Thermal Conductivity Of Silicon Nanowires Research Articles

Atomistic wave packet investigation of phonon scattering at rough surfaces

Investigating the phonon-surface scattering mechanism is essential for the evaluation of thermal transport in nanostructures. The theoretical description to quantify this mechanism remains to be developed at the atomic scale. This work presents a phonon wave packet method to study the phonon-surface scattering behavior at rough surfaces. We obtain the specularity distribution dependent on phonon polarization, wavelength, and surface roughness. The reflection of the diffuse wave packet is primarily attributed to the surface shadowing effect at a higher incident angle, surface disorder, and surface-induced localized modes. Taking the wavevector-dependent specularity data as input, the thermal conductivity of silicon nanowires is calculated based on the Boltzmann Transport Equation. Our specularity model provides an accurate evaluation for predicting thermal conductivity. This work offers an atomic-level analysis for phonon-surface interaction, which is helpful for the understanding of thermal transport in nanostructures.

The influence of Surface Roughness on the Lattice thermal Conductivity in Silicon Nanowires

The influence of Surface Roughness on the Lattice thermal Conductivity in Silicon Nanowires

Remarkable Thermal Conductivity Reduction of Silicon Nanowires during the Bending Process.

The one-dimensional geometry of silicon nanowire helps to overcome the rigid and brittle nature of bulk silicon and enables it to withstand substantial bending stresses. This provides exciting opportunities for the development of flexible electronics. The bending strain introduces atomic displacement in the lattice structure, which inherently has a significant impact on the thermal conductivity. The strain-dependent thermal conductivity of silicon nanowire is crucial to the thermal management and performance of flexible electronic devices. However, in situ thermal conductivity measurement of bending silicon nanowires remains challenging and unreported due to the varying thermal contact resistances between the sample and sensor/heat sink. In this study, the Raman spectroscopy-assisted steady state thermal conductivity measurement method is coupled with a micromanipulation system to successively monitor the thermal conductivity variation of silicon nanowires during the bending process. The result shows that the thermal conductivity of silicon nanowires steeply decreases 55-78% owing to the strain-induced structural deformation during bending. Furthermore, the proposed in situ thermal conductivity measurement method can also be extended to other nanomaterials.

Giant Isotope Effect of Thermal Conductivity in Silicon Nanowires.

Isotopically purified semiconductors potentially dissipate heat better than their natural, isotopically mixed counterparts as they have higher thermal conductivity (κ). But the benefit is low for Si at room temperature, amounting to only ∼10% higher κ for bulk ^{28}Si than for bulk natural Si (^{nat}Si). We show that in stark contrast to this bulk behavior, ^{28}Si (99.92% enriched) nanowires have up to 150% higher κ than ^{nat}Si nanowires with similar diameters and surface morphology. Using a first-principles phonon dispersion model, this giant isotope effect is attributed to a mutual enhancement of isotope scattering and surface scattering of phonons in ^{nat}Si nanowires, correlated via transmission of phonons to the native amorphous SiO_{2} shell. The Letter discovers the strongest isotope effect of κ at room temperature among all materials reported to date and inspires potential applications of isotopically enriched semiconductors in microelectronics.

Manipulating thermal conductivity of silicon nanowires through surrounded fins and Ge dopant

Manipulating the phonon transport using nanotechnologies is one of the commonly adopted ways to reduce the thermal conductivity and enhance the thermoelectric performance of thermoelectric materials. In this work, we proposed a resonant structure, surrounded fins, for Si nanowires. The effects of both surrounded fins and Ge dopant on the thermal transport in Si NWs are studied using the molecular dynamics simulations. The root-mean-square (RMS) displacement, phonon dispersion, density of states and transmission function have been calculated to understand the thermal conductivity reduction in Si NWs. The calculated results show that both the surrounded fins and Ge dopants could significantly decrease the thermal conductivity of Si NWs. The thermal conductivity of finned Si NWs decreases with increasing the height of the surrounded fins. The more surrounded fins added, the more significant the thermal conductivity decreases. The thermal conductivity of SiGe NWs decreases initially and then increases with increasing Ge concentration. Through the analysis of RMS displacement and phonon dispersion, we found that surround fins could not only enhance anharmonicity by activating atoms near to the edge, but also increase the low frequency phonons and decrease the group velocities by modifying phonon dispersion relationship. The phonon transmission function suggests that the surrounded fins and Ge dopants would mainly suppress the transport of low-frequency and high-frequency phonons, respectively. Phonon transport in Si NWs could be suppressed over the whole frequency range by combining the surrounded fins and Ge dopants. Our results provide useful guidance in the design of efficient thermoelectric devices made of nanowires.

