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Enhanced ionic conductivity and mesoscopic size effects in heterostructures of BaF2 and CaF2
Solid State Ionics 154 – 155 (2002) 497 – 502 www.elsevier.com/locate/ssi
Enhanced ionic conductivity and mesoscopic size effects in heterostructures of BaF2 and CaF2 N. Sata a, N.Y. Jin-Phillipp b, K. Eberl a,1, J. Maier a,* a
Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany b Max-Planck-Institut fu¨r Metallforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany Accepted 7 March 2002
Abstract Ionic heterolayers of CaF2/BaF2/CaF2 have been prepared by molecular beam epitaxy (MBE). The spacing has been varied from f 1 nm to f 1 Am. In the range of 1 Am to 5 nm, the conductivity (measured effective conductivity parallel to the interface) increases progressively with the increased interfacial density. This is even true for spacings in the sub-Debye range. For comparatively large spacings (>50 nm), semi-infinite space charges provide a quantitative description, while the behavior at smaller spacings reveals nano-size anomalies. At spacings smaller than f 5 nm, the conductivity decreases. The results clearly demonstrate the possibility to prepare artificial ion conductors and the potential of mesoscopic ion conduction. The paper describes transmission electron microscopy (TEM), X-ray diffraction (XRD), X-ray pole figure, secondary ion mass spectrometry (SIMS) and impedance spectroscopic characterization. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Space charge; Heterostructure; Artificial ion conductor; Nano-size effect; Molecular beam epitaxy
1. Introduction The introduction of interfaces into ionically conducting systems has been proven to be a powerful possibility to tune defect chemistry and ion conductivity properties. This is particularly valid for composites. In the case of composites of ion conductors and insulating but subsurface active second phases, the defect chemistry is modified by internal
* Corresponding author. Tel.: +49-711-689-1720; fax: +49-711689-1722. E-mail address: [email protected] (J. Maier). 1 Present address: Lumics, Carl-Scheele-Str. 16, 12489 Berlin.
defect adsorption, while in the case of two coexisting ion conductors, a redistribution of the mobile ions (or a combination of both effects) is expected [1]. The latter effect is analogous to the electron redistribution in the case of semiconductor/semiconductor contacts (of course, both effects occur simultaneously in the general case). Large conductivity anomalies within the miscibility gap of Aghalides can be explained in this way. Nano-sized systems are of particular significance in this context since they (i) provide extremely high interfacial proportions and (ii) might exhibit size effects on the local transport properties. 7H-stacking faults occurring at certain AgI interfaces indicate the potential of nano-sized ionic heterolayers: they can
0167-2738/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 2 7 3 8 ( 0 2 ) 0 0 4 8 8 - 5
498
N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
be conceived as heterolayers of g-AgI/h-AgI/g-AgI/. . . with a spacing of the order of 1 nm [2]. In Ref. [3], we reported about the preparation of defined heterolayers of CaF2/BaF2/CaF2. . . by molecular beam epitaxy (MBE). The increased F conductivity can be consistently explained by a fluoride ion redistribution at the individual boundaries, which will eventually seize the entire material (spacing of interfaces < 4 Debye length). In this paper, we discuss the conductivity properties and especially emphasize the structural characterization.
2. Experiments Heterostructures of CaF2/BaF2 layers were synthesized by the MBE technique [4]. The MBE system has a main UHV chamber connected with a load-lock chamber for substrate transfer to prevent the main chamber from exposure to the air. Pure powder or single crystals of CaF2 and BaF2 were sublimated at 1180 and 1000 jC, respectively, in the main chamber (base pressure of 10 11 Pa) with computer-controllable shutters to tune periodicity and thickness (individual layer thickness: S = 1 to 500 nm). Al2O3 (1102) single crystals were used as substrates. (For pure films of CaF2 or BaF2, we also used SiO2 substrates and
Fig. 1. Typical TEM image of a BaF2 – CaF2 heterostructure with a period of 18 nm.
