Ingot Completion

# Ingot Completion: Pulling Out Enough N-P-N Sandwiches to Matter

By the time ingot completion starts, both junctions already exist, base width is already fixed, and nothing left in this step can change a single electrical property of the devices already grown — what's left is purely a question of how much more usable crystal to pull before stopping, and how to get it out of the furnace without destroying what's already there. The puller keeps winding the crystal upward at the same constant rate $v_p$ that has governed every step since seed dip, now growing collector material on top of the completed base junction for as long as the operator lets it continue. Every additional centimeter pulled at this stage is pure yield — another slice's worth of n-p-n sandwich, repeating the same cross-sectional structure along the ingot's length, as long as the pull stays stable. The step ends with a decision, not a measurement: stop pulling, cool the crystal under control, and separate it from the melt without cracking it or letting thermal shock introduce dislocations into material that took the better part of an hour of continuous pulling to grow.

## 1. Ingot Length Is a Throughput Decision, Not a Physics Constraint

$$N_{\text{devices}} \approx \frac{L_{\text{ingot}} - L_{\text{seed}} - L_{\text{tail}}}{L_{\text{slice}}}$$

Once the sandwich is closed, the only variable left under the operator's control is how long to keep pulling before stopping — every additional unit of pulled length, divided by the slice thickness used in the next process step, is one more device's worth of n-p-n cross-section. This is a straightforward economic trade rather than a materials-science constraint: a longer pull means more devices per furnace cycle, but it also means more total time with a full crucible of molten germanium exposed to contamination risk, more cumulative thermal stress on the growing crystal, and a higher chance that some uncontrolled perturbation late in the pull (a temperature fluctuation, a vibration, a slight change in rotation speed) introduces a crystal defect somewhere along the ingot's length. Because the junctions near the seed end were grown earliest and have had the most total pull time to accumulate any such defect in material grown *after* them, ingot length is tuned against a real yield-versus-defect-rate curve, not pulled indefinitely just because the melt allows it.

## 2. Real Diagram: What Changes (and What Doesn't) During Completion

Ingot Completion — Growing Repeats of a Sandwich Already Closed pull continues at v_p, unchanged — no new dopant events, only accumulated length n (emitter) — grown, fixed p (base) — W_B fixed n (collector) growing now, no new dopant slice plane 1 slice plane 2 pull at v_p continues every slice plane below the base cuts a repeat of the same fixed n-p-n structure decision at stop: pull longer → more devices pull longer → more defect risk tuned against a yield/defect curve, not pulled to the melt's physical limit cooling and removal from the puller is itself controlled — thermal shock here can crack the whole ingot
Devices Pulled vs. Defect Probability, Same Ingot more pull length is pure yield, until accumulated risk starts eating into it ingot length pulled → devices / defect risk devices pulled, linear in length cumulative defect probability practical stop point stop before the defect curve starts eroding the yield curve's lead

## 3. Controlled Cooling Protects an Investment That Can No Longer Be Remade

$$\sigma_{\text{thermal}} \propto \alpha \, E \, \Delta T$$

Thermal stress in a cooling crystal scales with the coefficient of thermal expansion $\alpha$, the material's elastic modulus $E$, and the temperature differential $\Delta T$ across the crystal as it cools — which is exactly why ingot removal is a slow, ramped process rather than simply lifting a finished crystal out of a 938°C furnace into room-temperature air. A germanium ingot that has taken an hour or more of continuous pulling to grow, with every n-p-n repeat inside it already electrically fixed, represents a large, committed quantity of finished devices-in-waiting; a cracked ingot at this stage doesn't just lose the crystal, it loses every device that was going to be sliced from it, after all the earlier timing-critical steps already succeeded. Controlled cooling is the step that converts "a crystal that grew correctly" into "a crystal that survives to be sliced," and it's the last point in the process where a purely thermal/mechanical failure, rather than a dopant-timing failure, can still destroy the batch.

## Ingot Completion's Place in the Process Lineage

Ingot completion is step four of the six-step grown-junction transistor device process flow — after both pellet drops have closed the n-p-n sandwich, and before crosswise slicing and lead attachment. It is the step that converts a correctly-doped crystal into a controlled yield of repeated device cross-sections, and the last step where thermal mishandling — rather than dopant timing — can still destroy work already done.

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