Auger Theory at Defects—Application to States with Two Bound Particles in GaP

Auger transitions at defects in semiconductors are investigated with the objectives of determining the wave-function influence, carry out interimpurity comparisons, and apply the results to defects in GaP. As an aid to this, it is shown that in indirect-gap semiconductors the Auger transition matrix can be factored, approximately, into a product of overlap integrals over the periodic parts of the wave functions and an interaction integral with the nonperiodic parts. This result simplifies calculations and moreover shows that interimpurity comparisons should be quite reliable. Specific calculations are carried out for systems with two bound particles. A He-type defect is used to examine the role of the bound-state wave function by use of several He Hylleraas-type functions; it is concluded that the effect of wave-function variation is minor. The He system is then compared with an excitonlike defect for interdefect comparison. The results are applied to defects in GaP, with halide impurities as prototypes for He-like defects, and the Zn-O complex for exciton defects. It is shown that the theoretical Auger probability of the complex agrees with experimental values. It is also shown that Cl is an appreciably stronger Auger center than Zn-O.