Fig. 2. SIMS spectra of a BaF2 – CaF2 (total pressure: 10 10 Pa) heterostructure with a period of 103 nm as a function of etching time. Primary ion is Cs + ion with energy of 7.8 kV. BaF2 and CaF2 oscillations are clearly observed. The oscillation of F does not necessarily mean the concentration of F ion in each layer is not uniform. Carbon impurity probably stems from the graphite crucible of CaF2 effusion cell.
different growth conditions. Changes in the conductivity were very minor.) One side of the substrate was optically polished for the deposition. Since Al2O3 is transparent and the substrate is heated by radiation from the heater, the other side of the substrate was coated with Ti film to stabilize the temperature. The substrate was heated at 500 jC for the deposition and slowly cooled down at a rate of 10 jC/min after the growth. The growth rate of CaF2 and BaF2 was about 1 nm/min. The total thickness of the film packages ranged from 200 to 500 nm. The structural properties of grown films were characterized by transmission electron microscopy (TEM), X-ray diffraction (XRD) and secondary ion mass spectrometry (SIMS). TEM was carried out on a Philips CM200 microscope operated at 200 kV with a 0.27-nm point resolution. Cross-sectional specimens with foil normals parallel to h112i and h110i of the BaF2 and CaF2 layers were prepared for TEM observation. Conventional 2h –h scans were performed using the Cu Ka line for XRD. X-ray pole figures of heterostructures have been recorded by Bruker XRD spectrometer, D8 Advance. Secondary Ion Mass Spectroscopy (SIMS) has been performed on a SIMS machine, Atomika 6500. Thin gold coating (15 nm) was used to compensate charging effects.
N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
499
Rectangular platinum films, about 250 nm thick, were deposited parallel on the films by DC-sputtering at room temperature. The lateral conductivity of the film was measured by ac-impedance spectroscopy (1– 104 Hz, Ar atmosphere, 540– 100 jC).
3. Results
Fig. 3. Lattice spacings normal to the substrate surface, (111), as a function of hetero-periods in BaF2 – CaF2 heterostructure determined by X-ray diffraction analysis. Arrows indicate those parameters of bulk crystals and mixed film for comparison.
Fig. 1 shows a bright field micrograph of the sample with 18 nm period at many-beam condition. The BaF2 and CaF2 layers are well defined and demarcated by dark and bright contrasts, respectively. The interfaces are rather wavy (for a similar situation in semiconductor superlattices, see Ref. [5]). In addition to {111} lattice fringes parallel to the layers, moire´ fringes, marked with arrows, are present, indicating the coexistence of crystals with either different lattice constants or different orientations within individual layers. In the sample with a period of 2.2 nm, column-like sub-boundaries form (not shown here). TEM gives no indication of mixing.
Fig. 4. X-ray pole-figures of a heterostructured thin film, selecting the (111)-reflection (l.h.s.) and (220)-reflection (r.h.s.) of BaF2. In the r.h.s. picture, spots other than the six high intensity spots stem from the substrate.
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N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
The SIMS results in Fig. 2 may suggest a partial mixing; however, in how far they are influenced or even determined by lateral averaging effects (see Fig. 1) has to be checked by other methods. The evaluation of the X-ray reflections (see Fig. 3) shows—in view of the significant lattice mismatch, about 10%—a surprisingly small shift in the lattice constants. The lattice constant changes shown are overall values and may be explained by point defect variations and/or partial mixing. Further investigations are necessary to obtain detailed information and to draw more detailed conclusions on the dependence of strain on the distance from the interface. A very recent careful positional analysis of the TEM results gives a clearer picture: indeed, only a few interfacial lattice planes show
anomalous bonding distances, while otherwise, the spacing is very close to that of the bulk phases. This indicates (i) that mixing is restricted to the immediate interface, (ii) that the misfit stress is largely absorbed by dislocation formation in the interfacial area and (iii) that apparent bulk anomalies suggested by SIMS and X-ray are, to a great deal, artefacts of averaging. The detailed presentation will be given in a forthcoming paper [6]. X-ray pole figures in Fig. 4 indicate a very high degree of film orientation. The (111) pole figure shows the (111) reflection exclusively in its center indicating a high degree of orientation. The (220) pole figure shows six symmetrical centers instead of the three for ideal single crystal films pointing towards (111) twin structures as well known for the fluorite crystals [7].
Fig. 5. Arrhenius plots of the electrical conductivities of BaF2 – CaF2 heterostructured thin films (solid circle and open circle) and thin films of BaF2 (open square), CaF2 (open triangle) and their mixture Ba0.5Ca0.5F2 (+). The numbers in this figure give the BaF2/CaF2 period. The inset shows the conductivity dependency on individual thickness of heterostructures.
