Run-to-Run Control

R2R control operates on a discrete batch basis rather than continuous real-time adjustment. After a wafer or batch completes processing, post-process metrology measures critical quality characteristics. The R2R controller then calculates an updated recipe parameter for the next batch to minimize the deviation from target.

• Sampling interval: Between runs, not within a run
• Typical applications: Chemical Mechanical Planarization (CMP), etch depth control, deposition thickness
• Key advantage: Compensates for slow tool drift that real-time PID loops cannot address

The Exponentially Weighted Moving Average (EWMA) filter is the foundational algorithm in most R2R controllers. It applies a weighting factor (λ) between 0 and 1 to blend the current measurement with the historical estimate, creating a smoothed disturbance model.

• Formula: δ̂ₖ₊₁ = λ · δₖ + (1 - λ) · δ̂ₖ
• λ close to 0: Heavy filtering, slow response to real shifts
• λ close to 1: Light filtering, rapid response but noise-sensitive
• Tuning trade-off: Balance between noise rejection and responsiveness to genuine tool drift

Modern R2R systems maintain separate control threads for distinct process contexts. A single tool may run multiple products, each requiring independent disturbance tracking because different patterns and materials cause unique wear signatures.

• Context identifiers: Product ID, tool chamber, recipe name, reticle
• Thread management: Each context maintains its own EWMA state
• Cold start problem: New contexts lack historical data and require pilot wafers or global model initialization
• Context switching: Controller must seamlessly switch disturbance estimates when product mix changes

R2R controllers often employ gradual mode adjustments where recipe changes are intentionally dampened to prevent overcorrection. A deadband around the target prevents unnecessary adjustments when the process is within acceptable limits.

• Gain parameter (K): Scales the correction magnitude (typically 0.3-0.7)
• Deadband threshold: No adjustment if |error| < threshold
• Clamping limits: Maximum allowable recipe change per run to prevent process excursions
• Purpose: Prevents controller-induced variability from chasing measurement noise

When physical metrology is slow or expensive, R2R controllers integrate virtual metrology (VM) models that predict wafer quality from upstream sensor data. This enables wafer-to-wafer control without waiting for actual measurements.

• VM model inputs: Chamber pressure, RF power, gas flows, temperature traces
• Prediction target: Film thickness, etch depth, uniformity
• Confidence metrics: VM predictions include uncertainty estimates; low-confidence predictions may trigger a physical measurement
• Benefit: Reduces metrology burden while maintaining tighter control

R2R controllers are tightly integrated with Fault Detection and Classification (FDC) systems. If FDC flags a tool fault or an out-of-spec measurement, the R2R controller can suspend automatic updates to prevent corrupting the disturbance model with faulty data.

• Measurement validation: Outlier rejection before EWMA update
• Tool health gating: Recipe adjustments paused during maintenance recovery
• Alarm escalation: Persistent large corrections trigger engineering review
• Traceability: Every recipe change is logged with the metrology data and FDC status that triggered it

An advanced control algorithm that uses a dynamic process model to predict future outputs and compute an optimal sequence of control moves over a finite receding horizon. Unlike Run-to-Run control's batch-to-batch adjustments, MPC operates continuously within a single process run.

• Key Distinction: Solves a constrained optimization problem at each time step
• Application: Ideal for multi-variable processes with complex interactions
• Synergy: Often used for inner-loop control while Run-to-Run handles outer-loop recipe adjustments

A soft-sensing technique that predicts the quality characteristics of a manufactured wafer or product using upstream equipment sensor data without a physical post-process measurement. This provides the critical quality feedback signal that Run-to-Run controllers require, but with zero metrology delay.

• Benefit: Eliminates the time lag waiting for physical inspection results
• Enabler: Allows true wafer-to-wafer control rather than lot-to-lot
• Technology: Typically built on Gaussian Process Regression or deep neural networks

The most widely implemented Run-to-Run control algorithm in semiconductor manufacturing. The EWMA controller applies a discount factor (λ) to historical process disturbances, giving exponentially less weight to older data when calculating the recipe adjustment for the next batch.

• Tuning Parameter: λ balances responsiveness against noise sensitivity
• Stability: Guaranteed to converge for processes with a linear input-output relationship
• Limitation: Assumes a stationary disturbance model; struggles with abrupt shifts

A quality control methodology that uses statistical methods to monitor a process and distinguish between common cause variation (inherent noise) and special cause variation (assignable events). Run-to-Run control complements SPC by automatically correcting for common cause drift.

• Integration: SPC charts trigger alarms; Run-to-Run controllers execute corrections
• Tool: Control charts with Western Electric rules detect process shifts
• Philosophy: SPC identifies when intervention is needed; Run-to-Run automates the response

A non-parametric Bayesian inference method that models a distribution over possible functions to provide both predictions and calibrated uncertainty estimates for process variables. GPR is increasingly replacing linear models in advanced Run-to-Run controllers.

• Advantage: Naturally quantifies prediction confidence for risk-aware control
• Use Case: Modeling non-linear etch rates where traditional linear assumptions fail
• Output: Provides a mean prediction and a variance envelope for the next run's quality

A control technique that measures a measurable disturbance directly and preemptively adjusts the manipulated variable to cancel its effect before it impacts the process output. In Run-to-Run frameworks, feedforward handles incoming material variation while feedback corrects tool drift.

• Example: Adjusting etch time based on incoming film thickness measurements
• Combination: Feedforward + Run-to-Run feedback = complete disturbance rejection
• Requirement: Requires a reliable upstream metrology or virtual metrology signal