Overheating or overcooling of electrons in a metal because of the effect of an interface with an insulator

It has been shown that the temperatures of electrons and phonons are different at a heat flow through a metal-insulator interface. This effect leads to an additional contribution to the Kapitza thermal resistance because electrons transferring heat in the metal do not transfer it through the interface, but are rather involved in heat transfer only at a certain distance from it. Consequently, heat transfer near the interface is less efficient. The effect is independent of the insulator adjacent to the metal. An exact solution has been obtained in a linear approximation. The results explain the qualitative difference of predictions of previously accepted models from experimental data in the case of large transmission coefficients of phonons through the interface.