Rate Equations Description of the Asymmetric Double Barrier Electronic Cooler

Recent experimental results showed that an electron gas in an asymmetrical double barrier heterostructure can be effectively cooled down under resonant tunneling condition, thus leading to the realization of an electronic cooler. The cooling process is a multi-parameters phenomenon and it is desirable to handle this problem through a reasonably simple approach, in order to understand the role of each parameter. To this end, we present a rate equation modeling of the electron cooling. We model the resonant tunnel injection of the electrons in the well and their thermionic emission assisted by Longitudinal Optical (LO) phonons absorption and emission. The influence of several parameters on the electronic temperature is discussed. This simple model compares rather well to the predictions of non-equilibrium Green function approach and to the experiments.