Space Charge in Semiconductors Resulting from Low Level Injection

Abstract

A solution of the continuity equations is obtained for the space charge distribution by assuming (1) that deviations from neutrality are small, and (2) that the space charge fields, which are a consequence of the terms containing ▿·E in these equations give rise to pure diffusion and pure ``drift-wave'' terms with time dependent coefficients. It is, for equal numbers of holes and electrons initially injected, e[(p−p0)−(n−n0)]=−τρ∇ lim E·J[1−exp(−t/τρ)], where τρ equals K/4πσ, the relaxation time, J is the total current density including diffusion, as well as drift, and ∇ lim E means that the divergence does not operate on E (the electric field is held constant). In the differentiation ∂n/∂x and ∂p/∂x are considered to be equal, as are ∂2n/∂x2 and ∂2p/∂x2. Working independently, H. Brooks and W. van Roosbroeck arrived at expressions for both the ambipolar diffusion coefficient and the ``group mobility'' of the drift of a pulse of excess carriers. This theory yields the same results, and, in addition, transient expressions are gotten for each.