electronic properties of semiconductor surfaces and metal

Electronic properties of semiconductor surfaces and

metal/semiconductor interfaces

Inaugural-Dissertation

zur Erlangung der Doktorwiirde

am Fachbereich Physik

der Freien Universitat Berlin

vorgelegt, von

Massimo Tallarida

Berlin, Mai 2005

Arbeit eingereicht am: 24 Mai 2005

Tag der Disputation: 27 Juni 2005

1. Gutachter: Prof. K. Horn

2. Gutachter: Prof. M. Wolf

Angefertigt im Fritz-Haber-Institut der Max Planck Gesellschaft, Berlin

Ad Elvira

ed al divenuto Pietro

Contents

1 Introduction 31.1 Crystals, surfaces and interfaces............................................... 3

2 Experimental techniques for surface physics 92.1 Photoemission spectroscopy..................................................... 9

2.1.1 Angle resolved spectroscopy......................................... 122.1.2 Core level spectroscopy ............................................... 13

2.2 LEED and STM....................................................................... 152.3 Ultra high vacuum.................................................................... 17

3 SiC(0001) cleaved surface reconstructions 193.1 Semiconductor surfaces ........................................................... 193.2 Semiconductor surface reconstructions................................... 22

3.2.1 The IV group elements and the IV-IV compound semiconductors .................................................................... 24

3.2.2 6H-SiC(0001) polar surface.......................................... 263.3 Experimental set up................................................................. 293.4 6H-SiC(0001)(2x1): experimental results .............................. 29

3.4.1 LEED............................................................................. 293.4.2 Core level spectroscopy ............................................... 313.4.3 Discussion....................................................................... 35

3.5 Conclusions................................................................................ 37

4 Thin Manganese films on Si(111) 394.1 Transition metal silicides........................................................... 394.2 Experimental set up................................................................. 424.3 Experimental results................................................................. 43

4.3.1 Morphology.................................................................... 44

1

2 CONTENTS

4.3.2 Spectroscopy................................................................. 494.4 Conclusions................................................................................. 57

5 Al-Mg alloy thin films on Si(111) 595.1 Simple metals and binary alloys............................................... 61

5.1.1 Binary alloys................................................................. 625.2 Photoemission and QWS........................................................... 665.3 Experimental setup.................................................................... 685.4 Experimental results: ARUPS.................................................. 705.5 Collective excitations in simple metals and alloys................... 79

5.5.1 Experimental results: CIS spectroscopy..................... 855.6 Conclusions................................................................................ 91

Acknowledgements

I want to thank for his support, his stories, his availability and presence during experiments Prof. Karsten Horn.I acknowledge thankfully Prof. Martin Wolf for his interest and for coassessing this thesis.

All the Horn’s group with the former and the present members: Lucia, for the “red-shoes-team” on the 3m-NIM beamline; Ashwani, for the “coffee and cigarettes” and the “langsame” nightshifts; Sudipto for “It’s a surface state: let’s follow it!” at 4 a.m. in the night 22nd-23rd December 2001; Cha-hao for “ciao ciao, massimo massimo”; Martin for “walking in the snow storm” in Lund; Luis for the “never ended story”; Jeong Won for the “ko- reanische Woche”; Hugo for “gesellig”; Thorsten for “Ausstattung”: all you receive my thanks for being there.Special thanks go to Henrik for “espresso und Berlins Geschichte”.All the “new people” of the MP Department for the new verve.All the friends I have found in Berlin: David, Monica and Irene (Breakfast, lunch and dinner); Tiziano, Vanessa and Raffaello (Dinner, lunch and breakfast); Nacho, Judith and Jannis (Lunch, breakfast and dinner); Valentina and Felix (Brunch) and all the other imbisses.My family and attached: for oil, coffee and sun.Elvira: ... and all the rest.Pietro: ... and all the following.

AbstractThis thesis reports investigations of the electronic properties of a semiconductor surface (silicon carbide), a reactive metal/semiconductor interface (manganese/silicon) and a non-reactive metal/semiconductor interface (aluminum-magnesium alloy/silicon).

The (2x1) reconstruction of the 6H-SiC(0001) surface has been obtained by cleaving the sample along the (0001) direction. This reconstruction has not been observed up to now for this compound, and has been compared with those of similar elemental semiconductors of the fourth group of the periodic table. This comparison has been carried out by making use of photoemission spectroscopy, analyzing the core level shifts of both Si 2p and C 1s core levels in terms of charge transfer between atoms of both elements and in different chemical environments. From this comparison, a difference between the reconstruction on the Si-terminated and the C-terminated surface was established, due to the ionic nature of the Si-C bond.

The growth of manganese films on Si(111) in the 1-5 ML thickness range has been studied by means of LEED, STM and photoemission spectroscopy. By the complementary use of these surface science techniques, two different phases have been observed for two thickness regimes (<1 ML and >1 ML), which exhibit a different electronic character. The two reconstructions, the (1x1)-phase and the (V3 x V3)R30°-phase, are due to silicide formation, as observed in core level spectroscopy. The growth proceeds via island formation in the monolayer regime, while the thicker films show flat layers interrupted by deep holes. On the basis of STM investigations, this growth mode has been attributed to strain due to lattice mismatch between the substrate and the silicide.

Co-deposition of Al and Mg onto a Si(111) substrate at low temperature (100K) resulted in the formation of thin alloy films. By varying the relative content of both elements, the thin films exhibited different electronic properties, manifested by the observation of quantum well states and a surface state. The resulting shift in binding energy of both quantum well states and surface state has been interpreted in terms of the virtual crystal approximation model where the main effect of the alloying process is attributed to the change of electron density of the system. For this system, the variation of photoemission intensity as a function of photon energy has been also investigated and explained in terms of collective excitations.

KurzfassungDiese Dissertation befasst sich mit der Untersuchung der elektronischen Eigenschaften einer Halbleitersoberflache (Siliziumcarbid), einer reaktiven Metall/Halbleiter-Grenzflache (Mangan/Silizium) und einer nicht-reaktiven Metall/Halbleiter-Grenzflache (Aluminum-Magnesium-Legierung/Silizium).

Die (2x1) Rekonstruktion der 6H-SiC(0001) Oberflache wurde durch Spaltung der Probe entlang der (0001) Richtung erlangt. Diese Rekonstruktion ist fur diesen Verbundhalbleiter noch nie beobachtet worden. In dieser Arbeit wird SiC mit den Element-Halbleitern der 4. Gruppe des Perio- densystems verglichen. Dieser Vergleich wurde mittels Photoelektronenspe- ktroskopie durchgefuhrt, durch die Analyse von Verschiebungen des Si 2p und C 1s Rumpfniveaus im Sinne von Ladungsaustausch zwischen Atomen der beiden Elemente und in unterschiedlichen Umgebungen. Mittels dieses Vergleiches konnte ein Unterschied zwischen den Rekonstruktionen auf der Si-terminierten und der C-terminierten Oberflaache aufgrund der ionischen Eigenschaft der Si-C Bindung interpretiert warden.

Das Wachstum von dunnen Mangan-Schichten auf Si(111) im Bereich von 1-5 Monolagen wurde mittels LEED, STM und Photoemission untersucht. Durch den Einsatz dieser Methoden wurden zwei verschiedene Phasen im Bereich unterhalb einer Monolage sowie oberhalb dieser Schichtdicke beobachtet, welche eine unterschiedliche elektronische Struktur aufweisen. Die beiden beobachteten Rekonstruktionen, (1x1) und (\/3x\/3)R300 entste- hen durch Bildung von Mangan-Silizid, wie durch Rumpfniveau-Spektro- skopie nachgewiesen wurde. Das Wachstum geschieht durch Inselbildung im Bereich der Monolage, waahrend die dickeren Schichten flache Regionen zeigen, welche von tiefen Lochern unterbrochen werden. Dieser Wachs- tumsmodus wird auf das Auftreten von Verspannungen, aufgrund der Gitter- fehlanpassung zwischen Substrat und Schicht, zurackgeftihrt, deren Einflufi in den STM-Bildern zu beobachten ist.

Durch Kodeposition von Al und Mg auf Si(111) wurden Al/Mg-Legie- rungs-Schichten erzeugt. Durch Variation der Verdampfungsraten wurden Legierungen mit unterschiedlicher Zusammensetzung erzeugt, und deren elektronische Struktur durch Valenz Photoemission untersucht.In den Schichten werden Quantentopf-Zustande und Oberflachen-Zustande beobachtet. Deren Verschiebung als Funktion der Zusammensetzung wird im Rahmen der “virtual crystal approximation” analysiert.

Die Variation der Photoemissions-Intensitaat als Funktion der Photonen- Energie konnte durch die Anregung von Plasmonen erklaart werden, deren Energien von der Elektronendichte der Legierung abhaangen.

Chapter 1

Introduction

1.1 Crystals, surfaces and interfaces

Epitaxial films are of fundamental and technological interest. The growth mode of thin films depends both on the substrate and the adlayer properties, making the investigation of both surfaces and interfaces an important challenge in modern day surface science.

Crystalline and electronic structure are complementary properties of surfaces and thin films: only with the investigation of both characteristics is it possible to obtain a complete knowledge of the system. Such investigations form the basis of this thesis; various surface techniques have been adopted to analyse crystalline and electronic properties of a surface reconstruction and of two kinds of interfaces, a reactive and a non-reactive one.

In a crystal the position of atoms is given by the equilibrium among attractive and repulsive forces between atoms and, apart from the special case of quasi-crystals, follows a periodic order [1]. This particular order defines the crystalline structure that is a typical property of the crystal at certain physical conditions described by pressure and temperature. The knowledge of the crystalline structure of a material, determined by the crystal class and the coordination number, is important because it is derived from microscopic effects and is responsible for many macroscopic physical properties: one of the most instructive examples is represented by carbon, which crystallizes in two distinct conformations, diamond and graphite. The difference between the two crystals is due to the different bonds among the carbon atoms. The sp3, hybridization in diamond induces its tetrahedral structure, while the

3

4 Introduction

sp2 hybridization in graphite is responsible for its layered structure. This difference in structure is reflected in the different electrical resistance properties of diamond and graphite: the former has a large resistivity, ranging from 1011 to 1018 fi-m depending on the doping type, and the latter has a resistivity of about 8 /rfi-m [2]. Moreover, the conductivity in graphite is highly anisotropic, caused by the different bonding nature of atoms in the same plane from that of atoms in different layers.It is thus clear that the crystalline structure is one of the most important physical characteristics of a material, and an alteration of this property leads to a change of other physical variables. Such a typical structure alteration is present in every real crystal and is given by the surface, being formed by atoms with a reduced coordination number and allocated in a structure of reduced symmetry. Hence, at the surface of a solid, many novel and interesting physical properties are present [3]. For example, in a heteropolar semiconductor compound like GaAs the choice of a surface along a particular symmetry direction corresponds to the choice of having a surface terminated with either only one or both chemical species, i.e. the surface is either polar or non-polar. This difference is reflected in the geometrical ordering at the surface. In fact, the (110) surface with both Ga and As atoms does not change the overall translational symmetry, although bond lengths angles at the surface are modified, while the surfaces with Ga- or As-termination exhibit changes in the symmetry of the unit cell. This leads to a so-called surface reconstruction, with consequences on the electronic structure and other physical and chemical behaviour, such as, for example, adsorption processes.

Atoms and molecules adsorbed on a surface may grow in thin films in various ways, via island formation, or epitaxially in a 2D mode, depending on many physical and chemical variables, like the temperature of the substrata, or the chemical environment in which the evaporation is performed, the reactivity of both the substrate and the adsorbed species, or the presence of defects on the surface, etc. In a new sub-field of surface science, i.e. nanotechnology, various aspects of thin film growth and of molecular adsorption on surfaces are investigated in order to find new and promising features. In particular, the case of semiconductor substrates is very interesting, where a further complication is caused by surface reconstructions. Hence, a detailed knowledge of these systems can be obtained only by a

1.1 Coystals, suofaces and inteofaces 5

complete characterization of the surface reconstruction. This consideration stresses the importance of studying semiconductor surface reconstructions, and shows how intrinsically complex systems can be analyzed starting from simpler basic steps. In these terms we have studied the reconstruction of the semiconductor 6H — silicon caobide cleaved along the (0001) direction. The technique, used for obtaining the clean surface, leads to a reconstruction never observed up to now on this compound, and makes a comparison possible with similar elemental semiconductors such as Si, C and Ge [4].

Interfaces between solids or solids and molecules are of fundamental importance in many aspects, in semiconductor lasers, for example, formed by semiconductor heterostructures, or in field effect transistors (FET), made of semiconductor interfaces with either metal, semiconductor or oxide counterparts. Here, abrupt and lattice-matched interfaces are required and the operation characteristics of these devices is determined by the charge distribution in the spatial region next to the interface, the space-charge layer [5]. Electronic properties of such interfaces are widely studied because they are responsible for the correct operation of novel nanotechnology devices based on 2D-superstructures. The way the substrate-adlayer interface is formed is of extreme importance and may lead to different properties of the system. Reactive systems present a smooth interface, obtained by interdiffusion of the different species present at the interface. This is the case for the Mn/Si(111) system presented in this thesis: transition metals show a strong reactivity which results, upon adsorption on a silicon substrate, in the formation of a silicide. This silicide forms already at very low coverage, through the incorporation of manganese atoms into the silicon substrate, and continues until flat silicide films are formed. The way the Mn-Si silicide forms, and its electronic properties, are studied here by means of photoemission, and its structure is analyzed using the scanning tunneling microscope.

The reactivity of certain systems may be reduced by decreasing the temperature at which the interface is formed. This limits the diffusion of the adlayer atoms and can result in an abrupt interface. It has been demonstrated that reactive systems like Mg/Si and Al/Si obtained by deposition at low temperature have a very low reactivity [6]. The nearly free electrons of the metal adlayer are then confined between the vacuum and the interface, and show discretization of the electronic dispersion in close similarity with the “particle in a box” model. Thin metallic films thus provide a labora

6 Introduction

tory for basic quantum mechanical concepts and 2D systems. In addition, fine tuning of the microscopic sample structure can result in macroscopic effects, as in the case of the “electronic growth”, where the electronic contribution to the film energy plays a decisive role to determine film stability [7]. Here the study of quantum well states has been extended to thin films of Al — Mg/Si(111) alloys.

In this thesis, for each system studied, both the electronic and structural properties are investigated. The results obtained are the following: in SiC, the cleaved polar (0001) surface, with the two terminations, has in both cases a 2x1 reconstruction. Similarities with and differences between the 2x1 reconstruction observed in cleaved (111) surfaces of Si, C and Ge are discussed on the basis of photoemission data, and two distinct reconstruction models are proposed for the two respective surface terminations. In particular, for the Si-terminated surface, the buckling model seems to be adequate to explain the observed surface core level shifts. On the other hand, the C-terminated surface cannot be explained by the same model and more accurate calculations are required.

Silicide formation in manganese films on Si(111) was directly observed by means of STM and photoemission techniques. For < 1ML deposition, manganese atoms form small clusters on step edges and terraces. Consequently, the substrate order is destroyed by the inclusion of Si atoms in the clusters, in order to form the silicide. The composition of this phase is thought to be MnSii.r and shows semiconducting character.For > 1ML deposition, a (V3 x V3)R30° LEED pattern is observed. STM images show flat layers on a large part of the surface, but also strain relief represented by deep holes and Moire patterns. Contrary to the submonolayer deposition, the surface has a metallic character and is thought to be formed of MnSi silicide. Using core level spectroscopy, core level shifts from MnSi1.r, in the submonolayer, and from MnSi, in the monolayer range, are detected. Si surface-related components are detected as well. A detailed analysis led us to the conclusion that the silicide films are terminated with a layer of Si atoms.Finally, alloys of Al and Mg were grown on Si(111). Alloys in a wide range of composition were epitaxially grown, and were studied by means of angle resolved photoemission. For some compositions, the system Al-Mg/Si shows electronic confinement in the thin film, with the observation of quantum

1.1 Coystals, suofaces and inteofaces 7

well states and of a surface state in the photoemission spectra. For other compositions, only the surface state was observed. The binding energies of both quantum-well (when present) and surface states show a dependence on the alloy composition; the shifts are related to the electronic density of the system in a jellium-model approach. A deviation from this relation is explained by the formation of phases with different composition. Finally, the occurrence of collective electron excitations was investigated by means of photoemission used in the constant initial state mode, and the dependence of the bulk-like and multipole plasmon on both the alloy composition and the film thickness was observed.

8 Introduction

Chapter 2

Experimental techniques for surface physics

2.1 Photoemission spectroscopy

Photoemission spectroscopy is one of the most popular techniques for surface investigations. It is based on the photoelectric effect where the emission of electrons from a material is due to photon irradiation [8], and explained exactly 100 years ago by Einstein. In a photoemission experiment, a collimated beam of monochromatic photons of energy hu is directed towards a sample. Electrons are then optically excited from occupied to unoccupied states in the solid and some of them leave the sample if hu is larger than the sample work function $ and if their momentum is directed towards the surface.Their kinetic energy distribution, which reflects their binding energy distribution in the solid, is then analysed. A photoemission experiment can be carried out under various conditions depending on the photon energy range and characteristics of the electron analyser. One can separate, in this way, the study of valence bands and core level lines and can obtain information from electrons with either a well defined escaping angle or in an angle integrated mode. In the former case, it is possible to study the electronic valence band dispersion with wave vector or to vary the depth of escaping electrons by changing the emission angle. The two major classes of photoemission experiments are valence and core level spectroscopy. In the first case low energy photons (101eV- 102eV) are generally used, while in the second class

9

10 Experimental techniques for surface physics

of experiments a higher photon energy is required (102eV-104eV). 1 Photoemission is a many-body process involving electron-photon, electron- electron and electron-phonon interactions. Its full quantum-mechanical description, known as the one-step model, takes all these effects into account[9].

