Thermal strain during Czochralski growth

Abstract An analytical solution has been derived for the description of the stress and strain fields appearing under the inhomogeneous temperature distribution and boundary conditions characteristic to the Czochralski growth of single crystals. The pulled crystal was modelled by an elastic rod of constant radius and semi-infinite length, while its elastic and thermal properties were taken as being independent of temperature. The behaviour of the stress field is discussed both at the growth interface and far from it.