Germanium Island Size Distribution by Atomistic Simulation
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Germanium Island Size Distribution by Atomistic Simulation Richard J. Wagner and Erdogan Gulari Department of Chemical Engineering, University of Michigan Ann Arbor, MI 48103, U.S.A. ABSTRACT Strained epitaxial growth of Ge on Si(001) produces self-assembled, nanometer scale islands, or quantum dots. We study this growth by atomistic simulation, computing the energy of island structures to determine when and how islanding occurs. The distribution of island sizes on a surface is determined by the relation of island energy to size. Applying the calculated chemical potential to the Boltzmann-Gibbs distribution, we predict size distributions as functions of coverage and temperature. The peak populations around 80 000 atoms (35 nm wide) compare favorably with experiment. INTRODUCTION Heteroepitaxy of germanium on silicon is an important technology in microelectronic fabrication. Under certain conditions, the Ge self-assembles into arrays of small islands [1]. These islands are on the order of 30 nm wide [2], producing quantum confinement of electrons and leading to the name “quantum dots”. Such structures have unique electronic properties and can be made into novel lasers and photodetectors [3]. During epitaxial growth, as Ge is deposited onto a Si substrate, the adatoms attempt to conform to the underlying Si lattice. A two-dimensional film forms over the surface but the 4.2% lattice mismatch between Ge and Si leads to strain. Once 3–4 monolayers (ML) of Ge are deposited [4], the growth switches to three-dimensional coherent islands that partially relieve the strain. Scanning tunneling microscopy studies have revealed that during the early stages of growth these islands are pyramids with {105} facets [4]. We investigate the energetics of islanding by atomistic simulation. The first question to address is whether there exists a minimum-energy island size. The answer determines how islands ripen with time. The energy of an island is related to its volume, surface area, and edge length. If the volume component of relaxation dominates, then the chemical potential of an island will generally decrease with size. This leads to Ostwald ripening—islands can always decrease their chemical potential by coalescing. The other possibility is that Ostwald ripening does not occur—a decrease in surface energy upon islanding produces minimum-energy islands at some ideal size. The active mechanism is determined by growing Ge islands and then annealing—holding the samples at a constant temperature for a number of minutes. Many researchers have found a narrow size distribution for self-assembled Ge. For example, Liu et al. studied Ge islands on Si(001) by atomic force microscopy (AFM) [2]. They found a peak island volume around 2 000 nm3 (corresponding to a base width of 40 nm) after annealing at 825 K and concluded that the distribution matched models of thermodynamic rather than kinetic limitation. Kamins et al. also measured island size distributions by AFM and found stable configurations of roughly 2 000 nm3 pyramidal islands at
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