Nanostructured Semiconductors - Taylor & Francis eBooks

NanostructuredSemiconductors

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NanostructuredSemiconductors

edited by Petra Granitzer and Klemens Rumpf

From Basic Research to Applications

for the WorldWind PowerThe Rise of Modern Wind Energy

Preben MaegaardAnna KrenzWolfgang Palz

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Contents

Preface xv

1. AMetaModelforElectrochemicalPoreGrowthinSemiconductors 1

Malte Leisner, Helmut Föll, and Jürgen Carstensen

1.1 Introduction 1 1.2 The Essence of Crystallographic and

Currentline Pores in III–V Semiconductors 4 1.2.1 General 4 1.2.2 Crystallographic Pores 6 1.2.3 Currentline Pores 10 1.3 Experimental Insights into the Growth

Mode of Currentline Pores 15 1.3.1 ND Dependence 15 1.3.2 The Pore Tips 17 1.3.3 Mass Transport through Currentline

Pores 19 1.4 Experimental Insights into the Growth

Mode of Crystallographic Pores 24 1.4.1 ND Dependence 24 1.4.2 Monte-Carlo Simulation of

Crystallographic Pore Growth 25 1.4.2.1 Simulation procedure 25 1.4.2.2 Simulation results 27 1.5 Crysto–Curro Transition 30 1.6 Nucleation 34 1.7 Conclusion 38

vi Contents

2. NewApproachestotheProductionofPorousSiliconbyStainEtching 45

Kurt W. Kolasinski

2.1 Introduction 46 2.2 Surface Chemistry of Silicon 48 2.3 Carrier Dynamics 55 2.4 Requirements for Stain Etchants 63 2.5 Stain Etching in FE3+, MN O 4 –

, CE4+, and V O 2 + 66 2.6 Conclusion 72

3. SiliconNanostructuresbySelf-AssemblyandMetal-AssistedEtching 85

Luca Boarino, Giampiero Amato, Emanuele Enrico, Natascia De Leo, Federica Celegato, Marco Coïsson, Franco Vinai, Paola Tiberto, Angelica Chiodoni, and Michele Laus

3.1 Introduction 85 3.2 Polystyrene Nanospheres 87 3.3 Emulsion 87 3.4 Nanoemulsion 90 3.5 Surface Control 91 3.6 Self-Assembly 92 3.7 Nanofabrication by Self-Assembly of Colloidal

Spheres 95 3.8 Formation of 2D Arrays of Colloidal Spheres 97 3.9 Mask Modification 100 3.10 Metal-Assisted Etching 102 3.11 MAE with PSNS Pre-Patterning 106 3.12 Microstructural and Magnetic Characterization of

Antidot Magnetic Thin Films 109 3.13 MAE on Magnetic Thin Films 111 3.14 Conclusions 114

4. SynthesisandCharacterizationofGermaniumNanocrystals 119

Manash R. Das, Sabine Szunerits, and Rabah Boukherroub

4.1 Introduction 120 4.2 Germanium Nanocrystals 123

viiContents

4.2.1 Preparation of Ge Nanocrystals 123 4.2.1.1 Ion implantation 123 4.2.1.2 D.C. and RF magnetron sputtering 125 4.2.1.3 Chemical vapor deposition 127 4.2.1.4 Electron-beam and cluster-beam

evaporation 129 4.2.1.5 Molecular beam epitaxy 132 4.2.1.6 Pulsed laser deposition 133 4.2.1.7 Sol-gel 133 4.2.1.8 Solution phase 134 4.3 Functionalization of Ge Nanoparticles 138 4.3.1 Hydrogermylation 138 4.3.2 Halogenation/Alkylation 140 4.3.3 Ge−OBondFormation 148 4.3.4 Miscellaneous 149 4.4 Conclusions and Perspectives 153

5. SiGeNanostructures:FromFundamentaltoApplications 165

Isabelle Berbezier, Antoine Ronda, Jean-Noël Aqua, Luc Favre, and Thomas Frisch

5.1 Introduction 165 5.2 Experimental 168 5.3 Nucleation and Growth 170 5.4 Strain Control and Adjustment 180 5.5 Redistribution of Dopants 192 5.6 Self-Assembly on Nanostructured Substrate 194 5.6.1 Natural Structuration Based on Growth

Mechanisms 195 5.6.1.1 Si/Si instabilities 196 5.6.1.2 SiGe/Si instabilities 200 5.6.1.3 Self-assembly 202 5.6.2 Nanostructuration Based on Lithographic

Tools 208 5.6.2.1 FIB-patterned Si substrate 209 5.6.2.2 Self-assembly on SiO2/Si substrate 214

viii Contents

5.7 Physical Properties of SiGe Nanostructures 223 5.8 Conclusion 233

6. MesoporousSilicafromtheAnodizationofSilicon:PreparationandMorphologies 247

Jean-Noël Chazalviel and François Ozanam

6.1 Introduction 248 6.2 Preparation of Thick Porous Silica Films 250 6.2.1 Experimental Results 250 6.2.2 Theoretical Understanding 253 6.3 Macromorphologies 260 6.3.1 Characterization of the Bright Layers 260 6.3.2 Morphologies of the Dull Layers 262 6.3.3 Map of the Macromorphologies in

Preparation Space 264 6.3.4 Origin of the Macromorphologies 266 6.4 Ultimate Structure of the Porous Silica Layers 267 6.4.1 Evidence for a Stratified Structure by

X-RayReflectometry 268 6.4.2 Direct Evidence for a Stratified Structure

by SEM after Metal Electrodeposition 269 6.4.3 Origin of the Stratified Structure 271 6.5 Conclusions 275

7. FillingofPorousSiliconwithMetalsbyElectrochemicalReactions 279

Kazuhiro Fukami

7.1 Introduction 279 7.2 Electrodeposition within p-Type Macroporous

Silicon 280 7.2.1 Electrodeposition of Metals via Hole

Injection or Photo-Excitation 280 7.2.2 Effect of Solution Composition on the

Morphologies of Deposits 283 7.2.3 Effect of Pore Wall Resistance 286 7.3 Filling of Mesoporous Silicon by Electrodeposition 288

ixContents

7.3.1 Copper Filling within Mesoporous Silicon: From an Experimental Approach 288

7.3.2 Copper Filling within Mesoporous Silicon: From a Numerical Approach 290

7.3.3 Filling of Mesoporous Silicon with Other Metals by Electrodeposition 294

7.4 Concluding Remarks 295

8. MagneticNanostructuresEmbeddedinaPorousSiliconMatrix 299

Klemens Rumpf and Petra Granitzer

8.1 Introduction 300 8.2 Preparation of the Nanocomposite 301 8.2.1 Fabrication of the Porous Silicon Matrices 301 8.2.2 Electrodeposition of Ni and Co 304 8.3 Structural Characterization of the Nanocomposite 307 8.4 Magnetic Behaviour 310 8.4.1 Temperature Dependence 313 8.4.2 Dependence of the Coercivity on Magnetic

Interactions 314 8.5 Summary 315

9. ManifestationsoftheQuantumConfinementEffectinthePhototransportPropertiesofEnsemblesofSemiconductorQuantumDots 319

Isaac Balberg

9.1 Introduction 320 9.2 Basic Concepts in Photoconductivity 324 9.3 Experimental Details 334 9.3.1 Sample Preparation and Characterization 334 9.3.1.1 Ensembles of CdSe nanocrystallites 334 9.3.1.2 Ensembles of silicon

nanocrystallites 336 9.3.1.3 Light-emitting porous silicon 338 9.3.2 Experimental Techniques 339

x Contents

9.4 Manifestation of the QC Effect in the Phototransport Properties in the Steady State 341

9.5 The Mutual Exclusion of the PL and the PC in the Steady State 352

9.6 Possible Correlation between the PC and the PL Phenomena in the Transient Regime 362

9.7 Summary and Conclusions 378

10. SiliconNanocrystalsEmbeddedinSiO2Matrices:Abinitio

Results 393

Roberto Guerra and Stefano Ossicini

10.1 Introduction 393 10.2 Computational Methods 395 10.2.1 Beyond Density Functional Theory 396 10.2.2 Local Fields 397 10.2.3 The Effective Medium Theory 398 10.3 Structures 400 10.3.1 Silicon Nanocrystals Embedded in SiO2 400 10.3.2 Amorphous Structures 403 10.3.3 Suspended Nanocrystallites 405 10.4 Results 407 10.4.1 The Crystalline Embedded Nanocluster 408 10.4.2 The Amorphous Nanocluster in a Glass 411 10.4.3 Size 415 10.4.4 Effective Medium Approximation 420 10.4.5 Many-Body Effects 425 10.4.6 Local Fields 426 10.4.7 Strain 429 10.4.8 Oxidation 432 10.4.9 NC–NC Interaction 434 10.4.10 Emission Rates 436 10.5 Conclusions 442

xiContents

11. DesignofCompositeandMulti-ComponentOne-DimensionalPhotonicCrystalStructuresBasedonSilicon 453

Tatiana S. Perova, Vladimir A. Tolmachev, and Kevin Berwick

11.1 Introduction 454 11.2 Methods for Photonic Bandgap Design 456 11.2.1 Band Diagram Method 458 11.2.2 Transfer Matrix Method 460 11.2.3 The Gap Map Method 460 11.2.4 Gap Map and Real 1D Photonic Crystal 464 11.3 Gap Map of 1D Photonic Crystal with

