3ω Method Research Articles

A Robust Miniaturized Gas Sensor for H2 and CO2 Detection Based on the 3ω Method.

Gas concentration monitoring is essential in industrial or life science areas in order to address safety-relevant or process-related questions. Many of the sensors used in this context are based on the principle of thermal conductivity. The -method is a very accurate method to determine the thermal properties of materials. It has its origin in the thermal characterization of thin solid films. To date, there have been very few scientific investigations using this method to determine the thermal properties of gases and to apply it to gas measurement technology. In this article, we use two exemplary gases ( and ) for a systematical investigation of this method in the context of gas analysis. To perform our experiments, we use a robust, reliable sensing element that is already well established in vacuum measurement technology. This helix-shaped thin wire of tungsten exhibits high robustness against chemical and mechanical influences. Our setup features a compact measurement environment, where sensor operation and data acquisition are integrated into a single device. The experimental results show a good agreement with a simplified analytical model and FEM simulations. The sensor exhibits a lower detection limit of 0.62% in the case of , and only 0.062% in case the of at an excitation frequency of 1. This is one of the lowest values reported in literature for thermal conductivity sensors.

Effect of precipitation of silicone oil-based nanofluid on thermal conductivity

This study investigated the effect of the precipitation of nanofluid additives on thermal conductivity in various environments using a bidirectional 3 omega (3ω) method. Silicone oils with viscosities of 50, 500, and 1000 CS were used as the base fluid. Nanoparticles containing aluminium spheres of 100 nm diameter were added to the base fluid at a mass ratio of 0.5%. The experimental set-up was designed and fabricated, and the bidirectional 3ω method was verified by measuring the thermal conductivity of the well-known liquid. Using the nanofluids, thermal conductivities were measured at various temperatures and viscosities. The measurement results are discussed with respect to the elapsed time of precipitation. In addition, the effect of penetration depth on the thermal conductivity is investigated.

Determination of thermal conductivity, thermal diffusivity and specific heat capacity of porous silicon thin films using the 3ω method

Here the thermal transport properties of low thermal conductivity porous silicon thin films attached to high thermal conductivity silicon substrates are studied using the 3ω method implemented over the 100 Hz to 33 kHz frequency range. The thermal conductivity and thermal diffusivity of the films are extracted using temperature impedance monitoring of electrical contacts deposited on films, combined with an extended-frequency, multi-layer thermal model. From the extracted thermal conductivity and diffusivity of the films, the heat capacity could be determined. Validation of the approach is performed using the known properties of thick substrate glass and SU-8 layers spun on silicon substrates, the latter ranging in thickness from 1.35 to 12.5 µm. The technique was then applied to porous silicon films with porosities ranging from 45% to 77%. The extracted thermal properties for as-fabricated films show a reduction of thermal conductivity and diffusivity from 1.7 to 0.15 W/mK and 1.9 to 0.2 mm2/s, respectively as the porosity increases. After passivation by annealing in nitrogen and at 600 °C, the same films exhibited higher values of thermal conductivity and diffusivity ranging from 2.7 to 0.7 W/mK and 2.5 to 0.65 mm2/s. The ability to extract both thermal conductivity and thermal diffusivity for these films removes the need to make assumptions around specific heat capacity, commonly made during analysis of porous media. These results show for the first time a monotonic increase in specific heat capacity of porous silicon films as a function of porosity.

Anisotropic thermal conductivity of nanocolumnar W thin films

We report on thermal conductivity of W films 350 nm thick sputter-deposited by glancing angle deposition (GLAD). The 3ω method is used to measure the in-plane thermal conductivity kx and ky for films deposited with a deposition angle α of 0° and 80°. For classical films (α=0°), the thermal conductivity is 71 Wm−1K−1, whereas for GLAD films (α=80°) the in-plane conduction drops to kx=3.2 Wm−1K−1 and ky=4.8 Wm−1K−1. The in-plane thermal conductivity anisotropy corresponds to a heat conduction favored in the direction perpendicular to the deposition axis, which is related to the anisotropic columnar microstructure. Electrical conductivity is also determined leading to a significant deviation from the Wiedemann-Franz law for the GLAD films.

