Finish Growth and Cool

# Finish Growth and Cool: Not All Dislocations Cost the Same

Thermal stress during cooling can nucleate dislocations anywhere along the ingot's length, but a dislocation in the bulk of the emitter or collector region is a far more forgivable defect than the identical dislocation sitting inside the thin junction-bearing section this whole process spent eighteen steps building. A dislocation threading through otherwise-uniform n-type or p-type material mostly just locally disrupts carrier mobility — a minor, often tolerable defect in bulk material far from either junction. The same dislocation intersecting a depletion region is a different problem entirely: it introduces a physical pathway of disrupted lattice directly across the junction's electric field, creating a generation-recombination center that shows up as excess leakage current and degraded breakdown voltage in exactly the region steps fifteen through eighteen worked hardest to get right.

## 1. Dislocation Density Alone Doesn't Predict Device Failure — Location Does

$$I_{\text{leak}} \propto N_{\text{disl}}^{\text{(junction-proximal)}}, \qquad I_{\text{leak}} \not\propto N_{\text{disl}}^{\text{(bulk)}}$$

The same total dislocation density, generated by the same cooling-stress profile, produces wildly different electrical consequences depending on where those dislocations happen to land relative to the two junctions. A cooling schedule that passes a bulk-material dislocation-density inspection with ease can still produce unacceptable leakage current if even a small fraction of that density concentrates within the narrow axial section spanning both junctions and the base between them — a region that, on a typical ingot, is a small fraction of the total pulled length but carries essentially all of the electrical consequence from this step's thermal handling.

## 2. Real Diagram: Same Stress, Different Consequence by Location

Dislocations From Cooling Stress — Same Density, Different Stakes location relative to the junctions determines whether a dislocation matters electrically n region 1 junction-bearing section n region 2 bulk dislocation mostly benign junction-proximal dislocation — leakage path bulk dislocation mostly benign cooling the ends faster than the junction-bearing middle reduces stress where it matters most

## 3. Why Cooling Rate Can Be Non-Uniform on Purpose

$$\left.\frac{d\sigma_{\text{thermal}}}{dt}\right|_{\text{junction section}} < \left.\frac{d\sigma_{\text{thermal}}}{dt}\right|_{\text{bulk sections}}$$

Because the junction-bearing section's dislocations carry disproportionate electrical cost, controlled cooling schedules can deliberately hold a slower rate of temperature change specifically across that axial section, even while allowing faster, more aggressive cooling in the bulk emitter and collector regions where dislocation tolerance is higher. This is a refinement on the generic ingot-cooling thermal-stress control already established — not a different physical mechanism, but a location-weighted application of it, informed by exactly which part of the finished ingot the slicing step will cut into individual transistor bars from.

Leakage Current vs. Axial Position of a Dislocation same defect, same density — sensitivity spikes only across the junction-bearing section axial position along the ingot → leakage current from a dislocation there junction-bearing section bulk n₁ bulk n₂ cooling control should weight stress reduction toward the narrow peak, not the whole ingot equally

## Finish Growth and Cool's Place in the Process Lineage

Finishing growth and cooling is step twenty of the 1951 grown-junction transistor's full manufacturing sequence — the final step of crystal growth, after the second N-type region has completed, and before the ingot is handed off to be cut into individual transistor bars. It is the step where thermal stress management has to be weighted by location along the ingot, since a dislocation's electrical cost depends entirely on whether it lands in the junction-bearing section this whole process was built around, or in bulk material far more tolerant of the same defect.

Take finish growth and cool further

Ask the copilot about this term, or have our engineers assess it against your process.

Ask CFSGPT about this → Request a technical assessment → Open the CFS app