Omni-Directional Band Regions 466 11.3.1 Influence of the Optical Contrast

and Incident Angle on the PBG Regions 467 11.3.2 Comparison of BD and GM Approaches for

Calculation of Omni-Directional Bands 470 11.3.2.1 Photonic crystal with medium

optical contrast 470 11.3.2.2 Photonic crystal with small

optical contrast 471 11.4 Complex Photonic Crystals for PBG Extension 472 11.4.1 Addition of PBGs in Complex Photonic

Crystals 472 11.4.1.1 Comparison of photonic crystals

with the same A and different f 475 11.4.1.2 Comparison of photonic crystals

with the same fanddifferentA 477 11.4.1.3 Combined PC with omni-directional

PBG 480 11.4.2 Photonic Crystal with Structural Disorder

for Extension of PBG 482 11.5 Multi-Component PC with an Additional

Regular Layer 485 11.5.1 Features of Gap Map Formation for a

Three-Component PC 488

xii Contents

11.5.2 Influence of the Thickness of the Additional Layer on the PBGs 490

11.5.3 Influence of the Number of Lattice Periods for Multi-Component PC 492

11.5.4 Tuning of Optical Contrast 493 11.5.5 Gap Map and Reflection Spectra for

Oblique Incidence of Light and Formation of Omni-Directional Bands in Three-Component PCs 495

11.5.6 Suppression of PBGs and Formation of Regions of Transparency 501

11.6 Composite Tunable Photonic Structures Based on Silicon and Liquid crystals 507

11.6.1 Photonic Crystals with Tunable PBGs 508 11.6.2 Thermo-Tuning of the PBG’s Edge 513 11.6.3 Electro-Tuning of the PBG’s Edge 516 11.7 Conclusion 520

12. Silicon-BasedOpticalResonators 527

Alessandro Pitanti, Paolo Bettotti, Mher Ghulinyan, and Lorenzo Pavesi

12.1 Introduction 527 12.2 One-Dimensional Interference Filters 528 12.2.1 Porous Silicon Interference Filters with

a Thick Cavity 529 12.2.2 Thin l-Cavity 530 12.2.3 Thick 27l-Cavity 531 12.2.4 1D Coupled Cavities and Slow Light 532 12.3 Azimuthally Symmetric Optical Cavities: Microdisk

Resonators 536 12.3.1 Passive Si3N4 Microresonators 538 12.3.2 Active Microresonators and Strain

Engineering: The Micro-Kylix 541 12.4 Slow Light 545 12.5 Conclusion 551

xiiiContents

13. OpticalPropertiesofNanoscaleSi/SiO2Superlattices 555

David J. Lockwood and Leonid Tsybeskov

13.1 Introduction 555 13.2 Quantum Well Approach 559 13.3 Disordered Silicon Quantum Wells 560 13.4 Crystalline Silicon Quantum Wells 563 13.5 Nanocrystalline Silicon–Silicon Dioxide Superlattice

Fabrication and Post-Treatment 568 13.6 Structural Characterization 573 13.7 Strain-Induced Lateral Self-Organization in Si/SiO2

Nanostructures 578 13.8 Raman Spectroscopy 583 13.9 Thermal Conductivity and Laser Annealing 596 13.10 Photoluminescence 600 13.11 Future Directions 607

14. NanosiliconforAdvancedPost-ScalingApplications 619

Nobuyoshi Koshida and Bernard Gelloz

14.1 Introduction 619 14.2 Photonics 620 14.2.1 Photonic Crystal Structures 620 14.2.1.1 Passive structures 621 14.2.1.2 Active structures: sensing,

switching 624 14.2.2 Light Emission of Si Nanostructures 626 14.2.2.1 Luminescence of Si nanocrystals 626 14.2.2.2 Blue emission of Si-rich oxide 632 14.2.2.3 Useful functions 635 14.3 Ballistic Electron Emission 638 14.3.1 In Vacuum: Excitation/Probe 638 14.3.2 In Gases: Attachment/Internal Excitation 639 14.3.3 In Solutions: H2 Generation/Thin Film

Deposition 641

xiv Contents

14.4 Acoustic Emission: Sensor/Bioacoustics 643 14.5 Summary 644

15. SemiconductorNanowiresandAssociatedPolymericComposites:TherapeuticImplicationsforSmartTissueEngineeringScaffolds 655

Jeffery L. Coffer, Ke Jiang, and Dattatri Nagesha

15.1 Introduction 655 15.2 Nanowire Fabrication Routes 657 15.3 Initial Cytocompatibility Evaluation 658 15.4 Biorelevant Surface Modification of Nanowires

with Electrochemistry 660 15.5 Surface Modification with Known Anti-Osteoporodic

Drugs 662 15.6 Composite Blends of Nanowire Networks and

Established Biorelevant Polymers 665 15.6.1 Horizontal Nanowire Arrays on Biopolymer

Substrates 666 15.6.2 Nanowire Transfer onto Porous Polymer

Surfaces with Horizontally Oriented NWs 667 15.6.3 Cell Attachment Assays with Mesenchymal

Stem Cells 669 15.7 Future Improvements and Challenges 673

Index 677

Preface

Nanostructuring of materials is a key topic in many of today’s research fields. Owing to the novel obtained physical properties,nanostructured and low-dimensional materials are of interest in basic research as well as in applications such as integrated circuits at nanometric sizes, optoelectronic and magneto-optical devices, perpendicular media for high-density data storage, and nanostructures as functionalized sensors in nanobiology. Popular techniques to produce nanometric structures can be classifiedas top-down strategies or bottom-up growth mechanisms. Self-assembled and self-organized structures are important owing to the elementary fabrication processes. The miniaturization of semiconductor materials is a requirement not only in technologies such as microelectronics but also in many other fields such asphysics, chemistry, biology, materials science, and even medicine. A special interest exists in the changing properties of the material due to the nanoscopic size compared with bulk materials. Because of these emerging new properties, nanostructured materials and especially semiconductors are of paramount importance. Therefore, the fabrication of various nanostructured semiconductors plays a key role and is the focus of this book. This book presents an introduction to important aspects of nanostructured semiconductors, their fabrication, and their applica-tion invarious fieldssuchasoptics,acoustics,andbiomedicine. Itis designed for graduate students and also practicing scientists to get an overview of the recent developments in this widespread topic of nanostructured semiconductors. The book is structured into 15 chapters written by renowned scientists in these fields. The first six chapters deal with thefundamentals of pore growth in III–V semiconductors, differentformation techniques such as anodization, stain etching, and metal-assisted etching, and the fabrication of SiGe and Ge nanostructures. Especially, the chapters discuss the synthesis of nanocrystals and epitaxially grown nanostructures. Pore-filling is discussed in Chapters 7 and 8. Chapter 7 focuses on the deposition of noble

xvi

metals such as platinum, palladium, gold, and copper within macro- and mesopores. In Chapter 8, the authors electrochemically fillferromagnetic metals such as nickel and cobalt into high-aspect-ratio mesoporous silicon. In the remaining chapters, the physical properties of such nanostructured materials are discussed, and the focus is on the transportandopticalbehaviorstartingwithquantumconfinementeffects and phototransport properties followed by optical onessuch as one-dimensional photonic crystals, silicon-based optical resonators, and optical properties of Si/SiO2 superlattices. The last two chapters discuss the applications of the described materials, on the one hand, in electronics and acoustics and, on the other hand, in the emerging topic of biological applications of silicon nanowires, and their therapeutic implications for smart tissue engineering scaffoldsarehighlighted. We hope to present the reader a comprehensive survey of the topic of nanostructured semiconductors and to depict the high potential and broadness of the utilization of such materials. Finally, wearedeeplygrateful toall theauthors fortheireffort inwritingtheir outstanding chapters.

PetraGranitzerKlemensRumpf

Preface

Chapter 1

1.1 Introduction

Electrochemically etched pores in n-type III–V semiconductorscan be divided into two basic classes according to their appearance and properties: crystallographic pores (crystos) and currentline pores (curros). Crystallographic pores have first been observed in InP using an aqueous HCl electrolyte [1, 2]. Crysto pores always grow into the <111> B direction, independent of the substrateorientation. The pore tips and pore walls are typically facetted; a detailed overview can be found in [3]. In the meantime, crysto pores have also been etched into InP with electrolytes rather diff erent to acidic HCl, e.g., solutions of NaF [4], KOH [5], and NaCl [6], andinto other III–V crystals such as GaP (H2SO4 [2], H3PO4 [7],

A Meta Model for Electrochemical Pore Growth in Semiconductors

Malte Leisner, Helmut Föll, and Jürgen CarstensenChristian-Albrechts-University of Kiel, Institute for Materials Science,Kaiserstrasse 2, D-24143 Kiel, Germany

hf@ .uni-kiel.de

Nanostructured Semiconductors: From Basic Research to ApplicationsEdited by Petra Granitzer and Klemens RumpfCopyright © 2014 Pan Stanford Publishing Pte. Ltd. ISBN 978-981-4316-90-3 (Hardcover), 978-981-4411-10-3 (eBook) www.panstanford.com

mailto:[email protected]

2 A Meta Model for Electrochemical Pore Growth in Semiconductors

HNO3 [8], and bromine-based solutions [9]) and GaAs (HCl [2],NaCl [10], HF [11], and H2SO4 [2, 12]). Of course, most poresfound in Si and Ge have always been of the crystallographic type without this being mentioned in most publications; cf. [13–15]for details. An example of crystallographic pores in InP is shownin Fig. 1.1a.

