3ω Method Research Articles

Demonstration of Thermal Property Determination for a Suspended Wire Using 3ω Method Acquired by a High buffered Multimeter Applying a Discrete Fourier Transformation and a Window Function

Demonstration of Thermal Property Determination for a Suspended Wire Using 3ω Method Acquired by a High buffered Multimeter Applying a Discrete Fourier Transformation and a Window Function

In-plane thermal conductivity measurement of microscale polymer films using a reusable micro-thermocouple

Polymers serve as encapsulating materials for electronic devices, making it crucial to investigate their thermophysical properties. In this work, a novel 2ω method for assessing the in-plane thermal conductivity of polymer films is proposed. A reusable micro-thermocouple, serving as both a heating wire and a sensor, is used with silver paste as the interstitial material in contact with the test film. By comparing the 2ω voltages under both contact and non-contact conditions, the thermal impedance is determined. The thermal conductivity is directly calculated by determining the slope of the real part of the thermal impedance against the logarithm of frequency. Theoretical analysis shows that the influences of contact thermal resistance and radiation heat loss are negligible. To validate the accuracy of the method, measurements were repeated on polyimide and polyester films under various contact conditions. The results demonstrate consistency and align with those obtained using the laser spot periodic heating technique.

Electrical, Optical and Thermal Properties of Ge-Si-Sn-O Thin Films.

This work evaluates the electrical, optical and thermal properties of Sn-doped GexSi1-xOy thin films for use as microbolometer sensing materials. The films were prepared using a combination of a radio frequency (RF) magnetron and direct current (DC) sputtering using a Kurt J Leskar Proline PVD-75 series sputtering machine. Thin films were deposited in an O2+Ar environment at a chamber pressure of 4 mTorr. The thicknesses of the thin films were varied between 300 nm-1.2 µm by varying the deposition time. The morphology and microstructure of thin films were investigated by atomic force microscope (AFM) imaging and X-ray diffraction (XRD), while the atomic composition was determined using the energy dispersive spectroscopy (EDS) function of a scanning electron microscope. The thin film with an atomic composition of Ge0.45Si0.05Sn0.15O0.35 was found to be amorphous. We used the Arrhenius relationship to determine the activation energy as well as temperature coefficient of resistance of the thin films, which were found to be 0.2529 eV and -3.26%/K, respectively. The noise voltage power spectral density (PSD) of the film was analyzed using a Primarius-9812DX noise analyzer using frequencies ranging from 2 Hz to 10 kHz. The noise voltage PSD of the film was found to be 1.76 × 10-11 V2/Hz and 2.78 × 10-14 V2/Hz at 2 Hz and 1KHz frequencies, respectively. The optical constants were determined using the ellipsometry reflection data of samples using an RC2 and infrared (IR) VASE Mark-II ellipsometer from J A Woollam. Absorption, transmission and reflection data for a wavelength range of 900 nm-5000 nm were also determined. We also determined the optical constant values such as the real and imaginary parts of refractive index (n and k, respectively) and real and imaginary part of permittivity (ε1 and ε2, respectively) for wavelength ranges between 193 nm to 35 µm. An optical band gap of 1.03 eV was determined from absorption data and using Tauc's equation. In addition, the thermal conductivity of the film was analyzed using a Linseis thin film analyzer employing the 3ω method. The thermal conductivity of a 780 nm thick film was found to be 0.38 Wm-1K-1 at 300 K. From the data, the Ge-Si-Sn-O alloy was found to be a promising material for use as a sensing material for microbolometers.

Anisotropic Thermal Conductivity Enhancement of the Aligned Metal-Organic Framework under Water Vapor Adsorption.

Metal-organic frameworks (MOFs) exhibit high adsorption and catalytic activities for various gas species. Because gas adsorption can cause a temperature increase in the MOF, which decreases the capacity and adsorption rate, a strict evaluation of its effect on the thermal conductivity of MOFs is essential. In this study, the thermal conductivity measurement of the MOF under water vapor adsorption was performed using an oriented film of copper tetrakis(4-carboxyphenyl)porphyrin (Cu-TCPP) MOF. A recently developed bidirectional 3ω method enabled the anisotropic thermal conductivity measurement of layered Cu-TCPP while maintaining its ordered structure. The water adsorption was found to increase the thermal conductivity in both in-plane and cross-plane directions with different trends and magnitudes, owing to the structural anisotropy. Molecular dynamics simulations suggest that additional vibrational modes provided by the adsorbed water molecules were the reason for the thermal conductivity enhancement.

