Mixed vibrational modes of PbTe nanocrystallites

Far-infrared reflectance (20–700 cm^?1) and Raman spectra of porous PbTe were studied. The spectral dependences found significantly differ from those observed in the case of bulk single-crystal PbTe. Aside from the transverse (TO) and longitudinal (LO) optical phonon modes, additional vibrational modes were detected in the spectra, whose frequencies are close to those in a bulk material. Their number and spectral positions are in satisfactory agreement with the results of calculations carried out to determine the vibrational mode frequencies for nanocrystallites taking into account boundary conditions at their surface. The macroscopic continuum model allows calculation of the frequencies of the mixed phonon modes in quantum dots by the simultaneous consideration of atomic displacements and the accompanying change in the electrostatic potential. It was found experimentally that the detected modes are mixed (LO-TO), as was predicted by theory. The data of atomic-force microscopy allowed us to estimate the average radius of quantum dots, which form the nanorelief of the porous PbTe layer.