(b)

(a)

Figure 1.1 Cross–sectional view of typical (a) crystallographic poresand (b) currentline pores etched on (100) n-type InP.

Currentline pores in InP were also first discovered with aqueous HCl electrolytes [16]. Meanwhile they have been reproduced by several other groups, cf. e.g., [2, 17–20]. Curro pores, simply speaking, always grow perpendicular to the equipotential planes

3

enveloping the pore tips, i.e., quite often perpendicular to thesample surface independent of the surface orientation. Figure 1.1b shows the exception to this rule. The pore tips and cross sectionsare round and not facetted, as can be seen in Fig. 1.1b and the following figures. Currentline pores in InP have also beenobtained with a large variety of electrolytes and solutions, e.g.,HCl [2, 16, 17], liquid ammonia [21], and NaCl [6]. They also existin GaP using H2SO4 [2, 7], HNO3 [8], and bromine-containingsolutions [9] as electrolyte but have not yet been found in aconvincing way in GaAs.

As might be expected for something as complex as pore etching in semiconductors, pores have been observed that cannot be classified as either crysto or curro. There might be mixtures ofthe two kinds (e.g., in Si, see [22]), or pores that still defyclassification. Some pores found in GaP [7, 23] may serve asexamples; we will also come back to this issue in what follows.There exists, in particular, a subset of current line pores, named “curristos” for brevity, which will be described in what follows.

Nevertheless, there are strong indications that the crysto/curro classification might be generally valid for electrochemicallyetched pores in all semiconductors and not just for n-type III–V specimen. For example, pores etched in II–VI materials such as CdSe [10, 24] and ZnSe [25] are nearly a perfect match for currosin InP. Even in Si, where crysto pores dominate, currentlinepores can be etched using organic electrolytes [26].

Crysto and curro pores might be seen as the extremes or paradigms of pore growth modes in any semiconductor. Describing pores as either crysto or curro thus describes pores in semiconductors on a meta level. Since both pore types have been etched in several materials with a large variety of electrolytes, it follows that some meta principle that transcends detailedinterface chemistry and physics must govern pore growth on the meta level. In the concomitant meta model presented here, we,thus, do not concern ourselves with “details”, e.g., which growth direction is the preferred one for crysto pores in some material,or what kind of chemical reactions takes place at the interface.

InP is the semiconductor in which both pore types are presentin full splendor. It, thus, can serve as a model material for“meta” pore research. As will be demonstrated here, a thoroughinvestigation of pores in InP combined with quantitative modeling

Introduction


on the base of the meta model proposed here will elucidate the diff erences between the pore growth mechanisms of crysto and curro pores and yield valuable information about electrochemical pore etching on the meta level.

In what follows, we first describe some essentials of themeta model used. This allows the consistent interpretation of existing experimental data, as well as detailed simulations of some pore structures that will be presented in the following chapters.

1.2 The Essence of Crystallographic and Currentline Pores in III–V Semiconductors

1.2.1 General

As will be elaborated in this manuscript, the first major aspectof electrochemical pore growth in III–V semiconductors, if not in all semiconductors, must consider the passivation behavior of the semiconductor–electrolyte interface at the (freshly etched) pore tips and pore walls. Passivation in the conventional sense means that current flow at some fixed potential is more difficult through a passivated surface increment relative to an unpassivated one. Passivation in this general sense can occur by several mechanisms. It may happen, for example, by H, Cl, or OH coverage for Si, InP,or Ge surfaces, respectively, by the potential-driven formation of insulating layers such as SiO2 or just a temporary build-up of reaction products. In the first case, the passivation mechanism is typically linked to a removal of electronic semiconductor surface states by chemical species (e.g., the ones mentioned in this section above) ofthe electrolyte, allowing a space charge region to develop andthus reducing the potential drop at the interface. On the meta-level modeling proposed here, the exact mechanism must not matter. What matters is only that a passivation of some localsurface increment reduces the probability for initiating currentflow on this surface element and that passivation never occurs instantly but with some {hkl}-dependent time constant. Passivation is thus a function of the local concentration of the passivating species, the crystallography, and time. Note that in most cases passivation occurs by a purely chemical reaction independent ofthe local potential, i.e., the rate of passivation is proportional tosome concentration.

5

Passivation in this sense crucially interacts with the second major aspect of the meta model used here: Current flow throughthe tip region of a growing pore is never uniform in space and time but occurs in spatially and temporally localized “current bursts” (CB). In a nutshell, the so-called “current burst model” (CBM; discussed in detail and applied quantitatively to relevant cases in [14, 22, 27–29]) assigns two probability functions to anyinterface increment that describe the probability for starting and stopping current flow through that surface element, respectively. The major variable in these two probability functions is the local electrical field strength, which in turn depends on the local passivation state of the surface element. High field strengths tend to increase current flow by initiating CBs as given by the first probability function. Since current flow after its initiationalways alters the state of a surface increment mostly in such a way that the field strength decreases, current flow usually stops after some time with a probability given by the second probability function. Chemical changes in the now current-less surfaceelement plus an increasing potential (see in this section below)starts current flow once more and a dynamical current on-off situation develops locally. Local potential increases might occur because under typical galvanostatic etching conditions the total number of active current bursts, i.e., surface increments with current flowing through them, must be about constant and the localpotential (= external potential minus potential drop in the series resistance) must adjust to meet that condition. Even under potentiostatic conditions, the local potential is not constant but depends on (changing) series resistances. Local potential variations provide just one of several feedback mechanisms intrinsic to the current burst model that can lead to the wealth of self-organization features observed during pore growth in all semiconductors, and that therefore can also be understood by the meta model discussed here. This chapter, however, will not discuss self-organization very much; for details, the reader is referred to a recent review given in [22]. In the same vein, we will not discuss the many material- and pore-type-specific pore formation models that have been proposed;see [2, 30–40] for recent reviews.

A third major aspect needed for any meta model is the source of the holes necessary for the dissolution reactions in all semiconductors. Significant pores in all the III–V (and II–VI)

The Essence of Crystallographic and Currentline Pores in III–V Semiconductors


semiconductors investigated so far were only found in n-type materials (typically heavily doped), and it is safe to assume that the necessary holes are always generated by some local breakdownof the (reversely biased) electrolyte–semiconductor junction athigh electrical field strength. This essentially restricts hole generation to the pore tip area where the field strength hasmaximal values. It could and has been argued that local breakdownis the basic reason for pore formation, but that is an over-simplification as evidenced by pores in p-type semiconductorssuch as Si and Ge and by the general shape of the crystallographic pores treated here. The experimental results for III–V crystals essentially indicate that to a first-order approximation the hole supply to the growing pore tip is not a crucial part of pore formation. In a second approximation, the electrical breakdown producingholes is the same breakdown that initiates a current burst. In other words, hole production is already contained in the probability functions that are central to the current burst model.

In the following subsections, the basic properties of currentline and crystallographic pore growth will be outlined in the framework of the three points outlined in this section above that form the foundations of our meta model. In what follows, we present experimental results, mostly from InP, that will be discussed in the context of the model. The data include not only ideal curro (plus curristo) and crysto pore growth but also the self-induced or externally induced switchover between both pore types, as well as special ordering or self-organization phenomena.

1.2.2 Crystallographic Pores

In our meta model crystallographic pore growth results, whenever the passivation kinetics of (freshly etched) surfaces matters and shows some anisotropy. In this case, the probability for newcurrent bursts is reduced on some crystallographic planes and increased on others. The average current flow through a pore tip is thus anisotropic. Note that self-amplifying eff ects due to theintrinsic non-linearity of the CBM may lead to strong eff ects for only small diff erences in passivation. Figure 1.2 illustrates this by schematically showing how a crysto pore in {100}-orientedIII–V semiconductors grows into the depth along a <111>B direction (going from the group A atom to the group B atom). The starting

7

point is the fact that crysto pores consist of staggered {111} tetrahedrons as shown in Fig. 1.2a. After a tetrahedron has been well expressed, all available surfaces are the best-passivated ones (“stopping planes”) and current burst nucleation probabilities are low everywhere, except at the corners where maximum fieldstrength prevails. Eventually current bursts cluster at the edges, with the edge pointing in growth direction being favored, since ithas the smallest space charge region and thus the highest field strength (the upper edges are also somewhat shielded byneighboring pores not shown). In other words, the pore itself induces a symmetry breaking for the otherwise identical four edges of the tetrahedron. A new tetrahedron pointing in the prevalent growth direction thus nucleates with high probability at thebottom as shown in Fig. 1.2b. On occasion (dictated by theprobability functions) new tetrahedrons nucleate at other edges right at the pore tip or somewhere along the pore; in this case the pore would branch. Note that while the nucleation probability for CBs on some tetrahedron corner along the existing pore is rather low compared with the one at the tip, the branching rate can be appreciable since it is given by probability times the (large)number of eligible edges.

