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.