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Impurity microsegregation due to periodic changes in the temperature and pulling rate of crystal grown by the Stepanov method

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Abstract

A mathematical model is proposed to describe the behavior of a doping impurity concentration in a crystal grown by the Stepanov method from a melt and subjected to periodic changes in its pulling rate and temperature of the thermal node. Various modes of these effects are discussed. The results obtained are given by graphs that characterize their influence on concentration distribution.

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Abbreviations

V :

pulling rate of the crystal

V c :

crystallization rate

V l :

velocity of melt motion

h(t) :

position of the crystallization front at the timet

H(t) :

dimensionless height of the crystallization front

l 0 :

initial length of the crystal

R(t) :

crystal radius

k j (j=l, s) :

thermal conductivities of the melt and the crystal

c pj (j=l, s) :

specific heats of the melt and the crystal

ρ j (j=l,s):

densities of the melt and the crystal

ΔH f :

latent heat of melting

ε0 :

angle of growth

σ:

coefficient of surface tension

T m :

melting point

T j (j=l, s) :

temperatures of the melt and the crystal

T 0 :

temperature of the melt at the shaper outlet at the initial moment of time

l * :

length of the capillary channel

C l :

impurity concentration in the melt,k 0, coefficient of impurity distribution

b :

radius of the capillary channel

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Authors
  1. A. V. Zhdanov
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  2. L. P. Nikolaeva
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  3. B. S. Red'kin
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Additional information

Institute of Solid-State Physics, Russian Academy of Sciences, Chernogolovka, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 486–493, May–June, 1995.

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Zhdanov, A.V., Nikolaeva, L.P. & Red'kin, B.S. Impurity microsegregation due to periodic changes in the temperature and pulling rate of crystal grown by the Stepanov method. J Eng Phys Thermophys 68, 419–426 (1995). https://doi.org/10.1007/BF00859059

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  • DOI: https://doi.org/10.1007/BF00859059

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