- Email: [email protected]
Domain configurations in ferroelectric PbTiO3 thin films: The influence of substrate and film thickness
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Solid State Ionics 75 ( 1995 ) 43-48
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Domain configurations in ferroelectric PbTi03 thin films: The influence of substrate and film thickness S. Stemmer a,*,SK. Streiffer a, F. Ernst a, M. Riihle a, W.-Y. Hsu b, R. Raj b aMax-Planck-Institut ftir MetaNforschung, Institut ftir Werkstoffwissenschaft, Seestraje 92, 70174 Stuttgart, Germany b Cornell University, Department of Materials Science and Engineering, Bard Hall, Ithaca, NY 14853-1510, USA
Abstract Using transmission electron microscopy, we have compared the domain configurations in epitaxial, ferroelectric PbTiO, films grown on different substrates and to different film thicknesses. These configurations change considerably between the different samples. In addition, we have characterized the film/substrate interfaces by high-resolution transmission electron microscopy. It is proposed that the elastic properties of the substrate play a role in determining the domain configuration by influencing the accommodation of tilts of the film lattice. Keyworcis: Domain configuration; Film/substrate
interfaces; Ferroelectrics, HRTEM
1. Introduction
Domain configurations and domain walls in epitaxial, perovskite-type ferroelectric thin films play an important role in determining much of a film’s macroscopic behavior. For ferroelectrics such as PbTiOJ, film properties such as the saturation polarization and the coefficient of second harmonic generation depend strongly on the volume fraction of material with the c-axis of the tetragonal unit cell approximately parallel to the substrate surface, the so-called a-domains [ 2,6]. For many applications, films with the c-axis oriented normal to the substrate surface are necessary, because the spontaneous polarization lies along this axis, while the dielectric constant is smallest and the pyroelectric coefficient is largest in this direction. However, films generally contain a certain percentage of u-domains [ 1,2,6]. * Corresponding author.
The u-domains form during the cooling of a film, which is typically deposited at temperatures above its Curie temperature, Tc. The inclusion of u-domains in the film is a mechanism to relieve the strain generated by the phase transformation of the material from the high-temperature, cubic, paraelectric structure to the tetragonal, ferroelectric modification. Models based on free-energy considerations of this twinning transformation under the constraints imposed by a rigid substrate have been proposed. These models predict a-domain widths and volume fractions as a function of variables such as film thickness and epitaxial and thermal expansion mismatch with the substrate [3,5,8]. X-ray and transmission electron microscopy (TEM) studies show that the distribution and volume fraction of a-domains depend on the choice of substrate [ 2,9,11], in qualitative agreement with these models. We have used TEM to examine factors influencing the size and distribution of u-domains in epitaxial,
0167-2738/95/$09.50 0 1995 Elsevier Science Publishers B.V. All rights reserved. SSDIO167-2738(94)00151-O
44
S. Stemmer et al. / Solid State Ionics 75 (I 995) 43-48
ferroelectric PbTi03 thin films. To investigate substrate effects, PbTi03 films were grown on bare (001 )-oriented MgO single crystals and on (00 1) MgO single crystals covered with epitaxial SrTi03 or epitaxial Pt. In addition, the effects of film thickness on domain configuration were examined by characterizing films deposited to different thicknesses onto (00 1 ) SrTi03 single crystals.
2. Experimental The PbTiOJ films were grown by pulsed laser ablation at a substrate temperature of 600°C and were found to be stoichiometric and fully perovskite phase [ 21. Platinum interlayers of 300 nm thickness were deposited by rf magnetron sputtering, while pulsed laser deposition was used to grow 30 nm thick SrTi03 interlayers. The PbTi03 films on bare MgO, on Pt/MgO and on SrTiOJ/MgO had thicknesses of about 150 nm, while the PbTi03 films grown on SrTi03 were deposited to thicknesses of 87 and 200 nm. All deposited films grew predominantly with their unit cell axes aligned parallel to the cell axes of the substrate. Plan-view TEM samples were fabricated by back-side thinning and dimpling, and then ion-beam milling at 6 kV to perforation. Cross-sectional samples were prepared by a technique described in [ lo]. For conventional microscopy a JEM 2000FX (JEOL) operated at 200 kV was used, and a JEM 4000EX (JEOL) operated at 400 kV was used for high-resolution examination of the specimens.
