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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 Δe 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 Δe increased with decreasing R at fixed j and T. As T increased, both Δe 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. |
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