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Linköping Studies in Science and Technology

Dissertation No. 1303

Atomic and Electronic Structures of

Clean and Metal Adsorbed

Si and Ge Surfaces:

An Experimental and Theoretical Study

Johan Eriksson

Surface and Semiconductor Physics Division Department of Physics, Chemistry and Biology Linköping University, S-581 83 Linköping, Sweden

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The gure on the cover shows a top view of the calculated charge density redistribu-tion needed to reach self consistency on a c(4×2) Si(001) surface, see Fig. 1.6(a) on page 7. The blue large triangular shaped features are positioned at the sites of the dimer down atoms and illustrate volumes that are depleted of charge. The gure was rendered using the XCrysDen software.

Copyright © Johan Eriksson 2010, unless otherwise noted ISBN: 978-91-7393-433-6

ISSN 0345-7524

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Abstract

In this work, a selection of unresolved topics regarding the electronic and atomic structures of Si and Ge surfaces, both clean ones and those modied by metal ad-sorbates, are addressed. The results presented have been obtained using theoretical calculations and experimental techniques such as photoelectron spectroscopy (PES), low energy electron diraction (LEED) and scanning tunneling microscopy (STM). Si(001) surfaces with adsorbed alkali metals can function as prototype systems for studying properties of the technologically important family of metal-semiconductor interfaces. In this work, the eect of up to one monolayer (ML) of Li on the Si(001) surface is studied using a combination of experimental and theoretical techniques. Several models for the surface atomic structures have been suggested for 0.5 and 1 ML of Li in the literature. Through the combination of experiment and theory, critical dierences in the surface electronic structures between the dierent atomic models are identied and used to determine the most likely model for a certain Li coverage.

In the literature, there are reports of an electronic structure at elevated temper-ature, that can be probed using angle resolved PES (ARPES), on the clean Ge(001) and Si(001) surfaces. The structure is quite unusual in the sense that it appears at an energy position above the Fermi level. Using results from a combined variable temperature ARPES and LEED study, the origin of this structure is determined. Various explanations for the structure that are available in the literature are dis-cussed. It is found that all but thermal occupation of an ordinarily empty surface state band are inconsistent with our experimental data.

In a combined theoretical and experimental study, the surface core-level shifts on clean Si(001) and Ge(001) in the c(4×2) reconstruction are investigated. In the case of the Ge 3d core-level, no previous theoretical results from the c(4×2) reconstruction are available in the literature. The unique calculated Ge 3d surface core-level shifts facilitate the identication of the atomic origins of the components in the PES data. Positive assignments can be made for seven of the eight inequivalent groups of atoms in the four topmost layers in the Ge case. Furthermore, a similar, detailed, assignment of the atomic origins of the shifts on the Si surface is presented that goes beyond previously published results.

At a Sn coverage of slightly more than one ML, a 2√3 × 2√3 reconstruction

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can be obtained on the Si(111) surface. Two aspects of this surface are explored and presented in this work. First, theoretically derived results obtained from an atomic model in the literature are tested against new ARPES and STM data. It is concluded that the model needs to be revised in order to better explain the experimental observations. The second part is focused on the abrupt and reversible transition to a molten 1×1 phase at a temperature of about 463 K. ARPES and STM results obtained slightly below and slightly above the transition temperature reveal that the surface band structure, as well as the atomic structure, changes drastically at the transition. Six surface states are resolved on the surface at low temperature. Above the transition, the photoemission spectra are, on the other hand, dominated by a single strong surface state band. It shows a dispersion similar to that of a calculated surface band associated with the Sn-Si bond on a 1×1 surface with Sn positioned above the top layer Si atoms.

There has been extensive studies of the reconstructions on Si surfaces induced by adsorption of the group III metals Al, Ga and In. Recently, this has been expanded to Tl, i.e., the heaviest element in that group. Tl is dierent from the other elements in group III since it exhibits a peculiar behavior of the 6s2electrons called the inert

pair eect. This could lead to a valence state of either 1+ or 3+. In this work, core-level PES is utilized to nd that, at coverages up to one ML, Tl exhibits a 1+ valence state on Si(111), in contrast to the 3+ valence state of the other group III metals. Accordingly, the surface band structure of the1

3ML

3×√3reconstruction is found to be dierent in the case of Tl, compared to the other group III metals. The observations of a 1+ valence state are consistent with ARPES results from the Si(001):Tl surface at one ML. There, six surface state bands are seen. Through comparisons with a calculated surface band structure, four of those can be identied. The two remaining bands are very similar to those observed on the clean Si(001) surface.

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Populärvetenskaplig sammanfattning

Arbetet som presenteras i den här avhandlingen rör egenskaper hos ytor av kristallint kisel (Si) och germanium (Ge). Atomstrukturen hos dessa material är mycket lika och kan, likt de esta fasta grundämnen, beskrivas av en enhetscell bestående av en eller era atomer som upprepas med en periodicitet given av ett gitter i tre dimen-sioner. Periodiciteten i en riktning bryts vid en yta och den kan därför väsentligen betraktas som tvådimensionell. Den brutna periodiciteten ger upphov till lokaliser-ade elektrontillstånd, s.k. yttillstånd, som kan vara både fyllda och tomma. Kristall-ytornas orientering anges med beteckningar såsom t.ex. (001) eller (111). På grund av de brutna kristallbindningarna är det, för både Si och Ge, ofördelaktigt ur en-ergisynpunkt att låta ytatomerna behålla samma positioner som om de suttit i ett tredimensionellt gitter. En energisänkning kan åstadkommas genom att atomer på ytan spontant ändrar position och skapar nya bindningar, man säger att ytan rekonstrueras. Rena ytor, och de som är modierade av adsorbat, kan uppvisa en rad olika mer eller mindre komplicerade rekonstruktioner med olika egenskaper. I det här arbetet har egenskaper som laddningsfördelningen på ytan studerats med sveptunnelmikroskopi (STM), ytans periodicitet med elektrondiraktion (LEED) och yttillståndens egenskaper med vinkelupplöst fotoelektronspektroskopi (ARPES). Samma egenskaper kan studeras för olika atommodeller med hjälp av datorbaserade beräkningar. Genom att jämföra experimentella och beräknade data har man möj-lighet att identiera den atommodell som beskriver ytan och tolka de experimentella observationerna.

På de rena (001)-ytorna av Si och Ge bildas s.k. 2×1-rekonstruktioner när ytatomerna bildar par. Dessa ytor är föremål för två studier. I den ena visas att ett ovanligt fenomen, där elektroner besätter de vanligtvis tomma tillstånden, bäst förklaras av termiska eekter. Vid låga temperaturer övergår Si- och Ge-ytorna till att istället uppvisa c(4×2)-periodiciteter. Dessa undersöks i den andra studien där beräknade energiskillnader hos relativt hårt bundna elektroner används för att förklara experimentella data. Det visar sig att bidrag från grupper av atomer ända ner till fjärde lagret går att identiera.

Tre olika adsorbat har använts för att modiera Si-ytor. Gemensamt för de tre, litium (Li), tenn (Sn) och tallium (Tl), är att de tillhör gruppen metaller i det periodiska systemet. De kan dock antas bete sig olika vid adsorption på en Si-yta eftersom de skiljer sig markant på era sätt, till exempel storleksmässigt och i antalet

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elektroner som deltar i bindningarna. Ytor modierade genom adsorption av Li, Sn eller Tl bjuder därför på goda möjligheter att studera många olika fenomen.

I litteraturen nns era olika modeller för (001)-ytan på Si när den modierats med Li. I avhandlingen presenteras en studie där experimentella data från ARPES jämförs med beräknade elektronstrukturer och de mest troliga atommodellerna för två olika täckningsgrader av Li identieras.

