatively flat etch ground nearly without notching by etching in KOH-solutions with concentrations of about 40wt.%. Using a 50wt.% KOH leads to the reverse tendency, that means a hollow mirror is built. -3 6 0 -3 7 0

-3 7 0

D e p th [µ m ]

D e p th [µ m ]

-3 6 0 -3 8 0 -3 9 0 -4 0 0 0

P V 2 0 0 0

a) notching effect

4 0 0 0 P o s itio n [µ m ]

6 0 0 0

-3 8 0 -3 9 0 -4 0 0 -4 1 0 0

P V 5 0 0

1 0 0 0 1 5 0 0 P o s itio n [µ m ]

2 0 0 0

2 5 0 0

b) hollow mirror effect

Fig. 5.5. Deviations from a flat etch ground (top: measured profiles)

“Hollow mirror” effect The underetching of an -mask edge produces {100}-sidewalls and a weakly curved face is created in the concave edge between the sidewall and the etch ground, figure 5.5b. The cause is a shallow minimum of the etch rate distribution around {100} (see figure 3.5b). Generally, such curved faces can be cre-

88


ated if the etch ground extends because of underetching leading to the “hollow mirror effect”. The deviation from the flat etch ground increases with increasing concentration of the etchant (see figure 5.5b) [Früh03]. The dimension of this effect becomes larger with increasing etch depth, too. The underetching of compensation masks at convex corners leaves as a variant of the hollow mirror effect a blunt ridge on the etch ground [Kamp95] influencing the stiffness of a membrane for example. The hollow mirror effect is more pronounced in KOH than in TMAH etchants [Res03]. Defects Defects on the etch ground can be “micro pyramids” (hillocks) or “micro hollow mirrors”. Models for their generation are illustrated in figure 5.6. Many publications are concerned with micropyramidal hillocks, see [Baum97, Bhat93, Res03, Schröd99, Tan94, Thong01]. The cause of their generation can be a local and temporary masking by undissolved oxidation products, by hydrogen bubbles (generated by the chemical reaction, see section 3.2) or by precipitates of oxide as examples. Another explanation is based on the statistical occurrence of very small micro pyramids (at least 7 atoms) on the atomic rough {100}-face which can grow so long as the top atom is not attacked [Bres96]. Two kinds of hillocks are observed: octagonal pyramids (bordered by sidewalls similar to underetching) and quadratic pyramids. The hillocks can become smaller by fast etching faces or by a peeling with atomic steps. The occurrence of micro pyramids is more frequent in the case of etchants with low concentration (KOH: < 30 %; TMAH: < 20 %) or with relative small rates of underetching (KOH-IPA). The micro pyramids can be removed partially by a short re-etching step after rinsing and drying (long time re-etching produces new micro pyramids). Etching under ultrasound conditions or adding of oxidizing agents reduces the generation of H2-bubbles and of micro pyramids [Baum97]. Initialized by a temporary masking

Initialized by a surface damage

a) Micropyramids

b) Micro hollow mirrors

Fig. 5.6. Defects on the etch ground, top: series of simulated profiles illustrating the development of the defect, bottom: SEM pictures

5.2 Qualities of etch ground and sidewall-faces and of the edges between them

89

Micro hollow mirrors are created by surface damages which can result from the original surface preparation or from defects in the mask (pin holes). These are transmitted into the silicon surface if the process of structuring and stripping of the mask has an insufficient selectivity. During the orientation dependent etching process a local etch ground region develops which is weekly curved [Diet93]. Occurring with a high density both micro pyramids and micro hollow mirrors can overlap each other producing extremely high values of roughness. Roughness Tables 5.4, 5.5 and 5.6 give information on the roughness Ra occurring under typical conditions. Generally, the roughness of the etch ground increases from the original value of the polished wafer surface during the etching process with increasing depth. Further, the composition of the etchant influences the roughness, figure 5.7. Table 5.4. Surface qualities of the {100}-etch ground

roughness [nm]

Conditions KOH 30 % 80 °C KOH 30 % 60 °C KOH-IPA 35 % 70 °C EDP TMAH 25 % 70–90 °C TMAH 25 % 70–100 °C TMAH 20–25 % 90 °C, 20 min TMAH 20–25 % 70–80 °C TMAH 20 % 70–90 °C TMAH-IPA 25 % 70–80 °C TMAH-IPA 20 % 70–80 °C TMAH-NCW 5 % 70–80 °C

Etch depth [µm] 200 150 150 77 unknown 150 unknown 70 150 150 150 unknown

Ra [nm] 40 3 25 80 < 60 1014

1016– 1019 (1500)

1010– 1015 (530)

1000– 1100

450– 500

3.75– 4.20

4.0– 4.7

262– 310 1550– 2820

340– 480 0.5–0.6

45–50

Glass

790– 880 12–39

6.4–8.0

11 13 ∗ 10- 73 ∗ 10- 73 ∗ 10- 10 – 6 6 1016 1490 1460 1185 2046

276– 360

6

150

400– 900

400

1700– 1850 9.8–9.9

8.0–9.0

Physical Properties of Silicon

205

Table A.1. Continuation Properties

Density ρ [g/cm3] Elastic modulus E [GPa] Yield point Rp0.2 [N/mm2] Tensile strength Rm [N/mm2] Compressive strength σdB [N/mm2] Bending strength σbB [N/mm2] Elongation after fracture A5 or (A10) [%] Hardness HB [ - ] or HV [ - ] Knoop hardness HK [ - ] Specific heat cp [J/kgK ] Thermal conductivity λ [W/mK] Coefficient of thermal expansion α [10-6 /K] Electrical resistivity ρ [Ωcm] Melting point TS [°C] Temperature durability Tmax [°C] Dielectric constant ε[-]