Experimental setup for thermal measurements at the nanoscale using a SThM probe with niobium nitride thermometer.

Scanning Thermal Microscopy (SThM) has become an important measurement technique for characterizing the thermal properties of materials at the nanometer scale. This technique requires a SThM probe that combines an Atomic Force Microscopy (AFM) probe and a very sensitive resistive thermometer; the thermometer being located at the apex of the probe tip allows for the mapping of temperature or thermal properties of nanostructured materials with very high spatial resolution. The high interest of the SThM technique in the field of thermal nanoscience currently suffers from a low temperature sensitivity despite its high spatial resolution. To address this challenge, we developed a high vacuum-based AFM system hosting a highly sensitive niobium nitride (NbN) SThM probe to demonstrate its unique performance. As a proof of concept, we utilized this custom-built system to carry out thermal measurements using the 3ω method. By measuring the V3ω voltage on the NbN resistive thermometer under vacuum conditions, we were able to determine the SThM probe's thermal conductance and thermal time constant. The performance of the probe is demonstrated by performing thermal measurements in-contact with a sapphire sample.

Comprehensive assessment of thermoelectric properties in modules: Time-domain impedance spectroscopy considering heat leakage via attached lead wires

This study aimed to determine various thermoelectric properties, including the dimensionless figure of merit (zT0), resistivity (ρTE), thermal conductivity (κTE), and Seebeck coefficient (S), using a combination of 3ω and time-domain impedance spectroscopy (TDIS) methods for a thermoelectric module at absolute temperature (T0). The effective dimensionless figure of merit (zT0,eff), influenced by heat leakage through attached lead wires, was quantitatively and qualitatively assessed based on the TDIS method. The results demonstrated that zT0,eff/zT0 can be expressed as the ratio between the thermal conductance of the attached thermoelectric element and the lead wire. Thus, by considering heat leakage through the lead wire, the TDIS method can estimate not only zT0 and ρTE but also κTE and S after measuring the lead wire's thermal conductivity using the 3ω method. The study utilized a commercial Π-shaped bismuth-telluride-based thermoelectric module and derived representative values for its elements. zT0, ρTE, κTE, and |S| at 300 K were 0.871, 10.15 μΩ m, 1.71 W/mK, and 224 μV/K, respectively, consistent with previous reports on representative bismuth-telluride-based materials. In conclusion, the combination of the 3ω and TDIS methods is useful for determining all thermoelectric properties, considering heat leakage through attached lead wires.

Thermal conductivity reduction due to phonon geometrical scattering in nano-engineered epitaxial germanium

Nano-engineering crystalline materials can be used to tailor their thermal properties. By adding new nanoscale phonon scattering centers and controlling their size, one can effectively decrease the phonon mean free path, hence the thermal conductivity of a fully crystalline material. In this Letter, we use the 3ω method in the temperature range of 100–300 K to experimentally report on the more than threefold reduction of the thermal conductivity of an epitaxially grown crystalline germanium thin film with embedded polydispersed crystalline Ge3Mn5 nano-inclusions with diameters ranging from 5 to 25 nm. A detailed analysis of the structure of the thin film coupled with Monte Carlo simulations of phonon transport highlights the role of the nano-inclusions volume fraction in the reduction of the phononic contribution to the thermal conductivity, in particular its temperature dependence, leading to a phonon mean free path that is set by geometrical constraints.

Enhancement of ZT in Bi0.5Sb1.5Te3 Thin Film through Lattice Orientation Management.

Thermoelectric power can convert heat and electricity directly and reversibly. Low-dimensional thermoelectric materials, particularly thin films, have been considered a breakthrough for separating electronic and thermal transport relationships. In this study, a series of Bi0.5Sb1.5Te3 thin films with thicknesses of 0.125, 0.25, 0.5, and 1 μm have been fabricated by RF sputtering for the study of thickness effects on thermoelectric properties. We demonstrated that microstructure (texture) changes highly correlate with the growth thickness in the films, and equilibrium annealing significantly improves the thermoelectric performance, resulting in a remarkable enhancement in the thermoelectric performance. Consequently, the 0.5 μm thin films achieve an exceptional power factor of 18.1 μWcm-1K-2 at 400 K. Furthermore, we utilize a novel method that involves exfoliating a nanosized film and cutting with a focused ion beam, enabling precise in-plane thermal conductivity measurements through the 3ω method. We obtain the in-plane thermal conductivity as low as 0.3 Wm-1K-1, leading to a maximum ZT of 1.86, nearing room temperature. Our results provide significant insights into advanced thin-film thermoelectric design and fabrication, boosting high-performance systems.

