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SrTiO3 interfaces
PII:
Acta mater. Vol. 47, No. 1, pp. 183±198, 1999 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain S1359-6454(98)00334-6 1359-6454/99 $19.00 + 0.00
ATOMISTIC STRUCTURE OF MISFIT DISLOCATIONS IN SrZrO3/SrTiO3 INTERFACES F. ERNST1{, A. RECÏNIK1,2, P. A. LANGJAHR1,3, P. D. NELLIST4,5 and M. RUÈHLE1 1 Max-Planck-Institut fuÈr Metallforschung, Seestraûe 92, 70193 Stuttgart, Germany, 2Jozef Stefan Institute, Ceramics Department, Jamova 39, 1000 Ljubljana, Slovenia, 3UniversitaÈt Karlsruhe, Institut fuÈr Keramik im Maschinenbau, Haid-und-Neu-Str. 7, 76131 Karlsruhe, Germany, 4Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6030, U.S.A. and 5Nanoscale Physics Research Laboratory, School of Physics and Astronomy, The University of Birmingham, Birmingham B15 2TT, U.K.
(Received 13 May 1998; accepted 6 September 1998) AbstractÐThe atomistic structure of mis®t dislocations at heterointerfaces between two ionic crystals with the perovskite structure, SrZrO3 and SrTiO3, is investigated. The interfaces were fabricated by metal±organic deposition of SrZrO3 layers on (001) SrTiO3 single crystal substrates. Under appropriate conditions the SrZrO3 layer grows epitaxially, with its crystal lattice parallel to the lattice of the substrate (``cube-oncube'' orientation relationship). In the layer/substrate interface a square network of dislocations accommodates the mis®t between corresponding spacings in the two crystals. These mis®t dislocations have edge character, h010i line directions, and h100i Burgers vectors parallel to the interface. The SrZrO3/SrTiO3 interface has been imaged with the mis®t dislocations in end-on projection by high-resolution transmission electron microscopy and also by high-resolution scanning transmission electron microscopy. Quantitative image analysis has shown that a (002) layer of TiO2 terminates the SrTiO3 crystal, and the SrZrO3 crystal commences with a (002) layer of Sr±O. Concerning the {200} layers normal to the interface it was found that in interface regions of good match, between the mis®t dislocations, the perovskite structure continues straight through the interface: Sr±O layers of SrTiO3 continue as Sr±O layers of SrZrO3, and TiO2 layers continue as ZrO2 layers. Where the mis®t dislocations reside, however, in regions of poor match, a lateral oset exists between the two crystals and disrupts the perovskite structure: on the core plane (the symmetry plane) of the mis®t dislocations a (200) TiO2 layer of SrTiO3 continues as a (200) SrO layer in SrZrO3. # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
Langjahr et al. [1, 2] have shown that by means of MOD (metal±organic deposition [3]) one can grow epitaxial layers of SrZrO3 on (001) SrTiO3 substrates. Like SrTiO3 [4], the SrZrO3 layer adopts the perovskite structure (Fig. 1), even though the room temperature modi®cation only has pseudocubic Pnma symmetry [5, 6]. The SrZrO3 layer grows with its lattice parallel to the lattice of the SrTiO3 substrate. Thus, the mis®t of corresponding spacings across the SrZrO3/SrTiO3 interface coincides with the mis®t{ aT ÿ aZ ÿ4:9% aZ
dislocations have pure edge character, h100i Burgers vectors parallel to the interface, and h010i line directions (here and in the following, we refer to a cartesian reference frame parallel to the axes of the two crystal lattices, see Fig. 4). So far, however, details of the ion arrangement at the SrZrO3/ SrTiO3 interface have not been studied [7]. In this paper we analyze the mis®t dislocation core structures in MOD-grown SrZrO3/SrTiO3 interfaces from images we have obtained by HRTEM (highresolution transmission electron microscopy) and by high-resolution STEM (scanning transmission electron microscopy).
1
between the lattice parameter aT 0:39 nm of SrTiO3 and aZ 0:41 nm, the arithmetic mean of the three SrZrO3 lattice parameters. At the SrZrO3/ SrTiO3 interface, a square network of edge-type dislocations accommodates the mis®t (1). These mis®t {To whom all correspondence should be addressed. {Here, and in the following, the superscript ``T'' refers to strontium titanate, while ``Z'' refers to strontium zirconate. 183
2. EXPERIMENTAL PROCEDURES AND METHODS
2.1. High-resolution transmission electron microscopy To image the SrZrO3/SrTiO3 interface in cross section, viewing down the [010] line direction of one set of mis®t dislocations, we prepared TEM samples by applying the technique of Strecker et al. [1, 8]. For HRTEM we employed a JEM 4000 EX (JEOL) microscope, equipped with a top-entry objective lens (pole piece UHP-40H) and a LaB6 ®lament. Operating at an accelerating voltage of
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inner and outer radius, such HAADF images directly reveal the projected electron scattering power of individual atom columns in the specimen [10]. This is known as Z-contrast [11, 12]. The HB-603 U has an accelerating voltage of 300 kV, an objective lens with a small spherical aberration (Cs 1:0 mm), and can thus form an electron probe with a diameter as small as 0.13 nm. Scanning the specimen with this small electron probe and recording only electrons scattered under a minimum angle of 30 mrad we have obtained atomic resolution Z-contrast images of the SrZrO3/ SrTiO3 interface. Fig. 1. Perovskite structure of a crystal with the composition ABO3, as adopted by SrTiO3 (A = Sr, B = Ti) and SrZrO3 (A = Sr, B = Zr). Normal to any {100} plane the structure corresponds to an alternating sequence of ion layers a (AO) and b (BO2), which coincide with {200} planes of the cubic (or pseudo-cubic) lattice.
400 kV, this microscope achieves a point resolution of 0.175 nm. At several dierent defocus settings we recorded images of the interface on photographic ®lm. Subsequently, we digitized the negatives with an Eikonix diode array scanner, providing a dynamic range of 212. For HRTEM image simulations we used the EMS software package [9]. Apart from known electron optical parameters of the JEM 4000 EX, image simulations require the defocus of the objective lens and the local specimen thickness to be speci®ed. We have determined both parameters from defocus thickness tables (Section 5.2) and cross-checked the results against the values we obtained by independent experimental measurements: to estimate the local thickness t of the TEM specimen we measured the distance d between the region of interest and the edge of the specimen. Assuming that after ion beam milling the specimen edge has the shape of a wedge with surfaces parallel to the direction of the ion beams we obtain t from t 2d tang
2
where g denotes the inclination of the ion beams against the plane of the specimen (128). To verify the defocus setting we have evaluated optical diffractograms of image regions featuring the amorphous edge of the TEM specimen. 2.2. Scanning transmission electron microscopy Besides HRTEM, we employed high-resolution STEM to image the structure of the SrZrO3/SrTiO3 interface. Using an HB-603 U (Vacuum Generators) DSTEM (dedicated scanning transmission electron microscope) we recorded images with an HAADF (high-angle annular dark ®eld) electron detector. Provided that the specimen is suf®ciently thin and the detector has an appropriate
3. EXPERIMENTAL OBSERVATIONS
3.1. High-resolution transmission electron microscopy By means of HRTEM and high-resolution STEM we have recorded cross-sectional images of the SrZrO3/SrTiO3 interface in [010] projection. First, we discuss the results obtained by HRTEM. Figure 2 presents two cross-sectional HRTEM images of the same interface region, recorded at two dierent defocus settings Df. The upper image was recorded nearly at Gauû focus (Df10), while for the lower image the defocus corresponds to the ®rst reverse passband of the contrast transfer function (Df1 ÿ 70 nm). The interface region included in Fig. 2 lies between 8 and 16 nm away from the edge of the TEM specimen. Since the TEM specimen has been ion milled under g 128, equation (2) yields a local thickness between 3 and 7 nm. Figure 2 reveals a sharp and ¯at interface, which lies exactly parallel to the (001) planes of the SrZrO3 and the SrTiO3 crystal. Viewing the HRTEM images at an acute angle, normal to the trace of the interface, one recognizes strain ®elds of dislocations that accommodate the mis®t between the layer and the substrate: the (200) layers (vertical in Fig. 2) bend in order to maintain continuity across the interface. HRTEM observations of such (200) layer bending in regions where the local foil thickness exceeds the lateral period of the interface lead to the conclusion that the corresponding strain ®elds belong to mis®t dislocations parallel to the viewing direction. We de®ne their line direction as l 010:
3
The white arrows in Fig. 2 point to the mis®t dislocation cores. Apart from occasional irregularities the bending of the (200) layers at each dislocation exhibits mirror symmetry with respect to the ``core plane''Ðthe arrowed (200) plane that intersects with the mis®t dislocation core. Left and right from the core plane the SrTiO3 substrate features a (200) layer that does not continue in the SrZrO3 layer but ends at the interface. Accordingly, the mis®t dislocations have Burgers vectors
ERNST et al.: MISFIT DISLOCATIONS
185
Fig. 2. Cross-sectional HRTEM images of the SrZrO3/SrTiO3 interface in [010] projection, revealing mis®t dislocations along the viewing direction (arrows point to the mis®t dislocation cores).
b 100:
4
The spacing between each pair of mis®t dislocations in Fig. 2 amounts to 19 dZ100 20 dT100 dZ100
5
dT100
where and denote the spacing of the (100) planes in the SrZrO3 and in the SrTiO3 crystal, respectively. The mis®t dT100 ÿ dZ100 ÿ5:0% dZ100
6
between the (100) spacings coincides with the mis®t (1) between the standard lattice parameters of aT and aZ of SrTiO3 and SrZrO3, respectively. This
means that essentially no homogeneous coherency strains have remained in the SrZrO3 layerÐthe layer has fully relaxed. The regions halfway between the mis®t dislocations represent areas of ``good match'', where the interface structure corresponds to the ion arrangement of minimum energy. Viewing Fig. 2(a) or (b) at an acute angle reveals that in these regions the (200) fringes of SrTiO3 continue straight into (200) fringes of SrZrO3 without any oset. The same is true for the (101) and 101 fringes, both of which make an angle of 458 with the interface. On both sides of the interface the HRTEM images of Fig. 2 exhibit black or white spots with two dierent intensities; this gives rise to {100} fringes superim-
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Fig. 3. High-resolution STEM image of a mis®t dislocation in the SrZrO3/SrTiO3 interface (horizontal), recorded in the same projection as Fig. 2.
