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Hopping transport regimes and dimensionality transition: a unified Monte Carlo Random Resistor Network approach

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.