Numerical simulation of germanium single crystals grown with a low melt height and an axial vibration

In this study, antimony-doped germanium (Ge-Sb) crystal growth from the melt using three directional growth methods, the vertical Bridgman (VB), the axial heat processing (AHP), and the axial vibrational control (AVC), is investigated. In the VB method, the radial heat flux from furnaces leads to a natural convective flow near the s/l interface. The convective flow results in an inhomogeneous solute distribution. In the AHP method, immersing a high thermal conductivity baffle in the melt reduces the melt height and changes the convective flow pattern near the s/l interface. Consequently, the solute segregation is reduced and the single crystal length is increased. In the AVC method, an axial vibration of the immersed baffle generates a forced convective flow in growth region which affects the crystals quality. Varying amplitude and frequency of vibration result in various convective flow patterns near the s/l interface. Appropriate adjusted amplitude and frequency of vibration can improve the crystal quality. Six Sb-doped Ge crystals are grown experimentally with the aforementioned methods to investigate the effect of the melt height, pulling velocity, and amplitude and frequency of the vibrating baffle on the solute distribution, achieved single crystal length, and morphological stability of the grown crystals. Numerical simulations for all of the three mentioned methods with different growth parameters are performed and compared with experimental results. The interface shape obtained from the experimental results is verified by simulations. Extra simulations with parameters different than experiments are performed to better understand the melt flow characteristics and its influence on crystal growth from the melt. The flow pattern and temperature distribution are investigated by simulations with varying pulling velocities, melt heights, and vibrational parameters. The influence of natural convection flow in the VB and AHP methods and of forced flow in the AVC method on the solidification rate, interface shape, and grown crystal quality is analyzed. A reduced melt height and properly adjusted axial vibration amplitude and frequency improve crystal quality and production yield.