Conductivity Of Silicon Thin Films Research Articles

Surface phonons limit heat conduction in thin films

Understanding microscopic heat conduction in thin films is important for nano/micro heat transfer and thermal management for advanced electronics. As the thickness of thin films is comparable to or shorter than a phonon wavelength, phonon dispersion relations and transport properties are significantly modulated, which should be taken into account for heat conduction in thin films. Although phonon confinement and depletion effects have been considered, it should be emphasized that surface-localized phonons (surface phonons) arise whose influence on heat conduction may not be negligible due to the high surface-to-volume ratio. However, the role of surface phonons in heat conduction has received little attention thus far. In the present work, we performed anharmonic lattice dynamics calculations to investigate the thickness and temperature dependence of in-plane thermal conductivity of silicon thin films with sub-10-nm thickness in terms of surface phonons. Through systematic analysis of the influences of surface phonons, we found that anharmonic coupling between surface and internal phonons localized in thin films significantly suppresses overall in-plane heat conduction in thin films. We also discovered that specific low-frequency surface phonons significantly contribute to surface--internal phonon scattering and heat conduction suppression. Our findings are beneficial for the thermal management of electronics and phononic devices and may lead to surface phonon engineering for thermal conductivity control.

Mechanism of phonon scattering by under-coordinated atoms on surface

Because of high surface-to-volume ratio (SVR), the most prominent size effect limiting thermal transport originates from the phonon-surface scattering in nanostructures. Here in this work, we propose the mechanism of phonon scattering by the under-coordinated atoms on surface, and derive the phonon scattering rate of this mechanism by quantum perturbation theory combined with bond order theory. The scattering rate of this mechanism is proportional to SVR, therefore the effect of this mechanism on phonon transport increases with the feature-size of nanostructures decreasing. Due to the <i>ω</i><sup>4</sup> dependence of scattering rate for this mechanism, the high-frequency phonons suffer a much stronger scattering than the low-frequency phonons from the under-coordinated atoms on surface. By incorporating this phonon-surface scattering mechanism into the phonon Boltzmann transport equation, we calculate the thermal conductivity of silicon thin films and silicon nanowires. It is found that the calculated results obtained with our model are closer to the experimental data than those with the classical phonon-boundary scattering model. Furthermore, we demonstrate that the influence of this phonon-surface scattering mechanism on thermal transport is not important at a very low temperature due to the Bose-Einstein distribution of phonons. However, with the increase of the temperature, more and more phonons occupy the high-frequency states, and the influence of this scattering mechanism on phonon transport increases. It is astonished that the phonon scattering induced by the under-coordinated atoms on surface is the dominant mechanism in governing phonon heat transport in silicon nanostructures at room temperature. Our findings are helpful not only in understanding the mechanism of phonon-surface scattering, but also in manipulating thermal transport in nanostructures for surface engineering.

Study on thermal conductivities of Si thin films and porous Si structures based on a modified lattice Boltzmann method

In this work, a modified lattice Boltzmann method (LBM) is developed to predict the thermal conductivity of silicon thin films and porous silicon structures, in which a probability parameter is introduced to determine whether a phonon collision event happens at a specific lattice point. The thickness dependent silicon thin film thermal conductivity calculated using this method shows a good agreement with prior experimental and simulation results. We also use this approach to study the porosity and pore-size dependent thermal conductivity of porous silicon structures. Furthermore, the simulated results about thermal conductivity of porous silicon are found to agree well with the previously reported data. The modified algorithm offers substantial computational improvement as compared to current LBM models and enables us to a clearer understanding about the meaning of collision step and streaming step in the LBM model.

