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Auger recombination and impact ionization involving traps in semiconductors

1964; IOP Publishing; Volume: 84; Issue: 6 Linguagem: Inglês

10.1088/0370-1328/84/6/311

1747-3810

P. T. Landsberg, C Rhys-Roberts, Pyare Lal,

Advanced Chemical Physics Studies

Using Bloch and hydrogen-like wave functions calculations have been made of the recombination rates by Auger processes in which one localized and three band states are involved. Four essentially different processes have to be considered, depending on how many of the states are in the conduction band and how many are in the valence band. In addition, each transition rate depends on the quantum numbers (n, l) of the localized state involved in the transition. This problem is solved in zero-order which is valid when the energy change of an electron making a transition is large compared with kT. The validity of this calculation is considered by extending the calculations for the ground state to higher order. The zero-order results for the excited states and the higher order results for the ground states, as well as the detailed consideration of exchange effects at various points in the paper, appear to be new. Zero-order results for the ground state have been obtained by previous workers. These results however, must be amended to ensure a self-consistent theory. Formulae are given which enable impact ionization coefficients to be obtained from the recombination coefficients. The calculated recombination coefficients are presented in graphical form, and show (i) at low temperatures a fluctuating variation with the quantum number l of the excited state into which an electron is captured, (ii) an expected variation with the energy level of the donor, (iii) a negligible effect due to exchange, (iv) that the higher order terms can be important.