As shown in recent experiments, spectral properties of exciton-polaritons in optical microcavities with an embedded semiconductor quantum well are strongly affected by electron doping of the semiconductor.
Previous theoretical studies concerned with nonzero Fermi-energy mostly relied on the approximation of an immobile valence band hole, which is appropriate for low-mobility samples only. For high-mobility samples, one needs to consider a mobile hole with large but finite mass. We present an analytical diagrammatic approach to tackle this problem for a model with short-ranged (screened) electron-hole interaction, studying it in two complementary regimes. In the first regime, where the Fermi energy is much smaller than the exciton binding energy, excitonic features are enhanced by the finite mass. In the second regime, where the Fermi energy is much larger than the exciton binding energy, finite mass effects cut off the excitonic features in the polariton spectra, in qualitative agreement with experimental studies of high-density polaritons.