Carrier concentration-dependence of the Nottingham cooling of an n-type silicon semiconductor

Abstract

The authors investigated the Nottingham effect of an n-type silicon semiconductor cathode in a quest for a practical solid-state cooler. The dependence of field emission cooling on the carrier concentration n in the range from 1015 to 1020 cm -3 was analyzed. The potential profile was obtained for a spherical tip with a radius R = 0.5 nm and was used to calculate the energy exchange Δe and the cooling power density Γ as a function of n and the temperature T. The energy exchange Δe was found to remain almost constant for 1019 cm -3 and decrease slowly as n further increased. In contrast, the current density j increased continuously with increasing n. As a result, the cooling power density Γ increased with increasing n, more rapidly at higher T. For n = 1016, 1018, and 1020 cm -3, a bias of V = 6.0 volts yields Γ = 0.49, 49, and 3202 watts/cm2 at 600 K and 2.0, 201, and 16560 at watts/cm2 at 900 K, respectively. This predicts a field emission cooling for micro-electronic devices even with a bias equivalent to several dry cells.