Semiconductor Devices: Physics and Technology, 3rd Edition

Appendix I

Derivation of Recombination Rate for Indirect Recombination

A schematic diagram of the various transitions that occur in recombination through recombination centers is shown in Fig. 13 of Chapter 2. If the concentration of centers in the semiconductor is N_t, the concentration of unoccupied centers is given by N_t(1-F), where F is the Fermi distribution function for the probability that a center is occupied by an electron. In equilibrium,

where E_t is the energy level of the center and E_F is the Fermi level.

Therefore, the capture rate of an electron by a recombination center (Fig. 13a of Chapter 2) is given by

We designate the proportionality constant by the product v_thσ_n, so that

The product v_thσ_n may be visualized as the volume swept out per unit time by an electron with cross section σ_n. If the center lies within this volume, the electron will be captured by it.

The rate of emission of electrons from the center (Fig. 13b) is the inverse of the electron capture process. The rate is proportional to the concentration of centers occupied by electrons, that is, N_tF. We have ...