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Real-to-Sim Calibration of Bosch Etching Simulators with Few-Shot XSEM Data and Hybrid Search

Xinyu Jia, Jainil Shah, Rahul Tripathi, Vijay Gupta, Zhihong Chen

arXiv:2610.31904v1cs.CEcs.LG

TL;DR

Bosch etching prediction is difficult to calibrate because real measurements are sparse and costly. This work uses few-shot XSEM data to identify recipe-specific ViennaPS parameters and combines guided search with surrogate screening. The framework predicts held-out outcomes, while prediction errors decrease as more real samples are used for calibration.

  • Problem

    Accurate Bosch etching prediction requires calibration against real measurements, which are sparse and costly, while existing real-to-sim methods rely on continuous observations unavailable in this setting.

    Source: §1 · p. 2, §2.2 · p. 6

  • Method

    The framework uses few-shot XSEM measurements to identify recipe-specific ViennaPS parameters, combining local exploration, LLM-guided candidates, and XGBoost screening with ViennaPS verification.

    Source: §1 · p. 3, §6 · p. 30

  • Results

    The framework predicts held-out etching outcomes, and test depth MAE, sidewall-angle MAE, and global error all decrease as the calibration sample count increases.

    Source: §5.6 · p. 27, §6 · p. 30

  • Takeaways & Limitations

    The calibrated ViennaPS simulator serves as a physics-based predictor for held-out conditions within the same recipe using sparse terminal XSEM measurements.

    Source: §2.2 · p. 6, §6 · p. 30

    The framework uses a relatively low-dimensional parameter space; higher-dimensional calibration for future high-fidelity simulators remains a challenge.

    Source: §6 · p. 30

Abstract

from arXiv · show

The Bosch process is widely used in MEMS and TSV fabrication, but accurate prediction of etching outcomes remains difficult without calibration against real measurements, which are sparse and costly to obtain. This work presents a few-shot real-to-sim calibration framework that decouples simulator parameters from direct process variables to infer a recipe-specific simulator parameter vector from sparse measurements, enabling reliable prediction of etch depth and sidewall angle under held-out process conditions. We first formulate Bosch profile prediction as a few-shot real-to-sim calibration problem, where a small set of real XSEM measurements is used to identify a recipe-specific ViennaPS parameter vector $z_r^*$ that minimizes the discrepancy between simulated and measured etch depth and sidewall angle. To search this parameter space efficiently, the framework combines local exploration, LLM-guided candidate generation, and XGBoost-based surrogate screening, while retaining ViennaPS simulation as the final verification step for each selected candidate. Experiments on two Bosch etching recipes show that the proposed framework accurately predicts held-out etching results, achieving normalized global errors of 0.340 and 0.249 for the 2 recipes respectively.

1 Introduction

Accurate Bosch etching prediction requires calibration against sparse, costly real measurements, but existing models face data, parameter, or physics-specification constraints. The paper calibrates recipe-specific ViennaPS parameters from few-shot XSEM data and combines guided search with surrogate screening.

1 Introduction

  • Sparse real measurements make calibration—not prediction alone—the central challenge for models intended to match experimental Bosch etching behavior.Physical experiments are expensive and time-consuming, and uncalibrated simulation accuracy may not translate to practical value.Source: §1 · p. 2
  • Few-shot real-to-sim calibration identifies recipe-specific ViennaPS parameters to align simulated and measured etch depth and sidewall angle.The calibrated simulator is then used to predict outcomes under held-out conditions within the same recipe.Source: §1 · pp. 2–3
  • The framework decouples simulator parameters from process variables and jointly fits a recipe-specific parameter vector across multiple fitting conditions.It retains ViennaPS as an executable physics-based simulator rather than replacing it with a black-box model.Source: §1 · p. 3
  • LLM-guided proposals use process knowledge and residuals, while XGBoost screens candidates as calibration history grows; ViennaPS verifies selected candidates.The surrogate filters candidates, but the final parameter update is determined by ViennaPS evaluation on the fitting data.Source: §1 · p. 3
  • The paper situates its contributions across related work, formulation, framework, experimental evaluation, and conclusion.The experiments assess both fitting quality and held-out prediction ability.Source: §1 · p. 3

2 Related Work

Etching prediction approaches rely on unknown simulator parameters, labeled real data, or sufficiently specified governing equations. Real-to-sim calibration uses real observations to adjust simulator parameters, but prior approaches generally rely on continuous observations unlike terminal XSEM measurements.

