# Polaronic inter-acceptor hopping transport in intrinsically doped nickel oxide

## TL;DR

This paper investigates the electronic transport in intrinsically doped NiO, demonstrating that polaronic inter-acceptor hopping, rather than free small polaron hopping, best explains the conduction mechanism, with temperature-dependent regimes influenced by phonon interactions.

## Contribution

It introduces a polaronic inter-acceptor hopping model for doped NiO, contrasting with the traditional free small polaron model, and highlights the role of disorder and acceptor states in transport.

## Key findings

- Holes are localized at Ni vacancies forming bound polaron-like states.
- Two temperature regimes of conductivity are identified, separated by about 200 K.
- Structural disorder influences the hopping mechanism, favoring variable range hopping in high-disorder samples.

## Abstract

In this work, we revisit the issue of the nature of electronic transport in nickel oxide (NiO) and show that the widely used model of free small polaron hopping, initially raised to characterize transport in high-purity samples, is not appropriate for modeling intrinsically doped NiO. Instead, we present extensive evidence, collected by means of temperature- and frequency-dependent measurements of the electrical conductivity $\sigma$, that the model of polaronic inter-acceptor hopping can be used to consistently explain the electronic conduction process. In this framework, holes are localized to acceptors (Ni vacancies), forming a strongly bound, polaron-like state. They can only move through the film by hopping to a neighboring, at least partially unoccupied, acceptor. This renders the spatial overlap between neighboring polaronic wave functions a highly critical parameter. The signature of this process is the occurrence of two temperature regions of the DC conductivity, separated by about half the Debye temperature $\theta_D/2 \approx 200 K$. For $T > \theta_D/2$, holes are transferred by phonon-assisted hopping over the potential barrier between two sites, whereas phonon-assisted tunneling through the barrier dominates below that temperature. We also show that the degree of structural and electronic disorder plays a vital role in determining the characteristics of the transport process: high disorder leads to strong energetic broadening of the acceptor states such that hopping to more distant sites may be favored over transfer to nearest neighbors (variable range hopping). The assumption of high binding energies of the charge carriers at VNi is in accordance with the recent paradigm shift regarding the understanding of the electronic structure of NiO: holes doped into NiO couple to Ni 3d spins, thereby occupying deep polaron-like states within the band gap (Zhang-Rice bound doublets).