Size Effects on the Electrical Conductivity of Ceria: Achieving Low

Article pubs.acs.org/JPCC

Size Effects on the Electrical Conductivity of Ceria: Achieving Low Space Charge Potentials in Nanocrystalline Thin Films M. C. Göbel, G. Gregori,* and J. Maier Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany S Supporting Information *

ABSTRACT: Thin films of nominally pure and 10 mol % Gd-doped ceria were grown on Al2O3⟨11̅02⟩ (r-cut) and MgO⟨100⟩ substrates with pulsed laser deposition (PLD). Their electrical conductivity properties were measured using impedance spectroscopy. Oxygen partial pressure and temperature dependence indicate that the nominally pure films are contaminated with acceptor impurities whose concentration is found to vary perceptibly among the samples. Quite remarkably, the nanocrystalline 10 mol % Gd-doped thin films show conductivities that are, as expected, lower than those for epitaxial films but surprisingly much larger than those obtained previously from other comparable nanocrystalline films (e.g., grown on SiO2), indicating that the oxygen vacancies are much less depleted at the grain boundaries. Correspondingly, the space charge potential was found to be unusually small with a value of 0.19 ± 0.05 V.

1. INTRODUCTION Motivated by the worldwide energy challenge, increased efforts have been made concerning the search for new materials for more efficient power conversion devices, such as solid oxide fuel cells (SOFCs).1−3 SOFCs are particularly interesting because, in contrast to fuel cell technologies working at lower temperatures, they easily convert not only hydrogen but also different hydrocarbons.4,5 On the other hand, the high operation temperature leads to severe material problems. For example, ceramic interconnects are required instead of readily available stainless steel interconnects. Therefore a major goal in SOFC development is the reduction of the operation temperature to ∼500 °C6−8 or even below.9 The decrease of operation temperature is not only limited by the low oxygen exchange rate at the cathode; the electrolyte conductivity also becomes critical. As far as electrolytes are concerned, acceptor-doped cerium oxide (CeO2) exhibits, thanks to the low migration energy, a very high oxygen vacancy conductivity at intermediate temperatures10 and is thus a promising electrolyte in this respect.80 A parallel approach to lower the process temperature is the development of SOFCs in the microscopic range using thin film electrolytes. Such μ-SOFCs19−22 are supposed to replace batteries in portable devices in the future as hydrocarbons offer much larger energy densities. However, while high in the bulk, the ionic conductivity at the grain boundaries (GBs) is strongly reduced in acceptor-doped CeO2 because of a positive space charge layer (SCL) potential arising from a positively charged GB core,23−32 which leads also to an increase of the electronic conductivity.33,34 Notably, the SCL effects were found to dominate the overall conductivity properties particularly in nanocrystalline materials (e.g., ref 35−38). For acceptor-doped CeO2 with very small grains, the SCLs were found to drastically change the electrical transport © 2013 American Chemical Society

properties by many orders of magnitudes, leading to unusual features such as significant n-type electronic conductivity even in strongly acceptor-doped materials at low temperatures and high oxygen partial pressures (pO2).32,39 Also, heterojunctions such as film−substrate interfaces were observed to vary the conductivity of CeO2 and related materials because of both SCL and strain effects.40−46 The role of strain is quite controversial: recent publications show that strained ceria−zirconia (YSZ) multilayers did not exhibit any significant conductivity variation compared with the bulk properties.47 In addition, further studies recently pointed out that other contributions, such as leakage currents through the nominally insulating (but much thicker) substrate for in-plane measurements of very thin films48,49 or GB effects in polycrystalline films with a thickness-dependent lateral grain size, 31 lead to experimental results that can be easily misinterpreted as conductivity effects at the film−substrate interface. These uncertainties show that further systematic studies on boundary effects in CeO2 and related materials are necessary to clarify a number of important aspects, such as (i) the conditions under which the experimental data can be safely attributed to boundary effects, (ii) the microstructural origins of the boundary effects, (iii) the impact of boundary effects on the electrical conductivity, and (iv) the identification of the parameters that can be used to adjust the boundary properties. This paper deals with the first two aspects mentioned above: (i) the influence of the presence of impurities (particularly in nominally pure samples) on presumed boundary effects and (ii) Received: July 30, 2013 Revised: September 20, 2013 Published: September 23, 2013 22560

dx.doi.org/10.1021/jp407585w | J. Phys. Chem. C 2013, 117, 22560−22568

The Journal of Physical Chemistry C

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Figure 1. X-ray diffraction (XRD) patterns of the CeO2 thin films: (a) nominally pure cerium oxide on Al2O3⟨11̅02⟩, (b) 10 mol % Gd-doped cerium oxide on Al2O3⟨11̅02⟩, (c) nominally pure cerium oxide on MgO⟨100⟩, and (d) 10 mol % Gd-doped cerium oxide on MgO⟨100⟩. The curves have been smoothed for clarity.

