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Phys 48W

Physics and Chemistry at Surfaces

An electronic course offered at the Physics Department of theBogazici University to 4th-year and Masters-Degree students

Mehmet Erbudak

Physics Department, Bogazici University

and

Laboratorium fur Festkorperphysik, ETHZ, CH-8093 Zurich

[email protected]

[email protected]

February 2013

Phys 48W

Physics and Chemistry at Surfaces

2013 Spring Semester

An electronic course offered for the Bachelor- and Masters-degree students

Mehmet Erbudak

Physics Department, Bogazici University

[email protected]

and

Laboratorium fur Festkorperphysik, ETHZ, CH-8093 Zurich

[email protected]

Several different phenomena are observed at surfaces that do not have a counterpart

in bulk materials. Corrosion, epitaxial growth, heterogenous catalysis, or tribology

are just few of these. While all bulk processes can be accounted for on equal footing

owing to the universal description of electronic states, at surfaces symmetry is

broken, and we need to redefine the electronic and crystal structure. In this course,

we first study the geometric structure of the bulk and the surface. Then we deal

with the electronic structure and describe the magnetic ordering. The chapter on

magnetism is a valuable contribution from Prof. Danilo Pescia, ETH in Zurich. A

chemical analysis is part of the complete characterization of surfaces. We realize

that the atomic structure, the electronic properties, and the chemistry of surfaces

are all interrelated. During the course we get acquainted with the appropriate

experimental tools to observe surface-specific processes.

Every week, students obtain the script for the week, the exercises, and a short

video clip summerizing the material. During the semester, I plan to be present for

a few lectures personally and during the exam at the end of the semester.

Prerequisite: Modern Physics or Physical Chemistry

i

Preamble

I will place the learning material as well as exercises to your disposal in internet

in the pdf format every week. The learning material is planned to occupy your

attention during about 3 hours per week to justify the 3 credit hours. I will men-

tion to you some books as supporting material if needed, and will present relevant

publications. With some basic knowledge on Quantum Mechanics and Solid State

Physics , I assume you will appreciate the presented material as an introduction

to several directions of Surface Physics and Chemistry as well as modern Materi-

als Science. Similarly, the concepts you will be introduced correspond to those of

low-dimensional phenomena. Thus, this course is thought to be as an introduction

to your future research in many fields. I will mostly emphasize the experimental

achievements. For any question please do consult me per mail.

The presented material may be too extensive. My intention is to trigger your

interest on this subject. Interest and curiosity are required for innovative research

and progress. In the following you will find a comprehensive introduction followed

by chapters on the atomic structure of the bulk and the surface as well as their

determination. The following chapters are devoted to the electronic structure and

magnetism, likewise of the bulk and the surface. Last two chapters deal with

techniques used in determination of chemical composition and adsorption of foreign

atoms on the surface as well as their behavior. I appreciate any suggestions or

corrections on this material.

I suggest you follow some professional journals, such as Surface Science, Physical

Review Letters , Science, or Nature, and recommend few books as reading material:

AZ - A. Zangwill, Physics at Surfaces, Cambridge University Press, New York,

1988.

WD - D.P. Woodruff and T.A. Decker, Modern Techniques of Surface Science,

Cambridge University Press, New York, 1994.

EK - G. Ertl and J. Kuppers, Low-Energy Electrons and Surface Chemistry, Verlag

Chemie, Weinheim, 1974.

JSB - J.S. Blakemore, Solid State Physics , W.B. Sounders Co., Philadelphia, 1974.

CK - C. Kittel, Introduction to Solid State Physics , John Wiley, New York, 1966.

AM - N.W. Ashcroft and N.D. Mermin, Solid State Physics , Saunders College

Publishing, Fort Worth, 1976.

I hope you will find the course useful and enjoy it!

ii

Chapter 1

Introduction: Why surfaces?

The majority of processes, that played a crucial role in the development of our tech-

nological society, is based on physical and chemical properties of surfaces. Catalyt-

ical reactions and semiconductor (SC) structures are the most important examples.

A pertinent question is whether we can describe the elementary surface processes

of model catalysts on atomic scale and during the chemical reaction. Can we un-

derstand the basics of SC technology on microscopic scale? In all these issues, our

goal is the insight into the connection between the microscopic properties of matter

and its macroscopic behavior. What are the relevant concepts that help us reach

this goal?

