In this paper we apply a parallel adaptive solution algorithm to simulate nanoscale double-gate metal-oxide-semiconductor field effect transistors (MOSFETs) on a personal computer (PC)-based Linux cluster with the message passing interface (MPI) libraries. Based on a posteriori error estimation, the triangular mesh generation, the adaptive finite volume method, the monotone iterative method, and the parallel domain decomposition algorithm, a set of two-dimensional quantum correction hydrodynamic (HD) equations is solved numerically on our constructed cluster system. This parallel adaptive simulation methodology with 1-irregular mesh was successfully developed and applied to deep-submicron semiconductor device simulation in our recent work. A 10 nm n-type double-gate MOSFET is simulated with the developed parallel adaptive simulator. In terms of physical quantities and refined adaptive mesh, simulation results demonstrate very good accuracy and computational efficiency. Benchmark results, such as load-balancing, speedup, and parallel efficiency are achieved and exhibit excellent parallel performance. On a 16 nodes PC-based Linux cluster, the maximum difference among CPUs is less than 6%. A 12.8 times speedup and 80% parallel efficiency are simultaneously attained with respect to different simulation cases.

In this paper, we investigate the electron-hole energy states and energy gap in three-dimensional (3D) InAs/GaAs quantum rings and dots with different shapes under external magnetic fields. Our realistic model formulation includes: (i) the effective mass Hamiltonian in non-parabolic approximation for electrons, (ii) the effective mass Hamiltonian in parabolic approximation for holes, (iii) the position- and energy-dependent quasi-particle effective mass approximation for electrons, (iv) the finite hard wall confinement potential, and (v) the Ben Daniel-Duke boundary conditions. To solve the 3D nonlinear problem without any fitting parameters, we have applied the nonlinear iterative method to obtain self-consistent solutions. Due to the penetration of applied magnetic fields into torus ring region, for ellipsoidal- and rectangular-shaped quantum rings we find nonperiodical oscillations of the energy gap between the lowest electron and hole states as a function of external magnetic fields. The nonperiodical oscillation is different from 1D periodical argument and strongly dependent on structure shape and size. The result is useful to study magneto-optical properties of the nanoscale quantum rings and dots.