28
2 Theory: Bond-Electron-Energy Correlation
crystal potential in a Taylor series. The term ν (k, R) ∼ = sin
2 (kR/2) ≤ 1, for the fcc
structure instance, is a distribution function.
The exchange integral dominates the CLS. Typically,
ν (z b ) = α ν + z b β ν = α ν
1 + z b β ν
α ν
∝ E b
1 + E νW
2E b
≈ 3.0(1 + 0.2/6.0) = 3.0(1 + 3%).
A 3% contribution from the overlap integral to the CLS is negligibly small. For the
deeper bands, this ratio is even smaller. Thus, the bulk CLS depends mainly on the
bond energy E b in the first order approximation. Any relaxation of the interatomic
bond changes directly the E νW and the CLS accordingly.
Atomic ionization by X-ray radiation or by charging accumulation on the sample
changes the crystal potential throughout the course of measurements, which serves
as a removable background in calibration. In fact, charging effect exists only for
thick insulating samples in measurement because of the non-conductive character
of the specimen. The charging effect for conductors or thinner insulators becomes
negligible [10]. The charging effect can be minimized by grounding the specimen
during experiment [2, 11]. The electronic multi-body interaction also serves as an
average background as it exists throughout the specimen at quest. The final-initial
state relaxation effect exists throughout all the measurements so this effect can also
be averaged as background in the date processing.
The band width E νW = 2z b β ν ν (k, R) ∝ z b E b is proportional to the atomic
cohesive energy. As illustrated in Fig. 2.1a, if one moves from the valence band
downward, the ν (z b ) shift will turn from 10
0 to 10
−1 eV and the E νW will approach
0.0
0.5
1.0
1.5
2.0
E v (γ)/ E v (12)
B
P
T
Envelop
E v (0)
(a)
(b)
Fig. 2.1 a Evolution of the νth atomic energy level E ν (0) to the band E ν (z b = 12) with a shift of
ν (z b ) ∝ E b and an expansion E νW (z b ) ∝ z b E b of the νth band upon bulk formation. Artifacts
in measurements and charge polarization may change the amounts of BE shift and the width of
the components but not the nature of origin. b A typical XPS spectral peak shows components of
entrapment (T, or positive shift), polarization (P, or negative shift), and the bulk (B). Reprinted with
permission from [46]. Copyright 2006 American Physical Society
2 Theory: Bond-Electron-Energy Correlation
crystal potential in a Taylor series. The term ν (k, R) ∼ = sin
2 (kR/2) ≤ 1, for the fcc
structure instance, is a distribution function.
The exchange integral dominates the CLS. Typically,
ν (z b ) = α ν + z b β ν = α ν
1 + z b β ν
α ν
∝ E b
1 + E νW
2E b
≈ 3.0(1 + 0.2/6.0) = 3.0(1 + 3%).
A 3% contribution from the overlap integral to the CLS is negligibly small. For the
deeper bands, this ratio is even smaller. Thus, the bulk CLS depends mainly on the
bond energy E b in the first order approximation. Any relaxation of the interatomic
bond changes directly the E νW and the CLS accordingly.
Atomic ionization by X-ray radiation or by charging accumulation on the sample
changes the crystal potential throughout the course of measurements, which serves
as a removable background in calibration. In fact, charging effect exists only for
thick insulating samples in measurement because of the non-conductive character
of the specimen. The charging effect for conductors or thinner insulators becomes
negligible [10]. The charging effect can be minimized by grounding the specimen
during experiment [2, 11]. The electronic multi-body interaction also serves as an
average background as it exists throughout the specimen at quest. The final-initial
state relaxation effect exists throughout all the measurements so this effect can also
be averaged as background in the date processing.
The band width E νW = 2z b β ν ν (k, R) ∝ z b E b is proportional to the atomic
cohesive energy. As illustrated in Fig. 2.1a, if one moves from the valence band
downward, the ν (z b ) shift will turn from 10
0 to 10
−1 eV and the E νW will approach
0.0
0.5
1.0
1.5
2.0
E v (γ)/ E v (12)
B
P
T
Envelop
E v (0)
(a)
(b)
Fig. 2.1 a Evolution of the νth atomic energy level E ν (0) to the band E ν (z b = 12) with a shift of
ν (z b ) ∝ E b and an expansion E νW (z b ) ∝ z b E b of the νth band upon bulk formation. Artifacts
in measurements and charge polarization may change the amounts of BE shift and the width of
the components but not the nature of origin. b A typical XPS spectral peak shows components of
entrapment (T, or positive shift), polarization (P, or negative shift), and the bulk (B). Reprinted with
permission from [46]. Copyright 2006 American Physical Society