Impact of diameter fluctuations on thermal stresses during Czochralski silicon growth

Variation of crystal radius during the growth process is an inevitable feature of Czochralski crystal growth method. Fluctuation in the system i.e. heating power, pulling rate and melt level perturbs the stability of the growth process during Czochralski silicon growth. Highly uneven topographies are likely to act as concentrators for thermally induced stresses and deformations. This effect has been underestimated and neglected in stress studies and the crystal is assumed perfectly cylindrical. A set of 2D simulation were performed for an axisymmetric crystal with isotropic properties. The crystal boundary is perturbed complying a sinusoidal function. The impact of amplitude and frequency of crystal radius fluctuation on stress field inside the crystal has been studied. Simulation result shows that crystal surface undulation affects both thermal field and stress distribution inside the crystal. Sharp angels and profound perturbation found to generate high stresses at the crystal periphery.