Self-Consistent Fowler–Nordheim Tunneling Modeling in Si/GaAs Heterostructures with Optimized Nanoscale Meshing

Abstract

The Fowler–Nordheim (FN) tunneling current in GaAs was systematically analyzed as a function of electric field (25–50 MV/cm) and temperature (250–400 K) to evaluate its potential for high-sensitivity structural temperature sensing. Two physical descriptions were considered: a constant electron effective mass model and a field-dependent effective mass formulation. For the constant-mass approximation, the FN tunneling threshold appears at approximately 25.2 MV/cm, where the current rises rapidly from ~10⁻¹² to 10⁻⁶ A/cm² with increasing electric field. When field-dependent effective mass effects are incorporated, the threshold shifts to ~28.6 MV/cm and intermediate-field currents are suppressed by nearly one order of magnitude. Temperature variation increases the FN prefactor by approximately 30–35%, indicating measurable thermal sensitivity, although the exponential dependence on electric field remains the dominant factor controlling tunneling transport. These characteristics demonstrate the feasibility of exploiting FN tunneling mechanisms for nanoscale temperature sensing in high-field semiconductor structures. In addition, a self-consistent FN tunneling framework was developed for a p-Si/n-GaAs heterostructure to evaluate numerical stability and predictive accuracy for temperature-dependent tunneling simulations. Two tunneling formulations were compared: a conventional simplified FN model and an effective-mass-corrected model. A comprehensive mesh convergence analysis using rectangular and triangular discretizations with spatial resolutions from 0.5 to 20 nm shows that coarse meshes can introduce errors up to 12%, whereas sub-nanometer meshing ensures convergence below 1%. The effective-mass-corrected model consistently predicts 5–15% higher tunneling currents across the 0.5–3.0 V bias range, highlighting the importance of band-structure corrections for reliable sensor modeling. Furthermore, adaptive triangular meshes achieve comparable accuracy with up to 40% fewer elements, significantly improving computational efficiency. These results establish a robust numerical framework for simulating FN-based tunneling transport in semiconductor heterostructures and provide practical guidelines for mesh optimization in advanced TCAD studies. The proposed methodology supports the development of compact, high-sensitivity FN-based temperature sensors suitable for integration into nanoscale electronic, optoelectronic, and structural monitoring systems.