Combined effects of thickness, grain size and residual stress on the dielectric properties of Ba0.5Sr0.5TiO3 thin films

Accepted Manuscript Combined effects of thickness, grain size and residual stress on the dielectric properties of Ba0.5Sr0.5TiO3 thin films Tanja Pečnik, Sebastjan Glinšek, Brigita Kmet, Barbara Malič PII:

S0925-8388(15)30308-X

DOI:

10.1016/j.jallcom.2015.06.192

Reference:

JALCOM 34599

To appear in:

Journal of Alloys and Compounds

Received Date: 14 April 2015 Revised Date:

11 June 2015

Accepted Date: 22 June 2015

Please cite this article as: T. Pečnik, S. Glinšek, B. Kmet, B. Malič, Combined effects of thickness, grain size and residual stress on the dielectric properties of Ba0.5Sr0.5TiO3 thin films, Journal of Alloys and Compounds (2015), doi: 10.1016/j.jallcom.2015.06.192. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Combined effects of thickness, grain size and residual stress on the dielectric properties of Ba0.5Sr0.5TiO3 thin films Tanja Pečnika,b,1, Sebastjan Glinšeka,c,2, Brigita Kmeta, Barbara Maliča Electronic Ceramics Department, Jožef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia

b

Jozef Stefan International Postgraduate School, Jamova cesta 39, 1000 Ljubljana, Slovenia

School of Engineering, Brown University, 184 Hope Street, Providence, RI 02912, USA

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Corresponding author: E-mail address: [email protected], Postal address: Institut Jožef Stefan, Jamova cesta 39, 1000 Ljubljana, Slovenia, Phone: +386 1 477 3260. 2 Currently Sebastjan Glinšek is at CEA Grenoble, LETI, Minatec Campus, 17, Rue des Martyrs, F-38054 Grenoble, France.

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ACCEPTED MANUSCRIPT Abstract We studied the microstructure and dielectric properties of Ba0.5Sr0.5TiO3 thin films on polycrystalline alumina substrates with film thicknesses in the range 90–400 nm. Upon annealing at 900 °C in a rapidthermal-annealing furnace the films crystallized in a pure perovskite phase with uniform and dense

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microstructures consisting predominantly of columnar grains. As the film thickness increased from 90 to 170 nm, the average lateral grain size increased from 45 to 87 nm. In the same manner, the dielectric permittivity of the films increased from 650 to 1250, measured at 100 kHz and room

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temperature. In the thickness range between 170 and 240 nm, only a slight change of the grain size and the permittivity was observed. But with a further increase of the thickness to 400 nm the permittivity

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decreased, even though the grain size remained unchanged. A similar trend was also observed in the GHz range. The reduced dielectric permittivity in the thicker films is related to the tensile residual stress, which develops due to the thermal expansion mismatch between the film and the substrate. The measured tensile residual stress was above 300 MPa in the thickness range 90–170 nm, while it partially relaxed at greater thicknesses because of the formation of cracks. As a result, the dielectric

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permittivity of the films is reduced.

Keywords: Ferroelectric thin films, Chemical solution deposition, Thickness, Grain size, Residual stress.

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ACCEPTED MANUSCRIPT 1. Introduction Ferroelectrics possess a unique combination of functional properties, making them a technologically very important group of materials, with applications ranging from sensors, actuators, energy harvesters and industrial ink-jet printers to electrocaloric cooling devices, etc. Their strongly electric-field-

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dependent dielectric permittivity and relatively low microwave dielectric losses in the paraelectric state also make them attractive for various electrically tunable components. Compared to the competing wireless technologies, ferroelectrics-based varactors are characterized by a high tuning

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speed, small leakage currents, high breakdown fields and radiation hardness [1-3].