The last few atomic layers of a solid constitute the interface with its environ-

ment. On this interface, there is a multiple of atomic and molecular processes that

take place in the quasi two-dimensional (2DIM) stage. These processes are the basis

of our present-day technology. For example, without a detailed knowledge in the

production of SC devices, no progress could have been achieved in the information

and telecommunication technology. We also have access to nanostructured materi-

als with extraordinary functional properties, such as SC quantum dots and carbon

nanotubes. We have a growing understanding of how these structural features con-

trol the electronic properties. Throughout the years we have learned and mastered

the crystal growth. A real revolution was the invention of epitaxy. It allows the

fabrication of almost any material at will and makes possible the creation of any

alloy in 2DIM which otherwise does not exist according to the 3DIM phase diagram.

Most of the chemical reactions take place at the surface and heterogeneous catalysis

is a surface reaction, while the catalytic substance does not take part in the reac-

tion. A Ni-Fe-Cr alloy is called stainless steel because of its resistance to oxidation

and corrosion. In fact, owing to adsorption-induced segregation, Cr diffuses to the

surface and binds to oxygen forming a thin oxide layer. The cromiumoxide cover at

the surface of the alloy acts as a protection and prevents further oxidation. Similar

surface passivation processes are successfully used in SC devices, like an atomic

layer of Gd2O3 on a GaAs surface. Internal diffusion of impurities to the surface

results in segregation. In the worst case the grain boundary segregation of sulfur in

1

CHAPTER 1. INTRODUCTION: WHY SURFACES? 2

stainless steel is responsible for its brittleness. We lose so much energy due to the

friction, yet without friction we cannot even walk. Tribology deals with this surface

effect.

The atoms of the bulk material are arranged in a symmetrical way. This sym-

metry allows many simplifications. The ion cores constitute a periodic potential.

Under its influence the electrons of the material can be described as Bloch waves.

There is a universal behavior of the bulk owing to the symmetry in all the phase

transitions such that we can speak of universality. At the surface the symmetry

is broken, no regularities can be found analogous to the bulk. The 3DIM phase

diagram cannot be applied. Any observation has to be dealt with separately. These

points are in fact responsible why Surface Physics or Surface Chemistry have ad-

vanced not before the last 50 years.

I will now mention some processes specific of the surface.

1.1 Surface Processes

At a general surface, physical and chemical modifications can take place not known

of for the bulk.

Figure 1.1: When a SC crystal is cleaved the top atomic layer may relax

by x in either direction, as seen in the panel on the right-hand side.

One can cleave a SC perpendicular to a crystallographic direction and expose a

surface for which the least amount of bonds are broken. No charge separation takes

place as a result of cleavage. The surface atoms thereby have a reduced coordination

and may react to this change in order to reduce the total energy. The shift normal

to the surface of the top atomic layer is called relaxation as depicted in Fig. 1.1.

If atoms are shifted pairwise lateral to the surface to form surface dimers

the atomic symmetry of the surface will change and the periodicity is doubled

[Fig. 1.2(left)]. This is a simple example for reconstruction. Buckling is illustrated

in the Fig. 1.2(right).


Figure 1.2: (left) The top atomic layer may show reconstruction or (right) buckling.

There may also occur chemical modifications at a general surface. Foreign atoms

may arrive at the surface and stick to it. Consider the potential formed between

the foreign atom, the adsorbate, and the surface, the substrate, shown in (Fig. 1.3).

In the case of physisorption there is a weak binding between the adsorbate and

the substrate, as is in the noble-gas adsorption on surfaces or adsorption of gases

on noble-metal surfaces. By a moderate heating the foreign atoms will be desorbed .

The binding is strong for chemisorption, while the adsorbates are trapped by the

strong attractive potential well (see Fig. 1.3).

Figure 1.3: The potential formed by the adsorbate and the substrate.

In chemisorption there is an electron transfer between the substrate and the

adsorbate, while physisorption is typically formed by some van-der-Waals forces. If

chemisorption proceeds, a new compound, an oxide, can be formed that differs from

the bulk by chemical composition and atomic structure. Also surface segregation

leads to a similar situation. Thus, we need to fully characterize the surface from

scratch for its chemical composition, atomic geometry, and electronic properties.


