Nanoscale semiconductor quantum dots (QDs) have been intensively studied in their physics and applications. In addition to theoretical and experimental methods, numerical simulations can also provide useful insights into a QD's electronic and optical properties. However, effective and feasible numerical methods for three dimensional (3D) quantum structures are rarely available. We present novel methods for calculating bound state energies and their corresponding wave functions of a 3D QD model. The model assumes that a irregular shape single low-band-gap semiconductor QD island is embedded in a wideband-gap semiconductor matrix. The heterojunction of the QD can be approximated by an arbitrary smooth function to fit real world QDs nicely. The Schrödinger equation approximating the model in cylindrical coordinate is discretized by using a body fitting finitedifference method. The scheme comes from directly discretization of the Schrödinger equations in curvilinear coordinate system with a clever choice of coordinate axis in the computational domain that gives a sharp local truncation error estimate near the interface and at the same time guarantees the symmetry and positivity of the resulting matrix. As long as the grids are non-crossing, this procedure gives a symmetric and positive definite matrix, regardless of the regularity of the grids. The induced eigenvalue problems are then solved by the Jacobi-Davidson methods. Our numerical experiment results show that the proposed methods can be very efficient and achieve the second order convergence rate.
|出版狀態||已發佈 - 2004|
|事件||European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 - Jyvaskyla, 芬兰|
持續時間: 2004 七月 24 → 2004 七月 28
|會議||European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004|
|期間||2004/07/24 → 2004/07/28|
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