Thermal Diffusivity Of Thin Films Research Articles

Fourier Transform Thermoreflectance Method Under Front-Heat Front-Detect Configuration

The thermoreflectance method, which can measure thermal diffusivity in the cross-plane direction of thin films, mainly has two possible configurations; rear-heat front-detect (RF) and front-heat front-detect (FF) configuration. FF configuration is applicable to a wide variety of thin films including thin films deposited on opaque substrates, but this configuration has some problems in determination of the thermal diffusivity. One of the main problems is the effect of the penetration of pump beam and probe beam in thin film, which affects the initial temperature distribution near the sample’s surface after pulse heating. Several studies have tried to analyze the effect but there have been no practical analytical solutions which can solve this problem in FF configuration. In this paper, we propose a new analytical solution which considers the penetration of pump beam and probe beam into thin film, and by applying Fourier expansion analysis which we developed in a previous study to thermoreflectance signals, we have determined the thermal diffusivity of thin film in the thermoreflectance method under FF configuration. We measured platinum thin films with different thickness under both FF and RF configuration and obtained consistent thermal diffusivity values from both configurations.

Development of Fourier Transform Ultrafast Laser Flash Method for Simultaneous Measurement of Thermal Diffusivity and Interfacial Thermal Resistance

The thermoreflectance technique is one of the few methods which can measure thermal diffusivity of thin films as thin as 100 nm or thinner in the cross-plane direction. The thermoreflectance method under rear-heat front-detect configuration is sometimes called ultrafast laser flash method because of its similarity to laser flash method. Up to now it has typically only been possible to attempt to evaluate the interfacial thermal resistance between the thin films by preparing and measuring several samples with different thicknesses. In this study, a method to directly determine interfacial thermal resistance by a single measurement of a thin film on substrate is represented, by analyzing the shape of thermoreflectance signals with analytical solutions in frequency domain and time domain. Thermoreflectance signals observed from metallic thin films on sapphire substrate with different thickness steps were analyzed by Fourier analysis and fitted by analytical equations with four parameters: heat diffusion time across the first layer, ratio of virtual heat sources, characteristic time of cooling determined by interfacial thermal resistance and relative amplitude of the signal. Interface thermal resistance between the thin film and substrate was able to be determined reliably with smaller uncertainty.

A pre-time-zero spatiotemporal microscopy technique for the ultrasensitive determination of the thermal diffusivity of thin films.

Diffusion is one of the most ubiquitous transport phenomena in nature. Experimentally, it can be tracked by following point spreading in space and time. Here, we introduce a spatiotemporal pump-probe microscopy technique that exploits the residual spatial temperature profile obtained through the transient reflectivity when probe pulses arrive before pump pulses. This corresponds to an effective pump-probe time delay of 13ns, determined by the repetition rate of our laser system (76MHz). This pre-time-zero technique enables probing the diffusion of long-lived excitations created by previous pump pulses with nanometer accuracy and is particularly powerful for following in-plane heat diffusion in thin films. The particular advantage of this technique is that it enables quantifying thermal transport without requiring any material input parameters or strong heating. We demonstrate the direct determination of the thermal diffusivities of films with a thickness of around 15nm, consisting of the layered materials MoSe2 (0.18 cm2/s), WSe2 (0.20 cm2/s), MoS2 (0.35 cm2/s), and WS2 (0.59 cm2/s). This technique paves the way for observing nanoscale thermal transport phenomena and tracking diffusion of a broad range of species.

