Acoustic Phonon Spectrum Modification in Nanostructures and Its Effect on Lattice Thermal Conductivity

The feature size of conventional electronic devices has already fallen below the acoustic phonon mean free path (MFP) in silicon, which is estimated to be 50 nm – 300 nm at room temperature. The lateral dimensions of nanowires and the size of quantum dots in quantum dot superlattices (QDS) fabricated by different self-assembly techniques are approaching the wavelength of a dominant phonon mode, which is on the order of 1 nm – 2 nm at room temperature. As the feature size of nanostructures that consist of elastically dissimilar materials becomes smaller than MFP and approaches the length scale of the thermal phonon wavelength one can expect a significant modification of the acoustic phonon spectrum, e.g. flattening of dispersion branches and mini-band formation. This modification, in its turn, affects the lattice thermal conductivity via enhanced phonon relaxation rates [1] or reduction of phonon density of states in the relevant frequency range. In this talk we theoretically investigate phonon spectrum modification in arrays of semiconductor nanowires and three-dimensional regimented arrays of quantum dots, e.g. quantum dot superlattices (QDS). We present new results for QDS obtained without simplifying assumptions of freeor clamped surface boundary conditions [2]. We argue that phonon spectrum for nanostructures that consists of regimented and closely spaced quantum dots deviates significantly from the predictions based on Lamb’s model. It is shown that strong modification of acoustic phonon spectrum is accompanied by the decrease of the phonon group velocity and corresponding decrease of the lattice thermal conductivity. For model validation, we calculate Raman peak positions for QDS and compare them with available experimental data.