Chemical Papers 66 (8) 748–756 (2012)DOI: 10.2478/s11696-012-0190-y

ORIGINAL PAPER

Effect of substrate on phase formation and surface morphologyof sol–gel lead-free KNbO3, NaNbO3, and K0.5Na0.5NbO3 thin films

Helena Bruncková*, Ľubomír Medvecký, Pavol Hvizdoš

Institute of Materials Research, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia

Received 25 January 2012; Revised 28 March 2012; Accepted 29 March 2012

Environmentally acceptable lead-free ferroelectric KNbO3 (KN) or NaNbO3 (NN) andK0.5Na0.5NbO3 (KNN) thin films were prepared using a modified sol–gel method by mixing potas-sium acetate or sodium acetate or both with the Nb-tartrate complex, deposited on the Pt/Al2O3and Pt/SiO2/Si substrates by a spin-coating method and sintered at 650◦C. X-ray diffraction (XRD)analysis indicated that the NN and KNN films on the Pt/SiO2/Si substrate possessed a single per-ovskite phase, while NN and KNN films on the Pt/Al2O3 substrate contained a small amount ofsecondary pyrochlore phase, as did KN films on both substrates. Scanning electron microscopic(SEM) and atomic force microscopic (AFM) analyses confirmed that roughness Rq of the thinKNN/Pt/SiO2/Si film (≈ 7.4 nm) was significantly lower than that of the KNN/Pt/Al2O3 film(≈ 15 nm). The heterogeneous microstructure composed of small spherical and larger needle-likeor cuboidal particles were observed in the KN and NN films on both substrates. The homogeneousmicrostructure of the KNN thin film on the Pt/SiO2/Si substrate was smoother and contained finerspherical particles (≈ 50 nm) than on Pt/Al2O3 substrates (≈ 100 nm). The effect of differentsubstrates on the surface morphology of thin films was confirmed.c© 2012 Institute of Chemistry, Slovak Academy of Sciences

Keywords: sol–gel, (K,Na)NbO3 thin films, spin-coating, pyrochlore, perovskite phase, morphol-ogy

Introduction

Thin films of alkali metal niobates such as potas-sium niobate (KNbO3, KN), sodium niobate(NaNbO3, NN), and potassium sodium niobate(K0.5Na0.5NbO3, KNN) have been subjected to inten-sive study on ecological grounds (Weber et al., 2005;Wu et al., 2010). Environmental considerations dictatethat lead-free thin films be used in the new generationof functional devices (Lee et al., 2011). Several yearsago, Saito et al. (2004) emphasised the importanceof this material system by discovering a new mor-photropic phase boundary in the potassium sodiumniobate system. Environmentally friendly lead-freepiezoelectric materials are needed for application inthe form of thin films in many micro-electromechanicalsystems (MEMS) driven by miniaturisation and inte-gration (Soderlind et al., 2005).

The following physical and chemical methods arerecognised for thin film preparation onto different sub-strates: physical vapour deposition (PVD), e.g., mag-netron sputtering (Shibata et al., 2008), pulsed laserdeposition (PLD) (Yamazoe et al., 2010), and chemi-cal solution deposition (CSD) (Katsumata et al., 2010;Kang et al., 2011). The CSD method, based on thesol–gel process, proceeds in several steps: solution syn-thesis, coating on a substrate, pyrolysis, and crys-tallisation (Li et al., 2008; Chowdhury et al., 2010a).Many publications differ as to the manner in which thefilms are processed, mainly in relation to the precursor(solution) preparation and annealing steps and, con-sequently, development of a microstructure. Tanakaet al. (2006) and Nakashima et al. (2007) utilisedethoxide-based precursors and 2-metoxyethanol assolvent. KNN solutions have been prepared by thePechini method using an ammonium oxalate Nb-

