Photoelastic effect and mirage deflection in anisotropic materials

The collinear mirage technique is widely used to measure the thermal diffusivity of semi-transparent materials. However, in a recent paper [A. Salazar, M. Gateshki and A. Sánchez-Lavega: Appl. Phys. Lett. 76, 2665 (2000)], it was shown that for isotropic materials, because of the influence of photoelastic effect, the method was sensitive to the polarization state of the probe beam. The present paper extends the previous work to include anisotropic materials. In particular, we focus on the experimental conditions under which the thermal diffusivity of each crystal system can be measured using the phase method. Our theoretical model indicates that while the thermal diffusivity of isotropic materials can be measured using an unpolarized probe beam, for anisotropic materials, even the use of an unpolarized probe beam does not guarantee the validity of the method in all crystal systems. Experimental measurements performed on cubic, hexagonal and monoclinic crystals confirm the validity of the model. Received: 17 March 2001 / Accepted: 17 March 2001 / Published online: 25 July 2001     

A simple theoretical extension to the analysis of photothermal deflection signal for low thermal diffusivity evaluation

A modified amplitude method to analyze the photothermal probe beam deflection signal for the determination of low thermal diffusivity values of materials is proposed. This simple theoretical model, which is an extension of the amplitude method proposed by Quelin et al., takes into account the dependence of the photothermal signal on the height of the probe beam above the sample surface which affects mirage measurements when the thermal diffusivity of the coupling medium is greater than that of the sample. The present work is similar to the modification to the phase method proposed by Bertolotti et al. for determination of low thermal diffusivity. The method can be applied irrespective of whether the sample is optically transparent or optically opaque and is independent of thickness.     

An analytical model for thermal diffusivity measurements of film substrate composite using the mirage technique

The thermal diffusivity h of a thin film on a substrate is measured by using the mirage technique. The photothermal deflection of the probe beam is caused by the heat field and the substrate, heated by the pump beam. From the experimental data a two-dimensional algorithm is proposed to obtain the measurements of the diffusivity of film and substrate in one set of mirage detection.     

Theoretical study of thermal diffusivity of superlattices in measurements using “mirage” technique

A complete theoretical treatment for the determination of thermal diffusivity of superlattices by the mirage technique has been performed. An effective medium approximation model of the thermal conductivity and thermal diffusivity of both sublayers is presented, which is different from the simple models with the thermal diffusivity or thermal conductivity in series or parallel. The numerical calculation of the transverse component of the probe beam deflection in the mirage effect shows that the results obtained from the complete thermal-wave theory and the medium approximation model, for the optically and thermally thick superlattices, are in good agreement with each other. However, the further study on the thermally thin superlattices shows that either the series or the parallel model of the thermal conductivity should be chosen according to whether the thermal impedance of the superlattice is larger or less than that of substrate, respectively.     

Thermal Diffusivity of Film/Substrate Structures Characterized by Transient Thermal Grating Method

Transient thermal grating method is used to measure the thermal diffusivity of absorbing films deposited on transparent substrates. According to periodically modulated dielectric constant variations and thermoelastic deformations of the thin films caused by the transient thermal gratings, an improved optical diffraction theory is presented. In the experiment, the probing laser beam reflectively diffracted by the thermal grating is measured by a photomultiplier at different grating fringe spaces. The thermal diffusivity of the film can be evaluated by fitting the theoretical calculations of diffraction signals to the experimental measured data. The validity of the method is tested by measuring the thermal diffusivities of absorbing ZnO films deposited on glass substrates.     

Vector model analysis in nondestructive imaging by using the photothermal deflection methods

The noncontact imaging of the buried structures is carried out in the open-air atmosphere by using the photothermal deflection (PTD) method. We applied these techniques to the layered samples. Besides the PTD images for the optically opaque buried structures, the parameters of the materials such as thermal diffusivity can also be calculated from the PTD amplitude and phase signal in the PTD scanning images. When the PTD signals at two different modulation frequencies are used, the thermal diffusivity of the buried structure can be obtained from the PTD signal outside of the sample nondestructively. Received: 27 November 1998 / Accepted: 18 March 1999 / Published online: 7 July 1999     

Thermal diffusivity and Biot number: A new experimental method

A new simple method is presented for measuring thermal diffusivity and Biot number in cylindrical samples made of relatively highly conducting materials, subjected to laminar air flow. The basic idea is a heat source in the middle section of the sample, acting also as a thermocouple; only one additional temperature sensor at the cylinder basis is required to give all information, without requiring any hypothesis about the effective time dependence of the heat source.     

