The potential and electric field at the metallurgical boundary of an abrupt p-n semiconductor junction

Analytical equations are presented that rigorously establish the electrostatic potential and electric field at the metallurgical transition point of an abrupt p-n semiconductor junction. From these equations, the classical depletion-layer approximation is shown to be rigorously correct only when (NA= ND), although this solution remains adequate for engineering purposes if 1.0 ≤ NA/ ND≤ 10.0, approximately. It is also shown that mechanisms of operation take place within an asymmetrical abrupt junction (NA≥ ND) that cannot be deduced from the depletion-layer aproximation. For example, the asymmetrical junction is shown to contain an electrostatic potential and an electric field at its metallurgical transition point that are essentially constant throughout a wide range of reverse biasing voltage. These characteristics imply that the total electrostatic charge within its p-type and n-type space charge layers remain essentially constant, and that its p-type space-charge layer is of constant width, despite the application of a reverse biasing voltage. These heretofore unreported mechanisms of operation arise from a layer of mobile charge carriers residing at the low-doped side of the metallurgical transition between n-type and p-type semiconductor material.