posed on the {200} fringes. The symmetry of the perovskite structure (Fig. 1) implies that in each crystal the respective spots coincide with the positions of the cation columns (Sr and TiO columns in SrTiO3, Sr and ZrO columns in SrZrO3). Thus, the straight continuity of the (101), 101, and (200) fringes across the interface means that there is no lateral oset between the planes of corresponding cation layers in SrTiO3 and SrZrO3Ðthe cation layers continue straight through the interface. In other words, the experimental observations rule out a ``lock-in'' con®guration of the two crystals.
which have the highest scattering power, while the Ti±O columns appear weaker. In the region of SrZrO3, however, the Zr±O columns have the largest scattering power and appear even brighter than the Sr columns. The left side and the right side of Fig. 3 show regions of good match. Similar to the HRTEM images of Fig. 2, these regions feature straight continuity of cation layers across the interface. The central part of Fig. 3 shows a region of poor match between SrZrO3 and SrTiO3. The contrast reduction in the core region probably originates from a slight local misorientation of the specimen with respect to the optic axis.
3.2. Scanning transmission electron microscopy Figure 3 presents a high-resolution STEM image of the SrZrO3/SrTiO3 interface, recorded with a HAADF detector in the same cross-sectional [010] view as the HRTEM image of Fig. 2. The bright spots in this Z-contrast image originate from cation columns; the columns that contain only O ions do not produce sucient Z-contrast. In the region of the SrTiO3 the brightest spots represent Sr columns,
4. ATOMISTIC MODELS OF MISFIT DISLOCATION CORES
Without further analysis, the above experimental observations on mis®t dislocation cores appear to agree with a variety of atomistic models, which we deduce in this section. Figure 4 presents a schematic drawing of a mis®t dislocation in the SrZrO3/ SrTiO3 interface. Based on our experimental obser-
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187
Now consider the relative translation of SrZrO3 and SrTiO3 in regions of good match, in the centers of the square meshes of the mis®t dislocation network. Recalling the straight continuity of cation layers through the interface we distinguish between only two dierent translation states, ``perovskite translation'' and ``antiphase translation''. Perovskite translation implies that the cation sites of one crystal lattice coincide with the equivalent sites in the other lattice: AT $ AZ , B T $ B Z T
Z
9
where A and A refer to Sr sites, while B and BZ correspond to Ti and Zr sites, respectively. Antiphase translation, in contrast, implies coincidence of non-equivalent cation lattice sites: AT $ B Z , B T $ AZ : Fig. 4. Schematic drawing of a mis®t dislocation in the SrZrO3/SrTiO3 interface.
vations we assume that (i) the crystal lattices of SrZrO3 (top) and SrTiO3 (bottom) have the same orientation (``cube-on-cube orientation relationship''), (ii) the interface is sharp, ¯at, and lies parallel to the (001) planes of both crystals, (iii) the plane of the interface, which we denote as ``iplane'', resides between the (002) ion layers iZ and iT terminating the two crystals, (iv) the mis®t dislocation has edge character, a line direction of l 010 (antiparallel to the viewing direction), and a Burgers vector of b 100, (v) the ``d-plane'' (core plane) coincides with (200) ion layers dZ and dT in the two crystals, and (vi) the d-plane constitutes a mirror plane for the ion positions. Characterization of the interface structure at the atomic level requires to specify (i) the nature of the ``d-layers'' dZ and dT and (ii) the nature of the ``ilayers'' iZ and iT. Along any h100i direction the perovskite structure of SrTiO3 and SrZrO3 corresponds to an alternating sequence of two types of ion layers, a and b, which coincide with {200} planes (Fig. 1). In SrTiO3 these layers have the stacking sequence . . . aT bT aT bT . . .
7
T
where a represents a layer with the composition Sr±O and bT denotes a layer with the composition TiO2. Correspondingly, in the SrZrO3 epilayer the {200} layers along any h100i direction have the stacking sequence . . . aZ bZ aZ bZ . . . :
8
In analogy to (7), aZ and bZ represent layers with the composition Sr±O and ZrO2, respectively. According to (1), however, the ion spacings within aZ and bZ are 5% larger than the corresponding ion spacings within aT and bT.
T
10
Both perovskite translation and antiphase translation imply cation±anion bonding across the SrZrO3/SrTiO3 interface. So far, we have just considered the relative translation of the two crystal lattices in regions of good match, without regarding the nature of the i-layers that actually form the SrZrO3/SrTiO3 interface (Fig. 4). Two possibilities exist for each of the two potential translation states. For perovskite translation, the stacking pattern of the (002) layers across the interface corresponds to either . . . aT bT aT bT ±±aZ bZ aZ bZ . . .
11
. . . bT aT bT aT ±±bZ aZ bZ aZ . . .
12
or
where the Ð marks the position of the i-plane. Antiphase translation, in contrast, requires either . . . aT bT aT bT ±±bZ aZ bZ aZ . . .
13
. . . bT aT bT aT ±±aZ bZ aZ bZ . . . :
14
or
Dierent from the ``perovskite stacking'' con®gurations (11) and (12), the ``antiphase stacking'' con®gurations (13) and (14) correspond to interface stacking faults, which break the stoichiometry of the perovskite structure. Such ``planar'' non-stoichiometry, however, is not unusual in perovskite materialsÐrelated compounds are known as Ruddlesden±Popper phases [13] or MagneÂli phases [14]. Up to this point, we have discussed the structure of the SrZrO3/SrTiO3 interface in regions of good match. Now we focus on the regions of poor match. Compared to the hypothetical case of an ``unrelaxed interface'' (an interface with no lateral ion displacements), the real interface features mis®t dislocations. Mis®t dislocations constitute strain ®elds that extend the regions of good match by narrowing the regions of poor match. Whatever con®guration
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corresponds to ``good match'' at the SrZrO3/SrTiO3 interface, the mis®t dislocation cores reside in regions of poor match, halfway between the regions of good match. Without relaxation, a h100i projection of these regions of poor match would show the (200) ion layers on each side of the interface exactly ``out of register''. Since the i-plane component of the displacement ®eld associated with a mis®t dislocation vanishes at the core plane, we expect that even in the presence of relaxations the d-plane of a mis®t dislocation features (200) ion layers exactly ``out of register'' with respect to the con®guration in regions of good match. In Fig. 4, for example, good match corresponds to ``perovskite translation'': aT layers continue as aZ layers, and bT layers as bZ layers. This con®guration appears on the left and on the right side of Fig. 4Ðaway from the mis®t dislocation core in the center. On the dplane, in contrast, an a layer of SrTiO3 continues as a b layer of SrZrO3. Permutating the d-layers that meet at the d-plane in SrZrO3 and SrTiO3, respectively, we obtain four possible con®gurations: aT jbZ
15
bT jaZ
16
aT jaZ
17
bT jbZ :
18
In each case, the vertical bar symbolizes the dplane. For the regions of good match, con®gurations (15) and (16) imply perovskite translation, while (17) and (18) correspond to antiphase translation. Every possible combination of the i-layer con®gurations (11), (12), (13), and (14) with the d-layer con®gurations (15), (16), (17), and (18) yields another model for the mis®t dislocation cores in the SrZrO3/SrTiO3 interface. In the following, we refer to dierent combinations of i-layers and d-layers by symbols like iT ±±i Z dT jdZ :
19
In total, we obtain eight models. Perovskite translation in regions of good match requires either con®guration (11) or (12) for the i-layers and either (15) or (16) for the d-layers. The combination yields: aT ±±bZ aT jbZ
20
aT ±±bZ bT jaZ
21
bT ±±aZ aT jbZ
22
bT ±±aZ bT jaZ :
23
Antiphase translation, in contrast, requires con®guration (13) or (14) for the i-layers and (17) or (18) for the d-layers. This leads to aT ±±aZ aT jaZ
24
aT ±±aZ bT jbZ
25
bT ±±bZ aT jaZ
26
bT ±±bZ bT jbZ :
27
The next section describes in which way we have identi®ed the most realistic mis®t dislocation core con®guration among these eight models: by quantitative comparisons between experimental and simulated HRTEM images.
5. QUANTITATIVE ANALYSIS OF HRTEM IMAGES
5.1. Processing of experimental HRTEM images In order to compare our experimental HRTEM images with simulated images we have digitized the negatives and improved the signal-to-noise ratio of the images in the following three steps: First, we averaged over the intensity distributions of several dislocation images, which we have recorded under nearly identical HRTEM imaging conditions: in the same TEM specimen, at the same defocus, and in regions of similar specimen thickness. This procedure delivered best results (minimum level of information in the dierence image) when averaging over just two neighboring dislocations. After this ®rst step of noise reduction, however, the images still exhibited an inhomogeneous background. Since the experimental images suggest mirror symmetry of the ion arrangement with respect to the d-plane (Fig. 4), we further reduced the noise by computing the average intensity of the image obtained in the ®rst step and its mirror image. Finally, in the third step, we applied a Fourier ®lter to remove long-range intensity variations from the image without loosing the short-range structural information. The corresponding Fourier ®lter, a ``zero ®lter'', deletes the central intensity from the Fourier spectrum of the image intensity. Figure 5(a) and (b) present two images of mis®t dislocation cores after applying the above procedure to the unprocessed HRTEM images of Fig. 2. In the following we analyze the relative strength of dierent intensity maxima in these images. If the reproduction does not reveal the relevant intensity dierences the reader may verify our observations by means of the ``edge threshold images'' in Fig. 5(c) and (d). The black pixels in these images indicate those pixels of Fig. 5(a) and (b) where the intensity has reached 82% of the respective maximum; large circles represent strong intensity maxima and vice versa.
