Iterative compensation of nonlinear error of heterodyne interferometer

Xie, Jiandong; Yan, Liping; Chen, Benyong; Zhang, Shihua

doi:10.1364/oe.25.004470

Cited by 17 publications

(9 citation statements)

References 16 publications

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“…Due to ellipticity and nonorthogonality of the light source and misalignment or imperfection of the PB, 58 periodic nonlinear errors exist in the practical GIs. As shown in Figure 20, the spatially separated heterodyne GI has been proposed to reduce these errors 59 .…”

Section: Stage Position Measurementmentioning

confidence: 99%

“…For a heterodyne GI, the frequency difference (f 1 − f 2 ) contains displacement information, which makes it possible to use a single PD to determine the direction. 56 Due to ellipticity and nonorthogonality of the light source and misalignment or imperfection of the PB, 58 periodic nonlinear errors exist in the practical GIs. As shown in Figure 20, the spatially separated heterodyne GI has been proposed to reduce these errors.…”

Section: Stage Position Measurementmentioning

confidence: 99%

See 1 more Smart Citation

Mechanical system and dynamic control in photolithography for nanoscale fabrication: A critical review

Song

Chen

Huo³

et al. 2021

Int Journal of Mech Sys Dyn

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As one of the most advanced and precise equipment in the world, a photolithography scanner is able to fabricate nanometer-scale devices on a chip. To realize such a small dimension, the optical system is the fundamental, but the mechanical system often becomes the bottleneck. In the photolithography, the exposure is a dynamic process. The accuracy and precision of the movement are determined by the mechanical system, which is even more difficult to control compared with the optical system. In the mechanical system, there are four crucial components: the reticle and wafer stages, the linear motor, the metrology system, and the control system. They work together to secure the reticle and substrate locating at the correct position, which determines the overlay and alignment performance in the lithography. In this paper, the principles of these components are reviewed, and the development history of the mechanical system is introduced.

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Section: Stage Position Measurementmentioning

confidence: 99%

Section: Stage Position Measurementmentioning

confidence: 99%

Mechanical system and dynamic control in photolithography for nanoscale fabrication: A critical review

Song

Chen

Huo³

et al. 2021

Int Journal of Mech Sys Dyn

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“…The commonly used solutions include passive compensation method and active elimination method [29][30][31][32][33][34][35][36]. At present, iterative algorithm with a digital lock-in phase demodulator [37], spatially separated structure [38] and symmetric oblique incidence structure [39,40] have been studied. However, it is difficult to adjust the optical path or expand the 2-DOF measurement in the above scheme, so a scheme with strong extensibility and adjustability is needed.…”

Section: Introductionmentioning

confidence: 99%

A polarization adjustment module for frequency aliasing of heterodyne grating interferometer

Gao¹,

Zhu²,

Huang³

et al. 2022

Optical Metrology and Inspection for Industrial Applications IX

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Heterodyne grating interferometer is widely used in precision positioning due to its high precision and robustness. However, the polarization states of two frequency components in a dual-frequency laser are easy to overlap with each other because of the non-ideality of optical components. It will cause nonlinear error, which limits the measurement precision of the grating interferometer. To improve the frequency aliasing of heterodyne grating interferometer, a polarization adjustment module is proposed to adjust the polarization angle of the dual-frequency laser. The dual frequency system outputs two laser beams with different frequencies separately. The module realizes the polarization adjustment of the two frequency components through two groups of the polarizers and the half-wave plates (HWP). Finally, the polarization directions of two frequency components are orthogonal and combined by the beam splitter (BS). Thus, the nonlinear error caused by frequency aliasing is removed. The polarization adjustment module has the advantages of not changing the direction of the laser propagation and simple structure, which makes it easy to realize integration. It can provide a reference for the solution of frequency aliasing of heterodyne grating interferometer.

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“…Additionally, recent research indicates that these configurations still suffer from nonlinearities caused by multi-order Doppler frequency shift (DFS) arising from ghost reflection [ 11 ]. The second solution keeps the common optical paths and employs compensation algorithms, mainly the Heydemann correction [ 12 , 13 , 14 , 15 , 16 , 17 ]. This correction relies on the traditional model that first- and second-order nonlinearities are generated from optical mixing [ 18 , 19 , 20 ].…”

Section: Introductionmentioning

confidence: 99%

“…In theory, the correction is capable of eliminating nonlinearities through elliptical fitting. Nevertheless, residual nonlinear errors from hundreds of picometers to several nanometers are still found even after compensation [ 12 , 13 , 14 , 15 , 16 , 17 ], the cause and mechanism of which remain largely uninvestigated.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Errors Resulting from Ghost Reflection and Its Coupling with Optical Mixing in Heterodyne Laser Interferometers

Wang

et al. 2018

Sensors

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Even after the Heydemann correction, residual nonlinear errors, ranging from hundreds of picometers to several nanometers, are still found in heterodyne laser interferometers. This is a crucial factor impeding the realization of picometer level metrology, but its source and mechanism have barely been investigated. To study this problem, a novel nonlinear model based on optical mixing and coupling with ghost reflection is proposed and then verified by experiments. After intense investigation of this new model’s influence, results indicate that new additional high-order and negative-order nonlinear harmonics, arising from ghost reflection and its coupling with optical mixing, have only a negligible contribution to the overall nonlinear error. In real applications, any effect on the Lissajous trajectory might be invisible due to the small ghost reflectance. However, even a tiny ghost reflection can significantly worsen the effectiveness of the Heydemann correction, or even make this correction completely ineffective, i.e., compensation makes the error larger rather than smaller. Moreover, the residual nonlinear error after correction is dominated only by ghost reflectance.

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Iterative compensation of nonlinear error of heterodyne interferometer

Cited by 17 publications

References 16 publications

Mechanical system and dynamic control in photolithography for nanoscale fabrication: A critical review

Mechanical system and dynamic control in photolithography for nanoscale fabrication: A critical review

A polarization adjustment module for frequency aliasing of heterodyne grating interferometer

Nonlinear Errors Resulting from Ghost Reflection and Its Coupling with Optical Mixing in Heterodyne Laser Interferometers

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