Molecular Dynamics Simulations on Influence of Defect on Thermal Conductivity of Silicon Nanowires

A non-equilibrium molecular dynamics simulation method is conducted to study the thermal conductivity (TC) of silicon nanowires (SiNWs) with different types of defects. The impacts of defect position, porosity, temperature, and length on the TC of SiNWs are analyzed. The numerical results indicate that SiNWs with surface defects have higher TC than SiNWs with inner defects, the TC of SiNWs gradually decreases with the increase of porosity and temperature, and the impact of temperature on the TC of SiNWs with defects is weaker than the impact on the TC of SiNWs with no defects. The TC of SiNWs increases as their length increases. SiNWs with no defects have the highest corresponding frequency of low-frequency peaks of phonon density of states; however, when SiNWs have inner defects, the lowest frequency is observed. Under the same porosity, the average phonon participation of SiNWs with surface defects is higher than that of SiNWs with inner defects.

Tuning Thermal Conductivity in Si Nanowires with Patterned StructuresSupported by the National Natural Science Foundation of China (Grant No. 11875047).

Tuning the thermal conductivity of silicon nanowires (Si-NWs) is essential for realization of future thermoelectric devices. The corresponding management of thermal transport is strongly related to the scattering of phonons, which are the primary heat carriers in Si-NWs. Using the molecular dynamics method, we find that the scattering of phonons from internal body defects is stronger than that from surface structures in the low-porosity range. Based on our simulations, we propose the concept of an exponential decay in thermal conductivity with porosity, specifically in the low-porosity range. In contrast, the thermal conductivity of Si-NWs with a higher porosity approaches the amorphous limit, and is insensitive to specific phonon scattering processes. Our findings contribute to a better understanding of the tuning of thermal conductivity in Si-NWs by means of patterned nanostructures, and may provide valuable insights into the optimal design of one-dimensional thermoelectric materials.

Nonlocal heat conduction in silicon nanowires and carbon nanotubes

Experimental results showed that the effective thermal conductivity of silicon nanowire is smaller than the bulk thermal conductivity, while that of carbon nanotube (CNT) is usually much larger than its bulk counterpart. In order to resolve this paradox, a nonlocal heat conduction model for one-dimensional materials is proposed. This nonlocal model indicates that the different heat conduction boundary conditions of silicon nanowire and CNT lead to the different behaviour of their thermal conductivities in comparison with their bulk counterparts. Furthermore, the nonlocal effect of heat flux on the surfaces of the CNT makes the thermal conductivity of the single-wall CNT more than seven orders of magnitude higher than its bulk thermal conductivity. The thermal conductivities of the single-wall and multi-wall CNTs obtained by using the nonlocal model show an agreement with the experimental ones.

Ultra-low thermal conductivity of roughened silicon nanowires: Role of phonon-surface bond order imperfection scattering**Project supported by the National Natural Science Foundation of China (Grant No. 11874145).

The ultra-low thermal conductivity of roughened silicon nanowires (SiNWs) can not be explained by the classical phonon–surface scattering mechanism. Although there have been several efforts at developing theories of phonon–surface scattering to interpret it, but the underlying reason is still debatable. We consider that the bond order loss and correlative bond hardening on the surface of roughened SiNWs will deeply influence the thermal transport because of their ultra-high surface-to-volume ratio. By combining this mechanism with the phonon Boltzmann transport equation, we explicate that the suppression of high-frequency phonons results in the obvious reduction of thermal conductivity of roughened SiNWs. Moreover, we verify that the roughness amplitude has more remarkable influence on thermal conductivity of SiNWs than the roughness correlation length, and the surface-to-volume ratio is a nearly universal gauge for thermal conductivity of roughened SiNWs.

