International Society for Industrial Process Tomography

Numerical Aspects of Contactless Inductive Flow
Tomography for Crystal Growth

T. Wondrak^1*, R.T. Jacobs², V. Galindo¹, F. Stefani¹

¹Helmholtz-Zentrum Dresden - Rossendorf, Institute of Fluid Dynamics, 01328 Dresden, Germany

²Technische Universität Dresden, Elektrotechnisches Institut, 01062 Dresden, Germany

^*Email: t.wondrak@hzdr.de

ABSTRACT

The flow structure of liquid silicon in the crucible for Czochralski (Cz) crystal growth is important for the quality of the silicon crystal. However, the high temperature and the required cleanliness of the melt represent a challenge for any flow measurement device. A promising technique to reconstruct the flow of a conducting liquid is contactless inductive flow tomography (CIFT). The procedure relies on the measurement of the flow induced perturbation of a primary magnetic field and the inversion of the corresponding integral equation system. In this paper, the numerical challenges for the application of CIFT to Cz crystal growth will be investigated. This includes the treatment of the singularities of the integral equation system as well as the selection of appropriate integration techniques. The paper concludes with numerical investigation of the expected flow induced magnetic field for a reversal of the rotation in simple model of a typical crucible.

Keywords Contactless inductive flow tomography, Czochralski crystal growth, flow measurement, liquid metal

Industrial ApplicationCzochralski crystal growth