CMP removal-rate prediction moves to self-supervised pretraining: final-interval RMSE falls from 11.23 to 9.32 under temporal drift

CMP MRR virtual metrology can learn representations directly from raw multichannel sensor time series and then regress removal rate, instead of starting from hand-designed process features. Earlier approaches rely on simplified linear assumptions or handcrafted feature engineering, such as selecting 20 features from 68 engineered descriptors with an externally pretrained TabPFN model; such feature construction needs domain knowledge and may discard temporal information from the original signals. On the PHM 2016 CMP dataset, against a supervised baseline of process-level features plus tree models implemented following Li et al., GREP performs comparably across most labeled-data fractions and achieves lower error in selected limited-label settings.

Pretraining needs no MRR labels; the model learns the global statistical structure of the sensor sequences themselves. Self-supervised time-series representation learning has used contrastive learning, masked reconstruction, or regression targets built from predefined statistical, spectral and temporal features, the last requiring explicit feature selection and extraction. Each sensor channel is standardized and split into complete, first-half and second-half views, each projected onto 64 fixed Gaussian random vectors to form proxy targets, and the encoder plus auxiliary regression heads fit these targets by standardized mean squared error; pretraining uses only the designated training partition, followed by separate fine-tuning for low-speed and high-speed polishing modes.

When training data are restricted to the earliest chronological interval and testing moves to later intervals, GREP's prediction error stays below the baseline. Across four chronological intervals, GREP achieves lower RMSE than the baseline in all four. RMSE falls by 16.6% and 17.0% in the third and fourth intervals, and in the final interval GREP reaches 9.32 versus 11.23 for the baseline.

Evaluation is confined to the PHM 2016 CMP dataset, covering low-speed polishing in chambers 4–6 and high-speed polishing in chambers 1–3, with RMSE of average MRR as the metric. Noise experiments use controlled synthetic perturbations, namely Gaussian noise, random spikes and linear trends, rather than calibrated CMP sensor fault conditions, and models are evaluated on unmodified test data. Integration with advanced process control is outside the scope of this work.

Under noise neither method shows consistently lower noise sensitivity: at 30% labeled data the RMSE slopes per tenfold increase in noise power are 0.114 for GREP and 0.049 for the baseline, and at 40% they are 0.054 and 0.099. The reason for smaller prediction errors under temporal drift was not independently identified, and the physical causes of process drift remain undetermined.