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14 Principles: Bond-Band-Barrier Correlation
of the surface and the correlation among the parameters used in calculations constitute the complexity in de-coding VLEED data from the systems with chemisorbed
oxygen.
Therefore, besides the M 2 O bond geometry, a proper nonuniform-SPB for systems
with chemisorbed oxygen is necessary to:
• reduce the number of independent SPB variables to properly correlate the intrinsic
entities of the surface and to simplify VLEED optimization ensuring the certainty
of solution.
• allow the calculation code to automatically optimize the image plane z 0 (E) to
reproduce the experimental data.
• let the z 0 (E) profiles vary on-site with the crystal structure to reflect appropriately
the interdependence between the atomic geometry and the electronic structures;
and, eventually
• produce the essential DOS features in the energy range covered by VLEED.
14.4.2 Complex Form of the Surface Potential Barrier (SPB)
Electrons with energy E traversing the surface region can be described as moving in
a complex optical potential [53, 54]:
V(r, E) = ReV(r) + iImV(r, E)
= ReV(r) + iIm[V(r) × V(E)]
(14.2)
The V(r, E) satisfies the following constraints.
14.4.2.1 Elastic and Inelastic Correlation
The elastic potential ReV(r) correlates to the electric field ε(r), charge density ρ(r),
and the imaginary ImV(r, E) in the following form:
∇[ReV(r)] = −ε(r )
∇
2 [ReV(r)] = −ρ(r ) ∝ ImV(r, E) = ImV(r) × ImV(E)
The ReV(r) satisfies Poisson equation and the gradient of the ReV(r) equals the
electric field ε(r). If ρ(r) = 0, then the ReV(r) corresponds to a conservation field
without charging source being included; that is, the moving electrons will suffer no
energy loss and the spatial variation of the inelastic damping potential ImV(r) ∝ ρ(r)
= 0. Therefore, the ImV(r) and the ReV(r) are correlated each other uniquely through
the electron distribution ρ(r).
14 Principles: Bond-Band-Barrier Correlation
of the surface and the correlation among the parameters used in calculations constitute the complexity in de-coding VLEED data from the systems with chemisorbed
oxygen.
Therefore, besides the M 2 O bond geometry, a proper nonuniform-SPB for systems
with chemisorbed oxygen is necessary to:
• reduce the number of independent SPB variables to properly correlate the intrinsic
entities of the surface and to simplify VLEED optimization ensuring the certainty
of solution.
• allow the calculation code to automatically optimize the image plane z 0 (E) to
reproduce the experimental data.
• let the z 0 (E) profiles vary on-site with the crystal structure to reflect appropriately
the interdependence between the atomic geometry and the electronic structures;
and, eventually
• produce the essential DOS features in the energy range covered by VLEED.
14.4.2 Complex Form of the Surface Potential Barrier (SPB)
Electrons with energy E traversing the surface region can be described as moving in
a complex optical potential [53, 54]:
V(r, E) = ReV(r) + iImV(r, E)
= ReV(r) + iIm[V(r) × V(E)]
(14.2)
The V(r, E) satisfies the following constraints.
14.4.2.1 Elastic and Inelastic Correlation
The elastic potential ReV(r) correlates to the electric field ε(r), charge density ρ(r),
and the imaginary ImV(r, E) in the following form:
∇[ReV(r)] = −ε(r )
∇
2 [ReV(r)] = −ρ(r ) ∝ ImV(r, E) = ImV(r) × ImV(E)
The ReV(r) satisfies Poisson equation and the gradient of the ReV(r) equals the
electric field ε(r). If ρ(r) = 0, then the ReV(r) corresponds to a conservation field
without charging source being included; that is, the moving electrons will suffer no
energy loss and the spatial variation of the inelastic damping potential ImV(r) ∝ ρ(r)
= 0. Therefore, the ImV(r) and the ReV(r) are correlated each other uniquely through
the electron distribution ρ(r).