In this approach the photocurrent (or the transition probability per unit time) can be described in terms of the Fermi’s golden rule [10]:

; (R,E,hu) $*|dH|$i)|2d(E - hu - E/) (2.1)ioccup

where the final state is taken as a time-reversed LEED wave $<, $ represents the initial state, ioccup are the occupied states, and 5H, the perturbation, is the dipole operator of the optical transition, given by the vector potential A of the field and the electron momentum operator p = -ihV as:

5H x A • p + p • A. (2.2)

The matrix element M/i x |( ^^Hl#^2 describes all aspects of the photoemission process (optical excitation, transport through the solid and escape through the surface). One-step theories imply wave function matching at the surface, and allow the treatment of the whole set of situations encountered in photoemission: bulk and surface photoemission, adsorbates, etc.

A simpler and more instructive description, the semi-classical three-step model, accounts for many of the features observed experimentally. In this model, the photoemission process is regarded as separated into three consecutive events: optical excitation, transport to the surface and escape through the surface potential barrier [9]. In the first step, a photon with energy hu is absorbed and an electron is excited from an occupied to an unoccupied state within the crystal. The momentum carried by a photon is small and, therefore, the crystal momentum hk is conserved via the exchange of a reciprocal lattice momentum vector hG between the electron and the periodic lattice. The momentum conservation rule can thus be written:

kf = ki + G (2.3)

■ Of course this distinction is not as abrupt as it is may appear. For example, it is worth to remember that valence band studies can be done at very high energies, using the resonant phenomena of valence photoemission and Auger decay. Anyway, in the use of photoemission that we have done to study our systems, this distinction is still well defined.

2.1 Photoemission spectroscopy 11

W03 Au Au

5000 104.0 102 500 10:E, electron energy (eV)

Figure 2.1: Escape depth versus kinetic energy of the electron measured for different materials. After ref. [11].

while energy conservation imposes the condition:

%) = #(ki) + Aw, (2.4)

where kf and k; mean, respectively, the final and initial momentum. Thus, the transition is vertical and can take place only at positions where the energy difference between initial and final energy equals Aw.In the second step, the excited electron propagates through the crystal and eventually reaches the surface. Strong electron-electron interaction may result in scattering events in which both energy and direction of the traveling electron is changed. The probability for such a scattering event to occur is described by a parameter A called the “electron mean free path”, which represents the average distance a photoelectron travels between two inelastic scattering events, and determines the electron escape depth. The electron escape depth is dependent on the kinetic energy and, while it depends weakly on the actual material, has generally a minimum of about 5 A at a kinetic energy of about 50 eV (see figure 2.1).The third step, in which the photoelectron escapes through the surface, is characterized by the conservation of the electron surface-parallel wave vector component kf| to within a surface reciprocal lattice vector g|

q|| = kf|| +g|| (2.5)

where qn and kfii are the external and internal surface-parallel wave vector


z energyanalyser

Figure 2.2: Schematic representation of the angle resolved photoemission geometry.

components of the photoelectron, respectively. For an unreconstructed surface, gii is the surface-parallel component of a reciprocal bulk lattice vectorG.

2.1.1 Angle resolved spectroscopy

The principle and geometry for angle-resolved ultraviolet photoelectron spectroscopy or ARUPS is shown schematically in Fig. 2.2. The angle resolved analyzer collects electrons escaping from the surface with an angle 0. Since the translational symmetry of the crystal potential is broken in the direction normal to the surface, the wave vector component k^ perpendicular to the surface is not conserved as the electron escapes into the vacuum, but, as indicated before, the parallel components are conserved. Thanks to conservation of wave vector and energy for a photoelectron escaping without scattering, its kinetic energy and propagation direction in vacuum gives information about the initial state from which it was excited. Since an electron in vacuum is free, for an emitted photoelectron the following dispersion relation holds:

(2.6)

where E\r is the vacuum potential. Combination of the above relation with equations 2.3 and 2.5 gives the surface parallel component of the wave vector in the initial state as

(2.7)

2.1 Photoemission spectroscopy 13

Furthermore, using equations 2.3 and 2.6 together with the definition of the work function $ = EV — Ef, we obtain the initial state energy as:

E (ki) — ef = Ekin + — Aw (2.8)

where EF is the Fermi energy. Thus by knowing Ekin, © and $, the parallel wave vector component k^ and energy E(k;) of the initial state are easily calculated. Since kf± is not conserved upon transmission through the surface, the perpendicular wave vector component ki± cannot be directly obtained from an ARUPS measurement. However, the final state band is in many cases reasonably well described by a free-electron parabola with a constant inner potential, V0:

with

E(kf) ^ 2m (k/n+k2^ (2.9)

2 2mFo^ + A2 (2.10)

where q is the photoelectron wave vector outside the sample (the measured one). From this condition, ki± can be estimated using equations 2.3 and 2.5. Hence, angle resolved photoemission gives the possibility to study the bulk and surface band dispersion by varying the angle at which the electrons are detected by the analyzer, obtaining E(k).

2.1.2 Core level spectroscopy

The number of core levels and their binding energies are characteristic for a given chemical element. These parameters can therefore be utilized for an elemental analysis of the material being used. Moreover, the actual core level binding energy of an element in a solid is given by the chemical environment in which it lies. A comprehensive investigation of the core level line shape, thus, gives detailed information about the chemical environment of the atom studied [12]. The basic physics underlying the change in binding energy is simple. The energy of an electron in a tightly bound core state is determined by the attractive potential of the nuclei and the repulsive core Coulomb interaction with all the other electrons. A change in the chemical environment of a particular atom involves a spatial rearrangement of the valence charges of this particular atom and a different potential created by the nuclear and electronic charges on all the other atoms in the compound.


This simple picture is reflected in a similarly simple relationship connecting the binding energy difference AE°(A,B) of a core level c measured for an atom i in two different compounds A and B and the valence charges qA and qB, respectively,

AEf(A, B) = #c(qA — qB) + (%A — %B). (2.11)

The first term accounts for the charge transfer and the consequent difference in the electron-electron interaction between the core orbital and this valence charge.

The second term has the character of a Madelung potential. This term decreases the observed shift Ei so that shifts are usually only a few eV or less [4]. Particularly spectacular is the case when A is an elemental material and B a compound of A and a ligand. Figure 2.3 shows two of such cases where core level shifts are directly related to differences in electronegativity between Si and the ligand. However, it has to be pointed out that the system has to rearrange also because of the principal effect of photoemission: the ionization of the atom involved. This rearrangement involves a flow of negative charge towards the hole created in the photoemission process in order to screen the suddenly appearing positive charge. The screening lowers the energy of the hole state left behind and therefore lowers the measured binding energy as well. This binding energy defect is commonly referred to as the relaxation energy ER [9].

Thus, in core level photoemission, core level electrons are excited by photons and collected by the electron analyser. The typical energy resolution in an ESCA experiment is of the order of 100 meV, depending on the energy resolution of both the light source and the analyser, i.e. of the same order of the core level shifts. An accurate analysis of the core level shifts needs, therefore, a fitting procedure to decompose the core level line shape into various components corresponding to atoms in different chemical environment. The line shape of the core level for non-metallic samples can be described to a reasonable approximation by a Voigt function, which approximates a convolution of a Gaussian and a Lorentzian line shape. The Lorentzian curve accounts for the finite lifetime of the electron-hole pair, while the Gaussian curve is related to experimental broadening and surface disorder [12]. The Lorentzian distribution, with a width rfwhm , which can be called the intrinsic width of a line, and is related to the lifetime t of the hole left behind the photoemission process through Heisenberg’s uncertainty

2.2 LEED and STM 15

-1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5electronegativity difference with Si (eV)-6-4-2 0 2

energy (eV relative to bulk Si 2p3/2)

Figure 2.3: Photoemission spectra of the systems O/Si(001) and F/Si(111). Atoms in different environment (in this case with different liga.ncy) contribute with peaks of different shift (left). This is related more generally to the different electronegativity of Si and the ligand (right) [From Himpsel et al, NATO Varenna Summer School 1988, Ed. Compagna. and Rosei, North-Holla.nd Publ.].

relation T = t-1, has the character of a transition probability: a state with a core hole decays through a transition into a state of lower energy. Depending on the decay channels available to the core hole, it is possible to infer the dependence of the Lorentzian width on the core level excited: a Is core hole in a heavy atom will generally have a shorter life-time and will therefore be broader than a higher lying 4/ state because more levels are available to fill the deep-lying Is hole.

2.2 LEED and STM

As a complement to photoemission spectroscopy, in our work other two surface techniques have been used, i.e low energy electron diffraction (LEED) and scanning tunneling microscopy (STM).

The Scanning Tunneling Microscope (STM) is based on the quantum mechanical tunneling effect, in which electrons from one conductor may penetrate into another one passing through (“tunneling”) a potential barrier. The tunneling is granted by the leaking of the wave function of a surface


Sample(+)

sample

sample

Figure 2.4: Representation of a tunnel contact in STM. A positive bias is applied to the sample. The form of the potential tp(z) is rounded by the image potential.

electron into the vacuum. The tunneling probability T depends on the distance cl between the two conductors (the wave function decays exponentially into the vacuum) and on the barrier height <j>, the work function, as follows:

T(E) % exp (2.12)

For an arbitrary potential <p(z) the WKB quasi-classical approximation (when the potential varies slowly with respect to the electron wavelength) is given by the equation:

T(E) = exp a/2 m[ip(z) — E]clz (2.13)

In a STM experiment, the sample is held at a biased potential (Vb) to shift the Fermi edge of the sample with respect to the tip. In this way the barrier height and the spatial shape can be adjusted to produce a tunnel current I. A typical experimental situation is depicted in Fig. 2.4, in which a positive bias is applied, making possible the tunneling from the tip to unoccupied states in the sample. An STM image is obtained by maintaining either the current or the distance constant, and recording the variation of the free parameter to define the contour of the sample surface. In this way, the tip is moved in the lateral direction to scan a large region of the sample and the contour of this surface region is displayed.

2.3 Ultra high vacuum 17

The analysis of low energy electron diffraction (LEED) patterns from surfaces of solids is a well established technique for the investigation of surface periodicity. Electrons of kinetic energies in the range of 10 eV to 300 eV have de Broglie wavelengths comparable to interatomic distances. Illuminating a surface with a mono-energetic beam of such electrons will give rise to a well defined diffraction pattern of the elastically scattered electrons. As a result of the short mean free path of electrons in this energy region, this scattering only probes the surface layers. If only the top layer is involved in the scattering process, it can be shown that the diffraction spots appear when the parallel components of the wave vectors of incoming and outcoming electron waves fulfill the condition

k°ut - k|,n = G2D (2.14)

where G2D is a reciprocal surface-lattice vector. That is, periodic structures on the sample lead to constructive interference of the backscattered electrons and the diffraction pattern is therefore a representation of the reciprocal lattice vectors of the surface. Experimentally, a filament emits electrons which are accelerated by a variable voltage and focused on the sample surface with deflection electrodes. The diffracted electrons are retarded between a set of grids in front of a fluorescent screen, in order to discriminate inelastically scattered electrons. Finally, the electrons passing the grids are accelerated onto the fluorescent screen, where they are converted into visible intensity variations.

2.3 Ultra high vacuum

The short mean free path of the photoelectrons makes the preparation and preservation of a clean sample surface one of the main experimental tasks in photoemission. For example, at an escape depth of 10 A, assuming a lattice constant of 4 A, and an exponential decay of the photoemission intensity with depth, we find that the topmost layer of atoms contributes about 30% to the total spectrum. It is therefore clear that even partial changes in the topmost layer that are not intrinsic to the material under study (surface reconstruction, for example) can severely falsify the results. A foreign atom on the surface may add its own photoemission lines to the spectrum of the substrate; for example, oxygen contamination results in the addition of the


O 1s line at 534 eV in core level spectroscopy or the O 2p line around 6 eV binding energy and is therefore observable in the valence band spectra. However, the interaction between adatom and substrate may change the energy levels of the substrate as well and induce a substrate core level shift. The conservation of a clean sample requires, therefore, ultrahigh vacuum conditions (UHV). In fact, a sample exposed to a gas at a pressure of 10~6 Torr that has a sticking coefficient of unity will accumulate a monolayer of that gas in 1 s. The sticking probability can vary by several orders of magnitude depending on the material. The (111) surface of nickel, for example, has a sticking probability probability of 1 for CO, making the operation at pressures as low as 10~10- 10~n Torr necessary in order to have sufficient time for an experiment.

Chapter 3

SiC(0001) cleaved surface reconstructions

3.1 Semiconductor surfaces

The formation of a surface in a material leads to interesting changes in the crystal and electronic structure near the surface. The basic reason is the loss of periodicity in one direction of the crystal lattice, which is responsible for the creation of electronic localized surface states, surface relaxation and reconstruction. These are very important properties; for example, they can be decisive in the adsorption process of other species onto clean surfaces. The study of clean surfaces has been very productive in the past 40 years, leading to the creation of new fields with many subbranches [11]. The importance of new technologies in everyday life has underscored the importance of the semiconductor branch of surface science. In fact, the continuous miniaturization of electronic devices such as integrated circuits, optoelectronic and non-volatile memory devices, has made semiconductors a most important material for industry. The semiconductor silicon carbide (SiC) has gained much popularity in the scientific community relatively lately, although it was known already in 1907 that crystals of silicon carbide emit light when an electrical current passes through them, and it was used as detector crystal in early radio receivers [13]. Problems related with the growth of high quality SiC crystals slowed down the integration of this semiconductor in technologically important processes, and their solution still remain the major task in current research.

19

20 SiC(0001) cleaved surface reconstructions

Nevertheless, silicon carbide possesses very interesting and peculiar material properties which make it superior to silicon in a wide range of applications. The fundamental characteristic of a semiconductor, the bandgap, has a value of Eg ~3 eV for SiC and is hence about three times larger than that of Si. This allows device operation up to many hundred degrees C, while the operation temperature of Si-based electronic devices is limited to 150°C. Operation at elevated temperatures simplifies power dissipation problems and reduces cost. The high value of its band gap allows the production of blue light emitting diodes (LED), although GaN or InGaN are now preferred, but SiC is still useful as a substrate. A high thermal conductivity guarantees homogeneous heat distribution in devices and also a fast heat transfer to the mounting of the device. One more peculiar property of SiC-based devices is the possibility to operate them at much higher voltages than silicon ones, making the handling of high voltage direct currents much easier in energy transmission and distribution networks [14]. The cheap delivery of electrical power is an important issue in modern society. The extensive utilization of power electronics with improved properties such as, for example, switching at high frequencies, low losses and low manufacturing costs will be of extreme importance in the future. Unfortunately, with the current available power semiconductor devices based on silicon, the possibilities to meet these requirements are limited. Therefore, SiC-technologies have become more and more important in the past decades and, since the problem of producing at low cost and in large quantity defect-free SiC wafers now appears to be resolved, they will probably substitute Si-based devices in many applications.In a SiC crystal each atom is covalently bound to four atoms of the other chemical species in a tetrahedral coordination. The Si-C bonds are arranged in a hexagonal bilayer with carbon and silicon in alternating positions. The bilayers are stacked on top of each other along the direction perpendicular to the bilayer. The tetrahedral arrangement of Si-C bonds can be continued in two orientations differing by a 60° rotation. The different stacking sequence produces SiC crystals with various structural modifications called polytypes [15]. There are two extreme cases of the various possibilities, one is obtained when all the bilayers are oriented in the same direction and the corresponding crystal possesses a zinkblende structure; this corresponds to the cubic SiC modification and is called ,3-SiC. The other extreme case

3.1 Semiconductor surfaces 21

Figure 3.1: Fourexamples of Si-G bilayers stacking sequences. Changing the stacking sequence, different polytypes are formed. After ref. [15].

e

is when for every bilayer the stacking direction is rotated by 60° and the resulting crystal modification is the hexagonal wurtzite structure. Between these two extremes, there are about 170 different SiC poly types. They have completely different spatially oriented three-dimensional bulk unit cells, but their energy of formation is almost independent of the particular polytype [15]. The way to distinguish between different polytypes is to refer to the periodicity along the stacking direction: the zinkblende structure can be described by a planar hexagonal unit cell with a periodicity of three bilayers along the c-axis forming an ABC sequence, and is therefore called 3C-SiC. The wurtzite structure has an AB sequence and is called 2H-SiC. Here C and H are used to denote the cubic or the hexagonal unit cell symmetry. Most of the electrical applications have been reported for the 3C, the 4H and the 6H polytypes, while the 2H-SiC has not been observed to be stable in nature. The 4H-SiC has two bilayers of identical orientation followed by


two bilayers with the opposite orientation, with an ABCB sequence, while 6H-SiC has an ABCACB sequence and up to the third bilayer has the same sequence as the 3C-polytype. The hexagonal unit cell in the 4H and 6H polytypes has a height of 4 and 6 bilayers, respectively (see Figure 3.1).

3.2 Semiconductor surface reconstructions

The theory used to understand the crystal and electronic properties of solids is based on Bloch’s theorem which is applicable to the ideal case of an infinite perfect periodic lattice. The surface breaks this periodicity in one direction, producing new features which are not present in the bulk solid.

These modifications are particularly interesting in the case of semiconductors, where the existence of a bandgap in the volume is altered in the region next to the surface: new states can be possible within the gap, modifying the properties to the surface. While in the case of metals the electrons are highly delocalized all over the crystal, semiconductor elements and compounds are characterized by the strong directionality of their bonds. In fact, the surface in a semiconductor crystal is created by breaking the bonds between atoms on the surface, producing a strong increase in the surface free energy, and, therefore, in its reactivity.The occurrence of broken bonds (dangling bonds) is responsible for surface reconstruction and relaxation, which are frequently found on semiconductor surfaces. A typical example of surface reconstruction is given by the Si(111) surface with its two well-known reconstructions: the (7x7), which is a very complex reconstruction, and is explained by the dimer-adatomstacking fault (DAS) model proposed by Takayanagi et al. [16] on the basis of electron microscopy, and later confirmed by STM. A less complex but, nevertheless equally intriguing reconstruction is the Si(111)-(2x1) reconstruction which is a metastable reconstruction. In fact, when heated up to 600 K it undergoes an irreversible transition to the already cited Si(111)- (7x7) reconstruction. The (2x1) reconstruction has been subject of a long and intense scientific debate in the late 70’s. It was clearly observed for the first time in the famous work of Lander [17], where the low energy electron diffraction (LEED) pattern of a cleaved Si(111) surface exhibited extra spots in the mid-positions between the normal, integral order spots expected from the bulk crystals. They also observed that “transitions to different struc

3.2 Semiconductor surface reconstructions 23

tures occur at higher temperatures" that were called Si(111)-5 and Si(111)-7. This was in a sense the beginning of modern surface science.

