290
14 Principles: Bond-Band-Barrier Correlation
where E 0 = 12.04 eV and E F = 7.04 eV are the vacuum and Fermi level of a pure
Cu surface. For calibration n 0 was given by the data for the Cu(001) surface (V 0 =
11.56 eV, z 1 = z 0 = −2.5 Bohr radii, 1/α = λ = 0.9) [59]. Different calibrations
merely offset the φ L (x, y) value.
The work function depends on the occupied DOS and it is independent of the
dimensions of whatever sample is being considered. The concept of local work
function φ L has been employed to explain variations on the scale of patches of unit
cells with chemisorbed oxygen [30]. This concept can be extrapolated to the atomic
scale so that variations occur over the dimensions of a single atom.
For metal systems with chemisorbed oxygen, the usual concept of φ is no longer
valid due to the strongly “localized” features. It is even unlikely that the strongly
localized electrons with low mobility move from the site of “lower” φ L to the site of
“higher” φ L on the same surface described with φ L (x, y). Since the VLEED integrates
over a large area of surface, all the quantities depending on surface coordinates (x, y)
become energy-dependent. Accordingly, the n(x, y) in φ L becomes n(E). The n(E) is
precisely the occupied DOS that is characterized by z 0 (E). In the current modeling
approach, the φ L (E) becomes E dependent and it can also be extended to large surface
areas over which VLEED integrates for the DOS.
14.4.5.2 Parameterization of the 3D-SPB
One may define an inelastic potential to unify the effect that damping occurs in
the electron-occupied space (Fermi z decay) with any energy greater than the work
function, which depends on the occupied DOS [42]:
ImV(z, E) = Im[V (z) × V (E)]
= γ × ρ(z) × exp
E − φ L (E)
δ
=
γ × exp
E−φ L (E)
δ
1 + exp
−
z−z 1 (z0)
α(z 0 )
(14.10)
where γ and δ are constants depending on the calibration of the measured spectral
intensities. The z 1 (z 0 ) and the α(z 0 ) in the Fermi z function characterizes the electron
distribution.
Because single electron can be excited by an incident electron beam that has any
energy greater than the work function, i.e., E ≥ φ, we choose the form of [E −
φ L (E)] in the inelastic damping. It is to be noted that the surface electron density ρ(z)
is so important that it ties all the identities for surface electrons together meeting the
basic requirement. These identities are local work function φ L (x, y), elastic potential
ReV(z), spatial decay ImV(z) and energy dependent of the inelastic damping ImV(E)
of the electronic system.
14 Principles: Bond-Band-Barrier Correlation
where E 0 = 12.04 eV and E F = 7.04 eV are the vacuum and Fermi level of a pure
Cu surface. For calibration n 0 was given by the data for the Cu(001) surface (V 0 =
11.56 eV, z 1 = z 0 = −2.5 Bohr radii, 1/α = λ = 0.9) [59]. Different calibrations
merely offset the φ L (x, y) value.
The work function depends on the occupied DOS and it is independent of the
dimensions of whatever sample is being considered. The concept of local work
function φ L has been employed to explain variations on the scale of patches of unit
cells with chemisorbed oxygen [30]. This concept can be extrapolated to the atomic
scale so that variations occur over the dimensions of a single atom.
For metal systems with chemisorbed oxygen, the usual concept of φ is no longer
valid due to the strongly “localized” features. It is even unlikely that the strongly
localized electrons with low mobility move from the site of “lower” φ L to the site of
“higher” φ L on the same surface described with φ L (x, y). Since the VLEED integrates
over a large area of surface, all the quantities depending on surface coordinates (x, y)
become energy-dependent. Accordingly, the n(x, y) in φ L becomes n(E). The n(E) is
precisely the occupied DOS that is characterized by z 0 (E). In the current modeling
approach, the φ L (E) becomes E dependent and it can also be extended to large surface
areas over which VLEED integrates for the DOS.
14.4.5.2 Parameterization of the 3D-SPB
One may define an inelastic potential to unify the effect that damping occurs in
the electron-occupied space (Fermi z decay) with any energy greater than the work
function, which depends on the occupied DOS [42]:
ImV(z, E) = Im[V (z) × V (E)]
= γ × ρ(z) × exp
E − φ L (E)
δ
=
γ × exp
E−φ L (E)
δ
1 + exp
−
z−z 1 (z0)
α(z 0 )
(14.10)
where γ and δ are constants depending on the calibration of the measured spectral
intensities. The z 1 (z 0 ) and the α(z 0 ) in the Fermi z function characterizes the electron
distribution.
Because single electron can be excited by an incident electron beam that has any
energy greater than the work function, i.e., E ≥ φ, we choose the form of [E −
φ L (E)] in the inelastic damping. It is to be noted that the surface electron density ρ(z)
is so important that it ties all the identities for surface electrons together meeting the
basic requirement. These identities are local work function φ L (x, y), elastic potential
ReV(z), spatial decay ImV(z) and energy dependent of the inelastic damping ImV(E)
of the electronic system.