Subband structures and exciton and impurity states in V-shaped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-\mathrm{G}\mathrm{a}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum wires

The subband structures and exciton and impurity states in V-shaped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-\mathrm{G}\mathrm{a}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum wires (V-QWRs) are investigated by a coordinate transformation method with a variational procedure. The results show that the subband gaps are proportional to the curvature of V-shaped boundaries. Some “forbidden” transitions between electrons and heavy holes are found, due to lack of the inversion symmetry for V-QWRs. The exciton binding energies are different for different exciton transitions depending on the localization of exciton states. The theoretical exciton peaks are in good agreement with the recent experimental photoluminescence excitation (PLE) spectra [Phys. Rev. Lett. 78, 1580 (1997)]. The results also show that there is an asymmetrical distribution of impurity binding energy along the direction normal to the V-shaped boundaries. The impurity position corresponding to maximum binding energy deviates from the center, depending on the dimension and curvature of V-QWRs. The variation in impurity binding energy with impurity position is discussed.