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

J. Fr¨uhauf Shape and Functional Elements of the Bulk Silicon Microtechnique

Joachim Fr¨uhauf

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 Fr¨uhauf Technische Universit¨at Chemnitz Fakult¨at f¨ur 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 <110>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 <110>). 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 <1 <1 0,01 0,01 Roughness Ra (polished side) µm 0,01 a Different customer specific values and tolerances are possible. b AFM-Microroughness.

200 725 Notch

300 825 Notch

5 < 30 < 30 0,23 0,12 0,00015 b 0,0001 b

6

2 Technological Basis of Bulk-Silicon-Microtechnique [0 1 1 ]

[0 0 1 ]

[1 0 1 ]

[1 1 0 ]

[1 1 0 ]

[1 1 0 ] N o tc h F la t [1 1 0 ] {1 0 0 } - W a fe r

{1 1 1 } - W a fe r [0 1 1 ]

z

[1 1 0 ]

z

{1 1 0 } - W a fe r

[1 0 1 ]

[0 0 1 ]

z

[1 1 0 ] [1 1 0 ] y y x x ( 0 0 1 ) - P la n e

[1 1 0 ] y x

( 1 1 1 ) - P la n e

( 1 1 0 ) - P la n e

Fig. 2.1. Markings of orientation and doping of silicon wafers by flats or notches (no standardization in the case of {110}-wafer); position of second flat (short flat, not shown in figure 2.1 and not applied in the case of notches): 180° to the primary flat: {100}-wafer, ntype; 90° to the primary flat: {100}-wafer, p-type; 45° to the primary flat: {111}-wafer, ntype; no secondary flat: {111}-wafer, p-type

2.2 Technological processes

2.2.1 The basic conception of the bulk-silicon-microtechnique The technological basis for the bulk-silicon-microtechnology is borrowed from the microelectronics and profits of its reached development state. For this, several single chips with the same structure will be produced simultaneously on a silicon wafer (“batch process”). The following technological basic steps are used [Scha91]: - production of thin layers on the wafer surface (growing or deposition), - structuring of the layers or the wafer material (transfer of structures by photolithography and local or complete removing by etching- or dissolving steps), - modifying of the layer- or wafer material (doping, phase-transition, curing). The shape- and functional elements created by the bulk-silicon-microtechnique out of a wafer are mostly not complete functional systems. Usually, a microsystem

2.2 Technological processes

7

consists of several different chips which are combined to a sandwich stack. In order to get a complete unit packaging steps have to be carried out, e.g.: - completion or combination with other shape- and functional elements to a wafer or chip-sandwich (wafer bonding, see section 2.2.5), - hermetic sealing of some functional spaces, - cases with interfaces for electrical and some non-electrical signals and power (wires, windows and openings) as well for fluidic and chemical mass transport. After packaging the separation of the wafer stack into single chips has to be achieved. In the most cases this is carried out by sawing with a diamond blade. This kind of separation is preferred to the mounting of single chips after the separation. The packaging of these by gluing or soldering can not be avoided if a connection of silicon with other materials (gallium arsenide, PCB or ceramics) is favourable or necessary. 2.2.2 Deposition and structuring of passivation layers To create structures inside a substrate the mask technology is used. This mask covers and passivates (protects) selected regions of the substrate surface which should not be attacked by the following etch- or dissolution processes. Not protected regions are called “mask windows”. The most common wet Si etchants are KOH, TMAH, and EDP (see chapter 3). The etch resistant passivation layers (“etch mask”) mostly used in the bulk-silicon-microtechnique are silicon dioxide (SiO2) and silicon nitride (Si3N4). Specifying the thicknesses of the layers their etch rates in the Si etch media must be considered. The etch rate of thermal SiO2 in KOH (30 %, 80 °C) is about 7 nm/min. It decreases with decreasing KOH concentration, etching in TMAH (0.3 nm/min) or using CVD-oxide [Elw98, Seid86]. The etch rate of nitride is very low in KOH. The transfer of the structures into these layers is done by photolithography with a resist. To create the passivation layers on the surface of a silicon wafer, the following processes are used [Bütt91, Heu91, Scha91]: - thermal oxidation of the silicon surface (SiO2), - chemical vapor deposition – CVD (Si3N4, SiO2), - spin-on (resist). During thermal oxidation the substrate material (Si) is involved into the growth of the layer since it is changed into SiO2 in an oxidizing atmosphere. (A layer of 1 µm of Si is changed into a layer of 2.2 µm oxide.) The process can be performed in dry oxygen (O2) or humid atmosphere (O2/H2O) at temperatures between 700 and 1200 °C. It consists of the transport of the oxygen to the wafer surface and its adsorption there, its diffusion through the growing oxide layer and its reaction with the silicon at the boundary Si/SiO2. The thermally grown oxides can also be used as gate oxides (MOS), diffusion and implantation masks and insulating and dielectric layers [Bütt91].

8

2 Technological Basis of Bulk-Silicon-Microtechnique

Table 2.2. Process steps of the transfer of structures on a Si wafer Process step Deposition of light-sensitive organic layer (resist) on the substrate (Si with passivation layers) Exposure (UV light) of the resist throughout a Crmask (glass with structured Cr-layer): local modifications of the resist (positiv-resist: polymers inside the resist are broken open and therefore highly soluble, negativ-resist: resist is highly polymerized and therefore insoluble), developing

S i

R e s is t P a s s iv a tio n la y e r ( S iO 2 , S i3 N 4 )

C r- m a s k

Selective solution of the resist creating a “window” Transfer of the resist windows into the layer underneath e.g. by etching Stripping of the resist

During CVD a chemical reaction of gaseous components to a solid takes place by an external energy supply. This solid reaction product is deposited on a substrate. The supply of energy necessary for the reaction ensues thermally (APCVD – atmospheric pressure CVD, LPCVD – low pressure CVD) or by gas discharge (PECVD – plasma enhanced CVD). The process gases for silicon dioxide are for example SiH4 or Si(OC2H5)4 (TEOS) with CO2, O2 or N2O and for silicon nitride SiH4 with NH3 [Bütt91]. The deposition of the resist is done by the spin-on-process. A drop of material is given onto the substrate and spread out by rotation. The main process steps of photolithography for the bulk-silicon-technology are given in table 2.2. The structural transfer should happen before the threedimensional etching is done, because a deposition of the resist and the lithography is difficult on strongly profiled surfaces. 2.2.3 Wet and dry etching of silicon After transferring the structures onto the wafer, the Si can be etched by different processes: - anisotropic (orientation dependent) wet etching, - isotropic wet etching, - dry etching.

2.2 Technological processes

9

Wet etching Table 2.3. Example for the fabrication of a typical microstructure (one side-fastened cantilever-type, see section 6.1, type 6.1.1) No. Process step 1 Thermal oxidation SiO2, double-sided 2 Resist, double-sided

State after process step 2

3 Photolithography, back side 4 Wet etching of SiO2, back side 5 Stripping of resist

5

6 LP-CVD Si3N4, double-sided 7 Resist, double-sided

7

8 9 10 11 12

11 Photolithography, front side Wet etching of Si3N4 Wet etching of SiO2 Stripping of resist Wet etching of Si, front side (etch depth = 12 wafer thickness – 2 * cantilever thickness)

13 Etching of Si3N4, double-sided 14 14 Wet etching of Si, both sides until perforation of the wafer (etch depth = cantilever thickness) 15 Wet etching of SiO2 15

The orientation dependent wet etching is the most important technique to create structures of shape- and functional elements with an µm-precision and low expenditure and is described in detail in chapter 3. The technology of the fabrication of a typical Si microstructure by this anisotropic wet chemical etching is given in table 2.3.

Dry etching In the dry etching techniques the material is removed by gaseous etch media (plasmas) mostly on the base of the halogens F, Cl or Br. Different principles can be distinguished [Chung00, Elw98, Will98]: - chemical etching, - physical-chemical etching, - physical etching.

10

2 Technological Basis of Bulk-Silicon-Microtechnique

During the chemical process radicals are generated and transported from the plasma to the etch site, where a chemical reaction takes place. If the reaction products are volatile they can be sucked off and the reaction continues. If the products are solid, the reaction is stopped by itself and the material is resistent against further etching. From this a material selectivity arises. In the physical-chemical process (e.g. RIE - Reactive Ion Etching) the chemical reaction is initiated by an ion bombardement of the surface. During this process the surfaces can be passivated by polymer layers which originate from the present halogens and carbons inside the reactor gases at specific operation conditions. Then a further etching only is possible in vertical direction where the protection layer is removed by the ions. So a high anisotropy and selectivity is possible. This development is termed deep RIE (DRIE). It allows vertical etching of Si to depths of several hundred micrometers. The basic idea is an alternating passivation and etching step and is patented by the Robert Bosch GmbH [Lärm94]. The dry etching of Si according to this principle is also called High Aspect Ratio Silicon Etching (HARSE) [Kass96], Bosch deep silicon etching or Advanced Silicon Etching (ASE), a trademark of Surface Technology Systems LTD (STS) [Bhar95]. During physical plasma etching the atoms are striked out of the surface mechanically by chemically inert ions. This process only plays a subordinate role in the fabrication of microstructural elements. During DRIE different effects can be observed [Cra01, Elw98]: - RIE lag: the etch rate depends of the mask width (the aspect ratio increases with decreasing etch rate), - bowing: parabolic curvature of etched sidewalls, - micrograss: long-tailed spikes at the trench bottom. The dry etching process is often combined with the wet etching process. For example, mechanical elements like membranes or cantilevers (see chapter 6) are structured by wet etching the Si wafer from one side followed by a dry etching from the other one, e.g. [Esa94, Gui98, Kwon98, Lee03, McN00]. 2.2.4 Metallization Apart from the used mask films for structuring the wafers (SiO2, Si3N4, photoresist) further materials are used for thin layers with functional characteristics. One group of them are the metals whose application and generation is given in table 2.4. The generation of these layers is mainly performed by Physical Vapor Deposition – PVD (evaporation) or sputtering and wet chemical galvanic processes (electroplating or electroless plating inside of an electrolyte) [Bütt91]. During PVD and sputtering the building of the layers takes place by condensation of a vapor on the substrate. The vapor is physically produced, in evaporation by thermal energy and in sputtering by kinetic energy of ions which solve material out of a target.

2.2 Technological processes

11

Table 2.4. Metal layers Metal Cr

Al, Au

Application mask material for photolithography mask material for dry etching processes reflection layers

Ni, FeNi Al, Cu, Ni

ferromagnetic layers conductive layers (vias)

Pt TiN, TiW WSi2, MoSi2, TiSi2

resistor layers diffusion barriers gate electrodes, conductor path

Al

Generation PVD

Resistant in etchant KOH, TMAH

PVD PVD

Al: TMAH Au: KOH, TMAH electroplating KOH, TMAH PVD, electro- and Al: TMAH electroless plating Cu, Ni: KOH, TMAH sputtering sputtering KOH, TMAH sputtering KOH, TMAH

Electroplating can produce layers with new qualities compared to other techniques especially thick layers. Metal ions which are given by an external source of current (substrate = cathode, metal compound = anode) are reduced to a metal under absorption of electrons. In the electroless plating the electrons come out of a reduction media inside the electrolyte. The main advantage of electroless plating is the formation of an uniform layer thickness. In the field of metallization the electroplating is mainly used for the deposition of Cu. The metals Au, Cr, Pt, Ag, Cu, and Ta are resistant against the wet etchants KOH and EDP, Al against TMAH. Materials which are not resistant in the etch media must be covered during the etch process or must be deposited afterwards. For the production of structures layers two ways are possible: − The deposition of the layer is made on the whole wafer surface and afterwards the areas which should not be coated are etched selectively free with the help of lithographical processes. − The deposition procedure works selectively. This means, that the layer material is only deposited on special areas, whose surface is selectively exposed by lithographical processes. 2.2.5 Wafer bonding Processes of wafer bonding are applied to join two or more Si or glass wafers inseparably and over the whole area. Two main processes can be distinguished [Bütt91, Elw98, Gös99, Scha91, Wiem98]: Silicon Fusion Bonding (Silicon Direct Bonding) – SFB – and Anodic Bonding. Bond partners of the SFB are polished Si wafers of any crystal orientation and doping with thin layers of natural or thermal oxide (bond oxide). The bond process consists of three steps: - pre-treatment, - pre-bonding at room temperature, - heating to T = 200–800 °C.

12

2 Technological Basis of Bulk-Silicon-Microtechnique

The pre-treatment includes the cleaning and surface activation of the wafers. The used wafers must be of highest quality concerning roughness, flatness and number of particles in order to reach a high quality of bonding. In the second step the wafers are positioned to each other and brought into contact. Then the bond front which is based on hydrogen bonds between the surfaces spreads spontaneously. This step can be supported by mechanical or electrostatical pressure. By the final heating step the hydrogen bonds are converted into covalent bonds increasing the strength of the bonding extremely. If the heating to high temperatures is not possible in an advanced stage of technology because of the function of electronical devices, metal layers on those or metal structures (electrodes, pads for wire bonding) on the basic wafers an alternative is given by the Low Temperature Bonding [Wiem98]. This process is compatible with metals (e.g. Al) because high bond strengths are reached at temperatures below 400 °C. During Anodic Bonding Si wafers are joined with glass wafers (containing a sufficient number of alkaline ions) under the influence of an electrical voltage and temperature. The temperatures are 300–500 °C, the voltage is between 20 and 2,000 V. This kind of joining is based on the diffusion of alkaline ions resulting in a space-charged region and the building of Si-O-Si compounds at the boundary. The mechanical properties of the bonded interfaces are tested with different methods [Gös99, Rich02]. During the process technology the bonding step is possible at different stages. If two or more Si wafers are bonded at the beginning the produced stack can be handled as one wafer and can be easily structured by 3-dimensional orientation dependent etching. The bond oxide layer works as an etch stop but can be removed by an oxide etching. With the process of wafer bonding multiple wafer compounds, selective bondings, capsules of sensors or SOI-wafers can be realized. Additional bond processes work with intermediate layers like the eutectic bonding (Si – Au) or the seal-glassbonding. u p p e r p la te w ith tig h t e le c tr o d e in s u la tin g p la te m id d le p la te w ith m o v a b le e le c tr o d e a n d 2 s ilic o n s p r in g s in s u la tin g p la te

b o n d p a d s

a) Schematical sketch

lo w e r p la te w ith tig h t e le c tr o d e

b) SEM-picture

Fig. 2.2. Mounting of an acceleration sensor [Geß95]

2.2 Technological processes

13

As an example for a typical microstructural element in the bulk-siliconmicrotechnique with bonding steps within the process technology an acceleration sensor with multiple chip planes is shown in figure 2.2. 2.2.6 Plastic reshaping of silicon microstructures The shapes of microstructural elements realized by an etching process are limited by their given position completely inside the wafer or chip volume. Atoms are removed and the remaining ones are located at their original positions. By the process of plastic reshaping it is possible to transfer atoms into new positions. Therefore new shapes with elements, which partially can be located outside the wafer or chip plane can be created. Because of the brittleness of Si at room temperature the plastic reshaping of Si becomes possible at temperatures T > 700 °C [Früh1-99]. The microstructural elements which come into question for a plastic reshaping are those which are suitable for an elastic deformation, too. At this moment two different processes of plastic reshaping of Si are known [Früh2-99, Früh1-00, Gärt1-01], table 2.5. Examples of deformed structures are shown in figures 2.3 and 2.4. The deformation process in the furnace is performed with tools such as rods, stamps and rests, which also can be prepared out of Si. It requires the heating of the whole chip/wafer. The exact degree of bending can be reached by the choice of the corresponding height respectively depth of the stamp and rest, so that a high precision and reproducibility of the realized shapes is guaranteed. The process can be performed as a batch process (simultaneous deformation of several structures inside a wafer). Table 2.5. Different processes of reshaping Process of reshaping In a furnace with tools by heating the microstructures up to T > 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

3 Orientation Dependent Etching of Silicon

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.

3.1 Fundamental principles of the generation of shapes

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

3 Orientation Dependent Etching of Silicon

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 <110>-Zone

v

   e tc h g r o u n d

Sidewall along <110> 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 )

Rates of faces of the <100>-Zone

v

e tc h g ro u n d

       

Sidewall along <100> mask edge

(0 0 1 )

2 .5 2

m a s k

1 .5

Rates of faces of the <130>-Zone



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

Sidewall along <130> mask edge

Fig. 3.5. The use of the WJC illustrates the development of concave sidewalls along mask edges of different directions: <110>, <100>, <130> ({100}-Wafer, KOH-type etchant)

3.1 Fundamental principles of the generation of shapes

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

3 Orientation Dependent Etching of Silicon

< 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

3.1 Fundamental principles of the generation of shapes

25

Table 3.1. Fast etching faces at convex <110>-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 <110>-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

3 Orientation Dependent Etching of Silicon

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.

3.1 Fundamental principles of the generation of shapes

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 <110>-direction

    

    

e tc h g ro u n d

b) Sidewall along <100>-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

3 Orientation Dependent Etching of Silicon

Table 3.2. Fast etching faces on free convex edges on the {100}-silicon wafer (c curved) Sidewalls along <110>-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 <100>-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.

3.1 Fundamental principles of the generation of shapes

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

3 Orientation Dependent Etching of Silicon

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 <110>-directions perpendicular to each other exist in the wafer plane, figure 2.1. Along mask edges which are parallel to these <110>-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 <100>-directions which are also perpendicular to one another. With the primary flat respective with the <110>directions they include an angle of 45°. The formation of sidewalls along <100>edges of a mask is in control of the etch rates of faces belonging to the crystallographic <100>-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 <100>-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 <110>

mask II <100>

{100}-Si EDP-type etchant

mask II <110>

mask II <100>

31

{110}-Si KOH-type etchant

mask II <111> mask II <112>

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 <110>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 (<112>-direction: 54.74° to <110>), figure 2.1, because of their absolute minimum of etch rates of the <112>-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 <110>-direction which is perpendicular to the flat reflect the symmetry of the <110>-normal direction of the {110}-wafer, figure 3.15. Along mask edges in an angle of 90° relative to the primary flat (parallel to <110>) {111}-sidewalls are generated (absolute minimum of etch rates of the <110>-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 <110> respective parallel to <100>) the generation of sidewalls is controlled by the rates of the <100>-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

3 Orientation Dependent Etching of Silicon

< 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 <112>-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 <110>. Consequently, applications which need a smooth etch ground have to be ruled out.

Etching of {112}-wafers The {112}-face belongs to the <110>-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 <110> on the {112}-wafer the developing cross section will be defined by the etch rates of the <110>-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 <110>

(1 1 2 )

9 0 °

3 5 ,2 6 ° (0 0 1 )

_

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

cross section along <111>

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

3.1 Fundamental principles of the generation of shapes

33

Grooves along <110>-direction can result in a geometrical etch stop having a cross section like a saw tooth. The sidewalls of a groove in <111>-direction (90° to <110>) 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 <111>-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

3 Orientation Dependent Etching of Silicon

- the difference between a crystallographic axis (<001>, <111>, <110>) and the normal of the wafer surface, - the difference between a crystallographic direction (standard <110>) 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 <110>: 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 <110>-direction. The mask contains no edge near <110> which can confuse. 4 Test structure according to [Steck91] {111}-sidewalls developing at the outer concave corners mark the correct <110>-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

3.1 Fundamental principles of the generation of shapes

35

Etching of circular windows produces square deepenings (pyramids) dislocated by ∆x. The <110>-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 <110>. 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

3 Orientation Dependent Etching of Silicon

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 <110>direction, - the development of correctly <110>-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 Chemistry and techniques of wet silicon etching

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

3 Orientation Dependent Etching of Silicon

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:

3.2 Chemistry and techniques of wet silicon etching

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)

3 Orientation Dependent Etching of Silicon

< 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.

3.2 Chemistry and techniques of wet silicon etching

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

3 Orientation Dependent Etching of Silicon

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]

3.2 Chemistry and techniques of wet silicon etching

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

3 Orientation Dependent Etching of Silicon

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

3.2 Chemistry and techniques of wet silicon etching

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

3 Orientation Dependent Etching of Silicon

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.

3.3 Etch mask design and simulation of silicon etching

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 <110>- or <100>-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 <110> KOH- or EDP-type

along <100> KOH-type

along <100> 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

3 Orientation Dependent Etching of Silicon

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

3.3 Etch mask design and simulation of silicon etching

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 <110>-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

<100>-beam

l

b

b = 2d l ≥ 3d

50

3 Orientation Dependent Etching of Silicon

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 <110>-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 <110>-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 <112>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

3.3 Etch mask design and simulation of silicon etching

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].

52

3 Orientation Dependent Etching of Silicon

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.

3.4 Basic processes of the bulk-silicon-microtechnique

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

3 Orientation Dependent Etching of Silicon

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

3.4 Basic processes of the bulk-silicon-microtechnique

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

3 Orientation Dependent Etching of Silicon

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

3.4 Basic processes of the bulk-silicon-microtechnique

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

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3 Orientation Dependent Etching of Silicon

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

3.4 Basic processes of the bulk-silicon-microtechnique

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

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3 Orientation Dependent Etching of Silicon

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

3.4 Basic processes of the bulk-silicon-microtechnique

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

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3 Orientation Dependent Etching of Silicon

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

3.4 Basic processes of the bulk-silicon-microtechnique

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

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3 Orientation Dependent Etching of Silicon

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

3.4 Basic processes of the bulk-silicon-microtechnique

65

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Abu-Zeid MM (1984) Corner undercutting in anisotropically etched isolation contours. J Electrochem Soc 131, 9: 2138–2142 Acero MC et al. (1995) Electrochemical etch-stop characteristics of TMAH:IPA solutions. Sensors and Actuators A 46–47: 22-26 Alavi M, Schumacher A, Wagner HJ (1992) Laser machining and anisotropic etching of <111>-silicon for applications in microsystems. Micro System Technologies ’92: Proc of the 3rd Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 227–231 Allongue P, Kosta-Kieling V, Gerischer H (1993) Etching of silicon in NaOH solution: II. Electrochemical studies of n-Si(111) and (100) and mechanism of the dissolution. J Electrochem Soc 140: 1018–1026 Ashruf CMA et al. (1998) A new contactless electrochemical etchstop based on a gold-silicon-TMAH galvanic cell. Sensors and Actuators A 66: 284–291 Bäcklund Y, Rosengren (1992) New shapes in (100) Si using KOH and EDP etches. J Micromech Microeng 2/75-79:75–79 Barycka I, Zubel I (1995) Silicon anisotropic etching in KOH-isopropanol etchant. Sensors and Actuators A 48: 229–238 Bean KE (1978) Anisotropic etching of silicon. IEEE Transactions on Electron Devices 10: 1185–1193 Beyer V (1996) Anisotropes selektives naßchemisches Ätzen von monokristallinen Siliciummembranen unter Verwendung MeV-implantierter Strukturen. Diploma Thesis, Technische Universität Chemnitz Chang WS (1998) A new method to find the <110> crystal orientation on a (100) silicon wafer by pre-etching process. Micro System Technologies ’98: 6th Int Conf & Exhibition on Micro Elektro, Opto, Mechanical Systems and Components, Germany: 658–660 Choi WK et al. (1998) Characterisation of pyramid formation arising from the TMAH etching of silicon. Sensors and Actuators A 71: 238–243 Dorsch O, Hein A, Obermeier E (1997) Effect of the silicon content of aqueous KOH on the etching behaviour of convex corners in <100> single crystalline silicon. Transducers ‘97: Proc of the 9th Int Conf on Solid-State Sensors and Actuators, USA: 683–686 Dziuban JA (2000) Microwave enhanced fast anisotropic etching of monocrystalline silicon. Sensors and Actuators 85: 133–138 Elwenspoek M, Jansen H (1998) Silicon Micromachining. Cambridge University Press, Cambridge Ensell G (1995) Alignment of mask patterns to crystal orientation. Transducers ’95: Proc of the 8th Int Conf on Solid-State Sensors and Actuators, Sweden: 186–189 Frühauf J et al. (1993) A simulation tool for orientation dependent etching. J Micromech Microeng 3: 113–115 Frühauf J et al. (1993) Entwurfswerkzeuge zur Strukturierung von SiliciumEinkristallscheiben durch nasschemisches Ätzen für Mikrotechnik. Final Report AIF-Project 298D, Technische Universität Chemnitz

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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 <110> 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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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.