Photoacoustic measurements of the thermal properties of AlyGa1-yAs alloys in the region 0<y<0.5

y Ga_1-yAs alloys grown by liquid phase epitaxy on GaAs substrates, by means of the open photoacoustic cell detection technique and the temperature-rise method under continuous light illumination. The values of the thermal conductivity, diffusivity and specific heat were obtained in the 0<y<0.5 region, where the Al_yGa_1-yAs band gap is mainly direct. The technique presented here is based upon an effective sample model which is shown to be suitable for the determination of the thermal properties of two layer semiconductor specimens. Received: 15 November 1996/Accepted: 5 March 1997     

Study on thermal diffusivity of materials by laser photothermal reflection technique

A method of measuring thermal diffusivity of materials at room temperature by photothermal reflection technique is described. An intensity-modulated Ar+ laser beam is used as incident light. The beam is focused to about 1 mm diameter spot and illuminates the sample surface. HgCdTe infrared detector is used to receive photothermal signal. Using this technique, the photothermal signals are experimentally measured as the function of different frequencies. The thermal diffusivities can be obtained by fitting the experimental data. On the other hand, the thermal diffusivities of one-way composite and orthogonal symmetric arranged composites Al2O3/Al are measured in transverse, longitudinal and arbitrary directions. The results show that the diffusivity of one-way material decreases with the increase of the measurement angle; the diffusivity of orthogonally arranged material almost keeps the same when measurement angle changes.     

The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model

The stability of a couple stress fluid saturated horizontal porous layer heated from below and cooled from above when the fluid and solid phases are not in local thermal equilibrium is investigated. The Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of the thermal non-equilibrium Darcy model for the Newtonian fluid case can be recovered in the limit as couple stress parameter C→0. We also present asymptotic analysis for both small and large values of the inter phase heat transfer coefficient H. We found an excellent agreement between the exact solutions and asymptotic solutions when H is very small.     

Photothermal probe beam deflection measurement of thermal diffusivity of atmospheric air

We have used a modified photothermal probe beam deflection system with a back pumping configuration for the measurements of the temperature-dependent thermal diffusivity of atmospheric air. The results are consistent and reasonably well agree with the literature values. The measured thermal diffusivity values are the same for the same measuring temperature regardless of the beam offsets and the deflecting surface temperatures. For the gas with known temperature-dependent thermal diffusivity, this method can be used to deduce the temperature of a gas from the measured thermal diffusivity value.     

Laser-induced thermal lens study of the role of morphology and hydroxyl group in the evolution of thermal diffusivity of copper oxide

The paper explores the evolution of thermal behavior of the material by studying the variations in thermal diffusivity using the single beam thermal lens (TL) technique. For this purpose, the decomposition of Cu(OH)₂ into CuO is studied in a time range up to 120 h, by subjecting the sample to morphological, structural, and spectroscopic characterizations. The time evolution of thermal diffusivity can be divided into three regions for demonstrating the dynamics of the reaction. When the reaction is complete, the thermal diffusivity is also found to be saturated. In addition to the morphological modifications, from rods to flakes, the variations in the amount of hydroxyl group are attributed to be responsible for the enhancement of base fluid's thermal diffusivity by 165%. Thus the study unveils the role of hydroxyl groups in the thermal behavior of CuO.     

Phonon Transport and Thermal Conductivity in an Acoustic Filter

We investigate the phonon ballistic transmission and the thermal conductivity in a dielectric quantum structure. It is found that these observable quantities sensitively depend on geometric parameters, and are of quantum character. The total transmission coetfficient as a function of the reduced waveguide-length exhibits periodical behaviour and the reduced thermal conductance decreases below the ideal universal value for the low temperature. Our results show that one can control the thermal conductivity of the structure and make all kinds of acoustic filters to match practical requirements in devices by adjusting the geometric parameters.     

Nonlinear photoacoustic imaging dedicated to thermal-nonlinearity characterization

We proposed a nonlinear photoacoustic(PA) technique as a new imaging contrast mechanism for tissue thermalnonlinearity characterization. When a sine-modulated Gaussian temperature field is introduced by a laser beam, in view of the temperature dependence of the thermal diffusivity, the nonlinear PA effect occurs, which leads to the production of second-harmonic PA(SHPA) signals. By extracting the fundamental frequency PA and SHPA signal amplitudes of samples through the lock-in technique, a parameter that only reflects nonlinear thermal-diffusivity characteristics of the sample then can be obtained. The feasibility of the technique for thermal-nonlinearity characterization has been studied on phantom samples. In vitro biological tissues have been studied by this method to demonstrate its medical imaging capability,prefiguring great potential of this new method in medical imaging applications.     

