Atomic-size tip enhanced cooling of field emission from the n-type silicon semiconductor

• This work describes how field emission from the n-type semiconductor produces cooling at all temperatures.
• This work explains how the energy exchange, called the Nottingham effect, takes place in field emission from the n-type semiconductor. The Nottingham effect is comparable to the Peltier effect.
• This works suggests how to find the potential energy for a system of a spherical semiconductor tip and a planar metallic anode. The vacuum potential is obtained as the product of that for the planar cathode and the curvature-dependence.
• This works shows what amount of cooling can be obtained using a sharp n-Si tip. It is found that a field emission array of tips produces the maximum cooling power density of 6148 W/cm2 or cooling power of 62 W at 900 K.
• This works suggests that a field emission device can be fabricated as a practical solid state cooler, especially for the use at high temperatures.

The Nottingham effect of an n-type silicon semiconductor tip was theoretically investigated for use as a practical solid state cooler. The vacuum potential was obtained in the form which explicitly included the semiconductor cathode geometry. This leads to a relatively exact dependence of the energy exchange Δε and the cooling power density Γ on the geometry of the device. By systematic calculations of the field emission cooling, Γ was obtained as a function of the bias V, the tip radius R, and temperature T. The current density j increased with decreasing R at fixed V and T. The Δε increased with decreasing R at fixed j and T. As T increased, both Δε and Γ increased considerably. When an atomic-size silicon tip was taken, a meaningful cooling was obtained at V as small as several volts. At V = 6.8 V, a sharp tip of R = 0.5 nm yielded the maximum Γ = 250, 1941, and 6148 W/cm2 at T = 300, 600, and 900 K, respectively. This implies that an optimized configuration of an n-Si cathode produces a useful field emission cooling for micro-electronic devices with a low bias.