N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
Conductivity results derived from impedance spectroscopy are given in Fig. 5. The measured effective parallel conductivity (i.e. derived from the measurement parallel conductance via total thickness f 400 nm with distance of 1 mm of the heterostructures) progressively increases with the interfacial density. To rule out that the conductivity enhancement might be due to the formation of mixed phases, we also generated films by the simultaneous deposition of BaF2 and CaF2. These films, which should exhibit a maximum mixing in addition to a high density of interfaces, have only moderately enhanced conductivity values. The enhanced conductivities (overall value denoted by rm) are also not due to oxygen contamination which is known to affect the defect chemistry via formation of OFV and VFS . (The spectrum of 16O in the SIMS results in Fig. 2 shows that the impurity level of O is not very low for the samples grown with a base pressure of 10 6 Pa; note that the SIMS results do not allow a quantitative statement in this case.) Instead, deliberate oxygen contamination led to a decrease in the rm values in the heterostructures which was the larger the smaller the spacing. The inset of Fig. 5 shows that there is a decrease of rm if the spacing is smaller than 5 nm.
4. Discussion From our experience and expectations concerning heterogeneous ionic systems, two reasons for the conductivity effects appear plausible. One is the thermodynamically expected redistributions of fluoride ions from one phase to the other according to the different ‘‘energy levels’’ in the two phases. This leads to an increase of the fluoride vacancy concentration in one conductor and of the fluoride interstitial concentration in the other conductor. The second mechanism is a unilateral or bilateral F transfer to or from the interface layer in order to lower the interfacial core free energy. Note, however, that the first mechanism can also be beneficial with respect to the misfit aspect (based on the distinctly greater molar volume of BaF2 compared to CaF2). As far as the slopes are concerned, the conductivity results are in line with the space charge conception. The results indicate an enhanced conductance primarily in the BaF2 part; there, the migration energies of fluoride vacancies
501
VFS and fluoride interstitials FiVare very similar (VFS : 0.75 eV and FiV: 0.83 eV [8]). The low temperature slope of 0.7– 0.8 eV would be in agreement with both directions of a fluoride ion transfer. The conductivity relation [1]
rm ¼
2 rBaF rCaF2 1 N 1 m þ m þ S N 2" 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# BaF2 e RT e eCaF2 e0 RT 0 CaF2 2uBaF2 ; BaF2 þ 2u 2Vm 2VmCaF2
ð1Þ (u: mobility of the respective fluoride defect in the indicated phase, ee0: dielectric constant, Vm: molar value, the superscripts CaF2 (or BaF2) refer to the defect enriched in CaF2 (or BaF2), N: number of layers) describes both T- and S -dependence (S denoting the spacing). Eq. (1) is based on semi-infinite space charges and assumes a maximum interfacial effect in a simple continuum model [1]. The linear increase with S 1 is due to the fact that the space charge layers approach each other and comparatively insulating bulk portions are eliminated. As can be seen from Fig. 5, the effect does not saturate if S f 4k (k: Debye length assessed to be f 60 nm from impurity level and conductivity behavior of the pure phase). Rather, the conductivity increases more steeply. In terms of space charge conductivity hDrjjiscl, this reads as follows: hDrjjiscl does not stay constant with S 1, but it increases. An increase of hDrjjisc is expected according to an overlap of space charge regions in the subDebye regime, characterized by
4k gðS 1 Þ ¼ S
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c0 c* : c0
ð2Þ
(c0: concentration at the interface, c*: concentration in the center which is implicitly correlated with c0 and S via elliptical integrals [9]). The fact that the results indicate an even higher increase than expected if the boundary concentrations are considered to be constant with spacing (increased slope in rm vs. S 1), has to be tackled in greater detail. An in-depth consideration of this is in preparation.
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N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
The effect of oxygen contamination on the slope may provide an additional support of the space charge overlap [10]. Since it directly influences k, it has a profound influence on the transition between the regime of semi-infinite boundary conditions to the regime of finite boundary conditions as indeed observed. A remarkable feature is the steep slope at high temperatures (0.95 eV). It is far flatter than the intrinsic slope. A natural explanation is provided by including the conduction contribution of CaF2 into the analysis (migration energy of FiV: 0.92 eV [11]). In fact, if we assume FiV to be enriched there, the high temperature behavior naturally follows from the quantitative analysis as a consequence of the steeper activation energy of the boundary transport in CaF2 (last term in Eq. (1)). The high temperature behavior is then to be attributed to an interstitial conduction in the CaF2 films. This favors a fluoride ion redistribution mechanism from BaF2 to CaF2 as the defectinducing process. In how far local boundary peculiarities explain the rm decrease for extremely tiny films or if this is simply due to a loss of coherency has to be investigated in more detail.
