Thermal Conductivity Of Nanostructures Research Articles

Thermal Conductivity of Nanostructure in Microelectronic Equipment and the Enhancement of Its Thermo-Physical Properties

To optimize the heat dissipation performance of microelectronic equipment, optical instrument, and optoelectronic devices, it’s necessary to explore the heat transfer mechanism of the nanostructure in them, however, due to the limitation of the research objects, there isn’t a uniform simulation method for the thermo-physical properties of such nanostructure. Therefore, this paper aims to study the thermo-physical properties of nanostructure in microelectronic equipment. At first, by structuring Si super lattice nanowires in a specific direction and then using the Ge atoms to replace the Si atoms in the nanowires, this paper built a model for the periodic Si/Ge super lattice nanowires. Then, this paper performed integral operation on the dynamic equations of the two types of atoms using the time integration algorithm to attain the trajectories of Si and Ge atoms in the nanowire structure of the microelectronic equipment, and discussed the influence of the size and geometrical shape of the cross section of nanowires on thermal conductivity. After that, this paper simulated the structure of the nano-scale SiC material, selected appropriate cut-off radius, and optimized the structure of the nanostructure model based on the Discover Minimization module. At last, the thermal conductivity of the nanostructure was calculated and its thermo-physical properties were analyzed.

Enhancing the Thermal Conductivity of Amorphous Carbon with Nanowires and Nanotubes.

The thermal conductivity of nanostructures can be obtained using atomistic classical Molecular Dynamics (MD) simulations, particularly for semiconductors where there is no significant contribution from electrons to thermal conduction. In this work, we obtain and analyze the thermal conductivity of amorphous carbon (aC) nanowires (NW) with a 2 nm radius and aC nanotubes (NT) with 0.5, 1 and 1.3 nm internal radii and a 2 nm external radius. The behavior of thermal conductivity with internal radii, temperature and density (related to different levels of hybridization), is compared with experimental results from the literature. Reasonable agreement is found between our modeling results and the experiments for aC films. In addition, in our simulations, the bulk conductivity is lower than the NW conductivity, which in turn is lower than the NT conductivity. NTs thermal conductivity can be tailored as a function of the wall thickness, which surprisingly increases when the wall thickness decreases. While the vibrational density of states (VDOS) is similar for bulk, NW and NT, the elastic modulus is sensitive to the geometrical parameters, which can explain the enhanced thermal conductivity observed for the simulated nanostructures.

Nanoscale limit of the thermal conductivity in crystalline silicon carbide membranes, nanowires, and phononic crystals

Silicon carbide (SiC) aims to be the number one material for power microelectronics due to its remarkable thermal properties. Recent progress in SiC technology finally enabled the fabrication of crystalline SiC nanostructures. Yet, the thermal properties of SiC at the nanoscale remain overlooked. Here, we systematically study heat conduction in SiC nanostructures, including nanomembranes, nanowires, and phononic crystals. Our measurements show that the thermal conductivity of nanostructures is several times lower than that in bulk and that the values scale proportionally to the narrowest dimension of the structures. In the smallest nanostructures, the thermal conductivity reached 10% of that in bulk. To better understand nanoscale thermal transport in SiC, we also probed phonon mean free path and coherent heat conduction in the nanostructures. Our theoretical model links the observed suppression of heat conduction with the surface phonon scattering, which limits the phonon mean free path and thus reduces the thermal conductivity. This work uncovers thermal characteristics of SiC nanostructures and explains their origin, thus enabling realistic thermal engineering in SiC microelectronics.

Enhanced thermal conduction by surface phonon-polaritons.

