Interaction of the thermocapillary, thermal and forced convection in the Czochralski-configuration of the silicon crystal growth Jelena Aleksic1, Janusz A. Szymczyk1, Alfred Leder2 1 University of Applied Sciences of Stralsund, Department of Thermofluiddynamics and Turbo Machines, Zur Schwedenschanze 15, 18435 Stralsund, Germany 2 University of Rostock, Department of Mechanics and Shiptechniques, Albert-Einstein-Str.2, 18059 Rostock, Germany Abstract There are three separate systems of thermal and kinematic circuits with the Czochralski crystal growth method: wall heating, rotating and pulling of the melt as well as rotating and pulling of the growing crystal. However, the movement of the crucible with the melt and the crystal itself can be defined as a fourth and fifth system where the heat is discharged. All these conditions cause a very complicated flow that has a big influence on the homogeneity of the growing crystal. It is a great challenge to investigate this flow and to try to determine its influence on the whole process. 1. Introduction The majority of the semiconductor monocrystals used nowadays (ca. 80%) are produced with the Czochralski method. Thermocapillary and forced convection accrue in the melt due to the thermal and kinematic boundary conditions. Thermocapillary effects accrue due thermal, solute or electro-kinetic inhomogeneity on the free liquid surface and/or the boundary layer. The existence of the inhomogeneity leads to a boundary layer movement which at the same time causes an impulse transport due to friction between lower liquid layers. Boundary layers and transport phenomena in themselves and their interaction with thermal convection are from a common interest because of their frequent occurrence in many technical systems. They often accrue in disciplines like metallurgy, crystal growth, physical chemistry, production technologies, glass production and others and give the basis for further investigations. It is also of interest to investigate these phenomena under Microgravity (for example in space laboratories) because it is a chance to explore the buoyancy driven convection separately, without the influence of thermal convection. Beside the widespread elimination of thermal convection, the result of the vanishing hydrostatic pressure and sediment build-up allows the implementation of well directed experiments. Due to limited experimental possibilities under Microgravity, it is of preference that the primary aims of the investigations are derived from day practice, with the effect that such investigations are led by a wide range of Plateau simulations in order to ensure the scientific success of the experiments in space. 2. State of the art Nowadays there is no doubt of interest that thermal and thermocapillary convection play the dominant role in impulse, heat and material transfer in technical processes with boundary layers. Therefore it is not enough just to predict the expectant buoyancy driven convection – but also the interesting and technically relevant exercise of active manipulation of the convection during the course of the process is necessary thereby making it possible to use the convection to optimize the process. Most investigations are of an experimental and theoretical nature. The numerical simu lations of the most widely used semiconductors have already been made. Theoretical experiments are based mostly on the investigation of the boundary layer, instabilities and oscillations of the surface. Szymczyk [11] showed in his experiments from 1992, that the instability of the surface liquid/gas occurs immediately after a radial temperature gradient has been created on the interface of the melt. Bakovetsa [3] and Hintz [6] have shown that the crystal growth meniscus (where the crystal is slightly pulled out from the melt) is often the cause for the appearance of turbulence in the melt. On the other hand this meniscus is ideal for the form, the purity and the grid structure of the growing monocrystal and must not be changed during the growth process.

Many experiments were made to determine the influences of other external components on the growing process. Hashim [5] tested the influence of magnetic fields on the convection in the melt. His numerical calculations showed that the presence of magnetic field leads to oscillatory rather than to stable convection.. Nevertheless, he proved a relative stabilising effect of a magnetic field (compared to no magnetic field) on the surface layer of the fluid. The investigations of the influence of point formed magnets on the crystal growth showed that the configuration with the magnetic field within the melt [8] makes most sense, as this causes the most homogeneous distribution of the oxygen in the crystal. Other experiments showed clearly that adding of dope substances does not lead to abnormal phenomena in the process. By experiments under Microgravity conditions [10], the frequency of the temperature oscillations in the melt was lower in space (ca. 0,1 Hz) then on the earth (0,2 Hz). 3. The experimental equipment The experimental equipment was designet in a way, that it best matches the real Czochralski process (Figure 1). To provide the thermal and kinematic boundary conditions, the experimental equipment allows setting the temperature of the stick, surrounding fluid bath and measuring cubicle bottom. There is also the possibility of heating the upper margin of the experimental fluid, which is considered to be a modification of the real process. In addition, it is possible to rotate the measuring cubicle and the stick independently of each other at variable speed and direction of rotation. Different glycerine-water mixtures and silicone oil are used as experimental fluids. Liquid crystals are put In the experimental fluid. These are little particles which change colour with temperature (and in this way visualise the temperature fields) and they act as tracer for the velocity measurement.

