First-Principle Model of the Electron Field Emission From Silicon Nano-Scale Tip

Abstract

Prediction of electron field-emission current of nano-scale devices is of significant importance in the field of vacuum nanoelectronics. Nowadays, modified Fowler-Nordheim model (F-N) being widely used to estimate electron field-emission current of various systems. Nevertheless, it was shown that experimental values of the emission current from nano-scale emitters can differ from such values obtained within F-N theory. Moreover, the F-N formalism is not entirely suitable for describing field emission from silicon nanostructures, where it is important to take into account the interaction of electrons with impurities, phonon scattering, temperature effects (Joule heating), and the penetration depth of the electric field in the semiconductor. For the accurate simulation of electron field emission in the case of nano-scale silicon tip, first-principle quantum-mechanical models based on Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) formalisms should be used. In this work, we calculated within first-principle approach the field-emission current in a system consisting of the silicon nanoscale tip (emitter) and collector of the same type, which are separated by a nanoscale vacuum gap. The calculations were performed using time-dependent perturbation theory for non-zero external electric field within the non-equilibrium Green functions (NEGF) formalism to describe the electron transport and inelastic scattering in the emitter, where pseudopotentials and Kohn-Sham equations are explored in a self-consistent manner. This theoretical approach can serve as an important step towards the consideration of field-electron emission process beyond the F-N theory to describe correctly field-emission experimental data at the nanoscale.