Surface Topography of Si/TiO₂ Stacked Layers on Silicon Substrate Deposited by KrF Excimer Laser Ablation

Abstract

This study investigates the surface topography of the deposited thin films versus the distance between target and substrate (d_TS) inside a laser ablation equipment. The profile of the rough surface was obtained by atomic force microscopy data analysis based on power spectral density and the roughness-length scale (RLS) functions. The roughing on the top film is analyzed considering the previous topography of the underneath surface for each consecutive TiO₂ and Si deposition onto Si (100) wafer. The buried oxide layer inside of Si/TiO₂/c-Si structure, obtained by KrF excimer laser ablation was characterized by complementary techniques as spectral ellipsometry, X-ray reflectometry, and X-ray diffraction.

1. Introduction

The ever-increasing demand for very small devices has led to an important growth of the microelectronics market and, subsequently, research interest. In the last years, the interest for buried oxides layers increased exponentially due to this market demand for devices such as 7 nm field effect transistor (FET) technology available now. There are several types of technologies associated to buried oxide layer (BOX) structures which are currently used in the microelectronics industry, that make the integration easier by offering the sharp barrier of the silicon/insulator and by yielding much smaller parasitic capacitance than their bulk counterparts, since the dielectric constants of the oxides are lower than that of silicon [1].

BOX technology innovation was one of the main improvements for low power electronics. The preliminary improvements regarding the fabrication of silicon on insulator like: zone melting re-crystallization of silicon deposited layer on insulator [2] and hetero-epitaxial technique as silicon on sapphire [3] paved the way to the more efficient technologies. The built of an embedded oxide layer by using oxygen ion implantation called Separation by IMplanted Oxygen (SIMOX) [4] and Bond an Etch Silicon on Insulator (BESOI) meaning bond and etch oxidized substrates technology [5] were the main improvements after the 1980s for low power electronic devices. At this stage the Silicon on Insulator (SOI) solution produced standard wafer fabrication with dedicated new equipment [6]. A revolutionary technique proposed by Bruel in 1995 leads to high performance results compared with those obtained by both SIMOX and BESOI. The application of ion implantation in “Smart Cut” technology was extended to protons for the delamination of very thin silicon layer at the top of the Si wafer. The removal of the Si layer happening during wafer bonding [7] is facilitated by the irradiation defects aggregation at the averaged depth in silicon of the stopped protons. The ultimate technology of building BOX layer gives a high uniformity of the Si-SiO₂ stacked layer on the whole wafer surface with low Si crystal defects at a reasonable cost for a large technological flexibility [8].

A different approach in creating the buried oxide layers can be provided by a versatile technique, which is pulsed laser deposition (PLD) [9,10,11,12]. This study focuses on the preparation and characterization of silicon-oxide-silicon structures obtained as stacked thin films deposited on silicon wafer by PLD.

The wide bandgap and high dielectric constant (high-k) oxides, as are Al₂O₃ and TiO₂ have drawn great attention in the electronic, optical devices and chemical sensors industries [13,14,15].

One challenge is to control the flatness of the deposited hyper thin stacked layers comparable with those usually achieved in planar technology processing. This demand is especially required for low scale FET, using high-k gate oxide as TiO₂ [16] needed to avoid gate e-charge leakage due to quantum tunneling [17].

The integration of PLD technique in the frame of Complementary Metal–Oxide–Semiconductor (CMOS) technology sustains the development of integrated biosensors based on TiO₂ used as electric charge transport media between source and drain in FET transistors, built on insulator [18]. Furthermore, buried oxide layer has the advantage of building double gate FET sensors of interest in biology [19]. Thus, PLD based deposition of TiO₂ layer, instead SiO₂ usually growth by silicon oxidation in CMOS technology, improves the development of new integrated sensors for photo-chemical and biodetection.

In this work we report the successful deposition of TiO₂ thin films with brookite signature by PLD on a n-Si (100) wafer, which was annealed at 600 °C in ultra-high vacuum (UHV) and heated during deposition at 500 °C. The TiO₂ thin film deposited on c-Si substrate was then covered by a Si layer using the same PLD technique to obtain a buried oxide layer.

