Thermal conductivity of amorphous and crystalline thin films by molecular dynamics simulation

This paper reports, for the first time, the cross-plane thermal conductivity of amorphous and crystalline templated cubic mesoporous titania thin films from 30 to 320 K. Both sol-gel and nanocrystal-based films were synthesized by evaporation-induced self-assembly with porosity of 30% to 35%, respectively. The pore diameter in sol-gel mesoporous films ranged from 14 to 25 nm and film thickness from 120 to 370 nm. Crystalline domains in crystalline mesoporous films were 9 to 13 nm in diameter. The thermal conductivity was measured between 30 and 320 K using the 3ω method. The experimental setup and the associated analysis were first validated by comparing experimental measurements with data reported in the literature for high purity silicon substrate and thermal oxide films over the temperature range considered. The thermal conductivity of sol-gel dense and mesoporous TiO2 films was found to increase with increasing temperature. The thermal conductivity of polycrystalline dense film was strongly dependent on temperature while that of dense amorphous and mesoporous films increased slowly with increasing temperature. The amorphous mesoporous TiO2 films featured very small thermal conductivity due to the fact that heat was mainly transferred by very localized non-propagating vibrational modes. Despite the particles crystallinity, the nanocrystal-based film showed significantly lower thermal conductivity than that of the sol-gel polycrystalline mesoporous thin films due to the strong phonon scattering at the nanocrystal boundaries.

This paper reports the room temperature cross-plane thermal conductivity of pure silica zeolite (PSZ) MEL and MFI thin films. PSZ MEL thin films were prepared by spin coating a suspension of MEL nanoparticles in 1-butanol solution onto silicon substrates followed by calcination and vapor-phase silylation with trimethylchlorosilane. The mass fraction of nanoparticles within the suspension varied from 16 to 55%. This was achieved by varying the crystallization time of the suspension. The thin films consisted of crystalline MEL nanoparticles embedded in a non-uniform and highly porous silica matrix. They featured porosity, relative crystallinity and MEL nanoparticles size ranging from 40 to 59%, 23 to 47% and 55 to 80 nm, respectively. PSZ MFI thin films were made by in-situ crystallization, were b-oriented, fully crystalline and had a 33% porosity. Thermal conductivity of the PSZ thin films was measured at room temperature using the 3ω method. The cross-plane thermal conductivity of the MEL thin films remained constant around 1.02 ± 0.10 Wm−1K−1 despite increases in (i) relative crystallinity, (ii) nanoparticle size and (iii) yield as the nanoparticle crystallization time increased. Indeed, the effect of increases in these parameters on the thermal conductivity was compensated by the simultaneous increase in porosity. PSZ MFI thin films were found to have the same thermal conductivity as MEL thin films even though they had smaller porosity. Finally, the average thermal conductivity of the PSZ films was three to five times larger than that reported for amorphous sol-gel mesoporous silica thin films with similar porosity and dielectric constant.

The photoacoustic (PA) technique is one of many techniques for measuring thermal conductivity of thin films. Compared with other techniques for thermal conductivity measurement, the photoacoustic method is relatively simple, yet is able to provide accurate thermal conductivity data for many types of thin films and bulk materials. In this work, the PA measurement in a high frequency range is made possible by a newly developed PA apparatus, which extends the limit of the PA technique. Thermal conductivities of SiO2 with thicknesses from 0.05 to 0.5 μm on Si wafer, e-beam evaporated thin nickel film on Si wafer, and thermal barrier coatings are obtained. In addition to the commonly used phase shift fitting, which is only appropriate for thermally-thin films, an amplitude fitting method is developed and employed for measuring both thin films and bulk materials with smooth or rough surfaces. Comparing results by amplitude fitting to those obtained by other methods and reference values shows good agreements. Applications and limitations of the photoacoustic technique are discussed.

Ionic conductivity of lithium alumino-silicate thin films on SiO 2 glass and Al 2O 3 substrates

The present work measured the thermal conductivities of the silicon nitride films prepared by lower pressure chemical vapor deposition (LPCVD) with thicknesses ranging from 100 nm to 200 nm. The measurements were made at room temperature using the transient photothermal reflectance technique, which is a non-contacting and non-destructive optical approach. The data measured were fitted by genetic algorithm to get the thermal conductivity of thin films and interfacial thermal resistance simultaneously. The results show that thermal conductivities of these films are lower than corresponding bulk material values. The interfacial thermal resistances are in the order of 10−8 m2K/W. It cannot be neglected for the very thin films. Some comparison and analysis for the results were discussed.

