Wetting Angles and Surface Tension in the Crystallization of Thin Liquid Films
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WETTING ANGLES AND SURFACE TENSION FILMS
IN THE CRYSTALLIZATION OF THIN LIQUID
ELI YABLONOVITCH, T. GMITTER Exxon Research and Engineering Company Annandale, New Jersey 08801 ABSTRACT The behaviour of thin liquid films is known to be dominated by surface tension forces. We show that the crystallization of thin liquid films requires that two wetting angle conditions be simultaneously satisfied: (i) relating to the liquid-vapour interface and (ii) relating to the crystal-liquid interface. The balance between capillary pressure and thermal gradient forces shows that the equilibrium freezing point of thin films is actually depressed below the bulk freezing point. The magnitude of the effect is 10 K in an 800 A thick film. These observations suggest that small-scale thickness fluctuations may be responsible for the initiation of sub-grain boundaries in the growth of crystalline silicon films. INTRODUCTION The crystallization of thin liquid silicon films is a promising method1 to produce single crystal films of good electronic quality. These films will have important device applications in radiation hardening, dielectric isolation, high voltage integrated circuits, etc. It is well known that capillary forces, surface tension and wetting play a vital role in the behaviour of thin liquid films. In this article we will derive the wetting angle requirements which permit the crystallization of thin liquid films to proceed. We will see that the success with liquid silicon films encapsulated in silicon dioxide is the result of a particularly fortuitous combination of wetting angles for those two materials. WETTING ANGLE REQUIREMENTS In general there is no assurance that a thin liquid film will be stable. There is the well known tendency for the liquid film to "ball up" and form droplets on the surface of the substrate. The condition for spreading of the liquid film on a substrate is that its wetting angle should be identically zero. Since this is very rare, a different approach is used. We will show that a solid capping layer on the liquid film greatly relaxes this severe wetting angle constraint, and permits wetting under more easily satisfied conditions. For practical stability, the liquid film should spread to fill any possible voids in the film as shown in Fig. 1. Let -Is and ylc be the surface energy (or tension) of the liquid with respect to 1he substrate and capping layer. Let yvs and yvc be the surface energy of the bare substrate and capping layer respectively. The spreading of the liquid film should result in a net reduction of surface energy. Therefore:
Yls + Ylc - (Yvs + Yvc) < 0 2
The Young-Dupre equation for wetting angles; used to simplify inequality (1):
(1)
yvs - yls = Yvlcoso may be
Mat. Res.Soc. Symp. Proc. Vol. 23 (1984) 0Elsevier Science Publishing Co.,Inc.
390
ta)
'isp
,0,{
Growth Drection
LJiquid•
Crystalline
Silicon
Srilcon (b)
FIG.
1:
A vertical cross-section through the thin liquid film. The liquid-vapor wetting angle, 0, is required to provide absolute stability against any voids
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