Glass

Polymeric material

Sodalime silica glass 2.47– 2.58 60–74

PVC-U (hard)

PEHD

PMMA

PTFE

Epoxy resin

1.38 2.7–3.0

0.941– 0.965 1.0–1.4

1.17– 1.20 3.0–3.3

2.15– 2.20 0.40– 0.75

1.20– 1.90 3.4–4.0

50–80

50–60

20–30

60–80

25–40

40–80

500– 1000

80

40–120

70–120

38

100–170

18–20

80–130

10–50

80–550

3.5–5.5

350–480

6

100–130

46–50

180–200

30

120

1880 0.35– 0.47

1400– 1500 0.16– 0.19

1000– 1050 0.22– 0.25

1050

0.70– 1.25

850– 1000 0.14– 0.16

8.0–10.0

70–80

180–200

70–80

100–120

20–70

108–1013

1015

1015–1016 1014–1015 1016–1018 1014– 1016 126–135 325

500

55–65

60–80

70–100

200–250

80–130

5.0–9.0

3.0–3.5

2.4

3.3–3.8

2.1

3.5–5.0

400–800

100–130

100–140

4.6–5.3 770

(500)

0.13– 0.20

206

Appendix

Density [g/cm 3]

Mechanical properties

2.34 2.33 2.32 2.31 2.3 2.29 -400 -200

0

200 400

600 800 1000 1200 1400

Temperature [°C] Fig. A.1. Dependence of density on temperature [Lyon77, Okad 84] Table A.2. Constants of elasticity Elastic modulus C11 [GPa] 167.54 165.64

C12 [GPa] 64.92 63.94

C44 [GPa] 80.24 79.51

T [K] 4.2 298

dC11/C11*dT [K-1] -9.40E-05

dC12/C12*dT [K-1] -9.80E-05

dC44/C44*dT [K-1] -8.30E-05

T [K]

S44 [GPa-1] 1.258E-14

T [K] 298

T [°C] 25

T [K] 298

T [°C] 25 [Heub91]

Elastic coefficient S11 [GPa-1] S12 [GPa-1] 7.691E-15 -2.142E-15

Young’s modulus for special stress directions E [GPa] E [GPa] E [GPa] 130 169 188

T [°C] Reference -268.8 [Hall67] 25 [Hall67]

300–1000

Torsional modulus for special torsional axises (round stick) [GPa] [GPa] [GPa] 79.5 62 57.8 Sliding modulus for the stress of an {100}-face for directions of G [GPa] G [GPa] 79.51 50.85

[Over77]

Physical Properties of Silicon

207

Table A.3. Bending strengths Bending strength [GPa] Orientations Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

6.1 (0.8)

18

3.9

19 20

2.2 3.5

Weibullmodulus {100}

{111} 0.37 (0.25–0.59) 0.265

0.76 0.17 0.28

3.68 4.4 2.1

0.22 0.9 1.486 0.986

3.38 2.21 3 (0.87) 3.18 3.73

2.1 (0.8)

4.41 3.73 4.41

3.04 6.18 8.23 6.18 8.23

2–3.7 10.1 2

208

Appendix

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Shape and functional elements of the bulk silicon microtechnique: a manual of wet-etched silicon structures

Silicon Devices: Structures and Processing

Silicon

Silicon Avatar

The Silicon Mage

The Silicon Tongue

Silicon Karma

Optimizing the Shape of Mechanical Elements and Structures

Silicon Psalm

Silicon photonics

The Silicon Mage

The Silicon Mage

Handbook of Silicon Semiconductor Metrology

Handbook of Silicon Semiconductor Metrology

Handbook of Semiconductor Silicon Technology

Handbook of Semiconductor Silicon Technology

Thomas A. Easton - Silicon Karma

The Silicon Jungle

The Silicon Mage

The Silicon Mage

The chemistry of organic silicon compounds

The Silicon Mage

The Silicon Jungle

The Silicon Mage

Structural Chemistry of Boron and Silicon

Electrochemistry of Silicon and Its Oxide

Electrochemistry of Silicon and Its Oxide

Measurement and Modeling of Silicon Heterostructure Devices

Measurement and Modeling of Silicon Heterostructure Devices

Bioactive Organo-Silicon Compounds

Tom Easton - Silicon Karma

Shape and functional elements of the bulk silicon microtechnique: a manual of wet-etched silicon structures

Silicon Devices: Structures and Processing

Silicon

Silicon Avatar

The Silicon Mage

The Silicon Tongue

Silicon Karma

Optimizing the Shape of Mechanical Elements and Structures

Silicon Psalm

Silicon photonics

The Silicon Mage

The Silicon Mage

Handbook of Silicon Semiconductor Metrology

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