the role of the microstructure on the origin of the space charge potential. In model systems such as SrTiO3 bicrystals, it is known that the structure of the GB (the misorientation angle between two adjacent grains) crucially controls their conductivity properties (e.g., ref 37). For thin films, the microstructure and thus also the misorientation angles depend (among other influences) on the chosen substrate. An example for well-investigated polycrystalline CeO2 films are thin films grown on SiO2⟨0001⟩ substrates for which it was found that the GB effects dominate the ionic conductivity.31,32,50 Here the SiO2 substrate has a large structural mismatch compared with CeO2 (the lattice parameter of SiO2⟨0001⟩ is a = 4.91 Å). Therefore, one way to address the GB structure-SCL potential relationship is the investigation of films grown on substrates that show a lattice mismatch which is smaller than with SiO2 but large enough to cause polycrystalline growth. Two well-suited candidates for a substrate which fulfill these conditions and which are utilized in this study are MgO⟨100⟩ and Al2O3⟨11̅02⟩ (r-cut). For both materials the lattice mismatch is about 10%. Hence, the present study deals with the investigation of the electrical conductivity of polycrystalline acceptor-doped and nominally pure ceria thin films grown on Al2O3⟨11̅02⟩ (r-cut) and MgO⟨100⟩ substrates. It is worth briefly summarizing the main features of the defect chemistry of ceria starting from the oxygen excorporation reaction OOX =

1 O2 + VO•• + 2e / 2

K = pO21/2 cVO••n2

2cVO•• = n

(3)

σn ∝ n = (2K )1/3 pO2−1/6

(4)

with σn being the electronic conductivity and pO2 being the oxygen partial pressure, from which Nn =

∂log σ 1 =− 6 ∂log pO2

⎛ ⎞ Δ H ⎜and correspondingly Ea = R + hn⎟ ⎝ ⎠ 3

(5)

with Nn being the pO2 dependence of σn, Ea the activation energy, ΔRH the reduction enthalpy, and hn the electron hopping energy. For acceptor-doped ceria, 2cV••O = cA holds and thus σn ∝ n = 2K1/2cA−1/2pO2−1/4 Nn = −

(6)

1 4

⎛ ⎞ Δ H ⎜and correspondingly Ea = R + hn⎟ ⎝ ⎠ 2

(7)

For strongly acceptor-doped ceria: 2cVO•• = cA ≫ n

(8)

Nv = 0 (and correspondingly Ea = hVO• •)

(9)

(1) (2)

where Nv is the oxygen partial pressure dependence of the ionic (oxygen vacancy) conductivity, hV••o the migration enthalpy of the oxygen vacancy, and cA the concentration of a trivalent dopant such as gadolinium.

where K is the corresponding equilibrium constant and cV••O and n are the equilibrium concentrations of oxygen vacancies and electrons, respectively. For pure ceria 22561



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Table 1. Results of the XRD and TEM Investigation of the Ceria Thin Films Al2O3⟨11̅02⟩

substrate doping

nominally pure

TEM: film thickness XRD: lattice constant (Å) crystallinity

63

TEM: lateral grain size (nm)

29 ± 1 5.42 ± 0.01 epitaxial no grains

284 ± 14 5.42 ± 0.01

MgO⟨100⟩ 10 mol % Gd

nominally pure

45 ± 2 5.45 ± 0.01

309 ± 15 5.43 ± 0.02

33 ± 2 5.47 ± 0.05

polycrystalline with columnar grains 18 ± 9

poly crystalline >50

polycrystalline with columnar grains 16 ± 6

272 ± 14 5.47 ± 0.05

10 mol % Gd

58 ± 19

39 ± 2 5.49 ± 0.05

16 ± 11

431 ± 22 5.47 ± 0.02

59 ± 26

The films grown on MgO (both nominally pure and acceptordoped) also exhibit a polycrystalline columnar structure, as indicated by the XRD patterns (Figure 1c,d), which show several orientations. Owing to the high intensity ratio between the (111) and (100) signals, the Gd-doped CeO2 films on MgO appear to be preferentially oriented along the (111) direction. This polycrystalline microstructure is expected given the quite large lattice mismatch between MgO and ceria (the lattice parameter of MgO is 4.21 Å).62 Interestingly, according to the XRD pattern, the films on MgO exhibit a slightly larger lattice constant compared with the films on Al2O3⟨11̅02⟩ (increase about 1%). However, this difference is not statistically significant in view of the corresponding large measurement error caused by the weak intensity of the CeO2 XRD reflexes for films on MgO (thus the difficulty in assigning the precise position of the signal maximum). High-resolution TEM analysis (Supporting Information) indicated these grain boundaries are clean without segregation or a second phase. The lateral grain sizes were measured using the TEM micrographs. As summarized in Table 1 this value is significantly larger for the thicker films (about 60 nm for films thicker than 270 nm) compared with the thinnest prepared films (about 15−20 nm for films thinner than 50 nm). 3.2. The 10 mol % Gd-Doped Films. Figure 2 shows representative impedance spectra collected from the Gd-doped