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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

73

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 <110>-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 <100>-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

5 Simple Shape Elements

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.

5.1 Definitions of shapes by the combination of sidewalls

77

{111}-Sidewalls along <110> 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 <100> 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 <112> 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 <110> (perpendicular to the flat) also {111}-sidewalls develop inclined by 35.26° relative to the wafer surface. The type of sidewalls arising along <100> (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

5 Simple Shape Elements

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 <110> mask edges. This asymmetry can be seen assuming a rotation of the wafer surface from the {001}-situation by 35.26° about the <110>-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 <110>-direction are parallel to the <111>-direction. Consequently, they must consist of faces of the <111>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.

5.1 Definitions of shapes by the combination of sidewalls

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 <110>-parallel mask edges. In this case the shapes are qualitatively independent on the type of etchant. Along <100>-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

5 Simple Shape Elements

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 <110>-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 <100>-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 <100>-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.

5.1 Definitions of shapes by the combination of sidewalls

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 <110>-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 <100> (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

5 Simple Shape Elements

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.

5.1 Definitions of shapes by the combination of sidewalls

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

5 Simple Shape Elements

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 <100>-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

5 Simple Shape Elements

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 <5 < 20 < 35 < 15 < 10 <40 25

70 60 50 40 30 20 10 0

Reference own values [Find92] [Früh2-97] [Früh2-97] [Merl93] own values [Chen01] [Shik2-01] [Früh2-97] [Früh2-97] [Früh2-97] [Sar00]

KOH, depth 400 µm

KOH, depth 200 µm

TMAH, depth 400 µm

TMAH, depth 150 µm

10

20

30

40

50

60

concentration [%]

Fig. 5.7. Influence of etchant and etch depth on the roughness of the {100-etch ground (etching temperature 80 °C)

90

5 Simple Shape Elements

Other wafer orientations The {110}-etch ground is composed of two symmetrical facets of the type {144} or {155} [Sato2-99] (see figure 3.3c) resulting in a furrowed texture with large values of roughness. Using KOH with a concentration in a narrow interval of 45–47 % and at the high temperature of 135 °C a relative smooth etch ground was found [Tana03]. The {112}-etch ground develops a relative smooth basic ground partially covered by overlapping hillocks which are shown in figure 5.8. Faces of the <110>zone change the surface quality from atomic rough in the case of {100} to microscopic stepped near {111} with a border near {112} [Veen01]. The {111}-etch ground shows steps depending on the misorientation and defects, see figure 3.3a. Practically it is very difficult (or nearly impossible) to produce an atomic flat etch ground by orientation dependent etching with micro- or macroscopic dimensions. The etchant attacks the steps removing layer by layer but new steps are created at defects [Nij00, Veen01].

Fig. 5.8 Overlapping hillocks on an {112}-etch ground etched in 30 % KOH at 80 °C Table 5.5. Surface qualities of the {110}-etch ground Conditions KOH 30 % 80 °C KOH 34 % 70 °C KOH-IPA 27 % 70 °C TMAH 25 % 90 °C TMAH 25 % 70 °C

Etch depth [µm] 250 150 115 155 80

Roughness Ra [nm] 610 500 535 190 675

Reference own values [Sato2-99] own values own values [Shik2-01]

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

91

Table 5.6. Surface qualities of the {112}- and {111}-etch ground Conditions {112}-Si: KOH 30 % 80 °C {112}-Si: KOH 34 % 70 °C {112}-Si: TMAH 25 % 80 °C {111}-Si: KOH 34 % 70 °C

Etch depth [µm] 200 200 77 205

Roughness Ra [nm] 5–100 500–2400 55 200 120

Comment Reference flat area hillocks flat area hillocks steps

[Kuhn02] [Sato2-99] own values [Shik00]

5.2.2 Quality of sidewalls Table 5.7 gives information on the inclination γ and the roughness Ra of sidewalls occurring under typical conditions. The most important ones are pictured in figure 5.9. The inclination of sidewall faces has a theoretical value provided that the Miller indices are known. On the other hand the crystallographic orientation can be identified by measurements of the inclination and directions of the edges of the sidewalls which must not be of a low index type. Such measurements are difficult because of the small dimensions and deviations from an ideal flat face (roughness, defects). {100}-sidewalls assumed as vertical are weekly curved resulting in an overall inclination smaller than 90°. This fact is analogous to the hollow mirror effect of the etch ground. Table 5.7. Surface qualities of sidewall faces Sidewall {111} along <110>

Wafer {100}

{100} along <100> {110} along <100>

{100} {100}

{110} along {100} <110> {111} along {110} <110> {100} along {110} <100> fast etching faces {113} along {110} <110> {113} along {110} <110>

Conditions KOH 30 % 80 °C KOH 33 % 90 °C (FZ) TMAH 25 % 80 °C KOH 20–50 % 80 °C TMAH 20–25 % 80–90 °C KOH-IPA KOH-IPA 35 % 70 °C TMAH-IPA 20–25 % 70–80 °C TMAH-NCW 22 % 90 °C EDP KOH 10–50 % 80 °C KOH 30 % 80 °C KOH 30 % 80 °C TMAH 25 % 90 °C KOH 30 % 80 °C TMAH 25 % 90 °C KOH 35 % 80 °C TMAH 25 % 80 °C

n. m. not measured, unkn. not measured

γ [°] 54.65

45 n. m. 45.4–45.8

Ra [nm] 170 <70 315 20 unkn. 80 613 121-840

References [Früh03] [Kwa95] own values [Früh03] own values [Shie99] [Früh2-97] [Dötz00]

45 n. m. 45.7 about 90 about 90 35.15 35.20 44.4 44.3

50 93 unkn. 350-660 115 190 30 15

[Seki2-99] [Dötz00] [Zav94] own values [Dötz00] [Dötz00] [Dötz00] [Dötz00]

24±2

60-100

[Res00]

24±2 (curved)

10-30

[Res00]

54.60 87–89 89.3–89.6

92

5 Simple Shape Elements

{111}, all etchants

{100}, KOH

{110}, KOH-IPA

{110}, TMAH-IPA

{100}, TMAH

Fig. 5.9. Quality of sidewall faces on the {100}-wafer: sidewall type, etchant (mentioned faces are marked with arrows)

<110>-mask edge

{113}-near, KOH

{113}-near, TMAH

{113}-near, TMAH-IPA

{103}-near, TMAH

{103}-near, TMAH-IPA

<100>-mask edge

{103}-near, KOH

Fig. 5.10. Quality of fast etching faces at convex edges on the {100}-wafer: sidewall type, etchant (mentioned faces are marked with arrows)

Typical defects are shallow, terraced etch pits on the {111}-sidewalls or hollow mirrors on the {100}-sidewalls. They can be caused by defects of the mask edge (small deviations of the mask edge from a straight line) and by defects inside the silicon. Terraced etch pits were found more frequently in Czochralski-Silicon as in Floating-Silicon [Hein00]. Also high temperature processes in oxygen atmosphere stimulate the creation of this defect. Assuming an inhomogeneous distribu-

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

93

tion or a precipitation of oxygen an increased etch rate in oxygen rich regions could be the explanation [Müll00]. In any case the use of wafers from Floatingsilicon yields the best quality of the{111}-sidewalls [Kwa95]. Fast etching sidewall faces resulting from a maskless etching of convex edges (see section 3.1.2) develop different surface qualities but only little information exists. The quality changes partially also during the growth of these faces. So in the case of the {113}-near faces along <110>-edges the quality is improved with increasing etching time in KOH. On the other hand etching in TMAH the surface quality of the growing {112}-…{113}-near faces is smooth direct at the beginning [Res00], table 5.7 and figure 5.10. The fast etching faces along <100> show a surface which is coarsely furrowed perpendicular to <100>. 5.2.3 Quality of edges Some applications make requirements to the sharpness of edges. Only little information exists about this feature. The quality of edges can be characterized by the radius of curvature and by defects. The last ones are the result of deviations of the mask edge from a straight line corresponding to the defects of the sidewall faces. Most edges are very sharp. Their radius of curvature Rc cannot be measured sufficiently exact by the SEM technique. The high resolution TEM investigation of thinned cross sections must be used, figures 5.11 and 5.12. Available values of important edges are summarized in table 5.8. The concave 70.5°-notch created by the geometrical etch stop on the {100}wafer was found to be the sharpest edge. The radius estimated from a TEM picture is an upper limit. The atomic structure of this notch is not investigated at this time. The convex 70.5°-knife produced by the mask inversion technique is slightly blunted by the interface oxidation below the nitride mask (“birds beak effect”) resulting in an asymmetrical flattening. Table 5.8. Quality of edges Edge Built by the {111}-sidewall with {100}-surface {100}-etch ground {111}-sidewall neighboured 70.5° (geometrical etch stop) {111}-sidewall neighboured 70.5° (after mask inversion) Built by the {100}-sidewall with {100}-surface {100}-etch ground

Type

Etch depth [µm]

Rc [nm]

convex edge concave edge (concave) notch

2 1 2

about 50 about 25 <5

(convex) knife

2

about 30

convex edge concave notch

1 1

about 15 about 95

94

5 Simple Shape Elements

a) {100}-{111} convex edge

b) {100}-{111} concave edge

c) {111}-{111} 70.5°-notch

d) {111}-{111} 70.5°-knife

Fig. 5.11. <110>-sidewall edges on the {100}-wafer (TEM-pictures)

a) {100}-{100} convex edge

b) {100}-{100} concave edge

Fig. 5.12. <100>-sidewall edges on the {100}-wafer (TEM-pictures)

5.3 Shape elements made by one-step etch processes 5.3.1 Hollows (Deepenings) Simple hollows or deepenings are the most used shape elements made by orientation dependent wet etching for diverse applications of the resulting cavities or of the remaining silicon below the etch ground. Examples are cavities for fluidic elements, membranes as support for thermal or caloric elements and membranes as mechanical springs. In numerous cases the membrane will be structured by a second process (mostly dry etching) starting at the back side. If the etched depth exceeds the wafer thickness a hole is created. Examples of application are holes for optical or fluidic elements. Holes in the silicon can also be used for the production of membranes consisting in the back side passivation layer stack. Only the wafer orientations {100} and {110} are of interest. Shapes of the resulting hollows are collected in tables 5.9 and 5.10. The real shape results from the layout of the mask window. The bottom of the hollows (etch ground) can show deviations from a flat face, see section 5.2. More complex hollows can arise from joining two or more hollows resulting from different windows if suitable underetchings occur, see section 3.1.2.

5.3 Shape elements made by one-step etch processes

95

{100}-wafer <110>-mask edges (α = 0° or 90°): The most important shape of a hollow corresponds to the concave combination of four {111}-sidewalls along the <110>directions at the same side of the {100}-wafer (rectangular window in the mask) resulting in a rectangular reverse pyramidal stump or roof, types 5.9.1a and 5.9.3a, table 5.9. If the depth dT exceeds the amount d T = w / 2.

(5.1)

inside a window of the width w the opposite {111}-faces meet in the depth, types 5.9.2a and 5.9.4a, table 5.9 ("geometrical etch stop", see also section 3.1.2). Inside of small, square mask windows “stopping” reverse pyramids are formed, figure 5.1. Windows which are long, narrow and rectangular lead to trenches with V-shaped cross sections (“V-grooves”) discussed in section 5.3.3. <100>-mask edges (α = 45°): In the case of a rectangular mask layout along the <100>-direction on the {100}-wafer the dominant sidewalls depend on the used etchant, see section 5.1. Because of the considerable etch rates of these sidewalls the slowly etching {111}-faces arise in the concave corners leading to a final shape which is completely bound by these faces, figure 5.13. In KOH-type etchants the vertical {100}-sidewalls arise, types 5.9.1b and 5.9.3b, table 5.9. To hinder the development of {111}-borders in KOH-type etchants a special pattern of windows near the concave corners is proposed (“concave corner compensation”) [Nik97]. In EDP-type etchants the 45°-inclined {110}-sidewalls are developed, types 5.9.1c and 5.9.3c, table 5.9. Opposite {110}-sidewalls can meet resulting in a configuration analogous to the geometrical etch stop by {111}-faces but different because of the considerable etch rate. No real etch stop occurs but the depth corresponds no more to the rate of the {100}-etch ground, types 5.9.2c and 5.9.4c, table 5.9. The situation should be called “geometrical etch delay”. Additional etch ground at an interim depth: In regions suffering a geometrical etch stop or delay a new etch ground can be created by raising the situation of stop or delay. This is possible by fast etching faces coming from top as consequence of a complete underetching of misoriented masked stripes [Vang2-96]. Similar an opening of stopping regions by an underetching front creates a new etch ground, figure 5.14. Note, that the rough quality of the new etch ground is strongly influenced by the delaying structures. By this method regions of different depths can be produced using only one mask and one etch step.

96

5 Simple Shape Elements Fig. 5.13. Etched groove with rectangular mask layout along the <100>direction; in the concave corners the {111}-sidewalls are built (the final shape is not yet reached, so the shape is not yet completely bounded by the {111}-faces); (light areas: underetched mask)

a)

b)

Fig. 5.14. Regions of different depths produced with only one mask and one etch step (nominal etch depth: 265 µm – groove a, etch depth in groove with etch delay: 105 µm – groove b)

5.3 Shape elements made by one-step etch processes

97

Table 5.9. Hollows (deepenings) in the {100}-wafer (unique depth) {100}-wafer

Dominant angle of the mask edge to the flat a) α = 90° or 0° b) α = 45° etchant of KOH- or etchant of KOH-type EDP-type

c) α = 45° etchant of EDP-type

A

Type 5.9.1 Quadratic window A

B B

A

A B B

A

A

A-A

Type 5.9.2 Quadratic window: Geometrical etch stop or etch delay

A-A

A-A

B-B

B-B A

A A

A

A-A

A-A Type 5.9.3 Rectangular window

A

A

B

A

A B

A A

A-A

A-A

A-A

B-B Type 5.9.4 Rectangular window: Geometrical etch stop or etch delay

A

A A

A

A-A

A-A

98

5 Simple Shape Elements

Fig. 5.15. Type 5.9.1a: Square deepening along <110> (α = 0 or 90° to the flat) with etch ground

Fig. 5.16. Type 5.9.2a: Deepening along <110> (α = 0 or 90° to the flat) with geometrical etch stop

Fig. 5.17. Type 5.9.3a: Rectangular deepening along <110> (α = 0 or 90° to the flat) with etch ground

Fig. 5.18. Type 5.9.4a: Rectangular deepening along <110> (α = 0 or 90° to the flat) with geometrical etch stop

Fig. 5.19. Type 5.9.3b: Rectangular windows along <100> (α = 45° to the flat) with etch ground, KOH-type etchants

Fig. 5.20. Type 5.9.3c: Rectangular windows along <100> (α = 45° to the flat) with etch ground, EDP-type etchants

5.3 Shape elements made by one-step etch processes

99

{110}-wafer Table 5.10. Hollows (deepenings) in the {110}-wafer (unique depth) {110}wafer

Dominant angle of the mask edge to the flat a) α = 0° resp. 90° b) α = 0° resp. 90° c) α = 35.26° etchant of KOH-type etchant of EDP-type etchant of KOH- or EDP-type B (4 5 ° )

Type 5.10.1

B

B

{1 0 0 }

A

A A

A

B

A A

B B

3 5 ,2 6 °

A -A

A -A

B -B

B -B

A -A

B -B

Type 5.10.2 Stop in depth

{1 0 0 }

A A

A A

A -A

A -A

Type 5.10.3 Geometrical etch stop

A A

A -A

A A

A

A -A

A

A -A

A A

A -A

100

5 Simple Shape Elements

Etching a rectangular window with edges orientated parallel and perpendicular to the flat inside a wafer three types of sidewalls are generated: - perpendicular to the flat: 35.26° inclined {111}-sidewalls (little underetching), - parallel to the flat: 45° inclined {100}-sidewalls by KOH-type etchant; vertical {110}-sidewalls by EDP-type etchant, - in concave corners: vertical {111}-sidewalls. The resulting hollow has always a mirror symmetry, table 5.10. It is not possible to create a quadratic hollow. If the depth dT exceeds the amount (5.2) dT = ½ w / 2 an etch stop in depth is reached by meeting of the opposite {111}-faces. This situation is not the ultimate geometrical etch stop (type 5.3.7a) because of the presence of {100}-sidewalls, type 5.10.2a, table 5.10.

Fig. 5.21. Type 5.10.2a: Hollow on an {110}-wafer with stop in depth (etchant of KOH-type); mask window along 0° respective 90° to the flat

Fig. 5.22. Type 5.10.1a: Hollow on an {110}-wafer with etch ground (etchant of KOH-type); mask window along 0° respective 90° to the flat

Fig. 5.23. Type 5.10.3a: Hollow on an {110} wafer with geometrical etch stop (etchant of KOH-type); mask window along 0° respective 90° to the flat

5.3 Shape elements made by one-step etch processes

101

Fig. 5.24. Type 5.10.1b: Hollow on an {110}-wafer with etch ground (etchant of EDP-type); mask window along 0° respective 90° to the flat

Using a rhombic mask window with edges along <112>-directions (35.26° relative to the flat) a rhombic hollow with vertical {111}-sidewalls results in all orientation dependent etchants, types 5.10.1c-3c, table 5.10. A minimum underetching occurs along these directions. 5.3.2 Mesas (Elevations) Etching of a masked island produces a mesa or elevation above the etch ground limited by a convex combination of sidewalls at the same side of the wafer. Because of the relative minimum etch rate of the sidewall faces, new sidewalls are developed at the convex corners. Here, fast etching faces are generated underetching the convex corners of the mask island and removing a considerable volume. This effect appears to be the main problem in the production of high mesas. It can be compensated by extensions of the mask around the convex corners (compensation masks), see section 3.3.2. After the period over which the compensation is effective the underetching progresses as in the case of uncompensated islands resulting in a column dominated by the corners. If the fast etching corner faces meet each other directly below the mask, the top level area is reduced to zero. A tip is produced and completely separated from the mask [LiuJH95]. Afterwards the fast etching faces lower the height and finally leave a residual shape bounded by faces of week curvature (FWC), see section 3.1.2. Examples of application of mesas are electrodes for electrostatic actuators, columns as support of other components or tips (for atomic force microscopy) in the case of complete underetching. Shallow mesas can be used for the definition of selected regions for wafer bonding processes. Only wafer orientations {100} and {110} are of interest. Shapes of the resulting mesas are collected in tables 5.11 and 5.12. More complex mesas can arise from a partitioning of a mesa into two or more mesas if suitable underetchings occur, see section 3.1.2.

102

5 Simple Shape Elements

{100}-wafer <110>-mask edges (α = 0° or 90°): A rectangular island of the mask with edges along <110> results in a mesa with {111}-sidewalls forming a rectangular pyramidal stump or roof, a sufficient corner compensation provided. Using an <100>-beam an approximately perfect pyramidal shape can be achieved, section 3.3.2. Note that the corner compensation always corresponds to the etching time. Consequently the quality of the resulting edges depends on the accurate keeping of the etching time. Because of the considerable differences of the underetching at convex corners it must be also distinguished between the mesa shapes along the <110>directions etched in KOH- and EDP-type etchants. The relative small inclinations of the sidewalls arising in EDP-type etchants (54.74–45°) leads to residuals of the compensation structures around the corners at the etch ground, type 5.11.1a and 2a. <100>-mask edges (α = 45°): Mesas with <100>-orientated edges suffer a considerable underetching particularly in KOH-type etchants. With it the convex corners are less clearly blunted. Using a triangular compensation mask a sharp edge between the vertical sidewalls can be realized resulting in a rectangular solid. In EDP-type etchants a pyramidal stump with rounded corners at the etch ground arises.

5.3 Shape elements made by one-step etch processes Table 5.11. Mesas (elevations) on the {100}-wafer (unique height)

103

Dominant angle of the mask edge to the flat a) α = 90° or 0° b) α = 45° etchant of KOH- or etchant of KOH-type EDP-type KOH-type Type 5.11.1 A Corners not compenA A sated

EDP-type

Type 5.11.2 Corners compensated

A

A

KOH-type A

A

A

A

EDP-type A

A

A

A

A

c) α = 45° etchant of EDP-type

104

5 Simple Shape Elements

Fig. 5.25. Type 5.11.1a: Mesa on an {100}-wafer; dominant angle of the mask edge to the flat 0 or 90°; corners not compensated, etchant of KOH-type

Fig. 5.26. Type 5.11.1a: Mesa on an {100}-wafer; dominant angle of the mask edge to the flat 0 or 90°; corners not compensated, etchant of EDP-type

Fig. 5.27. Type 5.11.2a: Mesa on an {100}-wafer; dominant angle of the mask edge to the flat 0 or 90°; corners compensated, etchant of KOH-type

Fig. 5.28. Type5.11.2a: Mesas on an {100}-wafer, dominant angle of the mask edge to the flat 0 or 90°; corners compensated, etchant of EDP-type

Fig. 5.29. Type 5.11.1b: Boss on an <100>-orientated cantilever (dominant angle of the mask edge to the flat 45°); corners not compensated; etchant of KOH-type

Fig. 5.30. Type 5.11.2b: Mesa on an {100}-wafer; dominant angle of the mask edge to the flat 45°; corners compensated, etchant of KOH-type

5.3 Shape elements made by one-step etch processes

105

{110}-wafer Etching a rectangular mask island with edges orientated parallelly and perpendicularly to the flat two types of sidewalls are generated: - perpendicular to the flat: 35.26° inclined {111}-sidewalls (little underetching), - parallel to the flat: 45° inclined {100}-sidewalls in KOH-type etchants or vertical {110}-sidewalls in EDP-type etchants. The convex corners are underetched. The resulting mesa has always a mirror symmetry, table 5.12. To construct an approximately quadratic shape the underetching of the flat-parallel edges must be considered. It is not possible to create a mesa with exact quadratic symmetry because of the different sidewalls. Using a rhombic mask island with edges along <112>-directions (35.26° relative to the flat) a rhombic mesa with vertical {111}-sidewalls results in all orientation dependent etchants. A minimum underetching occurs along this directions but the convex corners are attacked which can be minimized by a rhombic compensation mask [Kim98]. Table 5.12. Mesas (elevations) on the {110}-wafer (unique height) {110}wafer

Dominant angle of the mask edge to the flat a) α = 0° resp. 90° b) α = 0° resp. 90° etchant of KOH-type etchant of EDP-type

c) α = 35.26° etchant of KOH- type (EDP-type similar)

Type 5.12.1 Corners not compensated

Fig. 5.31. Type 5.12.1a: Mesa on an {110}-wafer; dominant angle of the mask edge to the flat 0° respective 90°; corners not compensated; etchant of KOH-type

Fig. 5.32. Type 5.12.1b: Mesa on an {110}-wafer; dominant angle of the mask edge to the flat 0° respective 90°; corners not compensated; etchant of EDP-type

106

5 Simple Shape Elements

5.3.3 Grooves (Trenches) Grooves or trenches are built by a narrow left-right combination of sidewalls - inside a long and narrow window resulting in a closed groove, - between two mask islands or peninsulas resulting in an open groove, - inside a long and narrow bay resulting in a mixed open/closed groove. The closed type ends with concave corners corresponding to the sidewalls of hollows. The open type ends with convex corners corresponding to the sidewalls of mesas. The most important feature of a groove is its cross section. Because of the narrow distance of the mask edges the opposite sidewalls can meet if low underetching is combined with relative small inclination resulting in a geometrical etch stop in the case of {111}-sidewalls, equation (5.1) and (5.2), or geometrical etch delay in other cases. A characteristical parameter of the cross section is the aspect ratio rA defined as the ratio of the maximum depth dT and width w: rA = dT / w

(5.3)

Table 5.13 shows grooves feasible by one-step etch processes considering the wafer orientations {100}, {110} and {112}. Isotropic and dry etching processes produces in all wafer orientations approximately the same cross section depending on the depth and the process characteristics. Only the isotropically etched groove is represented in table 5.13 (type 5.13.4). A low depth provided the shapes of the sidewalls are a quarter of a circle. The resulting aspect ratio corresponds to equation (5.4). The main fields of application of grooves are channels for fluidic elements, grooves for mechanical guiding, for positioning optical fibres or for chip separation. Optical slits can be realized by etching up to the wafer perforation or the ground of the groove is perforated from the back side by a second etch process. Arrays of parallel groove-wall pairs build gratings for optical or metrological applications.