5. Conclusions TEM, SIMS, X-ray and impedance spectroscopy demonstrate that defined highly oriented heterostructures of CaF2/BaF2/CaF2. . . can be prepared. They rely on the morphological metastability of the interfacial arrangement and make use of the ionic contact equilibria which are thermodynamically demanded. The results can be consistently explained by an internal charge transfer (presumably a fluoride ion transfer from BaF2 to CaF2) and show the relevance of the space charge effects. If S b4k, space charges overlap and penetrate the heterolayer package throughout leading to artificial ion conductors in which novel properties emerge. In this regime, strain
effects and defect interactions are likely to play an additional role. The decrease at extremely tiny systems may be due to structural effects or to morphological nonidealities. Further, extremely worthwhile information is expected from conductivity results perpendicular to the interface which requires an appropriate substrate. At present, we are exploring the possibility to use the heterostructure concept for the preparation of other systems of ion conductors.
Acknowledgements We would like to express our gratitude to W. Kussmaul for the experimental assistance. We are indebted to Dr. Bilger and to Dr. De Souza for SIMS experiments, to Dr. Kerber for the X-ray pole-figure and to Dr. Adams for helpful discussions.
References [1] J. Maier, Prog. Solid State Chem. 23 (1995) 171. [2] J.-S. Lee, S. Adams, J. Maier, J. Electrochem. Soc. 147 (6) (2000) 2407. [3] N. Sata, K. Eberman, K. Eberl, J. Maier, Nature 408 (2000) 946. [4] K. Eberl, P.M. Petroff, P. Demeester (Eds.), Low Dimensional Structures Prepared by Epitaxial Growth or Regrowth on Patterned Substrates, NATO Science Series: E: Applied Sciences, vol. 298, Kluwer Academic Publishing, Dordrecht, 1995. [5] N.Y. Jin-Phillipp, F. Phillipp, T. Marschner, W. Stolz, J. Mater. Sci., Mater. Electron. 8 (1997) 289. [6] N.Y. Jin-Phillipp, N. Sata, J. Maier, in preparation. [7] W. Kleber, H.-J. Bautsch, J. Bohm, Einfu¨hrung in die Kristallographie, 17th ed., Verlag Technik, Berlin, 1990. [8] W. Bollmann, Phys. Status Solidi, A 18 (1973) 313. [9] J. Maier, Solid State Ionics 23 (1987) 59. [10] Y.-M. Chiang (Ed.), Special Issue on Nanostructured Materials for Energy Applications, J. Electroceram. vol. 3, Kluwer, Dordrecht, 1997, p. 205. [11] W. Bollmann, R. Reimann, Phys. Status Solidi, A 16 (1973) 187.
Enhanced ionic conductivity and mesoscopic size effects in heterostructures of BaF2 and CaF2 N. Sata a, N.Y. Jin-Phillipp b, K. Eberl a,1, J. Maier a,* a
Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany b Max-Planck-Institut fu¨r Metallforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany Accepted 7 March 2002
Abstract Ionic heterolayers of CaF2/BaF2/CaF2 have been prepared by molecular beam epitaxy (MBE). The spacing has been varied from f 1 nm to f 1 Am. In the range of 1 Am to 5 nm, the conductivity (measured effective conductivity parallel to the interface) increases progressively with the increased interfacial density. This is even true for spacings in the sub-Debye range. For comparatively large spacings (>50 nm), semi-infinite space charges provide a quantitative description, while the behavior at smaller spacings reveals nano-size anomalies. At spacings smaller than f 5 nm, the conductivity decreases. The results clearly demonstrate the possibility to prepare artificial ion conductors and the potential of mesoscopic ion conduction. The paper describes transmission electron microscopy (TEM), X-ray diffraction (XRD), X-ray pole figure, secondary ion mass spectrometry (SIMS) and impedance spectroscopic characterization. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Space charge; Heterostructure; Artificial ion conductor; Nano-size effect; Molecular beam epitaxy
1. Introduction The introduction of interfaces into ionically conducting systems has been proven to be a powerful possibility to tune defect chemistry and ion conductivity properties. This is particularly valid for composites. In the case of composites of ion conductors and insulating but subsurface active second phases, the defect chemistry is modified by internal
* Corresponding author. Tel.: +49-711-689-1720; fax: +49-711689-1722. E-mail address: [email protected] (J. Maier). 1 Present address: Lumics, Carl-Scheele-Str. 16, 12489 Berlin.