3. Results and discussion Fig. 1 shows plan-view TEM images for PbTi03 films grown on bare MgO, Pt/MgO and SrTi03/ MgO. The four types of equivalent { 101) twin boundaries between the c-axis oriented matrix and the u-domain lamellae exhibit a fringe contrast in the thicker parts of the TEM sample because they are inclined at an angle to the plane of the substrate surface. The films grown on the three different types of substrates show differences in average width W, length L, and number density D of the a-domains. Films grown on Pt contain u-domains that are larger in width and length and lower in density than those
Fig. 1. Plan-view TEM image showing 90” domain walls in PbTi03 films on (a) bare MgO, (b) SrTiOJMgO, and (c) Pt/MgO. The 90” domain walls are tilted 47” with respect to the film plane (wall planes lie along the { 101) twin planes) and project along the indicated [ 1001 and [OlO] directions, respectively.
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S. Stemmer er al. /Solid State Ionics 75 (1995) 43-48
Table I Measured a-domain lengths, widths and densities for the three different kinds of samples and the standard error for the measurements, defined as the standard deviation divided by the square root of the number of measurements (given in parentheses).
average a-domain length (nm) average a-domain width (nm) average a-domain density (m-‘)
PbTiO,/MgO
PbTiOJSrTiOJMgO
PbTiO,/Pt/MgO
130?12(32) 17+ 1.9( 17) 1.2* lOI
174f9(49) 18*0.9(42) 6.5x lOI
587+35(78) 32*2.7(44) l.lXlO”
in the other films. Table 1 summarizes average values taken from different micrographs for the parameters W, L, and D. For our three types of samples the lattice mismatches (defined as 2 (dPb=ioj - dsubstrate)/ ( dPbTiO3 + &bstrate ) ) between the lattice parameter of the substrate and the bulk value of the c-axis (u-axis) of PbTi03 are: 1.4% (7.7%) for growth on MgO, -5.7% (0.54%) for growth on Pt, and -6.2% (0.15%) for growth on SrTi03. Pt and SrTi03 match closely the u-axis of PbTi03 below T, and with the cubic lattice parameter of PbTi03 above T,:. Large differences in a-domain size and density are observed between the films on Pt and on SrTi03 despite similar lattice mismatches for the two substrates. The films on MgO and on SrTi03 appear rather similar. Fig. 2 shows typical TEM images obtained from plan-view samples of the two films grown on SrTi03. In the thicker film the average width and length of the u-domains are larger, while the average u-domain density is smaller than in the thinner film. Table 2 gives the values for the three parameters W, L and D for these two film thicknesses. In thicker films with larger u-domains, internal twinning of the a-domains is occasionally observed, resulting in a-u-domain walls. In order to understand these variations, the different, competing free energy terms, whose minimization determines the domain structure under equilibrium conditions, must be known. Among these free energies are: (i) the thermodynamic free energy of the phase transformation, (ii) the energy associated with the interaction of the film polarization with either an insulating (bare MgO or SrTiOJMgO) or conducting (Pt/MgO) substrate [ 41, (iii) the strain energy resulting from thermal contraction differences between film and substrate, (iv) the energy stored at the film-substrate interface, (v) the strain energy resulting from elastic accommodation of the
Fig. 2. Plan-view TEM images of PbTiO, films with two different film thicknesses on SrTiOr: (a) 87 nm and (b) 200 nm.
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S. Stemmer
et al. /Solid
State Ionics
75 (1995) 43-48
Table 2 Measured a-domain lengths, widths and densities for the two different film thickness of PbTi03 on SrTiO, and the standard error fat. the measurements, defined as the standard deviation divided by the square root of the number of measurements (given in parentheses) PbTi03 film thickness
87 nm
200 nm
average a-domain length (nm) average a-domain width (nm) average a-domain density (mW2)
120+7(39)
310+26(87)
llk4(39) 8.23+ lOI
19f 1.6(93) 2.67f lOI
Fig. 3. Cross-sectional HRTEM image of PbTiOs on MgO along the ( 100) zone axis. The image shows an a-domain intersecting the film/substrate interface, and the lattice tilt (indicated by a solid line) in the a-domain. The 90” domain walls enclosing the a-domain are marked by arrows.
