Tip-geometry enhanced cooling of field emission from semiconductor cathodes

Abstract

The tip-geometry effect of the Nottingham effect was theoretically investigated for use as a practical solid state cooler. A vacuum potential was first obtained for a spherical tip of an n-type semiconductor cathode. This made it possible to calculate the energy exchange Δe and the cooling power density Γ as a function of the emission configuration. When an atomic-size silicon tip was taken, a meaningful cooling was obtained at the bias V as small as several volts. At V=6.8 volts, a sharp tip of the radius R=0.5 nm yielded the maximum Γ= 1941 and 6148 watts/cm2 at temperature T= 600 and 900 K, respectively.