Tip-geometry enhanced cooling of field emission from the n-type semiconductor

Abstract

The cooling effect of field emission from an n-type semiconductor was theoretically investigated in quest for a solid state cooler. The vacuum potential was exactly expressed in terms of the semiconductor cathode geometry. This leaded to the more accurate configuration-dependent calculations of the energy exchange and the cooling power. It has been shown that a sharper tip of semiconductor can yield either a larger field emission current density or a larger energy exchange, according to the applied bias. For an atomic size tip, the n-Si cathode yielded the cooling power density Γ = 2.0, 75, and 713 W/cm2 at temperature T = 300, 600, and 900 K, respectively. This implies that an optimized configuration of an n-Si cathode produces a significant electron emission cooling, especially at high temperatures.