Calculation of band alignments and quantum confinement effects in zero- and one-dimensional pseudomorphic structures

The strain field distributions and band lineups of zero-dimensional and one-dimensional strained pseudomorphic semiconductor particles inside a three-dimensional matrix of another semiconductor have been studied. The resulting strain in the particle and the matrix leads to band alignments considerably different from that in the conventional two-dimensional (2D) pseudomorphic growth case. The models are first applied to an ideal spherical and cylindrical ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ particle in a large Si matrix. In contrast to the 2D case, the band alignments for both structures are predicted to be strongly type II, where the conduction-band edge and the valence-band edge of the Si matrix are both significantly lower than those in the ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ inclusion, respectively. Band lineups and the lowest electron–heavy-hole transition energies of a pseudomorphic V-groove ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ quantum wire inside a large Si matrix have been calculated numerically for different size structures. The photoluminescence energies of a large ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ V-groove structure on Si will be lower than those of conventional 2D strained ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ for similar Ge contents.