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,

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

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

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

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 $\tau <0$, there will be a tendency to increase the trijunction radius; while if $\tau >0$, the tendency should be to reduce the trijunction radius.