The Effect of Barrier Height on the Design of GaAs/Al_xGa_1-xAs Quantum Cascade Lasers

We develop and present guidelines for selecting an optimal barrier height and alloy composition, i.e. the mole fraction x in GaAs/Al_xGa_1-xAs, for Quantum Cascade (QC) lasers. We investigate the effect of barrier height on the figure-of-merit (FOM), which is proportional to the laser gain. In a two-level system, we present a maximum FOM which occurs at x = 0.17. This maximum occurs at zero applied electric field, an energy difference between the first excited and ground states (E₂₁) of 78.2 meV, barrier widths of 200 Å, and a well width of 100 Å. Then, we vary both x and the well width of the two-level such that E₂₁ = 100 ± 2 meV is held constant. The minimum x needed to produce an energy difference E₂₁ of 100 meV is x = 0.15 with a corresponding well width of 64 Å. The maximum FOM occurs at this x value. Most importantly, we investigate the optimal barrier height for a three-level system, the fundamental building block for a laser. We adjust x, the well widths, and inner barrier width so we have the two-coupled QW system needed to achieve this three-level system. Additionally, we adjust these values such that the energy difference between the second and first excited state, E₃₂ = 100 ± 2 meV, and E₂₁ = 40 ± 1 meV are constant, as would be required for most laser applications. The optimum parameters to achieve these energy differences are: x = 0.19, well widths of 60 Å, and an inner barrier width of 10 Å. The maximum FOM for E₃₂ of 510 ps Ų, or 112872.3 ps meV Ų, also occurs at x = 0.19. This FOM corresponds to a maximum gain of 36.4 cm/kA, a sizeable gain for QC lasers. Therefore, we found an optimal barrier height of x = 0.19 for a three-level system for a laser omitting photons of 100 meV. This value is almost 50% smaller than the optimal barrier height reported in earlier literature [1] that primarily relied on experimental trial-and-error or temperature considerations. As a result, future QC laser design needs to include x as a critical design parameter.