The Statistics of Charge Carrier Fluctuations in Semiconductors

The statistical fluctuations in the number of charge carriers (conduction electrons of valence band holes) in a given volume of semiconductor in the steady state is calculated from the transition probabilities of electrons between the conduction and valence bands or between either band and impurity levels The case in which one independent fluctuating variable (either n or p ) specifies the electronic state of the system is considered. Simple general formulae are developed for the mean value n 0 of n and its variance and it is shown that for large numbers n tends to be normally distributed about n 0 . The relaxation time for small deviations from equilibrium is evaluated. These results are applied to three cases: (i) the intrinsic semiconductor, (ii) the strongly extrinsic semiconductor and (iii) the slightly extrinsic semiconductor with all impurity atoms ionized. The relation between the statistical approach and the thermodynamical treatment (given in another paper) is indicated.