Photoionization spectrum in double-barrier quantum wells: Exact expansion over resonances and natural line shape

The photoionization spectrum of a double-barrier quantum well is resolved exactly as a sum of independent (but in general overlapping) resonance contributions. Each contribution to the photoionization cross section is a naturally asymmetric band whose maximum is blue-shifted with respect to the quasienergy. In practice, the method amounts to the replacement of the normalized Lorentzian in the linear absorption coefficient by a sum of a Lorentzian and a dispersive curve, all whose parameters are fixed by the model. We give a simple algorithm for the calculation of these contributions and illustrate our results with numerical examples for ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}/\mathrm{GaAs}$ quantum wells typically used as infrared detectors.