Hot electron relaxation in periodic type-II quantum well

In hot carrier photovoltaic devices, photoexcited electrons and holes are spatially separated in "Type II" quantum wells to reduce their recombination rate. The excess energy of the hot electrons can be lost to optical phonons through electron-phonon interactions. These optical phonons decay into acoustic phonons and eventually leave the system as heat. Previously, we have calculated the phonon modes of the repeated quantum well/barrier supercell and shown that the energy escaping rate is significantly reduced in this structure compared to a pure semiconductor. We build on this to develop a model to predict the steady-state of the hot electrons. We describe the electron dynamics with a fermionic Boltzmann rate equation, where an external light source pumps the hot electron population, and the electron-phonon interaction changes the population distribution of electrons in energy space. The distribution for the relevant optical phonon is modeled with a bosonic rate equation, including their decay into acoustic modes and leaking to a normal mode of the supercell and leaving the system. Solving these coupled equations with realistic parameters can predict and possibly optimize the steady-state, non-equilibrium, hot electron distribution.