2.1 Etching Prediction and Simulation

  • Physics-based simulators, ML models, and PINNs respectively require calibration of unknown parameters, large real datasets, or sufficiently complete governing equations.The section compares these approaches for etching prediction and simulation.Source: §2.1 · p. 3, Table 1 · p. 4

Physics-based simulators

  • Physics-based simulators provide interpretable physical priors, but internal parameters are not directly available from recipes and require calibration against measurements.Examples include ViennaPS, commercial tools, and models of plasma etching processes.Source: Physics-based simulators · p. 4

ML models

  • Data-driven ML can predict process outcomes, but Bosch XSEM studies have costly, scarce labels and these models do not capture etch-profile physical structure.The cited work includes neural-network etch-depth prediction and domain adaptation for endpoint detection.Source: ML models · pp. 4–5

PINNs

  • PINNs embed physical constraints to improve data efficiency, but existing approaches rely on prescribed equations or simulation data rather than calibrating ViennaPS to real measurements.The full plasma chemistry and effective parameters can be difficult to specify for a particular tool and recipe.Source: PINNs · p. 5

2.2 Real-to-Sim Calibration

  • Robotics real-to-sim methods use real observations to adjust simulators, but their reliance on continuous observations does not fit Bosch etching's sparse terminal XSEM data.The etching samples provide measurements only after processing, so the section motivates calibration designed for feature-level simulation.Source: §2.2 · pp. 5–6

3 Background and Problem Formulation

The paper describes Bosch etching as a cyclic process and formulates calibration as identifying a shared ViennaPS parameter vector for each recipe. Few-shot measurements guide that vector, which is then used to predict etch depth and sidewall angle for held-out conditions in the same recipe.

3.1 Bosch Etching Process

  • Bosch etching alternates C4F8-based deposition and passivation with SF6-based etching stages that clear the trench bottom and extend the trench.Repeated cycling protects sidewalls while enabling deep anisotropic etching and producing a scalloped profile.Source: §3.1 · p. 6

3.2 Real-to-Sim Calibration Formulation

  • A process input comprises cycle count, opening size, and the recipe's process-parameter vector.These are denoted c, o, and pr, respectively.Source: §3.2 · p. 6
  • ViennaPS maps a process input and simulator parameter vector to a simulated profile, from which etch depth and sidewall angle are extracted.The real profile is characterized by corresponding measured depth and angle.Source: §3.2 · pp. 6–7
  • Real observations are divided into non-overlapping fitting and test sets, with the fitting set used for parameter identification and the test set reserved for final evaluation.The supplied passages specify the roles of the sets but not their sizes.Source: §3.2 · p. 7
  • Calibration identifies a recipe-specific simulator parameter vector that aligns ViennaPS outcomes with real Bosch measurements across considered process conditions.The same parameter vector is shared across fitting conditions within a recipe.Source: §3.2 · p. 7
  • After calibration, the recipe-specific simulator predicts etch depth and sidewall angle for new process conditions within that recipe.The calibrated simulator serves as a physics-based predictive model under held-out conditions.Source: §3.2 · pp. 6, 8

4 Methods

The methods calibrate a shared, recipe-specific ViennaPS parameter vector against sparse measurements across fitting conditions, then use the calibrated simulator to predict etch depth and sidewall angle. A hybrid search proposes and screens candidates, while ViennaPS determines the final parameter updates.

4.1 Real-to-Sim Calibration Framework

  • A shared recipe-specific ViennaPS parameter vector is refined across fitting conditions using local exploration, LLM guidance, and surrogate screening; ViennaPS evaluations determine each update.The surrogate screens candidates, but the selected update is based on the lowest global error from ViennaPS evaluation.Source: §4.1 · pp. 8–10

4.2 ViennaPS and Parameter Space

  • Calibration varies eight ion- and neutral-flux parameters across ignition, deposition, and two etching stages, constraining the search to factors selected to shape Bosch profiles.Other ViennaPS settings are not covered by this section's parameter-space description.Source: §4.2 · p. 10

