Transport across nanogaps using semiclassically consistent boundary conditions

TL;DR

This paper investigates charge transport across nanogaps using a semiclassical boundary condition approach, revealing quantum effects on limiting current that differ from classical predictions and aligning with recent experimental observations.

Contribution

It introduces a self-consistent boundary condition using a first order WKB wavefunction, providing new insights into quantum transport in nanogaps.

Findings

Quantum limiting current density scales with voltage and gap size as J_c ~ V_g^alpha / D^{5-2alpha}

Exponent alpha approaches 3/2 in the classical regime, indicating classical behavior at small de Broglie wavelengths

Results align with experiments showing classical space charge limited scaling in nanogaps

Abstract

Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework and the existence of limiting current investigated. It is shown that the choice of a first order WKB wavefunction as the transmitted wave leads to self consistent boundary conditions and gives results that are significantly different in the non-classical regime from those obtained using a plane transmitted wave. At zero injection energies, the quantum limiting current density, J_c, is found to obey the local scaling law J_c ~ (V_g)^alpha/(D)^{5-2alpha} with the gap separation D and voltage V_g. The exponent alpha > 1.1 with alpha --> 3/2 in the classical regime of small de Broglie wavelengths. These results are consistent with recent experiments using nanogaps most of which are found to be in a parameter regime where classical space charge limited scaling holds away from the emission dominated regime.