Study on Lattice Thermal Conductivity of Silicon Thin Film with Aligned Nano-pores

A frequency-dependent phonon Boltzmann transport equation solver is presented to numerically study the lattice thermal conductivity of nano-porous silicon thin film based on the Discrete Ordinates Method. We find that not only characteristic size and porosity, but also the shapes of both unit cell and pore do affect the lattice thermal conductivity. Therefore, we arranged a series of computational cases by the orthogonal design method to investigate the influence of geometric parameters Lx, Ly, ax/Lx and ay/Ly (Lx is unit cell length, Ly unit cell width, ax pore length and ay pore width). Furthermore, a non-linear regression model is established depending on the data obtained from those computational cases. The result shows that lattice thermal conductivity of nano-porous silicon thin film decreases obviously with the increase of ax/Lx and ay/Ly. Among these four geometric parameters, ay/Ly is the most significant factor while Lx and Ly have little effect on lattice thermal conductivity. The proposed regression model can offer useful suggestion for the fabrication of nano-porous silicon thin film with lower lattice thermal conductivity.

Thermal Conductivity of Silicon Thin Films Deposited On Porous Alumina by PECVD

In this paper we have studied the thermal properties of silicon thin films deposited by plasma enhancement chemical vapor deposition (PECVD) on porous aluminum using the phothermal deflection technique (PTD). The aim of this work is to investigate the influence of anodisation current (between 200 to 400 mV) on the thermal conductivity of samples. We present a computational model to determine the thermal conductivity K. The coincidences between the experimental and theoretical curves permit to deduce the values of thermal conductivity with a good accuracy. In fact, it was found that K decrease with the anodisation current.

The effect of phonon anisotropic scattering on the thermal conductivity of silicon thin films at 300K and 400K

Previous studies have shown that anisotropy in phonon transport exist because of the difference in phonon dispersion relation due to different lattice directions, as observed by a difference in in-plane and cross-plane thermal conductivities. Our current work intends to study the effect of anisotropy scattering on silicon thermal conductivity at 300K and 400K. We adopt the Henyey and Greenstein probability density function in our phonon Monte Carlo simulation to investigate the effect of highly forward and backward scattering events. The impact of applying the anisotropy scattering using this approach is discussed in detail. While the forward and backward scattering will increase and decrease thermal conductivity respectively, the extent of the effect is non-linear such that forward scattering has a more obvious effect on thermal conductivity than backward scattering.

Out-of-Plane Thermal Conductivity of Silicon Thin Film Doped with Germanium

The out-of-plane thermal conductivity of silicon thin film doped with germanium is calculated by non-equilibrium molecular dynamics simulation using the Stillinger-Weber potential model. The silicon thin film is doped with germanium atoms in a random doping pattern with a doping density of 5% and 50% respectively. The effect of silicon thin film thickness on its thermal conductivity is investigated. The simulated thicknesses of silicon thin film doped with germanium range from 2.2 to 10.9 nm at an average temperature 300K. The simulation results indicate that the out-of-plane thermal conductivity of the silicon thin film doped with germanium decreases linearly with the decreasing film thickness. As for the film thickness of 9.8nm and the average temperature ranging from 250 to 1000 K, the investigation shows that the temperature dependence of the film thermal conductivity is not sensitive.

Isotope and strain effects on thermal conductivity of silicon thin film

In this paper, non-equilibrium molecular dynamics simulations (NEMD) are employed to study the effects of isotope and in-plane strain on the thermal conductivity of silicon thin film. The results show that the thermal conductivity of silicon thin film decreases with the isotope concentration at the lower concentration and increases with the isotope concentration at the higher concentration, respectively. In addition, simulations on the strained film indicate that the thermal conductivity decreases monotonously with the applied strain. To achieve a fundamental understanding of the physical mechanisms, phonon density of states (DOS) and phonon dispersion are analyzed in details. High frequency phonons are found to be sensitive to the impurity, which leads to the reduction of phonon group velocity. For the strained thin film, high frequency phonons, especially of transverse optical (TO) phonon branch, play an important role in the change of thermal conductivity. Our findings suggest the great potential of tailoring the thermal properties by isotope and mechanical strain.