Improving heat dissipation in increasingly miniature microelectronic devices is a serious challenge, as the thermal conduction in nanostructures is markedly reduced by increasingly frequent scattering of phonons on the surface. However, the surface could become an additional heat dissipation channel if phonons couple with photons forming hybrid surface quasiparticles called surface phonon-polaritons (SPhPs). Here, we experimentally demonstrate the formation of SPhPs on the surface of SiN nanomembranes and subsequent enhancement of heat conduction. Our measurements show that the in-plane thermal conductivity of membranes thinner than 50 nm doubles up as the temperature rises from 300 to 800 kelvin, while thicker membranes show a monotonic decrease. Our theoretical analysis shows that these thickness and temperature dependencies are fingerprints of SPhP contribution to heat conduction. The demonstrated thermal transport by SPhPs can be useful as a previously unidentified channel of heat dissipation in a variety of fields including microelectronics and silicon photonics.

Thermal conductivity of silicon nanowire forests

A large amount of parallel silicon nanowires, placed perpendicularly to a silicon substrate (silicon nanowire forests), have been contacted and assembled in order to fabricate legs of a thermoelectric generator. This paper reports the measurement of the main parameter for thermoelectric applications, which is the thermal conductivity. The reported value, which confirms the strong reduction of the thermal conductivity in nanostructures, is measured on a large amount (>107) of parallel nanowires with a diameter variable in the range 60–120 nm, and takes into account eventual non-uniformities which are unavoidable on surfaces of several mm2. As silicon nanowire forests are very thin, it has been necessary to develop a suitable measurement apparatus. The fabrication of devices based on silicon nanowire forests, the apparatus and the measurement procedure, as well as the the results, are illustrated and discussed.

Shape, size and phonon scattering effect on the thermal conductivity of nanostructures

A phenomological model is described here to study the effect of size, shape and phonon scattering on the thermal conductivity of nanostructures. Using the classical model proposed by Guisbiers et al (Phys. Chem. Chem. Phys. 12, 7203 (2010), J. Phys. Chem. C 112, 4097 (2008)) in terms of the melting temperature of nanostructures, the expression for variation of thermal conductivity is obtained in terms of shape and size parameter. An additional term is included in the expression of thermal conductivity to consider the impact of phonon scattering due to the surface roughness with a decrease in size. The expression of thermal conductivity is obtained for spherical nanosolids, nanowires and nanofilms. The thermal conductivity is found to decrease in nanostructures in comparison with the counterpart bulk material. The values of thermal conductivity obtained from the present model are found to be close to the available experimental data for different values of roughness parameter which verifies the suitability of the model.

Impact of thermally dead volume on phonon conduction along silicon nanoladders.

Thermal conduction in complex periodic nanostructures remains a key area of open questions and research, and a particularly provocative and challenging detail is the impact of nanoscale material volumes that do not lie along the optimal line of sight for conduction. Here, we experimentally study thermal transport in silicon nanoladders, which feature two orthogonal heat conduction paths: unobstructed line-of-sight channels in the axial direction and interconnecting bridges between them. The nanoladders feature an array of rectangular holes in a 10 μm long straight beam with a 970 nm wide and 75 nm thick cross-section. We vary the pitch of these holes from 200 nm to 1100 nm to modulate the contribution of bridges to the net transport of heat in the axial direction. The effective thermal conductivity, corresponding to reduced heat flux, decreases from ∼45 W m-1 K-1 to ∼31 W m-1 K-1 with decreasing pitch. By solving the Boltzmann transport equation using phonon mean free paths taken from ab initio calculations, we model thermal transport in the nanoladders, and experimental results show excellent agreement with the predictions to within ∼11%. A combination of experiments and calculations shows that with decreasing pitch, thermal transport in nanoladders approaches the counterpart in a straight beam equivalent to the line-of-sight channels, indicating that the bridges constitute a thermally dead volume. This study suggests that ballistic effects are dictated by the line-of-sight channels, providing key insights into thermal conduction in nanostructured metamaterials.

Hierarchy of models for calculating the thermal conductivity in nanostructures

This work is devoted to the problem of the thermal conductivity calculation in nanostructures. Various models for thermal conductivity determination are discussed, including the original one. The results of calculations are presented.