We have estimated the thermal conductivity of nanocrystalline bismuth telluride thin films using the differential 3ω method, taking into account the thermal contact resistance (TCR) between the substrate and thin-film layers. The thin films were prepared on alumina substrates by radio-frequency (RF) magnetron sputtering at temperature of 200°C. Film thickness varied between 0.8 μm and 3.1 μm. The structural properties of the films were analyzed using x-ray diffraction analysis. Their electrical conductivity, Seebeck coefficient, and power factor were evaluated. For measurement of thermal properties by the differential 3ω method, SiO2 thin films were deposited onto the samples, to act as insulating layers. Thin aluminum wire was then patterned onto the SiO2 layer. The observed variations in temperature amplitude as a function of film thickness indicated that the TCR contribution was very small and could therefore be neglected when estimating the thermal conductivity of the thin films. The thermal conductivity of the nanocrystalline bismuth telluride thin films with thickness of 0.8 μm and 2.1 μm were determined to be 0.55 W/(m K) and 0.48 W/(m K), respectively.

Summary form only given. In this talk we present a self-consistent model for calculating the lattice thermal conductivity in semiconductor thin films and nanowires. The model is based on the solution of the phonon Boltzmann equation. It rigorously takes into account modification of the acoustic phonon dispersion in low-dimensional structures with the lateral feature size of 10 nm - 30 nm, and change in the non-equilibrium phonon distribution due to partially diffuse scattering from rough boundaries and interfaces. It is shown that the presence, of distinctive boundaries in such structures leads to a transformation of the acoustic branches of phonon dispersion to quasi-optical branches characterized by a low group velocity and different cut-off frequencies. This transformation affects both in-plane and cross-plane thermal conduction in low-dimensional structures. In this talk we also analyze three-phonon Umklapp scattering processes in thin films and nanowires and compare them with those in bulk semiconductors. The predictions. of the thermal conductivity. values based on our model are in good agreement with available experimental data for silicon thin films and nanowires. The described changes in phonon transport in semiconductor thin films and nanowires bear important consequences for nanostructure and device simulation since neither Fourier beat theory nor Debye approximation are accurate at nanometer length scale. The observed modification of the thermal resistance of the low-dimensional structures has to be taken into account in simulation of thermal transport in deep-submicron devices since, it strongly affects the electrostatic, discharge voltage (EDS) and other reliability characteristics. The change in the acoustic phonon dispersion and group velocity may be partially responsible for the experimentally observed drop of EDS in devices based on thin-film silicon-on-insulator (SOI) wafers.

We use the 3ω method to measure the effective thermal conductivity of thin films of a-Ge with thicknesses of 20–150 nm in the temperature range of 30–300 K. By using a moving shadow mask, the films are grown on the same Si (001) substrate in a single deposition run to minimize changes in the microstructure. We observe a reduction in the effective conductivity of the films with the decreasing layer thickness. From the measured data we estimate values for both the film thermal conductivity and the thermal boundary resistance (TBR) between SiO2/a-Ge/Si at the different temperatures. An experimental value of the interface resistance of 2×10−8 m2 K/W is obtained at 300 K. The temperature dependence of the TBR differs appreciably from calculations based on the diffusive mismatch model. The values derived for the intrinsic thermal conductivity of the films, kfilm(300 K)=0.64 W/mK, agree with predictions from the minimum thermal conductivity model and with values measured by Cahill and Pohl [Phys. Rev. B 37, 8773 (1988)] for thicker films.

The out-of-plane (c-axis) thermal conductivities of high-temperature superconducting thin films (YBa2Cu3O7-δ: YBCO) have been measured by photothermal radiometry (PTR) at room temperature. The YBCO samples are in c-axis-aligned epitaxially grown thin films with thicknesses of 250, 500, and 1000 nm. PTR is a noncontact measurement technique for the thermal conductivity and is based on the detection of infrared radiation emitted from a sample heated by a frequency-modulated laser beam. By changing the modulation frequency up to about 1 MHz, the thermal conductivity of thin film can be determined by a curve-fitting analysis of phase-lag data in the frequency domain. The uncertainty of measured thermal conductivity is estimated to be better than ±7%. The experimental results for thermal conductivity exhibit apparently positive film thickness dependence, and their absolute values are less than half of those for single crystal at the smallest thickness. The results indicate a size effect that cannot be explained by the very short phonon mean free path that the kinetic theory predicts. By employing a simple model taking into account phonon boundary scattering, the possible mean free path to interpret the present results is substantially larger than the prediction. The conclusion supports the validity of quite broad spectral distribution of phonons responsible for the thermal conductivity of YBCO.