Atomic Force Microscopy (AFM) and light scattering techniques used for surface topography characterization became, by using power spectral density (PSD), very powerful methods that fit nanotechnology requirements. PSD function describes in a statistical manner the existing hills and valleys on the sample’s surface with dimensions ranging from 10⁻⁹ to 10⁻⁵ m. Initially PSD was applied to the investigation of the electric signals and noise. This field of a large accumulation of work was turned successfully from the analysis of signals versus time to the investigation of the rough surface profiles versus space. The improved control on surface layer topography especially for random or regular features at nanometric scale, represents an important requirement for the actual silicon-based nanotechnology [20]. Thus, the development of appropriate methods based on PSD applied to both AFM and light scattering techniques are useful for monitoring of rough surface profile.

2. Materials and Methods

2.1. Pulsed Laser Deposition and Materials

The PLD technique is a versatile research tool that permits the deposition of a broad range of materials [10,11] like complex oxides, high-temperature superconducting coating, polymer, or organic thin films, which can be used in different applications [21,22]. A unique feature of our PLD system is the ability to work at UHV base pressure (8.5 × 10⁻¹¹ Torr) being very useful in controlling unwanted film impurities. Another important feature consists in the laser target manipulator that can accommodate up to four targets of two inches in diameter which are selectable one by one.

There are many parameters which can be tuned for the ablation process, like deposition time, target-substrate distance (d_TS), substrate temperature, laser pulse energy, the repetition rate of the laser pulse, laser spot area, speed of rotation targets, and substrates. The depositions of TiO₂ thin films on n-Si (100) and of Si on TiO₂ were carried out using a KrF excimer laser produced by Coherent-Compex pro 205 F (Coherent Inc., Santa Clara, California, USA) with wavelength (λ_L = 248 nm), using a pulse duration of 20 ns and at 45° incidence angle to the target. The schematic of the ablation is provided in Figure 1.

During laser ablation, the targets were rotated (10 rpm) and, furthermore, the laser spot was slightly scanned so that fresh surface is exposed to the laser beam during the thin film deposition. The resulting ablation zone on the target surface is shown in Figure 1 inset.

The substrates n-Si (100) were positioned parallel to the target surface at distance d_TS. During deposition the substrates were rotated (3 rpm) and heated up 500 °C.

The coupons 10 × 30 mm² cut from 2 inches n-Si wafer (100) substrate purchased from Merck (Merck KGaA, Darmstadt, Germany), were cleaned in Hydrofluoric Acid (HF, Merck KGaA, Darmstadt, Germany) 10% for 10 min to eliminate the native oxide (SiO₂) from the surface, after being ultra-sonicated in acetone and dried under nitrogen flow followed by UHV annealing at 7 × 10⁻⁹ Torr, 600 ℃ for 3 h (SVTA, Eden Prairie, MN, USA). The TiO₂ target 99.99% with 5 mm thickness was purchased from Testbourne Ltd. (Hampshire, UK) and as Si target, we used a wafer, 0.5 mm thick, from Merck (Merck KGaA, Darmstadt, Germany). Both targets were 2 inches in diameter.

2.2. Characterization Techniques and Methods

The morphological properties of TiO₂ and Si films have been studied using a multimode commercial AFM (SOLVER Next—NT-MDT, Spectrum Instruments, Zelenograd, Moscow, Russia). Cone-shaped tips from monocrystalline silicon (tip radius ~10 nm) on cantilevers with a stiffness of about 34 N/m were used to perform the measurements. The AFM measurements were successfully carried out in tapping mode in which height (topography) signal was acquired.

The sample obtained in optimal conditions was analyzed using a Rigaku SmartLab X-ray Diffractometer (XRD) (Tokyo, Japan) with a copper target (λ_X = 0.1540598 nm), tube voltage of 45 kV, at 200 mA, and a K_β filter. The obtained diffractogram was fitted using SmartLab Studio Software from Rigaku (Tokyo, Japan) and compared with existing data from the PDF2 database and scientific articles. The X-ray reflectivity (XRR) measurements on both roughness and thickness of the thin film was performed with the same Rigaku XRD equipment (Tokyo, Japan). The results were obtained using the Integrated Thin Film Analysis Software Global Fit from Rigaku (Tokyo, Japan).