1.2 Surface-Induced Chemical Reactions

In a heterogenous catalysis, the catalyzer does not take part in the reaction, it

just triggers the reaction. It provides the electron wave functions with the required

symmetry in order to combine the reaction components. An extremely important

example is the Haber-Bosch reaction for the synthesis of ammonia which dates back

to a time prior to the advent of surface physics or chemistry. It is an exothermal

reaction:

3H2 + N2 −→ 2NH3 + 22.1 kcal. (1.1)

We need small Fe crystals for the reaction to proceed at 200 atu and 475−600 C.

This reaction is used to produce artificial fertilizer without which a great proportion

of mankind would have starved during the 20. century. Fritz Haber received the

Nobel Prize in 1918 for his achievement and Carl Bosch in 1931. The microscopic

description of the reaction came as late as in 1975 by Gerhard Ertl. He is a surface

physicist from Munich and could explain the process with proper wave functions

upon which he received a professorship in Berlin at the Fritz-Haber-Institute. Later

he was awarded with the Nobel Prize 2007 in Chemistry.

Similarly, Fischer-Tropsch synthesis, is a collection of chemical reactions that

converts a mixture of carbon monoxide and hydrogen into liquid hydrocarbons.

The process produces synthetic fuel typically by burning low-cost coal, natural gas,

or biomass.

(2n+ 1)H2 + nCO −→ CnH(2n+2) + nH2O (1.2)

The Fischer-Tropsch process operates in the temperature range of 150−300 C and

uses Ni or Co catalysts. A modern treatment of heterogenous catalysis is given by

Rupprechter.1

1.3 Epitaxy

The thermodynamics of 3DIM structures are governed by their phase diagram.

This limitation does not apply to 2DIM systems, and therefore a wealth of different

materials can be fabricated at the surface with tailored properties. The growth

method is called epitaxy (epi = ‘top’ and taxis = ‘order’ in Greek).

Figure 1.4: (left) Wetting of the surface by the adsorbate and (right)

island formation.

1G. Rupprechter, Adv. Catal. 51, 133 (2007).


In epitaxy2 the surface is exposed to a gas, e.g., metal vapor, which condenses on

the surface. This way the surface becomes a contact place between two solids which

is called the interface. The fundamental question in epitaxy is whether the gas

atoms adsorbed on the surface will wet the surface or form islands. Figure 1.4(left)

schematically shows a monoatomic layer of adsorbate. This case occurs as a result

of strong forces between adsorbate and surface atoms at T = 0. This is a typical

case of adhesion. If, on the other hand, the adsorbate-adsorbate interaction is

stronger than adsorbate-surface interactions, island form on the surface which are

termed clusters . Hence, the wetting property of a gas upon a specify surface is the

necessary condition for the epitaxial growth.

Figure 1.5: Schematic illustration of the three epitaxial growth modes. From

R. Kern et al., In Current Topics in Materials Science, ed. E. Kaldis, Vol. 3,

Chapter 3, North-Holland, Amsterdam, 1979.

Epitaxial growth can basically be classifies in three modes, illustrated in Fig. 1.5.

In the simplest case, we may assume that the growth proceeds in a 2DIM fashion,

one layer after the next, up to some required film thickness. This is called layer-

by-layer growth, also termed Frank-Van der Merwe (FV) growth, named after the

investigators first described the process. However, this is not always the case. One

often finds that the deposited material coagulates into clusters which at a stage may

form a polycrystalline layer. This is Volmer-Weber type growth; 3DIM crystallites

form upon deposition and some surface area remains uncovered at the initial stages

of deposition. Stranski-Krastanov (SK) growth is inbetween, few layers may grow

in FV fashion before 3DIM clusters begin to form.

2J.R. Arthur, Surface Sci. 500, 189 (2002).


We can in fact estimate in advance which growth mode is more probably for

a given adsorbate-substrate system. We need to know three macroscopic quanti-

ties, namely the three surface tensions: γa, γi, γs, the free energy per unit area at

the adsorbate-vacuum interface, the adsorbate-substrate interface, and substrate-

vacuum interface, respectively. We expect an ideal wetting of the substrate, FV

growth, for ∆γ = γa + γi − γs < 0, VW growth for ∆γ > 0, and SK growth for

∆γ = 0. For thicker films, γi contains the contribution of the strained adsorbate

layer and therefore depends on the film thickness. This is the case for pseudomorphic

growth.

In epitaxy, atoms or molecules are deposited on the substrate and some struc-

tures evolve as a result of a multitude of processes. This is a non-equilibrium

phenomenon and any growth scenario is governed by the competition between ki-

netics and thermodynamics. Self assembly and self organization are modes through

which desired nanometer-size structures grow on the surface.