Measurement of Thermal Diffusivity of Thin Film in Thickness Direction Using an Ordinary Dielectric Film as the Sensor

Accurate thermal parameters of thin films are beneficial for the engineering thermal design and thermal management of electronic devices to improve the operating stability and prolong service life. In this article, a novel method for measuring the thermal diffusivity of thin films is proposed based on the thermal pulse method (TPM) for mapping space charge distribution, whose thermal response current is strongly determined by the temperature profiles within thin film. A multi-layer thin film structure is adopted, in which the tested film layer is thermally coupled on the dielectric film substrate with thermal parameters known. The thermal pulse by laser pulse excites the tested film and then penetrates into the dielectric film substrate. By analyzing the thermal response current of the dielectric film substrate, one can deduce the temperature profiles in both layers and therefore the thermal diffusivity of the tested film. The proposed method can determine the thermal diffusivity of both insulating and electric conduction films with the thickness tens of micrometers in through thickness direction. The obtained values of the thermal diffusivity of polyimide (PI), bi-oriented polypropylene (BOPP), polyethylene 2,6-naphthalate (PEN), tin(Sn) foil, and lead (Pb) foil are well consistent with the data provided in the literatures. By the analyzing heat boundary conditions, the interface thermal resistance between the tested film and the dielectric film substrate can be also determined at the same time.

Determination of thermal diffusivity of thin films by applying Fourier expansion analysis to thermo-reflectance signal after periodic pulse heating

The flash methods, which are the most popular transient methods for measuring the thermal diffusivity of solid materials, have evolved into ultrafast laser flash methods by using picosecond or nanosecond pulse lasers as a heating source and a thermo-reflectance technique such as high-speed thermometry. In conventional ultrafast laser flash methods, thermal diffusivity is determined by fitting an analytical equation after single pulse heating to observe thermo-reflectance signals, although actual thermo-reflectance signals are observed after periodic pulse heating. This paper presents an exact analytical solution of the temperature response expressed by Fourier series for one-dimensional heat diffusion after periodic pulse heating. These Fourier coefficients are directly related to the Laplace transformation of the temperature response after single pulse heating. The signal observed for a 100 nm thick platinum thin film on a fused quartz substrate was analyzed by this Fourier expansion analysis and fitted by analytical equations with three parameters: heat diffusion time across thin film, the ratio of heat effusion of the substrate to thin film, and the amplitude of the signal over the entire range of pulse interval in the time domain. Robustness in determining the thermal diffusivity of the thin film by the ultrafast laser flash method can be improved by this new analysis approach.

Microscopic infrared thermography for fast estimation of the thermal properties of thin films

The thermal properties of polyimide thin films govern the temporal response of electric devices in highly integrated circuits. An innovative advanced method, called the Modal-Method, has been developed to investigate the in-plane anisotropic thermal diffusivities of 4 homopolymers of aromatic polyimide thin films, widely used in microelectronics. The proposed method is based on microscopic infrared thermography and consists of a single non-destructive fast experiment. A photo-thermal excitation is applied on the center of the film rear surface. The thermal response of the front surface, recorded by using an infrared camera equipped with a unique microscope lens, allows reaching high resolutions. The Modal-Method is then applied on the recorded thermal emission data. This method is robust to the measurement noise and allows estimating the in-plane thermal diffusivities of thin films. This method affords also the estimation of the effective heat transfer coefficient. This parameter, representing the heat exchanges between the films and their environment, is directly related to the signal/noise ratio and hence related to the quality of the estimation. Eventually, this method has been validated by comparison with temperature wave analysis results.

Scanning thermal probe microscope method for the determination of thermal diffusivity of nanocomposite thin films.

A commercial scanning thermal microscope has been upgraded to facilitate its use in estimating the radial thermal diffusivity of thin films close to room temperature. The modified setup includes a microcontroller driven microhotplate coupled with a Bluetooth module for wireless control. The microcontroller board (Arduino Leonardo) is used to generate a bias of suitable voltage amplitude and pulse duration which is applied across the microhotplate contact pads. A corresponding heat pulse from the Pt heating element (1 mm(2)) embedded within the microhotplate is delivered to the lower surface of the thin film (25 mm(2)) deposited over it. The large difference in the dimensions of the heating source and the thin film surface causes heat to flow radially outwards on the top surface of the latter. The decay of this radial heat wave as it flows outwards is recorded by the scanning thermal microscope in terms of temperature-time (T-t) profiles at varying positions around the central heating zone. A fitting procedure is suggested to extract the thermal diffusivity value from the array of T-t profiles. The efficacy of the above setup has been established by evaluating the thermal diffusivities of Bi2Te3 and Bi2Te3:Si thin film samples. Further, with only minor alterations in design the capabilities of the above setup can be extended to estimate the axial thermal diffusivity and specific heat of thin films, as a function of temperature.

