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NASA NTRS2017

Growth Angle: A Microscopic View

A microscopic continuum mechanical model of the growth angle is proposed. It is based on the van der Waals type framework that is used for surface force phenomena. The obtained augmented Laplace type integro-differential equations are, in general, difficult to analyze. Here we focused primarily on the particular case of equal melt and crystal surface energies. We derived an approximate equation for the meniscus shape, and obtained an analytical relationship between the contact and the growth angle. Interestingly, the same result can be obtained using the macroscopic model of Herring. The case of a macroscopically sharp corner is also considered. For this case, the macroscopic angle is not defined and it can be any angle between the contact angles of both flat surfaces. The microscopic model yields the smooth shape for the meniscus that also is not unique, but depends on the initial position of the meniscus.

Mazuruk, Konstantin↗

NASA NTRS1999

Static Magnetic Fields in Semiconductor Floating-Zone Growth

Heat and mass transfer in semiconductor float-zone processing are strongly influenced by convective flows in the zone, originating from sources such as buoyancy convection, thermocapillary (Marangoni) convection, differential rotation, or radio frequency heating. Because semiconductor melts are conducting, flows can be damped by the use of static magnetic fields to influence the interface shape and the segregation of dopants and impurities. An important objective is often the suppression of time-dependent flows and the ensuing dopant striations. In RF-heated Si-FZ - crystals, fields up to O.STesla show some flattening of the interface curvature and a reduction of striation amplitudes. In radiation-heated (small-scale) SI-FZ crystals, fields of 0.2 - 0.5 Tesla already suppress the majority of the dopant striations. The uniformity of the radial segregation is often compromised by using a magnetic field, due to the directional nature of the damping. Transverse fields lead to an asymmetric interface shape and thus require crystal rotation (resulting in rotational dopant striations) to achieve a radially symmetric interface, whereas axial fields introduce a coring effect. A complete suppression of dopant striations and a reduction of the coring to insignificant values, combined with a shift of the axial segregation profile towards a more diffusion-limited case, are possible with axial static fields in excess of 1 Tesla. Strong static magnetic fields, however, can also lead to the appearance of thermoelectromagnetic convection, caused by the interaction of thermoelectric currents with the magnetic field.

Croll, Arne↗