The (111) is the plane where cleavage in silicon and germanium is possible. It happens between two double layers as shown in figure 3.2(a), and produces only one dangling bond per unit cell, while in the other two high symmetry directions (110) and (100), the surface produces two dangling bonds per unit cell. A first attempt to give a theoretical explanation of the half order spot in diffraction was given by Haneman [18] in 1961 on the basis of experimental data of Schlier and Farnsworth [19]. He explained the occurrence of a primitive rectangular mesh as a result of a displacement of the surface atoms in a configuration where “every second atom, counting along alternate close-spaced rows, is raised with respect to its neighbors, so that the actual surface layer consists of atoms whose spacing is exactly twice that of atoms in bulk (111) planes". The consequences of such displacement are very strong in the bonding properties of the surface atoms. While in the bulk every atom is bound to three atoms by tetrahedral sp3 bonds, the atoms raised in the direction perpendicular to the surface will experience an alteration of the quantum state of the dangling bond [18]. In this way, the total energy of the surface should be minimized, but the reconstructed surface becomes ionic. For many years this model was used to explain the (2x1) reconstruction in both silicon and germanium, although some experimental results were in clear contrast with its predictions. The most important disagreement between theory and the experiments were related to the ionicity of the surface. This predicts a large charge transfer between the atoms of the surface displaced in opposite directions. The charge transfer has to take place from the lowered atoms towards the raised ones. Tight-binding calculations gave in fact a net charge of -0.76e0 on the raised, +0.36e0 on the lowered and +0.4e0 on the second layer atoms [20]. In agreement with the basic physics of core level spectroscopy, the large charge transfer should cause appreciable core level shifts [12], but photoemission experiments conducted between the end of the 70’s and the beginning of the 80’s [21],[22] revealed little shift, a sign that the charge transfer was much lower than that predicted. The estimate of the charge transfer, responsible for the core level shifts, gave approximately 0.15e0 which is much smaller than the 0.76e0 calculated for the buckled reconstruction [21]. The solution to the puzzling (2x1) surface reconstruction of Si(111) and Ge(111) was later given

24 SiC(OOOl) cleaved surface reconstructions

Figure 3.2: (a) ideal lxl termination after cleave along the line, (b) Pa.ndey model of the 2x1 reconstruction. The bond between atoms #3 and #7 breaks and the bond #2-#7 is formed. In the 2x1 reconstruction the distance between the two pairs of dangling bonds is 2 times the distance in the ideal cleaved surface.

(a)

by Pa.ndey [23], who proposed a new model based on ir-bonded chains. A description of this model is given in Figure 3.2.According to Pa.ndey, the (2x1) PEED pattern does not result from a. buckling of the surface but from a. more general rearrangement of the atoms of the first two bilayers. This rearrangement happens through breaking of bonds (between the atoms #3 and #7 in figure 3.2) and creation of new ones (between the atoms #2 and #7). This new model predicts a. nonpolar surface reconstruction, in agreement with the core-level results and with other experimental results: with angle-resolved photoemission experiments that showed a. large distance between surface atoms in one direction of the surface unit cell and a. small one in perpendicular direction [24]; and with surface differential reflectance (SDR.) experiments which gave as result a. strong absorption with light polarized along the (110) direction and no signal with a. polarization along the (211) direction [25].

3.2.1 The IV group elements and the IV-IV compound semiconductors

The similarity between silicon carbide and the IV group semiconductors results mainly in an identical nearest-neighbour configuration, which also in SiC is tetrahedral with a. bond length of 1.89 A. The major difference lies in


Figure 3.3: Symmetric (a) and antisymmetric (b) components of the total valence charge densities of GaAs, SiC and ZnS along the anion-cation bonds. After ref. [28].

10 - /

GaAs:

C,As,S Si,Ga,Zn

the ionic nature of the Si-C bond, due to the extreme disparity of the covalent radii of Si (rsi=1.17 A) and C (rc=0.77 A) which originates from the different strength of the Si and C potentials. The ionic nature of the Si-C bond can be also understood in terms of the large difference of electronegativity of the two elements (e^=1.7; ec=2.5), leading to a charge transfer from Si to C atoms [26]. The ionicity of SiC gives rise to an ionic gap within the valence bands of the bulk-band structure, similarly to the case of III-V and II-VI heteropolar compound semiconductors. In SiC, hence, the Si atoms act as cations and the C atoms as anions. It is interesting to compare the ionicity of SiC with that of the III-V heteropolar semiconductor GaAs and the II-VI ZnS. To do this, it is appropriate to use the Garcia-Cohen scale, which gives, through the g value, the ionicity of many compounds taking into account the asymmetry of the charge density along the bonds [27]. It has been demonstrated that SiC is in some sense more similar to the heteropolar ionic compound ZnO than to the heteropolar covalent semiconductors GaAs and ZnS [28]. Calculations of the symmetric and antisymmetric components of the charge densities of GaAs, SiC and ZnS along the anion-cation bonds, predicted that the maximum position of the antisymmetric component is shifted closer to the anion in SiC than in GaAs or ZnS, and is similar to the case of ZnO (see Fig. 3.3). This asymmetry in the charge density of the two elements Si and C is one of the reasons for the distinctively different reconstruction behaviour of the Si- and C-terminated surfaces [26]. Due to the charge asymmetry, the angular forces occurring at the Si and C atoms are largely different. They are much larger at the C than at Si atoms, so that changes of the tetrahedral configuration around the C atoms involve much more energy than for Si atoms. Another difference between diamond, silicon and silicon carbide is the lattice constant. For C,


the bulk lattice constant is aC=3.57 A, and for Si it is aSi=5.43 A, while for SiC it has an intermediate value aSiC=4.36 A. This is very important in the surface reconstruction; at Si- (C-)terminated surfaces one encounters Si (C) orbitals on a two-dimensional lattice with a lattice constant that is much smaller (larger) than that of related silicon (diamond) surfaces. This can produce a substantial difference in the reconstruction behaviour of SiC surfaces with respect to the Si and the C surfaces. It is, therefore, of great interest to investigate how decisive these differences between SiC and the IV group seminconductors are, with respect to surface reconstructions and electronic properties.

3.2.2 6H-SiC(0001) polar surface

The most studied SiC polytypes are the 3C- and the 6H- which are identical in the stacking direction up to the fourth bilayer. For surface sensitive experimental techniques, the 3C-SiC(111) and the 6H-SiC(0001) surfaces are, therefore, indistinguishable. Most reconstruction models for these polar surfaces involve Si and C adatoms or trimers and may therefore be called adsorption-induced reconstructions. The reconstruction is strongly dependent on the surface preparation procedure, which in the case of SiC can be more complicated than for many other materials, and is dependent on the surface termination. Ion bombardment, for example, has been used in various studies on the Si-terminated surfaces, providing an atomically clean surface with a stoichiometry near to a 1:1 ratio of silicon and carbon [29], and therefore usually denoted as a “stoichiometric surface”. However, after ion bombardment, the surface presented a strong disorder, which could be removed only by annealing. This procedure produces a depletion of silicon because of the larger vapor pressure of silicon compared to carbon. A stoichiometric, well ordered surface is, therefore, not easily achieved by using a simple sputter/anneal preparation procedure.Chemical methods and more complex thermal treatments are needed to obtain well ordered surfaces (see ref. [15] and references therein). A prolonged heating in oxygen at atmospheric pressures and temperatures around 1000° C, and subsequent covering of the surface with an oxide layer removable by HF etching, was shown to yield well ordered and stoichiometric surfaces. The limitation of this method consists in the necessity of removing the oxide


cap outside of the UHV chamber. A possible alternative to HF etching is to anneal the samples in UHV. The problem is again carbon enrichment as mentioned above, which can be partially reduced by lowering the anneal temperature to 850° C. Another alternative is to evaporate silicon on the sample during annealing at 1000° C in order to compensate for the Si loss during annealing. It is clear that in this case the resulting surface structure strongly depends on the balance between the silicon depletion caused by the temperature treatment and the silicon compensation. This led to the observation of many different surface reconstructions. On the 3C-(111) and nH-(0001) surfaces, the stable reconstruction is the (3x3), which is Si-rich, but upon lower silicon flux or higher temperature annealing a C-rich (V3 x V3) — R30° phase can be obtained [15]. Upon further annealing, a (6V3 x 6V3)R30° has been observed, composed of several coexisting phases of different order. The C-terminated (0001) surface also has various reconstructions, such as the (1x1) after preparation under Ga flux at elevated temperatures and, upon further annealing, the (V3 x V3) phase. Also a carbon rich (3x3) reconstruction prepared by annealing has been found to be stable; upon further heating it transforms into a (V3 x V3) structure. The atomic structures of these various reconstructions are usually very complex and for many of them there is no complete agreement between the various investigations and the theoretical models yet, also because the particular atomic structure can be different for the various preparation procedures, even though the LEED images show the same symmetry. An example is the Si-rich (3x3) for which two models have been proposed (shown in Fig. 3.4) and for which the debate is still open [15]. The electronic structure of these reconstructions is equally puzzling and many experimental as well as theoretical investigations have been performed in the last years [30], but in many aspects no general agreement has been found. One particular question concerns the electrical character of the surface. All the above mentioned reconstructions have an odd number of electrons in the surface unit cell, which produces half-filled surface bands, conferring a metallic character to the surfaces. On the other hand, the experimental results show that the surfaces are semiconducting, in clear contrast to the simple electron counting rule. To resolve such discrepancy, it has been necessary to introduce electronic correlation, with a lower and upper Hubbard band, which gives to the (\/3 x \/3), for example, a semiconductor character.


a) DAS model

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Si adatoms

Si adlaycr

SiC substrate

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X Si adlaycrQ® SiC substrate

li) Single adatom model

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Figure 3.4: Example of two (3x3)-6H-SiC(0001) reconstruction structural models. The dimer-adat.om-stacking fault (DAS) model was proposed by Kaplan (a) and the single adatom model by Kulakov et al. (b). After ref. [15].

The difficulty to find a standard procedure in preparing the clean surfaces of SiC, and the use of techniques which cannot be well controlled, such as

3.3 Experimental set up 29

annealing under silicon flux, has caused a great amount of experimental work which led to different and sometimes contrasting results, making the study of the various reconstructions of the SiC surfaces very difficult. A way to overcome these problems is to produce the clean surface in a more direct way, without using any annealing, sputtering or etching procedures. This can be thought of as a going back to the origin of modern surface science, taking advantage of the simple technique of cutting (“cleaving”) the sample in UHV. The (0001) planes can be cleaved, in fact, producing one dangling bond per unit cell, when the cut is performed between two bilayers, similar to the case of Si, Ge and C(111) surfaces. The creation of the surface by cleaving is more difficult in SiC than in Si, because the Si-C bond is stronger than the Si-Si bond, but it is still possible. Indeed, here we report on the first study of cleaved SiC surfaces.

3.3 Experimental set up

Photoemission experiments have been carried out at the UE-56/2 beamline at the BESSY storage ring, in a typical UHV chamber with a base pressure of 1x10~10 mbar. Photoelectrons were analyzed in an angle-resolving hemispherical analyzer, Omicron AR65, equipped with three channeltron detectors. The total experimental resolution was set to 100 meV for the Si 2p core level and to 200 meV for the C 1s. All spectra were taken with an angle of incidence of 30° and at normal emission with an angular acceptance of about 1°.The chamber was equipped with a LEED optics by means of which the surface symmetry was determined. The primary electron energy could be varied remotely from a computer in a wide range (50-300 eV) and the image was recorded by a CCD camera, in order to obtain I(E) profiles of symmetry points.The samples were bulk 6H-SiC heavily-doped with nitrogen (n-type) as revealed by their dark colour. In order to avoid charging during photoemission experiments, an ohmic contact was formed with indium, with a resulting resistance as low as 500 fi.


Figure 3.5: FEED patterns of the Si and C-terminated surfaces: the primary electron energies are 113 eV (a), 162 eV (b), 170 eV (c) and 135 eV (d).

3.4 6H-SiC(0001)(2xl): experimental results

3.4.1 LEED

Samples of 6H-SiC were cleaved in UHV along the (0001) direction and in-situ studied by means of LEED. Four LEED pictures corresponding to the two terminations of the SiC surface are shown in Fig. 3.5. In the following, the Si-terminated surface will be indicated as (0001), while the C-terminated one as (0001). The presence of extra spots in the half-integer order positions of the LEED pattern is evident in Fig. 3.5, although their intensities are lower than those of the integer order ones. These (2x2) LEED patterns may represent either a true (2x2) super lattice or a superposition of three rotational domains of a (2x1) phase. The difference between the two possibilities lies in the equivalence of the spots of the (-j-j) order in the first case, while in the case of three domains the half order diffraction spots are inequivalent, because spots from the same domain are in the opposite position with respect to the (00) spot and in principle the occurrence of the different domains is inequivalent. Therefore, the spot intensity has been inspected in the following way: half-order spots at opposite positions are shown in the boxes in Fig. 3.6(left) with the same colour frames. Their intensities are plotted as a function of the primary electronic energy on the right in the same figure. The profiles look very similar in the sense that

3.4 6H-SiC(0001) (2x1): experimental results 31

Figure 3.6: (left) FEED image taken on the C-terminated surface with 147 eV. (right) 1(E) spectra (intensity vs energy curves) from individual half-integer spots plotted on identical scale. The colors of the curves are referred to the colors of the boxes of the FEED image (left).

Figure 3.7: Same FEED image of Fig. 3.6. Three domains 2x1 reconstruction is responsible for the 2x2 FEED pattern observed on both termination surfaces. Here it is shown how the three domains are arranged to form the 2x2 pattern.

the peaks are located at similar energy positions, but the intensity of the peaks depends on the particular spot taken. In addition, the intensities are similar for every pair. This is the conclusive evidence that the spots are inequivalent but are coupled in a way corresponding to a three-domain (2x1) reconstruction. It is also clear from the difference in the spot intensities that the population of the three domains is different and that they are rotated by 60° (see Fig. 3.7). This result suggests a strong similarity with the case of the Si(lll), Ge(lll) and C(lll) metastable (2x1) reconstructions. This is already a very important and unexpected result. It is the first time that a reconstruction involving an even number of atoms in the unit cell has been observed for SiC. It is therefore interesting to study in further detail the way this (2x1) reconstruction occurs. In the next section results from core level spectroscopy are shown, providing more information on the crystal and electronic structure.


(a) (b>hv=145eV hv=330eV

105 104 103 102 101 100 99 98 288 287 286 285 284 283 282 281Binding energy (eV) Binding energy (eV)

Figure 3.8: Si-2p (a) and G-ls (b) core level PE spectra of the C-terminated surface. Dashed lines correspond to spectra taken just after a new cleave; continuous lines to spectra taken after 80 minutes.

3.4.2 Core level spectroscopy

Our core level spectroscopy experiments have been performed after in situ cleaving the SIC sample. The samples, cleaved at a pressure of 4xlO~10

mbar, were quickly transferred to the measurement position. The complete alignment of the samples with the photon beam and the analyzer was performed within 15 minutes after the cleave. The clean surface presented chemical reactivity as is clear from Fig. 3.8, where the Si 2p (Fig. 3.8(a)) and the C Is (Fig. 3.8(b)) core level spectra of the SiC(0001) surface are shown. The dashed lines are referred to the just cleaved surface and the continuous ones after 80 minutes. The appearance of an extra shoulder on the higher binding energy side in the spectra taken after 80 minutes is due to contamination as is clear from the width and the energy position. In fact, contamination with either hydrocarbons or oxygen results in peaks at higher binding energies with respect to the bulk core level of both Si 2p and C Is. In Fig. 3.9 we show the peaks of the two species for the (0001) and the (0001) surfaces. The first evidence is that, while the Si 2p core levels are very similar for the two surfaces, the C Is spectra show strong differences: a new peak around 284.5 eV and a broad feature at 286 eV. The main C Is peak has a binding energy of 283.6 eV, i.e. more than 1 eV shifted towards lower binding energy with respect to the C Is bulk peak of diamond [31]. The Si 2p3/2 component of the Si 2p doublet has a binding energy of 101.2 eV, showing a shift of 1.4 eV towards higher binding energy. These shifts are due to the difference in electronegativity between Si and C, leading to


a charge transfer from silicon to carbon atoms, i.e. silicon atoms behave as cations and carbon atoms as anions. The values we have found are in good agreement with previous photoemission experiments on 6H-SiC(0001) and 3C-SiC(lll) surfaces [32] and will be considered from now on as reference for the surface core level shifts. In Figs. 3.10 - 3.13 the line shape analysis by means of a least squares fitting procedure are shown. Lorentzian peaks numerically convoluted by a Gaussian (for the description of instrumental and phonon broadening) are used to model the photoemission lines. Typical Lorentzian widths of the C Is and Si 2p are, respectively, 0.3 eV and 0.15 eV, as known from previous photoemission studies on SiC [33]. These are used to determine the Voigt line shape, taking Gaussian values as large as 0.8 eV for the C Is and 0.65 eV for Si 2p. These large values for the Gaussian widths are probably due to the disorder on the surface, which is produced by the cleaving, with a large density of steps. The spin-orbit splitting for the Si 2p doublet is fixed to 0.608 eV with a statistical ratio of 0.5 and the symmetry factor for all the spectra is zero. The results of the fitting procedure are reported in table 3.1.