{100}-wafer <110>-mask edges (α = 0° or 90°): The mostly important grooves of the silicon microtechnique are the so called V-grooves resulting from the geometrical etch stop along <110>-mask edges on the {100}-wafer (type 5.13.1a). Because of the very low underetch rate of the {111}-sidewalls the V-shaped cross section shows a minimum dependence on the etching time and is well defined by the distance w of the mask edges. Nevertheless for maximum precision a correct alignment must be realized . Because of the 54.74°-inclination of the {111}-faces the angle of opening of the V-grooves amounts 70.56°.

5.3 Shape elements made by one-step etch processes

107

Table 5.13. Grooves or trenches (unique depth)

{100}-wafer

Dominant angle of the mask edge to the flat a) α = 90° or 0° b) α = 45° etchant of KOH- or etchant of KOH-type EDP-type

c) α = 45° etchant of EDP-type

Type 5.13.1

{110}-wafer

a) α = 90° etchant of KOH- or EDP-type

Type 5.13.2

b) α = 0°: etchant of KOH-type c) α = 0°: etchant of EDP-type b)

d) α = 35.26° etchant of KOH-type

c)

{112}-wafer

a) α = 90° : <110>

etchant of KOHor EDP-type Type 5.13.3

All wafer orientations Type 5.13.4

a) all directions; isotropic etchant

Fig. 5.33. Type 5.13.1a: Grooves; {100}-wafer with a dominant angle of the mask edge to the wafer flat of 0 or 90°

Fig. 5.34. Type 5.13.2a: Grooves; {110}-wafer with a dominant angle of the mask edge to the wafer flat of 90°

108

5 Simple Shape Elements Fig. 5.35. Type 5.13.4a: Groove; isotropic etchant

A system of rectangular crossing V-grooves is used frequently for the limitation of chips to support the processes of cleavage or sawing. In this case four convex corners result around the crossing nodes producing underetched regions which lower the chip area. The corner compensation is not a simple problem in this case because of the limited area for compensation masks. Some complex solutions are presupposed [Hohm86, Schei95] but T-shaped compensation masks can be used also, figure 5.33. Junctions of grooves are further described in chapter 7. Along other directions of the mask edges different cross sections result depending on the used etchant (see table 5.3).

a) Etch mask with T-shaped corner com- b) SEM picture pensation Fig. 5.36. Corner compensation inside crossing V-grooves.

<100>-mask edges (α = 45°): In the case of the <100>-direction on the {100}wafer etched in KOH-type etchants the vertical {100}-sidewalls arise leading to a rectangular cross section of the groove (type 5.13.1b). The underetch rate is equal to the rate in depth resulting in a maximum aspect ratio of rA = dT / (w + 2 dT) < 0.5

(5.4)

Using EDP-type etchants {110}-sidewalls arise having an inclination of 45° and a rate of underetching which is not too large. This makes possible that the etch ground disappears and a geometrical etch delay occurs if

5.3 Shape elements made by one-step etch processes

dT > dU + w /2

respective

tRT > tRU + w /2

109

(5.5)

t > w / 2(RT - RU ). The resulting grooves can be regarded as V-grooves with an opening angle of 90° (type 5.13.1c) but the cross section depends strongly on the etching time. Note the problematic surface quality of these sidewalls.

{110}-wafer Along the <110>-directions (perpendicular to the flat) on wafers of {110}orientation {111}-sidewalls arise with an inclination of 35.26°. Analogous to the situation on the {100}-wafer a geometrical etch stop is possible, equation (5.2), resulting in precise V-grooves which have an angle of opening of 109.48°, type 5.13.2a. Grooves along the <100>-direction (parallel to the flat) are built by {100}sidewalls inclined by 45° using KOH-type etchants. A geometrical etch delay is possible, equation (5.5), resulting in V-grooves with an opening angle of 90°, type 5.13.2b. On the other hand using EDP-type etchants vertical {110}sidewalls are created leading to a rectangular cross section of the groove (type 5.13.2d) with a limited aspect ratio, equation (5.4). Vertical {111}-sidewalls along the <112>-direction (α = 35.26° to the flat) are the dominant feature of the application of the {110}-wafer. Grooves with an extreme aspect ratio and with high precision can be realized, a perfect alignment provided (type 5.13.2c).

{112}-wafer The importance of the {112}-wafer is based (and limited, too) on the possibility to produce grooves with a saw tooth-shaped asymmetrical cross section (type 5.13.3a). This is the consequence of the positions of the {111}-faces inside this wafer orientation (see section 5.1). 5.3.4 Walls Walls are built by a narrow left-right combination of sidewalls - by a long and narrow masked island resulting in an open wall, - between two mask windows or bays resulting in a connected wall, - by a long and narrow peninsula (beam) resulting in a mixed open/connected wall. The open type ends with convex corners corresponding to the sidewalls of mesas. The connected type ends with concave corners corresponding to the sidewalls of hollows. The most important feature of walls is their cross section shown in table 5.14.

110

5 Simple Shape Elements

Because of the narrow distance of the mask edges the opposite sidewalls can meet at sufficient underetching dU. In the case of vertical sidewalls a very high aspect ratio can be achieved (w: with of the mask): rA = dT / (w - 2 dU)

(5.6)

After a complete underetching (w = 2 dU) an annihilation of the wall occurs leaving a rim of weekly curved faces at the etch ground. Less steep sidewalls build a knife-shape after the complete underetching followed by a blunting by fast etching faces leaving a similar rim at the etch ground. In these cases (e.g. the 54.74°- inclined {111}-faces) the aspect ratio should be related to the width of the wall at the etch ground. Table 5.14 shows walls feasible by one-step etch processes considering the wafer orientations {100}, {110} and {112}. Isotropic and dry etching processes produce approximately the same cross sections in all wafer orientations depending on the depth and the process characteristics. Only the isotropically etched wall is represented in table 5.14 (type 5.14.4). At low depths the shapes of the sidewalls are a quarter of a circle. The minimum distance of two walls results from the aspect ratio of the groove in between corresponding to equation (5.4). An example of application of a wall structure is a mechanical bearing (knife) or guiding element. Walls separating neighboured hollows can be used for heat exchange in fluidic elements because of the large heat conductivity of silicon. Arrays of parallel groove-wall pairs build gratings for optical or metrological applications.

{100}-wafer The most important walls of the silicon microtechnique are walls resulting along <110>-mask edges on the {100}-wafer (type 5.14.1a). Because of the very low underetching rate of the {111}-sidewalls the trapezoidal cross section is well defined by the distance w of the mask edges and the etching time assuming a correct alignment. A defined misalignment can be used to achieve a complete underetching of the narrow mask region followed by a blunting of the wall by fast etching faces. Open <110>-walls end with a sharp tip because of the meeting of opposite fronts of the corner underetching, figure 5.36. Along <100>- directions the KOH-type etchants produce walls with an extreme aspect ratio because of the vertical {100}-sidewalls. By a well defined underetching very thin and high walls can be achieved. Note that deviations from the verticality (described in section 5.2) prevent exact parallel sidewall faces. In EDP-type etchants a trapezoidal cross section results along the <100>directions allowing the complete underetching described above.

5.3 Shape elements made by one-step etch processes

111

Table 5.14. Walls (unique height) {100}-wafer

Dominant angle of the mask edge to the flat a) α = 90° or 0° b) α = 45° etchant of KOH- or etchant of KOH-type EDP-type

c) α = 45° etchant of EDP-type

a) α = 90° etchant of KOH- or EDP-type

d) α = 35.26° etchant of KOHtype

Type 5.14.1

{110}-wafer

Type 5.14.2

b) α = 0°: etchant of KOH-type c) α = 0°: etchant of EDP-type b)

c)

{112}-wafer

a) α = 90°: <110>

b) α = 0° etchant of KOH- or EDP-type

Type 5.14.3

All wafer orientations Type 5.14.4

a) all directions; isotropic etchant

Fig. 5.37. Type 5.14.1a: Wall; {100}wafer with a dominant angle of the mask edge to the flat of 90°

Fig. 5.38. Type 5.14.1b: Wall; {100}wafer with a dominant angle of the mask edge to the flat of 45°

112

5 Simple Shape Elements

Fig. 5.39. Type 5.14.2a: Wall; {110}wafer with a dominant angle of the mask edge to the flat of 90°

Fig. 5.40. Type 5.14.4a: Wall; isotropic etchant

Simulation: A

A

A

A

A

A

SEM:

Fig. 5.41. Formation of open <110>-wall ends (KOH-type etchant)

{110}-wafer Along the <110>-directions (perpendicular to the flat) on wafers of {110}orientation {111}-sidewalls arise with an inclination of 35.26°. Analogous to the situation on the {100}-wafer the trapezoidal cross section is well defined by the distance w of the mask edges and the etching time assuming a correct alignment. Walls along the <100>-direction (parallel to the flat) are built by {100}sidewalls inclined by 45° using KOH-type etchants. On the other hand using EDP-type etchants vertical {110}-sidewalls are created leading to a rectangular cross section of the wall (type 5.14.2b and c). Note the bad surface quality of these sidewalls.

5.3 Shape elements made by one-step etch processes

113

Vertical {111}-sidewalls along the <112>-direction (α = 35.26° to the flat) are the dominant feature of the application of the {110}-wafer. Walls with an extreme aspect ratio and well defined by the distance w of the mask edges and by the etching time can be realized, a perfect alignment assumed (type 5.14.2d). 5.3.5 Front-back combinations By combinations of shape elements realized at the front and back side new elements can be constructed, see section 5.1.3. In the case that the sum of the etch depths of both sides is smaller than the wafer thickness the combined structures can be designed relatively independently. In the other case three different situations are of interest: - front-back combination of parallel sidewalls with the etch ground at the same side of the sidewalls resulting in a perforation inside a congruent region of the etch ground, - front-back combination of parallel sidewalls with dislocated etch ground (at different sides of the sidewalls), - front-back combination of crossing sidewalls. The following considerations include only shapes resulting from the {100}wafer illustrating the most important examples. The combined sidewalls can be seen as boundaries of hollows or grooves. From parallel sidewalls with congruent etch ground new shapes result in the moment of the perforation of the wafer and thereafter. Free convex edges arise followed by an attack of fast etching faces, types 5.15.1. Parallel sidewalls with dislocated etch ground produce walls between hollows or grooves situated at different wafer sides, types 5.15.2. These sidewalls can meet each other if they show an underetching leaving a horizontal perforation with free convex edges attacked by fast etching faces [Nij01, Off90]. The front back combination of crossing sidewalls produces complex shapes after the perforation of the wafer. Free convex edges arise which are afterwards increasingly attacked by fast etching faces. Table 5.16 illustrates crossing sidewalls using crossing grooves or hollows as examples. The analogous situations occur in the cases of crossing sidewalls resulting from islands or peninsulas

114

5 Simple Shape Elements

Table 5.15. Selected shapes of front-back combination of parallel sidewalls {100}-wafer

Dominant angle of the mask edge to the flat a) α = 90° or 0° b) α = 45° etchant of KOH- or etchant of KOH-type EDP-type

c) α = 45° etchant of EDP-type

Type 5.15.1 Congruent etch ground Type 5.15.2 Dislocated etch ground Table 5.16. Selected shapes of front-back combination of crossing sidewalls {100}-wafer

Type 5.16.1 Top view

Dominant angle of the mask edge to the flat a) α = 90° or 0° b) α = 45° etchant of KOH- or etchant of KOH-type EDP-type

C

B A

c) α = 45° etchant of EDP-type

A

B C

Cross section

5.4 Shape elements made by two-step etch processes 5.4.1 General remarks The shapes arising from a first etch step can be modified by a second etch step with - an alteration of the etch mask or - a change of the etchant in between. In section 5.1 the resulting sidewalls by the use of orientation dependent etchants are discussed. Alterations of the etch mask can be the expansion of a window (“putting back” of the mask edge) or the reducing (“putting back”) or the removing of the mask (“maskless etching”) of an island or a peninsula. Beside of the modifying of the profile of the sidewalls a terraced shape can be produced having an intermediate etch ground between the maximum depth and the top level of the chip. Change of the etchant means the use of orientation dependent wet etchants of different types (KOH-type, EDP-type), isotropic wet etchants and dry etching processes. The application of an isotropic etch step is limited to short times be-

5.4 Shape elements made by two-step etch processes

115

cause of the influences of convection. The combination of dry etching as the first step with wet etching as the second step is important in the case of the {111}wafer discussed in section 3.1.3. By the change of etchants the sidewalls are modified. In particular the change from KOH- to EDP-type produces undercut sidewalls along <100>-directions but the {111}-sidewalls along <110>directions remain uninfluenced. No information exist about two-step etch processes with {110}-wafer orientations. Consequently, the following considerations are only related to the etching of {100}-wafers. 5.4.2 Alteration of the etch mask

Sidewall corners The sidewalls occurring after alterations of the mask are described in figures 5.1 and 5.2. A large variety of shapes results. With exception of the concave corners of a hollow (or the ends of a groove) respective the convex corners of a mesa (or the ends of a wall) these shapes are well represented by their cross sections as left-right combination of the sidewalls. Therefore, the following considerations should be focused on hollows and their corners as combinations of sidewalls in concave angles respective on mesas and their corners as combinations of sidewalls in convex angles. Table 5.17. Faces occurring during the second etch step after putting back the mask and their intersection at corners by use of KOH-type etchants (see also table 3.2) Faces and corners of <110>-oriented sidewalls Face Inclination Concave corner Nearby con<110>/<110> cave corner γ [°]

Convex corner <110>/<110>

{111} 54,74 {001} 0 (ground) {11l} 22–32

sharp sharp

sharp sharp

Not compensated convex corner fuzzy blunted blunted

FWC

rounded

sharp ridge

sharp ridge

0…some

straight slightly curved curved

Faces and corners of <100>-oriented sidewalls (only KOH-type) Face Inclination Concave corner Nearby con- Convex corner <100>/<110> cave corner <100>/<100> γ [°] {100} {001} {10l} {l01} FWC

about 90 0 (ground) about 17 about 73 0...some

sharp fuzzy fuzzy rounded

straight uneven uneven curved

sharp fuzzy fuzzy rounded

Not compensated convex corner straight uneven uneven curved

116

5 Simple Shape Elements

The shape of the corners is predefined during the first etch step. At uncompensated convex corners or inside <100>-aligned concave corners new sidewall faces arise at these corners. The second etch step will modify these new corner sidewalls. Otherwise inside concave <110>-aligned corners or at compensated convex corners the sidewalls along the mask edge can directly intersect each other at the corner. Table 5.17 summarizes the characteristics of the observed corners. The quality of the corners depends strongly on the surface quality of the intersecting faces. In particular fuzzy corners result by intersecting of fast etching faces of different sidewall directions as in the case of <100>-oriented windows. EDP-type etchants are not included into the considerations because of a lack of information and of the bad quality of the fast etching faces in etchants with a content of isopropanol (IPA).

Hollows and grooves An obvious alteration of the etch mask is the expansion of a window (“putting back” of the mask edge) for modifying a hollow or a groove by a second etch step. The resulting groove is well represented by its cross section as left-right combination of the sidewalls. In view of hollows the concave corners are important as combinations of sidewalls in concave angles. Table 5.18 shows selected hollows resulting from two-step etch processes with a “putting back” of the mask The corners built by the concave combination of the sidewalls can be clearly seen. Inside concave corners of <110>-orientated sidewalls (α = 0° or 90°) no new faces arise apart of rounding effects. Table 5.18. Selected hollows and grooves with concave corners resulting after the second etch step with an expanded window. The sidewall types according to figures 5.1 and 5.2 and the resulting cross sections are included. <110>-oriented windows Type 5.18.1 Fig. 5.1-1.2b

Type 5.18.2 Fig. 5.1-1.3a

Type 5.18.3 Fig. 5.1-1.4b

Type 5.18.4 Fig. 5.1-1.5a

Type 5.18.5 Fig. 5.1-1.5b

Type 5.18.6 Fig. 5.1-1.9

<100>-oriented windows Type 5.18.7 Fig. 5.2-2.2

Type 5.18.8 Fig. 5.2-2.2

5.4 Shape elements made by two-step etch processes

117

Inside concave corners of <100>-orientated windows (α = 45°) {111}sidewalls are already produced during the first etch step resulting in eight concave corners combining <100>- with <110>-oriented sidewalls. Consequently, after expansion of the window these eight corners are modified resulting in intersections of different types of sidewall faces. Figures 5.42 – 5.45 show examples of hollows and grooves from table 5.19 etched in KOH. The quality of the fast etching faces can be improved by the use of TMAH instead of KOH, see figure 7.9.

Fig. 5.42. Type 5.18.1: Hollow resulting after two etch steps in KOH; mask directed along <110>; after the first etch step the mask was put back; the sidewall faces correspond to state 1.2b in figure 5.1

Fig. 5.43. Type 5.18.2: Hollow resulting after two etch steps in KOH; mask directed along <110>; after the first etch step the mask was put back; the sidewall faces correspond to state 1.3a in figure 5.1

Fig. 5.44. Type 5.18.3: Hollow resulting after two etch steps in KOH; mask directed along <110>; after the first etch step the mask was put back; the sidewall faces correspond to state 1.4b in figure 5.1

Fig. 5.45. Type 5.18.7: Hollow resulting after two etch steps in KOH; mask directed along <100>; after the first etch step the mask was put back; the sidewall faces correspond to state 2.2 in figure 5.2

Mesas and walls An obvious alteration of the etch mask is the reducing (“putting back”) or the removing (“maskless etching”) of the mask from an island for modifying a mesa or a wall by a second etch step. A resulting wall is well represented by its cross section as left-right combination of the sidewalls but in the case of mesas the convex corners are important as combinations of sidewalls in convex angles.

118

5 Simple Shape Elements

Table 5.19. Selected mesas and walls resulting after the second etch step at islands with back set or removed mask. The sidewall types according to figures 5.1 and 5.2 and the resulting cross sections are included. <110>-oriented islands Type 5.19.1 Fig. 5.1-1.6b Type 5.19.2 Fig. 5.1-1.12b <100>-oriented islands Type 5.19.3 Fig. 5.2-2.12b

In view of the convex corners it must be distinguished between compensated or uncompensated corners for the first etch step. Because of the occurrence of fast etching sidewall faces no new faces arise at the compensated convex corners. The underetching of uncompensated convex corners during the first etch step These new sidewalls are also modified in a similar manner. In the case of <110>orientated convex corners these additional sidewalls are shortened during the second step by the fast etching <11l>-sidewall faces which can intersect each other in a final stage [Li96]. Table 5.19 shows selected mesas resulting from two-step etch processes with “putting back” or “removing” of the mask. The corners built by the convex combination of the sidewalls can be clearly seen.

Fig. 5.46. Type 5.19.1: Mesa resulting after two etch steps in KOH; mask edge directed along <110>; after the first etch step the mask was put back; the sidewall faces correspond to state 1.6b in figure 5.1

Fig. 5.47. Type 5.19.2: Mesa resulting after two etch steps in KOH; mask edge directed along <110>; after the first etch step the mask was completely removed; the sidewall faces correspond to state 1.12 in figure 5.1

5.4 Shape elements made by two-step etch processes

Fig. 5.48. Type 5.19.3: Mesa resulting after two etch steps in KOH; mask edge directed along <100>; after the first etch step the mask was completely removed; on the top no plateau was built; the fast etching faces meet in a tip; the sidewall faces correspond to state 2.11 in figure 5.2

119

Fig. 5.49. Type 5.19.3: Mesa resulting after two etch steps in KOH; mask edge directed along <100>; after the first etch step the mask was completely removed; the sidewall faces correspond to state 2.12 in figure 5.2

Fig. 5.50. Type 5.19.3: Mesa resulting after two etch steps in KOH; mask edge directed along <100>; after the first etch step the mask was completely removed; the sidewall faces correspond to state 2.13 in figure 5.2; at the bottom a minimal facet exists

5.4.2 Change of the type of orientation dependent etchant

Sidewalls and corners 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.

The main emphasis of the following considerations is put on changes between anisotropically acting etchants of different types. Along the <110>-edges of the mask the change of the etchant type has no effect. Here always the {111}-sidewalls are produced. Consequently, the considerations of this section are concerned with sidewalls and corners resulting from mask edges along the <100>-direction (45° to the wafer flat).

120

5 Simple Shape Elements

Table 5.20. Concave corners inside <100>-orientated windows developing by two-step etching with change of the type of etchant Etch step first step second step first step second step

Type of etchant <100>-sidewall KOH {100} EDP {101}/{100}/{101} EDP {110} KOH {100}/{110}

135°-corner {100}-{111} {101}/{100}/{101}-{111} {110}-{111} {100}/{110}-{111}

The <100>-directed sidewalls produced by KOH-type etchants are different from the sidewalls produced by EDP-type etchants. Complex sidewalls can be formed by changing the etchant type described in figures 5.4. A very interesting shape can be made by the application of a KOH-type etchant in the first step developing vertical {100}-sidewalls followed by the second step using an EDP-type etchant. Thereby at the upper edge (directly under the mask) and at the lower edge at the etch ground the now slowly etching {110}-faces are generated forming an undercut sidewall shown in figure 5.3 [Früh2-00]. Inside the concave corners of an <100>-orientated window the very slowly etching {111}-faces develop. Consequently a rectangular corner degenerates into two 135°-corners. Each of the 135°-corner consists in the sidewall faces along <100> which intersect the {111}-sidewall along <110>. The sidewall faces along <100> are vertical {100}-faces by etching in KOH-type etchants or 45°inclined {110}-faces by etching in EDP-type etchants. Changing the type of etchant the {111}-sidewalls are conserved but the <100>-directed sidewalls are modified by growing of the alternative face {110} or {100}. The underetching at convex <100>-orientated corners is only a little stronger than the underetching of the sidewalls. By etching in a KOH-type etchant two steep facets arise with sharp corners whereas etching in EDP-type etchants a rounded corner is developed. Changing the etchant the alternative sidewall faces grow with their characteristical corners.

Hollows and grooves first step: KOH / second step: EDP <100>-directed sidewalls resulting after changing the etchant from KOH- to EDP-Type have an upper face undercutting the wafer surface. This means the extension of a hollow increases below the surface. Consequently, two neighboured hollows or grooves can have a connection in the inner of the wafer. first step: EDP / second step: KOH <100>-directed sidewalls resulting after changing the etchant from EDP- to KOH-Type are composed by a vertical upper face followed by a 45°-inclined lower face. Consequently, the so etched hollows inside an <100>-window are funnel shaped.

5.4 Shape elements made by two-step etch processes

121

Table 5.21. Selected <100>-orientated hollows or grooves resulting after the second etch step with a changed etchant. The sidewall types according to figure 5.4 and the resulting cross sections are included. first step: EDP, second step: KOH

first step: KOH, second step: EDP Type 5.21.1 Fig. 5.4-4.2

Type 5.21.2 Fig. 5.4-4.3

Type 5.21.3 Fig. 5.4-5.2

Fig. 5.51. Type 5.21.3: Groove after a two-step etch process with change of the etchant (KOHĺEDP); the sidewalls correspond to state 4.4 in figure 5.4

Mesas and walls first step: KOH / second step: EDP Because of the undercutting <100>-sidewalls the extension of a mesa decreases below the surface resulting in a waist. In the extreme case the upper part is detached leaving a tip or knife with a medium height. first step: EDP / second step: KOH <100>-directed sidewalls are composed by a vertical upper face followed by a 45°-inclined lower face. Consequently, the more shallow mesa produced during the first step build a socket for the steep mesa arising during the second step. In the case of a slender mesa defined by its corners a two stage tip can be produced [Tran95].