2. EXPERIMENTAL SECTION For each 10 × 10 × 0.5 mm3 substrate, Al2O3⟨11̅02⟩ and MgO⟨100⟩ (CrysTec GmbH, Germany), and each electrolyte composition (nominally pure and 10 mol % Gd-doped), four thin films of different thicknesses (ranging between 25 and 450 nm) were fabricated using pulsed laser deposition (PLD) as described in ref 31, including a 30 min postdeposition treatment at 720 °C in 1 bar pure oxygen (grade 5.0). To measure the film thicknesses for each set of films, cross sections of the respective thinnest and thickest films were cut with the focused ion beam (FIB) (Zeiss Crossbeam 1540 ESB electron microscope, gallium ion beam, acceleration voltage of 30 kV, 10 pA ion current for the final fine cut). These lamellae were investigated using transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) (Zeiss 912 Omega TEM microscope with acceleration voltage of 120 kV and a JEOL 4000FX with acceleration voltage of 400 kV). The thicknesses of the two intermediately thick films were linearly interpolated in accordance with the corresponding number of PLD pulses. For X-ray diffraction (XRD) analysis, a Philips Xpert XRD diffractometer 3710 HTK (Cu Kα radiation λ = 1.54056 Å) was utilized. The electrical conduction properties were determined via impedance spectroscopy upon deposition of 2 parallel platinum electrodes as described elsewhere.31 The measurements were performed at different temperatures ranging from 230 to 700 °C and at different pO2 ranging between 10−5 and 1 bar (using oxygen/nitrogen mixtures). The pO2 was monitored with a commercial oxygen sensor (Cambridge Sensotec, UK). Also, the conductance of the bare Al2O3⟨110̅ 2⟩ and MgO⟨100⟩ substrates was measured and found to be negligible in comparison to the thin film conductances. 3. RESULTS AND DISCUSSION 3.1. Microstructure Characterization. Figure 1 shows the XRD diffractograms of the thin films. Let us first discuss the nominally pure samples on Al2O3⟨110̅ 2⟩ (Figure 1a). For these films, only signals corresponding to the (100) orientation were found pointing toward epitaxial growth. Indeed, the TEM investigation also shows an epitaxial microstructure (cf. Supporting Information). On the one hand this is astonishing given that the relevant Al2O3[112̅0] axis is 12% larger compared with the CeO2[100] axis (CeO2[100], 5.41 Å; Al2O3[112̅0], 4.76 Å; Al2O3[1̅101], 5.21 Å).51 However, on the other hand there are many studies in the literature reporting epitaxial growth of CeO2 on Al2O3⟨11̅02⟩ (e.g. ref 52−58). On the contrary, the Gd-doped CeO2 films exhibit additional (111) and (222) signals (Figure 1b) while the TEM micrographs (Supporting Information) clearly show the presence of a polycrystalline columnar structure. Most likely it is the slight increase in the lattice constant upon doping59−61 (Table 1) that causes the variation of the microstructure.

Figure 2. Impedance spectra of 10 mol % Gd-doped CeO2 films of different thicknesses on MgO⟨100⟩ substrates (θ = 700 °C). The equivalent circuit used for fitting the data is shown in the inset.

films with different thicknesses. Notably, for all samples the impedance spectrum is characterized by a single semicircle. The reason for this is the stray capacitance of the measurement setup, which is several orders of magnitudes larger than that of the bulk and GB capacitances.31 As a consequence, the measured resistances, and thus the corresponding conductivities, are effective values that contain contributions from both bulk and GBs. These considerations also hold for the nominally pure samples. As expected, the 10 mol % Gd-doped films do not exhibit a pO2-dependent conductivity. Their activation energy between 0.7 and 0.9 eV (Figure 3 and Table 2) is slightly higher than the 22562



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Figure 3. Activation energy vs thickness diagrams of the CeO2 thin films on Al2O3⟨11̅02⟩ and MgO⟨100⟩. (a) Nominally pure CeO2; (b) 10 mol % Gddoped CeO2.

Table 2. Conductivity Data (at 700°C) and Activation Energies (between 700 and 580°C) for the Ceria Thin Filmsa Nominally Pure CeO2 Thin Films Al2O3⟨11̅02⟩

substrate thickness (nm) conductivity (S m−1)