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Fig. 5. (a), (b) Processed images of mis®t dislocation cores, obtained from the experimental HRTEM images of Fig. 2(a) and (b). (c), (d) Corresponding edge-threshold images.
In the processed image of Fig. 5(a) the SrZrO3 crystal features a superposition of {100} and {200} lattice fringes; the image reveals an alternating pattern of larger and smaller black spots. The SrTiO3 crystal, in contrast, mainly exhibits {200} fringes: here the black spots are nearly equal in size. The sharp transition between the image patterns of SrZrO3 and SrTiO3 indicates that practically no interdiusion has occurred. Unlike Fig. 5(a), Fig. 5(b) exhibits an alternating pattern of larger and smaller bright spots. Both crystals exhibit {100} and {200} lattice fringes, even though the contri-
bution of {100} fringes appears weaker in SrTiO3. Viewing Fig. 5(b) upwards the d-plane reveals that a row of large bright spots in SrTiO3 matches a row of large bright spots in SrZrO3. In the regions of good match at the outer left and the outer right of the image, however, rows of large bright spots in SrTiO3 continue as rows of small bright spots in SrZrO3, and vice versa. Another important feature of Fig. 5(b) concerns the lattice fringes parallel to the SrZrO3/SrTiO3 interface. The black marker lines on the left of Fig. 5(b) indicate where the image has horizontal rows of large bright spots.
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The pattern of these marker lines as well as the corresponding edge-threshold image in Fig. 5(d) reveal that the SrTiO3 crystal ends on a row of large bright spots and the SrZrO3 crystal begins on a row of large bright spots; there is no row of small bright spots next to the i-plane. 5.2. HRTEM image simulations To identify the i-layers and d-layers that give rise to the speci®c image patterns of Fig. 5(a) and (b) we have carried out HRTEM image simulations; we assume that the arrangement whose simulated images match best with the experimental images represents the best model for the real structure. Before actually simulating HRTEM images of mis®t dislocations we determined optimum values for the experimental specimen thickness t and defocus Df. For this purpose, we simulated images of undistorted SrTiO3 and SrZrO3 over large intervals of t and Df and arranged these images in thickness focus tables. Comparing the tables with the undistorted regions of Fig. 5(a) and (b) we found the best simultaneous match with both experimental images for a specimen thickness of 4.9 nm. This value agrees well with the experimental estimate presented in Section 3.1. For the defocus Df we determined ÿ9 nm for Fig. 5(a), and ÿ69 nm for Fig. 5(b), in good agreement with optical diractograms and the nominal adjustment of the microscope during the experiment. The simulations that reproduce the imaging conditions of Fig. 5(a) reveal that the cation columns appear as dark spots in both crystals. In SrTiO3 the Sr and the TiO columns produce spots of similar size. In SrZrO3, in contrast, the spots of the Sr columns appear much larger than those of the Zr±O columns. Under the imaging conditions of Fig. 5(b) the cation columns appear as bright spots in both crystals. In SrTiO3 the spots of the Ti±O columns look somewhat larger than those of the Sr columns, while in SrZrO3 the Sr columns appear substantially brighter than the Zr±O columns. To simulate HRTEM images of mis®t dislocations we modeled the real interface structure as a periodic repetition of an orthorhombic supercell. For each model, the A, B, and C translations of the supercell were chosen parallel to the [100], [010], and [001] axes of the coordinate system in Fig. 4, respectively. The supercells had dimensions of A = 8.2 nm, B = 0.4 nm, C = 8.0 nm and included about 2000 ions. In each supercell the interface lies parallel to (001) and divides the supercell volume into two nearly equal parts. The mis®t dislocation core lies parallel to B and resides in the center of the A C plane, while the left and the right side correspond to regions of good match. Along the A axis, the extension of each supercell corresponds to the lateral mis®t dislocation spacing (5). The C translation has nearly the same length (10 perovskite unit cells on each side of the interface), in
order to avoid interference eects from the neighboring interfaces in the periodic repetition of the supercell. In contrast to the large A and C dimensions, B only amounts to one average lattice parameter of SrTiO3 and SrZrO3. This means we do not account for the lattice mis®t between SrTiO3 and SrZrO3 along the viewing direction. However, the HOLZ (``higher order Laue zone'') eects we discard in this way are negligible compared to the eects of other approximations [15]. For each possible combination of i-layers and dlayers (Section 4) we set up a simulation supercell. Initially, the ion arrangement in each supercell was free of strain. To account for the strain ®eld of the mis®t dislocations we then re®ned the positions of the ion columns: by iterating (i) adjustment of the column positions and (ii) quantitative comparisons between simulated and experimental images we determined those column positions for which the simulated images of the respective supercell yield maximum similarity with the experimental images of Fig. 5. To quantify the similarity between a simulated image S and the corresponding experimental image E, we adjust the size of E to the size of S, consider both images as vectors of N pixel intensities, and evaluate the cross-correlation [16] CS,EM
S ÿ hSi E ÿ hEi sS sE
28
where hSi and hEi denote the mean values of the two images, respectively, and the symbols sS and sE represent the corresponding standard deviations. Depending on the images being compared, the cross-correlation can adopt values between ÿ1 and +1. The cross-correlation actually evaluates the contrast patterns of the images, irrespective of their mean values and standard deviations. A cross-correlation of +1 indicates perfect match between the patterns, 0 implies no match at all, and ÿ1 implies anticorrelation, which means that the two patterns are negatives of each other. In order to reduce the computation time we took advantage of the following simpli®cations: (i) Because the O ions have only a small electron scattering power compared to Sr, Zr, or Ti ions we re®ned only the cation positions and assumed that the oxygen ions reside halfway between the cations. (ii) We only considered displacements parallel to the SrZrO3/SrTiO3 interface. While the experimental images in Figs 2 and 5 reveal displacements normal to the interface, too, these displacements are small compared to the lateral displacements. (iii) The column shifts we applied during the re®nement initially pointed away from the d-plane in SrZrO3 (dilatation) and towards the d-plane in SrTiO3 (compression); only if such column shifts did not improve the image similarity we applied shifts in the opposite directions. (iv) Consistent with the pro-
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191
Fig. 6. Re®ned models with ``perovskite stacking''. The i-layers and d-layers in (a), (b), (c), and (d) correspond to the combinations (20), (21), (22), and (23), respectively.
cedure of noise reduction (Section 5.1) we enforced mirror symmetry of the ion column displacements with respect to the d-plane. (v) In every re®nement cycle we ®rst readjusted the ion columns near the mis®t dislocation core. From there we proceeded to columns farther away from the core until we reached columns that required no adjustment at all. (vi) Instead of re-calculating the scattering potential of the entire supercell after each column rearrangement we only re-calculated and replaced the local scattering potentials. 5.3. Results First we consider the re®ned models with ``perovskite stacking'', compare Fig. 6 and the corresponding simulated images in Fig. 7 (small underfocus) and Fig. 8 (large underfocus). Away
from the mis®t dislocation core, each simulated image agrees reasonably well with the corresponding experimental image in Fig. 5(a) or (b), respectively. However, only Fig. 7(b) and (d) reproduce the strong black spots originating from the dZ-layer of the SrZrO3 crystal in Fig. 5(a). Consistent with this result, only the images of Fig. 8(b) and (d) reproduce the bright spots of higher intensity this ion layer exhibits in Fig. 5(b). In the latter image, strong bright spots also appear on the SrTiO3 side of the d-plane, and Fig. 8(c) and (d) actually reproduce this feature. Therefore, only Fig. 8(d) correctly reproduces both characteristic features of the experimental image in Fig. 5(b). The cross-correlation numbers in Figs 7 and 8 quantitatively con®rm that the images of Fig. 7(d) and Fig. 8(d) constitute the best reproduction of the experimental images.
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Fig. 7. Simulated HRTEM images of the models in Fig. 6 (white frames) for the defocus of Fig. 2(a). Cross-correlating the framed region with the corresponding region of Fig. 5(a) yields: (a) 0.864; (b) 0.904; (c) 0.869; (d) 0.910.
Hence, we only retain the model of Fig. 6(d), in which the i-layers and d-layers correspond to con®guration (23). Now consider the models with ``antiphase stacking''. Figure 9 depicts the re®ned model structures, while Figs 10 and 11 show the corresponding simulated HRTEM images, obtained with the defocus of Fig. 5(a) and (b), respectively. Comparing the simulated images with the experimental images we ®nd that the images in Figs 10(a), 10(c), 11(a) and 11(c) reproduce the contrast of the d-layer in SrZrO3 but not in SrTiO3, while the opposite is true for Figs 10(b), 10(d), 11(b) and 11(d). Thus, none of the models in Fig. 9 yields a simulated image that satisfactorily matches any one of the experimental images on both sides of the interface. Among these models, the model in Fig. 9(a) yields the simulated images with the highest cross-correlation numbers
in Figs 10 and 11. In the model of Fig. 9(a) the ilayers and d-layers correspond to con®guration (24). Since the respective cross-correlation numbers are of the same order as those obtained for the ``perovskite stacking'' model of Fig. 6(d) we keep these two models for a more detailed inspection. Even though we obtain slightly dierent crosscorrelations, the simulated HRTEM images of the mis®t dislocation core structures in Figs 6(d) and 9(a) look rather similar. Therefore, we need an additional criterion to decide between these two models. For this purpose, we compare the simulated images of Figs 8(d) and 11(a) with the experimental image of Fig. 5(b) regarding the contrast of the iTlayer and the iZ-layer. When examining Fig. 5(b) in Section 5.1 we noted that both SrTiO3 and SrZrO3 exhibit image patterns consisting of alternating horizontal rows of large and small bright spots
ERNST et al.: MISFIT DISLOCATIONS
193
Fig. 8. Simulated HRTEM images of the models of Fig. 6 (white frames) for the defocus of Fig. 2(b). Cross-correlating the framed region with the corresponding region of Fig. 5(b) yields: (a) 0.823; (b) 0.831; (c) 0.825; (d) 0.851.
