Thermal-field emission in nanostructures with resonant tunneling

A model of thermal field emission in nanostructures with several barriers and potential wells between them is presented, based on a strict definition of the shape of the quantum potential and a strict solution of the Schrodinger equation, taking into account the thermal balance and the influence of spatial charge. Vacuum and semiconductor resonant tunneling diode and triode structures with two, three or more electrodes are considered. A formula is given for correcting the quantum potential due to the influence of spatial charge. In general, it is necessary to consider two-way tunneling and heating of electrodes with different temperatures due to current flow. Conditions are considered when the contribution of the reverse current is small, when thermal current or tunnel current can be neglected. The approach can be extended to the non-stationary case.