Engineering Physics

8.8 Einstein’s relations

Einstein showed the direct relation between the mobility (μ) and diffusion coefficient (D) of a semiconductor. Suppose a semiconductor is in equilibrium at some temperature T K with no applied electric field. The free electrons and holes distribution is uniform and there is no net current flow in any direction. Any disturbance in the carrier concentration leads to diffusion current in the material. As the material is at some temperature T K, it possesses electrical resistance due to thermal vibrations of ions. The product of resistance and diffusion current results in voltage and hence electric field in the material. Therefore, in equilibrium, the drift and diffusion currents due to excess concentration are equal. So, ...