Thermal Field Regulation of 6-Inch VGF-Ge Single Crystals: CGSim Simulation and Experimental Study on Defect Suppression

Abstract

The thermal field distribution in the vertical gradient freeze (VGF) process strongly influences the formation of dislocations, residual thermal stress, and twins in germanium (Ge) single crystals, and its effective control is essential for reducing defect density. In this study, a full-scale three-dimensional unsteady thermal–fluid–solid coupled model was developed for a 6-inch VGF furnace, and transient finite-element simulations combined with systematic experiments were performed to quantify the relationships among axial temperature gradient, growth rate, crucible cone angle, insulation configuration, melt flow, and defect evolution; an L9(34) orthogonal design was used to decouple the interactions of these factors. The simulations indicate that the crucible shoulder cone angle markedly affects thermal stress and dislocation density, while the stability of the solid–liquid interface is largely governed by the growth rate. With the optimized parameters (crucible cone angle 92°, 18 g cone insulation cotton, head-to-tail temperature difference of 15 K, growth rate 1.5 mm/h), the average etch pit density decreased to 238 cm−2 on the head wafer and 541 cm−2 on the tail wafer, with maximum values of 633 cm−2 and 1333 cm−2, respectively. The X-ray rocking-curve FWHM measured at the center of a wafer was 25.4 arcsec, corresponding to a mosaic tilt of only 0.007° and consistent with the low dislocation densities obtained; no twins were observed by visual inspection. These improvements are attributed to a symmetric flow field, enhanced melt thermal stratification, and a growth rate that balances latent-heat release against dislocation formation. The established simulation-guided optimization and validation approach offers a reproducible route toward large-sized, low-dislocation Ge single crystals.