Comparison of the heat-treatment effect on carrier dynamics in TiO2 thin films deposited by different methods

carrier dynamics in TiO2 thin films deposited by different methods Ramsha Khan,∗,†,§ Harri Ali Löytty,‡ Antti Tukiainen,¶ and Nikolai V. Tkachenko∗,†,§ †Photonic Compounds and Nanomaterials Group, Faculty of Engineering and Natural Sciences, Tampere University, P.O. Box 692, 33014 Tampere, Finland ‡Surface Science Group, Faculty of Engineering and Natural Sciences, Tampere University, P.O. Box 692, 33014 Tampere, Finland ¶Faculty of Engineering and Natural Sciences, Tampere University, P.O. Box 692, 33014 Tampere, Finland §A shared footnote

free of the sample is used to solve the problem, but there is no such a reference sample when a film sample is measured. However, one can measure reflectance (spectrum) and use it to account for the reflectance "losses". If the film reflectance is R, then the relative intensity of the monitoring light is reduced by 1 − R, and the relative light intensity after the sample is (1 − R)10 −A , where A is the film "true" absorbance also called optical density. Thus, the sample transmittance is T = (1 − R)10 −A (S1) and the absorbance can be calculated from measured transmittance T and reflectance R spectra as It has to be noted that this is an approximation which does not account for 1. interference of the monitoring light inside the sample due to multiple reflections from both film surfaces, 2. absorption of light reflected from the back side of the film which reduces the total sample reflection.
The first problem starts to play a role when the film thickness approaches quarter of the wavelength. Since we work with 30 nm films we do not expect the interference to have strong impact on the measurements.
The second has vanishing impact in transparent samples, or at wavelengths > 400 nm in the case of TiO 2 , which is the wavelength range of our main interest. And it will result in some overestimation of absorbance otherwise.

Steady state absorption spectra of flat films
The interference and reflection absorption can be accounted for but this requires more complex calculations. A model for accurate calculations of transmittance and reflectance spectra of a semitransparent film deposited on transparent substrate was developed by Barybin and Shapovalov. 1 The sample structure is air film substrate air ← d → n = 1 n = n = n s n = 1 Here the refractive index of the substrate is n s , and the film has complex refractive index n f +ik f with imaginary part, k f responsible for the film absorption; k f is also called extinction coefficient and it is directly proportional to the absorption coefficient α = 4πk λ . The substrate is assumed to be thick enough so that the interference inside the substrate can be ignored.
The transmittance and reflectance spectra, T (λ) and R(λ), can be calculated using eq. (43) in, 1 though the calculations and equations are bulky and we do not provide them here. The parameters needed for calculations are the film thickness, d, and spectra n f (λ), k f (λ) and n s (λ). We used single-term Sellmeier equation 2 to model refractive indexes of TiO 2 and quartz substrate where A and B are the constants specific to material and documented for a large variety of semiconductor and dielectric materials. 2 We have used A = 1190 and B = 0.2182 for TiO 2 anatase (wavelength in measured in nm) and amorphous TiO 2 was modelled by TiO 2 polyxtal with A = 8400 and B = 0.207. 2 The initial values for the substrate where take as fused silica but were adjusted to fit measured absorption spectra of our substrates and were A = 6276.61 and B = 0.91851. This model is complemented by a factor accounting for possible sample porosity, namely the refractive index of the film is presented as 3 where n is the refractive index of the bulk material, e.g. TiO 2 anatase, and the parameter p is in the range 0 < p ≤ 1 where p = 1 corresponds to the layer without voids, and smaller p means larger effective volume of voids. Within this approximation the voids are assumed to be much smaller than the wavelength and homogeneously distributed through the film.
In order for the model to work well in the blue and near UV parts of the spectrum, one need to account for the sample absorption, k f (λ). This is especially important for as grown sample when the crystal structures is not well formed and the film has detectable absorption due to high degree of disorder and large number defects and trap states. To account for the rising sample absorption at wavelengths approaching the band gap the absorption extinction coefficient k f was modelled by a step-like function having zero value at long wavelengths and approaching k 0 at short wavelengths where λ 0 is the wavelength at the middle of transition from 0 to k 0 and λ is the transition width (in the wavelength domain). Since the wavelength rage of our interest is above the wavelength corresponding the band gap, this equation will be used at λ > λ 0 , meaning that we will observe only the long wavelength tail of the function.