Figure 1.2 Schematic growth of a crysto pore. The colored part indicates the area with high current burst probability and thusaverage current density (symbolized by arrows).

The average current density at the pore tip in Fig. 1.2b is rather large since the available surface is small. New surface thusis generated faster than it can be passivated, and growth at this



stage proceeds by cleaning out spherically shaped volumes. As the size of the sphere increases, the current density, and thus the rate of freshly generated surface, decreases. Passivation becomes possible on some planes and the probability for current bursts decreases on these “stopping” planes ({111}A planes in III–V’s).A tetrahedron forms (Figs. 1.1c,d) and the process starts anew. If the stopping planes consist of all {111} planes, as in Si,octahedrons form accordingly (cf. [41]). Note that intrinsic meta features of this process are as follows:

(i) There is a probabilistic element in crysto pore growth that accounts for pore branching among other things.

(ii) The current (and the current density) in a single crysto pore cannot be constant all the time; it “oscillates” by necessity, again with a stochastic component.

(iii) What happens for one pore is also influenced by its surroundings, i.e., by neighboring pores. They influence the local field strengths and thus current burst probabilities (and thus also the local hole supply and density).

(iv) Correlation of the growth details between neighboring pores via changed probabilities for CBs is now possible. This correlation may induce synchronization of growth modes and thus self-organization phenomena; cf. [22].

More details to these points can be found in [14, 28, 29, 41–43]. Crystallographic pores result because the passivation kinetic

is fast enough on some crystallographic planes. The resulting diff erences in passivation, via the CB probability functions, lead to a non-uniform current flow through the interface and thus to non-uniform electrochemical dissolution rates. In III–V semiconductors, the {111}A planes (terminating in group III atoms) are most strongly passivated, whereas the {111}B planes (terminating in group V atoms) are most weakly passivated. Thus, tetrahedron-shaped pore tips consisting of the most stable {111}A planes are formed, andthe pore will be a sequence of staggered tetrahedra (cf. Fig. 1.2) with a preferential pore growth into the <111>B directions. Thestaggered tetrahedra are enveloped by {112} planes and thus acrysto pore can be said to be bounded by {112} planes [3], in particular if there is a dense stacking with a possible “washing out” of the sharp corners by small currents flowing through the pore

9

walls (leakage currents in a semiconductor sense) that are drivenby the need to minimize surface energy.

Which planes in a given semiconductor are most strongly or weakly passivated cannot be predicted on the meta level, since this involves knowledge about system-specific details (e.g., semiconductor material and electrolyte), which are not considered on the meta level. However, it is only important to know thatthere are diff erences. Experimental evidence or known system details then must supply the detailed information if needed.

It is thus essential for crystallographic pore growth that mass transfer of the passivating species through the pore length is not the rate determining process, i.e., pore tips and walls will alwayshave a sufficiently large concentration of passivating speciesnearby. This ensures that the passivation kinetics is interface dominated, leading to the aforementioned {hkl}-dependent passivation behavior. Note that the chemical species needed for passivation might also be involved in the dissolution reaction;this is most likely the case for InP in Cl-bearing electrolytes.

“Strong” and “weak” passivation can occur in two ways. Weak passivation, for example, could mean that it takes longer beforesome passivation level is reached and/or that the final passivation level is lower compared to strong passivation. The level ofpassivation, as mentioned before, is simply expressed by the probability that current flow through the passivated surface is initiated at some given potential. Since current flow through the pore tip is most important, the {hkl}-dependent time constant ofthe (purely chemical) passivation reaction is more important for pore growth than the final passivation level eventually reached on pore walls.

A characteristic feature of crystallographic pore growth is the occasional branching of pores either from pore tips or from pore walls. In what follows, it will be demonstrated that branching can be fully described by a simple stochastic model, which is a direct consequence of the current burst model as elaborated in this section above. Branching of a pore growing in one of the four possible <111>B directions can occur into the three remaining <111>B directions with certain probabilities that, once more, contain the local field strength at the three relevant tetrahedron corners and thus the local passivation state plus space charge region details and



the applied potential. This approach also allows understanding the branching behavior in diff erent semiconductor materials (InP, GaAs, GaP, ...) and the characteristic dependence on the semiconductor doping concentration ND, which has been extensively studied forInP as shown in Sections 1.3.1 and 1.4.1.

From the meta model alone, it is not possible to deduce much about the size and shape of the space charge region around pores. Experimental data typically show that a space-charge-region(SCR) will evolve around pore walls if enough time is given for passivation. This would be expected if passivation occurs byremoving interface states in the band gap and thus Fermi level pinning. It is thus safe to assume that passivation in III–V’s and other semiconductors occurs by saturating “dangling bonds” by some chemical species like H or Cl. The width of the SCR defines the minimum distance between pores and thus leads to doping concentration-dependent pore densities and morphologies.

1.2.3 Currentline Pores

The fact that pore walls and pore tips of current line pores are round and that their growth is independent of the crystallographic orientation of the InP substrate strongly indicates that passivation of specific crystallographic planes during the etching of currentline pores is not essential, in strong contrast to the case ofcrystallographic pores. In the meta model, we thus postulate that passivation in the pore tip region during currentline pore growth is so weak that it is of no consequence for the dissolution kinetics. In other words, the probability for current flow in some interface increment is determined by other parameters than {hkl}-dependent passivation. It follows that no crystallographicanisotropy of the etching rate will be observed. Moreover, the absence of passivation should allow for comparatively highaverage etching current densities at the pore tips. Indeed, current densities and thus pore growth rates far higher than for crystopores are easily possible at low potentials.

At high current densities, currentline pore growth may actually be seen as a special case of electropolishing that only occurs at the pore tips and not on the whole sample surface. In this case, the active area will be maximized and the typical straight closepacked currentline pores as shown, for example, in Fig. 1.6

11

and in results of reference [44]. Moreover, current bursts tend tosynchronize (see [27] for a fully quantitative modeling ofelectropolishing with CB theory) as is easily seen in the alwaysmore or less clearly repressed oscillations of the curro porediameter (often synchronized, cf. [45]; Figs. 1.4b and 1.5b). The factor restricting electropolishing to the pore tips in this case is thepresence of carrier depleted pore walls, which prohibits strong current flow through the pore walls and thus the merging of individual pores. Moreover, pore walls of neighboring pores also serve as a strait jacket, making individual deviations from the general growth direction difficult, since this would require that an aberrant pore must grow through its orthodox neighbors, which is impossible. However, at lower current densities, the need for close packing is relaxed and the independence of pre-determined growth directions of curro pores can express itself in other ways than just instraight hexagonal arrangements; see e.g. Section 1.3.1.

It follows that currentline pores cannot easily grow directlyfrom the surface. Some layer of diff erent pores (typically crysto pores) must always precede curro pores. Note that this nucleation layer may be etched off or lifted off during the etching of deep currentline pores so that the final sample appears to have only currentline pores. In other words, cross–sectional postmortemSEM pictures of pore structures do not necessarily show what happens during the initial stage of pore growth.

Like crysto pores, single curro pores are surrounded by an SCR, leading to a minimum distance between pores of about twice the width of the SCR. This follows from experimental observations of pore geometries and has been independently confirmed by Santinacci et al., who used photocurrent spectroscopy [20]. This (together with whatever level of passivation is eventually obtained) prevents to a large extent diameter increases during etching. Moreover, if curro pores grow in a close-packed hexagonal arrangement, the semiconductor material everywhere between the pores is almost completely depleted of carriers, and thus no additional pores can nucleate and grow between the older pores. In total, even so conditions close to electropolishing might prevail, a stable pore structure results. How a hexagonal close-packed arrangement evolves from the fourfold symmetry of the typically {100}-oriented samples is an interesting question that isillustrated in Fig. 1.3, following [44].



Figure 1.3 Illustration of the evolution of a hexagonal curro pore array by a nucleation layer of crysto pores. Multiple branching occurs in a given {110} plane, which leads to an alignment of the intersection point of pores and a {100}-type plane as, for instance, the source or the plane of a growth mode change.

If the absence of anisotropic passivation is essential for currentline pore growth, this absence has to be produced in some way. The absence or low concentration of a chemical species that is present in the electrolyte around the pore tip area can only mean that the supply of this passivating species is severely limited by mass transport through the upper part of the pores. This oncemore means that in principle currentline pores always require a porous top layer or nucleation layer that restricts the diff usional transport of the passivating species to sufficiently low values. Of course, if the concentration of the passivating species in the electrolyte is already low to begin and the current density rather large, a limitation of the passivation reaction rate might occur right away. It is clear that the necessary strong concentration gradient scales with the concentration in the electrolyte and the generation rate of fresh surfaces, i.e., the external current density. It followsthat currentline pore growth is more prevalent at high current

13

densities and that a sudden increase in the external current density might switch the system from growing crysto pores to growingcurro pores. This switchover is illustrated in Fig. 1.4a for a {111}-oriented sample with ND = 1 × 1018 cm–3 and in Fig. 1.4b for a {100}-oriented sample with ND = 8 × 1017 cm–3.