Microscopically, the primary mechanism in the growth of surface nanostructures

from adsorbate species is the transport of these species on a flat terrace, involving

random hopping processes at the substrate atomic lattice. This surface diffusion

is thermally activated. This means that diffusion barriers need to be surmounted

when moving from one stable (or metastable) adsorption site to another. The

diffusivity D, which is the mean square distance travelled by an adsorbate per

unit time, obeys an Arrhenius law. If the deposition rate F of atoms in a growth

experiment is kept constant, then the ratio D/F determines the average distance

that an adsorbate species has to travel to meet another adsorbate for nucleation.

Thus, the ratio of D/F is a key parameter characterizing the growth kinetics. If the

deposition is slow (large D/F at the high-temperature limit), growth occurs close to

equilibrium conditions: the adsorbates have sufficient time to explore the potential

energy surface so that the system reaches a minimum energy configuration. If the

deposition is fast (small D/F ), then the pattern of growth is essentially determined

by kinetics; individual processes leading to metastable structures are important.3

SC nanostructures are usually grown at intermediate D/F values and their

morphology is determined by the complex interplay between kinetics and ther-

modynamics. Strain effects are particularly important and can be used to active

mesoscopic ordering.

Low-temperature growth of metal nanostructures on metal surfaces is the pro-

totype of kinetically controlled growth methods. Metal bonds have essentially no

directionality that can be used to direct interatomic interactions. Indeed, kinetic

control provides an elegant way to manipulate the structure and morphology of

metallic nanostructures. On homogenous surfaces, their shape and size are largely

determined by the competition between different displacements the atoms can make

along the surface, such as diffusion on terraces, over and along step edges. Each of

these displacement modes has a characteristic energy barrier, related to the local

3J.V. Barth et al., Nature 437, 671 (2005).


Figure 1.6: Schematic energy band of a SC. The conduction band edge

is Ec and valence band edge is Ev. Analogous to metals, Φ is defined as

E∞ − EF, where EF is the Fermi level.

coordination of the diffusing atom. It is the natural hierarchy of diffusion bar-

riers that determines the details of the growth process. Terrace smoothening by

step-flow growth is one example. Supermolecular self assembly is achieved at the

high-temperature limit close to equilibrium.

Epitaxy is based on the revolutionary ideas of Leo Esaki and Raphael Tsu back

in 1960’s and today it is extensively used in research and development as well as

in technology. The fabrication of superlattice diodes is a prominent example. First

let us look at the energy-level diagram of a SC shown in Fig. 1.6.

It is essential to note that the vertical axis is the energy of electrons. E∞ − Evis called the ionization potential , and E∞−Ec the electron affinity . For an intrinsic

SC, EF is in the middle of the energy gap, Eg.

Superlattices are manufactured by alternate epitaxial deposition of GaAs and

(AlGa)As layers.4 GaAs quantum wells with small band gaps are found successively

between (AlGa)As layers that possess electrons confined in 2DIM, as displayed in

Fig. 1.7. Figure 1.8 shows a cross section observed in transmission electron micro-

scope, TEM, across a laser diode consisting of a superlattice structure.5 Observe

the precision in the production of numerous layers.

1.4 Surface Melting

Surface melting is a classical example for a surface-specific phenomenon. The slip-

periness of ice is widely referred to as premelting , which is the existence of liquid at

4L.J. Challis, Contemp. Phys. 33, 111 (1992).5D.D. Vvedensky, In Low-Dimensional Semiconductor Structures, ed. K. Barnham and D.D.

Vvedensky, CUP, Cambridge, 2008.


Figure 1.7: Energy bands of (a) narrow gap GaAs and (b) large band gap

(AlGa)As. If GaAs is placed between two (AlGa)As layers by molecular

beam epitaxy, a quantum-well structure is created. Ref. [4].

temperatures and pressures below the normal phase boundary.6 The atoms at the

surface are loosely bound compared to those in the bulk. As a result, the amplitude

of surface-atom vibrations is larger and hence the surface softer. There are super-

cooled liquids (like glass), but no superheated solids, possibly because the surface

melts at a lower temperature than the bulk does. In the scientific terminology we

may speak of lower Debye temperature.