Ultralow thermal conductivity of amorphous silicon–germanium thin films for alloy and disorder scattering determined by 3ω method and nanoindentation

Abstract The ultralow thermal conductivity (1.3 W/(m∙K)) of amorphous silicon–germanium films for alloy and disorder scattering was investigated using the 3ω method and nanoindentation. The films exhibited the lowest phonon mean free path (MFP) of 0.5 nm compared to that of amorphous silicon (1.1 nm) and germanium (0.9 nm) films, owing to alloy scattering in the silicon–germanium films. Based on Matthiessen’s rule, the phonon MFPs of the amorphous silicon–germanium films contributing to alloy and disorder scattering were calculated to be 1.0 nm for both. Therefore, alloy and disorder scattering contribute equally to the reduction in the phonon MFP.

Heat transport evaluation of amorphous Si, SiGe, and Ge thin films using 3ω method and minimum heat conduction model

Heat transport evaluation of amorphous Si, SiGe, and Ge thin films using 3ω method and minimum heat conduction model

Origin of ultralow thermal conductivity in amorphous Si thin films investigated using nanoindentation, 3ω method, and phonon transport analysis

The origin of the ultralow thermal conductivity in amorphous Si thin films was investigated by comparing their phonon transport properties with those of single-crystal Si. The group velocity and thermal conductivity were measured at 300 K using nanoindentation and the 3ω method, respectively. The phonon mean free path (MFP) and phonon frequency were determined using the measured properties and models. The scattering in the disordered structure of amorphous Si thin films caused a significant decrease in the phonon MFP with an increase in the phonon frequency, leading to ultralow thermal conductivity. However, the group velocity was unaffected by the disordered structure.

Assessing dispersion stability of alumina colloids via thermal characterization of the sediment layer

Colloidal suspensions incorporating particles are pivotal in diverse industries because of their distinct properties. However, challenges such as particle aggregation and sedimentation have impeded their widespread application. Existing techniques for assessing dispersion stability have limitations with respect to the particle type, concentration, and suspension properties. This study focuses on an innovative approach for assessing the dispersion stability and presents a streamlined method for analyzing the particle size and distribution. A theoretical model considering gravity, buoyancy, and viscous forces acting on the particles was developed to calculate the time-varying thickness of the sediment layer at the bottom of the sample colloid. The 3ω method is employed to measure thermal resistance changes at the sample droplet's bottom due to sedimentation. An empirical comparison utilizing Al2O3 particles in deionized water validates the efficacy of the method in understanding sedimentation mechanisms. In addition, a stability constant was proposed to quantitatively compare sedimentation phenomena, factoring in mixing methods, time, particle concentration, and shelf time. This study enhanced the quantification of the dispersion stability of colloids by enabling swift and precise assessment of particle concentration, size, and distribution inside a sample droplet.

Magnetic field dependent thermal conductivity investigation of water based Fe3O4/CNT and Fe3O4/graphene magnetic hybrid nanofluids using a Helmholtz coil system setup

Magnetic hybrid nanofluids are making a name of themselves in mainstream application areas such as heat transfer, solar systems, acoustic applications, etc. These nanofluids are highly favorable as their ability to advance the properties of their constituent particles such as their thermophysical properties. This study aims to investigate the magnetic field dependent thermal conductivity of Fe3O4/CNT – water and Fe3O4/Graphene – water magnetic hybrid nanofluids. The thermal conductivity investigations are carried out with the 3ω method under a uniform magnetic field generated by a 3D Helmholtz coil system. Fe3O4/CNT – water and Fe3O4/Graphene – water magnetic hybrid nanofluids were purchased commercially as 20 wt% colloids. Then, the samples with 1, 2, 3, 4, and 5 wt% were prepared by diluting them with DI water. Thermal conductivity measurements were carried out for the samples under the external uniform magnetic field in the range of 0–250 G in both parallel and perpendicular directions to the temperature gradient generated by the thermal conductivity measurement probe. The results pointed out that the thermal conductivity of the samples increases as the magnetic field and particle concentration increase for both magnetic hybrid nanofluids. Additionally, it is obtained that the thermal conductivity enhancement of Fe3O4/Graphene – water is up to 3 times higher than Fe3O4/CNT – water samples. Moreover, the maximum thermal conductivity enhancement was observed as ∼12 % and ∼9 % for Fe3O4/CNT – water, and ∼51 % and ∼21 % Fe3O4/Graphene – water under external magnetic field application with parallel and perpendicular direction, respectively.