parallel to the SrZrO3/SrTiO3 interface, and we found that the interface disrupts this pattern by a missing row of small bright spots. Figure 8(d) correctly reproduces this feature, while Fig. 11(a) does notÐcompare the marker lines at the simulated images with those in Fig. 5(b). Therefore, we conclude that the mis®t dislocations in the SrZrO3/SrTiO3 interface have the structure of Fig. 6(d), which corresponds to con®guration (23): bT ±±aZ bT jaZ :
29
Figure 12 depicts a larger view of this ®nal model: in the SrTiO3 crystal the i-layer and the d-layer consist of TiO2, while in the SrZrO3 crystal the i-layer and the d-layer consist of SrO. In the regions of good matchÐon the outer left and on the outer rightÐthe perovskite structure of the substrate con-
tinues straight into the perovskite structure of the layer without disruption. 5.4. Comparison with high-resolution STEM The STEM image of Fig. 3 allows us to crosscheck the above result of quantitative HRTEM image analysis. Having identi®ed the ion column types that produce the dierent types of intensity maxima on both sides of the interface (Section 3.2), we conclude from Fig. 3 that in regions of good match the perovskite structure continues straight across the interface. As shown by the inset on the left of the image the Sr substructure exhibits no disruption across the interface, and the Zr substructure of the epilayer continues the Ti substructure of the substrate. In agreement with the analysis of the HRTEM images, therefore, the STEM image indi-
194
ERNST et al.: MISFIT DISLOCATIONS
Fig. 9. Re®ned models with ``antiphase stacking''. The i-layers and d-layers in (a), (b), (c), and (d) correspond to the combinations (24), (25), (26), and (27), respectively.
cates perovskite translation in regions of good match. Since the central part of the image lacks contrast, it is dicult to determine the position of the i-plane and, even more so, the position of the dplane. The most likely position of the i-plane follows from the contrast of the ion layer marked by the horizontal line in Fig. 3. The contrast of this layer resembles the contrast of TiO2 layers in the substrate rather than the contrast of the ZrO2 layers in the epilayer. Hence, we conclude that the marked layer actually consists of TiO2 and constitutes the layer iT, which terminates the SrTiO3 crystal. Together with the straight continuity of the Sr substructure across the interface this means that the stacking sequence across the interface corresponds to (11). This result agrees with the conclusions we have drawn from our HRTEM images in Section
5.3. However, since we cannot locate the d-plane, the STEM image does not allow us to distinguish between the possibilities (22) and (23). 6. DISCUSSION
Our quantitative evaluation of HRTEM images shows that in regions of good match the ion arrangement at the interface maintains the perovskite structure. This result corresponds to what one would expect: the perovskite structure constitutes the equilibrium structure of both SrZrO3 and SrTiO3, and the mis®t between the corresponding interatomic spacings along the interface is rather small. Under the boundary condition of continuing the perovskite structure straight across the interface in regions of good match, two possibilities remain
ERNST et al.: MISFIT DISLOCATIONS
195
Fig. 10. Simulated HRTEM images of the models in Fig. 9 (white frames) for the defocus of Fig. 2(a). Cross-correlating the framed region with the corresponding region of Fig. 5(a) yields: (a) 0.907; (b) 0.901; (c) 0.870; (d) 0.868.
for the i-layer con®guration: either aT ±±bZ or bT ±±aZ . We observe bT ±±aZ ; the ion layer that terminates the SrTiO3 crystal consists of TiO2 rather than SrO. Previous experimental observations suggest that TiO2 termination of the SrTiO3 crystal, which we observe at the SrZrO3/SrTiO3 interface, actually constitutes the most likely con®guration for the surface of the SrTiO3 substrate prior to the deposition of the SrZrO3 layer: Henrich et al. [17] as well as Cord and Courths [18] have carried out Auger and photo electron spectroscopy, respectively, on the (001) surface of SrTiO3 single crystals after annealing them in ultra-high vacuum or in an oxygen atmosphere. The results imply that most of the top layer consists of TiO2 rather than SrO. More recent experiments of Kawai et al. [19] have con®rmed this tendency: coaxial impact-collision ion scattering spectroscopy of (001) SrTiO3 surfaces, cleaned by Bi deposition and desorption,
revealed more than 75% TiO2 termination. On a TiO2-terminated SrTiO3 substrate the ®rst atom layer of the SrZrO3 crystal must consist of SrO in order to realize the interface structure we observe. On the other hand, SrO layers of SrZrO3 dier from SrO layers in SrTiO3 only by the somewhat larger interatomic spacings. Thus, even if a layer of SrO, not TiO2, terminated the substrate, it seems possible that during epitaxial growth the ions in this layer rearranged their spacings and only then became what we regard as the ®rst layer of the SrZrO3 crystal. The particular types of d-layers we observe are more dicult to rationalize. Since we have no evidence for reconstruction or reduced column occupancy in the mis®t dislocation core we conclude that the d-layers of SrTiO2 experience lateral compression, while their counterparts, the d-layers of SrZrO3, experience lateral dilatation. We expect
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Fig. 11. Simulated HRTEM images of the models of Fig. 9 (white frames) for the defocus of Fig. 2(b). Cross-correlating the framed region with the corresponding region of Fig. 5(b) yields: (a) 0.849; (b) 0.832; (c) 0.826; (d) 0.824.
that the major contribution of strain to the interface energy originates from those ions that experience compression, because the energy of ion ensembles usually increases more rapidly with compression than with dilatation. Consequently, the ion column that terminates the d-layer in SrTiO3 plays a key role for the line energy of the mis®t dislocation and thus for the energy of the SrZrO3/ SrTiO3 interface. Suppose the d-layers were aT jbZ . Then the d-layers of both crystals would end on a column of O2ÿ ions, and the O2ÿ ions terminating the dZ-layer would have to sit ``ball-on-ball'' on the O2ÿ ions terminating the dT-layer. O2ÿ ions, however, have the largest size of all ions involved in the SrZrO3/SrTiO3 interface: in the six-fold coordination of the perovskite structure the O2ÿ ions have a radius of 140 pm, while the Sr2+, Zr4+, and Ti4+ ions have radii of only 116, 80, and 60 pm, respectively [20, 21]. Owing to the large radius of
the O2ÿ ions, the con®guration aT jbZ would cause a high mis®t dislocation core energy. In the experimentally observed con®guration bT jaZ , in contrast, the O2ÿ ions in the TiO column that terminate the dT-layer make a ball-on-ball con®guration with smaller ions: the Sr ions in the column that terminate an aZ-layer of SrZrO3. It seems plausible that this con®guration requires less energy. 7. CONCLUSION
From our study on SrTiO3/SrZrO3 interfaces fabricated by MOD of SrTiO3 on (001) SrTiO3 single crystal substrates we draw the following conclusions: a layer of TiO2 terminates the SrTiO3 substrate crystal. In interface regions of good match the interface maintains the perovskite structure also adopted by the two individual crystals. In regions
ERNST et al.: MISFIT DISLOCATIONS
197
Fig. 12. Final model for the structure of mis®t dislocations in the SrZrO3/SrTiO3 interface.
of poor match, mis®t dislocations form with h100i Burgers vectors and h010i line directions. On the {200} core plane of these mis®t dislocations a TiO2 layer of SrTiO3 continues as a SrO layer of SrZrO3. It appears that this con®guration develops because (i) prior to the growth of the SrZrO3 layer the SrTiO3 substrate ends on a layer of TiO2 and (ii) a column of small ions in the region of highest compression along the mis®t dislocation core constitutes an energetically favorable con®guration.
AcknowledgementsÐThe ®nancial support of the MZT, project No. Z1-7964-0106-96 10083 (Slovenia), is acknowledged (A.R.). We thank F. F. Lange (University of California, Santa Barbara) and T. Wagner (Max-PlanckInstitut fuÈr Metallforschung) for their collaboration on metal±organic deposition, S. J. Pennycook (Oak Ridge National Laboratory) for his assistance with the VG 603 DSTEM, and M. Wilson and M. Exner (Max-Planck-
Institut fuÈr Metallforschung) for helpful discussions on the compressibility of ions in perovskites.
REFERENCES 1. Langjahr, P. A., Lange, F. F., Wagner, T. and RuÈhle, M., Acta mater., 1998, 46, 773. 2. Langjahr, P. A., Wagner, T., RuÈhle, M. and Lange, F. F., Epitaxial Oxide Thin Films II, ed. J. S. Speck, D. K. Fork, R. M. Wolf and T. Shiosaki. Materials Research Society, Pittsburgh, 1996, p. 109. 3. Lange, F. F., Science, 1996, 273, 903. 4. SrTiO3, JCPDSÐInternational Centre for Diraction Data, Powder-Diraction-File, #35-724, 1992. 5. Carlsson, L., Acta crystallogr., 1967, 23, 901. 6. SrZrO3, JCPDSÐInternational Centre for Diraction Data, Powder-Diraction-File, #10-268, 1992. 7. RecÆnik, A., Langjahr, P. A. and Ernst, F., J. Computer-Assisted Microsc., 1997, 9, 35. 8. Strecker, A., Salzberger, U. and Mayer, I., Prakt. Metall., 1993, 30, 482. 9. Stadelmann, P. A., Ultramicroscopy, 1987, 21, 131.
