Low-temperature Thermal Conductance Research Articles

Modification of the Acoustic Mismatch Model and Diffuse Mismatch Model for Accurate Prediction of Interface Thermal Conductance At Low Temperatures

Abstract Houston's method for summing phonon modes in the Brillouin zone is applied to exclude specular transmission of phonon modes of specific symmetries, thus, modifying the Acoustic Mismatch Model when phonon heat flux is incident from a heavier to a lighter medium. The Houston method is also used to impose conservation of the number of phonons in each direction of high symmetry, thus modifying the detailed balance theorem and the Diffuse Mismatch Model. Based on the assumption that phonons are in equilibrium at the interface and are transmitted specularly or diffusely by two-phonon elastic processes, interpolation between the modified Acoustic Mismatch Model and the modified Diffuse Mismatch Model has led to a general analytical formalism for low-temperature interface thermal conductance. The Debye temperature, the only parameter in the derived formalism, is expressed as a function of temperature by assimilating numerically obtained specific heat values to the Debye expression for specific heat. Previous measurements of the thermal conductance of smooth and rough interfaces between dissimilar materials could be reproduced numerically without adjustment of model parameters, demonstrating the importance of modifications to the Acoustic Mismatch Model and the Diffuse Mismatch Model, and supporting the hypothesis that anharmonic processes play a minimal role in heat transport across interfaces below ambient temperature. The formalism developed is used to study the thermal conductance of the interface between silicon and germanium because of the potential of silicon-germanium nanocomposites for thermoelectric applications.

Low-frequency phonon dynamics and related thermal properties of axially stressed single-walled carbon nanotubes

Synthesis temperatures of composite materials are usually far less than the ones of their use, thus carbon nanotubes (CNTs) embedded into a polymer matrix undergo significant axial stress. We develop a continuous theory, which describes the dynamics of stressed single-walled (SW-) CNTs and predicts their low-frequency phonon spectra. The changes in dispersion laws of SWCNT low-frequency phonon modes due to the axial stress of different signs are discussed. Then, the results obtained are used to analyze low-temperature (T < 70 K) heat capacity and thermal conductivity of individual nanotubes. We demonstrate that compressive stress leads to increase in heat capacity CV of an individual SWCNT, while tensile stress causes CV to decrease. In the latter case at T → 0 heat capacity diminishes according to a linear law ~T instead of a power one ~T1/2. Nevertheless, according to our results, axial stress hardly affects low-temperature thermal conductance of SWCNTs. Influence of investigated effects on the corresponding macroscopic properties of CNT-based composite materials are also discussed.

Simple theory of low-temperature thermal conductivity in single- and double-walled carbon nanotubes

Low-temperature phonon thermal conductance (PTC) of any 1D system increases proportionally to the temperature. However, here we show that in single- and double-walled carbon nanotubes (CNTs), starting from 3--6 K, the PTC increases faster than the linear function, since the low-frequency modes of dispersion curves, which do not tend to zero together with the wave vector, are excited. To develop the PTC theory, we combine the Landauer's ballistic approach with the simple continuous model proposed for the calculation of the low-frequency phonon spectra of both free nanotubes and those interacting with an environment. The approach obtained is valid not only for commensurate double-walled CNTs, but also for incommensurate ones. The temperature-dependent relation between the PTC of double-walled CNT and those of its constituent SWNTs is obtained and discussed. The low-temperature heat transfer in bulk materials originated from CNTs is also considered and the upper limit of thermal conductivity of such materials is determined. We argue that the ideal material consisting of CNTs can challenge diamond only when the mean length of its defect-free nanotubes reaches at least one hundred of micrometers.

Influence of multi-cavity dislocation distribution on thermal conductance in graphene nanoribbons

