Noble Metals, Noble Metal Halides and Nonmagnetic Transition Metals

343 Pages·2003·12.99 MB·English

by  A. Goldmann (auth.), A. Goldmann (eds.)

Ref. p. 12] 1.1 Historical remarks 1
1 Introduction
1.1 Historical remarks
The photoelectric effect has been discovered already in 1887 by Heinrich Hertz [1887H], when he
observed that sparking of a spark gap was enhanced by ultraviolet light. Subsequent work [1888H, 1899T,
1900L, 1902L] revealed that electrons were emitted whose maximum kinetic energy was proportional to
the frequency of the incident light, and whose number was proportional to the light intensity. In 1905
Albert Einstein [1905E] published the quantum theory of the photoelectric effect, for which he received
the Nobel Prize in 1921. Several reviews give an account of the early and the further history of
photoelectron spectroscopy [32H, 77J, 78C1, 82S1, 82S2, 88M]. After more than 100 years since its
discovery, we may state that the photoelectric effect and the many photoelectron spectroscopies based on
it represent one of the most productive areas in solid state and surface science, with considerable impact
also to today's technology.
Modern photoemission spectroscopy, now representing one of the most important tools to investigate
the electronic structures of atoms, molecules, solids and surfaces (including interfaces), started 20 to 30
years ago. Several important experimental developments contributed (among others) to the rapid progress
of that field: The field of X-ray photoelectron spectroscopy (XPS) was pioneered by Kai Siegbahn and his
group, mainly by the development of high-resolution, high-sensitivity electron spectrometers and intense
soft X-ray line-sources (for details see Table 1, Section 1.3) [67S, 69S]. This work was awarded with the
Nobel Prize in 1981 [82S1]. The field of ultraviolet photoelectron spectroscopy (UPS) was pushed
forward mainly by three advances: First, the development of windowless high-intensity uv-lamps such as
the HeI and the HeII line-sources (for details see Table 1, Section 1.3). Second, the advent of high-
resolution, high sensitivity, electrostatic electron energy analyzers which allowed angle-resolved UPS
investigations in reasonable times [82P, 83H, 84C]. Third, the availability of synchrotron radiation from
"dedicated" storage rings as tunable, intense sources of linearly and/or circularly polarized photons [83K].
This instrumental progress allowed to develop experimental methods to measure both the energy and the
momentum of the electrons, i.e. to map the electronic energy band structure along many k-space directions
[82P, 83H, 84C, 92K, 95H1].
For the future we may predict further progress in the field of photoelectron and related spectroscopies.
A new generation of dedicated sychrotron radiation sources is now available. These are based on magnetic
insertion devices (wigglers, undulators) and improved monochromator concepts [97P1]. They supply us
with very intense, high-brilliance radiation of simultaneously high energy-resolution and tunable
polarization. These sources will allow measurements to be performed with photons in the energy range up
to about 1 keV at high photon energy resolution (10...100 meV), high lateral resolution (10...100 nm) and
spectroscopically relevant temporal resolution (pico- to nanoseconds). In conclusion, these sources will
enable us to collect data like those presented in this volume at, however, much improved resolution and
accuracy. This statement refers to core-level spectroscopy as well as to symmetry-resolved mapping of
energy bands.