122

5 Simple Shape Elements

Table 5.22. Selected <100>-orientated mesas, walls or tips resulting after the second etch step with a changed etchant. The sidewall types according to figure 5.4 and the resulting cross sections are included. first step: EDP, second step: KOH

first step: KOH, second step: EDP Type 5.22.1 Fig. 5.4-4.2

Type 5.22.2 Fig. 5.4-4.3

Type 5.22.3 Fig. 5.4-4.3

Fig. 5.52. Type 5.22.1: Mesa after a twostep etch process with change of the etchant (KOHĺEDP); the sidewalls correspond to state 4.2 in figure 5.4

Fig. 5.53. Type 5.22.2: Mesa after a two-step etch process with change of the etchant (EDPĺKOH); the sidewalls correspond to state 5.2 in figure 5.4

5.4.3 Change between orientation dependent and isotropic etchants

General remarks Isotropic etchants act in a transport controlled manner. Consequently the production of a large and homogenous depth is very difficult. Because of a lack of homogeneity isotropic etching as a first step has no importance except this lack can be avoided (grooves concentrically to the wafer with concentric stirring of the etchant [Ziel95]). On the other hand a short isotropic etching after the first step by orientation dependent etching can modify the structures. Principally, the predetermination of the resulting shape should be possible by the elementary wave construction, see section 3.1. The reality is different.

5.4 Shape elements made by two-step etch processes

123

Sidewalls and corners Concave edges and corners should be rounded with the radius corresponding to the isotropic etch depth. Because of a residual influence of the reaction kinetics at the sharp edges between the {111}-faces a small facet grows during a considerable etching time, figure 5.45a. Finally, the edges are really rounded but at the same time the first irregularities occur, figure 5.45b. Break outs from the underetched mask influence the convection of the etchant and originate the irregularities. At the convex corners of a mesa the edges between the intersecting sidewall faces remain relatively sharp, figure 5.46.

<110>

<100>

Fig. 5.54. Concave corners after etching in KOH-type etchant as the first step followed by isotropic etching as a second step

<110>

<100>

Fig. 5.55. Convex corners after etching in KOH-type etchant as the first step followed by isotropic etching as a second step

124

5 Simple Shape Element s

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[Kim98]

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5.4 Shape elements made by two-step etch processes [Kuhn02]

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[Nik97]

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Shikida M et al. (2001) Surface roughness of single-crystal silicon etched by TMAH solution. Sensors and Actuators A 90: 223–231 [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 [Tan94] Tan S et al. (1994) Morphology of etch hillock defects created during anisotropic etching of silicon. J Micromech Microeng 4: 147–155 [Thong01] Thong JTL et al. (2001) Evolution of hillocks during silicon etching in TMAH. J Micromech Microeng 11: 61–69 [Tran95] Tran E, Kim ES, Lee SY (1995) Fabrication of mesas and octagonal cones in silicon by wet chemical etching. J Micromech Microeng 5: 251–256 [Vang2-96] Vangbo M, Bäcklund Y (1996) Terracing of (100) Si with one mask and one etching step using misaligned V-grooves. J Micromech Microeng 6: 39–42 [Veen01] van Veenendaal E et al. (2001) Micromorphology of single crystalline silicon surfaces during anisotropic wet chemical etching in KOH and TMAH. Sensors and Actuators A 93: 219–231 [Zav94] Zavracky PM et al. (1994) Fabrication of vertical sidewalls by anisotropic etching of silicon (100) wafers. J Electrochem Soc 141, 11: 3182–3188 [Ziel95 ] Zielke D, Frühauf J (1995) Determination of rates for orientation-dependent etching. Sensors and Actuators A 48: 151-156

6 Elements for Mechanical Applications

6.1 Spring elements 6.1.1 Overview and used crystal faces Corresponding to the principles of microtechnology springs are created together with other components out of the whole silicon body. The realizable spring shapes and the crystal faces limiting them are derived from this fact. Therefore not all shapes and surface qualities are possible. The springs can be classified by the kind of main use (bending, torsion) [Krau93]: Table 6.1. Classification of springs one side fastened straight spring (cantilever)

Bending element two side polygon fastened spring straight spring

membrane

Torsion element one side two side fastened fastened

A further aspect is the dominant kind of movement (translation, rotation) relative to the wafer surface. There are two possibilities: - Translation direction resp. rotation axis within the wafer plane - Translation direction resp. rotation axis directed out of the wafer plane. The concrete shape of the spring element determines the kind of deformation and movement and the working spring characteristic. Bending springs are preferably developed by leaf springs. Torsion-bar springs can be produced from rotationbar-springs with different kinds of cross sections. All kinds of spring elements are fixed to a frame. Furthermore, the spring is often connected to a seismic mass, also called “boss” e.g. [Geß94, Min99, Xin01]. This mass is fitted in its shape and dimensions to the respective function of the element. Mainly the {100}-wafer is used for the production of components with springs. In tables 6.2–6.6 variants of springs with bosses are shown, but also variants without bosses are possible and easily imaginable. Only for the case of membranes (table 6.5) both variants are presented. The shapes are preferably built by the following crystal planes, see chapter 5: - {111}-faces as slowly etching faces parallel to <110> with high surface quality.

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6 Elements for Mechanical Applications

- {001}-surface or etch ground (parallel to the wafer plane) with high surface quality (small roughness). - {100}-faces (vertical to the wafer plane γ=90°) at α=45° directed mask edges for KOH-type etchants with high surface qualities (small roughness). - {110}-faces (γ=45° tilt to the wafer plane) at α=45° directed mask edges for EDP-type etchants with surface qualities which are strongly dependent on the used etchant. Further facets can occur on bounds and stiffenings: - {110}-faces as fast etching faces parallel to <110> with a very rough surface. - {11l}-faces as fast etching faces parallel to <110> with smooth and lightly wavy surface qualities. - {10l}-faces as fast etching faces parallel to <100> with a bad surface quality. - faces of weak curvature parallel to <110> or <100> with a high surface quality (small roughness). 6.1.2 Bending springs

Out-of-plane movement The movement out of the wafer plane can be realized by leaf springs parallel to the {001}-wafer surface respective parallel to the etch ground. There are two possible variants: Asymmetrical (types 6.2.1 and 6.2.2 in table 6.2) [Dau98, Kwon98, Cor98]: One boundary face is the wafer surface.This is the easiest and mostly used variant. The production of such shapes is possible with masks on the wafer front and back side each. Different etch steps are necessary from each side and the sum of both is the wafer thickness. After a first etch step from one wafer side up to the double of the wished spring thickness a second step must follow in which both sides are etched simultaneously (adjustment of spring thickness and realization of perforation areas). To avoid the undercutting of convex corners mask compensation corners must be added. Often the etch step from the second wafer side is done by RIE [Esa94, Schla96, Min99, Wibb98], see basic processes table 3.16. In most cases the perforated areas are created in this way. Then the first step by wet chemical etching must be directly realized up to final spring thickness and the arosen surface must be protected with a resist or a metal layer (Al). Symmetrical ( [Mat99]: Both boundary faces are produced by an etch ground. The production of such a shape needs two mask levels both on the front- and backside. Two different etch steps are necessary each with the same depth from each wafer surface. The first depth is produced until the half of the spring thickness, the second one until half of the wafer thickness is reached. In between one mask level must be removed. Please note that after this removing of the mask at the spring area, fast etching faces are produced at the sides [Geß92]. This has to be

6.1 Spring elements

129

considered for the mask design. In both variants the direction along the spring can be chosen as <110> (parallel or vertical to the wafer flat) or <100> (α=45° to the flat). For springs along the <110>-direction and one-step etch processes the sides are {111}-faces. After the perforation these {111}-planes can be blunted by {110}facets [Boch00, Hash94] by continuing the etch process. In the case of two-step etch processes {11l}-facets arise after the mask removing. Analogous to springs along the <100>-direction edges are blunted by {10l}-facets. Furthermore, the underetching in this direction has to be considered. Please note that the Young’s module is different for different directions (<110>: 169 GPa; <100>: 130 GPa). Special types of bending springs are for example: single and double cantilevers (types in table 6.2), two side fastened straight springs (types in table 6.3), polygon springs (types in table 6.4) [Horie95]. These structures can be considered as perforated membranes. By changing the area of perforation a wide range of varieties of spring forms are possible. The spring with a triangular cross section (type 6.3.5) is a special one with regard to its production and shape. The using of such a spring is not interesting from the view of its cross section, but from the possibility of producing such a spring in a distance over a panel area or over another spring (double spring). This can be realized by a two-step etch process with a change of the type of etchant (see section 5.12) [Früh2-00, Han98]. Membranes without perforation areas (type 6.5.1) are also used for an out-ofplane movement ({100}-faces). In the most cases they have thicknesses below 30 µm. They are only etched from one wafer side and time-, electrochemical- or p+etch stops are used to adjust the exact thickness [Chin96, DeBa00, Herm96, Ios02, Kab99, Lap98, Man99, Oost1-99, Puers01]. For some applications bosses are used (type 6.5.3) which must be designed with corner compensation [Büte01, Ngu98, Roß95, Shik03, Szi01]. Stiffenings on membranes (type 6.5.2) can be produced by two-step etch processes. First, the stiffening area is masked. After the first etch step this mask is removed. During the second etch step the elevation is flattened by fast etching faces and faces of weak curvature [Früh2-97]. It is also possible to create reinforcements at membrane edges [Götz98]. They consist of membranes with two different thicknesses with a smooth transition area. A special kind of membrane is the folded one. It is produced by revolving V-trenches, which are displaced at the front- and back side (table 5.3, section 5.1). For this, it is very important to take the underetching of the convex corners into account [Off90].

In-plane movement Springs for movements inside the wafer plane can be produced by vertical {100}faces [Gärt03, Hanf02, Schrö1-98, Schrö2-98]. For this, mask edges with α=45° against the flat and a KOH-type etchant are used (basic process table 3.14). The production requires matched masks on the front- and backside. Designing the spring the underetching in <100>-direction must be considered. Furthermore, the blunting of the convex edges created by {111}-faces at the frame is necessary after the perforation. This is possible by continuing the etch process after the perfo-

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6 Elements for Mechanical Applications

ration, see section 3.1, figure 3.12. The blunting is important to minimize the mechanical stresses at these points. Special types are: one side fastened straight springs (cantilevers and parallel springs, types 6.2.3, 6.2.4, 6.2.5), two side fastened straight springs (types 6.3.6 and 6.3.7), polygon springs (types 6.4.3, 6.4.4, 6.4.5, 6.4.6). The polygon spring can be especially used as a spiral spring for rotation with an axis vertical to the wafer plane. An <111>-orientated membrane for an in-plane movement is designed by [Oost2-99]. 6.1.3 Torsion-bar springs The production of torsion-bar springs is possible with the same procedure as described in chapter 6.1.2. It can also be distinguished between unsymmetrical and symmetrical positions of the spring inside the wafer plane as well as between the direction of the spring to the wafer flat. The special kind of spring cross section determines the spring behavior with regard to the torsion and other modes of movement [DiL00,Vuja96]. Please note that the G-module is different for different directions. The most common procedure is the technologically simplest variant of unsymmetrical springs parallel to <110> [Mark92]. However, a minimal bending can be reached with a cross-like cross section of the spring [Hill98]. To create such a shape a combination of geometrical etch stops along <110>-directed trenches and edges after a perforation of the wafer can be used (X-cross section). A further possibility realizing this cross section is the application of SOI-wafers [Breng99, Kurth01]. The springs are bounded by {111}-facets, which are etched from both wafer sides until the oxide layer of the wafer staple is reached. Another variant (+-shape) is developed along the <100>direction in a KOH-etchant with the help of a two-step etch process with a changing of the etch mask between the steps [Han98].

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131

Table 6.2. Mechanical elements I: Bending springs (cantilever-type) Dominant angle of the mask edge to the flat Cross section a) α = 0° or 90° b) α = 45° Etchant of KOH-type variants Bending out of the wafer plane (γ = 0°). unsymmetrical A Type 6.2.1 A Single cantilever Basic process: B B unsymmetrical 1.pK/1.1K, symmetrical table 3.15, A symmetrical B 1.1K/2.2K, A B table 3.17 unsymmetrical Type 6.2.2 A A Double cantilever Basic process: B B unsymmetrical 1.pK/1.1K, symmetrical table 3.15, symmetrical A B 1.1K/2.2K, A table 3.17 B

A B

A B A B

A B

Bending in the wafer plane (γ = 90°) Type 6.2.3 Single cantilever B B

Basic process: 1.1K, table 3.14

B

B B

Type 6.2.4 Parallel cantilever

B

Basic process: 1.1K, table 3.14

B

B

Type 6.2.5 Spring array B

Basic process: 1.1K, table 3.14 B

B B

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6 Elements for Mechanical Applications

Fig. 6.1. Type 6.2.1a: Single cantilevers (dominant angles of the mask edges 0 and 90°) with unsymmetrical cross section (the springs do not lie in the middle of the wafer height); a better compensation of the underetched corners can be done by changing the etch mask design

Fig. 6.2. Type 6.2.1b: Single cantilevers (dominant angle of the mask edges 45°) with unsymmetrical cross section; the springs in this example have different lengths but equal widths

Fig. 6.3. Type 6.2.2a: Double cantilevers (dominant angles of the mask edges 0 and 90°) with symmetrical cross section; the springs are positioned in the middle of the wafer height and are bounded at their sides by fast etching faces

Fig. 6.4. Type 6.2.2a: Double cantilever (dominant angles of the mask edges 0 and 90°) with unsymmetrical cross section (the springs are not positioned in the centre of the wafer heigth); it is possible to build rounded transitions in vertical direction between the ends of the springs and the boss or the frame to decrease the mechanical stresses

6.1 Spring elements

133

Fig. 6.5. Type 6.2.2b: Double cantilever (dominant angle of the mask edge 45°) with symmetrical cross section; the springs are rounded and bounded at their sides by faces of weak curvature

Fig. 6.6. Type 6.2.3b: Single cantilever (dominant angle of the mask edge 45°); the thin spring has nearly vertical sidewalls and the height is the wafer thickness; the mass piece which is formed like wings has additional structures on its surface

Fig. 6.7. Type 6.2.4b: Parallel cantilever (dominant angle of the mask edge 45°); after the perforation of the wafer the etching process is continued; by this the heigth of the springs are adjusted (28 µm) and the {111}-faces are flattened

Fig. 6.8. Type 6.2.5b: Spring array (dominant angle of the mask edge 45°); after the perforation of the wafer the etching process is continued; by this the heigth of the springs are adjusted (28 µm) and the {111}-faces are flattened

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6 Elements for Mechanical Applications

Table 6.3. Mechanical elements II: Bending springs (two and more side fastened straight springs) Dominant angle of the mask edge to the flat Cross section a) α = 0° or 90° b) α = 45° Etchant of KOH-type variants Bending out of the wafer plane (γ = 0°) Basic process for types 6.3.1-6.3.4: unsymmetrical 1.pK/1.1K, table 3.15, symmetrical 1.1K/2.2K, table 3.17 unsymmetrical A Type 6.3.1 A A Single straight B spring B

B

symmetrical A

Type 6.3.2 Double straight spring (side by side)

A B

A

B

B

unsymmetrical A

A B

A

B

B

symmetrical A B

A

Type 6.3.3 Double straight spring (crossed)

A

A

B B

unsymmetrical A A B

B B

symmetrical B

A

A

A

Type 6.3.4 Fourfold straight spring (side by side and crossed)

A

unsymmetrical A A

B

B B

symmetrical

A

B

B

A B

A

6.1 Spring elements single (unsymmetrical) B

Type 6.3.5 Double straight spring (crossed) or parallel straight spring (crossed)

135

B

B

B

double B B

Basic process: 1.1K/1.1E

Bending in the wafer plane (γ = 90°) Basic process: 1.1K, table 3.14 Type 6.3.6 Single straight spring C

C C

C

Type 6.3.7 Parallel straight spring

C C

C

C

Fig. 6.9. Type 6.3.1a: Two single straight springs with unsymmetrical cross section and dominant angles of the mask edges of 0 and 90°; the bosses are relatively small in these examples

Fig. 6.10. Type 6.3.1b: Single straight spring with unsymmetrical cross section and a dominant angle of the mask edge of 45°

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6 Elements for Mechanical Applications

Fig. 6.11. Type 6.3.3b: Double straight spring (crossed) with unsymmetrical cross section and a dominant angle of the mask edge of 45°

Fig. 6.12. Type 6.3.5b: Double straight spring (crossed) with unsymmetrical position of the springs in the wafer height; the springs have a triangular cross section and an angle of ± 45° between the spring axis and the wafer flat

Fig. 6.13. Type 6.3.5b: Parallel straight spring (crossed); the springs have a triangular cross section and an angle of ± 45° between the spring axis and the wafer flat; they are positioned symmetrically in the wafer height

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137

Table 6.4. Mechanical elements III: Bending springs (polygon springs) Dominant angle of the mask egde to the flat Cross section a) α = 0° or 90° b) α = 45° Etchant of KOH-type variants Bending out of the wafer plane (γ = 0°) Basic process: unsymmetrical 1.pK/1.1K, table 3.15, symmetrical 1.1K/2.2K, table 3.17 unsymmetrical

Type 6.4.1 Polygon spring double

A

A A

A

symmetrical A A

Type 6.4.2 Polygon spring fourfold

unsymmetrical A

A

A

A

symmetrical A A

Bending in the wafer plane (γ = 90°) Basic process: 1.1K, table 3.14 Type 6.4.3 Polygon spring fastened at one side

Type 6.4.4 Polygon spring fastened at two sides

Type 6.4.5 Double polygon spring fastenend at one side

Type 6.4.6 Double spiral spring

B

B B

B

B

B

B

B

B

B

B B

B B

B

B

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6 Elements for Mechanical Applications

Fig. 6.14. Type 6.4.1a: Fourfold polygon spring with unsymmetrical position of the springs in the wafer height; the four spring bands are angled only once in this example

Fig. 6.15. Type 6.4.5b: Double polygon spring which is fastened at one side; the spring bands have nearly vertical sidewalls and a dominant angle of the mask edges of ± 45°; the tongue pieces in the middle can be designed in different ways

6.1 Spring elements

139

Table 6.5. Mechanical elements IV: Membranes Dominant angle of the mask edge to the flat Cross section a) α = 0° or 90° b) α = 45° Etchant of KOH-type variants Membranes without boss unsymmetrical Type 6.5.1 B A Flat membrane A

Basic process: unsymmetrical 1.pK, table 3.10, symmetrical 1.1K, table 3.14

A

A B

B

symmetrical A

Type 6.5.2 Membrane with roundings and stiffenings

B

A

A B B

A

rounding

stiffening A

A

Basic process: 1.pK/K rounding stiffening Membranes with boss Type 6.5.3 Flat membrane with boss Basic process: unsymmetrical 1.pK, table 3.10, symmetrical 1.1K, table 3.14

unsymmetrical B

A A B

A A

B

symmetrical A

B

A B

B

Type 6.5.4 Folded membrane A

Basic process: 1.1K, table 3.14

A A

A

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6 Elements for Mechanical Applications

Fig. 6.16. Type 6.5.1a: Flat membrane with unsymmetrical position in the wafer height (dominant angles of the mask edges 0 and 90°)

Fig. 6.17. Type 6.5.2a: Membrane with roundings and stiffenings (dominant angles of the mask edges 0 and 90°) and with unsymmetrical position of the membrane in the wafer height; the membrane is stiffened with a ring structure in this example

Fig. 6.18. Type 6.5.2a: Membrane with roundings and stiffenings (dominant angles of the mask edges 0 and 90°) and with unsymmetrical position of the membrane in the wafer height; the membrane is stiffened with a grid structure in this example

Fig. 6.19. Type 6.5.3b: Membrane with boss and unsymmetrical position of the membrane in the wafer height (dominant angles of the mask edges 0 and 90°); the transitions from the membrane to the frame and boss can also be designed in a curved manner

6.1 Spring elements

141

Table 6.6. Mechanical elements V: Torsion-bar springs

Type 6.6.1 Trapezoidal shape

Dominant angle of the mask edges to the flat Cross section a) α = 0° or 90° b) α = 45° Etchant of KOH-type variants unsymmetrical (γ = 0°/55°) A

A

A

A

symmetrical (γ = 0°/2°)

Type 6.6.2 Hexagonal shape

A A

Type 6.6.3 Dodecagonal shape

(γ = 0°/55°/22°/90°) A

A

(γ = 0°/22°/90°)

Type 6.6.4 Octagonal shape

A A

(γ = 55°/22°) Type 6.6.5 Star like shaped

A A

(γ = 55°)

Type 6.6.6 Cross like shaped

A A

symmetrical (γ = 0°/90°) (1)

Type 6.6.7 Rectangular B

B B

(2) B

B B

(γ = 0°/18°/72°/90°)

Type 6.6.8 Dodecagonal

B B

(γ = 18°/72°) Type 6.6.9 Octagonal

Type 6.6.10 Cross like shaped

B B

(γ = 0°/90°) B B

Basic processes: all except types 6.6.6 and 6.6.7(2) 1.1K/2.2K, table 3.17, types 6.6.6 and 6.6.7(2) 1.1K, table 3.14

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6 Elements for Mechanical Applications

Fig. 6.20. Type 6.6.2: Torsion-bar spring; the shapes and dimensions of the mass pieces and spring bands can be varied; one can use also the possibilities of types 6.6.2 to 6.6.6

Fig. 6.21. Type 6.6.7 (1): Torsion-bar spring (dominant angle of mask edges to the flat 45°) with spring bands of quadratic cross section

Fig. 6.22. Type 6.6.7 (2): Torsion-bar spring (dominant angle of mask edges to the flat 45°) with spring bands of rectangular cross section [Schm02]

Fig. 6.23. Type 6.6.8b: Torsion-bar spring (dominant angle of mask edges to the flat 45°) with spring bands of dodecagonal cross section; the dodecagonal cross section raises from the rectangular one during further etching

6.2 Levers / Spring hinges

Fig. 6.24. Type 6.6.9b: Torsion-bar spring (dominant angle of mask edges to the flat ± 45°) with spring bands of octagonal cross section; the dodecagonal cross section will be changed into an octagonal one after longer etching times

143

Fig. 6.25. Type 6.6.10b: Torsion-bar spring (dominant angle of mask edges to the flat ± 45°) with spring bands of a cross like shaped cross section; the cross like shaped spring can be prepared with equal or unequal dimensions of vertical and horizontal bands

6.2 Levers / Spring hinges

6.2.1 Overview It is possible to create uni- and bilateral levers or polygon levers with arms along the <110>-direction (parallel α=0° or vertical α=90° to the wafer flat) or the <100>-direction (α=45° against the wafer flat). The lever can be designed for inplane or out-of-plane movements. Flexural solid hinges and other spring elements for an in-plane movement can be well fabricated out of silicon [Gärt1-03, Gärt2-03]. Thereby the high bending fracture strength at small loaded volumes is the prerequisite for high deflections. With decreasing spring heights the fracture strength increases at a constant spring length. With the silicon microtechnology it is not possible to produce rotating hinges with glide bearings. Such rotating hinges can only be realized with spring bearings in connection with bending- and torsion-bar springs. These springs have to withstand the loading of the forces which work on the levers. That is why the comments made in chapter 6.1 should be noted. Furthermore, it should be mentioned that only small rotation angles can be realized and only small forces and moments can be transferred.

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6 Elements for Mechanical Applications

From the use of a spring hinge it can be deduced, that - out-of-plane movements can be realized for bilateral levers only with torsion-bar springs or for unilateral levers with torsion-bar and bending springs, - in- plane movements can be only realized with bending springs. 6.2.2 Levers / Hinges for out-of-plane movements Such levers should be advantageously realized by torsion-bar springs with cross like cross sections. This can be the X-cross section along the <110>- or the + cross section along the <100>-direction. A very simple unilateral lever is built by bending springs from the cantilever type (table 6.2) with a short spring length. 6.2.3 Levers / Hinges for in-plane movements In order to prepare springs with nearly vertical sidewalls for in-plane bending, the structures must be designed in <100>-direction. In this design {111}-sidewalls develop at the fastening point of the springs at the frame and form a sharp tip at the moment of perforation of the wafer. By continuing the etch process this tip can be dulled and so multiaxiale stress states can be reduced (see section 3.1, figure 3.12). Simultaneously the spring height is reduced. This must be considered designing the mask.

