THEORY OF NOISE IN A MULTIDIMENSIONAL SEMICONDUCTOR WITH A P-N JUNCTION

Abstract
This thesis discusses the fluctuations of noise in a two and three dimensional semiconductor containing a p-n Junction. We consider a rectangular parallelepiped single crystal It is bisected in the longest dimension by a p-n Junction. Since this dimension is several diffusion lengths it can be considered infinite. In the transverse plane we investigate the case where both dimensions are finite, and then the case where one is finite and the other infinite. In the p-n junction the noise is the result of fluctuations in the minority carrier density. in a p-n Junction there are two classes of minority carriers: 1. holes in the n-type material, 2. electrons in the p-type material. Since both the and electron density fluctuations are similar, we discuss only the former in detail. We investigate the differential equations for a two and three dimensional semiconductor with a p-n Junction and find the inhomogeneous form of these equations. These equations are solved with the help of the scalar and tensor green's function. The noise problem is solved by using these equations as Langevin equations and interpreting the distributed sources as random forces. Then the noise current spectrum is determined with stochastic process theory after deriving the sources from basic physical models and the theory of stationary, ergodic, Markovian processes. We consider two cases of surface recombination velocity on the transverse surfaces: infinite s and finite s. For the infinite case, we get the exact solution which provides an upper bound for the noise spectrum for large a. For an arbitrary S we get a solution but have confidence in the solution for only small s. Therefore we have obtained a complete solution for the two cases of practical interest: large and small surface recombination velocity. These cases should prove of interest in the analysis of noise phenomena in semiconductors.

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