(b)

(a)

Figure 1.4 Externally induced switchover from currentline pores to crysto pores in (a) {111}-oriented InP with ND = 1 × 1018 cm–3 and (b) {100}-oriented InP with ND = 8 × 1017 cm–3. Note that the diameter oscillation inherent in densely packed curro pores is synchronized throughout the sample in the upper part of the curro layer; expressed in the faint horizontal lines.



It has been asked which current, exactly, determines the shape of currentline pores. Is it the currentline in the electrolyte,flowing up the pore, or the current in the semiconductor [46]?While this is a good question in principle, it is often moot in reality.In the beginning of an etching experiment, it is always rather clear how the current will flow through the sample. If, for example, the sample is covered with an insulating layer that only has a small opening somewhere, the current flow lines will crowd through the hole with a distribution like the spikes on one half of a sea urchin. Currentline pores will follow this symmetry, an example is shown

(a)

(b)

Figure 1.5 Examples for the geometrical predictability of currentline pore growth. (a) Hedgehog-like structure leading to spherical pore growth caused by a single nucleation point. (b) Waveguide structure produced by etching through a strip mask, cf.[47, 48]. Note the curro pore diameter oscillation in thelower part.

15

in Fig. 1.5a. On the next level of consideration, already existing pores will influence the current flow pattern and thus their own geometry. This is also seen in Fig. 1.5b, where etching through a strip mask (see [47, 48] for details) first produced crysto poresthat then were switched to curro pores by an increase in thecurrent. The currentline pores first grow exactly as one wouldexpect from the general current flow geometry until they meet each other, which forces them to grow downward, since pores cannot penetrate each other (except if the tips meet) as outlined in [49]. While it is not easy to calculate current flow and the poregeometry under these conditions, the concept of “currentlinepores” is, nevertheless, rather clear despite claims of the opposite [46]. There is yet another level of complexity with regard tocurrent line pores that is encountered, for example, when one looks at a self-induced growth mode change from crysto to curro that happens by definition at relatively low current densities. In thiscase, the current density is far below what a hexagonally closepacked curro pore system could support—and that can only mean that current bursts are “off ” most of the time. Which current direction is the pore following when it switches on again? A moreor less random direction as far as it is compatible with itsneighbors. In other words, a single curro pore may follow analmost random walk pattern as long as all the other pores aredoing it too and as long as the average walking direction isdownward. Pores matching that description are shown in Fig. 1.10.

1.3 Experimental Insights into the Growth Mode of Currentline Pores

1.3.1 ND Dependence

The morphology of currentline pores strongly depends on the InP doping concentration ND. Figure 1.6 illustrates this point. Itshows currentline pores etched under optimized conditions (see[50] for details) for ND = 1 × 1017 cm–3 in (a) cross–sectional viewand (b) top view after removal of the nucleation layer, and corresponding results for ND = 8 × 1017 cm–3 in (c) and (d), as well asfor ND = 3 × 1018 cm–3 in (e) and (f).

Growth Mode of Currentline Pores


(a) (b)

(c) (d)

(e) (f)

Figure 1.6 Cross–sectional and plan view (after removal of thenucleation layer) of currentline pores etched under optimized conditions on n-type InP with a doping concentration of (a), (b) ND = 1 × 1017 cm–3, (c), (d) ND = 8 × 1017 cm–3, and (e),(f) ND = 3 × 1018 cm–3.

For the highest ND, the pores are circular and ordered in a hexagonal close-packed arrangement. The pore shape deviates

17

slightly from ideal circular pores, as pores get more ellipsoidwith decreasing ND. The pore diameter is rather independent ofND and in the range of 130 nm. The hexagonal arrangement of pores is also visible for the lower ND samples. One major diff erence between the samples is the thickness of the pore walls, which decreases strongly with increasing ND. As demonstrated in [50],the pore wall thickness agrees well with twice the value of thespace-charge-region (SCR) width. These results strongly indicate that an SCR exists around the pore walls, and that the overlap of the SCRs of two neighboring pores defines the minimum distance between pores.

1.3.2 The Pore Tips

A closer look at the physico-chemical processes involved in the pore etching mechanism can be obtained by in situ Fast Fourier Transform Impedance Spectroscopy (FFT IS) [51]. A detailed FFTIS study of currentline pore growth in n-type InP has beenpublished in [50]. Other data not yet published indicate that the equivalent circuit model developed for curro pores in InP is justas good for curro pores in other systems, indicating once morethat meta level modeling is possible. As a result, a detailed viewof the situation at the pore tips during the etching experimenthas been obtained. From the FFT IS data, once more the necessity of a space-charge-region (SCR) at the pore tips can be deduced, necessitating a constant (but ND dependent) potential drop in the SCR that expresses itself in a constant (ND dependent) capacitancein the impedance. Figure 1.7a shows the SCR capacitance asmeasured by FFT IS [50] and compares these data with theoreticallycalculated values for two diff erent geometries: semispherical geometry, assuming a semispherical shape of the pore tips and planar geometry, assuming flat pore tips. It can be seen that the measured values lie well in between the boundaries defined bythe two geometries. Furthermore, with increasing ND, the measured values move from close to semispherical towards close to planar, a phenomenon that is in very good agreement with the changing shape of the pore tips. Pore tips become more planar indeedwith increasing ND, as is apparent in the SEM images presentedin Figs. 1.7b–d.



(a)

(b) (c) (d)

Figure 1.7 Space-charge-region at the pore tips. (a) Theoretically calculated SCR capacitance CSCR for semispherical and planar pore tip geometry. The stars represent the capacitance measured by FFT IS. (b) Magnified view of a curro pore tip for ND = 1 × 1017 cm–3, (c) for ND = 8 × 1017 cm–3, and (d) forND = 3 × 1018 cm–3. Pore diameter approximately 130 nmfor all three cases. The pore tip gets flatter with increasing ND.

The changing pore shape might be well understood by the decreasing width of the SCR with increasing ND. For the lowest doping concentration the SCR width is in the range of the pore diameter, while it is about ten times smaller for the highest doping concentration. In the former case it is thus understandable thatthe SCR cannot be bent around a “sharp” corner as it is the case forthe much thinner SCR in case of the highest ND. Thus, the pore tip shape can only get flatter (as expected for an essentiallyelectropolishing process), if sufficiently large enough doping concentrations ND are provided.

As stated before, it is generally assumed that in the case ofInP the hole generating mechanism is avalanche breakdown in the SCR at the pore tips. The question thus is if “flat” pore bottoms

19

can generate the required holes. This has been addressed in [50],where it has been demonstrated that the theoretically calculated field strength in the SCR is in good agreement with the literature values for the avalanche breakdown field strength in InP. The solution of Poisson’s equation for the range of doping investigated fits the observed ND dependence of the pore tip shape rather well.

1.3.3 Mass Transport through Currentline Pores

It has been stated in Section 1.2.3 that limited diff usional transport of (passivating) chemical species through the pores is a necessity in order to generate currentline pores in the first place. In what follows, several results will be presented that illustrate the roleand importance of the mass transport.

Figure 1.8 presents the pore depth dpore as a function of etching time t for experiments on n-type InP with diff erent doping concentrations and for diff erent constant etching potentials (potentiostatic conditions in this case), as indicated in the legend of the figure. The general information contained in Fig. 1.8 isthat the etching velocity decreases as pores get longer. All datacan be approximated very well by one master curve (dashed line), which has the form of a potential growth law

pore 0=d d t γ⋅ , (1.1)

with the pre-factor d0 = 40.3 μm and the exponent γ = 0.57. It isalso known that the pore depth at some time t decreases with decreasing electrolyte concentration and for decreasingtemperature, as is evident from data not presented here. Taken together, these results can be most easily explained if etching is limited by the mass transport through the pores. Of course, it would be desirable to calculate the relevant mass transport in full quantitative detail, but this is not possible at present, since the situation is not as trivial as it looks on first sight. The calculationof mass transport is complicated since the system cannot bedescribed by a simple diff usion problem, because a part of the external etching potential will always drop in the pores, leading to an intricate mixture of diff usion and drift phenomena for at least one chemical species, or in other words, a state that is far off from thermodynamic equilibrium. This strong non-equilibriumstate in the pores has also been present in the FFT IS data recorded



in [50], giving further evidence of the proposed situation in the pores. In this vein, it is also understandable that the factor γdeviates from 0.5, which should be expected to be present for a simple diff usion limited reaction. A more detailed treatment ofEq. 1.1 and its physico-chemical origin can be found in [26].

Figure 1.8 Curro pore depth dpore as function of etching time t under potentiostatic conditions for several doping levels and applied potentials. All data can be very well approximated by thesame growth law as given in Eq. 1.1.

