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 Delta epsilon and the cooling power density Gamma on the geometry of the device. By systematic calculations of the field emission cooling, Gamma 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 Delta epsilon increased with decreasing Rat fixed j and T. As T increased, both Delta epsilon and Gamma 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 Gamma = 250, 1941, and 6148 W/cm(2) 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. (C) 2015 Elsevier B.V. All rights reserved.