Experimental Control and Statistical Analysis of Thermal Conductivity in ZnO–Benzene Multilayer Thin Films

We have fabricated a model system of precisely layer-engineered inorganic–organic thin-film structures using atomic/molecular-layer deposition (ALD/MLD). The samples consist of nanoscale polycrystalline ZnO layers and intervening benzene layers, covering a broad range of layer sequences. The samples characterized in this study combined with previous publications provide an excellent sample set to examine thermal transport properties in inorganic–organic thin films. The cross-plane thermal conductivity is found to depend on multiple factors, with the inorganic–organic interface density being the dominating factor. Our work highlights the remarkable capability of interface engineering in suppressing the thermal conductivity of hybrid inorganic–organic materials, e.g., for thermoelectric applications.

The sandwich samples and the double benzene barrier do not fit into the [(DEZ-H2O)m+q + (DEZ-HQ)]n + (DEZ-H2O)p scheme and instead they have their cycle sequence explicitly written out. E.g. SW SL5(1) 200 nm has the recipe 300 x (DEZ+H2O) -> 5 x [100 x (DEZ+H2O) + 1 x (DEZ +HQ)] -> 400 x (DEZ +H2O). This indicates that first 300 cycles with diethylzinc and water were deposited (300 x (DEZ+H2O)), followed by a superlattice sequence starting with 100 cycles DEZ and water and 1 cycle with diethylzinc and hydroquinone, which was repeated 5 times (5 x [100 x (DEZ+H2O) + 1 x (DEZ +HQ)]) and finally 400 cycles of DEZ and water were deposited (400 x (DEZ +H2O)) The table contains only samples that were made during this study and doesn't include samples from previously published articles. Estimating the phonon mean free path in ZnO thin films:

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The thermal conductivity due to phonons can be expressed in first approximation from kinetic theory as ℎ = . CV being the heat capacity, ν the average phonon velocity (approx. speed of sound) and lmfp the mean free path 1 (page 122) . We approximate κ = κPhon in ZnO and with values for κPhon = 50 W m -1 K -1 , this value is estimated on the basis of Alvarez-Quintana et al. 2 who report 43 W m -1 K -1 for a 40 nm thick film and 56 W m -1 K -1 for a 180 nm thick film at 300K, the latter value is obtained by using the program plotreader 3 on their figure 4. The values of CV = 2900 kj/m³K and are taken from Wu et al. 4 . For we use 3700 m s -1 this has a great uncertainty as the speed of sound varies greatly depending on the crystal orientation it can be between 2760 -6090 m/s, however choosing a value at the lower end of this spectrum seems wise considering we don't have a single crystal. We get This is a very simple calculation, that tends to underestimate the lmfp, especially by approximating the phonon velocity ν to the speed of sound. However it can be expected that the correct lmfp is within an order of magnitude of the value estimated here. 5-7

Thermal conductivity values of all reported samples in the ZnO/benzene system
In this study SL48(1) 100 and SL96(1) 100 were not used because those samples are amorphous (the spacing between the ZnO blocks is too small) and GM12(1) Fib 100 was also excluded because the ALD ZnO cycle sequence follows the Fibonacci sequence and the first few barrier layers are seperated by 1,1,2,3,5.. ALD cycles which is not enough to treat them seperately (as already discussed in 8 where this sample was first reported). We still list them in the table for the sake of completeness as there no other table to list the complete set. SL5(1) 100 is an outlier (see multivariate analysis in the main text) and was not included in Figure 3 in the main text. We believe that SL5(b) 100 is the more representative sample of the two.  ** SL5(1) 100 is used in the Simca analysis but not in Figure 3, SL5(1)b 100 is considered the more representative sample.
An excel sheet with all variables used for the multivariate analysis can be obtained from the authors upon request.

Time domain thermoreflectance: modulation frequency and sensitivity
The measurement length scale of the TDTR technique is defined by the thermal penetration depth (TPD). Traditionally, thermal penetration depth is defined by the following equation: TPD = (Eq. S1) Here, k, C and f are thermal conductivity, volumetric heat capacity, and modulation frequency of the pump beam during TDTR measurements, respectively. However, thermal penetration depth calculated using this equation does not take into account the effects of the metal film transducer, the resulting thermal boundary conductance, the pump and probe spot size, and any finite thicknesses of films in multi-layer material systems. A more accurate representation of the thermal penetration depth can be obtained by solving the cylindrical heat diffusion equation, details of which were provided by Braun and Hopkins. 11 Though Eq. S1 does not provide an accurate value of the thermal penetration depth for the multilayered material systems, it qualitatively shows how TPD changes with modulation frequency. As the thickness of the films measured in this study range from ca. 50 to 200 nm, a high modulation frequency is desired during TDTR measurements. When the modulation frequency is high, the TPD is low. As a result, the sensitivity to the thin film thermal conductivity is higher compared to the substrate thermal conductivity. On the other hand, when the modulation frequency is low, the TPD is high and sensitivity to the substrate thermal conductivity is higher. This is shown by the sensitivity analysis of SL 12(1) 100 nm corresponding to 8.8 and 1 MHz in Figure S2. As shown in Figure S2, at 8.8 MHz, sensitivity to the thin film thermal conductivity is much larger than the substrate. Thus, using 8.8 MHz during TDTR measurements of the thin films, the influence and corresponding uncertainty propagation from the substrate thermal conductivity is minimized relative to that of lower modulation frequencies. Furthermore, in our current experimental setup, 8.8 MHz provides the best signal to noise ratio. That is why higher modulation frequencies (> 8.8 MHz) were avoided during the TDTR measurements.
In Figure S3, the thermal penetration depths for SL 12(1) 100 nm corresponding to 8.8 and 1 MHz have been provided. These thermal penetration depths have been calculated according to the definition provided by Braun and Hopkins. 11 As shown in Figure S3 (a) and (b), the thermal penetration depths for 8.8 and 1 MHz are 180 and 800 nm, respectively. This further shows that at 8.8 MHz, we are most sensitive to the film thermal conductivity. However, with 1.1 MHz, as TDTR would probe more than 600 nm of the sapphire substrate, TDTR measurements at this frequency would be most sensitive to the substrate thermal conductivity.

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The sensitivity analysis of TDTR measurements for SL 12(1) 100 nm is shown in Figure S4. TDTR measurements are most sensitive to the transducer thickness and the thicknesses of the thin films. In this study, the thickness of the transducer and thin films were determined by picosecond acoustics and X-ray reflectivity, respectively. The uncertainty associated with the transducer and thin film thicknesses were ca. 3 and 5 nm, respectively. Due to the high modulation frequency (8.8 MHz) used during the TDTR measurements, sensitivity to the substrate thermal conductivity is minimal. TDTR measurements are almost insensitive to the