Thermal Diffusivities of Bilayer Films Deposited on Substrates Characterized Simultaneously by Transient Reflecting Grating Technique

The transient reflecting grating (TRG) technique has been applied to characterize the thermal diffusivities of thin films in trilayered structures. Based on the TRG behavior in the trilayered structures of opaque film/transparent film/substrate, a two-dimensional theoretical model describing the thermal diffusion processes in the trilayed structures is presented and calculated by the finite-element method. The normalized TRG signals decayed with time can be expressed as a triple-exponential function with different time-dependent coefficients. The influences of the thermal properties of the first and second layer films on the TRG signals are calculated and discussed separately. By fitting the theoretical decay curves to the experimental measured data of a series of trilayered structures (Au/ZnO/Si and Al/ZnO/Si with different film thicknesses), the thermal diffusivities of both films in the trilayered structures can be evaluated simultaneously. The results show that the thermal diffusivities of the thin films are strongly dependent on the thickness of the thin films and significantly lower than the corresponding bulk materials, and decay with the decreasing thickness of the films.

Observation of thermal transfer across a Pt thin film at a low temperature using a femtosecond light pulse thermoreflectance method

We report the first systematic temperature responses of thermal energy transfer across a 90 nm Pt thin film at low temperature using a rear-heating front-detection-type (RF-type) femtosecond thermoreflectance measurement system. Thermal energy transfer across the thin film became faster as the temperature decreased from 273 K to 15 K. The obtained thermoreflectance curves showed two thermal energy transfer processes: a fast thermal energy transfer within the initial few picoseconds and a slow thermal energy transfer after a few picoseconds. The classical heat diffusion curves were fitted well to the slow temperature increase after a few picoseconds by introducing a ‘characteristic length’ that characterizes the thermal energy penetration depth at the ‘initial’ incident time instead of the given optical penetration depth. The obtained thermal diffusivities from 100 K to 273 K were consistent with the electrical resistivity of the film measured with the van der Pauw method. The characteristic lengths calculated from this analysis increased with the decrease of the temperature, and were larger than the optical penetration depth. The thermoreflectance signal over the initial several picoseconds is considered to be a non-diffusive process. The new RF-type system can not only give the classical thermal diffusivity of thin films at low temperature, but also new information related to the non-thermal energy transfer process.

Thermal diffusivity of aromatic polyimide thin films by temperature wave analysis

The heat transport properties of aromatic polyimide thin films have become more important in the use for the electric insulation in the microelectronic devices with highly integrated circuits. The various kinds of measuring methods have been applied to obtain the anisotropic thermal conductivity and thermal diffusivity of thin films, however, if the specimens are soft and transparent, the conventional methodology requires highly advanced technology in preparing the specimens for the measurement and the results obtained vary widely. The purpose of this study is to apply the temperature wave analysis (TWA) method to measure the thermal diffusivity of thin films and spin-coated layers of aromatic polyimide in the thickness direction at various temperatures. The TWA is an absolute method to determine the thermal diffusivity by using the phase shift of temperature wave. We have performed measurements on the five different chemical structures of aromatic polyimide, including polyimide isoindoloquinazolinedione (PIQ), pyromellitic dianhydride and 4,4′-oxydianiline (PMDA/ODA), 3,3′,4,4′,-biphenyltetracarboxylic dianhydride and p-phenylenediamine (BPDA/PPDA), 3,3′,4,4′-biphenyltetracarboxylic dianhydride and 4,4′-oxydianiline (BPDA/ODA), and 3,3′,4,4′-benzophenonetetracarboxylic dianhydride and 3,3′-diaminobenzophenone (BTDA/DAB). As a result, thermal diffusivity of thin films in a thickness range from 0.1 to 300 μm at a temperature range from 10 to 570 K is obtained. The thickness dependence of thermal diffusivity of spin-coated layers of PIQ exhibits a good coincidence with the tendency of molecular anisotropy observed by attenuated total reflection Fourier transform infrared spectroscopy. In the low temperature below 20 K the amorphous PMDA/ODA film exhibits a substantial increase, which can be understood by considering the phonon mean free path of amorphous systems as first noted by Kittel for inorganic glasses. The glass transition of BTDA/DAB is observed as a rapid decrease of thermal diffusivity. The results indicate the availability of TWA for the present needs of accurate but simple measuring technique to determine the thermal diffusivity of thin polymer films, which is strongly dependent on the chemical and anisotropic structures.

