3-omega Method Research Articles

Investigation of Heater Structures for Thermal Conductivity Measurements of SiO2 and Al2O3 Thin Films Using the 3-Omega Method.

A well-known method for measuring thermal conductivity is the 3-Omega (3ω) method. A prerequisite for it is the deposition of a metal heater on top of the sample surface. The known design rules for the heater geometry, however, are not yet sufficient. In this work, heaters with different lengths and widths within the known restrictions were investigated. The measurements were carried out on SiO2 thin films with different film thicknesses as a reference. There was a significant difference between theoretical deposited heater width and real heater width, which could lead to errors of up to 50% for the determined thermal conductivity. Heaters with lengths between 11 and 13 mm and widths of 6.5 µm or more proved to deliver the most trustworthy results. To verify the performance of these newfound heaters, additional investigations on Al2O3 thin films were carried out, proving our conclusions to be correct and delivering thermal conductivity values of 0.81 Wm−1 K−1 and 0.93 Wm−1 K−1 for unannealed and annealed samples, respectively. Furthermore, the effect of annealing on Al2O3 was studied, revealing a significant shrinking in film thickness of approximately 11% and an increase in thermal conductivity of 15%. The presented results on well-defined geometries will help to produce optimized heater structures for the 3ω method.

Anisotropic thermoreflectance thermometry: A contactless frequency-domain thermoreflectance approach to study anisotropic thermal transport.

We developed a novel contactless frequency-domain thermoreflectance approach to study thermal transport, which is particularly convenient when thermally anisotropic materials are considered. The method is based on a line-shaped heater geometry, produced with a holographic diffractive optical element, instead of using a spot heater as in conventional thermoreflectance. The heater geometry is similar to the one used in the 3-omega method, however, keeping all the technical advantages offered by non-contact methodologies. The present method is especially suitable to determine all the elements of the thermal conductivity tensor, which is experimentally achieved by simply rotating the sample with respect to the line-shaped optical heater. We provide the mathematical solution of the heat equation for the cases of anisotropic substrates, thin films, and multilayer systems. This methodology allows an accurate determination of the thermal conductivity and does not require complex modeling or intensive computational efforts to process the experimental data, i.e., the thermal conductivity is obtained through a simple linear fit ("slope method"), in a similar fashion to the 3-omega method. We demonstrate the potential of this approach by studying isotropic and anisotropic materials in a wide range of thermal conductivities. In particular, we have studied the following inorganic and organic systems: (i) glass, Si, and Ge substrates (isotropic), (ii) β-Ga2O3 and a Kapton substrate (anisotropic), and (iii) a 285 nm thick SiO2 thin film deposited on a Si substrate. The accuracy in the determination of the thermal conductivity is estimated as ≈5%, whereas the temperature uncertainty is ΔT ≈ 3 mK.

Estimating the uncertainty of measurements of thermal conductivity of thin films of thermoelectrics with the 3-omega method

Using the method of computer simulation, the uncertainty of measurements of the thermal conductivity of silicon, which is often used as substrates, and also thin films based on bismuth, is estimated. The influence of the application of an additional dielectric layer between the thermoelectric film and the resistive heater on the measurement results is shown.

