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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Coordinate measuring machine (CMM) is a universal measuring instrument in dimensional metrology. However, the CMM has many sources of errors and deviations that affect its precision and accuracy. Unfortunately, the accuracy of flatness measurement by the CMM is not studied which is very important feature in metrology and industry at present time. A method is introduced to evaluate the accuracy of the flatness measurement of the Zeiss CMM based on flatness measurement of an optical flat. The flatnesses of the optical flat are measured by four different techniques using the CMM. Moreover, the effects of CMM head probe's scanning speed and step width on flatness measurements are examined separately in special measuring subroutines. The flatness of the optical flat surfaces are calibrated using Zygo phase shifting interferometer since it is used as reference for this study. The experimental results show that the CMM's probing points technique can be used for accurate measurements of flatness.
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