1.
2.
We need to apply the boundary conditions for this problem:
where n B0 is the thermal equilibrium electron concentration in the p-type Si.
As the recombination velocity S is zero, we find in this case
With these boundary conditions we find the two equations
We find for the constants A and B
The full solution for the excess electron concentration is then
We find for the electron current density
When the emitter is much more highly doped than the base, the current is virtually only
carried by the electrons. This current should be constant anywhere in the device, so also
for x = 0, we find
Using
and
we finally find the saturation current density J 0 to be