12
2 What is the Work Function?: Definition and Factors …
vacuum
charge density
Electrons spreading out
Electrons spreading out
-
+
Ion core
Ion core
Fig. 2.6 Schematic illustration of the origin of the surface term of the work function. The left
picture depicts a schematic cross-sectional electron contour map near the surface and the right
picture shows the charge density of electrons across the surface region
the vacuum side, which is the origin of the surface electrostatic potential. This term
is called the “surface term” in the text.
Here we reintroduce the energy diagram of electrons near the surface by replacing
potentials with energy levels, i.e., the chemical potential μ with the Fermi level
E F , φ V with E V AC , and φ B with E V AC(bulk) (Fig. 2.7). The work function φ is the
energy difference E V AC − E F . We represent the surface term of the work function,
φ V − φ B = E V AC − E V AC(bulk) , as S and the bulk term of the work function,
E V AC(bulk) − E F , as B . According to density functional theory (DFT) applied to
the jellium model, the bottom of the valence band is located V XC below E V AC(bulk) ,
where V XC is the exchange–correlation energy. Valence electrons occupy energy
levels from the bottom of the valence band up to E F , which is located
2
2m
k
2
F above
the bottom of the valence band.
Fig. 2.7 Energy diagram of electrons near the surface obtained by replacing potentials with energy
levels, chemical potential μ with Fermi level E F , φ V with E vac , φ B with E vac(bulk)
2 What is the Work Function?: Definition and Factors …
vacuum
charge density
Electrons spreading out
Electrons spreading out
-
+
Ion core
Ion core
Fig. 2.6 Schematic illustration of the origin of the surface term of the work function. The left
picture depicts a schematic cross-sectional electron contour map near the surface and the right
picture shows the charge density of electrons across the surface region
the vacuum side, which is the origin of the surface electrostatic potential. This term
is called the “surface term” in the text.
Here we reintroduce the energy diagram of electrons near the surface by replacing
potentials with energy levels, i.e., the chemical potential μ with the Fermi level
E F , φ V with E V AC , and φ B with E V AC(bulk) (Fig. 2.7). The work function φ is the
energy difference E V AC − E F . We represent the surface term of the work function,
φ V − φ B = E V AC − E V AC(bulk) , as S and the bulk term of the work function,
E V AC(bulk) − E F , as B . According to density functional theory (DFT) applied to
the jellium model, the bottom of the valence band is located V XC below E V AC(bulk) ,
where V XC is the exchange–correlation energy. Valence electrons occupy energy
levels from the bottom of the valence band up to E F , which is located
2
2m
k
2
F above
the bottom of the valence band.
Fig. 2.7 Energy diagram of electrons near the surface obtained by replacing potentials with energy
levels, chemical potential μ with Fermi level E F , φ V with E vac , φ B with E vac(bulk)