doi:10.1038/nature17653 Supplementary Methods Electronic transport mechanism in H-SNO In pristine RNO, pronounced electron-phonon interaction results in polaron formation that dominates the electronic conduction mechanism. In H-SNO, both electronphonon and electron-electron interactions are important in determining its electronic transport mechanism. Extended Data Figure 5c shows the low-temperature transport properties of H-SNO, whose behavior deviates from that of activated transport mechanism as in a classical semiconductor. Extended Data Figure 5d plots w(t ) d ln ρ / d lnt as a function of T in log-log scale. The transport mechanism can be determined by the slope (p) of the w(t ) T curve on a log-log plot: p = 1/4 for Mott VRH in 3-dimensional systems, p = 1/2 for VRH in the presence of Coulomb interactions (also called Efros-Shklovskii VRH), and p = 1 for activated conduction. The dominant mechanism in H-SNO over the entire temperature range is ES-VRH signifying the presence of Coulomb interactions in the system as well as electron-phonon interactions. In ES-VRH, the temperature-dependent resistivity can be described as: ρ(t ) = ρ 0 exp T p 0 T where ρ 0 is a prefactor and T 0 is characteristic temperature given by: T 0 = 2.8e2 4πεk B ξ where ε is the dielectric constant, and ξ is the localization length. A linear fit to Extended Data Fig. 5d yields T 0 = 1.194 10 5 K. Using the above equation and taking the relative dielectric constant of H-SNO to be ~ 5 (Ref. 12), we determine ξ = 0.78 Å, which is smaller compared to the lattice spacing of bulk SNO (0.3796 nm). Thus the carriers are strongly localized within a unit cell due to electron correlation. In comparison, the transport mechanism in pristine SNO was also investigated. The w(t ) d ln ρ / d lnt curves of SNO show a switchover between two distinctive regions: activated type behavior (p = 1) for T > 180 K with an activation energy ~ 110 mev and Mott VRH (p = 1/4) at low temperatures, showing that the Coulomb gap is absent in pristine SNO (Extended Data Fig. 5e). Methods to calculate ionic conductivity of H-SNO The ionic conductivity of H-SNO in Pt/SNO/Pt configuration is measured in the open circuit condition by impedance spectroscopy with 3% humidified 5%H 2 /95%Ar as fuel and laboratory air as oxidant at various temperatures. The ionic conductivity of H- SNO in Pt/SNO/Pd configuration is measured in the open circuit condition by impedance spectroscopy with 3% humidified pure H 2 as fuel and laboratory air as oxidant at various temperatures. The ionic conductivity of epitaxial H-SNO is measured by impedance spectroscopy in a dry 5%H 2 /95%Ar gas mixture. The ASR (i.e. SNO electrolyte ASR, or ASR SNO ) is obtained from the value of the high frequency intercept on the real axis of the Nyquist plot. ASR SNO was found to be remarkably low (for example, 0.045 Ω cm 2 at 500 C in Fig. 2b). The total electrical WWW.NATURE.COM/NATURE 1
conductivity of the SNO electrolyte (σ SNO ) is defined as the ratio of the electrolyte thickness to ASR SNO, and was calculated to be 2.17 10-3 S/cm at 500 C. The measured total electrical conductivity consists of both electronic and ionic conductivity. Quantitative analysis is needed to extrapolate the ionic conductivity. The ionic transference number can be calculated in two ways. In the E.M.F. method, one considers the fuel cell using an equivalent circuit that has an ionic resistance and electronic resistance from the electrolyte. The underlying assumption is that interfacial processes are very fast. In this method, the ionic transference number is given by: t i = V OC /E N It should be noted that the non-zero electronic conductivity of the electrolyte itself can provide a pathway for the electronic current even under open circuit condition. Therefore, in the presence of current flow, the measured OCV is also affected by the electrode polarization resistance (R polarization ) (Ref. 15, 16). In this case, the ionic