| Summary: | 博士 === 國立中央大學 === 電機工程研究所 === 95 === In up-to-date development of nanoscale semiconductor devices, quantum mechanisms play an important role and have to be properly taken into account in the simulation and design. Therefore, it is necessary to develop the device simulator including quantum effects. The 1-D Schrodinger computation and density gradient model for quantum effect simulations will be introduced in this dissertation. We propose a simplified equivalent circuit model to solve the Schrodinger equation and an efficient eigenvalue and eigenvetor solver to solve the eigenvalue problem. Based on the equivalent circuit model of Schrodinger equation, the equivalent circuit model of the Poisson-Schrodinger equation can be created and can be simulated to show that the MOS device features of the quantum effects at strong inversion. Moreover, the Kronig-Penney approximation will be also applied to reveal the essential features of the energy band structure of semiconductors with the simplified numerical method and the equivalent circuit method. To make all variables in similar orders without scaling factors, we propose a log-scale method to help Newton-Raphson iterations to easily converge in device simulations. Also, we will propose a matrix solver using Banded incomplete LU method to improve the problem that the memory space is insufficient. Finally, the density gradient model will be converted to an equivalent circuit form and we use the decoupled method with a log-scale method to solve the self-consistent quantum drift-diffusion model.
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