defect adsorption, while in the case of two coexisting ion conductors, a redistribution of the mobile ions (or a combination of both effects) is expected [1]. The latter effect is analogous to the electron redistribution in the case of semiconductor/semiconductor contacts (of course, both effects occur simultaneously in the general case). Large conductivity anomalies within the miscibility gap of Aghalides can be explained in this way. Nano-sized systems are of particular significance in this context since they (i) provide extremely high interfacial proportions and (ii) might exhibit size effects on the local transport properties. 7H-stacking faults occurring at certain AgI interfaces indicate the potential of nano-sized ionic heterolayers: they can
0167-2738/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 2 7 3 8 ( 0 2 ) 0 0 4 8 8 - 5
498
N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
be conceived as heterolayers of g-AgI/h-AgI/g-AgI/. . . with a spacing of the order of 1 nm [2]. In Ref. [3], we reported about the preparation of defined heterolayers of CaF2/BaF2/CaF2. . . by molecular beam epitaxy (MBE). The increased F conductivity can be consistently explained by a fluoride ion redistribution at the individual boundaries, which will eventually seize the entire material (spacing of interfaces < 4 Debye length). In this paper, we discuss the conductivity properties and especially emphasize the structural characterization.
2. Experiments Heterostructures of CaF2/BaF2 layers were synthesized by the MBE technique [4]. The MBE system has a main UHV chamber connected with a load-lock chamber for substrate transfer to prevent the main chamber from exposure to the air. Pure powder or single crystals of CaF2 and BaF2 were sublimated at 1180 and 1000 jC, respectively, in the main chamber (base pressure of 10 11 Pa) with computer-controllable shutters to tune periodicity and thickness (individual layer thickness: S = 1 to 500 nm). Al2O3 (1102) single crystals were used as substrates. (For pure films of CaF2 or BaF2, we also used SiO2 substrates and
Fig. 1. Typical TEM image of a BaF2 – CaF2 heterostructure with a period of 18 nm.
Fig. 2. SIMS spectra of a BaF2 – CaF2 (total pressure: 10 10 Pa) heterostructure with a period of 103 nm as a function of etching time. Primary ion is Cs + ion with energy of 7.8 kV. BaF2 and CaF2 oscillations are clearly observed. The oscillation of F does not necessarily mean the concentration of F ion in each layer is not uniform. Carbon impurity probably stems from the graphite crucible of CaF2 effusion cell.
different growth conditions. Changes in the conductivity were very minor.) One side of the substrate was optically polished for the deposition. Since Al2O3 is transparent and the substrate is heated by radiation from the heater, the other side of the substrate was coated with Ti film to stabilize the temperature. The substrate was heated at 500 jC for the deposition and slowly cooled down at a rate of 10 jC/min after the growth. The growth rate of CaF2 and BaF2 was about 1 nm/min. The total thickness of the film packages ranged from 200 to 500 nm. The structural properties of grown films were characterized by transmission electron microscopy (TEM), X-ray diffraction (XRD) and secondary ion mass spectrometry (SIMS). TEM was carried out on a Philips CM200 microscope operated at 200 kV with a 0.27-nm point resolution. Cross-sectional specimens with foil normals parallel to h112i and h110i of the BaF2 and CaF2 layers were prepared for TEM observation. Conventional 2h –h scans were performed using the Cu Ka line for XRD. X-ray pole figures of heterostructures have been recorded by Bruker XRD spectrometer, D8 Advance. Secondary Ion Mass Spectroscopy (SIMS) has been performed on a SIMS machine, Atomika 6500. Thin gold coating (15 nm) was used to compensate charging effects.
N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
499
Rectangular platinum films, about 250 nm thick, were deposited parallel on the films by DC-sputtering at room temperature. The lateral conductivity of the film was measured by ac-impedance spectroscopy (1– 104 Hz, Ar atmosphere, 540– 100 jC).