4.3 Etch Profile Measurement

  • Etch depth excludes the ignition profile and measures vertical distance from the post-ignition reference to the trench bottom, converted to micrometers when opening size is known.Sidewall angle is fitted from the widest points of the first and last scallops on each side; positive angles indicate inward taper, and the reported angle averages both sides.Source: §4.3 · p. 11
  • Profiles with depth below 1 µm or sidewall angle below 70° are invalid, preventing failed simulations from appearing favorable through misleading numerical error.The validity check is applied during candidate evaluation.Source: §4.3 · p. 11

4.4 LLM-Based Parameter Guidance

  • The LLM proposes physically informed parameter updates from global error, validity information, and Bosch process knowledge, helping guide search before enough records support a reliable surrogate.Its structured prompt includes calibration state and process knowledge, and requests numerical updates with brief physical explanations.Source: §4.4 · pp. 12–13

4.5 XGBoost-Based Parameter Screening

  • An XGBoost surrogate learns ViennaPS depth, angle, and validity responses from accumulated simulations, screening a larger candidate pool before selected candidates undergo ViennaPS evaluation.Its historical records include process conditions, parameter vectors, simulated measurements, and validity labels.Source: §4.5 · pp. 13–14

5 Experiments

The experiments use measured XSEM profiles from two Bosch recipes to calibrate ViennaPS and assess prediction on separate held-out samples. They evaluate profile agreement and search efficiency using depth, sidewall-angle, and combined error measures.

Real Experiment Data

  • Each recipe’s real samples vary in cycle number and opening size, and fitting and test sets are non-overlapping.Calibration is performed independently for each recipe, with test samples excluded from parameter identification.Source: Real Experiment Data · p. 14, Table 2 · p. 15
  • XSEM measurements provide ground-truth etch depth and sidewall angle, measured from the profile while excluding the initial ignition opening.The sidewall angle averages the fitted directions of the left and right walls.Source: Real Experiment Data · pp. 14–15, Figure 3 · p. 16

ViennaPS Setup

  • ViennaPS simulates an ignition stage followed by repeated deposition, Etch A, and Etch B cycles; calibration updates eight flux-related parameters while holding other settings fixed.Recipe 1 illustrates the setup, and the procedure is independently applied to Recipe 2.Source: ViennaPS Setup · p. 16

Evaluation Metrics

  • Evaluation covers fitting and held-out prediction accuracy as well as search efficiency, including depth MAE, sidewall-angle MAE, relative depth error, and normalized global error.The global error weights relative depth error and sidewall-angle error normalized by tolerance equally; the search comparison tracks the best calibration error found over iterations.Source: Evaluation Metrics · pp. 16–17

5.2 Calibration Accuracy

The calibrated recipe-specific ViennaPS parameters predict held-out etching outcomes and improve agreement with fitting measurements. The reported errors quantify both prediction gains and calibration quality across the two recipes.

5.2 Calibration Accuracy

  • Recipe 1 calibration reduced normalized global error from 5.585 to 0.400, while Recipe 2 reduced it from 5.163 to 0.237.For Recipe 1, depth MAE decreased from 18.063 µm to 0.410 µm and sidewall-angle MAE from 5.367° to 1.207°.Source: §5.2 · p. 18, Table 3 · p. 19
  • Across shallow, intermediate, and deep fitting conditions, the same Recipe 1 parameter vector produced profiles well aligned with real XSEM measurements despite differing cycle numbers and opening sizes.Figure 4 pairs the real profile with its calibrated ViennaPS simulation.Source: §5.2 · p. 19, Figure 4 · p. 19
  • For both recipes and both measured outcomes, calibrated results were closer to ideal y = x agreement than default ViennaPS results across the fitting sets.The comparison includes etch depth and sidewall angle for each recipe.Source: §5.2 · p. 19, Figure 5 · p. 20

5.3 Prediction Accuracy

  • 0.340 and 0.249 normalized global errors were achieved on held-out test sets for Recipes 1 and 2, respectively, versus 5.798 and 5.198 with default parameters.For Recipe 1, depth MAE fell from 25.682 µm to 0.782 µm, relative depth error from 85.443% to 2.546%, and sidewall-angle MAE from 6.103° to 0.852°.Source: Table 4 · p. 21, §5.3 · p. 21
  • Residuals remained small across cycle number and opening size, while remaining local deviations may reflect XSEM measurement noise and simulator model-form limitations.Representative Recipe 1 test profiles also reproduced the main trench geometry without sample-specific parameter tuning.Source: §5.3 · p. 21

5.4 Ablation Study

The ablation compares candidate-generation strategies under a shared calibration budget and finds that combining LLM guidance, local exploration, and surrogate screening gives the fastest early error reduction and lowest final error. The components contribute at different stages: LLM guidance helps early, while XGBoost screening becomes useful after sufficient simulation history accumulates.