Using non-equilibrium Green's function method and keeping the zigzag carbon chains unchanged, we investigate the transmission rate of acoustic phonon and the reduced thermal conductance in the graphene nanoribbons with three cavities. The results show that the reduced thermal conductance approaches to 32kB2 T/(3h) in the limit T0 K. Due to the fact that only long wavelength acoustic phonons with zero cutoff frequency are excited at such low temperatures, the scattering influence on the long wavelength acoustic phonons by the dislocation distribution of three cavities in the graphene nanoribbons can be ignored and these phonons can go through the scattering region perfectly. As the temperature goes up, the reduced thermal conductance decreases. This is because the high-frequency phonons are excited and these high-frequency phonons are scattered easily by the scattering structures. With the further rise of temperature, acoustic phonon modes with the cutoff frequency greater than zero are excited, which leads to a rapid increase of the reduced thermal conductance. This study shows that in higher frequency region, the transmission spectra display complex peak-dip structures, which results from the fact that in higher frequency region, more phonon modes are excited and scattered in the middle scattering region with three cavities, and the scattering phonons are coupled with the incident phonons. When the three cavities are aligned perpendicularly to the edge of the graphene nanoribbons, the scattering from low-frequency phonons by the scattering structures is smallest, which leads to the fact that the reduced thermal conductance is largest at low temperatures; however, at high temperatures, the reduced thermal conductance is smallest when the three cavities is aligned perpendicularly to the edge of the graphene nanoribbons. This is because the scattering from high-frequency phonons by the scattering structures is biggest. These results show that the acoustic phonon transport and the reduced thermal conductance are dependent on the relative position of the three cavities. In addition, the dislocation distribution of the three cavities can only modulate obviously the high-temperature thermal conductance of the in-plane modes (IPMs). This is because the change of the relative position of the quantum dots can only modulate greatly the high-frequency phonon transmission rate and less modulate the low-frequency phonon transmission rate of the IPMs. However, the dislocation distribution of the three cavities can adjust obviously not only the high-temperature thermal conductance of the flexural phonon modes (FPMs), but also the low-temperature thermal conductance of the FPMs. This is because the change of the relative position of the three cavities can modulate greatly phonon transmission rates of flexural phonon modes in the low-frequency and high-frequency regions. These results provide an effective theoretical basis for designing the thermal transport quantum devices based on graphene nanoribbons.

Low-temperature thermal conductance in three-dimensional nanowire embedded with phonon cavity

In this paper, we investigate low-temperature thermal conductance in three-dimensional nanowire embedded with phonon cavity based on the full scalar model of elasticity. The results show that at very low temperatures, the cavity can enhance the thermal conductance in certain lateral-width range, just as the constructive coupling of more phonon-modes excited in the cavity with modes in the transport region. At higher temperatures, however, the scattering of more interfaces formed from the cavity become a dominant factor to suppress the phonon transmission. Moreover, it is found that while the material in the cavity is substituted for the material with higher sound velocity than that in the transport region, the thermal conductance is also enhanced.

Acoustic phonon transport and thermal conductance in quantum waveguide with abrupt quantum junctions modulated with double T-shapedquantum structure

By using the scattering matrix method, the transmission coefficient and thermal conductance of acoustic phonon through a quantum waveguide with abrupt quantum junctions modulated with double T-shaped quantum structure at low temperatures are studied. The results show that at very low temperatures, the double T-shaped quantum structure can enhance low-temperature thermal conductance; contrarily, at higher temperatures, the double T-shaped quantum structure can reduce low-temperature thermal conductance. However, in the whole low-temperature region, the low-temperature thermal conductance can be enhanced by adding the narrowest width c in the scattering region. Moreover, it is found that both the transmission coefficient and thermal conductance can be adjusted by changing the structural parameters of the the scattering region.

Enhanced low-temperature thermal conductance by quantum dot made of material with high sound velocity in a three-dimensional semiconductor nanowire

We investigate ballistic phonon transport and thermal conductance in a three-dimensional semiconductor nanowire modulated with different materials in a single quantum dot using elastic wave continuum model. In general, the acoustic discontinuities at such system cause the decrease of the thermal conductance. However, at very low temperatures, the material with higher sound velocity in quantum dot do enhance the thermal transport, despite that phonons are scattered due to the acoustic mismatch at the interfaces. The enhancement originates from the longer wavelength of the mode (0,0) in the material with higher sound velocity.