Application of 3-omega method for thin-film heat flux gauge calibration

Double-sided thin-film resistance temperature detector (RTD) heat flux gauges (HFGs) are commonly used to characterize heat transfer rates in high-heat flux environments with complex flow features. These gauges comprise two thin-film RTDs on opposing sides of a dielectric. To deduce accurate heat flux, the RTDs must be properly calibrated and the material properties of the dielectric must be characterized. This study presents a complete gauge characterization method for sensors of this type by applying standard calibration procedures with specially-designed RTDs capable of utilizing the 3-omega method. The 3-omega method quantifies the thermal conductivity and thermal product of a material by measuring the response of a specially designed heater/thermometer deposited on the substrate. This study shows the 3-omega method enables RTD calibrations and thermal property determination over a range of temperatures for individual gauges, reducing the uncertainty in calculated heat flux. Although the method is quite general, this study utilized platinum RTDs with a polyimide dielectric, which is common in turbomachinery applications. The thermal properties obtained through this method agree with previous characterization efforts; however, discrete characterization of seven gauges shows that gauge-to-gauge variation in the dielectric could influence measured heat flux by as much as 30%. This study also builds the framework to characterize the thermal conductivity of the adhesive layer beneath the gauge which is necessary to mount the sensors to the test article. Although often uncharacterized, the adhesive thermal conductivity has a significant impact on matching experimental measurements to simulations. Additionally, this study found that if the thermal conductivity of the dielectric is constant (an assumption that holds for the present study), an in-situ RTD calibration can be performed. In-situ RTD calibration and traditional method RTD calibration agreed to within 0.1%. Overall, this work has practical implications in obtaining high quality measurements from HFGs of this type.

Management of Phonon Transport in Lateral Direction for Gap-Controlled Si Nanopillar/SiGe Interlayer Composite Materials

The phonon transport in the lateral direction for gap-controlled Si nanopillar/SiGe interlayer composite materials was investigated to eliminate heat generation in the channel area for advanced MOS transistors. The gap-controlled Si NP/SiGe composite layer showed 1/100 times lower thermal conductivity than Si bulk. Then, the phonon transport behavior in lateral direction could be predicted by the combination between 3-omega measurement method for thermal conductivity and Landauer approach for phonon transport in Si NP/Si0.7Ge0.3 interlayer composite structure. We found that the NP structure could regulate the phonon transport in the lateral direction by changing the NP gaps. As such, this structure achieves the first step toward phonon transport management in the same electron transportation direction of planar-type MOSFETs and represents a promising solution to heat generation for advanced CMOS devices.

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.

Measurement of the thermal conductivity of flexible biosourced polymers using the 3-omega method

The thermal conductivity of flexible biosourced polymers was measured by the 3-omega method. Two biopolymers were investigated: the polylactic acid (PLA), a widely used commercial biodegradable one, and the cellulose palmitate (CP), a hydrophobic biosourced material developed in the laboratory, that could be used in electronic or microfluidic applications. The 3-omega method is based-on the use of a metal element as both heating device to thermally disturb the system and temperature sensor. A stencil lithography technique was applied to obtain metallic lines, since biopolymers are not compatible with classical photolithography method. Thermal conductivities of 0.19 and 0.30 W/m.K are obtained respectively for PLA and CP thick films, and 0.12 and 0.22 W/m.K for respectively PLA and CP thin films. These values are close to those measured for petro-sourced substrates or films and so give the possibility to address the applications mentioned.

Microfabricated sensor platform with through-glass vias for bidirectional 3-omega thermal characterization of solid and liquid samples

A novel microfabricated, all-electrical measurement platform is presented for a direct, accurate and rapid determination of the thermal conductivity and diffusivity of liquid and solid materials. The measurement approach is based on the bidirectional 3-omega method. The platform is composed of glass substrates on which sensor structures and a very thin dielectric nanolaminate passivation layer are fabricated. Using through-glass vias for contacting the sensors from the chip back side leaves the top side of the platform free for deposition, manipulation and optical inspection of the sample during 3-omega measurements. The thin passivation layer, which is deposited by atomic layer deposition on the platform surface, provides superior chemical resistance and allows for the measurement of electrically conductive samples, while maintaining the conditions for a simple thermal analysis. We demonstrate the measurement of thermal conductivities of borosilicate glass, pure water, glycerol, 2-propanol, PDMS, cured epoxy, and heat-sink compounds. The results compare well with both literature values and values obtained with the steady-state divided bar method. Small sample volumes (∼0.02 mm³) suffice for accurate measurements using the platform, allowing rapid temperature-dependent measurements of thermal properties, which can be useful for the development, optimization and quality testing of many materials, such as liquids, gels, pastes and solids.

