Optical Analysis of Oxygen Self‐Diffusion in Ultrathin CeO2 Layers at Low Temperatures

An optical in situ strategy for the analysis of oxygen diffusion in ultrathin ceria layers with a thickness of 2–10 nm at temperatures between 50 and 200 °C is presented, which allows for the determination of diffusion coefficients. This method is based on the sensitivity of the photoluminescence (PL) intensity of InGaN nanowires to adsorbed oxygen. The oxygen diffusion through an ultrathin CeO2 coating deposited on the InGaN nanowires is monitored by analyzing the transient PL behavior of the InGaN nanowires, which responds to changes of the oxygen concentration in the environment when the corresponding oxygen concentration is established at the CeO2/InGaN interface due to diffusion through the coating. Quantitative evaluation of the oxygen diffusion in CeO2 based on a model considering Langmuir Adsorption and recombination yields a diffusion coefficient D of (2.55 ± 0.05) × 10−16 cm2 s−1 at a temperature of 100 °C. Temperature‐dependent measurements reveal an Arrhenius type behavior of D with an activation energy of (0.28 ± 0.04) eV. In contrast, no oxygen diffusion is detected for an ultrathin layer (≥5 nm) of Al2O3, which is known as a poor oxygen ion conductor within the analyzed temperature regime.

the time-dependent photoluminescence intensity. Investigation of different layer thicknesses and quantitative modeling of the extracted transients allows for quantitative estimation of the diffusion coefficients. This nondestructive in situ technique is applicable for ultrathin layers and for temperatures below 200 °C.

Sample Design and Concept
InGaN/GaN nanowire structures which feature a PL quenching response upon exposure to oxygen and other oxidizing gases [14,15] were coated with a 2-10 nm thick homogeneous CeO 2 layer by ALD as displayed in the schematic and in the high-resolution transmission electron microscopy (HRTEM) image in Figure 1.
The PL characteristics of the resulting nanocomposite in atmospheres with different oxygen concentration were recorded at temperatures of 50, 100, 150, and 200 °C. Due to the dense, homogeneous ALD coating, the InGaN core of the nanowire composite was not in direct contact with the surrounding gas atmosphere. To cause a PL quenching response to the oxygen-containing atmosphere, oxygen has to diffuse through the CeO 2 coating until it reaches the CeO 2 /InGaN interface. The related time delay was detected in a transient PL measurement in direct comparison with the behavior of an uncoated InGaN/GaN reference. As the CeO 2 coatings show 97% transparence for the PL excitation wavelength of 405 nm (Section S1, Supporting Information), electron-hole pairs were almost exclusively photogenerated in the InGaN core.

Figure 2a
shows PL spectra of uncoated InGaN/GaN NWs for different oxygen concentrations and temperatures. An increase of the respective entity results in quenching of the PL with the spectral shape remaining unchanged. In Figure 2b, similar PL spectra are shown for a 5 nm CeO 2 -coated sample. Also in this case, thermal and oxygen-induced quenching is observed, but the relative response to oxygen is reduced. The observation that oxygen has an influence on the InGaN PL intensity of 5 nm CeO 2 coated samples indicates that oxygen passes the coating and reaches the CeO 2 /InGaN interface, where the PL quenching is induced due to interfacial oxygen adsorption.
Oxygen-induced relative PL intensity changes (responses) and their temporal evolution were investigated by a transient collection of PL spectra and evaluation of the PL intensities which were integrated over the spectral range between 400 and 700 nm.
In Figure 3a, the transient PL response for alternating intervals of pure nitrogen and 20.5% oxygen in nitrogen of the uncoated InGaN/GaN reference (black curve) and hybrid   T = 50 °C and T = 100 °C; gray-scale spectra were taken at 50 °C and bluescale spectra at 100 °C and measured in an atmosphere of 0%, 1%, 5%, or 20.5% oxygen in nitrogen respectively; a) uncoated InGaN/GaN NWs; b) 5 nm CeO 2 coated InGaN/GaN NWs. An enhancement of temperature T and oxygen concentration c O2 lead to a quenching of PL intensity. www.advenergymat.de www.advancedsciencenews.com structures with CeO 2 coatings of different thickness (colors indicated in the figure) are compared. A detail of the transient measurements is shown in Figure 3b, which displays a magnification of the first 30 s during exposure to oxygen. Here, the transients are normalized to their maximum intensity at the end of the nitrogen interval, t = 0 is the switching point between pure nitrogen and the nitrogen/oxygen mixture (synthetic air).