Polycrystalline ferroelectrics continue to be at the forefront of applied materials research and

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continuous miniaturization makes thin films of great interest. However, their functional response can be significantly different from their bulk counterparts. The main factors that modify the functional response of polycrystalline thin films include the interaction with the electrodes (i.e., the electrode effect [4]), porosity [5], chemical homogeneity [6, 7], texture [8-10] grain size and film thickness [11-

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18] as well as interactions with the substrates causing residual stresses [19-23]. These complex phenomena occur across various length scales and are still not completely understood [24, 25]. The dielectric grain-size effect, i.e., the change of dielectric permittivity with the grain size, has been

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comprehensively studied for bulk ceramics in their ferroelectric state. In the case of BaTiO3 the complex domain-wall motion results in a non-monotonic dependence, with a peak in the permittivity

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observed for a grain size of ∼1–2 µm, with a strong decrease at smaller grain sizes [13]. In the paraelectric phase, however, the dielectric permittivity continuously decreases with a decreasing grain size [11, 12]. The explanation for this effect is not trivial: the reduced response was explained by the core-shell structure of the grains, consisting of grain-boundary layers with a lower permittivity and the grain core with single-crystal properties. The volume fraction of the low-permittivity layers increases with a decreasing grain size, resulting in a lower permittivity. In thin films the dielectric grain-size effect also depends, on the one hand, on the electrode geometry, i.e., in-plane vs. out-of-plane [4, 17, 18], and, on the other, on the microstructure, i.e., granular vs. 3

ACCEPTED MANUSCRIPT columnar [26, 27]. The grain size is coupled with the film thickness and usually increases with an increasing thickness over a wide range, resulting in improved dielectric, piezoelectric and ferroelectric properties of the films. Such behavior has been reported for different systems and it seems to be universal for all deposition methods [14-18, 27]. Aygün and co-workers prepared BaTiO3 thin films by

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chemical solution deposition on Cu foils with thicknesses in the 500-nm range [27]. Using an optimized heating procedure (multi-step heating) they promoted the removal of organics, decreased the porosity and increased the lateral grain size from 100 to 185 nm. The kHz-range permittivity increased from ~1400 to a bulk-permittivity value of ~3000. Comparing their data to that in the

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literature and fitting the grain-size dependence of the permittivity with the brick-wall model, the authors concluded that a similar core-shell structure to that in the bulk ceramics is responsible for the

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decrease of the permittivity in Ba1-xSrxTiO3 films with a grain size below 1 µm.

An important parameter that distinguishes thin films from bulk materials is the presence of residual stresses, which may originate from specific growth conditions (growth stresses), defects present in the film, lattice mismatches between the film and the substrate (epitaxial stress) and mismatches in the

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thermal expansion coefficients (TECs) between both (thermal stress) [28]. In polycrystalline thin-film ferroelectrics the thermal stress, which develops upon cooling from the high processing temperatures, usually prevails. These stresses have an important influence on the behavior of ferroelectrics-based

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films and can cause the stabilization of ferroelectricity, i.e., an upward shift of the Curie temperature [29], induced ferroelectricity in SrTiO3 [30] and KTaO3 [31] incipient ferroelectrics, the orientation of

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the spontaneous polarization in certain directions [32], the modification of the domain state and the mobility of domain walls [19] and the stabilization of the phases with a preferred size of the cell in systems with the proximity of thermodynamically stable phases [33, 34], i.e., morphotropic phase boundaries and polymorphic phase transitions. The exact influence depends on the sign of the stress (tensile or compressive) and its magnitude [20, 22, 23]. As a consequence, the piezoelectric, dielectric and ferroelectric properties of the films are greatly modified [33, 34, 35]. The stress dependence of the tunable dielectric properties of polycrystalline films has also attracted attention. In particular, 200-nm-thick (100)-oriented Ba0.5Sr0.5TiO3 thin films prepared on different 4

ACCEPTED MANUSCRIPT substrates with a SrRuO3 bottom electrode showed a linear increase in the kHz permittivity with an increasing thermal expansion coefficient of the substrate, and a very similar dependence was also observed for the tunability, i.e., the electric field dependence of the permittivity [23]. Interestingly, the result is not in complete agreement with the phenomenological calculations, from which a non-

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monotonic, tunability stress dependence is predicted due to an electric-field-induced paraelectricferroelectric phase transformation [36].

