Analysis of key technologies for virtual instruments metrology

Liu, Guixiong; Xu, Qingsong; Gao, Furong; Guan, Qiuju; Fang, Qiang

doi:10.1117/12.819751

Cited by 3 publications

(3 citation statements)

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“…The interest in virtual experiments and virtual instruments is growing rapidly in recent years [1][2][3][4][5][6][7][8][9]. Virtual experiments provide a numerical model for real measurements and they are used, for example, to identify relevant sources of uncertainty [1,10], to specify tolerances required for reaching a desired accuracy [9] or for the design of novel measurement principles.…”

Section: Introductionmentioning

confidence: 99%

Virtual experiments for the assessment of data analysis and uncertainty quantification methods in scatterometry

Kok¹,

Dijk²,

Wübbeler

et al. 2023

Metrologia

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Geometrical dimensions in nanostructures can be determined through indirect optical measurements carried out by a scatterometer. This includes solving a nonlinear regression task in which a physical model is fitted to the observed optical diffraction pattern. We developed a virtual experiment which produces simulated diffraction patterns in coherent Fourier scatterometry measurements including perturbations due to various error sources. We utilize this virtual experiment to assess the suitability of data analysis and uncertainty quantification methods employed in scatterometry. In addition to investigating relevant physical parameters we explore the impact of deviations between the regression model utilized for the analysis and the scatterometry model used to produce the virtual diffraction pattern. We choose coverage probabilities of interval estimates of the geometrical dimensions as the main metric for the assessment. One of our findings is that the discretization level, expressed as the number of retained Fourier orders, can be relaxed up to order 9 in our case study, which is relevant as calculation times strongly depend on this parameter. Another result is that the least-squares approach considered here for solving the regression task in combination with the propagation of variances yields uncertainties which have somewhat lower coverage probabilities than the envisaged 95 %. It turned out that it was critically important to model the oxide layer in order to get proper estimates of the width, or ‘critical dimension’, of the sample, while the uncertainty of the side wall angle had the largest impact on the uncertainty of the measurands. Our findings can help establishing traceability of Fourier scatterometry and underline the usefulness of highquality virtual experiments in connection with complex measurement principles. At the same time the presented case study can be seen as a generic approach that could be followed for assessing uncertainty quantifications in other applications as well.

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Section: Introductionmentioning

confidence: 99%

Virtual experiments for the assessment of data analysis and uncertainty quantification methods in scatterometry

Kok¹,

Dijk²,

Wübbeler

et al. 2023

Metrologia

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“…It produces virtual data whose properties reflect those of the data observed in the corresponding real experiment. Virtual experiments have become increasingly important in modern metrology and industrial applications [2][3][4][5][6][7]. They are utilized, for example, to explore the accuracy of a measurement device, or to specify machine tolerances needed to reach a required accuracy [8].…”

Section: Introductionmentioning

confidence: 99%

GUM-Compliant Uncertainty Evaluation Using Virtual Experiments

et al. 2022

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A virtual experiment simulates a real measurement process by means of a numerical model. The numerical model produces virtual data whose properties reflect those of the data observed in the real experiment. In this work, we explore how the results of a virtual experiment can be employed in the context of uncertainty evaluation for a corresponding real experiment. The uncertainty evaluation was based on the Guide to the Expression of Uncertainty in Measurement (GUM), which defines the de facto standard for uncertainty evaluation in metrology. We show that, under specific assumptions about model structure and variance of the data, virtual experiments in combination with a Monte Carlo method lead to an uncertainty evaluation for the real experiment that is in line with Supplement 1 to the GUM. In the general case, a GUM-compliant uncertainty evaluation in the context of a real experiment can no longer be based on a corresponding virtual experiment in a simple way. Nevertheless, virtual experiments are still useful in order to increase the reliability of an uncertainty analysis. Simple generic examples as well the case study of a virtual coordinate measuring machine are presented to illustrate the treatment.

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“…In recent years, when measuring equipment has become much more powerful and software dependant, questions regarding software performance in metrology have been raised demanding further concern and research to establish its current status (Cox and Harris, 2000;Goulding, 2003;Esward et al, 2003;Greif et al, 2006;Richter, 2006;Carbone et al, 2008;Habra, 2008;Liu et al, 2008). The same applies when simulation models are integrated in the metrology software to be used to preview the CMM behavior, which is the case of the Virtual Coordinate Measuring Machines (VCMM) (Phillips et al, 2002;Takamasu, 2002;Levin, 2008).…”

Section: Introductionmentioning

confidence: 99%