``Thermoelectric Effect'' of Hot Carriers

A theory is developed for the voltage arising from a gradient in a high electric field, i.e., a field sufficient to change the average energy of the carriers, and applied to calculations for the warm-carrier region in a semiconductor. For a situation in which there is a region of constant field E next to a region, consisting of the same material, in which the field decreases to zero, it is found that, for E in the warm-electron range, the field-gradient voltage is proportional to E2. This dependence is found experimentally for both n and p germanium at room temperature. Because a region of inhomogeneous material at a contact also makes some contribution to the measured voltage, it is not possible to make a quantitative comparison between experiment and theory. The contribution of the contact is found to depend on the nature of the transition region between semiconductor and metal and, in the hot-electron region, upon the magnitude of the electric field.