Thermal Conductivity Of Silicon Nanowires Research Articles

Modeling thermal conductivity in silicon nanowires

AbstractThe complexity of heat transport in silicon nanowires (SiNWs) and, specifically, its dependence on temperature and the nanowire diameter, is beyond continuum models of heat conduction and necessitate consideration of atomic‐level heat‐conduction models. In this work, we specifically aim to ascertain the ability of models based on non‐equilibrium statistical mechanics to reproduce the observed anisotropy, temperature and size dependence of the thermal conductivity of SiNWs. In this approach, the atomic‐level kinetic relations are regarded as empirical and subject to modeling. Within this framework, we find that a simple model, based on the introduction of a thin amorphous layer at the surface of the SiNWs, yields effective thermal conductivities that are in excellent agreement with the experimental data over a range of temperatures and diameters. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of vacancy defects and axial strain on thermal conductivity of silicon nanowires: A reverse nonequilibrium molecular dynamics simulation

Thermal conductivity of silicon nanowires (SiNWs) is evaluated using the reverse nonequilibrium molecular dynamics simulation. The Stillinger–Weber (SW) and Tersoff interatomic potentials are employed to simulate thermal conductivity of SiNWs. In this work, the influence of random vacancy defects, axial strain, temperature and length on thermal conductivity and effective mean free path of SiNWs is investigated. It is found that by raising the percent of random vacancy defects, thermal conductivity of SiNWs decreases linearly for the results obtained form SW potential and nonlinearly for those obtained from Tersoff interatomic potential. Dependence of the thermal conductivity on axial strain is also studied. Results show that thermal conductivity increases as compressive strain increases and decreases as tensile strain increases. Influence of temperature is also predicted. It is found that the thermal conductivity of SiNWs decreases with increasing the mean temperature. Most of the simulations are performed for 4 UC×4 UC×40 UC silicon nanowires using ssp boundary condition.

Top-down fabrication of silicon nanowire devices for thermoelectric applications: properties and perspectives

In this paper, the most recent achievements in the field of device fabrication, based on nanostructured silicon, will be reviewed. Top-down techniques for silicon nanowire production based on lithography, oxidation and highly anisotropic etching (wet, plasma and metal assisted) will be discussed, illustrating both advantages and drawbacks. In particular, fabrication processes for a massive production of silicon nanowires, organized and interconnected in devices with macroscopic dimensions, will be shown and discussed. These macroscopic devices offer the possibility of exploiting the nanoscale thermoelectric properties of silicon in practical applications. In particular, the reduced thermal conductivity of silicon nanowires, with respect to bulk silicon, makes possible to obtain high efficiencies in the direct conversion of heat into electrical power, with intriguing applications in the field of green energy harvesting. The main experiments elucidating the electrical and thermal properties of silicon nanowire devices will be shown and discussed, and compared with the recent theoretical works developed on the subject.

Strain- and defect-mediated thermal conductivity in silicon nanowires.

The unique thermal transport of insulating nanostructures is attributed to the convergence of material length scales with the mean free paths of quantized lattice vibrations known as phonons, enabling promising next-generation thermal transistors, thermal barriers, and thermoelectrics. Apart from size, strain and defects are also known to drastically affect heat transport when introduced in an otherwise undisturbed crystalline lattice. Here we report the first experimental measurements of the effect of both spatially uniform strain and point defects on thermal conductivity of an individual suspended nanowire using in situ Raman piezothermography. Our results show that whereas phononic transport in undoped Si nanowires with diameters in the range of 170-180 nm is largely unaffected by uniform elastic tensile strain, another means of disturbing a pristine lattice, namely, point defects introduced via ion bombardment, can reduce the thermal conductivity by over 70%. In addition to discerning surface- and core-governed pathways for controlling thermal transport in phonon-dominated insulators and semiconductors, we expect our novel approach to have broad applicability to a wide class of functional one- and two-dimensional nanomaterials.

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.

(Invited) The Effects of Doping Pattern on Lattice Thermal Conductivity of Silicon Nanowires

The thermal conductivity of silicon nanowire doped with Germanium in different geometrical distributions was investigated with nonequilibrium molecular dynamics method. Five different geometrical arrangements of the impurities that influence the thermal conductivity properties of silicon nanowires were investigated, which include centralization doping, uniform doping, non-uniform doping, random doping and cubic pattern doping. The results demonstrate that the uniformity of the impurity positions has a substantial influence on the thermal conductivity of silicon nanowires under the same impurity concentration.

Phonon focusing and temperature dependences of the thermal conductivity of silicon nanowires

Phonon focusing and temperature dependences of the thermal conductivity of silicon nanowires

Analysis of phonon transport in silicon nanowires including optical phonons

The present study identifies and investigates the dominant phonon contribution to the thermal conductivity of silicon nanowires at room temperature. We have employed the full phonon dispersion model including the heat transfer by optical phonons and have conducted a phonon band-to-band analysis in order to elucidate the energy transport mechanisms of each phonon band with a different polarization and frequency. The longitudinal acoustic phonon bands of 4 ∼ 8 THz is found to mainly contribute to the thermal conductivity of silicon nanowires (approximately 60%), whose diameters range from 37 to 115 nm. Although the contribution of optical phonons to the thermal conductivity is less than 10% even at nanometer-scale diameters, optical phonons can interact with acoustic phonons and modify their contribution to the thermal conductivity, especially at high frequencies. The results obtained from this study provide detailed information on which phonons of a certain polarization and frequency are dominant heat carriers in silicon nanowires.