We may summarize that after more than a century of photoemission studies [95B] the kinematics of
the photoemission process is well understood. This refers to both one-photon photoemission [92K, 95H1]
and two-photon photoemission [95F, 95S]. Provided good quality single-crystals as well as recipes to
prepare surfaces with the desired stoichiometry and sufficient lateral order are available, the determination
of energies and energy bands is now almost routine using tunable photon sources. This business, however,
is only the lower level of every spectroscopy. The higher and more sophisticated level concentrates on
measurement and understanding of line shapes [98H, 98M, 99H, 99V, 00L, 00M] and peak intensities
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2 1.2 Arrangement of data, 1.3 Definition of quantities [Ref. p. 12
[98M, 99M, 01P]. In the last few years photoelectron spectroscopy has progressed to a point [98H, 98P,
99V, 00R], where these quantities are no longer exclusively determined by experimental resolution
constraints, but also by the "intrinsic" quantities like photohole-lifetime [98H, 00C2, 00P, 01G, 01Z, 02G,
02Z] and the lifetime of the excited electron [00C1, 00E, 00P, 02B]. Spoken more generally, the line
shape may give detailed information on the dynamics of the solid as a correlated many-particle system,
including electron-electron [97P3, 00C1, 00E] and electron-phonon [99H, 99P, 99V, 00L, 00R]
interactions. This development opens up a completely new field which recently got additional impetus by
the advent of two-photon photoelectron spectroscopies with time-resolution on the femtosecond scale
[95H2, 96O, 97O, 97P2, 97P3, 97W, 98A, 98K, 00E, 00P]. Moreover, free-electron-lasers with high-
intensity and high-brilliance specifications will be operating in the near future. We may therefore
anticipate further progress in photoelectron and related spectroscopies.
1.2 Arrangement of data
Each chapter has a separate introduction referring to special aspects of the materials under consideration.
Within each chapter the organisation is as follows. First, general data (as far as available) are summarized
on crystal structure, electronic configuration, work functions, plasmon energies, core level binding
energies, valence band critical point energies, and other relevant quantities. Then diagrams are collected
reproducing angle-integrated as well as angle-resolved valence-band and core level spectra, calculated
energy bands and corresponding densities of states, and in particular experimental electron energy
dispersion curves E(k). When considered necessary, also optical spectra and results obtained with other
experimental techniques are shown to supplement the electronic structure information.
Figures and tables within Chaps. 2.9, 2.10 and 2.11 are numbered consecutively through their
subsections.
In the tables of this volume, experimental errors are given in parentheses referring to the last decimal
places. For example 1.23(45) stands for 1.23 ± 0.45 and 9.9(11) stands for 9.9 ± 1.1.
1.3 Definition of quantities
Two features of photoemission spectroscopy (PES) and its time-reversed counterpart, inverse
photoemission spectroscopy (IPES) are of particular interest: First, initial and final state energies of
radiative transitions are directly determined by the experiment. Other methods, e.g. light absorption or
reflection, can in general only determine the energy difference between initial and final state. Second, the
electron momentum !k may be determined in angle-resolved experiments using single-crystal samples.
The schematics of PES and IPES are shown in Fig. 1. PES and IPES can supply information on the
electron energy eigenvalues E(k) and their dependence on the electron wave vector k. As is evident from
Fig. 1, the combination of both techniques can investigate all energy bands below and above the Fermi
level at EF.
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Ref. p. 12] 1.3 Definition of quantities 3
Fig. 1. Schematics of photoemission (top) and inverse photoemission
(bottom). The angles of photon (α) and electron (θ) are defined with respect
to the surface normal. The shaded region of the energy band structure is
accessible to the respective technique. Radiative transitions occur between
initial state | i〉 and final state | f〉.
