Arnoldi Codes Used for Finite Element Solution to Quantum Wells

Tsung-lung Li, University of Washington

Due to the development of modern crystal growth technology, crystals can be virtually grown layer by layer on semiconductor wafers, creating microstructures that can confine electrons in a space of .01 microns or less. The electrons confined in these microstructures exhibit quantized behavior with energy spectra being discretized rather than continuous. These microstructures are commonly referred to as "quantum wells." They can be manipulated to have desired properties, such as spectra range, and can be used in photodetectors, lasers, and fiber optic communication.

The codes are used to predict the discretized energies of the electrons in the quantum wells. The problem was identified as a generalized eigenvalue problem with a non-symmetric stiffness matrix. Although parallel computing is not necessary for the preliminary model, the solver does take advantage of the large computational potential that parallel computers provide.

This project is an example of how outside researchers benefit from CRPC work. The Arnoldi codes used in the solution were developed by Dan Sorensen, a CRPC researcher at Rice University, and were run on an IBM 3090 machine at the University of Washington. According to Tsung-lung Li, they were a "vital part of the solution."

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