SILICON SINGLE CRYSTAL PULLING CONDITION CALCULATION PROGRAM, SILICON SINGLE CRYSTAL HOT ZONE IMPROVEMENT METHOD, AND SILICON SINGLE CRYSTAL GROWING METHOD

摘要

A pulling condition calculation program enables a computer to perform the steps of: setting a plurality of sets of pulling conditions based on solid-liquid interface height and distance between a surface of a silicon melt and a heat shield plate; performing, for each set of the pulling conditions, the steps of: calculating a heat flux (q) (W/m²) and a crystal surface temperature (T); defining a reference temperature (Tref) given by an equation (1) below and a geometry of the solid-liquid interface as boundary conditions,recalculating an in-crystal temperature distribution; calculating a mean stress in the monocrystalline silicon; calculating a defect distribution in a pulling direction based on the mean stress and the in-crystal temperature distribution; determining a defect-free region in the pulling direction; and drawing a contour line showing a dimension of the defect-free region on a two-dimensional map defined by the distance and the solid-liquid interface height.; $$ \begin{array}{cc}\mathrm{Tref}=\sqrt[4]{T^4-\frac{q}{\mathrm{\varepsilon \sigma }}}& \left(1\right)\end{array}$$