SiC(0001): The Si 2p spectrum of the Si terminated surface has three components; the bulk (B), the Si at higher binding energy and the So at lower binding energy. The latter could be due to the dangling bond of the Si atoms at the surface (see Fig. 3.10). The C Is core level shows three main components: the bulk (B) and the surface related Si and S3 components (see Fig. 3.11). Here the Si component has a slightly stronger intensity compared to the S3 one. The weak component (So) at higher binding energy

Figure 3.9: Si-2p (left) and G-ls (right) core level spectra recorded, respectively, at 145 eV and 330 eV for the C-terminated and the Si-terminated surfaces.


Binding energy relative to bulk Si 2p3/2 (eV)

Figure 3.10: Silicon face: Si2p. Bulk Si2p=101.2 eV; S. =101.9 eV (+0.7 eV); S. =100.7 eV (-0.5 eV). Lorentzian width for all pea.ks= 0.15 eV. Gaussian for all peaks = 0.65 eV.

is probably due to sample contamination: it is always present, even in the just cleaved surfaces.

SiC(OOOl): The C Is spectrum on this surface termination is more complex compared to the one obtained from the other termination: it is characterized by the presence of one strong peak at higher binding energy, a peak with a very large shift (-2.4 eV) and a weak component at lower binding energy. The particularity of the C Is for this termination is the strong intensity of the component at 0.9 eV which has no analogy in any of the other core level spectra, hence making clear the difference of the two reconstructions. The Si 2p spectrum of this termination has a component at higher binding energy similar to that of the Si terminated surface, but no component at lower binding energies (Fig. 3.13).

3.4.3 Discussion

The intensity and core level shift is related to the position and the bond geometry of the Si atom: reconstruction models have to be in agreement with these experimental properties. The starting point of our discussion could be the Pandey model which described successfully the (2x1) reconstructions of C, Si and Ge (111) surfaces. This model predicts a displacement of the atoms from the first two layers: in Fig. 3.14 the atomic structures of the bulk truncated and of the possible Pandey reconstruction for both surface terminations are depicted. Clear is the symmetric behaviour of the


Figure 3.11: Silicon face: Gls. Bulk Cls=283.6 eV; S. =284.2 eV (+0.6 eV); S. =285.2 eV ( + 1.6 eV); S. =282.6 eV (-1 eV). Lorentzian width for all peaks = 0.3 eV. Gaussian width = 0.7 eV; 0.7 eV; 0.8 eV; 0.8 eV.

Pandey reconstruction by exchanging the surface termination: the first two layers of each reconstruction are composed by both Si and C atoms; the only difference between the two reconstructions is a specular exchanging of the chemical species in the surface structure (see Fig. 3.14, (b) and (d)). Let us now try to relate this specular behaviour of the Si and C atoms with the core level spectra of both surface terminations. The two terminations are, at least in the first two layers, very similar; Si and C atoms in the first layer have a dangling bond and the other three bonds are with atoms of the

9 -

I--------- 1---------- 1---------- 1---------- 1---------- 1---------- 1---------- 1---------- 14 3 2 1 0 -1 -2 -3 -4

Binding energy relative to bulk C is (eV)

Figure 3.12: Carbon face: Cls. Bulk Cls=283.6 eV; S. =284.5 eV (+0.9 eV); S. =286.0 eV (+2.4 eV); S. =282.6 eV (-1 eV). Lorentzian width for all peaks = 0.3 eV. Gaussian width = 0.8 eV; 0.8 eV; 0.9 eV; 0.8 eV.


Binding energy relative to bulk Si 2p3/2(eV)

Figure 3.13: Carbon face: Si2p. Bulk Si2p= 101.2 eV; S. =101.9 eV (+0.7 eV). Lorentzia.n width for all peaks = 0.15 eV. Gaussian for all peaks = 0.65 eV.

(a) ()

(b) ( )

Figure 3.14: Stick and ball representation of the bulk truncated and of the possible Pancley reconstruction of 6H-SiC(0001) surfaces: a) and b) Si terminated; c) and cl) G terminated.

3.5 Conclusions 37

other chemical species in the second layer. Hence the electronic properties of the atoms in the first two layers are very similar for the two terminations. Anyway, from the experimental core level spectra this similarity is not clear, at least the C 1s spectra are very different (see Fig. 3.9), with a strong surface component in the C termination. Moreover, both Si 2p and C 1s core level spectra should have surface components due to the dangling bonds in both surface terminations. For Si 2p the dangling bond causes a core level shift towards lower binding energies, while for C 1s the shift should be towards higher binding energies 1. The symmetric geometry of the two reconstructions by exchanging the surface termination is broken by the nature of the bond between atoms from the second and the third layer. As can be observed in Fig. 3.14 (b) and (d), every second bond there is a homopolar (bond 2-7) Si-Si bond in the Si termination and C-C bond in the C-termination. These differences in the reconstruction geometry could explain the differences in the core level spectra. From an energetic point of view, it is possible, anyway, to predict that the C-C bond is more stable than a C-Si one. This means that, provided the energy necessary to break the C-Si bond is available, the resulting reconstruction is stable if a C-C bond is created. For the Si-termination, this is not true, in fact, the Si-Si bond is energetically less stable than the Si-C one. It seems that the two reconstuctions, although giving the same LEED pattern, are generated by two distinct processes.

3.5 Conclusions

In order to establish a possible similarity between SiC and other group IV elemental semiconductors, clean surfaces were obtained by cleaving. As shown by the LEED result, cleaved 6H-SiC{0001} surfaces are reconstructed in (2x1) periodicity. In particular, the LEED pattern has been related to the existence of three rotationally equivalent domains with different statistical populations.

' The creation of the surface breaks the bond between Si and C, leaving a dangling bond on the Si termination atoms. The charge equilibrium between the central silicon atom in the tetrahedral C. Si-C basis and the carbon atoms is broken, now the silicon atoms on the surface recover back the charge that is coming from the dangling bond. This results in a core level shift towards lower binding energies.


Core level spectroscopy revealed a substantial difference of the (2x1) reconstructions compared with other reconstructions previously studied, and in particular it can be excluded in the (2x1) case, the formation of neither dimers nor trimers. One important aspect of the (2x1) reconstructions is their different nature on the two surface terminations as evidenced by the core level analysis. Anyway, a precise calculation of charge transfer and angular forces is needed in order to establish the real geometry of the reconstructions.

Chapter 4

Thin Manganese films on Si(111)

4.1 Transition metal silicides

The elements with unfilled d- or f-shells exhibit a strong chemical reactivity. For example, they react with silicon to form silicides, stable metal-silicon compounds of various stoichiometries. The deposition of transition metal (TM) atoms onto silicon surfaces is accompanied by a geometric rearrangement and formation of silicides, initially in the contact region and, if supported by sufficient annealing, all over a reacted region, many layers thick. The study of TM thin films on Si is important both for the implications for silicon and silicide technology and for fundamental reasons, since the understanding of the reaction mechanism involved in interface growth in this case is in principle simpler than for compound semiconductors. Nevertheless, the problem remains a difficult one mainly because the interface reaction takes place at temperatures well below the temperature usually needed to form silicides. The discussion of this problem is a prerequisite for any further progress in the understanding of junction formation and thus it has received a great experimental and theoretical effort [34].From a technological point of view, silicide formation and growth are very important topics because, for example, for microelectronics, micro-sized silicides with low and metal-like resistivity and high temperature stability, are arranged in very-large-scale-integrated (VLSI) circuits, while for optoelectronic devices, semiconductor silicides are used in combination with an in

39

40 Thin Manganese films on Si(111)

direct band gap semiconductor.Recently, the new field of “spintronics” devices for non-volatile memories brought great attention to the magnetic properties of semiconductors. The prototype device that is already in use in industry as a read head and a memory-storage cell is the giant-magnetoresistive (GMR) sandwich structure which consists of alternating ferromagnetic and non-ferromagnetic metal layers [35]. Depending on the relative orientation of the magnetizations in the metallic layers, the device resistance changes from small (parallel resistance) to large (antiparallel resistance). This change in resistance (generally called magnetoresistance) is used to sense changes in magnetic fields.In addition, semiconductors may enhance GMR devices with other properties [36]. While metal-based GMR devices do not amplify signals, semiconductor-based spintronics devices could in principle provide amplification and serve, in general, as multi-functional devices, being also much easier for semiconductor-based devices to be integrated with traditional semiconductor technology. For this reason, the recent discovery that GaAs presents ferromagnetic behaviour when doped with manganese, brought a new impetus in studying the structural and electronic properties of such semiconductors, where Mn impurities act, on the one side, as dopants for GaAs semiconductors and, at the same time, introduce the magnetic properties in this semiconductor [37]. Therefore, Gai_xMnxAs has been subject, in the last few years, of many investigations, which led to a good knowledge of many properties of this semiconductor, which is a member of the class of diluted magnetic semiconductors (DMS), composed by III-V semiconductors doped with manganese.Also different mechanisms for magnetoresistance have been proposed for other materials, and in particular for the intriguing narrow-gap insulator FeSi. This (Kondo) insulator, which already attracted attention for over 30 years because of its anomalous electrical, optical and magnetic properties [38], presents a metal-insulator transition when doped with either Al or Co. More recently it has gained renewed attention because, when doped by substitution of a single species, say Co or Mn, for Fe, it is a low carrier density magnetic metal with exceptional magnetoconductance [39]. In addition, a successive investigation of Fe1_xCoxSi and Fe1_xMnxSi showed a large anomalous Hall effect (AHE) [40], which does not seem to be related to the scattering of Co (or Mn) impurities, but most likely is intrinsic, de

4.1 Transition metal silicides 41

rived from band structure effects. In this sense (Fe,Co)Si and (Fe,Mn)Si represent a class of materials different from the (III,Mn)V in which the electrons involved in electrical conduction are different from those localized ones responsible for the magnetism, and act as scattering sites for the mobile electrons, such that field tuning of the scattering strength gives rise to the magnetoresistance observed in these materials. In FeSi-based ferromag- nets, the magnetoresistance arises from quantum interference effects, and the same electrons are responsible for both magnetic properties and electrical conduction. One more important characteristic of these newly discovered magnetic systems is the complete miscibility of FeSi with CoSi and MnSi (all three have the same cubic B-20 crystal structure), very different from the (Ga,Mn)As system for which the miscibility of Mn is limited by Mn segregation. Therefore, the main problems related to (Ga,Mn)As, i.e. the high defect density and the low compatibility with Si, can be overcome by the introduction of these new systems, although the disadvantage of a lower Curie temperature (Tc) still exists. In fact, the (Ga,Mn)As materials present a high Curie temperature, which, in (III,Mn)V semiconductors, depends on the carrier concentration, and a semiconductor of this class with a Tc of about room temperature has been found [41]. For FeSi doped with Co or Mn a Tc of about 60K has been observed. Hence the quest to find higher Tc doped semiconductors provides an incentive to study the isostructural CoSi and MnSi, and in particular their electronic properties.In view of this, we have studied the formation of manganese silicide by deposition of the metal onto the silicon surface. This may produce various silicide phases depending on the film thickness and the annealing procedure like, for example, Mn3Si, Mn5Si3, MnSi, MnSi2 and MnSi1,7. Among these, the most interesting phase from the point of view of the magnetic properties is bulk MnSi, which below 30K and at atmospheric pressure orders into a ferromagnetic state developing a long wavelength (180 A) helical modulation in magnetic fields below 0.6T [42]. Also the Mn5Si3 phase has interesting magnetic properties: it has been observed that a transition between a non-collinear anti-ferromagnetism and a collinear ferromagnetism-paramagnetism occurs depending on the field applied and on the temperature [43].The MnSi1.r phase is considered a promising thermoelectric material for high-temperature applications. It has been shown to grow epitaxially on silicon and could be used in optoelectronic applications such as silicon-based


infrared detectors and light sources [44]. MnSi1,7 is a class of superstructures MnxSiy where the ratio x is ~ 1.7; this class is called “higher manganese silicide” (HMS). It seems that depending on the structure it may present either a direct bandgap near 0.7 eV [45] or an indirect gap near 0.4 eV [46]. The reason is that it may be either a continuum of ordered phases, or perhaps a group of several distinct compounds. The usefulness of such a semiconductor as an optoelectronic material depends on its growth mode and has led to a large amount of experimental studies.

4.2 Experimental set up

Photoemission and STM experiments were carried out in two different vacuum chambers. In the photoemission experiment, synchrotron radiation from the UE-56/2 beamline at the BESSY storage ring has been used, with the system equipped with a VG Scientific electron spectrometer. The UE- 56/2 beamline provides for a very intense photon flux in the range of 60-1200 eV, giving the possibility to study both the VB and the core level electrons. The experimental total resolution was set to 100 meV for the Si 2p core level and to 250 meV for the valence band studies. The angular acceptance of the electron analyzer was 24°. All spectra were taken with an angle of incidence of 30° and at normal emission.For the STM experiments, a home-built STM [47] was used, in a UHV chamber with a base pressure of 5x 10-11 mbar with the STM operating at room temperature. Both UHV chambers are equipped with LEED for controlling and comparing the surface order.The use of both STM and photoemission spectroscopy in the study of surfaces and thin films is due to the different information that can be obtained by the two techniques. While the former gives information about the local properties of the surfaces, the latter operates on a larger spatial scale depending on the photon spot incident on the sample and the analyzer aperture.Due to the acceptance angle of the electron analyzer, photoemission is here used in such a way that the density of states (DOS) is measured and no angular information is possible. At a photon energy of about 65 eV, electrons escaping from the sample with an angle of 12° will have a corresponding wave vector of about 1 A"1 (see eq. 2.7), i.e. almost the width of the first

4.3 Experimental results 43

surface Brillouin zone.As anticipated in chapter 2, photoemission from core levels permits to check the chemical composition of the sample and to study the charge transfer between atoms at different positions with respect to the surface and bound to species with different electronegativities. Thus, a detailed analysis of the core level line shape offers the possibility to study the effect of formation of the Mn/Si interface and to determine the formation of manganese silicide. The Si samples were cut from a commercial p-type Si(111) wafer (Virginia Semiconductors). To produce clean Si(111) surfaces, the samples were first degassed to ~ 650° C for a few hours and then flashed at ~ 1200° C. The pressure burst during the flash was maintained in the 10"10 mbar range. The samples were then quickly cooled to ~ 900° C. The procedure ensured a good 7x7 reconstruction proved by the sharp 7x7 LEED pattern. Manganese deposition has been carried at room temperature from a water cooled Knudsen type MBE cell at a rate of 0.1 ML/min, where 1ML of manganese is defined as 7.88x1018 atoms/m2.

4.3 Experimental results

The deposition of manganese in the initial stages and its effect on the surface symmetry has been characterized by means of LEED, where, in the range 1-5 ML, two distinct phases are found. While the LEED picture of 1 ML of Mn on Si shows a diffuse (1x1) phase with high background in which a faint (7x7) superstructure is still present (Fig. 4.1a), for more than 1.5 ML of manganese films annealed at 400°, a (\/3 x \/3)R30° LEED pattern was observed, with no remaining substrate superstructure (Fig. 4.1c and d). The (1x1) spots become sharper after annealing at 250° C for 5 minutes, although very feeble remnant streaks of the (7x7) phase from the substrate are still visible (Fig. 4.1b). Any remaining doubt that the (\/3 x \/3) could be derived from the (1x1) structure is resolved by observing that the relative intensities of the (10) and (01) spots change in the two LEED patterns (cf. Fig. 4.1b and d). The existence of the above mentioned structural phases has been already reported by Evans [48], Nagao [49] and Kawamoto [50]. It has also been reported that up to 3 ML of Mn, deposited at RT at a slow rate of < 0.15 ML/min, and annealed at 350°C, a sharp (1x1) LEED pattern is observed. However, as shown here, we found that the (\/3 x \/3)

44 Thin Manganese films on Si(lll)

Figure 4.1: FEED images for (a) 1 ML Mn deposited on Si at room temperature, (b) same film as (a), annealed at about 250°C, (c) and (d) 2 ML Mn on Si annealed at about 400°G. The difference between (c) and (d) is only the electron energy.

reconstruction is already formed with 1.5 ML of Mn even with a lower deposition rate.

4.3.1 Morphology

Fig. 4.2 shows a STM image from a submonolayer Mn thin film on Si, after annealing at 250° C. Clusters of different sizes are present on the substrate, and the terraces of the silicon substrate, still distinguishable in this picture, are still very regular and have an average width of about 55 mn. Only about 1/3 of the largest clusters are formed on the terraces, while the steps are preferred, because of the necessity of incorporating Si atoms to form the silicide. In fact, when the clusters are formed on the terraces, they are surrounded by craters in the substrate, showing that silicide formation has already happened after a mild annealing, as expected from such reactive system.The incorporation of silicon atoms into the deposited layer seems to be the path to form the silicide, with the consequent loss of order of the substrate surface. This becomes clearer in the close-up image of this layer in Fig.


Figure 4.2: STM topography of about 0.5 ML Mn deposited on Si at RT and annealed at 250° C. The size of this image is 315x315 nm‘ and has been recorded at constant current I =1 nA, with sample bias voltage Vb = 1.7 V.

Figure 4.3: Atomic resolution STM image of clusters of different sizes. Some Si atoms from the substrate are incorporated in the clusters (dark holes in this image), while the others show disorder, with no trace of the (7x7) reconstruction. Image size is 27x27 mu'. I =1 nA, with sample bias voltage Vb = 1.7 V.

4.3. The corresponding LEED image for this layer is Fig. 4.1a, with the streaks from the 7x7 Si reconstruction coming from the terrace region with no silicide clusters.

