STRESSES IN STRAINED GESI STRIPES AND QUANTUM STRUCTURES - CALCULATION USING THE FINITE-ELEMENT METHOD AND DETERMINATION USING MICRO-RAMAN AND OTHER MEASUREMENTS

Stresses in heterostructures containing lattice mismatched GeSi stripe s (of half-width l and thickness h) deposited on Si substrates are cal culated using the finite element (FE) method. It is shown that the str ess distribution is a unique function of l/h, it does not depend on I and h separately or on the substrate dimensions if the substrate dimen sions are sufficiently large. Ratio E(E) = E(f)/E(s) of the Young's mo duli (E(f) is the Young's modulus of the stripe and E(s) is the Young' s modulus of the substrate) changes from 0.78 for Ge/Si to nearly 1 wh en the Ge fraction in the layer is small. The effect of this change on the stress distribution is calculated and is found to be small but no t negligible. Stress distribution in the surface layer of the stripe i s a weak function of R(E). Therefore values of stresses given in this paper can also be used for GaAs-based heterostructures. Analytical mod els are not capable of giving accurate values of the stresses in these structures. These values show that as h increases and I is kept const ant, stress at a constant height z in the stripe decreases and at a co nstant depth z in the substrate increases, first rapidly and then slow ly. It saturates and becomes practically constant for l/h < 0.5. Finit e element calculations of circular mesas (quantum dots) are also repor ted. Experimental values of stresses in stripes, quantum wires and qua ntum dots are found to be in good agreement with the values calculated by the FE method.