The ability to control thermal conductivity is important for a wide range of applications. For instance, advancements in both oxide thermal barrier coatings and thermoelectric materials hinge on engineering a thermally resistive material that is optimized in conjunction with other parameters such as thermal expansion, microstructure, toughness, or carrier mobility. Similarly, materials with high thermal conductivity are desirable for thermal management applications. The remarkable ability of perovskites to accommodate a wide range of materials opens avenues to tune material properties through an appropriate choice of elements 3 . In recent years, epitaxial growth of complex oxides with the perovskite crystal structure has figured prominently in studies of the physics of correlated electrons 4 and in the search for electronic materials for information technology and sensing 5,6 . Measurement of thermal conductivity of epitaxial thin films is another way to characterize the quality of epitaxial films, beside x-ray diffraction (XRD) 7 , transmission electron microscopy (TEM) 8,9 , and in situ reflection high energy electron diffraction (RHEED) 10 . The perovskite family of oxides shows promise for thermal barrier 11 and thermoelectric applications 12- 15 , because of its compositional tunability, which is accompanied by high-temperature stability.
One such material from the perovskite family is strontium titanate (Fig. 1) and its epitaxial thin This is the author9s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI: 10.1116/6.0003320 Sarantopoulos et al. demonstrated that STO thin films grown on DyScO3 substrate under tensile strain showed a significant reduction in thermal conductivity at room temperature to ~2.5 Wm -1 K - 1 , when compared to the STO on LSAT and STO substrates (~6 Wm -1 K -1 ) 30 . Katsufuji et al. measured thermal conductivity of two samples where one of them was a thin film of 70 nm SrVO3 on STO and the other samples was thin film of 30 nm SrVO3 and 30nm SrTiO3 on LSAT substrates with thermal conductivities of 8 Wm -1 K -1 and 2 Wm -1 K -1 respectively 31 looked at the thermal conductivity of nano grained STO thin films deposited on Sapphire substrates. Thin films with a thickness of 170 nm with varying grain sizes were deposited using a chemical deposition process. There was a reduction of 50%-60% across the grain sizes, as compared to the bulk values. A reduction in thermal conductivity with decreasing grain size was also observed in this work 34 .
Brooks et al. demonstrated the ability to tune the thermal conductivity of homoepitaxial STO thin films using MBE by varying deposition parameters such as growth temperature, oxidation temperature and cation stoichiometry. The study showed a 80% reduction in thermal conductivity from 11.5 Wm -1 K -1 for stoichiometric STO to 2 Wm -1 K - at low temperatures, an effect that was attributed to hydrodynamic phonon transport. Such an effect was lost with the introduction of any dopant 38 .
Data on thermal conductivity of STO thin films on Si substrate is lacking. STO on Si substrate serves as an epitaxial platform upon which other multifunctional oxides can be integrated for various device applications 39 . Understanding thermal transport of this material system is important to such applications 40 . In this study, we examine the thermal conductivity of four STO thin films of thicknesses of 12 nm, 50 nm, 80 nm, and 200 nm deposited on Si substrates.
The STO thin films were epitaxially grown on 2= diameter, undoped Si (100) wafers (Virginia Semiconductor) using oxide molecular beam epitaxy (MBE). Epitaxial growth was initiated through the crystallization of 2 unit-cells of amorphous STO deposited at room temperature, as discussed in detail elsewhere 41 . After crystallization of this seed-layer at ~ 500 o C in ultra-high
X-ray diffraction (XRD) confirms the epitaxial quality of the STO thin films on Si. The XRD measurements were taken on a Bruker D-8 system that is equipped with a standard Cu k³ x-ray source (λ = 1.54056 Å). Figure 3 shows survey scans of the 4 films with the various diffraction peaks labelled. The out-of-plane lattice constants of the 12 nm, 50 nm, 80 nm, and 200 nm films were 3.918 Å, 3.924 Å, 3.898 Å, and 3.910 Å, respectively, which largely compares well with the bulk lattice constant of STO (3.905 Å).