There has been a significant effort made to understand and control the functional properties of

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ferroelectric thin films. However, due to the complexity of the topic it is still difficult to predict the exact behavior of functional polycrystalline films and further investigations are needed. In the present

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study we prepared Ba0.5Sr0.5TiO3 thin films on polycrystalline alumina substrates by chemical solution deposition. We observed a strong non-monotonic dependence of the kHz and microwave dielectric properties on the thickness, which was varied from 90 to 400 nm, and explained it in terms of the

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grain-size effect and the presence of the residual tensile stress in the films.

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ACCEPTED MANUSCRIPT 2. Materials and methods The Ba0.5Sr0.5TiO3 (BST) films were prepared by chemical solution deposition. The solution was synthesized from the alkaline-earth acetates (Ba(CH3COO)2, 99.999 %, Sr(CH3COO)2, 99.81 %, both Alfa Aesar, Heysham, United Kingdom) and Ti-butoxide (Ti(OC4H8)4, 99.61 %, Fluka, St. Louis,

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United States). The acetates were dried before use and then dissolved in acetic acid (CH3COOH, 100 %, Merck, Darmstadt, Germany), while the Ti-butoxide was diluted by the 2-methoxyethanol (CH3OCH2CH2OH, 99.3+ %, Sigma Aldrich, St. Louis, United States). The two solutions were mixed

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for 2 hours at room temperature and the concentration of the solution was adjusted to 0.25 M.

The BST solution was deposited on polished alumina substrates (Al2O3, 99.6 %, Coorstek, Golden,

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USA), dried at 200 °C for 2 min, pyrolyzed at 350 °C for 2 min and annealed at 900 °C for 15 min in a rapid-thermal-annealing furnace (RTA, TM100-BT, LPT, Hermsdorf, Germany) with a heating rate of 15 K/s. The deposition/drying/pyrolysis/annealing steps were repeated several times and the final thicknesses were between 90 and 400 nm. For intermediate layers the time of the RTA annealing was

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5 min, although it was 60 min for the final layer. As a reference the BST solution was dried at 60 °C overnight to yield a gel and heated to 900 °C with a heating rate of 10 K/min (STA 409, Netzsch, Selb, Germany).

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The phase composition and orientation of the thin films were analyzed with an X-ray diffractometer (XRD, X'Pert PRO MPD, PANalytical, Almelo, Netherlands) using Cu–Kα1 radiation. The XRD

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patterns were recorded in the 2θ-region from 10 ° to 70 ° using a 1D detector (X'Celerator, PANalytical, Almelo, Netherlands) with a capture angle of 2.122 °. The exposure time for each step was 100 s and the interval between the obtained data points was 0.017 °. The residual stress analysis was performed using a Bruker D8 Discover diffractometer equipped with a VÅNTEC-500 twodimensional (2D) detector. The measurements were performed in the ∼17 to 47 ° and ∼-62 ° to -116 ° 2θ and γ regions, respectively. The samples were tilted in the ψ-range from 0 to 60° with a step of 6 °. At each ψ-angle the samples were rotated around their normal (ϕ-angle) by 360 ° with a step of 45 °. The acquisition time for each measurement was 100 s. A quantitative analysis was performed using

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ACCEPTED MANUSCRIPT LEPTOS Software (Bruker Corporation, Billerica, USA). The measured γ-range was divided into ten sub-ranges and the (110) peaks of the BST, obtained by integration, were fitted with the pseudo-Voigt function. In this way ∼800 points were generated for each sample. The final stress values were calculated from the set of fundamental equations linking the stress tensor components to the

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diffraction cone distortions using a least-square regression [37]. A Young’s modulus E of 80 GPa [38] and a Poisson ratio ν of 0.3 were used. Further details on the residual stress analysis using the 2D XRD method can be found in Ref. 36.

