Cpk

Cpk (Process Capability Index) is the statistical measure of how well a process meets specification limits, adjusted for process centering — quantifying whether a manufacturing process can consistently produce output within required tolerances, essential for semiconductor quality management and customer qualification.

What Is Cpk?

• Formula: Cpk = min((USL − μ) / 3σ, (μ − LSL) / 3σ).
• USL/LSL: Upper and Lower Specification Limits.
• μ: Process mean. σ: Process standard deviation.
• Interpretation: Higher Cpk = better process capability and centering.

Cpk vs Cp

• Cp: Measures process spread only (Cp = (USL − LSL) / 6σ).
• Cpk: Measures spread AND centering (always ≤ Cp).
• Example: Cp = 2.0 but Cpk = 0.5 means process is capable but off-center.
• When Cp = Cpk: Process is perfectly centered between specs.

Industry Standards

• Cpk < 1.0: Not capable — producing significant defects.
• Cpk = 1.0: Marginal — 2,700 DPPM (0.27% defect rate).
• Cpk = 1.33: Capable — 63 DPPM, minimum for most semiconductor processes.
• Cpk = 1.67: Good — 0.6 DPPM, typical automotive requirement.
• Cpk = 2.0: Excellent — 3.4 DPPM, Six Sigma level.

Semiconductor Applications

• Critical Dimensions (CD): Gate length, fin width Cpk requirements.
• Film Thickness: Oxide, nitride, metal layer uniformity.
• Overlay: Lithographic alignment accuracy between layers.
• Electrical Parameters: Vt, Idsat, leakage current distributions.
• Reliability: TDDB, electromigration lifetime distributions.

Calculating Cpk from Data

• Collect 30+ measurements from stable (in-control) process.
• Verify normality (Shapiro-Wilk test, Q-Q plot).
• Calculate within-subgroup σ (not overall σ which gives Ppk).
• Apply formula: Cpk = min(Cpu, Cpl).
• Report with confidence interval for sample size.

Cpk is the universal language of process quality — a single number that tells customers, engineers, and management whether a process can reliably meet specifications.