Electricity in Disordered Materials: Electron Hopping express
In disordered materials, such as organic semiconductors or inks made from two-dimensional materials, electrons don't move smoothly like water through a pipe. Instead, they hop from one spot to another, like a ball bouncing across a rough surface. This kind of motion is called hopping transport.
At different temperatures, electrons hop in different ways. At low temperatures, they prefer to jump farther but to sites with similar energy: this is known as variable-range hopping. At high temperatures, hops are short, only to the nearest sites. Scientists created a computer program that simulates these hops in a material. The program takes into account how the hopping sites are arranged and what their energies are. It turns out that these very properties determine which hopping regime dominates. The program was tested against real experiments: it accurately reproduces the transitions between regimes and the behavior in one, two, and three dimensions.
Now researchers have a tool to predict in advance how a new material will conduct electricity. This will speed up the development of flexible electronics, solar cells, and sensors.
Original abstract
as written by the authors arXiv:2601.01243
Hopping transport, characterized by carrier tunneling between localized states, is a key mechanism in disordered materials such as organic semiconductors, perovskites, nitride alloys, and 2D material-based inks. Two main regimes are typically observed: Variable Range Hopping and Nearest Neighbor Hopping, with a transition between them upon temperature variation. Despite numerous experimental observations, the modeling of this transition remain insufficiently explored and not fully understood. In this work, we present an in-house Monte Carlo Random Resistor Network-based simulator capable of capturing both hopping transport regimes. We demonstrate how material properties that define the network, such as localization length and the spatial and energetic distribution of sites, determine the dominant transport regime. The simulator has been successfully validated against experimental data, showing excellent agreement, reproducing the transition from one regime to the other and accurately capturing 1D, 2D and 3D variable range hopping behavior, providing both a theoretical framework for interpreting experiments and a powerful tool for studying transport mechanisms.
Hopping conductivity explains why some materials conduct better when heated — unlike metals, which conduct worse when heated.