Three-dimensional wave propagation through single crystal solid–liquid interfaces

Large differences in the ultrasonic velocity of the solid and liquid phases of semiconductors have stimulated an interest in the use of laser ultrasonic methods for locating and characterizing solid–liquid interfaces during single crystal growth. A previously developed two-dimensional ray tracing analysis has been generalized and used to investigate three-dimensional ultrasonic propagation across solid–liquid interfaces in cylindrical bodies where the receiver is located at an arbitrary position relative to the source. Numerical simulations of ultrasonic ray paths, wavefronts, and time of flight have indicated that ultrasonic sensing in the diametral plane is a preferred sensing configuration since the transmitted, reflected, and refracted rays all propagate in 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 the planes in which reflected and refracted rays propagate are not known a priori, and fewer ray paths are accessible for interface interrogation because of large refractions.