Micrologic 1960 Step 13 Cost per Good Die Yield Economics

# Price a Chip by Its Transistor Count, Not Its Function: The Cost Per Good Die Curve This Product Forced

## 1. Why Adding One More Transistor Costs More Than Adding One More Transistor

This step turns Step 7's whole-chip yield penalty into a number a sales catalog can actually print: the cost of one good die is the cost of processing an entire wafer divided by the number of dies on it that pass, and because the chance any one die survives falls exponentially as its transistor count rises, cost per good die rises far faster than transistor count does. A wafer costs roughly the same to process whether a die carries four transistors or forty, since the furnace cycles, masking steps, and metal deposition this series' earlier steps described run once per wafer regardless of what any single die contains. What changes is the fraction of dies on that wafer with no fatal defect anywhere in their now-larger area, and that fraction is exactly Step 7's Poisson survival probability, now plugged directly into a cost model for the first time in this project's history.

$$C_{\text{good die}} = \frac{C_{\text{wafer}}}{N_{\text{dies}} \cdot e^{-D A}}$$

where $C_{\text{wafer}}$ is the fixed per-wafer processing cost, $N_{\text{dies}}$ the number of dies patterned on the wafer, $D$ the defect density this series has tracked since Step 7, and $A$ a die's area — which grows directly with its transistor count. A die with twice the area of another does not cost twice as much to make good; because $A$ sits in the exponent's denominator, it can cost several times as much, and that nonlinearity is the economic fact this series' pricing has to respect.

Cost Per Good Die Rises Faster Than Transistor Count an exponential yield penalty applied directly to the price of a part transistors per die → cost per good die cost curve, exponential if cost only scaled linearly with count the gap between the two curves is the price this series must charge to cover scrap

## 2. Real Diagram: One Wafer, One Fixed Cost, a Falling Fraction of Winners

The wafer this series processes is the same wafer whether its dies are small and simple or larger and more complex. What a bigger die buys in function it spends in survival probability, and this diagram makes that trade visible: more area per die, fewer good dies per wafer, the same total wafer cost spread across a smaller winning fraction.

One Fixed Wafer Cost, Two Die Sizes a smaller die keeps more winners from the same processing bill SMALL DIE, LOW TRANSISTOR COUNT most dies pass LARGE DIE, HIGH TRANSISTOR COUNT most dies fail, same wafer cost the fixed cost is identical; the winning fraction is not

## 3. Why This Is the First Cost Model This Project Has Had to Build

Every earlier series priced reliability the way Step 9's military qualification measured it — pass or fail against a fixed specification, not as a continuous curve traded against a design choice. This step is the first place this project has had to say, explicitly, that a design decision as ordinary as adding one more gate to a function changes not just whether a part works but what it costs to make, in a way that compounds rather than adds. Step 11's choice to build every function from one NOR primitive matters here too: a smaller, simpler gate repeated many times keeps die area, and therefore cost per good die, closer to the left side of this curve than a dense, idiosyncratic layout ever could.

A catalog price, once this series starts publishing one, is not a markup over a component's value the way a resistor's price once was; it is a direct readout of this curve, and every customer who buys a Micrologic part is, whether they know it or not, paying for the exponential this step just made visible.

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