Shape-Independent Scaling of Excitonic Confinement in Realistic Quantum Wires

The scaling of exciton binding energy in semiconductor quantum wires is investigated theoretically through a nonvariational, fully three-dimensional approach for a wide set of realistic state-of-the-art structures. We find that in the strong confinement limit the same potential-to-kinetic energy ratio holds for quite different wire cross sections and compositions. As a consequence, a universal (shape- and composition-independent) parameter can be identified that governs the scaling of the binding energy with size. Previous indications that the shape of the wire cross section may have important effects on exciton binding are discussed in the light of the present results.