Figure 1: Diagram of the modified Czochralski configuration

4. Optical flow measurement systems Two optical measurement systems are simultaneously used to visualise the temperature and velocity fields (Figure 2). The Particle Image Thermometry (PIT) is used for qualitative determination of the temperature field. In PIT, the lightsheet from the white light source is pictured with the CCD camera. The light source for a 1,5 mm thin lightsheet is a halogen-lamp. The evaluation methods and their software were successfully developed by us. The determination of the velocity field was made using the Particle Image Velocimetry (PIV).

Heat in/output

Heat input

Heating ring

Gas convection

Experimental fluid

Heat in/output

Surrounding bath

Heat in/output

Crucible rotation

Stick rotation

Heat radiation

Stick

Temperature gradient

Fluid/gas Interface

Marangoni convection

Thermal convection

Measuring cubicle

Figure 2: Lightsheetmethod system in the experimental equipment

4.1 Particle Image Thermometry (PIT) The Particle Image Thermometry is based on the property of certain liquid crystals to reflect light in different colours depending on their temperature, the pressure and the observation angles. In our experiments, the pressure and the observation angle is constant so that the color of the liquid crystals only dependes on their temperature. The liquid crystals are characteris ed by their size, start and end temperature and their density. The start temperature, so called Red Start (RS), is the temperature at which the crystals begin to reflect red light. As the temperature increases, the crystals reflect the whole visible band of the white light colour spectrum beginning with red, over yellow, green and blue to violet. When reaching the end of the spectrum, i.e. the end temperature or Colourless (CL), the fluid becomes colourless. The temperature measurement is based on the Red-Green-Blue (RGB) images recorded with the camera. Only knowing this RGB information, there is no explicit correlation between colour and temperature possible because the colour system is three dimensional. To establish this correlation the Hue-Saturation-Intensity (HSI) model for temperature measurement is used. The HSI model is based on twisting the RGB coordinate system and the presentation in cylindrical coordinates. The Hue (coloration) is the pure light colour, i.e. the dominating light colour, which can be seen. It represents the dominant wave length which is directly dependent on the temperature (Figure 3)

Figure 3: Transformation from the RGB to the HSI colour model Thus an explicit correlation between temperature and colour can be established. The Hue is specified as an angle, which in practice lies in the interval [0,255]. In this way the colour red is assigned the Hue value of 0, the colour yellow of 42.5 and the colour blue of 170. The dependence of the Hue on the temperature is strongly non-linear and is described with a calibration curve (Figure 4). The saturation is a measure for the dilution of a colour with white. The intensity is a colour-neutral attribute and describes the relative brightness.

CCD camera

Lens system for producing

laser-lightsheet

Lens system for producing

white-lightsheet

Surrounding bath

Experimental cubicle

Experimental fluid

Quartz-glass windows

Cross-correlation camera

Figure 4: Calibration curve for KXN 2030 liquid crystals (Japan Capsular Products)

The conversion from the RGB to the HSI system can be done using the following formulas. The calibration polynomial is labelled t(h), whereupon t(h) is the temperature as a function of the Hue and an is the polynomial coefficients of the calibration polynomial.

( )

( )BGRIntensity

GBRBRGBGRSaturation

BGBGR

Hue

++=

−−−++=

−⋅−−

=

31

32

arctan21

222

π

01

11

1 ....)( ahanahaht nn

nn +⋅++⋅+⋅= −

−

4.2 Particle Image Velocimetry (PIV) The Particle Image Velocimetry allows contactless laser-based measurement of the flow velocity of the whole field. By generating a lightsheet, which binds the measurement volume, it is possible to visualise the flow process and in this way to calculate the flow velocity. The supposition for this is the transparency of the flow and the existence of tracers. The image analysis begins by splitting the investigated area to in a 2D raster. Onto every raster point one quadratic interrogation spot is placed. A cross-correlation camera, synchronised with the laser, records two digital images of the light reflected from the tracers (liquid crystals) placed in the experimental fluid. These two images show the displacement of the tracers in the time between two laser pulses. In the following step the software splits the two pictures into some small interrogation spots , the size of which depends on several criteria, and after splitting the second image the cross-correlation is done. Thereby the displacement of all tracers in the 2D interrogation spots is calculated and accumulated and the product is an occurrence field with a peak (i.e. a point with very high density) for every interrogation spot. The peak (Figure 5) represents the displacement of the tracers done for every interrogation spot. This distance is specified as a vector for an interrogation spot and indicates the speed of the tracers after dividing by the time between two taken images.

Figure 5: Cross-correlation determination of the velocity field

5. Presentation of the results The images of the velocity and temperature fields were gained and evaluated after setting the different thermal and kinetic boundary conditions. The experiments were made with 100%, 85 % and 75 % glycerine-water mixtures and diverse silicone oils . Different liquid crystals have been used as tracers. The example in Figure 6 shows the influence of forced convection on the flow topography and its interaction with the thermocapillary convection. As an experimental fluid 100% glycerine was used. In both cases the temperature fields are quasi-symmetrical. There is a larger warm area in the upper part of the rotating cubicle, because of the better shuffling of the experimental fluid during the rotation. The velocity field is laminar and rotational-symmetrical in the case of the non-rotating cubicle (Figure 6 A-D). Due to the radial temperature gradient dT/dr on the surface of the fluid between the wall and the middle of the cubicle, a tangential tension appears there, which causes the fluid to move towards the increasing interface tension from the edge to the middle of the cubicle. The flow thus created is transmitted by friction to deeper lying fluid layers. Due to continuity a closed large convection roll will be formed which dominates the whole volume. A swiftly, cold, downward flow (a so called jet) will be formed in the middle of the cubicle and will be reinforced trough thermal convection. Because of the very large Prandtl Number a stationary, stable flow with a stable flow topography will be established. For smaller Prandtl Numbers (Pr=7) and larger cubicle diameters an instability flow can be expected, with a permanently changing flow topography. It has to be proved whether this flow turns in to some other mode and whether it leads to an oscillatory buoyancy driven flow [11]. Because of the very similar Marangoni Numbers, a similar flow topography can be expected for the rotation of the cubicle at law rotation rates. Figure 6 E-H shows an destruction of the flow symmetry, the velocity fields and of the convection rolls of the rotating cubicle. In a numerical article about buoyancy driven convection, Jaszczur und Szmyd [7] showed that the forced flow in a vertical cylindrical vessel with a surface tension gradient is not axial symmetric. To prevent a great deal of destruction of axial symmetry, the cubicle should be turned at lower rotation rates and the temperature gradient between the wall and the crystal should be higher [14]. The rotatory Froude Number (i.e. the quotient of the centrifugal force and the gravity force) of the rotating cubicle is just 3.57⋅10-5..This means that the gravity force in the case of law rotation rates of 1min-1 is significantly more dominating than the centrifugal force. The destruction of the symmetry shows that the centrifugal force at the Czochralski configuration has a bigger influence than expected from the Froude Number. The reason for this is that the buoyancy driven flow dominates the whole volume. The symmetry cannot exist if the rotation influences or destroys the tangential force inducted in this way or the developed boundary layer.

ω=1min-1

A: Configuration schema 8

E: Configuration schema 24

B: Temperature field

F: Temperature field

C: Velocity field G. Velocity field

ω=1min-1 19.5°C 19.5°C

29.5°C 29.5°C

21.3°C 21.3°C

D: Streamlines

H: Streamlines

Mg = 590.9, Pr = 8226.8

No rotation Mg = 540.2, Pr = 8226.8

(Fr)ω = 3.57⋅10-5, (Re)ω = 0.44

Figure 6: Boundary conditions with the appendant temperature and velocity fields, streamlines and the dimensionless numbers