5.4 Ablation Study

  • The ablation tests Recipe 1 under a 10-iteration budget, with variants sharing the initial parameter vector, bounds, fitting set, seed, and evaluations per iteration.The comparison includes random-only, Random+LLM, Random+XGBoost, and the full method.Source: §5.4 · p. 22
  • Progressive evaluation screens candidates on shorter-cycle samples before full-set validation, reducing early simulation cost.Candidates advance from 10-cycle samples through 20- and 30-cycle samples when they meet the stated depth-error criterion; from iteration 8, all methods use the complete fitting set.Source: §5.4 · pp. 24–25
  • The full method achieves final error 0.400, versus 1.858 for random-only, 0.772 with LLM guidance, and 0.974 with XGBoost screening.The table compares candidate-generation strategies; the full method has the lowest final error.Source: §5.4 · pp. 22, 25, 26, Table 6 · p. 25
  • XGBoost screening activates after 36 sample-level evaluations, so its first three iterations follow the random-only trajectory.The surrogate is filled by local exploration during warm-up and becomes useful after enough evaluated candidates accumulate.Source: §5.4 · p. 25
  • The full method reduces best global error fastest, while Random+LLM also converges faster than random-only.The comparison uses the best validated calibration performance at each iteration; faster reduction indicates reaching a low-error region in fewer iterations.Source: §5.4 · p. 25, Figure 9 · p. 26

5.5 LLM Robustness Analysis

Across the robustness and sensitivity analyses, overall calibration performance remains similar across tested LLM backends, while fitting-data and batch-size choices affect prediction or search error. About 10 fitting samples mark a relatively stable regime, and moderate batch sizes preserve useful feedback updates.

5.5 LLM Robustness Analysis

  • Across tested LLM backends, held-out overall errors are similar, although llama4:latest has the lowest depth MAE (0.302µm) and qwen3.8:27b the lowest angle MAE (0.852°).The two backends show different depth-versus-angle error trade-offs; overall performance does not strongly depend on a specific backend.Source: Table 7 · p. 27, §5.5 · p. 27

5.6 Fitting Data Size Sensitivity

  • As Nfit increases, held-out depth MAE, sidewall-angle MAE, and global error decrease; gains become marginal beyond Nfit = 10.The analysis uses Recipe 1, three independent data splits, and a fixed held-out test set within each split; the reported regime is relatively stable beyond about 10 fitting samples.Source: §5.6 · pp. 27–28, Figure 10 · p. 28, Table 8 · p. 28

5.7 Batch Size Sensitivity

  • The batch-size comparison uses Recipe 1 and a fixed 60-candidate budget, with the best global error defined as the lowest fitting error found within that budget.The tested batch sizes are 4, 5, 6, 10, and 12.Source: §5.7 · pp. 28–29
  • Under 60 candidate evaluations, best global errors are 0.420, 0.390, and 0.408 for batch sizes 4, 5, and 6, versus 0.837 and 0.922 for sizes 10 and 12.The authors attribute the larger-batch results likely to fewer feedback updates under the same budget; batch size 6 allows 10 updates, compared with 6 for size 10.Source: §5.7 · pp. 28–29, Figure 11 · p. 29

6 Conclusion and Future Work

The paper proposes few-shot calibration of ViennaPS for Bosch etching, using sparse real XSEM measurements to align simulated depth and sidewall angle with measurements. The authors report reduced fitting error and generalization to test samples, while noting that substantially higher-dimensional simulators pose a future calibration challenge.

6 Conclusion and Future Work

  • The framework identifies a recipe-specific ViennaPS parameter vector from a small number of real XSEM measurements across cycle numbers and opening sizes within each recipe.It combines local exploration, LLM-guided candidate generation, and XGBoost surrogate screening, with ViennaPS simulation as the final verification step.Source: §6 · p. 30
  • Experiments show that calibrated parameters substantially reduce fitting error and generalize to test samples across Bosch recipe settings using few real XSEM measurements.The framework is intended for sparse terminal XSEM measurements and does not require fully specified Bosch plasma-chemistry equations or continuous observations such as trajectories or image sequences.Source: §6 · p. 30
  • The current framework operates in a relatively low-dimensional parameter space; high-fidelity simulators may introduce many more parameters and make calibration challenging.The authors identify scalable methods for limited-XSEM settings as future work.Source: §6 · p. 30

Appendix A Real Experiment Recipe and Samples

The appendix describes the real Bosch etching recipes and the 20-sample Recipe 1 dataset, including its fitting and held-out test assignments.

