Monte Carlo studies of ground-state & optical properties of multiexcitonic complexes in semiconductors
Excitonic complexes, consisting of several electron-hole pairs bound by mutual Coulomb interactions, play an important role in the photoluminesence of direct- and indirect-gap semiconductors and semiconductor impurities. We calculate the ground-state and optical properties of several multiexciton systems within the spherical effective mass approximation, focusing on the role of interparticle correlations which have not been adequately accounted for in previous calculations. We employ a model of these complexes including particle pair correlations and excitonic effects, using the variational method along with Monte Carlo methods to calculate binding energies and ground-state expectation values. Transition matrix elements are studied with various extensions of the Monte Carlo method to obtain information on optical properties. In particular, we first apply these techniques to the exciton bound to a shallow donor impurity. As a function of electron-hole mass ratio this system exhibits a transition between H2 molecule-, positronium-hydride- and H- ion-like behavior, providing a useful test of current theories of coulombic few-particle systems. The binding energy and oscillator strength for radiative recombination are calculated and compared with those of other theories, and with experimental binding energy and lifetime data from various direct-gap semiconductors. We then study the ground-state properties of polyexcitons, freely moving complexes of two, three, and four electron-hole pairs in indirect-gap semiconductors, calculating binding energies and single- and two-particle distributions. These are compared to the analogous situation of multiexciton complexes bound to an impurity, to study the role of the impurity as a perturbation to the free system. Finally we calculate the lineshape of phonon-assisted photoluminesence from polyexcitons. The average electron-hole coa.lesence probability Peh(O), which determines the radiative lifetime, is calculated with a new Monte Carlo method.
monte carlo method, excitonic complexes, semiconductors
University of Illinois - Urbana-Champaign
Networked Digital Library of Theses and Dissertations