6.2 Levers / Spring hinges Table 6.7. Mechanical elements VI: Levers and articulated springs Dominant angle of the mask edge to the flat Cross section α = 0° or 90° α = 45° Etchant of KOH-type variants Axis of rotation is a torsion-bar spring in the wafer plane Basic process: 1.1K, table 3.14 Type 6.7.1 Unilateral lever (cross like shaped torsion-bar springs)

B A

section A-A A

B

Type 6.7.2 Bilateral lever (cross like shaped torsion-bar springs) A

B

section B-B section A-A

A

B

section B-B

Axis of rotation is a bending spring in the wafer plane Basic process: 1.1K, table 3.14 Type 6.7.3 Unilateral lever

Type 6.7.4 Bilateral lever (straight)

Type 6.7.5. Bilateral lever (angled lever)

Type 6.7.6 Parallel hinge guide

145

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6 Elements for Mechanical Applications

Fig. 6.26. Type 6.7.4.b: Bilateral lever

Fig. 6.27. Type 6.7.6: Parallel hinge guide

Fig. 6.28. Microgripper using several hinges

Fig. 6.29. Microgripper using several hinges

6.3 Sliding guides

6.3.1 Overview Sliding guides with dove-tail shape in bulk-silicon-micromechanics are based on the generation of {111}-sidewalls with an inclination of 54.74° by anisotropic wet etching. For this, trenches are etched in different wafers which will be used as sledges and guides after sawing them in separate chips. The easiest way to produce sledges and guides is to use two wafers for each, which are bonded to each other (four-wafer-guide). With the help of additional technological steps, such as sawing of slits with a diamond saw, it is possible to produce sledges as well as guides each out of one wafer (two-wafer-guide). A further variant is a sledge which is formed out of one wafer and which slides between two bonded guidechips (three-wafer-guide).

6.3 Sliding guides

147

The process of plastic deformation can be used to realize sliders with bent cantilevers which are movable in a board representing another type of a two-waferguide. In every case a great attention must be put to keep the trench distances and widths at a level which will minimize the free play. This means, that the tolerances of the mask need to be minimized and the mask misalignment to the crystal as well as the etch rate of the {111}-plane has to be considered. Particularly, mask misalignments result in higher roughnesses and slight changes of the sidewall inclination. A possibility to minimize the friction is the coating of the silicon structures with thin layers, but there has been no experience until now. 6.3.2 Four-wafer-guide (type 6.8.3) First of all, trenches will be etched in a guide- and sledge-wafer. The position and dimensions of these trenches must be coordinated to each other. Afterwards additional wafers are bonded to each etched wafer surfaces and the guide- and sledgewafers are thinned from the backside (mechanically and/or chemically) until the ground of the etched trenches is removed. In this way undercut dove-tail guides are developed which fit into one another after sawing the wafers [Coll97, Gonz197, Gonz98]. 6.3.3 Two-wafer-guide (type 6.8.1) To create the guide-chip a trench is cut into the wafer (by sawing or laser ablation) which creates a deep slit in the mask and the silicon. The following etch process develops undercut sidewall structures which can be used as dove-tail guides [Gonz2-97]. 6.3.4 Three-wafer-guide (type 6.8.2) To create this guide the sledge chip is positioned into a lower guide-chip. Afterwards, the upper and the lower guide chip are bonded together without sticking the sledge-chip between them. 6.3.5 Sliding guide with plastically deformed elements (type 6.8.4) Sliding guides can be also realised applying the process of plastic deformation. Etched silicon cantilevers which are plastically deformed are mounted into a corresponding board with etched {111}-sidewalls meeting at an edge. The bent cantilevers grip under this edge and can be moved in the board. Walls in the slider and grooves in the board guarantee a straight moving. Only small forces are necessary. The sliders can work as carriers for other microstrucural elements [Gärt2-01].

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6 Elements for Mechanical Applications

Table 6.8. Mechanical elements VII: Sliding guides

Type 6.8.1 Two-wafer-guide

Dominant angle of the mask edges to the flat: α = 0° or 90° sledge guide sledge

Basic process: 1.pK (slit wafer)

Type 6.8.2 Three-waferguide

1 2

guide

lower guide

upper guide

upper side

lower side

upper guide

sledge

Basic process: 1.1K

lower guide Type 6.8.3 Four-wafer-guide

guide

sledge sledge 1 2

Basic process: 1.pK (bounded on an unstructured wafer) Type 6.8.4 Guide with plastically deformed cantilevers Basic process: board: 1.1K/2.1K, table 3.18 slider: 1.pk/1.1K/2.1K, table 3.20

3 4

guide

sliders

board back

front

s lid in g b a r s

6.4 Bearings

149

Fig. 6.30. Type 6.8.2: Parts of a three-wafer-guide; the sledge chips which are provided with bars can be positioned and moved in guide channels

Fig. 6.31. Type 6.8.4: Sliding guide: two sledges can glide horizontally in the board. The sliders consist of plastically bent cantilevers which grip under the edge at the board

6.4 Bearings

6.4.1 Overview With the help of bulk-silicon-microtechniques it is possible to produce bearings as edge- or tip-bearings. Unfortunately only little information exists about it. As an compromise the edge as well as the pan can be produced out of the material silicon. In principle a coating is imaginable to improve the mechanical behavior of the bearing. In most cases two problems need to be solved: -

Edges or tips can be produced with very narrow but flat or edged top planes. Such top planes only allow the edge to be tilted and not rolled on the pan. Normally, a rounding process has to follow. A suggestion to realize a radius from 1 to 10 µm is made in [Schäf92].

150

-

6 Elements for Mechanical Applications

The assembly of the bearings is realized by gluing or bonding the fixed chip areas. As the distance of the edge/tip and pan-plane is defined by technological parameters (e.g. thickness of the wafer, height of the tips and pans or height of the gluing layer), it is possible that the edge or tip does not touch the pan in every case. This is frequently the case because of the large tolerances in the edge- and tip-heights. A solution for this problem could be to raise the pan level slightly so that a small initial mechanical stress occurs. A flat plateau can be used as a pan. It is also possible to use concave pans produced by orientation dependent or isotropic etching.

6.4.2 Edge bearings An edge bearing (roll-edge-bearing) is described by Schäfer [Schäf92]. It serves as support for the spring of a torsion-bar pendulum. It is based on an wall parallel to <110> etched with a small mask strip resulting in an edge bounded by two {111}faces and a triangular cross section with an edge angle of 70.52°, type 6.9.1. For long edges the problem occurs that a mask misalignment produces a higher underetching. The result is a tapering of the narrow top-plane in the middle of the edge. For extreme conditions this tapering leads to a separation of the edge-areas in two parts. The pan is created with a flat plateau as a rectangular elevation on a second wafer. A line contact should be produced by positioning the narrow side of the pan area against the long side of the edge. 6.4.3 Tip bearings Tips with various shapes can be produced by etching in different ways. The easiest case is a square pyramid, type 6.9.2. This pyramid has a small plateau on the top so that a rounding process has to follow. A special problem for the design of tips is the right calculation of the compensation structures for convex mask corners. Because of the small mask area this is only possible for small etch depths. Etchants of EDP-type are advantageous because of their small underetching rates. A further problem of other possiblities of tip producing is the adjustment of the correct tip height. For instance, a large tip is created by a complete underetching of a mask area. Using KOH-type etchants the fast etching facets form a steep pyramid (tip angle 30°). But it is very complicated to find the correct time of complete underetching. Furthermore, there is the phenomenon that the pyramid has a small tapering below the top. At this position the silicon etches through so that the pyramid has an undefined height below the wafer surface. EDP-type etchants are more promising but the tip angles are higher (about 90°). Another solution is to remove the mask before the whole mask is underetched. In this case, fast-etching planes are produced on top of the pyramid, type 6.9.3. The height of the pyramid is also below the wafer surface, but better to calculate.

6.4 Bearings

151

Table 6.9. Mechanical elements VIII: Bearings Edge bearing

Dominant angle of the mask edges to the flat: α = 0° or 90° Edge Pan Cross section

Type 6.9.1 Edge: wall with small plateau Pan: plateau Basis process: 1.pK, table 3.10 Tip bearing

Tip

Pan

tip enlarged Cross section

Type 6.9.2 Tip: quadratic pyramid Pan: plateau Basis process: 1.pK, table 3.10 Type 6.9.3 Tip: octagonal pyramid, truncated Pan: plateau Basic Process: 1.pK/K tip enlarged Type 6.9.4 Tip: flat tip on faces of weak curvature Pan: plateau on a high truncated pyramid Basic Process: 1.pK/K

Tips with small heights (type 6.9.4) are produced if an unmasked elevation is etched back until the plateau and all flat sidewall faces are removed. Now faces with weak curvature originating from the etch ground produce a tip which is located very near to the etch ground [Weid97], see also chapters 3 and 5.

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Flat plateaus can be used as pans. For a large angle interval of the bearing movement, a sufficient height is necessary. The maximal height for the pan is the wafer thickness [Weid97].

Fig. 6.32. Type 6.9.3: Octagonal, slightly truncated pyramid useable as a tip of a bearing; the relation between height and basis width can vary largely so that relative high tips can be produced, too

Fig. 6.33. Type 6.9.4: Pan (plateau on a truncated pyramid) as a part of a bearing; the etch mask is not removed from the plateau in this example; a guide groove for the tip is not created here but it can be realized easily

Fig. 6.34. Type 6.9.3: Tip and edge prepared in a two-step etch process in KOH; the mask is completely removed after the 1st etch step; the sidewall faces correspond to those presented in stade 2.13 in figure 5.2

6.4 Bearings

153

Fig. 6.35. Type 6.9.4: Tip and edge prepared in a two-step etch process in KOH; the mask is completely removed after the 1st etch step; the etch process is continued compared to figure 6.33; the sidewall faces correspond to those presented in stade 2.14 in figure 5.2

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References [Boch00]

Bochobza-Degani O et al. (2000) Design and noise consideration of an accelerometer employing modulated integrative optical sensing. Sensors and Actuators A 84: 53–64 [Breng99] Breng U et al. (1999) µCORS – a bulk micromechined gyroscope based on coupled resonators. Transducers ‘99: Proc of the 10th Int Conf on Solid-State Sensors and Actuators, Japan: 1570–1573 [Büte01] Bütefisch S et al. (2001) Micromechanical three–axial tactile force sensor for micromechanical characterisation. Microsystem Technologies 7: 171–174 [Chin96] Chin A et al. (1996) A novel processing technique for thin diaphragms. Micro System Technologies ‘96: Proc of the 5th Int Conf and Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 223–228 [Coll97] Collins SD, Gonzalez C, Smith RL (1997) Microfabrication creates mesoscopic optical systems. Laser Focus World: 187–191 [Cor98] Corman T, Enoksson P, Stemme G (1998) Low-pressure-encapsulated resonant structures with integrated electrodes for electrostatic excitation and capacitive detection. Sensors and Actuators A 66: 160–166 [Dau98] Dauderstädt UA, Sarro PM, French PJ (1998) Temperature dependence and drift of a thermal accelerometer. Sensors and Actuators A 66: 244–49 [DeB00] De Bhailís D et al. (2000) Modelling and analysis of a magnetic microactuator. Sensors and Actuators 81: 285–289 [DiL00] DiLella D et al. (2000) A micromachined magnetic-field sensor based on an elctron tunneling displacement transducer. Sensors and Actuators 86: 8–20 [Esa94] Esashi M (1994) Encaspsulated micromechanical sensors. Microsystem Technologies 1: 2–9 [Früh2-97] Frühauf J et al. (1997) Konstruktionselemente der Silizium-Mikrosystemtechnik, Varianten ihrer ätztechnischen Herstellung und ihr rechnergestützter Entwurf. Final Report AIF–Project 9929B, Technische Universität Chemnitz [Früh2-00] Frühauf J, Hannemann B (2000) Wet etching of undercut sidewalls in {001}silicon. Sensors and Actuators 79: 55-63 [Gärt2-01] 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 [Gärt1-03] Gärtner E et al. (2003) Flexural solid hinges etched from silicon. Proc of the euspen Int Topical Conf, 1, Germany: 43–46 [Gärt2-03] Gärtner E et al. (2003) Festkörpergelenkführungen aus Si mit bis zu ± 5 mm Hub. Proc of the 6th Conf of Mikromechanik & Elektronik, Mikrosystemtechnik ´03, Germany: 118–121 [Geß92] Geßner T et al. (1992) Mikromechanische Technologieentwicklung für kinetische Sensoren. Gerätetechnik und Mikrosystemtechnik, VDI-Berichte 960, VDI-Verlag, Düsseldorf: 423–440 [Geß94] Geßner T, Vetter E, Wiemer M (1994) Technology tools for a high precision accelerometer in bulk micromechanics. Microsystem Technologies 1: 10–13 [Gonz1-97] Gonzalez A, Collins SD (1997) Magnetically actuated fibre-optic switch with micromachined positioning stages. Optics Letters 22, 10: 709–711

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155

[Gonz2-97] Gonzalez C et al. (1997) Microjoinery for optomechanical systems. Miniaturized Systems with Micro-Optics and Micromechanics II. Proc of SPIE, 3008, USA: 171–178 [Gonz98] González C et al. (1998) Micro Joinery: concept, definition and application to microsystem development. Sensors and Actuators A 66: 315–332 [Götz98] Götz A, Campabadal F, Cané C (1998) Improvement of pressure-sensor performance and process robustness through reinforcement of the membrane edges. Sensors and Actuators A 67: 138–141 [Han98] Hannemann B, Frühauf J (1998) New and extended possibilities of orientation dependent etching in microtechniques. IEEE, MEMS '98: Proc of the 11th Annual International Workshop on Micro Electro Mechanical Systems, Germany: 234–239 [Hanf02] Hanf M et al. (2002) Realization of electrostatically driven actuators using curved electrodes fabricated by using silicon bulk micromachining techniques. Actuator 2002: Proc of the Int Conf on new Actuators, Germany: 329–332 [Hash94] Hashimoto M et al. (1994) Silicon angular rate sensor using electromagnetic excitation and capacitive detection. Micro System Technologies ‘94: Proc of the 4th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 763–771 [Herm96] Hermes T et al. (1996) A micro mechanical system for liquid dosage and nebulization. Micro System Technologies ‘96: Proc of the 5th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 187–192 [Hill98] Hiller K (1998) A new bulk micromachined gyroscope with vibration enhancement by coupled resonators. Micro System Technologies '98: Proc of the 6th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 115-120 [Horie95] Horie M, Funabashi H, Ikegami K (1995) A study on micro force sensors for micro handling systems. Microsystem Technologies 1: 105–110 [Ios02] Iosub R, Moldovan C, Modreanu M (2002) Silicon membranes fabrication by wet anisotropic etching. Sensors and Actuators A 99: 104–111 [Kab99] Kabir AE et al. (1999) High sensitivity acoustic transducers with thin p+ membranes and gold back-plate. Sensors and Actuators 78: 138–142 [Krau93] Krause W (1993) Konstruktionselemente der Feinmechanik. Carl Hanser Verlag, München Wien [Kurth01] Kurth S et al. (2001) A new vacuumfriction gauge based on a Si tuning fork. Transducer´01: Proc of the 11th Int Conf on Solid-State Sensors and Actuators, Germany: 502–505 [Kwon98] 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 [Lap98] Lapadatu D et al. (1998) A model for the etch-stop location on reverse-biased pn junctions. Sensors and Actuators A 66: 259-267 [Manea] Manea E, Müller R, Popescu A (1999) Some particular aspects of the thin membrane by boron diffusion processes. Sensors and Actuators A 74: 91–94 [Mark92] Markert J et al. (1992) Elektrostatischer Mikroaktor. Gerätetechnik und Mikrosystemtechnik, VDI-Berichte 960, VDI-Verlag, Düsseldorf

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[Mat99]

Matsunaga T, Minami K, Esashi M (1999) Acceleration switch with extended holding time using the squeeze film effect. Transducers ´99: Proc of the 10th Int Conf on Solid-State Sensors and Actuators, Japan: 1550–1553 [Min99] Mineta T et al. (1999) Piezoresistive micro accelerometer for high g shock using air damping effect. Transducers ´99: Proc of the 10th Int Conf on SolidState Sensors and Actuators: 1530–1533 [Ngu98] Nguyen NT et al. (1998) Hybrid-assembled micro dosing system using silicon-based micropump/valve and mass flow sensor. Sensors and Actuators A 69: 85–91 [Off90] Offereins HL, Sandmaier H (1990) Stressfreie Chipmontage. Mikroelektronik, Heft 1,VDE-Verlag [Oost1-99] Oosterbroek RE et al. (1999) A micromachined pressure/flow sensor. Sensors and Actuators 77: 167–177 [Oost2-99] Oosterbroek RE et al. (1999) Characterization and optimization of monocrystalline in-plane operating check valves. Transducers ´99: Proc of the 10th Int Conf on Solid-State Sensors and Actuators, Japan: 1816–1819 [Puers01] Puers R, Reyntjens S (2001) Fabrication and testing of custom vacuum encapsulations deposited by focused ion beam direct-write CVD. Sensors and Actuators A 92: 249–256 [Roß95] Roßberg R, Schmidt B, Büttgenbach S (1995) Micro liquid dosing system. Microsystem Technologies 2/1: 11–16 [Schäf92] Schäfer A (1992) Kapazitiver mikromechanischer Beschleunigungssensor auf Basis eines schneidengelagerten Drehpendels. Dissertation Thesis, Technische Universität Chemnitz [Schla96] Schlaak H et al. (1996) Silicon-microrelay with electrostatic moving wedge actuator – new functions and miniaturisation by micromechanics. Micro System Technologies ´96: Proc of the 5th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 463–468 [Schm02] Schmiedel R (2002) Technologieentwicklung für einen neuartigen kapazitiven Beschleunigungssensor. Diploma Thesis, Technische Universität Chemnitz [Schrö1-98] Schröpfer G, de Labachelerie M, Ansel Y (1998) Investigations concerning the mechanical and capacitive sensitivity of lateral bulk accelerometers. MME '98: Proc of the 9th Micromechanics Europe Workshop, Norway: 295– 298 [Schrö2-98] Schröpfer G et al. (1998) Lateral optical accelerometer micromachined in (100) silicon with remote readout based on coherence modulation. Sensors and Actuators A 68: 344–349 [Shik03] Shikida M et al. (2003) Active tactils sensor for detecting contact force and hardness of an object. Sensors and Actuators A 103: 213–218 [Szi01] Szita R et al. (2001) A micropipettor with integrated sensors. Sensors and Actuators A 89: 112–118 [Vuja96] Vujanic A et al. (1996) Small torque measurements using micromachined sislicon cross-spring structure. Micro System Technologies ´96: Proc of the 5th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 261–266

6.4 Bearings [Weid97]

[Wibb98]

[Xin01]

157

Weidner J (1997) Untersuchungen zur Übertragbarkeit von Gestaltungsprinzipien der Feinwerktechnik auf Funktionselemente der Mikromechanik. Diploma Thesis, Technische Universität Chemnitz Wibbeler J, Pfeifer G, Hietschold M (1998) Parasitic charging of dielectric surfaces in capacitive microelectromechanical systems (MEMS). Sensors and Actuators A 71: 74–80 Xinxin L, Minhang B (2001) Micromachining of multi-thickness sensor-array structures with dual eching technology. J Micromech Microeng 11: 239–244

7 Elements for Fluidic Applications

7.1 Channels Channels are the most important structures of microfluidic elements [Ngu02]. Those etched in silicon can be divided into two groups relative to their course: - course of the channel inside the wafer plane, - course of the channel through the wafer plane. Consequently, channels with a course through the wafer plane have a very short length in the order of magnitude of the wafer thickness [Gerl94]. They are holes in the wafer. Produced by etching such channels can be compared with small caverns whose dimensions are related to the wafer thickness. With regard to possible shapes it can be referred to section 7.5 Channels inside the wafer plane can be etched principally as open grooves or trenches. A channel is built by mounting a second wafer (silicon or glass) with an even surface as a simple cover or with a congruent groove. Therefore the considerations can be reduced to grooves as simple shape elements. Principally the course of the grooves can be designed in any direction in the wafer plane. Thereby the cross section of the resulting shape and the quality of its surface depend on the direction and the used etchant. This is described in section 5 as a “left-right-combination” of sidewalls. Simple shapes of channels are characterized by directions of 0°, 90° or 45° relative to the wafer flat. Etchants of KOHor EDP-type can be used. The resulting cross sections are shown in table 7.1. Grooves in directions with an angle of 0° or 90° relative to the flat are limited by {111}-faces. Consequently, the cross sections of the covered channels correspond to an isosceles trapezium [Liu99, Yosh02] or triangle (in the case of a geometrical etch stop) [Rich01, Schwes94, Stri94] with an angle of 54.74° at the base. Congruent double grooves have a hexagonal cross section or (in the case of etch stop) a rhombic cross section [Dam01, vanB01] with the angles of 109.48° and 70.52°. In the case of an etch stop the width and depth of the channels have a definite ratio (covered groove: 2 :1, congruent double groove: 1: 2 ). In this direction the cross section is independent of the etchant. In the case that the channel is directed in an angle of 45° relative to the flat, the corresponding cross section depends on the type of the used etchant. Etchants of KOH-type produce a rectangular cross section limited by {100}-faces. The ratio of width to depth is larger than 2:1, so the width of channel is the width of the mask window plus two times the depth (distance of underetching = depth). Using

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EDP-type etchants the produced sidewalls are {110}-faces with an inclination of 45°. Resulting cross sections can be a trapezium, a triangle (covered groove), a hexagon or a quadratic diamond (congruent double groove). The dimensions depend on the width of the mask window, the distance of underetching and the ratio of this distance to depth. This ratio is always smaller than one. Note the bad surface quality of the {110}-sidewalls in 45°-direction of the channels if KOH-IPA is used as etchant (EDP-type). These faces are rough and corrugated perpendicularly to the direction of the channel. Table 7.1. Fluidic elements I: straight channels Channels in the wafer plane , Basic process: 1.pK, 1.pE or 1.pI, table 3.10 Dominant angle of the mask edges to the flat a) α = 0° or 90° b) α = 45° c) α = 45° etchant of KOH-or etchant of KOH-type etchant of EDP-type

EDP-type Type 7.1.1 Channels with flat etch ground A

B

B

A B

Type 7.1.2 V-grooves

section A-A, γ=54.74° with geometrical etch stop

section B-B, γ=90°

B

section B-B, γ=45° with geometrical etch delay B

A

A

section A-A, γ=54.74° B

section B-B, γ=45° Isotropic etchant: channels in all directions Type 7.1.3 U-grooves

A

A

section A-A Channels through the wafer plane see caverns

7.1 Channels

161

Using an isotropic etchant a semielliptical cross section with fluctuating width and depth will be produced. This results from a non-ideal isotropic process which is influenced by the convection in the etch bath. The fluctuations increase with increasing depth. Another technique to create thin channels is the sacrificial poly-silicon etching [Ber01, Kwon01]. The principle is to remove a polysilicon layer between two silicon nitride layers by KOH etching. At locations where the silicon nitride has been removed before, the KOH also etches into the silicon substrate, creating large, low resistance entrance and exit channels. For some applications crossing channels are required. In the case of Į = 0 or 90° four convex corners result around the crossing node which can be compensated by different techniques (see grooves, section 5.3). A further possibility getting sharp corners is a technique using a two mask system and two etch steps [Kwon01]. One of the two {111}-sidewalls forming the convex corner is covered with an etch mask.

