Theoretical analysis of the energy exchange and cooling in field emission from the conduction band of the n -type semiconductor

Field emission has been theoretically found to contribute to the cooling only for the semiconductor cathodes. Using the formal theory developed recently by authors, the authors have calculated the energy exchange Δε as a function of temperature T and field F. It is found that the obtained Δε is positive for all T and large enough for a considerable cooling at room temperature. Even when the Joule heating is considered, field emission yields the net cooling effect. It is also found that the cooling is more effective for the n-GaN cathode than for the n-Si.