3ω method in combination with a meander shaped heater: Theoretical and experimental investigation

The 3ω-method is usually applied to a line heater because it simplifies the analytical solution of the heat transfer equation. Other potentially beneficial heater geometries, such as meandering heater structures, have not yet been addressed in the literature to date. A meandering structure is advantageous when the available space is limited. This article presents the detailed investigation on meander shaped heater structures, in combination with the 3ω-method. A theoretical approach approximated the meandering structure as several parallel strips with a certain spacing. It investigates the influence of the spacing and compares it with the conventional line heater model. It was found that the conventional model is an accurate model when the thermal diffusivity of the surrounding area of the heater is high and the spacing between the heater lines is small. This finding was used in the experimental investigation. Due to the general expressions of the theoretical model, it can be used as a tool for future investigations. An experimental approach investigated the loss of invariance along the lateral axis, which is often assumed for a line heater where its length is much larger than its width and a two-dimensional description can be used. The boundary effect of the finite length is neglected. The basic idea of the experimental work is to fabricate several meandering structures with different length-width ratios, but with the same total path length of the structures, such that the structures with different length-width ratios can be compared. The results based on platinum thin film structures showed that the straight structure with a length-to-width ratio of 300 deviates from the prediction of the two-dimensional model by about 5%. The structures with a length-to-width ratio 50 match significantly poorer with the two-dimensional model. The deviation becomes larger than 10%. A strong signal helps regarding the resolution in the application. The theoretical findings showed that the signal is highest if the distance between the heater lines is as small as possible. Moreover, the experimental work showed highest performance if the length-width ratio is around 1.4.

Aerosol jet printed 3 omega sensors for thermal conductivity measurement.

The 3 omega (3ω) method is a trusted technique for measuring thermal conductivity-a fundamental material property of critical importance in a broad range of applications. However, traditional 3ω sensor processing requires some form of physical vapor deposition, such as metal evaporation or sputtering. These 3ω sensor deposition techniques limit the materials and sample sizes applicable to the 3ω method. This work demonstrates an aerosol jet printing method to directly printsilver 3ω sensors that yield accurate temperature-dependent measurement up to 300°C on materials with thermal conductivity ranging from 1 to 150 W/m K. The interrelationship between printed sensor geometry, sensor thermal stability, and applicability to the 3ω method is examined. Thermal conductivity measurement with 3ω sensors conventionally sintered at 300°C agrees to independent laser flash measurement within 4% from room temperature to 150°C. An unconventional rapid high-temperature sintering method is shown to produce sensors that agree within 3% of the laser flash measurements from room temperature to 300°C. The rapid sintering profiles also reduced the sensor-substrate thermal boundary resistance of the printed sensors by as much as 88%. The direct printing of 3ω sensors creates opportunities for measurement of thermal transport properties in applications previously inapplicable to the 3ω method.

Enhanced Electron Heat Conduction in TaS3 1D Metal Wire.

The 1D wire TaS3 exhibits metallic behavior at room temperature but changes into a semiconductor below the Peierls transition temperature (Tp), near 210 K. Using the 3ω method, we measured the thermal conductivity of TaS3 as a function of temperature. Electrons dominate the heat conduction of a metal. The Wiedemann–Franz law states that the thermal conductivity of a metal is proportional to the electrical conductivity σ with a proportional coefficient of L0, known as the Lorenz number—that is, . Our characterization of the thermal conductivity of metallic TaS3 reveals that, at a given temperature T, the thermal conductivity κ is much higher than the value estimated in the Wiedemann–Franz (W-F) law. The thermal conductivity of metallic TaS3 was approximately 12 times larger than predicted by W-F law, implying . This result implies the possibility of an existing heat conduction path that the Sommerfeld theory cannot account for.

Measurement of thermal boundary resistance between water and superhydrophobic surfaces by the bi-directional differential 3ω method

This study describes a new approach for measuring thermal boundary resistance between water and superhydrophobic surfaces with a thin air layer in between. This new bi-directional differential 3ω method was used to detect the small thermal boundary resistance due to superhydrophobicity. The superhydrophobic surface was prepared by spin-coating a commercial colloidal solution (Glaco Mirror Coat Zero) on the borosilicate glass substrate with a thin film-heater line for the 3ω measurements. The surface wettability was changed from superhydrophobic to superhydrophilic by plasma treatment of the coating surface to obtain the reference state without the air layer (thermal boundary resistance), required for the differential measurement. The obtained thermal boundary resistance was 7.5 × 10−6 [(K･m2)/W], and its equivalent air layer thickness was 0.2 μm and was consistent with the surface topology observed using an atomic force microscope. This measurement technique is considered useful for characterizing the thermal resistance of superhydrophobic structures used in heat transfer applications, such as phase-change heat transfer surfaces and microchannel heat exchangers.

