Optical investigation of oxygen diffusion in thin films of Gd-doped ceria

Solid State Ionics 277 (2015) 30–37

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Optical investigation of oxygen diffusion in thin films of Gd-doped ceria Guy Lazovski, Olga Kraynis, Roman Korobko 1, Ellen Wachtel, Igor Lubomirsky ⁎ Dept. Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel

a r t i c l e

i n f o

Article history: Received 24 January 2015 Received in revised form 9 April 2015 Accepted 10 April 2015 Available online xxxx Keywords: Ionic conductivity Ellipsometry Gd-doped ceria Thin films Impedance spectroscopy

a b s t r a c t We describe the use of null-ellipsometry with lock-in detection to monitor grain core oxygen diffusion in thin films of the solid-state ionic conductor Ce0.8Gd0.2O1.9. Application of an electric field perpendicular to the film surface—probe alternating voltage (UA) in addition to perturbation bias voltage (UB)—produces ellipsometer optical response at the probe frequency. The signal amplitude and time dependence can be interpreted in terms of changes in the local material polarizability. Since the ionic contribution to the material polarizability is much larger than that of electrons or protons, the diffusion of ions can be distinguished. Because grain cores occupy the majority of the film volume, ion diffusion in the grain cores dominates the optical response. This effect was studied as a function of temperature (75–160 °C), amplitude and frequency of the electric field. The activation energy for oxygen diffusion in the grain cores was found to be 1.1 ± 0.1 eV and 1.5 ± 0.1 eV for films with in-plane compressive strain of 0.34 ± 0.06% and in-plane tensile strain 0.16 ± 0.03%, respectively. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Oxygen ion-conducting materials in the form of thin films are central to a broad range of applications, ranging from oxygen sensors [1,2] to non-volatile memory devices [3]. While the study of conduction mechanisms in these films is of primary importance for device development, the technique most commonly used, impedance spectroscopy (IS), is unable to unambiguously distinguish between electronic and ionic carriers without imposed variation of oxygen partial pressure. It would also be clearly advantageous to exploit a property more directly related to the movement of ions within the grain cores than ‘total conductivity’. A major difference between the movement of ions in the grain cores of Gd-doped ceria films and other conduction mechanisms is the dominant contribution of the ions to the polarizability of the film, and therefore, to its refractive index (n). Because grain cores occupy the majority of the film volume, ion diffusion in the grain cores dominates the optical response. We have recently shown that null-ellipsometry with lock-in detection is able to monitor oxygen diffusion on a background of other conduction mechanisms, i.e. protonic and electronic, in ionic and mixed ionic/ electronic conductors, in ceramic pellets and single crystal forms [4]. In the current work, we explore its suitability for the study of grain core ionic conduction in the more commonly encountered thin film geometry, highlighting required changes in both instrumentation and analysis. We applied alternating probe voltage (UA) in addition to perturbation bias voltage (U B) to 300–600 nm Ce0.8 Gd 0.2 O1.9 (GDC20) films and monitored the optical response with null-ellipsometry ⁎ Corresponding author. E-mail address: [email protected] (I. Lubomirsky). 1 Currently at Swiss Federal Institute of Technology (ETH) in Zurich.

http://dx.doi.org/10.1016/j.ssi.2015.04.006 0167-2738/© 2015 Elsevier B.V. All rights reserved.

(Fig. 1). The amplitude and time dependence of the optical response to electric field-induced changes in the polarizability of the sample can be interpreted in terms of the mobility of the charge carriers (oxygen ions) as weakly influenced by the small, field-induced perturbation to the charge carrier concentration. This effect was studied as a function of temperature, amplitude and frequency of the applied electric field. From the temperature dependence of the decay time of the optical response to removal of the bias voltage, the activation energy (EA) for oxygen ion diffusion under our experimental conditions could be calculated [4]. The activation energy for oxygen diffusion in the grain cores of GDC20 thin films in the temperature range of 120–160 °C was found to be 1.1 ± 0.1 eV and 1.5 ± 0.1 eV for films with in-plane compressive strain 0.34 ± 0.06% and in-plane tensile strain 0.16 ± 0.03%, respectively. 2. Experimental procedures 2.1. Sample preparation Thin film samples were prepared as follows: a 200 ± 50 nm thick Cr film (the bottom electrode), was deposited by DC-magnetron sputtering on borosilicate glass slides. A 300–600 nm thick GDC20 film was then deposited via RF-magnetron sputtering without breaking the vacuum in the deposition chamber, in order to avoid contamination. Following deposition, the samples were annealed for 2 h at 450 °C (heating/cooling rates 3.5 °C/min) to relieve stress. Such sputtered, annealed GDC20 films have been shown by XPS to be fully oxidized [5]. Semitransparent Au films ~25 nm thick were then deposited by electron beam evaporation. Both Au and Cr electrodes are blocking for ions, but not for electronic charge carriers. Lastly, copper