Thermal conductivity of silicon nanowires: From fundamentals to phononic engineering

Abstractmagnified imageSilicon nanowires have attracted great interest in recent years due to their ideal interface compatibility with silicon‐based electronic technology and their various potential applications, such as energy harvest and generation, and thermal management. A variety of theoretical and experimental studies have been conducted to understand the thermal properties of silicon nanowires. In this review, we summarize the recent progress in this field from the perspective of both theoretical calculations and experiments. First, we introduce the fundamental physics underlying the thermal conduction of silicon nanowires. Then, the various approaches to manipulate the thermal conductivity of silicon nanowires are discussed. Finally, based on the understanding of dominant scattering mechanisms in different phonon frequency regimes, we present the basic concept of phononic engineering to control the thermal conductivity of silicon nanowires. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Spectral Phonon Scattering from Sub-10 nm Surface Roughness Wavelengths in Metal-Assisted Chemically Etched Si Nanowires

Frequency dependence in phonon surface scattering is a debated topic in fundamental phonon physics. Recent experiments and theory suggest such a phenomenon, but an independent agreement between the two remains elusive. We report low-temperature dependence of thermal conductivity in silicon nanowires fabricated using a two-step, metal-assisted chemical etch. By reducing etch rates down to 0.5 nm/s from the typical >100 nm/s, we report controllable roughening of nanowire surfaces and selectively focus on moderate roughness scales rather than the extreme scales investigated previously. This critically enables direct comparison with perturbation-based spectral scattering theory. Using experimentally characterized surface roughness, we show that a multiple scattering theory provides excellent agreement and explanation of the observed low-temperature dependence of rough surface nanowires. The theory does not employ any fitting parameters. A 5-10 nm roughness correlation length is typical in metal-assisted chemical etching and resonantly scatters dominant phonons in silicon, leading to the observed ~T(1.6-2.4) behavior. Our work provides fundamental and quantitative insight into spectral phonon scattering from rough surfaces. This advances applications of nanowires in thermoelectric energy conversion.

Significant reduction of thermal conductivity in silicon nanowires by shell doping

Reducing the thermal conductivity of silicon nanowires (SiNWs) can enhance the thermoelectric figure of merit. Applying non-equilibrium molecular dynamics simulation, we demonstrate that the thermal conductivity of SiNWs can be reduced remarkably by shell doping due to both impurity scattering and interface scattering associated with the peculiar structure of shell-doped SiNWs. In order to reveal the origin of the reduction of thermal conductivity, we perform the vibrational eigenmodes analysis and find the strong localization of phonon modes from 9.0 THz to 16.0 THz in shell-doped SiNWs. Furthermore, we evaluate the spatial distribution of localized modes and demonstrate that the strong localization of phonons in the shell-doped region suppresses thermal transport in shell-doped SiNWs greatly and is responsible for the significant reduction of thermal conductivity.

Phonon surface scattering controlled length dependence of thermal conductivity of silicon nanowires

We present a kinetic model to investigate the anomalous thermal conductivity in silicon nanowires (SiNWs) by focusing on the mechanism of phonon-boundary scattering. Our theoretical model takes into account the anharmonic phonon-phonon scattering and the angle-dependent phonon scattering from the SiNWs surface. For SiNWs with diameter of 27.2 nm, it is found that in the case of specular reflection at lateral boundaries, the thermal conductivity increases as the length increases, even when the length is up to 10 μm, which is considerably longer than the phonon mean free path (MFP). Thus the phonon-phonon scattering alone is not sufficient for obtaining a normal diffusion in nanowires. However, in the case of purely diffuse reflection at lateral boundaries, the phonons diffuse normally and the thermal conductivity converges to a constant when the length of the nanowire is greater than 100 nm. Our model demonstrates that for observing the length dependence of thermal conductivity experimentally, nanowires with smooth and non-contaminated surfaces, and measuring at low temperature, are preferred.

Understanding length dependences of effective thermal conductivity of nanowires

We have studied the length dependence of effective thermal conductivity of silicon nanowires by a thermon gas model and MD simulations. After modifications of the force term by considering the resistance enhancements from thermon gas interactions with the confined surfaces and the ends (inlet and outlet), the theoretical predictions of effective thermal conductivity agree well with the results of MD simulations in the length range of 4 to 550 nm. The result suggests that the resistance enhancement effect by thermon–boundary interactions, instead of the heat inertia, plays the dominating role in the non-Fourier heat conduction in silicon nanowires.

