Some Considerations on Energy Levels of Quantum Cascade Lasers

Conduction band non-parabolicity is taken into account and a numerical method is proposed to calculate the electron subband energy levels and corresponding wave functions in the active region of quantum cascade lasers. For a coupled double-well vertical transition mode active region, the calculated ΔE₂₁ = 32 meV, ΔE₃₂ = 270 meV correspond, respectively, to the energy of an optical phonon and that of a photon at wavelength λ = 4.5μm. For a coupled triple-well vertical transition active region, the calculated ΔE₂₁ = 32.4meV, ΔE₃₂= 250meV correspond to the energy of an optical phonon and the photon energy at wavelength λ= 5.0 μm.