Optical Properties 3

Landolt-Börnstein / New Series

Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology

New Series Editor in Chief: W. Martienssen Units and Fundamental Constants in Physics and Chemistry Elementary Particles, Nuclei and Atoms (Group I) (Formerly: Nuclear and Particle Physics)

Molecules and Radicals (Group II) (Formerly: Atomic and Molecular Physics)

Condensed Matter (Group III) (Formerly: Solid State Physics)

Physical Chemistry (Group IV) (Formerly: Macroscopic Properties of Matter)

Geophysics (Group V) Astronomy and Astrophysics (Group VI) Biophysics (Group VII) Advanced Materials and Technologies (Group VIII) Some of the group names have been changed to provide a better description of their contents.

Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology New Series / Editor in Chief: W. Martienssen

Group III: Condensed Matter Volume 34

Semiconductor Quantum Structures Subvolume C Optical Properties Part 3

E. Kasper, N. Koshida, T.P. Pearsall, Y. Shiraki, G. Theodorou, N. Usami

Edited by E. Kasper and C. Klingshirn

Online Version: ISSN 1616-9549 (Condensed matter) ISBN 978-3-540-47055-7 Springer Berlin Heidelberg New York

Print Version: ISSN 1615-1925 (Condensed matter) ISBN 978-3-540-29647-8 Springer Berlin Heidelberg New York

Library of Congress Cataloging in Publication Data Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie Editor in Chief: W. Martienssen Vol. III/34C3: Editors: E. Kasper, C. Klingshirn At head of title: Landolt-Börnstein. Added t.p.: Numerical data and functional relationships in science and technology. Tables chiefly in English. Intended to supersede the Physikalisch-chemische Tabellen by H. Landolt and R. Börnstein of which the 6th ed. began publication in 1950 under title: Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik. Vols. published after v. 1 of group I have imprint: Berlin, New York, Springer-Verlag Includes bibliographies. 1. Physics--Tables. 2. Chemistry--Tables. 3. Engineering--Tables. I. Börnstein, R. (Richard), 1852-1913. II. Landolt, H. (Hans), 1831-1910. III. Physikalisch-chemische Tabellen. IV. Title: Numerical data and functional relationships in science and technology. QC61.23 502'.12 62-53136 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 SpringerVerlag. Violations are liable for prosecution act under German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2007 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. Product Liability: The data and other information in this handbook have been carefully extracted and evaluated by experts from the original literature. Furthermore, they have been checked for correctness by authors and the editorial staff before printing. Nevertheless, the publisher can give no guarantee for the correctness of the data and information provided. In any individual case of application, the respective user must check the correctness by consulting other relevant sources of information. Cover layout: Erich Kirchner, Heidelberg Typesetting: Author and Redaktion Landolt-Börnstein, Darmstadt Printing and binding: AZ Druck, Kempten SPIN: 11901167 (Online) 11010500 (Print) 63/3020 - 5 4 3 2 1 0 – Printed on acid-free paper

Editors E. Kasper Universität Stuttgart Institut für Halbleitertechnik 70569 Stutttgart, Germany email: [email protected] C. Klingshirn Universität Karlsruhe (TH) Institut für Angewandte Physik 76131 Karlsruhe, Germany e-mail: [email protected]

Authors E. Kasper Universität Stuttgart Institut für Halbleitertechnik 70569 Stutttgart, Germany email: [email protected]

N. Koshida Tokio University of A&T Faculty of Electrical and Electronics Engineering Koganei, Tokyo 184-8588, Japan email: [email protected]

T.P. Pearsall 18, Rue des Petits Champs 75002 Paris, France email: [email protected]

Y. Shiraki Musashi Institute of Technology Tokyo 158-0082, Japan email: [email protected]

G. Theodorou Aristotle University Department of Physics Solid State Physics Section 54123 Thessalonoki, Greece email: [email protected]

N. Usami Tohoku University Institute for Materials Research Sendai 980-8577, Japan email: [email protected]

Editorial office Gagernstraße 8, 64283 Darmstadt, Germany fax: +49 (6151) 171760 e-mail: [email protected] Internet http://www.landolt-boernstein.com

Preface

The first two subvolumes III/34Cl and C2 on the Optical Properties of Semiconductor Quantum Structures have been well received by the scientific community. They concentrated on theoretical concepts (chapter 1), experimental methods (chapter 2), III-V semiconductors (chapter 4), I-VII semiconductors (chapter 6), and IV-VI semiconductors (chapter 7) in subvolume Cl. The II-VII materials (chapter 5) have been treated in subvolume C2. The present subvolume III/34C3 finishes the review on optical properties, by adding the chapter 3 on group IV materials. There are exhaustive data on bulk materials including optical properties, starting from diamond C and going over SiC, Si, Ge, to the semimetal grey Sn, and including their alloys—see e.g. Landolt-Börnstein, New Series, Group III, Vol. 41AlĮ1 and Į2, and A2Į1 and Į2. Silicon is the backbone of the worldwide semiconductor industry. It is an indirect gap material, which seriously hampers its use in light emitting or even laser diodes. There are some ideas to overcome this problem by forming group IV quantum structures like Si/Ge superlattices or nanocrystals. This hope triggers to a large extend the applied aspects of the research on the optical properties of group IV quantum structures. Though there are also relevant publications on the optical properties of group IV quantum structures involving C or Sn, the by far largest part of work in this field is devoted to the system Si/Ge. Therefore we concentrate here on this system. The outline of this subvolume follows essentially the concept of the two preceding ones Cl and C2, but with some differences in the details. The first section 3.1 brings again some basic properties like the energy gaps or the effective masses and proceeds then with in-depth information on the growth processes and the influence of the lattice misfit on the growth techniques. It is not possible in the Si/Ge system to circumvent this problem as it is in the ternary or quaternary systems like AlGaAs, InGaAsP or ZnMgSSe, where the values of band gap and lattice constant can be chosen within some limits independently. For this reason we bring in section 3.2 an overview of the influence of strain on the band structures of Si and Ge and on the relative band line up between the two materials, going in this field even more into depth in some of the following sections. After these two introductory sections we start, similar as in the other subvolumes, in section 3.3 with single, coupled, and multiple quantum wells. Section 3.4 is then devoted to the optical properties of superlattices. Section 3.5 combines the data on quantum wires and on a special group of quantum dots, namely those prepared by lithography of quantum wells, of selforganized quantum dots or –islands occurring in a similar way as in various III-V and II-VI systems such as InAs/GaAs or CdSe/ZnSe. Furthermore nanoclusters of e.g. Si in SiO2 are considered here. Nanoislands or localization sites occurring usually in quantum wells due to thickness and/or composition fluctuations and with lateral dimension which hardly result in quantization effects are only marginally treated in section 3.5. A separate section 3.6 is devoted to porous or nanocrystalline Si. The observation of visible luminescence from porous Si or Ge triggered a lot of research, caused again by the hope to obtain materials based on these group IV semiconductors which allow the fabrication of efficient light emitting devices. During the years of investigation it became obvious that not all light emission in these etched structures is due to Si

nanocrystals, but that there may be also contributions from siloxanes and similar SixOyHz compounds formed during the etching process. Since the latter lead beyond the scope of this compilation, section 3.6 is devoted to results where the important role of Si nanocrystals is rather well established. As in the two preceding subvolumes it is not the aim to cite and comment all work published so far on optical properties of group IV quantum structures but to explain and to highlight prominent examples. Some of the topics which are extensively studied in quantum structures of direct gap semiconductors such as four wave mixing, lasing processes etc. are of minor importance for the group IV semiconductors. Therefore the detailed structuring of this subvolume deviates in parts from the one of the chapters on e.g. direct gap III-V, II-VI or I-VII quantum structures. Acknowledgements The editors thank all co-authors of this subvolume for the committed and careful preparation of their manuscripts and the fruitful and stimulating cooperation during this book project. Thanks are due to Prof. Dr. W. Martienssen, the editor in chief of Landolt-Börnstein, for his steady and demanding interest in the progress of this work, and last but not least to Drs. R. Poerschke, W. Polzin and S. Scherer from Springer for their patient, competent and extremely helpful support during the production on this book. Stuttgart and Karlsruhe, January 2007

The Editors

Table of contents

Semiconductor Quantum Structures Subvolume C3: Optical Properties (Part 3) (edited by E. KASPER and C. KLINGSHIRN)

3

Group IV semiconductors

1

3.1

Basic properties, growth and preparation methods of group IV heterostructures (by E. KASPER) . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

3.1.1 3.1.2 3.1.3 3.1.4

Epitaxial growth processes . . . . . . . . . . . . . . . . . . . . Lattice mismatch and its implication on critical thickness and interface structure Virtual substrates and strain relaxation . . . . . . . . . . . . . . . . References for 3.1 . . . . . . . . . . . . . . . . . . . . . . .

. . . .

4 13 17 18

3.2

Influence of strain on bandstructure (by E. KASPER) . . . . . . . . . . . .

19

3.2.1 3.2.2 3.2.3 3.2.3.1 3.2.3.2 3.2.3.3 3.2.4

Hydrostatic strain. . . . . . . Uniaxial strain . . . . . . . . Band alignment of strained SiGe . Average valence band energy E0v,av Compressive strain . . . . . . Tensile strain . . . . . . . . References for 3.2 . . . . . .

. . . . . . .

19 20 22 22 23 24 25

3.3

Single and coupled quantum wells: SiGe (by N. USAMI and Y. SHIRAKI) . . . . .

26

3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 3.3.6 3.3.7 3.3.8 3.3.9 3.3.10 3.3.11 3.3.12 3.3.13 3.3.14 3.3.15 3.3.16 3.3.17 3.3.18 3.3.19 3.3.20

Introduction . . . . . . . . . . . . . . . . . . . . . Photoluminescence from SiGe/Si quantum wells: Spectral features Excitation power dependence of photoluminescence . . . . . Temperature dependence of photoluminescence . . . . . . . Quantum confinement effect . . . . . . . . . . . . . . Effect of post-growth annealing . . . . . . . . . . . . . Effect of electric field . . . . . . . . . . . . . . . . . Effect of external stress . . . . . . . . . . . . . . . . Fermi-edge singularity . . . . . . . . . . . . . . . . . Time-resolved photoluminescence . . . . . . . . . . . . Growth mode transition . . . . . . . . . . . . . . . . Type-II strained Si quantum well . . . . . . . . . . . . . Coupled quantum wells . . . . . . . . . . . . . . . . Electroluminescence . . . . . . . . . . . . . . . . . Interband absorption . . . . . . . . . . . . . . . . . Intraband absorption . . . . . . . . . . . . . . . . . Second-harmonic generation . . . . . . . . . . . . . . Phonon modes . . . . . . . . . . . . . . . . . . . . Cyclotron resonance . . . . . . . . . . . . . . . . . References for 3.3 . . . . . . . . . . . . . . . . . .

26 27 28 29 30 31 32 33 34 35 36 38 38 40 40 41 44 44 46 47

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .

Table of Contents

ix

3.4

Optical properties of Si/Ge superlattices (by G. THEODOROU and E. KASPER) . . .

50

3.4.1 3.4.2 3.4.2.1 3.4.2.2 3.4.2.3 3.4.3 3.4.3.1 3.4.3.2 3.4.3.3 3.4.4 3.4.5 3.4.5.1 3.4.5.2 3.4.6 3.4.6.1 3.4.7 3.4.8 3.4.8.1 3.4.9 3.4.10 3.4.11 3.4.12 3.4.13 3.4.14

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . The empirical tight-binding model . . . . . . . . . . . . . . . . . Uniaxial strain along the [001] direction . . . . . . . . . . . . . . . Uniaxial strain along the [111] direction . . . . . . . . . . . . . . . Optical properties. . . . . . . . . . . . . . . . . . . . . . . . Si/Ge SLs grown along the [001] direction . . . . . . . . . . . . . . Electronic properties . . . . . . . . . . . . . . . . . . . . . . Optical properties. . . . . . . . . . . . . . . . . . . . . . . . Interface intermixing . . . . . . . . . . . . . . . . . . . . . . Si/Ge SLs grown along the [111] direction . . . . . . . . . . . . . . Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . Zone-folded acoustic phonons . . . . . . . . . . . . . . . . . . . Confined optical modes and interface modes . . . . . . . . . . . . . Photoluminescence (PL) . . . . . . . . . . . . . . . . . . . . . Effect of hydrostatic pressure on the PL . . . . . . . . . . . . . . . Electroluminescence (EL) . . . . . . . . . . . . . . . . . . . . Photoconductivity (PC) and optical Junction Space Charge Techniques (JSCT) Wannier-Stark localization . . . . . . . . . . . . . . . . . . . . Spectroscopic ellipsometry . . . . . . . . . . . . . . . . . . . . Piezoreflectance and electroreflectance . . . . . . . . . . . . . . . Second-harmonic generation . . . . . . . . . . . . . . . . . . . Quantum dot superlattices (QDSL) . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . References for 3.4 . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

50 51 51 53 53 53 53 55 59 61 64 64 67 68 72 74 74 77 77 79 81 82 84 86

3.5

Si, Ge, and SiGe quantum wires and quantum dots (by T.P. PEARSALL) . . . . .

89

3.5.1 3.5.2 3.5.3 3.5.3.1 3.5.3.2 3.5.3.3 3.5.3.4 3.5.3.5 3.5.3.6 3.5.4 3.5.4.1 3.5.4.2 3.5.4.3 3.5.4.4 3.5.5 3.5.6

Introduction . . . . . . . . . . . . . . . . . . . . . . . . Silicon and germanium quantum-wire quantum-dot structures . . . . . Synthesis of quantum wires and quantum dots . . . . . . . . . . . Self-organized epitaxy of quantum dots . . . . . . . . . . . . . Lithographic definition of quantum structures . . . . . . . . . . . Synthesis of free-standing Si quantum dots . . . . . . . . . . . . Photoluminescence properties of Si nanoclusters . . . . . . . . . . Si quantum dots formed by controlled segregation of excess Si in SiO2 . Si quantum dots formed by the controlled segregation of excess Si in SiNx Applications of SiGe quantum-dot structures . . . . . . . . . . . SiGe quantum-dot photodetectors . . . . . . . . . . . . . . . Si quantum-dot light-emitting diodes . . . . . . . . . . . . . . Er-doped Si-SiO2 nanocluster optical amplification . . . . . . . . . Si quantum-dot memories . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . References for 3.5 . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

89 92 94 94 99 101 103 103 107 108 108 111 114 115 116 118

3.6

Luminescence and related properties of nanocrystalline porous silicon (by N. KOSHIDA) . . . . . . . . . . . . . . . . . . . . . . . . . . .

121

Introduction . . . . . . . . . . . An overview of nanostructured silicon . Fabrication technology. . . . . . . Nanocrystalline porous silicon . . . . Dry-processed silicon nanocrystallites .

121 121 122 122 123

3.6.1 3.6.2 3.6.3 3.6.3.1 3.6.3.2

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . . . . . . . . . . . . .

. . . . .

. . . . . . . . . . . . . . . .

. . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . .

. . . . .

x 3.6.4 3.6.4.1 3.6.4.2 3.6.4.3 3.6.4.4 3.6.4.4.1 3.6.4.4.2 3.6.4.4.3 3.6.4.5 3.6.5 3.6.6

Table of Contents Nanocrystalline porous silicon . . . . . Properties as a confined system . . . . Photoluminescence . . . . . . . . . Electroluminescent devices . . . . . . Related functions . . . . . . . . . . Carrier charging effects . . . . . . . Ballistic transport and emission . . . . Thermally induced acoustic emission . . Toward monolithic functional integration. Conclusions . . . . . . . . . . . . References for 3.6 . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

124 124 126 127 128 128 129 131 132 133 134

Ref. p. 18]

3.1 Basic properties, growth and preparation of group IV heterostructures

1

3

Group IV semiconductors

3.1

Basic properties, growth and preparation methods of group IV heterostructures by E. Kasper

In this section we present some basic properties of group IV semiconductors, methods of growth and preparation, the consequences of lattice mismatch, and strain relaxation. For more details see e. g. [05K1] and [00K1]. In silicon (Si) based systems quantum effect structures need small dimensions (typically less than 20 nm) because of the high effective masses. Such dimensions can be relatively easily obtained in growth direction (see below), but are difficult to obtain with lateral patterning methods. Lateral structures are usually first created in a surface resist layer and then transferred by etching, ion implantation, and/or diffusion. Microelectronic manufacturing is expected to reach 25 nm lateral feature sizes in the year 2010 (Table 3.1.1). Table 3.1.1. Lateral structure dimensions in processor manufacturing. (Source: International Technology Roadmap for Semiconductors (ITRS) 2003). Year

2003

2004

2005

2006

90

Node [nm]

2007

2008

2009

65

2010

2013

2016

45

32

22

Printed [nm]

65

53

45

40

35

32

28

25

18

13

Physical [nm]

45

37

32

28

25

22

20

18

13

9

For experimental research, however, several methods with high lateral resolutions are available, predominately electron beam lithography (EBL) and focused ion beam (FIB) methods. Standard EBL (Fig. 3.1.1) is now used routinely for mask preparation for optical lithography, but the writing time increases significantly as the resolution is increased, since EBL is a serial process. Using state of the art manufacturing methods, the vertical control of dimensions by deposition techniques can be at least ten times smaller than the lateral control. The reason is the intrinsic vertical atomic layer ordering present in most deposition methods. A good interface normally requires a single crystalline structure, which typically requires epitaxy conditions for the deposition. Epitaxy is the oriented growth on top of a substrate. The substrate is assumed to be single-crystalline, and the deposited epitaxial film can be single-crystal, poly-crystalline or amorphous. For the rest of this section we will only consider single-crystal epitaxial films. In the case of covalent bonded diamond type crystals the orientation of the film is the same as the substrate, e.g. a (100) oriented film is growing on a (100) substrate. The term heteroepitaxy is used when the deposited film material differs from that of the substrate. The deposited film is still homoepitaxial if the doping is different from the substrate. Epitaxial techniques, therefore, provide a number of options for producing structures designed for quantum based electronics.

Landolt-Börnstein New Series III/34C3

2

3.1 Basic properties, growth and preparation of group IV heterostructures

[Ref. p. 18

Electron gun Blanking electrode Illumination lens Aperture #1 Shaping deflector

Beam shaping lens

Aperture #2 Variable shaped beam Demagnifying lens Demagnified image of shaped beam

Projection lens

Position deflector Exposed pattern

Fig. 3.1.1. A schematic diagram of an electron beam lithography (EBL) system. An electron beam sensitive resist layer on top of the substrate is serially irradiated by a finely focused electron beam. The resolution depends on the focus width, on the resist thickness, on back scattering of electrons by the substrate, and on the development process. The resolution of the final structure is additionally dependent on the exact pattern transfer from the resist pattern (from [05K1]).

There are many material combinations which are interesting for quantum electronic devices, such as semiconductor/semiconductor, metal/semiconductor or insulator/semiconductor interfaces. Examples of crystalline insulator/Si structures and of metal/Si structures include the calcium fluoride (CaF2)/diamond lattice (Table 3.1.2) and the silicide materials (Table 3.1.3), respectively. Table 3.1.2. Lattice constant a0 of selected insulator materials and mismatch with Si (T = 300 K) [88K1]. Insulator

CaF2

SrF2

BaF2

Lattice constant a0 [nm] (at T = 300 K)

0.54629

0.57996

0.62001

Mismatch f with Si [%] (at T = 300 K)

+0.60

+6.8

+14.2

For comparison: Si: a0 = 0.543 nm; Ge: a0 = 0.565 nm.

Table 3.1.3. Lattice mismatch f of selected metal/Si interfaces [88K1]. Silicide

MnSi2

FeSi2

CoSi2

NiSi2

TiSi2

PtSi

Lattice type

tetragonal

cubic

cubic

orthorhombic

orthorhombic

Lattice mismatch f [%]

1.7

tetragonal 0.9

1.2

0.4

–

9.5

Different modifications, chemical instabilities, different layer stackings, thermal expansion and lattice mismatch are considerable obstacles for insulator application in single crystalline devices, whereas silicides are widely accepted as contact materials. Chemical similarity and good lattice match are the essential factors for the ability to grow high quality covalent semiconductor/semiconductor interfaces. Within the group IV column of the Periodic Table (Table 3.1.4) silicon and germanium (Ge) form a completely miscible alloy (Si1–xGex) with lattice mismatches ranging from 0 to 4.2% for a pure Ge lattice matched on silicon. Carbon (C) concentrations between 1018 cm–3 and 1021 cm–3 may be incorporated into Si or Ge on lattice sites under metastable growth conditions.

Landolt-Börnstein New Series III/34C3

Ref. p. 18]

3.1 Basic properties, growth and preparation of group IV heterostructures

3

Table 3.1.4. Properties of group IV compounds (diamond or zincblende lattice) [81S1, 05K1]. Compound

C (diamond)

α-SiC (3C)

Si

Ge

α-Sn

Lattice constant a0 [nm] Indirect bandgap Eg, ind [eV] Direct bandgap Eg, dir [eV] Miscibility with Si

0.3567 5.45 6.5 < 3%, metastable

0.436 2.2

0.5431 1.12 3.2 –

0.5646 0.66 0.80 complete

0.65 0 0 only metastable

< 20%

For additional data on group IV compounds, see [01L1].

Under equilibrium conditions, the carbon concentration is low (1017 cm–3 at temperatures below the melting point) with the carbon being mainly incorporated at interstitial sites. Some additional material properties of the SiGe system are given in Table 3.1.5. For more details see e.g. [01L1]. Table 3.1.5. Properties of Si and Ge [81S1, 05K1]. Material

Si

Ge

Bandgap [eV] Electron affinity χ [V] Effective masses of heavy holes mhh/m0 Effective masses of light holes mlh/m0 Effective masses of electrons in longitudinal direction ml/m0 Effective masses of electrons in transversal direction mt/m0

1.12 4.05 0.49 0.16 0.98 0.19

0.66 4.0 0.28 0.044 1.64 0.082

m0 = 9.1091·10–31 kg. Note: The conduction band minimum for Ge is in the [111] direction (L-point), but for nearly all strained SiGe alloys the minimum occurs in the [100] direction (X-point). For interpolation the properties of L-electrons in Ge (ml = 1.64 m0, mt = 0.082 m0) should not be used.

The completely miscible Si1–xGex alloy follows rather closely a linear dependence (Vegard’s law) (mismatch f to Si: f = 0.042 x) with a small quadratic deviation (Fig. 3.1.2). The lattice constant aSiGe is given exactly by [95K1] aSiGe [nm] = 0.5431 + 0.01992 x + 0.0002733 x2.

Si1-xGex

0.565 Lattice parameter aSiGe [nm]

(3.1.1)

0.560

0.555

0.550

0.545 0

Landolt-Börnstein New Series III/34C3

0.2

0.4 0.6 Ge content x

0.8

1.0

Fig. 3.1.2. The lattice parameter aSiGe of the SiGe alloy Si1-xGex as a function of the Ge content x. The solid line compares Vegard’s law with experimental values (crosses) [95K1].

4

3.1 Basic properties, growth and preparation of group IV heterostructures

[Ref. p. 18

In Si based microelectronics the most important surface orientation is the (100) orientation, at which the best controlled amorphous oxide/silicon structure for complementary metal oxide semiconductor (CMOS) transistors can be realized. A cut along the (100) plane gives two dangling bonds per atom (Fig. 3.1.3a). By a surface reconstruction (Fig. 3.1.3b) the number of dangling bonds is reduced, delivering a lower surface energy, lower symmetry and larger cell sizes, e.g. in the case of a (100) face a (2×1) a0 cell.

[100]- direction

a (100) - surface dangling bonds

b

Fig. 3.1.3. Reconstruction of the (100) surface. A cut through the bulk with two dangling bonds per atom (a) is compared with a ( 2 × 1 ) surface reconstruction (b). In the diamond lattice the distance between adjacent planes in the [100] direction is given by a0 /4 (0.136 nm for Si).

3.1.1 Epitaxial growth processes Epitaxy is performed at temperatures well below the melting point Tm of the deposited material (Tm = 1428 °C for Si), either from a metallic melt solution (liquid phase epitaxy, LPE), from the vapor phase by a chemical reaction (vapor phase epitaxy (VPE) or chemical vapor deposition, CVD) or from atoms and ions in a surrounding vacuum (physical vapor deposition, PVD). Molecular beam epitaxy (MBE), a sophisticated PVD method, and advanced CVD methods are the main fabrication techniques for quantum device structures in research and production [04M1]. A typical growth process will now be explained using as an example silicon MBE [88K1]. The principal design of a MBE system is shown in Fig. 3.1.4. The process is performed in a very clean ultra high vacuum (UHV) surrounding. The substrate is precleaned by a combination of ex-situ chemical treatment and in-situ thermal treatment. A thin (1 nm) chemical oxide is desorbed by a 5 minute anneal at 900 °C. Hydrogen covered substrates may be cleaned at lower temperatures (550 °C ... 650 °C). The epitaxial growth is started immediately after the cleaning by opening the shutters above the effusion cells, which are temperature stabilized to obtain a constant molecular flux density. Chemically aggressive materials like molten silicon are evaporated by electron beam heating of the center of a piece of material. The flux composition can be changed abruptly by opening and closing the corresponding effusion cell shutters. Two doping sources (n-type and p-type) and three matrix element sources (Si, Ge and C) are the minimum source configuration, with additional possibilities for other sources (metals, insulators, gases).

Landolt-Börnstein New Series III/34C3

Ref. p. 18]

3.1 Basic properties, growth and preparation of group IV heterostructures

5

QMS Substrate heater Substrate Molecular beams Dopanteffusion cells

Si-electronbeam evaporator

Ge-effusion cell

Fig. 3.1.4. A schematic diagram of the silicon MBE process. The substrate is mounted on top and heated from the backside by an infrared heater. The molecular beams are evaporated from separate thermal sources (effusion cells for the dopants and germanium or carbon, electron beam evaporators for silicon and sometimes also for germanium). In-situ monitoring is achieved by several methods. Here, a quadrupole mass spectrometer (QMS) for flux measurements is shown.

The growth process is monitored by in-situ analysis with electrons and optical beams [96H1]. Examples are reflection high energy electron diffraction (RHEED) to observe the surface; electron induced emission spectroscopy (EIES) or quadrupole mass spectrometry (QMS) for individual flux control; pyrometry or thermoelectric voltage measurement of temperatures; and ellipsometry or reflection interferometry for film thickness monitoring. A clean surface turned out to be an essential prerequisite for reducing the growth temperature from the usual 1050 °C ... 1150 °C to 500 °C ... 700 °C. Even lower temperatures are required if the limits set by amorphous growth at 100 °C ... 200 °C are to be reached. The substrate is radiation heated by a graphite meander mounted on the backside of the substrate. Several kilowatts of power are needed to operate the sources and the substrate heater. During operation the pressure raises from the base pressure 3·10–11 mbar ... 10–10 mbar range. This is acceptable as long as hydrogen (H2) is the dominating gas which has to be monitored by residual gas analysis (Note: The unit mbar is 100 times the international unit Pascal (Pa); 1 Pa = 1 Nm–2; atmospheric pressure (AP) is roughly 105 Pa). The pressure defines the molecular density which is about 1013 m–3 in the given pressure regime producing a mean free path for a molecule of about 100 km. This defines the impinging rate on a wall (1015 m–2s-1) and the time for monolayer coverage of a surface (104 s/S, where S is the sticking coefficient of a specific gas). A technical system (Fig. 3.1.5) needs in addition to the growth chamber additional UHV-chambers for a load lock, wafer storage, pretreatment and analysis. A wafer transfer system transports the wafer between the load lock and the wafer storage or the wafer holder.

Landolt-Börnstein New Series III/34C3

3.1 Basic properties, growth and preparation of group IV heterostructures

6

[Ref. p. 18

Main chamber

Storage chamber Load lock

Titanium sublimation pump Turbomolecular pump Turbomolecular pump Ion getter pump

Fig. 3.1.5. A three chamber Si-MBE system with the main chamber for growth, a storage chamber with a 25 wafer magazine, and a load lock. UHV-conditions are maintained by two turbomolecular pumps, a titanium sublimation pump and an ion getter pump. The transfer system operates from the storage chamber.

Standard silicon CVD (Fig. 3.1.6) is typically carried out at atmospheric pressure and involves the pyrolysis at an elevated temperature of the precursor gas of silane or silicon halide (SiH4–zClz, with 1 ≤ z ≤ 4). Radio frequency coils are used to heat the system to temperatures ranging from 900 °C to greater than 1100 °C to volatilize nominally contaminating species such as water, oxygen or carbon.

Vertical reactor

Wafer

RF -Heater Horizontal reactor Susceptor

SiCl 4 Thermostat AsH3 (PH 3 , B 2 H6)

H2

Fig. 3.1.6. A schematic diagram of a CVD epitaxy tool.

While such a high temperature can be tolerated for the homoepitaxial blanket growth of silicon onto a silicon wafer without dopants, the addition of either doping or germanium into the growth system requires significantly lower temperatures. Autodoping occurs at temperatures above 1000 °C, which involves the diffusion of dopants from the substrate into the epitaxial film creating unwanted anisotropic distortions in Landolt-Börnstein New Series III/34C3

Ref. p. 18]

3.1 Basic properties, growth and preparation of group IV heterostructures

7

Potential energy

the epitaxial layer. The reduction of the system operating pressure serves to eliminate a slowly floating boundary layer of gas immediately above the substrate, allowing the more rapid transport of evaporated dopant away from the substrate, thus reducing the autodoping effect. The reduction of the operating temperature also reduces both the rate of dopant evaporation into the gas stream and solid state diffusion. For strained Si1–xGex layers there are two main problems with high temperature. The first is the roughening or development of surface undulations from high-temperature growth, and the second is diffusion of the germanium. The activation energy E and diffusivity D of Ge from a Si0.7Ge0.3 layer into Si have been measured to be E = 4.7 eV and D = 0.04 m2/s, respectively, suggesting diffusion of some nanometers even at a temperature of 1000 °C for 1 min. As the growth temperature for CVD is reduced, lower background pressures are required to maintain an oxide free silicon surface to grow on [94N1]. Oxygen content in Si1–xGex films has been demonstrated to substantially reduce the minority carrier lifetime in the films, an important property for bipolar transistors. Chemical equilibrium data for the maintenance of an oxide free silicon surface demonstrate that it is the partial pressure of water which is the limiting effect and requires ultra-high vacuum background chamber pressures for low-temperature growth. A number of different CVD reactors have been developed for the low-temperature growth of strained Si1–xGex films. These can be conveniently divided into ultra-high vacuum CVD (UHV-CVD) at growth pressures of less than 10 Pa and low pressure CVD (LPCVD) with pressures ranging from 10 Pa ... 1000 Pa. Other systems do exist but most have been research tools and have not been developed into production tools. Source gases for CVD include SiH4, Si2H6, SiH2Cl2 and GeH4, while doping is achieved using AsH3, PH3 and B2H6. The majority of commercial LPCVD reactors are single wafer tools while the IBM UHV-CVD system is a batch tool allowing the growth of 25 wafers or more at a time. Whatever method of deposition of the epitaxial layer is used, the result is an atom sticking to the surface. These adsorbed atoms are called adatoms and are a precursor state before the atoms are incorporated into the lattice. The adsorption energy Ead is lower than the binding energy E of an atom in the crystal; usually Ead = ½ E ... Ҁ E. When an atom is moving toward the surface (Fig. 3.1.7) the balance of attractive and short ranged (atomic radius) repulsive atomic forces create a potential well at the equilibrium position for the adatom. In order to stick at this adatom position, the atom or molecule must transfer its energy, momentum and angular momentum to the solid. If this does not happen rapidly enough, as is often the case with molecules with an angular momentum, we refer to a sticking coefficient S smaller than unity.

Free atom

Ead dad Adatom position

Distance d to surface

Fig. 3.1.7. The potential energy as function of distance to the surface for the adsorption of adatoms.

Even if the adatom is adsorbed, the adatom may later escape by a desorption step caused by thermal vibrations. If there is an equilibrium between the solid and the vapor phases, the adsorption and desorption

Landolt-Börnstein New Series III/34C3

3.1 Basic properties, growth and preparation of group IV heterostructures

8

[Ref. p. 18

events are balanced. For growth the vapor pressure has to be higher than the equilibrium pressure (supersaturation). The flux F impinging on a surface is connected to the vapor pressure p by NA , 2ʌ MkBT

F= p

(3.1.2)

where NA = 6.022·1026 kmol–1 is Avogadro’s number and M is the molecular weight. In a simple picture the desorbing flux Fdes is proportional to the adatom surface density nS and the Boltzmann probability of an energetic thermal vibration, § E Fdes = nSωq exp ¨ − ad © kBT

· ¸, ¹

(3.1.3)

where ωq is the frequency of thermal vibrations, usually assumed as 1012 Hz ... 1013 Hz. A regular network of surface positions is available for the adatoms. Indeed, we have to assume that adatoms can easily jump from one position to another, a process which is described as surface diffusion with an activation barrier US. The diffusing atom may desorb or may be incorporated into the crystal. The energy gain for the incorporation from an adatom place is ES, where ES + Ead = E (Fig. 3.1.8). In a 70-year-old “Gedankenexperiment”, Kossel [27K1] showed that repeated joining of atoms to kinks on surface steps delivers continuous crystal growth with every atom gaining the binding energy when incorporated at the kink.

Potential energy E

Adsorbed

Free

Ead

Incorporated

US

E ES

Surface coordinate x

Fig. 3.1.8. A schematic diagram of the incorporation of adatoms. The process involves the adsorption of the adatom (with energy gain Ead), the surface diffusion (with energy barrier US) and the incorporation of the adatom in the crystal at a surface step (with binding energy E).

The equilibrium concentration of adatoms nS,0 is then given by the balance between the adatom position and any energetically favorable step positions,

§ E nS,0 = NS exp ¨ − S © kBT

· ¸, ¹

(3.1.4)

where NS is the surface density of atoms. The diffusion coefficient DS is given by DS =

§ U 1 ν exp ¨ − S NS © kBT

· ¸, ¹

(3.1.5)

where the mean distance between neighboring adatom places is given by 1/(NS)1/2. Before an adatom can be adsorbed, it walks on average for the desorption time IJdes, which defines a diffusion length ȜS on the surface,

λS = DSτ des =

§ E − US · 1 exp ¨ ad ¸. NS © 2kBT ¹

(3.1.6)

Landolt-Börnstein New Series III/34C3

Ref. p. 18]

3.1 Basic properties, growth and preparation of group IV heterostructures

9

Note that under growth conditions, the incorporation of the adatom in the crystal is a competing process to the desorption process, and therefore the majority of adatoms will walk distances smaller than ȜS. Let us now consider a growth experiment by supplying fluxes F of the different matrix and doping elements to a surface. For one element we define a linear supersaturation ı by

σ=

F −1, F0

(3.1.7)

where F0 is the equilibrium flux of the element given by F0 = nS,0/τ des. On the surface the adatom concentration nS will also increase above the equilibrium value nS,0. We define a surface supersaturation ıS by

σS =

nS −1 . nS,0

(3.1.8)

Depending on the composition, three different basic growth modes are possible (Fig. 3.1.9). Two-dimensional growth

Three-dimensional growth

Combination of 2D and 3D growth

Frank-v.d.Merwe e.g.Si on Si

Volmer-Weber e.g.Si on Ge

Stranski-Krastanov e.g.Ge on Si

Fig. 3.1.9. The basic growth modes of two-dimensional (or Frank-v. d. Merwe) growth (2D), three-dimensional (or Volmer-Weber) growth (3D), and a mixture from 2D to 3D growth, the Stranski-Krastanov mode.

A qualitative understanding is possible using the droplet model (Fig. 3.1.10), where the force balance at the rim of a droplet is considered. The surface tension Ȉ (specific surface energy) is composition dependent, while the interface energy Ȉi depends also on the strain and dislocation structure. One finds for 3D growth: Σ S − Σ i < Σ f , Σ S = Σ i + Σ f cos θ , 2D growth: Σ S − Σ i > Σ f Sf SS

q Si

Fig. 3.1.10. The droplet model of 3D island growth. The force between the surface tensions of ȈS and Ȉf is balanced by the interface energy Ȉi and leads to an island inclination angle θ when ȈS – Ȉi < Ȉf.

The most simple case is homoepitaxy, the growth of for example a Si epilayer on a Si substrate. The minimum surface energy is obtained by two-dimensional, flat growth. The surface morphology involves atomic steps of usually monolayer (h) or bilayer (2h) thickness. The low-temperature regime (below 100 °C for Si), where amorphous or highly defective growth proceeds, or the high-temperature regime (above 1250 °C for Si), where surface roughening occurs, are not taken into account, because these regimes are not presently used for the growth of epilayers which are used in quantum electronic structures. On silicon where the dislocation density is negligible, there are two sources which create surface steps. At higher temperatures (roughly above Tm/2, where Tm is the melting point; Tm = 1428 °C for Si), steps from the misorientation i of the substrate are present. Even with nominally oriented substrates, forming e.g. a (100) surface, a small misorientation (i < 0.5°, arc i ≅ tan i < 0.0085) is technically unavoidable, which leads to terraces of width L > 15 nm separated by monoatomic steps. At lower temperatures (roughly below Tm/2), adatoms are not fast enough to move to the steps and nucleate into 2D islands (Fig. 3.1.11). When all adatoms reach the already existing misorientation steps (in substrates which are not as perfect as Si the dislocation steps also act in a similar way) the monoatomic steps move laterally forward by the adatom capture (step flow).

Landolt-Börnstein New Series III/34C3

3.1 Basic properties, growth and preparation of group IV heterostructures

10

[Ref. p. 18

2D growth mode

Step flow

2D nucleation

Fig. 3.1.11. The two-dimensional growth by step flow or 2D island nucleation (side view).

At the lower temperatures, when 2D nucleation takes place, the adatoms can join to the steps at the rim of the nucleus within smaller distances. The nuclei grow and coalesce to form a single monolayer, so that the 2D nucleation is a periodic process. A critical nucleus (Fig. 3.1.12) is defined by the size in which the growth by the capture of adatoms is more probable than the decay of the nucleus.

Decay

Critical nucleus

Growth

Fig. 3.1.12. The two-dimensional nucleation (top view). The size of the nucleus fluctuations and a critical nucleus size is achieved when several adatoms have joined. The size and binding energy of this nucleus is high enough that a decay of the nucleus is less probable than the further growth by adatom capture.

Therefore with high supersaturation, resulting in high adatom density, the critical size of the nucleus is smaller. For the extremely high supersaturation which occurs during Si-MBE, two joining adatoms can be sufficient to create a critical nucleus. The basic picture is somewhat blurred by the loss of symmetry from the surface reconstruction which results in highly anisotropic diffusion and two step types with different kink densities (Fig. 3.1.13). A detailed discussion is beyond the scope of this volume. In either case the minimum step density is defined by the misorientation. In the step flow regime the number of steps is constant, whereas in the 2D nucleation regime the step density oscillates above the minimum step density. Using very sensitive surface monitoring methods like electron diffraction (RHEED), these oscillations in the 2D nucleation regime can be observed through intensity variations.

Fig. 3.1.13. A scanning tunneling microscopy (STM) image of a Si (100) surface depicting two different step types along with separation terraces with (2 × 1) and (1 × 2) reconstructions [90S1].

Landolt-Börnstein New Series III/34C3

Ref. p. 18]

3.1 Basic properties, growth and preparation of group IV heterostructures

11

We will treat as an example the simplest case of step flow within the framework of a theory developed by Burton, Cabrera, and Frank (BCF theory) [51B1]. Let us consider a regular array of misorientation steps (Fig. 3.1.14). The terrace width L is defined by the misorientation i, h = tan i ≈ arg i . L

(3.1.9)

Misorientation steps

L

h

i y

Step Kink

Adatom

Fig. 3.1.14. A regular array of misorientation steps. The misorientation (inclination i) leads to terraces of width L separated by steps with height h. The steps move by the capture of adatoms on sites with kinks.

The BCF theory is a surface diffusion theory with specific conditions for particle conservation at the steps. In general, particle conservation is described by the continuity equation dnS + ∇ ⋅ S = GS − RS , dt

(3.1.10)

where S = −∇nS

(3.1.11)

is the surface flux vector, and GS and RS are the generation and recombination rates, respectively. The trick in the BCF theory is the choice of the boundary conditions for (Eq. 3.1.10). Only the terraces are considered where the steps are outside. With this choice and the assumption that the adatoms are only captured at steps, the recombination term in the differential equation contains only the desorption term. The adatom incorporation, therefore, will be treated by the boundary conditions. In the one-dimensional (coordinate y perpendicular to the steps along the surface) and stationary form (dnS/dt = 0), the equation reads d 2 nS dy

2

λS2 − nS + F τ Des = 0 .

(3.1.12)

If we use the assumption that the step acts as a perfect sink for adatoms (Fig. 3.1.15), the boundary conditions at y = ±L /2 (the y-axis origin is given between two steps to obtain symmetrical solutions) may be written as nS = nS,0. The solution for the local surface supersaturation is given by y · § cosh ¨ nS λS ¸ σS = − 1 = σ ¨1 − ¸, nS,0 ¨ cosh L ¸ ¨ 2λS ¸¹ © with F 1 σ= − 1 , and cosh u = ( exp ( u ) + exp ( −u ) ) . F0 2

(3.1.13)

The adatom concentration has its maximum halfway between two steps. The local concentration gradient drives a diffusion flux | S | which is highest at the steps. Landolt-Börnstein New Series III/34C3

3.1 Basic properties, growth and preparation of group IV heterostructures

12 Step array

[Ref. p. 18

L

nS

nS,0

-L

- 2L

L 2

L

y

Fig. 3.1.15. Local concentration of adatoms on a step array. BCF theory with the assumption of steps as perfect sinks for adatoms.

The simple BCF theory of step flow describes the homoepitaxial growth of Si-MBE fairly well in the temperature regime between roughly 550 °C ... 900 °C. The lower temperature bound is caused by the onset of 2D nucleation which is well documented by the appearance of RHEED oscillations. The transition temperature depends on the misorientation i (with terrace length L) and growth rate R (for supersaturation σ ). The upper temperature bound is caused by surface defects and surface roughening, which allows adatoms to be incorporated also outside the steps and nuclei. This temperature value is uncertain, because MBE experiments usually are done well below 900 °C, and in CVD experiments the surface kinetics are overlapped by mass transport in the vapor phase, by chemical reactions and by adsorption of hydrogen and reaction products. In the typical Si-MBE temperature regime of step flow growth (typically 550 °C ... 750 °C) a further simplification of the BCF theory can be made. Si-desorption is very weak in this temperature regime and can be neglected, which is mathematically described by the inequality ȜS >> L. The differential equation (3.1.12) then reads DS

d 2 nS dy 2

+F =0,

(3.1.14)

with the solution for the step array nS − nS,0 =

2 · F §§ L · ¨ ¨ ¸ − y2 ¸ . ¸ 2 DS ¨© © 2 ¹ ¹

(3.1.15)

We will now give a simple example, where we choose a temperature T = 900 K (627 °C), F = 7·1014 cm–2s–1 (1 monolayer (ML) per second; a monolayer on (100) Si has a thickness of a0/4 = 0.136 nm), L = 30 nm (hence i = 0.25º), ES = 2.0 eV, US = 0.6 eV, ωq = 1013 Hz. Then we calculate a low value for the equilibrium adatom density nS,0 = 1.84·103 cm–2, a rather high surface diffusion coefficient DS = 4.8·10–6 cm2s-1 describing the good surface mobility of adatoms, and a maximum adatom density of nS,max between two steps (y = 0) of nS,max = 1.5·108 cm–2. The equilibrium adatom density is already low and decreases steeply with decreasing temperature (a 70 K decrease yields an order of magnitude decrease in nS,0). The diffusion coefficient also decreases with temperature, but more slowly (a 200 K temperature decrease is needed for an order of magnitude decrease in DS, corresponding to the lower activation energy). The maximum adatom density increases with decreasing temperature as (1/DS). This increase in adatom density favors 2D nucleation at lower growth temperatures. To prove the inequality ȜS >> L, we calculate IJdes = 60 s (Ead = 2.55 eV is assumed) and ȜS = 17 µm, which is 500 times higher than the step distance L. The diffusion length increases with decreasing temperature with an activation energy of (Ead – US)/2. The simple assumption that a step acts as a perfect sink for adatoms can be replaced by more sophisticated models. In one of these models the adatoms at the upper terrace have to overcome an energy barrier (Schwoebel barrier) to be captured. This model predicts step bunching where a step array is separated in regions with lower step densities and ripples with higher step densities. In Si, step bunching is probably also influenced by diffusion anisotropy and step energies.

Landolt-Börnstein New Series III/34C3

Ref. p. 18]

13

3.1 Basic properties, growth and preparation of group IV heterostructures

The BCF theory is not applicable to segregating dopants, because the steps then lose their sink properties, or to strained heteroepitaxial layers, because then the diffusion of adatoms is not solely controlled by the concentration gradients but also by chemical and strain gradients. In an epitaxial growth process the technologically controlled parameters are the substrate orientation, the material flux and the growth temperature. From the BCF theory we learned that the adatoms behave like a two-dimensional atom gas with much higher diffusivity in the plane of the surface than in the bulk. The laws of surface physics govern the movement of an atom to its final position in the crystal. At the moderate temperatures used for the epitaxial growth of quantum device structures, each atom is effectively fixed in its position in the bulk. The bulk diffusivity is determined by the diffusion of lattice defects (vacancies, interstitials) and the positional interchange between an atom and a defect. The equilibrium concentration and the mobility of these defects decreases with temperature, so the bulk diffusivity, D, of substitutional dopants reduces with temperature rather steeply (typical activation energies EA around 4 eV), § −E · D = D0 exp ¨ A ¸ . © kBT ¹

(3.1.16)

For example, with D0 = 0.1 m2s–1, EA = 4 eV, T = 900 K, time t = 3600 s, one obtains a bulk diffusion coefficient D = 4·10–26 m2s–1, which is 16 orders of magnitude lower than the calculated surface diffusivity. The diffusion length 2(Dt)1/2 amounts to 2.4·10–11 m. The processing of many quantum device structures may need high thermal budget processing including the annealing of any implants, thermal oxidation and silicide formation. Most of these processing steps require temperatures above 800 °C, where bulk diffusion cannot be neglected. The equilibrium diffusion may be masked at this temperature regime by what is known as transient enhanced diffusion (TED). Transient enhanced diffusion is caused by a nonequilibrium concentration of point defects (vacancies, interstitials) with which an atom can exchange its position. Implantation, oxidation, nitride formation and silicide formation, especially at lower temperatures, severely disturb the point defect equilibrium. A very precise method to measure TED is given by observing the out-diffusion of į-doped layers after point defect injection.

