Method and apparatus for controlling diameter of a silicon crystal ingot in a growth process

摘要

An improvement to a method and an apparatus for growing a monocrystalline silicon ingot from silicon melt according to the CZ process. The improvement performs defining an error between a target taper of a meniscus and a measured taper, and translating the taper error into a feedback adjustment to a pull-speed of the silicon ingot. The conventional control model for controlling the CZ process relies on linear control (PID) controlling a non-linear system of quadratic relationship defined in the time domain between the diameter and the pull-speed. The present invention transforms the quadratic relationship in the time domain between the diameter and the pull-speed into a simile, linear relationship in the length domain between a meniscus taper of the ingot and the pull-speed. The present invention applies a linear control (modified PID) which operates in the length domain, and controls a system that has a linear relationship between the ingot taper and the pull-speed in the length domain to control the diameter of a growing silicon ingot.