Enhanced thermoelectric properties of cobalt silicide-silicon heterostructured nanowires

Silicon nanowires (SiNWs) have attracted attention as promising high efficiency thermoelectric materials by significantly improving the thermoelectric efficiency of silicon. Here, we have fabricated cobalt silicide/silicon heterostructure on both ends of nanowires using self-aligned silicide (salicide) process. By forming cobalt silicide (CoSi2) layer on SiNWs, the thermal conductivity of SiNWs with diameters of 200, 350, and 500 nm decrease to 25.1, 31.3, and 38.1 W·m−1·K−1, respectively, which is about 8% reduction on average. Since the phonon nanoinclusion scattering is influenced by the density of the nanoinclusions, the thermal conductivity tends to decrease as the volume fraction of CoSi2 in SiNWs increases. The Seebeck coefficient of the heterostructured nanowires increases to 255 μV/K, which is mainly attributed to the low-energy charge carrier filtering effect due to the Schottky barrier at the CoSi2/Si interfaces. The measurements show that the figure-of-merit ZT of the heterostructured nanowires is improved by 10% on average compared with the conventional SiNWs. Consequently, the CoSi2/Si heterostructured nanowires enhance the thermoelectric properties of SiNWs effectively by suppressing phonon transport and improving electron flow.

(Invited) Cavity-Free Micro Thermoelectric Energy Harvester with Si Nanowires

Forthcoming trillion-sensors-network society demands the maturity of energy harvesting technology. Among various energy harvesting devices, thermoelectric generator (TEG), which utilizes the Seebeck effect of semiconductors, is anticipated as an ultimate one because it has a potential to provide a semipermanent power from almost unlimited heat energies. In a TEG, the efficiency of energy conversion from heat to electricity is determined by the thermoelectric figure of merit, ZT= S2σT/κ of the employed semiconductor, where S is the Seebeck coefficient, σ the electrical conductivity, κ the thermal conductivity, and T the average temperature between heat source and cold sink. Although higher ZT is favorable to achieve high conversion efficiency, only limited materials were known to have high ZT near the room temperature. Recently, silicon nanowires (Si-NWs) emerged as a promising thermoelectric material; the thermal conductivity of Si-NW was found to decrease drastically as the nanowire is thinned. [1,2] Since then, a number of fabrication examples of Si-based TEG has been reported. [3-5] Conventional demonstrations of planar type Si-based TEG employed long Si-NWs about 10-100 μm which were suspended on a cavity to avoid the bypass of the heat current, as shown in Fig 1a. The authors’ group proposed a new design of planar and short Si-NW TEG, which is illustrated as Fig. 1b. [6-9] Our proposed device is driven by a steep temperature gradient exuding around a heat flow perpendicular to the substrate, and the nanowires are not suspended on a cavity. Furthermore, the power density is scalable by shortening Si-NW to sub-μm length; the areal power generation density is inversely proportional to the square of the NW length. It has been experimentally confirmed that the thermoelectric power was enhanced by shortening the nanowire, and tens of µW/cm2-class power generation was achieved [6,7]. Fig. 2 shows an experimental Si-NW TEG fabricated on a silicon-on-insulator (SOI) wafer by the conventional CMOS process. The SOI layer was patterned into Si-NWs by ArF immersion lithography and reactive-ion etching. Both ends of Si-NW bundle are connected to Si-pads. Al/TiN/Ti electrode was deposited on the Si-pad. We prepared samples with different base Si-substrate thickness, by thinning with backside grinding. The hot side electrode was heated by a custom-made micro thermostat, and the base stage was maintained at room temperature by a water chiller. Fig. 3 shows the thermoelectric power density versus loading voltage curves, measured under an applied external temperature difference of 5 K. The measured power output is normalized by the area of the product of twice of the NW length and the NW pitch, supposing that the pads and NW arrays have a same footprint. The maximum power is obtained in the shortest NW device with 0.25 µm long. The thermoelectic power was drastically enhanced by reducing the Si-substrate thickness. Fig. 4 shows the dependence of the power density on the Si-substrate thickness. The power density of a sample with 50 µm thick Si-substrate reached 12 µW/cm2. The enhancement can be attributed to the increased temperature difference across Si-NWs by suppression of the series thermal resistance at the Si-substrate. Further improvement of thermoelectic power is expected by suppressing the thermal resistance at the Si-substrate. The temperature difference across Si-NW is expected to increase by partially replacing the Si substrate underneath the cold side edge of SiNW with Cu with higher thermal conductivity. According to our finite-element-simulation, [10] however, not only beneath the cold side edge of SiNW, replacing the whole substrate by Cu is the most effective way to improve the power generation density (Fig. 5). The results show that the thermal resistance of the entire substrate should be suppressed as a matter of first priority.

