Our first probability-style approach was too seductive. Multiplying guessed search dimensions can make almost any realized invention look astronomically improbable. The endpoint has already been selected by history, so the exact winning configuration is the wrong target.
Start by trying to destroy necessity claims
One provocative claim was that the 1947 point-contact transistor would have required the >100 microsecond minority-carrier lifetimes associated with later, better germanium crystals. A simple independent diffusion/recombination model already weakens that claim: at the historical tens-of-microns contact scale, 5–10 microsecond material does not fail the elementary carrier-survival test.
That does not reproduce transistor power gain. It does something narrower and more useful: it stops us from turning a later material improvement into a requirement merely because the later material was better.
The field changes the apparent requirement
The 2-D DEVSIM model then exposed another dependency. At low collector field, the fraction of injected minority holes reaching the collector depends strongly on assumed lifetime. Increase the collector field and the apparent lifetime requirement can collapse. In one matched low-injection control, the hole-transfer proxy moved from about 0.05 at 0.1 microseconds with zero collector bias to about 0.88 with a −5 V collector bias. At 5 microseconds the corresponding values were about 0.27 and 1.00.
They are model transfer proxies, not measured December 1947 current gain. The point is the dependency: “lifetime X was required” is meaningless unless the field geometry and bias are specified too.
Even the physical picture changes the result
A uniform n-type bulk model and a model with a thin p-type surface-layer proxy produce very different transfer at the same nominal lifetime and bias. At 0.1 microseconds and −1 V in one matched run, the minority-hole transfer proxy rose from roughly 0.55 to 0.89 when the surface-layer family was admitted. The surface layer is a model proxy, not a claim about a chemically doped layer in December 1947.
That difference is the result. If the inferred material requirement depends that strongly on how the surface is represented, no historical argument should talk about “the required lifetime” as if it were a free-standing constant.
The future target is an overlap problem
Historical research should reconstruct the set of material qualities, contact practices, geometry tolerances and instruments practically available by a date. Physics should independently map the set of parameters that produces a declared observable. Only then do we ask whether the two sets overlap. Later measurements may be used as sensitivity bounds, but the software now labels them as later calibration rather than silently placing them in 1947.
A simulation is strongest here when it makes an exciting anomaly disappear—or forces both sides to keep more variables in mind.
- DEVSIM — inspectable semiconductor device solver used for the 2-D controls.
- Gmsh — scripted point-contact geometry and mesh.
- NIST FiPy — independent finite-volume diffusion/recombination cross-check.
- US2524035A — post-discovery operating examples used only as a later calibration envelope.