Anisotropic thermal conductivity of sputtered Bi0.5Sb1.5Te3 films after current-assisted thermal treatment

Rhombohedral bismuth telluride exhibits highly anisotropic transport properties in different crystallographic directions. Although the degree of anisotropy is diminished in polycrystalline solids, the development of crystallographic texture will lead to distinct thermoelectric properties in the in-plane and out-of-plane directions of thin films. In this study, both in-plane and out-of-plane thermal conductivities of sputtered Bi0.5Sb1.5Te3 (BST) films subjected to thermal/electrical treatments were measured experimentally by the two-wire 3-omega method. The in-plane thermal conductivity of the electrically treated sample is nearly twice as high as that of the thermally treated sample, which is mainly attributed to the enhanced (00l) film texture of the electrically treated BST film. The understanding of anisotropic thermal transport behavior shall help the design and performance modeling of BST-based thermoelectric thin film devices.

Uncertainty Analysis of In- and Cross-Plane Thermal Conductivities of p-Bi0.5Sb1.5Te3 Thin Films by Changing Heater Widths in the Four-Point-Probe 3-Omega Method

Uncertainty Analysis of In- and Cross-Plane Thermal Conductivities of<i> p</i>-Bi_0.5Sb_1.5Te₃ Thin Films by Changing Heater Widths in the Four-Point-Probe 3-Omega Method

Enhancement of Thermal Conductivity of Polyvinyl Alcohol Membrane Using Nano-fiber

ABSTRACTThe thermal properties of organic membranes attract much attention due to the fact that heat dissipation in electronic devices limits their functionality and reliability. Here, we enhance the thermal conductivity of polyvinyl alcohol (PVA) membrane using nano-fibers fabricated by electrospinning. Measured by the 3-Omega method, the results show that the effective thermal conductivity of the electrospinning membranes (with/without Cu nanoparticles) are as high as 0.7 W/m-K at room temperature which is as twice as the value of thermal conductivity of amorphous spin-coated PVA membrane (0.35 W/m-K). The mechanism of enhancement are that, compared with amorphous membrane, the phonon scattering is attenuated and the crystallinity is improved in the electrospinning process. Our studies bring new insights in designing new kind of membrane with high thermal conductivity.

The 3-Omega Method for the Measurement of Fouling Thickness, the Liquid Flow Rate, and Surface Contact.

The 3-omega method is conventionally used for the measurement of thermal conductivity in solid samples. The present work includes the experimental characterization and proof-of-concept measurements of sensor concepts, based on the 3-omega method. It is shown that this method can be used to measure fouling layers with a thickness of 10 to 400 µm, to conduct the measurement of flow rates with a high precision, and finally, as a simple on-off contact sensor with a fast response time.

RETRACTED: Cross- and in-plane thermal conductivity of AlN thin films measured using differential 3-omega method

Thickness dependency and interfacial structure effects on thermal properties of AlN thin films were systematically investigated by characterizing cross-plane and in-plane thermal conductivities, crystal structures, chemical compositions, surface morphologies and interfacial structures using an extended differential 3ω method, X-ray diffraction (XRD) analysis, X-ray photoelectron spectroscopy, atomic force microscopy (AFM) and transmission electron microscopy. AlN thin films with various thicknesses from 100 to 1000 nm were deposited on p-type doped silicon substrates using a radio frequency reactive magnetron sputtering process. Results revealed that both the cross- and in-plane thermal conductivities of the AlN thin films were significantly smaller than those of the AlN in a bulk form. The thermal conductivities of the AlN thin films were strongly dependent on the film thickness, in both the cross- and in-plane directions. Both the XRD and AFM results indicated that the grain size significantly affected the thermal conductivity of the films due to the scattering effects from the grain boundary.