Transient absorption (TA) measurements in transmittance
and reflectance modes -estimation of the photoinduced absorbance change The TA measurement were carried out in two modes, transmittance and reflectance, by measuring either transmitted part of the probe pulse of reflected part of the probe, but using a standard pump-probe instrument and in otherwise identical conditions, i.e. the same spot on the sample and the same excitation density and wavelength. In both cases the probe light intensity is measured and the saved signal is − log I I , where I is the light intensity without excitation and I is the difference in light intensities with and without excitation at a particular delay time. The transmittance mode is a standard method of TA pump-probe experiments, and the measured signals will be denoted as A T . The results of reflectance mode TA measurements will be denoted as A R .
Here we will consider a transient absorption responses of a thin film deposited on an optically thick substrate. The responses are affected by both absorption change and refractive index change and our aim is to estimate a "pure" absorbance change form two types of TA measurements, a traditional transmittance and complementary reflectance TA measurements carried out in identical conditions as described above. The studied samples are thin (close to 30 nm) relative to the monitoring wavelength, therefore we will neglect by the probe light interference in the samples due to multiple reflectance from the film interfaces, and use approximation provided by eq. (S1). This approximation can be further extended to the transient absorption case. Photo-excitation result in a change of all three values, T , R and We are interested in A, Experimentally measured values are A T and A R therefore eq. (S7) can to be rearranged to Within this approximation the absorbance change can be estimated from the measured reflectance spectrum of the sample, R, and TA measurements carried out in transmittance, A T , and reflectance, A R , modes. Before applying eq. (S11) to calculate A, the measured A T (λ, t) and A R (λ, t) arrays were converted to dispersion compensated data with common delay time base.

Distributed decay model
The relaxation dynamics of thin semiconductor films is often non-exponential even when the relaxation mechanism is simple and a "single step". We have used stretched exponential decay function 4 f s (t) = exp − t τ β to fit the TA decays but in many cases the stretch- order of magnitude larger than the film thickness, while the apparent crystallite size derived from the XRD data was smaller than the film thickness.

Steady state spectra
The measured steady state transmittance and reflectance spectra of all samples are presented in Figure S3.
All the reflectance spectra have notable feature at roughly 850 nm. The origin of the feature is non-ideal reflectance of the reference mirror used to run base line of the spectrophotometer. To correct it, we used a clean quartz substrate (1 mm fused silica), recorded both transmittance, T and reflectance R spectra, and calculated "true" quartz reflectance spectrum as R = 1 − T , as presented in Figure S4. Comparison of R and R allows to calculate  Figure S4: Measured transmittance T and reflectance R spectra of quartz substrate. R = 1 − T is the reflectance spectrum calculated from T assuming that quartz does not absorb any light in the wavelength range of measurements. Comparison of R and R reveals the reference mirror reflectance spectrum marked as "mirror R".
The corrected reflectance spectra and measured transmittance spectra were used to calculate absorbance spectra shown in Fig. 1 of the main text using eq. (S2). The Tauc plot presentations of the same spectra in the photon energy range around the band gap are shown in Figure S5. These plots were used to estimate optical band gaps. (c) SPD thin films Figure S5: Tauc plots of TiO 2 thin films prepared by ALD, IBS and SPD, and slope linear approximations used to estimate optical band gaps.

Steady state absorption spectra modelling
The model given in Eq. S4 and Eq. S5 is applied to fit the measured absorbance spectra of the sample. The fitting parameters to model the measured absorbance spectra are p, the film thickness, d, and λ 0 , λ and k 0 . The results of the fit for all samples are presented in Table S1 and summarized in the main text in Table 2. The fit parameter λ if relatively large for as-deposited ALD and SPD samples and it points out at remaining shallow absorption of the samples extended from the band gap region to the visible wavelength range. However, this is reasonable for amorphous TiO 2 which may be strongly contaminated by the precursor compounds and their decomposition products.
The model gives very good approximation of the measured spectrum for ALD HT sample with standard deviation of only 0.0015, and fit parameters come close to the expected values.
Namely, the film thickness is 32.2 nm (intended thickness is 30 nm) and porosity factor p = 0.97, or virtually void free film. The sample absorption has an effect only at λ < 360 nm which agrees well with TiO 2 anatase band gap. Absorption spectrum of as-deposited sample is clearly different from the HT one. One obvious reason for the difference is the film crystallinity, the as-deposited can by identified as amorphous and thus having different refractive index spectrum. The polyxtal TiO 2 n model 2 had to be complemented with porosity factor and absorption "tail" (eq. (S5)) to obtain a reasonable absorption spectrum approximation. However, the result has a straightforward explanation: the low temperature ALD deposition does not result in formation of crystalline TiO 2 structure and has oxygen deficiencies with presence of precursor residuals, which leads to a tailing absorption in the visible part of the spectrum ( λ = 97 nm) and also voids in the film (p = 0.66). The HT fixes both of these problems.
The absorption spectra of IBS and SPD samples were analysed in a manner similar to that described above for ALD samples. The resulting spectra, modelled A calc and k are presented in Figs. S6 and S7, respectively. The IBS method results also in an amorphous film but it is much closer to TiO 2 than ALD, and the absorption spectra of as-deposited and HT samples are rather similar to each other (see Fig. S3). The most difficult for modelling turned out to be SPD samples (see Fig. S7). The large scale AFM imaging has shown that the problem is the film thickness homogeneity -the film looks as large number of overlapping disks with few tens on microns in diameter. However, at a qualitative level the difference between as-deposited and HT SPD samples is similar to that of ALD samples: HT removes tailing absorption in the visible and reduces film porosity.  Figure S7: Measured A meas and calculated A calc absorption spectra of HT and as-deposited SPD samples, together with modelled absorption extinction coefficients k (imaginary part of refractive index.)