The Woollam M-2000V ellipsometer (J. A. Woollam, Lincoln, Nebraska, USA) was used to evaluate the thickness of the TiO₂ buried layer. Ψ and Δ were acquired over the spectral range 550–1000 nm. Measurements were performed at three different angles (55°, 60°, 65°) and the experimental results were processed using a Cauchy mathematical model. The TiO₂ thin film with the smoothest oxide surface, in respect with the roughness over the full-length scale, was characterized by means of XRD, XRR, and spectrometric ellipsometry.

3. Results and Discussion

Two endeavors generated this contribution: PLD deposition of a buried TiO₂ layer as a part of Si/TiO₂/c-Si structure, and the application on the AFM data of an adequate approach to reveal the influence of d_TS deposition parameter on the topography of the films. The rough surface profile is determined after each consecutive fabrication of TiO₂ and Si film. Finally, the sample obtained at d_TS that gives the smoothest oxide layer was analyzed by means of XRD, XRR, and ellipsometry.

3.1. Deposition of the Stacked Si/TiO₂ Thin Films on (100) Si Wafer

In order to study the characteristics of the Si/TiO₂/n-Si (100) sandwiches structures, the samples were taken out after the TiO₂ deposition, and a Ti foil mask was applied to partially cover the surface before the deposition of the top Si layer [9]. Thus, access to both deposited layers was gained for further investigations.

The values of following deposition parameters were considered: substrate temperature 500 ℃, laser pulse energy 500 mJ and the repetition rate of the laser pulse 30 Hz. The surface topography of the deposited TiO₂ and Si thin films was investigated for several distances between target and substrate as d_TS: 4, 5, and 6 cm.

Before the Si deposition we set up the substrate temperature, then we waited for 3 h for the pressure to reach the lowest value (P_i~10⁻⁹ Torr), this being in fact the annealing of the preexisting TiO₂ layer in UHV.

In all performed depositions the laser spot was 3 mm², substrates rotation was 3 RPM and a deposition time of 600 s for each layer.

3.2. AFM Characterization of TiO₂ and Si Deposited Thin Films on (100) Si Wafer

In this work a special attention was paid to the optimization of the deposited thin films in terms of their surface roughness, which influences their optical and electronic properties.

The Root Mean Square roughness (σ_RMS) and the Roughness Average (σ_a) parameters were calculated from the acquired topographic images via an image processing software [23] being given in

Table 1. The deposition parameters as: substrate temperature, laser power and pulse frequency, pressure before and during films deposition, and the corresponding σ_RMS and σ_a roughness calculated for the 2D topography images recorded for TiO₂ and Si thin films (5 × 5 µm²).

Deposition Parameters								AFM Analysis
Sample	Deposited Thin Film	dTS (cm)	T (°C)	E (mJ)	RR (Hz)	Pi (Torr)	Pa (Torr)	σRMS (nm)	σa (nm)
S0	Si wafer	x	x	x	x	x	x	0.21 ± 0.026	0.19 ± 0.023
S1	TiO2	4	500	500	30	6.7 × 10−9	4.2 × 10−7	0.58 ± 0.098	0.46 ± 0.083
	Si	4	500	500	30	7.6 × 10−9	0.9 × 10−7	0.58 ± 0.077	0.44 ± 0.040
S2	TiO2	5	500	500	30	5.8 × 10−9	4.8 × 10−7	0.37 ± 0.063	0.29 ± 0.048
	Si	5	500	500	30	3.9 × 10−9	1.0 × 10−7	0.36 ± 0.024	0.29 ± 0.018
S3	TiO2	6	500	500	30	6.0 × 10−9	4.2 × 10−7	0.46 ± 0.024	0.35 ± 0.023
	Si	6	500	500	30	2.2 × 10−9	5.0 × 10−8	0.48 ± 0.090	0.32 ± 0.058

.

The AFM topography images recorded on annealed Si wafer (S0), TiO_2, and Si thin layers from three different sandwich structures (S1, S2, and S3) corresponding to d_TS of 4, 5, and 6 cm are presented in Figure 2 and Figure 3, respectively, all of them revealing a noteworthy uniformity.

