Mott-Schottky Model Research Articles

Determination of grain boundary potentials in ceramics: Combining impedance spectroscopy and inline electron holography

Abstract The electrostatic potential arising from charge bound at grain boundary cores in ceramics and the accumulation of space charge in their vicinity is in many cases made responsible for the ion blocking or conducting behavior of electroceramics. While interpretation of impedance spectra of nominally undoped and acceptor doped SrTiO3 ceramics and bicrystals implies that grain boundaries are positively charged and accompanied by fairly wide regions of negative space charge on both sides, a critical analysis of electron holography data available in the literature yields very narrow potential profiles of the opposite sign. This paper attempts to reconcile this apparent discrepancy by showing that within the Mott–Schottky model, impedance data which implies space charge dominated grain boundary resistivity must be interpreted in terms of even wider space charge regions than generally assumed. A review of electron holography results from grain boundaries in SrTiO3 is extended by new results which were obtained by a novel inline electron holography reconstruction algorithm at a near Σ13 grain boundary in nominally undoped SrTiO3. This work is dedicated to the memory of Prof. Rowland M. Cannon.

Proton transport properties at the grain boundary of barium zirconate based proton conductors for intermediate temperature operating SOFC

Proton transport properties across the grain boundary of barium zirconate based proton conductors were studied in accordance with the space charge concept. The analysis is performed at temperatures lower than 200 °C using a Mott-Schottky model. The barrier height of Y- and Gd-doped barium zirconate is in the range of 0.29 to 0.57 V, which higher than that of oxygen ionic conductors. The barrier height of the space charge layer shows a dependence on the dopant type and concentration. The dependence correlates with the enrichment of the dopant at the grain boundary. The results suggest that the enrichment of the dopant decreases the barrier height and is effective to improve proton transport properties across the grain boundary.

Comprehensive Modeling of Ion Conduction of Nanosized CaF2/BaF2 Multilayer Heterostructures

AbstractMolecular beam epitaxy‐grown CaF2/BaF2 heterolayers are a demonstration of the potential of nanoionics. It has been shown that ion conductivities both parallel and perpendicular to the interfaces increase with decrease in interfacial spacing. This size effect was attributed to the thermodynamically necessary redistribution of the mobile fluoride ions (N. Sata, K. Eberl, K. Eberman, J. Maier, Nature 2000, 408, 946; X. X. Guo, I. Matei, J.‐S. Lee, J. Maier, Appl. Phys. Lett. 2007, 91, 103102). On this basis, the striking phenomenon of an upward bending in the effective parallel conductivity as a function of inverse interfacial spacing ${\sigma}_{m}^{||} ({{\rm 1}/ \ell})$ for low temperatures (T ≤ 593 K) has been satisfactorily explained by application of a modified Mott–Schottky model for BaF2 (X.X. Guo, I. Matei, J. Jamnik, J.‐S. Lee, J. Maier, Phys. Rev. B 2007, 76, 125429). This model was further confirmed by measurements perpendicular to the interfaces that offer complementary information on the more resistive parts. Here a successful comprehensive modeling of parallel and perpendicular conductivities for the whole parameter range, namely for interfacial spacings ranging from 6 to 200 nm and investigated temperatures ranging from 455 to 833 K, is presented. The model is based on literature data for carrier mobilities and Frenkel reaction constants and the assumption of a pronounced F− redistribution. Given the fact that an impurity content that was experimentally supported is taken into account and apart from minor assumptions concerning profile homogeneity, the only fit parameter is the space charge potential. In particular, it is worth mentioning that in BaF2 the low temperature Mott–Schottky space charge zone which is determined by impurities changes over, at high temperatures, into a Gouy–Chapman situation owing to increased thermal disorder. (The situation in CaF2 is of Gouy–Chapman type at all temperatures.)

Defect chemical modeling of mesoscopic ion conduction in nanosizedCaF2∕BaF2multilayer heterostructures

Interfacial and mesoscopic size effects in molecular beam epitaxy-grown $\mathrm{Ca}{\mathrm{F}}_{2}∕\mathrm{Ba}{\mathrm{F}}_{2}$ heterolayers have been quantitatively analyzed on the basis of Gouy-Chapman and Mott-Schottky space-charge profiles. The linear dependence of the overall parallel conductivity on the inverse interfacial spacing found for large interfacial spacings $(\ensuremath{\ell}>50\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ can be obtained from both models being in good agreement with the experimental data. An upward bending occurring for small interfacial spacings $(\ensuremath{\ell}<30\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ can only be reproduced by the Mott-Schottky model based on the assumption of frozen-in impurity profiles.

Energy level alignment and band bending at TPD/metal interfaces studied by Kelvin probe method

In order to examine the validity of Mott-Schottky model at organic/metal interfaces, the position of the vacuum level (VL) of triphenyldiamine (TPD) film formed on five metal substrates was measured as a function of the film-thickness by Kelvin probe method in ultrahigh vacuum (UHV). At all the interfaces, sharp shifts of the VL were observed within 1 nm thickness. Further deposition of TPD up to 100 nm did not change the position of the VL indicating no band bending at these interfaces. These findings clearly demonstrate the Fermi level alignment between metal and bulk TPD solid in UHV is not established within a typical thickness of real devices.

Nature of the Schottky-type barrier of highly dense SnO2 systems displaying nonohmic behavior

The electrical characteristics of highly dense SnO2 ceramic varistors are believed to be caused by the existence of potential barriers at the grain boundary. A complex plane analysis technique (to eliminate the influence of trapping activity associated with the conductance term observed via depression angle of a semicircular relaxation in the complex capacitance plane), allied with an approached Mott–Schottky model, are used to demonstrate that the potential barriers at the grain boundary are Schottky-type barriers in SnO2 varistors such as those observed in the traditional ZnO varistor.

Energy level alignment and band bending at model interfaces of organic electroluminescent devices

The basic concepts of common vacuum level and band bending in Mott–Schottky (MS) model was experimentally examined for the model interfaces of organic electroluminescent devices by using UV photoemission spectroscopy (UPS) and Kelvin probe method (KPM). We found that interfacial dipole cannot be neglected at most organic/metal interfaces and that the potential shift at the interface due to such dipole sometimes reaches over 1 eV in contrast to the assumption of the common vacuum level in MS model. Based on the observed data, possible origins of the interfacial dipole and general trends of the potential shift against the work function of the electrode metal were proposed. The band bending and Fermi level alignment were also examined at the interfaces between metals (Au, Cu, Ag, Mg, Ca) and TPD( N, N′-bis(3-methylphenyl)- N, N′- diphenyl-[1,1′-bisphenyl]-4,4′-diamine).