Fig. 7.1. Type 7.1.1a: Channel with flat etch ground in the wafer plane with mask edges inclined by 0 or 90° to the flat; the channel walls are built by {111}-faces

Fig. 7.2. Type 7.1.1b: Channel with flat etch ground in the wafer plane; the channel walls are built by {100}-faces which are perpendicular to the wafer surface and the etch ground; the most slowly etching {111}-faces are stable at the end of the channel

Fig. 7.3. Type 7.1.1c: Channel with a flat etch ground in the wafer plane; the channel walls are built by {110}-faces which have an angle of ± 45° to the wafer surface and the etch ground; {111}-faces are stable in the corners at the ends of the channels

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7.2 Alterations of cross section of channels Table 7.2. Fluidic elements II: alteration of cross-sections Dominant angle of the mask edges to the flat a) α = 0° or 90° b) α = 45° c) α = 45° etchant of KOH- or etchant of KOH-type etchant of EDP-type EDP-type Abrupt alteration of cross section, Basic process: 1.pK or 1.pE, table 3.10 Type 7.2.1 KOH-type

EDP-type

Gradual alteration of cross section, Basic process: 1K or 1E, table 3.10 Type 7.2.2

Fig. 7.4. Type 7.2.1a: Channel with an abrupt alteration of the cross section (dominant angles of the mask edges 0 and 90°); KOH-type etchant; the etch stop is partially reached in the example, which results in different etch depths of the channels

7.2.1 General remarks Only the alterations of cross sections of channels with a course inside the wafer plane are considered. Channels with a course through the wafer plane are very short and alterations of their cross section are analogous to caverns or nozzles, see

7.3 Elbows

163

sections 7.5 and 7.6. It can be distinguished between abrupt and gradual alterations of the cross section. In the region of the alteration not only the magnitude, but also the shape of the cross section is changed. This results from the dependence of the sidewall shapes on the direction of the mask edge. In the case that at least in the narrow region of the channel no etch ground exists (geometrical etch stop or delay) the broader region must have a larger depth. This is not illustrated in table 7.2 but easy to reconstruct by means of other examples. 7.2.2 Abrupt alterations of the cross section In the case of abrupt alterations of the cross section (type 7.2.1 in table 7.2), convex corners occur in the sequence of the sidewalls. Especially with channels in 0° or 90° directions and etchants of KOH-type less abrupt alterations of cross section result. If necessary the underetching of these corners must be compensated by a suitable mask extension.

7.2.3 Gradual alterations of the cross section A gradual alteration of the cross section (type 7.2.2 in table 7.2) can be produced by the application of mask edges or sidewalls which are not directed in the preferential angles of 0°, 90° or 45° relative to the wafer flat. The shapes and the surface qualities depend on the used etchants. The mask layout presupposes the knowledge of the related etch rates.

7.3 Elbows

7.3.1 General remarks Elbows are the alterations of the direction of straight channels from a first direction into a second one. Two cases can be distinguished: - only one of the directions runs inside the wafer plane; the elbow guides the channel out of the wafer plane, - both of the directions before and after the elbow run inside the wafer plane. Possible variants are shown in table 7.3. With regard to the cross sections of the channels the considerations made in section 7.1 are valid.

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7.3.2 Elbows out-of-plane A straight channel inside a wafer plane leads into a short channel going out of the wafer plane (a hole or a small cavern, see section 7.5). The connection between these channels results if the channel with course inside the wafer plane ends in a narrow deepening etched from the backside of the wafer as a second channel (onewafer elbow, type 7.3.1). Another variant of elbow can be produced by mounting a second wafer with a narrow perforated cavern at the end of a channel in the first wafer (two-wafer elbow, type 7.3.2). The shapes of caverns shown in table 7.3 can be modified in agreement with table 7.5. 7.3.3 Elbows in-plane In the region of the alteration of direction the elbows have, along the sidewalls, concave and convex corners in pairs (see section 5). Here, during etching new sidewall faces are created. These faces are not parallel to the mask edge and have low or high etch rates and characteristical inclinations. Consequently in the region of an elbow the cross section of the first channel changes into the cross section of the second one in a manner depending on the used etchant. Principally, all directions of channels and all angles of alteration of directions can be realized. Preferential directions are 0°, 90° and 45° relative to the wafer flat. In the case of rectangular elbows with directions of 0° and 90° to the flat (type 7.3.3) the underetching of the convex corner leads to a local extension of the cross section. This can be avoided by compensation masks at the corners. Using EDPtype etchants this effect is minimized. In elbows between channels along directions with angles of -45/+45° (type 7.3.4) to the flat {111}-faces are created at the concave corner. At this place the cross section is locally decreased as a consequence of the very low etch rate of this face. Additionally in the case of elbows with 45° between the two directions of the cannels, the characteristical differences of the cross section between these directions must be considered.

7.3 Elbows

165

Table 7.3. Fluidic elements III: elbows Dominant angle of the mask edges to the flat a) α = 0° or 90° b) α = 45° etchant of KOH-type Elbows out-of-plane , Basic process: 1.1K or 1.1E, table 3.14 Type 7.3.1 B One wafer elbow A A

c) α = 45° etchant of EDP-type

B

B

section A-A

B

section B-B Type 7.3.2 Two wafers elbow

B

B

A A

section B-B

B

B

section A-A

section B-B Elbows in-plane, Basic process: 1.pK or 1.pE, table 3.10 Type 7.3.3 90°-angle

Type 7.3.4 45°-angle

section B-B

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Fig. 7.5. Type 7.3.3a: 90°-elbow inplane; the facets at the convex corners are built by underetching which can be compensated by another mask design and etchant

Fig. 7.6. Type 7.3.3b: 90°-elbow in-plane; the sidewalls are built by vertical faces

7.4 Branchings (Mixers)

7.4.1 General remarks A branching of a channel can be taken as a mixer in the case of the opposite flow direction [Ngu02]. Many different variants of branchings can be realized. Principally, we have to distinguish between: - branchings out-of plane, - branchings in-plane. For channels inside the wafer plane all directions are possible. Owing to the definite underetching the directions in an angle of 0°, 45° or 90° relative to the wafer flat are preferred. With regard to the cross sections of the channels outside the branching region the considerations of section 7.1 are valid. In connection with branchings the short channels guiding out of the wafer plane also correspond to narrow holes or caverns. In this section branchings with three channels should be preferentially discussed. Examples are shown in table 7.4. Further variants can be derived by generalization. This is illustrated by the star-shaped branching as an example. 7.4.2 Branching out-of-plane - One channel is located inside the wafer plane and two short channels lead out of the wafer plane, type 7.4.1 [Ehl98]. This branching is a combination of an one- and a two-wafer elbow variant, see section 7.3.

7.4 Branchings (Mixers)

167

- Two channels are located inside the wafer plane and one short channel leads out of the wafer plane, type 7.4.2. Two variants exist: a short channel meets a straight channel or an elbow. One- or two-wafer subvariants can be designed. - Many channels are located inside the wafer plane and one short channel leads out of the wafer plane (type 7.4.3): the branching is similar to the spokes of a wagon wheel with a short channel in the hub. The different underetching and different shapes of the cross sections of the channels in directions different from 0° or 90° relative to the flat must be taken into consideration. An EDPtype etchant is suitable to produce this branching. 7.4.3 Branching in-plane Three channels have a course inside the wafer plane. The layout can be T-like or Y-like, types 7.4.4 and 7.4.5). Analogous to the elbows extensions of the cross section result from the underetching of the convex corners in the region of branching. Application of compensation masks or the use of EDP-type etchants minimize this effect. Further a combination of different junctions is possible [Nehl96].

Fig. 7.7. Type 7.4.1a: Channel with a branching

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Table 7.4. Fluidic elements IV: channels with branchings Dominant angle of the mask edges to the flat a) α = 0°or 90° b) α = 45° c) α = 45° etchant of KOH-type etchant of EDP-type Branchings out-of-plane, Basic process: 1.1K or 1.1E, table 3.14 Type 7.4.1 B B One channel in A the wafer plane A

B B

section A-A

section B-B

section B-B Type 7.4.2 Two channels in the wafer plane A A

B B

section A-A

section B-B

Type 7.4.3 Star shaped directed channels in the wafer plane, e.g. 16 V- or trapezoidal grooves Branchings in-plane, Basic process: 1.pK or 1.pE, table 3.10 Type 7.4.4 T-branching

Type 7.4.5 Y-branching

B B

section B-B

7.5 Caverns (Cavities)

169

7.5 Caverns (Cavities) The basic shape of a cavern is an extended deepening or hollow in the silicon chip, type 7.5.1. The maximum height of a cavern in a single chip is the thickness of the wafer. Then the wafer is perforated. This deepening is completed to a cavern by covering with a cover chip – silicon, glass – (at one wafer side or at the front- and back side of the wafer) [Kondo99, Meck96] or with thin layers/membranes e.g. out of silicon, polysilicon, silicon nitride or others [Chév95, Dan98, Han99, Sato99, Zou99]. Assembling two chips with (congruent) grooves a cavern can be realized with an extended height [Gui01, Meck98]. In the most cases the concrete shape of a cavern and the inner surface qualities do not essentially influence the function of the fluidic element. To produce a perforation by etching two different processes can be used: -

etching of one hollow starting at one side of the chip until the perforation at the other side, ending at a masking layer (single hollow, type 7.5.2), etching of two hollows from both sides of the chip and perforation inside the volume of the chip (double hollow, type 7.5.3) [Pand00].

The maximum ratio of height to width of a cavern can be reached using a double hollow with a mask edge in an angle of 0° or 90° to the flat producing {111}sidewalls, type 7.5.3. To ensure the event of perforation (avoiding the geometrical etch stop) the width of the mask window must be larger than the wafer thickness divided by 2 2 . Then the maximum height of the cavern is 2 times the width. If the etch process is continued after the event of perforation the convex edges of the {111}-faces of the united hollows are flattened by nearly vertical but rough {110}-faces. A rectangular cavern is formed if the etching is finished in the moment of complete consuming of {111}-faces by the {110}-faces, type 7.5.4, see section 3.1.2, figure 3.12. After that, the continuation of etching produces new {111}-faces with an undercut inclination, type 7.5.5. Thereby, the volume will be enlarged essentially in the case of a cavern with a small width. The most shapes which can be found in literature are of type 7.5.1 or 7.5.2 (table 7.5). The etched cavities are not used as single elements. They are mostly combined in a system of channels, cavieties and holes [e.g. Chéc95, Gui01].

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7 Elements for Fluidic Applications

Table 7.5. Fluidic elements V: caverns (cavities) Dominant angle of the mask edges to the flat a) α = 0° or 90° b) α = 45° etchant of KOH-type Deepenings, Basic process: 1.pK or 1.pE, table 3.10 Type 7.5.1 B Deepening without perforation of the wa- A A A fer

c) α = 45° etchant of EDP-type B

A A

B

Type 7.5.2 Deepening with perforation of the wafer (broken line)

B

section A-A, γ=54.74° section A-A, γ=54.74° section A-A, γ=54.74°

section B-B γ=90° Double deepening, Basic process: 1.1K or 1.1E, table 3.14 Type 7.5.3 B Double deepening in the moA A A ment of perforation

section B-B γ=45° B A

B

section A-A, γ=54.74°

A A

B

section A-A, γ=54.74° section A-A, γ=54.74° section B-B, γ=90° section B-B, γ=45°

Type 7.5.4 Double deepening with vertical sidewalls (flattened convex edges)

section A-A, γ=90°

Type 7.5.5 Double deepening with under- section A-A, γ=54.74° cut sidewalls (etch stop)

7.6 Nozzles

171

Fig. 7.5. Type 7.5.1b: Deepening without perforation of the wafer; the share of the vertical, ± 45° to the flat directed {100}sidewall faces decrease with increasing etch depth in favour of the most slowly etching {111}-sidewall faces

7.6 Nozzles With regard of the flow direction it can be distinguished between - nozzles with a vertical flow (out-of-plane), - nozzles with lateral flow (in-plane). For a nozzle with an out-of-plane flow a perforated quadratic single hollow with {111}-sidewalls is well suitable. A simple square window in the etch mask parallel to <110> can be used. The window must be large enough to avoid a geometrical etch stop before the perforation of the chip. The pyramidal shape of this hollow gives a funnel-shaped alteration of the cross section, type 7.6.1 [Gerl98, Huang01, Lee02, Sim03]. The minimum etch rate of the {111}-faces makes it possible to realize very small square openings at the back side of the wafer after the perforation. Any other mask window produces a larger opening of the nozzle. The realization of extreme small openings is complicated by the deviations of the nominal wafer thickness or lack of parallelism of the wafer surfaces. The narrowest region of the nozzle can be transferred into the chip volume by etching a second small hollow from the opponent side of the chip (unsymmetrical double hollow, type 7.6.2). This also can be realized by a dry etching process [Zimm00]. The funnel shape of the nozzle can be modified to a convex or a concave shape using a two-step etch process with an extension of the mask window between the etch steps. Thereby, sidewall types consisting of {111}-faces and fast etching faces are combined. Different nozzles are designated as convergent, divergent and “de laval” nozzle according to their cross section [Ye01]. The convergent type is etched from two wafer sides with differently sized mask windows. The “de laval” type is etched in the same way, here the mask windows are identical. The divergent type is etched from one wafer side. Nozzles are often combined with channels [Lee99, Wit00]. According to Witvrouw et al. two distinct concepts of geometry can be distinguished: the edgeshooter and side-shooter concept. In the first one the channel and nozzle are inplane whereas in the second one the nozzle leads out-of-plane. The channels and nozzles are prepared by a combination of wet anisotropic and dry deep silicon etching.

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7 Elements for Fluidic Applications

Table 7.6. Fluidic elements VI: nozzles Dominant angle of the mask edges to the flat a) α = 0° or 90° b) α = 45° c) α = 45° etchant of KOH-type etchant of EDP-type Nozzles in vertical direction to the wafer plane Type 7.6.1 Truncated pyramid Basic process: 1.pK, table 3.10 A A

Type 7.6.2 Double pyramid, unsymmetrical Basic process: 1.1K, table 3.14 Type 7.6.3 Funnel concave

section A-A γ=54.74°

A A

Basic process: 1.pK/2.pK, table 3.12 section A-A γ=54.74°/22°

Type 7.6.4 Funnel convex

section A-A γ=54.74°/22°

Nozzles in the direction of the wafer plane, Basic process: 1.pK or 1.pE table 3.10 Type 7.6.5

7.6 Nozzles

173

Nozzles with a flow direction inside the wafer plane (types 7.6.5) are in principle alterations of cross sections of channels. The fabrication of such nozzles needs a cover by another chip. Using a plane cover, an unsymmetrical nozzle is produced. Using a cover chip with a congruent channel, the nozzle is symmetrical. In the case of a large underetching (along mask edges in angles of 45±30° relative to the wafer flat) a flat etch ground in the channel exists. Consequently, the opening of the nozzle has only a narrow height (slit-shaped cross section). Using directions of mask edges in symmetrical intervals of angle 0±10° or 90± 10° inclined V-grooves can be etched. Covering such a groove by a flat chip or by a chip with a congruent etched groove, a nozzle with a very small opening (triangle-shaped or rhombus-shaped) is produced. A new etching technique to produce {111}-faces as in-plane valves is suggested by Oosterbroek et al. [Oost].

Fig. 7.6. Type 7.6.3a: Concave funnel; the shape will be reached by a two-step etch process; the sidewalls are built by {111}faces in the upper part and by fast etching faces in the lower part

Fig. 7.7. Type 7.6.4a: Convex funnel; the shape will be reached by a two-step etch process; the sidewalls are built by fast etching faces in the upper part and by {111}-faces in the lower part (etched in TMAH)

Fig. 7.8. Type 7.6.5: Nozzle in the direction of the wafer plane (channel discharges into a groove); without compensation of corners

Fig. 7.9. Type 7.6.5: Nozzle in the direction of the wafer plane (channel discharges into a groove); with compensation of corners

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7 Elements for Fluidic Applications

Fig. 7.10. Type 7.6.5: Channel discharging into a groove; the channel becomes narrower; this is realized with sloped mask edges

Fig. 7.11. Channel discharging into a groove; the channel becomes narrower; this is realized by overlapping rectangular mask windows Fig. 7.12. Nozzle in the direction of the wafer plane (three channels discharge into a groove); with compensation corners

7.6 Nozzles

175

References [Ber01]

[Chév95]

[Dan98] [Ehl98]

[Gerl94]

[Gerl98] [Gui01] [Han99] [Huang01] [Kond99]

[Kwon01]

[Lee02] [Lee99]

[Liu99]

[Meck96]

[Meck99] [Nehl96]

Berenschot JW et al. (2001) Advanced sacrificial poly-si technology for fluidic systems. Transducers ’01: Proc of the 11th Int Conf on Solid-State Sensors and Actuators, Germany: 624–627 Chévrier JB et al. (1995) Micromachined infrared pneumatic detector for gas sensor. Microsystem Technologies1: 71–74 number for the fully developed laminar flow through hexagonal ducts etched in <100> silicon. Sensors and Actuators A 90: 96–101 Daniel JH et al. (1998) Silicon microchambers for DNA amplification. Sensors and Actuators A 71: 81–88 Ehlert A, Dauer S, Büttgenbach S (1998) Micro-optical fluidic analysis system for environmental and quality control. Micro System Technologies `98: Proc of the 6th Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 189–194 Gerlach T (1994) A simple micropump employing dynamic passive valves made in silicon. Micro System Technologies ‘94: Proc of the 4th Int Conf & Exibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 1025–1034 Gerlach T (1998) Microdiffusers as dynamic passive valves for micropump applications. Sensors and Actuators A 69: 181–191 Gui C et al. (2001) Selective wafer bonding by surface roughness control. J Electrochem Soc 148: G225–G228 Han J (1999) Novel fabrication and characterization method of Fabry-Perot microcavity pressure sensors. Sensors and Actuators 75: 168–175 Huang Y, Rubinsky B (2001) Microfabricated electroporation chip for single cell membrane permeabilization. Sensors and Actuators A 89: 242–249 Kondo S, Kano K, Shinohara E (1999) Reaction chamber for PCR made by microfabrication technologies. Transducers ’99: Proc of the 10th Int Conf on Solid-State Sensors and Actuators, Japan: 1718–1721 Kwon JW, Kim ES (2001) Microfluidic channel routing with protected convex corners. Transducers ’01: Proc of the 11th Int Conf on Solid-State Sensors and Actuators, Germany: 644–647 Lee SW et al. (2002) A monolithic inkjet print head: Dome Jet. Sensors and Actuators A 95: 114–119 Lee SW, Sim WY, Yang SS (1999) Fabrication of a micro syringe. Transducers ´99: Proc of the 10th Int Conf on Solid-State Sensors and Actuators, Japan: 1368–1371 Liu RH et al. (1999) A passive micromixer: three-dimensional serpentine microchannel. Transducers ’99 : Proc of the 10th Int Conf on Solid-State Sensors and Actuators, Japan: 730–733 Meckes A et al. (1996) Miniaturised air analyser. Micro System Technologies ‘96: Proc of the 5th Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 181–186 Meckes A et al. (1999) Microfluidic system for the integration and cyclic operation of gas sensors. Sensors and Actuators 76: 478–483 Nehlsen S et al. (1996) Lateral pyrex thin film anodic bonding and KOH deep etching of silicon substrates for micro fluid applications. Micro System

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Technologies `96: Proc of the 5th Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 217–222 [Ngu02] Nguyen NT, Werely ST (2002) Fundamentals and applications of microfluidics. Artech House, Boston London [Oost99] Oosterbroek RE et al. (1999) Designing, simulation and realization of inplane operating micro valves, using new etching techniques. J Micromech Microeng 9: 194–198 [Pand00] Pandraud G et al. (2000) Evanescent wave sensing : new features for detection in small volumes. Sensors and Actuators 85: 158–162 [Rich01] Richter M et al. (2001) A portable drug delivery system with silicon capillaries as key components. Transducers ’01: Proc of the 11th Int Conf on SolidState Sensors and Actuators, Germany: 970–973 [Sato99] Sato K et al. (1999) Fingerprint sensor with an arrayed microheater elements. Transducers ’99: Proc of the 10th Int Conf on Solid-State Sensors and Actuators, Japan: LN7, 1874–1875 [Sim03] Sim WY et al. (2003) A phase-change type micropump with aluminium flap valves. J Micromech Microeng 13: 286–294 [Schwes94] Schwesinger N, Burgold J, Ackermann H (1994) Piezoelectric micropumps based on a new deposition technology for ZnO-Films. Micro System Technologies `94: Proc of the 4th Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 1035–1044 [Stri94] Strike DJ et al. (1994) Glucose measurement using a micromachined open tubular heterogeneous enzyme reactor (MOTHER). Micro System Technologies 1: 48–50 [vanB01] van Baar JJ et al. (2001) Sensitive thermal flow based on a micro-machined two dimensional resistor array. Transducers ’01: Proc of the 11th Int Conf on Solid-State Sensors and Actuators, Germany: 1436–1439 [Wit00] Witvrouw A et al. (2000) Why CMOS-integrated transducers? A review. Microsystem Technologies 6: 192–199 [Ye01] Ye XY et al. (2001) Study of a vaporizing water micro-thruster. Sensors and Actuators A 89: 159–165 [Yosh02] Yoshida K et al. (2002) Fabrication of micro electro-rheological valves (ER valves) by micromachining and experiments. Sensors and Actuators A 95: 227–233 [Zimm00] Zimmermann S, Müller J (2000) Micro flame spectrometer. Microsystem Technologies 6: 241–245 [Zou02] Zou Q et al. (2002) Micro-assembled multi-chamber thermal cycler for lowcost reaction chip thermal multiplexing. Sensors and Actuators A 102: 114– 121 [Zou99] Zou Q et al. (1999) CoMSaT : a single-chip fabrication technique for threedimensional integrated fluid systems. Sensors and Actuators A 72: 115–124

8 Elements for Optical Applications

8.1 Grooves for fibre positioning

8.1.1 General remarks V-grooves are frequently used for holding and precise alignment of optical fibres. For extreme demands on the precision of position and direction an exact shape of the cross section of the groove must be created [Lutz86, Steck91]. Grooves for fibre positioning have to guarantee the correct direction and correct vertical position of the centerline of the fibre. The direction corresponds to the mask direction of the groove but the vertical position depends on the fibre diameter D, the width W of the groove and the inclination γ of the sidewalls. Two principles of fibre alignment can be used (figure 8.1): - face defined alignment and - edge defined alignment. The edge defined alignment is suitable if the grooves are dry etched having vertical sidewalls (γ = 90°). Moreover dry etching is not influenced by the crystallographic direction. On the other hand the centerline of the fibre must be located above the wafer surface. The face defined alignment can be realized by orientation dependently etched grooves. With it a precise alignment is possible with the centerline near or below the wafer surface. Using (110)-wafers long but narrow trenches can be fabricated [Hoff03, Bäck97]. The following sections are related to the {100}-wafer. w

fib r e

fib r e C

D h

C

D w

Condition: w < D sin γ, h < D/2 cos γ

Condition: w < D sin γ, h > 0

a) face defined alignment

b) edge defined alignment

Fig. 8.1. Principles of fibre alignment

h

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8 Elements for Optical Applications

Table 8.1. Optical elements I: grooves for face-defined fibre positioning Dominant angle of the mask edges to the flat Cross section a) α = 0° or 90° b) α = 45° Etchant of EDP-type variants Grooves parallel to the wafer plane Type 8.1.1 A Grooves for fibre B positioning section A-A γ=54.74° Basic process: A 1.pK or 1.pE, B table 3.10 section B-B γ=45° Type 8.1.2 Grooves rhombus A

shaped

Basic process: 1.pD/1.pK, table 3.13

section A-A A

Type 8.1.3 Grooves in a direction area ± ∆α around 0° or 90° A A

Basic process: 1.pK, table 3.10

A

A

section A-A γ=54.74°+∆γ

∆α < 15° Type 8.1.4 Grooves in any direction to the flat A

Basic process: 1.pE, table 3.10

A

section A-A γ=54.74°-∆γ



Grooves with inclined direction to the wafer plane Type 8.1.5 B

Basic process: 1.pK, table 3.10

A A B

C

C

section A-A

C @ s

e

c

t i o

n

sections

A

-

A

8.1 Grooves for fibre positioning

179

8.1.2 Grooves in an angle of 0 or 90° to the flat If the grooves on an {100}-wafer are parallel or perpendicular to the flat they are bordered by {111}-faces [Ono01, Hoff1-99, deLab01]. Any misorientation between the etch mask and the crystal lattice should be avoided. In these directions the underetch rate depends strongly on the angle of the mask edge and a misorientation yields wider and deeper V-grooves. The underetching has to be taken into account in the mask calculation although the underetch rate owns a minimum in <110>-direction which causes the so-called geometrical etch stop. The depth of the V-groove is well defined by the width of the mask. V-shaped grooves on pre-etched sidewalls can be obtained by a combination of DRIE and anisotropic etching [Har99, Hoff2-99]. After etching grooves with vertical sidewalls by DRIE an anisotropic wet etching step follows. The sidewalls become V-shaped and a rhombus-shaped fibre channel results. Different concepts of fibre positioning devices are presented [Gonz1-97, Arm91, Vand95]. 8.1.3 Grooves with an angle of 45° to the flat In this direction V-grooves can be only reached with etchants of the EDP-type. The value of the underetch rate is relatively large in comparison to the 0° or 90° directions and an etch stop of the V-cross section does not occur but only a geometrical etch delay. This must be considered in the mask layout [Han98, Früh197]. The dependence on the misorientation is relatively small because the etch rate minimum (around 45°) is wide and flat. The surface quality of the V-groove faces depends on the etchant and can also influence the precision of fibre positioning. In KOH-IPA etch solutions the arising faces are corrugated perpendicularly to the 45° groove direction. In EDP or TMAH-IPA etchants, the V-section is often disturbed by small vertical facets on the upper edges. Rectangular cross sections result using etchants of the KOH-type [Stra98, Bäck97]. Because of the relatively large underetching and the rectanular shape it is difficult to align and hold the fibre precisely. 8.1.4 Grooves in a direction range of ∆α around the 0° or 90° directions to the flat A concentric alignment of two or more fibres requires a fan-shaped arrangement of grooves. Thereby the different underetch rates and inclinations of the groove sidewalls in the direction range of α+∆α must be considered for the realization of such fibre grooves [Han98, Frü1-97]. In KOH-type etchants ∆α is limited by two factors: with increasing ∆α the sidewall faces become increasingly rougher with a more uneven stepped structure and the groove loses its V-shape if the mask edge comes closer to the direction of maximal underetch rate. This means that an etch

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8 Elements for Optical Applications

ground remains and a steep facet is built at the upper edge. A fibre guiding is no longer possible. Such ∆α-limitations do not occur in etchants of EDP-type. 8.1.5 Grooves in any direction to the flat They can be only created in EDP-type etchants. The effect of the underetch rate on the V-shaped cross section (width, depth, inclination of sidewalls) and the surface quality has to be taken into account as described in sections 8.1.3 and 8.1.4. 8.1.6 Grooves with inclined direction to the wafer plane Their realization succeeds with a wedge-shaped mask window so that the distance of the sidewalls and the depth of the V-groove increase continuously. The effect of the underetch rate on the V-shaped cross section (width, depth, inclination of sidewalls) and the surface quality has to be taken into account as described in sections 8.1.3 and 8.1.4 [Früh1-97]. The inclination angle į is limited by the wafer thickness dw and the needed guiding length lf of the fibre: tan į = dw / lf .

