シリコン単結晶の重回帰分析を用いたX線応力測定

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Multiple regression analysis was applied to the X-ray stress measurements of silicon single crystal wafer which has the [001] direction perpendicular to the surface. Using an X-ray diffractometer with parallel beam optics, X-ray profiles were recored by a scintillation counter while the specimen was oscillated around two axes. The X-ray measurement conditions were first determined, and then the method was successfully applied to measure the loading stress in a silicon single specimen subjected to four-point bending. The oscillation of the specimen between ±1 to 2 deg during recording was necessary to determine in peak position. An setting error of the specimen position of ±100 μm gave an error in diffraction angle of ±0.004 deg at most, corresponding to an error in stress of 3 MPa. The uniaxial stress was applied in [110] direction (longitudinal direction) of the specimen. Three stress components, σ_<11>, σ_<22> and σ_<12> were determined from the measurement of diffraction angles of five diffractions, 133, 133, 313, 313, 331, which had the same spacing between diffraction planes. The measured stress of σ_<11> is 0.993 of the applied stress and the two other components, σ_<22> and σ_<12>, were nearly zero. Multiple regression analysis was proved to be powerful to determine three stress components of single crystals under the plane stress state. The residual stress in polished silicone wafer was small tension of the order of 10 MPa.
社団法人日本機械学会の論文
2006-05-25

シリコン単結晶の重回帰分析を用いたX線応力測定

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