transference number can be determined using a modified E.M.F. method. The ionic transfer number can be expressed by (Ref. 15, 16): t i = 1 ASR SNO 1 V OC ASR T E N, where ASR T is the total area specific total resistance obtained from low-frequency intercept with the real axis of the impedance data on a Nyquist plot, V OC is the OCV, E N is the Nernst potential. For µsofcs with optimized electrode conditions, t i of H-SNO determined by the E.M.F. method is greater than 0.96 at 500 ºC, while t i of H-SNO determined by the modified E.M.F. method is greater than 0.98. This confirms the phase transition of SNO from an electronic conductor to an electron-blocking correlated insulator. With increasing operation temperature and increasing electrolyte thickness, the relative importance of the electrode polarization resistance decreases, and the OCV increases. Representative raw data sets from Pt/SNO/Pt devices used for the calculation are shown in Supplementary Table 3. For SNO SOFCs with dense Pd electrodes, only protons can pass through the Pd membrane and therefore the measured ionic conductivity only originates from proton conduction. On the other hand, the total electrical conductivity of epitaxial H-SNO thin films on LAO can be measured in 1 atmosphere of 5%H 2 /95%Ar as a reference. Using the ionic transfer number determined from the E.M.F. methods, the ionic conductivity of the epitaxial H-SNO can be also calculated as shown in Fig. 2c. The ionic conductivity of epitaxial H-SNO is higher than H-SNO in SOFC operation. This could be due to grain boundary conduction as SNO is polycrystalline when deposited on the Si 3 N 4 membranes. The conductivity of H-SNO in both membrane and thin film forms were measured from more than six different batches of samples grown over the course of the study and show consistent results. Calculation of the ideal OCV (Nernst potential E N ): The ideal open-circuit voltage developed by H 2 gradient is expressed using Nernst equation as follows: E N = RT 2F ln P (c) H 2 (a) P H2 2 2 WWW.NATURE.COM/NATURE
(c) P H2 where R is the ideal gas constant, T is the temperature, F is the Faraday constant, (a) and P H2 are the H 2 partial pressure at the cathode and anode, respectively. The equilibrium reaction between H 2, O 2, and water vapor (½ O 2(g) + H 2(g) = H 2 O (g) ) can be considered to express the H 2 partial pressure ( P ) in terms of O 2 partial pressure ( P ) and water vapor partial pressure ( P equilibrium constant. P H2 = P H 2 O K P O2 HO 2 H 2 ) in the following equation, where K is the O 2 In this study, the fuel used for testing Pt(c)/SNO/Pt(a) fuel cells was 3% humidified 5%H 2 /95%Ar, while the fuel used for testing Pt(c)/SNO/Pd(a) fuel cells was 3% humidified pure H 2. In both cases, the oxidant on the cathode side was laboratory air with ( ) a relative humidity of 60%, and therefore, the P c is determined to be 1.8%. Supplementary Table 2 shows the calculated values of E N at various temperatures ranging from 350-500 C. HO 2 Analysis of the ionic diffusivity and conductivity of H-SNO A general relationship exists between diffusivity D and conductivity σ because of their same origin of the electrochemical driving force: σ = c(ze)2 D k B T where c is the concentration of the mobile ions, e is the electron charge, Z is the number of electron charge each ion carries. Based on the relation between diffusion coefficient D, diffusion time t and diffusion length L D (from the optical microscopy image): L D ~ Dt, we can estimate the proton diffusivity to be 1.6 10-7 cm 2 /s at 300 ºC in SNO. Knowing the values of diffusivity and conductivity (based on electrical measurements), the concentration of mobile protons in H-SNO is estimated to be ~10 21-10 22 cm -3 (using the data from SNO polycrystalline fuel cell, and epitaxial thin films, respectively). Such concentration corresponds to 0.1 to 1 proton per unit cell, which agrees well with the valence state change of Ni indicated by the XANES studies. This verifies a high concentration of protons can be incorporated into SNO without the cation substitution commonly required for many other proton conducting oxides. WWW.NATURE.COM/NATURE 3