*Corresponding author, e-mail: hbrunckova@imr.saske.sk

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complex, together with potassium and sodium nitrates(Chowdhury et al., 2009). The phase heterogeneity inKNN films demonstrates carbonate phases formationin KNN gels prepared by an ethoxide-based sol–gelmethod (Chowdhury et al., 2010b, 2010c). Lai & Li(2007) added acetic acid, pentane-2,4-dione (acety-lacetone) as a stabiliser, chelating agent to an alkoxidesolution. Wang et al. (2008) reported a novel methodfor preparing KNN films with potassium and sodiumacetates as precursors. Ahn et al. (2008) and Yan etal. (2010) used alkaline acetates and applied acety-lacetone as a chelating agent. In an environmentallyacceptable sol–gel process dependent on the type ofinteraction between starting components (potassiumand sodium acetates) and polymeric Nb–citrate com-plex, solvent (acetic acid), and stabiliser (propan-1-ol), an amorphous film with metastable pyrochlorephase was formed at a calcination temperature of 300–400◦C, where pyrolysis of the organic compounds oc-curred, resulting in inorganic oxides K2O, Na2O, andNb2O5 (Soderlind et al., 2005). The perovskite phasewas formed during sintering at 500–700◦C.In the case of KNN films, the substrates seemed to

play an important role affecting phase formation andgrowth of the perovskite film on a substrate (SrTiO3,MgAl2O4, or Al2O3 and Pt/SiO2/Si) (Schroeter et al.,2007). Roscher et al. (2011) showed that KN and NNthin films on the Pt/SiO2/Si substrate displayed sub-stantially different crystallisation behaviour. The crys-tallisation of the KNN film was observed at tempera-ture as low as 500◦C. In the NN film, the pyrochloreNaNb3O8 phase was formed at about 620◦C and theNaNbO3 phase appeared at 440◦C and its quantityincreased proportionally upon reaching temperaturesof 700–800◦C. Various types of pyrochlore phases suchas K2Nb8O21 or K4Nb6O17 appeared at temperatureof 500◦C in the crystallisation process of the KN filmand perovskite KNbO3 phase formed at above 670◦C.A single KNbO3 perovskite phase in the KN/Al2O3film was obtained at 550◦C using sol–gel solutionswith K/Nb mole ratio equal to 1.25/1.50 (Weber etal., 2005). The KNN film (≈ 100 nm thickness), pre-pared by a sol–gel method on Pt/Ti/SiO2/Si substratewith a perovskite phase had a uniform microstructurewith particle size of about 100 nm (Yan et al., 2010).The particle shape of the KNN film prepared by thesol–gel method also depended on the presence of py-rochlore K4Nb6O17 and Na2Nb8O21 phases of approx-imately 10–20 nm (Tanaka et al., 2007).The present paper describes the phase composi-

tion and surface morphology formation of KN, NN,and KNN thin films deposited on the Pt/Al2O3 andPt/SiO2/Si substrates by the spin-coating methodusing a sol–gel process modified by polymeric Nb–tartrate complex. The effect of different substrates onphase formation and development of the perovskitephase and the microstructure thin films sintered at650◦C was investigated.

Fig. 1. Scheme of sol–gel method for preparation of 2-layeredKNN thin films.

Experimental

Three solutions (sols) of KN, NN, or KNN precur-sors were synthesised by a modified sol–gel method,by mixing potassium acetate, sodium acetate, or bothin an acetic acid solution with the Nb-complex. Allchemicals were of analytical grade and were pur-chased from Merck (Darmstadt, Germany). The poly-meric Nb–tartrate complex for the KN, NN, and KNNfilms synthesis was prepared by the modified Pechinimethod (Bruncková et al., 2008). The niobium(V)chloride was dissolved in ethanol and precipitated withaqueous NH3 to prepare hydrated niobium(V) oxide.The Nb–tartrate complex was formed by a reactionof Nb2O5 ·7H2O with 2,3-dihydroxybutanedioic acid(tartaric acid, TA) and H2O2. The solution thus ob-tained was dried at 80◦C and dissolved in ethane-1,2-diol (ethylene glycol, EG) (the mole ratio of EG/TAwas 0.04/0.073).The KNN precursor (sol) for the KNN thin film

preparation was derived using the modified sol–gelsynthesis shown in Fig. 1. K2CO3 and Na2CO3 wereallowed to dissolve in acetic acid (100 %) separatelyin two closed flasks at 80◦C for 1 h. After the additionof acetic acid, the alkali metals acetate solutions weredehydrated at 105◦C for 2 h and cooled to 80◦C andmixed with the niobium complex solution for 1 h. The

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Fig. 2. XRD diffractograms of KN (a), NN (b), and KNN (c) thin films deposited on Pt/Al2O3 substrate after sintering at 650◦Cand Pt/Al2O3 substrate (d): × – perovskite phase (KNbO3 (a), NaNbO3 (b), and K0.65Na0.35NbO3 (c)); pyrochlore phase(• – K4Nb6O17 (a); – Na2Nb8O21 (b); – Na2Nb8O21 (c)); (• – Pt and � – Al2O3) (d); S – Pt/Al2O3 substrate.