3.1.2 Lattice mismatch and its implication on critical thickness and interface structure In general, a lattice mismatch will occur between a film material (such as an epitaxial layer) and a substrate. We consider the thick substrate as the reference crystal and define the lattice mismatch f for cubic crystals as f =

af − a0 , a0

(3.1.17)

where af and a0 are the lattice constants of the film and the substrate, respectively. Nature has several answers for the growth of single crystalline mismatched films (see e.g. [01M1]) • • • •

Film accommodation by strain (elastic accommodation; pseudomorphic growth) Film accommodation by misfit dislocations at the interface (plastic relaxation) Morphological relaxation by surface undulations or Stranski-Krastanov growth Cracks

As a starting point, let us consider a strained film on a rigid substrate (Fig. 3.1.16).

Landolt-Börnstein New Series III/34C3

14

3.1 Basic properties, growth and preparation of group IV heterostructures

[Ref. p. 18

Fig. 3.1.16. Elastic accommodation of a film cell to the substrate mesh.

A larger film cell fits to the substrate cell by being compressed in the plane of the interface, and becomes a thinner film through tension. In the vertical direction, the opposite strain results following the laws of elasticity. A cubic cell will be transformed into a tetragonal one by the biaxial stress in the interface (Fig. 3.1.17) (stress ıx = ıy = ı, ız = 0). sy

sx

sx sy

Fig. 3.1.17. Biaxial stress leading to a tetragonal deformation.

z y x

The strain components İx,y,z follow from isotropic elasticity theory 1− Ȟ ı, E 2Ȟ 2Ȟ İz = − ı = − İ, E 1− Ȟ

İx = İ y = İ =

(3.1.18a) (3.1.18b)

with E the elastic modulus and Ȟ Poisson’s number. Both elastic moduli are connected with the shear modulus µ by E µ= . (3.1.19) 2(1 + Ȟ) For example, elastic relaxation of a film with lattice mismatch f and strain İ cancel each other if there is elastic accommodation of the strain in the film,

ε+f=0

(elastic accommodation).

(3.1.20)

The energy per area Ehom of a homogeneously strained layer is proportional to the square of the strain and linearly dependent on film thickness t,

Ehom = 2 µ

1+ Ȟ 2 İ t. 1− Ȟ

(3.1.21)

A finite substrate is bent by the stress. If equal elastic constants for the film and the substrate are assumed, the curvature (1/ȡ with ȡ radius of curvature) is a measure of the strain İ, 1 t = 6İ 2 , ȡ tS

where tS is the substrate thickness.

(3.1.22)

Landolt-Börnstein New Series III/34C3

Ref. p. 18]

3.1 Basic properties, growth and preparation of group IV heterostructures

15

With increasing thickness (and increasing elastic energy) other accommodation mechanisms start to be favorable. Let us first consider accommodation of strain by misfit dislocations at the interface (Fig. 3.1.18). When the film cell is larger than the substrate cell, some atomic planes will end at the interface without continuation into the film. This kind of atomic line defect is called a dislocation. Film and Substrate with different lattice constant

Fig. 3.1.18. Lattice mismatched films. Left side: a pseudomorphic film by elastic accommodation. Right side: a strain relaxed layer with a misfit dislocation in the centre.

T

The essential properties of a dislocation are shown in (Fig. 3.1.19). The dislocation line has a direction l, the deformation field around the dislocation is characterized by the Burgers vector b. 1

2

3

1’

8

b

2’

3’

8’ T 4

7 6

5

7’

4’

6’

5’

Fig. 3.1.19. Elements of a dislocation. Line direction l, Burgers vector b, glide plane.

Ideal crystal

Real crystal

The Burgers vector is easily found by surrounding the dislocation in a closed cycle (1, 2, 3, ..., 8 in Fig. 3.1.19) and then projecting the path into an ideal crystal (1’, 2’, 3’, ..., 8’ in Fig. 3.1.19). In the ideal crystal the path can be closed only with an additional vector b, the Burgers vector. The Burgers vector of a single dislocation is conserved whereas the direction may change. The plane defined by the line direction and the Burgers vector (b × l) is called the glide plane. Dislocations can easily move within this plane because only small atomic displacements are necessary for gliding. Movements outside the glide plane (called climbing) require generation or annihilation of point defects (vacancies, interstitials). The energy per unit length Eds of a single dislocation is given by Eds = A ln

ra , ri

with

A=

µb 2 4ʌ(1 − ν )

,

(3.1.23)

where µ is the shear modulus, b is the Burgers vector, Ȟ Poisson’s number and ra and ri are the outer and inner cutoff radii, respectively. The inner cutoff radius is of the order of the Burgers vector length, the outer cutoff radius is either determined by the nearby surface for single dislocations (ra = t), or by the distance p to neighboring dislocations in dense networks (ra = p/2). The areal energy Ed of an orthogonal network of dislocations – usually a network on (100) surfaces – is given by Ed =

2 Eds . p

(3.1.24)

Following the treatment of van der Merwe, we can calculate the minimum energy configuration of a film partly strained and partly relaxed by dislocations. The total energy per area Etot is the sum of the homogeneous strain energy Ehom and the dislocation network energy Ed, Landolt-Börnstein New Series III/34C3

16

3.1 Basic properties, growth and preparation of group IV heterostructures Etot = Ehom + Ed.

[Ref. p. 18 (3.1.25)

To find the minimum one has to know how the strain is reduced when the number of dislocations (1/p) per unit length is increased. Each dislocation displaces the atomic net by the effective length b’ of the Burgers vector. The effective length is smaller than the length b when the Burgers vector lies outside the interface, e.g. for the frequent b = ½ ¢111² one has a (111) glide plane dislocation in diamond lattices, and the effective length is b’ = b/2 for a (100) interface, thus f +ε =

b′ p

for a partially strained film.

(3.1.26)

Taking Eqs. (3.1.25) and (3.1.26) one can find the minimum energy configuration. An equivalent technique to the minimization of energy is to consider the forces on dislocations as first suggested by Matthews-Blakeslee [74M1]. Different numerical values stem from different choices of the cutoff radii ra and ri and the effective lengths b’. By this procedure one can also find a thickness, called the critical thickness hc, at which the first dislocations are energetically favorable. The relationship for this equilibrium critical thickness is given by the intrinsic equation hc f −

h b2 1 ln c = 0 . b′ 8π (1 + ν ) ri

(3.1.27)

In brittle materials (as Si and Ge are at temperatures below 750 °C) kinetic limitations (dislocation nucleation, dislocation movement) often prohibit the appearance of the first dislocations at their equilibrium thickness hc. The material grows pseudomorphic to higher thickness (metastable regime). The experimentally found critical thickness depends on the growth temperature (Fig. 3.1.20). In the SiGe system very often a curve is fitted to the experimental results as found by People-Bean [86P1]. This fit was found for a growth temperature of 550 °C. experimental thickness (MBE) at 750 °C and 550 °C

Critical thickness hc [nm]

1000

relaxed

100

metastable

10

theoretical thickness after v.d.Merwe

pseudomorphic

1 0.0001

0.001 Lattice mismatch f

0.01

Fig. 3.1.20. The critical thickness hc as function of lattice mismatch f. Shown are the regions of equilibrium pseudomorphic growth, metastable growth (also pseudomorphic up to a critical thickness which depends on growth temperature), and a (partly) relaxed regime.

The different values of critical thicknesses often confuse the reader. We give here in Eqs. (3.1.28) and (3.1.29) the index m for the equilibrium critical thickness hc,m with a certain choice of constants (essentially the choice Matthews-Blakeslee made [74M1]) and the index p for the curve fit given by People-Bean (hc,p, valid for about 550 °C growth temperature [86P1]). hc,m b

hc,p b

f − 5.78 ⋅10−2 ln f2−

hc,m b

hc,p 1 ln =0 200 b

=0

(equilibrium),

(3.1.28)

(550 °C fit curve).

(3.1.29)

Landolt-Börnstein New Series III/34C3

Ref. p. 18]

3.1 Basic properties, growth and preparation of group IV heterostructures

17

Beyond the critical thickness a network of misfit dislocations is created with increasing density up to a limiting dislocation spacing p0 (Fig. 3.1.21) p0 =

b′ . f

(3.1.30)

Fig. 3.1.21. A plan view electron microscope image of the two-dimensional network of misfit dislocations in a sample [75K1].

1.0 mm

3.1.3 Virtual substrates and strain relaxation A number of the quantum device concepts that will be reviewed in the later sections require the samples to be grown on relaxed Si1–yGey substrates to produce strain in heterolayers grown on top of these substrates, so that the correct band structure can be obtained [97S1]. There are many applications where a relaxed Si1–yGey substrate is therefore desirable. Unfortunately the liquidus solidus curves of the Si and Ge material system prevents the formation of Si1–yGey crystals with any value of y being pulled from the molten constituent elements. Some small diameter Si1–yGey wafers have recently become available with low values of y (below 0.10), but these wafers have used the constituent elements along with molten metals to allow SiGe crystals to be extracted. A significant problem is the contamination of the wafers with a number of non-group IV elements. Therefore as no bulk SiGe substrates are available, strain relaxation buffers must be grown on bulk silicon substrates. These are frequently called virtual substrates (or sometimes pseudo-substrates) as they produce the relaxed Si1–yGey substrate on top of a silicon substrate [04K1]. If a thick Si1–yGey layer is grown directly on top of a silicon wafer but well above the critical thickness (Eqs. 3.1.27, 3.1.28 and 3.1.29) the layer will relax. In particular as shown in Fig. 3.1.22, a misfit dislocation is produced with two segments which thread upwards at 60° on the (111) plane to the surface. It should be noted that relaxation can only occur through the formation of dislocations or defects. If there are no dislocations or defects then there can be no lattice mismatch between the two layers and the heterolayer cannot, therefore, be relaxed. SiGe epilayer

Threading dislocations

tion isloca

(111)

[001]

td Misfi

Si (100) substrate

[010] [100]

Landolt-Börnstein New Series III/34C3

Fig. 3.1.22. A schematic diagram of the relaxation of a compressively strained-Si1–yGey heterolayer by the formation of a misfit dislocation along the interface of the bulk-Si substrate and the Si1–yGey heterolayer along with the two threading segments of the dislocation which thread to the surface [05K1].

3.1.4 References for 3.1

18

3.1.4 References for 3.1 27K1 51B1 74M1 75K1 81S1 86P1 88K1 90S1 94N1 95K1 96H1 97S1 00K1 01L1 01M1 04K1 04M1 05K1

Kossel, W.: Nachr. Ges. Wiss. Goettingen, Math. Phys. Kl. (1927) 135. Burton, W.K., Cabrera, N., Frank, F.C.: Philos. Trans. R. Soc. London A 243 (1951) 298. Matthews, J.W., Blakeslee, A.E.: J. Cryst. Growth 27 (1974) 118. Kasper, E., Herzog, H.J., Kibbel, H.: Appl. Phys. 8 (1975) 199. Sze, S.M.: Physics of Semiconductor Devices, New York: Wiley, 1981. People, R., Bean, J.C.: Appl. Phys. Lett. 49 (1986) 229. Kasper, E., Bean, J.C.: Silicon Molecular Beam Epitaxy, Boca Raton: CRC Press, 1988. Schwarzentruber, B.S., Mo, Y.W., Kariotis, R., Lagally, M.G., Webb, M.B.: Phys. Rev. Lett. 65 (1990) 1913. Nijs, J.F.A.: Advanced Silicon and Semiconducting Silicon-Alloy Based Materials and Devices, Bristol: IOP publishing, 1994. Kasper, E., Schuh, A., Banu, G., Holländer, B., Kibbel, H.: J. Cryst. Growth 157 (1995) 68. Herman, M.A., Sitter, H.: Molecular Beam Epitaxy: Fundamentals and Current Status, 2nd Edition, Berlin: Springer-Verlag, 1996. Schaeffler, F.: Semicond. Sci. Technol. 12 (1997) 1515. Kasper, E., Lyutovich, K. (eds.): Properties of Silicon Germanium and SiGe:Carbon, EMIS Datareviews Series, Vol. 24, London: INSPEC (IEE), 2000. Landolt-Börnstein, New Series, Group III, Subvolumes 41 A1α and β, 41 A2α and β, Roessler, U., Schulz, M. (eds.), Berlin: Springer-Verlag, 2001 to 2003. Maiti, C.K., Chakrabarti, N.B., Ray, S.K.: Strained Silicon Heterostructures Materials and Devices, The Institution of Electrical Engineers, London, 2001. Kasper, E., Lyutovich, K.: Solid-State Electron. 48 (2004) 1257. Murota, J., Tillack, B., Caymax, M., Sturm, J., Yasuda, Y., Zaima, S.: Proc. First Int. SiGe Technology and Device Meeting, Appl. Surf. Sci., Vol. 224, 2004. Kasper, E., Paul, D.J.: Silicon Quantum Integrated Circuits, Berlin: Springer-Verlag, 2005.

Landolt-Börnstein New Series III/34C3

Ref. p. 25]

3.2

3.2 Influence of strain on bandstructure

Influence of strain on bandstructure

19

by E. Kasper

Application of strain is frequently used for the investigation of basic material properties. From such studies we understand the effects of hydrostatic pressure and uniaxial stress (see e.g. [05K1]). Strain has two main effects on the band structure: hydrostatic strain shifts the energetic position of a band, and uniaxial strain splits degenerate bands, if it reduces the symmetry of the crystal (Fig. 3.2.1).

Unstrained

Hydrostatic strain

Unaxial strain

Fig. 3.2.1. A schematic diagram representation of the strain on a triply degenerate band. Hydrostatic strain shifts the absolute energy position of the band. Uniaxial strain splits the degeneracy; illustrated is a case where the threefold degenerate band is split into a set of twofold degenerate bands at lower energy plus a singly degenerate band at higher energy. Note that the average over the three bands (dotted line) is unaffected by uniaxial strain.

The strain state of the semiconductor can be expressed by the strain tensor İ. The hydrostatic strain, corresponding to the fractional volume change ∆V/V, is given by the trace of the strain tensor, which amounts for biaxial strained epitaxial layers to ∆V = Tr(İ) = 2ε + ε z , V

(3.2.1)

where the normal strain İz in an isotropic notation is given by Eq. (3.1.18b). For simplicity we assume the z-direction in [001], a threefold degenerate valence band at k = 0 (we denote light holes with the index 1, heavy holes by 2, and spin-orbit split-off holes by 3), and an indirect conduction band with sixfold degenerate ∆ valleys (in the [100]) directions) as realized e. g. in Si. The effect of hydrostatic and biaxial strains on the bandstructures [95K1, 98D1] is expressed via deformation potentials. These deformation potentials have been determined experimentally and theoretically for Si and Ge; no direct determinations have been performed for SiGe alloys. Linear interpolation, however, tends to be a good approximation. The deformation potentials for hydrostatic strains will be denoted by the symbol a, and the deformation potentials for uniaxial strain in tetragonally distorted cubic lattice cells are denoted by b. For an overview, see e.g. [05K1], from which the following figures are extracted.

3.2.1 Hydrostatic strain Hydrostatic strain shifts the average position of the valence and the conduction band by ∆Ev,av and ∆Ec,av, respectively, ∆Ev,av = (2ε + εz ) av = 2 ε

1 − 2v av , 1− v

(3.2.2a)

∆Ec,av = (2ε + εz ) ac = 2 ε

1 − 2v ac , 1− v

(3.2.2b)

where Ȟ is Poisson’s ratio – see Eqs. (3.1.18a,b). Numerical values of the hydrostatic deformation potentials av and ac are given in Table 3.2.1. The selected values follow values recommended by C. van de Walle, who performed the basic studies on band offsets in the strained SiGe system.

Landolt-Börnstein New Series III/34C3

3.2 Influence of strain on bandstructure

20

[Ref. p. 25

Table 3.2.1. The deformation potentials av and ac for hydrostatic strain in Si and Ge [00K1]. The deformation potentials bv and bc are already given in a notation appropriate for tetragonal strain (E1, E2 in Kane’s notation, and Ȅd + ѿȄu, Ȅu in the van de Walle notation). Material

Deformation potential [eV] av

ac

bv

bc

Si

2.46

4.18

–2.35

9.16

Ge

1.24

2.55

–2.55

9.42

3.2.2 Uniaxial strain The biaxial strain in the epitaxial plane can be considered as hydrostatic deformation superposed by an uniaxial strain (İz – İ) perpendicular to the plane. This uniaxial strain component is written in isotropic notation as

εz − ε = − ε

1+ v 1− v

(3.2.3)

In the valence band the light-hole band is shifted by 3(İz – İ)bv with respect to the heavy-hole and spin-orbit split-off band. Compared to the average the shifts are given by ∆Ev,1 = 2(ε z − ε )bv = −2ε

1+ v bv , 1− v

∆Ev, 2 = ∆Ev,3 = −(ε z − ε )bv = ε

1+ v bv . 1− v

(3.2.4a) (3.2.4b)

Even in the absence of strain, the threefold degeneracy of the valence band is already lifted by the spin-orbit interaction, which splits the bands by an amount of ǻ0. With respect to the average band position Ev,av, two bands are shifted up by an amount of ǻ0/3 (the light-hole and heavy-hole bands, which are denoted Ev,1, Ev,2), while one band is shifted down by an amount of 2 ǻ0/3 (the spin-orbit split-off band, which we denote Ev,3). For completeness the relations are given for the lifting of the valence band degeneracy by both strain and band-orbit interaction. The superposition of both effects is nonlinear for the light-hole and spin-orbit split-off band: ∆Ev,1 = − 1 ∆0 + 1 (ε z − ε )bv + 1 ∆02 + 2 ∆0 (ε z − ε )bv + 9(ε z − ε ) 2 bv2 , 6 2 2

(3.2.5a)

∆Ev, 2 = 1 ∆0 − (ε z − ε ) bv , 3

(3.2.5b)

∆Ev,3 = − 1 ∆0 + 1 (ε z − ε )bv − 1 ∆02 + 2 ∆0 (ε z − ε )bv + 9(ε z − ε ) 2 bv2 . 6 2 2

(3.2.5c)

In the conduction band, the strain lifts the sixfold (6g) degeneracy into the fourfold degenerate (4g) bands with energy minima lying in-plane, and the twofold degenerate (2g) band energy minima lying perpendicular to the (001) plane. For (001) growth and ∆ type energy minima the energy shifts ∆Ec with respect to the average are easily written as

Landolt-Börnstein New Series III/34C3

Ref. p. 25]

3.2 Influence of strain on bandstructure

21

2 2 1+ v (ε z − ε )bc = − ε bc , 3 3 1− v

(3.2.6a)

1 1 1+ v ∆Ec (4g) = − (ε z − ε )bc = ε bc . 3 3 1− v

(3.2.6b)

∆Ec (2g) =

Let us now consider a model material with simple properties av = 2 eV, ac = 3 eV, bv = –2.5 eV, bc = 9 eV, ǻ0 = 0, Ȟ = 1/3, under either tensile or compressive biaxial strain İ of magnitude 0.01. First we investigate the valence band under the influence of strain (Fig. 3.2.2). The band average Ev,av is shifted up by tensile strain (+20 meV) and shifted down by compressive strain. Tensile strain further shifts up the light-hole (lh) energy levels by 100 meV, while heavy holes (hh) are lowered by 50 meV. In our model material the spin-orbit split-off holes (soh) are degenerate (ǻ0 = 0) with heavy holes at k = 0. As a result of tensile strain, the light-hole energy (Ev,1) is lifted by 120 meV, while the heavy holes (Ev,2 = Ev,3) are lowered by 30 meV. Ih e = 0.01 tensile strain

120 meV 150 meV

DEv,av = 20 meV 30 meV hh

hh 30 meV DEv,av = 20 meV 150 meV

e = 0.01 compressive strain

120 meV

Fig. 3.2.2. The valence band splitting under the influence of strain for | İ| = 0.01. For the properties of the model material see the text [05K1].

Ih

Under compressive biaxial strain (growth on a substrate with a smaller lattice constant) the heavy-hole band will be at the band edge; under tensile strain (growth on a substrate with a larger lattice constant) the light-hole band will be preferentially occupied. The different effective masses of the light-hole and heavyhole bands lead to different behavior in terms of the mobility of carriers or confinement shifts in the quantum wells. One can therefore use strain to tailor the band structure according to the needs of a particular application. Now, we investigate the Si-like conduction band (indirect, ∆ minimum) under the influence of tensile strain (İ = 0.01). The average energy Ec,av is shifted up by 30 meV. The twofold (2g) electrons perpendicular to the plane are shifted down by ∆Ec(2g) = 120 meV, the fourfold (4g) in-plane electrons are shifted up by ∆Ec(4g) = 60 meV (Fig. 3.2.3), resulting in a final energy position of Ec(2g) = –90 meV, Ec(4g) = +90 meV, with a 180 meV splitting. The dominant effect of band splitting compared to the shift of the average energy results in the band gap being reduced by the strain. With tensile strain the smallest gap is between the light-hole valence band and the twofold (2g) electrons with a band gap shrinkage of 210 meV (120 meV and 90 meV contribution from valence band and conduction band, respectively). With compressive strain the lowest gap is between hh states in the valence band and 4g electron states in the conduction band. The band gap shrinkage amounts to 120 meV (30 meV and 90 meV from the valence band and conduction band, respectively). Landolt-Börnstein New Series III/34C3

3.2 Influence of strain on bandstructure

22

e = 0.01 tensile strain

[Ref. p. 25

4g electrons 60 meV

90 meV

DEc,av = 30 meV 120 meV 90 meV

2g electrons 2g electrons e = 0.01 compressive strain

120 meV

90 meV

DEc,av = 30 meV 90 meV 60 meV

Fig. 3.2.3. The conduction band splitting under the influence of strain for | İ| = 0.01. The same model material has been used as in Fig. 3.2.2 [05K1].

4g electrons

3.2.3 Band alignment of strained SiGe When two semiconductors are joined at a heterojunction, discontinuities occur in the valence band and in the conduction band. In the absence of strain, i.e. for a lattice matched interface, the alignment simply requires one to determine how the band structures of the two materials line up at the interface; the lineup then produces values for the valence band discontinuity, ∆Ev, and the conduction band discontinuity, ∆Ec [01M1]. When the materials are strained, the strains will produce additional shifts (due to hydrostatic strain) and splittings (due to biaxial strain) as described in the forgoing section. We will follow here the treatment of van de Walle [00K1] who first considered the average energy E0v,av of the unstrained valence band and then added the influence of strain to obtain the individual energy levels. 3.2.3.1 Average valence band energy E0v,av The average valence band energy of Ge is roughly 0.58 eV above that value of Si (Note: Both, the experimental and theoretical values on that property are uncertain by about 0.1 eV). That would result in a valence band offset between unstrained Si and unstrained Ge of 0.662 eV, because the highest valence bands (lh, hh) are shifted up by ∆ 0/3. The spin-orbit splitting ǻ0 increases strongly from Si (ǻ0 = 44 meV) to Ge (∆ 0 = 290 meV). For both quantities, E0v,av and ǻ0, we will assume a linear relationship with the chemical composition of an Si1–xGex alloy (expressed by atomic Ge content x), thus E0v,av (Si1-xGex) [meV] = 580 x – 44/3 ,

(3.2.7)

ǻ0 (Si1-xGex) [meV] = 246 x + 44 . The valence band edge (lh, hh) of unstrained Si is taken as reference energy for edge Ev,1 = Ev,2 of unstrained SiGe is then given by E0v,av+ ǻ0/3 (Si1-xGex) [meV] = 662 x .

(3.2.8) E0v,av.

The valence band (3.2.9)

Landolt-Börnstein New Series III/34C3

Ref. p. 25]

3.2 Influence of strain on bandstructure

23

Remember that the indices 1, 2, and 3 are used to distinguish the light-hole, heavy-hole and spin-orbit split-off subbands of the valence band. The energetic position of the conduction band is more complicated, because of band bowing with Ge content x and because of Ge-like (eightfold, 8g) band minima for high Ge contents (x > 0.85) at the L points. We consider here only the mainly dominating Silike (6g, unstrained SiGe) states. The reader is referred to [04P1] with Ge-like states. The band gap Eg0 of unstrained Si1-xGex is roughly given by a parabolic law Eg0 (Si1-xGex) [eV] = 1.17 – 0.44 x + 0.206 x2 .

(3.2.10)

which is obtained by adding the binding energy of the free exciton (14.7 meV for Si, 4.15 meV for Ge) to the excitonic bandgap obtained from low-temperature photoluminescence measurements [89W1]. 3.2.3.2 Compressive strain A typical situation for compressive strain is given by a pseudomorphic SiGe film on a Si substrate. We consider only the energy offsets for the most occupied subbands (highest valence band, lowest conduction band). For compressive strain these are the heavy-hole valence band (Ev,2) and the (4g) inplane conduction band minima (Ec,4g). The typical contributions for the valence band offset are shown in Fig. 3.2.4 for the example of strained Ge on an unstrained Si substrate.

Ev2 Ev1 0 Ev,av Ev,av

Ev3

DEv

Ev Ev,av Si (unstrained)

Ge (strained)

Fig. 3.2.4. The theoretical valence-band lineups at an interface between unstrained Si and strained Ge (not to scale).

The Si substrate is on the left side with the average valence band energy Ev,av, an amount of ǻ0/3 = 44/3 meV (≅ 15 meV) below the valence band edge Ev (≡ Ev,1 = Ev,2). On the Ge side the hypothetical unstrained average E0v,av is 0.58 eV above the average Si level (chemical composition shift). The hydrostatic strain (compressive strain has negative sign) shifts down the average level to Ev,av. The uniaxial component splits the valence bands with the Ev2 energy (heavy-hole states) as the upper level for compressive strain. The conduction band offset may be constructed in the same way by adding the band gap to the average valence band energy and then applying the strain. With compressive strain the fourfold degenerate (4g) in plane conduction band minima Ec4 are lowest in energy. Figure 3.2.5 shows the valence band offsets ∆Ev(v2) and the conduction band offset ∆Ec(4g) as function of the Ge content for strained Si1-xGex on Si.

Landolt-Börnstein New Series III/34C3

3.2 Influence of strain on bandstructure

24 2.0

[Ref. p. 25

2g L

Band offset DE [eV]

1.5 4g

1.0

v2 v1

0.5

v3 0

Si /Si1-x Gex -0.5

0

0.2

0.4 0.6 Ge content x

0.8

1.0

Fig. 3.2.5. The band offsets ∆Ev, ∆Ec for a pseudomorphic Si/Si1–xGex heterojunction as a function of alloy composition x in the overlayer. ∆Ev is defined by the heavy-hole (v2) level, ∆Ec by the in-plane (4g) level. For better readability the conduction band offset ∆Ec is shifted up by the bandgap difference of Si (1.17 eV).

For comparison the offsets for the other subbands which do not define the band edge are also shown. The valence band discontinuity ∆Ev increases rather linearly to the strained Ge value of 0.78 eV, while the conduction band discontinuity is clearly nonlinear, because of the band gap bowing and it is quite small (Note that the band offset ∆Ec in Fig. 3.2.5 is shifted by 1.17 eV to separate it from ∆Ev). It is noteworthy that even for x = 1, i.e. pure Ge, the L minimum is not the lowest state due to strain in contrast to unstrained Ge. 3.2.3.3 Tensile strain A typical situation for tensile strain would be a strained-Si channel on a relaxed SiGe buffer (virtual substrate). Here the light-hole (v1) states mark the valence band edge while the perpendicular (2g) states mark the conduction band edge. The treatment is similar to the compressive strain treatment, but one has to consider that the energy splitting of the light-hole (v1) states is more complicated than that of the heavy holes (v2), because of interference with spin-orbit interaction (see Eqs. (3.2.5a,b) the forgoing section). The results of the calculation for a strained-Si quantum well on a relaxed Si1–yGey substrate heterojunction are given in Fig. 3.2.6. The larger band gap overlayer of Si is lower in the valence band edge (v1), which is as expected, but is also lower in the conduction band edge (2g) energy, which is a characteristics of a type II heterostructure. 1.5 4g

Band offset DE [eV]

1.0 2g 0.5

0

v1 v3

-0.5

v2

Si1-x Gex /Si -1.0

0

0.2

0.4 0.6 Ge content x

0.8

1.0

Fig. 3.2.6. The band offsets ∆Ev, ∆Ec for a pseudomorphic relaxed-Si1–yGey/strained-Si heterojunction as a function of alloy composition y of the substrate. The valence band offset ∆Ev is defined by the v1 (light-hole) state, the conduction band offset ∆Ec is defined by the 2g (⊥ to the interface plane) states. ∆Ec is shifted up by 1.17 eV as in Fig. 3.2.5.

Landolt-Börnstein New Series III/34C3

3.2.4 References for 3.2

25

3.2.4 References for 3.2 89W1 95K1 98D1 00K1 01M1 04P1 05K1

Weber, J., Alonso, M.I.: Phys. Rev. B 40 (1989) 5683. Kelly, M.J.: Low Dimensional Semiconductors: Materials, Physics, Technology, Devices, Oxford: Oxford University Press, 1995. Davies, J.H.: The Physics of Low Dimensional Semiconductors, Cambridge: Cambridge University Press, 1998. Kasper, E., Lyutovich, K. (eds.): Properties of Silicon Germanium and SiGe:Carbon, EMIS Datareviews Series, Vol. 24, INSPEC (IEE), London, 2000. Maiti, C.K., Chakrabarti, N.B., Ray, S.K.: Strained Silicon Heterostructures Materials and Devices, London: The Institution of Electrical Engineers, 2001. Paul, D.J.: Semicond. Sci. Technol. 19 (2004) R59. Kasper, E., Paul, D.J.: Silicon Quantum Integrated Circuits, Berlin: Springer-Verlag, 2005.

Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

26

3.3

Single and coupled quantum wells: SiGe

[Ref. p. 47

by N. Usami and Y. Shiraki

3.3.1 Introduction Advanced crystal growth techniques allow to realize a single thin layer of material sandwiched between two thick layers of another material. Depending on the choice of materials, carriers can be confined in the thin layer, and their motion along the growth direction is restricted in a well-defined two-dimensional space, which leads to the quantization of energy, momentum, and wave function. This “quantum well” (QW) structure provides unique electronic and optical properties compared with those of bulk crystal, and has been widely used for devices such as quantum well lasers and high electron mobility transistors in III-V materials (see also Landolt-Börnstein III/34C1). QWs can be realized also in SiGe/Si heterostructures. However, unlike lattice-matched III-V systems such as AlGaAs/GaAs, the existence of lattice-mismatch between the constituents of QWs complicates the situation. Epitaxial growth of SiGe/Si heterostructures is necessarily accompanied by the introduction of strain, which drastically affects the band gap as well as the band alignment. Therefore, the control of the band alignment must be done by paying careful attention to the status of the strain (see also the discussion in section 3.2). The strain-induced modification of the band gap as well as the band alignment can be predicted by the model solid theory developed by van de Walle and Martin [86V1, 89V1]. The hydrostatic component of the strain gives a shift of the band edges, and the shear strain modifies the crystal symmetry and lifts partially the degeneracy of the conduction band minima. The strain effects on the valence band are similar to those on the conduction band. The hydrostatic strain shifts the average position of the valance band, and the biaxial strain leads to a splitting of the valence bands in addition to the splitting introduced by the spin-orbit interaction. The relevant equations for the strain effects are documented in section 3.2 in terms of deformation potentials [68P1]. Additionally, the confinement influences the degeneracy, splitting and ordering of the bands. The confinement always pushes the light-hole (lh) bands below the heavy-hole (hh) bands, while tensile strain may partly compensate this effect. Fig. 3.3.1 shows the calculated conduction and valence bands in strained Si1–xGex pseudomorphically grown on Si(100). As a result, the conduction band minima are seen to be located at the Si-like ǻ valleys, irrespective of the Ge composition [86V1, 85P1]. This is in contrast to unstrained SiGe, where the crossover from the Si-like to Ge-like band structures is known to occur around a Ge composition of x ≈ 0.85 [58B1]. Furthermore, it can be seen that strained Si-rich Si1-xGex sandwiched between Si constructs a type-I QW, where both electrons and holes are confined in the SiGe layer, as illustrated in Fig. 3.3.2(a). On the other hand, epitaxial growth of a Si (Ge) layer on unstrained SiGe results in biaxial tensile (compressive) strain in Si (Ge), leading to type-II band alignment where electrons (holes) are confined in the Si (Ge) layer, as shown in Fig. 3.3.2(b). Both type-I and type-II band alignments are very useful from the viewpoint of device applications. Since the band discontinuity at the conduction band of the type-I strained-SiGe/Si QW is very small, the type-II alignment is especially important when the band engineering for electrons is intended. As illustrated in the examples above, various QWs can be realized by SiGe/Si heterostructures with careful control of the constituents as well as the status of the strain. This chapter is intended to give an overview of fundamental optical properties of single and coupled QWs based on SiGe/Si heterostructures. Data from multiple QWs (MQWs) are also included, where electronic coupling between neighboring wells is not important. Superlattices (SLs) are treated in section 3.4.

Landolt-Börnstein New Series III/34C3

Ref. p. 47]

3.3 Single and coupled quantum wells: SiGe

27

2.0 L

conduction bands

Band offset DE [eV]

D 1.17 1.0 0.84

Si /Si1-x Gex 0.5 valence bands

Fig. 3.3.1. Calculated conduction and valence band edges in compressively strained Si1-xGex lattice-matched to Si(100). All energies are referred to the top of the valence band in unstrained Si. The dashed lines show the mean values of each band [86V1].

0 0.2

0 Si

0.4 0.6 Ge content x

C.B.

Compressively strained SiGe hh

V.B.

1.0 Ge

D4

D4

C.B.

0.8

D2 Tensilely strained Si

Compressively strained Ge hh

V.B. Unstrained Si

SiGe Si

a

Unstrained Si

Unstrained lh SiGe

Unstrained SiGe

Si

Ge

SiGe

SiGe

Unstrained SiGe

b

Fig. 3.3.2. The band alignment of (a) compressively strained Si-rich SiGe on unstrained Si and (b) tensilely (compressively) strained Si (Ge) on unstrained SiGe.

3.3.2 Photoluminescence from SiGe/Si quantum wells: Spectral features Well-resolved band-edge photoluminescence (PL) of excitons confined in strained SiGe/Si quantum wells was first reported by Sturm et al. [91S1] – see Fig. 3.3.3. The samples were grown by a combination of rapid thermal annealing and chemical vapor deposition (RTCVD) on Si(100) substrates. The grown MQW structures consisted of 10 ... 50 periods of strained SiGe/Si QWs with Ge compositions in the range x = 0.17 ... 0.19, and well widths of 2.3 nm ... 3.4 nm as summarized in Table 3.3.1. Well-resolved PL, involving no-phonon transitions (NP) followed by phonon replicas, was observed. Although NP transitions are inhibited in indirect semiconductors such as SiGe and Si, the selection rule is partially relaxed in the presence of translational symmetry breaking mechanisms such as alloy disorder, interface roughness and impurity scattering. Phonon replicas consisted of transverse acoustic (TA) and three distinct transverse optical (TO) phonons with Si-Si, Si-Ge, and Ge-Ge modes. The observed phonon energies were 17.8 ± 0.5 meV (TA), 35 ± 1.5 meV (TO, Ge-Ge), 50.5 ± 1.0 meV (TO, Si-Ge), and 58.2 ± 0.5 meV (TO, Si-Si), which are in good agreement with those of relaxed bulk alloys [89W1].

Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

28

Si Ge/Si

T = 2K

[Ref. p. 47

NP

TO

Photoluminescence intensity I

Si-Si Si-Ge

TA

Ge-Ge 416-1B 416 489-4 489 950

Photon energy hw [meV]

1050

Fig. 3.3.3. Photoluminescence (PL) spectra of the four samples listed in Table 3.3.1 taken at T = 2 K [91S1].

Table 3.3.1. Summary of structural measurements of the four samples used in Fig. 3.3.3 (see text) [91S1]. Sample No.

SiGe [nm]

Si [nm]

Number of periods

Ge composition x

416-1B

3.4

6.5

10

0.18±0.02

416

2.9

5.4

10

0.17±0.02

489-4

2.5

2.3

50

0.19±0.03

489

2.3

2.3

50

0.18±0.03

3.3.3 Excitation power dependence of photoluminescence Lenchyshyn et al. reported that the decrease of excitation power results in the appearance of new broader and asymmetric PL peaks at lower energies [92L1]. Fig. 3.3.4 shows the semi-logarithmic plot of the excitation power dependence of PL spectra from a single 10 nm Si0.75Ge0.25/Si quantum well. It is seen that the peak shifts toward higher energies with increasing excitation power, reflecting that excitons fill a density of states. The lower energy tail of the PL line shape can be reproduced by an exponentially decaying function. These facts suggest that the PL process can be attributed to the recombination of excitons localized at alloy fluctuations. The energy separation between the usual luminescence and the localized exciton was found to decrease with decreasing well width [93L1]. However, the very long decay time at low excitation suggested that a localization process is important also in the very thin QWs. Furthermore, Steiner et al. [93S1] observed visible PL caused by the recombination of two electron-hole pairs yielding a single photon from a variety of SiGe/Si QWs. The excitation power dependence of the visible PL intensity was found to be close to linear over two orders of magnitude, which suggests that a major component of the luminescence consists of biexcitons, especially under high excitation and at low temperature [93S1, 94S1].

Landolt-Börnstein New Series III/34C3

Ref. p. 47]

Log (PL intensity) [arb.units]

10

3.3 Single and coupled quantum wells: SiGe

29

Si0.75 Ge0.25 /Si T = 2K EQ = 9.1 meV Iexc = -2 2400 mWcm 240 24 2.4

1

900

Fig. 3.3.4. Excitation power dependence of the PL line shape. The PL amplitudes are normalized to give equal intensity in the low energy tails. The low-energy edge is found to decrease exponentially as a function of energy,, with a 1/e slope of 9.1 meV [92L1].

930 910 920 Photon energy hw [meV]

3.3.4 Temperature dependence of photoluminescence Fig. 3.3.5 shows the temperature dependence of PL spectra of 50 periods of Si0.84Ge0.16/Si QWs with a well width of 7.3 nm grown by gas-source molecular beam epitaxy [92F1, 92F2]. In contrast to the rapid decay of PL from Si around 1100 meV, PL from MQWs survived up to higher temperatures.

Si0.84 Ge0.16 /Si

T = 116 K 100 K 90 K

70 K 60 K 50 K 45 K

Integrated PL intensity

Photoluminescence intensity I

80 K

38 K Si SiGe (NP) SiGe (TO)

31 K 20 K 950

a

1000 1050 1100 Photon energy hw [meV]

1

b

4 2 3 -1 Inv.temperature 100 / T [K ]

5

Fig. 3.3.5. Temperature dependence of (a) PL spectra of a 50-period Si0.84Ge0.16/Si MQW structure with a well width of 7.3 nm, and (b) integrated PL intensity for no-phonon (NO, full circles) and transverse-optical (TO, full triangles) phonon transitions in the MQW structure compared to Si (open circles) [92F1].

Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

30

[Ref. p. 47

The integrated PL intensity from the MQW was found to decay with an activation energy Ea = 130 meV. This energy is in good agreement with the theoretical prediction given by Ea = ǻEv – Eh,

(3.3.1)

where ǻEv and Eh are the valence band discontinuity (ǻEv = 136 meV for Ge composition of x = 0.16) and the confinement energy of the heavy holes (Eh = 10 meV). Therefore, the confinement of the heavy holes is concluded to be a controlling mechanism of the QW emission. Thermal quenching of PL from SiGe/Si QWs with a low activation energy is related also with grown-in nonradiative defects [97B1]. These defects can be partially removed by thermal annealing.

3.3.5 Quantum confinement effect Xiao et al. [92X1], Vescan et al. [92V1], and Fukatsu et al. [92F3] independently reported the quantum confinement effect of SiGe/Si quantum wells. Fig. 3.3.6 shows the PL peak energies as a function of the well width of strained Si0.84Ge0.16 quantum wells grown by gas-source molecular beam epitaxy reported by Fukatsu et al. [92F3]. Open and solid symbols are data points from multiple and single quantum wells (MQWs and SQWs), respectively. The PL emission energy was measured at T = 18 K. It is seen that the emission energy shifts toward higher energies with decreasing well width Lz, reflecting the quantum confinement effect. The solid and dashed lines show calculated results assuming a standard square potential and type-I band alignment. The conduction and the valence band offsets were assumed to be 10 meV and 136 meV, respectively, after van de Walle and Martin [86V1]. The calculated transition energy agrees with the experimental data if an offset of 13 meV was given to lower energies. This energy difference is considered to be the binding energy of excitons. Xiao et al. utilized the quantum confinement effect to predict the effective mass of the heavy holes in strained Si1–xGex, and obtained the expression mhh, eff = (0.278 – 0.07 x) m0 [92X1].

T = 18K

Si0.84 Ge0.16 /Si

1150

Photon energy hw [meV]

MQW 1100

SQW

1050

NP TO NP TO alloy bandgap

1000

950

0

5

10 15 Well width L z [nm]

20

25

Fig. 3.3.6. Emission energy as a function of well width, showing the systematic blueshift of no-phonon (NP) and transverse-optical phonon (TO) energies. The dotted line represents the alloy emission energy. The solid (NP) and dashed (TO) lines are calculated assuming a standard square potential and type-I band alignment with an energy offset of 13 meV to lower values [92F3].

Usami et al. reported PL from strained SiGe/Si SQWs grown by solid-source molecular beam epitaxy, and showed that a standard square potential cannot explain the experimental results in contrast to the gas-source MBE grown samples [92U1]. This was revealed to be due to the surface segregation of Ge Landolt-Börnstein New Series III/34C3

Ref. p. 47]

3.3 Single and coupled quantum wells: SiGe

31

during growth, and the resulting modification of the potential profiles. By taking this phenomenon into account and using the two-state exchange model developed by Fukatsu et al. [91F1], experimental results were fully reproduced, as shown in the solid line in Fig. 3.3.7. The segregation of Ge can be avoided without losing material quality by exploiting “surfactant mediated epitaxy” [89C1] or “segregant assisted growth” (SAG) [90F1]. In this growth technique, a foreign atom with smaller surface energy than that of Ge is deposited to suppress the segregation of Ge. Open circles in Fig. 3.3.7 show PL peak energies of SiGe/Si SQWs with an antimony (Sb) adlayer. In this case, an abrupt SiGe/Si interface can be obtained, and the PL peak energy was well reproduced by the numerical calculation considering a square well potential [93U1]. The effect of Sb on the optical properties and the interface abruptness in SiGe/Si SQWs was reported in [95Z1].

Si Ge /Si 1140

experiment MBE SAG calculation with segregation square potential

PL peak energy [meV]

1120 1100 1080 1060 1040 1020 1000 0

2

4 Well width L z [nm]

6

8

Fig. 3.3.7. Well width dependence of the NP transition energy from SiGe/Si SQWs grown by solid-source molecular beam epitaxy. Solid and open circles were obtained from samples grown without and with a Sb adlayer, respectively [93U1].

3.3.6 Effect of post-growth annealing An effect of post-growth annealing was reported by Sunamura et al. [93S2]. They annealed Si0.84Ge0.16/Si SQWs with a well width of 7.3 nm in vacuum at various temperatures, and observed a systematic blueshift of the peak energy and an increase in the integrated PL intensity (Fig. 3.3.8). The former is due to the potential modulation induced by the interdiffusion. Numerical calculation of the quantized energy coupled with the one-dimensional diffusion equation permits to obtain the diffusion coefficient, and the activation energy was estimated to be 2.47±0.4 eV. The increase in the PL intensity originates from the elimination of nonradiative pathways, and the amount of the improvement is more drastic for low-temperature grown samples [95S1]. A strong initial enhancement of the diffusion was observed for low-temperature grown samples [96L1].

Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

32

NP

Ta = 900 °C

Si0.84 Ge0.16 /Si

[Ref. p. 47

Si

PL intensity

TO

700

800

900 1000 hw [meV]

NP

TO

Photoluminescence intensity I

1100

T = 20 K

Ta = 900 °C

TA

850 °C

800 °C

as-grown 960

Fig. 3.3.8. PL spectra of strained Si0.84Ge0.16/Si (Lz = 7.3 nm) SQWs annealed in vacuum for 20 min at different temperatures Ta. The inset is the PL spectrum of the sample annealed at Ta = 900 °C [93S2].

×3

1000 1040 Photon energy hw [meV]

3.3.7 Effect of electric field Miyake et al. reported the influence of an external electric field on the recombination in strained Si0.82Ge0.18/Si SQWs with a well width of 2.8 nm [96M1] (Fig. 3.3.9). Although the ground state energy of a square quantum well is known to show gradual decrease with increasing electric field (quantum confined Stark effect), they observed a systematic blueshift.

Si0.82 Ge0.18 /Si 1.5 DEb DEQCS

1.5 1.0

L z = 7 nm

0.5

Binding energy shift

Energy shift DE [meV]

Energy shift DE [meV]

2.0

calc exp 1.0 L z = 7 nm

0.5

0 Stark shift - 0.5

0 0

a

0.5

1.5 1.0 Electric field E [kV/cm]

2.0

0

b

0.5

1.5 1.0 Electric field E [kV/cm]

2.0

Fig. 3.3.9. (a) Spectral shifts due to exciton binding energy reduction with increasing electric field calculated by a variational method (solid line) and due to the quantum confined Stark effect (dashed line). (b) The net spectral shift obtained from (a) (solid line) and the experimental values (dots) [96M1]. Landolt-Börnstein New Series III/34C3

Ref. p. 47]

3.3 Single and coupled quantum wells: SiGe

33

This was first explained in terms of a decrease of the binding energy of excitons, which overcompensates the decrease of the quantum confinement energy. Kim carried out a numerical calculation based on an Airy function method [98K1], and predicted the “Stark blueshift” region for a moderate field applied in a shallow well. This observation was originally found in the calculation by Austin et al. [85A1].

3.3.8 Effect of external stress Houghton et al. developed a substrate bending scheme to apply in-plane uniaxial stress along the [100] and the [110] directions, and attempted to utilize this technique to verify the band alignment in strained SiGe/Si (001) QWs with Ge compositions in the range x = 0.15 ... 0.38 [95H1]. The idea is to observe the direction of the energy shift in PL from SiGe, since the introduction of uniaxial [110] stress results in the peak shift toward the opposite directions depending on the band alignment. Fig. 3.3.10 shows the PL shifts as a function of the external [110] uniaxial stress. Dotted and dashed lines are calculated transitions for a type-I band alignment without and with the confinement effect, respectively. The chained line corresponds to the type-II band alignment. Since all the experimental results followed the calculations with type-I band alignment, it was concluded that SiGe/Si has a type-I band alignment. 10

SiGe/ Si

s II [110]

Energy shift DE [meV]

5 1 nm

0

type II SiGe - Si v2’ - D001

-5

Si v2 - D001 -10 -0.3

-0.2

Tension

-0.1

Si v1’

v2’

- D010

SiGe - D010 - D100

- D100

0 0.1 Stress s [GPa]

0.2

0.3 Compression

Fig. 3.3.10. PL peak shift as a function of external [110] uniaxial stress. Solid lines are calculated shifts of Si. Open symbols are PL shifts from Si0.85Ge0.15 QWs with well widths of 2.5 nm (circles), 3.7 nm (triangles base down), 6.0 nm (diamonds), 2 nm (triangles base up) and 4 nm (squares), Si0.80Ge0.20 QWs with a well width of 6 nm (pluses), and Si0.62Ge0.38 QWs with a well width of 1.2 nm (crosses). Full lines (calculation) and full squares give the results for strained silicon [95H1].

