Investigation of bulk and surface properties of Si and Si-Ge systems using Monte Carlo simulations and classical potentials

by 1968- Tavazza, Francesca M.

In this dissertation the study of Si and Si-Ge systems is conducted to provide answers to both statistical mechanics and material science questions. The compressible Ising model provides a general framework for describing phase transitions in alloys where the ordering is accompanied by a displacive structural change. Its behavior in the case of ferromagnetic interactions and constant volume conditions is investigated here using a model of binary alloys driven by elastic interactions. Classical Monte Carlo simulations in the semi-grand-canonical ensemble are utilized, and the two species composing the alloy are modeled by Si and Ge interacting via the Stillinger-Weber potential. A volume much closer to pure Ge than to pure Si is chosen to introduce a significant difference between the two species. The phase diagram contains a closed first order line which divides a “phase-segregated” (“ordered”) phase from a disordered one. In the “ordered” phase the most unfavorable species (Si in this case) congregates forming planes in-between which the other species is located. When interested in the study of technological important materials, few, if any, are more relevant than Si and Ge. In this work a classical, hybrid MC-MD algorithm is introduced for the study of surface phenomena (2D island stability or step-edge evolution) on (001) Si or Ge surfaces. This method is very general and can be easily expanded to other semiconductors and different surfaces. With respect to previously developed algorithms, this presents the advantage of working off-lattice and utilizing bulk-fitted potentials. It is based on the introduction of collective moves, such as dimer jumps, into the MC algorithm. MD-driven local relaxations are considered as trial moves for the MC. Results on early stages of island formation, island stability versus temperature and system size, and step-edge evolution are obtained in good qualitative agreement with experimental results. Index words: Si, Ge, Monte Carlo, surface, Compressible Ising Model Investigation of bulk and surface properties of Si and Si-Ge systems using Monte Carlo simulations and classical potentials by Francesca M. Tavazza B.A., Università Statale degli Studi di Milano, 1993 M.D., Università Statale degli Studi di Milano, 1995 A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Athens, Georgia 2003 c? 2003 Francesca M. Tavazza All Rights Reserved Investigation of bulk and surface properties of Si and Si-Ge systems using Monte Carlo simulations and classical potentials by Francesca M. Tavazza Approved: Major Professor: David P. Landau Committee: Michael Geller Uwe Happek Steven P. Lewis H.-Bernd Schüttler Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia August 2003 “Considerate la vostra semenza: nati non foste a viver come bruti, ma per seguir virtute e conoscenza.” (Dante Alighieri, Inferno, Canto XXIV, 118) “Consider ye the seed from which ye sprang: ye were not made to live like brutes, but for the pursuit of excellence and knowledge.” (Dante Alighieri, Inferno, Canto XXIV, 118)