3. Results
Fig. 3. Lattice spacings normal to the substrate surface, (111), as a function of hetero-periods in BaF2 – CaF2 heterostructure determined by X-ray diffraction analysis. Arrows indicate those parameters of bulk crystals and mixed film for comparison.
Fig. 1 shows a bright field micrograph of the sample with 18 nm period at many-beam condition. The BaF2 and CaF2 layers are well defined and demarcated by dark and bright contrasts, respectively. The interfaces are rather wavy (for a similar situation in semiconductor superlattices, see Ref. [5]). In addition to {111} lattice fringes parallel to the layers, moire´ fringes, marked with arrows, are present, indicating the coexistence of crystals with either different lattice constants or different orientations within individual layers. In the sample with a period of 2.2 nm, column-like sub-boundaries form (not shown here). TEM gives no indication of mixing.
Fig. 4. X-ray pole-figures of a heterostructured thin film, selecting the (111)-reflection (l.h.s.) and (220)-reflection (r.h.s.) of BaF2. In the r.h.s. picture, spots other than the six high intensity spots stem from the substrate.
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N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
The SIMS results in Fig. 2 may suggest a partial mixing; however, in how far they are influenced or even determined by lateral averaging effects (see Fig. 1) has to be checked by other methods. The evaluation of the X-ray reflections (see Fig. 3) shows—in view of the significant lattice mismatch, about 10%—a surprisingly small shift in the lattice constants. The lattice constant changes shown are overall values and may be explained by point defect variations and/or partial mixing. Further investigations are necessary to obtain detailed information and to draw more detailed conclusions on the dependence of strain on the distance from the interface. A very recent careful positional analysis of the TEM results gives a clearer picture: indeed, only a few interfacial lattice planes show
anomalous bonding distances, while otherwise, the spacing is very close to that of the bulk phases. This indicates (i) that mixing is restricted to the immediate interface, (ii) that the misfit stress is largely absorbed by dislocation formation in the interfacial area and (iii) that apparent bulk anomalies suggested by SIMS and X-ray are, to a great deal, artefacts of averaging. The detailed presentation will be given in a forthcoming paper [6]. X-ray pole figures in Fig. 4 indicate a very high degree of film orientation. The (111) pole figure shows the (111) reflection exclusively in its center indicating a high degree of orientation. The (220) pole figure shows six symmetrical centers instead of the three for ideal single crystal films pointing towards (111) twin structures as well known for the fluorite crystals [7].
Fig. 5. Arrhenius plots of the electrical conductivities of BaF2 – CaF2 heterostructured thin films (solid circle and open circle) and thin films of BaF2 (open square), CaF2 (open triangle) and their mixture Ba0.5Ca0.5F2 (+). The numbers in this figure give the BaF2/CaF2 period. The inset shows the conductivity dependency on individual thickness of heterostructures.
N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
Conductivity results derived from impedance spectroscopy are given in Fig. 5. The measured effective parallel conductivity (i.e. derived from the measurement parallel conductance via total thickness f 400 nm with distance of 1 mm of the heterostructures) progressively increases with the interfacial density. To rule out that the conductivity enhancement might be due to the formation of mixed phases, we also generated films by the simultaneous deposition of BaF2 and CaF2. These films, which should exhibit a maximum mixing in addition to a high density of interfaces, have only moderately enhanced conductivity values. The enhanced conductivities (overall value denoted by rm) are also not due to oxygen contamination which is known to affect the defect chemistry via formation of OFV and VFS . (The spectrum of 16O in the SIMS results in Fig. 2 shows that the impurity level of O is not very low for the samples grown with a base pressure of 10 6 Pa; note that the SIMS results do not allow a quantitative statement in this case.) Instead, deliberate oxygen contamination led to a decrease in the rm values in the heterostructures which was the larger the smaller the spacing. The inset of Fig. 5 shows that there is a decrease of rm if the spacing is smaller than 5 nm.
