ANALYTICAL SOLUTION OF THE SUBBANDS AND ABSORPTION-COEFFICIENTS OF ALGAAS-GAAS HYPERBOLIC QUANTUM-WELLS

A hyperbolic function is used to model the carrier confinement potential profile of a disordered Al0.3Ga0.7As-GaAs single quantum well produced by interdiffusion of group III atoms across the well-barrier interfaces. The confined states are determined analytically for the hyperbolic profile and their wavefunctions and energies are shown to compare well with the results obtained numerically using an error function profile. These analytical expressions allow a more convenient way to investigate the physical properties, which are due to the non-linear confinement profile. The subband edge energy in the hyperbolic quantum well is found to increase initially for a small diffusion length and then decreases for larger diffusion lengths. A relaxed selection rule for the allowed transitions is predicted in the case of the hyperbolic quantum well. The absorption coefficient is calculated for different interdiffusion lengths to demonstrate the model. The results show that the first (lowest transition related) absorption peak of the TM polarization has a larger magnitude than does the corresponding peak of the TE polarization, which is in agreement with measurements performed on quantum-well waveguide structures, and a similar trend is observed for the higher-order transitions. The magnitude of the second absorption peak also varies with the amount of interdiffusion in the case of TM polarization.