Inverse response behaviour in the bright ring radius measurement of the Czochralski process II: Mitigation by control

Abstract

This is the second part of a two-article series investigating the presence of an inverse response in the measurement of the ingot radius in the Czochralski process for monocrystalline silicon production, when the ingot radius is deduced from a camera image of the bright ring at the meniscus connecting the solid crystal to the silicon melt. Such inverse responses are known to pose a fundamental limitation in achievable control performance. However, for the bright ring radius measurement, the inverse response is an artefact of the measurement technique and does not appear in the physical variable one wants to control (the actual crystal radius). The present article addresses control for the mitigation of the inverse response behaviour, using a combination of parallel compensation and feedback control. The proposed design is validated against simulations where the production process is subjected to temperature disturbances.