Semiconductor Manufacturing

Machine Learning and Uncertainty Quantification Semiconductor Manufacturing

The semiconductor industry faces a number of challenges that can be addressed using analytics and uncertainty quantification. Each generation of electronics and chip manufacturing demands greater levels of precision and consistency, effectively mandating an understanding of uncertainty’s effects on both the performance of the final product and the manufacturing process. Engineers must address unique challenges in maintaining this exacting quality, tracing complex root causes, and optimization and verification of manufacturing processes and equipment. As process monitoring techniques and data collection become more sophisticated and allow for increasing quantities of data to be captured, the need for a powerful, user-friendly, engineering analytics tool to analyze the data accurately and efficiently has never been greater.

SmartUQ provides cutting-edge technologies which can accelerate efforts to handle variation and uncertainty from all sources, help trace problems to their source, and improve process control through robust design. Understanding and reducing uncertainty can lead to improved product performance, faster design cycles, and lower costs.

Key Applications for Foundries

Some of smartUQ's key application areas at semiconductor foundaries include:

TCAD Acceleration & Process Window Exploration

At leading-edge nodes (e.g., N3, N2, and A16), Technology Computer-Aided Design (TCAD) simulations for nanosheet GAAFETs and backside power delivery networks (BSPDN) are computationally prohibitive.

• High-Accuracy Surrogate Modeling: SmartUQ builds Gaussian process-based emulators from limited high-fidelity TCAD runs, replacing multi-hour physical simulations with near-instantaneous predictions across multi-parameter spaces.
• Space-Filling DOEs: Advanced sampling (e.g., Latin Hypercube, Sobol sequences) maps multi-variable process windows (such as source/drain epitaxy, gate oxide thickness, and dopant implant profiles) using minimal simulation evaluations.

Statistical Yield Optimization & Variability Analysis

Managing process variability (stochastic effects, line-edge roughness, threshold voltage shifts) across 300mm wafers is vital to ramping up production yields.

• Global Sensitivity Analysis (GSA): Uses Sobol indices to isolate which tool tolerances or lithography/etch variations drive yield loss, enabling engineers to target specific steps for quality control.
• Uncertainty Propagation & RBDO: Propagates aleatory tool variations and epistemic model uncertainties to run Reliability-Based Design Optimization, establishing robust design-technology co-optimization (DTCO) rules.

Fab Tool Metrology & Digital Twins

• Multi-Fidelity Data Fusion: Fuses large quantities of coarse 2D multi-physics tool simulations with sparse, high-fidelity in-line metrology and physical wafer CD-SEM data to build accurate hybrid predictive models.
• Bayesian Statistical Calibration: Calibrates multiphysics models against fab sensor arrays, isolating unobservable process discrepancies to speed up recipe tuning.
• Digital Twins & FMU Export: Exports trained models as Functional Mock-up Units (FMUs) or Python API endpoints to serve as virtual sensors for fab yield monitoring and predictive equipment maintenance.

Manufacturer Quality Control and Yield Optimization Case Note

A semiconductor manufacturing company was having difficulty with quality control and production optimization in a multistage batch plating process. SmartUQ took the manufacturer’s existing data, built processing scripts, and conducted both traditional analysis and advanced statistical modeling. These analyses teased out previously unknown correlations between multiple reactant concentrations, consumable status, and deposition rate. By understanding these relationships, previously unexplained process deviations were made clear and could be controlled, and further experiments for process optimization were identified.

Many useful insights into the nature of the manufacturing process and the relationships between inputs like consumables and output quality can be derived with statistical analysis once data sets are being collected and automatically processed into a suitable form. This type of analysis includes conducting sensitivity and variance analysis on existing manufacturing data to identify important inputs for use in process optimization and quality control.

In addition, advanced statistical model generation uses both existing data and intentional Designs of Experiment to train predictive models to mimic the behavior of the manufacturing process. This allows rapid prediction of the results from changes to processing steps, easier identification of root causes in failure analysis, and rapid process optimization.