29

65

138

284

33

67

135

272

0.27 0.13 0.073 0.048 0.027 0.016

0.15 0.067 0.039 0.025 0.014 0.0090

0.100 0.046 0.027 0.017 0.0097 0.0060

0.084 0.038 0.022 0.014 0.0081 0.0051

0.97 0.47 0.30 0.19 0.112 0.069

0.69 0.36 0.23 0.15 0.091 0.056

0.67 0.35 0.22 0.14 0.088 0.054

0.76 0.38 0.25 0.17 0.103 0.065

−1/4.4

−1/4.4

−1/4.4

−1/4.3

−1/4.6

−1/4.8

−1/4.8

−1/5.0

pO2 = 10−5 bar

1.71

1.74

1.79

1.88

1.39

1.34

1.40

1.37

pO2 = 10−4 bar pO2 = 10−3 bar pO2 = 10−2 bar pO2 = 10−1 bar pO2 = 1 bar

1.74 1.76 1.78 1.78 1.76

1.76 1.81 1.90 1.77 1.82 1.91 1.78 1.84 1.92 1.77 1.83 1.91 1.71 1.81 1.88 10 mol % Gd-Doped CeO2 Thin Films

1.48 1.56 1.61 1.64 1.65

1.44 1.53 1.58 1.61 1.63

− − 1.61 1.63 1.66

1.44 1.52 1.58 1.62 1.65

pO2 = 10−5 bar pO2 = 10−4 bar pO2 = 10−3 bar pO2 = 10−2 bar pO2 = 10−1 bar pO2 = 1 bar

pO2 dependence at 700 °C activation energy (eV)

Al2O3⟨110̅ 2⟩

substrate

a

MgO⟨100⟩

MgO⟨100⟩

thickness (nm)

45

83

158

309

39

95

207

431

conductivity (S m−1) activation energy (eV)

1.8 0.75

3.1 0.72

2.5 0.84

3.3 0.69

1.9 0.93

2.3 0.91

2.1 0.91

2.4 0.87

Errors: conductivity, ± 10%; activation energy, ± 0.02 eV; reciprocal pO2 dependence, ± 0.3 (e.g., −1/(4.4 ± 0.3).

Figure 4. Conductivity vs thickness diagrams of the CeO2 thin films on Al2O3⟨11̅02⟩ and MgO⟨100⟩. (a) Nominally pure CeO2; (b) 10 mol % Gddoped CeO2.

films on SiO2⟨0001⟩ substrates 31 (≈ 1.1 eV). Similarly, their conductivity values (Figure 4) amount to ∼2−3 S m−1, a value smaller than that of epitaxial films (e.g., 4 S m −1 for films grown

value of about 0.7 eV observed in single crystals10,64 and epitaxial films65,66 but lies well in the range for polycrystalline samples. Notably, it is significantly smaller than the activation energy of 22563



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Figure 5. Conductance vs thickness diagrams of the CeO2 thin films on Al2O3⟨11̅02⟩ and MgO⟨100⟩ in comparison with the results of ceria films on Al2O3⟨0001⟩ and SiO2⟨0001⟩ discussed in ref 31. (a) Nominally pure CeO2; (b) 10 mol % Gd-doped CeO2.

on Al2O3⟨0001⟩ 31) but definitely larger than those of the polycrystalline films on SiO2⟨0001⟩ ranging between 0.3 and 1 S m−1. As shown for the films on SiO2⟨0001⟩, the thicknessdependent lateral grain size (Table 1) leads to a small slope and a negative intercept in the conductance versus thickness plot.31 The same effect can also be observed for the films grown on Al2O3⟨11̅02⟩ and MgO⟨100⟩ (Figure 5, right panel); however, it is less pronounced compared with the films on quartz. This reduced effect of the GBs on the conductivity is astonishing given that the GB density between the films grown on Al2O3⟨11̅02⟩, MgO⟨100⟩, and SiO2⟨0001⟩ (ref 31) is very similar. Therefore, the microstructure of the GBs, i.e., their SCL potential, must be different. Here, the SCL potential was calculated by numerically solving the Poisson equation49,67,81 and using the well-established brick layer model.68,82 The potential was calculated to be 0.19 ± 0.05 V. This value not only is considerably smaller than the potential for the films on quartz calculated from conductivity data acquired under very similar conditions (0.32 ± 0.05 V)31 but also is at the lower limit of other literature values for the SCL potential in ceria obtained for different doping contents, pellets, or thin films grown under different conditions (between 0.20 and 0.34 V).26,32,69,70 The low potential corresponds to a low positive charge in the GB core. Typically, the origin of the core charge is ascribed to local deviation of the cation/anion stoichiometry (e.g., a deficiency of oxide ions71). For SrTiO3, it was observed that the misorientation angle between the grains leads to different resulting core charges and SCL potentials.37 The data of the present study show that it is not unlikely that the situation is the same for cerium oxide. Because of the smaller lattice mismatch between ceria and the Al2O3⟨11̅02⟩ and MgO substrates (in comparison with quartz), the grains appear to be arranged in a way such that at their boundaries only a small cation/anion stoichiometry variation (and thus GB core charge) is created. 3.3. The Nominally Pure Films. The measured pO2 dependence (Nm) of the nominally pure films lies between the expected value for pure (−1/6) and slightly acceptor-doped (−1/4) CeO2 ( Figure 6). Because, under consideration of the measurement error, the pO2 dependence of the films shows no significant thickness dependence, this deviation from the value of −1/6 cannot be ascribed to the film−substrate interface effect, but rather it is ascribed to the bulk of the material.83 Thus, this indicates that the samples are contaminated by a small concentration of acceptor dopant. In this case the charge neutrality condition is 2cVO•• = n + cA

Figure 6. Oxygen partial pressure dependence of the conductance G of the nominally pure CeO2 thin films.