G. Lazovski et al. / Solid State Ionics 277 (2015) 30–37

31

0.8

Voltage

UA 0.6 0.4

UB 0.2 0.0

Time

(a)

(b)

Fig. 1. (a) Scheme of a manual nulling ellipsometer with lock-in detection. To increase sensitivity, the analyzer was shifted from the null position by ~2°. (b) The sample is subjected to an electric field−probe voltage (UA) in addition to perturbation voltage (UB). Only the alternating component of the current in the photo-detector (P.D.) is recorded.

wires were connected to the bottom and top electrodes using silver paint (two wires were connected to the top electrode to permit monitoring of its integrity) and connections were made to a function generator and multi-meter. These films were used for both null-ellipsometry and impedance spectroscopy measurements. For comparison, a film with an alternative electrode geometry was also prepared for impedance spectroscopy. A 300–600 nm thick GDC20 film was deposited via RF-magnetron sputtering on a glass microscope slide. Following deposition, the sample was annealed under the same conditions as described for the ellipsometry samples. Two interdigitated electrodes were then defined on the film surface by optical lithography. The interdigitated electrodes consisted of 20 pairs of opposing contact fingers 4 μm wide, 100 μm long and separated by 4 μm spaces. The contacts consisted of a 5 nm Cr adhesion layer and a 100 nm Au layer (Fig. 2), deposited by electron beam evaporation. This arrangement permitted measurement of the motion of charge carriers parallel to the film surface. 2.2. Sample characterization The phase content of the samples was measured by X-ray powder diffraction (XRD, Rigaku® TTraxIII). In-plane strain was measured by the sin2(ϕ) method (ϕ is the inclination angle) as described in [6]. To investigate the integrity of the layers, grain size and shape and the quality of deposition, the samples were examined by scanning electron microscopy (SEM, Zeiss Ultra). The impedance spectra of each sample were measured using a high-resolution impedance analyzer (Alpha, Novocontrol) under the same conditions of temperature and environment as the optical measurements in order to allow comparison of the activation energies of ion diffusion and conductivity [4].

2.3. Lock-in ellipsometry measurements. Measurements were performed on a manual null-ellipsometer with He–Ne laser light source (λ = 632.8 nm) similar to that described in [4]. Voltages UA (0–1 V, 0.5 Hz–1 kHz) and U B (− 0.6 to 0.6 V) were applied directly to the sample using a function generator (DS345, Stanford Research) (Fig. 1). The ellipsometer photodetector is connected to a lock-in amplifier (SR830, Stanford Research) referenced to input from the function generator, in order to monitor the oscillating component of the photocurrent. Control measurements were performed to characterize the dependence of the detector response: on UA amplitude at fixed frequency and at different temperatures, UB = 0; on UA frequency at fixed amplitude and at different temperatures, UB = 0; on UB amplitude and polarity. As described previously [4], there are several reasons why detector current is the measured quantity of choice rather than ellipsometer angles, Ψ and Δ. Since lock-in detection detects only the periodically varying ellipsometer signal, the measured response is resistant to signal drift due to temperature fluctuations, power supply ripple, or mechanical vibrations. This stability is essential given the small signal amplitude. In fact, ellipsometry with lock-in detection is capable of measuring changes in the refractive index (n) of 1 part in 10 6. As noted previously [4], 0.5% change in the oxygen ion concentration of Gd-doped ceria produces a relative change in n of 10− 3. Therefore, our instrumental sensitivity allows us to measure changes in the ion concentration which are even three orders of magnitude smaller. In our experimental setup (Fig. 1), the changes in the angular settings of the ellipsometer polarizer and analyzer, which correspond to changes in the RMS nanoampere current, are on the order of 10−4 degrees (see Section 4). The accuracy with which nanoampere current can be measured is far in excess of the accuracy with which a 10−4 degree rotation of the optical elements of the manual ellipsometer can be measured.

3. Theoretical background

Fig. 2. Interdigitated 100 nm thick Au electrodes deposited on a GDC20 thin film for inplane impedance spectroscopy measurements as described in the text.

A theoretical basis for using ellipsometry to monitor ion diffusion in GDC20 has been detailed in [4]. To ensure reversibility, the voltage drop at the interface(s) with the electrodes must be a fraction of the applied voltage and less than the thermal voltage Vth = k B · T / q ~ 0.05 V in the temperature range relevant for this work. Changes in ion concentration induced by application of external voltage modify the local polarizability and hence the real part of the material refractive index [7]; the imaginary part of the refractive index of GDC20 for incident light photon energies below 3 eV is negligible [8]. Because the volume of the film consists primarily of grain cores and because the grain boundaries have significantly lower ionic conductance than the grain cores [9,10], monitoring the change in refractive index with the ellipsometer provides information that is specific to the polarizability changes arising from ion movement within the grain cores.

