A Review of the Automation of the Czochralski Crystal Growth Process

Abstract

On the occasion of the centennial of the invention of the Czochralski crystal growth process by the Polish scientist Jan Czochralski, a review of selected strategies for the automatic control of this process is given. This review provides a sketch of the fundamental challenges of controlling the Czochralski process and the basic concepts of feedback control. Both early and modern approaches to the control of the Czochralski process are described.The discussion focuses on questions related to feed-forward control, feedback control, and state estimation. The presented methods rely on simple mathematical process models in contrast to the nite element model-based approaches typically used in crystal growth process design and analysis. Such mathematical models motivate both the structure and parameters of the chosen controller. A comprehensive list of references to background literature on this topic completes this survey.

Improving the Dipping Step in Czochraski Process Using Haar-Cascade Algorithm

“…Many studies have been published regarding the application of computer science to this procedure. For example, Winkler et al used a mathematic algorithm to calculate the crystal diameter and introduce the automatic CZ process with a nonlinear-state smart sensor, or soft sensor, or virtual sensor for controlling the quantities in the Czochralski crystal growth [8,9]. Jing et al used a 3D-simulation method for investigating the relationship among the melting temperature at the melt or crystal surface, the rotation rate and efficiency of the final crystal product [10], and Kim et al used an auto-seeding system and image processing technology to optimize the manufacturing of sapphire crystal growth via the Kyropoulos (KY) method [11].…”

Automation of Crystal Growth from Melt

“…For this purpose, the essential components of a control system are briefly summarized according to [14,18,19]. This is done by appropriately manipulating the inputs of the process, in the following referred to as the manipulated variables.…”

“…This is done by appropriately manipulating the inputs of the process, in the following referred to as the manipulated variables. The approaches and requirements differ quite a lot [19] between both fields. The intention of this section is to introduce some of the basic concepts used in control technology as far as they are required for an understanding of the numerous strategies for control of the discussed crystal growth processes.…”

“…A short example is given as follows illustrating this strategy [19]. A short example is given as follows illustrating this strategy [19].…”

Diameter Control for Silicon Rod Growth

“…A quantitative evaluation of the observed approaches is difficult because of the absence of the ground truth data for the meniscus radii. Even though the radius of the grown rod can be thoroughly measured after the process, it doesn't represent the meniscus radius exactly [8]. Therefore, we perform two different experiments.…”