Micrologic 1960 New Yield Problem Whole Chip Fails

# Confront a New Yield Problem: One Bad Transistor Now Fails the Entire Chip

## 1. Why the Poisson Yield Model Now Has to Count a Whole Circuit's Area, Not One Die's

This step forces an honest accounting of what Step 6's functional test actually revealed across a batch of wafers: a single defect anywhere within a chip's area — one transistor's junction, one resistor's contact, one isolation island's spacing — fails the entire circuit, because the function Step 6 tests depends on every component cooperating, and a circuit with even one bad component produces a wrong truth table rather than a merely degraded one. This project's own yield model, established in the 1957 series at Step 9, already described how yield falls exponentially with the product of defect density and die area; this step does not need a new model, only a recognition of what "area" now has to mean. A single-transistor die's area was the area of one device. This circuit's effective area, for yield purposes, is the sum of every component's area on the chip, because a defect striking any one of them is fatal to all of them at once:

$$Y_{\text{circuit}} = e^{-D_0\,A_{\text{chip}}}, \qquad A_{\text{chip}} = \sum_i A_{\text{component}, i}$$

where $D_0$ is the same defect density this project has tracked since 1957, and $A_{\text{chip}}$ the sum of every transistor's, every resistor's, and every isolation island's area on one circuit. A logic gate with five components does not have roughly the yield of one component; it has, to a first approximation, the yield of a single die five times the area — and every additional component this series' layouts add from here forward multiplies that effective area again, which is precisely the constraint that will decide how complex a circuit this process can actually afford to build.

Component Count Multiplies Into the Area the Yield Model Sees circuit yield versus number of components, same exponential model as 1957 CIRCUIT YIELD VERSUS COMPONENT COUNT number of components on one chip → Ycircuit one transistor, 1959's yield five components, far lower yield Ycircuit = e−D₀A, Achip = ΣAi — the same exponential, now summed across every component no new model was needed; the area this model multiplies against simply grew

## 2. Real Diagram: Five Working Components, One Dead Chip

A wafer map from this batch shows something 1957's own wafer maps never had to show: dies where every individual component, tested on its own, would have passed, marked bad anyway, because one component among several failed and the circuit's function depended on all of them together.

Four Good Components, One Bad One, One Dead Chip a single defect anywhere in the layout fails the whole circuit T1, good R1, defective T2, good R2, good isolation, good entire chip fails, because every component is part of the same circuit this kind of failure did not exist when every die held only one device

## 3. Why 1959's Yield Was the Best This Series Will Ever See Again

The 1959 series' planar transistor enjoyed the full benefit of this project's reliability improvements with none of this series' yield penalty, because a single-device die's effective area was simply that device's own area, and the yield model this project established treated each die independently. This series inherits every reliability gain 1959 fought for, but trades part of it back by asking several devices to succeed together on one chip, where failure is no longer independent from device to device within that chip — it is correlated by the simple fact that they all have to work for any of them to matter. That correlation, not any new defect mechanism, is the entire content of this step's yield problem, and it is a cost this project's story will keep paying, in a worse form, every time a future circuit adds another component to its layout.

Step 7 does not discover a new kind of failure; it discovers that combining several already-reliable components does not multiply their reliability upward, it divides it down, by exactly the amount Poisson's own exponential already predicted.

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