Vid en täckning som motsvarar cirka en Sn-atom per Si-atom (ett monolager) på en Si(111)-yta bildas en 2√3 × 2√3-rekonstruktion. Denna uppvisar en enhetscell som är tolv gånger större än den för en orekonstruerad yta. Trots den stora enhets-cellen med många atomer, har STM bara påvisat fyra atomer. En dubbellagermodell för ytan nns beskriven i literaturen. I avhandlingen kombineras alla ovan nämnda experimentella och teoretiska tekniker för att testa om modellen är rimlig. Nya STM-resultat visar att det undre lagret förmodligen har en annan struktur och att modellen bör revideras. Arbetet har också fokuserat på, en för ytan, karaktäris-tisk övergång till en smält fas vid ca 190 ◦C. Observationer av förändringar hos

ytans elektronstruktur, mätt något under respektive över övergångstemperaturen, kombineras med beräknade resultat och nya slutsatser dras om ytans beskaenhet. Ovanför övergångstemperaturen uppvisar ytan egenskaper som kan förknippas med en blandning av en ytande och en fast fas.

Ordnade efter ökande atommassa består grupp III-metallerna i periodiska sys-temet av aluminium, gallium, indium och tallium. De har alla tre valenselektroner som kan delta i atombindningar (trivalenta). Tl-atomen skiljer sig från de övriga grupp III-metallerna då den ibland kan bete sig som om den bara hade en valenselek-tron (monovalent). Den här märkliga egenskapen kommer av en relativistisk eekt som ger sig till känna för tyngre grundämnen. I tre studier, en på Si(001) och två på Si(111), visas att Tl uppträder i den monovalenta formen för täckningar upp till ett monolager. Ytans elektronstruktur skiljer sig från den som uppvisas vid adsorption av de lättare, trivalenta, metallerna i grupp III. En jämförelse med en beräknad elektronstruktur visar att vid en täckning motsvarande ett monolager av Tl, bildas en rekonstruktion som liknar den som de monovalenta alkalimetallerna ger upphov till på Si(001).

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Preface

This doctorate thesis presents results that were obtained from experimental and computational work performed between 2004 and 2009 within the Surface and Semi-conductor Physics Division at the Department of Physics, Chemistry and Biology (IFM) at Linköping University, Sweden. The photoemission and electron diraction measurements were conducted at beamlines 33, I311 and I4 at the MAX-lab syn-chrotron radiation facility in Lund, Sweden. Scanning tunneling microscopy data was acquired using a variable temperature microscope at IFM. Density functional theory calculations were performed on a computer cluster at IFM and later also on the Neolith cluster at the National Supercomputer Centre in Linköping.

The thesis contains three parts. First a brief introduction to the topic and a presentation of the experimental and theoretical methods used. It is followed by a section with summaries and additional comments to the included papers. The last section contains the scientic output in the form of seven papers that have either been published, or have been submitted for publication.

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List of papers

Paper I

Lithium-induced dimer reconstructions on Si(001) studied by pho-toelectron spectroscopy and band-structure calculations

P.E.J. Eriksson, K. Sakamoto and R.I.G. Uhrberg Physical Review B 75, 205416 (2007)

Paper II

Origin of a surface state above the Fermi level on Ge(001) and Si(001) studied by temperature-dependent ARPES and LEED P.E.J. Eriksson, M. Adell, K. Sakamoto and R.I.G. Uhrberg

Physical Review B 77, 085406 (2008)

Paper III

Surface core-level shifts on clean Si(001) and Ge(001) studied with photoelectron spectroscopy and DFT calculations

P.E.J. Eriksson and R.I.G. Uhrberg Submitted to Physical Review B

Paper IV

Atomic and electronic structures of the ordered 2√3×2√3 and the molten 1×1 phase on the Si(111):Sn surface

P.E.J. Eriksson, J. R. Osiecki, K. Sakamoto and R.I.G. Uhrberg Submitted to Physical Review B

Paper V

Electronic structure of the thallium induced 2×1 reconstruction on Si(001)

P.E.J. Eriksson, K. Sakamoto and R.I.G. Uhrberg Submitted to Physical Review B

Paper VI

Core-level photoemission study of thallium adsorbed on a Si(111)-(7×7) surface: Valence state of thallium and the charge state of surface Si atoms

K Sakamoto, P.E.J. Eriksson, S. Mizuno, N. Ueno, H. Tochihara and R.I.G. Uhrberg

Physical Review B 74, 075335 (2006)

Paper VII

Photoemission study of a thallium induced Si(111)-√3×√3surface K. Sakamoto, P.E.J. Eriksson, N. Ueno and R.I.G. Uhrberg

Surface Science 601, 5258 (2007)

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My contribution to the papers

Paper I

Performed the experimental work in collaboration with the co-authors, per-formed the calculations, analyzed the data and wrote the manuscript.

Paper II

Performed the experimental work in collaboration with the co-authors, an-alyzed the data and wrote the manuscript.

Paper III

Performed the experimental work in collaboration with the co-authors, per-formed the calculations, analyzed the data and wrote the manuscript.

Paper IV

Performed the experimental work in collaboration with the co-authors, per-formed the calculations, analyzed the data and wrote the manuscript.

Paper V

Performed the experimental work in collaboration with the co-authors, per-formed the calculations, analyzed the data and wrote the manuscript.

Paper VI

Participated in the experimental work and in the discussion of the data.

Paper VII

Participated in the experimental work and in the discussion of the data.

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Papers not included

1

Abrupt rotation of the rashba spin to the direction perpendicular to the surface

Kazuyuki Sakamoto, Tatsuki Oda, Akio Kimura, Koji Miyamoto, Masahito Tsujikawa, Ayako Imai, Nobuo Ueno, Hirofumi Namatame, Masaki Taniguchi, P. E. J. Eriksson, and R. I. G. Uhrberg

Physical Review Letters 102, 096805 (2009)

2

Electronic structure of the Si(110)-(16×2) surface: High-resolution ARPES and STM investigations

Kazuyuki Sakamoto, Martin Setvin, Kenji Mawatari, P. E. J. Eriksson, Kazushi Miki, and R. I. G. Uhrberg

Physical Review B 79, 045304 (2009)

3

Surface electronic structures of the Eu- and Ca-induced so-called Si(111)-(5×1) reconstructions

Kazuyuki Sakamoto, P. E. J. Eriksson, A. Pick, Nobuo Ueno, and R. I. G. Uhrberg

Physical Review B 74, 235311 (2006)

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Acknowledgments

This work would have been impossible without the help of several individuals and organizations. They have, in dierent ways, supported me through the ups and downs during the studies. I would therefore like to acknowledge:

My supervisor, Prof. Roger Uhrberg. I am truly grateful for all his help and support in every aspect of my work through the years. His positive spirit has been invaluable and I have always felt welcome with my concerns, big or small.

Dr. Kazuyuki Sakamoto. I want to thank him as I have had the opportunity to learn much from his expertise on photoemission and labwork in general. His endless patience and good humor has been an inspiration and motivation during the MAX-lab weeks we shared.

Mainly Dr. Balasubramanian Thiagarajan, but also Dr. Martin Adell and the other members of the MAX-lab sta, for their technical support and trou-bleshooting skills.

Dr. Jacek Osiecki, for the time we shared at the STM.

Dr. Alexander Pick, for our friendship during my rst year at IFM. My mentor Prof. Bo Ebenman, for keeping an eye on my progress. Kerstin Vestin, for her immaculate administrative skills.

The Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation (KAW), for nancial support.

Andreas G. I am thankful for the time we spent together and for his unreserved way of kindly sharing his opinions on everything.

Arvid L and the other students, for making life at IFM enjoyable.

My wife Ylva, for her love and support, and our children Hedvig and Arvid, for showing me the meaning of life.