A very characteristic observation in the etching of currentline pores in InP is the presence of a thin nucleation layer under most etching conditions even if the experiment is started with “curro conditions” from the beginning. Figures 1.9a,b give an impressionof the nucleation layer. Figure 1.9a shows the top view of currentline pores etched in a viscous electrolyte; in the upper part, the nucleation layer is still present, whereas in the lower part, it has been removed and currentline pores are visible. The nucleationlayer consists of elongated small openings and has a lower porosity than the currentline pores region. In Fig. 1.9b, a cross–sectionalview of currentline pores is presented. On top, a 0.5–1 μm-thick nucleation layer is present, which is neither fully crysto nor curro but shows more similarity to crysto pores than to currentline pores. It is safe to assume that in these cases, the comparably low

21

porosity of the nucleation layers leads to a limitation of the masstransport, which subsequently allows for the formation of “proper” currentline pores. An observation that is supporting thisassumption is the fact that such kind of nucleation layers alsoexist when currentline pores are etched into GaP [7, 9, 12], whereas no such nucleation layers exist on GaAs, where almost exclusively fully developed crysto pores have been found so far, cf. [2].

(b)

(a)

Figure 1.9 (a) Top view of curro pores etched in a viscous electrolyte, a thin nucleation layer is present in the upper part of the image. (b) Cross–sectional view of curro pores with a thin nucleation layer of the “curristo” type on top.



From what has been presented so far, it is clear that the basic assumption in Section 1.2.3 is justified: It is indeed the transport of the passivating species that must be limited in order to grow curro pores. This will leave the pore tips weakly passivated, allowing for large currents and thus dissolution rates at the pore tips compared with crysto pores. The dissolution, moreover, is not dependent on the crystallography since all planes are equal. At the same time, the supply of dissolving species, while also limited by mass transfer, is still large enough to allow large currents forming currentline pores. With increasing pore depth, however, under potentiostatic conditions, a decrease of the etching current should be observed due to a decreasing supply of reactants and a reduction of thelocal potential at the pore tip due to ohmic losses in the pore. Thisis exactly what is manifested in Fig. 1.8.

At this point, it becomes clear once more that beyond crystos and closely packed currentline pores, a third kind of pore should exist, especially under galvanostatic conditions: If the supply of reactants falls below what is needed to support the current in currentline pores, the system cannot switch back to crysto pores because the supply of passivating species has long since ceasedto exist. The system thus must find new ways to support the current and the first way out is to increase the potential in order toincrease the ionic current of the necessary species to the growing pore tip. In other words, transport of the reactants must beassumed to be not purely diff usional, driven by concentration gradients, but to have a component that is driven by the electricfield. In yet other words, a part of the applied potential is used for driving ions down the pore. This view is corroborated by FFT ISdata, but it is too early for a detailed analysis.

Another strategy for the system is to induce the lift-off of the porous layer followed by regular electropolishing. The formation of the curristos (c.f. Fig. 1.5 (b) and Fig. 1.9 (b)) in the context of theself-induced switchover from crystos to curros essentiallyfollows the same logic without needing an increased potential to assure the supply of (ionic) reactants. Since the new kind of pores postulated here are not crystallographic, but go wherever the current they induce will take them, owing to a lack of a better short name, we dubbed them “curristos.” Figure 1.10 provides examples of the curristos observed by the self-induced crysto–curristo growth

23

mode transition, always occurring if given enough time undergalvanostatic conditions, for three diff erent doping levels.

(b)

(c)

(a)

Figure 1.10 Examples of curristo pores in (100) n-type InP obtainedafter etching for 30 min under galvanostatic conditions. (a)ND = 1 × 1017 cm–3, j = 5 mA/cm2, (b) ND = 8 × 1017 cm–3,j = 8 mA/cm2, and (c) ND = 3 × 1018 cm–3, j = 40 mA/cm2, respectively.

While a meta model cannot predict exactly what will happen when a crysto–curro growth mode transition is indicated due to disappearing {hkl}-dependent passivation at the pore tip region,



it can be stated with confidence that pores, if still produced atall, will have no preferred growth direction anymore and that the area between pores will be carrier denude due to the spacecharge region enveloping the pore since “older” pore parts will still be passivated. Growing pores then still cannot cross other pores. Taken everything together, possible pore arrangements are then severely restricted. Highly ordered parallel running pores—the “classic” curros—are possible, or the almost randomly arranged curristos as shown in Fig. 1.10.

1.4 Experimental Insights into the Growth Mode of Crystallographic Pores

1.4.1 ND Dependence

Crystallographic pore growth on n-type InP strongly depends on the doping concentration of the InP substrate. Figure 1.11 gives a comparison for experiments with three diff erent doping concentrations and similar experimental conditions otherwise. Figure 1.11a shows a detail of the resulting crysto layer forND = 1 × 1017 cm–3. Figure 1.11b shows the corresponding resultsfor ND = 8 × 1017 cm–3, and Fig. 1.11c for ND = 3 × 1018 cm–3.

(a) (b) (c)

Figure 1.11 Crysto pores in n-type InP with diff erent doping concentra-tions ND. Shown is the (1

__ 1 0) cleavage plane. All experiments

were galvanostatic with j = 0.4 mA/cm2 for 30 min and a5 wt.% HCl electrolyte at T = 20°C. A short “high voltage”pulse in the beginning was applied to ensure uniformnucleation. (a) ND = 1 × 1017 cm–3, (b) ND = 8 × 1017 cm–3, and(c) ND = 3 × 1018 cm–3, respectively.

With increasing doping concentration the thickness of the crysto pore layer decreases significantly for a given current density

25

and etching time. On the other hand, the pore density increases strongly with increasing ND, while the minimum distance between pores decreases. The average pore diameter increases for the three studied doping concentrations with increasing ND from 90 nm, via 140 nm to 160 nm.

The ND dependence of the minimum distance between pores can be explained by the presence of a space-charge-region (SCR) around the pore walls. This is generally expected for all pores in all semiconductors, because pore walls will always be passivated eventually. The concomitant reduction of electronic interface states then allows the formation of an SCR. Since the width of an SCR is proportional to ND

–1/2, the closer packing of pores with increasing ND can be easily understood.

A more detailed investigation of the chronological evolution of the crysto pore structures (not shown here) also reveals increased branching frequencies with increasing ND. This increased branching can be understood in the framework of the argument presented in Section 1.2.2, if the passivation depends on ND. This is indeed the case since the increased doping concentration leads to a smaller SCR width if the Fermi level is not pinned due to insufficient passivation.

1.4.2 Monte-Carlo Simulation of Crystallographic Pore Growth

1.4.2.1 Simulation procedure

The model for crystallographic pore growth in III–V semiconductors is based on the assignment of probabilities for the events of branching at pore tips and walls, respectively. This essentially current burst–induced stochastic nature of the model allows a three-dimensional Monte-Carlo simulation of crysto pore growth.

The simulation has been carried out on a three-dimensional cubic simulation array consisting of 1024 × 1024 × 1024 voxels. The topmost plane of this array represents the (100)-oriented surface of the InP sample. Correspondingly, the diagonal planes of the cube, which are also perpendicular to the surface, are the (1

__ 1 0) and (110) planes. An illustration of the (1

__ 1 0) plane of the

simulation array is presented in Fig. 1.12a. The downward-growing pores can be identified as chains of black voxels, whereas the upward growing pores, illustrated in blue, are intersecting the (1

__ 1 0) plane and are thus only present as individual voxels.

Growth Mode of Crystallographic Pores


(b)

(a)

Figure 1.12 Illustration of crysto pore growth in the simulation array.(a) View of the (1

__10) plane, downward-growing pores

are black chains of voxels, whereas upward growing pores(blue) are intersecting the plane. Branching at pore tipsandoutofporewallscanoccur.(b)Viewofthe(110)plane,upward growing pores are blue chains of voxels, whereasdownward-growingpores(black)areintersectingtheplane.Branchingatporetipsandoutofporewallscanoccur.

Shown are three subsequent iterations of the simulation to dem-onstrate the operating principle. In each iteration, the simulationarray is scanned and transformed into a new state according tospecific rules: (1) Eachporetipgrowsonforonemorevoxelintoitsrespective

poregrowthdirectionandtheformerporetipbecomesaporewall.

(2) Growth (and also branching) can only occur, if there is freespaceinthegrowthdirection.Ifthereareanyporespresentinanadjustabledistancelfreefromtheporetip,theporewillstoptogrow.

(3) Porescanbranchattheporetips(see(m+1)-thiteration).Thenewporewillalsogrowdownward.Theprobabilityktips forbranchingatatipperiterationisproportionaltothecurrentdensityattheporetipsjtipsandtoabranchingparameterptips,which is the first free input parameter of the simulation.

(4) Pores can also branch out of the pore walls (see blue voxelintheblackporein(m+2)-thiteration).Thenewporewillbeanupwardgrowingpore,growingoutofthe(1

__10)plane.

Theprobabilityforbranchingoutofwallsperiterationkwallsisproportionaltothecurrentdensityattheporetipsjtipsandtoabranchingparameterpwalls,whichisthesecondfreeinputparameter.

27

(5) If two pore tips meet in one voxel, one tip will continue to grow, whereas the other one will stop to grow.

(6) If branching has occurred at one voxel, no branching can occur out of the neighboring voxels, which will be set to a “dead” pore wall state. The number of aff ected neighbor voxels can be adjusted by the parameter lpass.

In Fig. 1.12b, the corresponding scenario is presented for the (110) plane. The upward growing pores are again shown in blue, but are now present as chains of voxels, whereas the downward-growing pores are intersecting the (110) plane and are thus individual black voxels. The rules given above also apply here: Upward growing pores that branch at tips produce upward growing pores, and branching out of walls produces pores that grow in the downward directions.

