Transport across nanogaps using self-consistent boundary conditions

Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework. The determination of self-consistent boundary conditions across the gap forms the central theme in order to allow for realistic interface potentials (such as metal-vacuum) which are smooth at the boundary and do not abruptly assume a constant value at the interface. It is shown that a semiclassical expansion of the transmitted wavefunction leads to approximate but self consistent boundary conditions without assuming any specific form of the potential beyond the gap. Neglecting the exchange and correlation potentials, the quantum Child-Langmuir law is investigated. It is shown that at zero injection energy, the quantum limiting current density (J c ) is found to obey the local scaling law J c ∼ V g α /D 5-2α with the gap separation D and voltage V g . The exponent α > 1.1 with α → 3/2 in the classical regime of small de Broglie wavelengths. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012