For the reference sample the typical decrease of the PL intensity in oxygen containing atmosphere, attributed to the enhancement of nonradiative surface recombination due to oxygen adsorption, [14,15] is observed. The magnification in Figure 3b shows that the reference sample immediately responds to oxygen, with a response time as fast as the resolution of the transient measurement (below 4 s). In Figure 3c (black symbols) the thermal quenching of PL intensity is displayed, whereas in Figure 3d the increase of PL quenching response to oxygen with increasing temperature is depicted. The latter is also mirrored by an increase in the effective adsorption energy E ads eff with increasing temperature, a fitting parameter that can be extracted from fits of the response curves according to the Langmuir Adsorption and Recombination (LAR) model that has recently been introduced in ref. [15].
InGaN/GaN nanowires coated with 2, 5, and 10 nm of ceria respectively (colored curves in Figure 3a) also show a decrease in PL intensity upon exposure to oxygen that is qualitatively comparable to the uncoated InGaN/GaN nanowires. As the InGaN core is separated from the gas environment by the CeO 2 coating, this result indicates that oxygen diffuses through the ceria film and causes quenching of the PL intensity when reaching the InGaN/CeO 2 interface. In the magnified presentation of Figure 3b, it is seen that the time delay for the first measurable response to oxygen increases with increasing film thickness. However, similar to the uncoated sample, the sample with the 2 nm CeO 2 coating does not show any time delay and immediately responds to the oxygen exposure.
The PL intensity ( Figure 3c) and the magnitude of the relative oxygen response (Figure 3d) are reduced and systematically decrease with increasing film thickness. The temperature dependence remains qualitatively comparable to that of uncoated nanowires.
In contrast, InGaN/GaN nanowires coated with ultrathin Al 2 O 3 layers do only show a response to oxygen for an Al 2 O 3 thickness of 2 nm. This response is qualitatively similar to that of samples coated with 2 nm of CeO 2 , but already for a thickness of 5 nm the response of Al 2 O 3 -coated samples is completely suppressed (cf. inset in Figure 3a). As Al 2 O 3 is known as a weak oxygen conductor with an oxygen self-diffusion coefficient of 5 × 10 −17 cm 2 s −1 at 1500 °C, [16] which is by a factor of 10 10 smaller than that of CeO 2 (5 × 10 −7 cm 2 s −1 at 1500 °C; approximated from ref. [8]), the absence of an oxygen response for the sample with the 5 nm coating is assigned to the fact that the oxygen diffusion proceeds too slow to cause a measurable decrease of the PL intensity at the temperatures applied here. This result further supports the interpretation that the delayed oxygen response of CeO 2 -coated InGaN nanowires with a coating thickness of 5-10 nm indeed corresponds to the oxygen diffusion through the coating material. However, for a 2 nm Al 2 O 3 coating a response to oxygen was observed, even though it is not expected due to the small diffusion coefficient. As displayed in Figure 3b, the sample with 2 nm Al 2 O 3 coating shows an immediate decrease in PL intensity upon oxygen exposure rather than a delayed response, and thus a comparable behavior as the 2 nm CeO 2 and the uncoated samples, indicating that the detection mechanism is different for 2 nm thin coatings and not induced by oxygen diffusion.