Inorganic Thermoelectric Fibers: A Review of Materials, Fabrication Methods, and Applications.

Thermoelectric technology can directly harvest the waste heat into electricity, which is a promising field of green and sustainable energy. In this aspect, flexible thermoelectrics (FTE) such as wearable fabrics, smart biosensing, and biomedical electronics offer a variety of applications. Since the nanofibers are one of the important constructions of FTE, inorganic thermoelectric fibers are focused on here due to their excellent thermoelectric performance and acceptable flexibility. Additionally, measurement and microstructure characterizations for various thermoelectric fibers (Bi-Sb-Te, Ag2Te, PbTe, SnSe and NaCo2O4) made by different fabrication methods, such as electrospinning, two-step anodization process, solution-phase deposition method, focused ion beam, and self-heated 3ω method, are detailed. This review further illustrates that some techniques, such as thermal drawing method, result in high performance of fiber-based thermoelectric properties, which can emerge in wearable devices and smart electronics in the near future.

A two-sensor 3ω-2ω method for thermal boundary resistance measurement

Thermal boundary resistance (TBR), which measures an interface's resistance to the thermal flow, is of critical importance among various areas, such as electronics cooling and thermoelectric materials. As for measuring TBR, electrical techniques are generally less sensitive compared to optical ones, but they are easily operable and compatible with the measurement of other electric properties; thus, it is highly desirable to develop electrical methods with higher accuracy and larger measurement range. Here, a two-sensor 3ω-2ω method with a novel experimental procedure design is proposed, which can well address those deficiencies in the conventional 3ω method. Two parallel metal sensors are fabricated, with one of them being wide and the other being narrow. The temperature changes of these two sensors are measured by detecting the 3ω and 2ω signals, respectively. The measurement includes three steps: (1) obtain thin film's thermal conductivity from the wide sensor's 3ω thermal response; (2) obtain substrate thermal conductivity from the narrow sensor's 2ω thermal response; and (3) derive an effective TBR from the narrow sensor's 3ω thermal response. Moreover, it is found the TBRs of metal/dielectric and dielectric/substrate interfaces are distinguishable due to the considerable difference between their contact areas, which enables us to separate these two TBRs by varying the contact area (heater's width). Then, our method is employed to probe the TBRs between the Al2O3 nanofilm and Si as well as SiC substrates at room temperature and good agreement with the previous measurements is achieved, verifying its feasibility. Our present scheme will be helpful for the experimental study of interfacial thermal transport.

Experimental Characterization and Model Verification of Thermal Conductivity from Mesoporous to Macroporous SiOC Ceramics

Based on the chemical cross-linking method, this paper uses polydimethylsiloxane with various viscosities of 10 cSt, 20 cSt, 50 cSt, and 100 cSt to synthesize mesoporous and macroporous SiOC ceramics. Their thermal conductivities are measured by using 3ω method with high accuracy. Three typical models for their thermal conductivities, i.e., series model (SM), maxwell-Eucken 1 model (ME1), and effective medium theory (EMT) model, are utilized to derive the empirical formula through the multi-parameter linear optimization algorithm, which agrees well with the experimental results. The effects of pore size and specific surface area on the overall thermal conductivity of the porous structure are explored. Interestingly, it is found that the thermal conductivities of both gas phase and solid phase inside the porous structure increase with the increasing pore size at the nanometer scale, but the overall thermal conductivity of the porous structure decreases with the increasing pore size. Scanning electron microscopy graphs corroborate that the extension of the heat transfer route and the barrier of more pores between the solid phases together cause the reduction of the gas-solid coupling thermal conductivity of SiOC ceramics with larger pore size. On the contrary, the miniaturization of individual particles through modulating the synthesis parameters can increase the number of small pores in the sample itself to meet the pseudo-lattice vibration conditions, which results in the increment of the gas-solid coupling thermal conductivity and the overall thermal conductivity of the porous structure. These findings would provide meaningful guidance for designing SiOC porous ceramic super-insulation materials with extremely low thermal conductivity.

