Second Pellet Drop

# Second Pellet Drop (n): Re-Dosing the Melt to Close the Sandwich

The second pellet drop does to the gallium-dominated melt exactly what the first pellet drop did to the antimony-dominated melt — it dumps in enough of the opposite dopant to overwhelm whatever is already dissolved, and lets the still-pulling crystal keep freezing straight through the flip. By the time this pellet goes in, the puller has been drawing p-type germanium for some scheduled interval, and the base region of the eventual transistor has already been growing, layer by layer, at thickness $W_B = v_p \cdot \Delta t_{\text{switch}}$ since the first drop. This second drop does not create a new mechanism — it reuses the identical melt-dosing trick, but now with antimony re-entering a melt that gallium currently dominates, and now carrying the weight of closing the sandwich rather than opening it. Once this pellet dissolves and the net melt chemistry flips back to n-type, the crystal that keeps growing on top is the collector region, and the base region that got frozen in between the two drops exists permanently, fixed in both doping and thickness, the instant this pellet finishes dissolving.

## 1. Why the Second Drop Is Not Just "Pellet Drop, Again"

The physics of overwhelming a melt's net doping sign is the same equation as step two:

$$N_D^{\text{melt,eff}} - N_A^{\text{melt,eff}} = \frac{m_{\text{Sb}}}{M_{\text{Sb}}} \cdot \frac{N_{\text{Av}}}{V_{\text{melt}}} - N_A^{\text{(Ga, residual)}}$$

but the residual term is no longer the clean, known pre-growth melt concentration from step one — it's whatever gallium remains in the melt *after* some of it has already been consumed growing the base region, which itself depends on how much of the melt solidified during that interval. The antimony pellet has to be sized against a melt whose gallium content has already partially depleted through growth, not against the original pre-doped baseline. Undersize it and the melt only partially re-flips, producing a graded, uncertain second junction; oversize it and the final n-type region carries a higher net donor concentration than the original seed melt did, which changes the collector's resistivity from what the device's electrical specification assumed.

$$W_B = v_p \,(t_{\text{Sb,drop}} - t_{\text{Ga,drop}})$$

Base width — the single most sensitive electrical parameter in the finished transistor — is entirely determined by the *time between the two pellet drops*, multiplied by a pull rate that was fixed back at seed dip and never changes. There is no step anywhere in this process where base width gets measured and corrected; it is scheduled, once, as the operator's decision about when to drop the second pellet relative to the first, and then simply happens as the crystal grows through that interval.

## 2. Real Diagram: Closing the N-P-N Sandwich

Second Pellet Drop — the Base Region Is Now a Fixed Fact Sb re-doses the melt, overwhelms Ga, crystal keeps pulling — collector growth begins crystal cross-section at the moment of the second drop n (emitter region) grown before first drop N_D (Sb, original melt) p (base region) W_B = v_p · Δt — fixed now Sb pellet dissolving here n (collector region) growing now, after the flip pull continues at v_p, unchanged second junction forms here, now everything below the Sb layer has not been grown yet — only its doping target has been decided once this pellet finishes dissolving, base width and base doping are both permanently fixed — nothing in steps 4 through 6 can widen, narrow, or re-dope the region already grown
Base Width Is a Straight Line Through the Drop Interval W_B = v_p · Δt — a late second drop adds directly to base width, with no later fix Δt, time between Ga drop and Sb drop → base width, W_B slope = v_p, fixed at seed dip intended drop time dropped late — base now wider, permanently every point on this line is a decision, not a measurement taken after the fact

## 3. Why This Drop Carries More Risk Than the First

The first pellet drop only had to flip a known, uniform melt; the second has to flip a melt that has already been depleted and stirred by one growth interval, and it has to do so inside a tight window, because every extra second the pull continues past the intended drop time adds directly to base width through $W_B = v_p \cdot \Delta t$. A technician who drops the antimony pellet even slightly late does not get a chance to fix it — the base region has already grown wider than specified, and there is no furnace step, no regrowth, no later correction anywhere in the remaining process that can narrow a base that grew too wide. This is the single point in the six-step flow where a timing error directly becomes an electrical specification error in the finished device, rather than a cosmetic or yield defect that downstream inspection might catch and discard.

## Second Pellet Drop's Place in the Process Lineage

Second pellet drop is step three of the six-step grown-junction transistor device process flow — immediately after first pellet drop, and the event that closes the n-p-n sandwich by fixing base width and base doping permanently, ahead of ingot completion, crosswise slicing, and lead attachment.

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