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10. Hartel, P., Rose, H. and Dinges, C., Ultramicroscopy, 1996, 63, 93. 11. Pennycook, S. J., Browning, N. D., McGibbon, M. M., McGibbon, A. J., Jesson, D. E. and Chisholm, M. F., Phil. Trans. R. Soc. Lond. Ser. A, 1996, 354, 2619. 12. Pennycook, S. J., Browning, N. D., McGibbon, M. M., McGibbon, A. J., Chisholm, M. F. and Jesson, D. E., Diusion Defect Data Part B, 1996, 47, 561. 13. Ruddlesden, S. N. and Popper, P., Acta crystallogr., 1958, 11, 54. 14. Anderson, S., ColleÂn, B., Kuylenstierna, U. and MagneÂli, A., Acta chem. scand., 1957, 11, 1641.
15. Ernst, F. and RuÈhle, M., Current Opinion Solid St. Mater. Sci., 1997, 2, 469. 16. Frank, J., in Computer Processing of Electron Microscope Images, ed. P. W. Hawkes. Springer, Berlin, 1980, p. 187. 17. Henrich, V. E., Dresselhaus, G. and Zeiger, H. J., Phys. Rev. B, 1978, 17, 4908. 18. Cord, B. and Courths, R., Surf. Sci., 1985, 162, 1. 19. Kawai, M., Liu, Z. Y., Hanada, T. and Katayama, M., Appl. Surf. Sci., 1994, 82-83, 487. 20. Shannon, R. D. and Prewitt, C. T., Acta crystallogr., 1969, B25, 925. 21. Pauling, L., The Nature of the Chemical Bond. Cornell University Press, Ithaca, New York, 1960, p. 514.
Acta mater. Vol. 47, No. 1, pp. 183±198, 1999 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain S1359-6454(98)00334-6 1359-6454/99 $19.00 + 0.00
ATOMISTIC STRUCTURE OF MISFIT DISLOCATIONS IN SrZrO3/SrTiO3 INTERFACES F. ERNST1{, A. RECÏNIK1,2, P. A. LANGJAHR1,3, P. D. NELLIST4,5 and M. RUÈHLE1 1 Max-Planck-Institut fuÈr Metallforschung, Seestraûe 92, 70193 Stuttgart, Germany, 2Jozef Stefan Institute, Ceramics Department, Jamova 39, 1000 Ljubljana, Slovenia, 3UniversitaÈt Karlsruhe, Institut fuÈr Keramik im Maschinenbau, Haid-und-Neu-Str. 7, 76131 Karlsruhe, Germany, 4Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6030, U.S.A. and 5Nanoscale Physics Research Laboratory, School of Physics and Astronomy, The University of Birmingham, Birmingham B15 2TT, U.K.
(Received 13 May 1998; accepted 6 September 1998) AbstractÐThe atomistic structure of mis®t dislocations at heterointerfaces between two ionic crystals with the perovskite structure, SrZrO3 and SrTiO3, is investigated. The interfaces were fabricated by metal±organic deposition of SrZrO3 layers on (001) SrTiO3 single crystal substrates. Under appropriate conditions the SrZrO3 layer grows epitaxially, with its crystal lattice parallel to the lattice of the substrate (``cube-oncube'' orientation relationship). In the layer/substrate interface a square network of dislocations accommodates the mis®t between corresponding spacings in the two crystals. These mis®t dislocations have edge character, h010i line directions, and h100i Burgers vectors parallel to the interface. The SrZrO3/SrTiO3 interface has been imaged with the mis®t dislocations in end-on projection by high-resolution transmission electron microscopy and also by high-resolution scanning transmission electron microscopy. Quantitative image analysis has shown that a (002) layer of TiO2 terminates the SrTiO3 crystal, and the SrZrO3 crystal commences with a (002) layer of Sr±O. Concerning the {200} layers normal to the interface it was found that in interface regions of good match, between the mis®t dislocations, the perovskite structure continues straight through the interface: Sr±O layers of SrTiO3 continue as Sr±O layers of SrZrO3, and TiO2 layers continue as ZrO2 layers. Where the mis®t dislocations reside, however, in regions of poor match, a lateral oset exists between the two crystals and disrupts the perovskite structure: on the core plane (the symmetry plane) of the mis®t dislocations a (200) TiO2 layer of SrTiO3 continues as a (200) SrO layer in SrZrO3. # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
Langjahr et al. [1, 2] have shown that by means of MOD (metal±organic deposition [3]) one can grow epitaxial layers of SrZrO3 on (001) SrTiO3 substrates. Like SrTiO3 [4], the SrZrO3 layer adopts the perovskite structure (Fig. 1), even though the room temperature modi®cation only has pseudocubic Pnma symmetry [5, 6]. The SrZrO3 layer grows with its lattice parallel to the lattice of the SrTiO3 substrate. Thus, the mis®t of corresponding spacings across the SrZrO3/SrTiO3 interface coincides with the mis®t{ aT ÿ aZ ÿ4:9% aZ
dislocations have pure edge character, h100i Burgers vectors parallel to the interface, and h010i line directions (here and in the following, we refer to a cartesian reference frame parallel to the axes of the two crystal lattices, see Fig. 4). So far, however, details of the ion arrangement at the SrZrO3/ SrTiO3 interface have not been studied [7]. In this paper we analyze the mis®t dislocation core structures in MOD-grown SrZrO3/SrTiO3 interfaces from images we have obtained by HRTEM (highresolution transmission electron microscopy) and by high-resolution STEM (scanning transmission electron microscopy).
1
between the lattice parameter aT 0:39 nm of SrTiO3 and aZ 0:41 nm, the arithmetic mean of the three SrZrO3 lattice parameters. At the SrZrO3/ SrTiO3 interface, a square network of edge-type dislocations accommodates the mis®t (1). These mis®t {To whom all correspondence should be addressed. {Here, and in the following, the superscript ``T'' refers to strontium titanate, while ``Z'' refers to strontium zirconate. 183
2. EXPERIMENTAL PROCEDURES AND METHODS
2.1. High-resolution transmission electron microscopy To image the SrZrO3/SrTiO3 interface in cross section, viewing down the [010] line direction of one set of mis®t dislocations, we prepared TEM samples by applying the technique of Strecker et al. [1, 8]. For HRTEM we employed a JEM 4000 EX (JEOL) microscope, equipped with a top-entry objective lens (pole piece UHP-40H) and a LaB6 ®lament. Operating at an accelerating voltage of
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ERNST et al.: MISFIT DISLOCATIONS
inner and outer radius, such HAADF images directly reveal the projected electron scattering power of individual atom columns in the specimen [10]. This is known as Z-contrast [11, 12]. The HB-603 U has an accelerating voltage of 300 kV, an objective lens with a small spherical aberration (Cs 1:0 mm), and can thus form an electron probe with a diameter as small as 0.13 nm. Scanning the specimen with this small electron probe and recording only electrons scattered under a minimum angle of 30 mrad we have obtained atomic resolution Z-contrast images of the SrZrO3/ SrTiO3 interface. Fig. 1. Perovskite structure of a crystal with the composition ABO3, as adopted by SrTiO3 (A = Sr, B = Ti) and SrZrO3 (A = Sr, B = Zr). Normal to any {100} plane the structure corresponds to an alternating sequence of ion layers a (AO) and b (BO2), which coincide with {200} planes of the cubic (or pseudo-cubic) lattice.
400 kV, this microscope achieves a point resolution of 0.175 nm. At several dierent defocus settings we recorded images of the interface on photographic ®lm. Subsequently, we digitized the negatives with an Eikonix diode array scanner, providing a dynamic range of 212. For HRTEM image simulations we used the EMS software package [9]. Apart from known electron optical parameters of the JEM 4000 EX, image simulations require the defocus of the objective lens and the local specimen thickness to be speci®ed. We have determined both parameters from defocus thickness tables (Section 5.2) and cross-checked the results against the values we obtained by independent experimental measurements: to estimate the local thickness t of the TEM specimen we measured the distance d between the region of interest and the edge of the specimen. Assuming that after ion beam milling the specimen edge has the shape of a wedge with surfaces parallel to the direction of the ion beams we obtain t from t 2d tang
2
where g denotes the inclination of the ion beams against the plane of the specimen (128). To verify the defocus setting we have evaluated optical diffractograms of image regions featuring the amorphous edge of the TEM specimen. 2.2. Scanning transmission electron microscopy Besides HRTEM, we employed high-resolution STEM to image the structure of the SrZrO3/SrTiO3 interface. Using an HB-603 U (Vacuum Generators) DSTEM (dedicated scanning transmission electron microscope) we recorded images with an HAADF (high-angle annular dark ®eld) electron detector. Provided that the specimen is suf®ciently thin and the detector has an appropriate
3. EXPERIMENTAL OBSERVATIONS
3.1. High-resolution transmission electron microscopy By means of HRTEM and high-resolution STEM we have recorded cross-sectional images of the SrZrO3/SrTiO3 interface in [010] projection. First, we discuss the results obtained by HRTEM. Figure 2 presents two cross-sectional HRTEM images of the same interface region, recorded at two dierent defocus settings Df. The upper image was recorded nearly at Gauû focus (Df10), while for the lower image the defocus corresponds to the ®rst reverse passband of the contrast transfer function (Df1 ÿ 70 nm). The interface region included in Fig. 2 lies between 8 and 16 nm away from the edge of the TEM specimen. Since the TEM specimen has been ion milled under g 128, equation (2) yields a local thickness between 3 and 7 nm. Figure 2 reveals a sharp and ¯at interface, which lies exactly parallel to the (001) planes of the SrZrO3 and the SrTiO3 crystal. Viewing the HRTEM images at an acute angle, normal to the trace of the interface, one recognizes strain ®elds of dislocations that accommodate the mis®t between the layer and the substrate: the (200) layers (vertical in Fig. 2) bend in order to maintain continuity across the interface. HRTEM observations of such (200) layer bending in regions where the local foil thickness exceeds the lateral period of the interface lead to the conclusion that the corresponding strain ®elds belong to mis®t dislocations parallel to the viewing direction. We de®ne their line direction as l 010:
3
The white arrows in Fig. 2 point to the mis®t dislocation cores. Apart from occasional irregularities the bending of the (200) layers at each dislocation exhibits mirror symmetry with respect to the ``core plane''Ðthe arrowed (200) plane that intersects with the mis®t dislocation core. Left and right from the core plane the SrTiO3 substrate features a (200) layer that does not continue in the SrZrO3 layer but ends at the interface. Accordingly, the mis®t dislocations have Burgers vectors
ERNST et al.: MISFIT DISLOCATIONS
185
Fig. 2. Cross-sectional HRTEM images of the SrZrO3/SrTiO3 interface in [010] projection, revealing mis®t dislocations along the viewing direction (arrows point to the mis®t dislocation cores).