u-domains, and (vi ) the twin boundary energy. Because films on Pt and SrTi03 have similar lattice mismatches but different domain contigurations, we conclude that the elastic and electrical properties of the substrate, in addition to film/substrate lattice mismatch, are important in explaining the observed u-domain sizes and their spatial distribution. In particular, the elastic properties of the substrate affect the energy needed for accommodation of the lattice tilt of the different domains with respect to the substrate (discussed below), and the misfit dislocation energy for films thicker than the critical thickness for strain relief, h,. With regard to the films of different thicknesses, for thicker films the interfacial energy terms (electrical and elastic properties of the substrate, lattice mismatch between film and substrate) become less important compared to the remaining energy terms. For SrTi03 as a substrate, this
results in an increasing volume fraction of u-domains with thickness. We now consider tilts of the film with respect to the substrate. As a result of the tetragonality of PbTi03, upon crossing from an u-domain to a c-domain the crystal axes are interchanged through an angle different from 90”. This results in a geometrically necessary tilt of the film lattice relative to the substrate lattice. This can be seen in the HRTEM image of Fig. 3, which shows a finite width u-domain intersecting an MgO substrate. The lattice tilt introduces an interaction with the substrate that may be considered in terms of either a dislocation wall or a disclination dipole [ 71. Tilts opposite to those in the udomains are also required in the c-axis matrix to avoid the buildup of long-range strains. However the tilts in the u-domains are much larger because of their small width. Unfortunately, the roughness of the MgO
S. Stemmer et al. /Solid State Ionics 75 (1995) 43-48
substrate surface makes it impossible to determine the exact accommodation mechanism of the tilt from this image. Further, it is expected that the mechanism depends on the width of the a-domain. a-domains in PbTi03 grown on Pt/MgO were also observed to intersect the film/substrate interface with a finite width. Fig. 4 shows an interfacial region of a film on a SrTi03 single crystal. In contrast to MgO, this interface is atomically flat over a large part of the image. The a-domains are usually found to become narrow and form a point when they reach the SrTiOJtilm interface, as seen in this micrograph. De Veirman et al. [ 111 have found similar behavior for films grown on La0.,Sr0.,Co03. In contrast, for films grown on LaA103, they observe domains intersecting the substrate with a finite width as we do for films on Pt and on MgO. The Pt and LaA103 both appear as atomically smooth as the SrTi03; thus it is unlikely that substrate roughness is the sole factor contributing to this effect. Further, there is no obvious correlation of the a-domain width at the substrate with lattice mismatch or substrate conductivity. The different behaviors at the interfaces of the different substrates are not yet understood. The mechanism for the accommodation of the misfit strain resulting from the lattice mismatch between the film and the substrate must also be known
47
for the different domains. For the given film thicknesses it is reasonable to assume that the majority of the misfit strain is relaxed prior to the phase transformation. For the case of PbTi03 on SrTi03, the expected misfit dislocation spacing is large because of the small misfit and therefore the dislocations are difficult to detect. Another important aspect of domain structure that must be considered is the needle shape of the a-domain lamellae. To form the domain ends, defects must be incorporated into the coherent domain walls, e.g. dislocations and twinning steps [ 12 1. Fig. 5 is an HRTEM image of a domain end obtained from a cross-sectional sample and shows an edge dislocation at the termination. This wall termination energy must be included in the minimization of the free energy terms that determine the domain configuration.
4. Conclusion We have used TEM to study the variations in domain structures in PbTi03 films grown on different substrates and to different thicknesses, and characterized the substrate/film interfacial region by HRTEM. In addition to lattice mismatch, the elastic properties of the substrate influence the domain
Fig. 4. Cross-sectional HRTEM image of PbTi03 on SrTiOJMgO along the ( 100) zone axis, showing a c-axis oriented region of the film containing an a-domain which terminates before intersecting the substrate. The 90” domain walls enclosing the a-domain are marked by arrows.
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S. Stemmer et al. /Solid State Ionics 75 (1995) 43-48
Fig. 5. HRTEM image of an a-domain end in a cross-sectionalsample along the (010) zone axis. The 90” domain walls enclosing the adomain are marked by arrows.
structures because of the elastic interaction between film and substrate due to the tilt of the film lattice. Comparison between films on Pt/MgO and SrTiOJ MgO indicates that growth on an elastically softer and conducting substrate results in a film with larger adomains that are also fewer in number. To evaluate the influence of lattice mismatch between film and substrate on domain configuration, more work is needed to determine the amount of misfit strain relieved by dislocation formation and by domain formation respectively, as a function of temperature. More measurements of films with different film thicknesses are necessary to verify the existing models and to determine relevant energy terms.
