Three-omega Method Research Articles

Experimental Evidence of Superdiffusive Thermal Transport in Si0.4Ge0.6 Thin Films.

Superdiffusive thermal transport represents a unique phenomenon in heat conduction, which is characterized by a size (L) dependence of thermal conductivity (κ) in the form of κ ∝ Lβ with a constant β between 0 and 1. Although superdiffusive thermal transport has been theoretically predicted for SiGe alloys, direct experimental evidence is still lacking. Here, we report on a systematic experimental study of the thickness-dependent thermal conductivity of Si0.4Ge0.6 thin films grown by molecular beam epitaxy. The cross-plane thermal conductivity of Si0.4Ge0.6 thin films spanning a thickness range from 20 to 1120 nm was measured in the temperature range 120-320 K via a differential three-omega method. Results show that the thermal conductivity follows a consistent κ ∝ t0.26 power law with the film thickness (t) at different temperatures, providing direct experimental evidence that alloy-scattering dominated thermal transport in SiGe is superdiffusive.

A simple numerical method for evaluating heat dissipation from curved wires with periodic applied heating

In many situations, the dual-purpose heater/thermometer wires used in the three-omega method—one of the most precise and sensitive techniques for measuring the thermal conductivity of thin films and interfaces—must include bends and curves to avoid obstructions on the surface of a sample. Although the three-omega analysis assumes that the heating wire is infinitely long and straight, recent experimental work has demonstrated that, in some cases, curved-wire geometries can be used without introducing detectable systematic error. We describe a general numerical method that can be used to calculate the temperature of three-omega heating wires with arbitrary wire geometries. This method provides experimentalists with a simple quantitative procedure for calculating how large the systematic error caused by a particular wire asymmetry will be. We show calculations of two useful cases: a straight wire with a single bend of arbitrary angle and a wire that forms a circle. We find that the amplitude of the in-phase temperature oscillations near a wire that forms a circle differs from the prediction using the analytic straight-line source solution by <12%, provided that the thermal penetration depth is less than ten times the radius of curvature of the wire path. The in-phase temperature amplitude 1.5 wire widths away from a 90° bend in a wire is within 11% of the straight-line source prediction for all penetration depths greater than the wire width. Our calculations indicate that the straight-line source solution breaks down significantly when the wire bend angle is less than 45°.

Thermal Conductivity of Nano-Crystallized Indium-Gallium-Zinc Oxide Thin Films Determined by Differential Three-Omega Method.

The temperature dependence thermal conductivity of the indium-gallium-zinc oxide (IGZO) thin films was investigated with the differential three-omega method for the clear demonstration of nanocrystallinity. The thin films were deposited on an alumina (α-Al2O3) substrate by direct current (DC) magnetron sputtering at different oxygen partial pressures ([PO2] = 0%, 10%, and 65%). Their thermal conductivities at room temperature were measured to be 1.65, 1.76, and 2.58 Wm−1K−1, respectively. The thermal conductivities decreased with an increase in the ambient measurement temperature. This thermal property is similar to that of crystalline materials. Electron microscopy observations revealed the presence of nanocrystals embedded in the amorphous matrix of the IGZO films. The typical size of the nanocrystals was approximately 2–5 nm with the lattice distance of about 0.24–0.26 nm. These experimental results indicate that the nanocrystalline microstructure controls the heat conduction in the IGZO films.

Three-omega thermal-conductivity measurements with curved heater geometries

The three-omega method, a powerful technique to measure the thermal conductivity of nanometer-thick films and the interfaces between them, has historically employed straight conductive wires to act as both heaters and thermometers. When investigating stochastically prepared samples such as two-dimensional materials and nanomembranes, residue and excess material can make it difficult to fit the required millimeter-long straight wire on the sample surface. There are currently no available criteria for how diverting three-omega heater wires around obstacles affects the validity of the thermal measurement. In this Letter, we quantify the effect of the wire curvature by performing three-omega experiments with a wide range of frequencies using both curved and straight heater geometries on SiO2/Si samples. When the heating wire is curved, we find that the measured Si substrate thermal conductivity changes by only 0.2%. Similarly, we find that wire curvature has no significant effect on the determination of the thermal resistance of an ∼65 nm SiO2 layer, even for the sharpest corners considered here, for which the largest measured ratio of the thermal penetration depth of the applied thermal wave to radius of curvature of the heating wire is 4.3. This result provides useful design criteria for three-omega experiments by setting a lower bound for the maximum ratio of the thermal penetration depth to wire radius of curvature.

Thermal conductivity and interfacial effect of parylene C thin film using the 3-omega method

Parylene has attracted a great interest in the last years because of its potential use in many fields. Among all kinds of parylene, parylene C seems the most interesting one for a large range of applications. In this paper, we are interested in its thermal properties, and in particular the thermal conductivity of thin films. This later is determined by the so-called three-omega method. This technique makes use of a thin conducting strip, in contact with the material under test. The metal wire serves both as a heat source for applying a heat flux and a sensitive thermometer for measuring the surface temperature. The thermal conductivity of parylene C films of different thicknesses (210, 440 and 760 nm) deposited by CVD process on borosilicate substrates is investigated. It is demonstrated that the effective thermal conductivity increases as a function of the thickness of thin film (81.20 × 10−3, 88.37 × 10−3 and 92.81 × 10−3 W m−1 K−1 are measured, respectively). This effect is produced by the phonon scattering boundary at the interface between substrate/film and film/heater. To highlight the presence of contact thermal resistances and to estimate their value, a numerical approach, based on a finite element method using the software COMSOL® Multiphysics, is also proposed. This study shows that the main part (97%) of the interfacial thermal resistance is due to the contact between the parylene C film and the substrate.

Thermal Conductivity, Electrical Resistivity, and Microstructure of Cu/W Multilayered Nanofilms

Metallic multilayered nanofilms have been extensively studied owing to their unique physical properties and applications. However, studies on the thermal conductivity and electrical resistivity of metallic multilayered nanofilms, as their important physical properties, are seldom reported. In this work, Cu/W multilayered nanofilms with periodic thickness varying from 6 to 150 nm were deposited by magnetron sputtering. The resistivities of the Cu/W multilayered nanofilms increase with the decrease of periodic thickness, especially when the periodic thickness is smaller than 37 nm. The resistivities of the multilayered nanofilms fit well with the Fuchs-Sondheimer and Mayadas-Shatzkes (FS-MS) model, which considers both interface scattering and grain boundary scattering. The thermal conductivities of the Cu/W multilayered nanofilms were measured by the three-omega (3ω) method, which decrease with a decrease of periodic thickness initially and increase at the smallest periodic thickness of 6 nm. The Boltzmann transport equation (BTE)-based model was used, to explain the periodic thickness-dependent thermal conductivity of metallic multilayered nanofilms by considering the contributions from both phonon and electron heat transport processes, where the calculated thermal conductivities agree well with the measured ones. The electrical resistivity and thermal conductivity strongly depend on the microstructures of the multilayered nanofilms.

Characterisation of high thermal conductivity thin-film substrate systems and their interface thermal resistance

This paper characterises the high thermal conductivity thin-film substrate systems and the interface thermal resistances between the films. First, three-omega (3ω) method was proposed and verified, obtaining a reliable thermal conductivity measurement at shallow thermal-penetration depths. The method was then applied to a thin-film/substrate system to identify the individual thermal conductivities. The interface thermal resistance between the thin films was then successfully characterised with the aid of theoretical modelling and experimental measurements. As an example of the method application in the IC industry, the AlN/Si systems were investigated. The study identified that the thermal conductivity of the 2μm-thick AlN film in an AlN/Si system is 172.1W/mK and the AlN/Si interface thermal resistance is 1.796×10−9m2K/W.

Thermal characterization and analysis of microliter liquid volumes using the three-omega method.

Thermal phenomena in many biological systems offer an alternative detection opportunity for quantifying relevant sample properties. While there is substantial prior work on thermal characterization methods for fluids, the push in the biology and biomedical research communities towards analysis of reduced sample volumes drives a need to extend and scale these techniques to these volumes of interest, which can be below 100 pl. This work applies the 3ω technique to measure the temperature-dependent thermal conductivity and heat capacity of de-ionized water, silicone oil, and salt buffer solution droplets from 24 to 80 °C. Heater geometries range in length from 200 to 700 μm and in width from 2 to 5 μm to accommodate the size restrictions imposed by small volume droplets. We use these devices to measure droplet volumes of 2 μl and demonstrate the potential to extend this technique down to pl droplet volumes based on an analysis of the thermally probed volume. Sensitivity and uncertainty analyses provide guidance for relevant design variables for characterizing properties of interest by investigating the tradeoffs between measurement frequency regime, device geometry, and substrate material. Experimental results show that we can extract thermal conductivity and heat capacity with these sample volumes to within less than 1% of thermal properties reported in the literature.

Thermoelectric Properties of Small Bandgap Semiconductor Nanowires: The Effects of 1D Electron Subband Formation and Phonon Boundary Scattering

Nanomaterials such as nanowires or nanoribbons offer a promising platform for efficient thermoelectric energy conversion applications, owing to their greatly reduced thermal conductivity and potentially high power factor due to strong one-dimensional (1D) quantum confinement effects. While the thermal conductivity of nanomaterials is widely found to be suppressed, the 1D electronic quantum confinement effect tuned power factor remains elusive in experiment. Small diameter nanowires of InAs or InSb provides an opportunity to observe such 1D quantum confinement effect, thanks to their high electron mobility and small effective mass (i.e. long electron wavelength/large 1D subband spacing). We present a study of the thermoelectric properties of InAs nanowires where the gate was used to control the electrons' Fermi level. At temperatures below about 100K, oscillations in the thermopower and power factor due to the formation of 1D electron sub-bands are observed in semiconductor nanowires for the first time. We also discuss the limiting factors in the pursuit of 1D confinement enhanced thermoelectric performance in semiconductors and point out that disorder induced 1D energy level smearing sets the current bottleneck for achieving 1D quantum effect enhanced figure of merit or power factor at practical temperatures (e.g. 300K). We further discuss a recent study of Bi2Se3 nanoribbon's thermal conductivity by the three-omega method. The as measured thermal conductivity for a single Bi2Se3 nanoribbon is nearly two orders of magnitude smaller than the bulk value, which is attributed to enhanced phonon boundary scattering in nanostructured materials. This work is done together with M.R. Sakr, J.M. Kinder, M. J. MacDonal, D. Liang, G.D. Li, R. L.J. Qiu at CWRU and Y. Tian and H.J. Gao at Chinese Academy of Sciences. The authors acknowledge NSF CAREER Award (DMR-1151534), ACS PRF (48800-DNI10) and the NSF of China for support of this research.

Reduced temperature-dependent thermal conductivity of magnetite thin films by controlling film thickness

We report on the out-of-plane thermal conductivities of epitaxial Fe3O4 thin films with thicknesses of 100, 300, and 400 nm, prepared using pulsed laser deposition (PLD) on SiO2/Si substrates. The four-point probe three-omega (3-ω) method was used for thermal conductivity measurements of the Fe3O4 thin films in the temperature range of 20 to 300 K. By measuring the temperature-dependent thermal characteristics of the Fe3O4 thin films, we realized that their thermal conductivities significantly decreased with decreasing grain size and thickness of the films. The out-of-plane thermal conductivities of the Fe3O4 films were found to be in the range of 0.52 to 3.51 W/m · K at 300 K. For 100-nm film, we found that the thermal conductivity was as low as approximately 0.52 W/m · K, which was 1.7 to 11.5 order of magnitude lower than the thermal conductivity of bulk material at 300 K. Furthermore, we calculated the temperature dependence of the thermal conductivity of these Fe3O4 films using a simple theoretical Callaway model for comparison with the experimental data. We found that the Callaway model predictions agree reasonably with the experimental data. We then noticed that the thin film-based oxide materials could be efficient thermoelectric materials to achieve high performance in thermoelectric devices.

Carrier interactions and porosity initiated reversal of temperature dependence of thermal conduction in nanoscale tin films

Recently, tin has been identified as an attractive electrode material for energy storage/conversion technologies. Tin thin films have also been utilized as an important constituent of thermal interface materials in thermal management applications. In this regards, in the present paper, we investigate thermal conductivity of two nanoscale tin films, (i) with thickness 500 ± 50 nm and 0.45% porosity and (ii) with thickness 100 ± 20 nm and 12.21% porosity. Thermal transport in these films is characterized over the temperature range from 40 K–310 K, using a three-omega method for multilayer configurations. The experimental results are compared with analytical predictions obtained by considering both phonon and electron contributions to heat conduction as described by existing frequency-dependent phenomenological models and BvK dispersion for phonons. The thermal conductivity of the thicker tin film (500 nm) is measured to be 46.2 W/m-K at 300 K and is observed to increase with reduced temperatures; the mechanisms for thermal transport are understood to be governed by strong phonon-electron interactions in addition to the normal phonon-phonon interactions within the temperature range 160 K–300 K. In the case of the tin thin film with 100 nm thickness, porosity and electron-boundary scattering supersede carrier interactions, and a reversal in the thermal conductivity trend with reduced temperatures is observed; the thermal conductivity falls to 1.83 W/m-K at 40 K from its room temperature value of 36.1 W/m-K. In order to interpret the experimental results, we utilize the existing analytical models that account for contributions of electron-boundary scattering using the Mayadas-Shatzkes and Fuchs-Sondheimer models for the thin and thick films, respectively. Moreover, the effects of porosity on carrier transport are included using a previous treatment based on phonon radiative transport involving frequency-dependent mean free paths and the morphology of the nanoporous channels. The systematic modeling approach presented in here can, in general, also be utilized to understand thermal transport in semi-metals and semiconductor nano-porous thin films and/or phononic nanocrystals.

Thermal conductivity of single biological cells and relation with cell viability

This paper presents measurements of effective thermal conductivity of single biological cells (HeLa, NIH-3T3 J2, and hepatocyte). Such cellular-level measurements have not been performed previously, due to the small size (∼10 pl) of cells. The measurement uses the three-omega method with a nanoscale thermal sensor and a micro-well structure that confines the cell. The results provide a fundamental property to investigate the thermodynamics of cells. We also measured thermal conductivity of dead cells; results were significantly different from those of live cells. The difference means that thermal conductivity can be used for probing cell viability.

Gas thermal conductivity measurement using the three-omega method

A new approach for gas thermal characterization is presented. This method, based on a 3ω setup, is attractive because of its relatively simple implementation and its integration potentiality. A model referred to as an “apparent thermal conductivity” is presented as well as its scope of utilization. Measurements carried out on pure gas components are made to prove the relevance of the approach. The thermal conductivity of nitrogen, helium and carbon dioxide is measured at 298K under atmospheric pressure with a less of 5 % discrepancy compared to reference values.

Monitoring protein denaturation using thermal conductivity probe

We propose a method for probing denaturation of proteins by measuring the thermal conductivity of the solution. We use the three-omega method with a microfabricated ac thermal sensor to measure the thermal conductivity of lysozyme, β-lactoglobulin, and bovine serum albumin protein solutions over a range of temperature and pH. Results suggest that conformation transformation of the protein during denaturation changes the thermal network in protein solutions and thus changes the thermal conductivity for all the tested proteins. The proposed method of denaturation monitoring requires much simpler experimental setup than conventional methods such as differential scanning calorimetry and circular dichroism detection. We also demonstrate that the proposed analytical technique can detect the protein denaturation in real time. Consequently, it is expected to be useful in lab-on-a-chip (LoC) applications as the probe can be easily miniaturized for integration into LoC devices and allows real-time analysis.

Thermal Conductivity of Copper-Graphene Composite Films Synthesized by Electrochemical Deposition with Exfoliated Graphene Platelets

Samples of graphene composites with matrix of copper were prepared by electrochemical codeposition from CuSO4 solution with graphene oxide suspension. The thermal conductivity of the composite samples with different thickness and that of electrodeposited copper was determined by the three-omega method. Copper-graphene composite films with thickness greater than 200 μm showed an improvement in thermal conductivity over that of electrolytic copper from 380 W/m.K to 460 W/m.K at 300 K (27 °C). The thermal conductivity of copper-graphene films decreased from 510 W/m.K at 250 K (–23 °C) to 440 W/m.K at 350 K (77 °C). Effective medium approximation (EMA) was used to model the thermal conductivity of the composite samples and determine the interfacial thermal conductance between copper and graphene. The values of interface thermal conductance greater than 1.2 GW/m2.K obtained from the acoustic and the diffuse mismatch models and from the EMA modeling of the experimental results indicate that the interface thermal resistance is not a limiting factor to improve the thermal conductivity of the copper-graphene composites.

Influence of laser and thermal treatment on the thermal conductivity of In-graphene composites

Graphene processed by thermal, laser, and thermal plus laser treatments was used to synthesize the indium-graphene composite foils. The symmetric nature of the G’ band in the Raman spectrum was used to identify that the graphene was only few layers thick. Quantitative image analysis was used to determine the volume fraction of graphene. Electrical resistivity and temperature coefficient of resistance of the composite coupled with effective mean field approximation were analyzed to determine the volume fraction and resistivity of graphene. Thermal conductivity of the composite foils was measured using the three-omega method and multilayer analysis. The thermal conductivity of In-gr foils prepared by the three methods of processing graphene was found to be 1.8 W/cm.K. The results indicate that the improvement in the thermal conductivity of the composites was same by the three methods of treatment of graphene.