Application of the Langmuir Adsorption and Recombination Model
To explain the dependence of the PL quenching response of InGaN/GaN NW structures on the oxygen concentration for different temperatures, the LAR model was recently introduced by Maier et al. [15] According to that model the maximum oxygen response R [%] is given by the maximum relative intensity change induced by a certain oxygen concentration and can be described by Equation (1) Adv. Energy Mater. 2018, 8, 1802120 Here, transients are normalized to their maximum intensity at the end of the nitrogen-rich interval. t = 0 is the switching point between nitrogen and synthetic air. Extracted data from PL transients of different temperatures and CeO 2 coating thicknesses x: c) maximum intensity I max (measured at the end of first N 2 interval); d) relative change in PL intensity, R, upon exposure response to oxygen.
with PL N2 being the maximum PL intensity in the nitrogen interval and PL O2 being the saturation PL intensity in the oxygen-rich interval. According to the LAR model the dependence of the PL response on the surrounding oxygen concentration and temperature is described by Equation (2) The factor α(T) is the probability for nonradiative surface recombination according to the LAR model and depends on molecular properties of the adsorbate, the nanowire geometry, the potential barrier at the InGaN surface, the temperature, and the number of potential adsorption sites (cf. Section S2, Supporting Information). The term in square brackets is the oxygen surface coverage with values between 0 and 1, according to the Langmuir adsorption model. It depends on the oxygen partial pressure p, the thermal energy k B T, and the effective adsorption energy E ads eff , given by the difference of the activation energies of adsorption and desorption. p 00 stands for the Langmuir desorption pressure, which is in turn dependent on temperature and the molecular mass of oxygen (for exact expressions see ref. [15] and Section S2, Supporting Information). The LAR model provides a phenomenological evidence for the temperature and concentration dependence of the oxygen response and quantitative results for E ads eff and α(T) as temperature-dependent fitting parameters for the calibration curve in which R is plotted as a function of the oxygen concentration or p. The application of the LAR model to the experimental results discussed here implies that the adsorption behavior can be described by a Langmuir isotherm. This is justified by the assumption that a defined number of oxygen adsorption sites is available at the InGaN/coating interface whose occupation probability between 0 and 1 by diffused oxygen follows the Langmuir isotherm. In that line the oxygen concentration in the solid film can be treated analogue to the partial pressure of a gas atmosphere. As for further evaluation only the interfacial oxygen concentration in saturation is taken into account, the deviation from ideal gas conditions can be overcome.
Quantitative evaluation based on the LAR model was carried out for the response curves of the hybrid nanostructures investigated here. In Figure 4a-d the PL responses of the uncoated reference and the coated nanowires are shown as a function of the oxygen concentration for different temperatures. The circles in Figure 4 indicate the experimental data while the solid lines represent the fits according to Equation (2).
All curves show the typical S-shape behavior, with zero response at very low concentrations, a quasi-logarithmic increase of response, which covers approximately three orders of magnitude in concentration, and a saturation regime with a maximum response at high concentrations. The concentration, where 50% of the maximum response is reached (turning point of the curve) is analyte-and temperature-dependent and directly linked to the effective adsorption energy E ads eff in the LAR model.  In all cases the fitted curves show good agreement with the experimental data, demonstrating the applicability of the LAR model. The respective saturation levels and the applied oxygen concentration at the turning point of the calibration curves depend on the coating thickness and the measurement temperature.
The two extracted fitting parameters of the LAR model-the effective adsorption energy E ads eff and the nonradiative surface recombination probability α-are displayed as a function of temperature in Figure 5. A comparison of these parameters for uncoated and coated samples reveals that the former, directly linked to the turning point of the curves, is unaffected by the coating (Figure 5a). This indicates that the adsorption process on the natively oxidized InGaN surface and the CeO 2 coating exhibit a similar adsorption energy. The latter does not depend on the thickness of the CeO 2 film as it is solely determined by the chemical surface properties and the interface characteristics of the hybrid nanostructure.
The observed increase of E ads eff with temperature was previously attributed to a thermally activated transition of physi-to chemisorption on natively oxidized InGaN surfaces. [15] For the experiments reported here this evolution could indicate a thermally activated modification of interfacial adsorption sites and thus a stabilization of adsorbed oxygen.