b 100:
4
The spacing between each pair of mis®t dislocations in Fig. 2 amounts to 19 dZ100 20 dT100 dZ100
5
dT100
where and denote the spacing of the (100) planes in the SrZrO3 and in the SrTiO3 crystal, respectively. The mis®t dT100 ÿ dZ100 ÿ5:0% dZ100
6
between the (100) spacings coincides with the mis®t (1) between the standard lattice parameters of aT and aZ of SrTiO3 and SrZrO3, respectively. This
means that essentially no homogeneous coherency strains have remained in the SrZrO3 layerÐthe layer has fully relaxed. The regions halfway between the mis®t dislocations represent areas of ``good match'', where the interface structure corresponds to the ion arrangement of minimum energy. Viewing Fig. 2(a) or (b) at an acute angle reveals that in these regions the (200) fringes of SrTiO3 continue straight into (200) fringes of SrZrO3 without any oset. The same is true for the (101) and 101 fringes, both of which make an angle of 458 with the interface. On both sides of the interface the HRTEM images of Fig. 2 exhibit black or white spots with two dierent intensities; this gives rise to {100} fringes superim-
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ERNST et al.: MISFIT DISLOCATIONS
Fig. 3. High-resolution STEM image of a mis®t dislocation in the SrZrO3/SrTiO3 interface (horizontal), recorded in the same projection as Fig. 2.
posed on the {200} fringes. The symmetry of the perovskite structure (Fig. 1) implies that in each crystal the respective spots coincide with the positions of the cation columns (Sr and TiO columns in SrTiO3, Sr and ZrO columns in SrZrO3). Thus, the straight continuity of the (101), 101, and (200) fringes across the interface means that there is no lateral oset between the planes of corresponding cation layers in SrTiO3 and SrZrO3Ðthe cation layers continue straight through the interface. In other words, the experimental observations rule out a ``lock-in'' con®guration of the two crystals.
which have the highest scattering power, while the Ti±O columns appear weaker. In the region of SrZrO3, however, the Zr±O columns have the largest scattering power and appear even brighter than the Sr columns. The left side and the right side of Fig. 3 show regions of good match. Similar to the HRTEM images of Fig. 2, these regions feature straight continuity of cation layers across the interface. The central part of Fig. 3 shows a region of poor match between SrZrO3 and SrTiO3. The contrast reduction in the core region probably originates from a slight local misorientation of the specimen with respect to the optic axis.
3.2. Scanning transmission electron microscopy Figure 3 presents a high-resolution STEM image of the SrZrO3/SrTiO3 interface, recorded with a HAADF detector in the same cross-sectional [010] view as the HRTEM image of Fig. 2. The bright spots in this Z-contrast image originate from cation columns; the columns that contain only O ions do not produce sucient Z-contrast. In the region of the SrTiO3 the brightest spots represent Sr columns,
4. ATOMISTIC MODELS OF MISFIT DISLOCATION CORES
Without further analysis, the above experimental observations on mis®t dislocation cores appear to agree with a variety of atomistic models, which we deduce in this section. Figure 4 presents a schematic drawing of a mis®t dislocation in the SrZrO3/ SrTiO3 interface. Based on our experimental obser-
ERNST et al.: MISFIT DISLOCATIONS
187
Now consider the relative translation of SrZrO3 and SrTiO3 in regions of good match, in the centers of the square meshes of the mis®t dislocation network. Recalling the straight continuity of cation layers through the interface we distinguish between only two dierent translation states, ``perovskite translation'' and ``antiphase translation''. Perovskite translation implies that the cation sites of one crystal lattice coincide with the equivalent sites in the other lattice: AT $ AZ , B T $ B Z T
Z
9
where A and A refer to Sr sites, while B and BZ correspond to Ti and Zr sites, respectively. Antiphase translation, in contrast, implies coincidence of non-equivalent cation lattice sites: AT $ B Z , B T $ AZ : Fig. 4. Schematic drawing of a mis®t dislocation in the SrZrO3/SrTiO3 interface.
vations we assume that (i) the crystal lattices of SrZrO3 (top) and SrTiO3 (bottom) have the same orientation (``cube-on-cube orientation relationship''), (ii) the interface is sharp, ¯at, and lies parallel to the (001) planes of both crystals, (iii) the plane of the interface, which we denote as ``iplane'', resides between the (002) ion layers iZ and iT terminating the two crystals, (iv) the mis®t dislocation has edge character, a line direction of l 010 (antiparallel to the viewing direction), and a Burgers vector of b 100, (v) the ``d-plane'' (core plane) coincides with (200) ion layers dZ and dT in the two crystals, and (vi) the d-plane constitutes a mirror plane for the ion positions. Characterization of the interface structure at the atomic level requires to specify (i) the nature of the ``d-layers'' dZ and dT and (ii) the nature of the ``ilayers'' iZ and iT. Along any h100i direction the perovskite structure of SrTiO3 and SrZrO3 corresponds to an alternating sequence of two types of ion layers, a and b, which coincide with {200} planes (Fig. 1). In SrTiO3 these layers have the stacking sequence . . . aT bT aT bT . . .
7
T
where a represents a layer with the composition Sr±O and bT denotes a layer with the composition TiO2. Correspondingly, in the SrZrO3 epilayer the {200} layers along any h100i direction have the stacking sequence . . . aZ bZ aZ bZ . . . :
8
In analogy to (7), aZ and bZ represent layers with the composition Sr±O and ZrO2, respectively. According to (1), however, the ion spacings within aZ and bZ are 5% larger than the corresponding ion spacings within aT and bT.
T
10
Both perovskite translation and antiphase translation imply cation±anion bonding across the SrZrO3/SrTiO3 interface. So far, we have just considered the relative translation of the two crystal lattices in regions of good match, without regarding the nature of the i-layers that actually form the SrZrO3/SrTiO3 interface (Fig. 4). Two possibilities exist for each of the two potential translation states. For perovskite translation, the stacking pattern of the (002) layers across the interface corresponds to either . . . aT bT aT bT ±±aZ bZ aZ bZ . . .
11
. . . bT aT bT aT ±±bZ aZ bZ aZ . . .
12
or
where the Ð marks the position of the i-plane. Antiphase translation, in contrast, requires either . . . aT bT aT bT ±±bZ aZ bZ aZ . . .
13
. . . bT aT bT aT ±±aZ bZ aZ bZ . . . :
14
or
Dierent from the ``perovskite stacking'' con®gurations (11) and (12), the ``antiphase stacking'' con®gurations (13) and (14) correspond to interface stacking faults, which break the stoichiometry of the perovskite structure. Such ``planar'' non-stoichiometry, however, is not unusual in perovskite materialsÐrelated compounds are known as Ruddlesden±Popper phases [13] or MagneÂli phases [14]. Up to this point, we have discussed the structure of the SrZrO3/SrTiO3 interface in regions of good match. Now we focus on the regions of poor match. Compared to the hypothetical case of an ``unrelaxed interface'' (an interface with no lateral ion displacements), the real interface features mis®t dislocations. Mis®t dislocations constitute strain ®elds that extend the regions of good match by narrowing the regions of poor match. Whatever con®guration
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corresponds to ``good match'' at the SrZrO3/SrTiO3 interface, the mis®t dislocation cores reside in regions of poor match, halfway between the regions of good match. Without relaxation, a h100i projection of these regions of poor match would show the (200) ion layers on each side of the interface exactly ``out of register''. Since the i-plane component of the displacement ®eld associated with a mis®t dislocation vanishes at the core plane, we expect that even in the presence of relaxations the d-plane of a mis®t dislocation features (200) ion layers exactly ``out of register'' with respect to the con®guration in regions of good match. In Fig. 4, for example, good match corresponds to ``perovskite translation'': aT layers continue as aZ layers, and bT layers as bZ layers. This con®guration appears on the left and on the right side of Fig. 4Ðaway from the mis®t dislocation core in the center. On the dplane, in contrast, an a layer of SrTiO3 continues as a b layer of SrZrO3. Permutating the d-layers that meet at the d-plane in SrZrO3 and SrTiO3, respectively, we obtain four possible con®gurations: aT jbZ
15
bT jaZ
16
aT jaZ
17
bT jbZ :
18
In each case, the vertical bar symbolizes the dplane. For the regions of good match, con®gurations (15) and (16) imply perovskite translation, while (17) and (18) correspond to antiphase translation. Every possible combination of the i-layer con®gurations (11), (12), (13), and (14) with the d-layer con®gurations (15), (16), (17), and (18) yields another model for the mis®t dislocation cores in the SrZrO3/SrTiO3 interface. In the following, we refer to dierent combinations of i-layers and d-layers by symbols like iT ±±i Z dT jdZ :
19
In total, we obtain eight models. Perovskite translation in regions of good match requires either con®guration (11) or (12) for the i-layers and either (15) or (16) for the d-layers. The combination yields: aT ±±bZ aT jbZ
20
aT ±±bZ bT jaZ
21
bT ±±aZ aT jbZ
22
bT ±±aZ bT jaZ :
23
Antiphase translation, in contrast, requires con®guration (13) or (14) for the i-layers and (17) or (18) for the d-layers. This leads to aT ±±aZ aT jaZ
24
aT ±±aZ bT jbZ
25
bT ±±bZ aT jaZ
26
bT ±±bZ bT jbZ :
27
The next section describes in which way we have identi®ed the most realistic mis®t dislocation core con®guration among these eight models: by quantitative comparisons between experimental and simulated HRTEM images.