Increasing the manganese deposition to 2 ML and annealing this layer at 400°C, the reaction at the surface continues, destroying the terrace structure of silicon and making comparatively larger islands (see Fig. 4.4a). These are accommodated on patches of silicon substrate which are disordered and partially consumed by silicide formation. The growth of the silicide islands proceeds on the substrate in a Volmer-Weber mode [11], with the thin films covering the Si surface only partially. In the 3D image of another region


Figure 4.4: Deposition of about 2 ML Mn and annealing at about 400°C. (a) Substrate terraces are destroyed and elongated, flat islands cover partially the substrate surface. Image size is 315x315 nm'. (b) 3D image of islands in the same sample as (a). Islands with different height lie on terraces of the Si substrate. Image size is 39x39 nm". I = 1 nA, with sample bias voltage Vb = 1.7 V.

from the same sample, shown in Fig. 4.4(b), it is possible to see the silicide islands growing on the disordered silicon layer. The silicide islands have clearly different heights, varying, in this picture, between 1 and 3 ML. This confirms that the silicide formation takes place by incorporating silicon atoms into the deposited manganese layers.The islands have a well-ordered atomic structure as evident from another

closeup image in Fig. 4.5, of another sample obtained with a similar procedure. They exhibit perfect order in a (\/3 x \/3)R30o arrangement with a number of additional “adatoms” in a three-fold coordination (Fig. 4.5). The substrate also exhibits an atomically ordered surface structure with areas of 81(111)7x7 as well as of the metastable (5x5) reconstruction. This reordering of the substrate compared to the submonolayer deposition can be ascribed to the higher annealing temperature (400 °C) [49], which is close to the transition temperature where the (7x7) reconstruction forms from the metastable (2x1) phase on cleaved 81(111) [4],

By depositing more manganese onto the surface, the silicide islands start to coalesce, forming an almost closed film (Fig. 4.6), interrupted by deep holes. Nevertheless, most of the epitaxially grown surface area is flat with monatomic, 3 A high islands on top (Fig. 4.7(a)), exhibiting a (\/3 x \/3)R30o reconstructed surface as can be seen in Fig. 4.7(b).


Figure 4.5: STM image of a silicide island and the Si substrate. The island has a (\/3 X

V3)R30° order, with the presence of extra features due to adatoms. Also the substrate has various ordered regions, although with various atomic arrangements, varying from (7x7) to (5x5) and (9x9). The height of the large silicide stripe is about 6 A, corresponding to 2 ML (left). The sample procedure is similar to that of Fig. 4.4, but with Mn deposition less than 2 ML. Image size is 34x34 mn'. I =1 nA, with sample bias voltage Vb = 1.7 V.

The atomically resolved STM images of the silicide surface in the lower (1-2 ML) and in the higher (up to 5 ML) coverage regime reveal the frequent existence of adatoms which are three-fold coordinated and probably commensurate with the silicide crystal structure (Fig. 4.8(right)).Moreover, by a more accurate observation of the STM images of the 5 ML Mn silicide (cf. Fig. 4.6 and Fig. 4.8(left)), it is possible to note that, although most of the surface area is flat, large scale modulations in STM with a period of about 20 mn are present. These exhibit a hexagonal symmetry pattern which suggests that the modulation can be ascribed to the formation of a strain network in the silicide him due to a mismatch in the epitaxial growth of the silicide onto the silicon substrate. This modulation is an example of a Moire pattern which is obtained by superimposing two crystals with a small mismatch and with some degree of displacement [51]. The nature of the deep holes that can be found besides the hats is also interesting. The depth of these holes can be as much as 30 A. On the bottom, the holes consist of unreacted silicon as can be seen from the residual reconstruction patterns (Fig. 4.9). The holes are thought to act as local relief


Figure 4.6: STM image of 5 ML Mn deposition and annealing at about 400°G. The film is flat and covers almost completely the substrate, although holes are still present. Image size is 315x315 mn'. I =1 nA, with sample bias voltage Vb = 2 V.

to the strain due to lattice mismatch, as suggested by the presence of the Moire pattern.

Figure 4.7: STM image of 5 ML Mn deposition and annealing at about 400°C. Flat islands grow on top the thin film (left), showing (V3 x V3)R30° reconstruction (right). Islands are about 3 A high. Image sizes are 85 x 85 nm" and 29x29 mn', respectively. I = 1 nA, with sample bias voltage Vb = 1.7 V.


Figure 4.8: (left) The V3x V3)R30° reconstructed surface has many defects and three-fold coordinated adatoms, (right) The STM contours show modulations with an approximately hexagonal symmetry. The period of the network is of the order of 20 nm. The surface shows also a high density of defects and eventually deep holes. Image size is 16x14 nm" (left), and 86x86 (right). 7 =1 nA, with sample bias voltage = 1.7 V (left) and 2 V (right).

Figure 4.9: Several layer deep holes are present also in the 5 ML film. It never covers the surface completely because the silicide film is strained, due to a lattice mismatch with the silicon substrate. At the bottom of 30 A deep holes, unreacted silicon is still present (left). Image size is 58x58 nm" and 48 x 48 nm", respectively. 7 =1 nA, with sample bias voltage Vi, = 1.7 V.

4.3.2 Spectroscopy

STM topography reveals the growth mode via island formation and the morphology of the reacted films. However, to obtain information about the electronic properties of these films, this system has been studied also by photoemission. The results can be sorted into two different classes: from the angle integrated normal emission valence band spectra, it is possible to


4 2 0Binding energy (eV)

Figure 4.10: Valence band photoemission spectra taken with a photon energy of 65 eV for the (1x1) and the (VS x v/3)R30° phases obtained by annealing 1 ML and 2 ML of Mn epitaxial films on Si.

observe the difference in electronic character of the various phases inferring which particular silicide corresponds to the actual phase, while with core level spectroscopy, information about the charge transfer between silicon and manganese atoms and the composition of the silicide surface have been obtained.Valence band spectra have been recorded with a photon energy of 65 eV. In

Fig. 4.10, photoemission spectra of the clean Si(111)7x7, the Mn/Si(111)- (1x1) and the Mn/Si(111)(\/3 x \/3)R300 surfaces are shown. The valence band spectrum for clean Si(111)7x7 is characterized by three features next to the Fermi edge, corresponding to the three surface states at 0.2, 0.8 and 1.8 eV binding energy, which have been attributed to ad-atoms, rest atoms and back bonded atoms, respectively [52]. These peaks are very sensitive to the deposition of manganese. Just one ML of Mn is sufficient to destroy the surface states of Si(111)7x7, as is clear from the valence band spectrum relative to the (1x1) phase, where two very broad features at ~1.0 eV and ^2.0 eV are present and, at the Fermi level, the photoemission intensity is very low. The feature at 1.0 eV is derived from Mn 3d non-bonding states while the one at 2.0 eV is from the bonding Mn 3d - Si 3p states [34]. Taking into account the overall energy resolution of our spectrometer, the decreasing


photoemission signal is interpreted as a signature of the semiconducting character of the (1x1) reconstructed surface.

Very different from the (1x1) phase is the valence band spectrum from the (V3 x V3)R30° surface. In fact, in this case, a sharp Fermi edge is observed, which demonstrates the metallic character of this surface in agreement with STS results. The corresponding valence band spectrum is presented in Fig. 4.10(top), where a (V3 x V3)R30° LEED pattern is obtained by depositing 2 ML of manganese on Si and annealing at 400° C, but it does not change with further Mn deposition. The bulk silicides which have metallic character are MnSi and Mn5Si3, therefore it is possible to determine which particular phase is obtained by comparing the data present in the literature concerned with these two components.

In the experimental valence band spectrum of Mn5Si3, a sharp peak, close to E_p, and two broad peaks at 1.3 and 3.0 eV are observed [43], whereas a sharp peak close to E_p and a weak feature at ~2 eV have been reported for MnSi [53]. Thus, by comparing the valence band spectrum of the (V3 x V3)R30° - phase with one of the known bulk metallic phases as well as with the band structure calculations of the known bulk phases of manganese silicides [54], we believe that the electronic structure of this phase is similar to that of bulk MnSi.Such an inference is in agreement with the findings of Nagao et al. [49], who, from their scanning tunneling microscopy measurements, also concluded that in the (V3 x V3)R30° -phase, the ratio between Si and Mn atoms is 1:1. Therefore, in agreement with the band structure calculations for MnSi, we assign the feature close to E_p to Mn 3d states and the feature at 1.7 eV to Mn 3d - Si 3sp derived bonding states.

Si 2p core level spectra of Si(111)-(7x7), with 1 ML and 2 ML of Mn overlayers as-deposited and the (1x1) and (\/3 x \Z3)R30°-phases, obtained by annealing these thin films, are shown in Fig. 4.11. All spectra were recorded with a photon energy of 150 eV, which assures a good surface sensitivity for the 2p core-level. As is obvious from the core level spectrum of an as-deposited 1 ML thin film of Mn, all features due to surface components [55], which are clearly visible in the core-level spectrum of Si(111)-(7x7), almost disappear.The main peak is shifted by about 80 meV towards lower binding energy in comparison to the Si 2p main peak of Si(111)-(7x7) and has a weak shoulder


Si 2p core level

2 ML Mn, as

deposited

(1x1) phase

1 ML Mn,

as deposited

clean Si(111)(7x7)

Binding energy (eV)

Figure 4.11: Si 2p core level spectra obtained with a photon energy of 150 eV for (a) Si(111)-7x7, (b) and (d) as-deposited Mn epitaxial films of 1ML and 2ML thickness,respectively, (c) the (1x1) phase and (e) the (\/3 x \/3)R30° phase.

at ^-0.3 eV binding energy with respect to the main peak. It is therefore clear that the metal-silicon reaction occurs already at room temperature, and that it results in the formation of Mn silicide on the Si surface.On annealing the film to 200°C to obtain the (1x1)-phase, no big changes are observed, only a further chemical shift of about 20 meV and a small decrease in the peak-to-valley ratio of the Si 2p doublet of the main peak. At 2 ML of Mn the line shape changes, indicating an increase in the intensity of the reacted component with the result of a shift of the main peak increased to about 150 meV.For the (V3 x V3)R30°-phase, the main peak is shifted by -0.23 eV and is comparatively narrower. Further, it also exhibits a shoulder at ^-0.5 eV, which is very similar to the S2 surface component of Si(111)-(7x7). This suggests that the surface of this phase is terminated by Si atoms.

Apart from these first observations, more information can be obtained by exploring the contributions of various components to the Si 2p core-levels, analysing the spectra by means of a least squares fitting.To model the photoemission lines we used Lorentzian peaks numerically convoluted by a Gaussian (for the description of instrumental and phonon


as deposited ~1 ML Mn film

100 99Binding Energy (eV)

ha/VvAvvwxAvxA/VWvuV'00 99 91Binding Energy (eV)

Figure 4.12: The best fit spectra for Si 2p core levels recorded with photon energy of 150 eV for (a) as-deposited Mn epitaxial film of 1 ML Mn on Si(111)-(7x7), (b) 1x 1-phase, (c) as-deposited 2 ML Mn on Si(111)-(7x7) and (d) (VS x VS)RS0° phase. The experimental data are represented by open circles, while the fits to the data are given by the thick solid line; the contribution of various components to the respective Si 2p core levels are displayed underneath each spectrum.

broadening and surface disorder), as in the case of the SiC core level shifts in chapter 3.The Si 2p spectrum for clean Si was fitted (not shown) in terms of known surface and bulk components and the parameters obtained were found to be consistent with the earlier published results [55]. In each of the Si 2p core-levels, all the Si 2p doublets representing contributions from different environments of Si atoms are well described by a spin-orbit splitting of 0.608±0.003 eV and a Lorentzian width of 0.070±0.020 eV.The Si 2p core-level for the as-deposited 1 ML of Mn film is well described in terms of three components (Fig. 4.12a), with the main component at 99.15 eV binding energy and the other two having a chemical shift of 0.28 eV and -0.34 eV. Taking into account the relative binding energies of different bulk and surface contributions to Si 2p core-level of Si(111)7x7, we assign the component at 99.15 eV binding energy to emission from bulk Si atoms. The


second one at higher binding energy to the Si surface component represents the back-bonded atoms from the Si substrate.The third component at lower binding energy then can be ascribed to the silicide phase formed due to reaction between the Mn atoms from the thin film and Si atoms from the substrate. It may be noted here that in comparison to clean Si, relatively large Gaussian widths were found from the fitting procedure, implying that the interface is characterized by large disorder as would be expected for an as-deposited film and as observed in STM.One of the main reasons for the observed large disorder for the reacted component (manganese silicide, MnSix) could be due to the fact that the reaction between Mn and Si is not complete and MnSix exists with different values of x, leading to a large variety of nearest neighbour environments for the Si atoms. The contribution of large intensities from the substrate confirms that deposition of 1 ML of Mn does not lead to a uniform coverage of the complete substrate surface, which implies that during the initial stages of growth, island formation instead of uniform film takes place, in agreement with our result from the STM experiment.In case of the Si 2p core level for the 1 x 1-phase (Fig. 4.12b), obtained by annealing the 1 ML Mn film at 250° C for 5 minutes, the introduction of an extra component shifted by 0.58 eV with respect to the bulk Si contributions was found to be necessary to arrive at a good description of the line shape. This component has been ascribed as S2, due to emission from the adatoms. Further, a decrease in the intensity of bulk component and increase in the intensities of the MnSix and S1 components with a concomitant decrease in the Gaussian widths of all the three components is apparent from the figure. On annealing the 1 ML Mn film, the reaction between the Mn and Si atoms proceeds further, possibly leading to the formation of single phase MnSix, and the bare areas of the substrate between the silicide clusters become more ordered.The increase in the intensity of S1 and reappearance of S2 surface components would also imply that at least in some of these bare areas, the formation of the (7x7) superstructure has recurred, which may not have a completely perfect dimer-adatom-stacking fault (DAS) structure, as confirmed by the observation of feeble streaks of (7x7) in LEED pattern of this phase (Fig. 4.1b). The surface core-level, S2 in Si(111)-(7x7) is shifted by about 0.70 eV [55], while in the (1x1)-phase the shift has been found to be


0.58 eV with a relatively larger Gaussian width. This leads us to believe that the S2 component not only has the contributions from the (7x7) superstructure of the bare substrate, but the surface of the 1 x 1-phase is also terminated by Si atoms.

For the as-deposited ~2 ML Mn thin film, the Si 2p core-level is well described in terms of three components, identified as contributions from the bulk and back-bonded atoms of the substrate and the manganese silicide phase (Fig. 4.12c). As in the case of an as-deposited 1 ML Mn film, here also a large intensity for the contributions from bulk Si-atoms and back-bonded atoms of the substrate is observed, indicating that even after deposition of 2 ML of Mn, the film is not completely closed. This supports our earlier inference that the growth of Mn on Si(111)7x7 takes place by formation of islands, which is in agreement with the earlier STM findings [48],[49].The Si 2p core-level for the (V3 x V3)R30°-phase (Fig. 4.12d) is mostly dominated by a single peak attributed to the silicide phase, which is possibly MnSi, as observed above for the valence band spectrum. Apart from this, relatively small contributions from the Si bulk atoms and adatoms are also clearly evident from the figure.The occurrence, in the Si 2p core-level of this phase, of one component with high intensity, attributed to the reacted silicide MnSi, suggests that the annealing of the film at 350° C leads to completion of the reaction between Mn and Si, resulting in the formation of the silicide with almost complete coverage of the Si substrate. Nevertheless, the presence of some bare areas of the substrate, observed in STM also for films 5 ML thick, is also revealed in the core level PE spectrum of Fig. 4.12d, by the presence of the S1 component, although its intensity is only 1/4 of the MnSi peak.It has to be noted here that to arrive at a good agreement with the experimental Si 2p line shape for the (V3 x V3)R30°-phase, it was found to be necessary to describe the line shape of the MnSi component by a Doniach- Sunjic function [56], instead of a Lorentz function. This is not completely surprising considering the fact that MnSi is metallic. Similar results were obtained from the analysis of Si 2p line shape for the (V3 x V3)R30°-phase obtained from the 5 ML of Mn film.

The observation of a component similar to the S2 surface core level of Si(111)-(7x7) in the Si 2p core levels of (1x1) and (V3 x V3)R30° surface


100 99 98Binding energy (eV)

Figure 4.13: (Vs x v/3)R30°-phase recorded with a photon energy of 120 eV, with the corresponding line shape analysis shown underneath.

reconstructions is puzzling if not completely surprising. In a recent study, Ctistis et al. [57] in their RHEED studies on thin films of Mn on Si(111)- (V3 x V3):Bi observed that annealing of such films at 250° C results in ordered films with a Si layer on top of the Mn film. Similarly, the annealing of epitaxial Ni films on Si(111)-(2x1), have also been reported [58] to be accompanied with out-diffusion of silicon atoms having epitaxial arrangement of the silicide surface. More recently, in a theoretical work [59], Wu et al. predicted that ultrathin Si-Mn sandwich films grown pseudomorphically on Si(001) are obtained by a diffusion of a single Mn atom into a second layer interstitial site below the Si dimer, and present ferromagnetic character.In order to explicitly check that this component originates from the Si atoms on the surface of the silicide and not from the bare areas of the substrate, we recorded Si 2p core level PE spectra for the (\/3 x \/3)R30°-phase with a photon energy of 120 eV, thus increasing the escape depth of the electrons. The corresponding spectrum is shown in Fig. 4.13. Even without any detailed line shape analysis, it is evident from the experimental spectrum that the intensity of the leading clean Si peak is markedly decreased compared to the surface sensitive spectrum at 150 eV photon energy. Specifically, the results of the line shape analysis indicate that there is an attenuation of 30% in intensity of this component thus clearly proving that this component in

4.4 Conclusions 57

deed originates from emission from Si atoms on the surface of MnSi. Since in the LEED pattern, only the (\/3 x \/3)R30° structure is observed, we believe that the atomic structure of these surface Si atoms is commensurate with the (V3 x V3)R30°-phase of MnSi.

