Laser Ultrasonic Sensing of Solid-Liquid Interfaces during Bridgman Single Crystal Growth

"Using a 3-D ray tracing methodology combined with laser ultrasonically measured elastic constant data near the melting point, ultrasonic propagation in cylindrical single crystal bodies containing either a convex or a concave solid-liquid interface have been simulated and used to design new sensing concepts. Ray paths, wavefronts and time-of-flight (TOF) of rays that travel from a source to an arbitrarily positioned receiver have been calculated. Experimentally measured TOF data have been collected using laser generated/detected ultrasound on model systems with independently known interface shapes. Both numerically simulated data and experimental results have shown that the solidification (interfacial) region can be identified from ultrasonic transmission TOF data. Since convex and concave solid-liquid interfaces result in distinctively different TOF data. When TOF data collected in the diametral plane are used in a nonlinear least squares algorithm, the interface curvature has been successfully reconstructed and ultrasonic velocities of both the solid and liquid obtained. The reconstruction errors were found to be less than 5%.IntroductionMany of today's single crystal semiconductors are grown by variants of a vertical Bridgman technique in which a cylindrical ampoule of a molten semiconductor is translated through a thermal gradient, resulting in directional solidification and the growth of a single crystal, Fig. 1.1 It has long been recognized that during crystal growth the velocity and the shape of the solid-liquid interface, together with the local temperature gradient, control the mechanism of solidification (i.e. planar, cellular or dendritic), the likelihood of secondary grain nucleation/ twin formation (i.e. the loss of single crystallinity), solute (dopant) segregation, dislocation generation, etc. They thus determine the crystals' resulting quality.2-4 The solidification rate and the solid-liquid interface shape are also sensitive functions of the internal temperature gradient (both axial and radial) during solidification.5•6 This in turn is governed by the heat flux distribution incident upon the ampoule, the latent heat release at the interface, and heat transport (by a combination of conduction, buoyancy and surface tension driven convection, and radiation) within the ampoule. The solid-liquid interface's instantaneous position, velocity and shape during crystal growth are therefore difficult to predict and uncontrolled during growth, especially for those semiconductor materials with low thermal conductivity (e.g. CdTe).4-6 The development of technologies to non-invasively sense the interface position and shape throughout the vertical Bridgman crystal growth process has therefore become a key step toward developing a better understanding of the growth process, for enabling sensor-based process control, and thus ultimately for improving the yield and quality of difficult to grow semiconductor materials like CdTe."