We present a theoretical model of composite excitonic states in doped semiconductors. Many-body interactions between a photoexcited electron-hole pair and the electron gas are integrated into a computationally tractable few-body problem, solved by the variational method. We focus on electron-doped monolayer (ML)-$\mathrm{Mo}{\mathrm{Se}}_2$ and ML-$\mathrm{W}{\mathrm{Se}}_2$ due to the contrasting character of their conduction bands. In both cases, the core of the composite is a tightly bound trion (two electrons and a valence-band hole) surrounded by a region depleted of electrons. The composite in ML-$\mathrm{W}{\mathrm{Se}}_2$ further includes a satellite electron with different quantum numbers. The theory is general and can be applied to semiconductors with various energy-band properties, allowing one to calculate their excitonic states and to quantify the interaction with the Fermi sea.

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• Excitons
• Optical conductivity
• Trions
• Doped semiconductors
• Transition metal dichalcogenides