Similar experiments were repeated by Thewalt et al. for a coherently strained Si0.7Ge0.3/Si(001) QW with a wide range of excitation power densities [97T1]. Fig. 3.3.11 shows the PL peak shift as a function of the [110] uniaxial and the (001) biaxial stresses. The solid and dashed lines show the expected slope of the energy shift for type-I and type-II band alignments, respectively. It is seen that the 10–5 I 0 data showed a type-I blueshift only for a very low (001) stress, and that a further increase of the stress resulted in a shift toward the opposite direction, which indicates a transition to type-II band alignment. The 10–7 I 0 data clearly showed type-II PL without any external stress. Therefore, it was concluded that SiGe/Si has a type-II band alignment, and all previous studies indicating type-I band alignment are due to the cancellation of the small conduction band offset by band bending resulting from the charge accumulation.

Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

34 240

1

Energy shift DE [cm- ]

200 160

-1

Iexc = 4×10 I0

Si0.7Ge0.3/ Si

CB

-2

4×10 I0

I

II

[Ref. p. 47

VB

-2

2×10 I0 120 -1

80

1×10 I0

-2

10 I0

40

-5

10 I0 0

-7

10 I0 [110]

-40

(001) 0

50

50 100 Tensile stress s [MPa]

150

200

Fig. 3.3.11. Energy shift of the SiGe NP line over a wide range of excitation densities versus applied tensile stress. Energies are relative to the NP line at zero external stress. Solid (dashed) lines are theoretical predictions for the stress dependence of type-I (type-II) transition energies for a Si0.7Ge0.3/Si(001) QW. The inset illustrates the effects of external stress on type I/II transitions [97T1].

3.3.9 Fermi-edge singularity Buyanova et al. investigated the effect of modulation doping on the radiative recombination in SiGe/Si QWs [96B1]. Fig. 3.3.12 shows the normalized PL spectra from a strained Si0.8Ge0.2 QW with a well width of 3 nm placed between two B-doped layers separated by 25 nm wide Si spacers. The PL spectra showed a marked difference compared with those of undoped QWs, and a broad asymmetric line shape was observed. This was explained in terms of the filling of the two-dimensional (2D) hole subband of the SiGe QW. The cutoff energy on the high-energy side was about 50 meV, which was in good agreement with theoretical estimates of the Fermi level (45 meV) obtained from Poisson’s equation. Therefore, this behavior was attributed to the Fermi-edge singularity, caused by nearly resonant scattering of holes from states near the Fermi edge and the next unoccupied subband.

Si0.8 Ge0.2 /Si

Photoluminescence intensity I

TO

Iexc = 3.5 W/cm

2

3.5 W/cm

2

1.6 W/cm

2

0.2 W/cm 0.90

0.95

TA NP Si substrate

2

1.00 1.05 Photon energy hw [meV]

1.10

1.15

Fig. 3.3.12. Normalized PL spectra at T = 2 K from SiGe QWs with a 25 nm wide spacer as a function of the photoexcitation intensity. The dashed curve shows the PL spectrum recorded after the hydrogen treatment [96B1].

Landolt-Börnstein New Series III/34C3

Ref. p. 47]

3.3 Single and coupled quantum wells: SiGe

35

3.3.10 Time-resolved photoluminescence Zrenner et al. carried out time-resolved PL spectroscopy for 5-period Si0.72Ge0.28 MQWs with a well width of 5.9 nm grown by molecular beam epitaxy [95Z2]. Fig. 3.3.13 summarizes the temporal profiles of Si-related (TO and electron-hole droplet, EHD) and SiGe-related PL. The SiGe QW PL was found to closely follow the decay of the EHD, especially just after turn-off of the laser. The decay of the SiGe QW was controlled by the capture of the excitons from evaporating EHD. The exciton lifetime in the SiGe QW was determined by the onset of the NP-PL as nominally 100 ns, which was dominated by nonradiative recombination processes.

Si0.72 Ge0.28 /Si

Photoluminescence intensity I

Lz = 5.9 nm lL = 458 nm 2 PL = 1 kW/cm T = 10 K Si-TO SiGe-NP SiGe-TO EHD

0

3000 2000 Time t [ns]

1000

4000

5000

Fig. 3.3.13. Temporal profiles of various PL lines under the condition of pulsed optical excitation (P = 1 kW/cm2, pulse width 2000 ns) above the Si band gap [95Z2].

Fukatsu et al. observed more extended decay lifetimes as long as 1 µs for a series of strained Si0.85Ge0.15 SQWs with well widths of Lz = 1 nm ... 20.8 nm [95F1, 95F2] – see Fig. 3.3.14. The observed lifetimes showed a strong well width dependence, and reached a maximum for a well width of Lz = 3.5 nm ... 4.5 nm. Generally, the lifetime of the free excitons is inversely proportional to the binding energy of excitons. The observed well width dependence was explained by the calculated binding energy of excitons except for the samples with small well widths, where 2D confinement was not enough and the lifetime was affected by nonradiative channels in the Si barrier layer.

Si0.85 Ge0.15 /Si 1/ Eb

1400

Lifetime t [ns]

1200

0

5

10 Lz [nm]

15

20

1000

800

600 400

T > 7.6 K 0

Landolt-Börnstein New Series III/34C3

50

150 100 Well width Lz [nm]

200

Fig. 3.3.14. The decay lifetime IJ as a function of well width Lz. The inset shows the well width dependence of the exciton binding energy [95F2].

3.3 Single and coupled quantum wells: SiGe

36

[Ref. p. 47

The investigation of the temperature dependence of the lifetime is a tool to access the dimensionality of excitons since the thermal population of excitons, which affects the lifetime, reflects the density of states [87F1]. When the upper limit of the momentum allowed in the transition, ǻ0, is much smaller than the thermal energy kBT, the lifetime of 2D excitons is shown to be proportional to the temperature. Fig. 3.3.15 shows the temperature dependence of the decay lifetime of Si0.82Ge0.18 SQWs with a well width of Lz = 6.8 nm. It is seen that the lifetime is linearly dependent on the temperature, and this tendency persists up to T = 60 K. This clearly manifests the 2D nature of excitons.

Si0.82 Ge0.18 /Si

1400 1200

Lifetime t [ns]

1000 800 600 400 200 0

0

10

20 40 30 Temperature T [ K]

50

60

Fig. 3.3.15. Temperature dependence of the decay lifetime of excitons confined in Si0.82Ge0.18 SQWs with a well width of 6.8 nm [95F2].

3.3.11 Growth mode transition Owing to the lattice-mismatch of 4.2% between Si and Ge, growth of SiGe on Si results in internal strain. Beyond a critical amount of strain energy, the energetic gain in the strain energy due to the island formation overcompensates the increased surface energy. Therefore, a growth mode changeover from Frank-van der Merwe (FM) growth (layer-by-layer) to Stranski-Krastanov (SK) growth (islands with leaving wetting layer) is expected for an increasing Ge composition in Si1–xGex/Si with fixed well width, or for an increasing width in Si1–xGex/Si with fixed Ge composition (see section 3.1.1). Fig. 3.3.16 shows the Ge composition dependence of the NP peak energy and the activation energy of PL from Si1–xGex/Si with a nominal well width of 3.2 nm reported by Sunamura et al. [95S2]. A deviation from the calculations assuming the FM growth mode is seen around x ≈ 0.4. By using cross-sectional transmission electron microscopy, this effect was attributed to the growth mode transition from the FM to the SK mode. A similar result was reported also by Gail et al [95G1]. The growth mode transition from the FM to the SK mode was observed also in pure Ge on Si [95S3, 95S4]. Sunamura et al. grew a series of Si/pure Ge/Si heterostructures with various Ge coverages Q by gas-source molecular beam epitaxy, and carried out PL measurements – see Fig. 3.3.17. With increasing Q, the PL peaks shifted toward lower energies, reflecting the quantum confinement effect. However, a broad luminescence band (L) appeared for Q > 4.1 monolayers, which was accompanied by quenching of the confinement effect and an unexpected blueshift of the NP and TO lines. These behaviors were interpreted as the growth mode transition to the SK mode. The decrease of the wetting layer thickness played a role to account for the blueshift, which manifests surface migration of Ge adatoms from the wetting layer to the Ge islands. The Ge islands can be utilized to laterally modulate the potential of buried QWs [97K1]. Furthermore, optical properties have been reported of ordered Ge islands by selective epitaxial growth [98K2] and by growth on a patterned substrate [02V1], and of vertically stacked Ge islands [00S1]. Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

PL activation energy Ea [meV]

Ea = 200 meV

x = 0.47 0

600

37

1.0 2.0 -1 Inv.temperature 100/T [K ]

1200

3.0

ENP = 1155-840x+Ec [meV] Ea = 840x-Ec [meV] 1000

400 Lz = 3.2 nm

800

200

NP energy ENP [meV]

Si1-x Gex /Si

PL intensity I ( log scale)

Ref. p. 47]

600

0 0

0.2

0.4 0.6 Ge content x

0.8

1.0

Fig. 3.3.16. Ge composition dependence of the activation energy of the PL intensity rolloff (solid circles) and NP emission energies (open circles) of Si1–xGex/Si with a nominal well width of 3.2 nm. The solid and dotted lines are the theoretical calculations assuming FM growth mode. The inset shows the temperature dependence of the PL intensity for x = 0.47 QW [95S2].

Si /Ge / Si T = 22 K

L

Q = 11.8 ML TO

NP

Si 5.9 ML

Photoluminescence intensity I

4.4 ML 4.1 ML

×3 ×5

3.9 ML

× 2.5

3.7 ML

3.3 ML 3.0 ML 2.2 ML 1.5 ML 0.7 ML 700

800 900 1000 Photon energy hw [meV]

Landolt-Börnstein New Series III/34C3

1100

Fig. 3.3.17. PL spectra of Si/Ge/Si QWs with various Ge coverages Q [95S3].

3.3 Single and coupled quantum wells: SiGe

38

[Ref. p. 47

3.3.12 Type-II strained Si quantum well Pseudomorphic growth of Si on relaxed SiGe results in the introduction of tensile strain in the Si film, leading to the formation of type-II (staggered) band lineup, and the confinement of electrons in the Si layer is expected. Nayak et al. utilized step-graded SiGe virtual substrates (see section 3.1) grown on Si to realize Si0.82Ge0.18/strained Si/Si0.82Ge0.18 type-II QWs [93N1], and observed the quantum confinement effect as the systematic shift of PL peak energies (labeled X in Fig. 3.3.18) with the changing width of the quantum well [93N2]. Such a type-II QW was realized also on single-crystalline SiGe bulk substrates, and the PL properties have been reported [03S1].

Si / Si0.82 Ge0.18

B B

D4

NP

TO(Si-SI)

T = 4.2 K

Photoluminescence intensity I

f

X

e X

d X

c X

X

b X

X

a 700

800 900 1000 Photon energy hw [meV]

1100

Fig. 3.3.18. PL spectra from strained-Si/SiGe QWs with various well widths of (a) 1 nm, (b) 1.3 nm, (c) 1.6 nm, (d) 1.9 nm, (e) 2.1 nm, and (f) no quantum well [93N2].

3.3.13 Coupled quantum wells Fukatsu et al. grew a series of a strained Si0.82Ge0.18/Si symmetrically coupled QWs with various Si spacer widths [93F1]. The PL peak energies showed a systematic shift with changing Si barrier width (Fig. 3.3.19), and an attempt was made to determine the band alignment. It was found that a negative conduction band offset, meaning type-II alignment, could not explain the experimental results. By fitting the experimental data, type-I alignment with conduction and valence band offsets of ǻEc = 7.7 meV and ǻEv = 149 meV was suggested. A new class of coupled QWs to confine both types of carriers was proposed and realized by Usami et al. [95U1]. The fundamental idea is to confine electrons and holes separately in neighboring wells as shown in Fig. 3.3.20, and to optimize the mutual widths to enhance the desirable overlap of the wave functions, which leads to the enhanced radiative recombination. Such a structure, a so called neighboring confinement structure (NCS), can be realized by sandwiching a pair of tensilely strained Si and compressively strained Si1-yGey layers between relaxed Si1–xGex (y > x).

Landolt-Börnstein New Series III/34C3

Ref. p. 47]

3.3 Single and coupled quantum wells: SiGe

39

DEv = 146 meV DEv = 149 meV T = 19 K DEv = 152 meV

Si0.82Ge0.18 /Si

1060

PL peak energy [meV]

1050

1040

A S 2

1

1030

S

type I type II (DEc = 0)

1020 0

20

40 60 Si barrier width [nm]

A

80

100

Fig. 3.3.19. PL peak energies as a function of the Si barrier width for strained-SiGe/Si symmetrically coupled QWs together with the results of effective mass calculations assuming various band alignments [93F1]. The inset shows the band scheme for type-I alignment.

Fig. 3.3.21 shows that a drastic improvement of the PL intensity can be achieved by NCS compared to a type-I and a type-II QW. The decay time of the NP line in NCS was found to be almost independent of temperature below T = 30 K, indicative of the relevance of the localized excitons for the enhanced NP intensity [96U1]. Fabrication of strain-balanced Si/SiGe MQWs on SiGe virtual substrates and their optical properties are reported in [01K1].

NP

Compressively strained Si1-yGey (y>x)

D4

D2

hn

Relaxed Si1-xGex

Photoluminescence intensity I

T = 18 K

Dislocation - related PL D2 D1

TO

c b QW

800

Tensilely strained Si

Fig. 3.3.20. Schematic band alignment of a neighboring confinement structure (NCS). A pair of carrier confining layers for electrons and holes is sandwiched by barrier layers [95U1].

Landolt-Börnstein New Series III/34C3

900 1000 Photon energy hw [meV]

a 1100

Fig. 3.3.21. Comparison of PL spectra of three samples. (a) 1 nm wide strained-Si SQW on Si0.82Ge0.18, (b) 1 nm wide strained-Si0.64Ge0.36 SQW on Si0.82Ge0.18, and (c) a pair of 1 nm wide strained-Si/1 nm strained Si0.64Ge0.36 sandwiched by Si0.82Ge0.18 barriers (NCS). Strong enhancement of radiative recombination can be seen in the NCS sample [95U1].

3.3 Single and coupled quantum wells: SiGe

40

[Ref. p. 47

3.3.14 Electroluminescence Electroluminescence (EL) is a key issue to determine the device feasibility of the material system, and EL of SiGe/Si has been intensively studied [92M1, 93F2, 93E1, 96F1]. Fig. 3.3.22 compares PL and EL spectra from a pin Si0.7Ge0.3/Si SQW with well width of 4 nm. With increasing temperature above 110 K, the EL peak shifts toward lower energies, reflecting the temperature dependence of the SiGe band gap. The temperature dependence of the integrated EL intensity from SiGe showed a unique behavior, and a maximum was obtained at a medium temperature range. This feature was qualitatively explained by considering Auger and radiative recombination in all relevant regions of the pin diode [96F1]. The internal quantum efficiency of pin light-emitting-diode with strained Si0.8Ge0.2/Si was studied and showed a maximum value of 0.5% at 100 K and 0.1% at room temperature [03S2]. An attempt to fabricate erbium-doped SiGe/Si QWs and a study of their EL and PL properties was reported in [00N1]. -1

Photon energy hw [cm ] 7000 8000

6000

9000

pin Si0.7 Ge0.3 /Si L z = 4 nm

SiGe

Si

T = 250 K

Photoluminescence intensity I

175 K 60 K PL 4.2 K EL T = 300 K 265 K 235 K 180 K 110 K 60 K 4.2 K 800

TO

NP

900 1000 1100 Photon energy hw [meV]

Fig. 3.3.22. Comparison of PL and EL spectra of a pin Si0.7Ge0.3/Si SQW with a well width of 4 nm [96F1].

3.3.15 Interband absorption The bandgap of SiGe covers the wavelength range of 1.3 µm ... 1.55 µm used for optical communications. Therefore, SiGe/Si MQW photodetectors operating at this wavelength have attracted attention toward integrated Si photonic devices. Gail et al. fabricated pin structures with an intrinsic SiGe MQW region on a p-type Si substrate and an n-type Si cap layer [95G1]. Fig. 3.3.23 shows the photocurrent of Si0.49Ge0.51 MQW samples. A maximum external responsivity of 4·10–4 A/W was obtained at Ȝ = 1.3 µm in normal incidence by increasing both the number of QWs and the Ge composition up to almost the critical thickness of the generation of dislocations. To overcome the inherently low absorption coefficient, Li et al. Landolt-Börnstein New Series III/34C3

Ref. p. 47]

3.3 Single and coupled quantum wells: SiGe

41

attempted to insert the absorption layer into two mirrors to form a resonant-cavity enhanced (RCE) photodetector. Their device structures consist of 20 periods of Si0.7Ge0.3 QWs with a well width of 6 nm sandwiched between SiO2/Si and Al2O3 distributed Bragg reflectors, and a resonant peak of 4.4·10–2 A/W at Ȝ = 1.3 µm was obtained [02L1] (Fig. 3.3.24). Both Stark redshift and blueshift were observed in SiGe/Si MQW pin photodiodes in the photocurrent spectra depending on the electric fields applied to the QWs [00L1].

1.8

3

10

Wavelength l [mm] 1.6 1.4

0.98

1.2

40

Responsivity [mA/W]

R 353 R 327 2

R 442 10-2

T = 293 K

35

30

10-3 10-4 Current [A]

Photocurrent [pA]

0.92

Si0.7 Ge0.3 /Si MQW

3×

10

Photon energy hw [eV] 0.96 0.95 0.94 0.93

45

Si0.49 Ge0.51 /Si MQW

T = 293 K 1 mm

0.97

10

25

10-5 10-6

1260

10-7 10 10-9 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 Voltage [V]

1 0.7

0.8 0.9 1.0 Photon energy hw [eV]

1.1

1280

1300

1320

1340

1360

Wavelength l [nm]

-8

1.2

Fig. 3.3.24. Responsivity spectra of the Si0.7Ge0 . 3 / Si MQW RCE photodetector fabricated using wafer bonding process [02L1] at room temperature (RT). The wavelength Ȝ may be converted to energy E by E [eV] = 1240/ Ȝ [nm].

Fig. 3.3.23. Photocurrent of Si0.49Ge0.51/Si MQW samples with identical well widths of Lz = 5.8 nm, but different numbers of QWs and Si barrier widths [95G1]. The inset shows the current voltage characteristics of the pin diode.

3.3.16 Intraband absorption Karunasiri et al. reported the intersubband infrared absorption in 10 periods of strained Si0.6Ge0.4/Si QWs with a well width of 4 nm [90K1] (Fig. 3.3.25). The central 3 nm of the QWs were doped with boron (B) to about 1·1019 cm–3. The absorption measurements were carried out using waveguide geometry, and an absorption peak around 8.1 µm was observed. The energy was found to correspond to the transition between the ground state and first excited states of the heavy holes. The absorption strength was strongly dependent on the polarization angle, as expected by the selection rules.

Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

42

[Ref. p. 47

78

Si0.6 Ge0.4 /Si MQW 65

T = 293 K

20°

52 Absorbance [m abs]

0°

40° 39

26 60° 13

0 2400

2000

1600 1200 -1 Wavenumber n [cm ]

800

Fig. 3.3.25. Measured absorption spectra of a Si0.6Ge0.4/ Si MQW for different polarizations of the incident light [90K1].

Park et al. measured the photoresponse as a function of incident beam polarization [92P1], and observed that the intersubband absorption disappears at normal incidence, while another broad absorption occurs at a shorter wavelength similar to a SiGe/Si MQW [92P2]. With increasing Ge composition in the SiGe MQW, the peak wavelength shifted towards shorter wavelengths, accompanied by the increase of the absorption strength (Fig. 3.3.26). The origin of the transition was attributed to the intervalence-subband transition from the ground state of the heavy hole to another valence subband.

1.24 0.7

0.62

Photon energy hw [eV] 0.41 0.31 0.25

0.21

0.18

6.0

7.0

0.6 Si0.7 Ge0.3 / Si (10 periods)

Transmittance [%]

0.5 0.4 Si0.6 Ge0.4 / Si (10 periods) 0.3 Si0.4 Ge0.6 / Si (5 periods)

0.2 0.1 0 1.0

2.0

3.0 4.0 5.0 Wavelength l [mm]

Fig. 3.3.26. Normal incident transmission spectra of SiGe/Si MQWs with various Ge compositions [92P1].

Landolt-Börnstein New Series III/34C3

Ref. p. 47]

3.3 Single and coupled quantum wells: SiGe

43

Hertle et al. reported the intersubband absorption in the conduction band of 5 periods of undoped Si/Si0.5Ge0.5 QWs [91H1]. The center of 5 nm of the barriers was doped with Sb. They studied various samples (Table 3.3.2) with different well widths and carrier densities, and the measured transition energies were in good agreement with the self-consistent subband calculations (Fig. 3.3.27). Photoinduced infrared absorption in p-doped [95B1] and undoped [95W1] SiGe/Si MQWs was investigated, which can provide useful information on valence band mixing effects. This technique can be utilized also to investigate recombination processes in SiGe/Si QWs [97D1]. Fujita et al. utilized segregant assisted growth (SAG) to realize narrow Si/Si0.4Ge0.6 MQWs with abrupt heterointerfaces, and a systematic variation of the absorption peak due to the intersubband transition was observed (Fig. 3.3.28). The peak energy was calculated based on the Kronig-Penney model taking the interface smearing into account. By comparing the experimental results with the calculation, the amount of the interface smearing was estimated to be less than 0.4 nm [92F4]. Table 3.3.2. Summary of the sample structure and transition energies of modulation doped (Sb) Si/Si0.5Ge0.5 five-period MQWs [91H1]. Given are the SiGe well width dSiGe, the modulation doping nSb per barrier, and the experimentally found and calculated subband transition energies E01, respectively. Sample No.

dSiGe [nm]

nSb [cm–2]

E01,exp [meV]

E01,cal [meV]

C0660

5.0

2.1·1012

33.5

33.8

7.5

12

19.4

12.5

C0662

Photon energy hw [meV] 20 25 30 35 40

15

Si /Si0.4 Ge0.6 MQW

45

Si /Si0.5 Ge0.5

100

E01,exp

Lz = 1.4 nm

E12,exp

E01,exp 1.8 nm

80 Transmittance

Transmission [%]

1.9·10

60

2.0 nm

CO660 T = 100 K

CO662 80

160

240 320 -1 Wavenumber n [cm ]

2.6 nm

400

Fig. 3.3.27. Measured transmission spectra at T = 8 K of the samples C0660 and C0662 (see Table 3.3.2).

0.1

0.2 0.3 Photon energy hw [eV]

10 %

40

0.4

Fig. 3.3.28. Transmission spectra of n-type Si/Si0.4Ge0.6 MQWs with well widths of Lz = 1.4, 1.8, 2.0, and 2.6 nm [92F4].

Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

44

[Ref. p. 47

3.3.17 Second-harmonic generation Second-harmonic generation (SHG) from bulk Si is inhibited in the bulk due to its inversion symmetry. However, introduction of structural asymmetry by heterojunctions and QWs leads to the appearance of optical nonlinearities. Seto et al. attempted to observe intersubband related SHG in Si/SiGe asymmetric QWs [94S2]. The sample consisted of 15 periods of uniformly p-doped 3.6 nm wide Si0.75Ge0.25/1.9 nm wide Si0.57Ge0.43 stepped QWs. The sample was designed to provide the asymmetry for a finite Ȥ(2) and have three bound heavy-hole subbands separated by around 120 meV, which corresponds to the CO2 laser photon energy. Fig. 3.3.29 shows a result of room temperature measurements of second-harmonic power as a function of incident pump power. A clear quadratic dependence was confirmed as expected for SHG. Ȥ(2) was estimated to be 5·10–8 m/V, with an uncertainty of a factor of 2. SHG from interband transitions was studied by Zhang et al. using similar stepped QWs. The measurements were carried out using a pulsed Q-switched yttrium aluminum garnet (YAG) laser with a wavelength of 1.06 µm as the fundamental beam in the reflection geometry. The evaluated value of Ȥ(2) was 0.65·10–6 esu [97Z1]. 10

Si /SiGe MQW Second harmonic power [nW]

8

lw = 10.56 mm l2w = 5.28 mm

6

T = 293 K

4

2

0 0

10

20

30 40 50 Incident power [W]

60

70

80

Fig. 3.3.29. Incident power vs. second-harmonic power from 15 periods of uniformly p-doped 3.6 nm wide Si0.75Ge0.25/1.9 nm wide Si0.57Ge0.43 stepped QWs at room temperature [94S2].

3.3.18 Phonon modes The large difference in the atomic masses of Si and Ge results in the localization of the phonon modes, and Raman spectra from SiGe alloys generally consist of three main phonon modes: Si-Si (§ 500 cm–1), Si-Ge (§ 400 cm–1), and Ge-Ge (§ 300 cm–1) [66F1]. The relative intensities of each mode are roughly proportional to the relative numbers of the corresponding bonds. Therefore, rough estimation of the alloy composition is possible by the relative intensities. The Si-Si and Ge-Ge peak frequencies in relaxed SiGe alloys are known to vary linearly with composition (Ȧ Si-Si [cm–1] § 520 – 70 x [89A1], Ȧ Ge-Ge [cm–1] § 285 + 16 x [94T1]). This behavior can be qualitatively understood by a simple cluster model [88M1]. The average cluster size of each bond is dependent on the alloy composition, and affects the phonon frequency through variation of the confinement wave vector. Furthermore, the local strain gives an additional shift. The Si-Ge peak frequency varies slowly over most of the composition range. In addition to the three optical modes, Alonso et al. observed several weak features between 420 cm–1 ... 470 cm–1 in the Raman spectra Landolt-Börnstein New Series III/34C3

Ref. p. 47]

3.3 Single and coupled quantum wells: SiGe

45

of Si1–xGex (0.28 < x < 0.77) single crystal layers grown by liquid phase epitaxy [89A1] (Fig. 3.3.30). By calculations of the first order Raman spectra of completely random SiGe alloys, these phonons were shown to be due to localized Si-Si motion in the nearest neighborhood of several Ge atoms.

Si1-x Gex Si - Si

500

T = 293 K

-1

Raman shift Dn [cm ]

LPE Bulk

450

Si - Ge

400 0

0.2

0.4 0.6 Ge content x

0.8

1.0

Fig. 3.3.30. The composition dependence of phonon modes in relaxed SiGe alloys at room temperature [89A1].

The introduction of strain modifies the bond length and affects the phonon modes as studied by applying uniaxial stress to bulk Si and Ge [72C1]. In SiGe/Si heterostructures, the strain is necessarily introduced due to the lattice mismatch between them, which induces a strain-induced shift in addition to the shift owing to the alloying. The amount of the strain-induced shift ǻȦ is summarized as ǻȦ = bİ for compressively strained Si1–xGex alloys grown on Si(001). Table 3.3.3. The experimentally determined coefficient b [cm–1] for strain-induced wavenumber shifts in compressively strained Si1–xGex alloys grown on Si(001). Composition x

Si-Si

Si-Ge

Ge-Ge

Ref.

0.2

–850

–710

–810

92L2

0.3

–980

–990

–925

92L2

0.8

–1052

–895

–728

96S1

The influence of doping on the Raman spectra in bulk Si and Ge has been widely studied [74J1, 75B1, 81O1]. Since doping leads to a shift of the Fermi level, the interaction between the phonon states and continuum states can be altered. As a consequence, Raman spectra show a broadening and energy shift depending on the doping concentration. These features are well-known as the Fano effect [61F1]. Bendayan et al. investigated the influence of two-dimensional p-type doping in SiGe QWs [97B2]. They observed that the quantum confinement enhances the renormalization effect due to the intrasubband transition. In addition, the lattice dynamics in SiGe/Si QWs, Si/Ge superlattices, and Ge islands embedded in Si have been investigated to clarify the impact on the optical confinement [94S2, 94S3], internal strain [84C1, 92L2, 96S1], partial strain relaxation [99Z1, 02C1], and external stress [01Q1] in Ge islands.

Landolt-Börnstein New Series III/34C3

3.3 Single and coupled quantum wells: SiGe

46

[Ref. p. 47

3.3.19 Cyclotron resonance Cyclotron resonance measurements were performed for modulation-doped strained Si/SiGe MQWs [91S2]. The samples consist of five strained Si QWs embedded in 25 nm wide Si0.5Ge0.5 barriers on strain relaxed Si0.7Ge0.3. The center of 5 nm of the barriers was doped with Sb. Fig. 3.3.31 shows the experimental curves and fitted ones with a classical line shape measured for QWs with a well width of 7.5 nm. The measured cyclotron mass varied between 0.195 m 0 ... 0.21 m 0. This supports the view that the electrons occupy the twofold degenerated conduction band minima with an in-plane effective mass of meff = 0.19 m 0. The effect of strain on the effective mass in the strained Si channels of two-dimensional gases was investigated [98G1]. Plots of resonant frequencies against the magnetic field showed straight lines as expected by the cyclotron frequency Ȧc = eB/m*, where B and m* are the magnetic field and the effective mass, respectively. However, most of the fitted lines did not pass the origin. This phenomenon was explained by a zero-dimensional confinement, leading to the dispersion which can fit the experimental data. The extracted effective masses were approximately 0.196 m 0, and are independent of the strain. The zero-dimensional confinement originates from the electron localization owing to the in-plane inhomogeneous strain relaxation. Furthermore, the linewidth was found to be dependent on the carrier density and the filling of the quantized Landau level [93M1], and the effective mass is also dependent on the filling factor [01I1]. Hole Landau levels are more complicated due to the complex valence band structures. Fig. 3.3.32 shows cyclotron resonance of holes in strained 7.5 nm Ge layers between asymmetric Si1–xGex barriers with x = 0.5 and x = 0.7 [94E1]. To account for all relevant features, self-consistent hole subband calculations are necessary based on a 6×6 k·p Hamiltonian including coupling of ī8 and ī7 states. It is important to consider the effect of the strain originating from the lattice mismatch and the coupling to the split-off band [96W1]. 120

Si/Si1-x Gex MQW

L = 7.5 nm

Ge /Si1-x Gex

T = 1.2 K

C1072

B = 6T

B = 14T

12 10 8

Magnetic field B [ T ]

80

14

Absorption ( _ DT/T )

Transmission [%]

16

100

60 20

40 60 80 -1 Wavenumber n [cm ]

100

120

Fig. 3.3.31. Cyclotron resonance of electrons in strained Si/SiGe QWs [91S2].

6 10 %

4 20

40

60 80 100 120 140 160 180 Wavenumber n [cm-1]

Fig. 3.3.32. Cyclotron resonance of holes in strained Ge/SiGe QWs [94E1]. Absorption is measured as a relative change in transmission T.

Landolt-Börnstein New Series III/34C3

3.3.20 References for 3.3

47

3.3.20 References for 3.3 58B1 61F1 66F1 68P1 72C1 74J1 75B1 81O1 84C1 85A1 85P1 86V1 87F1 88M1 89A1 89C1 89V1 89W1 90F1 90K1 91F1 91H1 91S1 91S2 92F1 92F2 92F3 92F4 92L1 92L2 92M1 92P1 92P2 92U1 92V1 92X1 93E1

Braunstein, R., Moore, A.R., Herman, F.: Phys. Rev. 109 (1958) 695. Fano, U.: Phys. Rev. 124 (1961) 1864. Feldman, D.W., Ashkin, M., Parker jr., J.H.: Phys. Rev. Lett. 17 (1966) 1209. Pollak, F.H., Cardona, M.: Phys. Rev. 172 (1968) 816. Cerdeira, F., Buchenauer, C.J., Pollak, F.H., Cardona, M.: Phys. Rev. B 5 (1972) 580. Jouanne, M., Beserman, R., Balkanski, M., Jain, K.P.: Solid State Commun. 15 (1974) 255. Balkanski, M., Jain, K.P., Beserman, R., Jouanne, M.: Phys. Rev. B 12 (1975) 4328. Olego, D., Cardona, M.: Phys. Rev. B 23 (1981) 6592. Cerdeira, F., Pinczuk, A., Bean, J.C., Batlogg, B., Wilson, B.A.: Appl. Phys. Lett. 45 (1984) 1138. Austin, E.J., Jaros, M.: Phys. Rev. B 31 (1985) 5569. People, R.: Phys. Rev. B 32 (1985) 1405. van de Walle, C.G., Martin, R.M.: Phys. Rev. B 34 (1986) 5621. Feldmann, J., Peter, G., Göbel, E.O., Dawson, P., Moore, K., Foxon, C., Elliot, R.J.: Phys. Rev. Lett. 59 (1987) 2337. Menéndez, J., Pinczuk, A., Bevk, J., Mannaerts, J.P.: J. Vac. Sci. Technol. B 6 (1988) 1306. Alonso, M.I., Winer, K.: Phys. Rev. B 39 (1989) 10056. Copel, M., Reuter, C., Kaxiras, E., Tromp, R.M.: Phys. Rev. Lett. 63 (1989) 632. van de Walle, C.G.: Phys. Rev. B 39 (1989) 1871. Weber, J., Alonso, M.I.: Phys. Rev. B 40 (1989) 5683. Fujita, K., Fukatsu, S., Yaguchi, H., Igarashi, T., Shiraki, Y., Ito, R.: Jpn. J. Appl. Phys. 29 (1990) L1981. Karunasiri, R.P.G., Park, J.S., Mii, Y.J., Wang, K.L.: Appl. Phys. Lett. 57 (1990) 2585. Fukatsu, S., Fujita, K., Yaguchi, H., Shiraki, Y., Ito, R.: Appl. Phys. Lett. 59 (1991) 2103. Hertle, H., Schuberth, G., Gornik, E., Abstreiter, G., Schäffler, F.: Appl. Phys. Lett. 59 (1991) 2977. Sturm, J.C., Monoharan, H., Lenchyshyn, L.C., Thewalt, M.L., Rowell, N.L., Nöel, J.-P., Houghton, D.C.: Phys. Rev. Lett. 66 (1991) 1362. Schuberth, G., Schäffler, F., Besson, M., Abstreiter, G., Gornik, E.: Appl. Phys. Lett. 59 (1991) 3318. Fukatsu, S., Yoshida, H., Usami, N., Fujiwara, A., Takahashi, Y., Shiraki, Y., Ito, R.: Jpn. J. Appl. Phys. 31 (1992) L1319. Fukatsu, S., Yoshida, H., Usami, N., Fujiwara, A., Takahashi, Y., Shiraki, Y., Ito, R.: Thin Solid Films 222 (1992) 1. Fukatsu, S., Yoshida, H., Fujiwara, A., Takahashi, Y., Shiraki, Y., Ito, R.: Appl. Phys. Lett. 61 (1992) 804. Fujita, K., Fukatsu, S., Shiraki, Y., Yaguchi, H., Ito, R.: Appl. Phys. Lett. 61 (1992) 210. Lenchyshyn, L.C., Thewalt, M.L.W., Sturm, J.C., Schwartz, P.V., Prinz, E.J., Rowell, N.L., Nöel, J.-P., Houghton, D.C.: Appl. Phys. Lett. 60 (1992) 3174. Lockwood, D.J., Baribeau, J.-M.: Phys. Rev. B 45 (1992) 8565. Mi, Q., Xiao, X., Sturm, J.C., Lenchyshyn, L.C., Thewalt, M.L.W.: Appl. Phys. Lett. 60 (1992) 3177. Park, J.S., Karunasiri, R.P.G., Wang, K.L.: Appl. Phys. Lett. 60 (1992) 103. Park, J.S., Karunasiri, R.P.G., Wang, K.L.: Appl. Phys. Lett. 61 (1992) 681. Usami, N., Fuktasu, S., Shiraki, Y.: Appl. Phys. Lett. 61 (1992) 1706. Vescan, L., Hartmann, A., Schmidt, K., Dieker, Ch., Lüth, H., Jäger, W.: Appl. Phys. Lett. 60 (1992) 2183. Xiao, X., Liu, C.W., Sturm, J.C., Lenchyshyn, L.C., Thewalt, M.L.W., Gregory, R.B., Fejes, P.: Appl. Phys. Lett. 60 (1992) 2135. Engvall, J., Olajos, J., Grimmeis, H.G., Presting, H., Kibbel, H., Kasper, E.: Appl. Phys. Lett. 63 (1993) 491.

Landolt-Börnstein New Series III/34C3

48 93F1 93F2 93L1 93M1 93N1 93N2 93S1 93S2 93U1 94E1 94S1 94S2 94S3 94T1 95B1 95F1 95F2 95G1 95H1 95S1 95S2 95S3 95S4 95U1 95W1 95Z1 95Z2 96B1 96F1 96L1 96M1 96S1 96U1

3.3.20 References for 3.3 Fukatsu, S., Shiraki, Y.: Appl. Phys. Lett. 63 (1993) 2378. Fukatsu, S., Usami, N., Shiraki, Y., Nishida, A., Nakagawa, K.: J. Cryst. Growth 127 (1993) 1083. Lenchyshyn, L.C., Thewalt, M.L.W., Houghton, D.C., Noël, J.-P., Rowell, N.L., Sturm, J.C., Xiao, X.: Phys. Rev. B 47 (1993) 16655. Murphy, S.Q., Schlesinger, Z., Nelson, S.F., Chu, J.O., Meyerson, B.S.: Appl. Phys. Lett. 63 (1993) 222. Nayak, D.K., Usami, N., Sunamura, H., Fukatsu, S., Shiraki, Y.: Jpn. J. Appl. Phys. 32 (1993) L1391. Nayak, D.K., Usami, N., Fukatsu, S., Shiraki, Y.: Appl. Phys. Lett. 63 (1993) 3509. Steiner, T.W., Lenchyshyn, L.C., Thewalt, M.L.W., Houghton, D.C., Noël, J.-P., Rowell, N.L., Sturm, J.C., Xiao, X.: Mater. Res. Soc. Symp. Proc. 298 (1993) 15. Sunamura, H., Fukatsu, S., Usami, N., Shiraki, Y.: Appl. Phys. Lett. 63 (1993) 1651. Usami, N., Fukatsu, S., Shiraki, Y.: Appl. Phys. Lett. 63 (1993) 388. Engelhardt, C.M., Többen, D., Aschauer, M., Schäffler, F., Abstreiter, G., Gornik, E.: Solid-State Electron. 37 (1994) 949. Steiner, T.W., Lenchyshyn, L.C., Thewalt, M.L.W., Houghton, D.C., Noël, J.-P., Rowell, N.L.: Solid State Commun. 89 (1994) 429. Seto, M., Helm, M., Moussa, Z., Boucaud, P., Julien, F.H., Lourtioz, J.-M., Nützel, J.F., Abstreiter, G.: Appl. Phys. Lett. 65 (1994) 2969. Schorer, R., Abstreiter, G., de Gironcoli, S., Molinari, E., Kibbel, H., Presting, H.: Phys. Rev. B 49 (1994) 5406. Tsang, J.C., Mooney, P.M., Dacol, F., Chu, J.O.: J. Appl. Phys. 75 (1994) 8098. Boucaud, P., Gao, L., Moussa, Z., Visocekas, F., Julien, F.H., Lourtioz, J.-M., Sagnes, I., Campidelli, Y., Badoz, P.-A.: Appl. Phys. Lett. 67 (1995) 2948. Fukatsu, S., Shiraki, Y.: J. Cryst. Growth 150 (1995) 1025. Fukatsu, S., Akiyama, H., Shiraki, Y., Sakaki, H.: J. Cryst. Growth 157 (1995) 1. Gail, M., Brunner, J., Nützel, J., Abstreiter, G., Engvall, J., Olajos, J., Grimmeiss, H.: Semicond. Sci. Technol. 10 (1995) 319. Houghton, D.C., Aers, G.C., Eric Yang, S.-R., Wang, E., Rowell, N.L.: Phys. Rev. Lett. 75 (1995) 866. Souifi, A., Benyattou, T., Guillot, G., Brémond, G., Dutartre, D., Warren, P.: J. Appl. Phys. 78 (1995) 4039. Sunamura, H., Shiraki, Y., Fukatsu, S.: Appl. Phys. Lett. 66 (1995) 953. Sunamura, H., Fukatsu, S., Usami, N., Shiraki, Y.: Appl. Phys. Lett. 66 (1995) 3024. Schittenhelm, P., Gail, M., Brunner, J., Nützel, J.F., Abstreiter, G.: Appl. Phys. Lett. 67 (1995) 1292. Usami, N., Issiki, F., Nayak, D.K., Shiraki, Y., Fukatsu, S.: Appl. Phys. Lett. 67 (1995) 524. Wu, L., Boucaud, P., Lourtioz, J.-M., Julien, F.H., Sagnes, I., Campidelli, Y., Badoz, P.-A.: Appl. Phys. Lett. 67 (1995) 3462. Zeindl, H.P., Nilsson, S., Klatt, J., Krüger, D., Kurps, R.: J. Cryst. Growth 157 (1995) 31. Zrenner, A., Fröhlich, B., Brunner, J., Abstreiter, G.: Phys. Rev. B 52 (1995) 16608. Buyanova, I.A., Chen, W.M., Henry, A., Ni, W.-X., Hansson, G.V., Monemar, B.: Phys. Rev. B 53 (1996) R1701. Förster, M., Mantz, U., Ramminger, S., Thonke, K., Sauer, R., Kibbel, H., Schäffler, F., Herzog, H.-J.: J. Appl. Phys. 80 (1996) 3017. Lafontaine, H., Houghton, D.C., Rowell, N.L., Aers, G.C.: Appl. Phys. Lett. 69 (1996) 1444. Miyake, Y., Kim, J.Y., Shiraki, Y., Fukatsu, S.: Appl. Phys. Lett. 68 (1996) 2097. Stoehr, M., Aubel, D., Juillaguet, S., Bischoff, J.L., Kubler, L., Bolmont, D., Hamdani, F., Fraisse, B., Fourcade, R.: Phys. Rev. B 53 (1996) 6923. Usami, N., Shiraki, Y., Fukatsu, S.: Appl. Phys. Lett. 68 (1996) 2340.

Landolt-Börnstein New Series III/34C3

3.3.20 References for 3.3 96W1 97B1 97B2 97D1 97K1 97T1 97Z1 98G1 98K1 98K2 99Z1 00L1 00N1 00S1 01I1 01K1 01Q1 02C1 02L1 02V1 03S1 03S2

49

Winkler, R., Merkler, M., Darnhofer, T., Rössler, U.: Phys. Rev. B 53 (1996) 10858. Buyanova, I.A., Chen, W.M., Pozina, G., Monemar, B., Ni, W.-X., Hansson, G.V.: Appl. Phys. Lett. 71 (1997) 3676. Bendayan, M., Baserman, R., Dettmer, K.: J. Appl. Phys. 81 (1997) 7956. Dekel, E., Ehrenfreund, E., Gershoni, D., Boucaud, P., Sagnes, I., Campidelli, Y.: Phys. Rev. B 56 (1997) 15734. Kim, E.S., Usami, N., Shiraki, Y.: Appl. Phys. Lett. 70 (1997) 295. Thewalt, M.L.W., Harrison, D.A., Reinhart, C.F., Wolk, J.A., Lafontaine, H.: Phys. Rev. Lett. 79 (1997) 269. Zhang, X., Chen, Z., Xuan, L., Pan, S., Yang, G.: Phys. Rev. B 56 (1997) 15842. Griffin, N., Arnone, D.D., Paul, D.J., Pepper, M., Robbins, D.J., Churchill, A.C., Fernández, J.M.: J. Vac. Sci. Technol. B 16 (1998) 1655. Kim, J.Y.: Thin Solid Films 321 (1998) 215. Kim, E.S., Usami, N., Shiraki, Y.: Appl. Phys. Lett. 72 (1998) 1617. Zhu, J., Miesner, C., Brunner, K., Abstreiter, G.: Appl. Phys. Lett. 75 (1999) 2395. Li, C., Yang, Q., Wang, H., Wei, H., Yu, J., Wang, Q.: J. Appl. Phys. 87 (2000) 8195. Naveed, A.T., Evans-Freeman, J.H., Vernon-Parry, K.D., Wright, A.C., Houghton, D.C., Peaker, A.R.: Semicond. Sci. Technol. 15 (2000) 91. Schmidt, O.G., Eberl, K.: Phys. Rev. B 61 (2000) 13721. Ikaida, T., Miura, N., Shiraki, Y., Imanaka, Y., Takehana, K., Kido, G.: Physica B 298 (2001) 505. Kawaguchi, K., Shiraki, Y., Usami, N., Zhang, J., Woods, N.J., Breton, G., Parry, G.: Appl. Phys. Lett. 79 (2001) 344. Qin, L., Teo, K.L., Shen, Z.X., Peng, C.S., Zhou, J.M.: Phys. Rev. B 64 (2001) 075312. Cazayous, M., Groenen, J., Demangeot, F., Sirvin, R., Caumont, M., Remmele, T., Albrecht, M., Christiansen, S., Becker, M., Strunk, H.P., Wawra, H.: J. Appl. Phys. 91 (2002) 6772. Li, C., Huang, C.J., Cheng, B., Zuo, Y., Luo, L., Yu, J., Wang, Q.: J. Appl. Phys. 92 (2002) 1718. Vescan, L., Stoica, T.: J. Appl. Phys. 91 (2002) 10119. Sheng, S.R., Rowell, N.L., McAlister, S.P.: Appl. Phys. Lett. 83 (2003) 857. Stoica, T., Vescan, L.: Semicond. Sci. Technol. 18 (2003) 409.

