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Title:  Quantum Monte Carlo simulations of electrons and holes 
Author(s):  Shumway, John Beaumont 
Doctoral Committee Chair(s):  Ceperley, David M. 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Quantum Monte Carlo simulations
electron excitations hole excitations semiconductors Path integral Monte Carlo local spin density approximation density function theory 
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 electronhole 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 excitonexciton 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 electronhole plasma. Our primary interest is the Bose condensation of an excitonic gas. At low density and low temperature the spinunpolarized system forms biexcitons. Since we are interested in Bose condensation, we study a spinpolarized 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 excitonexciton 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 selfassembled InAsGaAs 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. 
Issue Date:  1999 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/31235 
Other Identifier(s):  4268649 
Rights Information:  ©1999 Shumway 
Date Available in IDEALS:  20120523 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois