Cryst. Res. Technol. 44, No. 10, 1101 – 1108 (2009) / DOI 10.1002/crat.200900435
© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Solutocapillary convection in germanium-silicon melts
A. Cröll*, A. Mitric, O. Aniol, S. Schütt, and P. Simon
Kristallographie, Institut für Geowissenschaften, University of Freiburg, Hermann-Herder-Str. 5, 79104
Freiburg, Germany
Received 20 July 2009, accepted 28 August 2009
Published online 25 September 2009
Key words germanium-silicon, Marangoni, solutocapillary convection.
PACS 47.55.nb, 47.55.pf, 81.05.Cy, 81.10.Mx
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 65
th
birthday
© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction
In crystal growth, free liquid surfaces are encountered in a variety of important melt growth or high-
temperature solution growth configurations, including Czochralski and top-seeded solution growth, the
horizontal Bridgman method, and the float-zone process. Heat and mass transfer in such systems are always
subject to the influence of surface tension (Marangoni) effects [1]. Microgravity (µg)- and ground-based
experiments as well as numerical simulations have shown that the impact on segregation can be quite
substantial [2-6]. The temperature dependence of the surface tension was so far the main contribution
considered, and this type of Marangoni effect is therefore defined as thermocapillary convection. However,
there are other contributions that influence the surface tension, especially its dependence on concentration.
This is called soluto- or chemocapillary convection.
Solutocapillary effects are mostly neglected in crystal growth, often due to a lack of data, although its
importance was predicted more than 20 years ago [7]. Just a few investigations point out that the impact of
solutocapillary convection on segregation can be of the same order of magnitude or even larger than that of
thermocapillary convection, especially for crystals of mixed composition or grown from nonstoichiometric
melts. As an example, in the solidification of steel solutocapillary convection can be a strong force [8]. Some
segregation effects now attributed to thermocapillary convection or other sources may actually be caused by
solutocapillary convection. Solutocapillary convection has been demonstrated in a few experiments with model
substances and metals [7-14] as well as numerical simulations [15-18]. Only very recently have semiconductor
experiments been reported that point directly to solutocapillary convection as a source of segregation [19-21].
These were done in the GaSb-InSb system [20, 21], and in the Ge-Si system [19].
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* Corresponding author: e-mail: arne.croell@krist.uni-freiburg.de