Phonons and Thermal Properties of Ge Nanowires: A Raman Spectroscopy Investigation and Phonon Simulations

Abstract

We have investigated phonon an harmonicity related thermal properties [e.g., coefficient of thermal expansion (α), Gruneisen parameter (γ), and phonon mean free path as limited by Umklapp scattering (Λ mfp )] for Ge nanowires (NWs) using temperature-dependent Raman spectroscopy as well as phonon dynamics simulations. The experiments were carried out in two types of NW ensembles. One type of NWs has only the native oxide layer on Ge, and the other type has relatively thicker GeO 2 on the surface forming a core−shell structure. The temperature-dependent shift of the LO/TO Raman line of Ge (300 cm −1 ) was used to determine the αγ product in the temperature range of 80−800 K. The αγ product is enhanced compared to that observed in the bulk crystalline Ge over the whole temperature range. The experimental work was complimented by phonon simulations with quasi-harmonic approximation using density functional perturbation theory. The simulation allowed us to determine the thermodynamic parameters like bulk modulus, specific heat capacity (C v ), α, and γ. We have determined the anharmonicity coefficients and phonon lifetimes in Ge NWs and also estimated the Λ mfp arising from phonon−phonon scattering (Umklapp process). Comparison of the computed thermal parameters with the experimental data allowed us to place a confidence limit on the calculated parameters, which was used to separate out the two parameters αandγ for the NWs from the observed αγ product. The enhancement of α, in particular, in the Ge NWs has been explained as arising from significant softening of θ D in the NWs as observed from the low temperature C v calculated from the phonon simulations. Comparison of the computed phonon density of states shows appearance of excess weights in the phonon spectrum, which contributes to enhancement of heat capacity in NWs compared to that in the bulk.

Lattice thermal conductivity of ZnO: experimental and theoretical studies

“…Thus, γ can be estimated using first principles calculations from isobaric thermal expansion. The γ can also be evaluated using a quasi-harmonic approach, considering ω is a function of only volume, and is given by the relation: 38 where α is the average thermal expansion coefficient. There are several reports on the experimental value of α (=2 α a + α c ) for ZnO, which is around 1.5 × 10 −5 K −1 .…”