Before the simulation can start, a nucleation layer of pores has to be put into the simulation array. Therefore, pores are randomly distributed in the first layer of the array.

1.4.2.2 Simulation results

In what follows the modeling of crysto pore growth on (100)n-type InP with a doping concentration of ND = 8 × 1017 cm–3 is presented. As primary simulation parameters a tip branching parameter ptips = 5 cm2/mA and a wall branching parameterpwalls = 50 cm2/mA were used. As secondary parameters the array mesh size dmesh = 100 nm was adjusted to the experimentally determined crysto pore diameter (i.e., the triangle side length).The current j was set to 0.4 mA/cm2 and the starting etchingvelocity vstart to 1.2 μm/min, just as in the electrochemicalexperiment. The nucleation tip density ρnucl was set to 1 μm–2. The free length parameter lfree was set to 0 voxel and the passivation length to lpass = 2 voxels.

Figure 1.13 shows a comparison of experimental and simulation results. Shown is the etched and simulated crysto pore structurein the (1

__ 1 0) plane for three diff erent etching times. On the left

hand side, the whole crysto layer is shown, the nucleation layerhas been excluded in the SEM images. On the right hand side, adetail of the crysto pore structure is shown at the same magnification for all three etching times. A very good agreement between pore structures in the experiment and the simulation is clearly visible qualitatively on first sight. A quantitative comparison is presented in Fig. 1.14.



Figure 1.13 Comparison of the etched and simulated crysto pore structure on InP with a doping concentration of ND = 8 × 1017 cm–3 in the (1

__ 1 0) plane for three diff erent etching times. The left-hand

side shows a comparison of the whole crysto layer, the right-hand side a detail of the structure at same magnification.

Figure 1.14a shows the maximum pore depth dpore as function of the etching time t; a symbol always represents the experimentaldata and lines the result from the simulation. A good agreement has been obtained. Figures 1.14b,c show the pore density ρpore as function of depth d for the upward and downward-growing poresfor three diff erent etching times, respectively. The characteristic shape of the pore density profiles can be matched very well, and the absolute numbers are also in good agreement; deviations are inthe range of the statistical error of the etching experiment. An exception might be the density for 360 min for the downward-growing pores, which might be slightly underestimated due to non-ideal SEM images.

Nevertheless, the general agreement of experiment and simulation is very good and shows that the simple model presented in Section 1.4.2.1 is capable of describing the essential featuresof crysto pore growth in full quantitative detail.

29

(a)

(b)

(c)

Figure 1.14 Comparison of experimental data with simulation results(InP,ND=8×1017cm–3).Symbolsrepresenttheexperimentaldata,linesthesimulationdata.(a)Maximumporedepthdporeasfunctionoftimet.(b)Poredensityrpore(ofupwardgrowingpores) as function of depth d for three different etching times. (c) Pore densityrpore (of downward-growing pores)asfunctionofdepthd for three different etching times.



It is noteworthy that the simulation required no direct consideration of the transport of chemical species through thepores, i.e., neither diff usion limitation nor ohmic losses had to be included. This strongly indicates that the transport of chemical species through the pores in the electrochemical experiment is indeed not essential during the growth of crysto pores, as has been stated in Section 1.2.2.

The physical nature of the branching probabilities can also be understood in the framework of the arguments presentedin Section 1.2.2; they simply reflect the {hkl}-dependent passivation behavior of the interface. In this vein, the diff erence in passivation strength of pore walls and tips can be understood, leading todiff erent branching probabilities. Further simulation of crysto pore growth on GaAs [52] has also shown that the diff erent passivation behavior between InP and GaAs is manifested in lower branching probabilities for GaAs, which reflect the stronger passivation as compared to InP.

1.5 Crysto–Curro Transition

A peculiar feature of the electrochemical pore etching in InP isthe easy switching of the pore growth mode from crysto to curro and back by a sudden increase or decrease, respectively, of theexternally fixed current density and/or potential. Figure 1.15a shows a very sharp curro–crysto transition and Fig. 1.15b a porous crysto/curro multilayer structure (from [2]). Note that theinterfaces between the pore types own their sharpness to the fact that all pores must do what one pore does because of the geometrical restrictions for pore arrangements discussed previously.

While our meta model predicts these externally induced growth mode transitions, it also predicts self-induced switches from crystos to curros, but not the reverse self-induced switches fromcrystos to curros, which are indeed observed, and this chapter reports detailed experiments to this topics for the first time. The findings were admittedly surprising: While a self-induced growth mode transition was indeed observed for a large number of doping levels and current densities, the currentline pores found were never of the close-packed straight type as observed after enforced switching, but always of the randomly arranged type, thus falling

31

under the “curristo” classification from c.f. Section 1.1 and Fig. 1.9 (b).Figure 1.15c shows an example.

(a) (b)

(d)(c)

Figure 1.15 (a) Externally induced switchover from currentline pores to crysto pores in (100) n-type InP. (b) Multilayer structure consisting of alternating curro and crysto pore layers. (c) Self-induced switchover from crysto pores to curristo pores in (100) n-type InP under galvanostatic conditions. (d) Transition depth dtrans of the self-induced crysto–curristo transition as function of the constant current density for diff erent InP doping concentrations.

On second thoughts, this new feature is easy to understand. In InP anodized in HCl or NaCl electrolytes, Cl– is very likely the passivating species and the reactant needed for dissolution. Assoon as the supply of Cl– is too low to allow for passivation and dissolution, passivation no longer dictates the pore growth mode and a transition is ready to take place. However, without external stimuli, the current density is far below what closely packed aligned curros could carry and random curristos result as pointed out inthis section above.

Crysto–Curro Transition


The self-induced switchover from crysto to curristo occurs at a certain depth dtrans that must depend on the doping and the current density chosen. Figure 1.15d gives first quantitative data about this transition depth dtrans. As expected from our meta model, dtrans decreases nearly linearly as j increases. Moreover, dtrans also depends strongly on the doping concentration of the substrate and increases significantly with increasing ND. This is also readily understood. The porosity increases with increasing doping, allowing easier mass transport through the porous layer. While it is too early to quantify these qualitative arguments, it should be not too difficult, in particular if the supporting detailed data from FFT IS (not shown here) are utilized.

If we now give the externally induced growth mode transition a second look, the difference from the self-induced crysto/curristo transition becomes clear. Right after the substantial increase of the current density, the bulk of the incoming Cl– is now needed for carrying the current via the dissolution reaction. The concentration gradient becomes extreme, with essentially zero concentration of Cl– at the pore tip, ensuring the largest possible diffusion current. Passivation, being tied to the local concentration, decreases instantaneously to negligible strength. If not enough Cl– is supplied to carry the increased current, the potential needs to increase in order to add a field driven ionic current down the pores. The switch to curros happens right away and is sharp. The only configuration that can meet the geometric restrictions (all curros must do the same) and is able to carry a large current density is a closely packed arrangement of straight pores. The reverse process, i.e., the switch from curros to crystos for suddenly decreased current densities, follows the same line of arguments just “in reverse” (sudden increase in the concentration of passivating species, ...).

It is tempting, if a bit mind-boggling, to consider what kind of curro arrangements could be possible besides “all straight” and “all random.” Experiments give some hints. Figure 1.16a, for example, shows what one could call a “pore bundle” oscillation. Note that the two-dimensional cut through the structure always present in an SEM picture is deceiving to some extent; a structure like this cannot look the same on any plane. Figure 1.16b illustrates what one could call self-induced synchronized pore bundle

33

oscillations in a crysto/curro multilayer arrangement; Fig. 1.16c shows the details. While these pore bundle oscillations are superimposed on a crysto/curro multilayer structure, it is clearly the curros that cause these instabilities from a straight growth downward. Figures 1.16d,e finally show extreme pore bundle oscillations in just curro pores; note also the much coarser scale in comparison with Fig. 1.16c and cf. [53]. We will not delve deeper into these peculiar structures except to note that they are simply expressions of self-organization inherent in the CB model together with the specific properties of the pore type encountered.

(e)

(d)

(a) (b) (a)

Figure 1.16 Examples of special curro pore arrangements. (a) Pore bundle oscillations in curro pores. (b) Pore bundle oscillations in a crysto–curro multilayer stack; (c) shows a detail. (d) Pore bundle oscillations of curro pores etched in a viscous electrolyte; (e) shows a detail.

Crysto–Curro Transition


1.6 Nucleation

Good, i.e., uniform nucleation behavior is an essential if not always appreciated part of electrochemical pore growth. At any given time, pores proceed from the pores already present and the complete “history” including nucleation is thus of prime importance for thefinal structure. True enough, branching of pores generates new geometries with increasing depth, nevertheless, the primary nucleation of pores still strongly determines the observed pore morphology. External measures to enforce uniform primary nucleation are therefore often part of a pore etching experiment.

The etching of macropores in silicon, for instance, relies heavily on lithographically defined nucleation patterns for the pores, which allows producing very regular pore arrays [13]. Pore etching then is possible within a wide process window, i.e., pores follow the nucleation pattern for a large range of pore spacing and pore array geometries (hexagonal, cubic, ...), without much aberration fromthe ideal pore array arrangement. Without lithography, the pore array is not periodic and the distance between macropores adjusts to some internal length scale determined mostly by the SCR dimensions and thus doping. It is noteworthy in this context thata rather long nucleation period is needed before the finalmacropore array emerges [54, 55].

