Effect of elastic constants on the stresses in stripes and substrates: a 2D FE calculation

We report results of the finite element (FE) calculations of strains and stresses in stripe-substrate (S-S) heterostructures for several values of Young's moduli (E-t for the stripe and E-s for the substrate), stripe halfwidth l and its thickness h. The normalized stress sigma(xx)/sigma(0) (ob is the stress in the large area layer where effect of edge induced relaxation is absent) in both the stripe and the substrate depends only on the ratio R-E = E-f/E-s and not on the individual values of E-f and E-s. Numerical values of sigma(xx)/sigma(0) are calculated by the FE method for nine values of l/h and five values of R-E. It is found that R-E has only a weak influence on the stress distribution. sigma(xx)/sigma(0) in both the stripes and the substrates decreases monotonically and approximately linearly as RE increases. The values reported in this paper can be used for other values of R-E, l and h by interpolation without the need of making fresh FE calculations for each case. Experimental values of the stresses determined from the luminescence and the micro-Raman data support strongly the conclusion that the dependence of stress on R-E is weak.