6. Further investigations In the future the topography of the flow and the interaction of the three types of convection, as well as the coupling of the velocity with temperature fields will be investigated. The oscillatory and turbulent Marangoni convection and the phase behaviour of velocity and temperature oscillations will be analysed, too. Moreover we will examine the appearance of the oscillatory and turbulent Marangoni convection for low viscosity fluids. Acknowledgement The authors would like to thank the Ministry of Education, Science and Culture of the Bundesland Mecklenburg-Vorpommern, Germany, for promoting the project, under number: 1704598. The first author wishes to express his thanks to the University of Rostock and the Stralsund Institute for Energy and Environment e.V., Germany, for the financial support. 7. References [1] Aleksic, J., J. A. Szymczyk, A. Leder, T. A. Kowalewski: Experimental Investigations on Thermal,

Thermocapillary and Forced Convection in Czochralski Crystal Growth Configuration, CMEM 2001, 4-6 Juni 2001, Alicante, Spain, Computational Methods and Experimental Measurements X, pp. 627-636, ISBN 1-85312-870-8, WIT Press, 2001

[2] Aleksic, J., P. Zielke, J. A. Szymczyk, A. Delgado: Diagnose des Geschwindigkeits- und Temperaturfeldes in einer Czochralski Simulation, 8. Fachtagung „Lasermethoden in der Strömungsmeßtechnik – neuere Entwicklungen und Anwendungen“ GALA 2000 Tagungsband, 37, ISBN 3-8265-7809-0, Shaker Verlag 2000

[3] Bakovetsa, V. V.: Growth and Wetting Angles as the Control Parameters of Crystal Shape in Czochralski Method, Journal of Crystal Growth 193 ,4, pp. 720-727 ISSN 0022-0248, 1998

[4] Czochralski, J.: Ein neues Verfahren zur Messung der Kristallisationsgeschwindigkeit der Metalle, Z. Physik. Chem. 92, pp. 219-221, 1918

[5] Hashim, I., S. K. Wilson: the effect of a uniform vertical magnetic field on the onset of oscillatory Marangoni convection in a horizontal layer of conducting fluids, Acta Mechanica 132, 129-146, Springer Verlag, 1999

[6] Hintz, P.: Konvektion im Czochralski- Tiegel, Dissertation, I. Physikalisches Institut der Justus-Liebig-Universität Giessen, 1999

[7] Jaszczur, M., J. S. Szmyd: An analysis of buoyancy driven convection in vertical cylinder, Progress in Engineering Heat Transfer, pp. 341-348, IFFM Publishers 1999

[8] Kim, J-S., T-Y. Lee: Numerical study of the ment-thermal effect on a silicon crystal in Cz growth system, Journal of Crystal Growth 209, pp. 55-67 ISSN 0022-0248, 2000

[9] Kobayashi, M.; Tsukada, T.; Hozawa, M.: Effect of Internal Radiative Heat Transfer on Transition of Flow Models in CZ Oxide Melt, Journal of Crystal growth 208, pp. 459-465, 2000

[10] Nakamura, S., T. Hibiya, K. Kakimoto, N. Imaishi, S. Nishizawa, A. Hirata, K. Mukai, S. Yoda, M. S. Morita: Temperature Fluctuation of the Marangoni flow in a liquid bridge of molten silicon under microgravity on board the TR-IA-4 rocket, Journal of Crystal Growth 186, pp. 85-94, ISSN 0022-0248, 1998

[11] Szymczyk, J.A.: Interaction between Thermocapillary and Buoyant driven Convection under Normal Gravity, Exp. In Fluids 12, pp. 151-156, 1992

[12] Szymczyk, J.A., J. Aleksic: Experimentelles Simulationsmodell zur Herstellung eines Silizium – Einkristalls, ZAMM, Z. für Angewandte Math. und Mechanik, zur Publikation eingereicht

[13] Szymczyk, J.A.; Ch.-H. Chun, J. Siekmann, K. Wozniak: Liquid Crystal Tracers as a Method for Thermocapillary Flow Diagnostics, Archives of Mechanics, Vol. 41, 2-3, pp. 351-360, 1989

[14] Yi, K.-W.; Booker, V. B.; Eguchi, M.; Shyo, T.; Kakimoto, K.: Structure of Temperature and Velocity Fields in the Si melt of a Czochralski Crystal Growth System, Journal of Crystal Growth 156, pp. 383-392, 1995