Landolt-Börnstein New Series III/34C3

3.4 Optical properties of Si/Ge superlattices

50

3.4

[Ref. p. 86

Optical properties of Si/Ge superlattices by G. Theodorou and E. Kasper

3.4.1 Introduction In 1974 Gnutzman and Clausecker [74G] made the theoretical prediction that the imposition of a proper new periodicity in an indirect-gap semiconductor will fold the bands and could bring the minimum of the conduction band to the ī-point of the Brillouin zone (BZ), thus producing a direct-gap material. Si is such an indirect-gap semiconductor with the minimum of the conduction band along the ǻ direction and at about 80% of the īX distance from the ī point of the BZ. The imposition of a new periodicity of five times the original one, along the [001] direction, would bring the conduction band minimum to the ī point. The appropriate modification of the lattice periodicity could be achieved by the construction of Si/Ge superlattices (SLs) [86K, 87F, 87H, 88F, 88S, 89F, 89P1, 89P2, 89P3, 90T, 90Z, 91S, 93E, 93T]. The lattice constants of bulk Si and Ge differ by 4.2%. The epitaxy of Si/Ge SLs results either in a strained-layer configuration with the layers coherently grown on the substrate, if they are sufficiently thin, or in strain relaxation basically by a misfit dislocation network [87K, 90J]. The critical thickness for Ge (Si) films coherently grown on a Si(001) (Ge(001)) substrate is about 4 to 6 monolayers (MLs). In addition, a second overall critical thickness exists, that is equal to the total thickness of the superlattice, beyond which the material again partly relaxes by forming misfit dislocations. For (Si)6/(Ge)4 SLs, coherently grown on a Si(001) substrate, the critical total thickness is about 20 nm [90K]. In order to remove the second restriction of the critical total thickness, Kasper et al. [86K] suggested the idea of strain-symmetrized or free-standing SLs. According to this idea, SLs are grown on a properly chosen substrate so that stresses in neighboring layers balance each other and the SL could stand alone after growth, since no external stress is applied to it by the substrate. In particular, a strain-symmetrized (Si)m/(Ge)n SL could be obtained by growth on an alloy Si1–xGex(001) substrate with x = n/(m + n) [86V]. In this and the following subsections we are going to review the electronic properties of strained SLs, for which the layer lattice constant parallel to the interface, a||, is equal to that of the substrate which is considered to be rigid, while that perpendicular to it, a⊥, is given to a very good approximation by the elastic theory [86V, 87F, 88F, 90C, 93K], and is equal to B

B

B

B

B

B

B

P

B

P

B

B

B

B

P

P

§ § a& · · ai⊥ = ai ¨1 − Di ¨ − 1¸ ¸ , © ai ¹¹ ©

(3.4.1)

with D i = 2 c1i2 /c1i1, and c1i1, c1i2 the bulk elastic constants and ai the lattice constant of the i (Si or Ge) material. Finally, the interlayer distance between Si and Ge atomic layers at the heterostructure interface is found to be very close to the mean value of the intralayer distance between atomic layers in the distorted materials [87F, 88F, 90C, 93K]. The room temperature values of the elastic constants are given in Table 3.4.1. P

P

B

PB PB

B

B

PB PB

B

B

PB PB

B

B

PB PB

B

B

B

Table 3.4.1. Room temperature elastic constants of Si and Ge [89V].

c11 [Mbar]

c12 [Mbar]

Si

1.675

650

Ge

1.315

494

B

B

B

B

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

51

The band alignments between Si and Ge are such that the highest valence band is that of Ge and the lowest conduction band that of Si [86V]. This type of band alignment is called type II, and implies that in a Si/Ge SL the highest valence band has mostly a Ge-like character and the lowest conduction band mostly a Si-like character. In order to obtain a direct-gap material the conduction band minimum along the ǻ line, in the growth plane, must be shifted, besides folding, to energies higher than those along the growth axis. This can be achieved by straining the Si layers in the growth plane and thus splitting the Si-like six-fold degenerate conduction band minimum into a two-fold degenerate minimum ǻz along the growth axis and a four-fold degenerate minimum ǻxy in the growth plane. Stretching (compressing) the Si layers in the growth plane reduces (increases) the energy of the ǻz minimum relative to that of the ǻxy minimum [93T]. From the above discussion it is concluded that the coherent growth of a (Si)m/(Ge)n SL with m + n = 10, on a Si1–xGex(001) substrate rich in Ge, is most likely to produce a direct-gap material. B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

3.4.2 The empirical tight-binding model Most of the theoretical results that will be presented in this review were obtained by the use of an Empirical Tight Binding (ETB) model Hamiltonian with an sp3 set of orbitals, including spin-orbit interaction [93T]. The three-center representation and interactions up to the third neighbor were used in this model in order to obtain a good description of both the valence and lower conduction bands. The tight-binding parameters for the unstrained materials (bulk Si and Ge) were obtained by fitting existing bands [76C, 93T], and are given in Table 3.4.2. For strained materials the modification of the above tight-binding parameters, produced by a change in the distance between the atoms, was taken into account by the scaling formula [93T] P

§ d· H α ,β ( d ) = H α ,β ( d 0 ) ¨ ¸ © d0 ¹

P

Ȟα , β

,

(3.4.2)

with Į, ȕ representing atomic orbitals and d0, d the unstrained and strained interatomic distances, respectively. B

B

3.4.2.1 Uniaxial strain along the [001] direction

Uniaxial strain along the [001] direction lifts the degeneracy between px, py and pz orbitals. The latter modification is taken into account by the linear formulae B

B

B

B

B

B

x,y

Ep = Ep + bp (İ|| í İ⊥),

(3.4.3)

P

B PB

B

B

B

B

B

B

B

B

z

Ep = Ep í 2 bp (İ|| í İ⊥),

(3.4.4)

P

B PB

B

x,y Ep

B

B

B

B

B

B

B

z Ep

where and are the on-site p-orbital integrals and İ|| and İ⊥ the strain components parallel and perpendicular to the growth plane. The values for the scaling indices ȞĮ,ȕ and the orbital splitting parameter bp were determined in such a way as to obtain the best values for the ī point deformation potentials. The obtained values of the above parameters are given in Table 3.4.3 [93T]. For the calculations in the ETB model of electronic and optical properties of a (Si)m/(Ge)n SL, the valence band offset (VBO) between strained Si and Ge is also needed. The VBO between strained Si and Ge, coherently grown on a Si1–xGex(001) alloy substrate, is given by [86V] P

P

B PB

B PB

B

B

B

B

B

B

B

B

B

B

B

Si

B

Ge

P

B

B

PB

B

(3.4.5 a)

P

B

B

B

¨Ev(x) = (1-x) ¨Ev + x ¨Ev , B

B

PB

Si ¨Ev

= 0.84 eV is the VBO for growth on Si, and where x is the concentration of Ge in the buffer alloy, Ge ¨Ev = 0.31 eV the corresponding value for growth on Ge. P

B

P

B

PB

Landolt-Börnstein New Series III/34C3

PB

3.4 Optical properties of Si/Ge superlattices

52

[Ref. p. 86

Table 3.4.2. Tight binding interaction parameters [in eV] of Si and Ge (the notation is that of Slater-Koster) [93T].

Silicon

Germanium

Ess (0, 0, 0)

–6.3193

–7.2114

Epp (0, 0, 0)

 2.2494

 1.6376

Ess (0.25, 0.25, 0.25)

–1.8376

–1.3711

Esx (0.25, 0.25, 0.25)

 1.0087

 0.9127

Exx (0.25, 0.25, 0.25)

 0.3209

 0.2979

Exy (0.25, 0.25, 0.25)

 1.4889

 1.2935

Ess (0.5, 0.5, 0.0)

 0.1940

 0.1150

Esx (0.0, 0.5, 0.5)

–0.0395

 0.0250

Esx (0.5, 0.5, 0.0)

–0.1840

–0.0724

Exx (0.5, 0.5, 0.0)

 0.0626

 0.0710

Exx (0.0, 0.5, 0.5)

–0.2646

–0.1683

Exy (0.5, 0.5, 0.0)

–0.0378

–0.0748

Exy (0.0, 0.5, 0.5)

–0.0829

–0.1298

Ess (0.75, 0.25, 0.25)

–0.0674

–0.1036

Esx (0.75, 0.25, 0.25)

 0.2717

 0.1710

Esx (0.25, 0.25, 0.75)

–0.1262

–0.0432

Exx (0.75, 0.25, 0.25)

 0.0869

 0.1287

Exx (0.25, 0.25, 0.75)

 0.0094

–0.0092

Exy (0.75, 0.25, 0.25)

 0.0152

–0.0076

Exy (0.25, 0.25, 0.75)

 0.0952

 0.0659

Ȝso

 0.0150

 0.1000

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

Table 3.4.3. Values for the scaling indices ȞĮ,ȕ and the orbital splitting parameter bp, defined in Eqs. (3.4.2) … (3.4.4) [93T]. B

Ȟs,s B

B

Ȟs,p , Ȟp, p

bp [eV]

B

B

B

B

B

B

B

B

B

Si

3

1.8

2.0

Ge

3

1.8

1.0

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

53

3.4.2.2 Uniaxial strain along the [111] direction

The VBO between the topmost valence band states of strained Si and Ge, coherently grown on Si Ge Si1–xGex(111) alloy substrate, has been introduced by the interpolation between the values ¨Ev and ¨Ev , the VBO for growth on Si(111) and on Ge(111) substrates respectively, P

B

B

B

B

B

Si

P

PB

B

Ge

¨Ev(x) = (1-x) ¨Ev + x ¨Ev , P

B

B

B

(3.4.5 b)

P

PB

B

PB

PB

Si

Ge

with x is the concentration of Ge in the buffer. The values for the parameters ¨Ev and ¨Ev are taken Si Ge equal to ¨Ev = 0.85 eV and ¨Ev = 0.37 eV [86V]. P

B

P

B

P

PB

B

PB

P

PB

B

PB

3.4.2.3 Optical properties

The imaginary part İ2(Ȧ) of the dielectric function was calculated by the use of the relation [72W] B

ε 2 (ω ) =

4ʌ 2 e 2 m 2ω 2

B

2

k, c | P ⋅ a | k, v

¦ (2ʌ)3

2

δ ( Ecv (k ) – =ω ) dk ,

(3.4.6)

c,v

where in SI units have been used, | k , c ² and | k ,v ² stand for the wavefunctions of the conduction (c) and the valence (v) bands respectively, and Ecv(k) for the energy difference between the conduction and the valence band. P is the momentum operator and a the polarization unit vector. In the present ETB scheme the momentum matrix elements were expressed in terms of the Hamiltonian matrix elements and distances between localized orbitals [79S, 83B, 94T1]. The integration in the Brillouin zone (BZ) was performed within the linear analytic tetrahedron method [71J, 72L]. The real part İ1(Ȧ) of the dielectric function was obtained from İ2(Ȧ) by the use of the Kramers-Kronig relations. The above calculations for the optical properties do not take into account many body effects, like electron-phonon and electron-electron interactions; therefore the exciton contribution is not taken into account in the present model. B

B

B

B

B

B

3.4.3 Si/Ge SLs grown along the [001] direction 3.4.3.1 Electronic properties

Fig. 3.4.1 shows the band structure of a strain-symmetrized (Si)5/(Ge)5 SL [93T], along symmetry lines of the BZ for the tetragonal D2d crystal structure of the material. The band structure reveals a direct-gap material with a gap equal to 0.75 eV. d i Fig. 3.4.2 shows the calculated variation for the direct (Eg) and indirect (Eg (¨xy)) gaps of a (Si)5/(Ge)5 SL, coherently grown on a Si1–xGex(001) alloy substrate, as a function of Ge content x in the alloy [93T]. The direct gap is going down with x, while the indirect one is going up, and for x > ~ 0.2, the material becomes a direct-gap material. These results indicate that a (Si)m/(Ge)n SL with m + n = 10, coherently grown on a Si1–xGex (001) alloy substrate rich in Ge, produces a direct-gap material [93T]. Experimental and theoretical results for the band gaps of strain-symmetrized (Si)n/(Ge)n SLs and for different superlattice half-periods n are given in Fig. 3.4.3. Note the much weaker dependence of absorption measurements on the superlattice period, compared to either photoconductivity measurements or theory, which shows the strongest variation. B

B

B

B

B

B

P

B PB

B

B

B

B

B

B

B

B

PB

P

B

B

B

B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

B

B

B

B

B

3.4 Optical properties of Si/Ge superlattices

54

[Ref. p. 86

4

2

Energy E [eV]

(Si)5 /(Ge)5

Dxy

0

-2

-4

G

N

G

X P Wavevector k

Z

Fig. 3.4.1. Band structure of a strain-symmetrized (Si)5/(Ge)5 SL [93T], showing a direct gap at ī. B

B

B

(Si)5 /(Ge)5

1.0

Energy E [eV]

B

0.8

0.6 i

Eg (Dxy) Eg

d

Fig. 3.4.2. Calculated variation for the direct and indirect gaps of a (Si)5/(Ge)5 SL, pseudomorphically grown on a Si1–xGex (001) alloy substrate, as a function of the Ge content x in the alloy [93T]. B

0.4

B

0

0.2 0.4 0.6 0.8 Ge content x (substrate Si1-x Gex )

1.0

B

B

B

B

B

B

In addition, experimental results by Zachai et al. [90Z] for strain-symmetrized (Si)6/(Ge)4 SLs reported strong photoluminescence close to 0.84 eV. This peak was attributed to a fundamental quasidirect gap. Theoretical calculations [93T] predicted that the ideal SL is an almost-direct gap material i d with indirect and direct gaps equal to Eg = 0.80 eV and Eg = 0.81 eV, respectively. The calculated values for ideal SLs are smaller than those obtained by experiment, most probably because the calculated values were obtained for an ideal SL, while the sample used in the experiment probably deviates from the ideal structure. B

P

B

BP

B

B

B

P

B BP

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

55

1.0

(Si)n /(Ge)n

Energy gap Eg [eV]

0.9

0.8

Fig. 3.4.3. Experimental and theoretical results for the band gap of strain-symmetrized (Si)n/(Ge)n SLs for different superlattice half-periods (n). The calculated values [93T] are designated by the closed circles (Ɣ), with the dotted line intended to guide the eye. The experimental results were derived from photoconductivity measurements [98P] (open circles), absorption measurements [98P] (open triangles), and photoconductivity and absorption measurements [92O] (open squares). B

0.7

0.6

0.5 1

2

4

3

5 n

7

6

8

9

B

B

B

For a finite asymmetrically strained (Si)4/(Ge)4 SL on Si, measurements were performed on a sample with a five period SL embedded in Si [87P], and energy structures in electroreflectance spectra were observed at 0.76, 1.03, and 1.23 eV. A second set of experimental values, using the photocurrent technique [88H], found the lowest transitions at 0.78 and 0.90 eV, attributing an indirect character to them. Theoretical results [93T] for the infinite SL on Si gave transition energies at the ī point equal to 1.09 and 1.20 eV, but with small transition probabilities, two to three orders of magnitude smaller than that of a typical E0 bulk-like transition. These transition energies differ significantly from the experimental value of 0.76 eV. On the other hand, theory also predicts that the infinite (Si)4/(Ge)4 SL is an indirect-gap material [93T] with the calculated gap equal to 0.80 eV, relatively close to the experimental value of 0.76 eV. Also, theoretical calculations for a finite crystal [92P1] revealed that the lowest direct transitions with appreciable probabilities appear at 1.1 eV and 1.21 eV, close to the corresponding experimental values. Finally, measurements were performed [89P1] for a finite (Si)4/(Ge)6 SL, grown on a Ge(001) substrate and consisting of a five-period SL separated by a Ge spacer of about 20 nm thickness, yielding transition energies at 0.88, 0.96, 1.18, and 1.22 eV. The transition energies at 0.88 eV and 1.18 eV were attributed to the E0 and E0 + ¨0 structure of the substrate, and the rest to SL transitions. Subsequent piezoreflectance measurements on the same structure [91Y] led to the conclusion that the observed structures (with the exception of those related to the substrate) result from transitions in the Ge spacer and not the SL. For a Ge spacer of 78 monolayers, the lower transitions occur at 0.947 eV and 0.967 eV, while for 127 monolayers the former values become 0.915 eV and 0.926 eV, respectively. In agreement with their interpretation, the transition energies go down with the increase of the width of the spacer. Theoretical calculations [92P1] for the finite SL [(Si)4/(Ge)4]5/(Ge)48 support this interpretation. More precisely, the calculations predict the lower transitions with appreciable probabilities to be localized in the Ge spacer, and to occur at 0.99 eV and 1.01 eV. B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

3.4.3.2 Optical properties

Fig. 3.4.4 shows the calculated [94T1] dielectric function of strain-symmetrized (Si)5/(Ge)5 SL, for polarization parallel and perpendicular to the growth plane. For comparison is also given the dielectric function for unstrained (bulk) Si0.5Ge0.5 alloy [94T2]. From these results for the SL, the existence of a significant polarization anisotropy is evident for energies up to the critical point E2, that diminishes at higher energies. In the low-energy spectrum, between the energy gap of the SL, equal to 0.75 eV, and about ≈2 eV, the imaginary part of the dielectric function for the SL is very small. B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

B

B

B

3.4 Optical properties of Si/Ge superlattices

56

[Ref. p. 86

60

(Si)5 /(Ge)5

II

E2

T

50

Alloy Dielectric constants e1, e2

40 30 e2

20 10 0

e1

Fig. 3.4.4. Calculated dielectric function for strainsymmetrized (Si)5/(Ge)5 SL, for polarization parallel ( || ) and perpendicular ( ⊥ ) to the growth plane [94T1]. In the same figure is also shown the dielectric function of the unstrained (bulk) Si0.5Ge0.5 alloy [94T2].

-10 -20

B

1

4 5 3 Photon energy h w [eV]

2

7

6

B

B

B

B

B

B

B

Fig. 3.4.5 shows, in the above region, the imaginary part of the dielectric function for the above SL. The latter results implies that in this SL, the transition probabilities from states near the top of the valence to those close to the bottom of the conduction band, at the ī point, are very small [94T1]. 0.03

0.02 II T

Dielectric constant e2

(Si)5 /(Ge)5

0.01

0 0.6

Fig. 3.4.5. Calculated imaginary part of the dielectric function, close to the gap, for the strain-symmetrized (Si)5/(Ge)5 SL, and polarization parallel ( ||) and perpendicular ( ⊥ ) to the growth plane [94T1]. B

0.8

1.4 1.0 1.2 1.6 Photon energy h w [eV]

1.8

2.0

B

B

B

Calculated values for the transition matrix elements between the upper valence and lower conduction bands for strain-symmetrized (Si)m/(Ge)n SLs with m + n = 10 and polarization parallel and perpendicular to the interface plane are presented in Table 3.4.4 [95T1]. For polarization in the growth plane, the lowest V1–C1 transition is allowed for m =3, 5, 6, 7, and is characterized by a transition probability about three orders of magnitude lower than the typical average crystal E0 like transition. For polarization perpendicular to the growth plane, the lowest V1–C1 transition is allowed only for m = 6, and 7, and the transition probability is about five orders of magnitude lower than the typical average crystal E0 like transition [94T1]. The reason for that lies in the fact that for Si/Ge SLs the lowest conduction states at ī are produced by folding of the Si-like conduction band minimum along the ¨z direction. For a Si like crystal, indirect transitions from the top of the valence to the bottom of the conduction band along the ¨ line are forbidden (in the absence of electron-phonon interaction), because of momentum conservation. Superlattice periodicity produces folding of the zones and brings the conduction band minimum from the ¨ line to the ī point. In addition, the superlattice potential makes the transitions from the top of the B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

57

valence band to the folded conduction states allowed, but with a small transition probability. In the case of (Si)4/(Ge)6 SL the V1–C1 transition is forbidden by symmetry for both polarizations, and the lowest allowed transition is the V1–C2 one, with an energy of 0.83 eV and a transition probability about two orders of magnitude smaller than that of the typical E0 transition. From Table 3.4.4 we also see that transition matrix elements are stronger for SLs richer in Ge. This result can be explained with the smaller band effective masses in Ge in comparison to these in Si. B

B

B

B

B

B

B

B

B

B

B

B

B

B

Table 3.4.4. Calculated transition matrix elements, | M c v | 2 in units of (h/aSi)2, for the lowest transitions V1–C1 and V1–C2 at the Γ point of the BZ for the strain-symmetrized (Si)m/(Ge)n SLs, and light polarization parallel and perpendicular to the growth axis [95T1]. B

B

B

B

B

B

B

B

B

P

P

B

B

B

P

P

B

|| 2 P

B

T

P

P

P

P

T

m/n

V1–C1

V1–C2

3/7 4/6 5/5 6/4 7/3

0.31 – 2.4 0.31 0.36

0.7 7.7 0.08 – 1.6

B

B

B

B

2

P

PB

B

⏐Mcv⊥⏐ [·103]

⏐Mcv⏐ [·103] T

B

B

B

B

B

B

B

PB

P

P

T

P

P

V1–C1

V1–C2

– – – 0.01 0.05

0.16 0.8 0.004 – –

B

B

B

B

B

B

B

B

Fig. 3.4.6 shows calculated values [94T3, 94T4] for the dielectric function of a (Si)6/(Ge)4 SL, coherently grown on a Si (001) substrate, as well as that of bulk Si. Since the (Si)6/(Ge)4 SL has an orthorhombic symmetry, there exists an anisotropy in the growth plane between the x and y axis. However, this anisotropy is negligible, and therefore, instead of separate values for İxx(Ȧ) and İyy(Ȧ), only the average value İxy(Ȧ) = (İxx(Ȧ) + İyy(Ȧ))/2 is given. Polarization perpendicular to the growth plane corresponds to İ z z ( Ȧ). For energies smaller than 1.5 eV, the real part İ1 of the superlattice dielectric function is larger than that for bulk Si for both polarizations. In particular, the difference is approximately equal to 0.5 for polarization parallel to the growth plane and 1.0 for polarization perpendicular to it. B

B

P

P

P

P

P

P

P

B

B

B

B

B

B

P

P

P

P

P

B

B

60

(Si)6 /(Ge)4 on Si (001)

II T

50

Si

Dielectric constants e1, e2

40 30 20

e2

10 0 -10 -20

Fig. 3.4.6. Calculated dielectric function [94T3, 94T4] for a (Si)6/(Ge)4 SL, pseudomorphically grown on a Si (001) substrate, for polarization parallel ( || ) and perpendicular ( ⊥ ) to the growth plane. In the same figure is also shown the dielectric function of bulk Si.

e1 2

6 4 Photon energy h w [eV]

B

8

B

B

B

Fig. 3.4.7 shows the calculated values [94T3, 94T4] of the refractive index for a (Si)6/(Ge)4 SL, coherently grown on a Si (001) substrate, as well as that of bulk Si. For polarization in the growth plane, the refractive index of the (Si)6/(Ge)4 SL is smaller than that for polarization perpendicular to the growth plane. In addition, the refractive index for bulk Si is smaller than the previously mentioned values for the SL, as can be expected from the higher values of İ1 mentioned above. B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

B

B

B

3.4 Optical properties of Si/Ge superlattices

58

[Ref. p. 86

4.0 II

(Si)6 /(Ge)4 on Si (001)

T Si

Refractive index n

3.8

3.6

3.4

Fig. 3.4.7. Calculated refractive index for a (Si)6/(Ge)4 SL, pseudomorphically grown on a Si (100) substrate, for polarizations parallel ( || ) and perpendicular ( ⊥ ) to the growth plane. In the same figure is also shown the refractive index of bulk Si [94T3, 94T4]. B

3.2 1.5 0.5 1.0 Photon energy h w [eV]

0

2.0

B

B

Fig. 3.4.8 shows the calculated values [94T3, 94T4] of the refractive index for the strain-symmetrized (Si)6/(Ge)4 SL, as well as that of the corresponding alloy Si0.6Ge0.4. For polarization perpendicular to the growth plane, the refractive index of the (Si)6/(Ge)4 SL is smaller than for polarization parallel to the growth plane. It is also important to note that for polarization perpendicular to the growth plane and energies smaller than 1.5 eV, the refractive index for the SL practically equals that of the alloy, i.e. nzz s = na. The reason for this coincidence can be understood as follows: polarization perpendicular to the growth plane forces the electrons to sample both Si and Ge layers, and therefore makes them “see” an effective potential similar to that of the corresponding alloy, implying equal refractive indexes for perpendicular polarization. B

B

B

B

B

B

PB

P

B

B

B

B

B

B

B

B

3.8

(Si)6 /(Ge)4 on Si 0.6 Ge0.4

3.7

II T

Refractive index n

Alloy 3.6

3.5 Fig. 3.4.8. Calculated refractive index for a (Si)6/(Ge)4 SL, pseudomorphically grown on a Si0.6Ge0.4 (001) substrate, and for polarizations parallel ( || ) and perpendicular ( ⊥ ) to the growth plane. In the same figure is also shown the refractive index of bulk Si0.6Ge0.4 alloy [94T3, 94T4]. B

3.4

B

3.3 0

0.5 1.0 Photon energy h w [eV]

1.5

B

B

B

B

B

B

B

B

B

Finally, Figs. 3.4.9(a, b) present results calculated [95T2] for the absorption coefficient for strain-symmetrized (Si)10–n/(Ge)n SLs, for polarization along the directions [100] and [001]. From these figures we obtain that the absorption coefficient increases slowly near the gap, and for an energy increase of 0.5 eV above the gap the absorption coefficient obtains the value about 400 cm–1 . Notice also that the absorption becomes stronger for strain-symmetrized (Si)10–n/(Ge)n SLs richer in Ge, that is for larger values of n. This is in agreement with the behavior of the transition matrix elements found before. B

B

B

B

P

B

P

B

B

B

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

59

800

(Si)6 /(Ge)4 (Si)5 /(Ge)5 (Si)4 /(Ge)6 E II [100]

400

200

0 0.6

0.8

a

1.4 1.0 1.2 Photon energy h w [eV]

(Si)6 /(Ge)4 (Si)5 /(Ge)5 (Si)4 /(Ge)6

-1

600

Absorption coefficient a [cm ]

-1

Absorption coefficient a [cm ]

800

1.6

600 E II [001] 400

200

0 0.6

1.8

1.4 1.0 1.2 Photon energy h w [eV]

0.8

b

1.6

1.8

Fig. 3.4.9. (a) Calculated absorption coefficient for strain-symmetrized (Si)10–n/(Ge)n SLs, for n = 4, 5, 6, and polarization along the direction [100]. (b) The same as in (a), but for polarization along the direction [001] [95T2]. B

B

B

B

3.4.3.3 Interface intermixing

Menczigar et al. [93M] performed photoluminescence (PL) measurements on strain-symmetrized (Si)3n/(Ge)2n. SLs and found strong luminescence in the infrared region. The luminescence signals were attributed to interband transitions of excitons localized at potential fluctuations in the superlattice, and from the transition energies the fundamental gap was determined. For the case of (Si)3/(Ge)2 SLs, the observed band gap was found to be identical to that of the corresponding Si0.6Ge0.4 alloy. This result is strong evidence that the sample is more of an alloy than a superlattice, and implies the existence of interface intermixing in the superlattice. Schorer et al. [94S] also found in Raman scattering experiments that phonon spectra of strain-symmetrized (Si)n /(Ge)n SLs, with n =4, 5, 6, 8, and 12, could not be explained with a model with abrupt-interface geometries. In addition, by taking into account interface intermixing, they recovered a general agreement between theory and experiment. Fig. 3.4.10 gives calculated values [95T2] of the fundamental gap of strain-symmetrized (Si)10–n /(Ge)n SLs. Results are given for ideal SLs, as well as for superlattices with interface intermixing over four atomic layers (configuration B), two at each site. In this configuration 50% of the positions in the first atomic layer from the interface are occupied by Ge atoms, and 50% by Si atoms, while in the second layer 75% of the positions are occupied by atoms of the host layer and 25% by atoms of the neighboring layer. We observe that interface intermixing of the atoms increases the energy gap of the material. This result can be explained as follows: Si/Ge SLs are type-II superlattices, with their valence band mostly determined by the Ge layers and the conduction band by the Si layers. Since the valence band energies of Si are lower than those of Ge, any diffusion of Si atoms into the Ge layers will modify the valence bands of the superlattice in the direction of approaching those of Si, thus reducing their energies. In addition, the lowest conduction band of Ge is higher than that of Si and any diffusion of Ge atoms into the Si layers will modify the conduction band of the SL in the direction of Ge conduction band, thus increasing its energy. Since the corresponding alloy of a given SL is the final stage of interface diffusion, it is clear that superlattices have also smaller gaps than the corresponding alloys. B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

B

B

B

3.4 Optical properties of Si/Ge superlattices

60

[Ref. p. 86

1.0

Energy gap Eg [eV]

(Si)10-n /(Ge)n 0.9

0.8

0.7

Fig. 3.4.10. Calculated values [95T2] of the fundamental gap of strain-symmetrized (Si)10–n/(Ge)n SLs. Results are shown for ideal SLs (full squares), and for superlattices with interface intermixing over four atomic layers (full triangles), as described in the text. B

2

4

3

5 n

7

6

8

B

B

B

Fig. 3.4.11 shows experimental results of Menczigar et al. [93M] for the fundamental gap of strain-symmetrized (Si)3n /(Ge)2n SLs. The case n = 0 represents the bulk alloy Si0.6Ge0.4. Theoretical results [95T2] for the same ideal SLs are also included in the figure, predicting the correct variation of the fundamental gap with n, but with smaller energy values than the experimental ones. In the same figure are also given theoretical results for non-ideal SLs, that is, SLs with interface intermixing of the atoms present. In particular, results were included for two sets of interface configurations, configuration A for which the interface intermixing is extended over two atomic layers, one at each site of the interface, and configuration B in which the intermixing is extended over four atomic layers, two at each site, as described before. As expected, the gap increases with the increase of interface intermixing. In particular, the experimental gap for the (Si)3/(Ge)2 SL is identical to that of the corresponding alloy Si0.6Ge0.4, implying that the measured sample is practically an alloy. In the case of the (Si)6/(Ge)4 SL, the experimentally obtained gap lies between the theoretical predictions for configuration A and configuration B, being closer to the latter. In the case of the strain-symmetrized (Si)9/(Ge)6 SL the experimental gap [93M] is even larger than the theoretical predictions for a configuration B superlattice, indicating that the sample used in the experiment is more drastically altered. B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

1.0

(Si)3n /(Ge)2n

Energy gap Eg [eV]

0.9

0.8

0.7

0.6

0.5

Fig. 3.4.11. Fundamental gap of strain-symmetrized (Si)3n/(Ge)2n SLs. Experimental results [93M] are given (crosses) together with theoretical predictions [95T2] for ideal SLs (full triangles), and for superlattices with interface intermixing over two (full squares) and four (full circles) atomic layers, as described in the text. B

0

1

2 n

3

4

B

B

B

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

61

Besides the gap, another characteristic quantity that describes the optical properties of a material is the absorption coefficient. Olajos et al. [92O] measured the optical absorption coefficient Į(E) near the gap Eg of the strain-symmetrized (Si)n /(Ge)n SLs with n = 5 and 6, and found the variation Į(E) ∝ (E í Eg)2 in a narrow region close to the gap. Theoretical predictions [95T2, 98P] for the absorption coefficient of an ideal 5/5 SL, as well as for the coefficient of a non-ideal 5/5 superlattice with a disordered interface (configuration B) are given in Fig. 3.4.12. Near the band edge, the strength of the absorption for the disordered SL is lower than that of the ideal SL. In addition, intermixing also produces a smoother variation of the absorption coefficient. The ideal SL shows a near-linear dependence, while in the case of disorder the dependence is nearly that of the square of the photon energy, in agreement with the experimental results [92O, 98P]. B

B

B

B

B

B

B

B

P

P

4

(Si)5 /(Ge)5

-1

Absorption coefficient a [cm ]

2

10

ideal 2

8 6

4

disorder 2

10 8 6

4 2

1 -2

10

2

10 Energy E - Eg [eV] 4

6

8

-1

2

4

Fig. 3.4.12. Calculated absorption coefficient for a strain-symmetrized (Si)5/(Ge)5 SL [95T2, 98P]. B

B

B

B

3.4.4 Si/Ge SLs grown along the [111] direction The growth of Si/Ge superlattices on substrates oriented along the [111] directions has been achieved successfully [89A, 89E, 95B]. We review the electronic and optical properties of these SLs, with the emphasis given to those SLs that may have a direct gap with appreciable transition probability [90B, 92R, 93B, 95T3, 96T]. The interplanar atomic bonds for these superlattices can be classified into two groups, those parallel to the growth direction ([111] bonds), and those not parallel to this direction ([Ǧ111], [1Ǧ11], Ǧ1] bonds). For (Si)m /(Ge)n SLs with m, n both even numbers, there exist two kinds of and [111 configurations, one with all interface bonds not parallel to the growth axis (R1 configuration), and one with all interface bonds parallel to the growth direction (R2 configuration). We are going to review results for (Si)m /(Ge)n SLs with m, n both even numbers in the R2 configuration. Imposing a new periodicity along the [111] direction produces folding of the bands along the ȁ line. For a SL with (m + n)/2 even, the L state along the growth axis of the bulk material is folded into the center of the superlattice BZ. However, a suitable choice of the SL composition and strain is needed in order to make this state the global conduction band minimum. Si/Ge SLs grown along the [111] direction are optically uniaxial, and therefore their optical properties are isotropic in the interface plane. We review results for the electronic and optical properties of the above mentioned SLs, and in particular for the energy gaps, the transition probabilities for transitions between the valence and conduction bands, the imaginary part of the dielectric function İ2(Ȧ), as well as the absorption coefficient Į(Ȧ). B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

3.4 Optical properties of Si/Ge superlattices

62

[Ref. p. 86

Calculated values [96T] for the gaps of (Si)2/(Ge)n SLs coherently grown on a Ge (111) substrate and belonging to the R2 configuration are given in Fig. 3.4.13 for n = 2 … 22, and show that these SLs are direct-gap materials. In the case of (Si)2/(Ge)10, the direct gap has the value of 0.78 eV. B

B

B

B

B

B

B

B

B

B

0.88

(Si)2/(Ge)n

0.84

d

Energy gaps Eg , Eg [eV]

0.86

i

i

Eg

0.82

d

Eg 0.80 0.78 0.76

Fig. 3.4.13. Calculated values [96T] of the direct (full square) and the indirect (full triangle down) gaps, for (Si)2/(Ge)n SLs coherently grown on a Ge (111) substrate. B

4

0

8

12 n

16

20

24

B

B

B

Calculated values [96T] for the transition matrix elements between the upper valence and lower conduction bands of (Si)2/(Ge)n SLs with n = 2 … 22, coherently grown on a Ge (111) substrate and belonging to the R2 configuration, are given in Fig. 3.4.14 for polarization parallel and perpendicular to the interface plane. From this figure we deduce that the transition matrix elements are quite strong, with a transition probability approximately only one order of magnitude smaller than that of the typical E0 transition. The significant transition matrix elements imply strong values for the optical absorption near the gap. B

B

B

B

B

T

B

B

B

E [111] E II [111]

(Si)2/(Ge)n

IMCV (k)I2

0.4

0.3

0.2

Fig. 3.4.14. Calculated values [96T] of the transition matrix elements between the top of the valence band and the bottom of the conduction band for polarizations parallel (full square) and perpendicular (full triangle down) to the growth axis, for (Si)2/(Ge)n SLs coherently grown on a Ge (111) substrate. B

0

4

8

12 n

16

20

24

B

B

B

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

63

Fig. 3.4.15 shows the calculated values [95T3] for the imaginary part of the dielectric function for a strained (Si)2/(Ge)10 SL, coherently grown on a Ge (111) substrate and belonging to the R2 configuration. In the same figure is also given the dielectric function for bulk Ge [93T]. The gross behavior of the dielectric function for both materials is the same. B

B

B

B

B

B

35

(Si)2 /(Ge)10

II T

30

Ge Dielectric constant e2

25 20 15 Fig. 3.4.15. Calculated [95T3] imaginary part İ2 of the dielectric function for a (Si)2/(Ge)10 SL, pseudomorphically grown on a Ge (111) substrate and belonging to the R2 configuration, for polarizations parallel (||, solid line) and perpendicular (⊥, dashed line) to the growth axis. For comparison the dielectric function for bulk Ge is also included (dotted line) [93T]. B

10

B

5

B

0 1

0

4 5 2 3 Photon energy h w [eV]

7

6

B

B

B

B

B

Finally, Fig. 3.4.16 shows the calculated values [95T3] of the absorption coefficient for the above SL, together with that for bulk Ge [93T]. In comparison to that of bulk Ge, the absorption coefficient of the SL shows a shoulder at low energies, just above the energy gap, with a plateau at a value of about 3000 cm–1. In addition, the absorption coefficient of the (Si)2/(Ge)10 SL increases relatively rapidly near the gap, and for an energy increase of about 0.1 eV above the gap, the absorption coefficient approaches the value of 3000 cm–1. The shown spectrum is due to the V1–C1 transitions taking place along the ΓZ direction. At about 1.05 eV, the absorption begins to increase steeply because the transitions V1–C2, V2–C2 and V3–C1, characterized by large oscillator strengths, start to contribute [95T3]. P

P

B

P

P

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

8000

6000

4000

II

2000

T

Absorption coefficient a [ cm−1]

(Si)2 /(Ge)10

Fig. 3.4.16. Calculated [95T3] values for the optical absorption of a (Si)2/(Ge)10 SL, coherently grown on a Ge (111) substrate and belonging to the R2 configuration, for polarization parallel and perpendicular to the growth axis. For comparison the absorption coefficient for bulk Ge is also included [93T]. B

Ge

B

B

B

B

0 0.7

Landolt-Börnstein New Series III/34C3

0.8

0.9 1.0 Photon energy h w [eV]

1.1

1.2

B

3.4 Optical properties of Si/Ge superlattices

64

[Ref. p. 86

3.4.5 Raman spectroscopy The band structure and the phonon dispersion of a single-crystalline solid depend on the size and the symmetry of the unit cell, which define the Brillouin zone (BZ) of the reciprocal lattice. In the case of a superlattice (SL), the original crystal symmetry is disturbed by the presence of longer-range periodicity superimposed on the regular lattice in the direction perpendicular to the SL layers (z direction). The effect of the SL periodicity can be accounted for by extending the unit cell in real space to accommodate a complete SL period. In the reciprocal lattice, this leads to a corresponding reduction of the BZ length in the kz direction. Since crystal momentum is only defined modulo G (where G Ł 2ʌ/L denotes the reciprocal lattice vector, and L is the real-space unit-cell length), the dispersion curves in the kz direction can be constructed to first approximation by folding back the original BZ into what is frequently called the “mini Brillouin zone”. Hence, electronic, optical, and phonon effects resulting from the superimposed periodicity of a SL are frequently referred to as “zone folding effects.” In the following, we will discuss phonon effects for the case of SiGe/Si strained-layer superlattices (SLSs) [91K]. B

B

B

B

3.4.5.1 Zone-folded acoustic phonons

The observation of folded longitudinal acoustic (LA) phonons by Brugger et al. [86B1] was probably the first experimental evidence for superlattice effects in the SiGe/Si system. In this study, which was extended in subsequent publications [86B2, 86D, 87L], Raman backscattering experiments on a variety of strained SiGe/Si SLs were performed in the regime of the acoustic phonons (Fig. 3.4.17). Si0.5Ge0.5 Si

lL = 501.7 nm T = 300 K z(x+y / x+y) z

buffer layer

Raman intensity I

Si folded LA - modes

SiGe (VS)

SiGe (buffer) Si (VS) Si (substrate)

×2

0

200 400 1 Energy shift Dn [cm- ]

600

Fig. 3.4.17. Typical Raman spectrum of optical and folded acoustic modes in a Si0.5Ge0.5/Si strained-layer superlattice. The arrows indicate the energy positions of optical phonon modes originating from the various layers. A schematic cross-sectional view of the sample is depicted in the inset [86B1]. Virtual substrate (VS) signals stem from the SiGe buffer layer. B

B

B

B

Due to the reduced Brillouin zone length 2ʌ/LSL (LSL is the SL period length) in kz-direction, phonons propagating perpendicular to the layers with wavevectors B

q = qs + m

2π , m = 0, ±1, ±2,! LSL

B

B

B

B

B

(3.4.7)

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

65

can become Raman active. Here, qs denotes the scattering wavevector, which is conserved in a one-phonon Raman process modulo a reduced reciprocal lattice vector GLS = 2ʌ/LSL. In backscattering geometry, qs is given simply by two times the photon momentum of the incoming laser light within the sample, i.e., qs =2(2ʌn/ȜL), where ȜL is the laser wavelength, and n is the refractive index of the sample at the laser wavelength. Hence, for a SLS with a relatively long period length, almost the entire reduced BZ may become accessible by varying the laser wavelength over the visible spectral range. As an example, the folded LA phonon dispersion of an asymmetrically strained Si0.5Ge0.5/Si SL with a period length of l6.3 nm is shown in Fig. 3.4.18. Folded LA phonon signals up to the m = –4 branch of the dispersion have been observed. Open symbols represent relatively weak signals, which occur for even values of m in SLs with almost identical layer thicknesses [85C]. Full symbols stand for very intensive signals, which can be comparable to, or even larger than those of the optical phonon modes. B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

Si /Si0.5Ge0.5 60

B

B

B

LSL = 16.3 nm

m

1

Energy shift Dn [cm- ]

+3 -3 40 +2 -2 +1

20

-1

Fig. 3.4.18. Dispersion of folded acoustic LA phonons for a Si0.5Ge0.5/Si SLS with a period length of 16.3 nm. Solid lines are calculated by using a sample elastic continuum model. Data points are derived from Raman experiments at various excitation wavelengths [86B1]. B

0 0

Wavevector (001)

p/LSL

B

B

B

The lines in Fig. 3.4.18 represent the branches of theoretical dispersion curves based on the elastic continuum model of Rytov [56R]. This approximation is, despite its simplicity, obviously fully capable of describing the experimental data within the energy range of Fig. 3.4.18. In the continuum limit, where the acoustic phonon dispersions are approximately linear and hence entirely characterized by the sound velocities, the energy dispersion of a SL is given by cos qd = cos

ω LSL 2v1

−

ωL ωL 1+ r2 sin SL sin SL , 2r 2v1 2v2

(3.4.8)

where v1, v2 are the sound velocities of the two constituent layers of the SL and r Ł v1d1/v2d2, where d1 and d2 are the densities of the two respective layers. It can be shown that in the case of equally thick layers, the average sound velocity v of the SL is directly related to the observed doublet splitting įȦ at a given scattering momentum qs by įȦ = 2qs v. For qs not too close to the BZ boundary, the doublet splitting is independent of the SL period length LSL, thus allowing a straightforward determination of the sound velocities of arbitrary Si1–xGex alloys. On the other hand, by fitting the data of a SL to the continuum dispersion relation, a precise evaluation of the SL B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

B

B

B

B

B

B

3.4 Optical properties of Si/Ge superlattices

66

[Ref. p. 86

period becomes possible. This appears to be an attractive and relatively simple technique, which is an alternative to the usual period determination by X-ray rocking analysis [88B]. The calculated dispersion curve in Fig. 3.4.18 reveals that the superimposed SL periodicity does not only fold back the original dispersion into the reduced BZ, but that energy gaps open between adjacent branches at the zone boundaries. Brugger et al. [86B2] showed that these gaps can actually be seen in a Raman experiment. For this purpose, a Si0.5Ge0.5/Si superlattice with a relatively large period length of LSL = 28 nm was grown, which shifts the zone boundary ʌ/LSL into a qs range that is easily accessible with standard laser lines. By tuning qs through the zone boundary, a finite energy gap of § 1 cm–1 between the Brillouin mode (m = 0) and the first folded mode (m = –1) could unambiguously be observed (Fig. 3.4.19). The experimentally found gap is in very good agreement with Rytov's theory, again demonstrating the adequateness of this simple model. B

B

B

B

B

B

B

B

B

B

B

B

P

P

4

Si /Si0.5Ge0.5 LSL = 28 nm 1

Energy gap Dn [cm- ]

3

2

1

0 0.6

0.8

1.0 1.2 Wavevector qs [ p/LSL ]

Fig. 3.4.19. Energy gap between the first folded LA phonon mode (m = –1) and the Brillouin mode (m = 0) near the reduced BZ boundary. The solid line is based on an elastic-continuum calculation. Data points are derived from Raman experiments [86B1].

1.4

The Raman studies of folded-phonon properties were extended to Si/Ge SLSs with extremely narrow period widths of only 5 to 20 monolayers (MLs) [88K]. Although the short period length LSL limits the range of the reduced BZ accessible by Raman excitation with visible laser light, the observation of the first LA, and also of the first transversal acoustic (TA) doublet (m = ± 1), suffices to determine the period length precisely. With decreasing period lengths the folded LA phonon signals from the first branch shift to higher frequencies (Fig. 3.4.20), as demonstrated in this series with period lengths from 20 ML … 5 ML. A monolayer on Si (100) has a thickness of a0/4 = 0.136 nm. That means the 5 ML period is slightly larger than a unit cell (0.7 nm), and indeed in this structure the folded phonons could not be detected because of interface smearing as discussed later. But the superlattices with 20 ML and 10 ML periods exhibited the first-order folded LA phonons at 74 cm–1 and 162 cm–1, respectively [88K]. A closer look (Fig. 3.4.21) reveals even the splitting of the m = ± 1 branch caused by the scattering wavevector qs and shows the much weaker m = 2 branch at around 150 cm–1 (20 ML period). Also, weak TA modes are visible which should be forbidden in backscattering geometry. With different wavelengths, for which the SL region was either transparent or opaque, the TA mode was explained as a forward scattered one which was reflected at the substrate interface [89A]. B

B

B

B

P

P

P

P

P

B

P

B

P

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

Si /Ge

67

lL = 501.7 nm

T m = 300 K Ge (SL)

Si (SL)

dSi / dGe

ImI = 1

Raman intensity I

Si (sub)

ImI = 2

12/8

ImI = 1 6/4

3/2

Si0.6 Ge0.4 0

Si /Ge

100 200 300 400 1 Energy shift Dn [cm- ]

lL = 476.5 nm nGe

m = ±1 LA TA

Fig. 3.4.20. Phonon spectra of SLSs with various period lengths. For comparison a spectrum of a SiGe alloy on a Si substrate is also shown [88K].

500

100 (011/011)100 T = 300 K nSi

gs

Raman intensity I

n [cm-1]

80 60 40 0 2p/d Wavevector

m = ±2

0

100

200

300

400

Fig. 3.4.21. Raman spectrum of a Si/Ge SLS with 12 MLs Si and 8 MLs Ge. The inset shows the calculated dispersion of acoustic phonons [88K].

500

-1

Energy shift Dn [cm ]

3.4.5.2 Confined optical modes and interface modes

In the wavenumber region between 300 cm–1 and 520 cm–1 the longitudinal optical (LO) phonon modes appear, along with the modes caused by interface vibrations [89A]. In Fig. 3.4.22 the experimental and theoretical Raman spectra of superlattices with periods from 8 MLs to 22 MLs are shown. Also given are for a specific SL with 8 MLs the vibrational eigenvectors of the Raman allowed LO modes. The higher wavevector (485 cm–1) is active within the Si layer (full circles), and the lower wavevector (296 cm–1) within the Ge layer (open circles). The mode at 358 cm–1 has the highest amplitudes at the interface. This interface mode is strongly dependant on the atomic perfection of the interface. Already roughening of the interface by one monolayer shifts this peak to about 400 cm–1 [89A]. P

P

P

P

P

P

P

P

P

P

Landolt-Börnstein New Series III/34C3

P

P

3.4 Optical properties of Si/Ge superlattices

68

[Ref. p. 86

Moreover, the optical phonons measured simultaneously give valuable information about the strain components within the respective layers. It is interesting to note that, in contrast to the acoustic phonons, the optical phonons develop modes confined to the individual layers. This is due to the missing overlap of the (relatively flat) optical-phonon dispersions of Si and Ge, which does not allow propagation within the respective other SL constituent.

