Stresses in selectively grown III-V semiconductor stripes and buried quantum wire lasers: Effect on optical properties

The problem of calculation of stresses in the strained layer stripes is simplified if attention is confined to the middle of the surface layer of the stripes. In this region the vertical component of the stress and the shear components of the stresses and strains are zero and the strain component ε'_yy (parallel to the length of the stripe) is known in the stripe coordinates. Hooke's equation is first solved in the stripe coordinates and the stress and strain components are then transformed into the crystal coordinates. An explicit relation between the stress components and the shift Δω₃ of the LO Raman mode and ΔE of the heavy hole luminescence band is established for different values of the misfit between the substrate and the stripe. The values of the shifts are calculated for thermally strained GaAs/Si and lattice mismatched InxGa_1-xAs/GaAs stripes. For In_xGa_1-xAs/GaAs stripes, the shifts are shown as surface plots in terms of the In concentration X (misfit parameter f_m is proportional to X) and the stress σ'_xx parallel to the width of the stripe. Using experimental values of ΔE and Δω₃, values of σ'_xx can be read directly from these plots. Values of σ'_xx in GaAs/Si and InGaAs/GaAs are determined using the surface plots and the existing experimental data. Finite element (FE) calculations are also made for the stresses in the stripes and the QWs. Values determined from the luminescence and Raman experiments are compared with those calculated by the FE method.