Molecular dynamics simulations of gold-catalyzed growth of silicon bulk crystals and nanowires
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Wei Cai Department of Mechanical Engineering, Stanford University, Stanford, California 94305 (Received 7 February 2011; accepted 27 April 2011)
The growth kinetics of Si bulk crystals and nanowires (NWs) in contact with Au–Si liquids is studied by molecular dynamics simulations using an empirical potential fitted to the Au–Si binary phase diagram. The growth speed v is predicted as a function of Si concentration xSi in the Au–Si liquid at temperature T 5 1100 K and as a function of T at xSi 5 75%. For both bulk crystals and NWs, the {111} surface grows by the nucleation and expansion of a single two-dimensional island at small supersaturations, whereas the {110} surface grows simultaneously at multiple sites. The top surfaces of the NWs are found to be curved near the edges. The difference in the growth velocity between NWs and bulk crystals can be explained by the shift of the liquidus curve for NWs. For both bulk crystals and NWs, the growth speed diminishes in the low temperature limit because of reduced diffusivity.
I. INTRODUCTION
Many semiconductor materials can be grown in the form of nanowires (NWs) by the vapor–liquid–solid (VLS) process using metal nanoparticles as catalysts. This has enabled a wide range of novel applications, such as nanoscale electronic, optical, and chemical-sensing devices,1–3 and has established semiconductor NWs as important potential building blocks of nanotechnology. However, many fundamental questions regarding the growth mechanisms still need to be answered to achieve better control of the orientation, yield, and quality of the NWs. Much of the studies on the VLS growth mechanism have been focused on Si and Ge NWs grown from Au catalysts, because of the relative simplicity of the Au–Si and Au–Ge phase diagrams and the anticipated compatibility of Si and Ge NWs with existing semiconductor industry. Most of the existing analyses of the VLS growth are based on the continuum theory of crystal growth.4–8 This approach has been successful in explaining certain features of NW growth, such as the modification of the chemical driving force of growth through the Gibbs– Thomson effect5,8 and the dependence of energetically favorable orientations on NW diameter caused by surface energies.9 However, many challenging and important questions remain to be answered. For example, how does the growth speed depend on NW orientation?10 Why some a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.155 J. Mater. Res., Vol. 26, No. 17, Sep 14, 2011
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catalyst particles fail to nucleate NWs?11 What causes growth anomalies such as kinking (i.e., sudden change of NW orientation during growth) ?12 What is responsible for the formation of metastable phases, such as hexagonal close-packed Au,13 upon growth termination? Answering these questions requires an understanding of the NW nucleation and growth mechanisms at the atomistic level. Atomistic simulations, such as molecular dynamics (MD) and Monte Carlo (MC
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