Shape-independent scaling of excitonic confinement in realistic quantum wires

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