Chemistry Reference
In-Depth Information
which means that under a steady-state condition the change of hole concentration
caused by diffusion, recombination, and photogeneration is zero. Using the boundary
conditions
and
p =
0 at
one obtains the solution for
as
Combining Eq. (1.84), (1.85), and (1.86), one obtains the expression for the absolute
value of photocurrent:
Equation (1.89) can be further simplified for the two extreme cases shown in Fig. 1.20.
For
in the case of weak absorption, Eq. (1.89) can be expanded and one obtains
For strong absorption, i.e.,
Eq. (1.89) becomes
i.e., all created carriers contribute to photocurrent and
is independent of doping
concentration and potential.
The ratio of the number of electrons transferred through the external circuit to
the number of photons striking the semiconductor surface is defined as quantum yield
or quantum efficiency:
The net photocurrent and the quantum yield are a function of a number of competing
processes
1154
as shown in Fig. 1.22. For an
n
-type semiconductor, the externally mea-
surable current
i
is the difference between the photocurrent and the forward current of
electrons. The electron current is decreased to zero under certain anodic bias. While
the flux of holes to the surface is exclusively controlled by the solid-state properties,
all the other reaction steps depend on the surface properties of the semiconductor. The
holes arriving at the surface can either (i) transfer to an electron donor in the solution,
(ii) be trapped at the surface states, or (iii) recombine with electrons in the conduction
band in the depletion region or at the surface. Process (iii) does not generate current in
the external circuit, whereas process (ii) produces only transient current charging up
the surface states. Only process (i) produces steady photocurrent. The measured pho-
tocurrent
can therefore be different from the flux of holes to the surface due to these
processes.
All these processes are strongly dependent on the band bending. In the absence
of surface recombination and with a fast kinetics of electron transfer, the photocurrent