Supplementary Table 1. Fitting parameters used for modeling the impedance spectrum in Fig. 2b using an equivalent circuit model. The electric double layers at the cathode and the anode act effectively as capacitance element C dl, and contribute to two of the semicircles. On the other hand, protons can be incorporated into or removed from the SNO lattice, which stores electrical charge/energy and effectively acts as another capacitance element C p (i.e. pseudocapacitance). The high-frequency semicircle corresponds to an effective area capacitance ~10 µf/cm 2. The pseudocapacitance related to the hydrogen incorporation reactions in thin film oxides typically ranges from tens to hundreds of µf/cm 2 (see for example Zheng and Jow, J. Electrochem. Soc. L6, 142, 1995). (Note that the measured capacitance is differential capacitance, and not the total charge stored divided by the voltage). The other two circles, in the lower frequency range, are due to the electrode polarization (electric double layer at the anode and cathode). This was verified by comparing Nyquist plots taken from two fuel cells with identical electrolyte deposition condition but different cathode and anode deposition conditions. A major difference in the two low-frequency semicircles can be observed between different electrode conditions, while the high-frequency semicircles are almost the same for different samples. Additional experiments measuring the Nyquist plot of a same fuel cell over different time during its operation also show that the two low-frequency semicircles change with time due to the agglomeration of porous metallic electrodes, while the highfrequency semicircle remains almost intact. The magnitude of these two circles can vary by more than one order of magnitude with a strong dependence on the fabrication parameters and morphology of the electrodes. Both of the two semicircles match well with typical values for Pt/YSZ/Pt µsofc samples, and show a clear thermally activated behavior, indicating that they indeed originate from the electrode EDL. These two semicircles correspond to even larger effective areal capacitance. For a perfectly smooth electrode-electrolyte interface, C dl is typically around 30 µf/cm 2. However, the value can be much larger, if the electrodes have high surface area, which is the case for the porous electrodes in our µsofcs. Area-specific ohmic resistance, ASR ohm (Ω cm 2 ) 0.045 Area-specific polarization resistance ASR 1 (Ω cm 2 ) 0.139 Area-specific polarization resistance ASR 2 (Ω cm 2 ) 0.400 Area-specific polarization resistance ASR 3 (Ω cm 2 ) 0.222 CPE constant T, CPE 1 -T (F) 6.19 10-8 CPE exponent p, CPE 1 -P 0.76 Capacitance, C 1 (F) 2.35 10-9 CPE constant T, CPE 2 -T (F) 2.12 10-7 CPE exponent p, CPE 2 -P 0.89 Capacitance, C 2 (F) 7.78 10-8 CPE constant T, CPE 3 -T (F) 3.52 10-6 CPE exponent p, CPE 3 -P 1.0 Capacitance, C 3 (F) 3.52 10-6 4 WWW.NATURE.COM/NATURE
Supplementary Table 2. The calculated Nernst potential used to extrapolate the ionic transference number. Temperature ( C) E N (3% humidified 5%H 2 /95%Ar) E N (3% humidified pure H 2 ) 350 1.108 1.188 375 1.102 1.185 400 1.095 1.182 425 1.089 1.179 450 1.082 1.175 475 1.075 1.172 500 1.069 1.168 Supplementary Table 3. Representative electrochemical data set from a Pt/SNO/Pt device to extrapolate the ionic transference number and the ionic conductivity T ASR SNO ASR T t ( C) (Ω cm 2 ) (Ω cm 2 V ) OC (V) E N (V) i σ i (S/cm) t i σ i (S/cm) (E.M.F.) (E.M.F.) (Liu) (Liu) 350 0.191 21.8 0.893 1.108 0.806 6.33 10-4 0.998 7.84 10-4 400 0.141 12.8 0.967 1.095 0.884 9.40 10-4 0.999 1.06 10-3 450 0.115 4.86 1.009 1.082 0.933 1.22 10-3 0.998 1.30 10-3 500 0.0640 1.92 1.03 1.069 0.964 2.26 10-3 0.999 2.34 10-3 WWW.NATURE.COM/NATURE 5