4.4 Conclusions

The deposition and reaction of ultrathin Mn films on Si-(7x7) were studied by means of LEED, STM and photoemission spectroscopy. While the reaction between Mn and Si begins already at RT leading to an incomplete silicide formation, annealing these Mn films results in the development of well ordered manganese silicide phases. At very low coverages, of less than about 1 ML of Mn, the development of silicide islands is observed in STM images resulting in a (1x1) LEED pattern. The valence band photoemission spectrum indicates that this film is semiconducting. At higher Mn coverages, up to 5 Ml, a (V3 x V3)R30° phase develops, as shown by LEED, in a Volmer-Weber mode, with islands interrupted by bare Si substrate patches at low coverages and the film being nearly closed at 5 ML. In this coverages range, a strain dislocation network is manifested as a large scale corrugation seen in STM. Photoemission experiments attributed these films to the metallic MnSi phase, terminated with Si adatoms.

Chapter 5

Al-Mg alloy thin films on Si(111)

An alloy is a liquid or solid solution of two or more elements. The structure of alloys varies, depending on their composition, temperature, pressure and forming elements. In the simplest case the elements are completely soluble and present a continuous variation of the structure with composition. However, this is not generally the case: usually the solubility is only partial. A particularly convenient way to represent the variation of the structure with the relative composition of the alloys is the phase diagram, where the different phases, i.e. domains of homogeneous concentration and structure, are presented in a temperature (or pressure) vs. concentration diagram. The simplest phase diagrams are those of completely soluble alloys, while the partially soluble systems are characterized by more complex phase diagrams, with transitions between different structures and coexistence of phases. Among the partially soluble alloys, the eutectic alloys, which are completely soluble in the liquid state but not in the solid state, are very important. Solidification of an eutectic alloy from the liquid phase produces two composite solid phases characterized by different solute concentrations. It is possible also for eutectic alloys to solidify into single phase compounds, but this happens only at certain particular compositions. Consider the phase diagram of the Al-Mg system shown in figure 5.1. The phases defined by

59

60 Al-Mg alloy thin films on Si(lll)

Atomic percent Mg

Figure 5.1: Phase diagram of the Al-Mg alloy system.

p, p1 and 7, represent three intermetallic compounds, namely the MgoAlg 1

and the AlioMgip. The a and e phases are the pure A1 and Mg.The binary alloys obtained by solution of simple metals are technologically very important materials, especially due to their mechanical properties, but they are also interesting from a more fundamental point of view, because the relative simplicity of the band structure of the forming elements can be tailored in the binary system.The Al-Mg alloys present similar features to other binary alloys, such as an excellent strength to weight ratio, good ductility and corrosion resistance, making them widely used in the mechanical industry.However, one more peculiarity of the Al-Mg system is the close similarity of their structure with many quasicrystals. Therefore the electronic properties of such systems can be of great importance in the study of the more complex quasicrystals obtained by alloying Al, Mg and a small amount of a transition metal or another simple metal (examples are the Al-Mg-Zn and the Al-Mg- Li alloys). Moreover, an interesting Al doping behaviour has been observed in the recently discovered high Tc superconductor MgBo doped with Al [60]. The resulting material Al^Mg^^Bo shows a dependence of Tc on the quan-

' The difference between the [3 and j3' phases is in the order and the extension of the unit cell, in fact, the former has a complex fee structure with a lattice constant of about 28 A and about 1100 atoms in the unit cell and the latter has an hexagonal structure with lattice parameters a=10.02 A and c=16.36 A.

5.1 Simple metals and binary alloys 61

tity x of doping Al [61]. From a theoretical point of view, ab initio virtual crystal approximation (VCA) calculations [62] demonstrated that electronic doping due to Al introduction raises the Fermi level to higher energies, leading to a band broadening and to a continuous variation of lattice constant with x, as result of the different Wigner-Seitz radius of Mg and Al.

5.1 Simple metals and binary alloys

A characteristic of the s-p metals is the simplicity of their electronic structure, which is essentially the s-p derived nearly free electron (NFE) band. This property determines the great mobility of the electrons which can move almost freely in the medium represented by the periodic ionic potential. Thin films of sp-metals are very interesting to study because their properties are strongly dependent on the size of the films, and in particular they can induce a discretization of the s-p band due to the confinement of the electrons in a 2D potential well. Because of the simplicity of the theoretical model, quantum size effects in s-p metals have been intensively studied and several thin film electronic structure calculations are available [63]. Aluminum and magnesium are two examples of s-p metals, and indeed many theoretical studies refer to them, although the experimental observation of quantum well states (QWS) for thin films of aluminum and magnesium has been published only very recently [64],[65].

Aluminum crystallizes in the face centered cubic structure (fcc) with lattice constant of 4.05 A. The corresponding reciprocal lattice is body centered cubic, with the first Brillouin zone represented in Fig. 5.2. Magnesium has a hexagonal close packed (hcp) structure with lattice constants a=3.19 A and c=5.18 A, thus with an almost ideal c/a ratio for a close packed structure. The Brillouin zone for Mg is shown in Fig.5.2 as well. The electronic structure of Al(111) and and Mg(0001) in the direction of interest for our study are shown in Fig. 5.3. The NFE band extends over a large energy region and for both metals a gap is present, due to the Bragg reflection of the wavefunction at the Brillouin zone boundary. Within this gap, a Shockley-type surface state has been predicted for both elements and, indeed, experimentally observed: at about 4.7 eV for Al(111) [66], and at about 1.7 eV for Mg(0001) [67].


Figure 5.3: band structures of Al(lll) and Mg(0001) in the direction of interest for confinement.

5.1.1 Binary alloys

The way a binary alloy behaves depends on the relative concentrations of the alloy components and on the electronic and atomic properties of both components in a complex way. Apart from the ordered compounds, a peculiarity of all the alloys is the loss of long-range periodicity leading to the inapplicability of Bloch’s theorem, at least in its direct formulation. However, the observation in the last decades of bulk and surface bands in systems with no translational symmetry, shows that the band picture can be modified to be applied to such systems [68].


Figure 5.4: Schematic illustration of the restoring of crystalline order with the introduction of effective atoms. This theory is known as virtual crystal approximation (VGA).

The effect of alloying of two metals consists in the variation of various properties: the lattice constant and the stable crystalline structure; the charge density n on which the Fermi energy Ep, the Fermi wave vector kp, the radius rg of the sphere which contains on average one electron, the work function $ and the potential V, depend. The different theories concerning the formation of alloys take care of all these effects in various ways depending on the approach to the problem.In order to tailor the powerful Bloch theorem to systems with no long range

order, it is possible to substitute the disordered crystal with an ordered one formed by atoms with averaged parameters depending on the composition of the system. In such a way, the order is restored and it is in principle possible to study the average properties of the disordered crystal with the same mathematical tools used for studying the ordered systems (see Fig. 5.4).The way the disordered crystal is approximated with an effective ordered one can be formulated in various manners: two of these are the virtual crystal approximation (VGA) and the coherent potential approximation (CPA). In the former one, the potentials VA and VB of the two different ions A and B are substituted by one effective potential, just by considering V(c) = VA(c) + VB(1 - c) where c is the concentration of element A in the alloy. The approach of the CPA is instead related to the scattering of the electrons, which is considered to be caused by the effective potential. In this case, the two different potentials are substituted by one which scatters in an effective way and, apart from this effective scattering, there are no further single-site scattering events.The VGA approximation is an extension of a simple model proposed by


Figure 5.5: Model used by Schliiter and Varma. to explain the changes due to alloying of two materials with different electronic properties [71].

Jones already in 1934 and called rigid band model [69], in which in the case of elements with similar band structure but different bandwidth, the alloying process results in a band structure similar to the two and with a bandwidth depending only on the relative concentration of the two elements. Hence, the valence band is rigidly shifted with respect to the Fermi edge by changing the composition. This result is indeed obtained also in the VGA model, but with the difference that a density of states profile dependence on the alloy composition is also taken into account, meaning that the alloying process is characterized also by a charge transfer.Neddermeyer [70] studied the Al-Mg alloy system by means of X-ray emission, and found that the bandwidth of the A1 and Mg Kfd bands have the same common value lying between those of the pure elements, while he could not gain any direct information about the density of states of both components, which would confirm the basic idea of the rigid band model of Jones. In order to understand how the density of states profile enters into the alloy process, a very intuitive approach to the VGA approximation has been proposed by Schliiter and Varma [71], who used a simple model based on the essential physics to calculate the stability of many binary alloys of simple metals.Their idea was that, starting from two s-p metals A and B with local density of states per unit volume 'IIa(E) and 'IIb(E) which are zero below the potentials Va and Vg, respectively, the alloy formation will result in an averaged local density of states ua(E) and ng(FJ). They calculated in a self-consistent


way the mean potential associated with the redistribution of the charge obtaining an averaged VAB . If, for example, VA <VB, the potential of element B will reduce to the averaged potential accumulating electrons, coming from element A, at the bottom of the spectrum, arriving at the situation depicted in Fig. 5.5. This model predicts thus an averaged, common Fermi level, dependent on the composition of the alloy.The other approach, which makes use of the CPA approximation, has been proposed by Bansil and Pessa [68] who used this approximation more specifically to explain their photoemission results in Cu%Ali_% alloys. In these alloys they observed the existence of both Tamm and Shockley-type surface states derived from the respective surface states of Cu, where the Shockley surface state on the (111) and (110) faces shifted by varying the Al concentration of the alloy, while the Tamm-type surface states on the (100) and (111) surface did not.The CPA theory predicts that the location, in a disordered way, of Al atoms in the Cu lattice sites produces bulk wave functions with k values with an imaginary component, resulting in the broadening of the electronic bulk bands and eventually in the shift of the gap position and of the surface state, with influences on the bandwidth given only by the broadening of the bands. The difference of behaviour between the Shockley and the Tamm state is given by their different nature: while the Tamm states are thought to be split off from the top of the Cu d-bands, the Shockley states are positioned in the gap which arises from the mixing of the states possessing s-p character, so the movements of the surface states on alloying follow those of the bulk states of corresponding symmetry [68].The reason why the CPA was used in the study of Bansil and Pessa is because it is more useful in treating the Cu d-bands. But, nevertheless, the result that only the gap position with respect to the Fermi edge influences the surface state energy, and therefore, only the Shockley-type surface states are influenced by the alloy composition, shows that the VCA approximation can be used as well. Indeed, we have also to note that in our case of AlMg alloys there are no d-bands involved, so the comparison between our system and that of Bansil and Pessa has to take into account this substantial difference.Except for some experimental studies done with Auger spectroscopy [72] aimed at studying the mechanical properties of the Al-Mg alloy and in par

66 Al-Mg alloy thin films on Si(111)

ticular Mg segregation, the only experimental study of the electronic properties of these alloys is the above cited X-ray emission work reported by Neddermeyer [70]. Photoemission is a very powerful tool for studying the electronic structure of the bulk and surface of solids, it is therefore very important to use this technique also for these systems and in particular for thin films of Al-Mg alloys to obtain more knowledge of the alloying process.

5.2 Photoemission and QWS

The simplest way to understand the formation of QWS is the 1D model of the “particle-in-a-box” where the electron is confined by two infinite barriers at a distance comparable with the particle wavelength, causing the discretization (quantization) of the energy values. The adaptation to the case of a thin film of thickness d is made through the 1D phase accumulation model [73],[74]. Here the electrons of the film are confined in the direction perpendicular to the surface by the image potential at the surface of the metal, and by the energy gap in the substrate, resulting in a reflection of the electron on both walls with a changing of the phase $ of the electron wave function #. In this direction the wave vector values k are allowed only if they fulfill the condition:

2kd + $B + $C = 2nn (5.1)

stating that the round trip phase accumulation of the electrons must be a multiple of 2n, similarly to the condition of constructive interference in the Bohr atomic model for a complete turnaround the atomic nucleus. Here $B is considered the phase shift at the vacuum barrier and $C the shift at the crystal substrate gap.The determination of $B and the $C as a function of binding energy E is a very important and indeed very complicated task. A useful approximation for the reflection phase shift at the surface is given by [75]:

$B=VEV5 -n (5-2)

where EV is the vacuum level, while for the phase shift at the interface there is an empirical formula which gives [73]:

E — El$C = 2 arcsinEu — El

— n (5.3)

675.2 Photoemission and QWS

|

Figure 5.6: Photoemission spectra taken at 15 eV photon energy for various film thicknesses of Al/Si(111).The substrate temperature during Al deposition was about 100K. The spectra were taken after annealing at 200K.

where EL and Eu are the energies for the lower and the upper parts of the band gap in the crystal substrate.The consequence of equation (5.1) is that the states for which the energy falls within the range of the gap in the surface projected band structure of the substrate are discrete. The band gap at the interface does not necessarily have to be an absolute gap, but may also be a symmetry-induced gap or maybe caused by a break in lateral symmetry due to lattice mismatch between the substrate and the overlayer thus causing a higher reflectivity. The effect of confinement is particularly clear in regions of the band structure where a NFE band is present, such as the s-p band of the simple metals Mg and Al (see Fig. 5.3): the quantization of the k values due to the reduced size of the thin film results in a split of the NFE bands into discrete energy values. In the energy distribution curves (EDC) obtained in photoemission, the quantization of energy values leads to separate peaks. In the case of Mg and Al the situation is advantageous because for a large range of binding energies, only the s-p bands are present, making the interpretation of the photoemission spectra simpler.In Fig. 5.6 we show photoemission spectra from the Al/Si(111) system. With increasing Al film thickness, there is an increase of the number of peaks and a shift of their binding energy as expected since the well is getting wider. From (5.1), it is possible to obtain the equation of k for the allowed

-5eV -4Binding energy (eV)


normal wave vector values of the film:

n n 1

N a N 2a (5.4)

where the thickness d of the film has been substituted by the number of layers N times the interatomic distance a. Another useful way to describe the QWS is the equation

m n 1 + $ck = (1 - N)' a - (5.5)

where the reduced quantum number m = N — n has been introduced. With this definition the state with m = 1 is always the closest to the valence band maximum and maintains its number m as the thickness increases. Increasing the number of layers, the value of k determined by equation (5.4) changes, leading to a shift of binding energy. At some point a new state crosses the E_p and a new peak is observed in the photoemission spectrum. The relation between the number of QWS and the thickness is given by the point where the bulk s-p band cuts: for example in the case of Al in r — L direction, there is a crossing of E_p at 1/3 of the Brillouin Zone (BZ), so a new QWS will cross E_p every 3 ML.

5.3 Experimental setup

The experiments were performed at BESSY on the beamlines 3m-NIM and TGM-4. These beamlines, located on bending magnets, have monochromators that offer the possibility to measure in the 5-30 eV range on the 3m-NIM and in the range 8-130 eV on the TGM-4, with a good energy resolution of ^30 meV and a photon flux of ~ 1011 photons/s. The use of low photon energy was decisive for obtaining good results, since, as will be shown later, in the range 10-15 eV the valence band cross-section has a huge enhancement due to collective electron excitations.The vacuum system used in these experiments was equipped with an ADES 400 hemispherical electron energy analyzer with a nominal radius of 50 mm and an angular acceptance of 1.5°. The estimate total energy resolution, determined by the width of the Fermi edge, was about 50 meV in the photon energy range used.The vacuum chamber was also equipped with low energy electron diffraction

5.3 Experimental setup 69

(LEED) for checking the periodicity of the clean surface of the Si substrate and of the thin films. The samples were cut from a commercial Si(111) wafer, p-type doping (B), 0.5 ficm resistivity (Virginia Semiconductors). The samples mounted on the manipulator could be degassed, annealed and flashed by direct resistive heating and cooled to liquid nitrogen (LN2) temperature through a cold finger. To produce clean Si(111) surfaces, the samples were first degassed at ~ 650°C for several hours and then flashed at ~ 1200°C, while the manipulator was cooled with LN2. The pressure burst during the flash was maintained in the 10~10 mbar range. The samples were then quickly cooled to ~ 900° C and then further cooled to low temperature within some minutes. The procedure ensured a good 7x7 reconstruction proved by the sharp 7x7 LEED pattern.The deposition of high purity (99.999%) aluminum and magnesium was realized with the use of home-made [76] water-cooled Knudsen cells. The two evaporators were mounted in the same plane, at an angle of 60° between them. The co-deposition took place with the sample face pointing towards the middle of the displacement angle, i.e. 30°. Thermocouples were spring- loaded to the crucible for temperature read-out and deposition rate control. The deposition rates were determined by a quartz micro-balance attached to the manipulator. The readings of the rate were made with the head of the micro-balance in front of the evaporators and multiplied by cos 30°.A further correction for the determination of the deposition rate of both metals is needed because of the different definition of ML for the two elements: if we define 1 ML as constituted by N0 atoms, it will correspond to 1.271 x 1019atoms/m2 in the case of Mg grown in the (0001) direction, and to 1.412 x 1019atoms/m2 in the case of Al(111), depending on the different in-plane lattice constants for the two elements; therefore we have to correct the value obtained by the calibrations and refer the ML unit of the alloys to that of pure Al2.The evaporations were performed on substrates cooled to liquid nitrogen temperature to make the reaction at the interface weak enough to avoid silicide formation. It has been observed by Aballe [64] that the highly reactive

' This means that 1 ML of Mg correspond to 0.9 ML of Al. Note that the definition depends on the structure parameters of the films which, depending on the alloy composition, can vary strongly. We have decide, for simplicity, to refer always to the definition of pure Al adding a discussion of the actual implication of such decision where it could give confusion.


Figure 5.7: Photoemission spectra of three Al-Mg alloy compositions: the Al-rich composition presents intensity modulations typical of QWS; the Mg-rich only a broad feature and the intermediate composition a huge peak with some modulation on both sides.

systems Al/Si and Mg/Si can productemperature of the substrate.

