Run-to-Run Control (R2R)

R2R operates on a wafer-to-wafer or lot-to-lot basis, not in real-time. After a batch completes processing, post-process metrology data is fed into a control algorithm that calculates updated recipe parameters for the next run. This contrasts with real-time feedback control, which adjusts actuators mid-process. The discrete nature makes R2R ideal for processes where in-situ measurement is impossible or too slow, such as Chemical Mechanical Planarization (CMP) or plasma etching in semiconductor fabrication.

The EWMA filter is the foundational statistical engine for most R2R controllers. It smooths noisy metrology data and provides a stable estimate of process drift. The controller updates the model intercept for the next run using:

a_{t+1} = w * (y_t - b*u_t) + (1 - w) * a_t

• w (lambda): The EWMA weight (0 < w ≤ 1). A high weight responds quickly to shifts but amplifies noise. A low weight filters noise but responds slowly to real drift.
• a_t: The estimated process offset at run t.
• y_t: The measured output.
• b: The process gain (sensitivity of output to input).

This simple yet robust method handles the non-stationary drift common in manufacturing tools like deposition chambers and etch reactors.

R2R controllers rely on a linear or non-linear process model that maps recipe parameters to quality outputs. The granularity of this model defines controller capability:

• Single-Input Single-Output (SISO): Controls one quality metric with one recipe parameter. Simple but ignores cross-variable interactions.
• Multi-Input Multi-Output (MIMO): Controls multiple correlated quality metrics simultaneously using multiple recipe parameters. Requires a gain matrix to model interactions.
• Non-Linear Models: Employs Gaussian Process Regression or neural networks when the process response is highly non-linear, such as in advanced etch depth control.

Model fidelity directly determines how accurately the controller can predict the required recipe adjustment to hit the target.

In high-mix, low-volume fabs, a single tool processes many different products with distinct process requirements. Threaded R2R control maintains separate EWMA state estimates for each unique context thread—a combination of product, technology, and tool chamber. When a context switches, the controller retrieves the correct thread's state, applies the appropriate recipe, and updates only that thread's model after metrology. This prevents cross-contamination of drift estimates between dissimilar products and enables precise control in flexible manufacturing environments.

A critical challenge in R2R is the measurement lag—the delay between processing a lot and receiving its metrology results. Several lots may be processed before the first lot's quality data arrives. The controller must handle this by:

• Predicting the current process state using the EWMA model and all available pre-metrology data.
• Retroactively updating the state estimate when delayed measurements finally arrive.
• Using virtual metrology to provide immediate, albeit less accurate, quality predictions based on equipment sensor traces, bridging the gap until physical measurements are available.

This ensures the controller can continue making informed adjustments even when physical metrology is hours or days behind.

R2R controllers are not autonomous black boxes; they operate within a supervisory control framework. Individuals and Moving Range (I-MR) charts monitor the controller's performance and the process stability. Key safeguards include:

• Deadband: A threshold around the target. If the predicted deviation is within the deadband, no recipe change is made, preventing unnecessary adjustments due to measurement noise.
• Rate Limits: Maximum allowed recipe change per run to prevent aggressive corrections that could overshoot or destabilize the process.
• Out-of-Control Action Plans (OCAPs): If the I-MR chart detects a violation (e.g., a point outside control limits), the controller is suspended, and an alarm triggers human intervention for root cause analysis.

This layered approach ensures the controller optimizes the process safely without masking catastrophic tool failures.

A predictive technique that estimates wafer or product quality characteristics without physical measurement, using equipment sensor data and machine learning models. In R2R contexts, virtual metrology replaces or supplements post-process metrology to reduce cycle time and enable more frequent control updates.

• Predicts thickness, critical dimensions, or etch depth from process signatures
• Eliminates queue time at physical metrology stations
• Enables wafer-to-wafer control rather than lot-to-lot
• Relies on Gaussian Process Regression or neural networks for uncertainty quantification

The Exponentially Weighted Moving Average filter is the mathematical backbone of most R2R controllers. It applies a discount factor (λ) to historical data, giving greater weight to recent runs while smoothing out high-frequency noise. This prevents the controller from overreacting to measurement noise while still tracking genuine process drift.

• Typical λ values range from 0.1 to 0.4 for stable processes
• Balances responsiveness against noise rejection
• Forms the basis of the threaded EWMA for multi-product contexts
• Critical for handling autocorrelated process disturbances

A methodology for managing R2R in high-mix manufacturing environments where multiple products or recipes share the same tool. Threaded control maintains separate EWMA state estimates for each product context, preventing cross-contamination of control signals when switching between different device types or layers.

• Each product-recipe combination gets its own control thread
• Prevents incorrect offsets when product mix changes
• Requires robust context identification from the factory MES
• Enables single-tool flexibility without sacrificing control quality

The practice of measuring workpieces directly within the process chamber during or immediately after processing, without removing the part. In-situ metrology provides the fastest possible feedback for R2R loops, eliminating wafer handling delays and enabling true wafer-to-wafer control in semiconductor manufacturing.

• Uses integrated sensors like spectroscopic ellipsometry or scatterometry
• Eliminates ex-situ queue time and handling variability
• Enables immediate rework decisions before the wafer leaves the tool
• Critical for atomic-scale processes like ALD and ALE

An advanced control algorithm that uses a dynamic process model to predict future behavior and optimize control moves over a finite horizon. While traditional R2R adjusts recipe parameters run-to-run, MPC operates on a faster timescale, handling within-run dynamics and multivariable constraints simultaneously.

• Optimizes over a receding horizon of future runs
• Handles input constraints explicitly (e.g., maximum temperature ramp rate)
• Can incorporate economic objectives beyond quality targets
• Often combined with R2R in hierarchical Advanced Process Control architectures

A stored time-series record of all critical process parameters from a historically optimal production run. In R2R systems, the golden batch serves as the reference trajectory that the controller attempts to replicate, adjusting recipe parameters to compensate for drift away from this proven ideal state.

• Captures multivariate interactions between parameters
• Used as the baseline for drift detection algorithms
• Must be periodically revalidated as tool hardware ages
• Forms the foundation for trajectory-based control strategies