Transport across nanogaps using semiclassically 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_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.

4 pages, 4 ps figures

References in corpus (1)

• Fabrication of graphene nanogap with crystallographically matching edges and its electron emission properties

Cited by in corpus (4)

• Improved transfer matrix methods for calculating quantum transmission-coefficient
• The Child-Langmuir law in the quantum domain
• Comment on "New Scaling of Child-Langmuir Law in the Quantum Regime"
• Calculating field emission currents in nanodiodes - a multi-group formalism with space charge and exchange-correlation effects