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ABSTRACT--We present a methodology correlating the group velocity of guided plate waves to temperature in anisotropic silicon substrate. The model is developed through numerical solution and manipulation of the dispersion relations, while elastic constants and plate thickness are treated as functions of temperature. Analytical results demonstrate that adequate thermal resolution is provided by both the lowest-order antisymmetric and symmetric dispersive Lamb wave modes to serve as an effective diagnostic in a noncontact thermometry scheme applicable during rapid thermal processing of silicon wafers. Validation is made through a combination of experimentation using laser-generated ultrasound in silicon wafers and analysis employing the Gabor wavelet transform to extract frequency-and temperaturedependent group velocities from the dispersive Lamb waves.

A methodology to characterize and quantify the thermo-mechanical properties of silicon wafers is presented. The method applies broadband Thermo-Acousto-Photonic (TAP) NDE techniques to both generate and detect analyzing guided Lamb waves in wafer structures. Optically induced, dispersive acoustic waves carry important information pertaining to the variation of mechanical properties due to temperature changes. To quantify the variation as functions of temperature, a spline-wavelet based fast integral wavelet transform is employed to identify the temporal progression of the multi-modal structure of dispersive waveguide modes. These results are then used to extract group velocities of particular frequency components of interest. Examples are given to demonstrate the effectiveness of the method on experimental data acquired using the Fiber Tip Interferometer (FTI) system developed at Texas A&M University.

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