Acknowledgment
SK. Streiffer would like to thank the Alexander von Humboldt-Stiftung for financial assistance. We also thank the Max-Planck Gesellschaft for support. R. Raj and W.-Y. Hsu received support from the National Science Foundation, Award No. DMR-9 I? 1654,
through the Materials University.
Science
Center
at Cornell
References [ 1] Y. Gao, G. Bai, K.L. Merkle, Y. Shi, H.L.M. Chang and D.J. Lam, J. Mat. Res. 8 (1992) 145. [2] W.-Y. Hsu, Ph.D. Thesis (Cornell University, 1994). [3] B.S. Kwak, A. Erbil, B.J. Wilkens, J.D. Budai, M.F. Chisholm and L.A. Boatner, Phys. Rev. Lett. 68 ( 1992) 3733. [4] W. Pompe, private communication. [ 51 W. Pompe, X. Gong, Z. Suo and J.S. Speck, J. Appl. Phys. 74 (1993) 6012. [ 6 ] R. Ramesh, T. Sands and V.G. Keramidas, Appl. Phys. Lett. 63 (1993) 731. [ 71 A.E. Romanov and V.I. Vladimirov, Disclinations in Crystalline Solids, in: Dislocations in Solids 9, ed. F.R.N. Nabarro (North-Holland, Amsterdam, 1992 ) . [ 8 ] J.S. Speck and W. Pompe, J. Appl. Phys. 76 ( 1994) 466. [9] S. Stemmer, S.K. Streiffer, E. Ernst, R. Raj and M. Riihle, J. Mat. Res., submitted for publication. [lo] A. Strecker, U. Salzberger and J. Maier, Prakt. Metallogr. 30 (1993) 482. [ll]A.E.M. de Veirman, J. Timmers, F.J.G. Hakkens, J.F.M. Cillesen and R.M. Wolf, Philips J. Res. 47 ( 1993) 185. [ 12 ] Yimei Zhu, M. Suenaga and J. Tafto, Philos. Mag. A 67 (1993) 1057.
L
B
SDllD
-3
me
.
_
STATE
_a
t
1
4,_
EISEVIEK
Solid State Ionics 75 ( 1995 ) 43-48
mms
Domain configurations in ferroelectric PbTi03 thin films: The influence of substrate and film thickness S. Stemmer a,*,SK. Streiffer a, F. Ernst a, M. Riihle a, W.-Y. Hsu b, R. Raj b aMax-Planck-Institut ftir MetaNforschung, Institut ftir Werkstoffwissenschaft, Seestraje 92, 70174 Stuttgart, Germany b Cornell University, Department of Materials Science and Engineering, Bard Hall, Ithaca, NY 14853-1510, USA
Abstract Using transmission electron microscopy, we have compared the domain configurations in epitaxial, ferroelectric PbTiO, films grown on different substrates and to different film thicknesses. These configurations change considerably between the different samples. In addition, we have characterized the film/substrate interfaces by high-resolution transmission electron microscopy. It is proposed that the elastic properties of the substrate play a role in determining the domain configuration by influencing the accommodation of tilts of the film lattice. Keyworcis: Domain configuration; Film/substrate
interfaces; Ferroelectrics, HRTEM
1. Introduction
Domain configurations and domain walls in epitaxial, perovskite-type ferroelectric thin films play an important role in determining much of a film’s macroscopic behavior. For ferroelectrics such as PbTiOJ, film properties such as the saturation polarization and the coefficient of second harmonic generation depend strongly on the volume fraction of material with the c-axis of the tetragonal unit cell approximately parallel to the substrate surface, the so-called a-domains [ 2,6]. For many applications, films with the c-axis oriented normal to the substrate surface are necessary, because the spontaneous polarization lies along this axis, while the dielectric constant is smallest and the pyroelectric coefficient is largest in this direction. However, films generally contain a certain percentage of u-domains [ 1,2,6]. * Corresponding author.
