An analytical model for the thermal conductivity of silicon nanostructures (original) (raw)
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Predictive Model for the Thermal Conductivity of Rough and Smooth Silicon Nanowires
Science of Advanced Materials, 2015
The thermal conductivity of semiconductor nanowires (NWs) is significantly reduced with respect to their bulk counterparts. It decreases when the NW diameter is reduced and in addition it is dependent on the NW surface morphology, resulting in very low thermal conductivities for rough NWs. The thermal conductivity is a crucial physical magnitude for the thermal management of the nanodevices based on NWs; therefore, a great research effort has been focused in constructing theories that account for the thermal conductivity of semiconductor NWs. However, among all of these approaches, it is still lacking the possibility of predicting the value of the thermal conductivity of the NWs by the alone knowledge of the nature and morphology of the NWs. We present herein a predictive approach for determining the thermal conductivity of Silicon NWs, both smooth and rough, based on a modified Callaway-Holland formalism. It correlates well with the existing experimental data, and greatly simplifies the complex evaluation of thermal conductivity at the nanoscale by means of simple mathematical expressions. These expressions allow for the estimation of the Si NW thermal conductivity for any combination of diameter and surface morphology parameters.
2008
The thermoelectric efficiency of a material depends on the ratio of its electrical and thermal conductivity. In this work, the cross-sectional dependence of electron mobility and lattice thermal conductivity in silicon nanowires has been investigated by solving the electron and phonon Boltzmann transport equations. The effects of confinement on acoustic phonon scattering (both electron-phonon and phonon-phonon) are accounted for in this study. With decreasing wire crosssection, the electron mobility shows a non-monotonic variation, whereas the lattice thermal conductivity exhibits a linear decrease. The former is a result of the decrease in intervalley and intersubband scattering due to a redistribution of electrons among the twofold-degenerate ∆ 2 and fourfold-degenerate ∆ 4 valley subbands when the cross-section is below 5 × 5 nm 2 , while the latter is because of the monotonic increase of three phonon umklapp and boundary scattering with decreasing wire cross-section. Among the wires considered, those with a cross-section between 3 × 3 nm 2 and 4 × 4 nm 2 have the maximal ratio of the electron mobility to lattice thermal conductivity, and are expected to provide the maximal thermoelectric figure of merit.
Numerical simulation of transient phonon heat transfer in silicon nanowires and nanofilms
Journal of Physics: Conference Series, 2007
This work proposes a numerical simulation of heat conduction in silicon nanowires and nanofilms. Boltzmann equation for phonons is solved in the relaxation time approximation. The equation is integrated in an axisymmetric cylindrical two dimensional geometry. Solid angle integration is done by means of Discrete Ordinate Method. Moreover, in contrast to other models published in literature, spectral dependency of relaxation times and acoustic wave dispersion are taken into account in this numerical resolution. Consequently, thermal profiles are obtained for silicon nanowires and nanofilms in steady state allowing computation of thermal conductivity and/or thermal conductance. Besides, we solve the unsteady Boltzmann equation in order to obtain nanosystems temporal evolution. The results obtained with this code match nanofilms and nanowires already predicted thermal profiles in steady state. In unsteady condition, diffusive state (Fourier) is discussed for nanowires and nanofilms. At low temperatures, ballistic phenomenons are seen in nanofilms, whereas, in nanowires, due to boundary scattering, diffusion regime is observed.
Thermal Conductivity in Thin Silicon Nanowires: Phonon Confinement Effect
Nano Letters, 2007
Thermal conductivity of thin silicon nanowires (1.4−8.3 nm) including the realistic crystalline structures and surface reconstruction effects is investigated using direct molecular dynamics simulations with Stillinger−Weber potential for Si−Si interactions. Thermal conductivity as a function of decreasing nanowire diameter shows an expected decrease due to increased surface scattering effects. However, at very small diameter (<1.5 nm), an increase in the thermal conductivity is observed, which is explained by the phonon confinement effect.
Atomistic simulations of heat transport in real-scale silicon nanowire devices
Applied Physics Letters, 2012
Utilizing atomistic lattice dynamics and scattering theory, we study thermal transport in nanodevices made of 10 nm thick silicon nanowires, from 10 to 100 nm long, sandwiched between two bulk reservoirs. We find that thermal transport in devices differs significantly from that of suspended extended nanowires, due to phonon scattering at the contact interfaces. We show that thermal conductance and the phonon transport regime can be tuned from ballistic to diffusive by varying the surface roughness of the nanowires and their length. In devices containing short crystalline wires phonon tunneling occurs and enhances the conductance beyond that of single contacts.
Thermal Transport in Silicon Nanowires at High Temperature up to 700 K
Nano letters, 2016
Thermal transport in silicon nanowires has captured the attention of scientists for understanding phonon transport at the nanoscale, and the thermoelectric figure-of-merit (ZT) reported in rough nanowires has inspired engineers to develop cost-effective waste heat recovery systems. Thermoelectric generators composed of silicon target high-temperature applications due to improved efficiency beyond 550 K. However, there have been no studies of thermal transport in silicon nanowires beyond room temperature. High-temperature measurements also enable studies of unanswered questions regarding the impact of surface boundaries and varying mode contributions as the highest vibrational modes are activated (Debye temperature of silicon is 645 K). Here, we develop a technique to investigate thermal transport in nanowires up to 700 K. Our thermal conductivity measurements on smooth silicon nanowires show the classical diameter dependence from 40 to 120 nm. In conjunction with Boltzmann transport...
The Journal of Chemical Physics, 2019
Nonequilibrium molecular dynamics is widely used to calculate the thermal conductivity of various materials, but the influence of temperature gradient to thermal conductivity has received limited attention within current research studies. The purpose of this article is to explore the discrepancy between intrinsic and extrinsic thermal conductivities under different temperature gradients, which can be considered as external fields. The analyses of phonon density of states have shown that the temperature gradient plays a role in the external field, and a larger temperature gradient activates more low-frequency vibrational modes, which leads to larger thermal conductivities. Specially, the thermal conductivity increases linearly with the temperature gradient when using Stillinger-Weber (SW) potential. Moreover, a new formula was derived to satisfactorily fit the thermal conductivities of bulk Si and silicon nanowires (SiNWs) for various cell sizes, and the physical meaning of the formula was explained. It is shown that the SW potential and Tersoff potential of Si produce different thermal conductivities. By comparing the results of first principles simulations, the Tersoff potential gives rise to better description of vibrational modes.