Position the Base Wire

# Position the Base Wire: A Binary Outcome, Not a Continuous Tradeoff

Every positioning problem this process has solved so far has been a tradeoff between two competing continuous quantities — gain against punch-through, etch depth against base-width safety. Placing the base wire's tip is different in kind: the tip either lands on the p-type base, making the correct connection, or it lands on one of the flanking n-type regions, making a categorically wrong one. There is no partial credit and no graceful degradation — a wire bonded a few microns off-target doesn't produce a slightly worse base contact, it produces a base lead connected to the emitter or collector instead, a different circuit entirely.

## 1. Combined Positioning Error Determines a Real Placement Probability

$$P(\text{correct placement}) = P\!\left(|x_{\text{tip}} - x_{\text{base,center}}| < \frac{W_B}{2} - m\right)$$

The tip's actual landing position carries two independent error contributions — step twenty-nine's measurement uncertainty in where the base actually is, and the micromanipulator's own mechanical placement repeatability in driving the tip to that coordinate. Both errors stack into a single combined positioning uncertainty, and the probability of landing correctly depends on how that combined uncertainty compares to the base width itself, with a safety margin $m$ subtracted to avoid grazing the edge. This is the step where base width — set as far back as step sixteen's pull-time scheduling — finally determines a concrete yield number rather than an electrical specification: a narrower base, built deliberately for better gain, is mechanically harder to land a wire on correctly.

## 2. Real Diagram: Correct Landing Versus a Near-Miss

Correct Base Landing Versus a Near-Miss Onto the Wrong Region the difference is a categorical connection error, not a degraded contact correct landing tip lands inside the base, correct connection near-miss tip lands on n-region, wrong connection entirely the offset separating these two outcomes can be smaller than the base width itself

## 3. The Narrower the Base Grown for Gain, the Less Forgiving This Step Becomes

$$P(\text{correct}) \downarrow \text{ as } W_B \downarrow, \text{ holding positioning error fixed}$$

This creates a direct tension between two earlier design goals that never had to confront each other until now: step sixteen's gain-optimization pressure pushes base width narrower, while this step's placement yield depends on base width staying wide enough, relative to the micromanipulator's achievable precision, for reliable landing. A process pushing for maximum gain by minimizing $W_B$ without a corresponding improvement in positioning precision trades electrical performance directly against bonding yield — the two constraints this entire contacting phase exists to reconcile.

Correct-Placement Probability vs. Base Width holding combined positioning error fixed — a narrower base is a harder target base width, W_B → P(correct placement) narrow base, best gain, worst yield wide base, easy landing, lower gain this curve is the actual tradeoff step 16's gain target has to be weighed against

## Position the Base Wire's Place in the Process Lineage

Positioning the base wire is step thirty of the 1951 grown-junction transistor's full manufacturing sequence — immediately after the base has been located electrically, and before the wire is pulse-bonded in place. It is the step where positioning error, accumulated from measurement and mechanical placement alike, converts directly into a binary correct-or-wrong connection outcome, with base width itself setting how much error the process can tolerate before that outcome flips.

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