Strain effect in a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-\mathrm{I}\mathrm{n}}_{0.25}{\mathrm{Ga}}_{0.75}{\mathrm{A}\mathrm{s}-\mathrm{A}\mathrm{l}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{As}$ asymmetric quantum wire

We report a theoretical investigation of the strain effects on the electronic energy band in a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-\mathrm{I}\mathrm{n}}_{0.25}{\mathrm{Ga}}_{0.75}{\mathrm{A}\mathrm{s}-\mathrm{A}\mathrm{l}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{As}$ asymmetric quantum wire formed in a V-grooved substrate. Our model is based on the ${\mathrm{sp}}^3{s}^{*}$ tight-binding model. It includes different spatial distributions of the lattice-mismatch-induced strain. We solve numerically the tight-binding Hamiltonian through the local Green’s function from which the electronic local density of states (LDOS) is obtained. The detailed energy band structure (discrete localized states and energy bands of extended states) and the spatial distribution of the eigenfunctions (wave function amplitude of nondegenerate states or sum of the wave function amplitudes of degenerate states) are directly reflected in the LDOS. Spatial mapping of the LDOS’s shows a reduction of the lowest excitation energies in different regions of the system when the local lattice structure of the ${\mathrm{In}}_{0.25}{\mathrm{Ga}}_{0.75}\mathrm{As}$ layer relaxes from completely strained to completely relaxed. By comparing the calculated results with photoluminescence measurement data, we conclude that the strain in the ${\mathrm{In}}_{0.25}{\mathrm{Ga}}_{0.75}\mathrm{As}$ layer relaxes linearly from the heterointerface with the ${\mathrm{Al}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{As}$ buffer layer to the heterointerface with the top GaAs layer.