Analyses of Crystal Shape Monitoring of LEC-Grown InP Crystals by using a Disc Approximation Approach

Abstract

This paper analyzes crystal shape monitoring for automatic diameter control (ADC) during the liquid encapsulated Czochralski (LEC) growth of InP crystals. The crystal diameter (shape) is monitored numerically (diagrammatically) by using a disc approximation approach based on precise weight and pulling length measurements. The error in the diameter calculation based on the approximation is estimated to be sufficiently small for practical use. The monitoring accuracy was investigated for crystal bodies with nearly flat growth interfaces, and for their shoulder portions with largely convex growth interfaces. For the straight body portions, the accuracy depended on diameter, d, and improved from ±15% for d=10 mm to ±3% for d=50mm. For the shoulder portions, the diameter was monitored with nearly the same accuracy. This method has therefore made it possible to monitor the growing crystal visually in real time, and was applied to the growth of <111> InP crystals with a cone angle of less than 39° and a smooth appearance to avoid twinning.