342
17 Blouin Zones, Effective Mass, Muffin-tin Potential…
In the second layer, each Cu atom in every other row along the [100] direction
donates one electron to the oxygen adsorbate. In the case of a Cu atom that has lost
one electron, the residual ion core will also reduce the V 0 due to its residual positive
charge. Every loss of an electron equals taking two electrons away from the sum of
the negative charge, so that the relativistic variation of the V 0 of the second layer is:
[29e × 2(Cu) + (29 − 2)e × 2(Cu
+ )]/[29e × 4(Cu)]
= 112/116 = 96.5%
Thus, the net charge of the top and the second layer is reduced by 9.5% and 3.5%,
respectively. The net charge finally approaches to the bulk value in the third metallic
layer and below, the V 0 of which is less affected by the reaction according to the
current model. The V 0 gradually approaches to the bulk value of the clean Cu(001)
when getting inside into the crystal, but the deeper layers are beyond the scope of
VLEED. Agreement between the analysis and the numerical optimization of the V 0
for the top layer further evidences the reality and integrity of the Cu 3 O 2 bond model
for the Cu(001)–(
√
2 × 2
√
2)R45°–2O
−2 surface reaction.
Although the analysis is simply based on a number count of electrons for the
particular Cu(001)–(2
√
2 ×
√
2)R45°–2O
−2 phase, result reveals the correlation
between the bond forming and the reduction of V 0 and work function. The V 0 relates
to the charge quantity of the corresponding layer, and that at very-low energies the
exchange-interaction between the incident beams and the surface ion is insignificant.
The plasma excitation energy is often ~15 eV below the E F and the incident energy
is insufficient for ionization. This non-exchange-interaction adds another advantage
to the VLEED for nondestructive detection.
17.5.2 Oxygen Reduced Local φ L (E)
As justified, the z-directional integration of the ρ(x, y, z), from the second layer to
infinitely far away of the surface, yields the local DOS n(x, y) that contributes to
the SPB and the work function in the form of [n(x, y)]
2/3 [29]. Since the VLEED
integrates over large surface areas, all the quantities depending on coordinate (x, y)
become E dependent. Therefore, at certain energy the VLEED integration results
the n(x, y) into the n(E) that relates to the occupied DOS and hence the local work
function.
The work function is dimensionless and it depends uniquely on the electron density at surface. However, the concept φ L holds for large surface areas over which the
VLEED integrates for the DOS, and the φ L is also extended to being energy dependent. The work function depends uniquely on the n(E), a z-dimensional integration
of the ρ(x, y, z) at energy E. The z 0 is the boundary of the ρ(x, y, z) (ρ(z 0 ) = 0).
The work function is determined by the z 0 . An outward shift of the z 0 ∼ = 1.0 a.u.
(from −2.3 to −3.3 a.u., closing to the grey scale of the STM image) corresponds
to a φ ∼ = −1.2 eV reduction. This quantity is consistent with the PEEM results of
the O–Pt system due to oxygenation.
17 Blouin Zones, Effective Mass, Muffin-tin Potential…
In the second layer, each Cu atom in every other row along the [100] direction
donates one electron to the oxygen adsorbate. In the case of a Cu atom that has lost
one electron, the residual ion core will also reduce the V 0 due to its residual positive
charge. Every loss of an electron equals taking two electrons away from the sum of
the negative charge, so that the relativistic variation of the V 0 of the second layer is:
[29e × 2(Cu) + (29 − 2)e × 2(Cu
+ )]/[29e × 4(Cu)]
= 112/116 = 96.5%
Thus, the net charge of the top and the second layer is reduced by 9.5% and 3.5%,
respectively. The net charge finally approaches to the bulk value in the third metallic
layer and below, the V 0 of which is less affected by the reaction according to the
current model. The V 0 gradually approaches to the bulk value of the clean Cu(001)
when getting inside into the crystal, but the deeper layers are beyond the scope of
VLEED. Agreement between the analysis and the numerical optimization of the V 0
for the top layer further evidences the reality and integrity of the Cu 3 O 2 bond model
for the Cu(001)–(
√
2 × 2
√
2)R45°–2O
−2 surface reaction.
Although the analysis is simply based on a number count of electrons for the
particular Cu(001)–(2
√
2 ×
√
2)R45°–2O
−2 phase, result reveals the correlation
between the bond forming and the reduction of V 0 and work function. The V 0 relates
to the charge quantity of the corresponding layer, and that at very-low energies the
exchange-interaction between the incident beams and the surface ion is insignificant.
The plasma excitation energy is often ~15 eV below the E F and the incident energy
is insufficient for ionization. This non-exchange-interaction adds another advantage
to the VLEED for nondestructive detection.
17.5.2 Oxygen Reduced Local φ L (E)
As justified, the z-directional integration of the ρ(x, y, z), from the second layer to
infinitely far away of the surface, yields the local DOS n(x, y) that contributes to
the SPB and the work function in the form of [n(x, y)]
2/3 [29]. Since the VLEED
integrates over large surface areas, all the quantities depending on coordinate (x, y)
become E dependent. Therefore, at certain energy the VLEED integration results
the n(x, y) into the n(E) that relates to the occupied DOS and hence the local work
function.
The work function is dimensionless and it depends uniquely on the electron density at surface. However, the concept φ L holds for large surface areas over which the
VLEED integrates for the DOS, and the φ L is also extended to being energy dependent. The work function depends uniquely on the n(E), a z-dimensional integration
of the ρ(x, y, z) at energy E. The z 0 is the boundary of the ρ(x, y, z) (ρ(z 0 ) = 0).
The work function is determined by the z 0 . An outward shift of the z 0 ∼ = 1.0 a.u.
(from −2.3 to −3.3 a.u., closing to the grey scale of the STM image) corresponds
to a φ ∼ = −1.2 eV reduction. This quantity is consistent with the PEEM results of
the O–Pt system due to oxygenation.