Nanoscale Graphene Disk: A Natural Functionally Graded Material-How is Fourier's Law Violated along Radius Direction of 2D Disk.

In this Paper, we investigate numerically and analytically the thermal conductivity of nanoscale graphene disks (NGDs), and discussed the possibility to realize functionally graded material (FGM) with only one material, NGDs. Different from previous studies on divergence/non-diffusive of thermal conductivity in nano-structures with different size, we found a novel non-homogeneous (graded) thermal conductivity along the radius direction in a single nano-disk structure. We found that, instead of a constant value, the NGD has a graded thermal conductivity along the radius direction. That is, Fourier’s law of heat conduction is not valid in two dimensional graphene disk structures Moreover, we show the dependent of NGDs’ thermal conductivity on radius and temperature. Our study might inspire experimentalists to develop NGD based versatile FGMs, improve understanding of the heat removal of hot spots on chips, and enhance thermoelectric energy conversion efficiency by two dimensional disk with a graded thermal conductivity.

Indirect measurement of thermal conductivity in silicon nanowires

We report indirect measurements of thermal conductivity in silicon nanostructures. We have exploited a measurement technique based on the Joule self-heating of silicon nanowires. A standard model for the electron mobility has been used to determine the temperature through the accurate measurement of the nanowire resistance. We have applied this technique to devices fabricated with a top-down process that yields nanowires together with large silicon areas used both as electrical and as thermal contacts. As there is crystalline continuity between the nanowires and the large contact areas, our thermal conductivity measurements are not affected by any temperature drop due to the contact thermal resistance. Our results confirm the observed reduction of thermal conductivity in nanostructures and are comparable with those previously reported in the literature, achieved with more complex measurement techniques.

On the importance of optical phonons to thermal conductivity in nanostructures

The contribution of optical phonons to thermal conductivity has typically been ignored. However, when the system size decreases to the nanoscale regime, optical phonons are no longer negligible. In this study, the contributions of different phonon polarizations to the thermal conductivity of silicon are discussed based on the phonon lifetimes extracted from a first principles approach. The results indicate that around room temperature, optical phonons can contribute over 20% to the thermal conductivity of nanostructures as compared to 5% in bulk materials. In addition, the temperature and size dependence of the contributions from acoustic and optical phonons are fully explored.

Thermal conductivity of Si nanostructures containing defects: Methodology, isotope effects, and phonon trapping

A first-principles method to calculate the thermal conductivity in nanostructures that may contain defects or impurities is described in detail. The method mimics the so-called ``laser-flash'' technique to measure thermal conductivities. It starts with first-principles density-functional theory and involves the preparation of various regions of a supercell at slightly different temperatures. The temperature fluctuations are minimized without using a thermostat and, after averaging over random initial conditions, temperature changes as small as 5 K can be monitored (from 120 to 125 K). The changes to the phonon density of states and the specific heat induced by several atomic percent of impurities are discussed. The thermal conductivity of Si supercells is calculated as a function of the temperature and of the impurity content. For most impurities, the drop in thermal conductivity is unremarkable. However, there exist narrow ranges of impurity parameters (mass, bond strength, etc.) for which substantial drops in the thermal conductivity are predicted. These drops are isotope dependent and appear to be related to the vibrational lifetime of specific impurity-related modes.

