The characterization of the static behavior of p-n junction devices

This paper examines the static behavior of certain p-n junction devices that are governed by Van Roosbroeck's differential equations. It is found that this set of first-order differential equations accurately predicts semiconductor static behavior in both the bulk and the transition regions. The purpose of this model is to find the hole and electron concentrations, hole and electron currents, and electric field as functions of position and external excitation. For part of the paper, use is made of the quasi-neutrality approximation in the bulk regions and the quasi-equilibrium Boltzmann relations (QEBR) which relate the hole and electron concentrations at transition region edges to the applied voltage across the transition region. The unijunction transistor with intrinsic base, p-i and p-in diodes, and a new current gain device are examined using these concepts, and the results are compared with experiment. By applying boundary conditions only at the ohmic contacts, a p-i diode problem is solved on a computer. One especially important point in this problem is that quasi-neutrality of the base and the QEBR are not imposed upon the problem. However, the final results indicate that these concepts are good approximations, except for extremely short devices.