Binding energy (eV)

sharp interfaces just by lowering the

5.4 Experimental results: ARUPS

In Fig. 5.7 three representative photoemission spectra are shown, taken at normal emission for three alloys of different compositions and thicknesses. All spectra are normalized to the photon flux measured on the last mirror of the beamline. The differences between the three spectra are clear: for the Al-rich alloy the spectrum is similar to that of the Al/Si system, while the Mg-rich alloy spectrum is completely different and presents only one broad peak. The spectrum relative to the intermediate composition shows a large peak and some possible modulation on the low binding energy side. The compositions of the three alloys correspond to the three regions of the phase diagram for the Al-Mg system (see fig. 5.1), and it is therefore reasonable to divide the results into three groups corresponding to these three regions.

5.4 Experimental results: ARUPS 71

AI-18at%Mg/Si(111 17.5 ML AI-18at%Mg/Si(111

V 200K

-4 -2Binding energy (eV)

-5eV -4 -3 -2 -1Binding energy (eV)

Figure 5.8: Photoemission spectra at normal emission of the Al-18at%Mg alloy. (left) Dotted lines are for spectra taken after a new deposition and continuous lines after annealing at 200K; (right) spectra taken at different photon energies. The peak positions do not change with photon energy, i.e. peaks have localized nature.

Al-rich alloys

Spectra recorded in normal emission from films of various thickness of an Al-18at%Mg alloy (Mg atomic concentration is 18%) are plotted in Fig. 5.8. Dotted lines correspond to the spectra taken just after a new low- temperature deposition (at ~100K) while the continuous lines correspond to spectra after annealing at ~200K for 5 minutes. The effect of annealing is to order the films. Especially in the very thin ones, the formation of the surface state is obtained only upon annealing. The identification of the surface state and the QWS is clear by looking at the differences for the three thicknesses: the peak at eV binding energy does not shift by further deposition, while the other peaks do and their number increases as well.By varying the photon energy between 10 eV and 15 eV the peaks do not


, 0.0 n -0.2'-0.4 -0.6

-0.8 -1.0

1

©

©

© Difference 18%Mg-pure Al

©

© ©

Figure 5.9: Surface state (S) and quantum well state (QWS) binding energy in the 18at%Mg alloy and in the pure Al and their shift.

-5

o 1

+ 16.2 MLAI/Si(111)

o 17.5 MLAI-18at%Mg/Si(111)

S 1.QWS 2.QWS 3.QWS 4.QWS 5.QWS

peak

shift as can be seen on the right side of Fig. 5.8, i.e. they do not disperse with k±. In Fig. 5.9 we show a comparison of the growth of this alloy with that of pure aluminum (cf. Fig.5.6 with Fig. 5.8). The surface state is shifted towards lower binding energies and for the thickest film the shift reaches a value of about 0.8 eV (nearer to the Mg surface state). The QWS are shifted in the same direction, and for the almost identical thickness the number of QWS below the Fermi edge is one less. Also, the dependence of the number of QWS on the thickness is different. For our alloy there is a new QWS every ~4 ML while for Al it occurs every ML.To understand the shift of the surface state due to alloy formation, we can refer to the theory of Schluter and Varma where the substitution of the Fermi level of pure Al with an averaged EF has been analyzed via VCA. The adoption of this theory means to assume that the 18at%Mg alloy corresponds to a metal with NFE character similar to pure aluminum, but with different charge density n. This charge density is averaged over the alloy film:

n* = MMg(c) + n^(1 - c) (5.6)

where n* represents the effective charge density for the alloy of Mg atomic concentration c. In the free electron model, the electrons occupy states of increasing energy from the bottom of the spectrum up to the Fermi level


PE Spectrum:

s-p bands-pband

Intensity

(7 ML Film)(7 ML Film)

Figure 5.10: Band structure of A1 [63] in the F-L direction, (left) 7 ML Al/Si(111) case: the discretization is revealed by the existence of peaks in photoemission spectra, (right) The band structure of Al-18at%Mg is presumed to be similar to that of pure Ah The Fermi level is lowered because of the different charge density. In this case of 7 ML, the second quantum well, which in the case of pure A1 has a binding energy ~0.7 eV, in the case of the alloy stays above the Fermi level and is, therefore, not visible in photoemission.

E_p where all the electrons are accommodated. This value depends on the charge density through:

Jj2 _________EF = — V(37t2??.)2. (5.7)

In the case of Mg, the charge density is 8.6xl028ro~3 corresponding to the Fermi level at 7.12 eV, while for the A1 the charge density is 18.07x1028/??t3 and Ej? is at 11.66 eV [1], If we now calculate the value of the Fermi level in the case of c=0.18 we obtain z?.*=16.4x 1028ro~3 and Ef=10.9 eV, i.e. almost 0.8 eV lower than the Fermi edge of aluminum. This value is almost exactly the shift of the surface state with respect to the Fermi edge that we have observed, showing that this interpretation of our data gives already a good result.In Fig. 5.10 the fundamental idea of our model is represented: the effect of

varying the charge density of the alloy system results in a variation of the Fermi level with respect to the bottom of the spectrum, so that the bands are rigidly shifted towards lower binding energies.Looking at the phase diagram in Fig. 5.1 it may be thought that the Al- 18at%Mg alloy is given by a coexistence of the two stable phases named a and /?, where the a phase is the pure aluminum and the /?, also called /TMgoAls, has a very complex fee structure with 1,173 atoms per unit cell


and a lattice constant a=28.22 A.Van Agterveld [72], who studied the Al-Mg alloys with local probe scanning Auger and scanning electron microscopy (SAM and SEM), showed that in the case of bulk alloys with a concentration of magnesium of 20%, Mg segregates to the surface where there is formation of a texture of branched and dendritic disordered features. So the surface of such alloys presents areas with different magnesium concentration.On the other hand, the density of states is an average quantity, thus the possible presence of two phases does not change the interpretation of our results, it may give rise to a superposition of spectra. Anyway, this is not observed in our spectra, showing that the annealing temperature (about 200K) is still very low for the formation of separate phases and the result is a metastable alloy which has a 18at% Mg concentration throughout the film.The alloying process also produces other effects, for example a change of lattice constant is expected when Mg atoms are introduced in the array of Al, due to the difference in the atomic radii of the two elements: the value of rS for Mg is higher than that of Al3. The increase of the lattice constant corresponds to a decrease of the Brillouin zone in reciprocal space and then a possible shift of the surface state. The gap is formed by the Bragg reflection of the electron wavefunction at the border of the BZ, hence if the BZ is smaller, the gap has a shift towards higher binding energies, i.e. in a direction contrary to the shift we have observed.It has been demonstrated that the lattice constant increases by 0.0047 A per at%Mg [77], producing in the case of 18at% of magnesium an increase of the lattice constant of about 3%, with a correspondent shift of the gap of about 0.1 eV towards higher binding energy.One more quantity influenced by the alloying process is the work function $. This affects the surface state binding energy, as predicted by Smith [74], with calculations made within the phase accumulation model framework and observed by Neuhold and Horn [78] in the case of Ag. The change in this case was ^20% of the work function change. In our case the work function of Mg and Al is 3.6 eV and 4.2 eV respectively, so, at maximum a change

' rMg = 2.6, rg'= 2.07. rs changes depending on the concentration of the alloy and then changes the lattice constant, in fact, the value of rs is approximately the value of the interatomic spacing in nearest-neighbour pairs.


of 0.6 eV is possible leading to at maximum a shift of ~ 0.1 eV. In the case of c=0.18, and assuming a linear change of the work function with Mg concentration the shift should be about 20 meV.All these considerations are in agreement with our results and may explain some discrepancy between the VGA predictions (without considering other effects) and the experimental observations.

Photoemission spectroscopy is particularly useful in studying the dispersion E(k) of the bulk and surface bands, when applied in the angle resolved mode. By recording spectra at various emission angles it is possible to obtain the dispersion making use of the relation between k and the emission angle 6e:

|k||| = sing • ^m^2km. (5.8)

Fig.5.11(a) shows a collection of spectra taken with hu= 13 eV at various

AI-15at%Mg/Si(111)

28 ML

Binding energy (eV)

-0.5 0.0 0.5 1.0kpar(1/A)

Figure 5.11: (a) Photoemission spectra taken at various emission angles of the 15at% Mg alloy, (b) Gray scale intensity plot of the 15at% Mg alloy. The lines represent the parabolic fit. The values of m*/me are also reported.

emission angles on a 28 ML thick him of a Al-15at%Mg alloy. It is obvious that the seven peaks, present in normal emission, disperse with emission angle. The same spectra are also presented in a gray scale representation,


where the second derivative of the photoemission intensity is plotted (Fig. 5.11(b)). In this figure the brightest points correspond to the peaks; in this way it is easier to follow the peaks in the first BZ up to ~1.1 A-1. Also presented are the parabolic fits of the in-plane dispersion of the surface state and the QWS, which visibly present a parabolic dispersion and can be therefore characterized in terms of an effective mass m* where Eb = .The result of the fit for the surface state gives a value of me=1.21. This value is similar to the value obtained for a 23 ML thick film of Al/Si(111) [64] showing that the introduction of Mg atoms in the Al array does not affect the scattering process because the film is made by a large ordered Al-rich phase, which gives rise to the QWS. The values of the effective masses for the dispersion of the QWS decrease in going towards the Fermi edge from m* = 1.13me to m* = 0.92me.

Intermediate composition alloys

In the intermediate concentration, 0.32< c <0.55 there is another problem to deal with, given by the instability of the structure in this composition range. In the bulk, at ~38at%Mg there is the transition to the 3 phase, at ~42at%Mg to the 3' phase and at ~55at%Mg the 7 phase. Fig. 5.12 shows

hv=13 eV

Mg (%)34 ML

16 ML

15.5 Ml

Binding energy (eV)

Figure 5.12: Photoemission spectra taken at normal emission of alloys with intermediate composition.


I'2

Figure 5.13: Gray scale direct intensity "3 plot of the 45 at % Mg alloy. The number is the m*/me values obtained by the "4

parabolic fit (black line). At higher binding energy a peak dispersing with NFE character is observed.

spectra, of alloys in the range 32-47a,t%Mg for various thicknesses and preparation procedures. These three spectra look very different, and especially the one for the Al-32at%Mg is very complicated. As in the other alloys, all the peaks are stationary with photon energy (not shown). In the case of the Al-32a.t%Mg, the spectrum is made up of an overlap of two different features, one of which gives the more intense peaks at -4.35 eV, -2.6 eV and -1.1 eV, while the other one gives the broader and less intense peaks at -3.5 eV, -2 eV and -0.5 eV. Also in the spectrum from the 37a.t%Mg there is a similarity with the first one: in this case the peaks are located at -3.95 eV, -2.45 eV, and -0.9 eV, and at -3.26 eV, -1.7 eV, but in this case all have similar intensity. The him of the Al-32at%Mg alloy has been obtained after a deposition of about 15 ML at 100K and subsequent annealing to RT, while for annealing at lower temperatures the him presented only broader features (not shown). The 45a.t%Mg alloy has a large peak at -2.45 eV. This spectrum has been also obtained just after a prolonged annealing at room temperature, with a broad feature at lower temperature. This seems to be typical of the alloys in this range of composition.As is clear from Fig. 5.12, a shift of the surface state with respect to the Fermi level is produced by the alloying process. This shift, due to the decrease of the density of states, should give the values 5Ej?=1.33, 1.55 and 1.9 eV, for the three alloys with 32a.t%, 37a.t% and 45a.t%Mg4, respectively. However, the apparent surface state shifts in these three cases are: 0.4, 0.5 and 2 eV, and therefore much less than the predicted ones, with the exception of the Al-45at%Mg alloy. This means that in this region of the phase

" In the case of 32at%Mg and 37at%Mg the shift is referred to the first set of peaks, being more intense, while for the 45at%Mg, the reference is the large peak.


diagram, the VCA cannot be used in its simple formulation.For the alloys considered here phase separation occurs, and both phases contribute to the spectra. This happens clearly in Al-32at%Mg and Al- 37at%Mg, giving rise to two sets of peaks which are very near to one another and have comparable intensity. But this happens also in Al-45at%Mg, where the two sets of peaks are more distant (in binding energy) and have different photoemission intensity, as can be seen in Fig. 5.13 where at about 4.4 eV a peak is dispersing with NFE, which also comes from a different alloy phase.It is therefore clear that in this range of alloy composition, the separation of phases is very efficient and both alloy phases contribute to the photoemission spectra, and both present band discretization and a surface state. It has to be noted that, if the two phases are connected, the Fermi level has to be the same, and is determined by the average of the charge density present in the two phases, although every phase has a different charge density because of the different composition. The fact that we observe surface states with different binding energy tells us that the thin film has patches of different alloy phases which behave as independent systems. The formation of unconnected phases is reasonable if we observe that the order and formation of discrete electronic bands is obtained only after an anneal at relatively high temperature. The intensity of the two sets of peaks is related to the lateral extension of the patches; by increasing the Mg content in the alloy, the peaks from the phase with more Mg (with peaks at lower binding energy) become more intense.

Mg-rich alloys

An example of a Mg-rich alloy is given in Fig. 5.14(a) where the growth of a Al-71at%Mg alloy is shown. The photoemission spectra are dominated by a broad peak at about 1.5 eV. The variation of photon energy does not affect the binding energy of this feature, making clear that it has a localized nature (see Fig. 5.14(b)). Also for this composition the prediction of the rigid band model can be tested by comparing the Fermi edge shift with the shift of the surface state with respect to the Fermi edge. The 5E_p is in this case 3.1 eV, predicting a surface state at about 1.55 eV, very near to the position of the broad peak in Fig. 5.14. The presence of a broad peak is

5.5 Collective excitations in simple metals and alloys 79

AI-71at%Mg/Si(111 AI-71at%Mg/Si(111

200K

Binding energy (eV) Binding energy (eV)

Figure 5.14: (a) Photoemission spectra taken at 10 eV of as deposited (dotted lines) film and after annealing (continous lines). (b) Spectra taken at various photon energies show the localized character of the peak.

likely to be the result of the two phases present in this range, which are the 7-AlMg with fcc structure and the hcp Mg-rich phase (see phase diagram). It is clear that these phases are more disordered than the Al-rich ones and therefore, the band discretization is not efficient. From this point of view, the Mg-rich alloys are less interesting. Moreover, upon increasing the Mg content, the VCA should not work anymore because of the transition to the hcp structure. In fact, the value of the surface state energy in pure magnesium is 1.65 eV [65], higher than that found in the Al-71at%Mg alloy. The broadness of the peak we have found could, therefore, be due to the existence of two narrower peaks, one due to the hcp phase with high Mg content and one with less magnesium and with a fcc structure.

5.5 Collective excitations in simple metals and al

loys

In the previous sections it has been shown that the Al-Mg alloy results in nearly free electron (NFE) systems with an average charge density and average properties over a wide range of composition. For these systems it is,


therefore, possible to refer to the jellium model to describe many electronic properties. The basic idea of the jellium model is that the lattice of positive ionic charges is replaced by a semi-infinite uniform background:

n+(z) = n#(—z), (5.9)

where 6(z > 0)=1 and 6(z < 0)=0 and the only free parameter is n, or equivalently, the average electron radius rS introduced in the previous sections.Among other important properties, the jellium model can be used to explain the electronic response of a metal to an incident electromagnetic field. This is a many-body effect and is due to collective excitations, where the electrons behave as a plasma, oscillating with the plasmon frequency wp. The dielectric function e(w), which describes the electronic response to the external field with frequency w, has the form e(w) = 1 — (wp/w2). The plasmon frequency in an infinite metal in the Drude model depends on the bulk charge density n, through:

Wp —4^ne2 (5.10)

Apart from the bulk plasmon excitation, the existence of a surface in a real solid introduces collective excitations due to the charges present at the surface. These are very important not only from a theoretical point of view, but also for a comprehensive understanding and the correct interpretation of all surface spectroscopies that use electromagnetic fields or charged particles. In fact, a very strong modification of both photoemission line shape and intensity has been found in various metals near their bulk plasmon frequency, which has been explained by the excitation of collective modes at the metal surface [79].The explanation of this behaviour is related to the form of the matrix element in the photoemission process that has been introduced in the second section of this thesis. In fact, if the spatial variations of the photon field V • A are neglected, the matrix element Mj in the Fermi’s golden rule:

;(R,2,Aw) x ^]|( $^|A • p + p • A|$i)|2d(# — Aw — 2/) (5.11)ioccup

can be assumed to be:

