Chemistry Reference
In-Depth Information
found to be significant for silicon electrodes in HF solutions, where the dissolution
intermediates are further oxidized by injecting electrons in the conduction band, result-
ing in current that is much larger than the minority dark limiting current.
8,38
1.4.5. Potential Distribution
The statically charged region at the silicon/electrolyte interface is composed of a
space charge layer in the silicon and double layer in the electrolyte. Any potential
change across the interface must be accomondated by one of the two layers or shared
by them. The partition of potential under a reverse bias when the current is very small
is determined by the relative value of the capacitance at the space charge layer, the
surface state capacitance, and the Helmholtz layer capacitance. On the other hand, under
a forward bias the partition of potential depends not only on the relative values of the
capacitances, but also on the kinetics of charge transfer across each layer. When there
is an oxide present, the potential may further be partitioned among the oxide film and
the two double layers.
In general, in the absence of an oxide the partition of the applied potential
across the space charge layer and the Helmholtz layer depends on doping concentra-
tion and current range. There are also two different potential distributions depending
on whether it is under a forward bias or a reverse bias. Under a forward bias for an
anodic process on a
p
-type semiconductor electrode the current density can be described
as follows
724
:
where is the exchange current density,
and
are the surface concentration of holes
under current flow and at equilibrium, and
is the overpotential for the anodic reac-
tion. The total applied voltage,
under anodization is the sum of the potential drop
in the Helmholtz layer,
in the space charge layer,
and concentration overpoten-
tial in the electrolyte,
That is,
According to the calculation by Kang and Jorne,
724
the fraction of the potential drop
across the space charge region depends on the doping level and exchange current
density. Under the same current density, decreases with increasing doping level.
When the doping level is the voltage drop in the space charge region is very small,
on the order of millivolts, and most of the potential drop occurs in the Helmholtz layer.
As the doping level decreases, a relatively larger fraction of the total overpotential
occurs in the space charge region as shown in Fig. 1.18. At a very low doping level,
when the concentration of holes is very small, the potential drop occurs almost entirely
in the space charge layer. The plot of logarithmic current versus potential then gives a
60 mV/decade relationship.
