16.2 VLEED Capacity and Reliability
327
Results in Figs. 16.6 and 16.7 indicate the following [3]:
(1) The elastic potential ReV(z; z 0 , λ, V 0 ) dominates the shape of the fine structures.
The integration of the ReV(z; z 0 , λ, V 0 ) makes more sense than the individual
limit in determining the phase change of the diffracted beam. Only a 20% change
in these parameters leads to a phase change of π, resulting in an alteration from
spectral maximum to spectral minimum at given energies, see Fig. 16.6a–c.
(2) The shape of the fine structures is insensitive to the inelastic damping, ImV(z).
All the parameters in the inelastic damping, however, affect the absolute reflectivity or the amplitude of the wave function of the spectrum. Therefore, all the
ImV(z) parameters can be functionally dependent on the characteristic variable
of the image plane z 0 (ρ(z 0 ) = 0; ρ(z 1 ) = 0.5ρ M ). The inelastic potential parameters could be used conveniently to compensate for the accuracy in calibrating
the measured data.
(3) By comparing the spectral intensity modulated by γ (for the whole range of
z-dimension in ImV(z, E)) with the resultant of η and β, one can find easily that
electrons out of the second atomic layer (z > z SL ) dominates the damping. The
resultant of β(z ≤ z 1 ) and η(z 1 < z ≤ z SL ) has the same quantitative effect as
γ on the reflectivity. So electrons below the second atomic plane never come
into play in the VLEED spectra. The ImV(z, E) describes the valence DOS
distribution in real and energy domains.
(4) The spectrum is, however, insensitive to the variations of α, β and z 1 . Thus,
approaches in the functional dependence of the insensitive parameters on the
characteristic one are substantially necessary. Although the effect of changing
parameter δ (slope) in ImV(E) was not considered, one may use it to compensate
for the assumption in data acquisition that the incident current be constant during
increasing the incident beam energy.
(5) It is noticed that only the inelastic damping modulates the spectral intensity at
energies being deeper than the valence band (>12.0 eV). This fact suggests that
the electrons in deeper bands are less affected by the surface bonding, and as a
result, they affect insignificantly the elastic potential at the surface.
(6) Another important fact is that the spectral intensity above 7.0 eV (E F ) is modulated neither by the bond geometry nor the shape of the elastic potential (z 0 and
λ) as indicated in Figs. 16.5 and 16.6. The intensity at this region is however
sensitive to the inner potential V 0 constant and parameters in the inelastic damping. Therefore, spectral features above 7.0 eV varies with the surface electron
density rather than the bond geometry or the barrier shape.
327
Results in Figs. 16.6 and 16.7 indicate the following [3]:
(1) The elastic potential ReV(z; z 0 , λ, V 0 ) dominates the shape of the fine structures.
The integration of the ReV(z; z 0 , λ, V 0 ) makes more sense than the individual
limit in determining the phase change of the diffracted beam. Only a 20% change
in these parameters leads to a phase change of π, resulting in an alteration from
spectral maximum to spectral minimum at given energies, see Fig. 16.6a–c.
(2) The shape of the fine structures is insensitive to the inelastic damping, ImV(z).
All the parameters in the inelastic damping, however, affect the absolute reflectivity or the amplitude of the wave function of the spectrum. Therefore, all the
ImV(z) parameters can be functionally dependent on the characteristic variable
of the image plane z 0 (ρ(z 0 ) = 0; ρ(z 1 ) = 0.5ρ M ). The inelastic potential parameters could be used conveniently to compensate for the accuracy in calibrating
the measured data.
(3) By comparing the spectral intensity modulated by γ (for the whole range of
z-dimension in ImV(z, E)) with the resultant of η and β, one can find easily that
electrons out of the second atomic layer (z > z SL ) dominates the damping. The
resultant of β(z ≤ z 1 ) and η(z 1 < z ≤ z SL ) has the same quantitative effect as
γ on the reflectivity. So electrons below the second atomic plane never come
into play in the VLEED spectra. The ImV(z, E) describes the valence DOS
distribution in real and energy domains.
(4) The spectrum is, however, insensitive to the variations of α, β and z 1 . Thus,
approaches in the functional dependence of the insensitive parameters on the
characteristic one are substantially necessary. Although the effect of changing
parameter δ (slope) in ImV(E) was not considered, one may use it to compensate
for the assumption in data acquisition that the incident current be constant during
increasing the incident beam energy.
(5) It is noticed that only the inelastic damping modulates the spectral intensity at
energies being deeper than the valence band (>12.0 eV). This fact suggests that
the electrons in deeper bands are less affected by the surface bonding, and as a
result, they affect insignificantly the elastic potential at the surface.
(6) Another important fact is that the spectral intensity above 7.0 eV (E F ) is modulated neither by the bond geometry nor the shape of the elastic potential (z 0 and
λ) as indicated in Figs. 16.5 and 16.6. The intensity at this region is however
sensitive to the inner potential V 0 constant and parameters in the inelastic damping. Therefore, spectral features above 7.0 eV varies with the surface electron
density rather than the bond geometry or the barrier shape.