Epitaxial Process 1961 Verify Thickness Resistivity Uniformity

# Verify Epitaxial Layer Thickness and Resistivity Uniformity: Two New Numbers This Process Has Never Had to Measure Together

## 1. Why a Single Passing Number No Longer Proves This Layer Is Right

Step 2 grew a layer; this step proves the layer it grew is the layer the series actually needed, and for the first time in this project's history that proof requires two independent measurements to agree at once, not one. Thickness is measured by infrared reflectance interference, the same fringe-counting principle the 1957 series used to read oxide thickness off a wafer's color, and resistivity is measured separately, by a four-point probe or a capacitance-voltage sweep, at the same sites across the wafer's surface. Neither number alone says anything about whether Step 1's conflict was actually resolved: a layer at the right thickness but the wrong resistivity still hands the breakdown-voltage requirement a doping level it cannot satisfy, and a layer at the right resistivity but the wrong thickness leaves too little lightly-doped silicon between the surface junction and the heavily-doped substrate beneath it. Both numbers must land inside their own tolerance, at the same site, simultaneously, or the wafer that looked fine on either measurement taken alone is not actually fine at all.

where $t_{\text{epi}}$ is the measured epitaxial thickness at a site, $\rho_{\text{epi}}$ the measured resistivity at that same site, and the right-hand side is a rectangle in a two-dimensional space rather than an interval on a line — a wafer passes only if every sampled site's $(t_{\text{epi}}, \rho_{\text{epi}})$ pair falls inside that rectangle, and it can fail by missing on either axis alone or on both axes together, which no single-property check in this project's history before this step has ever had to express.

## 2. Real Diagram: A Wafer Carrying Two Numbers at Every Site Instead of One

The wafer map below samples the epitaxial layer at several points across the surface, echoing the five-point oxide-thickness sampling this project first used in 1957's own Step 2 — but where that earlier map recorded a single thickness figure at each site, every site here carries a thickness-and-resistivity pair, because this step cannot pass or fail a site on either number alone.

## 3. Why 1957's Oxide Check Could Only Ever Fail in One Direction

The 1957 series' own Step 2 sampled a wafer's oxide at several points and compared each reading against a single acceptable range — a site either fell inside that interval or it did not, and the furnace drift behind a bad reading, when it occurred, showed up as one number moving the wrong way. The gas-flow and temperature non-uniformity this step now contends with is, mechanically, the same kind of reactor drift this project first characterized for diffusion furnaces in 1958's own Step 2, only now it acts on a gas-phase reactor rather than a solid-source furnace, and it rarely moves just one property. A temperature excursion at the wafer's edge nearest the gas inlet changes the local growth rate, which shifts thickness, and simultaneously changes how much dopant incorporates into the growing layer, which shifts resistivity — the same underlying drift reaching two different measured numbers through two different mechanisms, at the same site, in a way a single-axis check could never fully register even if it happened to catch one of the two symptoms.

Step 3 does not confirm that the epitaxial layer merely exists at roughly the right dimension; it confirms that the two properties Step 1 split apart — the breakdown voltage's doping and the series resistance's doping — have each landed where they need to be, independently, at every site a reactor's own drift could have disturbed.