Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid

Chu, Jiyoung; Griesmann, Ulf; Wang, Quandou; Soons, Johannes A.; Benck, Eric C.

doi:10.1364/ao.49.001849

Cited by 8 publications

(5 citation statements)

References 16 publications

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“…To eliminate the effect of gravity, Chu et al proposed the liquid floating method in which the measured object is floated on the surface of a solution [24]. The effect of gravity is canceled out by the buoyancy force.…”

Section: Deformation Measurement Of Polished Silicon Wafers Using Thr...mentioning

confidence: 99%

Evaluation of polishing-induced subsurface damage based on residual stress distribution via measured global surface deformation for thinned silicon wafers

Liu¹,

Zhou²,

Han³

et al. 2021

Surf. Topogr.: Metrol. Prop.

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Polishing is widely used to obtain smooth thinned wafer surfaces and the process-induced subsurface damage is often evaluated by scanning electron microscope or transmission electron microscope images. However, the difference of microscope images is very slight and subtle between wafers and affected by the location selection of the measured points. In this study, we explored the method of evaluating the polishing-induced subsurface damage based on residual stress distribution via measured global surface deformation. The surface deformation was first measured and then the polishing-induced residual stress distribution was calculated from the surface topography data by solving the system of linear equations. The polishing-induced subsurface damage could be evaluated independent of the dimension of the silicon wafer by the proposed method. How the thinned silicon wafer was supported during measurement process greatly affected polishing-induced wafer deformation and gravity-induced deformation should be separated from the measured data. Regularization method should be introduced in the calculation of residual stress to reduce the errors caused by the multi-collinearity of the system of linear equations. The calculated residual stress distribution was found to be an obvious centrosymmetric figure and exhibited a quasi-axisymmetric pattern with the axis of symmetry correlated with certain crystalline directions, indicating the effect of anisotropy of monocrystalline silicon in the polishing process. The proposed method could also be used in the evaluation of polishing-induced subsurface damage of other large and thin substrate plates.

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Section: Deformation Measurement Of Polished Silicon Wafers Using Thr...mentioning

confidence: 99%

Evaluation of polishing-induced subsurface damage based on residual stress distribution via measured global surface deformation for thinned silicon wafers

Liu¹,

Zhou²,

Han³

et al. 2021

Surf. Topogr.: Metrol. Prop.

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show abstract

“…The (100) silicon wafer was used in the measurement. When the coordinate axes were parallel to the crystal orientation [100], the stiffness constants were c 11 = 1.657×10 5 GPa, c 12 = 0.639×10 5 GPa and c 44 = 0.796×10 5 GPa. [9] The wafer thickness was assumed uniform as the thickness deviation was considerably smaller than the wafer warp.…”

Section: Measurement Methods and Equipment Setupmentioning

confidence: 99%

“…The main disadvantage of the phase shift reflection grating method is the requirement of specular surface for the test wafer [4]. Chu et al described a method to measure the warp of the wafers with an interferometer by floating them on high-density aqueous metatungstate solutions to reduce the effects of gravity-induced deformations [5]. The warp of a 300 mm diameter silicon wafer was measured when it was supported by a uniform pressure that did not distort the shape [6].…”

Section: Introductionmentioning

confidence: 99%

Development of a Measuring Equipment for Silicon Wafer Warp

Liu

Kang

Gao

et al. 2013

AMR

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Larger diameter wafers are used to decrease the cost of IC manufacturing and the wafer thickness is decreasing for form factor and thermal power dissipation considerations. The larger wafer requires a large scanning area to inspect the warp, and warp measurement of large and thin silicon wafers is greatly affected by the gravity-induced deflection. In this paper the gravity-induced deflection was calculated using finite element method by supporting the wafer horizontally with three steel balls. A laser displacement sensor based on triangulation principle was used to measure the warp and an air bearing stage was developed to achieve high straightness. The shape of the wafer was obtained using the silicon wafer warp measuring equipment.

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“…To eliminate the effect of GID in the flatness measurement, Chu et al proposed a method to obtain the shape of wafers with an interferometer while the tested wafer was floated on the surface of the high density aqueous meta-tungstate solutions [9,10]. The front surface of the wafer was above the liquid level and the flatness was measured directly by an interferometer while the gravity was balanced by the buoyancy force.…”

Section: Introductionmentioning

confidence: 99%

Analysis Of Factors Affecting Gravity-Induced Deflection For Large And Thin Wafers In Flatness Measurement Using Three-Point-Support Method

Liu

Dong

Kang

et al. 2015

Metrology and Measurement Systems

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Accurate flatness measurement of silicon wafers is affected greatly by the gravity-induced deflection (GID) of the wafers, especially for large and thin wafers. The three-point-support method is a preferred method for the measurement, in which the GID uniquely determined by the positions of the supports could be calculated and subtracted. The accurate calculation of GID is affected by the initial stress of the wafer and the positioning errors of the supports. In this paper, a finite element model (FEM) including the effect of initial stress was developed to calculate GID. The influence of the initial stress of the wafer on GID calculation was investigated and verified by experiment. A systematic study of the effects of positioning errors of the support ball and the wafer on GID calculation was conducted. The results showed that the effect of the initial stress could not be neglected for ground wafers. The wafer positioning error and the circumferential error of the support were the most influential factors while the effect of the vertical positioning error was negligible in GID calculation.

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Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid

Cited by 8 publications

References 16 publications

Evaluation of polishing-induced subsurface damage based on residual stress distribution via measured global surface deformation for thinned silicon wafers

Evaluation of polishing-induced subsurface damage based on residual stress distribution via measured global surface deformation for thinned silicon wafers

Development of a Measuring Equipment for Silicon Wafer Warp

Analysis Of Factors Affecting Gravity-Induced Deflection For Large And Thin Wafers In Flatness Measurement Using Three-Point-Support Method

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