Effect of screening on the optical absorption of a two-dimensional electron gas in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures

The optical-absorption spectrum is calculated for a quasi-two-dimensional electron gas interacting with polar optical phonons in a GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructure. The importance of dynamical screening, the effect of the finite width of the two-dimensional electron layer, and the temperature dependence are investigated. The polaron mass is derived and is found to decrease with increasing electron density. For electron densities around ${10}^{12}$ ${\mathrm{cm}}^{\mathrm{-}2}$ the absorption spectrum shows in addition to the usual structure a shoulder at energy $E_F$+ħ${\omega }_{\mathrm{LO}}$ with $E_F$ the Fermi energy and ħ${\omega }_{\mathrm{LO}}$ the optical-phonon energy.