Stresses in strained GeSi stripes: Calculation and determination from Raman measurements

Three mechanisms by which edges induce stress relaxation in GeSi strained stripes are described and their relative importance is discussed. Relaxation of stresses in the middle of the layers with l/h(=half-width/thickness) varying from 3 to 100 is calculated including the effect of the two mechanisms which are important in this range. The values calculated in this manner agree with our recent finite element calculations. Since the stresses in the stripes in the two orthogonal directions are not equal and since the stripes are usually grown in the [110] direction on a (100) substrate, determination of stress and strain using Raman measurements is not straightforward. A relation between the shifts Δ${\mathrm{\omega }}_3$ in the LO Raman frequency and stresses and strains in the stripe is established. With the help of this relation, a single measurement of Δ${\mathrm{\omega }}_3$ is sufficient to determine all the stresses and strains in the middle of the top layer of the stripe. Using recently measured values of Δ${\mathrm{\omega }}_3$ and known values of phonon deformation potentials, stresses in ${\mathrm{Ge}}_{0.14}$ ${\mathrm{Si}}_{0.86}$ stripes are determined. The values determined in this manner agree with the calculated values within the uncertainty in the available values of deformation potentials. The method developed is general and can be used for other semiconductor stripes irrespective of whether the strain is thermal or due to lattice mismatch.