Band Variations Caused by Strain Effects for Quantum Wires With Arbitrary Orientations

We develop a 2-D continuum elasticity model to study semiconductor band variations caused by strain effects for quantum wires (QWRs) with arbitrary orientations on the (001) plane. The model is implemented by the finite-element method, considering the anisotropic properties of semiconductor crystals and the geometric shapes of QWRs. Using this model, we systematically investigate the changes of band profiles and band gaps as the orientation of an InAs/GaAs QWR varies. We find that band energy deformations due to hydrostatic strain, biaxial strain, and piezoelectric effects are all orientation dependent. In particular, the piezoelectric energy changed dramatically with the orientation. These effects, in turn, cause the bandgap to be orientation dependent. The QWR along [100] or [010] has the minimum bandgap; and the QWR along the [110] or [11̅0] direction has the largest bandgap. For some cases, such as the triangle-based QWR, the bandgap change can be significant; and the heavy-hole and light-hole bands may cross or even flip at certain orientations. We also observe that the bandgap profile or pattern inside the QWRs is not sensitive to the orientation. For cylindrical QWRs, the bandgap is uniform, but for the triangle-based QWR, the bandgap has strong location dependence.