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The spatial extents of the wave functions of the collective plasmon-longitudinal optical (LO) phonon excitations have been studied as a function of the doping concentration and the temperature in the AlGaAs alloy, where the short-range alloy potential fluctuations, together with the impurity random potential, are responsible for the disorder. A strong increase of the localization length was found with increase of the doping, where the plasmons substitute for phonons as collective excitations. A further decrease of the localization length of the plasmon-like excitations detected with increase of the doping level at high electron densities was attributed to the interaction of the plasmons with the impurities. A theoretical analysis based on the variational principle showed that the ionized impurities are responsible for the observed modification of the localization length.

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