Correspondence and requests for materials should be addressed to

J.-H.C. (#) and C.S.H. (*)

Supplemental Information for

Strain evolution of each type of grains in poly-crystalline (Ba,Sr)TiO3 thin films grown by sputtering

Woo Young Park,1 Min Hyuk Park,1 Jong Ho Lee,1Jung Ho Yoon,1Jeong Hwan Han,1 Jung-Hae Choi,#2 and Cheol Seong Hwang*1

1WCU hybrid materials program, Department of Materials Science and Engineering, and Inter-university Semiconductor Research Center, Seoul National University, Seoul 151-744, Korea,2Electronic Materials Research Center, Korea Institute of Science and Technology, Seoul 130-650, Korea

Table SI shows the film thickness, measured by ellipsometry, and cation composition ratio, measured by XRF, of the BST films deposited at different substrate temperatures.

Table SI. Thickness and cation composition ratios of the BST films deposited at different substrate temperatures

Substrate Temp.
(Dep. Time) / Thickness (nm)
(growth rate) / / /
338 oC (175 min) / 120.2 (0.687 nm/min) / 1.12 / 0.482 / 0.529
402 oC (140 min) / 124.6 (0.890 nm/min) / 1.08 / 0.477 / 0.519
431 oC (135 min) / 120.2(0.890 nm/min) / 1.05 / 0.475 / 0.513
462 oC (156 min) / 119.3(0.765 nm/min) / 1.08 / 0.467 / 0.518
505 oC (180 min) / 124.1(0.689 nm/min) / 1.15 / 0.473 / 0.535

Error range of the XRF measurement

-Ti/(Ba+Sr): ~0.0020

-Ba/(Ba+Sr): ~ 0.0005

-Ti/(Ba+Sr+Ti): ~ 0.0006

Figure S1 shows the -2 XRD patterns of the BST films deposited at different substrate temperatures.

Figure S1.The -2 XRD patterns of the BST films deposited at different substrate temperatures.

The following shows the procedure for calculating the strain and stiffness tensors along the different crystallographic directions based on the classical elastic theory. The calculation results are included in table I of the main text.

Figure S2 shows the microstructures of the Pt and BST films. The atomic force microscopy image of the Pt film is shown in Fig. S2a. Figure S2b and c show the atomic force microscopy images of the BST films grown at a Tsof 338 and 505 oC, respectively. Figure S2d and e show the cross-section TEM image of the BST film grown at 505 oC. The upper panels show the selected area diffraction patterns of the grains indicated by triangles in the bright field TEM images in lower panels. The arrows indicate the direction which is normal to the film surface. Grains indicated in 2d and 2e have [011]and [111] directions, respectively, along the direction normal to the surface. The rougher grains are mostly [111]-oriented while flat grains are mostly [011]- or [100]-oriented. The BST film shows a highly dense and columnar microstructure with no notable voids.

Figure S2. (a)The AFM image of the Pt film (top view). (b) and (c) show the AFM images of the BST films grown at a Ts of 338 and 505 oC, respectively (bird’s eye view). (d) and (e) show the cross-section TEM image of the BST film grown at 505 oC. The upper panels show the selected area diffraction patterns of the grains indicated by triangles in the bright field TEM images in lower panels. The arrows indicate the direction which is normal to the film surface. Grains indicated in (d) and (e) have [011]and [111] directions, respectively, along the direction normal to the surface.

Below in Fig. S3, the possible reasons for different strains along different orientations under the in-plane stress are discussed. For an easier understanding, the orientation of the TiO6 octahedron in Fig. S3a and b is set as that the 002 and 110 directions, pointing upwardswhereas the [111] direction in Fig. S3c is perpendicular to the paper plane. When a tensile stress is applied along the x-y plane, in Fig. S3a, the four oxygen ions on that plane become farther away but the other two oxygen ions above and below the plane become closer. At the center of the TiO6 octahedron a Ti4+ ion presents so that this contraction in the distance between the two oxygen ions may increase the total energy less compared to the other cases. For Fig. S3b, the contraction along the z-direction results in a decrease in the distance between the two O2- ions with no intervening Ti4+ ion. Thus, this may impose a larger energy increase in the system. Moreover, this may be even more serious for Fig. S3c. For this case, the contraction along the z-direction results in a decrease in the distance between the two oxygen planes where the intervening Ti4+ ions displaces from the location,which directly connects upwards and downwards oxygen ions. This comparison may provide the qualitative understanding on the different compliance along the different crystallographic directions.

