Rate Grown Transistor 1954 Prepare High Purity Germanium

# Prepare High-Purity Germanium: The Same Lifetime Floor, Now Banked Against a Melt That Never Changes Composition

This series builds General Electric's rate-grown variant of the grown-junction transistor this project has already documented twice — once in germanium in 1951, once in silicon in 1954 — and it is the first of the three to never add or remove a dopant species mid-pull at all. Both earlier series change the melt's composition deliberately, dropping a new pellet to shift what the crystal incorporates next. This process instead loads both donor and acceptor dopants into the melt together, from the very first step, and will later encode the junction entirely in how fast the crystal is pulled through that unchanging, compensated melt — which means this step's purity target has to anticipate two dopant species contaminating the lifetime budget simultaneously, not one species added later.

## 1. Lifetime Still Depends on Recombination Centers, Now With Two Dopant Species Already in the Melt

$$\frac{1}{\tau_n} = \sigma\,v_{\text{th}}\,N_t$$

As in both earlier grown-junction series, minority-carrier lifetime $\tau_n$ is governed by recombination-center density $N_t$, not by a chemical-purity grade alone. What differs here is which impurities are already present while $N_t$ is being driven down: the germanium series purifies a melt that will later receive one new dopant; the silicon series does the same. This process purifies a melt that already carries both dopant species it will ever use, which means any impurity-related recombination site either dopant source itself introduces is baked into the bar from the very first pull, with no later step able to dilute it the way a single-dopant melt's later addition might.

## 2. Real Diagram: One Melt, Two Dopants, No Later Correction Opportunity

A Compensated Melt Carries Both Dopants From the Start neither earlier grown-junction series in this project loads two dopants before pulling even begins 1951 germanium / 1954 silicon one dopant, added later purity banked against a melt that will change this series both dopants, present now purity banked against a melt that already carries everything it ever will N_t must clear the same floor, with twice the opportunity for an impurity source to contribute to it

## 3. The Diffusion-Length Target Is Unchanged; What It Has to Survive Is Not

$$L_n=\sqrt{D_n\,\tau_n}$$

The target relationship is identical to both earlier series: this bar's diffusion length $L_n$ must exceed whatever base width this process's later pull-rate schedule leaves behind, with purification driving $N_t$ as low as the apparatus allows. What makes reaching that target harder here is a fact neither earlier series' purification step had to account for — this melt's donor source and acceptor source are both present simultaneously from the first charge, so any contamination either dopant's own feedstock carries is already active in the melt before a single centimeter of crystal has been pulled, rather than arriving only when a later series' own pellet-drop step chooses to introduce it.

Same Target Curve, an Earlier Point Where Contamination Can Enter L_n ∝ 1/√N_t — the equation this project has used since 1951 is unchanged trap density, N_t → diffusion length, L_n single-dopant melt, contamination arrives later compensated melt, contamination risk starts here instead the operating point target is identical; the window for a defect to form is wider

## Prepare High-Purity Germanium's Place in the Process Lineage

Preparing high-purity germanium is step one of this project's rate-grown series — mechanically close to step one of the 1951 germanium grown-junction series, and distinguished by what this bar's purity has to survive: a single compensated charge carrying both the donor and acceptor species this entire process will ever use, established before any crystal has been pulled and never revised afterward. Step two, establishing the compensated melt's initial composition, is where both dopant concentrations — not one, set now and changed later, but two, set together and never changed at all — are actually decided.

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