Mij x Ao(^/ |VV|^) (5.12)


where V is the potential felt by the electrons. For photon energies commonly used in a photoemission experiment, for example 20 eV, the wavelength is 50 nm, i.e. large compared to the atomic distances, and the assumption V • A—0 is correct. However, for photon energies near the collective excitations the response of the metal electron to the electromagnetic field cannot be neglected, since it causes the fluctuation of the charge density in the surface region, leading to strong variations of the vector potential A. Hence the initial assumption becomes V • A =0, and the exact solution of the equation (5.11) requires a calculation of the effective electromagnetic field in this region. The theoretical and experimental proof of the importance of the response to the incident field has been given by Levinson et al. [80], who observed a strong enhancement of the photoyield at about 0.8 wp and attributed it to the V • A term on the basis of self-consistent field calculations within the random-phase-approximation (RPA).In classical terms, the solid, represented by the frequency dependent dielectric constant e(w), is separated from the vacuum by an infinitely sharp boundary. Maxwell’ s equations give a continuous radiation field in the direction parallel to the surface and a discontinuity of the perpendicular component of the transverse field when e(w) = 1.The resulting charge density n is described by a delta function sheet in the surface plane n(r,w) = elq\rW^(z,^'> where q|| is the wave vector parallel to the surface. This fluctuating surface charge has dipolar character along the plane of the surface because the metal surface remains neutral. Hence the resulting electric field varies continuously in the direction parallel to the surface and has a discontinuity in the direction perpendicular to the surface: Ez(z = 0^) « %.Considering the vacuum described by a dielectric constant eo=1, the discontinuity of the electric field can be written as e(w)Ez(0_) = Ez(0+), which implies e(w)=-1. As mentioned above, the Drude model of an infinite metal gives e(w) = 1 — (wp/w2), so, considering the abrupt boundary with the vacuum, a surface plasmon results whose frequency ws = wp/\f2, is dependent on the bulk property wp (and is hence not a surface property).This result, derived from the assumption of an abrupt charge density profile, is certainly far from being realistic. Bennett [81] attempted to take into account a charge distribution across the surface, and calculated the electronic response to a linearly decreasing charge density through a surface


region from the bulk value to zero, using a simple hydrodynamic model. For a sufficiently diffuse electron charge at the surface, he observed additional plasmon modes.Contrarily to the “classical” surface excitation, which is monopolar (i.e. the charge distribution has a simple peak in the direction z) the new modes have multipole character and have a frequency between those of the surface and the bulk plasmon. It is easy to imagine that the next step for obtaining more complex plasmon modes is to describe the charge density profile at the surface of a metal in a better way, and this means to use the ground-state charge distribution of a jellium-like surface calculated by Lang and Kohn [82] within the local density approximation (LDA).Here, because of the sharp cutoff of the electronic wave vector at the Fermi surface, the charge density presents decaying Friedel oscillations in the bulk side with wavelength n/kF =1.64 rS. On the vacuum side, the charge density has the form:

n(z) cos(2kF z + a) ^nz (5.13)

where a and a depend on the shape of the surface potential [82]. Also here the actual profile depends on the parameter rS through the kF value. In Fig. 5.15(a) the LDA profiles for two rS values are shown.It should be also noted that the classical field, due to the charge density

induced by the external electromagnetic field, does not consider the effect of the dynamical screening due to the charge near the surface. The fields in the vicinity of the surface have to be calculated self-consistently by taking the response of the electron density into account. The single particle wavefunctions for the ground state description of the solid are used, and the many-body screening aspects of the response are put into an “effective” field [83],[84].Hence, due to the dynamical screening of the external field, the surface electromagnetic field varies rapidly and deviates appreciably from the classical Fresnel field, as shown schematically in Fig. 5.15(b), where the dashed line indicates the classical (Fresnel) field and the solid curve indicates the microscopic field. Beyond zi and z2 are the asymptotic regions where the classical description is adequate. The main feature of the microscopic surface field is the smooth variation between bulk and vacuum, and the displacement of the effective surface [84]. This dielectric response is a manifestation of


Positivebackground,

p forr,= 2

Distance z (Fermi wavelengths)

b)

2 screened^’

Fresnel,

Figure 5.15: (a) Ground-state charge distribution obtained by Lang and Kohn for jellium- like surfaces with two different values of 13. (b) Comparison of the Fresnel and themicroscopic held (from ref. [84]).

many-body effects, leading to the large differences between the screened field and the incident field. The oscillations of the charge profile at the surface set up longitudinal fields. The field enhancement is connected with the new collective mode of the electron gas at the surface. This is the mode predicted by Bennett [81] for the linear charge profile (see Fig. 5.16(a)).For a metal-adlayer system, Inglesfeld and Wikborg [85] found a charge density profile resembling that described in Fig. 5.15(a) for a clean metal surface, obtaining, within the RPA framework, a surface multipole excitation. More recently, the understanding of collective excitations on both clean metal surfaces and alkali adlayers has made great progress, by introducing the study of such systems within the jellium based time dependent local density approximation (TDLDA) [86],[87].In this way, Liebsch found the existence of an adlayer multipole plasmon which is related to the formation of a well-defined charge density plateau corresponding to the alkali-metal adlayer. This new feature has been identified with a bulk-like plasma oscillation but is not present in the bulk samples. It is rather similar to a surface plasmon and is due to the confinement of the charge along the direction normal to the film growth, for this reason and because of the smoothness of the charge variation through the interface, the frequency of this plasmon is slightly different from the bulk plasmon. The


Figure 5.16: (a) Representation of the multipole plasmon made by Inglesfeld and Wikborg with a linear charge-density profile. (b) TDLDA calculations of the charge induced in a 2 ML Li/Al film. For this thickness the bulk-like plasmon is stronger than the multipole. By increasing the thickness, the confinement of charge in the bulk-like plasmon is less efficient and it becomes weaker. From this picture it can be noted the localized nature of the multipole plasmon.

a)model charge density

used to derive the field-induced charge

/ positive background

oscillatory part of surface and monopole plasmon

parallel to surfacecharge spill-out

monopole (surface) plasmonmulti pole

plasmon ©m

b)field-induced charge

bulk-like plasmonsubstrateLi overlayer

multipole plasmon

Li layer

field induced charge density for a 2 ML thin Li him on A1 substrate is shown in Fig. 5.16(b), for both multipole and bulk-like plasmon.Since the thin films exhibit both the multipole surface and the bulk-like plasmon excitation, one can examine the relative strength of these excitations and the influence of the him and the substrate on these modes. Thin films of alkali metals like Na, Iv, and Li deposited on A1 have been object of many of such studies, where the changes in frequency, full width at half maximum (FWHM), and intensity of the alkali collective excitations as a function of smooth adlayer coverage are investigated [88] by means of photoemission spectroscopy.


Figure 5.17: Beamline photoyields obtained by measuring the photo-current on a Ga.AsP diode, with two different gratings. The flux is then normalized by the diode photoyield and by the ring current to take into account also its natural decreasing with time.

5.5.1 Experimental results: CIS spectroscopy

Photoemission spectroscopy is capable to detect both the bulk-like (in thin films) and the multipole plasmons, while bulk and surface plasmons at q=0

cannot be excited by the electromagnetic waves, because of their monopolar character. This gives a great advantage for detecting the multipole and bulk-like plasmons because the spectra are not overloaded by the real bulk and surface plasmons, as happens in the case of Electron Energy Loss Spectroscopy (EELS). In order to measure the yield of photoelectrons as a function of photon energy, the Constant Initial State (CIS) mode is used, meaning that both the photon energy and the analyzer energy are moved in parallel so that the signal is always taken from the same initial state. In all the following CIS spectra, states near the Fermi level (about -0.3 eV binding energy) have been chosen.The spectra are then normalized by the beamline flux curve that depends on the monochromator characteristics and can be obtained in two ways: by measuring the photocurrent on the last mirror of the beamline or by introducing a photodiode between the last mirror of the beamline and the sample, measuring in this way the beamline flux. The first case allows us to measure the CIS spectrum and normalizing flux at the same time, on the other hand, the use of the photodiode resulted in a more efficient method, giving a precise beamline photoyield.

• 2400 l/mm + 600 l/mm

/V

\AV

10 12 14 16Photon energy (eV)


15MLAI(111 )/Si(111)100-

10 11 12 13 14 15 16 17 18 19 20photon energy (eV)

Figure 5.18: CIS spectra of a 18 ML and a 15 ML thin film of Al/Si(lll) measured on two different beamlines: 3m-NIM (open circles) and lm-Seya Namioka (dots, from ref. [64]). The different monochromators used in the two experiments are responsible for the different shape of the spectra. In fact, the peaks observed in the 3m-NIM spectrum at about 10 and 12 eV are due to the normalization.

In Fig. 5.17 we show the beamline photoyield after normalization with the flux obtained from the GaAsP diode, for two different gratings. As is clear from the plot, the 3m-NIM monochromator has a very complex photoyield with intense maxima and deep minima in the energy range where plasmons are expected for our system. This means that the shape of the beamline photoyield can introduce unphysical features in the measurement of the CIS spectra. To check this possibility we measured the CIS spectra for the pure Al/Si system and compared it with previous measurements.In Fig. 5.18 we report two spectra of a 15 ML Al/Si( 111) thin film. Our spectrum, measured on the 3m-NIM beamline with the 2400 1/mm grating, has four peaks at ~10 eV, 12.4 eV, 13 eV and 14.1 eV. The reference spectrum has been measured on the lm-Seya Namioka beamline at Bessy I (from ref. [64]) and has two peaks at 13.1 eV and 14.4 eV, assigned to the adlayer multipole surface plasmon and bulk-like plasmon, respectively. Hence it is clear that the normalization introduces artifacts in the spectra.This is very important when the expected plasmon peaks have lower energy, like in the case of Mg. In fact, magnesium has a lower charge density than aluminum and has therefore a lower plasmon energy, i.e. 11 eV [1]. The multipole surface plasmon is expected at ~9 eV, in the spectrum region where the monochromator introduces a systematic error. This is evident in


Figure 5.19: CIS spectrum of a 27 ML thin film of Mg/Si(111). The bulk-like (wp) and the multipole (wm) plasmon are respectively at ~11 eV and ~9.5 eV. In this spectrum they are very weak shoulder of the more intense peak at 8.5 eV due to the normalization.

|0 5x1012

T5

to

1S'CO

I0

8 10 12 14 16 18

Photon energy (eV)

Figure 5.20: Photoyield of twoMg/Si(111) thin films, measured on the 3m-NIM beamline with the 600 l/mm grating. The relative intensity of the two plasmons depends strongly on the thickness of the film, because the bulk-like plasmon (wp) depends on the confinement of the charge in the thin film.

6 8 10 12 14Photon energy (eV)

Fig. 5.19 where a 27 ML Mg/Si(111) thin film is shown.To overcome the problem of flux normalization on the 3m-NIM beamline, we have performed the same experiments on another beamline, the TGM-4 for which the toroidal grating monochromator offers a more regular photoyield in the energy range of interest. Although the lowest photon energy that can be reached with the TGM-4 monochromator is only 10 eV, for the purpose of studying the collective excitation the use of this monochromator has been preferred because in the energy range between 10 eV and 15 eV the monochromator has a monotonous photoyield.As seen from the ARUPS experiments, alloy formation leads to the variation of the charge density of the system, with consequences on the surface state


and the quantum well states position. Also the bulk plasmon frequency depends on the averaged value of the charge density (see equation (5.10)). Thus, alloys with different charge density values may present distinct collective excitations in the photon energy range between the plasmon frequencies of magnesium ^Mg and aluminum uai.In addition, analyzing the relative intensity of the multipole and the bulklike plasmon in CIS spectra, it is possible to obtain informations on the nature of these collective excitations, especially when comparing thin films of different thickness, like in Fig. 5.20. As it is clear, the relative intensity is strongly dependent on the thickness and the ratio between the bulk-like and the multipole plasmon decreases as the thickness increases.To understand the reasons for this behaviour, one has to consider that the multipole surface plasmon is given by the charge density at the surface and it depends on the screening property of the surface electrons only, i.e. it is localized on the surface. On the contrary, the bulk-like plasmon is due to the confinement of the charge in the entire thin film and it has a more delocalized nature (see Fig. 5.16(b)). The latter excitation is, therefore, very important for very thin films, where the confinement is on a small region, and its intensity decreases for thicker films.By simulating the experimental CIS spectra of Al-13at%Mg/Si(111) thin films of Fig. 5.21(a), with two Voigt functions, corresponding to the bulk and the multipole plasmons, and a flat background, using a least-square minimization routine, it is possible to follow the Ap/Am ratio as a function of film thickness (shown in Fig. 5.21(c)).

Although no theoretical calculations exist on the line shape variation of the photon-excited adlayer plasmons, we used the Voigt function because it gave better fits than either a purely Gaussian or a Lorentzian function and because it has been successfully used in other experimental studies [88]. Both Lorentzian and Gaussian components of the Voigt function line-width were varied during the fitting. A representative fit for the 7 ML thick film is shown in Fig. 5.21(b).While the bulk-like plasmon is described by a narrow Voigt function (with a FWHM«0.6 eV), the multipole plasmon has a very broad line shape with a FWHMw1.2 eV. This result is not new in free-electron-metal adlayers, in fact, Barman et al. found a similar behaviour in the case of Li/Al, K/Al and Na/Al [88] for film thicknesses larger than 6 ML.


10 12 14 16 18Photon energy (eV)

Photon energy (eV)

< 5

-14.5-

0)13.5-

Film thickness (ML)

Figure 5.21: (a) Photoyield of four Al-13at%Mg/Si(lll) thin films. The CIS spectra have been measured at the TGM-4 beamline, and normalized with the synchrotron ring current. By increasing the film thickness the CIS line shape changes with a decreasing of the up component, which is shifted as well, and a relative increasing of the um component, (b) CIS spectrum of the 7 ML thin film fitted with two Voigt functions, (c) Peak positions and ratio of areas of the multipole and bulk-like plasmon component as a function of film thickness.

The reason of the narrow bulk-like plasmon is that this mode may couple with the smooth adlayer-vacuum interface and, for relatively thick films, very weakly with the adlayer-substrate interface, with a correspondent reduction of the possible decay channels. The multipole plasmon couples with the excitations localized at the surface and, due to the high degree of localization, presents an enhanced decay with the consequent broad peak.The Al-Mg/Si system is more complex than the alkali/Al systems studied


IFigure 5.22: Photoyield of three alloy thin films, measured on the ® TGM-4 beamline. The bulk-like — plasmon (up) is present in all three spectra, while the multipole plasmon (uj,n) is not distinguishable in the 40at%Mg alloy because the film is very thin and the bulk-like plasmon is very strong. In the pure Mg film the multipole plasmon is out of energy range of this monochromator.

+ pure Mg/Si O 40at%Mg alloy/Si A 17at%Mg alloy/Si

14Photon energy (eV)

by Barman et al., because the Al-Mg alloy has a single phase only in a restricted region of the phase diagram. When the thin him is formed by two phases, a double feature, similar to what is observed in angular resolved energy distribution curve (EDC) spectra, is present, making the width of the Voigt function broader.This is shown in Fig. 5.22, where CIS spectra from alloys with different composition are plotted. The spectrum of the 17at%Mg alloy presents two peaks easily distinguishable, at ~14.3 eV and ~13 eV; for the 40at%Mg alloy, the main peak is at ~ 13.4 eV and for the pure Mg him, the bulk-like peak is at about 10.6 eV.From average charge density considerations, it is possible to obtain an estimate of the bulk plasmon energy. In fact, considering the charge density nAl-Mg = n.41 • (1 — c) + iiMg -(c), where c represents the Mg atomic content in the alloy, and considering the dependence of up on the charge density (5.10), we obtain in the two cases reported in Fig. 5.22, ujp7%= 14.5 eV and ajp0%= 13.6 eV, in very good agreement with the experimental result.In the latter case the line shape on the high photon energy side is very different from that of a 17at%Mg alloy, showing that the peak is broader and eventually composed of two peaks corresponding to the two alloy phases.

5.6 Conclusions 91

This is not the case with the 17at%Mg alloy, where only one phase is present, as observed in ARUPS experiments. The peak at ~13 eV is due to and has a ratio wm/wp=0.91.The ratio um/up for free-electron-metals has values similar to 0.8 independently of the charge density and the surface [88]. The reason for this dependence is still not clear but a large body of available literature shows this coupling with a ratio varying between 0.8 and 0.89, making it an empirical result. Anyway, the um/up ratio from our data is higher (0.9-0.93) than those found for the alkali adlayers and this could be due to the reduction of wp by the core polarization effect. The multipole plasmon, on the other hand, is localized on the surface and it is therefore less influenced by the core polarization effect.Another feature, observable from Fig. 5.21(b), is that the bulk-like plasmon shifts towards lower energy. This is related to the dispersion of the bulk plasmon with wave vector q and in particular with the existence of higher- order modes of the bulk plasmon, that have been predicted theoretically [89] to have a wavelength A^ = 2a/n, where n is an odd positive number and a is the thickness of the layer, and to follow a quadratic dispersion given by

Wp(q) = Wp + aq2, (5.14)

where a=0.6ep/up. Thus, with increasing thickness of the adlayer, the wavelength of the higher plasmon modes increases, resulting in the redshift observed in our spectra. The multipole plasmon has also a redshift with increasing thickness, and this is associated with the dependence of onWp.

5.6 Conclusions

We have studied thin films of Al-Mg alloys over a wide range of composition, obtained by co-depositing aluminum and magnesium on a Si(111) substrate at low temperature. The alloying process gives rise to ordered epitaxial films for the Al-rich alloys (up to 30at%Mg) and two ordered alloy phases for higher magnesium contents. These ordered systems form a surface state and discretization of the s-p bulk band due to electronic confinement, as revealed by QWS in the photoemission spectra. The binding energies of both the surface and quantum well states depend on the alloy composition.


i ’Surface state position'

--------VGA

0 20 40 60 80 100

Atomic Mg (%)

Figure 5.23: Surface state experimental binding energy (squares) as a function of the alloy composition and VCA prediction (continuous line). The prediction and the experimental data are in good agreement in most part of the phase diagram, with the exception of the alloys with composition 32-45 at%Mg, where two phases with distinct Mg content are formed. For Mg-rich alloys, the VCA is not valid, because of the different atomic structure.

The interpretation of the observed behaviour was done on the basis of the virtual crystal approximation which predicts a continuous decreasing of the charge density by increasing the Mg content in the alloy. In Fig. 5.23 we summarize the experimental data and the VCA prediction for the surface state binding energy. As is clear, the binding energy very closely follows the VCA prediction, with the only exception in the intermediate alloy compositions, where the phase separation leads to two peaks, one at higher binding energy and the other one at lower binding energy, similar to the predicted one. The alloys with higher Mg content form a surface state, although the relative phases should be very disordered. Their binding energy is also very close to that predicted by the VCA, showing that this is related only to the alloy composition. These results indicate a strong similarity with the behaviour of Al-doped MgB2 and show that the electronic properties of these materials can be tailored by the actual composition in a relatively smooth way.The study of collective excitations in these alloys reveals also an interesting behaviour of both bulk-like and surface plasmons, with a direct proportionality of plasmon energy to the actual composition of the alloys. This is in agreement with the nature of both excitations where their behaviour is dominated by the charge profile in the surface region and at the interface and therefore, is strongly related with the rS value of the system. Anyway, the

5.6 Conclusions 93

existence of two alloy phases in thin films of particular compositions results in broad peaks where two components are present.

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