The u-domains form during the cooling of a film, which is typically deposited at temperatures above its Curie temperature, Tc. The inclusion of u-domains in the film is a mechanism to relieve the strain generated by the phase transformation of the material from the high-temperature, cubic, paraelectric structure to the tetragonal, ferroelectric modification. Models based on free-energy considerations of this twinning transformation under the constraints imposed by a rigid substrate have been proposed. These models predict a-domain widths and volume fractions as a function of variables such as film thickness and epitaxial and thermal expansion mismatch with the substrate [3,5,8]. X-ray and transmission electron microscopy (TEM) studies show that the distribution and volume fraction of a-domains depend on the choice of substrate [ 2,9,11], in qualitative agreement with these models. We have used TEM to examine factors influencing the size and distribution of u-domains in epitaxial,
0167-2738/95/$09.50 0 1995 Elsevier Science Publishers B.V. All rights reserved. SSDIO167-2738(94)00151-O
44
S. Stemmer et al. / Solid State Ionics 75 (I 995) 43-48
ferroelectric PbTi03 thin films. To investigate substrate effects, PbTi03 films were grown on bare (001 )-oriented MgO single crystals and on (00 1) MgO single crystals covered with epitaxial SrTi03 or epitaxial Pt. In addition, the effects of film thickness on domain configuration were examined by characterizing films deposited to different thicknesses onto (00 1 ) SrTi03 single crystals.
2. Experimental The PbTiOJ films were grown by pulsed laser ablation at a substrate temperature of 600°C and were found to be stoichiometric and fully perovskite phase [ 21. Platinum interlayers of 300 nm thickness were deposited by rf magnetron sputtering, while pulsed laser deposition was used to grow 30 nm thick SrTi03 interlayers. The PbTi03 films on bare MgO, on Pt/MgO and on SrTiOJ/MgO had thicknesses of about 150 nm, while the PbTi03 films grown on SrTi03 were deposited to thicknesses of 87 and 200 nm. All deposited films grew predominantly with their unit cell axes aligned parallel to the cell axes of the substrate. Plan-view TEM samples were fabricated by back-side thinning and dimpling, and then ion-beam milling at 6 kV to perforation. Cross-sectional samples were prepared by a technique described in [ lo]. For conventional microscopy a JEM 2000FX (JEOL) operated at 200 kV was used, and a JEM 4000EX (JEOL) operated at 400 kV was used for high-resolution examination of the specimens.
3. Results and discussion Fig. 1 shows plan-view TEM images for PbTi03 films grown on bare MgO, Pt/MgO and SrTi03/ MgO. The four types of equivalent { 101) twin boundaries between the c-axis oriented matrix and the u-domain lamellae exhibit a fringe contrast in the thicker parts of the TEM sample because they are inclined at an angle to the plane of the substrate surface. The films grown on the three different types of substrates show differences in average width W, length L, and number density D of the a-domains. Films grown on Pt contain u-domains that are larger in width and length and lower in density than those
Fig. 1. Plan-view TEM image showing 90” domain walls in PbTi03 films on (a) bare MgO, (b) SrTiOJMgO, and (c) Pt/MgO. The 90” domain walls are tilted 47” with respect to the film plane (wall planes lie along the { 101) twin planes) and project along the indicated [ 1001 and [OlO] directions, respectively.
45
S. Stemmer er al. /Solid State Ionics 75 (1995) 43-48
Table I Measured a-domain lengths, widths and densities for the three different kinds of samples and the standard error for the measurements, defined as the standard deviation divided by the square root of the number of measurements (given in parentheses).