(Si)10 /(Ge)12

Si4

Ge4

-1

n [cm ] 485 Raman intensity I

(Si)12/(Ge)8 358

(Si)4 /(Ge)4

296 y z

300

a

500

Wavenumber n [cm- ] 1

b

Fig. 3.4.22. (a) Experimental (upper curve) and calculated (lower curve) Raman spectra for several (Si)m/(Ge)n superlattices taken at Ȝ = 457.9 nm. (b) Vibrational eigenvectors calculated for the three Raman allowed longitudinal optic modes in a (Si)4/(Ge)4 superlattice [89A]. B

B

B

B

B

B

B

B

3.4.6 Photoluminescence (PL) Experimentally, two types of strained layer superlattices could be realized. First, pseudomorphic Si/Ge SLs [87B, 87P] were grown on Si substrates. In this asymmetrically strained SLs (Si layers are unstrained, Ge layers are compressively strained) the maximum period length is limited by the critical thickness of about 6 MLs for Ge on Si, and moreover the total thickness should not exceed 5 nm … 10 nm which is the critical thickness of the corresponding alloy. Unlimited total thicknesses are allowed with symmetrically strained superlattices introduced by Kasper [87K]. In this concept, the Si layers are tensilely strained, whereas the Ge layers are compressively strained. The critical thickness of the single period is also increased (roughly by a factor 2) because of the lower absolute values of the strain levels. The strain is adjusted by a so-called virtual substrate (VS), which is composed of the Si substrate and a relaxed SiGe buffer layer which adjusts the in-plane lattice constant of the following SL structure (see section 3.2). Band gap transitions and band gap related transitions may be probed with photoluminescence (PL). The majority of work was performed with symmetrically or near-symmetrically strained SLs because only with them thicker stacks (0.1 µm … 1 µm) could be realized. Moreover, from theoretical considerations only Si/Ge SLs with strained Si layers are expected to have the zone-folded electron states in the lowest conduction band position. The first experimental evidence of PL from zone-folded states was given by Zachai [90Z]. He compared (Fig. 3.4.23) the response of (Si)m/(Ge)n SLs with period B

B

B

B

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

69

lengths of 5 ML … 20 ML, and a common layer thickness ratio m/n = 1.5. The strain situation in these samples was near-symmetric (Si strain: 1.45 %, Ge strain: –2.75 %).

Si/Ge

lL = 457.9 nm

T=5K

2

PL = 1W/cm

Photoluminescence intensity I

(Si)3/(Ge)2 (alloy-like)

(Si)6 /(Ge)4

2

1W/cm

(Si)12/(Ge)8

1W/cm 100W/cm

2

Fig. 3.4.23. Photoluminescence of various symmetrically strained (Si)m/(Ge)n SLs grown on a Si (100) substrate with periods of 5, 10 and 20 MLs, a common layer-thickness ratio m/n = 1.5, and biaxial strain İ||Si ≈ 1.4 % and İ⊥Ge ≈ –2.7%. The (Si)3/(Ge)2 structure has a more alloy-like behavior [90Z]. B

2

× 0.1

0.7

B

B

B

B

B

0.8 0.9 1.0 Photon energy h w [eV]

1.1

PB

P

B

B

B

P

PB

B

The perfect symmetric strain for the given mean composition (m/n = 1.5) would be Si: 1.7%, Ge: –2.5%. Strong luminescence (at 0.8 eV) was found for the 10 ML period samples. The 5 ML period sample turned out to be more like an alloy from Ge segregation during growth. The 20 ML period sample exhibited only a response after strong excitation. Other 10 ML period samples with different strain showed a decreasing PL energy with increasing Si strain (Fig. 3.4.24). The principal dependence of the PL energy on period length, strain and thickness ratio could be explained within the framework of a Kronig-Penney type model.

DII

1.1

1

1

- hh

D

1 T

1

- hh

0.9 0.8 0.7

D

1 T

PL peak energy [eV]

1.0

1

- lh

B

(Si)6 /(Ge)4 (Si)4 /(Ge)6

0.6

Fig. 3.4.24. Photoluminescence peak energies of (Si)6/(Ge)4 superlattices (dots) and a (Si)4/(Ge)6 superlattice (open circle) compared with calculated values of the relevant band gaps for (Si)6/(Ge)4 (solid lines) and (Si)4/(Ge)6 (dashed lines) as a function of biaxial strain in the Si layers [90Z]. B

B

B

B

B

0

Landolt-Börnstein New Series III/34C3

1

2 Si Strain eII [%]

3

4

B

B

B

B

B

B

B

B

B

3.4 Optical properties of Si/Ge superlattices

70

[Ref. p. 86

The slight polarization dependence (Fig. 3.4.25) of the PL signal (measured in backscattering geometry from the edge of the 10 ML sample) was interpreted as a hint for the crossover of light hole (lh) and heavy hole (hh) minibands. lL = 457.9 nm

T=5K

PL = 50 W/cm y

Photoluminescence intensity I

x (z, z)x x (z, y)x

2

x z

Si Ge

(Si)6 /(Ge)4

Fig. 3.4.25. Polarization dependency of the photoluminescence of a (Si)6/(Ge)4 superlattice with biaxial strain İ||Si ≈ 1.4 % and İ⊥Ge ≈ –2.7%, measured in backscattering geometry from the edge of the sample; the spectra are normalized to the polarization-dependent efficiency of the grating, which leads to identical intensities of the Si luminescence peaks [90Z]. B

B

0.7

1.1

0.8 0.9 1.0 Photon energy h w [eV]

P

B

B

B

PB

PB

B

P

A few years later, Si/Ge SLSs with a higher quality (lower threading dislocation density, higher interface smoothness) were available [93M]. Nevertheless, the 5 ML period sample behaved like a SiGe alloy with concentration modulation yielding only about five times the PL intensity of the corresponding SiGe alloy (Ge content x = 0.4). But the 6/4 ML and the 9/6 ML Si/Ge SLSs proved enhanced PL intensities (about 100 times higher no-phonon (NP) transition probabilities than the alloy) with clear separation of the stronger NP localized exciton (LE) peak from the TO phonon replica (Fig. 3.4.26). 1.1

NR

NP

LE

Photoluminescence intensity I

(Si)6 /(Ge)4

PL peak energy [eV]

LE (Si)9 /(Ge)6

(Si)m /(Ge)n

m/n = 3/2

1.0 0.9 hh®D2 lh ®D2

0.8

5 15 0 10 Period length m+n [ML]

(Si)3 /(Ge)2 TO

LE

×5 TO

LE

NP ×5

0.7

Fig. 3.4.26. Photoluminescence spectra for (Si)9/(Ge)6, (Si)6/(Ge)4, (Si)3/(Ge)2 SLSs, and Si0.6Ge0.4 alloy [93M]. The inset shows the no-phonon (NP) transition energies as a function of the period length for heavy hole (hh) and light hole (lh) transitions to ǻ(2) electron states. The experimental values (empty dots) follow the predicted trend, but with slightly lower amounts. B

TO Si-Si

B

Si0.6 Ge0.4

0.8 0.9 1.0 Photon energy h w [eV]

B

B

B

B

B

B

B

B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

71

In order to identify the nature of the NP and TO lines, the Si/Ge SLSs were subsequently annealed at temperatures of 600 °C, 650 °C, and 780 °C, which resulted in increasing intermixing by diffusion. The NP line (Fig. 3.4.27) was shifted to higher energies (for the 6/4 ML SLS from 0.78 eV to 1.01 eV) with intermixing in agreement with expectations from band edge calculations (see subsection 3.4.3.3). The band edge calculations (inset in Fig. 3.4.27) as a function of the assumed Si content 1-x in the interdiffused Ge layer confirm the experimental finding. The energy difference of 52 meV between the NP and the TO replica line, respectively, compares very well with the energy of Si-Ge optical phonons measured with Raman spectroscopy.

NP

LE

hh®D4 PL peak energy [eV]

(Si)6 /(Ge)4

1.00 lh®D4 0.95 hh®D2 lh®D2 0.90

TO

Photoluminescence intensity I

LE

0 0.1 0.2 0.3 0.4 0.5 0.6 (1-x) [Ge layers]

a

NP

LE

TO

LE

L

b c

Fig. 3.4.27. Photoluminescence spectra for a (Si)6/(Ge)4 SLS: Spectrum (a) for the as-grown sample, spectra (b), (c) and (d) after subsequent annealing for 1 h at 600 °C, 650 °C, and 780 °C, respectively. The inset shows results of an EM calculation. Dots mark the positions of the NP line for spectra (a) and (d) [93M].

NP

B

LE

NP

D1

d 0.7

alloy

D2 0.8 0.9 1.0 Photon energy h w [eV]

1.1

B

B

The TO signal could therefore be attributed to a phonon replica due to local Si-Ge modes at the Si/Ge interface. After the highest annealing step at 780 °C defect lines (D1, D2) appear in the spectrum which are due to fresh dislocations generated by the relief of the residual strain (–0.3%) of the not perfectly strain-symmetrized SL. A further broad peak (marked with L) appears at 0.977 eV, which looks similar to PL signals in annealed SiGe quantum wells. The dependence on temperature and excitation power, and the line shape (Fig. 3.4.28) are consistently described in terms of the recombination of excitons localized at random potential fluctuations (energy E0 = 10 meV) which are expected due to slight variations, both in strain and composition. The PL line shape of localized excitons (LE) can be written [85O] as B

B

(

I ( E , T ) = e E / E0 1 + v e − ( E − E0 ) / kBT

Landolt-Börnstein New Series III/34C3

)

B

B

B

B

(3.4.9)

3.4 Optical properties of Si/Ge superlattices

Log10 (PL Intensity) [arb.units]

72 PL = 50 mW/ mm2 5 E0 = 10 meV 0.5 0.05

Photoluminescence intensity I

10

[Ref. p. 86

(Si)6 /(Ge)4 NP

T = 5K

LE

1

T= 5K

0 0.8 0.2 0.3 0.4 0.5 0.9 h w [eV]

TO

LE

8K

×1.4

9K

×1.6

10 K 13 K 17 K 22 K 29 K

×2.1 ×3.0 ×7.0

Fig. 3.4.28. Photoluminescence spectra for a (Si)6/(Ge)4 SLS at different temperatures. The inset shows PL spectra at T = 5 K taken with different excitation power densities [93M]. B

×17 ×41

0.7

0.9

0.8 Photon energy h w [eV]

B

B

3.4.6.1 Effect of hydrostatic pressure on the PL

The application of an external hydrostatic pressure results in a change in the bond lengths that influence the band structure and optical properties of the solid [94O]. The band offsets for a sample at atmospheric pressure calculated using actual structural data are shown in Fig. 3.4.29. The lowest energy transitions in the superlattice are between the zone folded electrons (called z minibands in [94O]) and the hh miniband.

(Si)9 /(Ge)6 on Si0.55 Ge0.45 1.6

Energy E [eV]

Ge z

x,y

x,y

Si0.55 Ge0.45 z

1.2

Si

x,y

z-miniband z hh lh

0.8 0.4 0

hh-miniband hh lh s-oh

lh hh s-oh

s-oh

Fig. 3.4.29. Diagram showing the calculated band offsets for a (Si)9/(Ge)6 sample, evaluated with the actual structural data [94O]. B

B

B

B

The NP lines shift linearly to lower energies (Fig. 3.4.30) with increasing pressure without any significant change in the amplitude. In addition, the PL spectra exhibited somewhat broader features at lower energies. These lines gained in intensity with increasing pressure and showed a positive pressure coefficient, suggesting that other recombination processes are involved in these features. These

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

73

experiments have made it possible to show experimentally that both defect related PL as well as band gap luminescence is observed in short period Si/Ge SLS. The calculated pressure dependencies for the band gap PL and the experimentally observed shifts are compared in Fig. 3.4.31.

(Si)6 /(Ge)4 p = 1bar

Photoluminescence intensity I

7.6 kbar 14.5 kbar

20.2 kbar

27 kbar 31.6 kbar

39.7 kbar 0.75

0.80

0.85 0.90 0.95 Photon energy h w [eV]

Fig. 3.4.30. Photoluminescence spectra as a function of applied hydrostatic pressure for a SLS sample (Si)6/(Ge)4 [94O].

1.00

B

B

B

B

The defect transitions observed below the NP line are most probably located in the relaxed SiGe buffer because they shift with pressure to energies above the SL band gap (Fig. 3.4.30). 0.90

(Si)6 /(Ge)4

PL peak energy [eV]

0.88 -1.44 meV/ kbar Si1-x Gex in-plane compliances

0.86

0.84 -1.45±0.05 meV/ kbar Linear regression to experimental data 0.82 -1.56 meV/ kbar Si and Ge in-plane compliances 0.80 0

5

Landolt-Börnstein New Series III/34C3

15 10 20 25 30 Hydrostatic pressure p [kbar]

35

40

Fig. 3.4.31. Comparison between the calculated pressure dependencies for the various superlattice structures and the experimental energy shifts of NP lines for the SLS sample (Si)6/(Ge)4. Filled circles denote experimental data [94O]. B

B

B

B

3.4 Optical properties of Si/Ge superlattices

74

[Ref. p. 86

3.4.7 Electroluminescence (EL) Electroluminescence pin diodes were fabricated [92P2, 93P] with the Si/Ge SL in the intrinsic or low p doped layer. Electroluminescence (EL) could be obtained (Fig. 3.4.32) both from mesa type and waveguide diodes.

(Si)5 /(Ge)5

B 2214

Injected power a) 180 mW b) 30 mW

40 mm ×10

0.5 mm

0.7

0.8

0.9 1.0 Photon energy h w [eV]

0m

m

b) 40

Electroluminescence intensity I

a)

SLS

1.1

Fig. 3.4.32. Electroluminescence (EL) spectrum from a mounted waveguide diode of a (Si)5/(Ge)5 SLS sample. Shown are the spectra for two different values of the injected electrical power, where a blueshift with higher injected power is observed. The inset shows the geometry and typical dimensions of the waveguide [93P]. B

B

B

B

The EL peak position shifts to higher energies with larger injected electrical power, and to lower energies with increasing temperature. The blueshift with injected power is assigned to a band filling process, the decrease of the EL energy is expected for a band to band as well impurity level to band transition. In high-quality samples the EL position is clearly different from the PL (Fig. 3.4.33), which lets one believe the EL to stem from a defect related transition in the SLS.

3.4.8 Photoconductivity (PC) and optical Junction Space Charge Techniques (JSCT) Absorption of light in the visible and near infrared spectral region is connected with band-to-band transitions (fundamental absorption), localized states to band transitions and intraband transitions (free carrier absorption). The first two lead to the generation of free carriers which can be detected by photoconductivity (PC) and junction space charge techniques (JSCT). Photoconductivity is the simpler experiment, where in an intrinsic or nominally undoped semiconductor the parallel conductivity change caused by light incidence is detected by two biased electrical contacts. In junction space charge techniques [81G] a pn junction either short-circuited or reversely biased is subjected to electrical signals, capacitance–voltage (C–V), admittance spectroscopy, deep level transient spectroscopy (DLTS) or optical signals (optical JSCT). Here, we only discuss the latter one. The example of absorption spectra from 0.7 eV to 1.1 eV as obtained by photoconductivity is shown in Fig. 3.4.34. Here, different SLSs with periods from 8 MLs to 12 MLs are compared with the corresponding SiGe alloy. One has to take into consideration that the photogenerated signal may not necessarily originate in the SLS region only, but also in other parts of the sample, i.e. the buffer layer. The transitions in the SLS are shifted to lower energies with increasing period length in accordance with the modeling results.

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

(Si)6 /(Ge)4

75

B2460 PL T=5K

a 0.8

0.7

0.9

1.0

1.1

1.2

1.1

1.2

50 mm

40 0m

Luminescence intensity I

m

EL T=5K 0.5 mm

SLS

b 0.8

0.7 EL T = 77 K

0.9

1.0

Mesa diode: Vertical emission

Fig. 3.4.33. Comparison of the PL and EL spectra of different fabricated mesa and waveguide diodes from pin diode (Si)6/(Ge)4 SLS sample. (a) PL at T = 5 K from mesa diode; (b) EL at T = 5 K from waveguide diode; (c) EL at T = 77 K from mesa diode [93P]. B

c 0.8 0.9 1.0 Photon energy h w [eV]

0.7

1.1

1.2

B

B

B

B2210 (6:6) T = 77 K

Absorbance (log scale)

B2209 (5:5) B2208 (4:4)

B2211 (50% alloy)

0.7 0.8 0.9 1.0 1.1 Photon energy h w [eV]

Landolt-Börnstein New Series III/34C3

Fig. 3.4.34. Absorption spectra as measured with parallel photoconductivity for the superlattices B 2210 (Si)6/(Ge)6, B 2209 (Si)5/(Ge)5, B 2208 (Si)4/(Ge)4, and the Si0.5Ge0.5 alloy B 2211 [81G]. B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

3.4 Optical properties of Si/Ge superlattices

76

[Ref. p. 86

The short-circuit current in the junction space charge technique is generated mainly in the SLS when the pn junction is appropriately doped, which is a serious technical problem because of the different dopant incorporation in Si and Ge. A typical measurement result and the applied fitting procedure are shown in Fig. 3.4.35. The experimental curves consist of two parts, each of them following the (ʄȦíE)2 dependence of an indirect semiconductor. One part is thought to stem from the SLS band gap transition, the other one from the buffer layer, or from defect states.

4

Absorption coefficient a [arb.units]

10

3

10

a 1/2[arb.units]

P

T = 150 K

B2214 T = 150 K

B2214

B2215

0.6

0.8 1.0 h w [eV]

B2215

2

P

2

( h w - 0.94 eV)

10

× 70

10 2

( h w - 0.76 eV)

1

2

( h w - 0.67 eV) 0.7

Fig. 3.4.35. Fitting procedure for two typical samples, B 2215 (Si)6/(Ge)6, and B 2214 (Si)5/(Ge)5. The additional onset in the spectrum of B2214 originates from the thick alloy buffer layer [81G]. B

0.8 0.9 1.0 Photon energy h w [eV]

1.1

B

B

B

B

B

B

B

The group of H. Grimmeis [91P, 92O, 92G] performed extensive JSCT investigations of Si/Ge SLSs. Fig. 3.4.36 shows the measurement scheme and photocapacity results. Photocapacity is especially sensitive to defect-band transitions because of charging (decharging) of the defects. hw

5

B 1589/5b hw = 0.49 eV

n

space charge region p*

Photocapacity signal [arb.units]

front contact

back side contact

a

4

3

2

1

b

T = 35 K

0

0.2

0.8 0.4 0.6 Reverse bias voltage [V]

1.0

Fig. 3.4.36. Junction space charge techniques. Scheme (a) and photocapacity result (b) from a (Si)4/(Ge)4 SLS. After Grimmeis [92G]. B

B

B

B

Landolt-Börnstein New Series III/34C3

Ref. p. 86] 3.4.8.1

3.4 Optical properties of Si/Ge superlattices

77

Wannier-Stark localization

Wannier-Stark localization occurs where a strong electric field breaks the mini band of a superlattice down into a series of localized states [92G]. The principal energy scheme is shown in Fig. 3.4.37. (Si)4 (Ge) 4 (Si) 4 (Ge) 4 (Si) 4 (Ge)4 (Si)4 ~0.8 eV

-0.3 eV

~0.2 eV

~0.3 eV

~0.9 eV

hh

a

+1 -1 -1/2

Fig. 3.4.37. Sketches of the conduction and valence band potential profiles for a (Si)4/(Ge)4 superlattice under (a) small and (b) high electrical fields [92G]. B

B

B

B

b

The spectral distribution measured in a Si/Ge SLS is not smooth, but exhibits oscillatory structures. The low threshold of 0.35 eV suggests that the signal arises due to transitions from localized states into the carrier wells. The expected spectrum is given by E = E0 + n q F LSL (n = 0, ±1, ±2, …), B

B

B

(3.4.10)

B

where E0 is the transition energy at zero field strength F, and LSL is the superlattice period. In ҏorder to study the field dependence of the photoionization cross section, the signal was measured for constant photon energies as a function of the reverse bias (Fig. 3.4.38). Analysis of the data is obtained by plotting the peaks as function of the square root of the reverse bias, which is a measure of the field strength. The authors conclude that there are good reasons to believe that a Wannier-Stark ladder from transitions via defect levels is observed in Si/Ge SLS. The assignment is, however, not unambiguous because the field strength in the space charge region varies considerably. B

B

B

B

3.4.9 Spectroscopic ellipsometry The simultaneous determination of both the real and the imaginary parts of the dielectric function İ(Ȧ) = İ1(Ȧ) + iİ2(Ȧ) has been proved to be efficiently done by spectroscopic ellipsometry. Interference effects lead to complications in the interpretation if the thickness of the top layer is below the penetration depth of the incident light. The group of Cardona [91S, 92S] investigated thoroughly the ellipsometric spectrum in terms of the amplitude ratio ȥ and the phase angle ¨. Interference effects were observed below an energy of 2.0 eV to 2.6 eV (Fig. 3.4.39), depending on thickness and Ge content of the SLS [92S]. B

B

B

B

Landolt-Börnstein New Series III/34C3

3.4 Optical properties of Si/Ge superlattices

78

[Ref. p. 86

40

(Si)4 /(Ge)4

30

hw= 0.350 eV

Photocapacity signal [arb.units]

20

30 0.390 eV

20 30

20 0.419 eV

Fig. 3.4.38. Photoionization cross section at constant photon energy as a function of the reverse bias for different photon energies in a (Si)4/(Ge)4 SLS [92G].

10 0

0.05

0.10 0.15 0.20 0.25 Reverse bias voltage [V]

0.30

0.35

B

B

B

B

y [deg]

26 22 18 14

(Ge)4 / (Si)6 Model calc.with alloy

a

40

D [deg]

30 20 10

Fig. 3.4.39. Raw ellipsometric data of the nominal (Ge)4/(Si)6 SLS (circles) and model calculation (solid lines) in which the dielectric function of an unstrained Ge0.4Si0.6 alloy has been used instead of the SLS [92S].

0 -10 b

B

1.8

2.2 2.6 3.0 Photon energy h w [eV]

3.4

B

B

B

B

B

B

B

The critical points (CP) in the spectra were analyzed in the second derivative spectrum d2İ/dȦ2. The best fit is obtained with a splitting of the E1 and E2 transitions (Fig. 3.4.40). The E0´ transition is very close to the E0´ values interpolated from bulk Si and Ge. The proximity of these values probably prevents localization, i.e. the observation of two separate values. P

B

B

B

B

P

P

P

BB

BB

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

79

30 e2

Dielectric constants e1, e2

20

10

0

Fig. 3.4.40. Real (ε1) and imaginary (ε2) parts of the dielectric function of the nominal (Ge)4/(Si)6 SLS (solid lines) compared to that of the Ge0.4Si0.6 alloy. Below 3 eV, ε (ω) has been derived from a multiphase least-square fit method, using the multiple angle of incidence measurements. Above 3 eV, a three-phase model (SLS + oxide over layer) has been used [92S]. B

B

B

B

(Ge)4 / (Si)6

-10

Ge0.4 Si0.6 alloy

e1

B

B

-20 4 3 Photon energy h w [eV]

2

5

B

B

B

B

B

B

B

B

3.4.10 Piezoreflectance and electroreflectance Useful methods for investigating direct band-to-band transitions are piezoreflectance and electroreflectance where the reflectivity is either modulated by applied stress or electric fields. Stress modulation is achieved by mounting the sample on a piezoelectronic transducer, and field modulation is usually achieved by a biased Schottky contact. A typical example of piezoreflectance data [91Y] is shown in Fig. 3.4.41. T = 77 K Ge Substrate

(×2)

0

Piezoreflectance DR /R

[(Si)m /(Ge)n ]5 /(Ge)N 0 m/n/N = 3/7/143 0 m/n/N = 3/7/29 0 m/n/N = 4/6/126

Fig. 3.4.41. The piezoreflectance spectra (solid lines) of a Ge (001) substrate and [(Si)3/(Ge)7]5/(Ge)143, [(Si)3/(Ge)7]5/(Ge)29, [(Si)4/(Ge)6]5/(Ge)126 and [(Si)4/(Ge)6]5/(Ge)78 short-period SL samples at T = 77 K. The dotted lines are least-square fits which yield the transition energies denoted by the arrows [91Y]. B

0 Exp Line-shape fit 0.8

Landolt-Börnstein New Series III/34C3

0.9

m/n/N = 4/6/78

1.1 1.0 1.2 Photon energy h w [eV]

1.3

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

3.4 Optical properties of Si/Ge superlattices

80

[Ref. p. 86

Ge T = 40 K

Electroreflectance DR /R

Electroreflectance DR /R0

Here the piezoreflectance (the relative change ¨R/R of the reflectance caused by an external stress modulation with 1 kHz) of a Ge substrate is compared with that of different pseudomorphic Si/Ge superlattices on this substrate. The notation of these pseudomorphic SLs is given by m/n/N, where m and n are the numbers of Si and Ge monolayers, respectively, and N counts the spacer monolayers in-between the repeated structures. The spacer layers are necessary to avoid dislocation generation and stress relaxation in the asymmetrically strained pseudomorphic SL. These repeated spacers between the SLs can be considered as quantum wells with SL barriers. Indeed, the authors [91Y] assign most of the spectral signatures to direct transitions in the quantum well, blueshifted compared to Ge by the confinement energy. Fig. 3.4.42 shows for comparison the electroreflectance [89P2] of a similar set of samples.

0

0.5

1.1 0.9 Photon energy h w [eV]

0.7

a

0

[(Ge)7 /(Si)3 ]/Ge T = 40 K

1.5

1.3

[(Ge)6 /(Si)4 ]/Ge T = 40 K

0.5

b

0.7

1.1 0.9 Photon energy h w [eV]

1.5

1.3

Fig. 3.4.42. Electroreflectance spectra at T = 40 K. (a) Electroreflectrance spectrum of the bulk Ge substrate in the region of the E0 and E0 + ∆0 transitions. Transition energies are determined from a lineshape fitting procedure. (b) Electroreflectance spectra of the (Ge)6/(Si)4 (upper) and (Ge)7/(Si)3 (lower) SLs in the same spectral range and under the same modulation conditions as in (a). The two spectra are similar because of the type II band alignment. Both samples show an additional strong oscillation near 0.95 eV not seen in the Ge spectrum. This feature is the superlattice transition near 0.95 eV. Precise values for the SL transitions as well as the Ge transitions in these samples are determined by lineshape analysis [89P2]. B

B

B

B

B

B

B

B

B

B

B

B

B

B

The interpretation of the spectra is complicated by the presence of Franz-Keldysh oscillations. Similarly, the spectra of pseudomorphic (Si)m/(Ge)n SLs on Si shown in Fig. 3.4.43 exhibit, besides the Si signals at 3.37 eV (E1) and 3.10 eV (E0´), the signatures of the SL/Si spacer quantum well structure. B

Electroreflectance DR /R [arb.units]

B

3

B

B

B

B

BB

[Ge/Si]/Si

2

8

7

6

5 4

3 1 2

1 0 -1 -2 -3 0.5

Fig. 3.4.43. Direct experimental recording of the electroreflectance spectrum of [Ge/Si]/Si alternating four-monolayer structure from 0.6 to 4.0 eV. The spectrum shows transitions occurring both in Si and in the GeSi ordered structure. The two lowest-energy Si transitions occur at 3.37 eV (E1) and 3.13 eV (E0´). All of the structure at lower energies comes from the 5.1 nm alternating four-monolayer structure. New transitions are resolved at 0.76, 1.26 and 2.31 eV [89P2]. B

1.0

1.5 2.5 3.0 2.0 Photon energy h w [eV]

3.5

4.0

B

B

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

81

3.4.11 Second-harmonic generation Short period (Si)m/(Ge)n SLSs offer the possibility of a change in the linear and nonlinear properties of group IV semiconductors. In particular, there exists the possibility of tailoring the structures to produce non-centrosymmetric materials if m and n are both odd. Second harmonic generation (SHG) was observed from a variety of superlattices, pseudomorphic ones [93B] and strain-symmetrical ones. Fig. 3.4.44 shows SHG from pseudomorphic 4:4 and 5:5 monolayer SLS. Given is the SHG intensity as function of the sample azimuth during a 360° rotation. B

B

B

B

SHG intensity

[(Si)4 /(Ge)4 ]5

a

0

[(Si)5 /(Ge)5 ]4

b

0 0

Fig. 3.4.44. Second-harmonic generation (SHG) (ȥ) from (a) [(Si)4/(Ge)4]5 and (b) [(Si)5/(Ge)5]4 SLSs (symbols). The solid curves are best fits. The two data sets are not to scale [93B]. B

90

180 y [deg]

270

360

B

B

B

B

B

B

B

B

B

B

B

The fundamental wavelength in this experiment was 775 nm using a femtosecond Ti:sapphire laser. The absorption depths of the fundamental, second-harmonic and third-harmonic radiation in the SL were 300 nm, 20 nm, and 5 nm, respectively. Third-harmonic generation (THG) is observed in the symmetric-strain SL, which is considered as a proof of good crystallinity (Fig. 3.4.45).

THG intensity

(Si)3 /(Ge) 2

Fig. 3.4.45. Third-harmonic generation (THG) (ψ ) from the (Si)3/(Ge)2 SLSs. The solid curve is a best fit using sin2(4ψ ) [93B]. B

0 0

Landolt-Börnstein New Series III/34C3

90

180 y [deg]

270

360

P

P

B

B

B

3.4 Optical properties of Si/Ge superlattices

82

[Ref. p. 86

3.4.12 Quantum dot superlattices (QDSL) The experimental realization of Si/Ge SLs suffers from low critical thicknesses and corrugated surfaces of the strained layers. The carriers in these superlattices are confined by the strain and Ge fluctuations as shown in the previous section on photoluminescence. Therefore, in a different approach [06T], the localized states from islands are arranged in a column (Fig. 3.4.46), creating a quantum dot superlattice (QDSL).

Ge /Si

20

z [nm]

40

Fig. 3.4.46. Cross sectional TEM image of the Si/Ge QDSL (left). The average height of a quantum dot in a column is B = 4.5 nm. Ge content profile along the growth direction z for the same sample (right) [06T].

0

Si buffer 0

0.5 1.0 Ge content

Photoluminescence and electroluminescence (Fig. 3.4.47) from the QDSL was observed and assigned to transitions from the wetting layer (WL), but dominantly from the quantum dot column. The large valence band offsets in the Si/Ge dot SL suggest intravalence band spectroscopy and possible detector applications in the mid-infrared (3 µm … 6 µm) spectral range [02B].

Photon energy h w [eV] 0.8 0.7

Electroluminescence intensity I

0.1 0

Integr.intensity J

0.9

Current I [A]

1.0

0.6 J=j

m

101

m = 4.8

100

0 1.0 Bias voltage Vb [V]

0.5

1.0 2.0 Current density j [A/cm2 ]

Ge /Si

1200

1600 Wavelength l [nm]

2000

Fig. 3.4.47. Electroluminescence (EL) spectra measured at room temperature for a Si/Ge QDSL, with a height of the quantum dot of B = 3.8 nm, and a cap width between QDs of W = 2.5 nm. Current densities are j [A·cm–2]: 0.9, 1,0, 1.1, 1.2, 1.4, 1.6, and 1.8 from bottom to top. Left inset: dark current-voltage characteristics. Right inset: double logarithmic plot for the EL integrated intensity J vs. current density j. The factor m is deduced from the fit J = jm. Full circles correspond to the EL measurement points shown in the main graph [06T]. P

P

P

P

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

83

The mid-infrared (MIR) photocurrent spectra measured from a ten-period Ge QD/Si SL with large Si spacers (50 nm) is shown in Fig. 3.4.48. On a similar twenty period Si/Ge QDSL, a MOS gate injection of carriers was used [06L] to obtain electroluminescence at around 0.85 eV (Fig. 3.4.49).

6.0 2.8

5.0 TM

4.0

Wavelength l [mm] 3.0

2.0 N.I.

-5.0 V TE

2.4

TM

2.0 -3.0 V

1.6

Ge /Si

Responsivity [mA/W]

1.2 -1.0 V

0.8 0.4 0 2.8

0V TE

2.4 2.0

-5.0 V

1.6 1.2

-3.0 V

0.8

-1.0 V

0.4 0

0V 200

300 400 500 Photon energy h w [meV]

1.7 1.6 1.5

Wavelength l [mm] 1.4 1.3 1.2

Electroluminescence intensity I

P

P

P

P

1.1

QD MOS experiment QD pin - experiment

T ~ 110 K

~160 K

600

Fig. 3.4.48. Mid-infrared photocurrent spectra at different bias voltages and T = 20 K from the Si/Ge dot pip structure in multipass waveguide geometry with transverse magnetic (TM) and transverse electric (TE) polarized light. The structural parameters are ten periods (8ML Ge/50 nm Si), 70 nm diameter, 6.5 nm height and 5·109 cm–2 areal density of dots. The nominal B doping of dots corresponds to about 130 holes per dot [02B].

Al Ec ~1.5mm Ev + + ~1.1mm Ge QD

~ 250 K Oxide

0.7

0.8

Landolt-Börnstein New Series III/34C3

0.9 1.0 Photon energy h w [eV]

1.1

1.2

Fig. 3.4.49. Electroluminescence (EL) spectra of Ge QDs MOS LED at different temperatures. The inset shows the energy band diagram of the Ge QDs MOS LED at accumulation bias. The EL spectra of the Ge QD pin diode are also shown for reference [06L].

3.4 Optical properties of Si/Ge superlattices

84

[Ref. p. 86

With resonant-cavity enhanced photodetection the spectral response of QDSL detectors may be shifted to technical interesting wavelengths (e. g. 1.55 µm for fiber communication). This is demonstrated in Fig. 3.4.50 for a ten-period QDSL with 8 ML Ge / 6 nm Si. The complete structure is grown pseudomorphically, which results in low dark currents. The resonant cavity enhanced (RCE) photodiode has a 3 dB bandwidth as small as 5 nm at a central wavelength of 1543 nm. Photon energy h w [eV] 0.81 0.80

0.82

0.03

0.79

Responsivity [mA/W]

Ge /Si

0.02

0.01 1510

1520

1530 1540 1550 Wavelength l [nm]

1560

Fig. 3.4.50. Responsivity of a Ge QDSL resonant-cavity enhanced photodiode (RCE-PD) [06Y].

3.4.13 Conclusions The development of epitaxial techniques [90H, 90K] has enabled us to control the growth of individual semiconductor layers on an atomic scale. As a result, a strong basis for designing semiconductor materials with tailored electronic and optical properties has been established. The combination of different composites in the form of heterostructures and superlattices has opened up exciting possibilities for manufacturing novel devices and has increased our basic understanding of electronic behavior in reduced dimensions. Development of Si based photonic components and subsequent integration of optic and electronic components on the same substrate will create optoelectronic integrated circuits and “superchips” that will perform much better than optical or electronic circuits alone. In addition, Si based optoelectronic technology could find applications in fiber-optic transmitters and receivers, optical computer integrations, optical controllers, information display panels, and numerous other devices. One of the exciting prospects for these SLs is the possibility of engineering new direct-gap materials from two constituent materials (Si and Ge) that are indirect-gap semiconductors [74G]. The technological importance of this prospect lies in the expectation of using the direct-gap Si/Ge SLs as components in integrated optoelectronic devices, in conjunction with the already well-established and highly advanced silicon technology. In the present article, we reviewed the modeling of electronic and optical properties of Si/Ge SLs grown along the [001] and [111] directions. The conclusions are that for ideal (Si)m /(Ge)n SLs with m + n = 10, coherently grown on a Si1–xGex (001) alloy substrate rich in Ge, a direct-gap material is obtained [93T]. The transition probabilities across this gap are 2 … 3 orders of magnitude lower than typical E0 bulk-like transitions [95T1]. Calculations [95T2] show that the absorption coefficient of strainsymmetrized (Si)10–n /(Ge)n SLs increases slowly near the gap, and for an energy increase of 0.5 eV above the gap the absorption coefficient gets the value of about 400 cm–1 . Furthermore, the absorption gets B

B

B

B

B

B

B

B

B

B

B

B

B

B

P

P

Landolt-Börnstein New Series III/34C3

Ref. p. 86]

3.4 Optical properties of Si/Ge superlattices

85

stronger for strain-symmetrized (Si)10–n /(Ge)n SLs richer in Ge, that is for larger values of n. This is in agreement with the behavior of the transition matrix elements found before. The presence of interface intermixing of the atoms influences the electronic properties of Si/Ge SLs. For strain-symmetrized Si/Ge SLs grown along the [001] direction, the interface intermixing increases the fundamental gap of the SL. Besides the gap, interface intermixing of the atoms changes the behavior of the absorption coefficient near the gap [92O, 95T2, 98P]. Near the band edge, the strength of the absorption for the disordered SL is lower than that of the ideal SL. In addition, intermixing also produces a smoother variation of the absorption coefficient. For growth along the [111] direction, theory predicts that (Si)2/(Ge)n SLs with n = 2 + 4k (k = 0, …, 5), grown on substrates rich in Ge are direct-gap materials. In this case the lowest transitions at the ī point of the SBZ have very large oscillator strengths, making these SLs candidates for optoelectronic applications [96T]. Finally, we should mention the efforts of obtaining direct band alloy semiconductors with the desirable materials properties: a very close lattice match to silicon and a direct band gap in the 0.7 eV … 1.0 eV range. Theoretical calculations predict that the alloys CGe3Sn and CSi2Sn2 pose the required properties [01Z]. B

B

B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

B

B

B

B

B

3.4.14 References for 3.4

86

3.4.14 References for 3.4 56R 71J 72L 72W 74G 76C 79S 81G 83B 85C 85O 86B1 86B2 86D 86K

86V 87B 87F 87H 87K 87L 87P 88B 88F 88H 88K 88S 89A 89E

89F 89P1 89P2

Rytov, S.M.: Akust. Zh. 2 (1956) 71; Sov. Phys. Acoust. (English Transl.) 2 (1956) 68. Jepsen, O., Andersen, O.K.: Solid State Commun. 9 (1971) 1763. Lehmann, G., Taut, M.: Phys. Status Solidi (b) 54 (1972) 469. Wooten, F.: Optical Properties of Solids, New York: Academic Press, 1972. Gnutzman, U., Clausecker, K.: Appl. Phys. 3 (1974) 9. Chelikowsky, J.R., Cohen, M.L.: Phys. Rev. B 14 (1976) 556. Smith, N.V.: Phys. Rev. B 19 (1979) 5019. Grimmeis, H.G., Ovren, C.: J. Phys. E 14 (1981) 1032. Brey, L., Tejedor, C.: Solid State Commun. 48 (1983) 403. Colvard, C., Gant, T.A., Klein, M.V., Merlin, R., Fisher, R., Markoc, H., Gossard, A.C.: Phys. Rev. B 31 (1985) 2080. Oueslati, M., Zouaghi, M., Pistol, M.E., Samuelson, L., Grimmeis, H.G., Balkanski, M.: Phys. Rev. B 32 (1985) 8220. Brugger, H., Abstreiter, G., Jorke, H., Herzog, H.J., Kasper, E.: Phys. Rev. B 33 (1986) 5928. Brugger, H., Reiner, H., Abstreiter, G., Jorke, H., Herzog, H.J., Kasper, E.: Superlattices Microstruct. 2 (1986) 451. Dharma-wardana, M.W.C., Lockwood, D.J., Baribeau, J.-M., Houghton, D.C.: Phys. Rev. B 34 (1986) 3034. Kasper, E., Herzog, H.J., Dambkes, H., Abstreiter, G.: Layered Structures and Epitaxy, Gibson, J.M., Osbourn, G.C., Tromp, R.M. (eds.), Mater. Res. Soc. Symp. Proc., Vol. 56, Pittsburg, PA: Materials Research Society, 1986. van de Walle, C.G., Martin, R.M.: Phys. Rev. B 34 (1986) 5621. Bevk, J., Ourmazd, A., Feldman, L.C., Pearsall, T.P., Bonar, J.M., Davidson, B.A., Mannaerts, J.P.: Appl. Phys. Lett. 50 (1987) 760. Froyen, S., Wood, D.M., Zunger, A.: Phys. Rev. B 36 (1987) 4547. Hybertsen, M.S., Schlüter, M.: Phys. Rev. B 36 (1987) 9683. Kasper, E., in: Physics and Applications of Quantum Wells and Superlattices, Mendez, E.E., von Klitzing, K. (eds.), NATO ASI Series B 170, New York: Plenum Press, 1987, p.101. Lockwood, D.J., Dharma-wardana, M.W.C., Baribeau, J.-M., Houghton, D.C.: Phys. Rev. B 35 (1987) 3243. Pearsall, T.P., Bevk, J., Feldman, L.C., Bonar, J.M., Mannaerts, J.P., Ourmazd, A.: Phys. Rev. Lett. 58 (1987) 729. Baribeau, J.-M.: Appl. Phys. Lett. 52 (1988) 105. Froyen, S., Wood, D.M., Zunger, A.: Phys. Rev. B 37 (1988) 6893. Hybertsen, M.S., Schlüter, M., People, R., Jackson, S.A., Lang, D.V., Pearsall, T.P., Bean, J.C., Vanderburg, J.M., Bevk, J.: Phys. Rev. B 37 (1988) 10195. Kasper, E., Kibbel, H., Jorke, H., Brugger, H., Friess, E., Abstreiter, G.: Phys. Rev. B 38 (1988) 3599. Satpathy, S., Martin, R.M., van de Walle, C.G.: Phys. Rev. B 38 (1988) 13237. Abstreiter, G., Eberl, K., Friess, E., Wegscheider, W., Zachai, R.: J. Cryst. Growth 95 (1989) 431. Eberl, K., Wegscheider, W., Friess, E., Abstreiter, G., in: Heterostructures on Silicon: One Step Further with Si, Nissim, Y.I., Rosencher, E. (eds.), Dordrecht, Boston: Kluwer Academic Publishers, 1989, p. 153. Friedel, P., Hybertsen, M.S., Schluter, M.: Phys. Rev. B 39 (1989) 7974. Pearsall, T.P.: Crit. Rev. Solid State Mater. Sci. 15 (1989) 551. Pearsall, T.P., Vandenberg, J.M., Hull, R., Bonar, J.M.: Phys. Rev. Lett. 63 (1989) 2104.

Landolt-Börnstein New Series III/34C3

3.4.14 References for 3.4 89P3 89V 90B 90C 90H 90J 90K 90T 90Z 91K 91P 91S 91Y 92G 92O 92P1 92P2 92R 92S 93B 93E 93K 93M 93P 93T 94O 94S 94T1 94T2 94T3 94T4 95B 95T1 95T2 95T3 96T 98P

87

Pearsall, T.P., Bevk, J., Bean, J.C., Bonar, J.M., Mannaerts, J.P., Ourmazd, A.: Phys. Rev. B 39 (1989) 3741. van de Walle, C.: Phys. Rev. B 39 (1989) 1871. Bass, J.M., Matthai, C.C.: J. Phys. C 2 (1990) 7841. Ciraci, S., Baratoff, A., Batra, I.P.: Phys. Rev. B 41 (1990) 6069. Hull, R., Bean, J.C., in: Semiconductors and Semimetals, Vol. 33, Willardson, R.K., Beer, A.C. (eds.), New York: Academic Press, 1990. Jain, S.C., Willis, J.R., Bullough, R.: Adv. Phys. 39 (1990) 127. Kasper, E., Kibbel, H.: Vacuum 41 (1990) 929. Turton, R.J., Jaros, M.: Mater. Sci. Eng. B 7 (1990) 37. Zachai, R., Eberl, K., Abstreiter, G., Kasper, E., Kibbel, H.: Phys. Rev. Lett. 64 (1990) 1055. Kasper, E., Schäffler, F., in: Semiconductors and Semimetals, Vol. 33, Willardson, R.K., Beer, A.C. (eds.), New York: Academic Press, 1991. Presting, H., Kibbel, H., Kasper, E., Grimmeis, H.G., Nagesh, V.G.: Mater. Res. Soc. Symp. Proc. 220 (1991) 327. Schmid, U., Cristensen, N.E., Alouani, M., Cardona, M.: Phys. Rev. B 43 (1991) 14597. Yin, Y., Yan, D., Pollak, F.H., Hybertsen, M.S., Vandenberg, J.M., Bean, J.C.: Phys. Rev. B 44 (1991) 5955. Grimmeis, H.G., Nagesh, V.G., Presting, H., Kibbel, H., Kasper, E.: Phys. Rev. B 45 (1992) 1236. Olajos, J., Engvall, J., Grimmeiss, H., Kibbel, H., Kasper, E., Presting, H.: Thin Solid Films 222 (1992) 243. Polatoglou, H.M., Tserbak, C., Theodorou, G.: Thin Solid Film 222 (1992) 212. Presting, H., Menczigar, U., Abstreiter, G., Kibbel, H., Kasper, E.: Mater. Res. Soc. Symp. Proc. 256 (1992) 83. Ren, S.Y., Dow, J.D., Gui-Lin Yang: Phys. Rev. B 45 (1992) 6628. Schmid, U., Humlicek, J., Lukes, F., Cardona, M., Presting, H., Kibbel, H., Kasper, E., Eberl, K., Wegscheider, W., Abstreiter, G.: Phys. Rev. B 45 (1992) 6793. Bass, J.M., Matthai, C.C., Milman, V., Payne, M.: Semicond. Sci. Technol. 8 (1993) 2121. Engvall, J., Olajos, J., Grimmeiss, H.G., Presting, H., Kibbel, H., Kasper, E.: Appl. Phys. Lett. 63 (1993) 491. Kelires, P.C., Tserbak, C., Theodorou, G.: Phys. Rev. B 48 (1993) 14238. Menczigar, U., Abstreiter, G., Olajos, J., Grimmeiss, H., Kibbel, H., Presting, H., Kasper, E.: Phys. Rev. B 47 (1993) 4099. Presting, H., Menczigar, U., Kibbel, H: J. Vac. Sci.Technol. B 11 (1993) 1110. Tserbak, C., Polatoglou, H.M., Theodorou, G.: Phys. Rev. B 47 (1993) 7104. Olayos, J., Jia, J.-B., Engvall, J., Grimmeis, G., Kasper, E., Kibbel, H., Presting, H.: Phys. Rev. B 49 (1994) 2615. Schorer, R., Abstreiter, G., de Gironcoli, S., Molinari, E., Kibbel, H., Presting, H.: Phys. Rev. B 49 (1994) 5406. Tserbak, C., Theodorou, G.: Phys. Rev. B 50 (1994) 18179. Theodorou, G., Kelires, P.C., Tserbak, C.: Phys. Rev. B 50 (1994) 18355. Theodorou, G., Vlachos, N.D., Tserbak, C.: J. Appl. Phys. 76 (1994) 5294. Theodorou, G., Tserbak, C., Vlachos, N.D.: J. Appl. Phys. 78 (1994) 3600. Bernhard-Höfer, K., Zrenner, A., Brunner, J., Abstreiter, G., Wittmann, F., Eisele, I.: Appl. Phys. Lett. 66 (1995) 2226. Theodorou, G., Tserbak, C.: J. Cryst. Growth 157 (1995) 45. Theodorou, G., Tserbak, C.: Phys. Rev. B 51 (1995) 4723. Tserbak, C., Theodorou, G.: Semicond. Sci. Technol. 10 (1995) 1604. Tserbak, C., Theodorou, G.: Appl. Surf. Sci. 102 (1996) 288. Pearsall, T.P., Colace, L., DiVergilio, A., Jäger, W., Stenkamp, D., Theodorou, G., Presting, H., Kaspar, E., Thonke, K.: Phys. Rev. B 57 (1998) 9128.