Strain effects on the thermal conductivity of nanostructures

Applying stress/strain on a material provides a mechanism to tune the thermal conductivity of materials dynamically or on demand. Experimental and simulation results have shown that thermal conductivity of bulk materials can change significantly under external pressure (compressive stress). However, stress/strain effects on the thermal conductivity of nanostructures have not been systematically studied. In this paper, equilibrium molecular-dynamics (EMD) simulation is performed to systematically study the strain effects on the lattice thermal conductivity of low-dimensional silicon and carbon materials: silicon nanowires (one dimensional) and thin-films (two dimensional), single-walled carbon nanotube (SWCNT, one dimensional) and single-layer graphene sheet (two dimensional). Spectral analysis of EMD is further developed and then applied to avoid the numerical artifacts such as the neglect of long-wavelength phonons that are often encountered when using EMD with periodic boundary conditions. Intrinsic thermal conductivity of the simulated bulk and nanostructures can be obtained using spectral analysis of EMD. The thermal conductivity of the strained silicon and diamond nanowires and thin films is shown to decrease continuously when the strain changes from compressive to tensile. However, for SWCNT and single-layer graphene, the thermal conductivity has a peak value, and the corresponding applied strain is at $\ensuremath{-}0.06$ or $\ensuremath{-}0.03$ for SWCNTs depending on the chirality and at zero for graphene, respectively. The following two reasons could explain well the effects of strains on the thermal conductivity of the nanowires and thin films that decreases continuously from compressive strain to tensile strain: (1) mode-specific group velocities of phonons decrease continuously from compressive strain to tensile strain and (2) the specific heat of each propagating phonon modes decrease continuously from compressive strain to tensile strain. However, for SWCNT and single-layer graphene, the mechanical instability induces buckling phenomenon when they are under compressive strains. The phonon-phonon scattering rate increases significantly when the structure buckles. This results in the decreasing behavior of thermal conductivity of SWCNT and graphene under compressive stress and explains the peak thermal conductivity value observed in SWCNT and single-layer graphene when they are under strain. The results obtained in this paper has important implications of challenging thermal management of electronics using advanced materials such as carbon nanotubes and graphene. It also points to a potentially new direction of dynamic thermal management.

Energy dissipation and transport in nanoscale devices

Understanding energy dissipation and transport in nanoscale structures is of great importance for the design of energy-efficient circuits and energy-conversion systems. This is also a rich domain for fundamental discoveries at the intersection of electron, lattice (phonon), and optical (photon) interactions. This review presents recent progress in understanding and manipulation of energy dissipation and transport in nanoscale solid-state structures. First, the landscape of power usage from nanoscale transistors (∼10−8 W) to massive data centers (∼109 W) is surveyed. Then, focus is given to energy dissipation in nanoscale circuits, silicon transistors, carbon nanostructures, and semiconductor nanowires. Concepts of steady-state and transient thermal transport are also reviewed in the context of nanoscale devices with sub-nanosecond switching times. Finally, recent directions regarding energy transport are reviewed, including electrical and thermal conductivity of nanostructures, thermal rectification, and the role of ubiquitous material interfaces.

Analytical law for size effects on thermal conductivity of nanostructures

The thermal conductivity of a nanostructure is sensitive to its dimensions. A simple analytical scaling law that predicts how conductivity changes with the dimensions of the structure, however, has not been developed. The lack of such a law is a hurdle in ``phonon engineering'' of many important applications. Here, we report an analytical scaling law for thermal conductivity of nanostructures as a function of their dimensions. We have verified the law using very large molecular dynamics simulations.

Longitudinal thermal conductivity of radial nanowire heterostructures

Thermal conductivity of tubular nanowires and radial nanowire heterostructures is analytically modeled along the longitudinal direction by using Boltzmann transport equation. This work is on the basis of Dingle [Proc. R. Soc. London, Ser. A 201, 545 (1950)] and Lucas [J. Appl. Phys. 36, 1632 (1965)] formalisms on thin wires and films, respectively. To investigate the thermal conductivity dependence on the interface conditions, we have generalized Prasher’s analytical solution [Appl. Phys. Lett. 89, 063121 (2006)] to cover the case where the scattering events at the interfaces are not totally diffuse scattering. The calculation of the size-dependent thermal conductivity includes the partly diffuse and partly specular scatterings at both internal and external interfaces of the tubular nanowires. It is found that the calculated thermal conductivities are in good agreement with the numerical solution of Yang et al. [Nano Lett. 5, 1111 (2005)]. Comparison is also made with the thermal conductivity of thin films and solid nanowires with the same dimensions. Results show that the thermal conductivity of the structures can be modulated by changing the radius ratio between the shell layer and the core layer of the radial nanowire heterostructures. The obtained results may serve as a possible way for tuning the thermal conductivity in nanostructures.

