Perspective Cite This: J. Phys. Chem. Lett. 2018, 9, 132−137
pubs.acs.org/JPCL
Ionic−Electronic Ambipolar Transport in Metal Halide Perovskites: Can Electronic Conductivity Limit Ionic Diffusion? Ross A. Kerner† and Barry P. Rand*,†,‡ †
Department of Electrical Engineering and ‡Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *
ABSTRACT: Ambipolar transport describes the nonequilibrium, coupled motion of positively and negatively charged particles to ensure that internal electric fields remain small. It is commonly invoked in the semiconductor community where the motion of excess electrons and holes drift and diffuse together. However, the concept of ambipolar transport is not limited to semiconductor physics. Materials scientists working on ion conducting ceramics understand ambipolar transport dictates the coupled diffusion of ions and the rate is limited by the ion with the lowest diffusion coefficient. In this Perspective, we review a third application of ambipolar transport relevant to mixed ionic−electronic conducting materials for which the motion of ions is expected to be coupled to electronic carriers. In this unique situation, the ambipolar diffusion model has been successful at explaining the photoenhanced diffusion of metal ions in chalcogenide glasses and other properties of materials. Recent examples of photoenhanced phenomena in metal halide perovskites are discussed and indicate that mixed ionic−electronic ambipolar transport is similarly important for a deep understanding of these emerging materials.
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halide perovskites. [A simple example of illumination affecting a solid-state electrochemical measurement is discussed in the Supporting Information (SI).] In addition, there are reports that the ion migration activation energy, Em, is dependent on illumination, often referred to as light or photoenhanced ion migration.14,15 The origin of the illumination dependence has been attributed to many effects including increased rotations of the organic cation and photogenerated electronic carriers decreasing the energy barrier for an ion to hop sites.14,15 However, the rotation of the polar organic cations may be of lesser importance than previously thought.16
etal halide perovskite materials have recently garnered immense attention for semiconducting and, in particular, optoelectronic applications due to their unique electronic and optical properties.1,2 These materials possess the unique property of being mixed conductors with the ionic and electronic conductivities being approximately equal under certain conditions.3,4 As a result, many long time scale transients (on the order of seconds to hours) are attributed to mobile ions. These effects include current−voltage hysteresis,5 photocurrent or photoluminescence decay,6 giant dielectric constant,7 device degradation,8 switchable/polarizable devices,9 and others. Therefore, it is critically important to fundamentally understand the ionic transport properties of metal halide perovskites to systematically mitigate or exploit these phenomena. The ionic transport properties appear to be dependent upon extrinsic factors. For example, the ionic diffusion coefficient has been reported to change by orders of magnitude depending on the substrate, electrode, or interface layer choice.10 However, it has recently been proposed that reversible and irreversible interfacial chemistry strongly affects the composition and properties near the interface.11−13 If unaccounted for, a measurement of a bulk property could easily be misconstrued. Interfacial chemistry, which can affect properties such as the capacitance by multiple orders of magnitude, may instead dominate the measurement. The chemical equilibrium or steady state concentrations at an interface where electrochemical reactions occur will also be affected by voltage and illumination conditions since free carriers are a main reactant. Understanding this chemistry is often helpful for explaining “anomalous” properties measured on devices composed of © XXXX American Chemical Society
One mechanism of coupling illumination to ionic mobility has been alluded to but largely overlooked: ambipolar transport. One mechanism of coupling illumination to ionic mobility has been alluded to but largely overlooked: ambipolar transport. Ambipolar transport is the phenomenon of coupled motion of positively and negatively charged carriers in a material under nonequilibrium conditions. Its origins lie in ceramic materials, but is most often applied to excess hole and electron transport in semiconductors. To be able to describe ambipolar transport, we need to assume quasi-neutrality to Received: September 8, 2017 Accepted: December 14, 2017
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DOI: 10.1021/acs.jpclett.7b02401 J. Phys. Chem. Lett. 2018, 9, 132−137
The Journal of Physical Chemistry Letters
Perspective
ensure that no large internal fields develop in the material as charge carriers migrate. In a semiconductor, a single charged species cannot diffuse freely because insufficient screening by its surroundings (due to the limited density of mobile charges) will lead to the development of a space charge, which counteracts the concentration gradient of the specific charged species and quickly stop the charge’s motion. Instead, oppositely charged carriers must migrate together in which case their mobility will be dictated by the minority carrier. Note that it is entirely possible that the minority carrier has a mobility much greater than that of the majority carrier, but the conductivity of the minority carriers is much lower owing to their relative scarcity. Ambipolar transport applied to mixed ionic−electronic conductors couples a single migrating ionic species to mobile electronic carriers. Increasing the electronic conductivity would ensure no space charges develop, decoupling cation and anion motion, and permitting maximal ion mobility. Mixed ionic− electronic ambipolar transport has been well characterized in chalcogenide glasses where the equilibrium electronic conductivity is much smaller than the ionic conductivity.17−20 Under illumination, this condition can be easily reversed. It is quite likely that halide perovskites, which have been shown to have ion transport numbers (tion, ratio of ionic to total conductivity) between 0.5 and 1 in the dark, are subject to ionic−electronic ambipolar transport as well.3,4 And, being relatively low bandgap materials with strong absorption coefficients, supra-bandgap illumination generates a considerable steady-state density of electronic carriers and can therefore facilitate the independent motion of ions. As such, ionic−electronic ambipolar transport may explain many of the observations made in the literature on halide perovskites and should be considered for the proper interpretation of results. Ionic−Electronic Ambipolar Transport Derivation. First, we must define what the mobile species are and what their properties depend on. It has been argued that the intrinsic mobile ionic species is the halide vacancy, just as it is at low temperature for the lead halides.3,4,21 This is logical since the halide sublattice is the only network that percolates the crystal with no other ions significantly blocking the pathways of halide motion. In the following discussion, it is assumed that halide defects are the most mobile, but it should be noted that definitive evidence for the most mobile species is still lacking. Usually, in a given material, one ion will be much more mobile than others. Interstitial (which has been all but ruled out4) and vacancy defect diffusion coefficients are the only properties that can be measured that are independent of other variables such as defect density. Note that the diffusion coefficient of the halide ions themselves, Dion, depends strongly on the concentration of vacancies, Cvac, while the vacancy diffusion coefficient, Dvac, is nearly constant over a wide range of defect densities (related to Cion),22 and can be related by the following expression: DionC ion = DvacCvac
other defects) is nearly independent of temperature at low temperatures (
