The Capillarity Influence On Shape Of Small Liquid Inclusions Enclosed In A Solid Under Non-Stationary Thermal Condition
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The Capillarity Influence On Shape Of Small Liquid Inclusions Enclosed In A Solid Under Non-Stationary Thermal Conditions
Vladimir Yu. Gershanov, Sergey I. Garmashov, Andrey R. Minyaev, Nickita E. Ivanov, and Irina Yu. Nosuleva Dept of Physics, Rostov State University, 5 Zorge st., Rostov on Don, RUSSIA ABSTRACT An analytical model taking into account the influence of capillarity on the process of changing the cross-sectional shape of a cylindrical liquid inclusion enclosed in an anisotropic crystal under non-stationary thermal conditions is suggested. It is shown that the capillary effect confines the possibilities for controlling the inclusion shape under non-stationary thermal conditions. The capillarity influence becomes stronger with decreasing cross-sectional area and increasing interfacial energy. The results of calculations of the limit inclusion shape under different thermal conditions are presented and discussed.
INTRODUCTION The migration of discreet liquid inclusions under the action of a temperature gradient through a crystal (the thermomigration process) is of interest as a method of fabrication of threedimensional p-n-junctions and heterostructures within a semiconductor wafer [1,2]. Controlling the liquid inclusion shape which determines the sizes of recrystallized region, it is possible to form geometrically complicated 3D structures. The shape of a liquid inclusion migrating through a crystal is usually considered as a function of the interfacial energy, interface kinetics, and temperature gradient in the liquid [3-5]. From this standpoint, the inclusion shape can be controlled by using the temperature dependence of the interfacial energy, interface kinetics, and the temperature gradient in the liquid. From our point of view, a more effective method for controlling the inclusion shape is the usage of weak temperature oscillations to which interface kinetics is very sensitive [6]. In this case, there is no necessity to change the average temperature of the process or the thermal gradient. The character of changing the inclusion shape is determined by the magnitude and the profile of temperature oscillations [7,8]. The anisotropy of interface kinetics, the non-linearity of the supersaturation dependence of growth velocity and the presence of asymmetric temperature oscillations (when absolute rates of heating and cooling are different) are the conditions of the existence of the shape change effect shown in [8]. It should be noted that the capillary effect is not taken into account within model [8] to demonstrate the possibility of the inclusion shape modification under non-stationary thermal conditions obviously. However, the capillary effect must inhibit a deviation of the inclusion shape from equilibrium. In other words, the model [8] is correct only in the case of small deviation of the inclusion shape from equilibrium, and therefore requires refinement to estimate the limit possibilities of controlling the inclusion shape under non-stationary thermal conditions.
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