Basic equations for statistics, recombination processes, and photoconductivity in amorphous insulators and semiconductors

Abstract

The original work of Shockley and Read, which described the statistic of a single trapping level in terms of four simple processes, is applied to insulators and semiconductors containing an arbitrary distribution of trapping levels. These statistics formerly involved solving an arbitrary number of rate equations; however, by the use of a mathematical artifice, a simple formal solution is obtained. The solution is also shown to be generally valid for an arbitrary dependence in energy of the cross sections σn(E) and σp(E) and to be independent of the effects of band to band recombination. Using the statistics, expressions are derived for the rate of recombination and the lifetimes of free carriers in such systems. Also, the ground rules for photoconductivity in amorphous materials are presented; these rules are summarized by two general equations. The first is the steady-state rate equation giving the total net rate of recombination of photoexcited carriers via all the trapping levels in the energy gap. The second is a general statement of charge neutrality, which shows that the excess charge contained in trapping levels above EF0 (the equilibrium Fermi level) is equal to the charge that has been removed from trapping levels below EF0. © 1972.