Hybrid PINN–TCAD Framework for Sub-Percent p-n Junction Simulation with Spill-Over Error Quantification

Abstract We present a comprehensive framework for p-n junction simulation that bridges analytical models, numerical methods, and machine learning approaches. A hybrid finite-difference–Physics-Informed Neural Network (PINN) solver is developed and validated across 12 silicon devices with doping concentrations ranging from 1015 to 1019 cm−3. The surrogate model reproduces Sentaurus TCAD results with 0.48% RMS potential error while revealing that analytical models systematically underestimate the built-in potential by up to 8 mV at high doping concentrations. This error leads to a 3% overestimation of solar-cell short-circuit current in predictive models. The framework achieves a 47× speed-up compared to conventional TCAD simulations and is successfully extended to 2D geometries (50 × 50 mesh) without architectural modifications, maintaining 0.62% RMS error with 12× acceleration. All implementation code, datasets, and reproduction scripts are openly available under an MIT license.