Scaling laws and minimum threshold currents for quantum-confined semiconductor lasers

Basic scaling laws are derived for bulk, two-dimensional (quantum well) and one-dimensional (quantum wire) semiconductor lasers. Starting from quantum derivation of the optical properties of confined carriers, the dimensional dependencies of the scaling laws are made explicit. Threshold currents of ∼100 and 2–3 μA are predicted for single quantum well and quantum wire lasers, respectively. The basic considerations of this analysis were used recently to obtain ultralow threshold quantum well lasers [P. L. Derry, A. Yariv, K. Lau, N. Bar-Chaim, K. Lee, and J. Rosenberg, Appl. Phys. Lett. 50, 1773 (1987)].