Dhruv Singh

Mechanism of thermal conductivity reduction in few-layer graphene

Using the linearized Boltzmann transport equation and perturbation theory, we analyze the reduction in the intrinsic thermal conductivity of few-layer graphene sheets accounting for all possible three-phonon scattering events. Even with weak coupling between layers, a significant reduction in the thermal conductivity of the out-of-plane acoustic modes is apparent. The main effect of this weak coupling is to open many new three-phonon scattering channels that are otherwise absent in graphene. However, reflection symmetry is only weakly broken with the addition of multiple layers, and out-of-plane acoustic phonons still dominate thermal conductivity. We also find that reduction in thermal conductivity is mainly caused by lower contributions of the higher-order overtones of the fundamental out-of-plane acoustic mode. The results compare remarkably well over the entire temperature range with measurements of graphene and graphite.

Spectral phonon conduction and dominant scattering pathways in graphene

In this paper, we examine the lattice thermal conductivity and dominant phonon scattering mechanisms of graphene. The interatomic interactions are modeled using the Tersoff interatomic potential and perturbation theory is applied to calculate the transition probabilities for three-phonon scattering. The matrix elements of the perturbing Hamiltonian are calculated using the anharmonic interatomic force constants obtained from the interatomic potential as well. The linearized Boltzmann transport equation is applied to compute the thermal conductivity of graphene for a wide range of parameters giving spectral and polarization-resolved information. The complete spectral detail of selection rules, important phonon scattering pathways, and phonon relaxation times in graphene are provided. We also highlight the specific scattering processes that are important in Raman spectroscopy-based measurements of graphene thermal conductivity, and provide a plausible explanation for the observed dependence on laser spot size.

Effect of Phonon Dispersion on Thermal Conduction Across Si/Ge Interfaces

We report finite-volume simulations of the phonon Boltzmann transport equation (BTE) for heat conduction across the heterogeneous interfaces in SiGe superlattices. The diffuse mismatch model incorporating phonon dispersion and polarization is implemented over a wide range of Knudsen numbers. The results indicate that the thermal conductivity of a Si/Ge superlattice is much lower than that of the constitutive bulk materials for superlattice periods in the submicron regime. We report results for effective thermal conductivity of various material volume fractions and superlattice periods. Details of the nonequilibrium energy exchange between optical and acoustic phonons that originate from the mismatch of phonon spectra in silicon and germanium are delineated for the first time. Conditions are identified for which this effect can produce significantly more thermal resistance than that due to boundary scattering of phonons. [DOI: 10.1115/1.4004429]

On the accuracy of classical and long wavelength approximations for phonon transport in graphene

This paper presents a critical evaluation of the approximations usually made in thermal conductivity modeling applied to graphene. The baseline for comparison is thermal conductivity computations performed using a rigorous calculation of three-phonon scattering events and accounting for the anharmonicity of interatomic forces. Three central assumptions that underlie published theories are evaluated and shown to compromise the accuracy of thermal conductivity predictions. It is shown that the use of classical phonon occupation statistics in place of the Bose-Einstein distribution causes the overprediction of specific heat and the underprediction of phonon relaxation time; for ZA phonons, the classical approximation can underpredict the relaxation time by a factor of approximately 2 at room temperature across a broad frequency band. The validity of the long wavelength (Klemens) approximation in evaluating the strength of phonon scattering events is also examined, and the findings indicate that thermal condu...

Revisiting the structure zone model for sculptured silver thin films deposited at low substrate temperatures

In this study, we examined the low substrate temperature (Ts) growth mechanism of Ag thin films in the atomic shadowing regime (Ts ≪ melting point Tm). The Ag thin films were deposited using glancing angle deposition (GLAD) at different substrate temperatures varying from 320 K to 100 K. Interestingly, it is observed that on lowering the substrate temperature instead of showing a monotonic variation, the Ag film morphology changes from the ordered nanocolumns to random and distorted columns, and then to the columnar bunches of nanowires. These growth results suggest that this temperature regime of effective adatom shadowing does not hold a unique growth mechanism for the GLAD within the low temperature range from 320 K to 100 K and depending on the observed temperature dependent variation in morphological and structural properties of the Ag film, it can be sub-divided into three characteristic zones. The observed growth mechanism of the Ag film is explained in terms of the temperature dependent change in ...