Thermal conductivity measurements were performed using the frequency domain thermoreflectance method (FDTR). A sinusoidally modulated pump laser (wavelength λ = 473 nm) with a power of 51.41 mW was used to create a periodic heat source at the sample surface. The frequency range for the modulation of the pump laser is from 2000 Hz to 50 MHz. A probe laser (λ = 532 nm) was used to measure the change in phase of the temperature response of the surface with respect to the phase of the input heat signal. This is achieved by measuring the surface temperature through a measurement of the reflected probe beam's intensity which is dependent on the surface temperature of gold transducer layer through a thermoreflectance coefficient. The For a n layer system, the number of properties associated with the system are 5n-1 resulting in 14 parameters for a 3-layer material system. By eliminating the parameters with known values (such as silicon thermal conductivity), the number of unknown parameters to be obtained by the fitting process between measured and computed phase lag are reduced. Another important parameter for the fitting analysis is the laser spot size. The laser spot size determines the size of the heat source on the sample surface, which is an important parameter used in the calculation of the phase lag using the 2D heat conduction model. The estimate of these parameters is described next.
Transducer is a device which converts one form of energy to another. In our case, the Au thin film converts the energy from the laser to create a periodic heat source at the sample's surface. The periodicity of the heat source corresponds to the frequency at which the pump laser beam is
modulated. The Au film is deposited using a pellet (99% purity) as a target, for the deposition [42][43][44] purchased from Kurt. J Lesker Company. We use Lesker Nano36 Evaporator thermal evaporator, Based on this, Table . 1 compiles the results for the Au layer properties for reference sapphire samples, used in the analysis of the STO samples. The value of Cp (also pre-determined in the fitting analysis software) for gold is 2.484 MJm -3 K -1 46 .
Figs. 5 a) and b) are the best curve fit figures for the transducer layer analysis of reference sapphire samples for 200 and 50 nm STO samples, and 80 and 12 nm STO samples respectively. Since the 200 and 500 nm samples share the same sapphire reference sample, the reference sample curve fit analysis is represented by the same figure for both the samples. This is also true for the 80 and 12 nm STO samples. We observe that the best curve fit line for the measured data fits near perfectly for both the measurements. This indicates the fitted values of the thermal conductivity and the thickness for the transducer layer, determined during this analysis is the correct solution. The following table is the properties of the Au thin film, which are used in the analysis of the STO samples.
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The SrTiO3 thickness is measured as a function of the deposition rate, which is computed from the rates of SrO and TiO2 fluxes, which are measured and controlled during the STO thin film deposition process. Volumetric heat capacity values for Au and Si layers are taken from the literature.
The volumetric heat capacity (Jmol -1 K -1 ) for STO is calculated using the above formula mentioned in the literature 47,48 , where the values of a, b, c, and d, are 134.581 Jmol -1 K -1 , 0.0045567 Jmol -1 K - 2 , 11.979e 5 Jmol -1 K, and -414 Jmol -1 K -1/2 respectively. Using a molecular weight of 189.49 gmol - 1 and a density of 4.81 gcm -3 for strontium titanate, the volumetric heat capacity is obtained to be 2.77 MJm -3 K -1 . Experimentally, the volumetric heat capacity of STO was determined to be around 2.78 MJm -3 K -1 49 .
A. Thermal conductivity analysis In Figs. 6 a,b,c,d, the slope of the phase lag plot and its best fit curve in the mid to high-frequency range changes from a trough to a slight crest as the sample thickness decreases (indicated in Fig. The measurement is found to be sensitive to cross-plane thermal conductivity (TC), with the extent of sensitivity remaining relatively constant in all the cases. This is an indication that the values of cross-plane conductivity obtained by the curve fitting analysis will be accurate. We also observe that the solution is relatively insensitive to the thermal boundary conductance (TBC) G1 and G2 in all the cases. Therefore, we assign a high value to G1 and G2 equal to 1000 MWm -2 K -1 and consider them to be fixed input parameters with a known value, for our analysis. This clears up the fact that there is little to no resistance to heat flow across these thermal boundaries and the effective resistance to the heat flow comes predominantly from the material's thermal conductivity.
In this analysis we also consider the anisotropy ( ∥ ⊥ ⁄ ) as 1, implying that the materials are isotropic. Under this imposed isotropic condition, the analysis software outputs the thermal conductivity value (either the cross-plane or in-plane) based on the measurement's sensitivity to the specific parameter. In our case, the system is sensitive to the cross-plane thermal conductivity of the STO thin films and is insensitive to the in-plane thermal conductivity. Hence, by keeping the anisotropy to be 1 (essentially not decoupling) the cross and the in-plane thermal conductivities), we reduce another fitting parameter, aiding us in the fitting analysis.
