Barrier enhancement mechanisms in heterodimensional contacts and their effect on current transport

It has been shown that in a Three-dimensional (3D) to two-dimensional (2D) contact system, the quantized nature of the energy of the 2D system imposes important changes on the thermionic emission of carriers from a 3D metal to a 2DEG. These include changes in the Richardson constants, temperature dependence behavior, and metal to semiconductor barrier height. Interestingly in actual devices, barrier heights higher than what is theorized based on the first confined state, are measured. In this paper we propose an additional mechanism of barrier height enhancement in 3D-2D contacts which is due to the repulsive Coloumbic force that is exerted by the 2DEG on the thermionically emitted electrons. An analytical derivation of the barrier height due to this effect is given which parallels that of the image force barrier lowering mechanism. Thermionic current conduction is then derived based on this enhanced barrier height as well as 3D-2D transport. These results are important for design and understanding of device behavior for low noise applications