We characterize a phase with an appropriate order parameter (OP). In a phase

transition, e.g., solid/liquid, OP is best chosen in such a way that it is zero in one

phase and finite in the other. An abrupt change in OP at the critical temperature,

Tc, is characteristic of a first-order phase transition. In this case the two independent

curves of free energy cross each other and the system jumps from one state to the

other one, like in the case of nucleation and growth. In this type of the transition,

a seed is required to trigger the transition. In a continuous phase transition, two

equivalent phases coexist and become indistinguishable. OP changes continuously

with temperature, and near Tc it behaves like (T −Tc)β. Figure 1.9 illustrates these

two kinds of phase transitions schematically.

6J.G. Dash et al., Rep. Prog. Phys. 58, 115 (1995).


Figure 1.8: An electron micrograph of a superlattice structure. Ref. [5].

The numerical value of β, the critical exponent, only depends on some physical

properties, like symmetry of the system or dimensionality of the order parameter.

The property that the phase transition behaves similarly for all systems with the

same dimensionality is called universality and suggests that unexpected phenomena

might take place at the surface (2DIM) in contrast to the bulk (3DIM).

OP

Tc

T

OP

Tc

T

tβ

Figure 1.9: (left) A typical first-order and (right) second-order phase

transition. OP is plotted as a function of temperature T , where t is the

reduced temperature and β the critical exponent.

Melting is a first-order phase transition for which the surface acts as a 2DIM

seed. In all investigations so far, the OP for the surface behaves like that in a

second-order phase transition so that we may say that the surface at temperatures

much lower than Tc anticipates the bulk melting. Depending on crystallographic

orientation, different melting temperatures have been observed for some metals.7

As yet, there is no universal microscopic theory for surface melting.

7J.F. van der Veen et al., Phys. Rev. Lett 59, 2678 (1987).


Figure 1.10: Conventional cubic cell of the diamond lattice. A sixfold-

symmetric planar honey-comb unit is highlighted.

1.5 Carbon-Based Structures

Graphene8 is a flat monolayer of carbon atoms tightly packed into a 2DIM hon-

eycomb lattice. It is the basic building block for graphitic materials of any DIM.

Carbon is the first element of Group IV in the periodic table. It has the 1s22s22p2

electronic configuration. In the case of 3DIM diamond structure, the outer 2s22p2

electrons form an sp3 hybrid which has a tetrahedral symmetry with the extremely

stable 109.47 the bond angle. It is a compact structure, macroscopically the hard-

est lattices. Diamond is an insulator with a large energy band gap. The diamond

structure is shown in Fig. 1.10. Nearest-neighbor bonds are drawn in. The four

nearest neighbors of each point form the vertices of a regular tetrahedron. In the

3DIM structure, a (111) plane is highlighted in order to emphasize the relation

to graphene. Hence, diamond structure can be thought of a special way of stack-

ing graphene layers along the [111] direction under consideration of the tetrahedral

symmetry.

Figure 1.11: Graphite is formed by periodic stacking of individual graphene layers.

8A.K. Geim and K.S. Novoselov, Nature Mat. 6, 183 (2007).


Figure 1.12: Fullerenes with 60, 70, 76, and 78 carbon atoms. Ref. [9].

Another 3DIM carbon-atom morphology is the graphite. In graphite, carbon

atoms occupy a 2DIM hexagonal lattice with 120 bond angles formed by the sp2

hybridization. The additional electron fixes the hexagonal layers within a loose π

bonding. The distance between the planes is almost 4.8 times the nearest-neighbor

distance within planes. The graphite material is soft, black, and shows a metallic

conduction along the graphene sheets. The graphite structure is schematically

illustrated in Fig. 1.11. On the right-hand side, the sp2 electron orbitals are shown

where the σ orbitals are 120 apart on a plane, while the π orbitals are perpendicular

to this plane.

Fullerene is a 0DIM cluster of carbon atoms arranged on the vertices of its typical

dome-like structure in icosahedral symmetry, as shown in Fig. 1.12. Fullerenes are

found as a by-product of carbon burning. They show spectacular properties when

doped with metallic species from being magnetic to superconducting.9

Nanotubes10 are 1DIM cylindrical structures based on the hexagonal lattice of

carbon atoms that forms crystalline graphite. By rolling up the graphene sheet a

chiral vector C is defined by C = na1 +ma2 (chiral, cheir = ‘hand’ in Greek). The

chiral angle γ is defined between C and a1. For the chiral nanotube, γ is between

0 and 30. The nanotube is termed armchair if n = m and γ = 30, zigzag for

m or n = 0 and γ = 0. This situation is illustrated in Fig. 1.13. The electronic

properties of nanotubes are determined by their diameter and the chiral angle. For

the motion of electrons, a nanotube is metallic if n − m = 3q with q an integer.

