15.2 Code Validation
305
clean Cu(001) surface suggests that the multiple-diffraction approach is sufficiently
accurate and complete to allow for the inclusion of all necessary diffraction events.
Importantly, the conventional SPB model for pure metal (ideal Fermi system) is
adequate to produce the correct intensity for the high-order diffraction events in the
SPB region.
15.2.2 Oxygen on Cu(001): Model Comparison
To examine the code validity for the O-Cu(001) surface, calculations were performed
with the same convention for clean Cu(001) surface by using geometries of several
missing-row structural models to optimise the SPB parameters. The best model is
then assigned to the one that provides the closest fit to the measured data.
Simulation was conducted to two typical VLEED I–E curves for 300-L oxygen
chemisorbed Cu(001) surface. The incident angle (relative to the normal of the surface) is 69.0° and the azimuth angles of the compared curves are 23.5° (near <21>
direction) and 43.5° (near <11> direction), respectively. Figure 15.2 compares the
atomic positions in the compared models. The side view above shows atomic positions viewing along the -Cu-O-Cu- chain; the bottom is a top view of the Cu(001)(
√
2 × 2
√
2) R45°-2O complex unit cell denoting the azimuth angle of incident
beams. Table 15.1 lists the structural parameters used in calculations. Model A is
derived from the M 2 O tetrahedron structure. The five calculation parameters (D 12 ,
DCu x , DCu z , DO x , DO z ) for model B and C were optimized in earlier LEED calculations [8]. Parameters for structure D are derived from the effective-medium theory
predictions [9].
By using the one-dimensional SPB with nine parameters, qualitative agreement
between measurement and calculation is achieved for the spectrum collected only at
23.5° azimuth angle, far away from the <11> direction for all the compared structural
models, as given in Fig. 15.3. The broken lines are the measured VLEED spectra.
For the 23.5° azimuth, violent features on the curves at about 6.8 and 13.5 eV come
from band-gap Bragg diffraction. The main Rydberg peak on the calculations (solid
lines) at 13.0 eV is very sensitive to the SPB.
All the structures provide the match of the peak position at 13.0 eV but not ideally
the intensities or the FWHM of this peak. The minor inconsistency below 12.0 eV
and the FWHMs of all the simulations suggest the essentiality of SPB modification
by involving the 3D effect and the energy dependent damping processes. The sharp
peak at 15.5 eV and the intensity-difference between measured and calculated results
from 14.0 to 16.0 eV of curves B, C and D could not be eliminated by adjusting SPB
parameters. The main peak at 13.0 eV would disappear before a close match being
reached, like curve A, in the range over 14.0–16.0 eV. The VLEED calculations
at 23.5° azimuth suggest that the atomic positions in model A are closer to the
true situation than those assigned in others. Unfortunately, none of the models can
provide acceptable simulation at 43.5°, near the <11> direction. This indicates the
305
clean Cu(001) surface suggests that the multiple-diffraction approach is sufficiently
accurate and complete to allow for the inclusion of all necessary diffraction events.
Importantly, the conventional SPB model for pure metal (ideal Fermi system) is
adequate to produce the correct intensity for the high-order diffraction events in the
SPB region.
15.2.2 Oxygen on Cu(001): Model Comparison
To examine the code validity for the O-Cu(001) surface, calculations were performed
with the same convention for clean Cu(001) surface by using geometries of several
missing-row structural models to optimise the SPB parameters. The best model is
then assigned to the one that provides the closest fit to the measured data.
Simulation was conducted to two typical VLEED I–E curves for 300-L oxygen
chemisorbed Cu(001) surface. The incident angle (relative to the normal of the surface) is 69.0° and the azimuth angles of the compared curves are 23.5° (near <21>
direction) and 43.5° (near <11> direction), respectively. Figure 15.2 compares the
atomic positions in the compared models. The side view above shows atomic positions viewing along the -Cu-O-Cu- chain; the bottom is a top view of the Cu(001)(
√
2 × 2
√
2) R45°-2O complex unit cell denoting the azimuth angle of incident
beams. Table 15.1 lists the structural parameters used in calculations. Model A is
derived from the M 2 O tetrahedron structure. The five calculation parameters (D 12 ,
DCu x , DCu z , DO x , DO z ) for model B and C were optimized in earlier LEED calculations [8]. Parameters for structure D are derived from the effective-medium theory
predictions [9].
By using the one-dimensional SPB with nine parameters, qualitative agreement
between measurement and calculation is achieved for the spectrum collected only at
23.5° azimuth angle, far away from the <11> direction for all the compared structural
models, as given in Fig. 15.3. The broken lines are the measured VLEED spectra.
For the 23.5° azimuth, violent features on the curves at about 6.8 and 13.5 eV come
from band-gap Bragg diffraction. The main Rydberg peak on the calculations (solid
lines) at 13.0 eV is very sensitive to the SPB.
All the structures provide the match of the peak position at 13.0 eV but not ideally
the intensities or the FWHM of this peak. The minor inconsistency below 12.0 eV
and the FWHMs of all the simulations suggest the essentiality of SPB modification
by involving the 3D effect and the energy dependent damping processes. The sharp
peak at 15.5 eV and the intensity-difference between measured and calculated results
from 14.0 to 16.0 eV of curves B, C and D could not be eliminated by adjusting SPB
parameters. The main peak at 13.0 eV would disappear before a close match being
reached, like curve A, in the range over 14.0–16.0 eV. The VLEED calculations
at 23.5° azimuth suggest that the atomic positions in model A are closer to the
true situation than those assigned in others. Unfortunately, none of the models can
provide acceptable simulation at 43.5°, near the <11> direction. This indicates the