Inverse response behaviour in the bright ring radius measurement of the Czochralski process I: Investigation

Abstract

This is the first part of a two-article series that deals with the investigation of the anomalous behaviour in the radius measurement signal of the Czochralski (Cz) process and its mitigation in a feedback control system. The inverse or anomalous behaviour is indeed a measurement signal response, which initially is opposite to that of the expected response. This is a crucial and limiting factor in feedback control system design. The paper presents the development of a rigorous 3D ray-tracing method to investigate the inverse response behaviour in the measurement signal. The results of this study provide an insight into the dynamic behaviour of the Cz growth process. It can serve as a guideline for achieving effective crystal radius control, which is addressed in the second part of this article series.