Comparison of impurity induced disordering potential profiles

The effect of the different functions, used to describe the potential profile of a disordered quantum well structure, on its electronic dispersion relations, has been investigated. The error function, and the hyperbolic secant function, have been applied to the envelope function approximation. The results obtained suggest that the hyperbolic secant profile is a valid approximation of the error function only for long annealing times. Comparison with results obtained from analytic calculations of the effective mass equations, for the hyperbolic secant profile, show that their validity is restricted to bandgap calculations for long annealing times and not for calculations of optical properties.<
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