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List of abbreviations

1D, 2D, 3D One, two, three dimension

ARPES Angle resolved photoelectron spectroscopy

BZ Brillouin zone

DFT Density functional theory

EF Fermi level

ESCA Electron spectroscopy for chemical analysis

GGA Generalized gradient approximation

LAPW Linearized augmented plane wave

LDA Local density approximation

LDOS Local density of states

LEED Low energy electron diraction

ML Monolayer

PES Photoelectron spectroscopy

RT Room temperature

SBZ Surface Brillouin zone

SCF Self consistent eld

SCLS Surface core-level shift

STM Scanning tunneling microscopy

STS Scanning tunneling spectroscopy

UHV Ultra high vacuum

UPS Ultraviolet photoelectron spectroscopy

UV Ultraviolet

VBM Valence band maximum

XPS X-ray photoelectron spectroscopy

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Contents

1 Crystal Structure and Surfaces 1

1.1 Crystal structure . . . 1 1.2 Electronic structure . . . 3 1.3 Si and Ge surfaces . . . 5 2 Methods 9 2.1 Experimental techniques . . . 9 2.1.1 Photoelectron spectroscopy . . . 10

2.1.2 Low energy electron diraction . . . 14

2.1.3 Scanning tunneling microscopy . . . 16

2.2 Computational techniques . . . 18

2.2.1 Slab geometry . . . 19

2.2.2 Electronic band structure . . . 20

2.2.3 Core-level shift . . . 22

3 Summary and Comments to the Papers 25 3.1 Paper I: Si(001):Li . . . 25

3.2 Paper II: Warm Ge(001) and Si(001) . . . 26

3.3 Paper III: Surface core-level shifts on clean Si(001) and Ge(001) . . . 28

3.4 Paper IV: Si(111):Sn . . . 29

3.5 Paper V: Si(001):Tl . . . 30

3.6 Paper VI and VII: Si(111):Tl . . . 32

Bibliography 35 4 The Papers 41 Paper I . . . 43 Paper II . . . 55 Paper III . . . 63 Paper IV . . . 79 Paper V . . . 103 Paper VI . . . 117 Paper VII . . . 125 xix

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1.0 Crystal Structure and Surfaces

CHAPTER

1

Crystal Structure and Surfaces

1.1 Crystal structure

All systems seek to minimize their energy. In nature, this is beautifully manifested by the crystalline structure of solids. The fundamental components of a crystal are the lattice and the primitive unit cell. In three dimensions there exist 14 fundamental lattice types [1], also known as the Bravais lattices, which dene the symmetry and periodicity of a crystal. The unit of repetition is dened by the primitive unit cell. It can contain a single atom, groups of atoms, ions or combinations of these [2]. Truncation of solids gives rise to surfaces. Through the study of the orientation of the surface planes in the late 18th century [3], the crystalline properties of solids were systematically investigated for the rst time. An important contribution came in 1839, when Miller presented [4] a convenient notation for the orientation of planes and directions in crystals. This index system is widely used and came to be known as the Miller indices.

In Fig. 1.1(a) is an example of a cubic structure. The Bravais lattice is simple cu-bic dened by the lattice vectors ¯a, ¯b and ¯c. The primitive cell contains one atom in this case. Two crystal planes are denoted by their Miller indices and two directions are illustrated with arrows in the gure. For many applications, where the momen-tum of the electron is important, e.g. diraction or electronic band dispersions, it is useful to also dene the reciprocal lattice, which is an arrangement of imaginary points in reciprocal space described by the vectors ¯a∗, ¯band ¯c. These vectors can

be generated from the three crystal lattice vectors using eq. 1.1. Figure 1.1(b) shows

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Chapter 1. Crystal Structure and Surfaces

Figure 1.1: (a) Crystal lattice of a simple cubic structure with lattice constant a0. The

Bravais lattice is dened by the vectors ¯a, ¯b and ¯c. Two crystal planes (shaded) are denoted by Miller indices in parenthesis. Two directions, corresponding to the normal directions of the crystal planes are shown with arrows and denoted by square brackets. (b) The

corresponding reciprocal lattice dened by ¯a∗, ¯band ¯c.

the corresponding reciprocal lattice of the simple cubic Bravais lattice in Fig. 1.1(a). The position of the reciprocal lattice points have the form ¯Ghkl, as given by eq. 1.2.

Two important concepts of the crystal are related to the reciprocal lattice. First, for every family of equidistant lattice planes in the crystal, there exists a vector be-tween two reciprocal lattice points that is parallel to the normal direction. Second, the interplanar spacing, d, in a family of equidistant crystal planes determines the length of its corresponding reciprocal lattice vector as 2π

d. ¯ a∗= 2π ¯b × ¯c ¯ a · (¯b × ¯c) ¯b ∗= 2π ¯c × ¯a ¯ a · (¯b × ¯c) c¯ ∗= 2π a × ¯b¯ ¯ a · (¯b × ¯c) (1.1) ¯ Ghkl= h¯a∗+ k¯b∗+ l¯c∗ (h, k, l = 0, ±1, ±2...) (1.2)

The primitive unit cell, containing one reciprocal lattice point, can be dened in many dierent ways. It is often convenient to choose the Wigner-Seitz cell as the primitive cell. The Wigner-Seitz cell is centered around a reciprocal lattice point and is comprised of all points in reciprocal space which are closer to that lattice point than to any other lattice point. Figure 1.2(a) shows the Wigner-Seitz cell (shaded) in the cubic case. Another, more commonly used, name for the Wigner-Seitz cell is the rst BZ.

It is possible to reach any reciprocal lattice point by translation using a reciprocal

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1.2. Electronic structure

Figure 1.2: (a) The Wigner-Seitz cell (rst Brillouin zone) of a simple cubic structure containing one reciprocal lattice point (dot). (b) High symmetry points and labels.

lattice vector. Due to the translational symmetry, an arbitrary vector, ¯k, can be translated (folded) back into the rst BZ. High symmetry points in the BZ are given special labels, as shown in Fig. 1.2(b) for the cubic case.

1.2 Electronic structure

An electron can be characterized by the wave vector, ¯k, or momentum, ~¯k. In free space, the electron has a kinetic energy, Ekin, given by eq. 1.3, and is described by

a traveling wave, eq. 1.4. The wave vector must be real-valued since ψ¯k(¯r)must be

nite. In 1D, the dispersion relation, E(k), has the shape of a parabola. Due to the requirement of conservation of energy and momentum, a free electron cannot absorb a photon as illustrated in the 1D case in Fig. 1.3(a).

Ekin=

~2

|¯k|2

2me (1.3)

ψ¯k(¯r) = ei¯k·¯r (1.4)

In a crystal the situation is dierent. Here, reciprocal space is partitioned by the BZ boundaries and momentum can be exchanged with the lattice in units of ~ ¯G. The parts of the parabola outside the rst BZ become accessible by folding, employing reciprocal lattice vectors, ¯G, see Fig. 1.3(b). This situation describes the electronic band structure of a crystal. Excitation by means of a photon is possible in this case, provided that the energy of the photon, hν, matches the energy separation between the initial state and an unoccupied state at higher energy. The transition is nearly vertical since the momentum carried by the photon,hν

c , is several

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Chapter 1. Crystal Structure and Surfaces

Figure 1.3: One dimensional example of electronic energy dispersions. (a) Energy disper-sion of an electron in free space. Excitation by a photon with energy hν is not possible as this would require a much larger addition to the momentum than what is provided by the photon. (b) Energy dispersion of an electron in a crystal with a weak periodic potential. Photoexcitations are possible through interaction with the lattice. Crystal momentum can

be transferred in units of ~ ¯G, where ¯Gis a reciprocal lattice vector. Bragg reections occur

where the wave vector is a multiple of 1

2G¯, dotted lines. As a consequence, forbidden

en-ergy gaps appear. (c) Schematic examples of three electron wave functions; 1) an electron in an innite crystal, 2) and 3) show a bulk state and a surface state, respectively, near a crystal surface.

orders of magnitude smaller than the crystal momentum, ~ ¯G. As the electrons are inuenced by a periodic potential, they are described by Bloch functions [1]. These are traveling waves modulated by a function, uk(¯r), as illustrated in Fig. 1.4. At

certain points, or planes in 3D, the electron wave vector fullls eq. 1.5. These are so called Bragg planes [2]. Electrons with such wave vectors cannot propagate as strong backscattering results in the formation of standing waves. This is referred to as Bragg reections, and it introduces further changes to the band structure. In Fig. 1.3(b) this is shown by the opening of band gaps at the BZ boundaries.

|¯k| = |¯k − ¯G| (1.5) When a crystal is terminated by a surface, the requirement that the wave vector is real-valued is lifted due to the partitioning of space that the surface brings about. Additional solutions are possible when the exponentially decaying wave function outside the crystal is matched to the Bloch functions inside. Exponentially decaying wave functions inside the crystal describe surface states when modulated by uk(¯r),

see Fig. 1.3(c). The energy levels associated with states localized at the surface can only exist in the band gap regions of the innite crystal [5]. A surface resonance is a state that is a mix of a surface state and bulk states. Energy levels of surface resonances can therefore overlap with the bulk band structure. The discovery of

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1.3. Si and Ge surfaces

Figure 1.4: Examples of the complex part of Bloch wave functions in 1D. (a) A function,

uk(x), with the same periodicity, a, as the crystal lattice. b) Wave functions of free

electrons, eq. 1.4, with various values of k are drawn with dotted curves. The solid curves illustrate the corresponding Bloch functions of electrons in a crystal.

surface states immediately started intense research activities. See Ref. [6] for a historical overview.

