Effects of Electrons and Holes on the Transition Layer Characteristics of Linearly Graded P-N Junctions

The dc theory of p-n junctions has been extended, taking into account the mobile carriers or electrons and holes in the transition region. The linearized Poisson-Boltzmann equation is solved by using a linearization parameter ¿, which is a measure of the relative importance of the fixed, ionized impurity space charge compared with the mobile carrier or electron and hole charges in the transition region of the p-n junction. It is found that both the transition layer width and the transition carrier capacitance associated with the electrons and holes in the transition region increase exponentially with applied voltage under forward bias condition. A calculation of the recombination-generation current at a forward bias beyond the built-in or diffusion voltage is now possible with the present theory. The dc theory of junction capacitance compares favorably with experimental measurements of a wide variety of nearly linear-graded diffused silicon junctions.