An Analysis of the Derivative Weight-Gain Signal From Measured Crystal Shape: Implications for Diameter Control of GaAs

Abstract

A commercially viable GaAs device technology for field-effect transistors, integrated circuits, and lasers is critically dependent on the availability of high-quality, single-crystal boules with controlled diameter. We have modeled a diameter control scheme based on the monitoring of crystal weight for liquid-encapsulated Czochralski (LEC) growth of GaAs. The presence of the B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> liquid encapsulant and significant capillary forces make the direct interpretation of the weight-gain signal and its time derivative (DWGS) more complicated in comparison with pulled materials such as oxide crystals. We have formulated a realistic model for the LEC growth of axisymmetric crystals and have derived the differential equation relating the time evolution of the DWGS to radius and length. We show that the magnitude of the DWGS at the crystal's “shoulder” is inversely related to the radius of curvature. Furthermore, the meniscus by itself gives rise to a precursor or early warning in the signal, which means that the maximum in DWGS precedes the maximum in shape by a few hundred seconds. The existence of a secondary maximum or aftershock in the signal that is the sole consequence of liquid encapsulation is also demonstrated. Excellent agreement has been obtained between DWGS and the signal predicted from the measured shape of a grown crystal. Thus, prospects for automatic diameter control are encouraging.