On the diffusion theory of rectification

It is pointed out that the Einstein relation eD = vkT between the mobility (v) and the diffusion coefficient (D) of current carriers has not so far been established theoretically or experimentally for the case of rectifying junctions which are carrying a current. It is shown that the theory can be developed without appealing to this relation, so that experimental characteristics can be utilized to test for the validity of the Einstein equation. When this is done experiment suggests different values of v, D and v/D for forward characteristics from those it does for reverse characteristics. This result has been discussed, taking into account Fermi-Dirac statistics, in the light of the formal theory of conduction. This has been shown to lead (a) to the diffusion equation and (b) to a slight modification of Einstein’s relation, provided v and D are regarded as averages for the barrier. Strictly, v and D depend on the concentration distribution of conduction electrons in the barrier. The shapes of the experimental curves are in agreement with theory.