Nanowire CVD Growth Designer (2D)

Precursor Gas

Growth temperature 550 °C

Precursor supersaturation 1.8×

Catalyst droplet diameter 28 nm

Run

Live Readouts

Growth rate

0.00 nm/s

Wire length

0 nm

Wire diameter

28 nm

Layers added

Driving force Δμ

0.000 eV

Critical diameter d꜀

0 nm

How it works

This is the 2D cross-section counterpart of the 3D Nanowire CVD Growth Designer, implementing the real Gibbs–Thomson-corrected VLS growth law. A molten catalyst droplet sits at the tip of the growing wire. Precursor gas supersaturation supplies a bulk driving force Δμ, but a thinner droplet has higher curvature and therefore a higher equilibrium vapor pressure (Gibbs–Thomson / Kelvin effect), which subtracts from that driving force — so thinner wires grow measurably slower, and below a critical diameter growth stops entirely.

Growth rate:  dL/dt = k(T) · [ Δμ − 4Ωσ / d ]₊
Driving force: Δμ = kB·T·ln(S)   (S = precursor supersaturation ratio)
Arrhenius:     k(T) = k0 · exp(−Ea / kB T),  Ea ≈ 1.6 eV (Si-VLS)
Critical diameter: d꜀ = 4Ωσ / Δμ   (growth = 0 when d ≤ d꜀)
Ω ≈ 0.020 nm³ (Si atomic volume), σ ≈ 1.0 J/m² (Au–Si droplet surface energy)

Supersaturation — sets the bulk driving force Δμ = kB·T·ln(S); higher S pushes more precursor into the droplet, raising the chemical-potential gradient that drives precipitation.
Droplet/wire diameter — smaller droplets have higher surface curvature, which (via the Gibbs–Thomson relation) raises the droplet's own equilibrium chemical potential and eats into Δμ as 4Ωσ/d. This is why very thin nanowires are hard to grow: below d꜀ = 4Ωσ/Δμ the correction term exceeds the driving force and growth rate hits exactly zero.
Temperature — sets both the Arrhenius kinetic prefactor k(T) and (through Δμ = kB·T·ln S) the driving force itself, so it has a double effect on rate.

The chart on the right plots growth rate against diameter for the current temperature and supersaturation, with the current droplet size marked — drag the diameter slider down and watch the marker slide toward, and then past, the critical-diameter cutoff.

Au catalyst droplet Nanowire (solid) Substrate

⛔ Below critical diameter — growth stopped