An Overview of the Application of Modern Statistical Techniques in Semiconductor Manufacturing

The semiconductor industry has long relied on Statistical Process Control (SPC) for yield and reliability management. In early technology nodes, classic univariate tools such as Shewhart charts, cumulative sums (CUSUM), exponentially weighted moving averages (EWMA), and the Cp/Cpk exponent could effectively monitor a finite set of key variables. However, sub-5nm and emerging 3 nm technologies have fundamentally changed the statistical environment. Advanced patterning, high-aspect-ratio etching, atomic layer deposition (ALD), chemical-mechanical polishing (CMP), and novel materials have drastically narrowed the process window. At these scales, nanometer-level deviations in critical dimensions (CD), overlay, or surface roughness can significantly impact yield. Simultaneously, modern wafer fabs generate massive amounts of high-frequency sensor data and high-dimensional metrology data. Traditional SPC assumptions—such as independence, normality, low dimensionality, and stationarity—often do not hold. Semiconductor data exhibits: (i) extremely high-dimensionality and strong intervariate correlations; (ii) a hierarchical structure encompassing fab → tooling → chamber → recipe → batch → wafer → field; and (iii) metrological delays and sampling limitations leading to incomplete and asynchronous observations. To address these challenges, this paper reviews advanced statistical methods applicable to wafer fabrication. These methods include multivariate statistical process control (MSPC) approaches such as Hotelling T2 statistics, PCA/PLS combining T2 and Q statistics, contribution diagnostics, time-series drift and change point detection, and Bayesian hierarchical modeling for uncertainty-aware monitoring in data-limited scenarios. Furthermore, we discuss how to integrate these methods with fault detection and classification (FDC), line-to-line monitoring (R2R), advanced process control (APC), and manufacturing execution systems (MES). This paper focuses on scalable, interpretable, and maintainable implementations that transform statistical analysis from a passive monitoring tool into an active component of data-driven fab control.