Alloy Junction 1952 Attach the Collector Lead

# Attach the Collector Lead: A Joint Already Made Is Now at Risk

Step 33 solved a one-sided thermal-safety problem: how much heat the emitter lead's own joint could tolerate before its pulse reached too close to the junction underneath it. Step 34 faces that identical local constraint again at the collector face — the same $T_{\text{solder}} < T_{E,\text{button}}$ ceiling, the same diffusion-limited penetration depth that has to stay shallow of $x_j$ — but it also introduces a risk Step 33 never had to consider, because Step 33 was the *first* lead attached. By the time this step runs, a finished solder joint already exists on the opposite face, and this step's own heat input is not the only heat that joint has to survive.

## 1. Local Penetration Was Never the Real Risk to the Other Side

Step 33's local thermal-penetration depth, $\delta_{\text{thermal}} \approx \sqrt{\alpha t_{\text{pulse}}}$, describes how far heat spreads from a brief, localized pulse before it dissipates — and for any short pulse, that distance stays far short of the full slice thickness $t_{\text{slice}}$ separating the two faces. A single collector-side solder pulse, taken on its own, essentially never reaches far enough to directly threaten the emitter joint by conduction alone. The real risk is different: it is not about *reach*, it is about *accumulation*. If the collector-side soldering operation runs for an extended total time, or the lead-attachment process repeats several passes, the heat delivered at each pass does not vanish — it raises the average temperature of the entire device, not just the region directly under the new pulse, and that bulk temperature rise is what can eventually threaten a joint on the far side that a single short pulse's local penetration depth never could.

## 2. A Different Kind of Thermal Budget — Total Heat, Not Local Depth

Where Step 33's equation tracked how far a single pulse's heat front advances, this step has to track something structurally different: how much the whole device warms up from the *cumulative* heat delivered across the entire collector-lead attachment operation. Treating the device as a single lumped thermal mass, the resulting bulk temperature rise is:

where $Q_{\text{total}}$ is the total heat delivered over the whole operation, $m$ is the device's mass, and $c_p$ is its specific heat capacity. This is an entirely different failure mode from Section 1's local penetration-depth concern: even a process whose individual pulses are each too brief and too localized to threaten anything by direct conduction can still, through enough repetition or enough total dwell time, raise $\Delta T_{\text{bulk}}$ high enough that the *entire* device — including the already-finished emitter joint sitting on the far face — approaches the same $T_{E,\text{button}}$ ceiling Step 33 established, this time from a uniform rise in ambient temperature rather than a local heat front.

## 3. Real Diagram: Two Different Ways the Same Limit Gets Approached

## 4. Real Diagram: Why Sequencing and Pacing the Pulses Matters

## Attach the Collector Lead's Place in the Process Lineage

Attach the Collector Lead follows directly from Step 33, Attach the Emitter Lead, whose finished joint is the specific thing this step's own heat input now has to avoid disturbing; it precedes Step 35, Connect the Base Tab to Its Terminal, which completes the device's third and final electrical connection under what should by then be a fully exhausted thermal budget. It is the seventh step of Phase 4 and the point where this series' running thermal-safety reasoning splits into two genuinely separate concerns for the first time — a local penetration-depth limit, already characterized in Step 33, and a new, global bulk-temperature limit that only exists because, unlike every prior lead or tab attachment in this series, this is the first operation performed on a device that already has something finished elsewhere on it to protect.