It is not intended here to describe the techniques and theories of PES and IPES in detail, since many
excellent reviewing articles and detailed monographs are available [70T, 72S, 77B, 77I, 78C1, 78C2,
78C3, 78F, 79B, 79C, 80W, 83D, 83S, 83W, 84B, 84D, 85D, 86H, 86S, 87B, 87L, 88S, 95S]. Therefore,
only a very brief overview of the methods will be given. The typical PES [82P, 83H, 84C, 92K, 95H1]
experiment is illustrated in Fig. 1. Photons of energy !ω impinge on the sample. If a photon is absorbed in
an occupied state | i〉, at energy Ei below the Fermi level EF (Ei = 0 at EF), an electron is excited into an
empty state | f〉 at energy Ef. Energy conservation requires Ef − Ei = !ω (The sign convention used in this
volume is summarized in Fig. 2). If Ef > Evac, the energy of the vacuum level, the electron in the excited
state may leave the sample. The emitted electrons are then analyzed with respect to their intensity, kinetic
energy Ek, and other variables of interest like: direction and polarisation of incident light, emission
direction of electrons with respect to incident photon direction and/or with respect to the crystal lattice
coordinates, and (sometimes) the electron spin-polarization [85K, 86F, 94D]. PES gives thus information
on the occupied states below EF and empty states above Evac. Energy conservation states that !ω = Ef − Ei
= Ek + φ − Ei, where φ = Evac − EF is the work function. If φ is known [79H] or measured (the width of the
experimental photoelectron distribution is given by !ω − φ, compare Fig. 3) both Ei and Ef are uniquely
determined. IPES [83D, 83W, 84D, 85D, 86H, 86S, 88S] is illustrated in Fig. 1 (bottom). The electron at
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Ei = Ek + φ impinges on the crystal, penetrates the surface and enters the previously empty state | i〉 at Ei >
Evac. By emission of a photon, the state at Ei is connected with state | f〉 at Ef ≥ EF = 0. The emitted photon
of energy !ω is registered in an energy-resolving detector [84D, 86H, 86D, 86S]. Again, Ei and Ef are
determined by the kinematics of the experiment.
Fig. 2a. Sign convention for energies in case of Fig. 2b. Sign convention for energies in case of
metallic samples, where the position of EF is clearly semiconductors and/or insulators, where in general the
observed in the photoelectron spectra. If not stated upper valence band edge at EVBM (valence band
otherwise, the energy zero is at EF. In the literature on maximum) is better defined in the experimental spectra
PES, the term "binding energy" is often used, with the than the position of EF. If not stated otherwise, the
convention that | Ei | = Eb ≥ 0. energy zero is at EVBM. In the literature on PES, the
term "binding energy" is often used, with the
convention that | Ei | = Eb ≥ 0.
Most PES experiments measure an electron distribution curve (EDC), i.e. the number I(Ek) of emitted
electrons, see Fig. 3. If !ω is sufficiently large, emission out of core levels is observable. The area of the
corresponding peak (shaded in Fig. 3, and superimposed to a continuous background of inelastically
scattered electrons) is proportional to the number of emitting atoms. Its energy Ei identifies the emitting
element and very often ("chemical shift") also the chemical environment. Emission from occupied valence
states in PES or into empty valence states in IPES yields information on the density of states. In general,
however, even the angle-integrated EDC does not directly reflect the density of states D(Ei), as idealized
in Fig. 3. In the following we will discuss this point for PES in some detail. Angle-integrated PES of bulk
states can transparently be described by a three-step model [68S] (for more refined treatment we refer to
[83H, 84C, 92K, 95H1]): photoexcitation of an electron, travelling of that electron to the surface, and
escape through the surface into the vacuum. Beyond the low-energy cutoff at Evac travelling through the
solid and escape are described by smooth functions of E and will not give rise to structure in I(Ek).
Therefore primarily the photoexcitation process determines the shape of the EDC. For bulk states, where
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Ref. p. 12] 1.3 Definition of quantities 5
crystal momentum !k is a quantum number conserved in the reduced zone scheme ("vertical transitions"
in Fig. 1) we then find for the distribution of photoexcited electrons
3 2 .
I(Ek, !ω) ≈ ∑ ∫ d k |〈f | p | i〉| · δ1 δ2 (1)
i, f
where δ1 = δ{Ef(k) − Ei(k) − !ω} and δ2 = δ{Ef(k) − φ − Ek}, and the k-space integral is to be extended
only over occupied states | i〉. The δ1-function assures energy conservation, while δ2 selects from all
transitions possible with photons of energy !ω only those that are registered by the electron energy
analyser. If we take for the moment the transition matrix element Mfi = 〈f | p | i〉 to be constant, eq. (1)
reduces to the so-called energy distribution of the joint density of states
3 .
