Numerical optimization of the interface shape at the VGF growth of semiconductor crystals in a traveling magnetic field

For the first time the efficiency of a traveling magnetic field (TMF) generated inside a vertical gradient freeze (VGF) equipment of industrial scale is computed numerically. The TMF is induced in a combined heater-magnet module consisting of three coil segments operating with phase shift. A charge of 6 kg Ge in a cylindrical pBN container with diameter of 110 mm is taken as model arrangement. In the focus is the study of the interaction between the induced Lorentz force field and the buoyancy-driven convection to find out the optimal field parameters, like frequency and phase shift, for achievement of a slightly convex melt–solid interface and temperature stable growth regime. The flow patterns and interface morphology as functions of the H/D aspect ratio (H — melt height, D — melt diameter) in the course of the crystallization process are investigated. It turns out that there is only a narrow Lorentz force region at low frequencies that is able to control a laminar time-independent melt flow regime. The validity of the numerical results is supported by magnetic force measurements on a dummy within the heater-magnet module positioned inside the industrial VGF furnace “Kronos”.