Inline quality monitoring of diesel exhaust fluid (AdBlue) by using the 3<i>ω</i> method

Abstract. Because diesel combustion processes produce harmful detrimental nitrous oxides, the selective catalytic reduction, an after-treatment method using diesel exhaust fluid (AdBlue) to reduce these emissions, is an important part in the cycle of the combustion process. Therefore, it is crucial to continuously monitor the quality of the diesel exhaust fluid to secure the ideal selective catalytic reduction. This article presents a platinum thin-film sensor using the 3ω method which is able to characterize the diesel exhaust fluid. By means of the 3ω method, information about the concentration of urea in water can be extracted. In this investigation, a digital lock-in amplification technique is used to execute the measurements. The results show that this sensor can determine the urea content within 1 % by weight. Moreover, besides the analysis of the 3ω signal, the 1ω signal is analyzed in depth to receive additional information about the temperature. Because the same structure can measure multiple parameters, such as concentration, temperature, and flow, the sensor might be a good alternative to the state-of-the-art diesel exhaust fluid sensor.

Thermal conductivity measurement of VO2 nanofluid using bidirectional 3ω method

Nanofluids containing vanadium dioxide (VO2) are used in applications such as actuators, smart windows, and gastrointestinal tracts. Therefore, measuring the thermal conductivity of nanofluids with VO2 characteristics is important in various environmental industries. In this study, the bidirectional 3 omega (3ω) method was used to measure the thermal conductivity of nanofluids. Experimental equipment for measuring VO2 nanofluids in various environments was designed and fabricated. The effectiveness of the bidirectional 3ω equipment was verified by measuring the thermal conductivity of ethylene glycol, which has been extensively reported in the literature. The effects of elapsed time, specimen thickness, and operation temperature on the thermal conductivity are discussed in this paper. In addition, the measuring error was investigated with regard to the precipitation of particles in the suspension.

Analysis of thickness and interfacial thermal resistance of Au microheater on glass or polyimide substrate

The 3ω method is widely used for measuring the thermal properties of a substrate or thin film on which a microheater is deposited. Recently, samples with non-formal shapes and has a thermal conductivity of 1 W/mK or below have been analyzed using the bidirectional 3ω method. In measuring the thermal conductivity of such samples, the measurement sensitivity and accuracy can be increased using a 3ω sensor fabricated on a low thermal conductivity substrate such as glass or polyimide. In this study, thermal characterization is conducted on a microheater deposited on glass and polyimide substrates for a 3ω sensor. The effects of the microheater thickness and the interfacial thermal resistance between the substrate and microheater, on the temperature amplitude and phase lag are analyzed. Results from analytic solutions considering the microheater thickness and the interfacial thermal resistance are compared with results from numerical analysis of two-dimensional conduction heat transfer and experiment.

Thermal barrier effect from internal pore channels on thickened aluminum nanofilm

High thermal conductivity nanofilms play a key role in the heat dissipation of microdevices, and the preparation process greatly influences the thermal conductivity of the nanofilms. In this study, four Al nanofilms with different thicknesses were fabricated via the electron beam evaporation method, and their effective thermal conductivity (ETC) values were measured using a specially designed microsensor-based third harmonic 3ω method. Due to the internal pore channels and nanometer-level feature size, the ETC of nanofilms exhibited a downward trend when the thickness increases. Significantly, the pores produced by the preparation induce the electron-phonon nonequilibrium effect inside the film, resulting in an anomalous change of the film thermal conductivity versus the thickness.

Anisotropic thermal conductivity of AlGaN/GaN superlattices

High thermal conductivity is an important parameter for nitride-based power electronic and deep-UV light emitters. Especially in the latter case short period superlattices and multicomponent alloys are used and the knowledge of the thermal properties of the binary compounds is sufficient. In-plane and cross-plane thermal conductivity of AlGaN/GaN superlattices were measured by differential two-wire 3ω method in the temperature range from 147 to 325 K. Samples were grown by metalorganic vapor phase epitaxy; the structure quality and accuracy of superlattice structures preparation were verified by means of HRXRD and transmission electron microscopy. It was observed, that value of thermal conductivities decrease with decreasing period thickness, while temperature dependencies differ from each other—in-plane thermal conductivity decreases, and cross-plane—increases with increasing temperature. Callaway method was used for thermal conductivity calculation; dependence of boundary scattering rate on the phonon wavelength was taken into account. Minimum thermal conductivity was added to calculated values to include the influence of high frequency acoustic phonons and optical phonons on the heat transport. Calculations are in good agreement with experimental results.