Fig. 8.2. Type 8.1.3a: Grooves for fibre positioning in a direction area of ∆α; the grooves are turned with steps of 1.5° around the 0° or 90° mask edge and designed to give identical axis heights of the guided fibres

Fig. 8.3. Type 8.1.6a: Groove for fibre positioning; the fibre axis is inclined with an angle of 3.3° to the wafer plane and guides to an {111}-mirror face in this example

8.2 Micro mirrors

8.2.1 Useable mirror faces on the {100}-wafer The following crystal faces, which are producible by etching, can be used as mirror planes (see also chapter 5.1):

8.2 Micro mirrors

-

-

-

-

181

The {001}-wafer surface and the etch ground parallel to it respectively: The surface of polished wafers normally has a small roughness of about few nanometers and is easily usable as a mirror face. The {100}-etch ground reveals a greater roughness in most etchants. This can be decreased by additives to the etch solution (e.g. K3 [Fe (CN)6 ] [Früh2-97]), so that the etch ground is suitable for a mirror face, too. The {111}-face along <110>-mask edges: {111}-faces are inclined to the wafer plane in an angle of 54.74°. They should have a small roughness of about few nanometers. As a result of misorientations between the crystal and the wafer plane or the mask, steps can occur in the {111}-faces decreasing the optical quality. Such steps are strongly built in the KOH-etchant. By using TMAH- or EDP-etchants the steps are submicroscopically small. The {100}-face along <100>-mask edges: The building of such faces vertical to the wafer plane demands etchants of KOH-type. Their inclination to the wafer plane is not exactly 90° but varies between 87 and 89° and can change in vertical direction (a small curvature occurs). The roughness lies between that of the polished wafer surface and the etch ground. The {110}-face along <100>-mask edges: These faces are inclined to the wafer plane in an angle of 45°. Their generation needs etchants of EDP-type. In KOH-IPA solutions corrugated faces occur, which are nearly unsuitable for optical applications (Ra about 5 µm). If the etching is done with EDP or TMAH-IPA solutions the corrugation is suppressed and a good optical quality with roughnesses about 70 nm can be reached.

8.2.2 Reflection at the {100}-wafer surface or {100}-etch ground The (100)-wafer surface [Asa99, Geß96, Hill99, Kurth98, Lang99, Mark93, Yan01] or the (100)-etch ground [Frank98] are the most frequently used mirror faces, especially in oscillating mirrors. The mirror faces - often coated with metals (Al or Au) for a better reflection - are situated on thin membranes which are connected with torsional springs. To fabricate these membranes a dry etching process is applied in the most technological processes or SOI-wafers [Graf00] are used. Such systems serve as periodical beam deflectors. 8.2.3 Reflection at sidewall faces out of the {100}-wafer plane Light beams directed parallel to the wafer plane (e.g. from LEDs or from fibres in V-grooves, see section 8.1) can be reflected out of the wafer plane by mirrors which are inclined to the wafer plane. A reflection of a beam at the 54.74° inclined {111}-faces leads to a deflection of 19.48° relative to the normal of the wafer, type 8.2.1 [Sad97]. These faces are etched in <110>-direction in etchants of KOHtype. A beam deflection perpendicular to the wafer plane can be reached if an {110}face which is inclined by 45° to the wafer plane is used as a mirror face [Bäck92,

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8 Elements for Optical Applications

Bäck93, Hill88, Jac93, Seki2-99, Stra95]. These faces arise in <100>-orientation in etchants of EDP-type. In order to smooth the initial ridged {110}-surfaces etched in KOH-IPA multiple cycles of oxidation and isotropic etching are utilized [Shie99]. A deflection normal to the wafer plane can also be reached at a 54,74° inclined {111}-face if the inclination angle is changed by 9,7°. This can be realized by plastic deformation of a cantilever with a boss with {111}-faces at its end [Früh01], see also section 2. So the 45° inclination is achieved. A double mirror is created by the combination of two mirrors. In the case of 45° inclined {110}-mirror faces, a double reflection in antiparallel direction occurs [Bäck92, Bäck93] and a vertical beam can be displaced in horizontal direction respectively (vertical double mirror, type 8.2.2). With a horizontal double mirror a horizontally directed beam is displaced vertically, that means in another level of the wafer plane, type 8.2.3. Such a mirror combination needs a two-step etch process, see section 5.4. Double mirrors built with 54.74° inclined {111}-faces (type 8.2.3) can be created in the same way. The horizontal double mirror is reached by etching from both wafer sides longer than to the point of perforation with mask edges directed along <110>- exactly positioned one above another. First the {111}-faces disappear by the growth of a nearly vertical face with a high roughness. If this vertical face has reached the mask edges, new {111}-faces grow again with an inclination of 125.26° building the double mirror. The multiple reflection of double mirrors results in different directions and intensities of the light beam, dependent on its incidence direction and position. 8.2.4 Reflection at sidewall faces inside the {100}-wafer plane The {100}-mirror plane is situated perpendicularly to the wafer plane, and the normal of the mirror is in <100>-direction [Maek01]. If the incident direction is parallel or perpendicular to the flat a beam deflection about 90° results [Ros1-94]. The deviations of the mirror planes should be noted. This mirror type can be combined to form double or multiple mirrors.

8.2 Micro mirrors

183

Table 8.2. Optical elements II: sidewall-mirrors Dominant angle of the mask edges to the flat α = 0° or 90° α = 45° Etchant of EDP-type Reflections out of the wafer plane Type 8.2.1 Single mirror

Cross section variants

C = 5 4 .7 4 °

B

Basic process: 1.pK or 1.pE, table 3.10

section A-A A A

C = 4 5 ° B s e c t io n B - B

section B-B

Type 8.2.2 Double mirror, vertical Basic process: 1.pK or 1.pE, table 3.10

C = 5 4 .7 4 °

B

section A-A A A

C = 4 5 °

B

s e c tio n B - B

section B-B C = 5 4 .7 4 °

Type 8.2.3 Double mirror, horizontal B

section A-A Basic process: 1.pK/1.pE, table 3.11 A A

C = 4 5 ° B

section B-B Reflections inside the wafer plane a) α = 0° or 90° Type 8.2.4 Single mirror

b) α = 45° Etchant of KOH-type

Cross section variants

B C = 9 0 °

Basic process: 1.pK, table 3.10 B

sectional view B-B

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8 Elements for Optical Applications

Fig. 8.4. Type 8.2.1b: Single mirror for out-of-plane reflections; the mirror groove m is connected with a fibre groove g

Fig. 8.5. Type 8.2.1: {111}-face which is used as a mirror plane; the cantilever is plastically bent by about 9,7°; therefore a 90°-diffraction in direction of the wafer normal out-of-plane results

Fig. 8.6. Type 8.2.3b: Horizontal double mirror; the beam comes back parallel to the wafer plane in another level inside the wafer; the double mirror consists of two undercut and 45° to the wafer plane inclined {110}-faces m1, m2 and is connected with fibre grooves on the back- and front side of the wafer

Fig. 8.7. Type 8.2.4b: Single mirror for in-plane reflections; the vertical mirror face is inclined to the wafer flat in an angle of 45°; the example contains fibre grooves like type 8.1.4.a for coupling in and out

8.2.5 Useable mirrors on the {110}-wafer Beside of the polished wafer surface the following faces of structures etched out of an {110}-wafer can be used as mirrors [Corn91, Mill97, Mita99, Uen95]: - the {111}-faces: as sidewalls along <110>-directed mask edges with an inclination of γ = 35,26° for out-of-plane reflection as vertical sidewalls along <112>-directed mask edges for in-plane reflection - the {100}-faces: as sidewalls along <100>-directed mask edges with an inclination of γ = 45° for out-of-plane reflection. The etch ground and the vertical {110}-sidewalls developing along <100>-mask edges in KOH-type etchants cannot be used as mirrors because of their extreme roughness.

8.3 Beam Splitters

8.3 Beam Splitters Table 8.3. Optical elements III: beam splitters Dominant angle of the mask edges to the flat a) α = 0° or 90° b) α = 45° Etchant of KOH-type Beam splitting in-plane, Basic process: 1.pK , table 3.10 Type 8.3.1 Splitting of the A A beam

Cross section variants

section A-A Type 8.3.2 Splitting of the beam intensity B

B

section B-B

Beam splitting out-of-plane, Basic process 1.1K or 1.1E, table 3.14 Cross section a) α = 0° or 90° b) α = 45° Etchant of EDP-type variants Type 8.3.3 C Splitting of the beam B

section A-A A

C A B

section B-B Type 8.3.4 Splitting of the beam intensity A

B

section A-A A

B C

section B-B

185

186

8 Elements for Optical Applications

8.3.1 Principles of beam splitting and suitable crystal faces A beam splitting can take place in two different manners: - splitting of the beam cross section at a common edge of two mirrors, - splitting of the beam intensity at a semi-permeable mirror. With it the quality of the beam splitting and the directions of the beams are determined by the mirror faces as described in 8.2.1. Further, the geometrical quality of the common edge of two mirrors is important for the splitting of the beam cross section. Such convex edges are normally unstable in orientation dependent etching. So the etch process must be finished exactly at the point of incidence of the two mirror faces (the point of building of the common edge). If this time is not yet reached or exceeded, the edge shape is disturbed by other facets. In any case a central part of the beam cross section is not reflected into the proper direction resulting in an additional loss. The splitting of the beam intensity can be applied with silicon for wave lengths of more than 1.1 µm without any problems. The thickness of the mirrors must be very thin (< 10 µm) for visible light to secure the semi-permeability because the transmission is low. 8.3.2 Beam splitting at a membrane built by the etch ground and the wafer back side The requirement is a low roughness of the etch ground to minimize the scattering (see section 8.2.1). An oxide layer between two bonded wafers could also be an advantageous alternative. 8.3.3 Beam splitting out of the wafer plane A two-side etch process is needed to create either two nonparallel mirrors with a common edge parallel to the wafer plane in the moment of wafer perforation or two mirror faces which are parallel with a very small distance in between forming a semi-permeable membrane. If in the second case {111}-faces are used the membrane thickness is well defined by the mask and nearly independent on the etching time. In the other case (common edge) an exact keeping of the etching time is necessary. Another possibility is to etch a groove at one wafer side first, passivate it and then etch from the other wafer side up to the passivation layer. After removing this layer a sharp edge is received. For the beam directions parallel and perpendicular to the wafer plane the creation of two 45° inclined mirror faces is necessary. This can be done either with etchants of EDP-type [Früh1-97, Han98] or by the use of an {110}-wafer with sidewalls along <100> developing in KOH-type etchants.

8.3 Beam Splitters

187

8.3.4 Beam splitting inside the wafer plane The involved mirror faces must be perpendicular to the wafer plane, which means that {100}-faces have to be created along mask edges in 45° direction to the flat [Ros1-94, Ros2-94]. This is only possible with KOH-type etchants. The sharpness of the common edge is easily truncated by fast etching facets. This can be avoided with a triangular compensation structure at the convex mask corner which will be underetched completely at the moment the mirrors have reached the desired height and the two mirror faces meet themselves in a common edge. This condition is not achievable over the whole area of the edge at the same time but can be reached at the height of the incident beam. For splitting the beam intensity a membrane is built by underetching of a mask bridge. The etching time must exactly be kept, because the membrane thickness is important for the splitting behavior [Früh1-97].

Fig. 8.8. Type 8.3.1b: Beam splitter by splitting of the beam cross section parallel to the wafer plane; the fibre grooves for the splitter fibres (left and right) have such an angle to the coupling fibre (middle) that the splitting losses are minimal

Fig. 8.9. Type 8.3.2b: Beam splitter by splitting of the beam intensity parallel to the wafer plane; the splitting takes place at a semi-permeable membrane s with vertical sidewalls; the vertical {100}-faces are built on mask edges which are turned to the wafer flat in an angle of ± 45°; grooves are prepared for an exact fibre positioning, too; this example can be used also as a double mirror like type 8.2.5.b Fig. 8.10. Type 8.3.4b: Beam splitter by splitting of the beam intensity out-ofplane; the splitting takes place at a semipermeable membrane s which is inclined to the wafer plane in an angle of 45°; grooves are prepared for an exact fibre positioning at the front- and back side of the wafer, too; this example can be used also as a double mirror similar to type 8.2.3.b

188

8 Elements for Optical Applications

8.4 Concave Micro Mirrors

8.4.1 Introduction Concave mirrors can be produced with an axis perpendicular to the wafer plane. Generally a two-step etch process is necessary because the development of the mirror faces must start at one point. This point is built at the sharp end of a pyramid-shaped deepening between {111}-faces in the first etch step ending with a geometrical etch stop. 8.4.2 Parabolic concave mirrors If the mask window around the firstly etched deepening is enlarged for the second etch step then fast etching facets will grow from the mask-free upper edges of the pyramid and the {111}-faces disappear. When the fast etching faces meet one another at the sharp end of the deepening, the growing of a weak curvatured etch ground starts at this point and the fast etching faces begin to disappear [Diet93, Kend88, Kend94]. During further etching the shape of the deepening becomes rotational-symmetrical with parabolical cross section, type 8.4.1 [Früh4-97]. Diameters of more than 500 µm and focus lengths of around 1 mm can be realized. The roughness is relatively small with values around 10 nm and therefore suitable for optical applications. 8.4.3 Spherical concave mirrors If the second etch step is done isotropically (HF-HNO3-HAc-etchant) the sharp end of the pyramid will change into a spherical concave shape, type 8.4.2. But the reaction rate of the isotropic etching is determined by convection and so some hindrances in the change of reactants lead to different etch rates. To minimize this effect, the mask should also be removed around the deepening. Nevertheless, deviations from the isotropy occur with increasing etching time and asymmetries in the spherical shape are the consequence. There exist only few results in an unpublished manner.

8.5 Gratings

189

Table 8.4. Optical elements IV: concave mirrors Dominant angle of the mask edges to the flat Cross section a) α = 0° or 90° b) α = 45° variants Axis parallel to the wafer perpendicular Type 8.4.1 Parabolic concave mirror Basic process: A A 1.pK/2.pK, table 3.12 section A-A Type 8.4.2 Spherical concave mirror Basic process: 1.pK/2.pI A

A

section A-A Fig. 8.11. Type 8.4.1a: Parabolic concave mirror; deepenings with parabolic profile and a diameter-depth relation of 35:1 to 45:1 are built by faces of weak curvature

8.5 Gratings

Gratings are only realizable in the wafer plane, this means for beam directions which are not in the wafer plane. The minimum grating constant depends on the width of the structure which can be made by lithography (one to a few µm) and mainly on the attainable minimum of misorientation between mask and crystal. The smallest grating constants should be realizable with grooves on the {001}wafer along the <110>-direction bordered by the slowest etching {111}-faces, inclined by 54,7°. These grooves are parallel or perpendicularly directed to the wafer flat. It results in a symmetrical groove array with V-shaped cross sections with walls between the single grooves, type 8.5.1a [Cian00, Rajk95]. These walls can be minimized by underetching when an etchant is used having a relatively large {111}-rate (e.g. TMAH, type 8.5.2a). Using a special kind of a two-step etch process with intermediate oxidation and mask changing (see section 3.4.2) a zigzag profile results with halved grating constants, type 8.5.2a (the uniformity of

190

8 Elements for Optical Applications

neighboured grooves is hardly to realize [Neuz95]). The profile is independent on the type of etchant. Along <100>-mask edges V-grooves with 45° inclined walls can be fabricated using etchants of EDP-type. Using etchant of KOH-type a rectangular profile arises, type 8.5.1b. V-grooves can be used as starting point for an electrochemical etch process resulting in U-shaped grids [Lehm02]. {110}-wafer orientations are also possible for the preparation of gratings. In dependence on the etchant and orientation of the mask edge different profiles are etched, types 8.5.5 and 8.5.6. With the mask edge along <112> ( 35.26° tilt to the flat) a nearly rectangular cross section with a high aspect ratio is possible, type 8.5.5(35.26°). Further cross sections of the grooves or other grating profiles are possible as described in table 8.5 and section 5. In particular gratings are described which are etched in wafers with special orientations. If a crystal plane is used as the wafer surface which is tilt to the {001}-face around an axis parallel to the <110>direction the {111}-faces of the V-grooves do not have longer the same angle to the wafer plane. An unsymmetrical saw-tooth profile with an angle of 70.52 deg between the tooth will result, types 8.5.7 and 8.5.8 [Cian00, Kuhn 03, Klum95]. Table 8.5. Optical elements V: gratings

{100}-wafer Type 8.5.1 Plateau between the grooves Basic process: 1.pK, table 3.10 Type 8.5.2 No plateau between the grooves Basic process: 1.pK Type 8.5.3 No plateau between the grooves Basic process: see table 3.9b (section 3.4) Type 8.5.4 Basic process: 1.pK/1.pI

Dominant angle of the mask edges to the flat (in the wafer plane only) a) α = 0° or 90° b) α = 45° etchant of KOH-type

c) α = 45° etchant of EDP-type

8.5 Gratings Type 8.5.5 Basic process: 1.pK/K {110}-wafer Type 8.5.6

a) α = 0°°

Basic process: 1.pK Type 8.5.7 Basic process: see table 3.9b (section 3.4) {112}-wafer Type 8.5.8 Plateau between the grooves

a) α = 90°

Basic process: 1.pK Type 8.5.9 No plateau between the grooves Basic process: see table 3.9b (section 3.4) All wafer orientations Type 8.5.10 Basic process: 1.pI

a) all isotropic etchants

b) α = 90°,

c) α = 35,26°,

191

192

8 Elements for Optical Applications

Fig. 8.12. Type 8.5.1a: Grating with plateaus in between; mask edge along <110> on an {100}-wafer; one etch step KOH or EDP

Fig. 8.13. Type 8.5.1a: Grating of the same type as in figure 8.12; the grooves are further etched

Fig. 8.14. Type 8.5.3a: Grating without plateaus; mask edge along <110> on an {100}-wafer; twostep etch process KOH or EDP with mask-unmask inversion

Fig. 8.15. Type 8.5.6a: Grating with plateaus in between; mask edge along <100> on an {110}-wafer; one etch step KOH

Fig. 8.16. Type 8.5.7a: Grating without plateaus; mask edge along <100> on an {110}-wafer; twostep etch process KOH or EDP with mask-unmask inversion

Fig. 8.17. Type 8.5.9a: Grating without plateaus; mask edge along <110> on an {112}-wafer, twostep etch process KOH or EDP with mask-unmask inversion

Fig. 8.18. Type 8.5.10a: Grating isotropically etched (flat-arched-flat)

Fig. 8.19. Type 8.5.10a: Grating isotropically etched (arched-flat); higher etch depth than in figure 8.18

8.6 Infrared Prisms

193

8.6 Infrared Prisms

8.6.1 General remarks The transparency of silicon in the wavelength range between λ=1.1 µm to 6.5 µm allows its use for refractive optical elements [Gör94, Gör98]. Sidewall shapes of etched structures may be combined to prisms. The requirement is a well defined growth of sidewall faces with a good surface quality. Produced prisms can be divided according to the direction of the prism edge: the prism edge is situated inside or perpendicular to the wafer plane. The plane of the refracted beams is perpendicular to this prism edge in all cases. At this time Si microprisms are the least used of all optical microstructures. 8.6.2 The prism edge lies inside the wafer plane In this case the prisms are bordered by sidewall faces which have a defined inclination angle to the wafer plane, etch ground or wafer surface. These are the {111}-faces with an inclination angle of 54.74° along the <110>-directed mask edges (parallel or perpendicular to the flat). Such faces can be combined to prisms with angles of ∆γ = 54.74° (type 8.6.1), ∆γ = 109.48° (type 8.6.2) and ∆γ = 70.52° (type 8.6.3). Vertical {100}-sidewall faces can be realized with mask edges inclined by 45° to the flat (parallel to <100>) by using KOH-type etchants. They build, together with the wafer surface or the etch ground, a prism with ∆γ = 90° (type 8.6.5). The 45° inclined {110}-sidewall faces can be created using EDP-type etchants so that prisms with angles of ∆γ = 45° (type 8.6.4) (together with the wafer surface or the etch ground) or ∆γ = 90° (type 8.6.5) (two {110}-faces) can be made. 8.6.3 The prism edge lies perpendicular to the wafer plane Only sidewall faces which are vertical to the wafer surface are possible. Mask edges must be designed with an angle of 45° to the flat and an etchant of KOHtype has to be used. The prism angle is ∆α = 90°. The KOH-type etchants can produce nearly vertical sidewalls on mask edges in a direction area α=45±7,5°deg. Prisms can be realized with angles ∆α=75 to 105° (symmetrical to <110>) or prisms with angles ∆α=10 to 15° (symmetrical to <100>). Table 8.6 and the following figure illustrates shapes of prisms which can be realized with the {100}-silicon wafer. Analogously, possible shapes can be easily developed with the {110}-wafer. In this case the use of the etch ground must be avoided.

