Carrier Diffusion in a Semiconductor
A semiconductor crystal at T1 = 263 K, X1 = 1 mm thick, has one surface illuminated with light,
so that free carriers (electrons and holes) are generated at the surface.
The carriers diffuse away into the sample. (Note that the electrons appear to head
to the right only because there is nothing on the left.)
An observable number of carriers makes
it across the crystal, 1 mm (in the x-direction) after t1 = 125.4 μs.
When we illuminate an identical crystal, but at T2 = 300 K, and of an unknown thickness X2, we measure
that it takes an observable number of carriers t2 = 627.1 μs to cross it.
You may assume for this problem that all the carriers have the same mass, that of a
free electron (me = 9.11 X 10-31 kg), and that the mean scattering length
remains constant over the range of temperatures in the problem.
How thick is the second crystal ?
X2 = mm