Contents
. Introduction
Capture cross-sections and lifetimes
Recombination mechanisms3.1 Phonon mechanism 3.2 Impact mechanism 3.3 Plasmon, exciton, and spin mechanisms 4 . Capture by charged centres
. Radiative recombination as a tool of studying the energy s p e c t~u m of a solid
Append& ReferencesA review is given of various mechanisms of the charge carriers recombination in semiconductors. A theoretical estimate of the relative importance of various mechanisms is given as well as the relevant temperature dependences of the capture cross-sections. Influence of the static electric field upon the recombination rate is considered in connection with the electrical instability problem. An enlarged version of the report given by one of the authors (V.L.B.-B.) at the Tagung der Physikalischen Gesellschaft in der DDR, April 1967. The hospitality of the Physikalische Gesellschaft in der DDR and of the Humboldt-Universitiit in Berlin is gratefully acknowledged. c n = J f n (~) V ( P ) an(P) d~ * Here f,(p) is the electron distribution function normalized to unity, v ( p ) is the absolute value of the electron velocity if the crystal momentum is equal to p, a,(p) is the electron capture cross-section for the trap level in question. The integral is taken over the Brillouin zone. The same equation (with the obvious change of notation) holds for C,. The quantities C , and C, have dimensions of L3 T -l . Multiplying them by concentrations of the vacant (occupied) centres of the type considered one obtains the transition probabilities of the electron (hole) from the conduction (valence) band to the level in q~estion.~) Every level is thus characterized by the two capture coefficients, C, and C,. Sometimes they are written in the form c,, = v 7 r sn,, 3 (1.2)where V , is the thermal velocity of the free electron while S, and S, are the quantities having dimensions of La. They are called the average capture crosssections (or simply capture cross-sections), not to be mixed with the "mechanical" cross-section a,, a , ! The aim of the recombination physics is to study these quantities as functions of temperature, electric, and magnetic field strength, etc. ,The rate of the direct band-to-band recombination is conveniently expressed in terms of the recombination probability per unit time per unit volume, R. For 5, Usually q M lo-@ to 8. However, the situation may change under low enough temperatures (see, for example, [7] to [S]). 4, Equation (Ll), if taken literally, refers to the case of the carriers captured by Borne point defects (impurities included). However, the same formal equation is valid as well in ca8e of the linear imperfections, such as dislocations, the cross-section u , , being replaced by an "effective capture radius". 8, T M to