Effects of vacancy defects location on thermal conductivity of silicon nanowire: a molecular dynamics study

The improvement of thermoelectric figure of merit of silicon nanowire (SiNW) can be achieved by lowering its thermal conductivity. In this work, non-equilibrium molecular dynamics method was used to demonstrate that the thermal conductivity of bulk silicon crystal is drastically reduced when it is crafted as SiNW and that it can be reduced remarkably by including vacancy defects. It has been found that ‘centre vacancy defect’ contributes much more in reducing the thermal conductance than ‘surface vacancy defect’. The lowest thermal conductivity that occurs is about 52.1% of that of pristine SiNW, when 2% vacancy defect is introduced in the nanowire. The vibrational density of states analysis was performed to understand the nature of this reduction and it has been found that the various boundary scatterings of phonon significantly reduce the thermal conductivity. Also, larger mass difference due to voids induces smaller thermal conductivity values. These results indicate that the inclusion of vacancy defects can enhance the thermoelectric performance of SiNWs.

Effect of confinement on anharmonic phonon scattering and thermal conductivity in pristine silicon nanowires

The effect of confinement on the anharmonic phonon scattering rates and the consequences thereof on the thermal transport properties in ultrathin silicon nanowires with a diameter of 1--4 nm have been characterized using atomistic simulations and the phonon Boltzmann transport equation. The phonon density of states (PDOS) for ultrathin nanowires approaches a constant value in the vicinity of the $\mathrm{\ensuremath{\Gamma}}$ point and increases with decreasing diameter, which indicates the increasing importance of the low-frequency phonons as heat carriers. The anharmonic phonon scattering becomes dramatically enhanced with decreasing thickness of the nanowires. In the thinnest nanowire, the scattering rates for phonons above 1 THz are one order of magnitude higher than those in the bulk Si. Below 1 THz, the increase in scattering rates is even much more appreciable. Our numerical calculations revealed that the scattering rates for transverse (longitudinal) acoustic modes follow $\sqrt{\ensuremath{\omega}}$ ($1/\sqrt{\ensuremath{\omega}}$) dependence at the low-frequency limit, whereas those for the degenerate flexural modes asymptotically approach a constant value. In addition, the group velocities of phonons are reduced compared with bulk Si except for low-frequency phonons ($l1$--2 THz depending on the thickness of the nanowires). The increased scattering rates combined with reduced group velocities lead to a severely reduced thermal conductivity contribution from the high-frequency phonons. Although the thermal conductivity contributed by those phonons with low frequencies is instead increased mainly due to the increased PDOS, the total thermal conductivity is still reduced compared to that of the bulk. This work reveals an unexplored mechanism to understand the measured ultralow thermal conductivity of silicon nanowires.

Ultralow Thermal Conductivity of Single‐Crystalline Porous Silicon Nanowires

AbstractPorous materials provide a large surface‐to‐volume ratio, thereby providing a knob to alter fundamental properties in unprecedented ways. In thermal transport, porous nanomaterials can reduce thermal conductivity by not only enhancing phonon scattering from the boundaries of the pores and therefore decreasing the phonon mean free path, but also by reducing the phonon group velocity. Herein, a structure–property relationship is established by measuring the porosity and thermal conductivity of individual electrolessly etched single‐crystalline silicon nanowires using a novel electron‐beam heating technique. Such porous silicon nanowires exhibit extremely low diffusive thermal conductivity (as low as 0.33 W m−1 K−1 at 300 K for 43% porosity), even lower than that of amorphous silicon. The origin of such ultralow thermal conductivity is understood as a reduction in the phonon group velocity, experimentally verified by measuring the Young's modulus, as well as the smallest structural size ever reported in crystalline silicon (<5 nm). Molecular dynamics simulations support the observation of a drastic reduction in thermal conductivity of silicon nanowires as a function of porosity. Such porous materials provide an intriguing platform to tune phonon transport, which can be useful in the design of functional materials toward electronics and nanoelectromechanical systems.

