Luminescence kinetics and lifetime of excitons in quantum wells with interface roughness

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Abstract
Excitonic optical spectra in quantum structures are sensitive to fluctuations of the well width (interface roughness). Since it is generally accepted that the exciton luminescence linewidth reflects the interface quality, a reliable theory is highly desirable. A Schrodinger equation for the exciton center-of-mass motion is derived which contains a disordered potential being Gauss distributed and correlated over distances of the exciton Bohr radius. The optical density (OD) as well as the excitonic density of states (DOS) are obtained by numerical methods. The OD determining the absorption lineshape shows a distinct asymmetry and reduced linewidth compared to the underlying potential distribution (motional narrowing). The luminescence lineshape is given by the product of the OD and the distribution function. Using a kinetic equation with generation, recombination, diffusion, and drift we show that at low temperatures the lineshape is determined by topology only as the excitons diffuse to the next local potential minimum before they recombine. Time-dependent simulations following a short broad-band excitation pulse show that the spectrum narrows and shifts to the red, from the absorption towards the topological lineshape.

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