A skin layer made of cured polysilazane and yttria stabilized zirconia for enhanced thermal protection of carbon fiber reinforced polymers (CFRPs)

This study reported for the first time using cured preceramic polymer precursor and their composites as thermal protection layer for the carbon fiber reinforced polymer (CFRP). The fabricated composite skin consists of cured polysilazane (PSZ) and yttria stabilized zirconia (YSZ) as the reinforcements and has a low density of 1.67 g/cm3, which can be used for both aerospace and defense applications. The coated composite showed excellent bonding integrity at the interface between the composite skin and the CFRP substrate. Thermal studies revealed the cured PSZ has excellent thermal stability up to its cured temperatures. Using the 3ω method, the room temperature thermal conductivity of PSZ was measured as 0.17 ± 0.02 W/m·K along the through-thickness direction. Thermal conductance of the skin layer is around 940 W/m2·K, which is about 45% reduction in conductance compared to the CFRP. Thermal insulation test shows that the coated composite can be used up to 250 °C. Experiment results demonstrated the skin layer's effectiveness in protecting the CFRP in high-temperature environments.

In vivo skin thermophysical property testing technology using flexible thermosensor-based 3ω method

Thermophysical properties of human skin surface and subsurface can reflect the hydration state of the skin and the blood flow rate in the near surface microvessels, which reveals important physiological information related to dermatology and overall health status of human body. Although a few techniques have been developed to measure these signs, complicated devices are required and the subjects need to be completely fixed during the test period. Here, a flexible thermosensor-based 3ω technology was used to monitor thermal conductivity of human skins at different states. Through the analysis of these characteristics, the corresponding physiological state can be established, which can provide a new detection method for the evaluation or prediction of human health status.

An advanced 2ω method enabling thermal conductivity measurement for various sample thicknesses: From thin films to bulk materials

We developed an advanced 2ω method for thermal conductivity (κ) measurements that is also applicable to samples with a wide range of thicknesses, to which the flash method cannot be applied. The conventional 2ω method, which features a simple setup combined with thermoreflectance, is a κ measurement method for thin films on substrates. However, it is difficult to apply this method to bulk substrate samples without films because of the interfacial thermal resistance between the transducer metal film and the substrate. In the advanced 2ω method, the interfacial thermal resistance becomes negligible due to the coating of a bulk sample with a high-thermal-resistance film. We measured the κ values of various bulk samples (Si, Ge, fused quartz, and TiO2). Moreover, the κ value of thin (0.3-mm) bulk Si substrates, which is difficult to measure using the conventional flash method for bulk materials because of the high thermal diffusivity, could be measured. This study demonstrates that the range of sample thickness for the 2ω method is extended from thin films to bulk materials.

Thermal conductivity and thermal boundary resistance of amorphous Al2O3 thin films on germanium and sapphire

Sub-nanometer thickness accuracy and excellent conformity make atomic layer deposited films prevalent in modern electronics, continuously shrinking in size. The thermal resistance of these films plays a major role in the overall energy efficiency of miniaturized devices. We report very sensitive thermal conductivity measurements of amorphous Al2O3 thin films grown using atomic layer deposition in the temperature range of 100–300 K. The 3ω method is used to characterize these films ranging from 17.0 to 119.4 nm in thickness, using a series-resistor model to deconvolve the intrinsic thermal conductivity of the film from thermal boundary resistances inherently present in the multilayer system. The thermal conductivity of amorphous alumina films with a density of 2.77±0.14 g cm−3 is measured to be 1.73±0.08 W m−1 K−1 at 300 K. Measurements were carried out on germanium and sapphire substrates, leading to no substrate dependence of the films’ thermal conductivity, within experimental accuracy. On the other hand, thermal boundary resistances of the systems Pt/Al2O3/substrate are observed to be strongly substrate-dependent, with values ranging from 2.1×10−8 m2 K W−1 to 3.7×10−8 m2 K W−1 at 300 K for films deposited on sapphire and germanium, respectively. These results provide further insights into the significance of interfaces in thermal transport across layered materials, in particular, for potential germanium-based devices.