University of Illinois Urbana-Champaign

Quantum Monte Carlo simulations of electrons and holes

Shumway, John Beaumont

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Description

Title
Quantum Monte Carlo simulations of electrons and holes
Author(s)
Shumway, John Beaumont
Issue Date
1999
Doctoral Committee Chair(s)
Ceperley, David M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Quantum Monte Carlo simulations
  • electron excitations
  • hole excitations
  • semiconductors
  • Path integral Monte Carlo
  • local spin density approximation
  • density function theory
Language
en
Abstract
Electron and hole excitations in semiconductors may be approximated as particles with effective masses which interact via Coulomb potentials. We study systems of electrons and holes with quantum Monte Carlo (QMC) techniques, covering three related areas: (1) elastic scattering of excitons, (2) thermodynamics of electron-hole plasmas, and (3) electrons confined in a quantum dot. Excitons are bound states of an electron and a hole, and obey Bose statistics. A low density exciton gas is an experimentally realizable dilute Bose gas. The scattering length a8 of a dilute Bose gas determines its properties, but is difficult to calculate. We present an essentially exact QMC treatment of exciton-exciton scattering, and find scattering lengths for different spin orientations of the excitons. At some mass ratios mh/me the scattering lengths diverge in conjunction with the appearance of biexciton vibrational states, an effect not found by earlier perturbative treatments. Path integral Monte Carlo (PIMC) is used to model the thermodynamics of the electron-hole plasma. Our primary interest is the Bose condensation of an excitonic gas. At low density and low temperature the spin-unpolarized system forms biexcitons. Since we are interested in Bose condensation, we study a spin-polarized system, which has no biexcitons. Restricted paths are used to handle the Fermion sign problem. With an appropriate choice of paired nodes for the restricted path approximation we find an excitonic Bose condensate. The energy of the low temperature, low density exciton gas determined from PIMC agrees well with the theory of dilute Bose gases, in which our previously calculated scattering length is used to model the exciton-exciton interactions. At higher densities the excitons are less well defined and the transition changes character. Finally, we study electrons in the inhomogeneous environment of a self-assembled InAs-GaAs quantum dot. We combine our ground state QMC treatment with another method, density functional theory (DFT) within the local spin density approximation (LSDA). Our comparison shows that LSDA is acceptable for treating interactions in the case considered, but recommend further tests for application of LSDA to larger dots or coupled dot systems.
Type of Resource
text
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Copyright and License Information
©1999 Shumway

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