Radiative heat transfer at nanoscale: Closed-form expression for silicon at different doping levels

Radiative heat transfer at the nanoscale is becoming an important technological issue with the development of nano electromechanical systems (NEMS). In this article, we derive asymptotic expressions to compute near-field radiative heat transfer between two planes of silicon. We identify two physical mechanisms that give the dominant contribution at small gaps. For intrinsic and low-doped silicon, the main contribution is due to evanescent waves coming from propagating waves undergoing frustrated total internal reflections at the interfaces. For doping levels larger than Ne=1016cm−3 surface mode coupling contributes to the heat transfer. Asymptotic expressions are also given in that case. In all cases, we compare analytical formulas with exact numerical calculations when varying the temperature and the doping concentration. We also give their range of validity.