Some general properties of stress-driven surface evolution in a heteroepitaxial thin film structure

Heteroepitaxial thin films are subjected to very large stresses, typically in the giga-Pascal range, due to lattice mismatch. Their applications in microelectronic devices have drawn a growing research effort which involves, in part, a better understanding of the processes by which defects such as cracks and dislocations are nucleated in a thin layer structure. One of the possible defect mechanisms is related to a stress-induced morphological instability which tends to roughen the film surface by mass diffusion during film growth or annealing. A major objective of this paper is to show that a few invariance properties of the strain energy density and the chemical potential in a heteroepitaxial structure can be utilized to obtain some valuable information concerning the equilibrium profile, the stress concentration and the formation of cusp-like stress singularities without having to resort to full-scale numerical studies. The process of cusp-formation requires a critical film thickness Hcr which is independent of the Matthews critical thickness herfor misfit dislocation formation by propagation of threading dislocations within the film. Calculations show that Hcr is significantly larger than hcr for a wide range of misfit strain, suggesting that nucleation of threading dislocations via cusp-formation could be critical in the overall process of strain relaxation in this type of film. Finally, a “phase” diagram is constructed to categorize important consequences of the surface evolution based on the instability wavelength and average film thickness.