I (Ek, !ω) ≈ ∑ ∫ d k · δ1 δ2 (2)
i, f
Fig. 3. Illustration of the fact that in angle-integrated
PES the density of occupied states D(Ei) is often
approximately reflected in the emitted electron energy
distribution curve I(Ek).
We will then expect that at low photon energies (typically !ω < 20 eV) the angle-integrated EDC does
generally not reflect the density of occupied states, since only few final states for photoexcitation are
available. However, at increasing !ω, the number of accessible final states increases and the intensity
modulation through these | f〉 states becomes less important. The EDC will then progressively become a
replica of the initial density of states (DOS), as long as Mfi = constant. If Mfi is not constant, the EDC
represents the initial DOS modulated by the matrix element varying in k-space. Similar considerations are
applicable to IPES.
The experimental method for mapping Ei(k) is angle-resolved PES, with vacuum-ultraviolet
excitation radiation [82P, 83H, 84C]. While Ei and Ef are easily determined, a problem [82P, 83H, 84C,
92K, 95H1] arises with k. Upon penetration of a single-crystal surface by an electron only k , the wave-
||
vector component parallel to the surface, is conserved and directly obtainable from the kinematical
2 l/2 l/2
parameters: k
|| = sinθ (2m/! ) Ek , where m is the free electron rest mass. The investigation of bulk
states E (k , k ) requires additional information on k which is not conserved. In most PES experiments
|| ⊥ ⊥
reasonable assumptions were therefore made (e.g. "free-electron-like", i.e. parabolic final state bands
[82P, 83H, 84C, 92K, 95H1]) to extract k from one EDC. However, several (albeit time-consuming and
⊥
tedious) "absolute" methods may also be applied to determine the full wave-vector (k , k ) experimentally
|| ⊥
from at least two ECD's viewing the k-space from different directions. A detailed discussion of such
methods has been presented in [82P, 83H, 84C, 92K, 95H1]. For a most elegant new strategy of band
mapping, which provides full control of the three-dimensional k-vector, see [00S, 01S].
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6 1.3 Definition of quantities [Ref. p. 12
Photoelectric cross sections at 1.5 keV for atomic levels are shown in subvolume a, see Fig. 3 of
section 2.5 (see also Fig. 13 of section 2.8 in subvolume b). Data for other excitation energies can be
found in [81G, 76S]. Calculated partial photoionization cross sections in the energy region 0...1500 eV
are given for all elements Z = 1...103 in [85Y]. A list of line sources commonly used in laboratory PES is
given in Table 1.
Table 1. Commonly used line sources for photoelectron spectroscopy [78C1].
Source Energy Relative Typical intensity at Linewidth
[eV] intensity the sample [meV]
–1
[photons s ]
12
He I 21.22 100 1 ⋅ 10 3
Satellites 23.09, 23.75, 24.05 < 2 each
a 11
He II 40.82 20 ) 2 ⋅ 10 17
a
48.38 2 )
a
Satellites 51.0, 52.32, 53. 00 < 1 ) each
11
Ne I 16.85 100 8 ⋅ 10
16.67
a
Ne II 26.9 20 )
a
27.8 10 )
a
30.5 3 )
Satellites 34.8, 37.5, 38.0 <2 each
11
Ar I 11.83 100 6 ⋅ 10
a
11.62 80...40 )
a
Ar II 13.48 16 )
a
13.30 10 )
11
Y M
ζ 132.3 100 3 ⋅ 10 450
12
Mg K
α1, 2 1253.6 100 1 ⋅ 10 680
Satellites K
α3 1262.1 9
K
α4 1263.7 5
12
Al K
α1, 2 1486.6 100 1 · 10 830
Satellites K
α3 1496.3 7
K
α4 1498.3 3
a
) Relative intensities of the lines depend on the conditions of the discharge. Values given are therefore only
approximate.