The smoothest TiO₂ surface is the one deposited at a d_TS of 5 cm with a σ_RMS = 0.37 nm and σ_a = 0.29 nm. The layers deposited at a d_TS of 4 cm and 6 cm, revealed higher surface roughness (Table 1). As it can be seen the Si films showed similar behavior than in the case of oxide films deposition. The smoothest Si surface revealed a σ_RMS = 0.36 nm and σ_a = 0.29 nm was obtained for 5 cm d_TS.

In Table 1, we show the parameters’ values associated to samples preparation, highlighting the optimal conditions. For each sample the first line corresponds to the fabrication of the TiO₂ layer and the second one to the top Si layer. The values in the table correspond to index of sample, d_TS, substrate temperature, laser pulse energy, repetition rate of laser pulses, pressure before ablation, pressure during ablation, calculated σ_RMS, and σ_a from AFM analysis. As it can be noticed, in all cases, even during ablation, pressure was in UHV interval being lower than 5 × 10⁻⁷ Torr.

According to all the AFM results, the optimal deposition d_TS for both type of materials (TiO₂ and Si) is d_TS = 5 cm (see Table 1, sample S2).

The Roughness Versus the Length-Scale Related to the Target-Substrate Distance

PSD analysis of the AFM images are the most appropriate procedure on revealing the morphological changes on the surface of thin films according to the deposition conditions. The description of sample roughness using σ_a and σ_RMS parameters cannot reveal the modifications of the surface features distribution, associated to their sizes and geometry. Samples characterized by almost the same value of σ_a and σ_RMS could show very different rough surface profiles, being the signatures of specific growth mechanisms of the thin films. The PSD function is defined for continuous topography data h(x, y) based on Fourier transform (1) [24]:

$$C_{2D}^{PSD}\left(q_x,q_y\right)=\underset{L\to \infty }{\lim }\frac{1}{L^2}{\left|\underset{-\frac{L}{2}}{\overset{\frac{L}{2}}{{\displaystyle \int }}}dx\underset{-\frac{L}{2}}{\overset{\frac{L}{2}}{{\displaystyle \int }}}h\left(x,y\right)e^{-i2\pi \left(x{q}_x+y{q}_y\right)}dy\right|}^2$$

(1)

where q_x and q_y are the projection on rectangular axes of spatial frequency; L is the maximum value of x and y. The RMS roughness can be calculated using 2D-PSD function (2):

$${\sigma }_{RMS}^2=\underset{-\infty }{\overset{+\infty }{{\displaystyle \iint }}}{C}_{2D}^{PSD}\left(q_x,q_y\right)d{q}_{x}d{q}_y$$

(2)

In the case of isotropic surfaces, the RMS roughness can be expressed by the following relation:

$${\sigma }_{RMS}^2=2\pi \underset{0}{\overset{+\infty }{{\displaystyle \int }}}{C}_{Iso}^{PSD}\left(q\right)qdq$$

(3)

where q = (q_x² + q_y²)^1/2 is the radial spatial frequency [24]. The 1D-PSD function is often used being obtained from 2D isotropic one by imposing to $C_{1D}^{PSD}$ to give the same result in (4) as in (3):

$${\sigma }_{RMS}^2=\underset{0}{\overset{+\infty }{{\displaystyle \int }}}{C}_{1D}^{PSD}\left(q\right)dq;\hspace{1em}\hspace{1em}\hspace{1em}{C}_{Iso}^{PSD}=\frac{1}{2\pi q}{C}_{1D}^{PSD}\left(q\right)$$

(4)

The AFM image of the surface is represented by discrete height values h(x_i, y_j), associated to in plane rectangular coordinates given by N_x and N_y, number of steps on x and y axis respectively. The calculation of the 1D-PSD function (4) in the case of discrete data series is based on changing from integration to summation in the frame of fast Fourier transformation algorithm FFT [25].

These investigations focus on the determination of thin films surface morphology as the contribution of both substrate roughness, and the d_TS deposition parameter. Therefore, we search for appropriate ways of using PSD on quantitative determination in terms of roughening to be associated with spectral distribution of frequencies [26].

