The electron temperature in nanostructures subjected to a high electric field

The drift-diffusion characteristics that limit the drift velocity to thermal velocity, appropriate to the dimensionality of nanostructures, are described. The concept of a hot electron and its temperature in a given context is discussed and simple analytical expressions extracted. These contextual definitions include: energy temperature, mobility temperature, Einstein-relation temperature both under ac and dc conditions, quantum temperature, and two-band intrinsic temperature. The dependence on the electric field is given in each case and the role of electric-field-induced quantum emission is delineated.