Numerical study of silicon crystal ridge growth

Analysis of the geometry of the growth ridges and correlation to the thermal gradient during growth of silicon crystals by the Czochralski-method

“…Actually, the solution of the Young-Laplace equation (see e.g. [11]) can yield a similar shape. Another possible explanation for this shape could be a slight variation of growth velocity in the different crystallographic directions.…”

“…Voronkov [3,9,10] was the first to develop a detailed theoretical understanding for the growth phenomena at the edge facets and the related growth ridges. Later on, Barinovs [11] obtained a simple analytical expression for the geometry of the growth ridge from Voronkovs' theoretical model and implemented it in a numerical algorithm to calculate the size of the growth ridge from known temperature gradients. These theoretical works predict a strong correlation between growth ridge geometry and thermal field.…”

Floating Zone Growth of Silicon

“…However, the calculated quantities can be further used to analyze the processes on micro and atomistic scales [67]. The models are macroscopic, i.e., they consider the material with continuum properties and do not describe the atomistic scale of crystal growth.…”

Three-dimensional modelling of thermal stress in floating zone silicon crystal growth

“…Morphology of the ridges for FZ crystals of 1 1 1 orientation up to 5" diameter has been described and a loss of particular ridge shapes when the crystal dislocates is suggested [11]. Size of the ridge has been theoretically calculated for a 1 0 0 4" Cz crystal depending strongly on the temperature gradient by the crystallization interface at the triple point [12]. The model predicts larger ridge size for a smaller temperature gradient.…”