Electron-Phonon Interactions in a single modulation doped Ga$_{0.24}$In$_{0.76}$As/InP Quantum Well

A series of Ga$_{0.24}$In$_{0.76}$As/InP modulation doped single quantum well (QW) structures have been investigated using cyclotron resonance experiments. The far-infrared magneto-transmission experiments are analyzed with a multidielectric model allowing the extraction of the imaginary part of the response function, revealing strong interactions with the different phonon energies of the mixed compound. For carrier densities n$_{S}$ higher than about 3.4x10$^{11}$ cm$^{-2 }$the only observed interaction is with the TO modes of the system whereas for lower densities, in addition to this interaction, a clear polaronic interaction with the LO phonons develops and increases as n$_{S}$ decreases. Due to the specific dielectric character of this compound these different types of interaction can be clearly indentified and even quantified.