Component mode synthesis approaches for quantum mechanical electrostatic analysis of nanoscale devices

In this paper, two component mode synthesis (CMS) approaches, namely, the fixed interface CMS approach and the free interface CMS approach, are presented and compared for an efficient solution of 2-D Schr?dinger-Poisson equations for quantum-mechanical electrostatic analyses of nanostructures and devices with arbitrary geometries. In the CMS approaches, 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 Schr?dinger 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 Schr?dinger and Poisson equations, a self-consistent solution for charge concentration and potential profile can be obtained. Numerical calculations show that both CMS approaches can largely reduce the computational cost. The free interface CMS approach can provide significantly more accurate results than the fixed interface CMS approach with the same number of retained wave functions in each component. However, the fixed interface CMS approach is more efficient than the free interface CMS approach when large degrees of freedom are included in the simulation.