Landolt-Börnstein New Series III/34C3

88 01Z 02B 06L 06T 06Y

3.4.14 References for 3.4 Zhang, P., Crespi, V.H., Chang, E., Louie, S.G., Cohen, M.L.: Nature (London) 409 (2001) 69. Brunner, K.: Rep. Prog. Phys. 65 (2002) 27. Liao, M.H., Yu, C.-Y, Guo, T.-H, Lin, C.-H, Liu, C.U.: IEEE Electron Device Lett. 27(4) (2006) 252. Talalaev, V.G., Cirlin, G.E., Tonkikh, A.A., Zakharov, N.D., Werner, P., Gösele, U., Tomm, J.W., Elsaesser, T.: Nanoscale Res. Lett. 1 (2006) 137. Yu, J., Kasper, E., Oehme, M.: Thin Solid Films 508 (2006) 396.

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5

3.5. Si, Ge, and SiGe quantum wires and quantum dots

89

Si, Ge, and SiGe quantum wires and quantum dots by T.P. Pearsall

3.5.1 Introduction Quantum wires and quantum dots refer to structures that confine electrons to some degree. There are several dimensional scales that may apply. The transition from a macroscopic to a quantum-confined environment first occurs when charge carriers are confined to a space smaller than the mean free path for elastic scattering. In silicon this length is several hundred nanometers at 4.2 K and around 20 nm ... 40 nm at room temperature. State-of-the-art silicon integrated circuits have transistors that could qualify as quantum confinement structures in this regime. Quantum behavior of carriers in this size regime can be seen in the current-voltage characteristic in the form of fluctuations in the conductance as a function of gate bias voltage and applied magnetic field. These fluctuations are measuring the specific structure of the current-carrying channel in terms of surface roughness, impurities and defects. Because the carriers are transported in the elastic scattering regime, they retain a memory of the path followed. Scattering events change the conductance by quantum steps of e2/h. The first experiments of this type were carried out by Skocpol and co-workers [82S1]. The original intent was to study a silicon metal oxide semiconductor field effect transistor (MOSFET) with an ultra-short channel. This structure is shown in Fig. 3.5.1

e Gat 1 mm

SiO

2

Si

Fig. 3.5.1. This scanning electron micrograph shows a series of fingers defined by reactive-ion etching in a silicon MOSFET structure, giving a perspective view of several of the narrow channels. The inset shows the position of the silicon inversion layer that carries the current across the finger region. The gate length is the width of the finger. For the first experiments carried out by Skocpol, gate lengths in the range of 100 nm ... 200 nm were explored [82S1].

The current is confined to the two-dimensional electron gas in the inversion layer between SiO2 and Si. The gate width is several microns, while the gate length is about 200 nm. Skocpol recognized that it would be even more interesting to study the conductance along the finger that forms the gate width, forming a quantum wire as shown in Fig. 3.5.2.

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

90

[Ref. p. 118

V24 3

2

5

4

1

6 I D

L24

S

W

0.5 mm Fig. 3.5.2. Measurement of conductance along the direction of the finger shown in Fig. 3.5.1 is achieved by placing electrodes (numbered 2 through 5) along the finger. Measurement of the voltage difference (here V24) between two electrodes and the current I between the drain (D) and the source (S) gives the conductance g = I/V. Skocpol [86S1] used this configuration to study quantum wire effects in a silicon inversion layer.

Studies of the conductance at low temperatures showed fluctuations of the conductance that depend on the magnetic field intensity—repeatable, but specific to the sample, proving that coherent electron transport is observed [86S1]. The results of such an experiment are shown in Fig. 3.5.3. The conductance in units of e2/h is plotted as a function of the perpendicular magnetic field for three different gate voltages. The gate voltage and the magnetic field determine the physical part of the sample that is measured. The fluctuations are not noise, but give a “fingerprint” of the sample. They are reproducible, and in particular mark the deviations from a perfect silicon crystalline structure. These results represent some of the first measurements of conductance of quantum-confined electrons in silicon. The reduced dimensional environment results in a quantized density of states. When the lattice temperature is significantly less than the energy separation between adjacent states, electrons flowing through the sample will follow a specific trajectory that is defined by the voltage and the magnetic field. The resulting conductance specific to the voltage and magnetic field is determined by the presence of scattering sites along that trajectory. 14

Si

VG [V] 6.0

12 Conductance g

5.9

12

5.8

12

10 0

2

4 Magnetic field B [ T]

6

8

Fig. 3.5.3. Measurement of electronic conductance (g) of a silicon quantum wire at T = 4.2 K for three different gate voltages VG [86S1]. The vertical scale is calibrated in units of e2/h, and has been extended so that the traces taken on the same sample at different magnetic field strengths can be compared. Each trace shows wellbehaved fluctuations on the order of e2/h. These fluctuations are due to scattering by fixed obstacles in the conduction path. Different values of the magnetic field cause the electrons to avoid some obstacles and encounter others.

In this first quantum size regime, the physical size of the sample is smaller than the mean free path of the electron for elastic scattering. The conductance carries information about the internal elements of the sample that provoke changes in the momentum of the electron under conditions of dissipation-free transport. A second regime occurs when an electron or a hole is confined to a space that is similar to its de Broglie wavelength. This effect can be viewed as a consequence of the Heisenberg uncertainty

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

91

principle. For a free electron confined to a three-dimensional box of dimensions Lx, Ly, Lz,, the electron energy levels are quantized according to the expression En, k ,l =

π 2 =2 § n2 2m*

k 2 l2 · ⋅¨ 2 + 2 + 2 ¸, ¨ Lx Ly Lz ¸ © ¹

(3.5.1)

where n, k and l are integers and m* is the.effective mass of the electron. The de Broglie wavelength of an electron or hole depends on its kinetic energy and its effective mass:

λdB =

h 1 = 2π = . p 2 m∗ E

(3.5.2)

For the case of charge carriers in either Si or Ge, this second regime is reached for sample dimensions on the order of 7 nm or less. Studies of conductance in silicon MOSFET inversion layers in the presence of a magnetic field led to the discovery of the quantized Hall effect, and the Nobel Prize for Klaus von Klitzing in 1985. These studies were carried out in silicon structures having electrons confined to a two-dimensional sheet. This discovery introduced many new insights and questions about the properties of electrons in confined states. The application of a magnetic field perpendicular to the two-dimensional sheet confines the electron to a circular orbit in the sheet. The radius of this orbit is inversely proportional to the magnetic field strength. At sufficiently low temperatures, and sufficiently high magnetic fields, electrons are confined in all three dimensions in a special kind of quantum dot. The radius of the quantum dot in the plane of the sheet is given by rII =

2= ≈ 10 nm in a magnetic field of 13 Tesla. eB

(3.5.3)

The quantum dot is thus defined, but not confined, in the two-dimensional sheet. The quantum dot is both defined and confined by the MOS interface in the direction perpendicular to the sheet. Thus, the quantum dot is free to move around in the two dimensional plane, and so it can carry current. The magnetic field quantizes the allowed energy levels for these electrons, although in each level, there are many available states for electrons. The separation in energy between these quantized levels is proportional to the magnetic field strength, and for values of a few Tesla, the energy separation can be tens of meV, a value significantly larger than kBT at the temperature of liquid helium. When the energy separation between levels is much larger than kBT, electrons can not scatter by collisions between these quantized states. Within a particular quantized level there are typically states that are occupied by electrons, and unoccupied states. Electron scattering between an occupied state and an unoccupied state produces the usual electrical resistance. However, when the electron density is large enough so that all these states are occupied, then scattering is forbidden, and the resistance vanishes. The quantum dot, however, is free to move in the two-dimensional sheet, and so it can still carry current. In his original experiments, von Klitzing systematically increased the density of electrons in a Si MOS structure until this zero-resistance state could be observed and studied [80K1]. This behavior is called the quantized Hall effect. The experiments represent the first creation and observation of quantum dots in any semiconductor. Most of the subsequent studies of electrons confined to a quantum dot by a three-dimensional potential have focused on the formation of quantum dots that are fixed spatially in all three dimensions by the sample geometry. Epitaxial growth by molecular beam deposition, which has precision on the atomic scale, enables the synthesis of silicon-based structures where electrons can be confined to zero (quantum dot) or one dimension (quantum wire). This technology has given a major impetus to the continuation and development of research on electronic and optical behavior of silicon-based structures in this second quantum size regime.

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

92

[Ref. p. 118

3.5.2 Silicon and germanium quantum-wire quantum-dot structures Silicon and germanium share the same crystal structure, but there is a 4% lattice mismatch between them. A pure germanium film deposited on silicon is subject to a significant compressive stress. Only about 4 monolayers of Ge can be deposited before this stress provokes the formation of dislocations as a way to relieve the strain from lattice mismatch—see e.g. the discussion in sections 3.1.2 and 3.1.3. A similar effect occurs for all Si-Ge alloy films grown epitaxially on silicon substrates. There is a critical thickness for such a film, beyond which dislocations are generated to relieve the strain [89P1]. For an alloy film containing only 10% Ge, the critical thickness is 10 nm. At this thickness quantum confinement effects are readily observed. Thus, the growth of coherently strained epitaxial films of Si-Ge alloys on either silicon or germanium naturally introduces a two-dimensional structure, or quantum well, leading to quantum confinement effects. There have been many studies of the mechanical, the optical and the electronic properties of these quantum wells, and the reader is referred to a number of reviews covering this subject [89P1, 99H2, 00K1, 02B1]. If the criteria for critical thickness are exceeded, the deposited material no longer maintains a two-dimensional planar geometry. The equilibrium state in the presence of strain on the one hand and surface tension on the other favors the formation of a three-dimensional dome. These structures are straightforward to produce by either chemical vapor deposition (CVD) or by molecular beam epitaxy (MBE). Early work to demonstrate and characterize such structures was carried out by Eaglesham [90E1] and by Lagally [90M1]. Such domes of Ge deposited on Si generally have a diameter of about 40 nm and a height of about 5 nm. The precise dimensions are determined by the conditions of deposition, such as material flux and substrate temperature. For deposition at fixed temperature, flux and exposure time, the RMS size distribution is typically on the order of 5%. These structures are referred to as self-organized quantum dots.

a

b

c Fig. 3.5.4. Formation of self-organized quantum dots by epitaxial deposition is accomplished by deposition of one semiconductor, such as germanium, on a substrate with a smaller lattice constant, such as silicon. Lattice mismatch strain is partially relieved by the creation of a free surface in three dimensions. This structure is the quantum dot. The size of the quantum dot is determined by an interaction involving the lattice mismatch strain, the surface tension of the free surface, and surface diffusivity, which depends on temperature. Since temperature plays an important driving role, there is always a size distribution for the resulting dots, according to diffusion statistics. The three basic phases of quantum dot formation are (a) deposition of a wetting layer, with 2…4 atomic layers in thickness, (b) growth from roughening and 3-dimensional nucleation, (c) growth of three-dimensional islands by diffusion of atoms on the surface, accompanied by a depletion of the wetting layer thickness.

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

93

The geometry of these self-organized quantum dots is dictated by the crystalline orientation of the silicon surface. For deposition on Si (001), the base of the dot is rectangular, and the sides are parallel to [110] surface directions. The dome of the “dot” is formed by well-defined surface planes generating a hut-like appearance. An image of such a “hut” obtained by scanning tunneling microscopy (STM) is shown in Fig. 3.5.5.

Fig. 3.5.5. Scanning tunneling microscopy (STM) image of a Ge nanocrystal (“hut”) grown coherently on Si (001) [90M1]. The hut is § 3 nm in height, § 20 nm on the short edge, and § 40 nm along the orthogonal base direction.

This kind of quantum-dot structure has electronic and optical properties that are similar to a twodimensional quantum well. Conditions for quantum confinement effects occur in only one dimension, due to the shallow height of the hut-like structure. The scanning tunneling microscope, and more recently the atomic force microscope (AFM) are the tools of choice for studying the formation of such hut-like structures, since the aperiodic location of huts on the surface requires real-space characterization methods. Study of the details of facet orientation is a valuable clue to the energetic balance between the accommodation of strain, surface diffusion, and surface tension. The formation of such huts is an important “nano-laboratory” for experiments that are creating a better understanding of the surface and interface physics of silicon, with significance for the design of silicon-based integrated circuits. Self-organized deposition of Ge quantum dots on Si produces a structure with a characteristic size of 20 nm ... 40 nm, but the de Broglie wavelength for electrons in the conduction band of Ge is about 7 nm. For silicon, a dot size of less than 5 nm is required before quantum size effects can be seen in the energy spectrum. Fabrication of nanostructures in which quantized electronic or optical behavior can be observed requires special attention in Si-based materials. An elegant demonstration of these features is given by the experiment of Batson and Heath [93B1]. Self-assembled silicon quantum dots were prepared by a photolysis-based aerosol synthesis, producing a population of hydrogen-terminated free-standing silicon nanoclusters with a wide size distribution. The clusters were imaged in transmission electron microscopy. Simultaneous characterization by electron energy loss spectroscopy (EELS) enabled any cluster of interest to be interrogated individually. The key result, reproduced in Fig. 3.5.6, shows the conduction band density of states for clusters of different diameters. For the cluster with a diameter of 8 nm, the density of states shows all the features associated with three-dimensional bulk silicon. For the 4 nm cluster this structure has disappeared, and a smooth parabolic density of states characteristic of a single simple conduction band minimum appears. In addition the oscillator strength of the transition from the valence band to the conduction band increases sharply, and the transition energy starts to increase as 1/R2, where R is the cluster radius. The work of Littau et al. [93L1] is equally convincing, showing the onset of quantum confinement effects in the energy spectrum for dimensions below 5 nm. Similar experiments have not yet been performed on germanium nanoclusters. Simple scaling using Eq. (3.5.1) shows that quantum confinement effects on the energy spectrum will be seen in Ge for dimensions less than 7.5 nm. This estimate is confirmed by calculations of Takagahara and Takeda [92T1].

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

94

[Ref. p. 118

Si L1

Normalized Si 2p3/2 intensity

8.8 nm

L3

D1

5.5 nm

4.0 nm 3.0 nm 2.4 nm 96

98

100 102 Energy loss [eV ]

104

Fig. 3.5.6. Electron energy loss spectra (EELS) taken on Si nanoclusters of various diameters [93B1]. The spectrum reproduces the energy dependence of the conduction band density of states, and shows the onset of the quantum-dot size regime below 5 nm. The solid line is a moving average of the experimental data points. The dashed line is a calculation of the density of states taking into account the features of the electronic band structure of silicon. ǻ1, L1, and L3 refer to energies where the joint density of states between the valence and conduction band reaches a maximum. For the sample with a diameter of 8.8 nm the data are fitted well using parameters of the bulk silicon bandstructure. For the sample with a diameter of 5.5 nm, it is necessary to introduce a damping term to model the proximity of the transitions to the surface. The effect of the surface tends to wash out the peaks in the density of states. For samples with diameters less than 4.0 nm, the structure in the density of states has disappeared, and the experiment shows the transformation to a smooth parabolic density of states for all energies measured.

These studies indicate that the quantum-dot regime for silicon nanoparticles lies below 5 nm, and that the quantum-dot regime for germanium nanoparticles lies below 10 nm. This is quite consistent with measurements made on SiGe quantum-well structures [86P1]. These limits are helpful to distinguish Si and Ge quantum dots from larger structures with characteristic dimensions of 20 nm and above which may be three-dimensional in geometry, but which have electronic structures similar to those of bulk materials.

3.5.3. Synthesis of quantum wires and quantum dots 3.5.3.1 Self-organized epitaxy of quantum dots Epitaxial deposition assures that the resulting quantum dots retain the basic crystalline structure presented by the deposition substrate, which in this case is single-crystal silicon. Epitaxy requires careful control of the substrate temperature, and a means for very precise metering of the Ge gas phase flux on the substrate, in the absence of impurities. Ge dots can be synthesized by various vapor-phase growth methods such as low-pressure chemical vapor deposition (LP-CVD) and molecular-beam epitaxy (MBE). In-situ analysis by reflection high-energy electron diffraction (RHEED) is quite helpful to see the transition between layer-by-layer growth to islanding, which occurs at 3 to 4 atomic monolayers thickness of the deposited material. However, RHEED can be used only in a high-vacuum environment such as MBE. Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

95

The size and the density of quantum dots are a function of the substrate temperature and the dose rate of Ge. Useful growth temperatures lie in the range of 500 °C ... 750 °C. Below 500 °C, the deposited Ge is no longer epitaxial, and the melting temperature of Ge is approached above 750 °C. The conditions for producing quantum dots of a certain size and density are specific to each growth reactor. However, the following trends prevail: The size (diameter) of the dots increases with increasing substrate temperature, reflecting increased surface diffusivity. The dot size decreases with increasing Ge flux, but the surface density increases [99S1]. The lattice mismatch between Ge and Si is about 4%, which is substantial. The presence of a single crystal Ge dot imposes a strain field that extends far into the Si substrate. If the layer of Ge dots is subsequently covered by a Si layer, this Si layer is also strained in the vicinity of the Ge dot. This strain field in Si creates sites that favor the nucleation of Ge dots that are aligned vertically to those of the layer below. This feature enables the ordered stacking of quantum dots in subsequent layers [99L1]. Such a stack is shown in Fig. 3.5.7.

Fig. 3.5.7. Transmission electron micrograph (TEM) showing the ordered stacking of ten Ge self-organized quantum dots on Si [00V1]. The intermediate Si layers are about 45 nm in thickness.

Self-organized quantum dots of Ge on Si are characterized by scanning tunneling microscopy (STM), usually in-situ during growth [91M1], and by transmission electron microscopy (TEM), low-energy electron diffraction (LEED) [91A1], and photoluminescence (PL) on structures after growth is completed. Studies by STM have contributed much to understand the mechanism of self-organized dot formation [99S2, 03L1, 04L1]. The clearly defined facets that are seen in Fig. 3.5.5 delineate the surfaces with the slowest growth rates. In the case of fcc materials like Si, these surfaces are typically [111] oriented, because this is the plane with the highest atomic density, so it takes more time to complete each layer. The growth rate in different crystal orientations is determined by an interaction between substrate orientation, temperature, diffusion, and surface energies. A full understanding of these interactions is still being developed. However, the first quantitative measurements of these facets was made by the Lagally group, taking advantage of the atomic resolution of the STM to determine the precise angle that the facets make relative to the substrate [91M1]. They determined the facet surface to be oriented [105]—quite distinct from the usual orientation of [111] that is typically found for surface defects on Si. This straightforward geometrical determination from real-space imaging was shortly afterward confirmed by LEED, a reciprocal-space technique that is highly sensitive to surface structures [91A1]. Photoluminescence spectra of self-organized quantum dots consist of three principal components: emission from the substrate, emission from the wetting layer, and emission from the quantum dot. Luminescence can be detected only at temperatures close to that of liquid He. Si and Ge are both indirect band gap materials. Reducing the temperature lengthens the lifetime for phonon-mediated recombination, thereby increasing the probability of direct radiative recombination across the band gap. Spectra of quantum dot samples are complicated by the presence of a complex strain field, consisting of both compressive and tensile elements. Fig. 3.5.8 is a schematic diagram of the situation, reproduced here from the work of Schmidt and Eberl [00S2]. This study identifies the key features of spectra measured under these conditions.

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

96

[Ref. p. 118

tensile strain

eII

2

compressive strain

compressive strain

Tensile strain eII

0

0

Ge Si

Fig. 3.5.8. A schematic diagram of the tensile strain parallel to surface (lower curve, İ||) and the tensile strain energy (upper curve, E ~ İ||2) of a Ge quantum dot buried in a Si matrix [00S2]. Above the island the Si matrix is laterally widened and the surface exhibits tensile strain. The tensile strain must be accommodated in neighbouring regions as compressive strain.

The low-temperature luminescence is dominated by the transverse optical (TO) phonon-assisted emission from the Si substrate at 1.1 eV. A weaker transverse acoustic (TA) line from Si substrate may also be observed near 1.135 eV. The non-uniform strain distribution in the Si layer can produce an electron-hole condensed liquid (EHD), and this emission occurs at a lower energy near 1.08 eV. The presence of this feature is sensitive to the photo-excitation intensity. The Ge wetting layer consists of two principal features: a no-phonon line and a TO shifted replica about 60 meV lower in energy. The combination of compressive strain and one-dimensional quantum confinement will act to shift the luminescence emission from the Ge band gap at 0.8 eV to more than 1 eV, overlapping the Si substrate luminescence. The amount of the shift cannot be predicted precisely because there may be some strain relaxation and compositional intermixing with Si. The luminescence from the Ge wetting layers gives considerable information about the formation of the Ge quantum dots. Luminescence has been detected from as few as three atomic monolayers of Ge (≈ 0.42 nm). Momentum conservation requirements are relaxed because of the reduced dimensionality, permitting optical recombination across the band gap, producing the no-phonon emission. With slightly increased deposition, the wetting layer increases in thickness, and the luminescence peak from the wetting layer evolves toward the Ge direct band gap at 0.8 eV. The thickness of the wetting layer can be calculated quite precisely from the position of the luminescence peak, using Eq. (3.5.1), and taking into account the compressive strain in the Ge layer. This measurement can be used to confirm and calibrate the metering of the Ge source. At continued deposition, quantum dots begin to form spontaneously at the equivalent of about 5 atomic monolayers. The formation of quantum dots proceeds by surface diffusion of Ge atoms to nucleation sites for quantum dots, thus depleting the thickness of the wetting layer. This in turn provokes a blueshift in the luminescence coming from the wetting layer. The presence of the quantum dots is signaled by a new photoluminescence peak near the band gap of Ge. The residual strain in the dot shifts this signal slightly higher in energy to about 0.85 eV. However, due to the three-dimensional size of the quantum dot, there is, ironically, little quantum confinement shift to the luminescence coming from the quantum dot. With continued deposition, the luminescence peak from quantum dots increases in amplitude, but does not change in its spectral position, the strain being unchanged. At even greater volume of deposition, the quantum dots become fully ripe, the wetting layer increases in thickness, dislocations will develop in order to relieve the strain, effectively destroying the luminescence. Many of these features can be seen in the spectra of Fig. 3.5.9. Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

97

WL TO T = 4.2 K × 0.5

Photoluminescence intensity I

4 ML

Dots

5 ML

5.33 ML

5.67 ML

×2

6 ML

×2

12 ML ×2

0.8

0.9 1.0 Photon energy h w [eV]

NP

Fig. 3.5.9. Photoluminescence spectra from a single layer of Ge quantum dots deposited on silicon. Spectra are taken at T = 4.2 K [00D1]. Luminescence from the Si substrate at 1.1 eV has been excluded from the spectrum. At 4 monolayers deposition, all the lattice mismatch strain energy is absorbed in the Ge wetting layer (WL). The luminescence from this layer has a nophonon (NP) component and a transverse optical (TO) shifted replica, shifted from the Ge band gap by the combined effects of strain and strong 1D quantum confinement. At an equivalent deposition of 5.7 monolayers, luminescence from the Ge quantum dot dominates the signal. At an equivalent deposition of 12 monolayers, dislocations have formed, the measured luminescence is coming from a mixture of fully relaxed quantum dots and layer-like deposition. Since most of the optical excitation radiation is absorbed in the Ge, the amplitude of the luminescence of the substrate is diminished.

The photoluminescence spectra of samples with several layers of quantum dots, as shown in Fig. 3.5.7, display additional features. Deposition of a series of layers containing quantum dots reduces the thickness of the dots, increasing quantum confinement effects. The thickness of the wetting layer and the height of the dots will vary from layer to layer. Schmidt and Eberl have made a study of a Ge quantum-dot system consisting of two layers, by varying the thickness of the intermediate Si spacer layer. These spectra show similar features to those seen in Fig. 3.5.9. However, the luminescence from the two layers occurs at slightly different energies, indicating different layer thicknesses, even though the nominal thickness of each layer should be the same (5 monolayers of Ge). These spectra are shown in Fig. 3.5.10. The spectra show a clear bimodal energy distribution of the luminescence attributed to the quantum dots, a feature that is also evident in Fig. 3.5.9. Schmidt and Eberl have proposed that this feature is due to a bimodal distribution of two dot geometries: pyramids and domes. They have obtained confirming data by atomic force microscopy [00S2]. To separate the influence of the wetting layer on the photoluminescence, Li et al. have devised a method for the deposition of self-organized Ge quantum dots on Si via a xenon wetting layer [04L2]. The Ge nanoclusters were grown on a Si (100) substrate in an ultra-high vacuum (UHV) system with a base pressure of 2⋅10í10 Torr. To inhibit direct interactions of deposited atoms with the substrate during Ge nanocluster growth, a layer of condensed Xe is used as a buffer between the clusters and the substrate. After cooling a clean Si (100) substrate to 10 K in UHV, buffer layers of condensed Xe ranging from 4 to 40 monolayers are formed by a exposure of ≈ 20 ... 200 Langmuir to pure Xe gas. Next, a flux of pure Ge atoms is deposited on top of the Xe buffer layer. Due to the low surface free energy of Xe, these atoms exhibit extremely high surface mobility compared to the surface mobility on a Si substrate, and easily nucleate into small three-dimensional nanoclusters. Finally, the sample is warmed to room temperature to remove the buffer layer and to softly land the nanoclusters onto the Si substrate.

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

98

NP, Ewl,1 WL

T=8K E’dots,1

Edots,1

Photoluminescence intensity I

Single Layer

[Ref. p. 118

SiTO

TO

Ewl,2

E’dots,2

t s = 60 nm Ewl,2

Edots,2

SiTA

30 nm E’dots,2

Ewl,2

Edots,2

Edots,1 15 nm

10 nm 0.7

0.8

0.9 1.0 Photon energy h w [eV]

1.1

Fig. 3.5.10. Photoluminescence spectra of two layer of Ge dots on a Si substrate [00S2]. Each Ge layer has a nominal thickness of 5 monolayers. The top trace shows the luminescence spectrum for a single layer of dots. Stacking layers of quantum dots has the effect of reducing the height of the dots in each layer. This reduction is seen by the quantum shift of the Ge layer luminescence toward higher energy. In the series of spectra, only the thickness tS of the Si intermediate spacer layer is changed. For the spectrum of the spacer layer with tS = 15 nm, the spectrum for the single layer has been superimposed in grey for convenience in evaluating the difference between a single layer and two stacked layers.

The photoluminescence of these unstrained Ge quantum dots at T = 15 K, for different equivalent surface coverages, is shown in Fig. 3.5.11. It can be compared to the photoluminescence spectra of strained Ge dots in Figs. 3.5.8 and 3.5.9.

T = 15 K

Photoluminescence intensity I

P1

P2 6 ML Ge

0.6 ML Ge 0.3 ML Ge

0.75 0.80

0.85 0.90 0.95 1.00 1.05 1.10 1.15 Photon energy h w [eV]

Fig. 3.5.11. Photoluminescence spectra of Ge nanoclusters with a nominal Ge thickness of (a) 0.3 monolayers (ML), (b) 0.6 ML, and (c) 6 ML. The spectra are measured at T = 15 K [04L1].

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

99

3.5.3.2 Lithographic definition of quantum structures Silicon and germanium nanostructures in the quantum regime have been accomplished by using lithography and by self-assembly techniques. In some cases both methods are combined. A schematic illustration of a lithographic method is shown in Fig. 3.5.12. Molecular beam epitaxy is used to define the thickness of the quantum well (Si, Si-Ge or Ge), and high-resolution lithography is used to define the lateral dimensions. This procedure is used to produce either quantum wires or quantum dots, starting from the same quantum well material. Photoresist + Exposure

Etching to form dot

Si

Si

Planar Quantum Well

Planarisation and Passivation

Metallisation

Quantum Dot Fig.3.5.12. Schematic procedure for fabricating a quantum wire or a quantum dot using epitaxial deposition and lithographic definition.

Seebohm and Craighead [00S1] have presented an excellent review of patterning techniques for nanostructures. There are two basic approaches: beam exposure of photoresist using electron-beam or deep-UV photons, and soft lithography, using a stamp either to print or emboss resist materials. Direct-write electron beam lithography (EBL) is widely used to define structures having dimensions of 50 nm or less. Conditions for exposure are discussed in [00S1]. There are three important properties for any lithographic process: resolution, registration, and throughput. Direct-write electron beam lithography is a method that represents a studied compromise between these properties. At the present time, this method is capable of producing feature sizes of about 10 nm under optimum conditions. Improvements in electron beam sources and electron optics are the key to higher resolution, although it appears unlikely for thermal reasons that electron beam lithography can reach the region of atomic resolution. There is considerable interest in developing alternatives to electron beam writing, because it is a relatively expensive tool, and it does not appear to be suitable either for exposure of substrates with a diameter larger than 100 mm, nor for fabrication in volumes large enough for commercial applications. Remarkable results have been demonstrated by imprint lithography [95W1]. Imprint lithography is implemented by a master stamp that is used to emboss a resist material by direct impression. The resulting material is used directly as an etching mask. This kind of micro-contact printing has the immediate appeal that it is a parallel printing process with a potential throughput much greater than that of electron beam lithography. The size of the printing area depends only on the rigidity of the stamp. The resolution depends on the process used to define the stamp. Chou has demonstrated features of 25 nm, putting imprint lithography in the same category as electron beam exposure methods [96C1]. Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

100

[Ref. p. 118

A significant evolution from the structure shown in Fig. 3.5.12 is the use of an electric field to confine electrons to a quantum-dot structure. A significant disadvantage of confinement by physical barriers is that surface roughness and interface states play a significant role in defining electronic and optical properties of the quantum-dot or quantum-wire structure. By using an electric field to achieve confinement, the energetic boundary that confines the electron is no longer synonymous with the physical boundary. What is more, the confinement volume can be modulated by the electric field. Such structures have implemented fruitful studies on the physics of quantum confinement.

Fig. 3.5.13. A Si-Ge quantum dot formed by an 8 nm thick quantum well embedded in silicon with lateral confinement by an electric field applied via the gates G1, G2 and G3. [04K1].

In the atomic force microscope image shown in Fig. 3.5.13, a quantum dot is created by the combination of confinement in the “vertical” direction by a Si-Ge quantum well and in the lateral plane by the application of an electric field. Note that the nominal dimension of the lithography is several hundred nanometers. This is an order of magnitude larger than the dimension of the dot. The use of an electric field permits access to confinement dimensions that are significantly smaller than the resolution of the lithography. Ishikuro and Harimoto [97I1, 99H1] have further developed electric field confined quantum-dot structures, using the Si-MOSFET inversion layer for confinement in the third dimension. A diagram of the electrode structure is shown in Fig. 3.5.14. [110] +

Source (n ) Gate poly-Si

[110]

+

Drain (n )

Point contact( p- ) W < 10 nm

SOI mesa Buried oxide

Fig. 3.5.14. Creation of a quantum-dot structure in silicon by electric field confinement. The electron distribution is first confined by a MOS inversion layer. Lateral confinement is achieved in the “neck region” between the source and drain of the structure. Measurements show that the dot dimension is less than 10 nm [97I1].

(111) Facet

The current-voltage characteristic from source to drain shows distinct regions where there is no increase in current for an increase in voltage. These current plateaux show that Coulomb blockade is occurring because of the quantization of electron energy levels. The dot size can be changed by the gate voltage. This gives access to a different range of source-drain voltages for the Coulomb blockade. The result of these measurements is shown in Fig. 3.5.15. For example, by increasing the source-drain voltage Vds while keeping the gate voltage Vg constant, the source-drain current increases until a plateau is Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

101

reached, indicating Coulomb blockage by electrons occupying states in the quantum dot. At even larger source-drain voltages, additional empty states can be accessed, and additional current can be transmitted by the structure. Ishikuro and Hiramoto have been able to demonstrate these quantum confinement effects at room temperature, precisely because electric field confinement allows access to ultra-small quantum dots. As the size decreases, the energy separation between adjacent states increases, allowing the quantum dot properties to be observed at room temperature—see Eq. (3.5.1).

Fig. 3.5.15. The drain current (vertical axis) shows regions of distinct plateaux as a function of drain-source voltage. A plateau occurs when a single electron occupying a state in the quantum dot can impede additional electrons from entering the dot at that energy. With sufficient drain-source bias, an unfilled energy level can be filled, allowing additional current. Applying a gate voltage changes the relationship between drain-source voltage and current [97I1].

This approach has been used to develop Si quantum-dot transistor arrays, and integrated circuits. It has several distinct advantages over other methods of producing three-dimensional quantum confinement of electrons in silicon: a)

The Si MOS inversion layer is a well-established method for creating one-dimensional confinement without introducing additional strain and defects.

b)

The use of electric field confinement in the lateral directions created no additional defects in the structure. The electrodes are deposited on the surface, and no precision etching is required.

c)

The fabrication methods are totally compatible with those used to make VLSI (Very Large Scale Integrated) circuits.

d)

The quantum dot size can be much smaller than the critical feature size of the confinement electrodes.

e)

The quantum dot dimension is electrically adjustable.

The properties of these transistors and circuits are discussed further in section 3.5.4 on applications. 3.5.3.3 Synthesis of free-standing Si quantum dots Si quantum dots with characteristic dimensions of 2 nm ... 10 nm can be fabricated in large quantities with reasonable control of the dot size. At the present time, two different methods have been developed for the fabrication of zero-dimensional quantum-dot structures: CO2 laser pyrolysis of silane in helium, followed by sizing using aerodynamic separation in a supersonic jet, and a procedure of implantation of excess silicon in SiO2, followed by annealing, thus inducing segregation of Si nanoclusters embedded in a SiO2 matrix. As remarked earlier with regard to the work of Heath and Batson, the pyrolysis method creates a population of silicon nanoclusters with a significant size distribution. Huisken and co-workers have developed a method for creating the nanocluster population, as well as a method for collecting and sizing the nanoclusters [03H1, 97E1, 95E1, 00H1]. The pyrolysis method is generally quite straightforward. A Landolt-Börnstein New Series III/34C3

102

3.5. Si, Ge, and SiGe quantum wires and quantum dots

[Ref. p. 118

molecular beam of silane and He is injected into a flow reactor, where the stream is irradiated by a CO2 laser, pyrolyzing some of the silane into Si + H2. The apparatus is illustrated in Fig. 3.5.16.

Fig. 3.5.16. Silicon nanoclusters are created in the source chamber by pyrolysis of silane. Nanoclusters diffuse to the spectrometer where they are separated according to mass, permitting the selection of nanoclusters all having the same mass (size) within a narrow range [00H1].

The procedure developed by Huisken and co-workers [00H1] enables the production of Si nanoclusters with a well-defined particular size and size distribution. The Si nanoclusters are extracted from the reaction zone into a high-vacuum chamber to form a freely propagating pulsed molecular beam. Size selection is achieved by exploiting the correlation between mass and velocity (small nanocrystals have a higher velocity than the larger ones) and employing a chopper properly synchronized with the CO2 laser. The chopper selects the desired cluster size which is finally deposited on a substrate positioned behind the chopper. The size of the Si clusters transmitted by the chopper is determined with the help of a time-of-flight mass spectrometer. The selected nanoclusters are typically collected on a quartz window for further study. After preparation in vacuum, the samples are exposed to air, allowing the Si nanocrystals to be surface-passivated by a naturally grown oxide layer. An atomic-resolution electron micrograph of a 10 nm nanocluster, formed in this way, is shown in Fig. 3.5.17. The single-crystal structure of the nanocluster is evident. In addition, an amorphous layer of SiOx, about 2 nm thick, can be seen to cover the exterior surface.

3 nm

Fig. 3.5.17. Electron micrograph of a single-crystal Si nanocluster formed by pyrolysis of silane [00H1]. The nanocluster is about 10 nm in diameter and is covered by an amorphous SiOx layer about 2 nm thick.

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

103

3.5.3.4 Photoluminescence properties of Si nanoclusters The basic characterization methods for Si quantum dots are transmission electron microscopy (TEM) to determine the structure, and optical spectroscopy (absorption and photoluminescence) in order to define the electronic energy levels and to determine the photoluminescence yield. Weak photoluminescence from bulk Si can be observed at room temperature near 1.1 eV in the infrared. Si quantum dots (d < 10 nm) exhibit stronger photoluminescence, with a peak near 1.7 eV. For dots with a diameter less than 4 nm, this luminescence is visible. This situation is quite distinct from that of Ge quantum dots deposited on Si, where luminescence can be observed only at low temperatures. In Fig. 3.5.18, we show spectra of different ensembles of dots, each a having a different mean size. These photoluminescence spectra show two important results. The larger dots (d > 5 nm) exhibit negligible quantum confinement effects in the photoluminescence signal. The photoluminescence peak at 1.4 eV shows that the electronic energy structure of Si quantum dots is quite distinct from that of Si, where the photoluminescence peaks at 1.1 eV. The electronic levels that are responsible for this luminescence are still a subject of debate. There is evidence that the interface states between the Si core and the SiO2 cladding may be the primary source of this emission. A second important feature is that the energy of the photoluminescence peak increases due to the quantum confinement effect for Si dot sizes less than 5 nm.

Fig. 3.5.18. Room temperature photoluminescence spectra for three different groups of Si quantum dots with different mean size distributions. The quantum confinement shift in energy from 1.4 eV upwards is seen as the mean diameter of the Si quantum dots is reduced below 5 nm [00H1].

3.5.3.5 Si quantum dots formed by controlled segregation of excess Si in SiO2 Silicon quantum dots can be created in-situ by the introduction of excess silicon in silicon dioxide, followed by a subsequent heat-treatment to induce segregation of the metastable silicon. Excess Si can be introduced in many ways. The most often used methods are chemical vapor deposition of SiO2 with an excess Si concentration, sputtering of SiO2 in the presence of excess Si, and ion implantation of Si into SiO2. Following deposition, the samples are annealed for several minutes to several hours to precipitate the excess silicon out of solution forming clusters of Si buried in SiO2. These techniques are both straightforward and potentially compatible with Si-VLSI processing. Silicon nanoclusters formed in this way have been widely investigated for both electronic and optoelectronic applications. The density and size of the silicon quantum dots depend on the excess Si concentration introduced (typically 10% ... 20 % above stoichiometric conditions), the annealing temperature (typically between 900 °C ... 1100 °C) and the time. For some examples of specific procedures, the reader can consult references [93K1, 94S1, 94D1, 98I1, 05P2]. While the general conditions for producing Si quantum dots are well-known, the specific relationship between the details of dose and annealing conditions on the one Landolt-Börnstein New Series III/34C3

104

3.5. Si, Ge, and SiGe quantum wires and quantum dots

[Ref. p. 118

hand, and the size and density of quantum dots on the other, are still somewhat obscure, remaining as “know-how” of individual research groups. The optical recombination spectra of freely-formed Si quantum dots, shown in Fig. 3.5.18, appear to be different from those displayed by Si quantum dots nucleated in SiO2 (see Fig. 3.5.19 through 3.5.21). Although fabrication parameters enable the synthesis of Si nanoclusters of different sizes, there appear to be fewer differences in optical recombination properties of the Si-SiO2 heterostructures that are formed by the process of the introduction of excess Si and subsequent ripening into Si nanoclusters. Experimental evidence suggests that several sites for optical recombination are active, including defects in the SiO2 matrix and states created at the Si-SiO2 interface. It is straightforward by using nucleation of excess Si to produce quantum dots in the size range of 3 nm ... 5 nm, embedded in SiO2. Under controlled conditions, the size dispersion is less than 15%, allowing the synthesis of an ensemble of quantum dots over a macroscopic area with well-defined size and optical properties. Fig. 3.5.19 shows high-resolution transmission electron micrographs (TEM) of such samples, produced by ion implantation of Si following annealing at 1100 °C [04G1]. Nanoclusters with a diameter of about 4 nm can be seen imbedded in the SiO2 matrix. These studies confirm that these clusters are crystalline. The formation dynamics of the cluster depend on the implant dose, the annealing temperature and the annealing time during formation. Once the excess Si in solution has been depleted, there is no ripening process, as is the case with self-organized Si quantum dots, and the clusters cease to grow.

Fig. 3.5.19. This high resolution transmission electron micrograp (TEM) shows the result of the plasmaenhanced chemical vapor deposition (PECVD) of SiO2 and excess Si following annealing. A distribution of single-crystal Si quantum dots can be seen (encircled) embedded in the sample, made manifest by the periodic contrast having the same atomic layer spacing as that of Si crystalline material. The average diameter of these single crystal nanostructures is about 5 nm. The inset shows an expanded view of a cluster [04G1].

Photoluminescence (PL) and electron spin resonance (ESR) have been used to complement the structural characterization by TEM. Photoluminescence studies by Garrido et al. on the samples of Fig. 3.5.19 show two main luminescence bands, one centered at ≈ 2.5 eV and the other at ≈ 1.7 eV [02G1]. These results, shown in Fig. 3.5.20, illustrate that luminescence is present following annealing at 690 °C even in the SiO2 control sample where no excess Si has been introduced. Samples that are implanted with Si show a stronger luminescence amplitude, but the presence of Si does not shift the energy of the emission. These results are not consistent with the model of luminescence that originates from an ensemble of quantum dots of different sizes. First of all the luminescence spectrum is bimodal, and the same peaks can be resolved in unimplanted, but annealed SiO2. Second, the spectrum does not shift to longer wavelengths, which would reflect an increase in mean dot diameter as a result of annealing. Instead, implantation of excess Si, followed by annealing is seen to amplify the optical recombination from levels that exist in unimplanted SiO2. These measurements support the model that the implantation of excess Si, and the subsequent nucleation of nanoclusters, enhance the transfer of excited state electrons to optical recombination levels in the SiO2 matrix.

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

Photoluminescence intensity I [arb.units]

3.0 2.75 2.50 6

Photon energy h w [eV] 2.25 2.0 1.75 not implanted 10% 2h 10% 2h+2h 20% as-implanted 20% 2h 20% 2h+2h

4

105

1.5 l exc = 325.11 nm

2

0 400

500

600 700 Wavelength l [nm]

800

900

Fig. 3.5.20. Photoluminescence (PL) of SiO2, excited in the UV at 325 nm [02G1]. Note that annealed, unimplanted SiO2 shows the same PL bands. Implantation of excess Si followed by annealing enhances this photoluminescence, suggesting that the Si quantum dots provide a more efficient pathway for the population of luminescent states in SiO2.

Valakh and co-workers have traced the evolution of the two photoluminescence bands as a function of annealing temperature following implantation [99V1]. The implantation dose used was 6⋅1016 cm-2. The implant energy was 150 keV. The resulting implant range and straggle were ¢230 nm² and ¢70 nm², respectively. Their results, shown in Fig. 3.5.21, show that following implantation, the luminescence signal is centered almost entirely near 2 eV. Following successively higher annealing temperatures, this band decreases in amplitude, but does not shift significantly in wavelength. Then, at 1100 °C, it can be seen that the 2 eV luminescence band has entirely disappeared, and the luminescence has shifted to the band near 1.7 eV. These results show that there is not a gradual evolution from one band to the other, as would be expected if the luminescence had its origin in Si quantum dots the size of which is increasing as the annealing temperature is raised. The results do support the idea that a new state is created in the annealing process, due to the nucleation of the excess silicon. They conclude that the photoluminescence recombination process takes place at surface localized states of the nanocrystals or even in the interfacial layer between the crystalline Si core and the amorphous SiO2 surface layer.

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

106

Photon energy h w [eV] 2.0 1.75

2.25

2.50

[Ref. p. 118

1.5

Photoluminescence intensity I [arb.units]

1.2 6

1 1.0 0.8 0.6

2

0.4

3

Fig. 3.5.21. Room temperature photoluminescence from silicon nanoclusters in a SiO2 matrix [99V1]. The curves correspond to different annealing temperatures: (1) as-implanted, (2) 300 °C, (3) 400 °C, (4) 500 °C, (5) 600 °C, (6) 1200 °C.

4

0.2

5

0

600 650 700 Wavelength l [nm]

550

500

750

800

Using samples that were prepared under similar conditions, Tetelbaum and co-workers have shown that a negligible shift in the 1.7 eV photoluminescence peak occurs as a function of annealing time at 1000 °C [02T1, 02T3]. This group has demonstrated that co-implantation with phosphorus ions (dose variations from 1⋅1015 cm-2 ... 30⋅1015 cm-2, implant energy 100 keV) increases significantly the PL yield in proportion to the phosphorus dose, but introduces no shift in the wavelength.

1.8

Photoluminescence intensity I [arb.units]

4000

Photon energy h w [eV] 1.7 1.6

1.2 6

4 3

3000

2

2000

1000

0 600

a

Photon energy h w [eV] 1.6 1.4

Photoluminescence intensity I [arb.units]

2.0

1

700

800 900 Wavelength l [nm]

1000

5

b

1.4

1.3

1.2

5 4 3

4 3 2 2 1 0 700

1100

1.5

1 800

900 1000 Wavelength l [nm]

1100

Fig. 3.5.22. (a) Photoluminescence (PL) yield as a function of annealing time in Si nanoclusters in a SiO2 matrix. The annealing temperature is 1000 °C [02T2]. The annealing times are (1) 30 min, (2) 60 min, (3) 120 min, and (4) 180 min. Longer annealing time improves the yield, but does not change the energy of the peak photoluminescence emission at 1.57 eV. (b) Room temperature PL yield of Si nanocluster in SiO2 matrix structures [02T1]. Dependence of the yield on level of phosphorus co-implant doping flux Ɏp: (1) Ɏp = 0, (2) Ɏp = 1015 cm-2, (3) Ɏp = 3·1015 cm-2, (4) Ɏp = 10·1015cm-2, (5) Ɏp = 30·1015 cm-2 . In all cases the peak of the luminescence remains fixed at 1.59 eV.

