The statistics for an arbitrary distribution of traps under nonequilibrium steady-state conditions is derived, and it is seen to be identical in form to the Shockley-Read expression for a single trapping level. The energy dependence of the statistics has been investigated, and several interesting features have been deduced. It has been found appropriate to describe the occupancy of the traps in terms of two modulated Fermi-Dirac functions-one associated with trapped electrons, the other with trapped holes. It has been found possible to categorize the traps (into species) in terms of the ratio of their electron and hole capture cross sections. Detailed discussions are given for the electron and hole fillings of the traps as a function of energy, temperature, and illumination intensity for various trap distributions. The distinctions between shallow traps, recombination centers, and dead states are defined and discussed in detail.

• Received 10 December 1970

DOI:https://doi.org/10.1103/PhysRevB.4.502