194

8 Elements for Optical Applications Fig. 8.20. Type 8.6.7: 75°-prism; the mask edge is directed in an angle of 45-7,5° to the flat; with greater deviations from the 45°-directed mask edge the facets at the etch ground will become more distinct

Table 8.6. Optical elements VI: IR-prisms ({100}-wafer) Dominant angle of the mask edges to the flat α = 0° or 90° α = 45° (KOH-type) α = 45° (EDP-type) Prism edge in the wafer plane (beam direction out of the wafer plane) Basic process: 1.pK or 1.pE resp. 1.1K or 1.1E, table 3.10 resp. 3.14 Type 8.6.1 ∆γ = 54.74° Type 8.6.2 ∆γ = 109.48° Type 8.6.3 ∆γ = 70.52° Type 8.6.4 ∆γ = 45° Type 8.6.5 ∆γ = 90° Prism edge perpendicular to the wafer plane (beam direction in the wafer plane) Basic process: 1.pK, table 3.10 Type 8.6.6 prism angle 15° α = 45 + ∆ α

α = 45 - ∆x Type 8.6.7 prism angle 90°±2∆α

α = 45 + ∆ α

α = -(45 + ∆ α)

α = 45 - ∆ α

α = -(45 - ∆ α)

8.6 Infrared Prisms

195

References [Arm91]

Armiento CA et al. (1991) Passive coupling of InGaAsP/InP laser array and singlemode fibres using silicon waferboard. Electronics Letters 27: 1109– 1111 [Asa99] Asada N, Takeuchi M (1999) Silicon micro-optical scanner. Transducers `99: Proc of the 10th Conf on Solid-State Sensors and Actuators, Japan: 778–781 [Bäck92] Bäcklund Y, Rosengreen L (1992) New shapes in (100) Si using KOH and EDP etches. J Micromech Microeng 2: 75–79 [Bäck93] Bäcklund Y, Rosengreen L, Smith L (1993) Optical planes and reflectors, anisotropically etched in silicon. Transducers `93: Proc of the 7th Conf on Solid-State Sensors and Actuators, Japan: 1031–1033 [Bäck97] Bäcklund Y (1997) Micromechanics in optical microsystems – with focus on telecom systems. J Micromech Micreng 7: 93–98 [Cian00] Cianci E et al. (2000) Fabrication and performance of a prism coupled silicon transmission grating for near infrared spectroscopy. Proc of the Micro.tec VDE World Microtechnologies Congress, Germany: 685–689 [Corn91] Cornely RH, Marcus RB (1991) Formation of silicon micromirrors by anisotropic etching. Sensors and Actuators A 29: 241–250 [deLab01] de Labachelerie et al. (2001) A micromachined connector for the coupling of optical waveguides and ribbon optical fibres. Sensors and Actuators A 89: 36–42 [Diet93] Dietrich D, Frühauf J (1993) Computer simulation of the development of dish-shaped deepenings by orientation dependent etching of {100}-silicon. Sensors and Actuators A 39: 261–262 [Frank98] Frank T, Wurmus H (1998) A new principle for micro-opto-mechnaical scanners. Micro System Technologies ‘98: Proc of the 6th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 177–182 [Früh01] Frühauf J, Gärtner E, Jänsch E (2001) Plastic reshaping of silicon microstructures: process, characterisation and application. Microsystem Technologies 7, 4: 155–160 [Früh1-97] Frühauf J, Hannemann B (1997) Mikromechanische und optische Funktionselemente hergestellt durch anisotropes Ätzen von Silizium. Mikrosystemtechnik ’97: Proc of the 3rd Conf on Mikromechanik & Mikroelektronik, Germany: 88–98 [Früh2-97] Frühauf J, Hannemann B, Gerber M (1997) Ätzraten und Oberflächenqualitäten beim Silizium-Ätzen in der Mikrotechnik. Internal Report SMWKProjektförderung 0380/509, Technische Universität Chemnitz [Früh4-97] Frühauf J et al. (1997) Konstruktionselemente der Mikrosystemtechnik, Varianten ihrer ätztechnischen Herstellung und ihr rechnergestützter Entwurf. Final Report AIF-Project 9929B, Technische Universität Chemnitz [Geß96] Geßner T et al. (1996) Design, technology and characterization of a mirrorarray in silicon-micromechanics. Micro System Technologies ‘96: Proc of the 5th Int Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 657–662 [Gonz1-97] Gonzáles C, Collins SD (1997) Magnetically actuated fibre-optic switch with micromachined positioning stages. Optics Letters 22, 10: 709–711

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8 Elements for Optical Applications

[Gör94]

[Gör98] [Graf00] [Han98]

[Har99]

[Hill88] [Hill99]

[Hoff03] [Hoff1-99] [Hoff2-99]

[Jac93] [Kend88] [Kend94]

[Klum95] [Kuhn03]

[Kurth96] [Lang99] [Lehm02]

[Lutz86]

Göring R, Molzahn U (1994) Miniaturized optical systems for beam deflection and modulation. Micro System Technologies ’94: Proc of the 4th Conf & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, Germany: 1073–1080 Göring R et al. (1998) Complex microprism structures and their application to multichannel fibre optics switches. Proc of SPIE 3276: 167–175 Graff JW, Schubert EF (2000) Flat free standing silicon diaphragms using silicon-on-insulator wafers. Sensors and Actuators 84: 276–279 Hannemann B, Frühauf J (1998) New and extended possibilities of orientation dependent Etching in Microtechniques. IEEE-MEMS '98: Proc of the 11th Int Micro Electro Mechanical Systems Conference, Germany: 234–239 Hara K et al. (1999) Si micromechanical fibre-optic switch with shape memory alloy microactuator. Transducers `99: Proc of the 10th Int Conf on SolidState Sensors and Actuators, Japan: 790–793 Hillerich B, Geyer A (1988) Self-ligned flat-pack fibre-photodiode coupling. Electronics Letters 24: 918–919 Hiller K et al. (1999) Fabrication of high frequency microscanners by using low temperature silicon wafer bonding. Transducers `99: Proc of the 10th Conf on Solid-State Sensors and Actuators, Japan: 1448–1501 Hoffmann M et al. (2003) Fibre-optical MEMS switches bases on bulk silicon micromachining. Microsystem Technologies 9: 299–303. Hoffmann M, Kopka P, Voges E (1999) Bistable micromechanical fibre-optic switches on silicon with thermal actuators. Sensors and Actuators 78: 28–35 Hoffmann M, Dickhut S, Voges E (1999) Silicon fibre ribbon Pigtails with rhombus-shaped fibre channels and integrated photodiodes. MOEMS `99: Proc of the 3rd Int Conf on Micro Opto Electro Mechanical Systems, Germany: 206–209 Jacobs-Cook AJ, Bowen MEC (1993) Novel optical fibre/microresonator interfacing technology. Sensors and Actuators A 37–38: 540–545 Don Kendall L et al. (1988) Chemically etched micromirrors in silicon. Appl Phys Letters 52, 10: 836–837 Don Kendall L et al. (1994) Micromirror arrays using KOH-H2O micromachining of silicon for lens templates, geodesic lenses, and other applications. Optical Engineering 33, 11: 3578–3588 Klumpp A et al. (1995) Anisotropic etching for optical gratings. Sensors and Actuators A 51: 77–80 Kuhn M et al. (2003) Herstellung und Charakterisierung von mikromechanischen Scannern mit integrierten Beugungsgittern. Mikrosystemtechnik ’03: Proc of the 6th Conf on Mikromechanik & Mikroelektronik, Germany: 73–78 Kurth S et al. (1998) Silicon mirrors and micromirror arrays for spatial laser beam modulation. Sensors and Actuators A 66: 76–82 Lang W et al. (1999) Electrostatically actuated micromirror devices in silicon technology. Sensors and Actuators 74: 216–218 Lehmann V, Rönnebeck S (2002) MEMS techniques applied to the fabrication of anti-scatter grids for X-ray imaging. Sensors and Actuators A 95: 202–207 Lutzke D (1986) Lichtwellenleitertechnik. Pflaum Verlag, München

8.6 Infrared Prisms [Maek01]

[Mark93] [Mill97]

[Mita99]

[Neuz95]

[Ono01]

[Rajk95] [Ros1-94] [Ros2-94] [Sad97]

[Seki2-99]

[Shie99]

[Steck91]

[Stra95]

[Stra98]

[Uen95]

[Vand95]

197

Maekoba H et al. (2001) Self-aligned vertical mirror and V-grooves applied to an optical-switch: modeling and optimization of bi-stable operation by electromagnetic actuation. Sensors and Actuators A 87: 172–178 Markert J et al. (1993) Elektrostatischer Mikroaktor. Feinwerktechnik & Meßtechnik 101, 5: 193–196 Miller RA et al. (1997) An electromagnetic MEMS 2*2 fibre optic bypass switch. Transducers `97: Proc of the 9th Conf on Solid-State Sensors and Actuators, USA: 89–92 Mita M et al. (1999) Optical and surface characterization of poly-Si replica mirors for an optical fibre switch. Transducers `99: Proc of the 10th Conf on Solid-State Sensors and Actuators, Japan: 1–4 Neuzil P, Serry FM, Maclay GJ (1995) Fabrication of sharp ridges on single crystal silicon wafers. The Electrochemical Society Inc, Extended Abstracts 95-2, 975: 1534–1535 Ono H et al. (2001) Fabrication of an electrostatic lens array with separate electrodes and shield membranes using the UV-LIGA process. Transducers ’01: Proc of the 11th Int Conf on Solid-State Sensors and Actuators, Germany: 4C2.05, 1586–1589 Rajkumar N, McMullin JN (1995) V-groove gratings on silicon for infrared beam splitting. Applied Optics 34: 2556–2559 Rosengren L, Smith L, Bäcklund Y (1994) Micromachined optical planes and reflectors in silicon. Sensors and Actuators A 41–42: 330–330 Rosengren L (1994) Silicon microstructures for biomedical sensor systems. Dissertation Thesis, Uppsala University Sadler DJ et al. (1997) Optical reflectivity of micromachined {111}-oriented silicon mirrors for optical input-output couplers. J Micromech Microeng 7: 263–269 Sekimura M, Naruse H (1999) Fabrication of 45° optical mirrors on [100] silicon using surfactant-added TMAH solution. Transducers ’99: Proc of the 10th Conf on Solid-State Sensors and Actuators, Japan: 550–551 Shie JS, Yu SH (1999) A micromachined silicon submount package for vertical emission of edge emitting laser diodes. Transducers `99: Proc of the 10th Conf on Solid-State Sensors and Actuators, Japan: 1490–1493 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 Strandman C et al. (1995) Fabrication of 45° mirrors together with welldefined V-grooves using wet anisotropic etching of silicon. J Microelectromechanical Systems 4, 4: 213–219 Strandman C, Bäcklund Y (1998) Passive and fixed alignment of devices using flexible silicon elements formed by selective etching. J Micromech Microeng 8: 39–44 Uenishi Y, Tsugai M, Mehregany M (1995) Micro-opto-mechanical devices fabricated by anisotropic etching of (110) silicon. J Micromech Microeng 5: 305–312 Vandewege J, Tan Q, de Pestel G (1995) A fibre-ribbon positioning device. J Micromech Microeng 5: 313–318

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[Yan01]

Yang LJ, Liu CW, Chang P (2001) Phase synchronization of micro-mirror arrays using elastic linkages. Sensors and Actuators A 95: 55–60

Appendix

Physical Properties of Silicon

201

Physical Properties of Silicon Survey and comparison with properties of other materials In the context of this manual the provision of some data about the physical properties of silicon serves the purpose of - the estimation of the suitability of silicon as a material for a desired function, - the support of the functional design of a microtechnical component. After an overall view for comparison with the properties of other selected materials (metals, glasses, ceramics, polymers) dates of the following properties are enclosed in tables and diagrams:

Mechanical properties − − − −

density elastic constants and moduli and their dependence on temperature hardness and its dependence on temperature bending strength and its dependence on the dimensions

Thermal and caloric properties − linear coefficient of thermal expansion and its dependence on temperature − heat conductivity and its dependence on temperature − specific heat and its dependence on temperature

Optical properties − refraction index and its dependence on wave length − coefficient of reflection and its dependence on wave length − coefficient of absorption and its dependence on wave length The values of properties shown in the overall view in table A.1 are based on data from a large number of books which are not referred to in detail here. Representative materials applicated to the construction of devices of precision engineering are selected. This table serves as a comparison of the properties of silicon with those of other materials and cannot be used as a source of concrete values. The values in tables A.2–A.14 are based on the data of [Hull99] or on original publications referred to in [Hull]. They are given at the end of the tables, too. The values are related to pure or “intrinsic” silicon. In the case of highly doped silicon the values differ more or less. Those values are not implemented in the tables. The values of bending strength are assembled from the given publications together with own results especially with regard to the dependence on the dimensions of the tested structures.

202

Appendix

Table A.1. Mechanical and physical properties of silicon at room temperature in comparison with other materials Properties

Density ρ [g/cm3] Young’s 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 durabiltiy Tmax [°C] Dielectric constant ε[-]

Si

Al

Monocrystal

Polycrystal

2.33

2.33

130–188

112

50–200

< 690

Al-alloys AlSi12 (castingalloy)

AlCu (agehardenable)

AlZn (agehardenable)

2.70

2.65

2.80

2.80

66–72

74–78

70–73

68–73

20–160

80–110

220–400

270–500

65–190

170–260

340–480

350–570

3–35

5–12

5–20

2–8

18–42

50–65

75–120

80–145

865–875

862

175–370

6.9-10.3

240

7.5-10.8 715

1.3 707

156

890–905 209–225

120–190

130–200

125–160

14.0– 21.6

22.8– 23.8

23.1– 24.0

83.7 2.3–2.6

2.2–4.2

23.5– 25.4

(6–20) ∗104 1412– 1417

10-4–104

2.7–2.9 ∗ 3.7–5.9 ∗ 3.4–5.8 ∗ 4.3–5.8 ∗ 10-6 10-6 10-6 10-6 660

1412– 1417 1000– 1200 11.7– 12.1

150–200

150

150–200

125

Physical Properties of Silicon

203

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 durabiltiy Tmax [°C] Dielectric constant ε[-]

Cu

Cu-alloys

Ni

FeNi-alloys

8.93

FeNi36 FNi28 Co18 (Invar) (Kovar) 8.2 8.3

CuZn 30 (brass)

CuSn6 (bronze)

8.96

8.53

8.85

117–130

105– 98–120 125– 120 135 90–460 160– 140– 590 1020 270– 340– 410– 560 710 1230

189– 135– 214 148 70–710 250– 490 385– 450– 750 630

140– 170 300– 450 450– 610

2–48

5–55

3–55

22–45

36–110

55–160 80–230 65–370 85–240 130– 265 2.3

140– 250

385

398

60–80

284–398

117– 121

67–71

502– 670 16.7– 19.3

16.8

18.6

17.0– 18.0

1.7–2.5 ∗ 10-6 1084

5.5–6.4 10–12 ∗ 10-6 ∗ 10-6

2.9–8.3 6.5–9.5 77 ∗ ∗ 10-6 ∗ 10-6 10-6 1454 1425

200–300

200– 250

200– 250

40–350 150–430

3–58

200– 320

CuBe2 (agehardenable) 8.3

2–46

20–43

90–200 444– 540 84–105 61–92

502– 523 12.6– 14.7

17.1

1.2–1.5 4.3– 6.1

13.1– 13.3

600– 800

250

45–77 ∗ 10-6 1450

204

Appendix

Table A.1. Continuation Properties

Steel/Cast iron Ck67

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[-]

Ceramic

(ferritic) 7.85

X5CrNi 18-10 (austenitic) 7.9

GG-25 (grey cast iron) 7.5

206

203

103– 118

350– 1400 530– 1600

185 490– 685

245 685– 980

175– 490 1–35

Al2O3

AlN

3.89– 3.99 255– 390

3.25– 3.30 300– 330

379– 552

130– 180 6.5–6.6

165– 295

1500– 1750 19–21

477

502

460

46

14.7

42–48

11.1

16.0

10.5– 11.0

175– 515

Silica glass (quarz glass) 2.20– 2.22 71.1– 74.3

Borosilicate glass 2.23– 2.50 61–66

50–115

70

420– 2300

840

50–60

50

650

11.8

710– 750 6.2–6.4

738

710

115– 170

1.15– 1.40

4.8– 6.6 750– 830 0.83– 1.13

3.8–5.7

0.48– 0.50

3.0– 5.0

> 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

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200–250

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3.0–3.5

2.4

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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 <100> [GPa] E <110> [GPa] E <111> [GPa] 130 169 188

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

300–1000

Torsional modulus for special torsional axises (round stick) <100> [GPa] <110> [GPa] <111> [GPa] 79.5 62 57.8 Sliding modulus for the stress of an {100}-face for directions of G <100> [GPa] G <110> [GPa] 79.51 50.85

[Over77]

Physical Properties of Silicon

207

Table A.3. Bending strengths Bending strength [GPa] Orientations <111> 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

<110>

<100>

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








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Physical Properties of Silicon Table A.4. Bending strengths in dependence on sample thickness

Bending strength Rm [MPa]

Thickness [mm] 0.012 0.017 0.031 0.043 0.106 0.400 0.400 0.530

Width [mm] 0.160 0.134 1.400 1.400 3.470 10.000 4.500 5.000

Bending 1-point 1-point 1-point 1-point 3-point 3-point 3-point 4-point

Rm [MPa] 3900 6100 1486 986 900 370 280 170

Reference [Joh88] [Eric90] [Eisn55] [Eisn55]

[Jän00] [Hu82] [Jän00] [Yasu82]

10000

1000

100 0.01

0.1

Sample thickness [mm]

Fig. A.2. Bending strength in dependence on sample thickness

1

209

210

Appendix

Table A.5. Hardness Vickers hardness T [°C] T [K] 25 298 25 298 25 298 25 298

H [GPa] 7–20 10.3 6.9 10.2

T [°C] 24 100 200 400 600 800

H [GPa] [Nayl] 10.2 9.8 9.3 5.6 2.6 1

T [K] 297 373 473 673 873 1073

Reference [Peth83] [Gilm73] [Sher85] [Nayl] H [GPa] [Gilm75] 7.9 7.4 7.1 6.2 2.3 0.8

Hardness H [GPa]

Knoop-micro-hardness on {111}-faces 7.49 GPa during 0.098 N load 8.41 GPa during 0.245 N load 7.7-10.8 GPa during 0.06 N load

[Burn86] [Leigh73]

12 10 8 6 4 2 0 24

100

200

400

600

Temperature T [°C] H [GPa] [Nayl]

Fig. A.3. Hardness

H [GPa] [Gilm75]

800

Physical Properties of Silicon

Linear coefficient of thermal expansion α [10 -6 K-1]

Thermal and caloric properties

5 4 3 [Soma98]

2

[Gibb58]

1 0 -1

0

500

1000

1500

2000

-2

Temperature T [K]

30

Thermal conductivity K [W cm

-1

K-1 ]

Fig. A.4. Linear coefficient of thermal expansion

25 20 15 10 5 0 0

500

1000

Temperature T [K]

Fig. A.5. Thermal conductivity of silicon [Wyb98]

1500

2000

211

212

Appendix

Specific heat Cp [J kg-1 K-1]

1200 1000 800 600 400 200 0 0

500

1000

Temperature T [K]

Fig. A.6. Specific heat [Honig62, Flub59, Kell49]

1500

2000

Physical Properties of Silicon

213

Optical properties

Refractive index n

8 7 6 5 4 3 0.1

1

10

Wavelength λ [µm]

Fig. A.7. Refractive index of silicon in dependence on the wavelength [Asp98]

Reflection coefficient R

0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.1

1

10

Wavelength λ [µm]

Fig. A.8. Reflexion coefficient of silicon at vertical incidence at room temperature [Asp98]

214

Appendix

10000000 1000000

Absorption coefficient a [cm-1]

100000 10000 1000 100 10 1 0.1 0.01 0.001 0.0001 0.1

1

10

Wavelenght λ [µm]

Fig. A.9. Absorption coefficient in dependence on the wavelength at room temperature [Asp98]

Physical Properties of Silicon

215

References [Asp98]

[Booth91] [Burn86] [Burn88] [Dien92]

[Eisn55] [Eric90] [Flub59]

[Gibb58] [Gilm73] [Gilm75] [Hall67] [Heu91] [Honig62] [Hu82] [Hull99] [Jän00]

[Joh88] [Kehr94] [Kell49] [Kies92] [Leigh73]

Aspnes DE (1998) Optical properties. In: Hull R (ed) Properties of crystalline silicon. University Virginia, INSPEC (No. 4) pp 677–696 Booth AS, Cosgrave M, Roberts SG (1991) The warm-prestressing effect in Si. Acta metall mater 39, 2: 191–197 Burnett PJ, Briggs GAD (1986) The elastic properties of ion-implanted silicon. J Mater Sci 21: 1828–1836 Burnett PJ (1988) Hardness of Si. In: Hull R (ed) Properties of crystalline silicon. University Virginia, INSPEC pp 21-26 Dienst W (1992) Festigkeitsprüfung an keramischen Mikroproben. Proc of the Conf Werkstoffprüfung, Deutscher Verband für Materialforschung und – prüfung, Germany: 281–290 Eisner RL (1955) Tensile tests on silicon whiskers. Acta Met 3: 414–415 Ericson F, Schweitz J (1990) Micromechanical racture strength of Si. J Applied Physics 68, 11: 5840–5844 Flubacher P, Leadbetter AJ, Morrison JA (1959) The heat capacity of pure silicon and germanium and properties of their vibrational frequency spectra. Phil Mag Ser 8, 4: 273–294 Gibbons DF (1958) Thermal expansion of some crystals with the diamond structure. Phys Rev 112: 136–140 Gilman JJ (1973) In: Westbrook JW, Conrad H (eds) The science of hardness testing and its research application. ASM, Ohio Gilman JJ (1975) Flow of covalent solids at low temperatures. J Applied Phys 46, 12: 5110–5113 Hall J (1967) Electronic effects in the elastic constants of n-type silicon. Phys Rev 161: 756–761 Heuberger A (1991) Mikromechanik. Springer Verlag, Berlin Honig RE (1962) Vapor pressure: data for the solid and liquid elements. RCA Rev 23: 567–586 Hu SM (1982) Critical stress in silicon brittle fracture and effect on ion implantation and other surface treatments. J Applied Physics 53, 5: 3576–3580 Hull R (ed) (1999) Properties of crystalline Silicon. INSPEC, University of Virginia, USA Jänsch E, Frühauf J, Gärtner E (2000) Biegebruchfestigkeiten von geätzten und verformten Mikrostrukturen. Freiberger Forschungshefte B321: 238– 253 Johansson S et al. (1988) Fracture testing in silicon microelements in situ in a scanning electron microscope. J Applied Physics 63, 10: 4799–4803 Kehr K (1994) Lebensdaueruntersuchungen an mikromechanischen Komponenten. Diploma Thesis. Technische Universität Chemnitz Kelly KK (1949) Contributions to the data on theoretical metallurgy. Bureau of Mines Bulletin Kiesewetter L et al. (1992) Wie belastbar ist Si in mikromechanischen Strukturen. F&M 100, 6: 249–254 Leighly HP, Oglesbee RH (1973) In: Westbrook JW, Conrad H (eds) The science of hardness testing and its research application. ASM, Ohio

216

Appendix

[Lyon77] [McL87] [Nayl]

[Okad84]

[Over77]

[Pear57] [Peth83] [Sher85] [Soma98]

[Wyb98] [Yasu82]

[Zhang94]

Lyon KG et al. (1977) Linear thermal expansion measurements on silicon from 6 to 340 K. J Applied Physics 48, 3: 865–868 McLaughlin JC, Willoughby AFW (1987) Fracture of silicon wafers. J of Crystal Growth, 85: 83–90 Naylor MGS, Page TF, Third Annual Technical Report, Grant no. DA-ERO78-G-010, European Research Office, United States Army, London, England Okada Y, Tokumaru Y (1984) Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K. J Applied Physics 56, 2: 314–320 Over HH (1977) Elastische und plastische Eigenschaften von einkristallinem Silicium in Abhängigkeit von der Temperatur und der Versetzungsdichte. Dissertation Thesis. RWTH Aachen Pearson GL, Read WT, Feldmann WL (1957) Deformation and fracture of small silicon crystals. Acta Met 5: 181–191 Pethica JB, Hutchings R, Olivier WC (1983) Hardness measurement at penetration depths as small as 20 nm. Philos Mag A, 48: 593–606 Sher A, Chen AB, Spicer WE (1985) Dislocation energies and hardness of semiconductors. Appl Phys Lett 46, 1: 54–56 Soma T, Kagaya K (1998) Thermal Expansion Coefficient of c-Si. In: Hull R (ed) Properties of crystalline silicon. University Virginia, INSPEC (No. 4) pp 153–154 Wybourne MN (1998) Thermal conductivity of c-Si. In: Hull R (ed) Properties of crystalline silicon. University Virginia, INSPEC (No. 4) pp 165–167 Yasutake K et al. (1982) Mechanical properties of heat–treated CZ-Siwafers from brittle to ductile temperature range. Jap J of Applied Physics 21, 5: L288–L290 Zhang J (1994) Verfahren und Einrichtungen zur Bestimmung mechanischer Eigenschaften mikromechanischer Werkstoffe. Fortschrittberichte VDI, Reihe 5: Grund- und Werkstoffe

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