1.930 1.928

d,Å

1.0

Tilt Angle, φ - 60O - 30O - 0O

1.926 1.924 1.922

0.00 0.25 0.50 0.75 (311) (222)

(220)

Au(111)

Cr(110)

sin2(φ)

0.5

(200)

In our previous report, null ellipsometry was applied to ceramics or single crystals [4]. These samples were sufficiently thick that only the change in polarizability at the upper electrode–film interface was detected. In contrast, in the current work, sample thickness is comparable to the wavelength of the ellipsometer light source (λ = 632.8 nm). Thus, changes in polarizability throughout the film cross-section may, in principle, contribute to the signal. Using methods that have been developed to calculate reflectance and transmittance of thin metal films deposited on a transparent dielectric substrate [11,12], we have determined the relative contribution of the upper interfaces to the measured optical response. Given the known angle of incidence of the laser light, the thicknesses and refractive indices of the Au electrode and of the GDC20 film, we determined that the majority of the incident light is reflected at the (air/ Au/GDC20) interfaces: the reflectance of the p and s polarizations are RP ≈ 45%, RS ≈ 90% (For the full derivation, see Appendix A). The optical response, therefore, originates predominantly from the top surface, although a minor contribution from the rest the film, as the light is reflected from the lower (GDC20/Cr) interface, is also likely present. To estimate the influence of the change in polarization on the optical signal, computational ellipsometry modeling of the GDC20 film was performed [13]. The perturbation to sample optical properties due to applied bias voltage was simulated with resulting changes in the ellipsometer angles, Δ and Ψ, as output. The initial state (UB = 0 V; zero built-in potential) was assumed to be a uniform layer with the refractive index of bulk GDC20 (n ≈ 2.07). The fieldperturbed state was modeled as a three-layer structure (i.e. space charge layers at the film/electrode interfaces), again without built-in potential: enriched layer\bulk\depleted layer, the directionality depending on the polarity of the perturbing voltage UB. Given the large concentration of ionic charge carriers in the bulk (2.5·1021 cm3), the thickness of both upper and lower interfacial regions, vacancy enriched or depleted, is taken to be a few Debye lengths ~1–2 nm. The concentration changes are modeled as a few percent of the bulk, considerably more than the experimental values, but nevertheless required by the demands of the calculation. With this model, the changes in the ellipsometer angles upon application/removal of the electric field do indeed depend on the polarity of UB (see additional information in Appendix A), yet because only the change in the photocurrent is detected, corresponding to the sum of the absolute values of the changes in the ellipsometer angles (|δΔ| + |δΨ|), this dependence cannot be distinguished experimentally. If, in addition to the ionic charge carriers, a high-mobility electronic charge carrier is present, as in GDC20, then the potential distribution and the ion distribution throughout the sample may be affected by Wagner–Hebb (W–H) stoichiometry polarization [14], determined here by the symmetric ion-blocking electrodes. In the bulk ceramics that we studied previously, sample thickness was on the order of 1 mm [3].

(111)

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Intencity, Counts/s

32

0.0 30

40

50

60

2θ, degrees Fig. 4. XRD patterns of a GDC20 film at three tilt angles (ϕ). The position of the (220) diffraction peak at each angle setting was used to determine the film in-plane strain as described in the text [6]. Inset: d-spacings of the (220) diffraction peak vs. sin2(ϕ).

Since the characteristic relaxation time for W–H polarization is τWH = L2 / D, where D is the chemical diffusion coefficient (see for instance [14]) and L is the thickness of the sample, a steady state corresponding to W–H polarization could not have been reached in the temperature range of the measurements (b300 °C). However, in thin films, W–H stoichiometry polarization may be significant. Nevertheless, for both space charge layer or W–H induced polarization, as long as the voltage drop at the interface is much smaller than Vth, the vacancy concentration gradient will be very small with respect to the absolute vacancy concentration and the ion diffusion may be approximated by the self-diffusion coefficient. Thus, the relaxation time of the ion distribution upon removal of the applied voltage will be inversely proportional to the ion selfdiffusion coefficient, with only a weak dependence on the amplitude of the applied voltage [4,14]. 4. Experimental results and discussion 4.1. Film structure and in-plane strain According to the SEM cross-section image, the GDC20 films, prepared by RF magnetron sputtering, have a columnar grain structure with a lateral grain size of ≈20 nm (Fig. 3a), which is similar to earlier reports [15]. According to XRD, the films are in the fluorite (Fm-3m) phase and have strong (111) texture (Fig. 4). The in-plane, dx, and the out-of-plane, dz, lattice spacings were determined from the position of the (220) (Fig. 4) or the (422) diffraction peak (data not shown) as a function of the inclination angle, ϕ, by [6]: ! 2 sin ðϕÞ ðdx −dz Þ : dðϕÞ ¼ dz ⋅ 1 þ dx

ð1Þ

Fig. 3. (a) SEM image of a GDC20 film deposited on SiO2\Cr. The lateral grain size is ≈20 nm. (b) The cross-section of the sample following deposition of the Au top electrode; columnar grain growth is clearly observable.

