Einstein showed that the parameters, mobility and diffusion coefficients are directly related. Here mobility describes drift of the charge carrier and diffusion coefficient describes diffusion of the charge carriers. Under equilibrium conditions these two forces are equal.
So, in p-type semiconductor drift current is equal to diffusion current of the electrons
Equating both the above equations we get
With the increase in concentration of electrons, pressure energy also increases. The force corresponding to pressure energy gradient is
By equating both the above forces we get,
from the above equation, the ratio of diffusion coefficient of the mobility is directly proportional to its temperature
This relation is called Einstein's relation