Various origins of the impurities might be possible. However, the fact that thin films prepared using the same target were found to exhibit quite remarkable differences in their conductivity84,85 suggests that the contamination occurs after the target preparation or during the film deposition using PLD. Let us now consider the epitaxial films on Al2O3⟨11̅02⟩, whose pO2 dependence is about −1/4.4. Two explanations of such a “mixed” slope are possible depending on the detailed doping (impurities) level: (i) CeO2 is in a mixed conductivity regime in which excess electrons and oxygen vacancies contribute perceptibly to the overall conductivity; (ii) CeO2 is electronically conducting but between the intrinsic and the extrinsic regime. In the case of a mixed conductivity (ionic and electronic) situation, the following equation holds72 Nm = Nntn + Nvtv

(11)

with tn and tv = 1 − tn being the electron and the oxygen vacancy transference numbers, respectively. As Nv= 0 and, in this case Nn= −1/4, for a slope of −1/4.4, tn = 0.9 results (and hence tv = 0.1), meaning that 10% of the total conductivity should be ionic. It is worth noting that a similar value of Nm was observed in epitaxial 0.15 mol % Gd-doped CeO2 films,49 which indeed unequivocally exhibited mixed conduction. Let us assume for a moment the films on Al2O3⟨11̅02⟩ to be in the same situation; then the ionic conductivity should be on the order of 6 × 10−2 S m−1 (obtained by considering the conductivity data of Figure 7a

(10) 22564



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MgO (see Table 2): ΔE increases by about 0.2−0.3 eV upon a change of pO2 from 10−5 to 1 bar. Such considerations are relevant for the interpretation of the thickness dependence of the electric transport properties as shown in the left panels of Figure 4 (conductivity vs thickness), Figure 3 (activation energy vs thickness), and Figure 5 (conductance vs thickness). It is worth noting that Figure 5 offers the possibility to separate the bulk properties (the slope of the linear fit) from film−substrate interface effects (the intercept on the y-axis of the linear fit) (see ref 31). These three figures show a somewhat weaker thickness dependence of the conduction parameters. As an example, the films grown on Al2O3⟨11̅02⟩ exhibit an increase of conductivity and a decrease of activation energy with decreasing film thickness. Correspondingly, the intercept on the y-axis in the conductance versus thickness plot is positive. However, although at first the data seem to suggest a conductivity effect at the film−substrate interface, this conclusion cannot be drawn because of the high influence of the impurities on the conductivity. As was shown above, the impurity content in the films on Al2O3⟨11̅02⟩ is considerably larger than that on MgO (according to the Nm values), leading to a larger activation energy, a steeper pO2 dependence, and a reduced conductivity. This shows that (even small) variations of the impurity concentration (in nominally undoped samples) can perceptibly affect the electrical conduction properties. In addition, one should also note that because the films on Al2O3⟨110̅ 2⟩ and MgO are contaminated differently, we cannot exclude the impurity content to vary also within one batch of films (grown on Al2O3 or MgO). Actually, the different pO2 dependences within one batch of samples point toward slight variations of cA from film to film. This obviously affects the interpretation of boundary effects (both (i) the film−substrate interface in epitaxial films and (ii) grain boundaries in polycrystalline films), which can easily result from a subtle change in the impurity concentration.88

in ref 31 and taking into account the different dopant concentrations), whereas the ionic conductivity obtained from both the measured conductivity (Table 2) and tv is lower than 2.7 × 10−4 S m−1 (we consider here the conductivity of the thinnest film at pO2 = 10−5 bar). This discrepancy of about 2 orders of magnitude indicates that the pure epitaxial ceria films investigated here are not in a mixed conductivity situation. Moreover, such a rather large fraction of ionic conductivity would result in a decrease of the activation energy with increasing pO2, which is actually not observed for this set of films. This means that the measured pO2 dependence points toward a situation in which the conductivity is electronic and in-between the pure CeO2 case (Nn = −1/6) and slightly doped CeO2 (Nn = −1/4) case (correspondingly, Ea lies between ΔRH/3 + hn and ΔRH/2 + hn). At this point, it is convenient to evaluate the impurity concentration. However, as ΔRH and thus the corresponding equilibrium constant are known to be quite different in thin films31 as well as in nanocrystalline systems25 compared with the single crystal64 or doped microcrystalline ceria,73 ΔRH cannot be utilized to evaluate the acceptor content. Therefore, we use here an alternative approach based on the measured pO2 dependence Nm, which allows for the estimate of cA without the knowledge of K (eq 2). When the charge neutrality condition (eq 10) is inserted in eqs 2 and 4, a remarkable relationship between n, cA, and Nm holds: 6N + 1 cA =− m n 4Nm + 1

