Theoretical analysis of a field emission enhanced semiconductor thermoelectric cooler

Abstract

In this paper a novel field emission enhanced thermoelectric type cooler is proposed and theoretically analyzed. The thermoelectric cooler device proposed here uses an electric field modulated current to transport energy (i.e., heat) from a cold source to a hot source via n- and p-type carriers. This device is fabricated by combining the standard n- and p-channel solid-state thermoelectric cooler with a two-element field emission device inserted into each of the two channels to eliminate the solid-state thermal conductivity. In the proposed cooler, the heat removed from the cold source is the energy difference, Δ ε, of field emitted electrons from the n-type and p-type semiconductors. The cooling efficiency is operationally defined as η=Δ ε/ eV where V is the anode bias voltage. This implies that the grid modulated field emission process enhances the cooling effect by increasing Δ ε at fixed V. It is found that Δ ε increases with decreasing doping concentration and with increasing local field at the emission tip. Furthermore, the cooling rates increase with doping concentration and field. With realistic values of doping and field, the cooling rates exceed those of standard thermoelectric coolers. The cooling device here is shown to have an energy transport (i.e., heat) per electron of about 500 meV depending on concentration and field while, in good thermoelectric coolers, it is about 50–60 meV at room temperature.