Appendix A Real Experiment Recipe and Samples

  • Each Bosch recipe fixes its process parameters, while cycle number, GDS design, and opening size vary across samples.Source: Appendix A · p. 30
  • The Recipe 1 sample list records cycle number, opening size, measured etch depth, measured sidewall angle, and data split for 20 real samples.Source: Appendix A · p. 30
  • Of the 20 Recipe 1 samples, 12 are assigned to fitting for parameter identification and 8 are held out for final evaluation.Source: Appendix A · p. 30

Appendix B ViennaPS Recipe

The ViennaPS recipe treats cycle number and opening size as sample-specific inputs, while calibration updates only eight flux-related parameters. Geometry, numerical settings, process template, sticking probabilities, and effective reaction coefficients remain fixed.

Appendix B ViennaPS Recipe

  • Calibration updates only the eight flux-related parameters; cycle number and opening size are set for each measured process condition.All other ViennaPS settings remain fixed across candidate parameter vectors.Source: Appendix B · p. 30
  • Geometry and numerical settings, process template, sticking probabilities, and effective reaction coefficients are fixed across simulations.The process template applies ignition once at the start, then repeats deposition, Etch A, and Etch B according to the sample-specific cycle number.Source: Appendix B · p. 30, Table B3 · p. 32, Table B4 · p. 32
  • The real samples are organized by Bosch process recipe, and Table B7 lists the flux-related parameters’ initial ViennaPS configuration.The supplied table captions do not provide the recipe or parameter values.Source: Table A1 · p. 31, Table A2 · p. 31

Appendix C LLM-Based Parameter Guidance Prompt

The prompt guides an LLM to propose small, physically reasoned updates to a restricted set of flux parameters. It supplies simulated and measured depth and sidewall angle, residuals, and calibration status for candidate generation.

Candidate constraints

  • The LLM may update only eight named Flux_* parameters and must leave alpha*, beta*, sticking*, ionSourceExponent, step times, geometry, numCycles, and etchStep unchanged.Each proposal must include a short physical reason for the change.Source: Appendix C · p. 33

Residual interpretation

  • A positive depth residual indicates simulated etching is too shallow, while a negative residual indicates it is too deep.The prompt recommends increasing etching fluxes or reducing protection for positive residuals, and the reverse for negative residuals.Source: Appendix C · p. 33

Physical guidance

  • Ion fluxes mainly strengthen directional ion-assisted etching, while neutral fluxes mainly strengthen chemical or more isotropic etching.Ignition fluxes mainly affect initial opening and early profile; deposition fluxes mainly affect polymer deposition and sidewall protection.Source: Appendix C · p. 34

Candidate output

  • The LLM returns one to three strict-JSON candidate updates, each changing only a small number of fluxes with numeric values, change magnitudes, and a reason.The candidates are intended for the next calibration iteration.Source: Appendix C · pp. 34–35

Prompt inputs

  • The prompt supplies current flux values, simulated and real depth and sidewall angle, their residuals, and global calibration information.The stated global information includes global error, validity label, and worst-sample residual.Source: Appendix C · pp. 33–34

Appendix D Extended 20-Iteration Ablation Study

In the 20-iteration ablation, the hybrid search reaches a high-quality calibration result earlier than the alternatives, while random-only remains weakest. The extended study tests whether conclusions from the 10-iteration setting hold over a longer search horizon.

Appendix D Extended 20-Iteration Ablation Study

  • The extended ablation applies the same experimental setting to all variants while increasing the search horizon from 10 to 20 iterations.The extension examines sensitivity to the short search horizon; each calibration iteration requires multiple ViennaPS evaluations.Source: Appendix D · p. 35
  • Random only remains the weakest variant; Random+LLM and Random+XGBoost improve with 20 iterations but need more simulation budget to approach the hybrid method’s earlier error level.The results support the hybrid search’s search efficiency and ability to produce a high-quality calibration result.Source: Appendix D · pp. 35–36
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