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

cs.CEOct 22, 2026

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

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

Organizations: Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana, USA · Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, USA · Micron Semiconductor Asia Operations Pte. Ltd., 1 North Coast Drive, Singapore, 757432, Singapore

Abstract

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.

Figures & tables

Approach	Modeling basis and data requirement	Limitation for Bosch etching
Physics-based simulator Reiter and Filipovic (2025) ; Bobinac et al. (2023) ; Rodrigues et al. (2023) ; Synopsys, Inc. (2023) ; Silvaco, Inc. (2023)	Uses explicit physical models of particle transport, surface reactions, and profile evolution.Calibration against measured data is required to determine internal simulator parameters.	The internal parameters cannot be directly obtained from experimental recipes and may vary across process conditions.
ML models Kang et al. (2026) ; Kim et al. (2025) ; Breidung et al. (2025)	Learn mappings from process inputs or sensor measurements to process outcomes, typically using large labeled datasets or extensive sensor data.	Real XSEM measurements are scarce, while purely data-driven models provide limited physical interpretability under small-data settings.
PINNs Dighamber (2024) ; Zhong et al. (2022) ; Leng et al. (2025)	Combine training data with governing equations by embedding physical constraints into the learning objective.	Existing methods rely on prescribed governing equations or simulation data, but do not calibrate simulator parameters against real measurements.

Table 1: Comparison of existing approaches for etching prediction and simulation.

Figure 1: Parameter Identification Framework

Figure 2: Etch Profile Measurement.

Cycle	No. of samples	GDS design	Opening sizes ( $\mu$ m)	Depth range ( $\mu$ m)	Angle range ( ∘ )
Recipe 1
10	3	6,10,10	6.20, 10.60, 11.00	7.05–7.84	88.74–90.91
20	3	7,8,9	7.589, 8.344, 9.263	14.152–14.790	89.73–91.49
30	4	7,8,9,9	7.15, 8.12, 9.10, 9.858	19.49–20.475	89.94–90.31
40	4	7,8,9,10	7.552, 8.256, 9.116, 10.193	23.95–25.732	90.54–91.64
70	6	6,7,8,9,10,15	6.95, 7.64, 8.72, 9.80, 10.81, 15.82	38.86–46.57	89.60–90.36

Table 2: Real Bosch etching samples used in this work. For each recipe, the cycle number, GDS design, and opening size vary across samples.

Panel of Figure 3 — Figure 3: Representative real XSEM profiles used in this work. The top horizontal line indicates the opening size, the vertical line indicates the etch depth, and the red dashed sidewall lines are fitted by connecting the first and last scallop positions on each side, from which the sidewall angle is measured.

Recipe	Parameter vector	MAE d ( $\mu$ m)	RE d (%)	MAE α ( ∘ )	$\epsilon$	Improvement d (%)	Improvement α (%)
Recipe 1	Default $z_{1}^{(0)}$	18.063	84.858	5.367	5.585	–	–
	Calibrated $z_{1}^{*}$	0.410	1.970	1.207	0.400	97.729	77.512
Recipe 2	Default $z_{2}^{(0)}$	11.308	81.93	4.265	5.163	–	–
	Calibrated $z_{2}^{*}$	0.079	0.59	0.830	0.237	99.301	80.54

Table 3: Calibration accuracy on two recipes. The improvement is computed relative to the default ViennaPS parameter vector

z^{(0)}

for each recipe.

Panel of Figure 4 — Figure 4: Three representative fitted profiles for Recipe 1. Covering shallow, intermediate, and deep etching. Each paired comparison shows the real XSEM profile on the left and the corresponding calibrated ViennaPS simulation on the right. The examples correspond to different cycle numbers and opening sizes, demonstrating that the same calibrated parameter vector $z_{1}^{*}$ can reproduce real profiles across multiple fitting conditions.

Figure 5: Real measurements versus simulated measurements on the fitting sets of Recipe 1 and Recipe 2. The dashed line denotes the ideal $y=x$ agreement. Gray circles indicate the default ViennaPS results, and blue circles indicate the calibrated ViennaPS results. (a) Etch depth for Recipe 1. (b) Sidewall angle for Recipe 1. (c) Etch depth for Recipe 2. (d) Sidewall angle for Recipe 2.