The nonradiative surface recombination probability α(T) shows similar values and temperature dependence for uncoated and 2 nm CeO 2 coated samples, again indicating a similar detection mechanism for these samples. The observed temperature dependence is mainly determined by the potential barrier the carriers need to overcome, if they recombine nonradiatively over the adsorbed oxygen (cf. Section S2, Supporting Information).
However, for 5 and 10 nm CeO 2 coated samples, the absolute values of α(T) and the temperature dependence are both reduced. As α is linked to the number of surface states (cf. Section S2, Supporting Information), the smaller values indicate that the number of adsorption sites at the InGaN/coating interface is reduced compared to an InGaN surface while it is not further influenced by the coating thickness. Consequently, full occupation of available adsorption sites is achieved at lower oxygen concentrations. The difference in temperature dependence can be assigned to a different potential barrier for coated and uncoated samples.

Determination of Diffusion Coefficients
Based on the quantitative relation between each PL response value and the respective oxygen concentration provided by the LAR-evaluation, the transient PL response measurements can serve as a base for modeling the oxygen diffusion applying the following strategy (exemplarily shown for a 10 nm CeO 2 coating measured at 150 °C in Figure 6): (1) Figure 6a shows the time-dependent response to oxygen obtained by converting the measured PL(t)-to an R(t)-curve by Equation (1). t = 0 is the last point of the N 2 interval. The subsequent increase in oxygen response is caused by the exposure to an atmosphere containing 20.5% of oxygen (synthetic air). (2) The measured response is linked to the oxygen concentration at the InGaN/coating interface by the LAR model. By converting the R(t) into a curve that displays the temporal evolution of the interfacial oxygen concentration, c (x = 10 nm, t), represented by the data points in Figure 6b (cf. schematic in Figure 6b). As α(T) differs for uncoated and differently coated samples, the LAR fit result for the specific sample and temperature must be used for this conversion. The error bars in Figure 6b are derived from the maximum deviation of experimental values from the LAR fit.
(3) The c (x = 10 nm, t) data points in Figure 6b are fitted using Fick's second law of diffusion (solid line in Figure 6b), expressed in detail in Equation (3), if an infinite reservoir of oxygen with a fixed surface concentration c s is assumed Here, x is the penetration depth and given by the thickness of CeO 2 coating, c s is given by the offered oxygen concentration   This fitting procedure is applicable only for those samples where the time delay in the PL response is dominated by the diffusion process. For those samples with a fast PL response, the response time is determined by the exchange of the gas volume in the measurement chamber and hence a fit based in the law of diffusion is not meaningful (this is demonstrated in Section S3, Supporting Information).
For the example shown in Figure 6 a diffusion coefficient of D = (6.00 ± 0.07) × 10 −16 cm 2 s −1 is obtained for a 10 nm CeO 2 -coated sample at a temperature of 150 °C. The error was derived by the standard error of the fit by Fick's law, which was applied to the concentration values including their respective errors.
Following this procedure, diffusion coefficients for coatings with a thickness of 5 and 10 nm at temperatures of 50, 100, 150, and 200 °C were determined and are displayed in an Arrhenius plot in Figure 7. For comparison values for higher temperatures that are reported in literature are also shown. It is evident from the inset in Figure 7 that the 5 and 10 nm coated samples show similar diffusion coefficients independent of the film thickness, which increase with increasing temperature in an Arrhenius type behavior. A linear fit of these results is indicated in Figure 7 and its inset and reveals an activation energy of E act = (0.28 ± 0.04) eV.
The comparison to existing literature values for the diffusion coefficient D, derived from different experimental and theoretical methods, indicated by the solid symbols in Figure 7, [5,8,9,[11][12][13] shows that our results fit into the range which is covered by the extrapolation to the investigated temperature regime of 50-200 °C, as indicated by the yellow area in Figure 7.
Experimental literature values do only exist for elevated temperatures above 500 °C and were obtained for bulk material.
