![]() ![]() In Section 3, the physics behind discrete impurities in the bulk is discussed, and a discrete impurity model appropriate for nanostructures where the interface effect between two different materials on the potential is inevitable is proposed. In Section 2, theoretical foundations imposed on the DD device simulations are discussed with emphasis on the length-scale involved in the scheme. The present paper is organized as follows. A detailed analysis of the other simulation schemes along this line will be reported elsewhere. Although the physical issues are common to any kind of device simulations in which the Poisson equation is self-consistently coupled with the transport equations, we restrict our discussion here to the DD simulation scheme. In the present paper, we thoroughly discuss the fundamental aspects of device modeling of randomly-doped discrete impurities within nanoscale device structures where the interface, as well as discreteness of impurities is of crucial importance. Nevertheless, almost no attention has been paid to the physical aspects of such discrete impurities, except the present authors’ group. In other words, a naive introduction of point charges or similar ones into the Poisson equation may lead to a logical inconsistency with self-consistently-coupled transport equations. An introduction of localized impurities into the device simulations implies a transition from the conventional continuous (long-wavelength limit) picture, which is a primary assumption of all device simulations mentioned above, to the discontinuous (discrete) picture. We would like to stress that the physical modeling of such potential fluctuations under the framework of device simulations is not trivial. ![]() ![]() Most simulations are, however, somewhat empirical discrete impurities are introduced into the Poisson equation as point charges or by simply replacing the atoms of the substrate with charged ions, and the variability in device characteristics has been evaluated by brute-force means. The approaches employed in these studies scatter from the conventional drift-diffusion (DD) method to the Monte Carlo (MC) or the nonequilibrium Green’s functions (NEGF) methods. Intensive studies on the variability associated with discrete impurities have been, therefore, carried out in the past few decades. This is called the random dopant fluctuations (RDFs) and a dominant factor that prevents further miniaturization of the present Si-based electron devices. Localized and, thus, discrete impurities doped in the device substrate induce surface potential fluctuations at the gate-oxide interface, which leads to threshold voltage fluctuations. Local potential fluctuations induced by localized impurities, interface or line edge roughness, localized defects, etc., are just a few examples of such problems. In order to predict device characteristics accurately, it is essential to model physical phenomena based on the basic principles of physics. Because of increasing complexity inherent to such advanced devices, the role of device simulation is getting more and more important. Even atomic layers such as MoS 2 are also suggested as an alternative channel material. The methodology is extended to the case of nanostructure devices so that the effects of the interface between different materials are taken into account.Īlthough device miniaturization by following the traditional scaling rule has already ended, the pursuit of the scaling merit of Si-based electron devices is now directed toward utilizing three-dimensional gate-surrounding structures of the channel substrate and/or replacing the channel material by a new material such as Ge or compound semiconductors. We describe a systematic methodology for how to treat the Coulomb potential consistently with both the Poisson and current-continuity (transport) equations. We then show that a naive introduction of localized impurities into the Poisson equation leads to a logical inconsistency within the framework of the drift-diffusion simulations. In the present paper, we discuss the details of the physics associated with localized impurities in nanostructure devices, which are inherent, yet nontrivial, to any device simulation schemes: The physical interpretation and the role of electrostatic Coulomb potential in device simulations are clarified. Modeling discrete impurities under the framework of device simulations is, therefore, an urgent need for reliable prediction of device performance via device simulations. Localized impurities doped in the semiconductor substrate of nanostructure devices play an essential role in understanding and resolving transport and variability issues in device characteristics. ![]()
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