Optical Response, nA

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0.5

75 °C 90 °C 105 °C 120 °C 130 °C

0.4 0.3 0.2 0.1 0.0

1

10

100

Frequency, f, Hz Fig. 5. (a) Frequency dependence of the ellipsometer photo-detector root mean square (RMS) current for the SiO2\Cr\Ce0.8Gd0.2O1.9\Au sample with in-plane tensile strain at different temperatures, UB = 0, UA = 0.2 V.

Even after annealing, dx was not equal to dz, indicating the presence of residual in-plane strain. An accurate determination of the in-plane strain using [6,16]:

ε xx ¼

ð1−dz =dx Þ dz =dx þ 2⋅ν=ð1−νÞ

ð2Þ

cannot be made because the Poisson ratio (ν) of Gd-doped ceria films is itself a function of time and of the strain state. Literature values vary from 0.334 [17,18] to 0.48 [16]. With these two values as limits, the in-plane strain, εxx, is obtained for the two samples described below: 0.34 ± 0.06% compressive and 0.16 ± 0.03% tensile. The out-of-plane strain, εzz, is of the opposite sign with amplitude again dependent on the Poisson ratio (εzz = 2·ν·εxx / (ν − 1)). 4.2. Null-ellipsometry measurements In response to application of probe voltage, UA (0.2 V(7 Hz)) and step-wise, perturbing bias voltage, UB , both thin film samples SiO2 \Cr\Ce0.8 Gd 0.2 O1.9\Au, with either tensile or compressive inplane strain, placed in the experimental setup (Fig. 1), generated well detectable AC current in the ellipsometer photo-detector at the same frequency as UA. The frequency-dependent RMS optical response shows clear dependence on temperature (Fig. 5) and, as in the case of bulk Ce0.8Gd0.2O1.9 ceramics [4], decays with reciprocal frequency (1/f). The detection threshold was measured as a function of the frequency and amplitude of UA within the temperature range of 75–120 °C (Fig. 6). The detection limit measured at 7 Hz decreased markedly with increasing temperature (Fig. 6a). The maximum frequency for the detection limit at UA = 0.2 V increased exponentially with temperature (Fig. 6b). The fact that in the temperature range of interest the species responsible for the optical response ceases to fol-

33

low the electric field at frequencies greater than a few tens of Hz is characteristic of ion diffusion. The amplitude of the response increases linearly with UA (Fig. 7a), and is dependent on temperature (Fig. 7b). The RMS photocurrent also depends on UB; in the measurement shown in Fig. 8, it is symmetric with respect to polarity at all values of |UB| b 0.6 V. Modeling described in Section 3 showed that the optical response should not be sensitive to the polarity of UB in the absence of a built-in potential. Fig. 8 also demonstrates that, although UB NN Vth, the voltage drop at the interface(s) is necessarily much smaller—relative changes in interface polarizability due to ion accumulation/depletion are symmetric only when changes in ion concentration are small and built-in potential is absent. This outcome also excludes other polarization mechanisms, such as fieldinduced crystallographic phase changes or Ce4 +/3 + redox reactions in the near electrode regions due to the non-reversible and nonsymmetrical nature of such mechanisms. Measurement of the relaxation time of the enriched/depleted charge distribution upon removal of the bias voltage was conducted at temperatures ranging from 120 °C to 160 °C (Fig. 9a). Although measurements at higher temperature would permit comparison with a broader range of literature data, we found that, while the optical response could be readily measured at temperatures as high as 375 °C, relaxation times were too short for the lock-in amplifier to follow. The relaxation time (τ) could be evaluated by fitting to a single exponential decay curve [4] and was found to decrease exponentially with reciprocal temperature (Fig. 9b, c). Having measured bulk GDC20 samples in both wet and dry states in our earlier work [4], the single exponential decay of the relaxation curves observed here for the thin films attests to the contribution of a single ionic charge carrier: in particular, protons derived from adsorbed water molecules are not present. The linear form of the Arrhenius plots provides evidence that the relaxation time, and therefore also the diffusion coefficient, depend exponentially on the inverse temperature. We are therefore provided with a measure of the energy of activation of the ion motion. The activation energies determined from the Arrhenius plots are 1.1 ± 0.1 eV and 1.5 ± 0.1 eV for the films with in-plane 0.34 ± 0.06% compressive strain and 0.16 ± 0.03% tensile strain, respectively. Films with in-plane compressive strain experience out-of-plane tensile strain, determined by the Poisson ratio, and vice versa. Since the measured activation energies relate to ion diffusion perpendicular to the film plane, it appears that out-of-plane tensile strain facilitates the diffusion of ions, while out-of-plane compressive strain impedes it. These results are consistent with predictions of the DFT calculations [19,20] that describe the effect of mechanical strain on the migration of oxygen vacancies in ceria. Similarly, in recently published experimental works [21–23], Rupp and coworkers demonstrate that lattice compaction and associated strain reduction in acceptor doped ceria give rise to increase in the activation energy of ionic conduction.

