2026-05-28T20:28:47Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1588662024-12-23T18:01:48Zoai_pmh:alloai_pmh:repo_items158866
https://hdl.handle.net/2286/R.I.63056
http://rightsstatements.org/vocab/InC/1.0/
2020
82 pages
Masters Thesis
Academic theses
Text
eng
Baikadi, Pranay Kumar Reddy
Vasileska, Dragica
Goodnick, Stephen
Povolotskyi, Mykhailo
Arizona State University
Masters Thesis Electrical Engineering 2020
The quest to find efficient algorithms to numerically solve differential equations isubiquitous in all branches of computational science. A natural approach to address<br/>this problem is to try all possible algorithms to solve the differential equation and<br/>choose the one that is satisfactory to one's needs. However, the vast variety of algorithms<br/>in place makes this an extremely time consuming task. Additionally, even<br/>after choosing the algorithm to be used, the style of programming is not guaranteed<br/>to result in the most efficient algorithm. This thesis attempts to address the same<br/>problem but pertinent to the field of computational nanoelectronics, by using PETSc<br/>linear solver and SLEPc eigenvalue solver packages to efficiently solve Schrödinger<br/>and Poisson equations self-consistently.<br/>In this work, quasi 1D nanowire fabricated in the GaN material system is considered<br/>as a prototypical example. Special attention is placed on the proper description<br/>of the heterostructure device, the polarization charges and accurate treatment of the<br/>free surfaces. Simulation results are presented for the conduction band profiles, the<br/>electron density and the energy eigenvalues/eigenvectors of the occupied sub-bands<br/>for this quasi 1D nanowire. The simulation results suggest that the solver is very<br/>efficient and can be successfully used for the analysis of any device with two dimensional<br/>confinement. The tool is ported on www.nanoHUB.org and as such is freely<br/>available.
Electrical Engineering
Computational Physics
AlGaN-GaN
Heterostructures
PETSc
Schrödinger-Poisson solver
self-consistent
SLEPc
Efficient Schrödinger-Poisson Solvers for Quasi 1D Systems That Utilize PETSc and SLEPc