Thermal diffusivity measurement of low- k dielectric thin film by temperature wave analysis

Thermal diffusivity of thin film with low dielectric constant ( k), what is called low- k dielectric thin film, 0.31–1.14 μm, including hydrogen-silsesquioxane (HSQ), methyl-silsesquioxane (MSQ), and poly(arylen ether) was examined by temperature wave analysis. The phase shift of temperature wave was observable up to 100 kHz. Thermal diffusivity of HSQ was 4.7 × 10 −7 m 2 s −1, on the other hand it was not higher than 1.1 × 10 −7 m 2 s −1 for MSQ or poly(arylen ether) at room temperature. Temperature dependence of thermal diffusivity/thermal conductivity of MSQ was obtained, thermal diffusivity decreased but thermal conductivity increased in a heating scan at 30–150 °C. It was shown that the thermal diffusivity of low- k thin film was correlated with the chemical and the physical structures, the latter was formed in the spin-coating and the curing process.

A Novel Method for Determination of the Thermal Diffusivity of Thin Films Using a Modulated CO2 Laser

The thermal diffusivity of thin metal films has been measured by combining a fast infrared radiation thermometer with a mercury cadmium telluride (MCT) detector and a CO2 laser modulated at a radio frequency up to 2 MHz. The laser output beam modulated by an acousto-optic modulator (AOM) is directed to the front surface of the blackened copper thin film (10μm thick, 9.5 mm in diameter). The thermal radiation from the back surface of the sample is detected. From the observed phase delay in the detected signal of 0.68 radian to the input laser beam, the thermal diffusivity is determined to be 1.11 × 10-4m2·s-1, which agrees well with the value of 0.99 × 10-4m2·s-1 calculated from literature results. The method is generally applicable for measurements of thermal properties of nano/micro materials.

Development of a thermal diffusivity measurement system for metal thinfilms using a picosecond thermoreflectance technique

A picosecond thermoreflectance measurement system has been developed in theNational Metrology Institute of Japan in order to measure thermaldiffusivities of metal thin films. A laser beam from a picosecond Ti-sapphirelaser is focused onto the surface of a metal thin film with a spot size of100 µm and absorbed within the skin depth of the order of 10 nm. Then, heatdiffuses towards the opposite side of the thin film one-dimensionally, and thetemperature of the heated face decreases over the time scale from tenpicoseconds to several hundreds of picoseconds. This ultrafast temperatureresponse is observed with a thermoreflectance method using probe picosecondpulses from the same source of the Ti-sapphire laser. Thermoreflectancesignals for aluminium thin films with the thickness of 50 nm, 100 nm, and500 nm sputtered on Pyrex 7740 glass substrates were observed under the frontheating front detection (FF) configuration. We also developed a rear heatingfront detection (RF) type picosecond thermoreflectance measurement system.Thermoreflectance signals of molybdenum thin films and aluminium thin filmswith nominal thickness of 100 nm deposited on Pyrex 7740 glass substrates wereobserved at room temperature under RF configuration. Thermal energy transferinside the molybdenum and aluminium thin films is dominated by the classicalFourier law. In-plane thermal diffusivities of the thin films are close tothose of the bulk materialsalthough out-of plane electrical resistivities measured by the four-probemethod are larger than the resistivities of the bulk materials.