Transient absorption measurements and interpretation
The primary measured data in transmittance, A T (λ, t), and reflectance modes, A R (λ, t) were first recalculated to transient absorption (TA) response, A(λ, t) using eq. (4). This TA data presents "true" absorption change and can be analysed using standard methods such as global (or multi-wavelength) data fitting. The aim of the global fitting is to obtain decay associated spectra (DAS) which can be used to calculate the species associated spectra (SAS), which in turn can be used to identify intermediate states. However, the practical implementation requires a mathematical model describing transition from one to another state. In the case of homogeneous system with thermally activated transitions the state populations follow (multi)exponential low, but the films are polycrystalline and composed of crystalline domains of different size, or they are intrinsically inhomogeneous. As the result, the (multi)exponential fitting may result in erroneous results. An empirical alternative is to use the so-called stretched-exponential instead, which often gives better results. 4 Yet another alternative we have tested is distributed decay model as described in Section 2.
Different combination were tests to find the minimum number of component with the lowest sigma value (average standard deviation between the data and fit). As an example, the fit model justification will be outlined for ALD as-deposited sample in the following section.
It was found that all HT samples can be fitted using a fast (< 1 ps) exponential term, a exponential term with a few tens of ps time constant, and a long-lived distributed decay term. The ALD as-deposited sample required only distributed decay term, and two other as-deposited samples required a picosecond exponential and a longer-lived distributed decay terms.

TA measurements, A calculations and fits
ALD as-deposited sample. Dispersion compensated raw measured TA data in transmittance, A T (λ, t), and reflected modes, A R (λ, t), are presented in Figs. S8a and S8b, respectively. The absorbance data, A(λ, t), were calculated using eq. (S11) and the result is presented in Figs. S8c. This data were fitted using different decay models as presented in Table S2. There was a statistically significant increase in fit goodness (decrease in σ value) when switching from mono-exponential fit to bi-exponential fit, and only a minor improvement on switching to three exponential fit. However, the DAS spectra of all the components were virtually the same. A single component stretch-exponential fit gives virtually the same fit goodness as bi-exponential fit. This means that this data allow us to identify only one spectral component. The distributed decay model gives a minor, statistically insignificant σ value improvement, but since we observe somewhat better fit goodness with distributed decay for all samples the it is reported for all the samples. In conclusion, the TA data for ALD as-deposited sample can be finely fitted by a single distributed decay component with center time constant of 0.93 ± 0.03 ps, and the resulting decay associate spectrum (DAS) is shown in Fig. S8d.
IBS as-deposited sample. The raw TA measured data (after group velocity compensation), A T and A R , calculated A, and A fits are presented in Fig. S9. To obtain a Table S2: Comparison of the fit results using different fit models for ALD as-deposited sample. Fit parameters are the time constant, τ , and stretched parameter, β, and the relative distribution width, b (eq.(S12)). SPD as-deposited sample. The raw TA measured data (after group velocity compensation), A T and A R , calculated A, and A fits are presented in Fig. S9. To obtain a reasonably good fit a sum of exponential and distributed decays had to be used. The time constant of exponential component is 1.6 ps which is much sorter than the central time constant of the distributed decay, 50 ps, but the shapes of the components are only marginally different.

Lifetime of thicker samples
Thicker films of 200 nm were prepared by ion beam sputtering to study the effect of TiO 2 film thickness on the lifetime of different charge carrier components. The decay spectra of these samples were also fitted by two exponential and one distributed decay component.
It was seen that increasing thickness of TiO 2 layer does not play any significant role in increasing the lifetime of photogenerated charge carriers and hence thicker films of TiO 2 will not provide any benefit to photocatalytic applications.

Methylene blue degradation
The excitation spectrum (300-400 nm) has only minor overlap with the methylene blue absorption spectrum as shown in Figure S13, and therefore, the filter effect in the test was small.