Steady-state thermal transport in anharmonic systems: Application to molecular junctions

We develop a general theory for thermal transport in anharmonic systems under the weak system-bath coupling approximation similar to the quantum master equation formalism. A current operator is derived, which is valid not only in the steady state, but in the transient regime as well. Here we focus on the effects of anharmonicity on the steady-state thermal conductance of a mono and diatomic molecular junctions. We also study molecules being confined in a double-well potential. We find that when the molecules have a non-linear on-site potential the low-temperature thermal conductance is dramatically affected by the strength of non-linearity, whereas for the diatomic molecule connected by an anharmonic spring the strength of anharmonicity plays almost no role in the low-temperature regime. In case of the molecules confined in a double-well potential we find that the height of the barrier greatly affects the thermal conductance; once the molecules can feel the effect of the barrier we observe negative differential thermal conductance at both high and low temperatures.

Numerical simulation of low temperature thermal conductance of corrugated nanofibers

In this work we numerically investigated the decrease of low temperature thermal conductance of cylindrical Silicon nanofibers with periodical and almost periodical corrugation on the boundary. We used 1D and 3D finite element models to study scattering of low frequency acoustic phonons from the corrugation. By assuming weak deformation and high enough cross-sectional symmetry it was found that 1D models yield a sufficiently good approximation and could be used in the calculation of thermal conductance for long nanofibers. Landauer 1D formalism was applied for the calculation of the thermal conductance of several long axially symmetric and elliptical fibers. Without significantly hindering the structural strength of the fiber we found boundary shapes which decrease the thermal conductance by each mainly contributing phonon down to 10% of the universal quantum on temperature range 0.1–1K. We concluded that the similar drop in total thermal conductance could be obtained by combining these designs in series.

Effects of controllable defects on thermal conductance in a nanowire with a quantum box

By using the scattering-matrix method and the scalar model of elasticity, we investigate the effect of controllable defects on low temperature thermal conductance in a nanowire with a quantum box geometry. It is found that the thermal conductance can be controlled by adjusting the parameters of the defects. The size and the position of the defect can induce the variation in thermal conductance. It is also found that the behavior of the thermal conductance versus temperature is different for different types of defects.

Quantum phonon transport of molecular junctions amide-linked with carbon nanotubes: A first-principles study

Quantum phonon transport through benzene and alkane chains amide-linked with single-walled carbon nanotubes (SWCNTs) is studied within the level of density-functional theory. The force-constant matrices are obtained from standard quantum chemistry software. The phonon transmission and thermal conductance are from the nonequilibrium Green's function and the mode-matching method. We find that the ballistic thermal conductance is not sensitive to small compression or stretching of the molecular junction. The terminating groups of the SWCNTs at the cutting edges only influence the thermal conductance quantitatively. The conductance of the benzene and alkane chains shows large difference. Analysis of the transmission spectrum shows that (i) the low-temperature thermal conductance is mainly contributed by the SWCNT transverse-acoustic modes, (ii) the degenerate phonon modes show different transmission probability due to the presence of molecular junction, and (iii) the SWCNT twisting mode can hardly be transmitted by the alkane chain. As a result, the ballistic thermal conductance of alkane chains is larger than that of benzene chains below 38 K and becomes smaller at higher temperature.

Low-Temperature Thermal Conductance in Superlattice Nanowire with Structural Defect

Using the scattering-matrix cascading method, we investigate the effect of structural defect on the acoustic phonon transmission and thermal conductance in the superlattice nanowire at low temperatures. In the present system, the phonon transmissions exhibit quite complex oscillatory behaviour. It is found that a lateral defect in an otherwise periodic structure significantly decrease the thermal conductance and completely washes away the transmission quantization. However, the appreciable transmission quantization survives in the presence of a longitudinal defect whereas a good quantization plateau of thermal conductance emerges below the universal level in a wide temperature range with the lateral defect.

Phonon-cavity-enhanced low-temperature thermal conductance of a semiconductor nanowire with narrow constrictions

We study the effect of the phonon cavity lying in a narrow constriction of a semiconductor nanowire on the ballistic phonon thermal conductance at low temperatures. At higher temperatures, the thermal conductance of the nanowire with phonon cavity is lower than that of the nanowire without phonon cavity since more discontinuous interfaces scatter phonons. On the contrary, it is found that the cavity can enhance the thermal conductance at very low temperatures despite phonons are scattered by its interfaces. The enhancement originates from the coupling between more excited cavity modes in the phonon cavity and phonon modes in the constrictions.

