Numerical modelling of the microscopic inhomogeneities during FZ silicon growth

Three-dimensional simulation of heat flow, segregation, and zone shape in floating-zone silicon growth under axial and transversal magnetic fields

“…Most of the numerical models for FZ crystal growth are 2D [6,7], in which the heat and mass transfer, fluid flow, and the zone shape are considered. Unfortunately, even with a perfect axisymmetric condition, many experimental and numerical evidences [1,8] indicated that unsteady 3D heat flows prevail in the molten zone.…”

“…Several 3D simulations were reported as well [8], but the phase boundaries were not taken into account. Recently, a 3D simulation of time-dependent melt convection was carried out by Ratnieks et al [9] based on a zone shape from their 2D selfconsistent model [7]. The coupling of timedependent convection with the growth rate was also reported, where back melting due to oscillatory rotational flow was illustrated.…”

3D Numerical Analysis of the Asymmetric Three-Phase Line of Floating Zone for Silicon Crystal Growth

“…The flow separation point, which is the origin of accumulated dopant, also changes repeatedly. These calculation results can explain the asymmetric distribution of the measured radial resistivity distribution in the as-grown crystal [4]. Crystals 2020, 10, x FOR PEER REVIEW 6 of 10 of current supplies does not strongly affect the symmetric flow pattern in the Y plane.…”

“…The first 2D numerical study on the FZ was published by Mühlbauer et al [2]. The 2D global numerical studies were later conducted and were found to provide a good fit with experimental results [3][4][5][6][7]. However, the physical phenomena along the azimuthal direction cannot be analyzed with a 2D numerical model.…”

Floating Zone Growth of Silicon

“…Riemann et al calculated the shapes of the free surface and the crystallization interface, and the thermal stress in the crystal [36]. Mü hlbauer et al extended the model [34] and calculated transient dopant transport in the melt [37] and compared the calculated resistivity distributions with experiments [38,39]. The influence of different additional magnetic fields on the resistivity distribution is studied by Raming et al in [40][41][42].…”