Being conned to the surface plane implies that the surface states have a 2D character, i.e., the surface bands show no dispersion in the direction perpendicular to the surface. Utilizing this property, and the fact that they appear in bulk band gaps facilitate an identication of the surface states experimentally. Furthermore, surface states are more aected by contamination from the gas environment than bulk states.

1.3 Si and Ge surfaces

Si and Ge are very similar elements. They belong to the group of semiconductors in the periodic table and both exhibit a tetrahedrally bonded atomic structure. Both have attracted a lot of attention from a scientic point of view. Furthermore, Si has gained strong commercial interest as well [7]. Surface and interface properties of semiconductors play an important role in the development of electronic components. In the study of various surface and interface phenomena, Si and Ge surfaces oer several benets. They can provide well ordered surfaces with a low defect density [8] and can be used, clean or modied by adsorbates, as model systems for more com-plicated structures. The band gap of semiconductors enables the study of surface electronic states without interference from bulk states.

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Chapter 1. Crystal Structure and Surfaces

Figure 1.5: (a) Conventional cubic unit cell of the diamond lattice. Crystal axes and the (001) and (111) planes are indicated. (b) and (c) Reciprocal lattice and surface Brillouin zones of the (001) and (111) surfaces, respectively. The directions of the basis vectors are shown.

Si and Ge both exhibit the diamond structure, i.e., a face centered cubic struc-ture with two atoms in the basis as illustrated in Fig. 1.5(a). A layer of surface atoms shows no translational symmetry in the normal direction. As a result, the reciprocal lattice of a surface is a two-dimensional grid spanned by two reciprocal lattice vectors, ¯a∗and ¯b. The reciprocal lattices and SBZs of the two surfaces used

in this work, (001) and (111), are shown in Figs. 1.5(b) and (c).

The formation of a surface involves the breaking of atomic bonds. It is however energetically unfavorable to have unpaired electrons, dangling bonds, at the surface. As a consequence, the surface reconstructs. Bonds and atoms are rearranged at the surface to facilitate a lowering of the surface energy. If the periodicity of the surface is altered as a consequence of the reconstruction, a superlattice [9] is used to describe the new reconstructed surface. The commonly used notation is after Wood [10] and has the form (p × q) − R◦. The length of the basis vectors of the

superlattice are given by the integers p and q, in units of the lattice vector lengths of the bulk terminated structure. If there is any rotation of the superlattice vectors relative to the underlying lattice, it is indicated by an angle R◦.

Si(001) and Ge(001)

Ideal bulk truncated Si(001) and Ge(001) surfaces consist of atoms with two dangling bonds each in a square lattice. In 1957, Schlier and Farnsworth showed that Si(001) exhibits a (2×1) surface periodicity after cleaning in UHV. It was suggested that the surface atoms shift laterally to form pairs, dimers. By participating in the dimer bond, one dangling bond per atom is eliminated. In this model, a half lled dangling bond state would exist at each surface atom. Following these results there was a

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1.3. Si and Ge surfaces

Figure 1.6: (a) Atomic structure of the c(4×2) reconstruction on clean Si(001) and Ge(001). The dimer atoms are shown in gray and, in addition, the up-atom is drawn with a larger circle. The shaded area shows the unit cell. In (b), the c(4×2) and 2×1 SBZs are drawn by solid and dotted lines, respectively. Due to the existence of two surface domains, the c(4×2) and 2×1 SBZs appear with two orientations as illustrated by 1) and 2).

discussion on how these symmetric dimers could explain the semiconducting nature of the surface. This was resolved in 1979, when theoretical calculations by Chadi showed that tilted dimers are energetically preferable over symmetric ones. See Ref. [7] for a historical summary of the advancements in the understanding of the Si(001) surface.

Above a temperature of about 200 K the dimers change tilt direction rapidly. Ge(001) behaves in a similar way. At reduced temperature, the rate of ipping is reduced. Through interaction between neighboring dimers, both Si(001) and Ge(001) can then assume a c(4×2) reconstruction with alternating tilt direction both along and perpendicular to the dimer rows, as shown in Fig. 1.6(a). At elevated temperatures, on the other hand, both surfaces transform into a 1×1 phase.

The similarities between Si(001) and Ge(001) are also evident from the surface band structure. Figure 1.7 shows ARPES data from low temperature c(4×2) re-constructed Si(001) and Ge(001). The data was obtained along the [010] direction, see Fig. 1.6(b). This direction is special since identical ¯k||points in the SBZs of the

two domains on the surface, shown as 1) and 2) in the gure, are probed. The two domain surface is a consequence of ML high atomic steps that are always present.

Papers II and III deal with dierent aspects of the clean Si(001) and Ge(001) surfaces. In papers I and V, the Si(001) surface was studied when modied by adsorbates.

Si(111)

The ideal bulk truncated Si(111) surface consists of atoms in a hexagonal lattice with one dangling bond each. In UHV, it forms a metastable 2×1 reconstruction of π-bonded chains when prepared by cleaving [11]. Upon annealing to about 650 K, the Si surface irreversibly converts into a 5×5 phase, and at about 800 K it transforms

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Chapter 1. Crystal Structure and Surfaces

Figure 1.7: Band structure of the c(4×2) reconstructed Si(001) and Ge(001) surfaces, measured at 100 K using ARPES along the [010] direction as shown in Fig 1.6(b). The data was acquired using linearly polarized photons with 21.2 eV energy.

into a 7×7 structure [12]. In 1985, the 7×7 reconstruction was described by the dimer-adatom-stacking fault (DAS) model proposed by Takayanagi et al. [13]. The DAS model can be generalized to (2n+1)×(2n+1) models, and describes the 5×5 phase as well. At about 1100 K the Si(111) surface transforms to a 1×1 phase. Adsorbate modied Si(111) surfaces are discussed in Papers IV, VI and VII.

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2.0 Methods

CHAPTER

2

Methods

2.1 Experimental techniques

To minimize the disturbance from unintentional reactions during experiments a con-trolled environment is required for the study of the atomic and electronic properties of surfaces. Molecules in a gas environment will adsorb on surfaces until equilib-rium is reached. All experiments must therefore be conducted in vacuum in order to minimize the eect of adsorbed species. The quality of the vacuum ultimately determines the time until the surface becomes too contaminated for further exper-iments. Equation 2.1 [14] gives the adsorption time, τ, for one ML as a function of the partial pressure, p, and the molecular mass of the gas species, m. Also the number of atoms in a ML, n0, and the temperature, T , are important parameters.

Some typical values are given in Ref. [14].

τ (p) =n0 √

2πmkBT

p (2.1)

To maintain a sucently clean surface during the experiment, a base pressure of about 10−10-10−11 torr is required. This is what is referred to as the UHV regime.

See Ref. [14] for a review of UHV technology.

Synchrotron radiation sources, see Ref. [15] for a thorough introduction, have been used for the photoelectron spectroscopy studies in this work. These sources oer many advantages over conventional laboratory sources [14] such as gas discharge lamps or X-ray tubes. The ability to tune the photon energy is perhaps the most

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Chapter 2. Methods

striking one, but also the high ux and polarization of the photons are important properties.

