Monte Carlo Simulation of Electron Transport in Degenerate Semiconductors

TL;DR

This paper introduces a simplified Monte Carlo algorithm incorporating the Pauli exclusion principle to accurately simulate electron transport in degenerate semiconductors, revealing effects on band profiles, electronic temperature, and quasi Fermi levels.

Contribution

A novel, efficient Monte Carlo method that explicitly includes Pauli exclusion, improving simulation accuracy for degenerate semiconductors under high fields.

Findings

Electronic distribution can be approximated by a shifted Fermi sphere at moderate fields.

Including Pauli exclusion reduces carrier heating at high fields.

Quasi Fermi level becomes valley dependent in high fields.

Abstract

A modified algorithm is proposed to include Pauli exclusion principle in Monte-Carlo simulations. This algorithm has significant advantages to implement in terms of simplicity, speed and memory storage. We show that even in moderately high applied fields, one can estimate electronic distribution with a shifted Fermi sphere without introducing significant errors. Furthermore, the free-flights must be coupled to state availability constraints; this leads to substantial decrease in carrier heating at high fields. We give the correct definition for electronic temperature and show that in high applied fields, the quasi Fermi level is valley dependent. The effect of including Pauli exclusion principle on the band profile; electronic temperature and quasi Fermi level for inhomogeneous case of a single barrier heterostructure is illustrated.