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.
The equations for electron and hole currents are: where the js are the current densities of electrons (e) and holes (p), the μs the charge carrier mobilities, E is the electric field, n and p the number densities of charge carriers, the Ds are diffusion coefficients, and x is position.
We define so the upper equations can be rewritten as: In a simple approximation, we can consider the electric field to be constant between the left and right electrodes and neglect ∂E/∂x.
, where β is the inverse of the product of temperature and the Boltzmann constant, these two equations can be combined: where for D*, μ* and τ* holds: Considering n >> p or p → 0 (that is a fair approximation for a semiconductor with only few holes injected), we see that D* → Dp, μ* → μp and 1/τ* → 1/τp.
The final equation for the carriers is: This can be interpreted as a Dirac delta function that is created immediately after the pulse.