2.1.1 Photoelectron spectroscopy

PES is one of the most important techniques in surface science [9], and has been so for many decades. The method is based on fundamental discoveries in the late 19th and early 20th centuries by Hertz (1887), Lenard (1894), Thomson (1899) and Einstein (1905), see Ref. [16] for a historical review. The use of PES in material analysis was however delayed due to technical challenges like the construction of electron energy analyzers, electron detectors, UHV compatible photon sources and general UHV equipment. Eventually the technology matured and, with the work led by Siegbahn [17], sucient resolution was reached to turn X-ray PES into a truly useful tool in 1957. Shortly thereafter, in 1962, Turner [18] demonstrated a setup with UV excitation. It was in 1964, in the group led by Siegbahn, that PES in the form of ESCA [19] was rst used as a method to study material properties like chemical composition and chemical environment of atoms.

In PES, electrons in a sample are excited by photons with a well dened energy, hν, that is higher than the work function, φ, of the material studied. The intensity of the emitted electrons is measured as a function of their kinetic energies, Ekin,

using an electron analyzer either in the spatial domain, hemispherical or cylindrical mirror analyzers [20], or in the temporal domain, time-of-ight analyzer [21].

For the analysis of the electronic states in a material, it is often useful to display the recorded electron distribution curves as a function of electron binding energy, Eb, instead of Ekin. The expression for Eb is given by eq. 2.2.

Eb= hν − φ − Ekin (2.2)

Of the emitted photoelectrons, those originating from states at EF will have the

highest kinetic energy, hν − φ. The Fermi energy is used as the reference level, corresponding to Eb= 0, as illustrated by the schematic spectrum in Fig. 2.1. The

energy position of EFcannot be determined from spectra recorded from all materials,

e.g., in non-metallic samples there are no electronic states at the Fermi energy, and hence no photoelectron intensity. Instead the position of EF can be measured on a

metallic part of the sample holder that is in electrical contact with the sample.

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2.1. Experimental techniques B in di ng e ne rgy Photoelectron intensity Valence band ARPES Core states XPS Inelastically scattered electrons Valence band Fermi level Vacuum level Core states K in te ti c e ne rgy 0 B in di ng e ne rgy 0

Sample Electron analyzer Spectrum

Figure 2.1: Schematic overview of the energy levels involved in photoelectron spec-troscopy. Electrons in bound states in a sample with a work function, φ, are excited by photons with energy hν. The intensity of the photoemitted electrons are measured as a

function of their kinetic energies, Ekin. Electrons from states at EF have a kinetic energy

of hν − φ. This energy position is used as the zero level in the resulting spectrum, where kinetic energy has been converted to binding energy.

Angle resolved photoelectron spectroscopy

By adding the ability to control and measure the angle at which the photoelectrons are detected, one enters the eld of ARPES. This technique is particularly useful for studying electronic structures in surface science. Figure 2.2 shows the geometry of an ARPES experiment. Emitted electrons are characterized by their wave vector, ¯

k, in momentum space, the polar angle, Θe, and the azimuthal angle, ϕ. The wave

vector can be decomposed into two components as shown in eq. 2.3, one parallel and one perpendicular to the surface.

¯

k = ¯k||+ ¯k⊥ (2.3)

Transport across the material boundary changes the perpendicular component as a consequence of the energy loss due to the work function. The two-dimensional character of the surface states implies that their dispersion relations are functions

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Chapter 2. Methods

Figure 2.2: Geometry of an ARPES experiment. Photons hitting the sample at an

incidence angle of Θiemit electrons from the sample. The electron intensity is analyzed

as a function of ¯k and the polar, Θe, and azimuthal, ϕ, emission angles. The surface band

structure is obtained when these parameters are converted to binding energy and ¯k||.

of ¯k||. This component remains unchanged, modulo a two-dimensional reciprocal

lattice vector ¯G||, when electrons cross the sample boundary. Using the geometry in

Fig. 2.2, the parallel component can be extracted from eq. 2.4.

|¯k||| = |¯k|· sin Θe (2.4)

By combining eq. 2.4 with the expression for the kinetic energy of a free electron, eq. 1.3, an expression relating the momentum parallel to the surface to the kinetic energy of the electrons is obtained, see eq. 2.5.

k||=

√ 2me

~ pEkin· sin Θe (2.5) The photoelectron intensity in the entire 2D ¯k||-space can be probed by varying

Θeand ϕ. Figure 1.7 shows two examples of ARPES data, where the surface band

structures of the Si(001) and Ge(001) surfaces were probed along the [010] direction using 21.2 eV photons from beamline I4 at the MAX-III synchrotron radiation source at MAX-lab in Lund, Sweden.

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2.1. Experimental techniques

Figure 2.3: The universal mean free path curve calculated in units of ML equivalents. The curve is valid for both Si and Ge since their ML spacings ac-cording to eq. 2.6, Si: 0.272 nm and Ge: 0.282 nm, are very similar.

Core-level photoelectron spectroscopy

Core electrons are more tightly bound than valence electrons and their wave func-tions are more localized. As a consequence, they do not show any energy dispersion and are of limited interest for ARPES studies. Instead they can be used to examine composition of a sample and the chemical environment of the atoms in a crystal [19]. Core-level spectroscopy can also be used to determine the contamination of a surface during sample preparations. No intensity from the C 1s or O 1s core-levels indicates that the surface is atomically clean. Core-levels are accessible using both XPS (e.g. C 1s, Eb=284 eV and O 1s, Eb=543 eV) and UPS (Ge 3d, Eb=29.8-29.2 eV

and Sn 4d, Eb=24.9-23.9 eV) [22].

Core-level spectra consist of a background and superimposed contributions from atoms in dierent environments. They can be analyzed through a peak tting procedure where the spectra are decomposed into components with a suitable line shape. The background can be modeled as proportional to the integrated spectral intensity of photoelectrons with higher kinetic energy [23], or as an exponential function if the kinetic energy of the core-level electrons is low so that inelastically scattered electrons constitute the major part of the background.

Information of the depth from which the measured electrons originate is valuable since it allows for a characterization of dierent atomic layers. The degree of surface sensitivity in an experiment is determined by the energy of the incoming photon beam and by the geometry of the experiment. The photon energy determines the kinetic energy of the photoelectrons.

It has been found empirically [24] that the mean free path of the electrons, λm,

as a function of their kinetic energy follows what is often referred to as the universal curve. It quite accurately describes the behavior of electrons with kinetic energies between a few to a few thousand eV. Figure. 2.3 shows the electron mean free path in

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Chapter 2. Methods

units of ML. It was calculated using the best t expression for elemental solids, see eq. 2.6 [24], and is valid for Si and Ge since their ML spacings, a, are very similar.

From the geometry of the experiment it follows that at a higher emission angle, Θe, electrons originating from a depth z must travel a longer distance of z

cos Θe

before they reach the surface. This results in an enhanced surface sensitivity as electrons from sub surface layers suer a greater risk of energy loss through scattering before being emitted.

λm(M L) = 538

E2 kin

+ 0.41 ·√a ·pEkin

where a(nm) =µ M olecular weight(g/mol) ρ(kg/m−3) · N

A(mol−1)

¶1/3

· 108 (2.6)

Knowing the mean free path, one can use a Beer-Lambert type expression, eq. 2.7 [25], to estimate the photoelectron yield, I, from dierent depths, z.

I(z) ∝ e

−z λ·cos Θe

(2.7) Most electrons suer losses through inelastic scattering on their way out. Using PES, these electrons can be seen as a high background at lower kinetic energies. This is shown schematically in Fig. 2.1.

2.1.2 Low energy electron diraction

LEED is a quick and simple tool, which can provide information on e.g. surface quality, geometry of the unit cell and the disposition of atoms in the unit cell on the surface [26]. In a LEED experiment, electrons, with kinetic energies usually in the range 30 to 300 eV and a momentum vector ¯k0, typically hit the sample surface

at normal incidence. It is the wave nature of the electrons that is utilized as they are diracted by the atoms in the rst few layers of the surface due to the short mean free path. To make the analysis of the diracted electrons feasible, those that have suered energy losses due to some inelastic process are ltered out by metallic meshes at dierent voltages in the LEED optics. The remaining, elastically scattered, electrons pass through and hit a uorescent screen which is monitored either by a camera or inspected directly by eye.

