Supplementary Material for Structure-Thermal Property Correlation of Aligned Silicon Dioxide Nanorod Arrays S. Dynamic shadowing growth (DSG) technique Figure S depicts a schematic of the DSG setup. For this study, a customized electron beam evaporator was used to deposit SiO2 NR arrays with the DSG approach at various deposition angles, defined as the angle between the incident vapor flux and the normal of the substrate (d in Fig. S). The base pressure was 0 4 Pa, and the deposition rate was 0.4 nm s for DSG of aligned SiO2 NR arrays and 0.3 nm s for the base layer and the capping layer. The fabrication employed a bottom-to-top approach: first, a dense base layer was deposited at a deposition angle of 0 (d = 0) with a thickness of 40 nm. Second, the SiO2 NR arrays were deposited at d = 84to form slanted NR arrays. To obtain vertical NR arrays, the substrate was rotated at 2 rpm during deposition. Third, a capping layer of 250 nm SiO2 was deposited at sequentially decreased d of 84, 70, 60, 50, 35, 20 and 0. No substrate rotation was applied during the growth of the capping layer. The fabrication procedures of capping layers are similar to those of the SiO2 NR arrays with DSG, only with different deposition conditions. The structures of the capping layers can be considered as much denser SiO2 NR arrays with porosities ranging from 0% to 20%. A smooth and continuous capping layer is required for two purposes: () for thermal characterization with TDTR, such a smooth and continuous capping layer is crucial for obtaining a uniform layer
of a metal transducer and (2) for fabrication of microbolometer devices, the capping layer serves as a base for the deposition of functional layers such as metal electrode stripes and the IR absorbent layers. Thus, a smooth and continuous capping layer is of vital importance to ensure electrical performance of the device as well as promote the growth of a high quality IR absorbent layer. FIG. S. Schematic of the dynamic shadowing growth. The sample substrate can be tilted (deposition angle of d) to induce the geometric shadowing effect. The random nucleation centers act as shadowing seeds that result in a preferable growth of the nucleation centers towards the incident vapor, ultimately forming an array of slanted NR structures. The sample substrate is rotated for vertically aligned NR arrays, and is kept still for growing slanted NR arrays. S2. Sample structure characterization The surface morphologies of SiO2 NR arrays were characterized with atomic force microscopy (AFM). Atomic force microscopy measurements were conducted with Veeco Dimension 300 in the tapping mode. The typical scanning area was 5 μm 5 μm at a 2
scanning voltage of.2 V. A first-order flattening was applied during AFM image analysis using Bruker NanoScope Analysis.40. The representative AFM characterizations of Samples - 3 on the surface morphology are depicted in Fig. S2. It is demonstrated that the film density of the layered SiO2 NR arrays can be easily controlled with sufficiently smooth surfaces for ellipsometry and thermal characterization. The root-mean-square surface roughness (rms) ranges from 6 to 30 nm for all five samples. (A) (B) (C) FIG. S2. Atomic force microscopy images of the top surface of SiO2 NR arrays: (A) Sample -capping layer, (B) Sample 2-slanted, and (C) Sample 3-vertical. The height variation from black-to-white is 5 nm for (A), and 25 nm for (B) and (C). Scale bars are μm for all three AFM images. Sample porosity was characterized by collecting the ellipsometry spectra (J.A. Woollam M2000DI ellipsometer) in the wavelength range of 9-670 nm at incident angles from 60 to 70 with a step of 5. WVASE3.2 software was used to fit the data. A Bruggemann effective medium approximation (EMA) based on a Cauchy dummy layer was employed to extract the porosities of the SiO2 NR arrays and the capping layer. Up to thirty iterations of normal fitting were conducted until the mean square error (MSE) fully converged with no observable changes between two sequential iterations. Figure S3 illustrates the parametric fitting of ellipsometry data measured for Samples - 3 to extract the 3
volumetric fraction of pure SiO2 NRs without the capping layer, x (or, equivalently porosity, x). (degree) (degree) (degree) 80 60 40 20 0 80 60 200 600 000 400 40 20 0 80 60 200 600 000 400 40 20 (A) (B) (C) Expt.60 Expt.65 Expt.70 0 200 600 000 400 700 Wavelength (nm) FIG. S3. Representative ellipsometry measurement data (symbols) of (A) Sample -capping layer, (B) Sample 2-slanted without the capping layer, and (C) Sample 3-vertical without the capping layer. The best fittings from the graded model are presented in (solid lines. The fitted xnr are listed in Table II. S3. Analysis on the anisotropic effect of SiO2 NR arrays Due to the inhomogeneity nature of the geometrical structure, the NR arrays are expected to exhibit anisotropic thermal transport along the through-plane and in-plane directions. In this part, we will discuss how much the anisotropic structure would affect the effective through-plane thermal conductivity measured by TDTR. 4