Orientation dependence of thermal conductivity in copper-graphene composites

Copper and graphene multilayer films were deposited on a copper substrate. The surface of the multilayer film was covered with another film of copper by electrochemical deposition. An electrically insulating film of polymer followed by films of silicon and yttria-stabilized zirconia were deposited to isolate the sample electrically from a gold heater line deposited on the top. The three-omega method was used to determine the cross-plane thermal conductivity in the sample. The effective planar thermal conductivity in the sample was determined from two gold heater lines deposited adjacent to each other on the surface. The gradient of temperature between the heater lines was evaluated under steady state to determine the planar thermal conductivity. The results show that the cross-plane thermal conductivity in the copper-graphene layers is reduced as a result of the lower thermal conductivity normal to the graphene planes. The planar thermal conductivity in the copper-graphene layers was not reduced below that in copper. The interface thermal resistance between copper and graphene was evaluated from the planar thermal conductivity. The interface thermal resistance either in the cross plane direction or in the planar direction is found to be not a limiting factor for the improvement in the thermal conductivity in the copper-graphene composite films.

Thermal Conductivity of Indium–Graphene and Indium-Gallium–Graphene Composites

Samples of graphene composites with a matrix of indium or indium-gallium alloy were prepared in the form of foils using exfoliated graphene dispersions. The thermal conductivity of the composite samples with different thicknesses was determined using the three-omega method. Indium–graphene composite samples with a thickness of 430 μm exhibited a twofold increase in thermal conductivity, whereas indium-gallium–graphene composite samples with a thickness of 330 μm exhibited a threefold improvement in thermal conductivity over that of the matrix at 300 K. The effective medium approximation (EMA) was used to model the thermal conductivity of the composite samples. The graphene platelet size distribution was used to determine the average thermal conductivity of graphene in the composite samples. The interfacial thermal conductance between graphene and indium or indium-gallium alloy determined from EMA was not the limiting factor in the improvement of the thermal conductivity of the composite samples, although the increase in thermal conductivity was found to be slightly lower than predicted theoretically using acoustic and diffuse mismatch models. The smaller size of the graphene platelets obtained by exfoliation prior to dispersion in the matrix appears to be the limiting factor.

Development of a micro liquid-level sensor for harsh environments using a periodic heating technique

This paper describes the development and testing of a novel micro thermal sensor for point sensing of lubrication oil level in industrial compressors. The results reported in this work can be applied to various harsh environments that feature high temperature/pressure, limited space and flow/vibration. The sensor employs an ac (alternating current) thermal technique with a single heating/sensing element. As the sensing scheme is based on the so-called three-omega method, the sensing signal is noise-resistant and hardly affected by flow in the liquid being measured. Experiments with DI water, ethanol and ethylene glycol confirm that the sensor performance is satisfactory under atmospheric pressure. Also, to mimic harsh conditions as in an industrial compressor, tests are performed in a pressure vessel containing R410A gas and polyvinylether lubrication oil under high temperatures and pressures. The results indicate that the sensitivity and response time of the developed sensor are appropriate for practical usage in harsh environments. As the sensor can be easily mass-produced at low cost using photolithography, it has strong potential for industrial applications.

Development of a micro thermal sensor for real-time monitoring of lubricating oil concentration

We report development of a micro thermal sensor and sensing techniques for monitoring the oil concentration in a refrigeration system. The sensor acquires the thermal response of the mixture to ac heating and then the concentration can be determined using one of the two different methods. In the first method, the thermal conductivity of the mixture is obtained using the three-omega method and the concentration is determined using the correlation between the mixture concentration and thermal conductivity. In the alternative fast-detection method, the concentration is determined by directly calibrating the sensor output signal to the mixture concentration. The performance of the sensor was tested using the R410A/polyvinyl ether (PVE) oil mixture. The uncertainty of the oil concentration measurement was estimated to be 5.8–7.3 wt.%, depending on the sensing scheme. Especially, the simple structure of the sensor makes the technique cost effective and adequate for miniaturization, i.e., for installation in a limited space.