Monte Carlo study of temperature-dependent non-diffusive thermal transport in Si nanowires

Non-diffusive thermal transport has gained extensive research interest recently due to its important implications on fundamental understanding of material’s phonon mean free path distributions and many nanoscale energy applications. In this work, we systematically investigate the role of boundary scattering and nanowire length on the non-diffusive thermal transport in thin silicon nanowires by rigorously solving the phonon Boltzmann transport equation (BTE) using a variance reduced Monte Carlo technique across a range of temperatures. The simulations use the complete phonon dispersion and spectral lifetime data obtained from first-principle density function theory calculations as input without any adjustable parameters. Our BTE simulation results show that the nanowire length plays an important role in determining the thermal conductivity of silicon nanowires. In addition, our simulation results suggest significant phonon confinement effect for the previously measured silicon nanowires. These findings are important for a comprehensive understanding of microscopic non-diffusive thermal transport in silicon nanowires.

Ballistic thermal transport in silicon nanowires

We have experimentally investigated the impact of dimensions and temperature on the thermal conductivity of silicon nanowires fabricated using a top-down approach. Both the width and temperature dependences of thermal conductivity agree with those in the existing literature. The length dependence of thermal conductivity exhibits a transition from semi-ballistic thermal phonon transport at 4 K to fully diffusive transport at room temperature. We additionally calculated the phonon dispersion in these structures in the framework of the theory of elasticity and showed that the thermal conductance increases with width. This agrees with our experimental observations and supports the pertinence of using the modified phonon dispersion at low temperatures.

Thermal conductivity of silicon nanowires embedded on thermoelectric platforms

In this study, we propose a simple method for obtaining the thermal conductivity of silicon nanowires (SiNWs) embedded on a thermoelectric platform. The approximation of the heat flux in SiNWs with temperature differences enables the determination of thermal conductivity. Using this method, the thermal conductivities of our n- and p-type SiNWs are found to be 18.06 ± 0.12 and 20.29 ± 0.77 W m−1 · K−1, respectively. The atomic weight of arsenic ions in the n-type SiNWs is responsible for a lower thermal conductivity than that of boron ions in the p-type SiNWs. Our results demonstrate that this simple method is capable of measuring the thermal conductivity of thermoelectric nanomaterials embedded on thermoelectric devices.

Blocking Phonon Transport by Structural Resonances in Alloy-Based Nanophononic Metamaterials Leads to Ultralow Thermal Conductivity.

Understanding the design rules to obtain materials that enable a tight control of phonon transport over a broad range of frequencies would aid major developments in thermoelectric energy harvesting, heat management in microelectronics, and information and communication technology. Using atomistic simulations we show that the metamaterials approach relying on localized resonances is very promising to engineer heat transport at the nanoscale. Combining designed resonant structures to alloying can lead to extremely low thermal conductivity in silicon nanowires. The hybridization between resonant phonons and propagating modes greatly reduces the group velocities and the phonon mean free paths in the low frequency acoustic range below 4THz. Concurrently, alloy scattering hinders the propagation of high frequency thermal phonons. Our calculations establish a rationale between the size, shape, and period of the resonant structures, and the thermal conductivity of the nanowire, and demonstrate that this approach is even effective to block phonon transport in wavelengths much longer than the size and period of the surface resonant structures. A further consequence of using resonant structures is that they are not expected to scatter electrons, which is beneficial for thermoelectric applications.

High-power thermoelectric generators based on nanostructured silicon

The low thermal conductivity of silicon nanowires and nanostructures opens interesting opportunities for energy harvesting through the direct, high-efficiency, conversion of waste heat into electrical power. We present solutions for the fabrication and interconnection of a high number of suspended silicon nanostructures, within CMOS compatible top-down processes. Mechanical stability and thermoelectric properties of these devices will be analysed by means of finite element simulations, and opportunities for practical applications will be discussed. It will be shown that, despite the reduced dimensions needed for a strong suppression of thermal conductivity, a considerable amount of electrical power can be delivered to the load as a result of the presence of many interconnected devices on the same chip.

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)