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The surface and cross-section microstructures of the films were analyzed with a field-emission scanning electron microscope (FE-SEM, JSM-7600F, JEOL, Tokyo, Japan). The average lateral grain

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sizes of the films, calculated as the Feret’s diameter, and their standard deviations were determined with a stereological analysis of the surface micrographs on ∼350 grains using ImageTool software (University of Texas Health Science Center at San Antonio).

For the RF-range dielectric characterization, the 750 × 750 µm2 planar capacitors with 3-µm gaps were

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patterned using lift-off photolithography and the Cr/Au electrodes were deposited using magnetron sputtering (5Pascal, Milano, Italy). The capacitance C and the dielectric losses tanδ of the films were measured using an impedance analyzer (HP 4284 A, Keysight, Santa Rosa, USA) at 100 kHz and

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room temperature. The capacitance-voltage characteristics were determined with the following DCbiasing scheme: 0V → + 40 V → 0 V → - 40 V → 0 V. The dielectric permittivity ε' of the films was

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calculated using the modified partial capacitance method (PCM) [39, 40]. The MW-range dielectric properties were determined on non-electroded samples with split-post dielectric resonators (QWED, Warsaw, Poland). The resonators were connected to a network analyzer (HP 8720 ES, Keysight, Santa Rosa, USA) and the 10- and 15-GHz properties were calculated using the numerical method and the software provided by the supplier of the resonators.

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ACCEPTED MANUSCRIPT 3. Results The thickness dependence of the dielectric properties measured at 100 kHz, 10 and 15 GHz is shown in Figure 1. The kHz-permittivity ε' increases from 650 to 1300 as the film thickness increases from 90 to 170 nm, and remains approximately constant up to 240 nm. With a further thickness increase the

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permittivity drops to 970. The kHz-losses tanδ of all the films are below 2 %. The GHz-permittivity follows a similar trend, although the values are slightly lower. The GHz-losses are rather high and range between 0.07 for the thinnest films and 0.16 at 15 GHz for the 210-nm-thick films.

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The DC-voltage dependence of the 100-kHz permittivity of the selected films is shown in Figure 2. The 90-nm-thick film shows the lowest DC-voltage dependence and its tunability n, calculated as the

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ratio of permittivities at 0 and 40 V, is 2.2. The plateau with the highest values of almost 4.0 is observed in the thickness range between 115 and 170 nm. The tunability of the 240-nm-thick films is 3.3; however, with a further thickness increase the DC dependence becomes less pronounced and a tunability of 2.4 is observed in the 400-nm film. In all the films the voltage dependences are

can be observed.

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symmetrical, although a slight hysteresis, which is more evident in the films with a higher permittivity,

The cross-section and plane-view FE-SEM micrographs of selected BST films are presented in Figure

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3. The cross-section microstructure of the 90-nm-thick film consists predominantly of one grain per film thickness. Its surface microstructure is uniform, with an average lateral grain size of 45 nm and

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fine intergranular pores. The columnar cross-sectional microstructure is to a large extent retained with the increasing film thickness; however, some fine, equiaxed grains are also present. The average lateral grain size increases with the increase in the thickness, reaching ∼100 nm in the thickest films. Note the presence of intergranular nano-cracks in the thickest film (marked with an arrow in Figure 3). Figure 4a shows XRD patterns determined in the Θ-2Θ geometry for all the films. Upon annealing at 900 °C all the films crystallize in a pure pseudo-cubic perovskite phase and their peaks have been indexed [41].«

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ACCEPTED MANUSCRIPT With an increasing thickness the intensities of the perovskite peaks increase and a careful comparison of the intensities of the (110) and (200) peaks (Figure 4b) reveals a change in the preferred orientation with the thickness of the films. Up to a thickness of 170 nm the films seem to be randomly or (200) oriented, while above this thickness a clear (110) orientation is observed. Furthermore, as the film

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thickness increases from 90 to 170 nm, the perovskite peaks shift toward higher 2Θ-angles, while with a further increase of the thickness the shifting appears in the opposite direction. Because the films were processed under exactly the same conditions, the shifting of the peaks has to be related to the

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residual stresses.