5. QUANTITATIVE ANALYSIS OF HRTEM IMAGES
5.1. Processing of experimental HRTEM images In order to compare our experimental HRTEM images with simulated images we have digitized the negatives and improved the signal-to-noise ratio of the images in the following three steps: First, we averaged over the intensity distributions of several dislocation images, which we have recorded under nearly identical HRTEM imaging conditions: in the same TEM specimen, at the same defocus, and in regions of similar specimen thickness. This procedure delivered best results (minimum level of information in the dierence image) when averaging over just two neighboring dislocations. After this ®rst step of noise reduction, however, the images still exhibited an inhomogeneous background. Since the experimental images suggest mirror symmetry of the ion arrangement with respect to the d-plane (Fig. 4), we further reduced the noise by computing the average intensity of the image obtained in the ®rst step and its mirror image. Finally, in the third step, we applied a Fourier ®lter to remove long-range intensity variations from the image without loosing the short-range structural information. The corresponding Fourier ®lter, a ``zero ®lter'', deletes the central intensity from the Fourier spectrum of the image intensity. Figure 5(a) and (b) present two images of mis®t dislocation cores after applying the above procedure to the unprocessed HRTEM images of Fig. 2. In the following we analyze the relative strength of dierent intensity maxima in these images. If the reproduction does not reveal the relevant intensity dierences the reader may verify our observations by means of the ``edge threshold images'' in Fig. 5(c) and (d). The black pixels in these images indicate those pixels of Fig. 5(a) and (b) where the intensity has reached 82% of the respective maximum; large circles represent strong intensity maxima and vice versa.
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189
Fig. 5. (a), (b) Processed images of mis®t dislocation cores, obtained from the experimental HRTEM images of Fig. 2(a) and (b). (c), (d) Corresponding edge-threshold images.
In the processed image of Fig. 5(a) the SrZrO3 crystal features a superposition of {100} and {200} lattice fringes; the image reveals an alternating pattern of larger and smaller black spots. The SrTiO3 crystal, in contrast, mainly exhibits {200} fringes: here the black spots are nearly equal in size. The sharp transition between the image patterns of SrZrO3 and SrTiO3 indicates that practically no interdiusion has occurred. Unlike Fig. 5(a), Fig. 5(b) exhibits an alternating pattern of larger and smaller bright spots. Both crystals exhibit {100} and {200} lattice fringes, even though the contri-
bution of {100} fringes appears weaker in SrTiO3. Viewing Fig. 5(b) upwards the d-plane reveals that a row of large bright spots in SrTiO3 matches a row of large bright spots in SrZrO3. In the regions of good match at the outer left and the outer right of the image, however, rows of large bright spots in SrTiO3 continue as rows of small bright spots in SrZrO3, and vice versa. Another important feature of Fig. 5(b) concerns the lattice fringes parallel to the SrZrO3/SrTiO3 interface. The black marker lines on the left of Fig. 5(b) indicate where the image has horizontal rows of large bright spots.
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The pattern of these marker lines as well as the corresponding edge-threshold image in Fig. 5(d) reveal that the SrTiO3 crystal ends on a row of large bright spots and the SrZrO3 crystal begins on a row of large bright spots; there is no row of small bright spots next to the i-plane. 5.2. HRTEM image simulations To identify the i-layers and d-layers that give rise to the speci®c image patterns of Fig. 5(a) and (b) we have carried out HRTEM image simulations; we assume that the arrangement whose simulated images match best with the experimental images represents the best model for the real structure. Before actually simulating HRTEM images of mis®t dislocations we determined optimum values for the experimental specimen thickness t and defocus Df. For this purpose, we simulated images of undistorted SrTiO3 and SrZrO3 over large intervals of t and Df and arranged these images in thickness focus tables. Comparing the tables with the undistorted regions of Fig. 5(a) and (b) we found the best simultaneous match with both experimental images for a specimen thickness of 4.9 nm. This value agrees well with the experimental estimate presented in Section 3.1. For the defocus Df we determined ÿ9 nm for Fig. 5(a), and ÿ69 nm for Fig. 5(b), in good agreement with optical diractograms and the nominal adjustment of the microscope during the experiment. The simulations that reproduce the imaging conditions of Fig. 5(a) reveal that the cation columns appear as dark spots in both crystals. In SrTiO3 the Sr and the TiO columns produce spots of similar size. In SrZrO3, in contrast, the spots of the Sr columns appear much larger than those of the Zr±O columns. Under the imaging conditions of Fig. 5(b) the cation columns appear as bright spots in both crystals. In SrTiO3 the spots of the Ti±O columns look somewhat larger than those of the Sr columns, while in SrZrO3 the Sr columns appear substantially brighter than the Zr±O columns. To simulate HRTEM images of mis®t dislocations we modeled the real interface structure as a periodic repetition of an orthorhombic supercell. For each model, the A, B, and C translations of the supercell were chosen parallel to the [100], [010], and [001] axes of the coordinate system in Fig. 4, respectively. The supercells had dimensions of A = 8.2 nm, B = 0.4 nm, C = 8.0 nm and included about 2000 ions. In each supercell the interface lies parallel to (001) and divides the supercell volume into two nearly equal parts. The mis®t dislocation core lies parallel to B and resides in the center of the A C plane, while the left and the right side correspond to regions of good match. Along the A axis, the extension of each supercell corresponds to the lateral mis®t dislocation spacing (5). The C translation has nearly the same length (10 perovskite unit cells on each side of the interface), in
order to avoid interference eects from the neighboring interfaces in the periodic repetition of the supercell. In contrast to the large A and C dimensions, B only amounts to one average lattice parameter of SrTiO3 and SrZrO3. This means we do not account for the lattice mis®t between SrTiO3 and SrZrO3 along the viewing direction. However, the HOLZ (``higher order Laue zone'') eects we discard in this way are negligible compared to the eects of other approximations [15]. For each possible combination of i-layers and dlayers (Section 4) we set up a simulation supercell. Initially, the ion arrangement in each supercell was free of strain. To account for the strain ®eld of the mis®t dislocations we then re®ned the positions of the ion columns: by iterating (i) adjustment of the column positions and (ii) quantitative comparisons between simulated and experimental images we determined those column positions for which the simulated images of the respective supercell yield maximum similarity with the experimental images of Fig. 5. To quantify the similarity between a simulated image S and the corresponding experimental image E, we adjust the size of E to the size of S, consider both images as vectors of N pixel intensities, and evaluate the cross-correlation [16] CS,EM
S ÿ hSi E ÿ hEi sS sE
28
where hSi and hEi denote the mean values of the two images, respectively, and the symbols sS and sE represent the corresponding standard deviations. Depending on the images being compared, the cross-correlation can adopt values between ÿ1 and +1. The cross-correlation actually evaluates the contrast patterns of the images, irrespective of their mean values and standard deviations. A cross-correlation of +1 indicates perfect match between the patterns, 0 implies no match at all, and ÿ1 implies anticorrelation, which means that the two patterns are negatives of each other. In order to reduce the computation time we took advantage of the following simpli®cations: (i) Because the O ions have only a small electron scattering power compared to Sr, Zr, or Ti ions we re®ned only the cation positions and assumed that the oxygen ions reside halfway between the cations. (ii) We only considered displacements parallel to the SrZrO3/SrTiO3 interface. While the experimental images in Figs 2 and 5 reveal displacements normal to the interface, too, these displacements are small compared to the lateral displacements. (iii) The column shifts we applied during the re®nement initially pointed away from the d-plane in SrZrO3 (dilatation) and towards the d-plane in SrTiO3 (compression); only if such column shifts did not improve the image similarity we applied shifts in the opposite directions. (iv) Consistent with the pro-
ERNST et al.: MISFIT DISLOCATIONS
191
Fig. 6. Re®ned models with ``perovskite stacking''. The i-layers and d-layers in (a), (b), (c), and (d) correspond to the combinations (20), (21), (22), and (23), respectively.
cedure of noise reduction (Section 5.1) we enforced mirror symmetry of the ion column displacements with respect to the d-plane. (v) In every re®nement cycle we ®rst readjusted the ion columns near the mis®t dislocation core. From there we proceeded to columns farther away from the core until we reached columns that required no adjustment at all. (vi) Instead of re-calculating the scattering potential of the entire supercell after each column rearrangement we only re-calculated and replaced the local scattering potentials. 5.3. Results First we consider the re®ned models with ``perovskite stacking'', compare Fig. 6 and the corresponding simulated images in Fig. 7 (small underfocus) and Fig. 8 (large underfocus). Away
from the mis®t dislocation core, each simulated image agrees reasonably well with the corresponding experimental image in Fig. 5(a) or (b), respectively. However, only Fig. 7(b) and (d) reproduce the strong black spots originating from the dZ-layer of the SrZrO3 crystal in Fig. 5(a). Consistent with this result, only the images of Fig. 8(b) and (d) reproduce the bright spots of higher intensity this ion layer exhibits in Fig. 5(b). In the latter image, strong bright spots also appear on the SrTiO3 side of the d-plane, and Fig. 8(c) and (d) actually reproduce this feature. Therefore, only Fig. 8(d) correctly reproduces both characteristic features of the experimental image in Fig. 5(b). The cross-correlation numbers in Figs 7 and 8 quantitatively con®rm that the images of Fig. 7(d) and Fig. 8(d) constitute the best reproduction of the experimental images.
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ERNST et al.: MISFIT DISLOCATIONS
Fig. 7. Simulated HRTEM images of the models in Fig. 6 (white frames) for the defocus of Fig. 2(a). Cross-correlating the framed region with the corresponding region of Fig. 5(a) yields: (a) 0.864; (b) 0.904; (c) 0.869; (d) 0.910.