Photoelectron spectroscopies and related or complementary techniques are looking through a
particular surface into the bulk of a solid material. Therefore unavoidably surface and bulk information
are superimposed in the experimental data. Although this volume concentrates on the electronic bulk
properties (for detailed information on the surface electronic and geometric properties see Landolt-
Börnstein III/24a-d) careful inspection of the spectra as well as sufficient understanding of the literature
quoted in this volume require some understanding of the surface as well. To support the reader we
reproduce the relevant bulk and surface Brillouin zones in Figs. 4 - 10.
For further details concerning unit cells, reciprocal lattices and first Brillouin zones see Landolt-Börnstein
III/13c, p.451.
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Ref. p. 12] 1.3 Definition of quantities 7
Fig. 4. fcc(100). (Bottom) Bulk Brillouin zone (BBZ)
Fig. 5. fcc(110). (Bottom) BBZ and (top) SBZ showing
and (top) Surface Brillouin zone (SBZ) showing the
the projection of the bulk onto the (110) surface.
projection of the bulk onto the (001) surface. The bulk
vectors are given by ΓX = [1,0,0] (2π/a), ΓL = [½, ½,
½] (2π/a), ΓK = [¾, ¾, 0] (2π/a), ΓW = [1,½,0] (2π/a)
where a is the lattice constant.
Fig. 6. fcc(111). (Bottom) BBZ and (top) SBZ showing
the projection of the bulk onto the (111) surface.
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8 1.3 Definition of quantities [Ref. p. 12
Fig. 7. bcc(100). (Bottom) BBZ and (top) SBZ
showing the projection of the bulk onto the (001)
surface. The bulk vectors are given by ΓH = [0,0,2]
(π/a), ΓN = [1,1,0] (π/a), ΓP = [1,1,1] (π/a) where a is
Fig. 8. bcc(110). (Bottom) BBZ and (top) SBZ
the lattice constant.
showing the projection of the bulk onto the (110)
surface.
←
Fig. 9. bcc(111). (Bottom) BBZ and (top) SBZ
showing the projection of the bulk onto the (111)
surface.
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Ref. p. 12] 1.3 Definition of quantities 9
Fig. 10. hcp(0001). (Bottom) BBZ and (top) SBZ
showing the projection of the bulk onto the (0001)
surface.
Fig. 11. hcp(1010). (Bottom) BBZ and (top) SBZ
showing the projection of the bulk onto the (1010)
surface.
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10 1.4 Frequently used symbols
1.4 Frequently used symbols
Symbol Unit Property
a, b, c Å lattice parameters
−1 −1
DOS eV atom , density of states
−1 −1 −1
eV atom spin ,
−1 −1
atom Ry
e C elementary charge
E eV, Ry energy
Eb binding energy (Eb ≥ 0)
EF Fermi energy
Ef final state energy (of radiative transition), (Ef ≥ 0)
Eg energy gap, band gap
Ei initial state energy (of radiative transition), (Ei ≤ 0 in
PES, Ei > 0 in IPES), electron incidence energy
Ek kinetic (photoelectron) energy
Evac vacuum energy level
EVBM energy of valence band maximum
∆E eV energy resolution
fi Phillips ionicity
−1
I arb. units, counts s intensity in spectral distribution
−1
k Å wavevector (of electrons)
k||, k⊥ wavevector components parallel and perpendicular
to the surface
kF Fermi surface radius
−1
NOS electrons atom number of states
R reflectivity
T K, °C temperature
Z atomic number
−1
α cm absorption coefficient
α deg angle of incidence of photons in PES, photon
emission angle in IPES
Γ center of Brillouin zone
Γe, Γh inverse life time of electrons, holes
ε2 imaginary part of dielectric constant
q deg angle of incidence of electrons in IPES, electron
emission angle in PES
−1
ν s frequency
hν eV photon energy
σ b cross section
−1
σ s optical conductivity
φ eV work function φ = Evac − EF
−1
ω rad s circular frequency
ωp plasmon frequency
!ω eV photon energy
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