As discussed in this work, the thermal channels along NRs are in parallel with the through-plane direction for the vertical alignment. While for the tilting alignment, heat flux sees a series of NR-air-NR-air structural arrangement as it propagates downwards. For the latter case, the NR-air interfacial thermal resistance could possibly reduce the effective through-plane thermal conductivity of the slanted NR arrays compared with the vertical ones. To set up boundaries, we quantitatively compare the interface contributions in serial and parallel structures to the effective through-plane thermal conductivity of the NR array (Fig. S4). Both structures have the same dimensions (L is the thickness and S is the area) and volumetric fractions of SiO2 NRs (x). The total thermal resistance of the serial (Rs) and parallel (Rp) structures can be expressed as: R s xl ( x) L L ng 2 s-eff, (S) R p L L x ( x) 2 L p-eff, (S2) where and 2 are the thermal conductivities of SiO2 and air, respectively; s-eff and p-eff are the effective thermal conductivities of the serial and parallel structures; n is the number of the NR-air interfaces inside the structures; and G is the thermal resistance of the NR-air interface. Rearrangement of Equations (S) and (S2) gives: s-eff x x ngl 2, (S3) x ( x). (S4) p-eff 2 5
The value x for SiO2 NR arrays in this work ranges from 0.33 to 0.47 as listed in Table II. Considering the much lower thermal conductivity of air compared with SiO2 (2), Equations (S3) and (S4) can be simplified as: s-eff 2, (S5) x 2 ngl p-eff x. (S6) Based on Equations (S5) and (S6), it is apparent that the effective thermal conductivity of the serial structure is lower than that of the parallel structure, due to both the much lower thermal conductivity of air and the influence from the interfacial thermal resistance at the NR-air interfaces. The slanted NR arrays studied in this work falls in the intermediate range between these two types; thus, the values calculated based on Equations (S5) and (S6) essentially set up the lower and upper limits of the effective through-plane thermal conductivity of the NR array. Heat flux SiO 2 Air L S (A) Serial S (B) Parallel FIG. S4. Schematic of (A) serial and (B) parallel structures for evaluating the lower ( serial ) and upper ( parallel ) limits of the effective through-plane thermal conductivity. The red arrows indicate the directions of heat flux deposited by the laser. 6
To discuss the anisotropic effect in our measurements, we simulate TDTR signals using the 2D thermal model. As shown in Fig. S5, the ratio signals of Vin/Vout on Sample 2 (Slanted ) are plotted as a representative example. The parameters used in the simulation are all the same except for the in-plane thermal conductivity of the SiO2 NR array, which is purely determined by air (0.025 W m K, red solid lines) or SiO2 (.3 W m K, blue dashed lines). These two values are selected as the upper and lower limits of the possible in-plane thermal conductivity of SiO2 NR array. From Fig. S5, there are no observable differences in the simulated TDTR signals calculated with the lower and upper limits of the in-plane thermal conductivities. This suggests the anisotropic structures of our SiO2 NR arrays samples do not affect the effective through-plane thermal properties obtained from TDTR measurements. Model predicted -Vin / Vout 3 2 0.5 0.3 8 MHz 9 MHz.6 MHz 00 000 Time delay (ps) FIG. S5. Comparison of the predicted Vin/Vout signals simulated by the 2D thermal model on Sample 2 (Slanted ). The parameters used in the simulations are all the same except for the in-plane thermal conductivity of the SiO2 NR array. The effective in-plane thermal conductivity is set to be 0.025 W m K for the red solid lines and.3 W m K for the blue dashed lines, respectively. These two values correspond to the lower and upper limits of the possible in-plane thermal conductivity of the SiO2 NR array. 7
S4. Uncertainty analysis of the TDTR measurements on SiO2 NR arrays The uncertainties of TDTR measurements come from the individual error sources of all parameters used in the thermal model, including the thermal conductivity and heat capacity of the Al transducer, the film thicknesses of Al and SiO2 NR array. The thermal conductivity of the Al transducer was derived from its electrical conductivity measured with the four-point probe technique together with the Wiedemann-Franz Law. The heat capacity of the Al transducer was taken from literature. The Al thickness was measured from picosecond acoustics. 2 The NR array layer thickness was characterized by ellipsometry. The overall uncertainty was estimated with a sensitivity-analysis method previously described. 3 With 5% uncertainties for the thermal conductivity, heat capacity, and thickness of the Al transducer, and a 2% uncertainty for the thickness of NR arrays, the overall uncertainty of the through-plane thermal conductivity is ~0% for the capping layer, and ~30% for the rest of four samples consisting of NR arrays. References: D. A. Ditmars, C. A. Plint, and R. C. Shukla, Int. J. Thermophys. 6 (5), 499 (985). 2 C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34 (6), 429 (986). 3 Y. K. Koh, S. L. Singer, W. Kim, J. M. O. Zide, H. Lu, D. G. Cahill, A. Majumdar, and A. C. Gossard, J. Appl. Phys. 05 (5), 054303 (2009). 8