*3.1. Film Structure and Morphology*

It is evident from the diffractograms shown in Figure 1a that the as deposited films are completely amorphous. In contrast the heat-treated films consist only of anatase phase (Figure 1b). The different ratio between the <101> and <004> peaks in the two samples (<004> is here referred to as the <001> direction using conventional Miller indexing) suggests that they are textured and have different preferential orientation. To gain further insight, the diffractograms were Rietveld refined [30] using the PowderCell package [31] and compared with anatase crystallographic files [32]. The preferential orientation was approximated with the March-Dollase model [33], as implemented in PowderCell. This model is appropriate for films sputtered under rotation because it implies a cylindrical texturing symmetry. Rietveld refinement showed that the films consisted of polycrystalline anatase grains with mean crystallite size of 24.2 nm at *P*O2 = 0.65 mTorr, and 22.1 nm at *P*O2 = 1.3 mTorr. The <004> March-Dollase (MD) parameter was found to be 0.966 in the former case (*R*p = 5.9, *R*exp = 3.49) and 0.637 in the latter (*R*p = 5.7, *R*exp = 2.94). Using the Zolotoyabko equation [34], the MD parameters were converted into percentages of preferred orientation, viz.

$$
\eta\_{\{\mu\nu\}} = \frac{\left(1 - r\_{\{\mu\nu\}}\right)^3}{\left(1 - r\_{\{\mu\nu\}}\right)^3} \cdot 100\% \text{ @} \tag{1}
$$

where Ș<*hkl*> is the degree of preferential orientation in the <*hkl*> direction in % and *r*<*hkl*> is the MD parameter calculated for this direction. The results from this analysis showed 2% preferential <001> orientation for the film sputtered at *P*O2 = 0.65 mTorr, while 25% preferential orientation was found for the film sputtered *P*O2 =1.3 mTorr. The 2% oriented film thus corresponds to almost randomly oriented grains, yielding a stronger <101> peak, due to the high relative abundance of these crystal planes in the equilibrium anatase structure. Since the measurements were done at a grazing angle of 0.5° only the topmost 165 nm of the films are penetrated (and the information depth is even less). Thus, we can safely assume that the structure of the surface structure is consistent with the results from the GIXRD measurements. Considering a mean crystallite size of approximately 20 nm this implies that only a thin layer corresponding to 8 "particle layers" are probed. Below we refer to the sample sputtered at *P*O2 = 0.65 mTorr to the <101> sample, and the one sputtered at *P*O2 =1.3 mTorr to the <001> sample.

Qualitative comparison of the Ti KĮ and O KĮ peaks ratio from EDX showed that the heat treated samples have the same stoichiometry. For each partial O2 pressure the ratio between the Ti and O peak was approximately constant at 0.65, confirming that the calcination in air oxidizes the substoichiometric films to an equilibrium structure (Table 1). Corresponding data for as-deposited films showed varying results due to bleaching (indicating gradual re-oxidation) of the films in the course of EDX analysis.

The SEM images shown in Figure 2 show that the films are composed of densely packed spherically shaped particles. No significant difference was observed between the two sets of films prepared at different O2 pressures. Cross section images were obtained at 30° tilting angle and showed a dense film structure with no evidence of columnar growth.

**Figure 1.** XRD diffractograms of post-annealed (**a**) non-oriented and (**b**) <001> oriented films (the intensity ordinates for the two samples are shifted and given in arbitrary units). Photographs of the corresponding as-deposited films are shown on as insets on the right.

**Figure 2.** Scanning electron microscope micrographs showing top-view and cross sections (taken at 30° angle of incidence) of the post-annealed films sputtered at (**a**,**c**) *P*O2 = 0.65 mTorr, and (**b**,**d**) *P*O2 = 1.3 mTorr.

It is apparent from the AFM images (Figure 3) that the surface morphology appears similar to the results from SEM. The raw data was treated to correct for *Z*-scanner error in the *Y* direction and exported as numerical values for statistical treatment in the *R* environment [35] using homemade scripts. Two surface morphology parameters were calculated: the root mean square (rms) surface roughness, *Rq*, and the average surface roughness wavelength, Ȝ*q*, where the latter is defined as

$$
\lambda\_q = 2\pi \frac{R\_q}{\Delta\_q} \tag{2}
$$

where ǻ*q* is the rms surface slope, defined as

$$
\Delta\_q = \sqrt{\frac{1}{N-1} \sum\_{N-1} \left(\frac{\Delta Z}{\Delta x}\right)^2} \tag{3}
$$

where ǻ*Z* is the change in height for every tip movement; ǻ*x*, in the *x* direction. The data for both *Rq*, ǻ*<sup>q</sup>* and Ȝ*q* were averaged for each of the 256 scan lines, then over the trace and retrace images, and then for three different measurements at random positions over the sample surface. Typical images for both films are shown in Figure 3. The rms surface roughness was estimated to be *Rq* = 1.31 ± 0.04 nm and 1.41 ± 0.04 nm, respectively, for the films sputtered at *P*O2 = 0.65 and 1.3 mTorr. The ǻ*q* values were determined to be ǻ*<sup>q</sup>* = 0.105 ± 0.003 nm and 0.123 ± 0.004 nm, respectively, which yielded an average surface wavelength of Ȝ*<sup>q</sup>* = 77.9 ± 4.03 and 73.9 ± 3.72 for films prepared at *P*O2 = 0.65 and 1.3 mTorr, respectively. Based on these results we can conclude that the films are smooth and are similar for the two sets of films, with slightly larger surface roughness and surface roughness wavelength for the preferentially <001> oriented films (within 8%). The physical properties of the anatase TiO2 thin films are compiled in Table 1.

**Table 1.** Thin film deposition parameters and their effect on the physical properties of three samples deposited at similar conditions, but at different partial O2 pressure, *P*O2.