K/Na/Nb mole ratio was 1 : 1 : 2. After addition of theNb-complex at a temperature of 80◦C, the yellow solwas formed. Finally, the KNN sol was diluted with astabilising solution (propan-1-ol/propane-1,2-diol, ϕr= 10 : 1) (Bruncková et al., 2011). The resulting yellowsolution was transparent and remained stable at labo-ratory temperature for two months. Analogously, theKN or NN solution was synthesised by the modifiedsol–gel method by mixing potassium or sodium ac-etate (prepared by dissolution of potassium or sodiumcarbonate in acetic acid) with the Nb–tartrate com-plex at temperature of 80◦C. The K/Nb or Na/Nbmole ratio was 1 : 1.Two different platinised substrate types, alu-

mina and silicon, were applied to deposit the films.Oxidised P-type silicon (100) single-crystal waferswere used as substrates with a Pt (50 nm) elec-trode layer (sputtered as a bottom electrode). TheSiO2 (250 nm) layers were present between Ptand Si. Pt/Al2O3 (50 nm/630 µm) and Pt/SiO2/Si(50 nm/250 nm/270 µm) substrates were spin-coatedwith the sol precursor at 2000 min−1 for 30 s fol-lowed by calcination at 400◦C for 3 min. The coating-pyrolysis process cycle was repeated twice to obtain2-ply thin films. Finally, the films were allowed tocrystallise via sintering at 650◦C for 1 h in air toform the perovskite phase in KN, NN, and KNNthin films, respectively. Heating and cooling rateswere ± 5◦C min−1. The thin films deposited onPt/Al2O3 (A) substrate (KN/A, NN/A, and KNN/A)and Pt/SiO2/Si (S) substrate (KN/S, NN/S, andKNN/S) were denoted accordingly.The phase composition of KN, NN, and KNN

films was determined by X-ray diffraction analysis(XRD), (model: X’Pert Pro, Philips, the Netherlands)using CuKα radiation. The surface and cross-sectionof KN, NN, and KNN thin films microstructureswere characterised by scanning electron microscopy(SEM) (model: JSM-7000F, Jeol, Japan) and atomicforce microscopy (AFM), dimension Icon from Veeco(USA).

Results and discussion

The XRD diffractograms of KN, NN, and KNNthin films deposited on substrates A and S and sin-tered at 650◦C and Pt thin films on Al2O3 andSiO2/Si substrates are shown in Figs. 2 and 3, re-spectively. XRD diffractograms of KN, NN, and KNNthin films on both substrates verified the formationof perovskite KNbO3 (PDF4 00-009-0156, accordingto Joint Committee on Powder Diffraction Standards(JCPDS)) (Figs. 2a and 3a), NaNbO3 (PDF4 00-014-0603) (Figs. 2b and 3b), and K0.65Na0.35NbO3(PDF4 01-077-0038) phase with monoclinic symme-try (Figs. 2c and 3c). In addition, secondary py-rochlore phases in KN films were found in the pat-terns K4Nb6O17 (PDF4 00-014-0287) in the KN/Afilm (Fig. 2a) and (PDF4 00-014-0287+ PDF4 00-021-1295) in the KN/S film (Fig. 3a), Na2Nb8O21 (PDF400-013-0329 + PDF4 00-030-1229) in the NN/A film(Fig. 2b), and Na2Nb8O21 (PDF4 00-013-0329) phasein the KNN/A film (Fig. 2c). The two peaks at 40◦ and46◦ corresponding to the Pt (111) and (200) planes, re-spectively (JCPDS 04-0802) appeared in Pt thin filmsdeposited on crystalline Al2O3 (Fig. 2d) and amor-phous SiO2/Si (Fig. 3d) substrates after sintering at650◦C. Significations of the perovskite and pyrochlorephases from the XRD diffraction patterns (Figs. 2and 3) are shown in Table 1. Note that the crys-tallinity of the secondary phases in particular was verylow and it is complicated and practically impossibleto carry out a accurate quantitative analysis of thephase composition of the films. In addition, some de-gree of the preferential growth of individual particlesin films cannot be excluded. In the films on substrateS, the XRD peaks exhibit weaker intensities. The ef-fect of different substrates on the phase formation ofthin films was determined from Figs. 2 and 3 andthe pure perovskite phase in NN and KNN films onsubstrates S was revealed, while the NN/A film con-tained a small amount of secondary pyrochlore phase,as did KN films on both substrates. A marked differ-ence was observed in XRD diffractograms of the KN