Analysis of two-dimensional effect in the measurement of thermal diffusivity of thin films with an AC calorimetric method

An ac calorimetric method for measuring the thermal diffusivity of thin-film materials has been widely applied. In the application of this method, the systematic errors caused by the heat loss effect, the edge reflection effect, etc., have been analyzed and corresponding correction methods have been developed. But when measuring films with low thermal diffusivity or with thickness comparable to the thermal diffusion length, a two-dimensional effect which will also result in a systematic error of the measurement is present. In this paper, the mechanism of two-dimensional heat conduction within a thin sample which is supplied a periodic heat flux by a chopped light beam is analyzed. A numerical analysis method is developed to study the effect of the two-dimensional heat conduction on the measured thermal diffusivity values. The relations between the measured thermal diffusivity and independent parameters such as frequency, thickness of sample, width of light spot, etc., are demonstrated to indicate the two-dimensional effect. The experimental precondition for minimizing the systematic error caused by the two-dimensional effect is determined. In addition, the analysis method presented in this paper should be useful for more difficult problems such as error estimation of the thermal diffusivity measurement of coatings or composite films.

NONEQUILIBRIUM HEATING IN METAL FILMS: AN ANALYTICAL AND NUMERICAL ANALYSIS

Ultrashort pulsed laser heating of metals at room temperature is commonly studied using the parabolic two step (PTS) model. An analytical solution of the PTS is presented and compared to numerical results. The analytical solution assumes constant thermophysical properties, which is appropriate for applications such as nondestructive testing using low laser fluences. The assumption of constant thermophysical properties is discussed, and appropriate regimes are established. Numerical and analytical solutions of the PTS model are compared to experimental data in order to demonstrate the utility of these solutions for determining the thermal diffusivity of thin films.

Thermal diffusivity by modified ac calorimetry using a modulated laser beam energy source

Modified ac calorimetry, a variation of the Angstrom method, has been shown to be a precise tool for measuring the in-plane thermal diffusivity of thin films (thickness less than 300 μm) of a wide variety of materials and layered composites. The property is determined from an analysis of the decay curve of the ac temperature waves generated by irradiation of a specimen using uniform chopped light (at frequencies from 1 to 20 Hz) from a halogen lamp source. To address certain limiting factors, especially to improve the signal-to-noise ratio and to eliminate heat losses, an improved form of measurement instrument has been developed. It is based on the use of a modulated laser beam heating to provide a higher intensity energy source plus a special optical system to ensure that one-dimensional ac temperature wave propagation is obtained. Measurements can now be made using frequencies in the range of 0.01 to 10 Hz, i.e., 10 times lower than in the traditional method. The performance of the improved measurement instrument will be illustrated by results on various materials of known thermal properties such as nickel and stainless steel, proposed reference materials such as a glassy carbon and alumina, plus a comparison of results obtained on CVD diamond films used in an international round-robin series with those obtained by the traditional technique.

Measurement of thermal diffusivity of thin films by the AC calorimetric method

Measurement of thermal diffusivity of thin films by the AC calorimetric method

Measurement of thermal diffusivities of thin metallic films using the ac calorimetric method

The thermal diffusivities of thin films of evaporated metal less than 1×10−6 m thick have been measured using the light-irradiation ac calorimetric method. The thermal diffusivities of metallic thin films become smaller than those of the bulk as the thickness of the metallic thin films decreases. It is determined, using x-ray diffraction measurement, that the decrease of thermal diffusivity of thin films of evaporated metal is caused by a decrease in crystalline size.

Measurement of the thermal diffusivity of thin films by an AC joule-heating method

A new thermal analysis named TWA (Temperature Wave Analysis) is proposed. This technique is based on the AC joule-heating method developed in our laboratory, and makes it possible to obtain thermal diffusivity precisely as a function of temperature at a constant frequency. The theoretical background and the calculation procedure for this technique are reported. This technique was applied to the study of the first order transition of high density polyethylene and the glass transition of glycerin.

A review of techniques for measuring the thermal diffusivity of thin films and coatings

A review of techniques for measuring the thermal diffusivity of thin films and coatings