Fluctuations of the Numbers of Electrons and Holes in a Semiconductor

Abstract

In calculations of certain types of noise in semiconductors it is required to know the fluctuation in the number of mobile charge carriers (electrons and holes). These fluctuations are calculated for a non-degenerate semiconductor in thermal equilibrium by two different methods: the first in terms of the electronic free energy of the system whose minimal properties are used to determine the equilibrium distribution and fluctuations of electrons between the conduction and valence bands and the impurity levels. The second approach is purely statistical and is based on the probabilities of the elementary processes of electron transitions between energy levels. The results of the two methods are identical but the thermodynamical method yields the solutions for complex cases which are not readily dealt with by the statistical method. Both intrinsic and extrinsic semiconductors are discussed, as well as the important practical case of a nearly intrinsic semiconductor.