Theoretical Considerations About the Generation and Properties of Narrow Electron Flows in Solid State Structures

TL;DR

This paper presents a theoretical method to evaluate and optimize the generation of extremely narrow electron beams in solid state structures, based on quantum mode analysis in nanoconstrictions.

Contribution

It introduces a new theoretical approach for analyzing and optimizing narrow electron beam generation in nanoconstrictions using adiabatic approximation and mode quantization.

Findings

Derived an asymptotically exact solution for linear widening constrictions.

Established the relationship between electron angular distribution and quantum states.

Verified semi-quantitative results on beam angular characteristics.

Abstract

A method for the evaluation of the angular width of an electron beam generated by a nanoconstriction is proposed and demonstrated. The approach is based on analysis of a narrow-width electron flow, that quantizes into modes inside a confining constriction which is described in the adiabatic approximation, evolving into a freely propagating electronic state after exiting the constriction. The method that we developed allows us to find the parameters and the shape of the constriction that are optimal for generation of extremely narrow electron beams. In the case of a constriction characterized by a linear widening shape an asymptotically exact solution for the injection problem is found. That solution verifies semi-quantitative results related to the angular characteristics of the beam, and it opens the way for determination of the distribution function of the electrons in the beam. We have found the relationship between the angular distribution of the electron density in the beam and the quantum states of the electrons inside the constriction. Such narrow electron beams may be employed in investigations of electronic systems and in data manipulations in electronic and spintronic devices.