Residual Stresses of Czochralski-Grown Crystal

Abstract

The residual stresses in a Czochralski-grown crystal during and after pulling are obtained analytically by using a linear isotropic thermoelastic model. It is assumed that the physical properties of crystal are independent of temperature and that the crystal has a semi-infinite cylindrical shape as it is withdrawn from a melt with a constant pulling rate. Moreover the problem is considered to be a quasi-stationary one. Numerical results show that the Biot number is a prime factor affecting the residual stress and that the maximum residual stress occurs at the cylindrical surface when the Biot number is small and at the center of the crystal when it is large, respectively. An explanation for the experimental results is given.