Summary of Nanowire Growth Mechanism

Summary of Nanowire Growth Mechanism

Yanming Wang and Seunghwa Ryu

Isotropic Material Nanowire Statics

No line tension at trijunction

$V_{L}={\frac {\pi }{3}}({\frac {r}{sin(\beta )}})^{3}(1-cos(\beta ))^{2}(2+cos(\beta ))$

Force balance is always kept as,

$\sigma _{LV}cos(\beta )=\sigma _{SV}cos(\alpha )-\sigma _{LS}$

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle tan(\alpha)=-\frac{dh}{dr} }

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h(\alpha')=-\int_0^{\alpha'}{tan(\alpha)\frac{dr}{d\alpha}d\alpha},V_L = const }

Solving the above integral, we can get the equilibrium shape of the nanowire grown by steady state process.

Non-zero line tension

The force balance equation in this situation will change as

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma_{LV} cos(\beta) = \sigma_{SV} cos(\alpha)-\sigma_{LS}-\frac{\tau}{r} }

if Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau<0} , there will be a tendency to increase the trijunction radius; while if Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau>0} , the tendency should be to reduce the trijunction radius.