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

By G. Müller (auth.)

1 The content material ofthis article is predicated on a German publication model ) which seemed on the finish of the 12 months 1986. the writer attempted to include - so far as attainable - new vital 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 should still make allowance for any incompleteness, additionally within the case that their vital contributions haven't been pointed out. this is able to for instance carry for difficulties regarding the Czochralski progress. yet specifically for this subject the reader should be refered to the impending quantity of this sequence, which incorporates targeted contributions on "Surface pressure pushed move in Crystal development Melts" through D. Schwabe and on "Convection in Czochralski Melts" by means of M. Mihelcic, W. Uelhoff, H. Wenzl and ok. Wingerath. The coaching of this manuscript has been supported by means of a number of ladies whose assistance is gratefully said via 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 analyzing corrections. additionally the great cooperation with the Springer Verlag, specifically Mrs. Bohlen and with the coping with editor of Crystals, Prof. H. C. Freyhardt, who seriously learn the manuscript, is acknowledged.

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8 . 5 solidified fraction g 57 Avoidance of Macroscopic Inhomogeneity Therefore, the remaining alternative is an increase of Oe, which means a reduction of the convective material transport. This finding has already been given in the monography of Pfann68 ) and is plotted for a typical example in Fig. 47. The concentration profile of curve a) corresponds to the case of pure diffusive material transport of Fig. 27( e). After the inhomogeneous transient region a relatively homogeneous dopant distribution is obtained when the concentration at the phase boundary becomes CL = CoIk.

Their model has the following essential features: - It describes only the steady state. - The model is one-dimensional and can therefore only describe the impurity distribution along the growth direction (longitudinal segregation). - In the interface a constant value ko of the distribution coefficient is assumed. - Impurity diffusion is not considered in the crystal but only in the melt (with constant value D). - The transport of heat is only included indirectly by a constant translation rate R of the phase boundary.

I / I I J I ! - " ~ "- , \ \ \ \ , 1 1 1 t I ! -" o \ ~ ,, , t ? 5 radius r / I , .... 0 ...... ///--'. - .... \ I "\ \ r r ! , I I f \ \ \ '\ / I \ \ t t . - / ~ I / I j J 1 1 I 1 ! _.. - - . I / I \ \ \. --. 1 J 1 J J 1 I I 1 I t J \ \ l \ I I I I \ \ I I \ \ \ \ \ t 1 \ 1 1 1 1 1 I I I I o I I . \ \ , , \ \ . , , \ I ! 5 radius r 10 >, ...... ~ ...... 'QJ > Fig. 39. 5 and Ra = 5 . lIP in two perpendicular sections: e = 001180° (above), e = 90°1270° (middle). Below: vertical velocity component w in the horizontal midplane82) Inoue84) in Si-melts in a Czochralski puller.

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