Spontaneous radiative recombination and nonradiative Auger recombination in quantum-confined heterostructures

General approach is described to the rates, fluxes and current densities associated with spontaneous radiative and nonradiative Auger recombinations in heterostructure lasers with different types of a quantum-confined active region (quantum wells, quantum wires, and quantum dots). The proper way of defining the spontaneous radiative and Auger recombination coefficients and their dimensionality are discussed. It is shown that only in a quantum dot, true time constants can be introduced for spontaneous radiative and nonradiative Auger recombinations, which are independent of the injection level. Closed-form elegant expressions are presented for the radiative recombination coefficient as an explicit function of temperature and parameters in bulk and quantum-confined structures. These expressions clearly demonstrate inappropriateness of the common practice of deriving the recombination coefficients in low-dimensional heterostructures from the bulk values.