Minoru Eguchi

Surface tension measurement of molten silicon by the oscillating drop method using electromagnetic levitation

The surface tension of molten silicon was successfully measured by an oscillating drop method using electromagnetic levitation over a wide temperature range from 1100 to 1500°C including the undercooling condition of ΔT ≈ 300 K. Single crystals of silicon heavily doped with B and Sb (resistivity as low as 1 × 10−4 Ω·m) were successfully melted and levitated. The surface tension of molten silicon was 783.5 × 10−3 N/m at the melting point of 1410°C within the measurement accuracy of 3–4%; its temperature coefficient was −0.65 × 10−3 N/m·K. Secondary ion mass spectroscopy (SIMS) analysis showed that O and Sb evaporated during melting, while the B concentration after melting was unchanged. This means that surface tension and its measured temperature dependence correspond to those for a contamination-free silicon melt.

Direct observation by X-ray radiography of convection of molten silicon in the Czochralski growth method

Abstract Convection of molten silicon during Czochralski single crystal growth was directly observed using X-ray radiography. The melt flow pattern was monitored using a tracer method. The tracer, whose density and wettability were adjusted to that of the molten silicon, was developed. The observed convection of the molten silicon in the crucible was not only steady but also transient, and not axisymmetric but asymmetric. This asymmetry is attributed to the asymmetric temperature distribution within the crucible. The flow velocity of the molten silicon in the 75 mm diameter crucible was 10 to 20 mm/s.

Spoke patterns on molten silicon in Czochralski system

Abstract Asymmetric temperature profiles similar to the spoke patterns and related asymmetric flow in Si melts of the Czochralski (CZ) system are verified for the first time by three-dimensional (3D) numerical simulation of heat and momentum transfer and by X-ray radiography technique. These profiles appear as the temperature difference between the wall and the crystal becomes large with symmetric boundary conditions. The 3D simulation leads to the conclusion that the vertical temperature gradient in the unstable layer near the free surface is an important cause of making the asymmetric profile. The profile is estimated to be caused by both Rayleigh-Benard and Marangoni-Benard instabilities in the Si melt. It is shown that the relative strength of these two instabilities depends on the coefficients of temperature dependence of the density and surface tension. If the temperature coefficient of surface tension (∂γ/∂T) is greater than 1 x 10-4 N/m ⋅, the Marangoni-Benard instability mainly causes asymmetry, while if ∂γ/∂T is less than this value, the Rayleigh-Benard instability mainly causes asymmetry.

The role of surface-tension-driven flow in the formation of a surface pattern on a Czochralski silicon melt

Spoke patterns on shallow silicon melts and polygonal cellular patterns on the surface of Czochralski (CZ) silicon melts were observed by CCD camera. The dark stripes of the spoke patterns in the CCD images indicate the lower temperatures. We found that the number of spokes depends on the depth of the silicon melt. When the thermocapillary flow in a 3-mm-deep silicon melt was dominant, a spoke pattern was clearly observed on the surface. On a CZ silicon surface of a 200-mm-deep melt not under a vertical magnetic field, polygonal-shape patterns were observed to move toward the melt center. However, under a vertical magnetic field, the polygonal patterns only changed to be more longitudinal but did not disappear. These observations indicate that the surface flow of a CZ melt and its instability cannot be fully suppressed by a magnetic field and that the surface flow plays a significant role in forming the surface patterns.

Natural and forced convection of molten silicon during Czochralski single crystal growth

Abstract Natural and/or forced convection of molten silicon during Czochralski single crystal growth was directly observed using X-ray radiography with solid tracers for various crystal and crucible rotation speeds, and temperature distribution in a crucible holder. Downflow attributed to natural convection in the center of a crucible which had been simulated by numerical calculation was scarcely observed with and without crucible rotation. Numerical simulation of the molten silicon was carried out by a packaged code of “FLUENT”; in the calculation, measured non-axisymmetric temperature distribution in a crucible holder was adopted. Unidirectional flow with and without crucible rotations can be qualitatively explained by the numerical simulation with non-axisymmetric temperature distribution in the crucible holder. The particle path attributed to natural convection near the solid-liquid interface was suppressed downward with increase in crystal rotation speed. The phenomena can be explained by a generation of forced convection beneath the rotating crystal.

