Transport across nanogaps using self-consistent boundary conditions

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 α g /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. 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.

Ang Replies:

“…In their recent publication [4], they also claimed that the reported quantum scaling law for the CL law, J QCL / V 1=2 g =D 4 , only holds under the assumption that the potential is constant beyond the gap [or at the anode], where D and V g is the gap spacing and voltage across the gap.…”

The Child-Langmuir law in the quantum domain

“…giving the scaling J ∼ V α g /D 5−2α as shown in [9]. The scaling law above is based on numerical observations.…”

Calculating field emission current in nanodiodes—A multi-group formalism with space charge and exchange-correlation effects

“…To understand this, note that a self-consistent solution of the 1-Schrödinger-Poisson system does not exist at any arbitrary value of J. In other words, there is a limiting mechanism that allows a self-consistent solution only upto a maximum current-density J max k at an energy E k [13][14][15] . Note that at J max k , the tunneling electrons see a broader and higher effective potential barrier compared to values of J k < J max k .…”