Carrier concentration-dependent cooling of field emission from the N-type semiconductor cathodes

We 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 was analyzed for a spherical tip with a radius R = 0.5 nm. The energy exchange Δε was found to remain almost constant for n ≤ 10
¹⁹
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 = 10
¹⁶
, 10
¹⁸
, and 10
²⁰
cm
^-3
, the bias of V = 6.0 volts yields Γ = 0.49, 49, and 3202 watts/cm
²
at 600 K and 2.0, 201, and 16560 at watts/cm
²
at 900 K, respectively.