Czochralski Silicon Crystal Puller

Puller Controls

Pull rate 1.0 mm/min

Thermal gradient G 3.5 K/mm

Crystal rotation 15 rpm

Dopant

Live Readouts

Diameter

— mm

Grown length

0 mm

Voronkov ratio ξ=v/G

— mm²/min·K

Critical ξ_c

0.130

—

How it works

In the Czochralski (CZ) process a seed crystal is dipped into molten silicon and slowly withdrawn while both seed and crucible rotate, freezing melt onto the seed one atomic layer at a time. The boule's diameter is not set directly — it is a consequence of the heat balance at the solid-melt interface, so this sim relaxes the visible radius toward a target with a finite response length, exactly like a real puller's diameter-control loop:

R_target ≈ R0 · (v0 / v)      (heat/mass balance: faster pull ⇒ thinner crystal)
dR/dL = (R_target − R) / L_relax

The point-defect population that freezes into the lattice is governed by the Voronkov criterion: the ratio of pull rate v to the axial thermal gradient G at the interface.

ξ = v / G
ξ > ξc  →  vacancy-rich   (voids / COPs — Crystal-Originated Particles)
ξ < ξc  →  interstitial-rich (dislocation loops)
ξ ≈ ξc  →  narrow "perfect" / defect-lean band
ξc ≈ 0.130 mm²/(min·K) for silicon

Pull rate — withdrawal speed of the seed; raises v and shrinks the target diameter.
Thermal gradient G — set by heater power and heat shielding; higher G lets you pull faster while staying near ξc.
Rotation — mixes the melt for a flatter, more axisymmetric interface; low rotation shows up here as visible diameter ripple (striations).
Dopant — boron (p-type) or phosphorus (n-type) added to the melt sets majority-carrier type; shown here only as boule tint, since dopant segregation itself follows a separate (much slower) diffusion process.

Real-world relevance: essentially every silicon wafer used in modern electronics — CPUs, memory, solar cells — starts as a CZ boule grown exactly this way, and fabs actively steer v and G to stay inside the narrow vacancy/interstitial-balanced band because both defect types degrade device yield.

Silicon boule Molten silicon

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