Resolution of the discrepancy between temperature indicated interface and radiographically determined interface in a vertical Bridgman furnace

• Published in: Journal of crystal growth 1993-07, Vol.131 (1-2), p.75-82
• Main Authors: Hubert, James A., Fripp, Archibald L., Welch, Christopher S.
• Format: Article
• Language: English
• Subjects: Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Materials science; Methods of crystal growth; physics of crystal growth; Physics; Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation
• ISSN: 0022-0248; 1873-5002
• DOI: 10.1016/0022-0248(93)90398-G

The melt-solid interface position was measured during the Bridgman growth of germanium both by X-ray imaging and by temperature measurements. X-ray imaging displayed an interface location through a change in image intensity representing the difference in density between liquid and solid germanium. The temperature measurements were obtained with thermocouples inserted into a centerline capillary tube in the germanium sample and translated to varying positions. The temperature profile indicated an interface location at the change in slope of temperature representing the difference in thermal conductivity between liquid and solid germanium. Comparisons between these measurement techniques showed a 3 mm difference in position of the interface. The position measured via radiography was lower (i.e. colder) than that measured by the temperature profile. The measured temperature was expected to be lower due to conduction of heat along the thermocouples but a spatial shift of the gradient discontinuity was not anticipated. The temperature field of the ampoule, growth material and measurement thermocouples was analyzed via numerical analysis. It was found that both the lower temperature and the spatial shift of the discontinuity in temperature gradient were a result of an end effect in the thermocouples. This end effect is caused by the low heat flux to the thermocouples which causes the temperature gradient at the tip of the thermocouples to be significantly lower than the temperature gradient of the environment. With this insight, a simple extension was made to the heat equation for a thin cylindrical rod in a temperature gradient. This analytical solution provided a good fit to both the numerical solution and the radiography data. This work provides a new insight into temperature measurement in a high gradient region.