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

107

These results demonstrate that the properties of the observed luminescence depend on the presence of Si clusters, but not on their geometry. A model that is consistent with experimental results is that the Si nanoclusters act to absorb the excitation radiation, creating an electron-hole pair which is transferred to an interfacial site or defect where recombination occurs. Co-doping may act to align energy levels between the excited state and the recombination level so that resonant energy transfer occurs. Quantum dots of germanium in a SiO2 matrix have been prepared by magnetron sputtering [05R1]. Deposition followed by annealing produces nanoclusters that are similar in physical size to the Si nanoclusters discussed above. These samples display photoluminescence at room temperature with a peak intensity at 1.75 eV and a lineshape that resembles that shown in Fig. 3.5.21. From the studies of photoluminescence of strained quantum layers with a thickness less than 1 nm, it has been determined that the band-to-band luminescence occurs at 1.05 eV (see Fig. 3.5.10). If quantum confinement in the germanium were determining the emission energy, the Ge quantum dots studied in the work of Roy and Das [05R1], having a diameter almost one order of magnitude larger, would not be the source of radiative recombination at higher energies than that shown in Fig. 3.5.10. In fact the spectra measured by Roy and Das are composed of several features, the most prominent of which occurs near 1.7 eV. It appears that the radiative recombination center is located elsewhere, either at interface states or at defects in the SiO2 created during the deposition and annealing process. 3.5.3.6 Si quantum dots formed by the controlled segregation of excess Si in SiNx In the previous section, evidence is presented for the determining role that Si-SiO2 interface states play regarding optical properties of Si nanoclusters. In particular the optical recombination energy is pinned near 1.7 eV, and the recombination lifetime is on the order of microseconds or even longer, further supporting the model of optical recombination from localized states, such as defects or interface states. Park et al. have developed a thin film CVD deposition procedure using a silane-ammonia mixture. This deposition produces Si-rich SiN with Si nanoclusters spontaneously embedded in the SiNx matrix [02P1]. The size and density of nanoclusters depend on the growth conditions, particularly on the Si excess and the nitrogen flow rates. More precise details of the thin film deposition have yet to be published. The characterization of this material shows significant differences with respect to those obtained for silicon-rich silicon oxide (SRSO). The quantum size effect on photoluminescence can be fit by the relationship E ( d ) [ eV ] = 1.16 +

11.8 . d2

(3.5.4)

The measurements are shown in Fig. 3.5.23a [04K2]. The significance of this measurement can be seen in Fig. 3.5.23b, where it is seen that photoluminescence spectra which span the entire visible spectrum can be obtained with these Si-rich SiNx materials [06S1]. The direct dependence of the peak luminescence energy on the nanocluster size supports the model of electronic transitions in the Si nanocluster, rather than recombination from surface states. The spectral width of these emission lines (ranging from 350 meV for the emission line that peaks at 950 nm to 1000 meV for the emission line peaking at 500 nm) is many times larger than the photoluminescence linewidth of a direct band gap semiconductor that has a well-defined band gap. This result is a consequence of the variation in the size of the nanoclusters in the SiNx matrix. The quadratic dependence of the band gap energy on the nanocluster size will tend to amplify variations in cluster size. In Fig. 3.5.23a, the data points at 2.6 nm and 3 nm differ in size by 10%. However, the corresponding peak emission wavelengths, 440 nm and 520 nm, differ by almost 20%. While these characteristics of the spectra may not be optimal for device applications, they give strong support to the model of light emission from the Si quantum dot cluster, rather than from defect or interface states.

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

108

[Ref. p. 118

6

Band gap E [eV]

5

Photoluminescence intensity I [normalized]

measured data for Si nanocrystals fitted PL energy for Si nanocrystals PL energy for amorphous Si quantum dots

4

3

2

1 1

a

2

3

4 5 Dot size d [nm]

6

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 300 400

7

b

500 600 700 800 900 1000 1100 Wavelength l [nm]

Fig.3.5.23. (a) Optical bandgap as measured by photoluminescence versus cluster size for Si nanocrystals embedded in a SiNx matrix [04K2]. The solid line is given by Eq. (3.5.4). (b) Room temperature photoluminescence spectra from a range of samples each having a different characteristic band gap energy [06S1]. It can be seen that a large range of peak emission wavelengths can be spanned by this Si nanocrystals in SiNx system. The visible range is 400 nm to 650 nm.

The measured time-decay of photoluminescence lies in the range 0.2 ns < IJ < 2.8 ns. However, the quantum efficiency of emission is low, ≈ 2%. These two results indicate that the luminescence decay is dominated by a non-radiative lifetime (≈ 3 ns) that is much shorter than the radiative lifetime (≈ 200 ns).

3.5.4 Applications of SiGe quantum-dot structures Applications of quantum-dot structures tend to be the simplest kind of electronic or opto-electronic devices, reflecting the emergent state of knowledge about the properties of quantum-dot materials. One of the principal interests is the use of quantum-dot structures to introduce photonic functionality in a silicon VLSI-compatible environment [02E1, 05R2]. Both light-emitting diodes and photodetectors have been demonstrated. In addition there is encouraging evidence that silicon-based quantum dots may provide the pathway to an electrically pumped laser based on silicon [05F1]. 3.5.4.1 SiGe quantum-dot photodetectors Quantum-dot photodetectors represent an extension of photon absorption by electrons excited from one quantum-confined subband to another. Such photoconductors, based on quantum wells with onedimensional confinement, have been widely developed for mid to far infra-red detection, because the typical energy spacing between adjacent subbands falls in this wavelength range. This device is referred to as a quantum-well infrared photodetector, or QWIP. However, the use of SiGe brings distinct performance advantages compared to III-V materials for implementing a QWIP. Efficient absorption of light in a simple planar quantum-well structure requires that the photons are polarized in a direction perpendicular to the plane of the quantum wells. Intersubband absorption in conduction band quantum wells of III-V materials obeys this rule. This is a significant impediment to making a detector in the usual configuration, where light is directly incident on the detector surface. However, the energy band alignments between Si and Ge are such that there is little confinement of Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

109

conduction band states, so useful QWIP-type detectors based on intersubband transitions in the conduction band cannot be made. However, quantum wells with excellent confinement properties can be formed in the valence band. The electronic states in the valence band are more complicated and numerous than those in the conduction band of III-V materials, and so allow efficient absorption by light of any polarization, enabling photodetectors where the light is incident on the detector surface. The use of quantum dots brings additional advantages relative to quantum wells: • •

Photoexcited electron-hole pairs have a longer lifetime, leading to improved efficiency, and There is a lower dark current, permitting operation at higher temperature.

The longer carrier lifetime is the direct result of a reduced cross section for electron-phonon scattering because the availability of states for scattering in a quantum dot is severely restricted. In a similar way, a lower dark current results from a sharply reduced overlap between the Fermi function and available states in the quantum subbands, making it more difficult for a thermal excitation of carriers to occur. There are also new problems: •

The geometrical cross section represented by a layer containing an ensemble of quantum dots is much lower than that represented by a quantum well having the same thickness.

•

There is a difficulty to collect the photoexcited electron-hole pairs from each quantum dot, where they are 3D confined. A solution proposed by Elfving et al. at the University of Linköping has been to create a multilayer structure consisting of alternating layers containing quantum dots and quantum wells. If the quantum dots are sufficiently close to the wells, photoexcited electrons in the quantum dots can tunnel into the quantum wells where they can be collected under the influence of an electric field [03E1]. A responsivity of 140 mA/W has been measured at 1350 nm. At 1500 nm, the measured responsivity is lower, about 35 mA/W.

This detector is a multilayer structure consisting of a silicon layer with Ge quantum-dot islands, silicon buffer/spacer layers, and Si-Ge quantum wells. A schematic diagram is shown in Fig. 3.5.24. The energy separation between the level for holes in the quantum dot and the conduction band represents the minimum interband energy. Photons with energy corresponding to this difference are absorbed, creating a hole that is localized in the quantum dot. The hole is excited out of the dot by the action of an applied electric field. It is then collected in the Si-Ge quantum well which provides a continuous electrical channel between source and drain of the photoconductive detector. Ec QW Gate +

S

QD

G D

S

Ev QD

QW

Fig. 3.5.24. In this detector structure, photons are absorbed by promoting an electron from a zero-dimensional quantum dot, leaving behind a trapped hole. The localized hole is field-ionised by the gate potential and promoted from the quantum dot into the two-dimensional quantum well “express transport layer”. This layer serves as the channel for conduction. Once in the quantum well, the hole is then transported to the contacts by an electric field between the source and drain of the structure [03E1].

Work on development and improvement of Si-Ge quantum dot detectors has been carried out in a number of research groups. In Table 3.5.1 we give a summary of some of the main results.

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

110

[Ref. p. 118

Table 3.5.1. Survey of Si-Ge photodetectors based on nanostructure designs. pin refers to a sequence of semiconductor layers which are doped with impurities: p-type, intrinsic (undoped ), and n-type. First Author and References

Institution

Detector Structure

A. Elfving [03E1]

Linköping University

M. Elkurdi [02E1]

Responsivity at 0.95 eV [mA/W]

Responsivity at 0.8 eV [mA/W]

Dark-current density [mA/cm-2]

Waveguide Ge dot– 500 Heterojunction Bipolar Transistor (HBT)

25

0.004 (at –1 V) 0.04 (at –5 V)

Université Paris XI, Orsay

Waveguide Ge dot pin diode

50

0.13

0.42 (at –1 V)

M. Elkurdi [02E2]

Université Paris XI, Orsay

Waveguide Ge dot pin diode on a Silicon on Insulator (SOI) substrate

25

0.25

K. Brunner [02B1]

Walter Schottky Institut

Normal incident Ge (110) dot layer pin diode

S. Tong [02T2]

UCLA

Normal incident Ge dot pin diode

J . Yu [06Y1]

Universität Stuttgart

Resonant-cavity Ge dot pin

G. Masini [00M1]

Università Roma 3 and MIT

Waveguide thick Ge epitaxial-layer pin diode

D. Buca [02B2]

Forschungszentrum Jülich

D. Buca [02B3]

Forschungszentrum Jülich

5

8 (at 1.4 µm)

0.03 (at –1 V) 0.03

10-7 (at –5 V)

250

20 (at –1 V)

10 Si/SiGe superlattice 5 Metal-SemiconductorMetal (MSM) detector with 16 ps response

~1

15 (at –1 V)

300 nm Ge epitaxial160 layer Schottky detector with 10 ps response

9

400

In general, the response time of these photodetectors is very rapid. Response times of 10 ps ... 20 ps have been demonstrated by several groups. This short response time is due in part to the thickness of the absorption region, which has dimensions on the order of several hundred nanometers for the largest detectors. This is significantly less than a diffusion length. It is also much less than the absorption length, and all quantum-dot detectors suffer from responsivity that is far below that of unity quantum efficiency, which would be about 1300 mA/W for the detection of light at 1500 nm. Some approaches that may help to improve performance are (1) a waveguide geometry so that light can be channeled and absorbed over a longer distance, or (2) a resonant cavity geometry where the incident light passes several times through the absorbing region [06Y1]. Much work is still needed to optimize these designs to obtain a performance that is competitive with that of other photodetector materials in this wavelength range.

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

111

3.5.4.2 Si quantum-dot light-emitting diodes The photoluminescence [95L1] generated by structures of Si nanoclusters precipitated in SiO2 is the basis for the development of light-emitting diodes (LEDs). Study of the LEDs is a starting point for the development of an electrically pumped injection laser. Attainment of laser action in a silicon structure is one of the “Grand Challenges” of semiconductor optoelectronics. While some advances have been obtained which are promising, there has not yet been a successful demonstration of a silicon-based injection laser. Attention has focused on the measurement of optical gain in these nanostructures, because gain is a precondition for observing laser action. Detailed and controlled studies of optical gain in these structures has been carried out by several groups around the world, notably in Italy, the US and Australia [05F2, 03D1, 03R1, 04L3, 02N1]. Pavesi et al. have measured small, but positive optical gain coefficients in these materials [00P1, 03P1]. A spectrum of this gain is shown in Fig. 3.5.25. Free carrier absorption and Auger recombination are each significant in Si and can turn gain into loss as the excited carrier density increases. The excitation power density is a key parameter in the observation of optical gain. By comparison, a direct bandgap semiconductor like GaAs shows gain near its bandgap energy of about 104 cm-1, which is three orders of magnitude larger. Laser action can take place in the presence of optical gain, population inversion and a resonant cavity. If the measured gain in Si-SiO2 structures remains below 100 cm-1, then the resonant cavity would have to be two orders of magnitude larger than that of a typical semiconductor laser diode, that is, on the order of cm in length. The intra-cavity loss, as a result, would need to be two orders of magnitude lower, on the order of 0.01 dB cm-1. Waveguides in silicon with this low level of loss have yet to be demonstrated. These considerations indicate that additional breakthroughs are needed before an injection laser based on these materials can be demonstrated. 2.75 120

2.5

Photon energy h w [eV] 2.25 1.75 2.0

1.5

Optical gain coefficient G [cm-1]

80 40 0 - 40 -80 -120

fit to full equation spectra difference

-160 -200 450

500

550

600

650 700 750 Wavelength l [nm]

800

850

900

950

Fig. 3.5.25. Optical gain spectrum in the Si-SiO2 system. For comparison, the optical gain coefficient of GaAs near its band gap energy is about 104 cm-1 [03P1].

Optical gain exists because optical pumping the Si-SiO2 structure results in optical emission that exceeds absorption over a specific range of wavelengths. We observe this result as photoluminescence. Optical gain and the accompanying luminescence have also been demonstrated in this medium by electrical pumping. The Si-SiO2 system does not behave like a typical semiconductor. Instead, special structures are needed to create electroluminescence, and these are based on excitation by hot electrons. A layer of SiO2 is inserted in the depletion region of a Si pn diode. To excite electroluminescence, the diode Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

112

[Ref. p. 118

is put into reverse bias until breakdown occurs, and hot electrons are injected into the Si-SiO2 layer. These electrons dissipate their energy by both non-radiative energy loss and by radiative recombination. By co-doping the Si-SiO2 region with specific rare-earth ions, the wavelength of the radiative recombination can be tuned to a wavelength particular to that ion. An additional advantage of this codoping is that the radiative lifetime is reduced, thereby increasing the luminescence yield. Coffa and coworkers have demonstrated electroluminescent diodes using the p-type Si/(Si-SiO2)/n-type Si sandwich structure, co-doped with Er ions, to produce light emission at 1550 nm, or an energy of 0.8 eV, respectively [96C2, 98C1]. Their experiments show that the Si-SiO2 structure is excited in a layer about 50 nm in thickness immediately adjacent to the Si p-type and n-type regions bordering on each side. Castagna has measured a quantum efficiency of several percent for these devices [03C1]. Quantum efficiency is the ratio of photons emitted per electron injected, bearing in mind in the present case of excitation by impact ionization, one injected electron is capable of generating more than one photon. However, the power efficiency is lower. Electrons are injected at a potential of 20 V ... 40 V. They are used to create photons with an energy of about 1 eV. Even if the quantum efficiency were 100%, the power efficiency would be only a few percent. Thus most of the energy that is used to operate these diodes is released as heat. In a conventional light-emitting diode, the electrons are injected at a potential that is usually quite close to the energy of the photon being emitted, and the power efficiency is closer numerically to the quantum efficiency. Such Si-based LEDs emit light in different regions of the spectrum, depending on the rare-earth ion that is used to co-dope the Si-rich oxide layer (Table 3.5.2). Table 3.5.2. Optical emission energies for Si-based LEDs co-doped with rare-earth ions. Rare-earth ion

Emission wavelength [nm]

Cerium: Ce3+ Terbium: Tb

3+ 3+

Ytterbium: Yb

Praseodymium: Pr Erbium: Er

3+

3+

Emission energy [eV]

530

2.34

540

2.30

983

1.26

1088

1.14

1550

0.8

The room temperature electroluminescence spectra of some LEDs are shown in Fig. 3.5.26 and 3.5.27, respectively. The LED in Fig. 3.5.26 is made from the Si-SiO2 system with 42% excess Si, but no codoping [02F1]. Both the electroluminescence and photoluminescence peak near 1.51 eV. When the Si-SiO2 nanocluster region is co-doped with rare-earth ions, the emission spectrum changes and represents the characteristic spectrum of the rare-earth ion. In Fig. 3.5.27, the results of Iacona et al. are shown for the case of erbium (Er) co-doping [02I1]. The electroluminescence peak occurs at 0.8 eV (Ȝ = 1550 nm). The linewidth is significantly more narrow (26 meV) and displays the characteristics of an atomic emission, as opposed to band-to-band emission. The time decay of the electroluminescence measured in this LED is 1.5 ms. While rare-earth ions offer a variety of emission wavelengths, at the present time there is not sufficient tenability to cover the visible wavelength range, even using a combination of diodes. This situation represents a significant difference compared to that of LEDs made from other direct-gap semiconductor materials or made from organic films. At this writing there have not been published quantitative device lifetime studies. The quantum efficiency improves with the reduction of the Si content in the SiO2, but the devices then degrade faster. Reducing the thickness of the Si-rich oxide, on the other hand, does not change degradation properties or the quantum efficiency, but it reduces operation voltages, thus improving the power efficiency.

Landolt-Börnstein New Series III/34C3

Ref. p. 118]

1.8

Photon energy h w [eV] 1.6 1.4

Electroluminescence intensity I [arb.units]

350

3000 2500 2000

250 200

1500

150 1000 100 500

50 0

0 600

700

Electroluminescence intensity I [arb.units]

0.85

113

T = 293 K

PL EL

300

1.2

800 900 1000 Wavelength l [nm] Photon energy h w [eV] 0.80 0.775 0.825

1100

Photoluminescence intensity I [arb.units]

2.0

3.5. Si, Ge, and SiGe quantum wires and quantum dots

Fig. 3.5.26. Comparison between the photoluminescence (PL) and the electroluminescence (EL) spectra of an LED based on Si-SiO2 with a Si content of 42 atomic percent in the Si oxide layer [02F1]. The Si-SiO2 has not been co-doped. The PL spectrum was measured with a laser pump power of 10 mW. The EL spectrum was measured with a voltage of 48 V and a current density of 4 mA/cm2. The emission linewidth is 207 meV.

0.75

300 T = 300 K 200

100

0 1.4

1.5 1.6 Wavelength l [mm]

1.7

Fig. 3.5.27. Room temperature electroluminescence spectrum of an Er-doped Si-SiO2 nanocluster MetalOxide-Semiconductor device [02I1], obtained under a forward bias of 32 V with a current density of 20 A/cm2. The emission peak occurs at 0.8 eV, which is characteristic for Er ions in SiO2. The emission linewidth is 26 meV.

The outlook for Si-based LEDs should take into account two principal considerations. One is the degree to which such diodes can be integrated into real Si integrated circuits (ICs). Requirements for integration include a close respect for the thermal schedule in IC manufacture as well as compatibility with the materials used throughout the IC process cycle. The second condition is performance. Si-based LEDs lack the brightness, the efficiency, the color gamut, and the lifetime of either direct bandgap semiconductor LEDs or organic LEDs. We will discuss the origin of some of these difficulties in the following section on the use of Si-SiO2 nanoclusters, co-doped with Er ions, for the application of thinfilm optical amplifiers.

Landolt-Börnstein New Series III/34C3

3.5. Si, Ge, and SiGe quantum wires and quantum dots

114

[Ref. p. 118

3.5.4.3 Er-doped Si-SiO2 nanocluster optical amplification The introduction of erbium (Er) ions into SiO2 creates centers with strong luminescence at 1550 nm. Er-doped glass optical fiber amplifiers are a technological success and a mainstay of long-haul optical fiber telecommunications. The excitation cross-section of the Er3+ ions is low, requiring about 100 meters of gain medium to be optically excited in order to fabricate a practical amplifier. The excellent low-loss optical transmission properties of optical fibers make this possible. To make a more compact amplifier, based on Si-SiO2 co-doped with Er3+ ions, the challenge is to increase the gain coefficient well above that for Er3+ in SiO2 alone. Silicon nanoclusters are being explored as an energy transfer agent to pump Er3+ ions in SiO2 with much greater efficiency than is possible in an optical fiber, thus enabling a more compact planar waveguide optical amplifier. A simplified excitation configuration diagram is shown in Fig. 3.5.28. The energy structure shows that it is possible to obtain net gain, but also shows that there are loss mechanisms, such as free-carrier (fc) absorption of the signal, so that net positive gain from this composite material is not assured. The amplifier design concept calls for the gain region to be processed into the core region of a planar waveguide. The waveguide losses in the best planar waveguides are orders of magnitude larger than those measured in optical fibers. To compensate, the excitation of the Er3+ ions must be orders of magnitude larger than the situation in optical fiber amplifiers. sfc

signal

ttr ~1ms sexc pump

ttr ~1ms Si - nc 3+

Er SiO2

650 nm 800 nm 980 nm 1535 nm

sabs signal

4 F9/2 4 I9/2 4 I11/2 4 I13/2

tem~9ms sem 4

I15/2

Fig. 3.5.28. A schematic excitation diagram for the Si-SiO2 system with co-doping and excitation by optical pumping for application as an optical amplifier. Optical pumping excites electrons in the Si-SiO2 nanocluster (nc) system. This excited-state electron transfers its energy to the Er3+ ion with a decay time of about 1 µs. The energy transfer excites one of the upper level energy states of the Er3+ ion. The electron decays relatively rapidly to the 4I13/2 state which has a long lifetime of § 1…3 ms. This long lifetime favors the build-up of a population inversion relative to the lowerlying 4I15/2 state. A signal photon incident on this structure provokes several reactions. The desired interaction is the excitation of stimulated emission by the Er3+ ions. However, a competing effect is free-carrier (fc) absorption by the excited-state electrons in the Si-SiO2 clusters.

Referring to Fig. 3.5.28, the excitation of electrons in the Si nanoclusters can be accomplished by optical pumping or by electrical pumping, as discussed previously. These hot electrons lose their energy to the surroundings, generating heat, and some will populate the ≈ 1.7 eV radiative state in SiO2. This initial energy transfer process has a much longer lifetime, about 1 microsecond, than thermal relaxation. However, electrons that reach this state can transfer their energy to the Er3+ sites. It has been proposed by Pavesi et al. that the Si-SiO2 system permits a more efficient excitation of the Er3+ than would be the case if the Er3+ ions were present only in a SiO2 matrix, as in a glass optical fiber [05P1]. Energy transfer to the excited state levels is followed by thermal relaxation to the 4I13/2 state. This energy level has quite a long radiative lifetime of about 10 ms. Otherwise said, the probability of optical recombination is even lower than is the case in undoped Si nanoclusters. The long lifetime makes it possible to imagine collecting many electrons in this state, which is favorable for obtaining a population inversion relative to the lower level, 4I15/2. An important consideration is the presence of non-radiative Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

115

recombination channels that would compete with radiative recombination. A final consideration is the evacuation of electrons from the lower level as recombination occurs. This discussion illustrates several important features of the Si-SiO2:Er3+ system as a candidate for solid-state light generation or amplification. On the negative side: a)

It is energetically inefficient. The various steps that require thermal relaxation mean that much of the electrical (or optical) energy used to excite the electrons is being dissipated as heat. This has implications for the use of Si nanoclusters for lighting applications.

b) The quantum efficiency is low. Non-radiative channels compete with population of radiative levels. Thus a fraction of the excitation electrons (or photons) injected into the structure will actually end up in a radiative recombination level. This has implications for using these LEDs in information transmission. c)

The long lifetimes for radiative recombination do not favor the use of the LEDs in applications where they are directly modulated.

On the positive side: a)

The achievement of population inversion in the Er3+ ions would lead immediately to an optical amplifier. A functioning waveguide optical amplifier on Si would be a significant advance toward practical optoelectronic components on Si. Low efficiency would be a secondary concern.

b) The achievement of population inversion in the Si-SiO2:Er3+ would lead directly to a Si-based injection laser. This accomplishment would have a revolutionary effect on the Si electronics industry. 3.5.4.4 Si quantum-dot memories Non-volatile memory devices are used for a wide variety of information storage applications. Current technology is based on a floating-gate memory. A charge induced on the gate contact determines the state of the channel for an indefinite period of time, provided there is no leakage of the charge through the gate oxide to the source or drain. One defect in the oxide of a memory cell would result in the failure of the cell. To ensure that such leakage does not occur, the current limits on the gate oxide thickness are 10 nm. Tiwari and co-workers showed that Si quantum dots can be used to mitigate the consequences of such leakage by using the quantum dots to store charge instead of the gate itself [96T1, 96T2]. In this structure the memory function is distributed among a population of electrically isolated quantum dots imbedded in oxide. If it should happen that one dot loses its charge, the memory function is no longer impaired. The result of this invention is that memory retention time and thus overall reliability are improved. At the same time the control oxide thickness can be reduced to 5 nm, allowing a reduction of the drive voltage from 9 V ... 6 V and an accompanying reduction in both power consumption and in read-write access time. The structure of the nano floating gate memory is shown in Fig. 3.5.29. Floating gate Si quantum dots Tunnel oxide

Control oxide

Source

Drain

Channel Landolt-Börnstein New Series III/34C3

Fig. 3.5.29. In the nano floating-gate memory, charge is stored in Si quantum dots that are located precisely a few nanometer from the C-MOS channel. Charges are accumulated or discharged by quantum mechanical tunnelling between the dots and the channel. The tunnelling is controlled by the gate. The quantum dots are electrically isolated from each other. Thus, the unintentional discharge of one dot will not affect the conductivity of the channel.

3.5. Si, Ge, and SiGe quantum wires and quantum dots

116

[Ref. p. 118

The operation of the nano floating-gate memory can be understood from Fig. 3.5.30. The write function (b) is accomplished by applying positive bias to the gate. Tunneling occurs from an occupied state in the channel to an unoccupied state in the quantum dot. The read function (c) occurs in a quiescent bias condition, as required for a non-volatile memory. Electrons stored in the quantum dot find no unoccupied states for tunneling into the channel. The erase function (d) is achieved by applying a negative bias, so that the trapped electron in the quantum dot can tunnel into an unoccupied state in the channel. In the original demonstration by Tiwari, the tunneling oxide was 1.6 nm in thickness. The quantum dots were deposited on the oxide by CVD, with a mean diameter of 5 nm and a density of 1012 cm-2, and encapsulated in a subsequent oxide deposition, forming the control oxide 7.3 nm in thickness on top. The measured threshold shift between the charged and discharged state was 0.25 V with a static gate bias of 1.25 V. Write Channel

Gate

a

Control oxyde

Drain Nanocrystals

Tunnel oxide

Gate

b

Store

c

Source

Erase

Fig. 3.5.30. Structure of the Si nano floating gate memory cell. In (b), (c), and (d), the write, read, and erase cycles are diagrammed [96T1].

d

Since the pioneering work of Tiwari, there has been a considerable effort to engineer state of the art memory chips using this technology [04L4]. In particular, Freescale Semiconductor has announced a 4 Mbit memory using Si quantum dots, achieving 6 V operation, with a 3 V threshold swing, and a 50% reduction in chip surface area compared to conventional floating-gate memories at the 90 nm node [03M1].

3.5.5 Conclusions Si quantum-dot structures cover a large range of sizes, from diameters of 3 or 4 nm, where true quantum confinement effects on the energy structure are measured, to several hundred nanometers, where electrons and holes are confined spatially to a region much less than a typical collision length. A significant effect of three-dimensional confinement is to increase the probability for electron-hole radiative recombination relative to structures where carriers are unconfined in one or more dimensions. Photoluminescence is the characterization method of choice for determining the electronic energy level structure. Significant and detailed structural analysis has been carried out primarily by scanning probe methods, because the dots are confined in real space, whereas traditional tools like X-ray or TEM analysis are designed for studying extended structures in real space. Electronic and optoelectronic device applications of quantum dots of Si or Ge have been developed. Efficient photoconductive detectors have been designed and demonstrated, based on the ionization energy of a hole from a Si-Ge quantum dot well into the Si valence band. The range of detection sensitivity covers a broader range of infrared energies than can be obtained with most other materials, including GaAs/InAs quantum dot materials. Landolt-Börnstein New Series III/34C3

Ref. p. 118]

3.5. Si, Ge, and SiGe quantum wires and quantum dots

117

Measurement of optical gain in silicon nanoclusters with sizes of a few nm embedded in SiO2 raises the tantalizing prospect of a being able to make an optical amplifier or even a laser from these quantum dot materials. However, experiments have not yet confirmed either of these possibilities. The measured properties of silicon nanoclusters embedded in Si3N4 suggest that this materials system may offer the pathway to efficient Si-based optoelectronic functionality. The use of Si quantum dots as the storage element in high-density, non-volatile memories has shown that quantum dots improve performance by increasing reliability and by enabling reductions in power dissipation and size.

Landolt-Börnstein New Series III/34C3

3.5.6 References for 3.5

118

3.5.6 References for 3.5 80K1 82S1 86P1 86S1 89P1 90E1 90M1 91A1 91M1 92T1 93B1 93K1 93L1 94D1 94S1 95E1 95L1 95W1 96C1 96C2 96T1 96T2 97E1 97I1 98C1 98I1 99H1 99H2 99L1 99S1 99S2

99V1 00D1

von Klitzing, K., Dorda, G., Pepper, M.: Phys. Rev. Lett. 45 (1980) 494. Skocpol, W.J., Jackel, L.D., Hu, E.L., Howard, R.E., Fetter, L.A.: Phys. Rev. Lett. 49 (1982) 951. Pearsall, T.P., Pollak, F.H., Bean, J.C., Hull, R.: Phys. Rev. B 33 (1986) 6821. Skocpol, W.J., Mankiewich, P.M., Howard, R.E., Jackel, L.D., Tennant, D.M., Stone, A.D.: Phys. Rev. Lett. 56 (1986) 2865. Pearsall, T.P.: Crit. Rev. Solid State Mater. Sci. 15 (1989) 551. Eaglesham, D.J., Cerullo, M.: Phys. Rev. Lett. 64 (1990) 1943. Mo, Y.-W., Savage, D.E., Swartzentruber, B.S., Lagally, M.G.: Phys. Rev. Lett. 65 (1990) 1002. Aumann, C.E., Mo, Y.-W., Lagally, M.G.: Appl. Phys. Lett. 59 (1991) 1061. Mo, Y.-W., Lagally, M.G.: J. Cryst. Growth 111 (1991) 876. Takagahara, T., Takeda, K.: Phys. Rev. B 46 (1992) 15578. Batson, P.E., Heath, J.R.: Phys. Rev. Lett. 71 (1993) 911. Kanemitsu, Y., Ogawa, T., Shiraishi, K., Takeda, K.: Phys. Rev. B 48 (1993) 4883. Littau, K.A., Szajowski, P.J., Muller, A.J., Kortan, A.R., Brus, L.E.: J. Phys. Chem. 97 (1993) 1224. Dinh, L.N., Chase, L.L., Balooch, M., Terminello, L., Wooten, F.: Appl. Phys. Lett. 65 (1994) 3111. Shimizu-Iwayama, T., Fujita, K., Nakao, S., Saitoh, K., Fujita, T., Itoh, N.: J. Appl. Phys. 75 (1994) 7779. Ehbrecht, M., Ferkel, H., Smirnov, V.V., Stelmakh, O.M., Zhang, W., Huisken, F.: Rev. Sci. Instrum. 66 (1995) 3833. Lu, Z.H., Lockwood, D.J., Baribeau, J.M.: Nature (London) 378 (1995) 258. Wang, D., Thomas, S., Wang, K., Xia, Y., Whitesides, G.M.: Appl. Phys. Lett. 70 (1995) 2658. Chou, S.Y., Krauss, P.R., Renstrom, P.J.: J. Vac. Sci. Technol. B 14 (1996) 4129. Coffa, S., Franzò, G., Priolo, F.: Appl. Phys. Lett. 69 (1996) 2077. Tiwari, S., Rana, F., Hanafi, H., Hartstein, A., Crabbé, E.F., Chan, K.: Appl. Phys. Lett. 68 (1996) 1377. Tiwari, S., Rana, F., Chan, K., Shi, L., Hanafi, H.: Appl. Phys. Lett. 69 (1996) 1233. Ehbrecht, M., Kohn, B., Huisken, F., Laguna, M.A., Paillard, V.: Phys. Rev. B 56 (1997) 6958. Ishikuro, H., Hiramoto, T.: Appl. Phys. Lett. 71 (1997) 3691. Coffa, S., Franzò, G., Priolo, F., Pacelli, F.A., Lacaita, A.: Appl. Phys. Lett. 73 (1998) 93. Inokuma, T., Wakayama, Y., Muramoto, T., Aoki, R., Kurata, Y., Hasegawa, S.: J. Appl. Phys. 83 (1998) 2228. Hiramoto, T., Ishikuro, H.: Superlattices Microstruct. 24 (1999) 263. Hull, R., Bean, J.C. (eds.): Germanium Silicon: Physics and Materials, Semiconductors and Semimetals, Vol. 56, San Diego: Academic Press, 1999. Liu, F., Davenport, S.E., Evans, H.M., Lagally, M.G.: Phys. Rev. Lett. 82 (1999) 2528. Sullivan, J.S., Mateeva, E., Evans, H., Savage, D.E., Lagally, M.G.: J. Vac. Sci. Technol. A 17 (1999) 2345. Savage, D.E., Feng Liu, Zielasek, V., Lagally, M.G.: Fundamental Mechanisms of Film Growth, Ch. 2, in: Hull, R., Bean, J.C. (eds.): Germanium Silicon: Physics and Materials, Semiconductors and Semimetals, Vol. 56, San Diego: Academic Press, 1999, pp. 49-100. Valakh, M.Ya., Yukhimchuk, V.A., Bratus', V.Ya., Konchits, A.A., Hemmentan, P.L.F., Komoda, T.: J. Appl. Phys. 85 (1999) 168. Darhuber, A.A., Bauer, G., Schittenhelm, P., Abstreiter, G.: Structural Characterization of SelfOrganised Ge Islands, Ch. 6, in: Pearsall, T.P. (ed.): Quantum Semiconductor Devices and Technologies, Boston: Kluwer Academic Publishers, 2000, p. 234-258.

Landolt-Börnstein New Series III/34C3

3.5.6 References for 3.5 00H1 00K1 00M1 00P1 00S1

00S2 00V1 02B1 02B2 02B3 02E1 02E2 02F1 02G1 02I1 02N1 02P1 02T1 02T2 02T3 03C1 03D1 03E1 03H1

03L1 03M1

03P1

119

Huisken, F., Hofmeister, H., Kohn, B., Laguna, M.A., Paillard, V.: Appl. Surf. Sci. 154-155 (2000) 305. Kasper, E., Lyutovich, K. (eds.): Properties of Silicon Germanium and SiGe:Carbon, London: INSPEC, 2000. Masini, G., Colace, L., Assanto, G., Luan, H.C., Kimerling, L.C.: Electron. Lett. 36 (2000) 2095. Pavesi, L., Dal Negro, L., Mazzoleni, C., Franzò, G., Priolo, F.: Nature (London) 408 (2000) 440. Seebohm, G., Craighead, H.: Lithography and Patterning for Nanostructure Fabrication, Ch. 3, in: Pearsall, T.P. (ed.): Quantum Semiconductor Devices and Technologies, Boston: Kluwer Academic Publishers, 2000, p. 98-138. Schmidt, O.G., Eberl, K.: Phys. Rev. B 61 (2000) 13721. Vescan, L., Goryll, M., Stoica, T., Gartner, P., Grimm, K., Chretien, O., Mateeva, E., Dieker, C., Holländer, B.: Appl. Phys. A 71 (2000) 423. Brunner, K.: Rep. Prog. Phys. 65 (2002) 27. Buca, D., Winnerl, S., Lenk, S., Buchal, Ch., Xu, D.-X.: Appl. Phys Lett. 80 (2002) 4172. Buca, D., Winnerl, S., Lenk, S., Mantl, S., Buchal, Ch.: J. Appl. Phys. 92 (2002) 7599. El kurdi, M., Boucaud, P., Sauvage, S., Kermarrec, O., Campidelli, Y., Bensahel, D., SaintGirons, G., Sagnes, I.: Appl. Phys. Lett. 80 (2002) 510. El kurdi, M., Boucaud, P., Sauvage, S., Fishman, G., Kermarrec, O., Campidelli, Y., Bensahel, D., Saint-Girons, G., Sagnes, I., Patriarche, G.: J. Appl. Phys. 92 (2002) 1858. Franzò, G., Irrera, A., Moreira, E.C., Miritello, M., Iacona, F., Sanfilippo, D., Di Stefano, G., Fallica, P.G., Priolo, F.: Appl. Phys. A 74 (2002) 1. Garrido, B.: SINERGIA Year One Report (unpublished), European Commission Project: IST– 2000-29650, 2002, p. 24. Iacona, F., Pacifici, D., Irrera, A., Miritello, M., Franzò, G., Priolo, F., Sanfilippo, D., Di Stefano, G., Fallica, P.G.: Appl. Phys. Lett. 81 (2002) 3242. Nayfeh, M.H., Rao, S., Barry, N.: Appl. Phys. Lett. 80 (2002) 121. Park, N.M., Kim, S.H., Sung, G.Y., Park, S.J.: Chem. Vap. Deposition 8 (2002) 254. Tetelbaum, D.I., Burdov, V.A., Mikhaylov, A.N., Trushin, S.A.: Proc. SPIE Int. Soc. Opt. Eng. 5023 (2002) 186. Tong, S., Liu, J.L., Wan, J., Wang, K.L.: Appl. Phys. Lett. 80 (2002) 1189. Trushin, S.A., Mikhaylov, A.N., Tetelbaum, D.A., Gorshkov, O.N., Revin, D.G., Gaponova, D.M.: Surf. Coat. Technol. 158-159 (2002) 717. Castagna, M.E., Coffa, S., Monaco, M., Caristia, L., Messina, A., Mangano, R., Bongiorno, C.: Physica E 16 (2003) 547. Dal Negro, L., Cazzanelli, M., Pavesi, L., Ossicini, S., Pacifici, D., Franzò, G., Priolo, F., Iacona, F.: Appl. Phys. Lett. 82 (2003) 4636. Elfving, A., Hansson, G.V., Ni, W.-X.: Physica E 16 (2003) 528. Huisken, F., Ledoux, G., Guillois, O., Reynaud, C.: Investigation of the Influence of Oxidation and HF Attack on the Photoluminescence of Silicon Nanoparticles, in: Jutzi, P., Schubert, U. (eds.): Silicon Chemistry: From the Atom to Extended Systems, Weinheim: Wiley-VCH, 2003, pp. 293307. Lagally, M.G.: J. Vac. Sci. Technol. A 21 (5) (2003) S54. Muralidhar, R., Steimle, R.F., Sadd, M., Rao, R., Swift, C.T., Prinz, E.J., Yater, J., Grieve, L., Harber, K., Hradsky, B., Straub, S., Acred, B., Paulson, W., Chen, W., Parker, L., Anderson, S.G.H., Rossow, M., Merchant, T., Paransky, M., Huynh, T., Hadad, D., O-Min Chang, K., White jr., B.E.: Proceedings IEDM, 2003, paper 26.2, 2003, pp. 26.2.1-26.2.4. Pavesi, L., Gaburro, Z., Dal Negro, L., Bettotti, P., Vijaya Prakash, G., Cazzanelli, M., Oton, C.J.: Opt. Lasers Eng. 39 (2003) 345.

Landolt-Börnstein New Series III/34C3

120 03R1 04G1

04K1

04K2 04L1

04L2 04L3 04L4 05F1 05F2 05P1 05P2 05R1 05R2 06S1 06Y1

3.5.6 References for 3.5 Ruan, J., Fauchet, P.M., Dal Negro, L., Cazzanelli, M., Pavesi, L.: Appl. Phys. Lett. 83 (2003) 5479. Garrido, B., López, M., Pérez-Rodríguez, A., García, C., Pellegrino, P., Ferré, R., Moreno, J.A., Morante, J.R., Bonafos, C., Carrada, M., Claverie, A., de la Torre, J., Souifi, A.: Nucl. Instrum. Methods Phys. Res. Sect. B 216 (2004) 213. Klein, L.J., Slinker, K.A., Truitt, J.L., Goswami, S., Lewis, K.L.M., Coppersmith, S.N., van der Weide, D.W., Friesen, M., Blick, R.H., Savage, D.E., Lagally, M.G., Tahan, Ch., Joynt, R., Erikssona, M.A., Chu, J.O., Ott, J.A., Mooney, P.M.: Appl. Phys. Lett. 84 (2004) 4047. Kim, T.Y., Park, N.M., Kim, K.H., Sung, G.Y., Ok, Y.W., Seong, T.Y., Choi, C.J.: Appl. Phys. Lett. 85 (2004) 5355. Lagally, M.G., Eriksson, M.A., Liu, F., Ma, Z.-Q., Celler, G.K., Savage, D.E., Klein, L.J., Slinker, K., Roberts, M.M., Yang, B., Zhang, P.P., Huang, M.-H.: Proc. Electrochem. Soc. 2004-7 (2004) 1135. Li, A.P., Flack, F., Lagally, M.G., Chisholm, M.F., Yoo, K., Zhenyu Zhang, Weitering, H.H., Wendelken, J.F.: Phys. Rev. B 69 (2004) 245310. Luterov, K., Dohnalov, K., Svrcek, V., Pelant, I., Likforman, J.-P., Cregut,O., Gilliot, P., Honerlage, B.: Appl. Phys. Lett. 84 (2004) 3280. Lombardo, S., De Salvo, B., Gerardi, C., Baron, T.: Microelectron. Eng. 72 (2004) 388. Fauchet, P.M.: Mater. Today 8 (2005) 26. Fauchet, P.M., Ruan, J., Chen, H., Pavesi, L., Dal Negro, L., Cazzaneli, M., Elliman, R.G., Smith, N., Samoc, M., Luther-Davies, B.: Opt. Mater. 27 (2005) 745. Pavesi, L.: Mater. Today 8 (2005) 18. Pellegrino, P., Garrido, B., Garcia, C., Arbiol, J., Morante, J.R., Melchiorri, M., Daldosso, N., Pavesi, L., Scheid, E., Sarrabayrouse, G.: J. Appl. Phys. 97 (2005) 074312. Roy, S.K., Das, K.: Opt. Mater. 27 (2005) 948. Rizk, R. (ed.): Si-based Photonics: Towards True Monolithic Integration, Symposium Proceedings 158, E-MRS; Opt. Mater. 27 (2005) 731. Sung, G.Y., Park, N.M., Shin, J.H., Kim, K.H., Kim, T.Y., Cho, K.S., Huh, C.: IEEE J. Selected Topics Quantum Electron. 12 (2006) 1545. Yu, J., Kasper, E., Oehme, M.: Thin Solid Films 508 (2006) 396.

Landolt-Börnstein New Series III/34C3

Ref. p. 134]

3.6

3.6 Luminescence and related properties of nanocrystalline porous silicon

121

Luminescence and related properties of nanocrystalline porous silicon by N. Koshida

3.6.1 Introduction As the scaling of silicon-based ultra-large-scale integrated devices comes into the region of nanometer sizes, the physical and chemical properties of nanostructured silicon have attracted particular attention from scientific and technological viewpoints. The fabrication and properties of nanocrystalline silicon (nc-Si) have been intensively investigated as a novel nano-material. The fundamental properties of singlecrystalline silicon (c-Si) are substantially modified in nc-Si, and then some useful functions are induced in various manners. For instance, a significant band gap widening occurs in nc-Si due to enhanced quantum confinement, in which the conventional indirect/direct transition regime in semiconductors becomes less meaningful. The most remarkable effect is efficient room-temperature visible photoluminescence [90C] and electroluminescence [92K] observed in anodized porous silicon (PS). Taking into account other effects [03K] observed to date, nc-Si should be regarded as a novel functional material. This article reviews the present status of studies on optoelectronic and related properties of nc-Si material, including their device applications. The scientific and technological significances of the quantum properties in this material are described in relation to the optical, structural, electrical, and thermal characterizations.

3.6.2 An overview of nanostructured silicon The ways for altering the properties of c-Si are divided into four approaches as shown in Fig. 3.6.1: introduction of disorder, decrease in structural dimension, modulation of lattice periodicity, and decrease in the crystalline size. In all cases, the band structure is varied from that of c-Si in terms of both the band gap and the transition scheme. Amorphous structures, wires, planes, superlattices, and quantum dots with various band gap energies have been obtained by many different ways of dry or wet processing [03K]. All these structure-modified silicon-based materials exhibit efficient luminescence even at room temperature. From a viewpoint of luminescence property, c-Si seems to be an exceptional material, since all other materials are luminescent due to their modified band gaps. Si-Si alloy (~2.5 eV)

a-Si:H (~1.7 eV) Disorder Dimension c-Si

Polysilane

2D polymer (~2.5 eV)

(~3-4 eV)

Superlattice

Quantum well

Disilane (~6.5 eV)

Periodicity Size Nanowire Cluster (~1.8 eV)

Landolt-Börnstein New Series III/34C3

Nanocrystal (~2.6 eV)

Fig. 3.6.1. Band gap modification of silicon-based materials along four approaches.

122

3.6 Luminescence and related properties of nanocrystalline porous silicon

[Ref. p. 134

The nonluminescent optical property of c-Si is due to the indirect band structure shown in Fig. 3.6.2(a), related to the diamond-type lattice configuration of silicon atoms. The most straightforward band modification is to decrease the size of c-Si, leading to strong quantum confinement effects on which our interest is paid here. Under this situation, two effects appear as shown in Fig. 3.6.2(b). The one is the band gap widening due to a strong confinement. This becomes apparent as the nc-Si diameter is decreased down below about 4 nm, corresponding to the Bohr radius of excitons in c-Si. Another one is delocalization of carriers in momentum space due to the uncertainty principle, making it possible for electrons and holes to recombine directly. Thus efficient luminescence in the visible wavelength region can be obtained from nc-Si. 2 nc-Si confined gap ( D Egµ 1/m*d )

c-Si indirect gap

E

E

a

k

Eg + D E g

hn

Eg

b

k

Fig. 3.6.2. Band gap structure of (a) c-Si and (b) confined nc-Si.

3.6.3 Fabrication technology 3.6.3.1 Nanocrystalline porous silicon A typical approach for obtaining nanocrystalline silicon (nc-Si) materials is the electrochemical conversion of single-crystalline silicon into a low-density anodic film. The formation of this “anodic silicon film” was first reported in the 1950s in relation to the study on electrochemical etching of silicon wafer surfaces [56U, 58T]. When single crystalline silicon is galvanostatically anodized in hydrofluoric acid (HF) solutions under a moderate current density lower than a level of electropolishing in an electrochemical cell as shown in Fig. 3.6.3, local dissolution of silicon atoms proceeds at the surface such that nanometer-scale pores are grown into the bulk. As a consequence, the surface is rendered to a lowdensity crystalline layer termed “porous silicon” (PS).

Fig. 3.6.3. Schematic diagram of the electrochemical anodization system used to fabricate nanocrystalline porous silicon (PS) or porous polycrystalline silicon (PPS) layers. In the n-type substrate case, anodization is usually done under illumination.

Landolt-Börnstein New Series III/34C3

Ref. p. 134]

3.6 Luminescence and related properties of nanocrystalline porous silicon

123

A typical transmission electron microscope (TEM) photograph of as-prepared PS is shown in Fig. 3.6.4. The PS layer consists of a large number of interconnected or isolated quantum-sized nc-Si dot arrays with a relatively high packing density. The formation of PS is promoted by a steady supply of holes from the substrate into the reactive surfaces. The PS structure strongly depends on both the original electrical properties of the silicon substrates (conduction type and resistivity) and the anodization parameters (HF concentration, anodization current density, illumination condition, and solution temperature). In the ntype case, anodic polarization corresponds to the reverse bias condition in the liquid-silicon junction. So, in general, the anodization for n-type c-Si substrates is made under illumination in order to supply holes.