4. Discussion From our experience and expectations concerning heterogeneous ionic systems, two reasons for the conductivity effects appear plausible. One is the thermodynamically expected redistributions of fluoride ions from one phase to the other according to the different ‘‘energy levels’’ in the two phases. This leads to an increase of the fluoride vacancy concentration in one conductor and of the fluoride interstitial concentration in the other conductor. The second mechanism is a unilateral or bilateral F transfer to or from the interface layer in order to lower the interfacial core free energy. Note, however, that the first mechanism can also be beneficial with respect to the misfit aspect (based on the distinctly greater molar volume of BaF2 compared to CaF2). As far as the slopes are concerned, the conductivity results are in line with the space charge conception. The results indicate an enhanced conductance primarily in the BaF2 part; there, the migration energies of fluoride vacancies
501
VFS and fluoride interstitials FiVare very similar (VFS : 0.75 eV and FiV: 0.83 eV [8]). The low temperature slope of 0.7– 0.8 eV would be in agreement with both directions of a fluoride ion transfer. The conductivity relation [1]
rm ¼
2 rBaF rCaF2 1 N 1 m þ m þ S N 2" 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# BaF2 e RT e eCaF2 e0 RT 0 CaF2 2uBaF2 ; BaF2 þ 2u 2Vm 2VmCaF2
ð1Þ (u: mobility of the respective fluoride defect in the indicated phase, ee0: dielectric constant, Vm: molar value, the superscripts CaF2 (or BaF2) refer to the defect enriched in CaF2 (or BaF2), N: number of layers) describes both T- and S -dependence (S denoting the spacing). Eq. (1) is based on semi-infinite space charges and assumes a maximum interfacial effect in a simple continuum model [1]. The linear increase with S 1 is due to the fact that the space charge layers approach each other and comparatively insulating bulk portions are eliminated. As can be seen from Fig. 5, the effect does not saturate if S f 4k (k: Debye length assessed to be f 60 nm from impurity level and conductivity behavior of the pure phase). Rather, the conductivity increases more steeply. In terms of space charge conductivity hDrjjiscl, this reads as follows: hDrjjiscl does not stay constant with S 1, but it increases. An increase of hDrjjisc is expected according to an overlap of space charge regions in the subDebye regime, characterized by
4k gðS 1 Þ ¼ S
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c0 c* : c0
ð2Þ
(c0: concentration at the interface, c*: concentration in the center which is implicitly correlated with c0 and S via elliptical integrals [9]). The fact that the results indicate an even higher increase than expected if the boundary concentrations are considered to be constant with spacing (increased slope in rm vs. S 1), has to be tackled in greater detail. An in-depth consideration of this is in preparation.
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N. Sata et al. / Solid State Ionics 154 – 155 (2002) 497–502
The effect of oxygen contamination on the slope may provide an additional support of the space charge overlap [10]. Since it directly influences k, it has a profound influence on the transition between the regime of semi-infinite boundary conditions to the regime of finite boundary conditions as indeed observed. A remarkable feature is the steep slope at high temperatures (0.95 eV). It is far flatter than the intrinsic slope. A natural explanation is provided by including the conduction contribution of CaF2 into the analysis (migration energy of FiV: 0.92 eV [11]). In fact, if we assume FiV to be enriched there, the high temperature behavior naturally follows from the quantitative analysis as a consequence of the steeper activation energy of the boundary transport in CaF2 (last term in Eq. (1)). The high temperature behavior is then to be attributed to an interstitial conduction in the CaF2 films. This favors a fluoride ion redistribution mechanism from BaF2 to CaF2 as the defectinducing process. In how far local boundary peculiarities explain the rm decrease for extremely tiny films or if this is simply due to a loss of coherency has to be investigated in more detail.
5. Conclusions TEM, SIMS, X-ray and impedance spectroscopy demonstrate that defined highly oriented heterostructures of CaF2/BaF2/CaF2. . . can be prepared. They rely on the morphological metastability of the interfacial arrangement and make use of the ionic contact equilibria which are thermodynamically demanded. The results can be consistently explained by an internal charge transfer (presumably a fluoride ion transfer from BaF2 to CaF2) and show the relevance of the space charge effects. If S b4k, space charges overlap and penetrate the heterolayer package throughout leading to artificial ion conductors in which novel properties emerge. In this regime, strain
effects and defect interactions are likely to play an additional role. The decrease at extremely tiny systems may be due to structural effects or to morphological nonidealities. Further, extremely worthwhile information is expected from conductivity results perpendicular to the interface which requires an appropriate substrate. At present, we are exploring the possibility to use the heterostructure concept for the preparation of other systems of ion conductors.
Acknowledgements We would like to express our gratitude to W. Kussmaul for the experimental assistance. We are indebted to Dr. Bilger and to Dr. De Souza for SIMS experiments, to Dr. Kerber for the X-ray pole-figure and to Dr. Adams for helpful discussions.
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