The direction of growth of the surface of a crystal in contact with its melt

Revisiting the constant growth angle: Estimation and verification via rigorous thermal modeling

“…Measurements belonging to this last type are especially appealing due to their simplicity and reported relative high accuracy. Examples include Surek and Charmer's [9] analysis of radially frozen zones in single crystalline wafers, Antonov and Selin's [10] elegant diagnosis of cone angles associated with directional solidification of small drops of semiconductor materials, and Satunkin's [11] discussion of different approaches to the determination of the growth angle using the same type of solidified drops.…”

Crystal Shape Stability in Meniscus-Controlled Growth Processes

“…The data points represent average values of 10 separate experiments each using {t11} orientation silicon and germanium wafers, respectively. The results encompass crystal growth rates which vary by nearly two orders of magnitude (from ....,0.002 cm S-l to ..... 0.09 cm S-l), a factor of two variation in water thickness, and various initial meniscus profiles [12,13].…”

“…Then, from eq. (5), we obtain (11) where the phase factor E is given by (12) The complete solution for the time dependence of the fluctuation in the crystal dimension is, of course, given by the sum of eqs. (10) and (11).…”

Crystal Growth: Substructure and Recrystallization

“…The reason is that the crystallization rate never coincides with the growth rate (or the rate of the EB gun displacement). In fact, the crystallization rate affects significantly the hydrodynamic processes developing in the liquid zone (Kobayashi, 1970;Kobayashi & Wilcox, 1982;Murphy, 1987;Surek & Chalmers, 1975). These processes give rise to oscillations in the growth rate; moreover, the instantaneous crystallization rate in these moments of time can be significantly greater than the cooling rate, as shown by estimates for molybdenum and tungsten.…”