Efficient Quantum-Mechanical Modeling of Nonradiative Charge Transfer Processes
Nonradiative charge transfer processes play a central role in a wide range of physical phenomena, including reliability phenomena in semiconductor devices such as bias temperature instability, hysteresis, random telegraph noise, and trap-assisted tunneling. nonradiative multiphonon (NMP) theory provides a physically rigorous framework for describing such charge transitions, but its full quantum-mechanical formulation is computationally too demanding for large-scale simulations. In this work, we present a systematic and implementation-oriented treatment of NMP-based models for practical large-scale simulations. Starting from the quantum-mechanical foundations of coupled electron--phonon dynamics, we derive computationally efficient approximations for charge capture and emission rates and clearly identify the underlying assumptions and validity regimes. In particular, we introduce an effective crossing-preserving approximation that yields fully analytic, numerically stable, and computationally inexpensive transition rates while retaining the essential quantum-mechanical physics. The resulting expressions are therefore well suited for large-scale device simulations, where capture coefficients must be evaluated repeatedly over broad multidimensional parameter spaces. Furthermore, we derive continuum formulations for transitions between localized defect states and extended electronic bands, enabling direct incorporation into semiconductor-device simulations. The resulting framework bridges microscopic defect physics and practical large-scale simulations of charge transfer processes in complex semiconductor devices. At the same time this work serves as a practical guide for implementing physically grounded NMP-based models, providing both a systematic derivation of the underlying theory and a clear guidance on the validity limits.