Spontaneous Radiative Recombination in Semiconductors

Abstract

The mechanisms by which electrons and holes recombine with the emission of radiation are examined. Expressions are derived for the radiative recombination lifetimes due to direct and indirect transitions and are applied to Ge and Si. Matrix elements in the transition probability for direct and indirect transitions are obtained from analyses of the cyclotron resonance effective mass data and the optical absorption data close to the band edge, respectively. For indirect transitions the calculated lifetimes were of the order of seconds and agreed within a factor of 3 with lifetimes calculated by the method of Van Roosbroeck and Shockley. It is shown that in Ge at room temperature, while the density of filled states in the conduction band at k=0 is very low, the rate of recombination by direct transitions is nevertheless somewhat greater than that by indirect transitions. This is consistent with the findings of Haynes. The role of radiative recombination in the observed lifetimes of excess carriers is questioned. It is concluded that for those semiconductors which have a rather high absorption constant close to the band edge (InSb), an emitted photon is usually reabsorbed before it can escape from the crystal, producing another hole-electron pair, without contributing to the macroscopically observed lifetime. In the limit of a very high absorption constant, this emission and absorption of photons acts as an additional mechanism for the diffusion of hole-electron pairs.