Localized impurities doped in the semiconductor substrate of nanostructure devices play an\nessential role in understanding and resolving transport and variability issues in device characteristics.\nModeling discrete impurities under the framework of device simulations is, therefore, an urgent need\nfor reliable prediction of device performance via device simulations. In the present paper, we discuss\nthe details of the physics associated with localized impurities in nanostructure devices, which are\ninherent, yet nontrivial, to any device simulation schemes: The physical interpretation and the role\nof electrostatic Coulomb potential in device simulations are clarified. We then show that a naive\nintroduction of localized impurities into the Poisson equation leads to a logical inconsistency within\nthe framework of the drift-diffusion simulations. We describe a systematic methodology for how to\ntreat the Coulomb potential consistently with both the Poisson and current-continuity (transport)\nequations. The methodology is extended to the case of nanostructure devices so that the effects of the\ninterface between different materials are taken into account.
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