3-DIMENSIONAL WAVE-PROPAGATION THROUGH SINGLE-CRYSTAL SOLID-LIQUID INTERFACES

Large differences in the ultrasonic velocity of the solid and liquid p hases of semiconductors have stimulated an interest in the use of lase r ultrasonic methods for locating and characterizing solid-liquid inte rfaces during single crystal growth. A previously developed two-dimens ional ray tracing analysis has been generalized and used to investigat e three-dimensional ultrasonic propagation across solid-liquid interfa ces in cylindrical bodies where the receiver is located at an arbitrar y position relative to the source. Numerical simulations of ultrasonic ray paths, wavefronts, and time of flight have indicated that ultraso nic sensing in the diametral plane is a preferred sensing configuratio n since the transmitted, reflected, and refracted rays all propagate i n this plane, significantly simplifying analysis of the results. While other sensing configurations can also provide information about solid -liquid interfaces, they require a more complicated analysis because t he planes in which reflected and refracted rays propagate are not know n a priori, and fewer ray paths are accessible for interface interroga tion because of large refractions. (C) 1998 Acoustical Society of Amer ica. [S0001-4966(98)00203-3].