Figure 4 shows the averaged 1D-PSDs of AFM images collected from the surface of TiO₂ and Si films deposited consecutively on (100) Si wafer. The plots correspond to different d_TS (4, 5, and 6 cm) inside laser ablation equipment. PSDs diagrams in Figure 4 represent the evolution of surface topography after each deposition from bare crystalline silicon up to the final double stacked layers samples. PSD values calculated from AFM data are given in Figure 4a in the case of TiO₂ thin films together with the UHV annealed (100) Si substrate in green, being considered as the reference [27].

Figure 4b gives the PSD data of the same samples, after the Si film deposition onto the previous TiO₂ layer. The PSD of the TiO₂/c-Si structures in green, was included to indicate the feeble changes of surface morphology after Si thin film deposition, in respect with the case of d_TS at 5 cm. Thus, appropriate data analysis has to amplify these differences searching for quantitative determinations.

The surface topography is given first by the deposited species involved in both smoothing and roughing mechanisms associated with the processing conditions as temperature, pressure, laser wavelength, pulse time, and d_TS [20]. Moreover, the contribution of the substrate roughness to the deposited film topography, especially at very small thickness, is revealed by the similarities between the coated and uncovered surface. Therefore, the estimation of the direct influences of the d_TS on the rough surface profile requires the extraction of the substrate imprinting features into the deposited thin film that could propagate from the interface up to the top of the sample. It means, to determine the changes of the roughness associated to spatial frequency range, determined by the coverage produced by the incoming particles relative to the initial topography. PSD associated to TiO₂ and Si films in Figure 4 have been used in the frame of mathematical expression that link the roughness to the spatial frequency or wavelength. We have considered the roughness versus length scale (RLS) function σ(λ; λ_min), defined in (5) [24,28].

$${\sigma }^2\left(\lambda ;{\lambda }_{min}\right)=\underset{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right. }{\overset{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${\lambda }_{min}$}\right.}{{\displaystyle \int }}}{C}_{1D}^{PSD}\left(q\right)dq$$

(5)

where λ_min = 1/q_max, it is the parameter associated to the length-scale Δλ = λ − λ_min, with λ representing the spatial wavelength. Λ_min has an imposed value of 10 nm, being required to reject the artifacts associated to the radius of the AFM tip used in this study. σ(λ; λ_min) has spectral significance being a function that can be defined versus spatial wavelength or spatial frequency. The graphical representations for all data calculated by relation (5) were plotted below using λ on abscissa instead of the length-scale Δλ = λ − λ_min that involve a fixed shift of 10 nm. Moreover, the above RLS function is used to express in percentages the variation of the roughness produced by the deposition of the TiO₂ layer relative to that of the c-Si substrate [29].

$${\epsilon }_{Ti{O}_2}\left(\lambda \right)=\frac{{\sigma }_{Ti{O}_2}\left(\lambda \right)-{\sigma }_{c-Si}\left(\lambda \right)}{{\sigma }_{c-Si}\left(\lambda \right)}\times 100\%$$

(6)

Figure 5a reveals the values of the RLS function on TiO₂ thin film, calculated for several values of d_TS. The changes of surface roughing by the oxide layer deposition, relative to the initial topography of the (100) Si substrate are shown in Figure 5b according to the relation (6). Titanium dioxide roughness is higher than that of Si wafer for all values of d_TS parameter: 4, 5, and 6 cm. These quantitative determinations indicate that for the length-scale associated to 20 nm < λ < 550 nm the smallest roughness is obtained at d_TS = 4 cm being almost the same as for Si substrate in between 70 nm and 200 nm. The spatial wavelength λ of the surface features below 550 nm indicates that the local roughing is increasing systematically as the substrate is placed far away from the ablation source as d_TS is modified from 4 to 6 cm. This effect corresponds to the diminishing of the incident particles number with orientations at large angles relative to the normal direction towards the substrate. Under these conditions the shadowing process it is expected to contribute on the increasing of roughness [30]. The wide angle distribution of the incoming particles at the smallest d_TS distance leads to the conformity of the rough surface profile on top of the deposited TiO₂ layer with that of the (100) Si substrate in between 70 and 250 nm.