Figure S3.The crystal structure with spherical ions (upper panel) and that with TiO6 octahedrons (bottom panel) of (a) [002]-, (b) [110]-, and (c) [111]-oriented (Ba,Sr)TiO3, respectively.

The following shows the method on how the unstrained lattice parameter, a0, for each type of grain was determined by the sin2 method. The specific sin2 value determined by the following equations corresponds to the direction where the a0 can be determined. The a0 value for each type of graincan be determined from the linear fitted graphs shown in Fig. 1 of the main text or Fig. S5. The necessary compliance values for calculating the specific sin2 values are listed in table SII, and the z/0values of Ba0.48Sr0.52TiO3 and Ba0.47Sr0.53TiO3 calculated from the elastic constants of BaTiO3 and SrTiO3 from literature are listed in table SIII. The calculated sin2 values are listed in table SIV., and the calculated a0 of BST (002), (110), (111) and Pt grains are tabulated in table S V.

Table SII. Elastic constants of BaTiO3, SrTiO3, Ba0.5Sr0.5TiO3, Ba0.48Sr0.52TiO3, Ba0.47Sr0.53TiO3, and Pt.

Parameters / BaTiO3 / SrTiO3 / Ba0.5Sr0.5TiO3 / Ba0.48Sr0.52TiO3 / Ba0.47Sr0.53TiO3 / Pt
S11(10-12m2/N) / 8.30 / 3.52 / 4.33 / 5.81 / 5.77 / 7.34
S12(10-12m2/N) / -2.70 / -0.85 / -1.39 / -1.74 / -1.72 / -3.08
S44(10-12m2/N) / 9.24 / 7.87 / 5.01 / 8.53 / 8.51 / 13.07

N.A. Pertsev, A. G. Zembilgotov, and A. K. Tagantsev, Phys. Rev. Lett. 80, 1988 (1998)

N.A. Pertsev, A. K. Tagantsev, and N. Setter, Phys. Rev. B 61, R825 (2000)

L. B. Freund and S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge, 2003.

Table SIII. z/0 of Ba0.48Sr0.52TiO3 and Ba0.47Sr0.53TiO3 calculated from the elastic constants of BaTiO3 and SrTiO3 from literature.

Ba/Sr = 48/52

SrTiO3
BaTiO3 / Pertsev et al. / Poindexter et al. / Boudali et al. (FP-LAPW) / Boudali et al. (PW-PP) / Bell et al. / Piskunov et al. (PPE) / Piskunov et al. (PWGGA)
Pertsev et al. / [002]: -0.853
[110]: -0.563
[111]: -0.431 / [002]: -0.836
[110]: -0.572
[111]: -0.455 / [002]: -0.847
[110]: -0.585
[111]: -0.469 / [002]: -0.842
[110]: -0.573
[111]:-0.453 / [002]: -0.852
[110]: -0.559
[111]: -0.425 / [002]: -0.840
[110]: -0.573
[111]: -0.454 / [002]: -0.844
[110]: -0.571
[111]: -0.449
Berlincourt & Jaffe / [002]: -0.831
[110]: -0.598
[111]: -0.498 / [002]: -0.817
[110]: -0.605
[111]: -0.516 / [002]: -0.827
[110]: -0.615
[111]: -0.526 / [002]: -0.823
[110]: -0.605
[111]: -0.513 / [002]: -0.831
[110]: -0.594
[111]: -0.493 / [002]: -0.821
[110]: -0.605
[111]: -0.514 / [002]: -0.824
[110]: -0.603
[111]: -0.510

