15.1 Decoding Methodology
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surface in the normal LEED energies [1]. The VLEED spectra are only active
in the upper valence band region, that is, 6.0–12.0 eV.
(2) Calculations revealed that the (00) beam reflectance (I 00 /I 0 ) greater than 12.5%
causes serious convergence problems. Measurements also showed that the
reflectivity is about 10%. Hence, the maximal value of I 00 /I 0 = 10% was
assumed as the maximal reflectivity to calibrate all of the I–E curves. In each
curve, the absolute intensity of the first and the last energy is vital to determine
the constants of γ and δ in the inelastic SPB. For instance, once the SPB functions are defined, we can solve the damping equation with the initial conditions
obtained by orthogonal-analysis technique.
(3) In the set of angular-resolved VLEED spectra [2], it was assumed that no structural change occurs to the bond geometry during the VLEED data acquisition. This assumption is also acceptable because increasing oxygen exposure
promotes more the reaction than sample aging.
(4) Earlier data simulation for Cu(001) surface [3] provided values of V 0 = 11.56 eV,
z 0 = −2.5 a.u. ( ∼ =1.32 Å approaches Cu atomic radius 1.276 Å) and λ = 0.9.
These data were used to calibrate the local work function and as references for
setting the SPB parameters.
(5) The z-scale difference of 0.45 Å in STM image offers reference for z 0 because
both STM image and z 0 (x, y) are the convolution of the surface electron distribution. Taking the lateral convolution for the finite size of STM tip and modification
by multiple diffraction and high-order diffraction in VLEED into consideration,
it is reasonable to assume that the z 0 and z STM are comparable and z 0
should be as small as possible.
15.1.2 Parameter Initialization
The second task before calculation is to initialize the SPB parameters. Orthogonal
optimization technique was used first at several energies E 0i with parameters of z 0i ,
λ i for the ReV(z) and ImV(E 0i ). Least-square optimization was used to fit the λ(z 0 )
plot for the constants. Both the STM image and barrier distribution imply that the
SPB increases its saturation degree with the outward shift of the image plane, z 0 . This
match serves as the physical basis for the relation between z 0 and λ. The optimized
z 0M and z 0m are −3.425 and −1.750 a.u., and the corresponding λ is 1.275 and 0.650.
There are four constants in the ImV(z, E). Matching the spectral intensities at
the VLEED energy terminals of 6.0 and 16.0 eV gives the γ and δ values. Given
the damping values at the energy terminals, one could solve the damping equation
to obtain the γ and δ. The FWHM of the Gaussian functions for z 1 (z 0 ) and α(z 0 )
are determined by obtaining the smallest z 0 (near the <11> direction presents the
maximal value).
301
surface in the normal LEED energies [1]. The VLEED spectra are only active
in the upper valence band region, that is, 6.0–12.0 eV.
(2) Calculations revealed that the (00) beam reflectance (I 00 /I 0 ) greater than 12.5%
causes serious convergence problems. Measurements also showed that the
reflectivity is about 10%. Hence, the maximal value of I 00 /I 0 = 10% was
assumed as the maximal reflectivity to calibrate all of the I–E curves. In each
curve, the absolute intensity of the first and the last energy is vital to determine
the constants of γ and δ in the inelastic SPB. For instance, once the SPB functions are defined, we can solve the damping equation with the initial conditions
obtained by orthogonal-analysis technique.
(3) In the set of angular-resolved VLEED spectra [2], it was assumed that no structural change occurs to the bond geometry during the VLEED data acquisition. This assumption is also acceptable because increasing oxygen exposure
promotes more the reaction than sample aging.
(4) Earlier data simulation for Cu(001) surface [3] provided values of V 0 = 11.56 eV,
z 0 = −2.5 a.u. ( ∼ =1.32 Å approaches Cu atomic radius 1.276 Å) and λ = 0.9.
These data were used to calibrate the local work function and as references for
setting the SPB parameters.
(5) The z-scale difference of 0.45 Å in STM image offers reference for z 0 because
both STM image and z 0 (x, y) are the convolution of the surface electron distribution. Taking the lateral convolution for the finite size of STM tip and modification
by multiple diffraction and high-order diffraction in VLEED into consideration,
it is reasonable to assume that the z 0 and z STM are comparable and z 0
should be as small as possible.
15.1.2 Parameter Initialization
The second task before calculation is to initialize the SPB parameters. Orthogonal
optimization technique was used first at several energies E 0i with parameters of z 0i ,
λ i for the ReV(z) and ImV(E 0i ). Least-square optimization was used to fit the λ(z 0 )
plot for the constants. Both the STM image and barrier distribution imply that the
SPB increases its saturation degree with the outward shift of the image plane, z 0 . This
match serves as the physical basis for the relation between z 0 and λ. The optimized
z 0M and z 0m are −3.425 and −1.750 a.u., and the corresponding λ is 1.275 and 0.650.
There are four constants in the ImV(z, E). Matching the spectral intensities at
the VLEED energy terminals of 6.0 and 16.0 eV gives the γ and δ values. Given
the damping values at the energy terminals, one could solve the damping equation
to obtain the γ and δ. The FWHM of the Gaussian functions for z 1 (z 0 ) and α(z 0 )
are determined by obtaining the smallest z 0 (near the <11> direction presents the
maximal value).