A seed crystal is dipped into molten silicon and slowly withdrawn while rotating. This cross-section view keeps the growing tip anchored at the melt surface and lifts the seed chuck as the boule lengthens, exactly like the diameter-control loop on a real puller: the radius doesn't get set directly, it relaxes toward a target set by the current heat/mass balance.
R_target ≈ R0 · (v0/v) · (1 + k·(Tmelt − T0))
dR/dL = (R_target − R) / L_relax
Faster pull (v↑) or a colder melt (Tmelt↓, closer to the 1414 °C freezing point) narrows the crystal; slower pull or a hotter melt widens it — negative feedback that mirrors the real solidification heat balance at the interface.
The interface thermal gradient G is estimated from melt superheat, and together with pull rate v it sets the Voronkov ratio ξ = v/G. Outside a safe band around the critical ξc ≈ 0.130 mm²/(min·K) the growth front becomes thermally unstable and dislocation loops nucleate — flagged here as red defect bands baked into the boule as it grows.
G ≈ G0 + kG·(Tmelt − 1414) (more superheat ⇒ steeper interface gradient)
ξ = v / G
|ξ − ξc| large → dislocation risk (flagged band)
- Pull rate — withdrawal speed of the seed; higher v narrows the target diameter and raises ξ.
- Melt temperature — heater setpoint above silicon's 1414 °C melting point; more superheat widens the target diameter and steepens G.
- Rotation — mixes the melt for a flatter interface; shown here as neck/body ripple amplitude and a spin indicator on the seed.
Real-world relevance: essentially every silicon wafer in modern electronics starts as a Czochralski boule grown exactly this way, with fabs actively steering pull rate and melt temperature to stay inside the narrow dislocation-free band.