Chemistry Reference
In-Depth Information
In the case of the valence band process, an electron transfer into the valence band
is only possible if holes are present at the surface. This means the density of empty
states equals the hole density at the surface,
Thus, the valence band anodic
current is
Integrals (1.52) and (1.53) can be analytically solved only by making some assump-
tions. Assuming for the conduction band process and for the valence
band process because electron transfer occurs mainly with 1
kT
of the band edges and
assuming is constant, integrals (1.52) and (1.53) can be approximated by the fol-
lowing equations for the anodic currents via the conduction and valence bands:
Similarly, one can obtain the approximate equations for the cathodic currents via the
conduction and valence bands:
For non-heavily doped semiconductors, the potential variation occurs only across the
space charge layer and the potential across the Helmholtz layer is constant. This means
that the exponential terms in Eqs. (1.54) to (1.57) are independent of applied potential,
that is, Thus, and are independent of the potential and can
be taken as constants: and The only quantities that are dependent on poten-
tial are and which are described by Eqs. (1.19) and (1.20). At equilibrium the
anodic and cathodic currents across each energy band must be equal, i.e.,
Also, the surface carrier concentrations at equilibrium can be described by
and
which are given by Eqs. (19) and (20):
where is the band bending at equilibrium. At potentials departing from equilibrium,
the surface carrier concentrations are described by
