Based on full quantum-transport simulations, we report a comprehensive study of the evaporative cooling process in a double-barrier semiconductor heterostructure thermionic refrigerator. Our model, which self-consistently solves the nonequilibrium Green’s function framework and the heat equation, is capable of calculating the electron temperature and electrochemical potential inside the device. By investigating the dependence of those thermodynamic parameters as a function of the barrier thickness and height, we answer open questions on evaporative cooling in solid-state systems, and give a clear recipe to reach high electron refrigeration. In particular, simulation results demonstrate that the best cooling is obtained when (i) the device operates at the maximum resonant condition; (ii) the quantum well state is symmetrically coupled with the contacts. The present results then shed light on physical properties of evaporative cooling in semiconductor heterostructures and will allow the development of thermionic cooling devices towards unprecedented performances to be sped up.
Fig. 1: (left) Sketch of the considered asymmetric double-barrier heterostructure. Lemit, LQW, and Lcoll refer to the thicknesses of the emitter barrier, the quantum well and the collector barrier, respectively. W is the activation energy, defining the gap between the QW state E0 and the top of the collector barrier. EFE and EFC are the Fermi levels of the emitter and collector, respectively. For all the considered devices, doping in the emitter and the collector is 1018 cm−3, LQW = 6 nm and Lcoll = 100 nm; (right) Emitter-barrier thickness (Lemit) dependence as a function of the applied bias V for the electron temperature in the QW—note that for all the devices, temperature exactly equals 300 K at V = 0 V. Temperature depicts similar profile for the six considered thicknesses. Starting from room temperature at equilibrium, it reaches a minimum before sharply increasing above 300K at large bias. However, the bias corresponding to the temperature minimum varies with Lemit. The red circles indicate the bias at which the resonant condition is fulfilled for each Lemit. Interestingly, we see that the temperature minimum coincides very well with the resonance condition. Indeed, current density being maximum at the resonant regime, the filtering of electrons on the collector barrier is the most relevant. Beyond the resonance, ballistic electrons are injected into the QW at higher energy, leading to a strong temperature increase.
Ref : M. Bescond, G. Dangoisse, X. Zhu, C. Salhani and K. Hirakawa, “Comprehensive analysis of electron evaporative cooling in double-barrier semiconductor heterostructures,” Phys. Rev. Appl. 17, 014001 (2022).