In the Haynes - Shockley experiment, a piece of semiconductor gets a pulse of holes, induced by voltage or a short laser pulse.
To see the effect, we consider a n-type semiconductor with the length "d". We are interested in determining the mobility of the carriers, diffusion constant and relaxation time. In the following, we reduce the problem to one dimension.
The equations for electron and hole currents are:
:
:
where is mobility, Einstein relation states: .
We consider the continuity equation:
:
:The electrons and the holes recombine with the time .
We define and so the upper equations can be rewritten as:
:
:
Let us consider the part with the gradient of the electric field. Laplace equation states:
:
:
Introducing and