This leaves us with only 2 unknown parameters, namely, STO cross-plane thermal conductivity and laser spot size. The reason we fit the spot size along with the thermal conductivity for our analysis is because the main source of experimental uncertainty comes from the estimation of spot size 50,51 .
This spot size can be determined in two ways, by using a knife edge method with a x-y piezo stage and by using Gaussian beam optics with a stationary sample stage. The knife edge method is an expensive method of determining spot size, as it requires a specially prepared knife-edge sample, a piezo stage and additional photodetectors, attached to the stage 52 . One can reduce the expense of spot size measurement, with a stationary stage, which would be less accurate. In this method, the pump laser spot is scanned over the probe layer spot, generating a Gaussian spot intensity profile, which is fitted to a calculated Gaussian spot intensity profile. This is done in both x and y directions. The curve fit analysis of these intensity plots provides us with a reasonable estimation of the spot size, at the cost of increased uncertainty.
Hence, for our analysis, a 2-parameter was essential to perform thermal conductivity measurements accurately. Thin films can generally show anisotropic nature due to their very small
thickness, but when we analyze the sensitivity plots, we see that there is no sensitivity to the inplane thermal conductivity property in any of the samples. This is because the substrate in use is Si (Cp = 1.64 MJm -3 K -1 , used in the fitting of STO measurements), which has a very high thermal conductivity value of ~145 Wm -1 K -1 (also used in the fitting analysis). This leads to quick dissipation of the heat into the Si substrate, diminishing the spreading of the heat in the radial direction, leading to insensitivity to the in-plane thermal conductivity. We then perform a 2parameter fit for the cross-plane thermal conductivity of STO and laser spot size, to find the best fit solution for the material systems with varying thickness. The values of STO thermal conductivity for different thicknesses are tabulated in Table . 2.
The value of thermal conductivity for STO thin film decreases with the decreasing thickness of the thin film. The reduction in the thermal conductivity across various thicknesses ranges from ~ 38% to 93%, when compared to the value of bulk single crystal of STO, purchased from MTI Corporation 53 . The thermal conductivity of bulk single crystal was also measured in our FDTR system, with a value of 12.5 Wm -1 K -1 . The approach for its analysis was like the one used in the case of thin films. These k values have an uncertainty of 10%, 11%, 11% and 13% respectively, from the thickest to the thinnest film.
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The 38% reduction in thermal conductivity value of 200 nm thin film relative to bulk sample is due to both finite-size effects associated with scattering of phonons at boundaries of the STO sample as well as due to presence of dislocations in the sample. Epitaxial films of STO on Si have dislocations due to the mismatch of not just the in-plane but also out-of-plane lattice constants between STO and Si. Steps on the Si surface associated with the miscut in the wafer are incommensurate in height relative to the lattice constant of STO.
Consequently, even very thin films, such as the 12 nm thick film studied here, have dislocations that give rise to anti-phase boundaries in the STO 54 . At present, the effect of such dislocations on thermal conductivity is not well established. We estimate the distance between dislocations to be ~ 25 nm in our films 55 . The even larger 93% decrease in the thermal conductivity value of the 12 nm thick film relative to the bulk sample, points to reduction in part from finite-size effects, as the density of dislocations due to steps on the Si surface in the 12 nm thick film and the 200 nm thick film are comparable. 7. Therefore, to accurately measure the volumetric heat capacity and to be confident in the value derived from analysis using FDTR, the film needs to be thick enough for it to be sensitive to Cp. The measured Cp values for the thickest film is 3.07 MJm -3 K -1 with an uncertainty of 6%.
The reason why the 3-parameter fit worked in this case is that phase lag sensitivities of cross-plane thermal conductivity and Cp shows us that they traverse a completely different trend, across the range of modulation frequencies of pump laser (2000 Hz -50 MHz), and the fact that there is a sensitivity difference between the two parameters at the lowest frequency.
Conclusions: The thermal conductivity values were measured to be 7.4, 3.86, 2.35 and 0.8 W m -1 K -1 for the 200 nm, 80 nm, 50 nm and 12 nm, respectively. The k value for the bulk STO sample was measured to be at 12.5 Wm -1 K -1 . A significant reduction of 93% in the thermal conductivity value was observed
This is the author9s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1116/6.0003320