Hence, we only retain the model of Fig. 6(d), in which the i-layers and d-layers correspond to con®guration (23). Now consider the models with ``antiphase stacking''. Figure 9 depicts the re®ned model structures, while Figs 10 and 11 show the corresponding simulated HRTEM images, obtained with the defocus of Fig. 5(a) and (b), respectively. Comparing the simulated images with the experimental images we ®nd that the images in Figs 10(a), 10(c), 11(a) and 11(c) reproduce the contrast of the d-layer in SrZrO3 but not in SrTiO3, while the opposite is true for Figs 10(b), 10(d), 11(b) and 11(d). Thus, none of the models in Fig. 9 yields a simulated image that satisfactorily matches any one of the experimental images on both sides of the interface. Among these models, the model in Fig. 9(a) yields the simulated images with the highest cross-correlation numbers
in Figs 10 and 11. In the model of Fig. 9(a) the ilayers and d-layers correspond to con®guration (24). Since the respective cross-correlation numbers are of the same order as those obtained for the ``perovskite stacking'' model of Fig. 6(d) we keep these two models for a more detailed inspection. Even though we obtain slightly dierent crosscorrelations, the simulated HRTEM images of the mis®t dislocation core structures in Figs 6(d) and 9(a) look rather similar. Therefore, we need an additional criterion to decide between these two models. For this purpose, we compare the simulated images of Figs 8(d) and 11(a) with the experimental image of Fig. 5(b) regarding the contrast of the iTlayer and the iZ-layer. When examining Fig. 5(b) in Section 5.1 we noted that both SrTiO3 and SrZrO3 exhibit image patterns consisting of alternating horizontal rows of large and small bright spots
ERNST et al.: MISFIT DISLOCATIONS
193
Fig. 8. Simulated HRTEM images of the models of Fig. 6 (white frames) for the defocus of Fig. 2(b). Cross-correlating the framed region with the corresponding region of Fig. 5(b) yields: (a) 0.823; (b) 0.831; (c) 0.825; (d) 0.851.
parallel to the SrZrO3/SrTiO3 interface, and we found that the interface disrupts this pattern by a missing row of small bright spots. Figure 8(d) correctly reproduces this feature, while Fig. 11(a) does notÐcompare the marker lines at the simulated images with those in Fig. 5(b). Therefore, we conclude that the mis®t dislocations in the SrZrO3/SrTiO3 interface have the structure of Fig. 6(d), which corresponds to con®guration (23): bT ±±aZ bT jaZ :
29
Figure 12 depicts a larger view of this ®nal model: in the SrTiO3 crystal the i-layer and the d-layer consist of TiO2, while in the SrZrO3 crystal the i-layer and the d-layer consist of SrO. In the regions of good matchÐon the outer left and on the outer rightÐthe perovskite structure of the substrate con-
tinues straight into the perovskite structure of the layer without disruption. 5.4. Comparison with high-resolution STEM The STEM image of Fig. 3 allows us to crosscheck the above result of quantitative HRTEM image analysis. Having identi®ed the ion column types that produce the dierent types of intensity maxima on both sides of the interface (Section 3.2), we conclude from Fig. 3 that in regions of good match the perovskite structure continues straight across the interface. As shown by the inset on the left of the image the Sr substructure exhibits no disruption across the interface, and the Zr substructure of the epilayer continues the Ti substructure of the substrate. In agreement with the analysis of the HRTEM images, therefore, the STEM image indi-
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Fig. 9. Re®ned models with ``antiphase stacking''. The i-layers and d-layers in (a), (b), (c), and (d) correspond to the combinations (24), (25), (26), and (27), respectively.
cates perovskite translation in regions of good match. Since the central part of the image lacks contrast, it is dicult to determine the position of the i-plane and, even more so, the position of the dplane. The most likely position of the i-plane follows from the contrast of the ion layer marked by the horizontal line in Fig. 3. The contrast of this layer resembles the contrast of TiO2 layers in the substrate rather than the contrast of the ZrO2 layers in the epilayer. Hence, we conclude that the marked layer actually consists of TiO2 and constitutes the layer iT, which terminates the SrTiO3 crystal. Together with the straight continuity of the Sr substructure across the interface this means that the stacking sequence across the interface corresponds to (11). This result agrees with the conclusions we have drawn from our HRTEM images in Section
5.3. However, since we cannot locate the d-plane, the STEM image does not allow us to distinguish between the possibilities (22) and (23). 6. DISCUSSION
Our quantitative evaluation of HRTEM images shows that in regions of good match the ion arrangement at the interface maintains the perovskite structure. This result corresponds to what one would expect: the perovskite structure constitutes the equilibrium structure of both SrZrO3 and SrTiO3, and the mis®t between the corresponding interatomic spacings along the interface is rather small. Under the boundary condition of continuing the perovskite structure straight across the interface in regions of good match, two possibilities remain
ERNST et al.: MISFIT DISLOCATIONS
195
Fig. 10. Simulated HRTEM images of the models in Fig. 9 (white frames) for the defocus of Fig. 2(a). Cross-correlating the framed region with the corresponding region of Fig. 5(a) yields: (a) 0.907; (b) 0.901; (c) 0.870; (d) 0.868.
for the i-layer con®guration: either aT ±±bZ or bT ±±aZ . We observe bT ±±aZ ; the ion layer that terminates the SrTiO3 crystal consists of TiO2 rather than SrO. Previous experimental observations suggest that TiO2 termination of the SrTiO3 crystal, which we observe at the SrZrO3/SrTiO3 interface, actually constitutes the most likely con®guration for the surface of the SrTiO3 substrate prior to the deposition of the SrZrO3 layer: Henrich et al. [17] as well as Cord and Courths [18] have carried out Auger and photo electron spectroscopy, respectively, on the (001) surface of SrTiO3 single crystals after annealing them in ultra-high vacuum or in an oxygen atmosphere. The results imply that most of the top layer consists of TiO2 rather than SrO. More recent experiments of Kawai et al. [19] have con®rmed this tendency: coaxial impact-collision ion scattering spectroscopy of (001) SrTiO3 surfaces, cleaned by Bi deposition and desorption,
revealed more than 75% TiO2 termination. On a TiO2-terminated SrTiO3 substrate the ®rst atom layer of the SrZrO3 crystal must consist of SrO in order to realize the interface structure we observe. On the other hand, SrO layers of SrZrO3 dier from SrO layers in SrTiO3 only by the somewhat larger interatomic spacings. Thus, even if a layer of SrO, not TiO2, terminated the substrate, it seems possible that during epitaxial growth the ions in this layer rearranged their spacings and only then became what we regard as the ®rst layer of the SrZrO3 crystal. The particular types of d-layers we observe are more dicult to rationalize. Since we have no evidence for reconstruction or reduced column occupancy in the mis®t dislocation core we conclude that the d-layers of SrTiO2 experience lateral compression, while their counterparts, the d-layers of SrZrO3, experience lateral dilatation. We expect
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Fig. 11. Simulated HRTEM images of the models of Fig. 9 (white frames) for the defocus of Fig. 2(b). Cross-correlating the framed region with the corresponding region of Fig. 5(b) yields: (a) 0.849; (b) 0.832; (c) 0.826; (d) 0.824.
that the major contribution of strain to the interface energy originates from those ions that experience compression, because the energy of ion ensembles usually increases more rapidly with compression than with dilatation. Consequently, the ion column that terminates the d-layer in SrTiO3 plays a key role for the line energy of the mis®t dislocation and thus for the energy of the SrZrO3/ SrTiO3 interface. Suppose the d-layers were aT jbZ . Then the d-layers of both crystals would end on a column of O2ÿ ions, and the O2ÿ ions terminating the dZ-layer would have to sit ``ball-on-ball'' on the O2ÿ ions terminating the dT-layer. O2ÿ ions, however, have the largest size of all ions involved in the SrZrO3/SrTiO3 interface: in the six-fold coordination of the perovskite structure the O2ÿ ions have a radius of 140 pm, while the Sr2+, Zr4+, and Ti4+ ions have radii of only 116, 80, and 60 pm, respectively [20, 21]. Owing to the large radius of
the O2ÿ ions, the con®guration aT jbZ would cause a high mis®t dislocation core energy. In the experimentally observed con®guration bT jaZ , in contrast, the O2ÿ ions in the TiO column that terminate the dT-layer make a ball-on-ball con®guration with smaller ions: the Sr ions in the column that terminate an aZ-layer of SrZrO3. It seems plausible that this con®guration requires less energy. 7. CONCLUSION
From our study on SrTiO3/SrZrO3 interfaces fabricated by MOD of SrTiO3 on (001) SrTiO3 single crystal substrates we draw the following conclusions: a layer of TiO2 terminates the SrTiO3 substrate crystal. In interface regions of good match the interface maintains the perovskite structure also adopted by the two individual crystals. In regions
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197
Fig. 12. Final model for the structure of mis®t dislocations in the SrZrO3/SrTiO3 interface.
of poor match, mis®t dislocations form with h100i Burgers vectors and h010i line directions. On the {200} core plane of these mis®t dislocations a TiO2 layer of SrTiO3 continues as a SrO layer of SrZrO3. It appears that this con®guration develops because (i) prior to the growth of the SrZrO3 layer the SrTiO3 substrate ends on a layer of TiO2 and (ii) a column of small ions in the region of highest compression along the mis®t dislocation core constitutes an energetically favorable con®guration.
AcknowledgementsÐThe ®nancial support of the MZT, project No. Z1-7964-0106-96 10083 (Slovenia), is acknowledged (A.R.). We thank F. F. Lange (University of California, Santa Barbara) and T. Wagner (Max-PlanckInstitut fuÈr Metallforschung) for their collaboration on metal±organic deposition, S. J. Pennycook (Oak Ridge National Laboratory) for his assistance with the VG 603 DSTEM, and M. Wilson and M. Exner (Max-Planck-
Institut fuÈr Metallforschung) for helpful discussions on the compressibility of ions in perovskites.
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