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Fig. 3. XRD diffractograms of KN (a), NN (b), and KNN (c) thin films deposited on Pt/SiO2/Si substrate after sintering at650◦C and Pt/SiO2/Si substrate (d); × – perovskite phase (KNbO3 (a), NaNbO3 (b), and K0.65Na0.35NbO3 (c)); • –, ◦– pyrochlore phase ((K4Nb6O17) (a)); (• – Pt � – Si) (d); S – Pt/SiO2/Si substrate.

Table 1. Signification of perovskite and pyrochlore phases of XRD diffraction patterns from Figs. (2 and 3)

Film Perovskite phase Pyrochlore phase XRD diffraction pattern

KN/A × – KNbO3 • – K4Nb6O17 × – PDF4 00-009-0156• – PDF4 00-014-0287NN/A × – NaNbO3 – Na2Nb8O21

× – PDF4 00-014-0603– PDF4 00-013-0329 + PDF4 00-030-1229

KNN/A × – K0.65Na0.35NbO3 – Na2Nb8O21× – PDF4 01-077-0038– PDF4 00-013-0329

KN/S × – KNbO3 • –, ◦ – K4Nb6O17 × – PDF4 00-009-0156• – PDF4 00-014-0287 + ◦ – PDF4 00-021-1295NN/S × – NaNbO3 – × – PDF4 00-014-0603

KNN/S × – K0.65Na0.35NbO3 – × – PDF4 01-077-0038

and NN films prepared on both substrates. The py-rochlore K4Nb6O17 phase coexists with the perovskiteKNbO3 phase at a temperature of 650◦C in KN filmson both substrates. The K4Nb6O17 is a compound de-void of potassium compared with KNbO3. PerovskiteK0.5Na0.5NbO3 single-phase in KNN thin films wasprepared by optimising the KxNaxNbO3 (x ≥ 0.5)composition of the precursor solution (Nakashima etal., 2007). Stoichiometric KNN films crystallised in theperovskite KNN phase with a small amount of theundesirable K4Nb6O17 phase. Several non-perovskitepeaks of pyrochlore K2Nb4O11 phase were found in

sol–gel-prepared KNN films after annealing at 800◦C(Lai & Li, 2007).Fig. 4 shows the SEM cross-section microstructures

of KNN thin films deposited on Pt/Al2O3 (Fig. 4a)and Pt/SiO2/Si (Fig. 4b) substrates sintered at 650◦C.The film surface roughness (≈ 150 nm thickness)is visible in the cross-section of the KNN thin filmon substrate A in contrast with the much smootherand uniform surface morphology of the KNN/S film(≈ 100 nm thickness), composed of densely packedparticles.The SEM images of the surface and the 2D AFM

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Fig. 4. SEM cross-section micrographs of KNN thin films deposited on Pt/Al2O3 (a) and Pt/SiO2/Si (b) substrates after sinteringat 650◦C.

