Mathematical Model of a Semiconductor Structure Based on Vanadium Dioxide for the Mode of a Conductive Phase

This study presents a comprehensive mathematical model of a semiconductor structure based on vanadium dioxide (VO₂), specifically in its conductive phase. The model was developed using the finite element method (FEM), enabling detailed simulation of the formation of a conductive channel under the influence of low-frequency alternating voltage (50 Hz). The VO₂ structure under investigation exhibits pronounced electric field concentration at the surface, where the field strength reaches approximately 5 × 10⁴ V/m, while maintaining a more uniform distribution of around 2 × 10⁴ V/m within the bulk of the material. The simulation results were validated experimentally using a test circuit. Minor deviations—no greater than 8%—were observed between the simulated and measured current values, attributed to magnetic core saturation and modeling assumptions. A distinctive feature of the model is its ability to incorporate the nonlinear dependencies of VO₂’s electrical properties on frequency. Analytical expressions were derived for the magnetic permeability and resistivity of VO₂, demonstrating excellent agreement with experimental data. The coefficients of determination (R²) for the frequency dependence of magnetic permeability and resistance were found to be 0.9976 and 0.9999, respectively. The current version of the model focuses exclusively on the conductive phase and does not include the thermally induced metal–insulator phase transition characteristic of VO₂. The study confirms that VO₂-based structures exhibit high responsiveness and nonlinear switching behavior, making them suitable for applications in electronic surge protection, current limiting, and switching elements. The developed model provides a reliable and physically grounded tool for the design and optimization components based on VO₂ in power electronics and protective circuitry.