Surface scattering controlled heat conduction in semiconductor thin films

Abstract

Phonon-surface scattering is the fundamental mechanism behind thermal transport phenomena at the nanoscale. Despite its significance, typical approaches to describe the interaction of phonons with surfaces do not consider all relevant physical quantities involved in the phonon-surface interaction, namely, phonon momentum, incident angle, surface roughness, and correlation length. Here, we predict thermal conduction properties of thin films by considering an accurate description of phonon-surface scattering effects based on the rigorous Beckmann-Kirchhoff scattering theory extended with surface shadowing. We utilize a Boltzmann transport based reduced mean-free-path model for phonon transport in thin-films to predict the wavelength and mean-free-path heat spectra in Si and SiGe films for different surface conditions and show how the thermal energy distribution can be tailored by the surface properties. Using the predicted wavelength spectra, we also introduce a measure to quantify phonon-confinement effects and show an enhanced confinement in Ge alloyed Si thin films. The impact of surface roughness and correlation lengths on thermal conductivities is also studied, and our numerical predictions show excellent agreement with experimental measurements. The results allow to elucidate and quantitatively predict the amount of thermal energy carried by different phonons at the nanoscale, which can be used to design improved optoelectronic and thermoelectric devices.

Enhancing Thermal Transport in Layered Nanomaterials

“…It is also observed that the larger the cladding thickness, the larger the increase in the thermal conductivity of the germanium thin film. This is because, for larger thicknesses of the silicon cladding layers, phonon scattering at the interfaces is reduced 31 – 36 and silicon phonon mean free paths are not shortened previously to their injection in germanium. Note that the enhancement of conductivity via injection of phonons is not unbounded with increasing cladding thickness, rather it begins to saturate as shown in Fig.…”

“…root-mean-square roughness and correlation lengths) between the cladding and internal layer. At the outer surfaces, the distribution function g k for a phonon leaving the surface is equal to the distribution function for the phonon striking the surface multiplied by the probability of specular surface scattering p ( k , θ , η , L ) where θ is the incident angle, η is the surface roughness and L is the correlation length 36 . On the other hand, at the silicon/germanium interface, the distribution function contains contributions from reflection and transmission events with probabilities P ( k , θ , η , L ) and Q ( k , θ , η , L ), respectively 38 .…”

“…The reflection P ij and transmission Q ij coefficients from a rough interface, where i and j denote the two solid media across the surface, can be written as and , where θ i and θ j are the incident and transmitted angles respectively, and R ij is the specular coefficient as given by Fresnel equations 38 . These expressions are extended for surface shadowing to account for the undulating nature of the surface 36 . Using these probabilities we perform an energy balance at the inner interfaces to obtain the functions f k for each material layer 38 .…”

Measurement of the phonon mean free path spectrum in silicon membranes at different temperatures using arrays of nanoslits

“…In thin two-dimensional structures, phonons experience additional scattering on the top and bottom surfaces [8][9][10]. Such surface scattering events should limit the phonon MFP in membranes as compared to bulk material [11], thus reducing the thermal conductivity and limiting the ballistic heat conduction. Indeed, the experimentally measured thermal conductivity of thin membranes are consistent with the MFP spectrum in bulk, assuming that the spectrum is limited by the membrane thickness [4].…”

Phonon Surface Scattering and Thermal Energy Distribution in Superlattices

“…We extend the electromagnetic wave scattering theory developed for rough surfaces by Beckmann and Spizzichino 36 to accurately model reflection and transmission at rough interfaces as well as phonon coupling between the layers by accounting for all the relevant physical variables such as phonon properties (e.g. momentum, incident angle) and surface characteristics (roughness, correlation lengths, and shadowing) 37 . By directly calculating the reduction in phonon relaxation times due to surface scattering through the rigorous solution of the Boltzmann transport equation, our analysis moves beyond the Mattheissen rule approximation for modelling surface scattering.…”