Chemical Tension in VLS Nanostructure Growth Process: From Nanohillocks to Nanowires
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1017-DD04-09
Chemical Tension in VLS Nanostructure Growth Process: From Nanohillocks to Nanowires Na Li1, Teh Y. Tan1, and Ulrich Gˆsele2 1 Mechanical Engineering and Materials Science, Duke University, Durham, NC, 27708 2 Max-Plank-Institute of Microstructure Physics, Halle, D-06120, Germany
ABSTRACT We formulate a global equilibrium model to describe the growth of 1-d nanostructures in the VLS process by including also the chemical tension in addition to the physical tensions. The chemical tension derives from the Gibbs free energy release due to the growth of a crystal layer. The system global equilibrium is attained via the balance of the static physical tensions and the dynamic chemical tension, which allows the system to reach the minimum Gibbs free energy state. The model predicts, and provides conditions for the growth of nanowires of all sizes exceeding a lower thermodynamic limit. The model also predicts the conditions distinguishing the growth of nanaohillocks from nanowires.
INTRODUCTION Semiconductor nanowires, in particular Si nanowires (SiNW), are of major interests for future applications in devices. Among many growth schemes, the vapor-liquid-solid (VLS) method is a most important one. Growth of SiNW starts from the nucleation of a thin layer underneath the metal-Si liquid alloy droplet on the substrate, and proceeds through a transition stage when the diameter shrinks as the length increases. Finally a nanowire will grow if a steady state can be reached when the diameter becomes constant. Otherwise, the diameter keeps shrinking; as a result a hillock will form and the growth will terminate. The transition stage is common to SiNW in the nanometer size range and Si whiskers in the µm size range.1 Recently, Schmidt et al.2 found that, besides SiNW, Si nanohillocks may also grow. They formulated a model to describe the transition process and identified the growth conditions of SiNW and Si nanohillocks. The model uses a stress balance scheme to account for the roles of a line tension τ and three surface tensions, σ LS , σ VL , and σ VS , respectively of the liquid-solid (LS), the vaporliquid (VL), and the vapor-solid (VS) interfaces. Though can be viewed as force quantities, these tensions are actually energy densities. The line, formed by the three interfaces, surrounds the wire growth front. The model is a quasi-static description of the SiNW (and nanohillock) growth process, which yielded quantitative fits to experimental results. The line tension value used was ~10-9 J/m, which seems to be too large: by as much as two orders of magnitude.3 Line tension values ranging from slightly positive to negative have to be used for growing SiNW. While a negative line tension is possible,4,5 it nonetheless means the line is more stable than the surfaces forming it, which is highly controversial.5 Moreover, to explain the same transition feature for SiNW and Si whiskers with size differences of several orders of magnitude, the line tension values must also span several orders of magnitude, in direct proportio
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