A general solution for step junctions with infinite extrinsic end regions at equilibrium

We present here a unified solution to determine the potential profiles for step junctions in equilibrium. The complete solution is determined by solving for the two sides of the junction separately. The generalized solution consists first of a curve corresponding to majority-carrier accumulation, i.e, the low side of high-low junction. Second, it consists of a family of curves corresponding to majority-carrier depletion, i.e., the high side of a high-low junction and either side of a p-n junction. The curves in the latter case approach a common asymptote that by itself constitutes a solution for all but lightly doped sides of asymmetric p-n junctions.