Influence of ion implantation on the thermal diffusivity of semiconductors

The influence of ion implantation on the thermal diffusivities of semiconductors are studied using the mirage effect. The dependences of the thermal diffusivities on the implantation doses are obtained. For silicon wafers implanted by boron, phosphorus and arsenic ions, with constant implantation energy, the thermal diffusivities decrease with increasing dose, when the doses are less than some critical values. The theoretical calculation results by using a one-dimensional multilayer model are in good agreement with the experimental ones. On the other hand, for gallium-arsenide wafers implanted with silicon ions, it is found experimentally that the thermal diffusivity increases with the implantation dose.     

Thermal conductivity and interface thermal resistance of Si film on Si substrate determined by photothermal displacement interferometry

An in situ, noncontact, photothermal displacement interferometer for performing thermal diffusivity measurements on bulk and thin-film materials has been developed. Localized transient surface motion is generated through photothermoelastic coupling of a pulsed, heating laser beam to the sample under investigation. The maximum surface displacement is found to be linearly dependent on the laser power while the proportionality is a function of the thermal diffusivity. Both thin-film conductivity and film/substrate interface thermal resistance are derived from the measured, effective thermal conductivity by employing simple heat-flow analysis. Wedge-shaped Si films, vacuum deposited on single crystal Si wafers are studied with this technique. A sample with oxide layer removed by ion bombardment of the wafer surface prior to film deposition shows the same film conductivity as a sample film deposited on an as-cast wafer, while the uncleaned sample exhibits higher interface thermal resistance. It is found that the thin-film thermal conductivity is somewhat smaller than the bulk value. However, the existence of an interface thermal resistance, when combined with film thermal conductivity, can result in an effective thermal conductivity as low as two orders of magnitude lower than the bulk value.Currently supported by the LLE fellowship     

THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMS

Carbon foams are being developed as a new class of thermal management materials. These foams are produced with a wide variety of thermo-mechanical properties; however, very few studies of the properties of carbon foams have been reported in literature. This article reports on an experimental study that was conducted to determine the thermal conductivity of various forms of graphitic carbon foam by using the flash diffusivity and guarded hot plate method. To reduce errors introduced by porous specimen, the test samples were vacuum infiltrated with epoxy. The thermal diffusivity results from the flash diffusivity instrument were used to determine the thermal conductivity of the samples. Some foam samples were determined to have large variations in thermal properties within the sample block. A theoretical and numerical model has been used to examine the effect of the filler epoxy on the experimental results and the influence of pore characteristics on the thermal conductivity of these foams. It was determined that accurate measurement of thermal properties of graphitic foam samples requires careful selection of sample size and measurement technique.     

Determination of doping effects on Si and GaAs bulk samples properties by photothermal investigations

The knowledge of doping effects on optical and thermal properties of semiconductors is crucial for the development of opto-electronic compounds. The purpose of this work is to investigate these effects by mirage effect technique and spectroscopic ellipsometry SE.

The near gap optical spectra are obtained from photothermal signal for differently doped Si and GaAs bulk samples. However, the above bandgap absorption is determined from SE. These spectra show that absorption in the near IR increases with dopant density and also the bandgap shifts toward low energies. This behavior is due to free carrier absorption which could be obtained by subtracting phonon-assisted absorption from the measured spectrum. This carrier absorption is related to the dopant density through a semi-empirical model.

We have also used the photothermal signal phase to measure the influence of doping on thermal diffusivity.     

Spectral and Non Radiative Decay Studies of Lead Di Bromide Single Crystals by Mode Matched Thermal Lens Technique

In the present paper, the investigations on the non radiative decay mechanism, optical band gap determination from absorption spectroscopic studies and fluorescence emission by photo luminescence techniques using different excitation wavelengths on gel derived lead di bromide single crystals are reported. Non radiative decay of the sample is studied using high sensitive dual beam mode matched thermal lens technique. For the thermal lensing experiment the crystal in solution phase is incorporated with rhodamine 6G dye for enhancing the absorption of the crystal sample. The thermal diffusivity of lead di bromide is determined using the probe beam intensity v/s time measurements.     

Efficient design considerations for end-pumped solid-state-lasers

The temperature distribution in the gain medium and key design parameters for an ideal-four level end-pumped solid-state laser have been analyzed depending on the crystal's length, absorption coefficient, and pump beam M² factor. The optimum key design parameters and thermal focal lens are obtained by minimizing the root mean square of pump beam radius in the laser crystal. It is found that the focal thermal lens and key design parameters are dependent on the gain medium characteristics and pump beam properties as well. By considering the Poisson equation in cylindrical coordinate and Top-Hat pumping profile, an analytical formula has been derived to introduce the thermal focal length in the end-pumped lasers. A formula is also presented to relate the requirements of pump source to the gain medium properties for working laser at the design point.