Minimum Detection Concentration of Hydrogen in Air Depending on Substrate Type and Design of the 3ω Sensor.

Hydrogen has emerged as a promising carbon-neutral fuel source, spurring research and development efforts to facilitate its widespread adoption. However, the safe handling of hydrogen requires precise leak detection sensors due to its low activation energy and explosive potential. Various detection methods exist, with thermal conductivity measurement being a prominent technique for quantifying hydrogen concentrations. However, challenges remain in achieving high measurement sensitivity at low hydrogen concentrations below 1% for thermal-conductivity-based hydrogen sensors. Recent research explores the 3ω method's application for measuring hydrogen concentrations in ambient air, offering high spatial and temporal resolutions. This study aims to enhance hydrogen leak detection sensitivity using the 3ω method by conducting thermal analyses on sensor design variables. Factors including substrate material, type, and sensor geometry significantly impact the measurement sensitivity. Comparative evaluations consider the minimum detectable hydrogen concentration while accounting for the uncertainty of the 3ω signal. The proposed suspended-type 3ω sensor is capable of detecting hydrogen leaks in ambient air and provides real-time measurements that are ideal for monitoring hydrogen diffusion. This research serves to bridge the gap between precision and real-time monitoring of hydrogen leak detection, promising significant advancements in the related safety applications.

Three-sensor 2ω method with multi-directional layout: A general methodology for measuring thermal conductivity of solid materials

Anisotropic thermal transport plays a key role in both theoretical study and engineering practice of heat transfer, but accurately measuring anisotropic thermal conductivity remains a significant challenge. To address this issue, we propose the three-sensor 2ω method in this study, which is capable of accurately measuring the isotropic or anisotropic thermal conductivity of solid materials. In this method, several three-sensor groups following the design guidelines are fabricated upon the sample along different characteristic directions, and each group consists of three parallel metal sensors with unequal widths and distances optimally designed based on sensitivity analysis. Among the three sensors, the outer two serve as AC heaters and the middle one as a DC detector. The 2ω voltage signals across the detector in each three-sensor group are measured, and then the data are processed by the proposed Intersection Method to derive thermal conductivities along directions of interest. The application of the detector's 2ω instead of the heater's 3ω voltage signals eliminates errors introduced by the uncertainties of thermal resistance in superficial structures (metal layer, insulation layer, interface, etc.). Meanwhile, by replacing the fitting algorithm with the Intersection Method, the local optimum trap of multivariate fitting is avoided. To verify the accuracy and reliability, four typical monocrystalline semiconductors, i.e., Si, GaN, AlN, and β-Ga2O3, are measured, and the results are consistent with the literature. This method will provide a comprehensive and versatile solution for the thermal conductivity measurements of solid materials.

Direct measurement of in-plane thermal conductivity of microscale suspended thin films using a novel 3ω method

A novel 3ω method has been developed for measuring the in-plane thermal conductivity of microscale suspended thin films. In this method, a heating wire makes contact with the test film using Ampere's force with the assistance of an interstitial material. The thermal impedance is determined by comparing the triple-frequency voltages across the heating wire with and without contact with the test film. The thermal conductivity can be directly obtained from the slope of the real part of the thermal impedance plotted against the logarithm of the heating frequency, even when the thermal contact resistance between the heating wire and the test film is unknown. This method has been successfully applied to determine the in-plane thermal conductivity of various thin films, including stainless-steel and Kapton films. The linear relationship is significantly improved for samples with low thermal conductivity, and its accuracy is verified through repeated measurements under different contact conditions.