The related activation energies for the self-diffusion process can be assigned to two diffusion mechanisms, as suggested by Kamiya et al. [8] High activation energies between 1.6 and 2.3 eV [3,8] are attributed to the formation of vacancies at elevated temperatures above 1000 K [8] and give rise to an intrinsic diffusion mechanism. Smaller activation energies between 0.4 and 0.6 eV are typically assigned to extrinsic diffusion Adv. Energy Mater. 2018, 8, 1802120   [11,8,9] d determined by conductivity measurements, [5] and e,f theoretical values for reduced ceria from molecular dynamics simulations. e considers CeO 1.95 [12] and f considers CeO 1.88 . [13] Yellow area indicates the range which is covered by the approximation of the literature values to the investigated low-temperature regime. Inset shows magnification of obtained results with error bars and linear fit.
processes observed for nonstoichiometric ceria already at lower temperatures. [8,11,13] This extrinsic diffusion process is dominated by impurity or defect diffusion, mainly assigned to the oxygen vacancy. These lower activation energies are similar to those obtained for Y-or Gd-doped CeO 2 [8] which supports the assumption that the diffusion process observed in the present experiments is impurity-dominated. [8] The activation energy of E act = (0.28 ± 0.04) eV extracted from our experiments agrees well with the values for extrinsic diffusion, as it is expected for the comparatively high density of oxygen vacancies due to high surface area and small film thickness. It has previously been shown that structural properties of the coating and particularly the presence of strain can influence the diffusion properties in oxide layers. [17] Figure 8 shows a detailed TEM analysis of the CeO 2 coating and the interfacial region to the GaN part of the nanowire, which is qualitatively similar to InGaN/ CeO 2 interface. The CeO 2 shell is composed of nanocrystals with ≈5 nm diameter. Those nanocrystals are mainly epitaxially attached to the GaN surface with a good alignment between the (111) CeO 2 and the (0002) GaN planes. It should be noticed that the geometric phase analysis (GPA) dilatation maps show a mismatch relation of about 20.4% between the above mentioned families of planes, which is in good agreement with a perfect relaxation of the CeO 2 structure, implying the creation of misfit dislocations every five (111) CeO 2 planes and six (0002) GaN planes. This relaxation mechanism is complex as also the interaction of the nanocrystals with their closest neighbors has to be taken into account. This is the reason, why in some cases there is also a rotation observed in the (111) CeO 2 planes, implying an elastic deformation of the planes, in competition to the plastic deformation due to the formation of misfit dislocations. In sum, the influence of strain to the oxygen diffusion in the CeO 2 coatings can be neglected, but grain boundary diffusion has to be considered besides the bulk diffusion process in the CeO 2 grains. Also, the anelastic properties of ceria [18,19] might have influence on the oxygen penetration and diffusion properties in the ceria film and therefore on the determined diffusion coefficient and activation energy.
Due to the fast response time an extraction of the diffusion coefficients for the samples with an Al 2 O 3 or CeO 2 coating thickness of 2 nm is not possible based on the existing experimental data. According to Figures 3 and 4 those samples show an almost instantaneous oxygen response with a similar magnitude, id est no time delay due to oxygen diffusion processes is observed for uncoated, 2 nm CeO 2 and 2 nm Al 2 O 3 coated samples. In combination with the different extracted α(T) parameter of the 2 nm CeO 2 coating in comparison to the samples with a thicker coating, shown in Figure 5b, it can be concluded that a different detection mechanism has to be taken into account for samples with a coating thickness of 2 nm. In particular, oxygen diffusion does not determine PL response time for a coating thickness of 2 nm. The similarity of the extracted α(T)-values and its temperature dependence for the samples with a 2 nm CeO 2 coating and the reference points toward a similar detection mechanism for those samples. Additionally, the observed oxygen response of 2 nm Al 2 O 3 -coated samples, even though oxygen diffusion is not likely to occur in Al 2 O 3 , supports this assumption.
A possible reason for the observed response characteristics of those structures could be that nonradiative recombination via oxygen atoms adsorbed at the surface that occurs via tunneling of photoexcited carriers through the oxide coating rather than the diffusion of oxygen determines the recombination process. The probability of this process is enhanced by the small oxide thickness and possibly further increased by monolayer thickness fluctuations. The strong temperature dependence of this process that rapidly decreases in probability for increasing coating thickness further supports this assignment.