average a-domain length (nm) average a-domain width (nm) average a-domain density (m-‘)
PbTiO,/MgO
PbTiOJSrTiOJMgO
PbTiO,/Pt/MgO
130?12(32) 17+ 1.9( 17) 1.2* lOI
174f9(49) 18*0.9(42) 6.5x lOI
587+35(78) 32*2.7(44) l.lXlO”
in the other films. Table 1 summarizes average values taken from different micrographs for the parameters W, L, and D. For our three types of samples the lattice mismatches (defined as 2 (dPb=ioj - dsubstrate)/ ( dPbTiO3 + &bstrate ) ) between the lattice parameter of the substrate and the bulk value of the c-axis (u-axis) of PbTi03 are: 1.4% (7.7%) for growth on MgO, -5.7% (0.54%) for growth on Pt, and -6.2% (0.15%) for growth on SrTi03. Pt and SrTi03 match closely the u-axis of PbTi03 below T, and with the cubic lattice parameter of PbTi03 above T,:. Large differences in a-domain size and density are observed between the films on Pt and on SrTi03 despite similar lattice mismatches for the two substrates. The films on MgO and on SrTi03 appear rather similar. Fig. 2 shows typical TEM images obtained from plan-view samples of the two films grown on SrTi03. In the thicker film the average width and length of the u-domains are larger, while the average u-domain density is smaller than in the thinner film. Table 2 gives the values for the three parameters W, L and D for these two film thicknesses. In thicker films with larger u-domains, internal twinning of the a-domains is occasionally observed, resulting in a-u-domain walls. In order to understand these variations, the different, competing free energy terms, whose minimization determines the domain structure under equilibrium conditions, must be known. Among these free energies are: (i) the thermodynamic free energy of the phase transformation, (ii) the energy associated with the interaction of the film polarization with either an insulating (bare MgO or SrTiOJMgO) or conducting (Pt/MgO) substrate [ 41, (iii) the strain energy resulting from thermal contraction differences between film and substrate, (iv) the energy stored at the film-substrate interface, (v) the strain energy resulting from elastic accommodation of the
Fig. 2. Plan-view TEM images of PbTiO, films with two different film thicknesses on SrTiOr: (a) 87 nm and (b) 200 nm.
46
S. Stemmer
et al. /Solid
State Ionics
75 (1995) 43-48
Table 2 Measured a-domain lengths, widths and densities for the two different film thickness of PbTi03 on SrTiO, and the standard error fat. the measurements, defined as the standard deviation divided by the square root of the number of measurements (given in parentheses) PbTi03 film thickness
87 nm
200 nm
average a-domain length (nm) average a-domain width (nm) average a-domain density (mW2)
120+7(39)
310+26(87)
llk4(39) 8.23+ lOI
19f 1.6(93) 2.67f lOI
Fig. 3. Cross-sectional HRTEM image of PbTiOs on MgO along the ( 100) zone axis. The image shows an a-domain intersecting the film/substrate interface, and the lattice tilt (indicated by a solid line) in the a-domain. The 90” domain walls enclosing the a-domain are marked by arrows.
u-domains, and (vi ) the twin boundary energy. Because films on Pt and SrTi03 have similar lattice mismatches but different domain contigurations, we conclude that the elastic and electrical properties of the substrate, in addition to film/substrate lattice mismatch, are important in explaining the observed u-domain sizes and their spatial distribution. In particular, the elastic properties of the substrate affect the energy needed for accommodation of the lattice tilt of the different domains with respect to the substrate (discussed below), and the misfit dislocation energy for films thicker than the critical thickness for strain relief, h,. With regard to the films of different thicknesses, for thicker films the interfacial energy terms (electrical and elastic properties of the substrate, lattice mismatch between film and substrate) become less important compared to the remaining energy terms. For SrTi03 as a substrate, this
results in an increasing volume fraction of u-domains with thickness. We now consider tilts of the film with respect to the substrate. As a result of the tetragonality of PbTi03, upon crossing from an u-domain to a c-domain the crystal axes are interchanged through an angle different from 90”. This results in a geometrically necessary tilt of the film lattice relative to the substrate lattice. This can be seen in the HRTEM image of Fig. 3, which shows a finite width u-domain intersecting an MgO substrate. The lattice tilt introduces an interaction with the substrate that may be considered in terms of either a dislocation wall or a disclination dipole [ 71. Tilts opposite to those in the udomains are also required in the c-axis matrix to avoid the buildup of long-range strains. However the tilts in the u-domains are much larger because of their small width. Unfortunately, the roughness of the MgO
S. Stemmer et al. /Solid State Ionics 75 (1995) 43-48
substrate surface makes it impossible to determine the exact accommodation mechanism of the tilt from this image. Further, it is expected that the mechanism depends on the width of the a-domain. a-domains in PbTi03 grown on Pt/MgO were also observed to intersect the film/substrate interface with a finite width. Fig. 4 shows an interfacial region of a film on a SrTi03 single crystal. In contrast to MgO, this interface is atomically flat over a large part of the image. The a-domains are usually found to become narrow and form a point when they reach the SrTiOJtilm interface, as seen in this micrograph. De Veirman et al. [ 111 have found similar behavior for films grown on La0.,Sr0.,Co03. In contrast, for films grown on LaA103, they observe domains intersecting the substrate with a finite width as we do for films on Pt and on MgO. The Pt and LaA103 both appear as atomically smooth as the SrTi03; thus it is unlikely that substrate roughness is the sole factor contributing to this effect. Further, there is no obvious correlation of the a-domain width at the substrate with lattice mismatch or substrate conductivity. The different behaviors at the interfaces of the different substrates are not yet understood. The mechanism for the accommodation of the misfit strain resulting from the lattice mismatch between the film and the substrate must also be known
47
for the different domains. For the given film thicknesses it is reasonable to assume that the majority of the misfit strain is relaxed prior to the phase transformation. For the case of PbTi03 on SrTi03, the expected misfit dislocation spacing is large because of the small misfit and therefore the dislocations are difficult to detect. Another important aspect of domain structure that must be considered is the needle shape of the a-domain lamellae. To form the domain ends, defects must be incorporated into the coherent domain walls, e.g. dislocations and twinning steps [ 12 1. Fig. 5 is an HRTEM image of a domain end obtained from a cross-sectional sample and shows an edge dislocation at the termination. This wall termination energy must be included in the minimization of the free energy terms that determine the domain configuration.
