Theory of hopping conduction in arrays of doped semiconductor nanocrystals

TL;DR

This paper develops a theoretical model explaining the transition from activated hopping to variable-range hopping in arrays of doped semiconductor nanocrystals, highlighting the role of quantum confinement and disorder.

Contribution

It introduces a simple theoretical framework that accounts for conduction regimes in doped NC arrays based on size, doping, and disorder effects.

Findings

Disorder from donor fluctuations induces Coulomb landscape leading to VRH.

Small NCs exhibit charge fluctuations causing transition to VRH.

Simulation identifies conduction regimes across temperature, doping, and size.

Abstract

The resistivity of a dense crystalline array of semiconductor nanocrystals (NCs) depends in a sensitive way on the level of doping as well as on the NC size and spacing. The choice of these parameters determines whether electron conduction through the array will be characterized by activated nearest-neighbor hopping or variable-range hopping (VRH). Thus far, no general theory exists to explain how these different behaviors arise at different doping levels and for different types of NCs. In this paper we examine a simple theoretical model of an array of doped semiconductor NCs that can explain the transition from activated transport to VRH. We show that in sufficiently small NCs, the fluctuations in donor number from one NC to another provide sufficient disorder to produce charging of some NCs, as electrons are driven to vacate higher shells of the quantum confinement energy spectrum. This confinement-driven charging produces a disordered Coulomb landscape throughout the array and leads to VRH at low temperature. We use a simple computer simulation to identify different regimes of conduction in the space of temperature, doping level, and NC diameter. We also discuss the implications of our results for large NCs with external impurity charges and for NCs that are gated electrochemically.