Phonon Transmission Probability Research Articles

Phonon thermal conduction in a graphene–C3N heterobilayer using molecular dynamics simulations

Two-dimensional (2D) graphene (GRA) and polyaniline (C3N) monolayers are attracting growing research interest due to their excellent electrical and thermal properties. In this work, in-plane and out-of-plane phonon thermal conduction of GRA–C3N heterobilayer are systematically investigated by using classical molecular dynamics simulations. Effects of system size, temperature and interlayer coupling strength on the in-plane thermal conductivity (k) and out-of-plane interfacial thermal resistance (R) are evaluated. Firstly, a monotonic increasing trend of k with increasing system size is observed, while a negative correlation between thermal conductivity and temperature is revealed. The interlayer coupling strength is found to have a weak effect on the in-plane thermal conductivity of the heterobilayer. Secondly, at T = 300 K and χ = 1, the predicted R of GRA → C3N and C3N → GRA are 1.29 × 10−7 K m2 W−1 and 1.35 × 10−7 K m2 W−1, respectively, which indicates that there is no significant thermal rectification phenomenon. It can also be observed that R decreases monotonically with increasing temperature and coupling strength due to the enhanced Umklapp phonon scattering and the phonon transmission probability across the interface. Phonon density of states, phonon dispersions and participation ratios are evaluated to reveal the mechanism of heat conduction in the heterobilayer. This work contributes the valuable thermal information to modulate the phonon behaviors in 2D heterobilayer based nanoelectronics.

A method to calculate thermal conductivity of a nonperiodic system, bamboo Si1−xGex nanowire with axially degraded components

For a nonperiodic system, a bamboo Si1−x Ge x nanowire with axially degraded components, it is impossible to obtain its phonon dispersion relations through lattice dynamic or the first principle calculation. Therefore, we present a simple and available method to solve this problem. At first, the Si1−x Ge x nanowire with axially degraded component is divided into several sections according to its component distribution like bamboos’ sections formed in the growth process. For each section with a given x value, we constructed a pseudo-cell to calculate its phonon dispersion relations. Thermal conductances of junctions and of each section are then calculated by the phonon mismatch model and the phonon transmission probability with diffusive and ballistic portions. The dependences of thermal conductivity on the length of each section and the gradient of degraded component between sections are presented. We studied thermal conductivity dependence on temperature, length and diameter of the Si1−x Ge x nanowire with axially degraded component. And we found κ ~ l 0.8, in which the exponent 0.8 is ascribed to the competition between phonons ballistic and diffusive transport. Furthermore, thermal conductivities along axial (100), (110), and (111) directions are discussed in detail. The method provides a simple and available tool to study thermal conductivity of a non-period system, such as a quasiperiodic superlattice or a nanowire with axially degraded component.

Erratum: Efficient approach for modeling phonon transmission probability in nanoscale interfacial thermal transport [Phys. Rev. B91, 174302 (2015)

Received 17 December 2015DOI:https://doi.org/10.1103/PhysRevB.93.019901©2016 American Physical Society

Efficient approach for modeling phonon transmission probability in nanoscale interfacial thermal transport

The Kapitza or interfacial thermal resistance at the boundary of two different insulating solids depends on the transmission of phonons across the interface and the phonon dispersion of either material. We extend the existing atomistic Green's function (AGF) method to compute the probability for individual phonon modes to be transmitted across the interface. The extended method is based on the concept of the Bloch matrix and allows us to determine the wavelength and polarization dependence of the phonon transmission as well as to analyze efficiently the contribution of individual acoustic and optical phonon modes to interfacial thermal transport. The relationship between the phonon transmission probability and dispersion is explicitly established. A detailed description of the method is given and key formulas are provided. To illustrate the role of the phonon dispersion in interfacial thermal conduction, we apply the method to study phonon transmission and thermal transport at the armchair interface between monolayer graphene and hexagonal boron nitride. We find that the phonon transmission probability is high for longitudinal (LA) and flexural (ZA) acoustic phonons at normal and oblique incidence to the interface. At room temperature, the dominant contribution to interfacial thermal transport comes from the transverse-polarized phonons in graphene (45.5%) and longitudinal-polarized phonons in boron nitride (47.4%).

Nanoscale transport of phonons: Dimensionality, subdiffusion, molecular damping, and interference effects

We examine heat transport carried by acoustic phonons in the systems composed of nanoscale chains of masses coupled to two thermal baths of different temperatures. Thermal conductance is obtained by using linearized Landauer-type formula for heat flux with phonon transmission probability calculated within atomistic Green's functions (AGF) method. AGF formalism is extended onto dissipative chains of masses with harmonic coupling beyond nearest-neighbor approximation, while atomistic description of heat reservoirs is also included into computational scheme. In particular, the phonon lifetimes and the phonon frequency shifts are discussed for harmonic lattices of different dimensions. Further, resonant structure of phonon transmission spectrum is analyzed with respect to reservoir-induced effects, molecular damping, and mass-to-mass harmonic coupling. Analysis of transmission zeros (antiresonances) and their accompanied Fano-shape resonances are discussed as a result of interference effects between different vibrational modes. Finally, we also predict subdiffusive transport regime for low-frequency ballistic phonons propagated along a linear chain of harmonically coupled masses.

Thermal boundary resistance for gold and CoFe alloy on silicon nitride films

Advances in microelectronics technology strongly depend on the thermal optimization of metal/dielectric interfaces, which requires precise modeling and thermal characterization of metal/dielectric structures. This work experimentally investigated the influence of metallic layers on the thermal boundary resistance of silicon nitride dielectric material. The results reveal that the thermal boundary resistance of silicon nitride thin films depends on the metallic layers. The thermal boundary resistance at the interface between Au and SiNx is larger than that between Co0.9Fe0.1 and SiNx. The reasons to cause this difference are discussed with phonon transmission probability and the ratio of the Debye temperature between metals and dielectrics.

