Oleg A. Louchev

The morphological stability in supercritical fluid chemical deposition of films near the critical point

Abstract In this paper, the results of experimental and theoretical studies of the chemical deposition of copper films from metalorganic compounds dissolved in supercritical C 2 F 6 are reported. The optimal conditions for the growth of highly adherent Cu films with good surface morphology have been determined. A theoretical analysis of the kinetics, the stability of the growth interface together with the transport phenomena inside the supercritical cell shows that the morphological stability is determined by the interplay of three factors. These are the bulk diffusion near the interface, the thermally activated kinetics, and the heat transfer across the deposited layer. It is shown that the morphological stability of the grown film is ensured by an enhanced turbulent convection occurring if the operation pressure and temperature are close enough to the critical point.

Diffusion, heat transfer, equilibrium molecular density and kinetic mechanism of morphological instability in physical vapor deposition

Abstract The growth interface stability in physical vapor deposition processes has been investigated. It is shown that in addition to (i) the gradient of the deposited substance in front of the growth interface, there are other reasons of the destabilization: (ii) the dependence of the kinetic coefficient on temperature, (iii) the dependence of the equilibrium molecular density (pressure) of the depositing substance on temperature and (iv) the temperature gradient across the deposited layer associated with the released sublimation heat and applied heat transfer conditions. The stability of the interface is shown to be determined by the interplay of these four effects together with the surface free energy depending on the local curvature. The breakdown of the morphological stability of the interface is shown to be possible even under a zero gradient of the molecular density of the deposited substance due to the interplay of kinetic coefficient and equilibrium molecular density perturbed in a temperature gradient. It is shown that the following transitions of growth modes can occur with increase of the layer thickness: (i) instability/stability, (ii) stability/instability and (iii) instability/stability/instability.

The influence of radiative heat transfer on the limit pull rate in Czochralski crystal growth of silicon

Abstract In this paper the results of an analytical study of the influence of the radiative heat transfer on the limit pull rate in Czochralski process are reported. An analysis of the contribution of the radiative heat transfer components shows that the limit pull rate depends non-monotonically on the effective temperature for radiation and, hence, at some temperature the limit pull rate has a maximum. For Czochralski crystal growth of silicon, the limit pull rate is shown to have the maximum when the effective temperature for radiation is within the 500–650 K range — depending on the convective heat transfer on the crystal surface. For commercially used apparatus, this temperature is evaluated to be about 1300 K. The most considerable contributions to this temperature are made by the radiative flux from the melt and crucible surfaces. The increase of the limit pull rate is possible (up to 50%) if the surface of the growing crystal can be protected from these surfaces, for example, by means of a special cooler installed around the crystal and kept at 500–650 K.

Radiative / conductive heat transfer mechanism of the limitation in α-HgI2 crystal vapor growth

Abstract An analytic study of the radiative / conductive heat transfer in α-HgI 2 crystal growth is performed. The considered model shows that the radiative / conductive limitation of the crystal size takes place in an large-diameter apparatus in which the IR radiation surrounding the growth surface may be larger than that on the source surface. However, the calculations performed show that this limitation can be eliminated in crystal growth by appropriate adjustment of the temperatures at ampoule walls.

The influence of natural convection on the formation of a molten zone under optical heating

Abstract The results of an experimental study of the formation of the molten zone in zone melting under optical heating are reported. It is shown that the molten zone enlarges symmetrically along with the incident heating flux increase only if the corresponding Rayleigh number Ra 103, the symmetry is destroyed. Namely, the molten zone extends only in the upward direction due to the loop of natural convection flow induced by the optical heating. It is shown that the convective stirring developed inside the melt leads to a linear increase of the total zone height along with an increase of the optical flux incident on the specimen.

Onset of supercooling in front of the solidification interface in zone melting materials processing

Abstract An analytical model of heat and mass transfer of zone melting materials processing for thermally thin bodies (Bi≪1) is developed. The influence of pull rate increase is considered with the aim to determine the onset of the melt supercooling in front of the solidification interface. It is shown that an increase of the pull rate leads to a displacement of the melt zone in the pull direction. As a consequence, the solidification interface gets out of the heating zone together with the adjacent melt layer. The heat transfer on the lateral surface leads to the cooling of this melt layer. This effect together with the conductive heat transfer and latent heat release leads to the onset of thermal supercooling in front of the solidification interface. The same effect, together with the segregation of solute, leads to the onset of the constitutional supercooling. Finally, analytical expressions for the threshold pull rates for the onset of thermal and constitutional supercooling are obtained. These expressions include the parameters of the heat and mass transfer and of the phase diagram involved in the process.

The incorporation of convection in 1D models of float zone and traveling solvent techniques

Abstract In the present paper we develop an analytically solvable 1D model of the thermal regime of float zone and traveling solvent zone processes with the incorporation of the convective transport to heat transfer inside the molten zone and with account of the dependence of the temperature of the solid/liquid transition on the melt composition. We consider two limiting cases of convective transport: (i) natural convection and (ii) thermocapillar, so-called Marangoni convection. The model matches well with two different sets of numerical simulation data. The calculations are carried out for the specific case of the float zone of LaB6 and the float zone traveling solvent technique of LaB6 in an excess of La as a solvent. The calculations show that convection transport plays a crucial role in the formation of the temperature regime in the melt. The Marangoni convection is important for the heat transfer in a molten zone of any height while the natural convection is important when the zone height becomes large enough. It is shown that the excess of La leads to a strong decrease of (i) the melting temperature, (ii) the heating power necessary to form the zone of a given height and (iii) the maximal temperature inside the melt.

The influence of solid phase conductive resistance on vapor growth of α-HgI2 crystals

The influence of the conductive heat resistance on the vapor growth of α-HgI2 crystals is studied in the steady-state one-dimensional approximation. It is shown that the conductive heat resistance leads to an increase of the temperature at the growth interface only under kinetic control of growth rate. Under mass transfer control, the increase of conductive heat resistance is offset by the sharp decrease of (i) growth rate and, as a consequence, (ii) released sublimation heat. Thus, the temperature at the growth interface does not change noticeably after onset of mass transfer control. It is shown that the temperature correction technique is only effective under kinetic control.

Thermal effects and kinetics in step-flow crystal growth of α-HgI2

Abstract In the present paper a step-flow problem accounting for adsorption and sublimation heat releases coupled with conductive heat transfer into the substrate is considered for the {110} vicinal face of α-HgI 2 crystal vapor growth. The crystal growth of α-HgI 2 on the {110} face proceeds under the combined control of (i) a high coverage factor (∼ 0.75−0.95), (ii) surface diffusion, (iii) thermally activated incorporation kinetics and (iv) thermal effects of adsorption and incorporation heats released in the vicinity of the steps coupled with conductive heat transfer through the growing crystal. It is shown that the sequence of steps moving across the crystal face produces a sequence of temperature waves with the amplitudes of 0.04 to 0.06 K. When the crystal thickness is small enough (less than ∼ 300 μm), the temperature fields of neighboring steps do not interfere, thus the steps are thermally isolated. However, when the crystal thickness is sufficiently large, the temperature field on the terraces becomes the superposition of thermal effects resulting from the whole sequence of steps.