Efficient Schrödinger-Poisson Solvers for Quasi 1D Systems That Utilize PETSc and SLEPc

The quest to find efficient algorithms to numerically solve differential equations isubiquitous in all branches of computational science. A natural approach to address
this problem is to try all possible algorithms to solve the differential equation and
choose the one that is satisfactory to one's needs. However, the vast variety of algorithms
in place makes this an extremely time consuming task. Additionally, even
after choosing the algorithm to be used, the style of programming is not guaranteed
to result in the most efficient algorithm. This thesis attempts to address the same
problem but pertinent to the field of computational nanoelectronics, by using PETSc
linear solver and SLEPc eigenvalue solver packages to efficiently solve Schrödinger
and Poisson equations self-consistently.
In this work, quasi 1D nanowire fabricated in the GaN material system is considered
as a prototypical example. Special attention is placed on the proper description
of the heterostructure device, the polarization charges and accurate treatment of the
free surfaces. Simulation results are presented for the conduction band profiles, the
electron density and the energy eigenvalues/eigenvectors of the occupied sub-bands
for this quasi 1D nanowire. The simulation results suggest that the solver is very
efficient and can be successfully used for the analysis of any device with two dimensional
confinement. The tool is ported on www.nanoHUB.org and as such is freely
available.