Finite-element analysis of quantum wires with arbitrary cross sections

A finite-element method is developed for the analysis of eigenstates in the valence band of quantum wires which have arbitrary potential profiles. Our method is basically based on the Galerkin procedure and triangle linear elements are used as finite elements. In our formulation the effect of the band mixing in the valence band is duly taken into account. Boundary conditions at heterointerfaces are also taken into account in the multiband envelope function space. Numerical examples are presented for circular, square, rectangular, and triangular quantum wire structures. The relation is clarified between the degeneracy in the ${\mathrm{E-k}}_y$ dispersion curve and the symmetricity of the confinement potential.