Capacitance–voltage and leakage-current characteristics of sol–gel-derived crystalline and amorphous SrTa2O6 thin films

Thermal conductivity of thin diamond films grown from d.c. discharge

We investigated the optical properties of amorphous and crystalline zinc tin oxide (ZTO) thin films grown on SiO2/Si substrates with varying compositions via a co-sputtering deposition method at room temperature. The co-sputtering targets consist of SnO2 and ZnO. By varying the relative power ratio of the two targets, we demonstrate the ability to control the Sn and Zn composition of the resulting ZTO thin films. The ratio of [Sn]/([Sn] + [Zn]) atomic compositions was estimated at 11%, 29%, 42%, 54%, and 60%. Using a 600 °C annealing process, the as-grown amorphous ZTO films were transformed into crystalline ZTO films. The dielectric functions were obtained based on the measured ellipsometric angles, ψ and Δ. We determined the dielectric functions, absorption coefficients, and optical gap energies of ZTO thin films with varying compositions. The dielectric functions, absorption coefficients, and optical gap energies of amorphous and crystalline Zn2SnO4 thin films were obtained at 29 at. % of Sn. Subgap states at 1.6 eV (A) and 2.8 eV (B) of ZnSnO alloys and Zn2SnO4 films were found in the imaginary part of the dielectric function spectra. The subgap state intensities were reduced via a nitrogen gas annealing. Possible origins of the observed subgap states will be discussed.

The micro-Raman method is a noncontact and nondestructive method for thin film thermal conductivity measurements. To apply the micro-Raman method, however, the thickness of the film must be at least tens of micrometers. An analytical heat transfer model is presented in this work to extend the micro-Raman measurement method to measure the thermal conductivity of thin films with submicrometer- or nanometer-scale thickness. The model describes the heat transfer process in the thin film and substrate considering the effects of thin film thickness, interface thermal resistance, thermal conductivity of the thin film and substrate. From this heat transfer model, an analytical expression for the thermal conductivity of the thin film is derived. Experiments were successfully performed to measure the thermal conductivity of 200, 300 and 500 nm thickness silicon dioxide films using the extended micro-Raman measurement method, with results confirming the accuracy and validity of the extended model.

Non-equilibrium molecular dynamics (MD) simulations were used to study the thermal conductivity of thin argon films. The MD simulations show that the argon film's thermal conductivity is affected by the thickness up to thickness of about 100 nm, which agrees with theoretical estimates. The results show that the MD method is very effective for modeling nanoscale thermal conduction. Besides pure argon films, the effect of vacancies on the argon film's thermal conductivity was also studied. The vacancies greatly reduce the thermal conductivity as a function of the vacancy concentration but not as a function of the vacancy distribution when the film's temperature is constant.

Thermal conductivity of undoped and Sn-doped β-Ga₂O₃ bulk and single-crystalline thin films have been measured by the 3ω technique. The bulk samples were grown by edge-defined film-field growth (EFG) method, while the thin films were grown on c-plane sapphire by pulsed-laser deposition (PLD). All samples were with (-201) surface orientation. Thermal conductivity of bulk samples was calculated along the in-plane and cross-plane crystallographic directions, yielding a maximum value of ~ 29 W/m-K in the [010] direction at room temperature. A slight thermal conductivity decrease was observed in the Sn-doped bulk samples, which was attributed to enhanced phonon-impurity scattering. The differential 3ω method was used for β-Ga₂O₃ thin film samples due to the small film thickness. Results show that both undoped and Sndoped films have a much lower thermal conductivity than that of the bulk samples, which is consistent with previous reports in the literature showing a linear relationship between thermal conductivity and film thickness. Similarly to bulk samples, Sn-doped thin films have exhibited a thermal conductivity decrease. However, this decrease was found to be much greater in thin film samples, and increased with Sn doping concentration. A correlation between thermal conductivity and defect/dislocation density was made for the undoped thin films.