# Theory of electron transport and emission from a semiconductor nanotip

## TL;DR

This paper develops a quantum-mechanical model to analyze electron transport and emission from semiconductor nanotips, incorporating effects of size quantization, scattering, and external fields, validated through Monte Carlo simulations.

## Contribution

It introduces a combined transfer matrix and Monte Carlo approach to accurately simulate electron behavior in semiconductor nanotips, considering quantum and scattering effects.

## Key findings

- Quantization and scattering significantly influence emission properties.
- Electron-phonon scattering affects transport efficiency.
- Diameter variation impacts electron emission probabilities.

## Abstract

An effective mass based model accounting for the conduction band quantization in a high aspect ratio semiconductor nanotip is developed to describe injected electron transport and subsequent electron emission from the nanotip. A transfer matrix formalism is used to treat electron scattering induced by the variation in the tip diameter and the electron emission. Numerical analysis of the scattering and emission probabilities is performed for the diamond parametrized nanotip model. Our scattering and emission models are further combined with a Monte Carlo (MC) approach to simulate electron transport through the nanotip. The MC simulations, also accounting for the electron-phonon scattering and externally applied electric field, are performed for a minimal nanotip model and an equivalent width diamond slab. An effect of the level quantization, electron scattering due to the nanotip diameter variation, and electron-phonon scattering on the nanotip emission properties is identified and compared with the case of bulk slab.