Modelling of conduction degradation kinetics in nanostructured low-dimensional semiconductor layers under long-term DC exposure

Background and Objectives: Percolation models are widely employed to analyze electrical transport in disordered systems, particularly near critical thresholds. While substantial research has focused on static percolation properties, the dynamic evolution of such networks under external stimuli, such as constant current, remains less explored. This paper addresses the kinetics of conductivity degradation in nanostructured low-dimensional semiconductor layers (exemplified by nanodispersed In₂O₃ layers) under prolonged DC exposure. A discrete three-dimensional percolation model is developed to simulate the irreversible transition from conducting to dielectric states, driven by carrier trapping at defect sites. Materials and Methods: The model implements bond percolation on a cubic lattice of size 300×300×15 nodes, with lognormal distributed edge conductivities. The initial configuration ensures 32 continuous conducting paths between electrodes, matching experimental data. Kirchhoff’s equations are solved numerically to compute node potentials and local current densities. Degradation dynamics are introduced via time-dependent edge conductance reduction, governed by carrier trapping kinetics proportional to local current density. Results: Simulations have revealed a two-stage degradation kinetics: an initial quasi-linear voltage increase followed by accelerated growth due to percolation path fragmentation. The model quantitatively reproduces experimental voltage-time characteristics, with deviations under 5% over most of the temporal range. The critical reduction in conducting bond density leads to catastrophic loss of connectivity, consistent with percolation threshold behavior. Conclusion: The results demonstrate the applicability of dynamic percolation models to describe nonequilibrium degradation processes in nanostructured semiconductors. The approach provides a foundation for predicting lifetime and reliability of devices based on dispersed semiconductor materials, relevant for sensor and transparent electronics applications. Further model refinements incorporating additional degradation mechanisms (e.g., local heating, electrochemical effects) are suggested for improved late-stage accuracy.