Generation-Recombination and Mobility
The chapter illustrates the main contributions to the transitions of the inter-band type, that give rise to the generation-recombination terms in the continuity equations for electrons and holes, and to those of the intra-band type, that give rise to the electron and hole mobilities in the current-density equations. The inter-band transitions that are considered are the net thermal recombinations (of the direct and trap-assisted type), Auger recombinations, impact-ionization generations, and net-optical recombinations. The model for each type of event is first given as a closed-form function of the semiconductor-device model’s unknowns, like carrier concentrations, electric field, or current densities. Such functions contain a number of coefficients, whose derivation is successively worked out in the complements by means of a microscopic analysis. Some discussion is devoted to the optical-generation and recombination events, to show how the concepts of semiconductor laser, solar cell, and optical sensor may be derived as particular cases of non-equilibrium interactions between the material and an electromagnetic field. The intra-band transitions are treated in a similar manner: two examples, the collisions with acoustic phonons and ionized impurities, are worked out in some detail; the illustration then follows of how the contributions from different scattering mechanisms are combined together in the macroscopic mobility models. The material is supplemented with a brief discussion about advanced modeling methods.