2.2 Origin of the Work Function
13
We see that the origin of the surface term of the work function is the charge
distribution of valence electrons, which generates an electric dipole at the surface.
For metals where the density of carriers is large, the length of the dipole is in the
range of the Fermi wavelength (typically ~1 nm). However, for semiconductors with
carrier density orders of magnitude less than that of metals, the electron redistribution
extends far below the surface. The dipole due to the electron redistribution causes the
electrostatic potential to extend rather deeply in the case of semiconductors, resulting
in so-called “band bending” (Fig. 2.8a). The depth of band bending W is expressed
as [3]
W =
ε
2π e 2 ×
eφ
N
.
(2.5)
Fig. 2.8 a Band bending on the surface of a semiconductor. b Flat-band realization by surface
treatment. c Band diagram for negative electron affinity. See text for explanation
13
We see that the origin of the surface term of the work function is the charge
distribution of valence electrons, which generates an electric dipole at the surface.
For metals where the density of carriers is large, the length of the dipole is in the
range of the Fermi wavelength (typically ~1 nm). However, for semiconductors with
carrier density orders of magnitude less than that of metals, the electron redistribution
extends far below the surface. The dipole due to the electron redistribution causes the
electrostatic potential to extend rather deeply in the case of semiconductors, resulting
in so-called “band bending” (Fig. 2.8a). The depth of band bending W is expressed
as [3]
W =
ε
2π e 2 ×
eφ
N
.
(2.5)
Fig. 2.8 a Band bending on the surface of a semiconductor. b Flat-band realization by surface
treatment. c Band diagram for negative electron affinity. See text for explanation