Modelling of phase boundaries for large industrial FZ silicon crystal growth with the needle-eye technique

Three-dimensional modelling of thermal stress in floating zone silicon crystal growth

“…The physical parameters of the heat transfer are temperature of the ambient space 600 K, temperature of the inductor 400 K and emissivities of the inductor and the reflector 0.3 . Average temperature of the reflector 1150 K is obtained without any cooling and is close to estimated 1000 K for a realistic FZ process [16]. However, water cooling would be preferable in order to avoid deformation of the silver reflector near its melting point.…”

“…To have realistic interface shapes and temperature field in the crystal, initially a converged state of quasi-steady calculations using the program FZone [16] with inductor shape from [7] is obtained for the given crystal diameter and the pull rate. Shape of the crystallization interface is found by solving global heat transfer problem which couples the temperature field in the silicon with radiation on the surfaces using view factors, and the heat sources are taken from 3D high-frequency electromagnetic field calculation [17].…”

Influence of reduced working frequencies on the floating‐zone growth of silicon single crystals

“…In this case the phase shift was maintained by tuning the inductance of the grid circuit. Melting behaviour Depending on the working frequency and the thickness of the liquid silicon layer at the open melting front, some fraction of the volume currents are induced into the liquid layer and the other fraction is induced into the subjacent solid (a model is proposed in [4]). The melting behavior is more favorable if the power is mainly induced into the liquid layer.…”

“…is therefore only relevant at the open melting front, where the penetration depth is in the order of the thickness of the liquid film and, hence, the change of the electric conductivity σ along the surface normal into the material has to be taken into account [4]. Applying the high frequency approximation and assuming the EM field is penetrating only the liquid silicon, the voltage is…”

Numerical study and comparisons with experimental data for transient behaviour of phase boundaries during industrial FZ process for silicon crystal growth

“…First, the equilibrium state (serves as initial geometry for transient calculations) was calculated with the stationary model [2]. The crystal pull rate was set constant to V C ¼ 3:24 mm=min: The feed rod radius was R F ¼ 55:5 mm; the crystal radius R C ¼ 52:95 mm and the HF current frequency f ¼ 2:8 MHz: Other parameters were set similar as in the example in Ref.…”