Phonon Transport Across Mesoscopic Constrictions

Phonon transport across constrictions formed by a nanowire or a nanoparticle on a substrate is studied by a numerical solution of the gray Boltzmann transport equation (BTE) resolving the effects of two length scales that govern problems of practical importance. Predictions of total thermal resistance for wire/substrate and particle/substrate combinations are made for the entire range of Knudsen number, with an emphasis on resolving transport in the mesoscopic regime where ballistic-diffusive mechanisms operate and analytical expressions are not available. The relative magnitudes of bulk and constriction resistance are established, and a correlation for overall thermal resistance spanning the range of practical Knudsen numbers is provided. DOI: 10.1115/1.4002842

NON-GRAY PHONON TRANSPORT USING A HYBRID BTE-FOURIER SOLVER

Non-gray phonon transport solvers based on the Boltzmann transport equation (BTE) are frequently employed to simulate sub-micron thermal transport. Typical solution procedures using sequential solution schemes encounter numerical difficulties because of the large spread in scattering rates. For frequency bands with very low Knudsen numbers, strong coupling between the directional BTEs results in slow convergence for sequential solution procedures. In this paper, we present a hybrid BTE-Fourier model which addresses this issue. By establishing a phonon group cutoff (say Kn = 0.1), phonon bands with low Knudsen numbers are solved using a modified Fourier equation which includes a scattering term as well as corrections to account for boundary temperature slip. Phonon bands with high Knudsen numbers are solved using a BTE solver. Once the governing equations are solved for each phonon group, their energies are then summed to find the total lattice energy and correspondingly, the lattice temperature. An iterative procedure combining the lattice temperature determination and the solutions to the modified Fourier and BTE equations is developed. The procedure is shown to work well across a range of Knudsen numbers.Copyright

Frequency Resolved Phonon Transport in Si/Ge Nanocomposites

In this paper, we analyze cross plane phonon transport and thermal conductivity in two-dimensional Si/Ge nanocomposites. A non-gray BTE model that includes full details of phonon dispersion, the spread in phonon mean free paths and the frequency dependent transmissivity is used to simulate thermal transport. The general conclusions inferred from gray BTE simulations that the thermal conductivity of the nanocomposite is much lower than its constituent materials and interfacial density as the parameter determining thermal conductivity remain the same. However, it is found that the gray BTE significantly overpredicts thermal conductivity in the length scales of interest and quantitatively reliable results are obtained only upon inclusion of the details of phonon dispersion. The transition of phonon transport from ballistic regime to near diffusive regime is observed by looking at a large range of length scales. Non-equilibrium energy exchange between optical and acoustic phonons and the granularity in phonon mean free paths are found to significantly affect thermal conductivity leading to departures from the frequently employed gray approximation. It is also found that the frequency content of thermal conductivity in the nanocomposite extends out to a much larger frequency range unlike bulk Si and Ge. Scattering against heterogeneous interfaces is very effective in suppressing thermal conductivity contribution from the low frequency acoustic phonons but less so for high frequency phonons, which have much smaller mean free paths.© 2011 ASME

Gas‐Phonon Interaction Model for Subcontinuum Thermal Transport Simulations

Subcontinuum thermal transport problems such as the contact thermal resistance of semiconductor‐gas interactions may play an important role in micro/nano‐scale devices. In present work, a gas‐phonon interaction modeling approach is suggested based on Boltzmann transport equations. Verification has been conducted by comparisons with asymptotic analytical solutions as well as previously reported numerical results and experimental data. Thermal transpiration in nano‐sized channels and thermal resistance of nano‐sized constrictions has been studied using the current model Thermal transpiration is the main mechanism for temperature driven pumps in nano/micro‐devices. In order to maintain higher temperature ratio between the two ends of the gas path (capillaries), the choice of membrane material is very important, and the gas‐solid interaction must be understood. It is shown from the calculations that the temperature gradient, capillary geometry, gas/solid Knudsen conditions, and the gas/solid thermal conductiv...

Design and Fabrication of a Mock Circulatory System for Reliability Tests on Aortic Heart Valves

The dynamic stress analysis and response of artificial heart valves — specifically the aortic valve is impending following the increasing number of artificial valve failures. This calls for the development of a mock circulatory system in order to establish clearly the parameters associated with the circulatory system in the heart and their effects on the robustness of a prosthetic implant.Copyright