An analytical model is developed to evaluate the critical electric field in Si and GaAs p-n junctions, with particular focus on the influence of incomplete dopant ionization. Two scenarios are considered: complete ionization and incomplete ionization. The model accounts for temperature- and doping-dependent ionization across a broad doping range and the temperature interval of 50–400 K. The analysis reveals that while incomplete ionization has little effect at room temperature, its impact becomes increasingly pronounced at lower temperatures, particularly in heavily doped junctions. Furthermore, the peak electric field within the depletion region is examined and compared with conventional analytical models, demonstrating the enhanced accuracy and predictive capability of the proposed approach under diverse thermal and doping conditions.
Abdullayev et al. (2026) studied this question.