The diracted electrons, with momentum vector ¯k, fulll the 2D analog of the Laue equations in the surface plane, eq. 2.8 [9], and give rise to a spot pattern

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2.1. Experimental techniques

Figure 2.4: a) A schematic representation of the two c(4×2) reconstructions with dierent orientations that are present on both Si(001) and Ge(001). b) The corresponding reciprocal lattices. c) The two reciprocal lattices superimposed. d) The experimentally observed LEED pattern of Ge(001) c(4×2).

on the screen. ¯Ghk is a reciprocal lattice vector in the surface plane, as dened

by eq. 2.9. The coherence length of the electrons in the incoming beam is usually around 100 Å [27]. This imposes two limitations on the size of the structures that can be resolved using LEED. First, only structures with a periodicity smaller than the coherence length can produce diraction spots in a LEED experiment. Second, ordered regions that are smaller than the coherence length will result in diuse spots. The smaller the ordered regions are, the more diuse the spots become.

¯

Ghk= ¯k||− ¯k0|| (2.8)

¯

Ghk= h¯a∗+ k¯b∗ (h, k = 0, ±1, ±2...) (2.9)

As an example of LEED, consider the c(4×2) reconstruction which was intro-duced in Sect. 1.3. Figure 2.4(a) schematically shows the surface with two orien-tations of the unit cell as a result of the two surface domains. In Fig. 2.4(b) are the corresponding reciprocal lattices. LEED is an area integrating technique due

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Chapter 2. Methods

Figure 2.5: Energy levels in an STM experiment with a semiconducting sample and a metallic tip. (a) A negative sample bias, V, results in a shift of the sample density of states to higher energy relative to the tip. Tunneling from occupied states of the sample

is possible within the energy range eV from EF. (b) Tunneling to unoccupied states of the

sample is illustrated for a positive sample bias.

to the spot size of the electron beam (∼1 mm2), thus the resulting LEED pattern

has contributions from both domains. Figure 2.4(c) shows two overlapping recipro-cal lattices and the real LEED pattern, in the case of Ge(001) c(4×2), is shown in Fig. 2.4(d). In the analysis of the pattern, the shape, size, position and intensity of the spots contain information on the surface structure.

2.1.3 Scanning tunneling microscopy

The quantum mechanical concept of tunneling can be used to obtain atomically resolved images of surfaces. Electrons in a solid sense a barrier, the work function, which prevents them from leaving the material. As this barrier height is nite, part of the electron wave function will extend outside the surface of the material, cf. Fig. 1.3(c). When two pieces of material are brought close to each other, electrons have a probability to tunnel through the barrier to the other side. By utilizing the

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2.1. Experimental techniques

Figure 2.6: Two constant current STM images acquired at RT showing the same 50×45

Å2area on a Si(111) sample with an average Sn coverage of approx. 1 ML. Empty and lled

states on the surface are probed using sample biases of +0.5 and -0.8 V in the respective

image. A 2√3 × 2√3unit cell is shown by dotted lines and an adjacent area with lower

Sn coverage shows a√3 ×√3reconstruction as seen in the top left corner of the images.

electron tunneling between a metallic tip and a sample surface separated by a very small distance, Binnig and Rohrer managed to construct the rst STM in 1981 [28]. In 1982 they could, together with Gerber and Weibel, present topographic pictures of surfaces on an atomic scale [29].

Using STM, the electronic states a few eV around EF can be probed. Two

modes of operation are commonly used as the tip is swept over the surface. In the constant current mode, a feedback system regulates the tip z position, i.e., the height over the sample, so that the tunneling current is kept at a preset value. The images are obtained from the z variation of the tip. In the constant height mode, no feedback is used and variations in the tunneling current are used to image the surface. By changing polarity of the bias voltage between the tip and the sample both occupied and unoccupied states can be probed as illustrated in Figs. 2.5(a) and (b). By acquiring images at dierent bias voltages, information about the spatial distribution of the orbitals, that are contributing to surface states at dierent energy positions relative to EF, can be obtained. Figure 2.6 shows two images where empty

and lled states on the 2√3 × 2√3 Si(111):Sn surface are probed. It is apparent that the empty and lled states are distributed dierently. Four features can be resolved inside the 2√3 × 2√3 unit cell in the image showing empty states, while essentially only one feature is seen when lled states are probed. The features in the STM images are the combined result of electronic and topographical variations on the surface and do not necessarily reect the atomic positions.

Current vs. voltage curves, I-V curves, can be obtained if the tip is held

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Chapter 2. Methods

tionary over the surface while the tunneling current is measured over a range of bias voltages. This is an STS method that can be used for estimating the LDOS according to eq. 2.10 [14].

LDOS ∝dI/dVI/V (2.10)

2.2 Computational techniques

All calculated material properties presented in this work were obtained using meth-ods in the DFT based software package WIEN2k [30]. The framework of DFT was established in two papers, by Hohenberg and Kohn [31] in 1964 and by Kohn and Sham [32] in 1965. With DFT, the complicated many-body Schrödinger equation is reduced to a series of single particle equations which are solved using a self con-sistent scheme. The total energy, E, is in DFT given as a functional of the electron density, ρ(¯r), as shown in eq. 2.11, see [33]. All material specic parameters, like geometry and atomic species, are contained in the external potential Vext(¯r). F [ρ] is

a universal functional of ρ, and the framework of DFT states that the ground state density yields the minimum value of E, i.e., the ground state energy.

E[ρ] = F [ρ] + Z

ρ(¯r)Vext(¯r)d¯r (2.11)

Even though DFT is formally exact (within the Born-Oppenheimer approxima-tion) [34], usually not all parts of the universal functional F [ρ] are known exactly [35]. More specically, it is the form of the exchange-correlation energy functional that is unknown. LDA and GGA are the two most common methods for approximations of this term.

The method implemented in WIEN2k for the practical use of DFT is LAPW, see [36]. Compared to pseudopotential methods, it is an all electron scheme. The electrons are divided into core electrons and valence electrons by a cut-o energy. Space is partitioned [33] into non-overlapping atomic spheres centered on the nuclei, called mun-tin spheres, where core electrons are described by linear combinations of radial functions and spherical harmonics. There is an interstitial region, with valence electrons described by plane wave expansions. The use of all electron meth-ods permits direct access to the core electrons for obtaining, e.g., surface core-level shifts.

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2.2. Computational techniques

Figure 2.7: Examples of symmetric and H-terminated Si(001):Tl 2×1 slabs are shown in (a) and (b). The shaded region is the unit of repetition. (c) shows the band structure

near EFobtained using the two slabs. The use of a symmetric slab can induce an articial

splitting of the surface bands as indicated by A and B.

2.2.1 Slab geometry

The calculations were performed on structures that, in the computational scheme, are repeated in all directions. To do a surface calculation, a slab structure with vacuum as spacing in one direction is necessary. Two examples of surface slabs are shown in Figs. 2.7(a) and (b). The unit of repetition, shaded, contains a vacuum region which separates the slabs in the direction perpendicular to the surface. The distance between consecutive slabs must be suciently large to avoid interaction between surfaces of neighboring slabs. The interior of the slab serves a similar purpose. It acts as a bulk buer region and separates the surface from the articial backside of the slab. It must therefore be suciently thick.

