17.3 Bond Geometry, Valence DOS, and 3D-SPB
339
(b) Band-gap reflection along the boundary of the second Brillouin zone is apparent, while such reflection at the boundary of the first Brillouin zone is invisible
near the symmetry point (45°). The invisible features are obviously due to the
strong overlap of the Cu 3d3p4s bands near the 11 direction, as illustrated
in Fig. 17.2.
(c, d) The damping surrounding the boundary of the second Brillouin zone features
electron excitation at the edges of different bands. The excitation of electrons
from the bottom of a band seems to be harder than that from the top edge of
a band where the electrons might be denser.
17.4 Inner Potential Constant and Work Function
17.4.1 Beam Energy Reduced V 0
The muffin-tin inner-potential constant V 0 is an important parameter required to
achieve best fit between theoretical calculations and the experimental measurements
of LEED spectra. Earlier investigations [17] revealed that the V 0 decreases with the
energy increases of the incident beams (so-called E-reduced V 0 ), and it was suggested
that the V 0 be affected by the formation of the surface dipole-layer. Investigating the
energy dependence of the V 0 of Ni and Cu surfaces, Jennings and Thurgate [17]
found that the V 0 decreases exponentially with the increase of the incident beam
energy in the normal LEED regime. This reduction was explained with free-electron
like scheme that the exchange-interaction between the ions of metal surface and the
incident electrons will be weakened as the electron velocity increases.
Measurements showed, however, the V 0 changes insignificantly at energies lower
than 40 eV for the Cu surfaces, indicating the insignificance of energy effect on
the V 0 at very-low energies. Rundgren and Malmstrom [18] suggested that the V 0
decreases as energetic incident beams bombard the surface and drag out the surface
ion cores to neutralize the surface negative charges. The sputtering of the surface by
the incident beams reduces the quantity of net charges. If one electron was sputtered
away from the surface, the residual ion core will also reduce the net negative charge.
Therefore, the quantity of surface charges dominates the V 0 .
17.4.2 Oxygen Reduced V 0
For system with chemisorbed oxygen, the variation of V 0 appeared to be much
more complicated. The amount of the reduction varies with crystal structure used
in calculation. The V 0 reduced by 1.21 eV for the Cu(001)–c(2 × 2)–2O and by
2.15 eV for the (2
√
2 ×
√
2)R45°–2O structure [19]. Best fit of the VLEED I–E
curves in this series using the Cu 3 O 2 structure requires a 1.06 eV (9.2%) reduction
339
(b) Band-gap reflection along the boundary of the second Brillouin zone is apparent, while such reflection at the boundary of the first Brillouin zone is invisible
near the symmetry point (45°). The invisible features are obviously due to the
strong overlap of the Cu 3d3p4s bands near the 11 direction, as illustrated
in Fig. 17.2.
(c, d) The damping surrounding the boundary of the second Brillouin zone features
electron excitation at the edges of different bands. The excitation of electrons
from the bottom of a band seems to be harder than that from the top edge of
a band where the electrons might be denser.
17.4 Inner Potential Constant and Work Function
17.4.1 Beam Energy Reduced V 0
The muffin-tin inner-potential constant V 0 is an important parameter required to
achieve best fit between theoretical calculations and the experimental measurements
of LEED spectra. Earlier investigations [17] revealed that the V 0 decreases with the
energy increases of the incident beams (so-called E-reduced V 0 ), and it was suggested
that the V 0 be affected by the formation of the surface dipole-layer. Investigating the
energy dependence of the V 0 of Ni and Cu surfaces, Jennings and Thurgate [17]
found that the V 0 decreases exponentially with the increase of the incident beam
energy in the normal LEED regime. This reduction was explained with free-electron
like scheme that the exchange-interaction between the ions of metal surface and the
incident electrons will be weakened as the electron velocity increases.
Measurements showed, however, the V 0 changes insignificantly at energies lower
than 40 eV for the Cu surfaces, indicating the insignificance of energy effect on
the V 0 at very-low energies. Rundgren and Malmstrom [18] suggested that the V 0
decreases as energetic incident beams bombard the surface and drag out the surface
ion cores to neutralize the surface negative charges. The sputtering of the surface by
the incident beams reduces the quantity of net charges. If one electron was sputtered
away from the surface, the residual ion core will also reduce the net negative charge.
Therefore, the quantity of surface charges dominates the V 0 .
17.4.2 Oxygen Reduced V 0
For system with chemisorbed oxygen, the variation of V 0 appeared to be much
more complicated. The amount of the reduction varies with crystal structure used
in calculation. The V 0 reduced by 1.21 eV for the Cu(001)–c(2 × 2)–2O and by
2.15 eV for the (2
√
2 ×
√
2)R45°–2O structure [19]. Best fit of the VLEED I–E
curves in this series using the Cu 3 O 2 structure requires a 1.06 eV (9.2%) reduction