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We have developed a very general and a powerful formalism to calculate the linewidths of excitonic transitions in semiconductor quantum well structures with arbitrary potential profiles in the presence of applied electric and magnetic fields. We assume that at low temperatures the dominant mechanism responsible for line broadening is the interface roughness which is always present even in the so called "perfect" samples. We have calculated the variation of the linewidth of the heavy-hole exciton (σ) as a function of well size and magnetic and electric fields in GaAs-Al0.3Ga0.7As based quantum well structures with three different potential well profiles, namely, rectangular, parabolic, and asymmetric triangular. We find that for a given value of the magnetic field the value of σ increases as the well width is reduced, in all three different structures. For well sizes larger than about 100 A°, the value of σ is the highest in the triangular wells and lowest in the rectangular wells. However, for well width less than 100 A°, the value of σ falls below those in rectangular or panbolic wells. Also, for a given value of the well size the value of σ increases with the magnetic field in all three different quantum well stmctures. It should be pointed out that our values of the excitonic linewidths are the lowest possible in these structures

A quantum statistical theory of excitonic linewidth in semiconductor quantum well structures