The above-observed shifts of the perovskite peaks are rather small, making quantification of the

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residual stresses using the 1D XRD geometry unreliable, while a more general 2D XRD method offers improved statistics for the measurement. The 2D XRD frames of the 170-nm-thick BST film measured at different ψ-angles are shown in Figure 5a. The (110) diffraction ring of the film is distinct in all the frames. The frames were integrated around this peak to obtain the conventional intensity-2Θ diffraction patterns and the result is shown in Figure 5b. The shift of the peak maxima towards a lower

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2Θ-angle with increasing ψ-angle is apparent. To evaluate the exact positions, the peaks were fitted with the pseudo-Voigt function and the obtained lattice parameter d vs. sin2ψ plot is shown in Figure 5c. A linear increase of the in-plane lattice parameter is observed, indicating a tensile residual stress in

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the 170-nm-thick BST film [42].

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As described in detail in the experimental part, the films were measured in the 0-60° ψ-range and in the 0-360° Φ-range, producing ∼800 experimental points per sample for the quantitative analysis of the stress. We did not observe any differences in the frames collected at different Φ-angles, indicating equi-biaxial stress in all the films. The analysis results are collected in Figure 6. All the films are under a significant tensile stress. The value is the highest in the thinner films, reaching 380 MPa in the 170nm-thick film, after which it drops sharply between the 170-nm- and 240-nm-thick films to 120 MPa in the 400-nm-thick film.

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ACCEPTED MANUSCRIPT 4. Discussion The dielectric permittivity of the studied films is high, especially in the thickness range between 170 and 240 nm, where a value above 1200 is observed at all frequencies and reaches a peak at 1350 (100 kHz, Figure 1) in the 240-nm-thick film with a grain size of 90 nm. This value is higher than the

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values reported for BST films with a similar composition and grain size, regardless of the deposition method and the electrode configuration. As examples, the reported out-of-plane permittivity of ∼300nm-thick RF-sputtered BST films prepared at 600 °C on platinized silicon substrates (Ba/Sr = 50/50)

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with 82 nm large grains is 760 at 100 kHz [17], while the in-plane permittivity of PLD-deposited 200nm-thick films (Ba/Sr = 60/40) on r-sapphire with grains in the 50–100 nm range is 830 at 10 GHz

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[21]. Besides the grain size and the thickness of the films, additional parameters that strongly influence the permittivity value are the grain morphology and porosity [26, 27, 43, 44]. We ascribe the good dielectric properties of the films to optimized processing conditions, i.e., the separation of the drying/pyrolysis/annealing steps for the efficient removal of the organics and the high heating rate and

[27].

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annealing temperature of 900 °C, resulting in a dense and predominately columnar microstructure

However, the non-monotonic thickness dependence of the permittivity (Figure 1) indicates that

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different effects control the permittivity value at different thicknesses. In Figure 6 we plotted the average lateral grain size G, the residual stress σ, the tunability n and the permittivity ε’, measured at

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100 kHz, as functions of the film thickness. The permittivity increases almost linearly in the thickness range between 90 and 170 nm, where the lateral grain size increases from 45 to 75 nm. In the same thickness range the porosity is reduced. However, the trend of permittivity increase is similar to the one observed in Ba0.3Sr0.7TiO3 thin films on alumina substrates, i.e., a grain-size increase from 40 to 80 nm results in a doubling of the dielectric permittivity, meaning that the grain size clearly controls the dependence of the dielectric permittivity [43]. The residual tensile stress in a 90-nm-thick film is 344 MPa, and this value increases to 378 MPa in the case of the 170-nm-thick film. The tensile stress in BST films is a consequence of the mismatch in the TECs of the alumina substrate and the film, with values of ~8×10-6 /K [45] and 10.5×10-6 /K [36], respectively. 10

ACCEPTED MANUSCRIPT As the thickness and grain size increase from 170 to 240 nm and from 75 to 90 nm, respectively, only a slight change in the permittivity is observed (Figure 1 and Figure 6), which indicates a deviation from the previously observed grain-size effect. Note that a strong decrease of the residual stress is observed in the same thickness range.

