  We show the operation of a Cu/Al_2O_3/Cu/n-Si hot-electron transistor for the
straightforward determination of a metal/semiconductor energy barrier height
even at temperatures below carrier-freeze out in the semiconductor. The
hot-electron spectroscopy measurements return a fairly temperature independent
value for the Cu/n-Si barrier of 0.66 $\pm$ 0.04 eV at temperatures below 180
K, in substantial accordance with mainstream methods based on complex fittings
of either current-voltage (I-V) and capacitance-voltage (C-V) measurements. The
Cu/n-Si hot-electron transistors exhibit an OFF current of ~2 * 10^-13 A, an
ON/OFF ratio of ~10^5 and an equivalent subtreshold swing of ~96 mV/dec at low
temperatures, which are suitable values for potential high frequency devices.