Ba/Sr = 47/53

SrTiO3
BaTiO3 / Pertsev et al. / Poindexter et al. / Boudali et al. (FP-LAPWa) / Boudali et al. (PP-PWb) / Bell et al. / Piskunov et al. (PBEc) / Piskunov et al. (PWGGAd)
Pertsev et al. / [002]: -0.850
[110]: -0.563
[111]: -0.433 / [002]: -0.833
[110]: -0.572
[111]: -0.457 / [002]: -0.844
[110]: -0.586
[111]: -0.472 / [002]: -0.839
[110]: -0.573
[111]: -0.456 / [002]: -0.849
[110]: -0.559
[111]: -0.427 / [002]: -0.837
[110]: -0.573
[111]: -0.456 / [002]: -0.840
[110]: -0.571
[111]: -0.451
Berlincourt & Jaffe / [002]: -0.829
[110]: -0.598
[111]: -0.499 / [002]: -0.815
[110]: -0.605
[111]: -0.517 / [002]: -0.825
[110]: -0.615
[111]: -0.527 / [002]: -0.820
[110]: -0.605
[111]: -0.515 / [002]: -0.828
[110]: -0.594
[111]: -0.494 / [002]: -0.818
[110]: -0.605
[111]: -0.515 / [002]: -0.822
[110]: -0.603
[111]: -0.511

N.A. Pertsev, A. G. Zembilgotov, and A. K. Tagantsev, Phys. Rev. Lett. 80, 1988 (1998)

D. Berlincourt and H. Jaffe, Phys. Rev. 111, 143 (1958)

N.A. Pertsev, A. K. Tagantsev, and N. Setter, Phys. Rev. B 61, R825 (2000)

E. Poindexter and A. A. Giardini, Phys. Rev. 110, 1069 (1958)

A. Boudali et al., Phys. Lett. A 373, 879 (2009)

R. O. Bell, and G. Ruppercht, Phys. Rev. 129, 90 (1963)

S. Piskunov, E. Heifets, R. I. Eglitis, G. Borstel, Comput. Mater. Sci. 29, 165 (2004)

aFP-LAPW: Full-Potential Linearized Augmented Plane Wave

bPP-PW: Pseudo-Potential Plane Wave

cPBE: Perdue-Burke-Ernzerhof method

dPWGGA: Perdue-Wang Generalized Gradient Approximation

Table S IV. Calculated sin2 values for each type of grainfor the cases of Ba/Sr ratios of 48/52 and 47/53

Ba/Sr / [002] / [110] / [111]
48/52 / 0.486 / 0.347 / 0.256
47/53 / 0.485 / 0.312 / 0.255

Table S V. The calculated a0(in nm) of BST (002), (110), (111) and Pt grains

Ts (oC) / (002) / (110) / (111) / Pt
338 / 0.4018 / 0.4019 / 0.4020 / 0.3922
402 / 0.4008 / 0.4013 / 0.4000 / 0.3921
431 / 0.4006 / 0.4008 / 0.3997 / 0.3921
462 / 0.3999 / 0.3999 / 0.3984 / 0.3921
505 / 0.3989 / 0.3984 / 0.3969 / 0.3922

Figure S4demonstratesthe XRD spectra in the -2 mode of the BST films with various thicknesses grown at a Ts of 505oC. The BST grains have three major orientations ([200], [110], and [111]) along the normal direction to the substrate surface, and did not show any notable difference in their XRD patterns with increasing thickness.

Figure S4.XRD spectra in the -2 mode of the BST films with various thicknesses grown at a Ts of 505oC. Right hand figure shows the schematics of the crystallographic structure of the polycrystalline BST film.

Figure S5 shows the variations of the cation composition ratio of the BST films with various thicknesses grown at a Ts of 505oC. The average Ba/(Ba+Sr) and Ti/(Ti+Ba+Sr) ratios are 0.47 and 0.54, respectively.

Figure S5. (a) The variations of the atomic ratio of Ba/(Ba+Sr) and (b) that of Ti/(Ba+Sr+Ti) of the BST films with various thicknesses grown at a Ts of 505oC, respectively.

Figure S6 shows the a0 vs. sin2 plots of the Pt (111) grains and BST (111), (110), and (002) type grains for the films with different thicknesses grown at 505oC.

Figure S6.The a0 vs. sin2plots of (a) the Pt (111) grains and (b) BST (002), (c) BST (110), and (d) BST (111) type grains for the films with different thicknesses grown at 505oC. Right hand figure shows the schematics for the experimental arrangement.

1