(12)

(For the derivation of eq 12, please refer to the Supporting Information). Note that the relationship is derived for a very small variation of pO2 (limΔpO2→0, for which Nm corresponds to the tangent in the log−log plots) and it becomes zero for Nm = −1/6, while the limit of cA as Nm approaches −1/4 is infinity, as expected. Because in eq 12 cA very sensitively depends on Nm, which here has an experimental error of ±0.3 (e.g., −1/(4.4 ± 0.3)), it can be used only for a rather rough estimation of cA. For the films on Al2O3, from Nm = −1/4.4 and the electron mobility data86 (here we assume single-crystal mobility data to hold also for the epitaxial films64,74) we obtain cAbetween 20 and 800 ppm, depending on the specific film.87 Considering the activation energy, Ea is expected to approach the value of ΔRH/2 + hn because n < cA. Quite remarkably, from Ea obtained experimentally, ΔRH ranging between 3 and 3.4 eV results, which is in fairly good agreement with the value (3.3 eV) obtained in a previous study on epitaxial, nominally pure CeO2 thin films exhibiting Nm = −1/6.31 Furthermore, the fact that, for a given film, Ea is pO2-independent can also be ascribed to n < cA. Let us now consider the nanocrystalline films grown on MgO. For these samples, the situation is more complex than for the previous set because (i) the films are nanocrystalline and (ii) although the impurity content is lower than in the films grown on Al2O3, it varies more pronouncedly from film to film. Nonetheless, it is noteworthy considering their activation energy. Under the conditions used here (oxidizing environment and θ ranging between 300 and 700 °C) the expected Ea should be between ΔRH/3 + hn (pure CeO2) and ΔRH/2 + hn (slightly acceptor-doped CeO2). With increasing pO2, the electron concentration decreases and the dopant concentration becomes more relevant in eq 10. Therefore, with increasing pO2 the resulting activation energy should rise toward higher values (close to ΔRH/2 + hn). This is indeed observed for the films on

4. SUMMARY AND CONCLUSIONS Nominally pure and 10 mol % Gd-doped CeO2 thin films of different thicknesses were deposited on Al2O3⟨11̅02⟩ and MgO⟨100⟩ substrates with PLD and investigated using impedance spectroscopy at various oxygen partial pressures and temperatures. The microstructure characterization showed that the nominally pure films on Al2O3⟨11̅02⟩ are epitaxial, whereas the doped films grown on sapphire and the films on MgO⟨100⟩ feature a polycrystalline columnar structure with average lateral grain sizes between 15 and 60 nm. For the nominally pure samples, a pO2 dependence close to −1/4 was detected indicating that these samples contain impurities acting as acceptor dopants. The electrical transport properties (conductivity, activation energy, and pO2 dependence) indicate that the impurity content varies from sample to sample, making the investigation of boundary effects not reliable. Importantly, a new approach is used to approximately evaluate the impurity (acceptor) content in the epitaxial films, which is based on the value of the pO2 dependence rather than the equilibrium constant of the oxygen excorporation reaction. Remarkably, despite their small grain size, the nanocrystalline 10 mol % Gd-doped thin films show a relatively large conductivity. It is still lower compared with epitaxial samples but significantly larger than other characteristic polycrystalline films (such as films on SiO2). The SCL potential in the films 22565



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grown on MgO was found to be rather low; its value is 0.19 ± 0.05 V. The results are significant for both basic research and applications. From the basic research point of view, the change of the SCL potential depending on the substrate (and thus on the microstructure) is interesting as it gives further insight into which parameters determine the value of the SCL potential. From the application point of view, it is the relatively high ionic conductivity for polycrystalline films and the low depletion of oxygen vacancies at the GBs that is of interest. While there have been complex attempts to lower the SCL potential (e.g., with heterogeneous doping by GB diffusion as well as through GB decoration75−79) the option just to use different substrates to enhance the ionic conductivity of polycrystalline thin films offers new, rather uncomplicated possibilities for the usage of doped ceria thin films in real applications.

