Mathematical modelling of charge transport in graphene heterojunctions

TL;DR

This paper develops a mathematical model for charge transport in graphene heterojunctions, combining classical drift-diffusion equations with quantum interface conditions, validated by numerical simulations matching experimental data.

Contribution

It introduces a novel combined classical-quantum model for graphene heterojunctions, integrating drift-diffusion equations with quantum scattering at interfaces.

Findings

Model accurately predicts charge transport behavior.

Numerical results align well with experimental data.

Provides a framework for analyzing quantum-classical interactions in graphene.

Abstract

A typical graphene heterojunction device can be divided into two classical zones, where the transport is basically diffusive, separated by a "quantum active region" (e.g., a locally gated region), where the charge carriers are scattered according to the laws of quantum mechanics.In this paper we derive a mathematical model of such a device, where the classical regions are described by drift-diffusion equations and the quantum zone is seen as an interface where suitable transmission conditions are imposed that take into account the quantum scattering process. Numerical simulations show good agreement with experimental data.