topography micrographs of KN, NN, and KNN thinfilms deposited on Pt/Al2O3 and Pt/SiO2/Si sub-strates prepared at 650◦C are shown in Fig. 5. Theheterogeneous microstructure of the KN film surfaceon substrate A (Fig. 5a) is characterised by the bi-modal particle size distribution and contains smallerspherical (≈ 30–50 nm) and bigger needle-like parti-cles of about 100–200 nm. On the surface microstruc-ture micrograph of the KN thin film deposited onsubstrate S (Fig. 5b), fine spherical particles of ap-proximately 30 nm and coarse cuboidal particles (≈80–150 nm) are shown. From the atomic force mi-croscope (AFM) analysis of the surface morphology,the root mean square roughness (Rq), and the av-erage roughness (Ra) were determined. Figs. 5a and5b show large-scale 2D AFM images of the KN thinfilm deposited on substrates A and S. From the AFMmeasurements, the values of root mean square rough-ness and average roughness within the scanned areasof 2.5 µm × 2.5 µm of thin films deposited on bothsubstrates were determined. The Rq values of the KNfilm on substrates A and S were approximately 20 nmand 11 nm, respectively (value of Ra = 15.0 nm and8.9 nm). On the other hand, bigger cuboidal parti-cle clusters (≤ 1 µm in length) composed of fine par-ticles with dimensions of less than 80 nm (Fig. 5c)were found in the heterogeneous microstructure of theNN/A thin film. In addition, the SEM surface imagesof the NN/S thin film (Fig. 5d), showed that the big-ger clusters of perovskite particles (representing ag-glomerates of smaller spherical particles of ≈ 50 nmin size) were surrounded by fine cuboidal particles ofabout 100 nm. The effect of substrate on the surfacetopography of NN films is apparent. The values ofsurface roughness Rq and Ra tended to improve inthe NN films from 51.5 nm to 39.2 nm on substrateA and from 15 nm to 14 nm on substrate S. Theroot mean square roughness of the PLD NN films was3 nm and 6 nm on Pt/SrRuO3 and Si/SrRuO3 sub-

strates, respectively (Aulika et al., 2007) and the aver-age particle size was 50 nm and 100 nm for NN on twodifferent substrates. The KNN/A thin film (Fig. 5e)had a uniform homogeneous microstructure and con-sisted of two particle forms: spherical with particle sizeof approximately 80–100 nm and cuboidal (≈ 100–150 nm). Small spherical particles with diameters ofapproximately 50 nm and approximately 80 nm wereobserved in the dense and uniform microstructure ofthe KNN/S thin film with the pure perovskite phase(Fig. 5f). Tanaka et al. (2006) observed similar smallparticles between large cuboidal particles in the mi-crostructure of the KNN film obtained by the sol–gelmethod. The results of AFM analyses confirmed thatthe values of Rq or Ra roughness of the KNN/S film(≈ 7.4 nm or 5.6 nm) were significantly lower thanthose (≈ 15 nm or 11 nm) of the KNN film depositedon substrate A. The Rq and Ra values of the preparedfilms deposited on the Pt/Al2O3 and Pt/SiO2/Si sub-strates and sintered at 650◦C are presented in Table 2.The surface morphology studies are consistent withthe structural and topography results. The roughnessof scanned areas of 2.5 µm × 2.5 µm of the Pt/Al2O3and Pt/SiO2/Si substrates was approximately 5.7 nmand approximately 1 nm, respectively. In the SEM sur-face images and AFM micrographs of topography ofthe Pt/Al2O3 substrate, Pt particles (≤ 100 nm) inthe Pt thin film of approximately 50 nm thickness wereobserved (Bruncková et al., 2011; Braunschweig et al.,2011). Our Pt thin film on smooth SiO2 was composedof small particles (≈ 10–20 nm). Mountain-like islandswith a roughness of about Rq (1.81 nm) and particlesize of about 10–20 nm were observed in the surfacetopography of the Pt/SiO2 film (Wei et al., 1998).The three-dimensional (3D) AFM micrographs of

KN, NN, and KNN films on both substrates (Fig. 6)showed that the film roughness and particle shapewere comparable with SEM observations of films. TheAFM acicular surface topography image of the KN/A

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Fig. 5. SEM surface micrographs and 2D AFM (small picture) surface topography micrographs of KN (a, b), NN (c, d), and KNN(e, f) thin films deposited on Pt/Al2O3 (a, c, e) and Pt/SiO2/Si (b, d, f) substrates after sintering at 650◦C.

film (Fig. 6a) was characterised by two types of sur-face, smooth (spherical particles) and rough (needle-like particles). In the spotted structure of the KN/Sfilm (Fig. 6b), elongated spherical and cuboidal par-ticles with smooth and rough surfaces were observed.The NN/A film (Fig. 6c) had island-like structures,representing the major portion of the rough surfacewith cuboidal particle clusters and a minor portion

of the smooth surface with spherical particles. Con-versely, the ridge-like structure of the NN/S film(Fig. 6d) contained the major portion of the smoothsurface (bigger clusters of perovskite particles) and aminor portion of the rough surface (cuboidal parti-cles). AFM uniform surface topography micrographsof KNN films on substrates A and S with dense andsmooth surfaces are given in Figs. 6e and 6f. The im-