■

(13) Trovarelli, A.; de Leitenburg, C.; Boaro, M.; Dolcetti, G. The Utilization of Ceria in Industrial Catalysis. Catal. Today 1999, 50, 353− 367. (14) Kharton, V. V.; Kovalevsky, A. V.; Viskup, A. P.; Figueiredo, F. M.; Yaremchenko, A. A.; Naumovich, E. N.; Marques, F. M. B. Oxygen Permeability of Ce0.8Gd0.2O2−δ-La0.7Sr0.3MnO3−δ Composite Membranes. J. Electrochem. Soc. 2000, 147, 2814−2821. (15) Kharton, V. V.; Kovalevsky, A. V.; Viskup, A. P.; Shaula, A. L.; Figueiredo, F. M.; Naumovich, E. N.; Marques, F. M. B. Oxygen Transport in Ce0.8Gd0.2O2−δ-Based Composite Membranes. Solid State Ionics 2003, 160, 247−258. (16) Fagg, D. P.; Shaula, A. L.; Kharton, V. V.; Frade, J. R. High Oxygen Permeability in Fluorite-Type Ce0.8Pr0.2O2−δ Via the Use of Sintering Aids. J. Membr. Sci. 2007, 299, 1−7. (17) Zhu, X. F.; Yang, W. S. Composite Membrane Based on Ionic Conductor and Mixed Conductor for Oxygen Permeation. AIChE J. 2008, 54, 665−672. (18) Leo, A.; Liu, S. M.; da Costa, J. C. D. Development of Mixed Conducting Membranes for Clean Coal Energy Delivery. Int. J. Greenhouse Gas Control 2009, 3, 357−367. (19) Huang, H.; Nakamura, M.; Su, P.; Fasching, R.; Saito, Y.; Prinz, F. B. High-Performance Ultrathin Solid Oxide Fuel Cells for LowTemperature Operation. J. Electrochem. Soc. 2007, 154, B20−B24. (20) Bieberle-Hutter, A.; Beckel, D.; Infortuna, A.; Muecke, U. P.; Rupp, J. L. M.; Gauckler, L. J.; Rey-Mermet, S.; Muralt, P.; Bieri, N. R.; Hotz, N.; Stutz, M. J.; Poulikakos, D.; Heeb, P.; Muller, P.; Bernard, A.; Gmur, R.; Hocker, T. A Micro-Solid Oxide Fuel Cell System as Battery Replacement. J. Power Sources 2008, 177, 123−130. (21) Kwon, C.-W.; Son, J.-W.; Lee, J.-H.; Kim, H.-M.; Lee, H.-W.; Kim, K.-B. High-Performance Micro-Solid Oxide Fuel Cells Fabricated on Nanoporous Anodic Aluminum Oxide Templates. Adv. Funct. Mater. 2011, 21, 1154−1159. (22) Ko, C.; Kerman, K.; Ramanathan, S. Ultra-Thin Film Solid Oxide Fuel Cells Utilizing Un-Doped Nanostructured Zirconia Electrolytes. J. Power Sources 2012, 213, 343−349. (23) Tschöpe, A.; Sommer, E.; Birringer, R. Grain Size-Dependent Electrical Conductivity of Polycrystalline Cerium Oxide I. Experiments. Solid State Ionics 2001, 139, 255−265. (24) Tschöpe, A. Grain Size-Dependent Electrical Conductivity of Polycrystalline Cerium Oxide II: Space Charge Model. Solid State Ionics 2001, 139, 267−280. (25) Tschöpe, A.; Birringer, R. Grain Size Dependence of Electrical Conductivity in Polycrystalline Cerium Oxide. J. Electroceram. 2001, 7, 169−177. (26) Kim, S.; Maier, J. On the Conductivity Mechanism of Nanocrystalline Ceria. J. Electrochem. Soc. 2002, 149, J73−J83. (27) Kim, S.; Fleig, J.; Maier, J. Space Charge Conduction: Simple Analytical Solutions for Ionic and Mixed Conductors and Application to Nanocrystalline Ceria. Phys. Chem. Chem. Phys. 2003, 5, 2268−2273. (28) Guo, X.; Sigle, W.; Maier, J. Blocking Grain Boundaries in YttriaDoped and Undoped Ceria Ceramics of High Purity. J. Am. Ceram. Soc. 2003, 86, 77−87. (29) Tschöpe, A.; Kilassonia, S.; Birringer, R. The Grain Boundary Effect in Heavily Doped Cerium Oxide. Solid State Ionics 2004, 173, 57− 61. (30) Guo, X.; Waser, R. Electrical Properties of the Grain Boundaries of Oxygen Ion Conductors: Acceptor-Doped Zirconia and Ceria. Prog. Mater. Sci. 2006, 51, 151−210. (31) Göbel, M. C.; Gregori, G.; Guo, X. X.; Maier, J. Boundary Effects on the Electrical Conductivity of Pure and Doped Cerium Oxide Thin Films. Phys. Chem. Chem. Phys. 2010, 12, 14351−14361. (32) Göbel, M. C.; Gregori, G.; Maier, J. Mixed Conductivity in Nanocrystalline Highly Acceptor-Doped Cerium Oxide Thin Films under Oxidizing Conditions. Phys. Chem. Chem. Phys. 2011, 13, 10940− 10945. (33) Chiang, Y. M.; Lavik, E. B.; Kosacki, I.; Tuller, H. L.; Ying, J. Y. Defect and Transport Properties of Nanocrystalline CeO2−X. Appl. Phys. Lett. 1996, 69, 185−187.