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A further increase of the thickness to 400 nm is accompanied by a stagnation of the grain size, a drop of the permittivity and reduced values of the residual tensile stress in the films. When the film thickness reaches some critical value, the internal stresses frequently relax as a result of the

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deformation processes induced by the thermally activated motion of the atoms and the defects, resulting in hillock formation, cracking of the film or in a film-substrate fracture [28, 46]. In our case,

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the stress relaxation occurs via the formation of intergranular cracks, as is evident from the surface micrographs of the films with thicknesses equal to, or greater than, 310 nm (Figure 7, Figure 3). Note that the cracks extend along many grains, extending up to the micron range. Based on the stress decrease we can reasonably assume that nano-cracks may also be present in the films with thicknesses between 170 and 240 nm films. A plateau of permittivity in the 170–240-nm film-thickness range and

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its further decrease for thicknesses greater than 240 nm is thus attributed to the existence of cracks, which behave as an additional low-permittivity phase. It was shown that a volume fraction of less than 1 % of intergranular cracks in PbZrO3 ceramics strongly reduced the permittivity. Such a decrease of

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the permittivity can be explained by the brick-wall model [5, 47].

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The high dielectric permittivity obtained with the improved microstructure, i.e., high density and predominantly columnar grains, leads to an enhanced voltage tunability, consistent with the literature [4]. The voltage tunability at 40 V for 90-nm-thick films is high, about 2, and it increases to around 4 in the thickness range from 115 to 170 nm. As the film thickness increases further, the tunability gradually decreases, which we attribute to the presence of cracks and the consequent reduction in the residual stresses. We note that in the 170–240-nm range the drop in the tunability coincides with the plateau of permittivity. The origin of a slight hysteresis, which is observed in the films with a higher permittivity, is not completely explained, but could be related to the presence of nano-polar regions

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ACCEPTED MANUSCRIPT [48], an electrically induced ferroelectric phase [36] or a slow dielectric relaxation appearing upon electric-field cycling. 5. Summary

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The dielectric properties of Ba0.5Sr0.5TiO3 thin films with thicknesses in the range from 90 to 400 nm were studied. The results show that the dielectric properties, measured in the kHz and GHz ranges, are strongly influenced by the grain size and the residual stress, but their contributions exhibit different thickness dependences, and may be divided into three groups. In particular, for the thinnest films, the

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increase of the grain size with increasing thickness, from 90 to 170 nm, coincides with the increase of permittivity and tunability, in agreement with the dielectric grain-size effect. The tensile residual

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stress, which develops as a consequence of the thermal expansion mismatch between the substrate and the film, is high and increases with increasing thickness.

In the next thickness range, between 170 and 240 nm, the grain size increases slightly with an increasing thickness and the permittivity reaches a plateau, while the tunability decreases. In parallel, a

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strong decrease of the initially high value of the tensile residual stress occurs, indicating some stress relaxation. The stress decrease becomes even more pronounced in the thickest films (> 240 nm). Here, the grain size remains almost unchanged, and the permittivity decreases. The quite abrupt drop

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in the residual stress indicates a progressive stress relaxation, evidenced by the formation of intergranular cracks in the thickest films, whose density increases with an increasing thickness. The

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reduction of the dielectric properties in this thickness range is thus related to the presence of cracks. The present systematic analysis of the main factors influencing dielectric properties of the polycrystalline (Ba,Sr)TiO3 thin films, i.e., grain-size and residual biaxial stress, reveals that these degrees of freedom are not independent but strongly correlated with the thickness of the films. This fact has to be carefully considered when the films are designed for use as varactors in microwave antennas – see for example Ref. 49.

