Efficient numerical simulation of electron states in quantum wires

Thomas Kerkhoven, Albert T. Galick, Umberto Ravaioli, John H. Arends, Youcef Saad

Research output: Contribution to journalArticlepeer-review


We present a new algorithm for the numerical simulation of electrons in a quantum wire as described by a two-dimensional eigenvalue problem for Schrödinger's equation coupled with Poisson's equation. Initially, the algorithm employs an underrelaxed fixed point iteration to generate an approximation which is reasonably close to the solution. Subsequently, this approximate solution is employed as an initial guess for a Jacobian-free implementation of an approximate Newton method. In this manner the nonlinearity in the model is dealt with effectively. We demonstrate the effectiveness of our approach in a set of numerical experiments which study the electron states on the cross section of a quantum wire structure based on III-V semiconductors at 4.2 and 77 K.

Original languageEnglish (US)
Pages (from-to)3461-3469
Number of pages9
JournalJournal of Applied Physics
Issue number7
StatePublished - Dec 1 1990

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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