In a slab geometry, two surfaces are created, i.e., the top and bottom ones. There are two ways of dealing with this situation. One can either use a symmetric slab, Fig. 2.7(a), or one can create an articial bulk termination using hydrogen atoms (H), Fig. 2.7(b). A disadvantage with the symmetric slab approach is shown in Fig. 2.7(c). Interaction between surface states on opposite sides of the slab can cause a splitting of the surface bands. The disadvantage with a H-terminated slab is the computational cost. The lack of inversion symmetry necessitates complex-valued calculations, instead of real-complex-valued in the symmetric case. Furthermore, the small bond length associated with the H-termination layer demands a small

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Chapter 2. Methods

Figure 2.8: Calculated band structure near EF of a Si(001) surface in a 2×1

reconstruc-tion as shown in (a). The path in the SBZ that is traversed is shown in Fig. 2.9(a). (b) Surface bands with contributions from U, D and the second layer atoms, S. In (c) the

contribution from atom U is decomposed into dierent orbitals, s, px, pyand pz. The size

of the circles is proportional to the contribution to the band from the respective atom and orbital.

mun-tin radius, that in turn results in an increased cut-o energy for the plane wave expansion. These calculations can be extremely time consuming since the computational time scales as the ninth power [36] of the plane wave cut-o.

2.2.2 Electronic band structure

Surface band structure calculations are useful for comparing with ARPES results. Surface band dispersions can be compared e.g. to test a theoretical model or to identify experimentally obtained bands. In Fig. 2.8 the contributions to the surface band structure of a Si(001) 2×1 surface, see Fig. 2.8(a), is resolved down to specic orbitals on individual atoms.

Two strong surface bands are associated with atoms U and D. Furthermore, a back bond state associated with atom U and a second layer atom, S, can be seen in the band structure around ¯Γ in Fig. 2.8(b). From the orbital decomposition of the contribution from atom U in Fig. 2.8(c) it is evident that the strong band mainly originates from dangling bond pz orbitals, but also some s contribution is seen near

the SBZ boundaries. The back bond contribution comes from py orbitals around ¯Γ.

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2.2. Computational techniques

Figure 2.9: Calculation of the bulk band projection onto the SBZ. (a) A path ¯Γ − ¯J−

¯

K− ¯J′− ¯Γ − ¯J

2is shown in a 2×1 SBZ (dotted lines). The underlying bulk truncated 1×1

SBZ is shaded. (b) The same path shown at three dierent heights, A-C, in the bulk BZ. (c) Band structures along the path at A, B and C. (d) The bulk band projection estimated by 26 superimposed band structures obtained at dierent heights between A and C.

Even though a study might be aimed at the surface band structure, it can also be useful to keep track of the bulk band structure. In Fig. 1.7 the shaded areas indicate the projection of the bulk bands onto the SBZ. Bands that are not inside the projection originates from surface states. The projection of the bulk band structure onto the 1×1 SBZ was calculated using a bulk 1×1×1 cell such as the one shown in Fig. 1.5(a). Figure 2.9(a) shows the same path in the SBZ as was traversed in the calculation presented in Fig. 2.8. In Fig. 2.9(b) this path is shown in the 3D conventional reciprocal lattice cell. The projection of the band structure onto the SBZ (shaded), is obtained by traversing this path at dierent heights in the BZ, i.e., at dierent k⊥ values. Figure 2.9(c) shows the band structure at three

dierent heights, A-C. The bulk band projection is built by superimposing several such images. Figure. 2.9(d) shows the situation when the BZ has been sampled at 26 dierent values of k⊥.

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Chapter 2. Methods Etotal Enon-ionized With screening Total energies Etot-bulk Etot D Etot U Ebinding D U E2p E2p-bulk E2p D E2p U No screening Core-state eigenenergies Ebinding D U E =0B E =0B

Figure 2.10: Energy levels in SCLS calculations. Results for the Si 2p SCLSs obtained for a Si(001) c(4×2) surface, see Fig. 1.6(a), are shown schematically in the gure. U and D refer to the up- and down-atoms of the dimer. In the case of no screening 2p eigenenergies are compared. The average of the 2p eigenenergies of atoms in the center

of the slab, ¯E2p−bulk, serves as bulk reference. The 2p SCLS of atoms U and D are 2p

eigenenergy deviations from this value. When screening is included, total energies are instead compared. The average total energy obtained when atoms in the center of the slab

are ionized ¯Etot−bulk is used as bulk reference. The 2p SCLS of atoms U and D are total

energy deviations from this value when atoms U and D are ionized, respectively.

2.2.3 Core-level shift

In core-level studies, the possibility to resolve the core-level shift of individual atoms is of great value. In theoretical calculations, these shifts can be computed with vari-ous degrees of screening included, i.e., relaxation of the valence electrons in response to the core-hole. When screening is included, the SCLS calculations can become computationally very demanding. There are three reasons for this. One stems from the fact that each atom must be treated individually. The second reason is the iso-lation of the core-hole, i.e., interaction laterally between core-holes in adjacent slabs should be avoided. Thus, the unit of repetition must in general be larger or have a lower symmetry than in a band structure calculation. Finally, the perturbation that the core-hole introduces can lead to slow convergence in the calculations. Fig-ure 2.10 illustrates the energy levels involved in the SCLS calculations, without and with screening. Screening eects are important for metals [37] where the valence electrons are very mobile and respond strongly to core-holes. It has also been shown to be important for Si and Ge surfaces [38].

In the case of Ge, the electrons in the 3d states are in the calculations normally treated as valence electrons. In experiments, however, they are considered as core electrons with no energy dispersion despite their low binding energy. Treating them as core electrons in the calculations results in core charge leakage out of the mun-tin spheres. Calculations with screening included can still be performed using a

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2.2. Computational techniques

two window semi-core approach [36]. The procedure starts with one electron being removed from a 3d state on one of the Ge atoms. One single iteration of the SCF procedure is run with the 3d states treated as core states, despite the charge leakage. The result is a shift of the 3d state of the ionized Ge atom to a slightly higher binding energy compared to the other, neutral, Ge atoms. In the next step, the 3d levels of the ionized atom as well as the neutral atoms, are then treated as valence states. The energy range of the valence states are separated into two windows by an energy cut-o, which is chosen to be between the down shifted 3d level and the 3d levels of the other Ge atoms. By keeping the occupancy one electron short in the window of the down shifted state, one is eectively creating a localized hole in the distribution of valence electrons. In the second window the occupation is not changed. This technique is applied to all individual atoms of interest and the corresponding SCF procedures are completed, this time with no core leakage. The SCLSs are extracted from the converged total energy dierences in the same manner as is illustrated in Fig. 2.10. The Si 2p core-level can be treated properly without core charge leakage with the regular approach as well as the two window technique. Tests have shown that the two methods produce very similar results of the SCLSs.

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3.0 Summary and Comments to the Papers

CHAPTER

3

Summary and Comments to the Papers

3.1 Paper I: Si(001):Li

Metal-semiconductor interfaces are important from a technological point of view. The alkali metals have a single s electron in the valence band and can, in com-bination with semiconductor surfaces, be used as prototype systems for studying such interfaces. In paper I, the adsorption sites of Li on Si(001) are investigated using photoelectron spectroscopy and band-structure calculations. In the literature, four dierent models of a 2×2 reconstruction with 0.5 ML of Li have been pro-posed [39, 40], while three dierent models for a 2×1 reconstruction with 1 ML of Li have been proposed [40, 41, 42]. ARPES results from the [110] and [¯110] directions were obtained through the use of a Si(001) sample with the surface normal 4◦ o

the [001] direction where the majority domain constitutes 80% of the surface area. These new ARPES results from the 2×2 and 2×1 reconstructions were compared to theoretical results from the literature. Using additional band structure calculations in the [010] direction and total energy comparisons we were able to discriminate between the dierent atomic models.

On the 2×2 surface, two models were found to be indistinguishable as they showed similar surface band structures and total energies. This stems from the very similar atomic structures of these two models. Both share a Si dimer structure with alternating strongly and weakly buckled Si dimers, and in addition, one Li atom positioned above a fourth layer Si atom in the trough between the Si dimers. The second Li atom occupies a bridge site above a second layer Si atom in one model,

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Chapter 3. Summary and Comments to the Papers

while it is instead positioned close to a pedestal site between the Si dimers in a dimer row but slightly shifted toward a bridge site in the second model.