Frequency, Hz

0.4

UA, V

0.3 0.2 0.1 0.0 70

(a)

80

90 100 110 Temperature, OC

120

10

1

(b)

80

100 120 Temperature, OC

Fig. 6. (a) The minimum value of UA (7 Hz) at which the optical response for the SiO2\Cr\Ce0.8Gd0.2O1.9\Au sample with in-plane tensile strain becomes detectable, UB = 0; and (b) the maximum frequency at which the response remains detectable for UA = 0.2 V as a function of temperature, UB = 0.

Optical Response, nA

G. Lazovski et al. / Solid State Ionics 277 (2015) 30–37

Optical Response, pA

34

60

40

20

0 0.0

0.1

0.2

0.3

0.4

200°C 180°C 165°C 155°C 145°C 125°C

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.05

0.5

0.10

(b)

UA, V

(a)

0.7

0.15

0.20

0.25

UA, V

Fig. 7. (a) Dependence of the photo-detector RMS current for the SiO2\Cr\Ce0.8Gd0.2O1.9\Au sample with in-plane tensile strain on the amplitude of UA (7 Hz) at 120 °C, UB = 0. The linear dependence indicates that the changes in ion concentration induced by the probe voltage, UA, are small. (b) Comparison of the dependence of the RMS optical response on the amplitude of UA (7 Hz) at different temperatures, UB = 0.

4.3.1. Electrical conductivity perpendicular to the film plane For comparison with the results of the null ellipsometry technique, impedance spectroscopy (IS) measurements at two excitation voltages, 0.05 V and 0.2 V, applied normal to the film plane were performed as a function of temperature (100–160 °C) on the sample with in-plane tensile strain (Fig. 10a). In this case, motion of charge carriers is parallel to the long axis of the columnar grains. With excitation voltage of 0.05 V, a nearly complete depressed semicircle dominates the Cole–Cole plot, with a small feature at higher frequencies and an incomplete arc below 10 Hz. The radii of the depressed semicircles, determined in the intermediate frequency range, were

4.3.2. In-plane conductivity The striking difference between the activation energies determined by IS and the null-ellipsometry technique was explored further by measuring total conductivity parallel to the film surface (perpendicular to the grain boundaries, cf. Fig. 3), i.e., across the columnar grains. Two interdigitated Au electrodes were deposited on a GDC20 thin film as described above, and impedance spectra were measured between 90 and 160 °C with excitation voltage of 0.05 V (Fig. 11a). The IS spectra contain only one depressed semicircle. The activation energy for total conductivity determined from these measurements is 0.83 ± 0.01 eV (Fig. 11b). Because charge carrier motion parallel to the film surface

Optical Response, pA

4.3. Impedance spectroscopy

plotted vs. the reciprocal temperature (Fig. 10c). The slope of the Arrhenius plot gives an activation energy of 0.4 ± 0.02 eV, a low value which has been attributed to electronic (polaronic) conductivity in both reduced and acceptor doped ceria [24,25]. The high frequency feature was too weak to permit reliable fitting. With excitation voltage of 0.2 V, IS measurement produces a low-frequency feature, which can be identified as negative capacitance (low frequency inductance) (Fig. 10b). As the frequency of the excitation voltage is reduced, the real component of the impedance decreases and the imaginary component becomes negative, i.e., inductive, producing a semicircle in the fourth quadrant. Such negative capacitance has been observed in a number of different organic and inorganic systems [26] but is not yet fully understood. However, even in this case, plotting the low frequency intercept of Re(Z) on the Im(Z) = 0 axis versus reciprocal temperature (Fig. 10d) gives the same activation energy, i.e. 0.4 ± 0.02 eV.