Thus, all armchair nanotubes are metallic, so are 1/3 of zigzag nanotubes; the

rest is semiconducting. The conductivity does nor depend on the length L of the

nanotube.

9G. Sun and M. Kertesz, J. Chem. Phys. A 104, 7398 (2000).10http://physicsweb.org/articles/world/11/1/9


Figure 1.13: Nanotube is a graphene sheet rolled into a 1DIM tube. Ref. [10].

1.6 Scattering Cross Section and Mean Free Path

According to the classical description, atoms consist of a positively charged nu-

cleus which is enclosed by an electron cloud. This model is also referred to as

the Rutherford model. Around 1910 experiments have been conducted with α par-

ticles to investigate the classical ideas about the electron cloud. Not much was

known about electron orbits microscopically, wave mechanics had not emerged yet.

Nevertheless, some ideas about scattering were developed which are still used suc-

cessfully today, as is done for scattering cross section. So we first deal with elastic

cross section in scattering.

A scattering event is elastic if the energy of the system is not changed. So if

a small particle with a mass m and initial velocity ~vo and initial momentum ~po

collides with a larger mass M initially at rest, we have after the collision ~v1 and ~p1

for the small mass and ~V2 and ~p2 for the larger mass. Consider central collision for

simplicity.

In elastic scattering momentum and energy are both conserved. Hence ~po =

~p1 +~p2 and Eo = p2o/(2m) = p2

1/(2m)+p22/(2M). For an energy transfer ∆E during

the collision we obtain

∆E =4mM

(m+M)2Eo (1.3)


This expression is smaller for a noncentral collision. For M m we can write

∆E ' 4m/MEo. For scattering of electrons at isolated atoms (m/M ≤ 10−4), we

obtain ∆E ≤ 10−4Eo. For scattering at a solid with 1023 atoms/cm3 the energy

transfer is even smaller ∆E ' 10−27Eo. We realize that there is practically no

energy transfer if a small particle collides with a larger one.

The differential cross section ∂σ/∂Ω is defined as the effective area per atom

scattering into the solid angle Ω. The number of scattered particles is given by

∆Ns(Ω,∆Ω) = Io∂σ

∂Ω∆ΩN, (1.4)

where Io is the intensity of incoming particles, N number of target particles. The

target area is R2∆Ω. Then the intensity of the scattered beam is given by

Is(Ω) ·R2∆Ω = ∆Ns(Ω,∆Ω). (1.5)

which leads to∂σ

∂Ω=Is(Ω)

Io

R2

N(1.6)

R2 and N are known quantities.

The scattering probability is

∂W

∂Ω=∂σ

∂Ω

N

Ao

=∂σ

∂Ωnd (1.7)

with Ao the area, n the density of target, and d the path length of scattering

particles. These ideas are valid for dilute targets where multiple scattering can be

neglected. Integration over Ω results in W = σnd. For W = 1 we obtain d = 1/nσ.

This quantity is called the mean free path or escape depth, Λ.

Actually, this derivation is valid for thin targets with d < Λ. Otherwise multiple

scattering will dominate. For an infinitesimally thin layer we may write ∂W =

σn∂d. If we scale with intensity, we obtain

∂I(d)

∂d= Io(d)σn. (1.8)

Considering the conservation of particles, i.e., Io(0) = I(d) + Io(d), leads to

Io(d) = Io(0)e−σnd = Io(0)e−d/Λ (1.9)

In all experiments that we use in our investigations, there are electrons, photons,

atoms, or ions involved. These particles interact with the solid with different inten-

sities. As a result, the mean free path is limited, and particles are either strongly

attenuated when they enter the solid or during escape. In any case, experiments are

more surface sensitive the shorter the mean free path is. Generally, Λ for photons

is quite long, while for electrons it has a typical trend in energy for most of the


Figure 1.14: The mean free path of electrons in metals as a function of their kinetic

energy. See, e.g., http://www.globalsino.com/micro/TEM/TEM9923.html.

metals, as seen in Fig. 1.14. Accordingly, in the energy range 30 < E < 300 eV, Λ

is as short as few-atomic distances. The reason lies in the fact that electrons inter-

act effectively with the solid and cause interband transitions thereby losing energy.