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Table 2. Values of root mean square roughness (Rq) and av-erage roughness (Ra) of scanned areas of 2.5 µm ×2.5 µm of substrates A (KN/A, NN/A, KNN/A) andsubstrate S, (KN/S, NN/S, KNN/S) thin films sin-tered at 650◦C and phase composition of films

Sample Rq/nm Ra/nm Phase composition of film

A 5.7 4.1 –KN/A 20.0 15.0 K4Nb6O17, KNbO3NN/A 51.5 39.2 Na2Nb8O21, NaNbO3,KNN/A 15.0 11.0 Na2Nb8O21, K0.65Na0.35NbO3S 1.0 0.8 –KN/S 11.0 8.9 K4Nb6O17, KNbO3NN/S 15.0 14.0 NaNbO3KNN/S 7.4 5.6 K0.65Na0.35NbO3

age of the KNN/S thin films verified that they hada smoother surface and contained only finer sphericalperovskite particles (≈ 50 nm) than those (≈ 100 nm)on substrate A. Similar AFM images of KNN filmswere obtained by the PLD method (Yamazoe et al.,2010). The effect of the Pt/SiO2/Si substrate causes asharper decrease in the rough surface portion betweenthe smooth surface than with Pt/Al2O3 substrates.We propose a hypothesis to explain the difference inthe behaviour of different (Pt/Al2O3 and Pt/SiO2/Si)substrates. The mechanism of the microstructure for-mation with morphologically varied perovskite parti-cles in alkali metals niobate thin films prepared from

Fig. 6. 3D AFM surface topography micrographs of KN (a, b), NN (c, d), and KNN (e, f) thin films deposited on Pt/Al2O3 (a,c, e) and Pt/SiO2/Si (b, d, f) substrates after sintering at 650◦C.

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the same sols on different substrates depends on thestructure of the Pt film deposited on crystalline Al2O3(rough surface) and amorphous SiO2 (smooth sur-face).

Conclusions

Lead-free KN, NN, and KNN thin films approxi-mately 100 nm in thickness were prepared by a sol–gelmethod modified using Nb–tartrate complex-obtainedsols, which were deposited by the spin-coating methodon Pt/Al2O3 and Pt/SiO2/Si substrates and sinteredat 650◦C.The effect of different substrates on the phase

formation in thin films was determined and thepure perovskite phases of NaNbO3 (in the NN film)and K0.65Na0.35NbO3 (in the KNN film) on thePt/SiO2/Si substrate were revealed. XRD diffrac-tograms showed that the NN and KNN films onthe Pt/Al2O3 substrate contained a small amountof secondary pyrochlore Na2Nb8O21 analogous withK4Nb6O17 in the KN films on both substrates.In the microstructures of thin films, the effect of

substrate on particle shape and sizes was clearly ob-served. The mechanism of the microstructure forma-tion with morphologically varied particles in the thinfilms on the Pt/Al2O3 and Pt/SiO2/Si substrates de-pends on the structure of the Pt film deposited oncrystalline Al2O3 and amorphous SiO2. The parti-cle morphology in the heterogeneous microstructureof KN or NN films was characterised by the bimodalparticle size distribution and small spherical nanopar-ticles on both substrates and larger needle-like (KN)or cuboidal (NN) particles on Pt/Al2O3 and cuboidal(KN) or spherical (NN) clusters on Pt/SiO2/Si wereobserved. The uniform homogenous microstructureof the KNN thin film on the Pt/SiO2/Si substratewas smoother and contained finer spherical particles(≈ 50 nm) than on Pt/Al2O3 substrate (≈ 100 nm).The results of AFM analyses confirmed that rough-

ness Rq of KN, NN, and KNN films on the Pt/SiO2/Sisubstrate (≈ 11.0 nm, 15.0 nm, and 7.4 nm, respec-tively) was significantly lower than roughness Rq ofKN, NN, KNN films deposited on the Pt/Al2O3 sub-strate (≈ 20.0 nm, 51.5 nm, and 15 nm, respectively).Acknowledgements. This work was financially supported by

the Slovak Grant Agency of the Ministry of Education of theSlovak Republic and the Slovak Academy of Sciences, ProjectNo. 2/0024/11.

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