Non-Markovian electron dynamics in nanostructures coupled to dissipative contacts

TL;DR

This paper develops a non-Markovian quantum transport model for quasiballistic semiconductor nanostructures, capturing long-timescale dynamics and contact interactions, demonstrated through a silicon n-i-n diode example.

Contribution

It introduces a non-Markovian master equation framework for transient quantum transport in nanostructures, extending beyond Markovian approximations and applicable on long timescales.

Findings

The approach accurately models carrier relaxation and transport dynamics.

Numerical solutions of coupled equations reveal detailed charge and current behavior.

Application to a silicon n-i-n diode demonstrates practical utility.

Abstract

In quasiballistic semiconductor nanostructures, carrier exchange between the active region and dissipative contacts is the mechanism that governs relaxation. In this paper, we present a theoretical treatment of transient quantum transport in quasiballistic semiconductor nanostructures, which is based on the open system theory and valid on timescales much longer than the characteristic relaxation time in the contacts. The approach relies on a model interaction between the current-limiting active region and the contacts, given in the scattering-state basis. We derive a non-Markovian master equation for the irreversible evolution of the active region's many-body statistical operator by coarse-graining the exact dynamical map over the contact relaxation time. In order to obtain the response quantities of a nanostructure under bias, such as the potential and the charge and current densities, the non-Markovian master equation must be solved numerically together with the Schr\"{o}dinger, Poisson, and continuity equations. We discuss how to numerically solve this coupled system of equations and illustrate the approach on the example of a silicon nin diode.