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This is the first part of a two-article series that deals with theinvestigation of the anomalous behaviour in the radius measurement signal ofthe 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 crucialand limiting factor in feedback control system design. The paper presents thedevelopment of a rigorous 3D ray-tracing method to investigate the inverseresponse behaviour in the measurement signal. The results of this study providean insight into the dynamic behaviour of the Cz growth process. It can serve asa guideline for achieving effective crystal radius control, which is addressedin the second part of this article series.

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