Thermal conductivity reduction of tungsten plasma facing material due to helium plasma irradiation in PISCES using the improved 3-omega method

The near-surface region of plasma facing material (PFM) plays an important role in thermal management of fusion reactors. In this work, we measured thermal conductivity of tungsten (W) surface layers damaged by He plasma in PISCES at UCSD. We studied the damage effect on both bulk, and thin film, W. We observed that the surface morphology of both bulk and thin film was altered after exposure to He plasma with the fluence of 1 × 1026 m−2 (bulk) and 2 × 1024 m−2 (thin film). Transmission electron microscopy (TEM) analysis reveals that the depth of the irradiation damaged layer was approximately 20 nm on the bulk W exposed to He plasma at 773 K for 2000 s. In order to measure the thermal conductivity of this exceedingly thin damaged layer in the bulk W, we adopted the well-established ‘3-omega’ method and employed novel nanofabrication techniques to improve the measurement sensitivity. For the damaged W thin film sample, we measured the reduction in electrical conductivity and used the Wiedemann-Franz (W-F) law to extract the thermal conductivity. Results from both measurements show that thermal conductivity in the damaged layers was reduced by at least ∼80% compared to that of undamaged W. This large reduction in thermal conductivity can be attributed to the scattering of electrons, the dominant heat carriers in W, caused by defects introduced by He plasma irradiation.

Thermal and Electrical Characterizations of Ultra-Thin Flexible 3YSZ Ceramic for Electronic Packaging Applications

Abstract This paper presents thermal and electrical characterizations of an ultra-thin flexible 3YSZ (3 mol% Yttria Stabilized Zirconia) ceramic substrate to explore its potential for electronic packaging applications. The thicknesses of the ultra-thin 3YSZ substrates were 20 μm and 40 μm. The flexible thin ceramic substrate can provide not only better modulus for higher robustness in manufacturing, especially in Z-axis direction of modules, but also low thermal resistance for high density 2D (two dimensional) / 3D (three dimensional) power module packaging applications. To better understand the thermal and electrical properties of the ultra-thin flexible ceramic, different measurements were employed. Thermal conductivity was measured at different temperatures by 3-omega method, the results were verified by thermo-reflectance measurement at room temperature. Relative permittivity was measured from 100 Hz to 10 MHz, with dielectric losses determined by dielectric spectroscopy. The dielectric breakdown of the ultra-thin flexible 3YSZ was measured, from room temperature to 150 °C. Weibull analysis was performed on 20 measurements for each temperature. The test results showed that the thermal conductivity of 3YSZ decreased from 3.3 W/mK at 235 K to 2.2 W/Mk at 600 K. The relative permittivity decreased from 30.9 to 27.3 for higher frequencies for both substrates with different thickness. The temperature-dependence of relative permittivity and dielectric loss was studied. The results showed that these two parameters increased slowly from −65 °C to 150 °C, but more repidly from 175 °C to 250 °C. The dielectric breakdown decreased at higher temperature, from 5.76 kV to 2.64 kV for thickness of 20 μm, 7.84 kV to 3.36 kV for thickness of 40 μm. SEM (Scanning Electron Microscopy), EDS (Energy-dispersive X-ray Spectroscopy) and XRD (X-ray Powder Diffraction) analysis was performed to compare the microstructure of 3YSZ ultra-thin substrate and that of AlN (Aluminum Nitride) substrate. The microstructure of 3YSZ consisted of smaller round particles and that of AlN contained larger columnar particles. FEA (Finite Element Analysis) simulations were also applied to demonstrate the thermal properties of 3YSZ in simplified model of power modules. Though the measurement results showed that it did not meet expectations for high temperature power modules, the present work showed potential applications of the ultra-thin 3YSZ substrates in low voltage power modules, LED modules.

Thermal Conductivity of ZnO Single Nanowire.

