Optical gain characteristics of quantum well heterostructure lasers are investigated in a broad range from a weakly quantized system to a strongly quantized one utilizing the band-to-band model with

selection rule, the detailed band structure of the quantum well heterostructures, and degenerate statistics. The results are compared to the experimentally observed threshold current densities in graded barrier single quantum well lasers. It is found that the threshold current densities of these quantum well lasers are well explained by the theoretical results in the range of well width from 75 to 300 Å. The lowest threshold current density observed is 245 A/cm
2in a heavily doped 100 Å single quantum well laser with a 150μm stripe width and 550μm length.