Thermal conduction in nano-porous silicon thin film

Controlling the thermal conductivity of thermoelectric materials continues to be a goal for energy conversion applications. The Phonon Boltzmann Transport Equation is solved by using the Discrete Ordinates Method to numerically study the phonon thermal conductivity of nano-structured silicon thin film with pores in this study. The effects of the film thickness, film porosity, and porous structure are concerned. The numerical results show that the nano-pores are able to reduce the thermal conductivity of the silicon thin film sharply by the phonon boundary scattering, and the scattering boundary area has significant effect on the thermal conductivity. The method of local angle distribution between heat fluxes is introduced for the first time to optimize the pore placement for reducing the thermal conductivity.

In-plane thermal conductivity determination through thermoreflectance analysis and measurements

A scanning thermoreflectance (TR) technique through which the surface temperature profile of heated thin films may be ascertained and modeled to yield the in-plane thermal conductivity (κip) is discussed. The TR intensity is shown to be a sensitive function of the film thickness, its thermo-optic materials properties, and the substrate geometry. A reduction in the thermal conductivity of silicon thin films is then demonstrated deploying the technique. A comparison of the estimated conductivity values to those obtained using other methodologies supports the validity of our method and suggests that complete isolation of the thin film from the substrate may not be required for extracting κip.

Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics Simulations and Theoretical Calculation

Molecular, dynamics simulation and the Boltzmann transport equation are used respectively to analyze the phonon transport in Si thin film. The MD result is in good agreement with the theoretical analysis values. The results show that the calculated thermal conductivity decreases almost linearly as the film thickness reduced and is almost independent of the temperature at the nanoscale. It was observed from the simulation results that there exists the obvious size effect on the thermal conductivity.

Effects of vacancy structural defects on the thermal conductivity of silicon thin films

Vacancy structural defect effects on the lattice thermal conductivity of silicon thin films have been investigated with non-equilibrium molecular dynamics simulation. The lattice thermal conductivities decrease with increasing vacancy concentration at all temperatures from 300 to 700 K. Vacancy defects decrease the sample thermal conductivity, and the temperature dependence of thermal conductivity becomes less significant as the temperature increases. The molecular dynamics result is in good agreement with the theoretical analysis values obtained based on the Boltzmann equation. In addition, theoretical analysis indicates that the reduction in the lattice thermal conductivity with vacancy defects can be explained by the enhanced point-defect scattering due to lattice strain.

A Nonequilibrium Molecular Dynamics Study of In-Plane Thermal Conductivity of Silicon Thin Films

We employed a nonequilibrium molecular dynamics (NEMD) simulator to calculate the in-plane thermal conductivity of silicon thin films. To avoid contamination of the temperature nonlinearity due to artificial heat addition/rejection, the selection of a proper linear range was investigated. It was found that the contaminated range was larger for thicker films and longer simulation lengths. To perform the quantum correction that is necessary when the MD simulation temperature is lower than the Debye temperature, we also attempted to obtain the confined phonon densities of states via equilibrium MD (EMD) simulations. The investigation showed that the thermal conductivities corrected by the thin-film density of states (DOS) agree excellently with theoretical predictions based on the phonon Boltzmann transport equation. A relationship between the surface roughness measurable in the laboratory and the specular fraction usually employed in the analysis was thus constructed.

Prediction of thermal conductivity of nanostructures: Influence of phonon dispersion approximation