60

40

20

0 -0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

UB, V

60 45

UB, V

0.4

30

0.2

0.0 0.0

(a)

15 0 0.3

0.6

0.9

1.2

Time, Hour

1.5

8

EA for GDC thin film 1.5 ± 0.1eV

5.5 5.0

7

6

Intercept Slope

4 2.35

(b)

4.0 3.5 3.0

5

1.8

EA for GDC thin film 1.10 ± 0.07 eV

4.5

lnTau

0.6

lnTau

75

Optical Response, pA

Fig. 8. The RMS response of the photo-detector current for the SiO2\Cr\Ce0.8Gd0.2O1.9\Au sample with in-plane tensile strain as a function of the superimposed voltage UB with UA = 0.2 V (7 Hz) at 145 °C.

2.40

2.45

Value -37.20128 17.74459

Standard Error 3.66604 1.52321

2.50

Reciprocal temperature, 1000/K

2.5 Intercept Slope

2.0

2.55

2.30

(c)

2.35

2.40

Value -27.51984 12.71338

2.45

Standard Error 2.078 0.873

2.50

2.55

Reciprocal temperature, 1000/K

Fig. 9. (a) Response of the photo-detector current for the SiO2\Cr\Ce0.8Gd0.2O1.9\Au sample with in-plane tensile strain to the on/off switching of UB = +0.6 V with UA = 0.2 V (7 Hz) at 153 °C. Relaxation of the optical response upon removal of bias can be observed. (b) and (c) Arrhenius plots for determining the activation energy. (b) The logarithm of the relaxation time as a function of the inverse temperature for the film with in-plane tensile strain. (c) The logarithm of the relaxation time as a function of the inverse temperature for the film with in-plane compressive strain.

-Im(Z), Ω

G. Lazovski et al. / Solid State Ionics 277 (2015) 30–37

2

15.0

160 °C 140 °C 120 °C 100 °C

-Im(Z), kΩ

7.5 24 28 Re(Z), Ω

-Im(Z), k Ω

1

35

160 °C 140 °C 120 °C 100 °C

1

0

0 0

1

2

0

3

2.5k 2k

Ea=0.41± 0.04 eV 1k

Au contact GDC20 film Cr contact 2.4

2.5

2.6

(c)

3

4

1k

Au contact GDC20 film Cr contact

500

2.3

2.7

Reciprocal temperature, 1000/K

2 Re(Z), k Ω

Ea=0.41±0.02 eV

1.5k

100 2.3

1

(b)

Resistance, Ω

Resistance, Ω

(a)

Re(Z), k Ω

(d)

2.4

2.5

2.6

2.7

Reciprocal temperature, 1000/K

Fig. 10. Cole–Cole plots of the Cr\Ce0.8Gd0.2O1.9\Au layered sample with in-plane tensile strain as a function of temperature in the frequency range of 1–106 Hz: (a) excitation voltage 0.05 V normal to the film surface; the dotted lines show the fit to a depressed semicircle; (b) excitation voltage 0.2 V. (c) and (d) Arrhenius plots for determination of the activation energy: logarithm of the resistivity deduced from the low frequency intercept on the Re(Z) axis in graphs (a) and (b) respectively, as a function of reciprocal temperature.

has minimal effect on the polarizability of the film, the analogous measurement cannot be made using the proposed optical technique. We suggest that the difference in the activation energy determined by IS for conduction parallel and perpendicular to the film surface may be due to the highly anisotropic shape of the crystal grains with the resulting different relative contributions of the grain cores and the grain boundaries to the total conductivity. 4.3.3. Comparison of activation energies It is not straightforward to compare the activation energies obtained for ion diffusion in the GDC20 thin films using the null ellipsometry technique with corresponding values reported in the impedance spectroscopy literature for other GDC20 samples. The activation energy for conduction in doped ceria depends on preparation protocol, overall morphology, i.e. film or bulk ceramic, grain size and shape, strain, partial pressure of oxygen, and temperature range of measurement [21–23, 27–29]. At temperatures in the vicinity of 500 °C, the activation energies reported for GDC20 thin films vary from 0.74 to 1.35 eV [21]. There do

not appear to be any reports of IS measurements on thin films of GDC20 in the low temperature range that we have used. We note that for T b 200 °C, GDC20 exhibits local structural distortions due to the interaction of the cerium host ions (Ce4+) and oxygen vacancies VO [15]. For films, this interaction has been measured to have an activation energy of 1.1 ± 0.2 eV [30]. The fact that relatively high activation energies are calculated from the optical relaxation times may indicate that the local lattice distortion in thin films impedes grain core oxygen diffusion within the measured temperature range. Nevertheless, we note the very similar low temperature activation energy for ion diffusion obtained by ellipsometry for GDC20 ceramics with isotropic 1.4 μm grains, i.e., 1.1 ± 0.1 eV [4]. 5. Conclusion Null ellipsometry with lock-in detection is able to directly measure the low temperature (b 200 °C) activation energy for oxygen ion diffusion in grain cores of 20 mol.% Gd-doped ceria thin films