Recipe	Parameter vector	$\mathrm{MAE}_{d}$	$\mathrm{RE}_{d}$	$\mathrm{MAE}_{\alpha}$	$\epsilon(z;D_{\mathrm{test}})$
		$(\mu\mathrm{m})$	$(\%)$	$(^{\circ})$
Recipe 1	Default $z_{1}^{(0)}$	25.682	85.443	6.103	5.798
Recipe 1	Calibrated $z_{1}^{*}$	0.782	2.546	0.852	0.340
Recipe 2	Default $z_{2}^{(0)}$	14.345	81.71	4.451	5.198
Recipe 2	Calibrated $z_{2}^{*}$	0.146	0.82	0.831	0.249

Table 4: Prediction accuracy on the held-out test sets for Recipe 1 and Recipe 2.

Panel of Figure 6 — Figure 6: Three representative prediction results on $D^{(1)}_{\mathrm{test}}$ for Recipe 1. Covering shallow, intermediate, and deep etching. Each paired comparison shows the real XSEM profile on the left and the corresponding calibrated ViennaPS prediction on the right. The examples correspond to different cycle numbers and opening sizes in $D^{(1)}_{\mathrm{test}}$ , showing that the same calibrated parameter vector $z_{1}^{*}$ can approximate the main real-profile geometry on test samples.

Figure 7: Real measurements versus predicted measurements on the held-out test sets of Recipe 1 and Recipe 2. The dashed line denotes the ideal $y=x$ agreement. Gray circles indicate the default ViennaPS results, and blue circles indicate the calibrated ViennaPS results. (a) Etch depth for Recipe 1. (b) Sidewall angle for Recipe 1. (c) Etch depth for Recipe 2. (d) Sidewall angle for Recipe 2.

Figure 8: Residual analysis of prediction results on held-out test set for Recipe 1 (blue circles) and Recipe 2 (orange squares). Each marker denotes one test sample ( $N=8$ per recipe), and the residual is computed as the value predicted with the calibrated parameters $z_{r}^{*}$ minus the real XSEM measurement. The residual is computed as predicted value minus real measurement. The dashed horizontal line denotes zero residual.

Variant	Candidate composition per iteration	Batch size $B$
Random only	Random $\times 6$	6
Random + LLM	LLM $\times 3$ + Random $\times 3$	6
Random + XGBoost	Random $\times 3$ + XGBoost $\times 3$	6
Ours	LLM $\times 3$ + Random $\times 1$ + XGBoost $\times 2$	6

Table 5: Candidate composition for each ablation variant.

Figure 9: Ablation study on candidate generation strategies using Recipe 1, with qwen3.8 used as the LLM for candidate generation.

Method	Local	LLM	XGBoost	$\epsilon_{\mathrm{final}}(D^{(1)}_{\mathrm{fit}})$
Random only	✓	–	–	1.858
Random + LLM	✓	✓	–	0.772
Random + XGBoost	✓	–	✓	0.974
Ours	✓	✓	✓	0.400

Table 6: Ablation study on candidate generation strategies.

LLM Backend	$\mathrm{MAE}_{d}$ ( $\mu$ m)	$\mathrm{MAE}_{a}$ ( ∘ )	$\epsilon(z^{*};D_{\mathrm{test}})$
gpt-oss:120b	0.681	0.915	0.344
qwen3.8:27b	0.782	0.852	0.340
gemma4:26b-a4b	0.754	1.058	0.401
llama4:latest	0.302	1.144	0.334

Table 7: Robustness analysis across different LLM backends.

Figure 10: Fitting data size sensitivity of the calibration framework. For each $N_{\mathrm{fit}}$ , the complete calibration framework is independently run over three data splits. Within each split, the same held-out test set is used for all $N_{\mathrm{fit}}$ settings. Markers denote the mean test performance over the three runs, and error bars indicate one standard deviation across runs.

$N_{\mathrm{fit}}$	Test $\mathrm{MAE}_{d}$ ( $\mu\mathrm{m}$ )	Test $\mathrm{MAE}_{\alpha}$ ( ∘ )	$\epsilon(z_{N}^{*};D_{\mathrm{test}})$
6	4.348	3.096	1.461
8	1.412	1.698	0.649
10	0.586	1.127	0.375
12	0.510	1.038	0.341
14	0.511	0.943	0.317

Table 8: Fitting data size sensitivity averaged over three independent runs.

