Transition to one-dimensional behavior in the optical absorption of quantum-well wires

We calculate the optical absorption of quantum-well wires for a large variety of wire widths, taking into account Coulomb interaction, unequal electron and hole effective masses, and continuum states. A transition from a two-dimensional semiconductor to a one-dimensional semiconductor is observed as the wire width is reduced. Absorption lines that are forbidden in the free-particle case appear as a result of Coulomb coupling. By comparison of different effective-mass ratios, we rigorously show that the dominant lines are related to the center-of-mass motion of excitons. The Influence of a finite length and a finite thickness is studied. The one-subband approximation is found to correctly describe the extreme one-dimensional limit. A comparison with realistic dimensions, however, demonstrates the shortcoming of that approximation for quantitative predictions.