Ultrasonic transmission at solid-liquid interfaces

New non-invasive solid-liquid interface sensing technologies are a key element in the development of improved Bridgman growth techniques for synthesizing single crystal semiconductor materials. Laser generated and optically detected ultrasonic techniques have the potential to satisfy this need. Using an anisotropic 3-D ray tracing methodology combined with elastic constant data measured near the melting point, ultrasonic propagation in cylindrical single crystal bodies containing either a convex, flat, or concave solid-liquid interface has been simulated. Ray paths, wavefronts and the time-of-flight (TOF) of rays that travel from a source to an arbitrarily positioned receiver have all been calculated. Experimentally measured TOF data have been collected using laser generated, optically detected ultrasound on model systems with independently known interface shapes. Both numerically simulated and experimental data have shown that the solidification (interfacial) region can be easily identified from transmission TOF measurements because the velocity of the liquid is much smaller than that of the solid. Since convex and concave solid-liquid interfaces result in distinctively different TOF data profiles, the interface shape (convex or concave) can also be readily determined from the TOF data When TOF data collected in the diametral plane is used in conjunction with a nonlinear least squares algorithm, the interface geometry (i.e. position and shape) has been successfully reconstructed and ultrasonic velocities of both the solid and liquid obtained with reconstruction errors less than 5%.