Defect Density from Yield

Infer defect density from measured chip yield and die area using the Poisson yield model. Formula: D0 [cm^-2] = -ln(Y [%]/100) / A [cm²], where Y is the measured die yield and A is the die area. Inputs: 0 < Y < 100 %, A > 0 cm². Output: D0 ≥ 0 cm^-2. Assumes uniformly random defects, Poisson statistics, and that every defect kills a die.

Description

Defect Density from Yield is a focused tool for the following task. Infer defect density from measured chip yield and die area using the Poisson yield model. Formula: D0 [cm^-2] = -ln(Y [%]/100) / A [cm²], where Y is the measured die yield and A is the die area. Inputs: 0 < Y < 100 %, A > 0 cm². Output: D0 ≥ 0 cm^-2. Assumes uniformly random defects, Poisson statistics, and that every defect kills a die. It reports Defect density from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.

When to use Defect Density from Yield

Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.

Measured yield (%): Required number in %. Measured die yield. Must be greater than 0 and at most 100%; exactly 100% yields zero inferred defects.
Die area (cm^2): Required number in cm^2. Die area. Must be greater than 0 cm².

The cited overview of Semiconductor device supplies background for the terminology and domain context used by this tool.^[1]

How Defect Density from Yield works

Defect density (defects/cm^2): Returned number in defects/cm^2. Extracted defect density. At least 0 cm^-2.

Limitations and assumptions

Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
Measured yield must be at least 5e-324.
Measured yield must be no greater than 100.
Die area must be at least 5e-324.
Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Alternative or Complementary approaches

Compare the estimate with measured process data, current device documentation, and a higher-fidelity circuit, field, thermal, quantum, or TCAD model when the decision requires it.

References

Semiconductor device — Wikipedia contributors

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