Summary of Nanowire Growth Mechanism

Summary of Nanowire Growth Mechanism

Yanming Wang and Seunghwa Ryu

Isotropic Material Nanowire Statics

No line tension at trijunction

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

Force balance is always kept 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} }

$tan(\alpha )=-{\frac {dh}{dr}}$

$h(\alpha ')=-\int _{0}^{\alpha '}{tan(\alpha ){\frac {dr}{d\alpha }}d\alpha },V_{L}=const$

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

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

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.