Elasto-viscoplastic wave propagation in single crystallographic silicon thin structure
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The thesis provides the required knowledge base for establishing Laser Induced Stress Wave Thermometry (LISWT) as a viable alternative to current infrared technologies for temperature measurement up to 1000Â°C with Â±1Â°C resolution. The need for a non-contact, high resolution thermal measurement methodology applicable to Rapid Thermal Processing (RTP) motivated the work. A stress wave propagation model was developed and a complex, temperature-dependent elasto-viscoplastic constitutive law was identified. A stagger-grid finite difference scheme was followed to approximate the solution field subject to temperature and plate thickness variations. Extensive numerical experiments were conducted to identify the proper time and spatial steps. A Gabor wavelet transform scheme was also employed for the extraction of wafer thermal and geometric information from exploring wave attenuation and dispersion. Researched results concluded that wave group velocity is a nonlinear function of temperature. Nonlinearity became more prominent at high temperatures and low frequencies. As such, for LISWT to achieve better thermal resolution at high temperatures, low frequency components of the induced stress wave should be exploited. The results also showed that the influence of temperature on attenuation is relatively small. It is not recommended to use attenuation for resolving temperature variation as small as several degrees Celsius. In addition to temperature, geometry also was found to have an impact on wave dispersion and attenuation. The results showed that the influence of thickness on wave velocity is significant, thus suggesting that for LISWT to achieve high temperature resolution, wafer thickness must be accurately calibrated in order to eliminate all possible errors introduced by thickness variation. The study established the basic framework for LISWT to be applicable to silicon wafer RTP at elevated temperatures. The model and methods developed for the course of the research can be easily adapted to account for other nondestructive evaluation applications involving the use of surface, plate or bulk waves for material characterization and thermal profiling.
Liu, Li (2003). Elasto-viscoplastic wave propagation in single crystallographic silicon thin structure. Master's thesis, Texas A&M University. Texas A&M University. Available electronically from