The strong electronic interaction is additionally caused by the creation of collective

excitations, plasmons, that is most effective above Ekin > 30 eV, and the emitted

electrons originate predominantly from a near-surface region making experiments

involving such electrons the basic tools in Surface Science.

1.7 Vacuum Technique

There are several reasons why Surface Chemistry and Surface Physics have devel-

oped relatively late. The most important one is the question how to prepare a clean

surface and how to keep it clean during the measuring time. In general, a clean

SC surface is exposed by cleavage. Unfortunately, only a few crystallographically

defined surfaces are thus accessible. Others, like those of all the metals, are first ori-

ented along the desired direction by x-ray methods and subsequently cut by spark

erosion to expose the net plane. Prior to introducing into the vacuum chamber,

the surface is polished with appropriate powders with decreasing grain size down

to 0.3 − 0.1 µm. In vacuum, surfaces are cleaned by bombardment with Ar+ ions

of 500 − 2000 eV and heated to elevated temperatures to restore the crystalline

structure. Once one has an appropriate surface, several systems, metals, alloys,

SC’s, can be generated by epitaxy.

A thus cleaned surface does not remain clean during long periods. The time

a one-monolayer (ML) of contamination reaches the surface is used as a measure


for the quality of the experiment and depends on the vacuum conditions. So the

question is, for given vacuum conditions, how long does a surface remain clean?

For an ideal gas, N = pV/kT is the number of particles in a volume V (l),

at a pressure p (Torr) and Temperature T (K) with the Boltzmann constant k.

Consider that the Maxwell distribution relates the average speed v =√

8kT/πm of

the particles with their mass m and the temperature T . Air molecules, CO or CO2,

at 20 C have an average speed of v ≈ 500 m/s.

Mean free path Λ of the particles is given by Λ = 1/(√

2πd2)(N/V )−1, while

d is the particle diameter. Thus, for air at p = 1 Torr, we have Λ = 4.5 µm at

room temperature. These particles move in the experimental chamber and hit all

exposed surfaces. The number of particles ∆n that hit a surface of area ∆F in a

time ∆t is given by ∆n/∆F/∆t = 1/4 v (N/V ) = v/4 (p/kT ), where the number

4 considers different directions.

Now we define the contamination time τ (s) as an interval during which an

originally clean surface is covered by 1 ML of adsorbed particles:

1015/(∆n/∆F/∆t) ≈ 3x10−6/p.

(1 ML ≈ 1015 atoms/cm2; 1 Pa = 10−5 bar; 1 Torr = 1.33 mbar = 1.33 x 10−2 Pa)

Thus, we have a stringent condition that we have to perform the experiments

in vacuum with the best possible conditions. For a pump, one defines the pumping

power Q = kTN (Torr·l/s) and pumping speed S = Q/p (l/s).

For the evacuation of an experimental chamber, we can write:

N = −dN/dt = −(V/kT )dp/dt and N = Q/kT = pS/kT , which results in:

p(t) = po exp (−S/V t). Hence, the decrease of pressure obeys an exponential law.

Consider a chamber of cubic volume of V = 1 m3 at a pressure of p = 10−5 Torr.

It contains N = 1017 atoms. The same chamber has ≈1020 atoms (6 x 104 cm2 x

1015 atoms/cm2) sticking at its inner walls if only 1 ML of adsorbates are present.

Hence, the number of atoms and molecules adsorbed at surfaces is much higher

than those present in the volume. Therefore, we have to get rid of the adsorbates

by making them desorb at elevated temperatures. So, we bake out the chamber to

attain good vacuo. This fact limits the choice of materials used to construct the

experimental chamber to those with high vapor pressure.

In this course we will deal with spectroscopic experiments and results. Every

spectroscopy has three ingredients. First, there is an initial disturbance, an excita-

tion. As a result, the system undergoes a transition from the ground state to an

excited state. This transition costs some energy and has a certain probability to

occur. We measure both, considering that the probability of the transition is the

intensity which is experimentally accessible. The excited state has some limited

life time that determines the accuracy of the observations. In the last step, the

system relaxes back to the ground state by emitting some energy. Also this time,

we observe the process. Our hope is that the measured quantities constitute the

dominant part of the transition. The major lesson is that we cannot ever measure

the ground state – observable are the excitations.

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