Gain and recombination dynamics in photodetectors made with quantum nanostructures: The quantum dot in a well and the quantum well

We consider the problem of charge transport and recombination in semiconductor quantum well infrared photodetectors and quantum-dot-in-a-well infrared detectors. The photoexcited carrier relaxation is calculated using rigorous random-walk and diffusion methods, which take into account the finiteness of recombination cross sections, and if necessary the memory of the carrier generation point. In the present application, bias fields are high and it is sufficient to consider the drift limited regime. The photoconductive gain is discussed in a quantum-mechanical language, making it more transparent, especially with regard to understanding the bias and temperature dependence. Comparing experiment and theory, we can estimate the respective recombination times. The method developed here applies equally well to nanopillar structures, provided account is taken of changes in mobility and trapping. Finally, we also derive formulas for the photocurrent time decays, which in a clean system at high bias are sums of two exponentials.