-Im(Z), Ω

0.50

23

0.25

bottom up 160°C 150°C 140°C 125°C 110°C 90°C

2.0

0

(a)

2

4

6

Re(Z),GΩ

EA = 0.83eV ± 0.01

22

1.0

Re(Z),GΩ

4.0

0.0

0.5

ln(Zre)

-Im(Z),GΩ

0.00 0.0

21 20 19 18

8

10

2.3

(b)

2.4

2.5

2.6

2.7

1000/T, 1000/K

2.8

Fig. 11. (a) Cole–Cole plots of the SiO2\Ce0.8Gd0.2O1.9 (300–500 nm)\Cr (5 nm)\Au (100 nm) sample vs. temperature: with excitation voltage 0.05 V parallel to the film surface, 1–106 Hz. The dotted lines show the fit to a depressed semicircle; (b) Arrhenius plot: logarithm of the resistivity deduced from the low frequency intercept on the Re(Z) axis as a function of reciprocal temperature.

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with columnar grains and strong (111) texture. Such information is not readily accessible by other popular techniques, e.g. impedance spectroscopy or tracer diffusion. The optical technique also provides data that are consistent with the idea that the activation energy for ion migration is sensitive to lattice strain: the activation energy in the out-of-plane direction is 1.1 ± 0.1 eV and 1.5 ± 0.1 eV for the films with in-plane compressive (out-of-plane tensile) and inplane tensile (out-of-plane compressive) strain of 0.34 ± 0.06% and 0.16 ± 0.03% respectively. We further note that 1.1 ± 0.1 eV is the value determined by null-point ellipsometry for bulk ceramics of 20 mol.% Gd-doped ceria. Impedance spectroscopic measurements on GDC20 thin films with the electric field both out-of-plane, i.e., along the grain boundaries, and in-plane i.e., perpendicular to the grain boundaries, produce two very different low temperature activation energies—0.4 eV and 0.83 eV respectively. This discrepancy strongly suggests the major influence of electronic conduction, of grain boundaries, and/or of grain anisotropy on the impedance spectroscopy results.

The Fresnel reflection coefficients:

r 01:p

r 12:p

    N2 ⋅ cos θe1 −N1 ⋅ cosðθ2 Þ N1 ⋅ cos θe1 −N2 ⋅ cosðθ2 Þ     ¼ ; r 12:s ¼ N 2 ⋅ cos θe1 þ N1 ⋅ cosðθ2 Þ N1 ⋅ cos θe1 þ N 2 ⋅ cosðθ2 Þ

The Fresnel transmission coefficients: 2N0 ⋅ cosðθ0 Þ 2N0 ⋅ cosðθ0 Þ   ; t 01:s ¼   N1 ⋅ cosðθ0 Þ þ N0 ⋅ cos θe1 N0 ⋅ cosðθ0 Þ þ N1 ⋅ cos θe1     2N1 ⋅ cos θe1 2N 1 ⋅ cos θe1     ¼ ; t 12:s ¼ N2 ⋅ cos θe1 þ N1 ⋅ cosðθ2 Þ N1 ⋅ cos θe1 þ N2 ⋅ cosðθ2 Þ

t 01:p ¼

t 12:p

Acknowledgments I.L. thanks the Minerva Foundation and the US–Israel Binational Science Foundation (2012237) for funding this research. I.L. specifically wishes to acknowledge the assistance of the Nancy and Stephen Grand Research Center for Sensors and Security. The research is also made possible in part by the generosity of the Harold Perlman Family.

    N1 ⋅ cosðθ0 Þ−N 0 ⋅ cos θe1 N0 ⋅ cosðθ0 Þ−N1 ⋅ cos θe1   ; r 01:s ¼   ¼ N1 ⋅ cosðθ0 Þ þ N0 ⋅ cos θe1 N0 ⋅ cosðθ0 Þ þ N1 ⋅ cos θe1

For θo = 75° and for the thicknesses and refractive indices of the Au electrode and of the GDC20 film as in Table A1, the total reflection/transmission coefficients and reflectance/transmittance are:

Rp ¼

Appendix A A.1. Optical reflectance and transmittance of a thin metal film on a transparent dielectric substrate Methods developed to calculate optical reflectance and transmittance of a thin metal film deposited on a transparent dielectric substrate [11,12] were applied to the layered sample—Au/GDC20 (parameters listed in Table A1). The variables in the calculation are: θe the complex angle of incix

dence (x indicating the lower of the two interfacial layers); rxy.p/s and txy.p/s are the Fresnel reflection and transmission coefficients (xy denotes the interface, and p/s, the polarization components of the electric vector of the incident light); Rp/s and Tp/s are the total reflection coefficients and the total transmission coefficients; and Reff.p/s and Teff.p/s are the reflectance and transmittance. β can be considered a phase shift. With the incident angle of the laser light at the airmetal interface θ0:     N N θe1 ¼ arcsin sinðθ0 Þ⋅ 0 ; θ2 ¼ arcsin sinðθ0 Þ⋅ 0 ; N1 N2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi3 2v " # u   2 u d N ⋅ sinðθ0 Þ β ¼ 2π 1 ⋅N1 ⋅4t1− 0 2 ⋅ðn1 −ik1 Þ 5 2 λ n 1 þ k1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2v #2ffi3 u "   u N ⋅ sin ð θ Þ 0 0 t cos θe1 ¼ 4 1− ⋅ðn1 −ik1 Þ 5 n1 2 þ k1 2

Table A1 Parameters for optical transmittance and reflectance calculations. Layer no.

Material

Thickness (nm), d

Complex refractive index (at 632.8 nm), N n

k

0 1 2

Air Au GDC20

∞ 25 300

1 0.19609 2.071

0 3.2558 0

r 01:p þ r 12:p ⋅ei2β

i2β

; Rs ¼

r 01:s þ r 12:s ⋅e 1 þ r 01:s ⋅r 12:s ⋅ei2β

; Ts ¼

t 01:s ⋅t 12:s ⋅eiβ 1 þ r 01:s ⋅r 12:s ⋅ei2β

1 þ r 01:p ⋅r 12:p ⋅e  2   2 Reff :p ¼ Rp  ¼ 0:451 ; Reff :s ¼ jRs j ¼ 0:88 Tp ¼ T eff :p

i2β

t 01:p ⋅t 12:p ⋅eiβ

1 þ r 01:p ⋅r 12:p ⋅e  2 N ⋅ cosðθ Þ   2 N ⋅ cosðθ2 Þ 2 ¼ 0:455 ; T eff :s ¼ jT s j ⋅ 2 ¼ 0:097 ¼ T p  ⋅ 2 N0 ⋅ cosðθ0 Þ N0 ⋅ cosðθ0 Þ i2β

Therefore, we determined that the majority of the light incident on the Au/GDC20 structure is in fact reflected before penetrating the film: the reflectance of the p and s polarizations are RP ≈ 45%, RS ≈ 90%. A.2. Computational ellipsometry modeling of the GDC20 film For the samples described in this report, the film thickness is comparable to the wavelength of the ellipsometer light source (λ = 632.8 nm). Therefore, before interpreting the optical signal, it is necessary to estimate the influence of contributions from both the upper and lower film interfacial regions. To this end, computational ellipsometry modeling of the GDC20 film was performed [13]. The perturbation to the sample's optical properties due to applied bias voltage was simulated, with resulting changes in the ellipsometer angles, Δ and Ψ, as output. The initial state (U B = 0 V; zero built-in potential) was assumed to be a uniform layer with the refractive index of bulk GDC20 (n = 2.071). The fieldperturbed state was modeled as a three-layer structure, again without built-in potential: enriched layer\bulk\depleted layer, the directionality depending on the polarity of the perturbing voltage UB. Given the large concentration of ionic charge carriers in the bulk (2.5·1021 cm− 3), the thickness of both the upper and lower interfacial regions, vacancy enriched or depleted, is taken to be a few Debye lengths ~ 1–2 nm (Table A2). With this model, the changes in the ellipsometer angles upon application/removal of the electric field do indeed depend on the polarity of UB, yet because only the change in the RMS photocurrent is detected, corresponding to the sum of the absolute values of changes

G. Lazovski et al. / Solid State Ionics 277 (2015) 30–37

37

Table 2 Parameters for computational ellipsometry modeling of the GDC20 film. Sample state

Initial Perturbed, UB b 0 V

Perturbed, UB N 0 V

Material

GDC (bulk) Vacancy enriched layer GDC (bulk) Vacancy depleted layer Vacancy depleted layer GDC (bulk) Vacancy enriched layer

Thickness (nm)

300 2.5 295 2.5 2.5 295 2.5

n (at 632.8 nm)

2.071 2.07095a 2.071 2.07105a 2.07105a 2.071 2.07095a

Ellipsometer angles (for incidence angle, θ = 75°) Δ

Ψ

δΔ

δΨ

|δΔ| + |δΨ|

−105.2521 −105.2520

25.8587 25.8587

– 0.0001

– 0

– 0.0001

−105.2521

25.8588

0

0.0001

0.0001

a It was necessary that the change in the refractive index due to the application of the perturbation voltage be larger than actually occurs in order to reach the sensitivity level of the software [13].

in the ellipsometer angles (|δΔ| + |δΨ|), this dependence cannot be distinguished experimentally. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

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