The role of interface thermal boundary resistance in the overall thermal conductivity ofSi–Ge multilayered structures

Nanoscale engineered materials with tailored thermal properties are desirable forapplications such as highly efficient thermoelectric, microelectronic and optoelectronicdevices. It has been shown earlier that by judiciously varying the interface thermalboundary resistance (TBR), thermal conductivity in nanostructures can be controlled. Inthe presented investigation, the role of TBR in controlling thermal conductivity at thenanoscale is analyzed by performing non-equilibrium molecular dynamics (NEMD)simulations to calculate thermal conductivity of a range of Si–Ge multilayered structureswith 1–3 periods, and with four different layer thicknesses. The analyses are performed atthree different temperatures (400, 600 and 800 K). As expected, the thermal conductivity ofall layered structures increases with the increase in the number of periods as well as withthe increase in the monolayer thickness. Invariably, we find that the TBR offered by theinterface nearest to the hot reservoir is the highest. This effect is in contrast to the usualnotion that each interface contributes equally to the heat transfer resistance in a layeredstructure. Findings also suggest that for high period structures the average TBR offered bythe interfaces is not equal. Findings are used to derive an analytical expression thatdescribes period-length-dependent thermal conductivity of multilayered structures.

Lattice thermal conductivity in a Si∕Ge∕Si heterostructure

We have developed a model of lattice thermal conductivity in a freestanding three-layered Si∕Ge∕Si heterostructure. This model takes into account the phonon confinement and interface scattering. Moreover, we derive an analytical expression of the interface scattering rate for phonon conduction in a semiconductor heterostructure. It is found that the phonon transport is reduced in the heterostructure. We further investigate the dependence of the thermal conductivity of the Ge well layer on the Si barrier layer thickness. We show that the thermal conductivity of the well layer can be modulated in a wide range by adjusting the barrier layer thickness. It is found that the thermal conductivity of the well layer increases with the barrier layer thickness in the case of highly specular scattering. The obtained results can be used for tuning the thermal conductivity in nanostructures.

Analytical model for the thermal conductivity of nanostructures

We present an analytical expression for the thermal conductivity in nanostructures which takes into account all phonon properties: the number of modes, the group velocity, the relaxation time due to the Umklapp process and the boundary surface scattering and their variation with the wave vector directions. Phonon properties can be determined from the known dispersion curves and the bulk thermal conductivity. For the example of a cube made of solid argon, the variations of the thermal conductivity with the system size obtained using the analytical model and nonequilibrium molecular dynamics (NEMD) are in good agreement. The model is also used to calculate the thermal conductivity of a single graphite sheet and carbon nanotubes as a function of their characteristic lengths. The variations of the thermal conductivity with size are compared with the theoretical predictions for one and two dimensional systems. Good agreement is obtained for the single graphite sheet, but not for carbon nanotubes, which reveals the limitation of the analytical model.

Analytical model for the thermal conductivity of nanostructures

We present an analytical expression for the thermal conductivity in nanostructures which takes into account all phonon properties: the number of modes, the group velocity, the relaxation time due to the Umklapp process and the boundary surface scattering and their variation with the wave vector directions. Phonon properties can be determined from the known dispersion curves and the bulk thermal conductivity. For the example of a cube made of solid argon, the variations of the thermal conductivity with the system size obtained using the analytical model and nonequilibrium molecular dynamics (NEMD) are in good agreement. The model is also used to calculate the thermal conductivity of a single graphite sheet and carbon nanotubes as a function of their characteristic lengths. The variations of the thermal conductivity with size are compared with the theoretical predictions for one and two dimensional systems. Good agreement is obtained for the single graphite sheet, but not for carbon nanotubes, which reveals the limitation of the analytical model.