It is interesting that the smallest values of RLS obtained at 70–550 nm for samples deposited at d_TS = 4 cm become greater than the other ones above 600 nm. The contribution of the large features to the overall roughness changes the top of the smoothness above 600 nm in Figure 5a,b. Thus, the best TiO₂ sample was obtained at d_TS = 5 cm, by considering entire length scale of spatial wavelength into expression (5).

Figure 6 shows the same type of data as those in Figure 5 but for silicon thin film deposited above the previous TiO₂ layer. Thus, Figure 6a gives the values of the RLS function associated to Si thin film, calculated for several values of d_TS. In this case, the variation of the rough surface profile from that of TiO₂ to the on top Si layer ${\epsilon }_{Si}\left(\lambda \right)$ is considered relative to that of titanium dioxide film, being this time like a new substrate (7). In this way the initial spectral roughness of the Si-TiO₂ interface is related to the surface profile of the on top deposited coverage.

$${\epsilon }_{Si}\left(\lambda \right)=\frac{{\sigma }_{Si}\left(\lambda \right)-{\sigma }_{Ti{O}_2}\left(\lambda \right)}{{\sigma }_{Ti{O}_2}\left(\lambda \right)}\times 100\%.$$

(7)

The negative values on the vertical axis in Figure 6b of all samples, indicate that silicon deposition on TiO₂ produces surface flattening along the full scale of the spatial wavelength.

The expected processes that lead to smoothing is surface migration of silicon atoms by reemission and diffusion, influenced by the oxide coverage. The smoothest samples corresponding to the spatial wavelength between 20 nm and 117 nm was obtained at d_TS of 6 cm. Contrary, above the crossing point at 117 nm the same sample turn to the highest roughness of all. Around this value the slope reaches the highest value. It is associated to surface features belonging to size distribution centered close to 8.5 μm⁻¹ as it is revealed by Figure 6c. Here the difference between PSD Si and PSD TiO₂ given in Figure 4, divided to PSD TiO₂ is plotted versus spatial frequency [26]. The peak corresponds to the length scale of 103 nm being close to the crossing point in Figure 6b.

The silicon films deposited at d_TS of 4 and 5 cm have similar dependence versus the length scale up to the crossing point. The smoothest silicon film was obtained at d_TS = 5 cm according with the roughness corresponding to entire length scale of spatial wavelength. The above data of the rough surface profile of TiO₂ and Si films remain unexplained at the length scale greater than 500 and 100 nm, respectively. Anyway, the interpretation lies on finding the dominant process of the front roughness formation during PLD deposition regarding shadowing, reemission, and surface diffusion [30], by similar investigations.

3.3. Structural and Optical Characterization of TiO₂ Thin Films

One goal of this contribution is to build TiO₂ layer buried in silicon by PLD consecutive depositions of the oxide and Si films on (100) Si wafer with thickness in the range of tens of nanometer. The improving of the roughness is critical for both interfaces of the buried TiO₂ layer in respect with electrical and elastic properties requested for applications in the field of sensors or electronic devices. Complementary techniques as XRD, XRR, and spectrometric ellipsometry were used for the characterization of the smoothest TiO₂ layer obtained by laser ablation deposition, according with the optimization of the d_TS parameter.

3.3.1. X-ray Diffraction and X-ray Reflectivity

The naturally occurred phases of TiO₂ are anatase, rutile, and brookite [31,32,33,34]. The last one is of high importance especially as photocatalysts, due to either oxidative or reductive manifestation of the exposed surface associated to (201) or (210), respectively. Brookite thin films of good quality are much more difficult to be obtained being in a mixture with anatase or rutile [31,35,36]. The XRD diffraction pattern of the TiO₂ film in Figure 7 is dominated by (100) Si substrate at 2ϴ = 69.15° [37,38]. The following peaks were associated to brookite phase in the diffractogram presented in Figure 7a: 31.37° (121), 44.93° (122), 63.3° (321), 82.02° (063) with magnification for the last two reflections shown in Figure 7b [31,36,39]. The intense peaks observed at 31.370 and that at 44.93° were reported in reference [31] being associated to brookite phase of PLD deposited films on Si (111) at 750 °C. Furthermore, in [40] are given similar results for ALD (atomic layer deposition) on the same substrate. Brookite-rich thin films of 95% were obtained by PLD after annealing at 290 °C [41]. The above-mentioned reports together with the partial XRD signature shown in Figure 7a,b suggests the formation of the brookite phase into the deposited TiO₂ layer. Moreover, the expected peaks of anatase or rutile phase were not identified as other studies reported in the case of deposited TiO₂ thin films [31,34]. Unfortunately, the resulted conclusion about the formation of a rich-brookite oxide [39] must be taken with care due to the very thin TiO₂ oxide layer combined with the missing of some expected XRD peaks.