The thermal conductivity of a single ZnO nanowire with diameter of ~150 nm was measured using a four-point-probe 3omega method over a temperature range of 140-300 K. The measured ther- mal conductivity of ZnO nanowire is strongly reduced compared to bulk ZnO crystal due to the enhanced phonon-boundary and impurity (isotope) scattering. The maximum of the thermal conductivity is shifted to a higher temperature than that of bulk counterpart. Temperature dependent measurements show that beyond the low-temperature maximum, the thermal conductivity decreases with temperature as T(-1.5) indicating strong impurity (isotope) scattering at intermediate and high temperatures.

(Invited) Tuning of Heat Transport across Thin Films of Polycristalline AlN via Multiscale Structural Defects

The effective thermal conductivity of nanocrystalline films of AlN with inhomogeneous microstructure is investigated experimentally and theoretically. This is done by measuring the thermal conductivity of the samples with the 3-omega method and characterizing their microstructure by means of electron microscopy. The relative effect of the microstructure and the interface thermal resistance on the thermal conductivity is quantified through an analytical model. Thermal measurements showed that when the thickness of an AlN film is reduced from 1460 to 270 nm, its effective thermal conductivity decreases from 8.21 to 3.12 WŸm−1ŸK−1, which is two orders of magnitude smaller than its bulk counterpart value. It is shown that the size effects of the phonon mean free paths and the intrinsic thermal resistance resulting from the inhomogeneous microstructure predominate for thicker films, while the contribution of the interface thermal resistance strengthens as the film thickness is scaled down. The obtained results demonstrate that the structural inhomogeneity in polycrystalline AlN films can be efficiently used to tune their cross- plane thermal conductivity. In addition, thermal conductivity measurements of epitaxially grown InP layers on silicon using Raman spectroscopy are reported.

Thermal conductance of thin film YIG determined using Bayesian statistics

Thin film YIG (Y$_3$Fe$_5$O$_{12}$) is a prototypical material for experiments on thermally generated pure spin currents and the spin Seebeck effect. The 3-omega method is an established technique to measure the cross-plane thermal conductance of thin films, but can not be used in YIG/GGG (Ga$_3$Gd$_5$O$_{12}$) systems in its standard form. We use two-dimensional modeling of heat transport and introduce a technique based on Bayesian statistics to evaluate measurement data taken from the 3-omega method. Our analysis method allows us to study materials systems that have not been accessible with the conventionally used 3-omega analysis. Temperature dependent thermal conductance data of thin film YIG are of major importance for experiments in the field of spin-caloritronics. Here we show data between room temperature and 10 K for films covering a wide thickness range as well as the magnetic field effect on the thermal conductance between 10 K and 50 K.

3-Omega Method for Thin Films with the Non-Fourier Boundary Condition

The effect of non-Fourier boundary condition on the 3-omega method for measuring the thermal conductivity of microscale thin films using the hyperbolic heat conduction equation and the Fourier equation is examined. Non-Fourier boundary condition with the Fourier equation leads to 80% error in the temperature oscillations and increases the error to 85% in the case of non-Fourier boundary condition with the hyperbolic heat conduction equation. The solution of the non-Fourier boundary condition with the hyperbolic heat conduction equation gives the most accurate thermal conductivity expression. The analysis also provides a method for determining the relaxation time of thin films.

Effect of grain size on thermal transport in post-annealed antimony telluride thin films.

The effects of grain size and strain on the temperature-dependent thermal transport of antimony telluride (Sb2Te3) thin films, controlled using post-annealing temperatures of 200°C to 350°C, were investigated using the 3-omega method. The measured total thermal conductivities of 400-nm-thick thin films annealed at temperatures of 200°C, 250°C, 300°C, 320°C, and 350°C were determined to be 2.0 to 3.7 W/m · K in the 20 to 300 K temperature range. We found that the film grain size, rather than the strain, had the most prominent effect on the reduction of the total thermal conductivity. To confirm the effect of grain size on temperature-dependent thermal transport in the thin films, the experimental results were analyzed using a modified Callaway model approach.