Nanowire Batch Yield & Uniformity Simulator (2D)

Batch & Process

Mean catalyst diameter 28 nm

Size dispersion (CV) 30%

Vapor supersaturation Δμ₀ 80 meV

Growth temperature T 550 °C

Time speed 1.0×

Run

Live Readouts

Critical diameter d꜀

6.2 nm

Batch yield

Mean wire length

0.0 nm

Length uniformity (CV)

Synthesis time

0.0 s

Stalled droplets

0 / 400

How it works

The 3D VLS Nanowire Growth Simulator shows why a handful of catalyst droplets of different sizes grow at different rates. This 2D companion asks the manufacturing-floor question that follows from it: if you dewet a whole wafer of gold into hundreds of droplets with some natural size spread, what fraction of your batch actually turns into usable nanowires, and how uniform are they?

Each of 400 droplets is drawn from a log-normal diameter distribution with the mean and dispersion (coefficient of variation) you set. Every droplet then grows under the same Givargizov / Gibbs-Thomson law used by the 3D model:

r_c = 2σΩ / Δμ₀              (critical radius — Gibbs-Thomson)
v(r) = v_max·(1 − r_c/r)      for r > r_c, else v(r) = 0
v_max(T) = v_ref · exp[ (E_a/k_B)(1/T_ref − 1/T) ]

Droplets below the critical diameter never grow at all — they cap the theoretical yield. Among the survivors, larger droplets still outrun smaller ones (v grows with r), so the batch's length distribution spreads out over time even when every droplet started above the cutoff. That spread, reported as a coefficient of variation, is exactly the uniformity metric real nanowire-array manufacturing lives or dies by.

Mean catalyst diameter — shifts the whole population toward or away from the critical cutoff.
Size dispersion — a tighter distribution (low CV) keeps more droplets clear of the cutoff and keeps the final lengths close together; a broad one trades yield and uniformity for a wider usable diameter range.
Supersaturation — raises Δμ₀, which shrinks d꜀ and can rescue previously-stalled droplets into the growing population.
Temperature — sets v_max through Arrhenius kinetics; it changes how fast the batch runs, not who grows.

The top panel is the population itself: every droplet's diameter, colored by whether it currently clears the critical cutoff. The bottom panel is the outcome: a live histogram of nanowire lengths across the batch, which starts as a single spike at zero and fans out as synthesis proceeds.

Above cutoff (will grow) Below cutoff (stalled)

Catalyst population (400 droplets)

Nanowire length histogram