Nonequilibrium Green’s Function Approach to Phonon Transport in Defective Carbon Nanotubes

We have developed a new theoretical formalism for phonon transport in nanostructures using the nonequilibrium phonon Green's function technique and have applied it to thermal conduction in defective carbon nanotubes. The universal quantization of low-temperature thermal conductance in carbon nanotubes can be observed even in the presence of local structural defects such as vacancies and Stone-Wales defects, since the long wavelength acoustic phonons are not scattered by local defects. At room temperature, however, thermal conductance is critically affected by defect scattering since incident phonons are scattered by localized phonons around the defects. We find a remarkable change from quantum to classical features for the thermal transport through defective carbon nanotubes with increasing temperature.

Effect of defects on the thermal conductivity in a nanowire

We investigate the effect of defects on the low temperature thermal conductance in nanowire structure by using the scattering-matrix method. It is found the behavior of the thermal conductance versus temperature is qualitatively different for different types of defects. When the defect is void, the universal quantum thermal conductance and the decrease of the thermal conductance at low temperature can be clearly observed. However, when the structural defect consists of clamped material, the quantized thermal conductance cannot be observed, and the thermal conductance increases monotonically with increasing temperature.

Universal Quantization Phenomena of Thermal Conductance in Carbon Nanotubes

The low-temperature thermal conductance of single-walled carbon nanotubes has been revealed by theoretical analysis based on the Landauer theory for thermal transports. The phonon-derived thermal conductance is quantized as a universal value of 4π2k2BT/3h in the low-temperature limit, independent of their radii and chiralities. The temperature range where the quantization is observable increases as the tube-radius decreases. For metallic carbon nanotubes, an electronic contribution to thermal conductance is also quantized as the same value as that of phonon in the low-temperature limit and becomes negligibly small compared with a phonon contribution as temperature increases. We also discuss the thermal transport properties of graphitic ribbons as a potential wiring material in nanoscale electronic devices as well as carbon nanotubes.

Empirical-potential study of phonon transport in graphitic ribbons

The thermal properties of graphitic ribbon are investigated based on Brenner's empirical potential. The reliability and usefulness of the empirical potential to address the thermal properties of covalent-bonded carbon nanostructures are verified through a comparison of phonon dispersion relations and the density of states of carbon nanotubes with first-principles calculations. The analysis reveals unique edge-phonon states that are highly localized at edge carbon atoms of both armchair and zigzag ribbons. Applying the phonon dispersion relations to the Landauer formula of phonon transport, the quantization and universal features of the low-temperature thermal conductance of graphitic ribbon are elucidated, and it is found that the width of the quantization plateau in the low-temperature region is inversely proportional to the ribbon width.

Photon-mediated thermal relaxation of electrons in nanostructures.

Measurements of the thermal properties of nanoscale electron systems have ignored the effect of electrical noise radiated between the electron gas and the environment, through the electrical leads. Here we calculate the effect of this photon-mediated process, and show that the low-temperature thermal conductance is equal to the quantum of thermal conductance, GQ = pi2kB2T/3h, times a coupling coefficient. We find that, at very low temperatures, the photon conductance is the dominant route for thermal equilibration, while at moderate temperatures this relaxation mode adds one quantum of thermal conductance to that due to phonon transport.

Low-temperature thermal conductance of carbon nanotubes

The universal behavior of low-temperature thermal conductance in single-walled carbon nanotubes is revealed within the framework of the Landauer theory of heat transport. The phonon-derived thermal conductance is quantized as a universal value of π 2 k B 2 T/3 h in the low-temperature limit, T→0, independent of radius or chirality. The temperature dependence follows a single curve given in terms of temperature scaled by the energy gap of the lowest optical mode. In contrast, the electronic contribution to thermal conductance at low temperature is found to be strongly dependent on the tube geometry responsible for the electronic states.

Phonon transport in nanowires coated with an amorphous material: An atomistic Green’s function approach

An approach is presented for the atomistic study of phonon transport in real dielectric nanowires via Green's functions. The formalism is applied to investigate the phonon flow through nanowires coated by an amorphous material. Examples for a simple model system and for real Si nanowires coated by silica are given. New physical results emerge for these systems, regarding the character of the transition from ballistic to diffusive transport, the low-temperature thermal conductance, and the influence of the wire-coating interface on the thermal transport. An efficient treatment of phonon scattering by the amorphous coating is also developed, representing a valuable tool for the investigation of thermal conduction through amorphous-coated nanowires.