X-ray Reflectivity (XRR) was used in order to examine the roughness and the thickness of the TiO₂ layer. The roughness determined in the XRR measurement shown in Figure 8a for the TiO₂ layer obtained in optimal conditions (sample S2) is 0.37 nm, being in agreement with the AFM data for the same layer (Table 1) [42].

The variation of the X-ray reflectivity shown in Figure 8a is related to the thickness of TiO₂ film [43]. The reflectivity oscillation profile (r) is described by the following expression:

$$r=\cos \left(\frac{4\pi d}{{\lambda }_x\sqrt{{\sin }^2\theta -2\delta }}\right),$$

(8)

where d is the thickness, λ_x is the wavelength, θ is the incident angle, and δ is the refractive index of X-ray.

The thickness of the layer is given by the peak position in the profile of Fourier transformation with the horizontal axis set as $\sqrt{{\sin }^2\theta -2\delta }$. The thickness of the TiO₂ layer was found to be 27 nm as it can be seen in Figure 8b.

3.3.2. Ellipsometry

Optical parameters and the thickness of the thin oxide layer were determined by means of spectroscopic ellipsometry, in order to corroborate with XRR results. The optimal fitting within the Cauchy model of the Ψ and Δ parameters, as it can be seen in Figure 9a, has found the TiO₂ layer thickness to be 26.5 nm which is in good agreement with XRR measurement mentioned above. It could be adequate to mention that the variation of thickness relative to the averaged TiO₂ and Si thin films thickness are lower than 7.2% and 10.1%, respectively.

The refractive index, namely, its real and imaginary parts, n, k, respectively, that result from the fitting procedure are given in Figure 9b versus the light wavelength. The high value of n and its dependence on the wavelength in Figure 9b is comparable to those reported about rich-brookite TiO₂ films [40].

4. Conclusions

This work investigates the profile of the rough surfaces for both TiO₂ and Si thin films deposited by PLD on silicon wafer. On top silicon film and the buried oxide layer, enclosed in Si/TiO₂/c-Si structures, were prepared for several target-substrate distances d_TS, ranging between 4 and 6 cm. We focused on the surface topography in relation with the deposition parameter d_TS, and with the initial substrate morphology, considering that at small thickness of the deposited layers their physical properties are more influenced by roughness. The change of d_TS value is associated to the modification of angular distribution of the incoming particles on substrate. Therefore, the RLS function associated to PSD-AFM analysis, has been proposed for its sensitivity that gives responses to the evolution of surface topography from bare (100) Si wafer up to on top deposited layer of the Si/TiO₂/cSi stacked structure. Thus, the spectral characteristic of the RLS function has the advantage of showing the changes of the roughness versus the length-scale after each deposition, highlighting the influences of the d_TS parameter. Furthermore, the topography of the deposited layer results as a combination of the initial roughness of the substrate and the deposition parameter d_TS. Relative RLS function takes into account both influences. Thus, we show that the TiO₂ deposition on Si(100) produced an increase of the roughness in the range of those features having spatial wavelength greater than 100 nm (Figure 5b). Contrary the Si deposition onto TiO₂ determine the smoothing of the initial oxide surface (Figure 6). Thus, the mechanisms of thin films growth can be revealed by adequate AFM data analysis, paving the way to useful physical models that correlate deposition parameters to the features built by particle assembling on surfaces.

In conclusion we show that relative RLS based on PSD function, used for AFM data analysis, reveals quantitatively the evolution of surface profile on top layer of the Si/TiO₂/(100) Si stacked films after their consecutive depositions, in relation with both substrate and with the d_TS distance.