By G. Müller (auth.)

ISBN-10: 3642732089

ISBN-13: 9783642732089

ISBN-10: 3642732100

ISBN-13: 9783642732102

1 The content material ofthis article is predicated on a German e-book model ) which seemed on the finish of the yr 1986. the writer attempted to include - so far as attainable - new very important effects released within the final yr. however the literature within the box of "convection and inhomogeneities in crystal development from the soften" has elevated loads meanwhile that the reader and the collegues may still make allowance for any incompleteness, additionally within the case that their very important contributions haven't been brought up. this is able to for instance carry for difficulties relating to the Czochralski progress. yet particularly for this subject the reader could be refered to the impending quantity of this sequence, which includes targeted contributions on "Surface rigidity pushed stream in Crystal development Melts" through D. Schwabe and on "Convection in Czochralski Melts" through M. Mihelcic, W. Uelhoff, H. Wenzl and okay. Wingerath. The coaching of this manuscript has been supported by way of numerous girls whose assistance is gratefully stated by way of the autor: Mrs. Gisela Neuner for the sort writing, Mrs. Abigail Sanders, Mrs. Fiona Eels and particularly Prof. Nancy Haegel for his or her assist in questions of the English language and Mrs. Christa Weber for interpreting corrections. additionally the nice cooperation with the Springer Verlag, particularly Mrs. Bohlen and with the dealing with editor of Crystals, Prof. H. C. Freyhardt, who significantly learn the manuscript, is acknowledged.

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Neglecting Vn in Eq. (22) therefore has no consequence. If Y' > (50, however, the concentration profile at the interface is governed by the convective transport. When that is the case 0 in Eq. (19) represents only a fit parameter for the description of experimental results by Eq, (19). 9 ..... l o () C 0 () c 0 ..... 0 1- g Fig. 21. Electron concentration n versus 1 - g (g = solidified fraction) of an S-doped InP crystal grown by the LEe technique in (111) direction69 ) do with the actual extension of the concentration profile Ce • vn now has to be evaluated from solutions of the Navier-Stokes equation, as was done for example in a treatment by Wilson70 ,71) which will be discussed in detail in Sect.

1. 8 1 (periphery) Fig. 50. Sherwood number Sh in dependence of the position across the interface for various strength of the magnetic field (Sh is defined in the caption of Fig. 49)92) strength91 ). Static magnetic fields have been used in crystal growth some years ago to avoid the occurrence of unsteady convection. This will be discussed in detail in Sect. 4. The use of static magnetic fields to avoid macrosegregation by the reduction of flow in steady convection has recently been considered.

C... T~ --:::;;;:o--T... x x Fig. 23. e. e. liquids (rightl 5) 35 Macroscopic Inhomogeneity 1/3 ~ n ~ 1 (25) Sc X Pe -=-=-=Le PeT Pr D Le is called the Lewis number, which represents the ratio of diffusive heat and diffusive particle flux. It is clear from the definition of Le and Eq. (25) that the thermal boundary layer of liquids is extended much further than the range of important changes of the concentration (Fig. 23). By the aid of Eq. (25) conclusions can be made from temperature profiles, 'which are more easily determined experimentally than concentration profiles.

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Crystal Growth from the Melt by G. Müller (auth.)


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