Films Stabilized by Long-Range Forces
Original entry by Hyerim Hwang, AP 226, Spring 2012.
Zhigang Suo and Zhenyu Zhang, "Epitaxial Films Stabilzed by Long-Range Forces", Physical Review B 1998 58, 5116-5120
Stability of an epitaxial film on a substrate of a different material is determined by the competition between surface tension and stress. This paper presents that thermodynamic driving forces of different physical origins which act over longer ranges than atomic length, can be strong. It shows that dispersion forces compete with the stress in thin films and the electrons in a metal film mediates a long-ranged force which can stabilize metal films of atomic layers.
Figure 1 illustrates a film thickness on a semi-infinite substrate. The surface tension of the film is taken to be isotropic and the stress in the film results from the difference of the film and the substrate. The model is based on a stability analysis.
All energies are computed for one period of the system, per unit thickness in the direction normal to the plane, to the leading order in the perturbation amplitude. We can know that the perturbation increases the surface energy and elastic energy stored in the system decreases when the surface undulates.
Long-range force effects should be included, as described by the interaction energy W(D) between the surface of the film and the film-substrate interface. Following expression is the change in the interaction energy associated with the surface undulation and it is reasonable when the wavelength of the perturbation is larger than the film thickness and the amplitude of the perturbation is small.
The first specific type of long-range force this paper considers is the dispersion force. In a system with many particles, the fluctuations in the polarization of one particle correlate, via electromagnetic waves, which gives rise to the dispersion dispersion force. In figure 2, first one describes the case when two identical media interact across a film of another medium the dispersion force is attractive. For the second figure, the dispersion force can be either attractive or repulsive when two dissimilar media interact across a film of a third medium. Furthermore, this research considers the effects of the stress and surface tension as shown in figure 3, which were ignored by the previous works.
We can know from this paper that long-range interactions can stabilize epitaxial films against stress. Dispersion forces can compete with the stress in thin films. We can know the dependence of the transition thickness on stress in the presence of the long-range forces.