Elasticity Studies of the Critical Thickness of an Epilayer Deposited on a Substrate with Finite or Infinite Thickness

The present work studies the critical thickness of an epilayer on a substrate with a finite or infinite thickness using both superposition and Fourier transformation. For the substrate with an infinite thickness we focus on the effects of the difference in elastic constants between the epilayer and the substrate. A closed formula determining the critical thickness is derived from isotropic elasticity study. The results show that it is easier to form a misfit dislocation in the interface if the substrate is softer than the epilayer, and consequently the critical thickness is smaller. For a substrate with a finite thickness, isotropic elasticity is adopted to investigate the critical thickness of an epilayer on a compliant substrate with the semiconductor-on-insulator configuration. The sliding boundary condition is assumed along the interface between the thin crystal substrate and the amorphous insulator layer where elastic constants differ from those of the crystal substrate. The results show that the thinner the crystal substrate, the thicker the epilayer, and the softer the amorphous insulator layer, the thicker the epilayer. This phenomenon becomes more significant when the mismatch is smaller than 1.2%