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

Abstract

Abstract.During the growth of large diameter silicon single crystals with the industrial floating zone method, undesirable level of thermal stress in the crystal is easily reached due to the inhomogeneous expansion as the crystal cools down. Shapes of the phase boundaries, temperature field and elastic material properties determine the thermal stress distribution in the solid mono crystalline silicon during cylindrical growth. Excessive stress can lead to fracture, generation of dislocations and altered distribution of intrinsic point defects. Although appearance of ridges on the crystal surface is the decisive factor of a dislocation-free growth, the influence of these ridges on the stress field is not completely clear. Here we present the results of thermal stress analysis for 4" and 5" diameter crystals using a quasi-stationary three dimensional mathematical model including the material anisotropy and the presence of experimentally observed ridges which cannot be addressed with axis-symmetric models. The ridge has a local but relatively strong influence on thermal stress therefore its relation to the origin of fracture is hypothesized. In addition, thermal stresses at the crystal rim are found to increase for a particular position of the crystal radiation reflector.

Containerless metal single-crystal growth via electromagnetic levitation

“…With an inner coil diameter of 3 mm, 20 bar of water pressure is required to reach a flow of 8 l/min necessary to transport a theoretical maximum power of 40 kW. The coil is attached to a sliding door (16), making it easy to service and replace.…”

“…On the contrary, in one way or another, all growth methods mechanically suspend the crystalline rod that is in contact with the melt, again leading to thermal stress-induced crystal defects. [3,16] 12 1…”

“…In contrast, the electromagnetic field providing lift in an EML setup is intrinsically coupled to sample heating. Furthermore, ESL 16 1…”

“…Actually, all growth methods, in one way or another, mechanically suspend the crystalline rod that is in contact with the melt, again leading to thermal stress-induced crystal defects. [3,16] To overcome these hurdles, it would be useful to grow crystals in a containerless environment. The absence of a crucible solves both the contamination problem and the thermal stress-induced crystal defect problem.…”

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

“…However, the physical phenomena along the azimuthal direction cannot be analyzed with a 2D numerical model. Therefore, 3D numerical simulation results for the EM field, heat transfer, and impurities have been conducted [8][9][10][11][12]. The asymmetric three-phase line analysis by numerical simulation has not yet been reported.…”