Quantum theory of space charge limited current in solids

TL;DR

This paper develops a quantum model for space charge limited current in trap-free solids, providing exact solutions and insights into quantum effects on mobility and current behavior.

Contribution

It introduces a novel quantum theoretical framework with exact solutions for space charge limited current in solids, extending classical models into the quantum regime.

Findings

Derived a quantum analog of the Mott-Gurney law.

Calculated quantum mobility of charge carriers.

Provided analytical solutions for steady-state current.

Abstract

We present a quantum model of space charge limited current transport inside trap-free solids with planar geometry in the mean field approximation. We use a simple transformation which allows us to find the exact analytical solution for the steady state current case. We use our approach to find a Mott-Gurney like behavior and the mobility for single charge carriers in the quantum regime in solids.