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HL: Fachverband Halbleiterphysik

HL 62: Quantum Dots and Wires: Transport Properties I (mainly Quantum Wires)

HL 62.8: Vortrag

Mittwoch, 28. März 2012, 16:45–17:00, EW 203

Optimal finite volume discretization of Schrödinger equations for cylindrical symmetric nanowires — •Paul Nicolae Racec — Weierstrass Institute Berlin, Mohrenstr. 39, 10117 Berlin, Germany — National Institute of Materials Physics, PO Box MG-7, 077125 Bucharest Magurele, Romania

We present a finite volume scheme for the one-particle effective mass Schrödinger equation with mixed boundary conditions, more precisely the Wigner-Eisenbud problem, on a bounded domain with cylindrical symmetry. Hence, we reduce the 3D problem to one in the (r,z) plane. We use linear triangular finite elements, structured meshing and the lumping approximation in the variational formulation of the discretized 2D problem. In order to remove the r⁻¹ singularity, we approximate within every element the metric r  dr  dz ≃ r_U^(e)  dr  dz and 1/r ≃ 1/r_U^(e), where r_U^(e) is the r-coordinate of the circumcenter of the triangular element. We analyze the influence of the size and shape of the finite elements on the accuracy of the eigenvalues and eigenfunctions. We study a free-particle case and a nanowire resonant tunneling diode. In case of equilateral finite elements, we obtain a second order convergence for the eigenvalues, which is independent of the ratio m_r^*/m_z^*, where m_r^* and m_z^* are the r and z components of the effective mass tensor of the nanowire. In case of anisotropic masses, the optimal finite element shape is obtained with a grid, which is finer in the direction of the smaller effective mass.

This is a joint work with Stanley Schade and Hans-Christoph Kaiser.