Keywords: Ionic conductivity, rectification, MIEC.

Abstract

Devices based on doped semiconductors with mobile ionic defects show qualitatively different current-voltage relations than ordinary semiconductor (SC) devices. Their different behavior arises from the movement of ionic defects which results in their redistribution, consequently changing the space charge distribution. This work evaluates theoretical I-V relations of a device of the form metal₁|doped-SC|metal₂ with mobile ionic defects, under steady state. We report here on doped SC of length of the order of a few Debye lengths. In the latter, both the bulk and the edge regions have non neglegible effects on the current voltage relations. Differently from the previously considered case [1], in the present case the electrodes of device allow exchange of material with the bulk. We find that the electrode impedance for ionic current has a significant impact on the device electrical properties.

The proposed model relies on drift-diffusion equations for ionic defects and holes which are coupled via the Poisson equation and mass action law. The transfer of the ionic defects through the electrodes and their reaction with the surroundings is described by a kind of Butler-Volmer relations [2]. Apart from these differential equations there are constrains on the defects concentrations which are dictated by the anode and cathode work functions and surroundings. The equation set plus boundary conditions form a boundary value problem which is solved numerically by a collocation method [3].

We examine the defects distributions, the inner electrical field and the resulting current voltage relations under steady state. The defects distributions and space charge change with V. The I-V relations exibit rectification. The influence of electrode work functions, different surroundings and electrode exchange current density on the parameters of interest, is analyzed in details. The key result is that the studied device shows rectification of the current for any asymmetrical boundary conditions both for depletion or accumulation of the relevant defects.

References

[1] Y. Gil, O. M. Umurhan and I. Riess 2008 J. App. Physics, Vol. 104. 084504.

[2] I. Riess, M. Gödickemeier and L. J. Gauckler 1996, Solid State Ionics, Vol. 90, pp. 91-104.

[3] J. Kierzenka, L.F. Shampine and M.W. Reichelt “Solving Boundary Value Problems for Ordinary Diferential Equations in MATLAB with bvp4c”. Apple Hill Drive, Natick : TheMathworks, Inc, 2000.