4. Conclusion We have used TEM to study the variations in domain structures in PbTi03 films grown on different substrates and to different thicknesses, and characterized the substrate/film interfacial region by HRTEM. In addition to lattice mismatch, the elastic properties of the substrate influence the domain
Fig. 4. Cross-sectional HRTEM image of PbTi03 on SrTiOJMgO along the ( 100) zone axis, showing a c-axis oriented region of the film containing an a-domain which terminates before intersecting the substrate. The 90” domain walls enclosing the a-domain are marked by arrows.
48
S. Stemmer et al. /Solid State Ionics 75 (1995) 43-48
Fig. 5. HRTEM image of an a-domain end in a cross-sectionalsample along the (010) zone axis. The 90” domain walls enclosing the adomain are marked by arrows.
structures because of the elastic interaction between film and substrate due to the tilt of the film lattice. Comparison between films on Pt/MgO and SrTiOJ MgO indicates that growth on an elastically softer and conducting substrate results in a film with larger adomains that are also fewer in number. To evaluate the influence of lattice mismatch between film and substrate on domain configuration, more work is needed to determine the amount of misfit strain relieved by dislocation formation and by domain formation respectively, as a function of temperature. More measurements of films with different film thicknesses are necessary to verify the existing models and to determine relevant energy terms.
Acknowledgment
SK. Streiffer would like to thank the Alexander von Humboldt-Stiftung for financial assistance. We also thank the Max-Planck Gesellschaft for support. R. Raj and W.-Y. Hsu received support from the National Science Foundation, Award No. DMR-9 I? 1654,
through the Materials University.
Science
Center
at Cornell
References [ 1] Y. Gao, G. Bai, K.L. Merkle, Y. Shi, H.L.M. Chang and D.J. Lam, J. Mat. Res. 8 (1992) 145. [2] W.-Y. Hsu, Ph.D. Thesis (Cornell University, 1994). [3] B.S. Kwak, A. Erbil, B.J. Wilkens, J.D. Budai, M.F. Chisholm and L.A. Boatner, Phys. Rev. Lett. 68 ( 1992) 3733. [4] W. Pompe, private communication. [ 51 W. Pompe, X. Gong, Z. Suo and J.S. Speck, J. Appl. Phys. 74 (1993) 6012. [ 6 ] R. Ramesh, T. Sands and V.G. Keramidas, Appl. Phys. Lett. 63 (1993) 731. [ 71 A.E. Romanov and V.I. Vladimirov, Disclinations in Crystalline Solids, in: Dislocations in Solids 9, ed. F.R.N. Nabarro (North-Holland, Amsterdam, 1992 ) . [ 8 ] J.S. Speck and W. Pompe, J. Appl. Phys. 76 ( 1994) 466. [9] S. Stemmer, S.K. Streiffer, E. Ernst, R. Raj and M. Riihle, J. Mat. Res., submitted for publication. [lo] A. Strecker, U. Salzberger and J. Maier, Prakt. Metallogr. 30 (1993) 482. [ll]A.E.M. de Veirman, J. Timmers, F.J.G. Hakkens, J.F.M. Cillesen and R.M. Wolf, Philips J. Res. 47 ( 1993) 185. [ 12 ] Yimei Zhu, M. Suenaga and J. Tafto, Philos. Mag. A 67 (1993) 1057.