ASSOCIATED CONTENT

S Supporting Information *

Representative results obtained from the TEM analyses and derivation of eq 12. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors thank G. Cristiani (Max Planck Institute for Solid State Research, Stuttgart, Germany) for assisting and maintenance of the PLD system. G. Götz and B. Fenk (Max Planck Institute for Solid State Research) are acknowledged for performing the XRD investigations and preparing the lamellae for TEM using FIB respectively. Special thanks also go to U. Salzberger, K. Hahn, B. Rahmati, and P. Kopold (Max Planck Institute for Intelligent Systems, Stuttgart, Germany) for performing the TEM analysis.

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REFERENCES

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to the presence of acceptor impurities rather than to a film−substrate interface effect.

(77) Litzelman, S. J.; De Souza, R. A.; Butz, B.; Tuller, H. L.; Martin, M.; Gerthsen, D. Heterogeneously Doped Nanocrystalline Ceria Films by Grain Boundary Diffusion: Impact on Transport Properties. J. Electroceram. 2009, 22, 405−415. (78) Gregori, G.; Rahmati, B.; Sigle, W.; van Aken, P. A.; Maier, J. Electric Conduction Properties of Boron-Doped Ceria. Solid State Ionics 2011, 192, 65−69. (79) Lupetin, P.; Giannici, F.; Gregori, G.; Martorana, A.; Maier, J. Effect of Grain Boundary Decoration on the Electrical Conduction of Nanocrystalline CeO2. J. Electrochem. Soc. 2012, 159, B417−B425. (80) Cerium oxide is not only of special interest for SOFCs, but also for a range of other applications such as catalysis11−13 and oxygen permeation membranes.15−18 (81) Usually the SCL potential can be calculated using an analytical approximation for the solution of the Poisson equation26,27,31,32,36

σVO••, ∞ σV⊥O••, m

=

1 de

εr ε0kBT exp[2eΔΦ0 /kBT ] cVO••, ∞ 4eΔΦ0 /kBT

Here σV••O ,∞ is the bulk ionic conductivity, σ⊥V ••O ,m the effective measured ionic conductivity of the polycrystalline sample, d the lateral grain size, e the elementary charge, εr the relative permittivity of ceria, ε0 the vacuum permittivity, kBT the Boltzmann term, cV••O ,∞ the bulk oxygen vacancy concentration, and ΔΦ0 the SCL potential. However, the above equation is valid only under the approximation of a strong oxygen vacancy depletion and thus a large change in conductivity. Here, for the only weak conductivity drop in the polycrystalline samples this condition is not fulfilled. For this reason we have used here a numerical approach.49,67 (82) Here the parameters of the two thinnest films in Tables 1 and 2 (which have similar grain sizes (≈17 nm) and conductivities (≈2 S m−1)) were used. The value typical for epitaxial films grown under the same conditions at these conditions (4 S m−1) was taken as bulk conductivity,31 leading to a conductivity change by a factor of 0.5. Furthermore, εr = 26 and T = 973 K were applied. (83) For the polycrystalline films on MgO also GB effects could - at least theoretically - be the origin of the changed pO2 dependence. However, it is worth noting that, as shown in Table 1, the lateral grain size strongly increases with increasing thickness. In such a situation also the electric transport properties should be significantly thicknessdependent as it was shown in a previous study.31 Because this is not the case for the films grown on MgO (Table 2), we can discard GB effects to be the origin of the steeper pO2 dependence. (84) For example, see Figure 5, left panel, and conductivity data from ref 31. (85) As an example, the nominally pure films studied in ref 32 were found to have an impurity content of less than 50 ppm. (86) In the following, ue is the electron mobility.

n=

ue ,0 −h / k T σ K· cm 2 ; ue = e n B ; ue ,0 = 390 ; hn = 0.40 eV eue T V·s

(87) The ratio cA/n varies here between 4 (for Nm = −1/4.4) and 5.6 (for Nm = −1/4.3). (88) In contrast to the results of films on grown Al2O3⟨0001⟩31 (negative intercept in the conductance vs thickness plot and steep slope) the films on Al2O3⟨11̅02⟩ show a positive intercept and a smaller slope in this plot (Figure 5, left panel). Therefore, both experiments were repeated. This included both the preparation of new thin films and the investigation with impedance spectroscopy. As a result, now both sets of samples show a nearly identical behavior. Their properties are similar to those of the films on Al2O3⟨11̅02⟩ discussed above. Given that these samples also show a pO2 dependence close to −1/4, their conductivity is also affected by the existence of impurities. However, the films on Al2O3⟨0001⟩31 which were prepared 3 years ago showed a pO2 dependence of −1/6, indicating the absence of impurities. This indicates that the positive intercept in the conductance versus thickness plot recorded here for the films on Al2O3⟨11̅02⟩ are most likely related 22568


Size Effects on the Electrical Conductivity of Ceria: Achieving Low

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