Oxygen transfer during single silicon crystal growth in Czochralski system with vertical magnetic fields

Oxygen transfer in silicon melts during crystal growth under vertical magnetic fields is investigated numerically and experimentally. A three-dimensional numerical simulation, including melt convection and oxygen transport, is carried out to understand how oxygen transfers in the melt under magnetic fields. Oxygen concentrations in single silicon crystals grown from the melt under these magnetic fields are experimentally measured by using an infrared absorption technique. The results obtained are compared to results from a numerical simulation. An anomalous increase is observed in the oxygen concentration of the grown crystals under a magnetic field of about 0.03 T. The cause of this anomaly is identified as Benard instability, since the temperature at the bottom of the crucible is higher than that at interface. When the temperature at the bottom is decreased, the Benard cell can be removed, and a monotonic decrease in the oxygen concentration in the single silicon crystals can be observed.

Flow instability of molten silicon in the Czochralski configuration

Abstract The flow instability of molten silicon in the Czochralski configuration has been studied by in-situ observation of melt convection using X-ray radiography and by temperature fluctuation measurement during crystal growth. Flow mode was dependent on an aspect ratio of the melt. For a deep, low aspect ratio melt, with growing crystal which is identical to shouldering process of the growth, the flow was unsteady and non-axisymmetric. For a shallow melt without crystal and crucible rotations, the flow was relatively steady and axisymmetric. However, flow became unsteady and non-axisymmetric for a shallow melt with crystal rotation. Amplitude of directly measured temperature fluctuation in the molten silicon for the case of unsteady and non-axisymmetric flow was larger than that for the relatively steady and axisymmetric flow. The flow instability area, which was also thermally unstable, was found to be larger in the crystal/crucible iso-rotation condition. In contrast Munakata and Tanasawa reported at the International Symposium on Supercomputers for Mechanical Engineering, September 1988, Tokyo that flow instability area was small for the silicone oil with larger Prandtl number.

Flow and temperature field in molten silicon during Czochralski crystal growth in a cusp magnetic field

Flow behavior of molten silicon and the oxygen-concentration distribution in crystals grown under three different types of cusp magnetic field (CMF) configuration were observed in order to investigate the effect of the magnetic field configuration on the heat and mass transfer in the melt during the crystal-growth processes. The molten-silicon flow in the CMF was directly observed by using an improved X-ray radiography system. The flow was strongly dependent on the CMF configuration, thus, the distribution of the oxygen concentration in the crystals grown under the CMF was also dependent on the CMF configuration. When the center of the CMF was positioned inside the melt, a homogeneous oxygen-concentration distribution was obtained due to the good axisymmetry and reduced flow velocity of the molten-silicon flow. In other cases, the oxygen concentration was inhomogeneously distributed in the crystals because the melt flow was not axisymmetric and its velocity fluctuated. The dependence of the molten-silicon flow on the CMF configuration is attributed to the magnetic field gradient in the melt.

Ordered structure in non-axisymmetric flow of silicon melt convection

Abstract This paper describes the three-dimensional non-axisymmetric flow of a silicon melt in a silicon Czochralski system. A stable vortex with almost the same angular velocity as the crucible is observed by in-situ detection of silicon melt convection using double X-ray radiography. To determine the flow structure in detail, three-dimensional numerical simulation is also carried out for the same geometry; this gives both the three-dimensional temperature and the velocity fields. The simulation predicts a stable vortex rotating with the crucible. The temperature field is also modulated in the azimuthal direction due to the stable vortex. The results of the experiments and numerical simulation show that the non-axisymmetric flow is due to a baroclinic instability.

The baroclinic flow instability in rotating silicon melt

Three-dimensional flow visualization experiments were used to observe the transition from axisymmetric to non-axisymmetric flow of molten silicon in the CZ crystal growth configuration at specific crucible rotation rates. Non-axisymmetric flow shows characteristics of the baroclinic instability when the flow pattern is observed from a rotating viewpoint. The transition from axisymmetric to non-axisymmetric flow due to the baroclinic instability is characterized by using two non-dimensional numbers, the thermal Rossby number (Ro T ) and the Taylor number (Ta)