DRAM-1968 Step 17 Model Wafer Scale Yield for a Repeated Cell Array

# Model Wafer-Scale Yield for an Array Built From One Repeated Cell

Step 9 qualified density against refresh complexity at the architecture level; manufacturing this array at volume raises a distinct question Steps 1 through 10 never addressed directly — how yield behaves when a single fabricated part contains thousands of nominally identical cells, any one of which can fail the whole part.

## 1. State the Yield Model a Repeated-Cell Array Actually Needs

A simple Poisson defect model treats yield as $Y = e^{-D_0 A}$, where $D_0$ is defect density per unit area and $A$ is the critical area exposed to that defect population. For an array built from one repeated cell (Step 9's own framing), $A$ scales directly with cell count, so a part with twice as many cells at the same defect density has a strictly lower raw yield — a mathematical consequence of repetition, not a flaw specific to this architecture.

Model Wafer-Scale Yield for an Array Built From One Repeated Cell Step 17 — dram-1968 State the Yield Model a Repeated-Cell Array Actu see Section 1 Show Why This Architecture Tolerates That Pressu see Section 2 Connect Yield Back to the Commercial Argument see Section 3 THREE-PART ARGUMENT, ONE STEP dram-1968 extension, step 17 of this project's DRAM lineage

## 2. Show Why This Architecture Tolerates That Pressure Better Than It First Appears

The repeated-cell property that drives $A$ up is the same property Step 9 identified as the source of this architecture's density advantage, so the yield pressure is not avoidable by a different cell design within this architecture — it is inherited from the same choice that makes the architecture valuable at all. What makes the tradeoff survivable in practice is redundancy at the array level (spare rows or columns substituted in for ones containing a defective cell, a technique this project does not need to re-derive here since it is a manufacturing-test practice, not a circuit-architecture one) and the sheer magnitude of the density advantage itself: even a yield loss proportional to array size still produces far more good bits per wafer than a latch-based array (Step 8's comparison) built at the same defect density, because the latch array's own larger per-bit area already costs it more die area for the same capacity.

Step 17 in the Dram-1968 Lineage what this step inherits and what it hands forward, by name Step 17 this step Inherits prior steps Hands Off named thread NO CELL-PHYSICS OR ARCHITECTURE RE-ARGUED each step adds a distinct angle; none re-derive settled prior content

## 3. Connect Yield Back to the Commercial Argument

Yield economics, not just raw area or cost-per-bit trajectory (Step 15), is what actually determined how fast a given fab could ship volume at an acceptable cost — a defect density too high for a given array size meant a fab simply could not sell parts of that capacity profitably yet, regardless of how favorable the architecture's density advantage looked on paper. This is the same manufacturing-economics lens this project applies in its Mesa Production (1958) series' own learning-curve and reject-pile arguments, now applied to a repeated-cell memory array instead of a discrete transistor product line.

Take dram-1968 step 17 model wafer scale yield for a repeated cell array further

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