Solutocapillary convection in germanium‐silicon melts

Abstract

Surface tension gradients in free crystal growth melts give rise to convective flow. If these gradients are due to thermal gradients, the well known thermocapillary (Marangoni) convection ensues. Concentration gradients due to segregation at the interface during growth can lead to additional solutocapillary convection. A system with large solutocapillary convection is Ge-Si due to the pronounced segregation and the strong difference in surface tension; solutal buoyancy convection is also present due to the large density difference between Ge and Si. Solutocapillary convection will oppose thermocapillary convection in the Ge-Si system since Si, having the higher surface tension, is preferentially incorporated into the crystal. A set of experiments directly proving and partially quantifying the effect has been conducted under microgravity during a parabolic flight campaign by recrystallizing Ge-Si mixtures of different compositions, between 3% and 9% Si, in a crucible with tracers to visualize the movement. Solutocapillary flow with initial flow rates in excess of 5.5 cm/s at the onset of crystallization was measured. A slight dependence of the flow velocity on the initial Si content has been found. Experiments on the ground showed the same effect but with overall smaller speeds; this difference can be explained by the additional action of solutal buoyancy convection. Dedicated to Prof. Wolfgang Neumann on the occasion of his 65th birthday

Three-Dimensional Numerical Simulation of Pure Solutocapillary Flow in a Shallow Annular Pool for Mixture Fluid with High Schmidt Number

“…Schwabe (2007) proposed a method to make dopants or impurities incorporate in the crystal by controlling the interaction of solutocapillarity and thermocapillarity deliberately. This feasibility has been proved by experimental investigations of solutocapillary convection (Cröll et al 2009;Arafune et al 2011;Schwabe et al 1996), numerical simulations (Abbasoglu and Sezai 2007;Minakuchi et al 2014;Lyubimova et al 2011) and linear stability analysis (Lyubimova 2007). As demonstrated experimentally by Cröll et al (2009) in a shallow rectangular crucible under microgravity, the measured velocity of the tracers is up to 55 mm/s at the onset of crystallization.…”

“…This feasibility has been proved by experimental investigations of solutocapillary convection (Cröll et al 2009;Arafune et al 2011;Schwabe et al 1996), numerical simulations (Abbasoglu and Sezai 2007;Minakuchi et al 2014;Lyubimova et al 2011) and linear stability analysis (Lyubimova 2007). As demonstrated experimentally by Cröll et al (2009) in a shallow rectangular crucible under microgravity, the measured velocity of the tracers is up to 55 mm/s at the onset of crystallization. Arafune and Hirata (1999) found that the surface velocity of solutocapillary flow is 3-5 times larger than that of the thermocapillary flow in In-Ga-Sb system in a rectangular open boat.…”

The Role of Marangoni Convection in Crystal Growth

“…According to Cröll et al [86], such mixed convection is explained below. According to Cröll et al [86], such mixed convection is explained below.…”

“…Cröll et al [86] carried out the directional solidification experiments of Ge x Si 1Àx mixtures of different compositions between 3% and 9% Si under microgravity condition during a parabolic flight campaign, where the samples of 2-3 mm in depth poured in a SiC-coated graphite crucible (inside dimensions 15 Â 30 mm 2 ) were heated by a doubleellipsoid mirror furnace whose two lamps were focused onto one end of the crucible. Figure 22.29 shows the three different experimental stages with a schematic view of the convective flow and the position of tracers put to visualize the flow direction of the solutocapillary flows: (a) the sample is completely melted by equally heating from both sides, and the cold spot is in the crucible center leading to two opposing thermocapillary convective rolls, (b) completely molten sample is reduced heating from the right side, and consequently the cold spot moves near the crucible wall, leading to a much reduced thermocapillary convective roll on the right, and (c) solidification starts from the right side, and solutocapillary flow caused by the concentration gradient along the surface due to segregation pushes the tracers away from the melt/crystal interface, where solutocapillary convection opposes thermocapillary convection in the Ge x Si 1-x system since Si, having the higher surface tension, is preferentially incorporated into the crystal during growth.…”

Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

“…For the compound semiconductor crystal growth, the coupling thermal and solutocapillarybuoyancy effects in the mixture are rather more complex than that of pure fluid. Cröll et al [38] conducted an experiment during the parabolic flight campaign to separate the buoyancy effect from the capillary convection. The solutocapillary convection was conclusively observed during the solidification of silicon-germanium.…”