Charge injection and transport in low-mobility mixed ionic/electronic conducting systems: Regimes of behavior and limiting cases

A comprehensive analysis of a model describing charge-carrier injection and transport in light-emitting electrochemical cells (LECs) and related mixed ionic electronic conductors (MIECs) is given. Ions are treated using a modified drift-diffusion transport equation that accounts for volume-exclusion effects, and electronic injection is treated using a spatially dependent tunneling mechanism that explicitly accounts for both forward and backward fluxes. Systems containing both one and two mobile ionic species are treated and compared. The unique physics of LECs stem from ionic polarization processes that can lead to field screening and narrowed injection barriers, producing increased electrode exchange currents via tunneling. The latter process promotes the establishment of electronic quasiequilibrium throughout the double-layer regions and hence promotes bulk-limited conduction. Explicit expressions are given describing the conditions necessary to assume field screening and bulk-limited conduction, which determine the applicability of either traditional semiconductor device models such as Fowler-Nordheim or electrochemical models such as the Nernst equation. Having established these conditions, several distinct regimes of bulk-limited LEC behavior are described. Explicit formulas for the biases delineating these regimes are given as well as formulas for the current in each regime. At low biases, the current generally increases exponentially with bias; the bulk remains field free, and the transport is predominantly unipolar and diffusive. At high biases, the current rises much less rapidly, and bulk transport is bipolar, occurring through a combination of drift and diffusion. The nature of the bulk region in the high-bias regime is markedly different in systems with one and two mobile ionic species. At intermediate biases, space charge effects preferentially drive injection of the minority carrier causing a transition from unipolar to bipolar injection. It is demonstrated that many of the models proposed to describe LECs exist upon a common continuum, and that the major factor separating them is simply the magnitude of the applied bias. This work allows one to estimate at what biases an idealized LEC with particular equilibrium concentrations of ionic and electronic carriers will transition from one mechanism to another. It also aids in conceptually mapping mechanisms and internal details of the system onto each regime of behavior.