Figure 11: Batch size sensitivity under a fixed simulation budget of $60$ candidate evaluations. Bars denote the mean final best global error over three independent runs, and error bars indicate one standard deviation.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Recipe 1
Step	C 4 F 8 (sccm)	SF 6 (sccm)	Ar (sccm)	Pressure (mTorr)	Time (s)	ICP (W)	Bias (W)
Ignition	–	75	30	20	10	1500	100
Deposition	150	–	30	25	2	2000	5
Etch A	–	150	30	60	2	2000	50
Etch B	–	150	30	60	2	2500	5
Recipe 2

Appendix

Table 9: Bosch process recipes used for the real etching samples.

Cycle number	Opening size ( $\mu$ m)	Real depth ( $\mu$ m)	Real angle ( ∘ )	Split
10	6.200	7.050	88.82	$D_{\text{fit}}$
10	10.600	7.780	88.74	$D_{\text{test}}$
10	11.000	7.840	90.91	$D_{\text{fit}}$
20	7.589	14.152	91.49	$D_{\text{fit}}$
20	8.344	14.770	89.73	$D_{\text{fit}}$
20	9.263	14.790	91.33	$D_{\text{test}}$

Appendix

Table 10: Full list of real Bosch etching samples for Recipe 1.

Parameter	Value	Unit / note
Grid spacing, gridDelta	0.025	$\mu\mathrm{m}$
Mask height, maskHeight	5.6	$\mu\mathrm{m}$
Taper angle, taperAngle	0.0	degree
Ion source exponent, ionSourceExponent	6000	–
Etch-step sequence, etchStep	both	Etch A followed by Etch B

Appendix

Table 11: Fixed geometry and numerical settings used in ViennaPS.

Step	Main gas	Pressure (R1)	Pressure (R2)	Time	Role
Ignition	SF 6 / Ar	20 mTorr	30 mTorr	10 s	Initial trench opening
Deposition	C 4 F 8 / Ar	25 mTorr	30 mTorr	2 s	Sidewall passivation
Etch A	SF 6 / Ar	60 mTorr	35 mTorr	2 s	Main etching step
Etch B	SF 6 / Ar	60 mTorr	35 mTorr	2 s	Secondary etching step

Appendix

Table 12: Fixed process template used in the ViennaPS Bosch simulation. The ignition stage is applied only once at the beginning of the simulation for initial trench opening, whereas the deposition, Etch A, and Etch B steps are repeated according to the sample specific cycle number.

Step	Parameter	Value
Ignition	stickingIgnitionMask	0.2
Ignition	stickingIgnitionSubs	0.2
Deposition	stickingDep	0.1
Etching	stickingEtchPoly	0.1
Etching	stickingEtchMask	0.2
Etching	stickingEtchSubs	0.2

Appendix

Table 13: Fixed sticking probabilities used in the ViennaPS Bosch simulation.

Step	Parameter	Value	Physical meaning
Ignition	alphaIgnitionSubs	-270	Ion-assisted etching of Si
Ignition	alphaIgnitionMask	-13.5	Ion-assisted etching of mask
Ignition	betaIgnitionSubs	-0.9	Chemical etching of Si
Ignition	betaIgnitionMask	-0.045	Chemical etching of mask
Deposition	alphaDep	10.0	Ion-assisted deposition coefficient
Deposition	betaDep	0.5	Neutral-assisted deposition coefficient

Appendix

Table 14: Fixed effective reaction coefficients used in the ViennaPS Bosch simulation.

Parameter	Step	Initial value	Unit
$\mathrm{Flux}_{ion}^{I}$	Ignition	$2.50\times 10^{15}$	atoms/cm ${}^{2}\cdot$ s
$\mathrm{Flux}_{neu}^{I}$	Ignition	$6.00\times 10^{18}$	atoms/cm ${}^{2}\cdot$ s
$\mathrm{Flux}_{ion}^{D}$	Deposition	$1.40\times 10^{15}$	atoms/cm ${}^{2}\cdot$ s
$\mathrm{Flux}_{neu}^{D}$	Deposition	$3.50\times 10^{18}$	atoms/cm ${}^{2}\cdot$ s
$\mathrm{Flux}_{ion}^{EA}$	Etch A	$4.00\times 10^{16}$	atoms/cm ${}^{2}\cdot$ s
$\mathrm{Flux}_{neu}^{EA}$	Etch A	$1.80\times 10^{19}$	atoms/cm ${}^{2}\cdot$ s

Appendix

Table 15: Flux-related simulator parameters updated during calibration. The listed values correspond to the initial ViennaPS configuration before calibration.

Figure 12: Extended 20-iteration ablation study on candidate generation strategies. All variants follow the same experimental protocol as the main 10-iteration ablation study.

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