Membrane fouling monitoring by 3ω sensing

Membrane fouling significantly reduces membrane permeability, leading to higher operational expenses. In situ monitoring of membrane fouling can potentially be used to reduce operation cost by optimizing operational parameters and cleaning conditions. In this study, a platinum wire with a diameter of 20 µm was attached to the surface of a ceramic ultrafiltration membrane, and by measuring the voltage across the wire while applying an AC current, the amplitude of the third harmonic wave, the so-called 3ω signal, was obtained. Results showed increasing 3ω signals during formation of fouling layers, which correlates directly to the hydraulic resistance of the formed fouling layer in semi-dead end filtration of polymeric core shell particles and crossflow filtration of diluted milk. This is explained by the insulating effect of the fouling layers which reduces heat convection by crossflow and the different thermal conductivity in the fouling layer compared with the feed. After membrane cleaning, the permeability and the magnitude of the 3ω signal were partly restored, showing that the 3ω method can be used to monitor the effect of cleaning. The frequency of the AC current was varied so it was possible to measure the heat conductivity in the fouling layer (high frequency) and heat convection due to cross-flow (low frequency). This may potentially be used to get information of the type of fouling (heat conductivity) and thickness of the fouling layer (AC frequency where heat conductivity becomes dominating).

High throughput, spatially resolved thermal properties measurement using attachable and reusable 3ω sensors.

The 3ω method is a well-established thermal technique used to measure the thermal conductivity of materials and the thermal resistance of interfaces. It has significant advantages over other steady state and transient thermal techniques in its ability to provide spatially resolved thermal property measurements over a wide range of thermal conductivity. Despite its advantages, it has been restricted to lab-scale use because of the difficulty involved in sample preparation and sensor fabrication and is limited to non-metallic substrates. High-throughput 3ω measurements with reusable sensors have not been realized yet. In this work, we demonstrate a method of applying reusable 3ω sensors fabricated on flexible polyimide films to measure bulk and spatially resolved thermal properties. We establish the limits of thermal conductivity measurement with the method to be 1 to 200 W/mK, and within the measurement limit, we verify the method by comparing the measured thermal conductivities of standard samples with established values. From the 3ω measurements, we also determine the thermal resistance of an interlayer of thermal grease as a function of pressure and compare it against the resistance calculated from direct thickness measurements to demonstrate the ability of this method to provide spatially resolved subsurface information. The technique presented is general and applicable to both metallic and non-metallic substrates, providing a method for high-throughput 3ω measurements with reusable sensors and without considerable sample preparation.

Measuring thermal conductivity of nanostructures with the 3ω method: the need for finite element modeling

Conventional techniques of measuring thermal transport properties may be unreliable or unwieldy when applied to nanostructures. However, a simple, all-electrical technique is available for all samples featuring high-aspect-ratio: the 3ω method. Nonetheless, its usual formulation relies on simple analytical results which may break down in real experimental conditions. In this work we clarify these limits and quantify them via adimensional numbers and present a more accurate, numerical solution to the 3ω problem based on the Finite Element Method (FEM). Finally, we present a comparison of the two methods on experimental datasets from InAsSb nanostructures with different thermal transport properties, to stress the crucial need of a FEM counterpart to 3ω measurements in nanostructures with low thermal conductivity.

Thermal contact resistance measurement between two intersecting PAN type carbon fibers using the T-type 3ω method

The prediction of the effective thermal conductivity of composites filled with carbon fibers requires the knowledge of the microstructure, the relative amount and thermal properties of filler and matrix materials, the orientation of non-isometric filler phases and the thermal contact resistances between fibers and matrix and also between fibers. However, information at small scale are often missing especially thermal contact resistances. The present work describes the measurement of the thermal contact resistance (TCR) between two crossed carbon fibers which is performed by an adaptation of the T-type 3ω method for thermal conductivity measurement of wires. The first carbon fiber is connected to two copper blocks supplied by a modulated electrical current providing a volumetric heating. The second fiber fixed on a U-shape holder is delicately implemented over the first one. After performing a secondary vacuum, the 3ω voltage V3ω of the first fiber is recorded as function of the frequency of the modulated current. Knowing the applied force, the contact area between the two carbon fibers is calculated from bending and deformations then a 3D numerical model describing heat transfer in two crossed carbon fibers is used to estimate the TCR at their intersection. In addition, a detailed sensitivity analysis of the unknown parameter TCR is performed allowing to find optimal operating conditions especially the frequency range. Measurements are performed with PAN type carbon fibers (FT300B) picked up from the same bundle. Different TCR estimations were performed by fitting numerical and computed V3ω voltage as function of frequency. Finally, values of TCR between crossed carbon fibers were found equal (10.4 ± 10.1) 105 kW−1 which provides an order of magnitude for such phenomenon.