Fundamental Aspects of Semiconductor Device Modeling Associated With Discrete Impurities: Drift-Diffusion Simulation Scheme

We discuss the fundamental aspects of how discrete impurities could be physically modeled under the framework of the drift-diffusion (DD) simulations. The detailed physical interpretations of potential fluctuations, impurity-limited mobility, and an appropriate modeling to represent the discrete nature of impurities are explained. The present analyses are validated by DD simulations with various types of discrete impurity models. The traditional mobility model, which reproduces the experimental mobility at various impurity densities, could be used in our long-range discrete impurity model, whereas localized impurity models in which impurity charge is spatially localized at each impurity site induce unphysical polarization fields in semiconductor substrate and are unable to predict the correct mobility.