The effect of the electron–phonon coupling on the thermal conductivity of silicon nanowires

The thermal conductivity of free-standing silicon nanowires (SiNWs) with diameters from 1–3 nm has been studied by using the one-dimensional Boltzmann’s transport equation. Our model explicitly accounts for the Umklapp scattering process and electron–phonon coupling effects in the calculation of the phonon scattering rates. The role of the electron–phonon coupling in the heat transport is relatively small for large silicon nanowires. It is found that the effect of the electron–phonon coupling on the thermal conduction is enhanced as the diameter of the silicon nanowires decreases. Electrons in the conduction band scatter low-energy phonons effectively where surface modes dominate, resulting in a smaller thermal conductivity. Neglecting the electron–phonon coupling leads to overestimation of the thermal transport for ultra-thin SiNWs. The detailed study of the phonon density of states from the surface atoms and central atoms shows a better understanding of the nontrivial size dependence of the heat transport in silicon nanowire.

Microscopic Origin of the Reduced Thermal Conductivity of Silicon Nanowires

We designed nanowires with a tailored surface structure and composition and with specific core defects to investigate the microscopic origin of the reduced thermal conductivity of Si at the nanoscale. We considered a diameter (15 nm) comparable to that of systems fabricated in recent experiments and we computed the thermal conductivity using equilibrium molecular dynamics simulations. We found that the presence of a native oxide surface layer may account for a tenfold to ~30-fold decrease in conductivity, with respect to bulk Si, depending on the level of roughness. However it is only the combination of core defects and surface ripples that enables a decrease close to 2 orders of magnitude, similar to that reported experimentally.

Phonon thermal conductivity in silicon nanowires: The effects of surface roughness at low temperatures

Using a Green’s function method based on an elastic wave equation, the effects of surface roughness and the nanowire-contact interface scattering on phonon thermal conductivity are studied at low temperatures. It is found that the interface geometry between a nanowire and its contacts affects the transmission function at small energies related to the gapless modes and it gives rise to deviated results from the universal conductance. It is also shown that the surface roughness is crucial in the suppression of phonon thermal conductivity with reducing the nanowire size by averaging the transmission function over the rough-surface configurations. Furthermore, the phonon mean free path is proportional to the ratio of the correlation length and roughness heights quadratically as well as the cross-section area of the nanowire.

A universal gauge for thermal conductivity of silicon nanowires with different cross sectional geometries

By using molecular dynamics simulations, we study thermal conductivity of silicon nanowires (SiNWs) with different cross sectional geometries. It is found that thermal conductivity decreases monotonically with the increase of surface-to-volume ratio (SVR). More interestingly, a simple universal linear dependence of thermal conductivity on SVR is observed for SiNWs with modest cross sectional area (larger than 20 nm(2)), regardless of the cross sectional geometry. As a result, among different shaped SiNWs with the same cross sectional area, the one with triangular cross section has the lowest thermal conductivity. Our study provides not only a universal gauge for thermal conductivity among different cross sectional geometries, but also a designing guidance to tune thermal conductivity by geometry.

Molecular dynamics simulations for the prediction of thermal conductivity of bulk silicon and silicon nanowires: Influence of interatomic potentials and boundary conditions

The reliability of molecular dynamics (MD) results depends strongly on the choice of interatomic potentials and simulation conditions. Five interatomic potentials have been evaluated for heat transfer MD simulations of silicon, based on the description of the harmonic (dispersion curves) and anharmonic (linear thermal expansion) properties. The best interatomic potential is the second nearest-neighbor modified embedded atom method potential followed by the Stillinger-Weber, and then the Tersoff III. However, the prediction of the bulk silicon thermal conductivity leads to the conclusion that the Tersoff III potential gives the best results for isotopically pure silicon at high temperatures. The thermal conductivity of silicon nanowires as a function of cross-section and length is calculated, and the influence of the boundary conditions is studied for those five potentials.

The effect of surface roughness on lattice thermal conductivity of silicon nanowires

A theoretic model is presented to take into account the roughness effects on phonon transport in Si nanowires (NWs). Based on the roughness model, an indirect Monte Carlo (MC) simulation is carried out to predict the lattice thermal conductivities of the NWs with different surface qualities. Through fitting the experimental data with the MC predictions, the scattering strength on phonons from the boundary, umklapp phonon–phonon processes and impurities can be estimated. It is found that the scattering on phonons by the roughness cell boundaries in a rough nanowire can reduce the phonon mean free path to be smaller than the nanowire diameter, the Casimir limit of the phonon mean free path in a flat nanowire for phonons engaged in completely diffused boundary scattering processes.

Remarkable Reduction of Thermal Conductivity in Silicon Nanotubes

We propose to reduce the thermal conductivity of silicon nanowires (SiNWs) by introducing a small hole at the center, i.e., construct a silicon nanotube (SiNT) structure. Our numerical results demonstrate that a very small hole (only 1% reduction in cross section area) can induce a 35% reduction in room temperature thermal conductivity. Moreover, with the same cross section area, thermal conductivity of SiNT is only about 33% of that of SiNW at room temperature. The spatial distribution of vibrational energy reveals that localization modes are concentrated on the inner and outer surfaces of SiNTs. The enhanced surface-to-volume ratio in SiNTs reduces the percentage of delocalized modes, which is believed to be responsible for the reduction of thermal conductivity. Our study suggests SiNT is a promising thermoelectric material with low thermal conductivity.