In this study, the influence of phonon dispersion approximation on the prediction of in-plane and out-of-plane thermal conductivity of thin films and nanowires is shown. Results obtained using the famous Holland dispersion approximation and the Brillouin zone boundary condition (BZBC) dispersion curves are compared. For (in-plane and out-of-plane) thermal conductivity predictions based on BZBC dispersion curves, new relaxation time parameters fitted from experimental data of bulk silicon thermal conductivity are reported. The in-plane thermal conductivity of nanostructures (films of thicknesses 20 nm, 100 nm, and 420 nm and nanowires of widths 22 nm, 37 nm, and 100 nm) in the temperature range 20–1000 K is calculated from the modified bulk thermal conductivity model by scaling the bulk phonon mean free path (MFP) by the Fuch–Sondheimer factor of boundary scattering developed for nanostructures with rectangular cross-section. The pseudo out-of-plane thermal conductivity of films of thicknesses 20 nm, 100 nm, and 420 nm and in the temperature range 150–1000 K is calculated from the solution of the Boltzmann transport equation (BTE) for phonons by using the Discrete ordinate method (DOM), and the Monte Carlo (MC) simulation. In order to confirm the current results, the calculated in-plane thermal conductivity of silicon thin films and silicon nanowires are compared with existing experimental data. Moreover, due to lack of experimental and theoretical data of out-of-plane thermal conductivity of thin films, comparison of the DOM and MC simulation is performed. The current work shows that a drastic simplification of dispersion curves can lead to wrong prediction of both in-plane and out-of-plane thermal conductivities of nanostructures, especially for ultra thin nanostructures and/or at high temperatures. Comparison with experimental data of in-plane thermal conductivity of silicon thin films and silicon nanowires proves that more refined dispersion approximation such as the BZBC is well adequate for phonon transport calculations when confinement has negligible effect. Moreover, the comparison between the thermal conductivity in the out-of-plane direction and that in the in-plane direction enables one to quantify the anisotropy of thermal conductivity of the film.

Nanoscale Thermal Transport and Microrefrigerators on a Chip

In this paper we review recent advances in nanoscale thermal and thermoelectric transport with an emphasis on the impact on integrated circuit (IC) thermal management. We will first review thermal conductivity of low-dimensional solids. Experimental results have shown that phonon surface and interface scattering can lower thermal conductivity of silicon thin films and nanowires in the sub-100-nm range by a factor of two to five. Carbon nanotubes are promising candidates as thermal vias and thermal interface materials due to their inherently high thermal conductivities of thousands of W/mK and high mechanical strength. We then concentrate on the fundamental interaction between heat and electricity, i.e., thermoelectric effects, and how nanostructures are used to modify this interaction. We will review recent experimental and theoretical results on superlattice and quantum dot thermoelectrics as well as solid-state thermionic thin-film devices with embedded metallic nanoparticles. Heat and current spreading in the three-dimensional electrode configuration, allow removal of high-power hot spots in IC chips. Several III-V and silicon heterostructure integrated thermionic (HIT) microcoolers have been fabricated and characterized. They have achieved cooling up to 7 degC at 100 degC ambient temperature with devices on the order of 50 mum in diameter. The cooling power density was also characterized using integrated thin-film heaters; values ranging from 100 to 680 W/cm2 were measured. Response time on the order of 20-40 ms has been demonstrated. Calculations show that with an improvement in material properties, hot spots tens of micrometers in diameter with heat fluxes in excess of 1000 W/cm2 could be cooled down by 20 degC-30 degC. Finally we will review some of the more exotic techniques such as thermotunneling and analyze their potential application to chip cooling

In-Plane and Out-Of-Plane Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics

The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relation, and the Stillinger-Weber interatomic potential. Three different boundary conditions are considered along the film surfaces: frozen atoms, surface potential, and free boundaries. Film thicknesses range from 2to217nm and temperatures from 300to1000K. The relation between the bulk phonon mean free path (Λ) and the film thickness (ds) spans from the ballistic regime (Λ⪢ds) at 300K to the diffusive, bulk-like regime (Λ⪡ds) at 1000K. When the film is thin enough, the in-plane and out-of-plane thermal conductivity differ from each other and decrease with decreasing film thickness, as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300K. In the ballistic limit, in accordance with the kinetic and phonon radiative transfer theories, the predicted out-of-plane thermal conductivity varies linearly with the film thickness, and is temperature-independent for temperatures near or above the Debye’s temperature.