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ACCEPTED MANUSCRIPT Acknowledgements This work was supported by the Research Agency of the Republic of Slovenia (P2-0105, PR-05026,

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J2-5482).

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ACCEPTED MANUSCRIPT [20] T. R. Taylor, P. J. Hansen, B. Acikel, N. Pervez, R. A. York, S. K. Streiffer, J. S. Speck, Impact of thermal strain on the dielectric constant of sputtered barium strontium titanate thin films, Appl. Phys. Lett. 80 (2002) 1978-1980. [21] E. A. Fardin, A. S. Holland, K. Ghorbani, E. K. Akdogan, W. K. Simon, A. Safari, J. Wang,

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ACCEPTED MANUSCRIPT [38] T. -H. Fang, W.-J. Chang, C. -M. Lin, L. -W. Ji, Y. -S. Chang, Y. -J. Hsiao, Effect of annealing on the structural and mechanical properties of Ba0.7Sr0.3TiO3 thin films, Mater. Sci. Eng. A. 426 (2006) 157-161. [39] O. G. Vendik, S. P. Zubko, M. A. Nikol’skii, Modeling and calculation of the capacitance of a

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Capacitors, IEEE Trans. Microw. Theory Tech. 63 (2015) 891-896.

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and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film

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ACCEPTED MANUSCRIPT Figure captions Figure 1: Dielectric permittivity ε’ and losses tanδ of the BST films with thicknesses from 90 to 400 nm measured at 100 kHz, 10 and 15 GHz. Lines between the experimental points are guides to the eyes only.

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Figure 2: Permittivity-voltage curves measured in the + 40 V to – 40 V range for the 90-, 115-, 170-, 240- and 400-nm-thick films, denoted with thickness values without the nm unit.

Figure 3: FE-SEM micrographs of the cross-section (left) and plane-view (right) microstructures of the

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the thicker films.

Figure 4: a) XRD patterns of the BST thin films on alumina substrates. The perovskite peaks are denoted with Miller indices. An XRD pattern of the bare alumina substrate is added. b) The (110) and (200) diffraction peaks of the BST thin films. Diffraction peaks of the BST gel heated to 900 °C are added as a reference together with the respective positions from the JCPDS database [41]. The arrows

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indicate shifting of the perovskite peaks. * - subtracted peaks of the alumina. Figure 5: a) The 2D-XRD frames of the 170-nm-thick BST film measured at different ψ-angles shown in the -62 ° to -116 ° γ-range and Φ = 0 °. b) The conventional XRD diffractograms around the (110)

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peaks obtained by the integration of 2D frames in the γ-range from -73 ° to -107 °. c) The d vs. sin2ψ In a) the (110)

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plot obtained from the positions of the peaks calculated from the 2D frames.

diffraction rings of the BST films are denoted. Other strong rings correspond to the Al2O3 substrate. In c) the line is a linear fit to the experimental points. Figure 6: The average lateral grain size G, residual stress σ, tunability n, calculated as a ratio of the 100-kHz permittivity at 0 V and at 40 V, and the low-frequency dielectric permittivity ε’, extracted from Figure 1, plotted against the film thickness. Lines between the experimental points are guides to the eyes only.

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ACCEPTED MANUSCRIPT Highlights The kHz dielectric permittivity of Ba0.5Sr0.5TiO3 thin films is as high as 1350.

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Broadband dielectric properties show non-monotonic film-thickness dependence.

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Dieletric grain-size effect is observed only in the thinnest films (≤ 170 nm).

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Residual biaxial stress was measured and its value decreases in thicker films.

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Stress relaxation occurs via crack formation in the films thicker than 170 nm.

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