| As the dimensions of commonly used semiconductor devices have shrunk into nanometer regime, it is recognized that the influence of quantum effects on their electrostatic and transport properties cannot be ignored. In the past few decades, various computational models and approaches have been developed to analyze these properties in nanostructures and devices. Among these computational models, the Schrödinger-Poisson model has been widely adopted for quantum mechanical electrostatic and transport analysis of nanostructures and devices such as quantum wires, metal–oxide–semiconductor field effect transistors (MOSFETs) and nanoelectromechanical systems (NEMS). The numerical results allow for evaluations of the electrical properties such as charge concentration and potential profile in these structures. The emergence of MOSFETs with multiple gates, such as Trigates, FinFETs and Pi-gates, offers a superior electrostatic control of devices by the gates, which can be therefore used to reduce the short channel effects within those devices. Full 2-D electrostatic and transport analysis enables a better understanding of the scalability of devices, geometric effects on the potential and charge distribution, and transport characteristics of the transistors. The Schrödinger-Poisson model is attractive due to its simplicity and straightforward implementation by using standard numerical methods. However, as it is required to solve a generalized eigenvalue problem generated from the discretization of the Schrödinger equation, the computational cost of the analysis increases quickly when the system's degrees of freedom (DOFs) increase. For this reason, techniques that enable an efficient solution of discretized Schrödinger equation in multidimensional domains are desirable.;In this work, we seek to accelerate the numerical solution of the Schrödinger equation by using a component mode synthesis (CMS) approach. In the CMS approach, a nanostructure is divided into a set of substructures or components and the eigenvalues (energy levels) and eigenvectors (wave functions) are computed first for all the substructures. The computed wave functions are then combined with constraint or attachment modes to construct a transformation matrix. By using the transformation matrix, a reduced-order system of the Schrödinger equation is obtained for the entire nanostructure. The global energy levels and wave functions can be obtained with the reduced-order system. Through an iteration procedure between the Schrödinger and Poisson equations, a self-consistent solution for charge concentration and potential profile can be obtained. In this work, the CMS approach is applied to compute the electrostatic and transport properties of a set of semiconductor devices including a quantum wire and several multiple-gate MOSFETs. It is demonstrated that the CMS approach greatly reduces the computational cost while giving accurate results. |