Fig. 3.6.4. A typical photograph of an anodized nanocrystalline PS structure observed with transmission electron microscopy.

The PS layer formation proceeds according to the following factors [97C1, 92S, 02L]: (a) (b) (c) (d) (e)

The dissolution reaction stochastically initiates at sites where holes are supplied. The effective valence for dissolution of one silicon atom is about 2. The micropores grow preferentially towards the [100] and its equivalent directions. The dissolution reaction occurs only at the tip of micropores. The minimum diameter of residual nc-Si dots in as-anodized PS is about 3 nm, which is close to the diameter of acceptor wave functions in c-Si. (f) The surfaces of nc-Si dots are automatically passivated by hydrogen atoms generated during anodization. Due to an enhanced surface chemical activity, the PS layer is efficiently oxidized even at relatively low temperatures. The controllable surface morphology also makes it possible to utilize the PS layer as device components with a mechanical flexibility. In fact, many studies on PS have been conducted for applications to field oxides in integrated circuits [76K], substrates for homo- or hetero-epitaxial growth [94K], and fabrication of silicon-on-insulator (SOI) structures [94Y]. Among them, the developed PSbased SOI technology is useful for providing a large-diameter substrate [00I]. Further investigations have been intensively conducted for the last fifteen years from viewpoints of scientific and technological interests in quantum properties of nc-Si in PS, as described in Section 3.6.4. 3.6.3.2 Dry-processed silicon nanocrystallites In addition to the above-mentioned wet approach, various dry processing techniques have been explored for the fabrication of nc-Si during recent years. These are based on plasma processing [96C, 97C2, 97E, 97G, 97D], sputtering [96B1, 98S1, 01G, 01B], chemical vapor deposition [98F, 98Z], gas decomposition [97H, 98H], ion implantation [98W, 99W, 97N, 94P, 96I, 95I], laser ablation [98L], synthesis reaction [93L, 96B2], spark processing [92H], cluster beam deposition [99H], and re-crystallization of deposited amorphous silicon films [99F].

Landolt-Börnstein New Series III/34C3

124

3.6 Luminescence and related properties of nanocrystalline porous silicon

[Ref. p. 134

It has been confirmed that from structural characterizations by TEM observation and Raman spectra, nc-Si particles are produced in specific embedded media. The width of the (Gaussian) nc-Si size distribution is comparable to that in PS. Some specimens show luminescence at room temperature, though the efficiency is still relatively low. Due to the embedded structure, the chemical activity of dryprocessed nc-Si is not so critical compared to PS, though microscopic passivation at nc-Si/medium interfaces is still crucially important. The major remaining subjects are to increase the spatial packing density of nc-Si and to establish the fabrication technology for precise control of the size distribution. It is also important to develop the technique for assembling uniform nc-Si films at lower temperatures on large-area substrates.

3.6.4 Nanocrystalline porous silicon 3.6.4.1 Properties as a confined system As mentioned above, PS consists of many micropores and residual nc-Si dots. The most important structural property of PS is that the single crystalline feature of the substrate is retained even when the size or width of silicon residuals is extremely decreased during anodisation. In many cases, the average diameter of crystallites is decreased down to the level of 3 nm. This is below a critical size for the occurrence of quantum confinement effects, since the exciton Bohr radius in silicon is 4.3 nm [93Y]. The band gap energy Eg, defined here as the transition energy from the lowest confined states, is a measure to determine whether or not carrier confinement effects are dominant in the physical process in PS. It has been shown from optical absorption [94M], L-edge X-ray absorption spectra (XAS) [94B], photoconduction [97R], and UV photoelectron spectroscopy (UPS) [96S] measurements that the band gap of luminescent PS is considerably larger than that of c-Si. Following the band gap widening, the photoluminescence (PL) peak energy of PS shows a blueshift. The UPS analysis shows that with increasing the anodisation current density, the valence and conduction band edges shift almost symmetrically toward the lower and upper side, respectively. This behavior is distinctly different from the situation in hydrogenated amorphous silicon, where the shift of the conduction band edge is comparably small due to the compensation effect of surface hydration [80A]. For band structure analyses, all PS samples should be transferred into an ultra-high-vacuum (UHV) system immediately after anodization without exposure to air, in order to avoid possible surface oxidation. According to the results of in-situ Auger electron spectroscopy (AES) for these samples, in fact, the signal of oxidation is below the detection limit, independent of the anodization conditions. Under this situation, the electronic structure of PS was analyzed by angle-resolved photoemission technique using synchrotron orbital radiation [98S2]. Figure 3.6.5 shows a Si LIIIedge X-ray absorption spectrum (XAS: 2p3/2 to conduction bands) and a valence spectrum obtained from PS formed on a p-type c-Si (001) substrate. In this figure, the result of the parent c-Si substrate is also shown for reference. The binding energies of these spectra are measured with respect to the Si 2p3/2 core sate. The position of the valence band maximum (EVBM) was determined from the leading edge of the valence spectrum, and the conduction band minimum (ECBM) from the onset of the LIII-edge absorption corresponding to the point of maximum slope. Three features denoted by a, b, and c in the LIII-edge XAS spectrum of c-Si correspond to the transitions to the conduction state density maxima X1, L1, and L3, respectively. These critical features remain in the XAS spectrum of PS, indicating that the single-crystallinity is retained in PS. This is different from the XAS spectra of both amorphous silicon (a-Si) and hydrogenated amorphous silicon (a-Si:H), wherein no critical features are observed. In the valence spectrum of c-Si, we can see three characteristic peaks denoted by I’, II’, and III’ which are attributed to the X4, L1, and L’2 symmetry points, respectively. In the case of PS, on the other hand, three weak peaks denoted by h1’, h2’, and h3’ are observed in addition to the original I’ feature. B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

B

BB

BB

B

BB

Landolt-Börnstein New Series III/34C3

Ref. p. 134]

3.6 Luminescence and related properties of nanocrystalline porous silicon

ECBM

h’1

h’2

I’

125

h’3

EVBM

Photoemission intensity I

PS I’

b c

a

II ’

III ’ c-Si

Fig. 3.6.5. Measured Si LIII-edge X-ray absorption spectrum (XAS: 2p3/2 to conduction band) and valence spectrum of nanocrystalline PS formed on a p-type c-Si (001) substrate [98S2]. The result of the c-Si substrate is also shown for reference. Binding energy is relative to EVBM of c-Si. B

B

L III XAS spectra (Si 2p3/2 ® CB) -5

Valence spectra h n = 55 eV

5 0 Binding energy [eV]

10

15

B

B

B

B

These three weak peaks are assigned to the characteristic states induced by monohydride and dihydride configurations on the nc-Si surfaces in PS. No oxygen-related signals are found in both the XAS and valence spectra in concordance with the AES spectra. The as-anodized nc-PS surface is terminated with hydrogen. The peak I’ that is also observed in a-Si as well originates from the p-derived states. This peak is less sensitive to the long-range order in comparison to the features II’ and III’. As shown in Fig. 3.6.5, the ECBM and EVBM positions of PS are spread out with respect with those of cSi toward a higher potential by 0.35 eV and a lower potential by 0.55 eV, respectively, . The consequent band gap widening is 0.90 eV in this sample. This is consistent with the peak wavelength of the PL spectrum. A significant shift in ECBM of PS is in contrast to the case of a-Si:H, in which the ECBM remains at the same position as that of c-Si. The shift in the EVBM position is presumably due to a steepening of the leading edge induced by the recession of the topmost valence states. The band edge distortion of PS is not caused by neither disordered lattice arrangements nor some surface chemical effects, but by the increased carrier confinement effect associated with the reduction in nc-Si sizes. This has been further supported by the fact that the band dispersion spectra of luminescent PS show the characteristic fine structure of c-Si. All of the direct transitions observed in a clean c-Si (001) sample are retained in luminescent PS independent of the anodization conditions. The above results provide the experimental evidence that PS retains the same band structure as c-Si with the exception that the band edges are shifted apart due to strong quantum confinement. In addition to the luminescent property, the most physical and chemical properties are changed in PS as indicated in Table 3.6.1. The widened band gap affects the spectral response of the photoconductivity and the optical constants. Optical characterization studies [97K] have shown that the dielectric constant of PS is significantly decreased in comparison to that of c-Si, and that the imaginary dielectric dispersion curve retains fundamental features of c-Si, reflecting the quantum properties of silicon nanocrystallites. Correspondingly, the refractive index of PS can be precisely controlled in a very wide range from 3.6 to 1.3 by increasing the porosity [97T]. The electron emission characteristics observed in PS diodes [95K1] suggest that there is a specific ballistic transport mode in nc-Si dot chains interconnected via tunnel oxide films. As a novel cold cathode, the PS emitter has various advantageous features over the conventional field emitter. Extremely lowered thermal conductivity of PS, on the other hand, can be applied to thermally-induced ultrasonic emission into air without using any mechanical vibrations [99S]. Furthermore, both the enhanced surface chemical activity and bio-degradability lead to another technological potential of PS [00L, 05P]. The photonic and electronic properties are presented in the following sections. B

B

B

B

B

B

B

B

Landolt-Börnstein New Series III/34C3

B

B

126

3.6 Luminescence and related properties of nanocrystalline porous silicon

[Ref. p. 134

Table 3.6.1. Physical effects induced in nanocrystalline PS and their technological potential. Effects

Phenomena

Functions

Applications

Confinement

Band gap widening

Visible luminescence

Electroluminescence, optoelectronic integration

Low refractive index

Low dielectrics, nonlinear optics

Isolation, waveguide and cavity

Carrier charging

Electrical hysteresis

Emissive non-volatile memory

Multiple-tunneling

Ballistic transport and emission

Display, ion source

Carrier depletion

Thermal insulating

Ultrasonic generation

Sensor, functional speaker

Surface effect

Chemical activity

Bio-compatibility

Bio-sensing, medical

Field effect

3.6.4.2 Photoluminescence Visible photoluminescence (PL) of PS is characterized as follows [97C3]. (1) Relatively high quantum efficiency at room temperature. (2) Necessity of high-quality surface passivation for efficient and stable PL, especially for nanoporous samples. (3) Broad-band PL emission spectra with full widths at half maximum of about 300 meV due to inhomogeneous broadening. (4) Tuning ability of the emission band from red to blue either with or without oxidation. (5) Stretched exponential behavior in the PL decay after a pulse excitation. (6) Emission-energy dependent PL lifetime at room temperature from 50 µs to 10 ns. The PL emission spectra can be controlled over the whole range of visible wavelengths by in-situ post-anodization photochemical etching alone [96M]. Even in the blue-emissive sample, no traces of surface oxide growth were detected in the Si 2p spectra of X-ray photoelectron spectroscopy (XPS). The observed continuous blueshift of the PL and photoluminescence excitation (PLE) spectra is assumed to be a result of band gap widening by the size reduction in silicon nanocrystallites possibly down to a level of 1 nm. The observed oxide-free blue PL is a strong indication that excitation and subsequent luminescence originate from wide-gap silicon nanocrystallites. The PL mechanism in PS has been investigated to date from various viewpoints: quantum confinement effects [90C], surface states [95K2], molecules [92B], surface defects [93K], and surface effects by hydride [92P]. The luminescence property was also analyzed by scanning probe microscopy [94W] in relation to the intrinsic PS nanostructure. Among the proposed models, the confinement scheme has given the most probable insights for the exploration of the visible PL emission. Quantum-sized nc-Si dots play an essentially important role in the excitation process [91C, 93M, 96B3, 96L], although it is still necessary to make clear how strongly excitons are localized therein and to explain all the experimental facts mentioned above. An especially important issue to be clarified is the correlation between surface termination and the PL efficiency. This should be done under well-controlled experimental conditions. As one practical approach, the effect of surface passivation on the PL characteristics of PS has been investigated by employing high-pressure water vapor annealing (HWA) [05G1, 05G2]. The PS samples with various porosities were prepared on (100)-oriented p-type c-Si wafers by conventional anodization. The PS samples were then annealed by HWA treatment at 0.5 ... 3 MPa and 200 .. 300 °C for 2...3 h. It has been shown that the HWA treatment leads to a drastic enhancement in the PL efficiency with no significant shifts of the peak wavelength, as shown in Fig. 3.6.6. Under the optimum condition, the PS sample exhibits an extremely high external quantum efficiency of 23% at room temperature. According to

Landolt-Börnstein New Series III/34C3

Ref. p. 134]

3.6 Luminescence and related properties of nanocrystalline porous silicon

127

analyses by the Fourier transform infrared (FTIR) spectra and electron spin resonance (ESR), nc-Si surfaces in HWA treated PS are covered with a high-quality SiO2 tissue. Obviously the improvement in PL is attributed to a drastic reduction in the concentration of non-radiative defects at the nc-Si/SiO2 interface. The PL decays are found to be longer than those of as-prepared PS, and become closer to a single-exponential behavior near the PL peak wavelength. The observed high efficiency and stability of PL emission from HWA treated PS in air ambience is attributed to (i) suppression in the density of nonradiative surface defects, (ii) uniform passivation by unstrained thin oxides, and (iii) strong localization of excitons in nc-Si dots. This low-temperature HWA treatment is very useful for obtaining highly efficient and stable luminescent PS and devices. B

B

B

2.4

2.2

Photon energy h w [eV] 2.0 1.8 1.6

B

1.4

Photoluminescence intensity I [arb.units]

150 p = 3.9 MPa

100

2.6 MPa 1.3 MPa

50

ECO-PS (× 20) PS (× 20) 0 500

600

700 800 Wavelength l [nm]

900

Fig. 3.6.6. PL spectra of PS with increasing pressure at high-pressure water vapor annealing (HWA). The PL spectra of as-prepared PS (72% in porosity) and electrochemically oxidized (ECO) samples are also shown for reference.

3.6.4.3 Electroluminescent devices Development of efficient and stable electroluminescence (EL) devices is one of the most important aspects in the PS technology. The structure of PS-based EL devices under study are divided into two groups [04G]. The first one utilizes a single PS layer as the active region. Another one employs layered or combined structures such as anodized pn junctions and/or partially oxidized PS. The evolution of the efficiencies and stability of PS-based EL devices reported to date is indicated in Fig. 3.6.7. Since the first report, the EL quantum efficiency has been increased by several orders of magnitude. As shown in the inset, a uniform bright red emission is discernible even under daylight. In the single PS devices, both p- and n-type substrates are available for the EL operation. For the ptype substrates, the EL emission is obtained under forward bias in which electrons and holes are injected into luminescent PS from the semitransparent top contact and the substrate, respectively. They recombine in PS radiatively as in conventional light-emitting diodes (LEDs). For the n-type substrates, in contrast, holes are generated in silicon nanocrystallites through high-field effects. Consequently, the EL emission can be observed at either the forward or reverse bias. Judging from the experimental result of excitation wavelength dependence of field-induced PL quenching, the high-field luminescent region in this diode is thought to be limited to a depth of about 500 nm just below the top contact. In the single-PS diode, it is very useful to employ a post-anodization electrochemical oxidation (ECO) technique in order to decrease the leakage current and to enhance the carrier injection into luminescent silicon nanocrystallites [98G1]. By applying this technique to PS formed on n+-type substrates, the external quantum efficiency has been dramatically improved beyond 1% [98G2]. The current dependence of the light output suggests that visible light emission is due to the intrinsic EL. The external power P

Landolt-Börnstein New Series III/34C3

P

128

3.6 Luminescence and related properties of nanocrystalline porous silicon

[Ref. p. 134

efficiency has been further enhanced to about 0.4% by reducing the contact and series resistances of the device [00G]. Especially the reduction in contact resistance at the semitransparent electrode by the formation of a compact superficial layer on the active luminescent PS layer is very useful for enhancing the power efficiency. According to the results of dynamic response analyses, the EL device with a partially oxidized PS layer has 3 dB frequencies higher than 1 MHz [95P]. It was reported that PS diodes fabricated by anodizing doped polycrystalline silicon films operate as LEDs with efficiencies comparable to the simple PS diodes, and that the devices can be driven by a poly-Si based thin-film transistor (TFT) [98K]. The TFT compatibility shows the availability of poly-Si based LEDs for large-area applications. The key subjects to be pursued further on PS-based EL are the improvement of the emission durability and the development of full-color devices. Regarding the former subject, there are two factors to be taken into account. The first is the suppression of current-induced oxidation. For this purpose, the encapsulation of the device surface with water-proof thin films of transparent materials (such as SiO2 film) is very effective [01K]. Another one is a complete and stable termination of nanocrystalline Si surfaces. This termination should be done without affecting both the emission band and the carrier injection efficiency. A possible approach is chemical functionalization by conjugated polymers [98B]. It has been confirmed from EL measurements that the formation of covalent Si-C bonding at the nc-Si surfaces, for instance, can significantly stabilize the EL intensity and spectrum under a continuous long-time operation [03G]. These stabilization effects would be further amplified by employing the HWA treatment mentioned above. B

B

Fig. 3.6.7. Progress in the performance of PS electroluminescent devices (EQE: external quantum efficiency, EPE: external power efficiency). The EL stability is defined as the half-life period measured under continuous operation. The inset shows that a uniform bright red emission is discernible even under daylight.

3.6.4.4 Related functions In addition to the optical properties, the quantum nature of PS as a strongly confined system appears in various ways. As indicated in Table 3.6.1, several useful functions are induced in PS due to different origins associated with modified optical, electrical, thermal, and chemical properties. Because of the semi-insulating property, the metal-PS-substrate device behaves like a metal-insulator-semiconductor (MIS) diode. The carrier transport in PS under high electric field conditions produces several useful functions to be discussed now which relate to carrier injection or ejection phenomena in nc-Si. 3.6.4.4.1 Carrier charging effects When relatively thin PS layers are used in fabricating diodes on either p- or n-type substrates, reversible negative resistance (NR) effects are observed [98U]. This becomes more significant at low temperatures due to an enhancement of the field effect. The diode current drops definitely at a critical forward voltage, and then the EL emission occurs. Landolt-Börnstein New Series III/34C3

Ref. p. 134]

3.6 Luminescence and related properties of nanocrystalline porous silicon

129

For the n-type substrates, electrons are injected from the n-type substrate into the PS layer under the forward bias condition, and then drift toward the top electrode. At a sufficient voltage, the electric field in PS becomes so strong that the electrons are injected into the silicon nanocrystallites. As the injected electrons play a role of fixed charges, the potential distribution along the thickness direction of the PS layer is distorted such that low- and high-field regions are produced near the substrate-PS and PS-Au interfaces, respectively. As a result, electrons in the PS region very close to the Au electrode have a chance of radiative recombination with holes generated there through a field-promoted mechanism. The EL emission is switched on despite a significant decrease in the diode current. This carrier injection model can be applied to the p-type substrate case as well. In the diodes with partially oxidized thin PS layers, the field effect is considerably enhanced. It causes a significant hysteresis in the current-voltage (I–U) curve. This behavior typically appears in the diode formed on p-type substrates [99U]. When the bias voltage is at first varied from 0 V toward the negative (reverse) direction, the diode current remains extremely low (denoted here by the “off-state”). At a threshold voltage, however, the diode current is abruptly increased, and then the diode operation turns on. This “on-state” is non-volatile, and can be kept for a long period of time (at least for a few weeks). When a sufficient positive bias voltage is applied, the diode is turned off again, and then the highly-resistive offstate is recovered. The difference in the diode current between the off- and on-states extends about four orders of magnitude even at room temperature. Under the on-state operation, the diode also exhibits visible EL, the intensity of which increases in proportion to the diode current as in the conventional light-emitting diodes. This means that the electrically stored information can be read out not only as an electrical signal, but also as an optical one. If the PS layer under the negative bias condition is illuminated through the semitransparent top contact by visible light like an Ar laser, the stored signal is further enhanced by the photoconduction effect. The oxidized-PS diode behaves as a non-volatile bistable memory. This is presumably due to increased carrier charging effects in nc-Si dots isolated by thin oxide films. The experimental results of the capacitance-voltage (C–U) characteristics suggest that positive carriers, i.e. holes, are stored in nc-Si at the on-state, and are removed from there at the off-state. We can assume that the holes are generated by electrons tunneling from the valence band of a nc-Si dot to the conduction band of a neighboring one. The moderate positive bias voltage under the on-state promotes radiative recombination of electrons with holes in the PS layer near the Au contact. Due to the strong electrical isolation property of nc-Si, the observed effect is potentially useful for pixel-free optical memory. 3.6.4.4.2 Ballistic transport and emission When the PS diode formed on the n+-Si substrate is driven in vacuum, electrons are emitted uniformly [95K1]. The bias voltage dependence of the emission current follows the Fowler-Nordheim scheme. In accordance with analyses of the output electron energy distribution, electrons injected from the substrate become hot in the PS layer during the drift toward the thin Au contact, and are ejected into vacuum by tunneling through the interfacial sub-band and thin Au film [99K1]. The field-induced drift in PS can be enhanced by appropriate oxidation treatment, and then the emission efficiency defined as the ratio of the output current to the diode current reaches 12% [98S3]. Similar cold emission was also observed in a diode formed on anodized polycrystalline silicon films as shown in Fig. 3.6.8. By the use of a structural control based on the anodization current modulation, the electron emission stability is significantly improved. Associated with the stable emission, the characteristic feature clearly appears in the energy distribution of emitted electrons. The feature of the energy distribution curves and the peak shift with increasing applied voltage suggest that quasiballistic electrons are generated in the nc-PPS layer [04I1, 04I2]. It is supposed that electrons are accelerated under a high electric field in the PS layer with a significantly enlarged drift length. At low temperatures below 150 K, where the tunneling mode is dominant, the energy distribution becomes narrower and more ballistic, since the low-energy tail component is further suppressed. P

Landolt-Börnstein New Series III/34C3

P

130

3.6 Luminescence and related properties of nanocrystalline porous silicon

[Ref. p. 134

10

10 IPS

-2

10 nc-Si Au

+

n -Si

Collector e-

Vc

-VPS

Ie

-4

10

h -6

10

1

Efficiency h [%]

Ie

2

Current density j [A/cm ]

Vacuum chamber

-8

10 10

-10

5

0

15 10 20 Bias voltage VPS [V ]

25

0.1 30

Fig. 3.6.8. Schematic experimental configuration of the PS cold cathode and its emission characteristics. The diode current IPS and the corresponding electron emission current Ie of a porous polycrystalline silicon (PPS) diode are given as a function of bias voltage. In this case, the PPS layer was produced by photoanodizing a non-doped poly-Si film (1.5 µm thick) deposited onto an n+-type Si (100) wafer. B

B

P

B

B

P

When a bias voltage is applied to the PS layer consisting of interconnected Si nanocrystallites, a major potential drop is produced only at the interfaces between them. Owing to spike-like interfacial high field and little scattering in the silicon nanocrystallites, electrons can travel for a long distance by a multipletunneling cascade without significant energy losses. In the region near the outer surface, electrons become hot enough, and are ejected quasiballistically into vacuum. The existence of a ballistic transport mode in the PS layer has been supported by picosecond width time-of-flight photoconduction measurements [05K], by which electrons with an extremely large mean free path (2 µm or more) are detected under a high electric field. Theoretical analyses of electron transport in nc-Si dot chains also suggest a possible suppression of phonon scattering losses due to a significant decrease in the deformation potential [05U1, 05U2]. This device has some advantageous features as a new type of surface-emitting cold cathode over the conventional ones such as field emitter arrays. In particular, less sensitivity to ambient pressure, smaller emission angle dispersion, low power consumption, and the compatibility with monolithic Si processing are very attractive from a viewpoint of applications to integrated vacuum microelectronic devices, including flat-panel displays. It has been demonstrated that this emitter is suitable as the excitation source of fluorescent screens. Using this technique, a 7.6-inches full-color flat-panel display has been developed on glass substrates [04K] under a simple-matrix drive as shown in Fig. 3.6.9. The PS ballistic emitter operates as a negative ion source in ambient air, since ejected electrons with kinetic energies of several eV are drifted in air with a mean free path of about 200 nm, and then possibly attached to oxygen molecules with a high probability [65E]. The negative ions thus produced reach the collector electrode. This effect is directly applicable to polymer film surface charging in air [05O]. In addition, energetic electrons generated in the nc-PS layer under a high electric field can be utilized for excitation of fluorescent films without ejection into vacuum. Actually, the diode composed of a thin Au film, a thin organic or inorganic fluorescent film, an nc-PS layer, an n-type Si, and an ohmic back contact, uniformly emits visible light by direct electron impact upon the fluorescent film [02N]. As a novel type of a surface-emitting light source, this solid-state cathodoluminescent device is attractive for a wide range of applications, since multicolor picture elements are easily arranged.

Landolt-Börnstein New Series III/34C3

Ref. p. 134]

3.6 Luminescence and related properties of nanocrystalline porous silicon

top electrode

ITO

131

Phosphor (P22) face plate

e-

e-

seal

nc --Si glass substrate bottom electrode

poly Si

Fig. 3.6.9. Schematic cross section of PS flat panel display (7.6 inches in diagonal) formed on a glass substrate (left) and the corresponding full color pattern image on a fluorescent screen (right). The vacuum spacing is 3 mm. The device is operated under a simple-matrix mode [04K].

3.6.4.4.3 Thermally induced acoustic emission Another important function of PS comes from its thermal property. Because of complete carrier depletion and phonon confinement in silicon nanocrystallites, the thermal conductivity Įof PS is decreased by two orders of magnitude in comparison with that of c-Si [97L]. The thermal capacity per unit volume, C, of PS is also extremely lowered. An exceptionally big contrast (about 1:1200) of the thermal effusivity (ĮC)1/2 is induced between the upper-side PS layer and the underlying c-Si substrate. This phenomenon makes it possible to promote the studies of the thermo-acoustic effect in PS devices [99S, 99K2]. The experimental device is composed of a patterned thin metal film electrode, a porous PS layer (10...50 µm thick), and a single-crystalline Si (c-Si) wafer as shown in the inset of Fig. 3.6.10. The PS layer is formed by a conventional anodization technique. When an electrical input is provided to the electrode as a sinusoidal current followed by Joule heating, a significant acoustic pressure is produced in front of the device as a result of an efficient heat exchange between PS and air without any mechanical vibrations. The measured acoustic pressures are plotted in Fig. 3.6.10 as a function of frequency. As expected from a theoretical analysis, the frequency response is completely flat in a wide range, in contrast to the resonant-type behavior of the conventional ultrasound generators. The limiting frequency is expected to be several-hundreds of MHz or more. This means that an ideal ultrasonic impulse signal can be generated by an impulse drive, and that the resolution for object sensing should be remarkably improved. It has been confirmed that the PS emitter is applicable as a probe for ultrasonic threedimensional object sensing in air [05T]. The impulsive output mode can also be used as a radiation pressure source for noncontact actuating [04H]. Another possible application of the flat frequency response is the use as an ultrasonic speaker. It has been demonstrated that a PS emitter can reproduce digitally recorded mouse-pup ultrasound vocalizations correctly in terms of call duration, frequency dispersion, and sound pressure level [06K]. The nc-Si device has a practical advantage for further experiments of ultrasound vocalizations, since a finely arrayed device configuration with a small size is easily fabricated by standard silicon planar processing. It would be possible to use this device as a directional ultrasound emitter with a function of acoustic wave manipulation. The nc-Si device provides a tool to explore the ultrasonic interaction and communication mechanisms between living organisms. P

P

Landolt-Börnstein New Series III/34C3

132

3.6 Luminescence and related properties of nanocrystalline porous silicon

[Ref. p. 134

Sound pressure level [dB SPL]

100

nc - Si

80

Sound Metal

60 c - Si 40

Input

40

60

80

Fig. 3.6.10. The device structure and frequency dependence of the emitted sound pressure for an electrical input power of 3 W. The acoustic output was measured at a distance of 2 mm from the device surface.

Frequency [kHz]

A further characteristic feature is that a scaling merit exists in the PS ultrasonic emitter, since the acoustic output is proportional to the input power density. If the size of the surface electrode is reduced by a factor of n, the emission efficiency, defined as the ratio of the acoustic pressure to the input power, is expected to increase by a factor of n. This becomes more apparent for a pulsed operation. The device configuration of fine electrode arrays with a size compatible with a standard microfabrication technology would be useful as a functional emitter under phased array operation. The above-mentioned advantageous features of the PS emitter over conventional piezo-electric transducers suggest the possibility for the development of integrated ultrasonic devices. 3.6.4.5 Toward monolithic functional integration As mentioned in section 3.6.4.1, the refractive index of PS can be controlled over a very wide range by changing the anodization conditions. This is directly applicable to the fabrication of photonic devices. For example, quarter-wavelength multilayered optical mirrors can be easily formed on c-Si substrates by periodic modulation of the anodization current. On a basis of this technique, we can obtain a Fabry-Perot resonator (FPR) with an optical length available for visible light. The fabricated device operates as a microcavity [96A1], and narrowed output light spectra are precisely and widely controlled as designed. The cavity operation has also been confirmed for the carrier injection scheme [96A2]. The variable feature of optical constants in PS is further developed into the fabrication of optical waveguides. If the p-type substrate is selectively and heavily doped by ion implantation and then anodized at a constant current, significant differences in both the refractive index and the growth rate of PS are induced between the doped (core) and original (clad) regions. Using this self-regulated process, a three-dimensionally buried optical waveguide has been fabricated by planar processing. Owing to a sufficiently big contrast in refractive indices between the core and cladding regions and consequent strong confinement of electromagnetic waves, polarized visible light propagates along the core with relatively low attenuation losses [99T]. Even in a bent waveguide with a width of 50 µm and a curvature radius of 250 µm, the light wave propagates along the bent core path without suffering serious bending losses despite a very small curvature radius. The PS layer also behaves as a nonlinear optical medium. This relates to the carrier population dynamics in nc-Si under photoexcitation [95M, 00T] or carrier injection [01T] followed by significant changes in the absorption and/or refractive index spectra. The measured nonlinear characteristics of a fabricated PS logic gate system [95M] are comparable to those of conventional materials. The controllability of the refractive index is available for the fabrication of a self-standing FPR optical cavity in which a PS layer is sandwiched with upper and lower multilayered Bragg reflectors. In the experimental configuration, the optical nonlinearity was observed more clearly. Electro-optical devices

Landolt-Börnstein New Series III/34C3

Ref. p. 134]

3.6 Luminescence and related properties of nanocrystalline porous silicon

133

such as the self-electro-optic effect devices or all-optical devices such as optical bistable Fabry-Perot etalons have been demonstrated by the excitonic absorption effect in the quantum wells of III-V semiconductors. Large-scale integration of these photonic devices, however, has not been established because of the difficulty of monolithic processing. From a viewpoint of fabricating Fabry-Perot resonators, it is an advantageous feature of PS that highly reflective multilayer mirrors can be obtained simply by controlling the anodization current density and time. Thus, PS offers the possibility of integrating optoelectronic devices on a c-Si substrate. Refining and combining all quantum functions of PS as optoelectronic components (such as LED, negative-resistance device, light-emissive non-volatile memory, ballistic electron emitter, ultrasound emitter, microcavity, waveguide, and logic gate) will result in a steady progress in the science and technology of this material toward silicon-based monolithic photonic and/or functional integration.

3.6.5 Conclusions Luminescent nanocrystalline PS is regarded as a kind of wide band gap semiconductor with the same band dispersion as that of c-Si. Besides efficient room temperature visible luminescence, PS shows some useful multifunctional properties as a quantum-confined system. These appear in various manners: nonlinear electrical and optical characteristics, ballistic transport and emission of electrons, and ultrasonic emission by thermo-acoustic effects. The PL external quantum efficiency has reached 23% by the introduction of complete surface termination. Based on analyses of ballistic electron emission and thermally induced ultrasound generation, their technological potential has been confirmed by prototyping devices such as flat panel display, 3D object sensing in air, and ultrasonic speaker for bio acoustics. The significantly decreased refractive indices of nc-Si, including their controllability in a wide range, produce another useful application of PS as a component of monolithic optical integration. It has been demonstrated that a three-dimensional buried optical waveguide can be fabricated on c-Si wafers, and that due to the obtained high contrast in refractive indices between the core and cladding PS layers, the visible light propagates along the bent waveguide with a very small curvature at a considerably lower bending loss than in the conventional fiber optics. Besides the operation as an optical filter, the FPR resonant cavity device is useful for observing a nonlinear optical response. Nanocrystalline silicon materials like PS are very attractive as a confined quantum system from scientific and technological viewpoints.

Landolt-Börnstein New Series III/34C3

134

3.6.6 References for 3.6

3.6.6 References for 3.6 56U 58T 65E 76K 80A 90C 91C 92B 92H 92K 92P 92S 93K 93L 93M 93Y 94B 94K 94M 94P 94W 94Y 95I 95K1 95K2 95M 95P 96A1 96A2 96B1 96B2 96B3 96C 96I 96L 96M

Uhlir, A.: Bell. Syst. Tech. J. 35 (1956) 333. Turner, D.R.: J. Electrochem. Soc. 105 (1958) 402. von Engel, A.: Ionized Gases, 2nd Edition, Oxford: Clarendon, 1965. Kuranari, K., Arita, Y.: Jpn. J. Appl. Phys. 15 (1976) 2279. Allan, D.C., Joannopoulos, J.D.: Phys. Rev. Lett.. 44 (1980) 43. Canham, L.T.: Appl. Phys. Lett. 57 (1990) 1046. Cullis, A.G., Canham, L.T.: Nature (London) 353 (1991) 335. Brandt, M.S., Fuchs, H.D., Stutzmann, M., Weber, J., Cardona, M.: Solid State Commun. 81 (1992) 307. Hummel, R.E., Chang, S.S.: Appl. Phys. Lett. 61 (1992) 1965. Koshida, N., Koyama, H.: Appl. Phys. Lett. 60 (1992) 347. Prokes, S.M., Glembocki, O.J., Bermudez, V.M., Kaplan, R., Friedersdorf, L.E., Searson, P.C.: Phys. Rev. B 45 (1992) 13788. Smith, R.L., Collins, S.D.: J. Appl. Phys. 71 (1992) R1. Kanemitsu, Y., Uto, H., Masumoto, Y., Matsumoto, T., Futagi, T., Mimura, H.: Phys. Rev. B 48 (1993) 2827. Littau, K.A., Szajowski, P.J., Muller, A.J., Kortan, A.R.: J. Phys. Chem. 97 (1993) 1224. Mihalecescu, I., Ligeon, M., Muller, F., Romestain, R., Vial, J.C.: J. Lumin. 57 (1993) 111. Yoffe, A.D.: Adv. Phys. 42 (1993) 173. van Buuren, T., Tiedje, T., Patitsas, S.N., Weydanz, W.: Phys. Rev. B 50 (1994) 2719. Kovyazina, T., Kutas, A., Khitko, V., Gaiduk, P.V., Komarov, F., Solov’ev, V., Bondarenko, V., Troyanova, G.: Mater. Sci. Forum 143/147 (1994) 583. Mauckner, G., Rebitzer, W., Thomke, K., Sauer, R.: Solid State Commun. 91 (1994) 717. Pavesi, L., Giebel, G., Ziglio, F., Mariotto, G.: Appl. Phys. Lett. 65 (1994) 2182. Wiesendanger, R.: Scanning Probe Microscopy and Spectroscopy, Cambridge: Cambridge University Press, 1994. Yonehara, T., Sakaguchi, K., Sato, N.: Appl. Phys. Lett. 64 (1994) 2108. Iwayama, T.S., Terao, Y., Kamiya, A., Takeda, M., Nakao, S., Saitoh, K.: Mater. Res. Soc. Symp. Proc. 388 (1995) 253. Koshida, N., Ozaki, T., Sheng, X., Koyama, H.: Jpn. J. Appl. Phys. 34 (1995) L705. Koch, F.: Microelectron. Eng. 28 (1995) 237. Matsumoto, T., Daimon, M., Mimura, H., Kanemitsu, Y., Koshida, N.: J. Electrochem. Soc. 142 (1995) 3528. Peng, C., Fauchet, P.M., Hirschman, K.D., Kurinec, S.K.: Mater. Res. Soc. Symp. Proc. 358 (1995) 689. Araki, M., Koyama, H., Koshida, N.: J. Appl. Phys. 80 (1996) 4841. Araki, M., Koyama, H., Koshida, N.: Appl. Phys. Lett. 68 (1996) 2999. Baru, V.G., Chernushich, A.P., Luzanov, V.A., Stepanov, G.V., Zakharov, L.Y., O'Donnell, K.P., Bradley, I.V., Melnik, N.N.: Appl. Phys. Lett. 69 (1996) 4148. Brus, L.E., Harkless, J.A.W., Stillinger, F.H.: J. Am. Chem. Soc. 118 (1996) 4834. Brus, L.: Phys. Rev. B 53 (1996) 4649. Cicala, G., Capezzuto, P., Bruno, G., Schiavulli, L., Perna, G., Capozzi, V.: J. Appl. Phys. 80 (1996) 6564. Iwayama, T.S., Terao, Y., Kamiya, A., Takeda, M., Nakao, S., Saitoh, K.: Thin Solid Films 276 (1996) 104. Letant, S., Vial, J.C.: J. Appl. Phys. 80 (1996) 7018. Mizuno, H., Koyama, H., Koshida, N.: Appl. Phys. Lett. 69 (1996) 3779.

Landolt-Börnstein New Series III/34C3

3.6.6 References for 3.6 96S 97C1 97C2 97C3 97D 97E 97G 97H 97K 97L 97N 97R 97T 98B 98F 98G1 98G2 98H 98K 98L 98S1 98S2 98S3 98U 98W 98Z 99F 99H 99K1 99K2 99S 99T 99U

135

Suda, Y., Koizumi, T., Obata, K., Tezuka, Y., Shin, S., Koshida, N.: J. Electrochem. Soc. 143 (1996) 2502. Canham, L. (ed.): Properties of Porous Silicon, EMIS Data Review Series No. 18, London: IEE, 1997. Cicala, G., Bruno, G., Capezzuto, P., Schiavulli, L., Capozzi, V., Perna, G.: Mater. Res. Soc. Symp. Proc. 452 (1997) 809. Cullis, A.G., Canham, L.T., Calcott, P.D.J.: J. Appl. Phys. 82 (1997) 909. Dutta, A., Kimura, M., Honda, Y., Otobe, M., Itoh, A., Oda, S.: Jpn. J. Appl. Phys. 36 (1997) 4038. Edelberg, E., Bergh, S., Naone, R., Hall, M., Aydil, E.: J. Appl. Phys. 81 (1997) 2410. Garrido, B., Achiq, A., Macia, J., Morante, J.R., Perez-Rodriguez, A., Ruterana, P., Rizk, R.: Mater. Res. Soc. Symp. Proc. 452 (1997) 785. Hinds, B.J., Banerjee, A., Johnson, R.S., Lucovsky, G.: Mater. Res. Soc. Symp. Proc. 452 (1997) 207. Koshida, N.: Dielectric Constant of Porous Silicon, in: EMIS Data Review Series No. 18: Properties of Porous Silicon, Canham, L. (ed.), London: IEE, 1997, pp. 234-237. Lang, W.: Thermal Conductivity of Porous Silicon, in: EMIS Data Review Series No. 18: Properties of Porous Silicon, Canham, L. (ed.), London: IEE, 1997, pp. 138-141. Normand, P., Tsoukalas, D., Kapetanakis, E., Van Den Berg, J.A., Armour, D.G., Stoemenos, J.: Microelectron. Eng. 36 (1997) 79. Romstad, F.P., Veje, E.: Phys. Rev. B 55 (1997) 5220. Theiss, W., Hilbrich, S.: Refractive Index of Porous Silicon, in: EMIS Data Review Series No. 18: Properties of Porous Silicon, Canham, L. (ed.), London: IEE, 1997, pp. 223-228. Buriak, J.M., Allen, M.J.: J. Am. Chem. Soc. 120 (1998) 1339. Fauchet, P.M., Tsybeskov, L., Zacharias, M., Hirschman, K.: Mater. Res. Soc. Symp. Proc. 485 (1998) 49. Gelloz, B., Nakagawa, T., Koshida, N.: Appl. Phys. Lett. 73 (1998) 2021. Gelloz, B., Nakagawa, T., Koshida, N.: Mater. Res. Soc. Symp. Proc. 536 (1998) 15. Hinds, B.J., Wang, F., Wolfe, D.M., Hinkle, C.L., Lucovsky, G.: J. Non-Cryst. Solids 227-230 (1998) 507. Koshida, N., Takizawa, E., Mizuno, H., Arai, S., Sameshima, T.: Mater. Res. Soc. Symp. Proc. 486 (1998) 151. Lowndes, D.H., Rouleau, C.M., Thundat, T., Duscher, G., Kenik, E.A., Pennycook, S.J.: Appl. Surf. Sci. 127-129 (1998) 355. Seifarth, H., Grtzschel, R., Markwitz, A., Matz, W., Nitzsche, P., Rebohle, L.: Thin Solid Films 330 (1998) 202. Suda, Y., Obata, K., Koshida, N.: Phys. Rev. Lett. 80 (1998) 3559. Sheng, X., Koyama, H., Koshida, N.: J. Vac. Sci. Technol. B 16 (1998) 793. Ueno, K., Koyama, H., Koshida, N.: Jpn. J. Appl. Phys. 37 (1998) 1096. Wu, M.H., Ueda, A., Mu, R., Henderson, D.O., Zuhr, R., Meldrum, A., White, C.W.: Proc. Electrochem. Soc. 19 (1998) 106. Zacharias, M., Tsybeskov, L., Hirschman, K., Fauchet, P.M., Bläsing, J., Kohlert, P., Veit, P.: J. Non-Cryst. Solids 227-230 (1998) 1132. Fujita, S., Sugiyama, N.: Appl. Phys. Lett. 74 (1999) 308. Huisken, F., Kohn, B., Paillard, V.: Appl. Phys. Lett. 74 (1999) 3776. Koshida, N., Sheng, X., Komoda, T.: Appl. Surf. Sci. 146 (1999) 371. Koshida, N., Nakajima, T., Yoshiyama, M., Ueno, K., Nakagawa, T., Shinoda, H.: Mater. Res. Soc. Symp. Proc. 536 (1999) 105. Shinoda, H., Nakajima, T., Ueno, K., Koshida, N.: Nature (London) 400 (1999) 853. Takahashi, M., Koshida, N.: J. Appl. Phys. 86 (1999) 5274. Ueno, K., Koshida, N.: Appl. Phys. Lett. 74 (1999) 93.

Landolt-Börnstein New Series III/34C3

136 99W 00G 00I 00L 00T 01B 01G 01K 01T 02L 02N 03G 03K 04G 04H 04I1 04I2 04K 05G1 05G2 05K 05O 05P 05T 05U1 05U2 06K

3.6.6 References for 3.6 White, C.W., Withrow, S.P., Meldrum, A., Budai, J.D.: Mater. Res. Soc. Symp. Proc. 507 (1999) 249. Gelloz, B., Koshida, N.: J. Appl. Phys. 88 (2000) 4319. Ito, M., Yamagata, K., Miyabayashi, H., Yonehara, T.: Proc. 2000 IEEE Int. SOI Conf. (IEEE, Massachusetts. 2000), pp. 10-11. Li, X., StJohn, J., Coffer, J.L., Chen, Y., Pinizzotto, R.F., Newey, J., Reeves, C., Canham, L.T.: Biomed. Microdevices 2 (2000) 265. Takahashi, M., Toriumi, Y., Matsumoto, T., Masumoto, Y., Koshida, N.: Appl. Phys. Lett. 76 (2000) 1990. Bera, S.K., Chaudhuri, S., Bandyopadhyay, A.K., Chakraborty, B.R., Pal, A.K.: J. Phys. D: Appl. Phys. 34 (2001) 273. Gago, R., Vazquez, L., Cuerno, R., Varela, M., Ballesteros, C., Albella, J.M.: Appl. Phys. Lett. 78 (2001) 3316. Koshida, N., Kadokura, J., Takahashi, M., Imai, K.: Mater. Res. Soc. Symp. Proc. 638 (2001) F 18.3.1. Toriumi, Y., Takahashi, M., Koshida, N.: Mater. Res. Soc. Symp. Proc. 638 (2001) F 8.3. Lehmann, V.: Electrochemistry of Silicon: Instrumentation, Science, Materials and Applications, Weinheim: Wiley-VCH, 2002. Nakajima, Y., Kojima, A., Koshida, N.: Appl. Phys. Lett. 81 (2002) 2472. Gelloz, B., Sano, H., Boukherroub, R., Wayner, D.D.M., Lockwood, D.J., Koshida, N.: Appl. Phys. Lett. 83 (2003) 2342. Koshida, N., Matsumoto, N.: Mater. Sci. Eng. R: Rep. 40 (2003) 169. Gelloz, B., Koshida, N.: Silicon and Porous Silicon, in: The Handbook of Electroluminescent Materials, Chap. 10, Vij, D.R. (ed.), Bristol and Philadelphia: IOP Publ., 2004, pp. 393-475. Hirota, J., Shinoda, H., Koshida, N.: Jpn. J. Appl. Phys. 43 (2004) 2080. Ichihara, T., Honda, Y., Baba, T., Komoda, T., Koshida, N.: J. Vac. Sci. Technol. B 22 (2004) 1784. Ichihara, T., Baba, T., Komoda, T., Koshida, N.: J. Vac. Sci. Technol. B 22 (2004) 1372. Komoda, T., Ichihara, T., Honda, Y., Hatai, T., Baba, T., Takegawa, Y., Watabe, Y., Aizawa, K., Vezin, V., Koshida, N.: J. Soc. Inf. Disp. 12 (2004) 29. Gelloz, B., Koshida, N.: J. Appl. Phys. 98 (2005) 123509. Gelloz, B., Kojima, A., Koshida, N.: Appl. Phys. Lett. 87 (2005) 031107. Kojima, A., Koshida, N.: Appl. Phys. Lett. 86 (2005) 022102. Ohta, T., Kojima, A., Hirakawa, H., Iwamatsu, T., Koshida, N.: J. Vac. Sci. Technol. B 23 (2005) 2336. Pacholski, C., Sartor, M., Sailor, M.J., Cunin, F., Miskelly, G.M.: J. Am. Chem. Soc. 127 (2005) 11636. Tsubaki, K., Yamanaka, H., Kitada, K., Komoda, T., Koshida, N.: Jpn. J. Appl. Phys. 44 (2005) 4436. Uno, S., Mori, N., Nakazato, K., Koshida, N., Mizuta, H.: J. Appl. Phys. 97 (2005) 113506. Uno, S., Mori, N., Nakazato, K., Koshida, N., Mizuta, H.: Phys. Rev. B 72 (2005) 035337. Kihara, T., Harada, T., Kato, M., Nakano, K., Murakami, O., Kikusui, T., Koshida, N.: Appl. Phys. Lett. 88 (2006) 043902.

Landolt-Börnstein New Series III/34C3