The total energy calculations favored two of the 2×1 models and the energy dierence between them was found to be very small. These are, like in the case of the 2×2 models mentioned above, quite similar in atomic structure. They share a structure with symmetric Si dimers and one Li atom at the pedestal sites between the dimers along the dimer rows. However, the position of the second Li atom in the trough dier. Surface band structure comparisons revealed that the ARPES data was better reproduced by the model where this second Li atom occupies the sites above the third layer Si atoms.

Analysis of the dimer atom components in high resolution Si 2p core-level spectra conrmed that the arrangement of the Si dimers in the models are indeed plausible.

3.2 Paper II: Warm Ge(001) and Si(001)

The surface band structures of clean Si(001) and Ge(001) are very similar as the example in Fig. 1.7 on page 8 shows. Filled, π, and empty, π∗, surface bands

are associated with dangling bond states of the up atom and the down atom of the dimers as illustrated for Si(001) 2×1 in Fig. 2.8 on page 20. In this paper, the empty band is in focus. In addition to calculations, it has been probed experimentally using inverse photoemission [43] and STS [44]. Following an early report [45] of a structure seen in normal emission with ARPES near EF on heated Ge(001), more

recent studies [46, 47] have shown that this structure is actually positioned above EF. It was attributed to the minima of the π∗surface band of the dimer down atoms

as it was found to show a ¯k|| dependence as expected from calculated dispersions

of that band [46]. Since the rst report, where the occupation of the structure was associated with the c(4×2) to 2×1 phase transition, the origin of the electrons in the band minima has been under discussion.

In paper II, ARPES and LEED data from Ge(001) at various temperatures are presented which show that the phase transition and appearance of the structure in photoemission are not connected. Furthermore, the intensity of the structure above EFmonotonically increases up to about 625 K, and becomes higher than that of the

π band positioned 0.17 eV below EF at ¯Γ. Above that temperature the intensity

drops steeply, possibly reecting a change in the dimer reconstruction. A similar structure, but much weaker in intensity, was found on Si(001). Here, no decrease

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3.2. Paper II: Warm Ge(001) and Si(001)

Figure 3.1: Normal emission ARPES

spectra from a highly n-doped (n+)

clean Si(001) sample at 100 K (gray) and a Si(001) sample with very low (dot-ted curve) and slightly higher Cs cov-erage (thin black curve) at RT. Data from a clean Si(001) sample at elevated temperature is shown with thick black curves.

in intensity could be observed up to 875 K, only a saturation. As neither the π, nor the π∗ surface bands on Ge and Si cross E

F, both surfaces must be considered

as semiconducting in the entire temperature range. By dividing by the Fermi-Dirac distribution function, the energy position of the structures were estimated to be 0.13 and 0.24 eV above EF for Ge(001) and Si(001), respectively. These values result in

separations between the VBM and the π∗ band minimum at ¯Γ that are consistent

with earlier reports.

More recent results have been published on Si(001), where the conclusion is that electron donation by thermal adatoms is the cause of the lling of the π∗ band

minima [48]. The authors argue that the temperature for the onset of the lling is too low to explain thermal excitations of electrons to the π∗ band. Furthermore,

the unusual energy position of the structure is explained by the number of donated electrons, which is thought to be too low to align the π∗ band minima to E

F [48].

The π∗band minima can be probed using ARPES by supplying additional

elec-trons to the surface. In Fig. 3.1, this is illustrated by the use of i) a highly n-doped sample (n+) and ii) Cs adsorption. The result when using an n+sample is shown

in gray. From this it is apparent that the photoemission cross-section of the π∗

band minima is very high in this geometry using 21.2 eV photons. It is therefore not unreasonable to have a measurable photoemission intensity from this structure at about 500 K, contrary to what was claimed in Ref. [48]. Both in the n+

spec-trum and in the spectra showing the two Cs adsorbed surfaces (dotted and thin solid curves), the energy position of the π∗ band minimum is very close to E

F. The

low coverage Cs case would correspond to the situation of initial lling by thermal adatoms. Despite the low intensity, the π∗ band minimum has been aligned with

EF. Compare this to the thick solid curves that show a spectrum from the Si(001) at

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Chapter 3. Summary and Comments to the Papers

elevated temperature. There is a clear dierence in energy position of the structure compared to the two Cs cases as well as compared to the n+ case.

3.3 Paper III: Surface core-level shifts on clean Si(001)

and Ge(001)

In paper III, the Si 2p and Ge 3d core-levels are studied using high resolution PES and DFT calculations. Both the Si(001) and the Ge(001) surfaces show a c(4×2) reconstruction at lower temperatures. Even though the atomic model, see Fig. 1.6 on page 7, is well established, calculated SCLSs in the literature only cover the Si surface. No results from Ge(001) in the c(4×2) reconstruction have been reported in the literature. Calculations on the similar p(2×2) surface structure have been presented in Ref. [38]. There it was found that screening plays an important role for the SCLSs on both the Si(001) and Ge(001) surfaces. Screening is a nal state eect, which is the result of the response from the valence electrons on the creation of a vacancy in the core state. The phenomenon of valence charge redistribution is always present when there are localized charges in solids. It becomes important in SCLS calculations when there is, as pointed out in Ref. [38], a site dependence, i.e., the eciency of the screening varies between dierent atoms.

When screening eects are included, the calculated SCLSs presented in this paper were found to describe the experimentally obtained core-level spectra from both Si and Ge very well. From the comparison between experiments and calculations, seven of the eight calculated components from the four topmost layers could be assigned to the components used to t the spectra in both the Si and Ge case. A strong site dependence of the screening was seen as the change in relative binding energy due to screening was signicantly larger for the dimer down atom compared to the other atoms. This has been attributed to occupation by screening electrons of the ordinarily empty dangling bond state at the down atom [38]. Figure 3.2 shows three examples of the spatial valence charge redistribution in the Si(001) c(4×2) case. The atoms with the core holes are recognized by the surrounding electron cloud, shown by large oversaturated red areas in the gure. In a larger shell around the core holes, beyond the relatively dense electron cloud, there is a depletion region that is, in many cases, followed by a region with excess charge in an oscillatory manner as shown in Fig. 3.2(b). The change in core-level shift due to screening was found to be more similar for atoms in deeper layers. Also, in contrast to the surface atoms,

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3.4. Paper IV: Si(111):Sn 0.01 e/Å-3 -0.01 e/Å-3 Up Down 4th layer 1 2 3 4 -0.5 0.5 1 1.5 0 -0.5 0.5 1 1.5 0 -0.5 0.5 1 1.5 0 Up Down 4th layer Radius (Å) ρ (r ) (e/ Å ) -3

Figure 3.2: In a), a cross sectional view of the valence charge density of Si(001) c(4×2) is showing the dierence between the charge distribution of a slab with a core hole and a neutral slab. The three panels show the situations when core holes are introduced in the

2plevel of the dimer up atom, dimer down atom and a fourth layer atom. Both the atom

with the core hole and the Si dimer are in the plane of the plot. Note that the color scale is heavily saturated in order to show small variations. In b) the spherical average of the charge density dierence around each of the three core-holes in a) is shown. Red (blue) indicate an accumulation (depletion) of charge in shells of dierent radius.

the accumulation/depletion oscillations in the spatial charge redistribution for these bulk-like atoms are virtually identical to that of the 4th layer atom in Fig. 3.2(b).

3.4 Paper IV: Si(111):Sn

When Sn is adsorbed on Si(111) a√3 ×√3reconstruction is initially formed. With increasing Sn coverage the surface starts to exhibit a 2√3 × 2√3 periodicity. In a narrow coverage interval slightly above 1 ML, the 2√3 × 2√3 reconstruction is present without coexistence of the√3 ×√3phase [49]. The 2√3 × 2√3phase shows a remarkable transition at 463 K. As observed in LEED, the entire surface abruptly, and reversibly, switches between the 2√3 × 2√3and a 1×1 diraction pattern at the transition temperature.

In this paper, calculated results obtained from an atomic two-layer model in the literature [50] are compared to detailed STM data and low temperature ARPES results from the 2√3×2√3surface. It is found that several of the six experimentally resolved surface state dispersions are not reproduced by the calculated surface bands. However, in calculated STM images the empty states, in combination with the

References

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