An analytical framework for field electron emission, incorporating quantum- confinement effects

Abstract

As field electron emitters shrink to nanoscale dimensions, the effects of quantum confinement of the electron supply and electric field enhancement at the emitter tip play a significant role in determining the emitted current density (ECD). Consequently, the Fowler-Nordheim (FN) equation, which primarily applies to field emission from the planar surface of a bulk metal may not be valid for nanoscale emitters. While much effort has focused on studying emitter tip electrostatics, not much attention has been paid to the consequences of a quantum-confined electron supply. This work builds an analytical framework from which ECD equations for quantum-confined emitters of various geometries and materials can be generated and the effects of quantum confinement of the electron supply on the ECD can be studied. ECD equations were derived for metal emitters from the elementary model and for silicon emitters via a more physically-complete version of the elementary model. In the absence of field enhancement at the emitter tip, decreasing an emitter's dimensions is found to decrease the total ECD. When the effects of field enhancement are incorporated, the ECD increases with decreasing transverse emitter dimensions until a critical dimension dpeak, below which the reduced electron supply becomes the limiting factor for emission and the ECD decreases. Based on the forms of the ECD equations, alternate analytical methods to Fowler-Nordheim plots are introduced for parameter extraction from experimental field emission data. Analysis shows that the FN equation and standard analysis procedures over-predict the ECD from quantum-confined emitters. As a result, the ECD equations and methods introduced in this thesis are intended to replace the Fowler-Nordheim equation and related analysis procedures when treating field emission from suitably small field electron emitters.