Physics of Discrete Impurities under the Frameworkof Device Simulations for Nanostructure Devices

Localized impurities doped in the semiconductor substrate of nanostructure devices play anessential role in understanding and resolving transport and variability issues in device characteristics.Modeling discrete impurities under the framework of device simulations is, therefore, an urgent needfor reliable prediction of device performance via device simulations. In the present paper, we discussthe details of the physics associated with localized impurities in nanostructure devices, which areinherent, yet nontrivial, to any device simulation schemes: The physical interpretation and the roleof electrostatic Coulomb potential in device simulations are clarified. We then show that a naiveintroduction of localized impurities into the Poisson equation leads to a logical inconsistency withinthe framework of the drift-diffusion simulations. We describe a systematic methodology for how totreat the Coulomb potential consistently with both the Poisson and current-continuity (transport)equations. The methodology is extended to the case of nanostructure devices so that the effects of theinterface between different materials are taken into account.