Energy exchange △εis investigated in field emission from semiconductors. For the first time, a formal theory is developed for the replacement process of the injected charge carriers. It leads to analytic expressions for As, which exhibit the dependence on field, temperature, and doping concentration in a parametric form. The analytic and numeric results reveal the important feature that △εis positive for all temperatures. This implies that field emission from semiconductors always produces cooling of an emitter. When Joule heating is included, there is still a net cooling for a wide range of emitted current densities.
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