Heat transfer in high volume fraction CNT nanocomposites: Effects of inter-nanotube thermal resistance

Monte Carlo simulations were employed to investigate the effective thermal conductivity of carbon nanotube–polystyrene (CNT–PS) nanocomposites at different wt.% of CNT loadings and temperatures. By validating with experimental data, values of phonon transmission probability as well as Kapitza resistance at the CNT–PS interface and at the CNT–CNT contact were calculated. In addition, the observed poor enhancement of thermal conductivity at high CNT concentrations was found to be the result of the CNT–CNT thermal resistance and of the bundle configuration.

Phonon confinement effects in ultrathin epitaxial bismuth films on silicon studied by time-resolved electron diffraction

The transient temperature evolution of ultrathin bismuth films, epitaxially grown on a silicon single crystal, upon femtosecond laser excitation is studied by time-resolved electron diffraction. The exponential decay of the film temperature is explained by phonon reflection at the interface, which results in a strongly reduced thermal conduction in the cross plane of the layered system. The thermal boundary conductance is found to be as low as $1273\text{ }\text{W}/(\text{K}\text{ }{\text{cm}}^{2})$. Model calculations, including phonon confinement effects, explain the linear relationship between the observed film-temperature decay constant and the film thickness. Even for 2.5 nm thin films the phonon transmission probability across the interface is given by bulk properties. Our simulations show that phonon confinement effects are negligible for bismuth-film thicknesses larger than 1 nm.

Mesoscopic phonon transmission through a nanowire-bulk contact

We calculate the frequency-dependent mesoscopic acoustic phonon transmission probability through the abrupt junction between a semi-infinite, one-dimensional cylindrical quantum wire and a three-dimensional bulk insulator, using a perturbative technique that is valid at low frequency. The system is described using elasticity theory, and traction-free boundary conditions are applied to all free surfaces. In the low-frequency limit the transmission probability vanishes as the frequency squared, the transport being dominated by the longitudinal channel, which produces a monopole source of elastic radiation at the surface of the bulk solid. The thermal conductance between an equilibrated wire nonadiabatically coupled to a bulk insulator should therefore vanish with temperature at temperature cubed.

Phonon transmission in III–V semiconductor superlattices and alloys

We have used the transfer matrix approach to investigate the LA phonon transmission along the [0 0 1] growth direction in GaAs/GaAlAs superlattices and in Ga1−xAlxAs alloys. Our calculated minigap in the phonon dispersion induced by the zone folding matches reasonably to the phonon filtering experiment. However, in the regime of phonon ballistic transport, we found insignificant effect of zone folding on phonon thermal conductance. On the other hand, the alloy scatterings largely suppress the phonon transmission probability and so lower the phonon thermal conductance of alloys.

Mesoscopic thermal transport through a weak link

We consider mesoscopic thermal transport between two bulk dielectrics joined by a narrow wire or weak mechanical link. In the “tunneling” regime where the phonon transmission probability through the link is small and the thermal conductance is much less than πk B 2 T/6ℏ, the thermal current is determined by a product of the local vibrational spectral densities of the two bodies. We derive an expression for the thermal current that is a thermal analog of the well-known formula for the electrical current through a tunneling barrier.

Kapitza resistance between silicon and helium-4

By simultaneously measuring the phonon scattering at or near a silicon surface and the phonon transmission from it into liquid helium, we have correlated quantitatively these two processes. For a clean polished silicon surface, the scattering of thermal phonons below 0.3 K becomes very small, and the transmission probability in this case approaches the prediction of the acoustic mismatch theory, which is 0.27%. The transmission probability increases, i.e. the thermal boundary resistance decreases, as the diffuse scattering increases either as a result of increasing the phonon frequency or the disorder at the surface. In the limit of completely diffuse scattering, the phonon transmission probability exceeds 30%, and the thermal boundary resistance approaches the value predicted by the diffuse mismatch model to within a factor of three.

Nonequilibrium conditions and diffusive transfer of primary excitations in superconducting tunnel-junction detectors.

The nonequilibrium behavior of superconducting tunnel junctions in the high-injection regime is examined. A model based on asymmetric coupled diffusion equations for quasiparticles and phonons, including a phonon escape term, is presented. A solution consisting of a two-dimensional perturbative algorithm to the equation of phonons and a self-iterative expansion to the quasiparticles equation has been developed. A characteristic length scale L = (D/sub p/d/u)/sup 1/2/ associated with phonon propagation and the detector geometry where D/sub p/ is the diffusion coefficient for the phonon pulse, d is the detector film thickness, and u is the average phonon velocity. The quasiparticles and phonon pulses almost uncouple with similar spatial and time distributions and with a minimum escape rate of the phonons when L/sup 2/ is equal to XT/..mu../sub min/, where X is a numerical factor, T is the intrinsic phonon transmission probability at the film substrate boundaries and ..mu.. is a phase-space factor defined by ..mu..(i,j) = (Pi/sup 2//4)((2i+1)/sup 2/ /a/sup 2/+(2j+1)/sup 2//b/sup 2/), when i,j = 0,1,2,. . . . The parameters a and b are half the longitudinal and transverse dimensions of the junction film. The implications of these new results on previous experimental measurements are discussed.

On the existence of the critical cone in Kapitza resistance experiments

The effects that arise on the phonon transmission probability through an interface between a solid and liquid helium when sound attenuation in the solid is described by a complex wave vector are discussed. The conclusion is that there is not enough reason to believe that total internal reflection vanishes in this case.