Electron energy level calculations for semiconductor nanostructures

Electron energy level calculations for semiconductor nanostructures Semiconductor nanostructures have attracted tremendous interest in the past few years because of their special physical properties and their potential for applications in micro- and optoelectronic devices. In such nanostructures, the free carriers are confined to a small region of space by potential barriers, and if the size of this region is less than the electron wavelength, the electronic states become quantized at discrete energy levels. The ultimate limit of low dimensional structures is the quantum dot, in which the carriers are confined in all three directions, thus reducing the degrees of freedom to zero.

We consider the problem to compute relevant energy states and corresponding wave functions of (three dimensional) semiconductor nanostructures. The governing equation characterizing the energy states E and corresponding wave functions \phi is the Schrödinger equation where the confinement potential V and the electron effective mass m are discontinous across the interface between the dot and the matrix. Assuming non-parabolicity for the electron effective mass, m depends nonlinearly on the energy state E, and the Schrödinger equation becomes a rational eigenvalue problem. Discretizing by FE or FV methods it results in a nonlinear matrix eigenvalue problem which is typically large and sparse. Iterative projection methods of Arnoldi and Jacobi-Davidson type are very efficient. One of the ongoing projects is to apply the automated multi-level substructuring to this type of problems.

• 4-13.115V
  Heinrich Voss: Electron energy level calculation for a three dimensional quantum dot pp. 586 -- 589 in T. Simos, G. Maroulis (eds.), Advances in Computational Methods in Sciences and Engineering 2005, Lecture Series in Computer and Computational Sciences, Vol. 4, Brill Academic Publishers, Leiden, the Netherlands 2005
• 4-13.118V
  Heinrich Voss: Numerical simulation of a three dimensional quantum dot. Proc.Appl.Math.Mech. 5, 783 -- 784 (2005)
• 4-13.120V
  Heinrich Voss: Numerical calculation of the electronic structure for three-dimensional quantum dots. Comput. Phys. Comm. 174, 441 -- 446 (2006)
• 4-13.121V
  Marta Markiewicz, Heinrich Voss: Electronic States in Three Dimensional Quantum Dot/Wetting Layer Structures pp. 684 -- 693 in M. Gavrilova et al. (eds.), Computational Science and its Applications -- ICCSA 2006, Lecture Notes in Computer Science 3980, Springer Verlag, Berlin, Heidelberg, New York 2006
• 4-13.124V
  Marta Markiewicz, Heinrich Voss: Electronic States in Three Dimensional Quantum Dot/Wetting Layer Structures on CD--ROM Proceedings of Computational Science and its Applications -- ICCSA 2006, Glasgow, UK, May 2006
• 4-13.125V
  Heinrich Voss: Iterative projection methods for computing relevant energy states of a quantum dot. J. Comput. Phys. 217, 824 -- 833 (2006)
• 4-13.133V
  Marta Betcke and Heinrich Voss: Electronic states of Quantum Dots. Eingereicht bei J. Comput. Phys.
• 4-13.135V
  Marta Betcke and Heinrich Voss: Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin--orbit splitting. Eingereicht bei Applications of Mathematics