On the other hand, lithographically pre-defined pore growth in III–V semiconductors or Ge has not been successful so far. Thisis probably due to a “stronger” internal length scale that expresses itself more forcibly than in Si and thus leads to a small process window for lithography. In other words, if the lithographicallydefined structure is not rather close to the structure that the crystal “makes” by self-organization, the system will not follow the pattern off ered. This view is corroborated by the observationthat currentline pores at high current densities always tend to grow in a well-defined self-organized hexagonal arrangement, as shown in Section 1.3.1. The observed thin nucleation layer shown in Section 1.3.3 will be formed independent of the presence of anynucleation mask; see Fig. 1.17a for a (first) illustration of this.

Homogeneous, if somewhat random, pore nucleation inIII–V semiconductors is not easy to obtain but can be optimized by suitable external measures. In InP, a short high current or voltage

35

pulse in the beginning of the experiment typically enhances the homogeneity of pore nucleation. This treatment is especiallyefficient (and necessary) for low doping concentration of the InP. Figure 1.17b shows an example for an inhomogeneous nucleation.

(a) (b)

Figure 1.17 (a) Etching of curro pores in n-type InP with a lithographically pre-defined etching mask (top). Currentline pores are formed in the same self-arranged hexagonal array (which is diff erent from the geometry of the mask) as without mask, since a nucleation layer forms below the mask. (b) Inhomogeneous nucleation on low doped InP etched with a viscous electrolyte.

A beneficial eff ect can also be obtained by front-side illumination of the sample [56]. In GaAs and especially in GaP, where uniform nucleation is more difficult than for InP, even stronger measures might be necessary. Samples have been subject to ionbombardment, for example, inducing surface defects that serve as nucleation sites for pore growth in a controlled way [57, 58]. The temperature also has a strong influence on the experiments,where it has been observed that increasing temperatures tend to benefit nucleation behavior. Compare also [15], where a wholearsenal of “tricks” for achieving homogeneous nucleation in Ge is described.

To sum up things, it can be stated that the nucleation of electrochemically etched pores depends on a large number offactors, which are altogether not yet very well understood. If ahomogeneous nucleation behavior will be obtained stronglydepends on the material used, its surface condition (polished or rough), the doping type and doping level, the electrolyte used, as well as details of the experimental conditions.

Nucleation


With InP homogeneous pore nucleation is comparatively easy; it is at least as good as on Si but happens much faster. On GaP and GaAs, nucleation gets harder and is often very inhomogeneous if no special pre-treatment is performed. In extreme cases, only a few very big holes are formed. In GaAs, a rather peculiar eff ect due to a low-density nucleation has been observed [2]: at a few primary nucleation points, an initial pair of crysto pores is formed that starts to branch heavily, generating a whole system of upward- and downward-growing crysto pores. The intersection points of the upward-growing pores with the surface form a readily observedpore domain, cf. Fig. 1.18a for an example. Figure 1.18c shows the result of a Monte-Carlo simulation; the only diff erence from the simulation pictures in Fig. 1.13 are far fewer nucleation points (only one) and diff erent values for the branching probability, required because we have a diff erent material and thus diff erentpassivation behavior in detail. The result not only speaks for itselfbut also demonstrates how a hexagonal array of curro pores can develop on a sample with cubic symmetry. As shown in Fig. 1.18d (taken from [44]), branching produces pore tips aligned alonga <112> direction on the surface, but also in the depth of thesample. The preferential direction formed thus serves as ordering direction for the hexagonal array; the rest is defined by the needfor close packing.

Pore domains resulting from difficult nucleation are ratherthe rule than the exception in pore etching in semiconductors.Figure 1.18b shows just one other example from Ge [15]. There are many ways of forming pore domains but the reason for domain formation is always the same: inhomogeneous nucleation or low density of nuclei.

In the meta model presented here, the nucleation behavior can be understood to some extent. The basic assumption is that it is also controlled by passivation. Passivation of InP, for example, isweaker in comparison with GaP or GaAs, as evidenced by therelative ease of currentline pore formation in InP and the general absence of current line pores in GaAs. Weak passivation allows for easy current burst nucleation on many sites of the original surface and thus for a uniform distribution of nuclei in a high density.GaAs, on the other extreme, is so strongly passivated that initial current bursts are only formed at weak spots (e.g., dislocations or micro defects), but not on “perfect” surface parts. Wherever

37

current flow starts first, tiny holes on the surfaces are formed. The development of these first holes into large branched pore systems due to the lack of passivation on freshly etched surfaces ismuch more favorable than at the other places of the surface, which are still strongly passivated. It is just a matter of probabilities. The probability of nucleating new current bursts at primary holes in InP is also higher than on the still perfect surface but the number of current bursts produced is probability times area. If the probability is not too low, large areas win over existing nuclei and uniform nucleation results.

(a) (b)

(c) (d)

Figure 1.18 (a) Crysto pore domain on the (100) surface of an n-type GaAs sample. (b) Surface domain etched on Ge. (c) Simulation result of the crysto pore domain shown in (a). (d) Illustration of the origin of the geometrical structure of the crysto pore domains (after [44]).

The reason for the diff erences of III–V semiconductors with respect to passivation might lie in the electronic nature of the

Nucleation


material, especially the group III element. It is well known [59] that planes terminated by group III elements are most stable. The higher atomic number of InP as compared with Ga leads to a less polar nature of the bond, which only allows for a comparatively weak passivation.

A second rather general nucleation phenomenon is that nucleation typically gets better with increasing doping concentration ND of the substrate. This behavior has also been found on other semiconductors, most prominently Si [54, 55], where it was found that nucleation proceeds slower with increasing ND but yields a stronger ordered nucleation layer. This dependency can again be understood if it is assumed that passivation gets weaker with increasing ND. This would obviously lead to a faster nucleationbut would also tend to produce unorderly pores with a lot ofbranches or side pores, since branching or side pore growth would also become much easier for the weaker passivated (high ND) case. The suggested relation between ND and passivation can be understood by two phenomena: (i) Passivation as defined here depends to some extent on the width of the space-charge-region (SCR), which decreases with increasing ND and would thus present a smaller obstacle for current flow, which translates into weaker passivation. (ii) Increasing ND will lead to an increased density of doping elements on the surface, which might be preferential for current flow, and thus would yield a weaker passivation.

1.7 Conclusion

It has been shown that a relatively simple meta model is able to account for many basic features of electrochemical pore growth in III–V semiconductors, if not in all types. The meta model essentially considers the diff erences in passivation behavior of the semiconductor–electrolyte interface together with the currentburst model to be accountable for much of the characteristic appearance and properties of porous structures. In this vein, it is possible to understand the diff erences between the major poretypes, crystallographical and currentline pores, the diff erences between semiconductor materials, as well as the specific dependencies of pores on the doping level of the semiconductor.

39

Acknowledgments

The work by Dr. Sergiu Langa was important for this chapter, and this is gratefully acknowledged. The authors appreciate the manyfruitful discussions with Drs. Georgi Popkirov and Ion Tiginyanu and would like to thank M.Sc. Emmanuel Ossei-Wusu and Dr. Ala Cojocaru for extensive SEM imaging.

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References

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References

1 Chapter 1: A Meta Model forElectrochemical Pore Growth inSemiconductors

1. Takizawa, T., Arai, S., and Nakahara, M. (1994).Fabrication of vertical and uniform-size porous InPstructure by electrochemical anodization, Japan J. Appl.Phys., 33(2, 5A), pp. L643–L645.

2. Föll, H., Langa, S., Carstensen, J., Lölkes, S.,Christophersen, M., and Tiginyanu, I.M. (2003). Review:pores in III–V semiconductors, Adv. Mater., 15(3), pp.183–198.

3. Spiecker, E., Rudel, M., Jäger, W., Leisner, M., andFöll, H. (2005). Morphology, interface polarity andbranching of electrochemically etched pores in InP, Phys.Stat. Sol. (A), 202(15), pp. 2950–2962.

4. Weng, Z., Zhang, W., Wu, C., Cai, H., Li, C., Wang, Z.,Song, Z., and Liu, A. (2010). Selective etching of InP inNaF solution, Appl. Surf. Sci., 256(7), pp. 2052–2065.

5. O’Dwyer, C., Buckley, D. N., Sutton, D., and Newcomb,S.B. (2006). Anodic formation and characterization ofnanoporous InP in aqueous KOH electrolytes, J.Electrochem. Soc., 153(12), pp. G1039–G1046.

6. Volciuc, O., Monaico, E., Enachi, M., Ursaki, V. V.,Pavlidis, D., Popa, V., and Tiginyanu, I. M. (2009).Morphology, luminescence, and electrical resistanceresponse to H 2 and CO gas exposure of porous InPmembranes prepared by electrochemistry in a neutralelectrolyte, Appl. Surf. Sci., 257(3), pp. 827–831.

7. Wloka, J., and Schmuki, P. (2006). Morphology of porousn-GaP anodically formed in diff erent mineral acids, J.Electroceram., 16(1), pp. 23–28.

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