Properties of solid state devices with mobile ionic defects. Part I: The effects of motion, space charge and contact potential in metal|semiconductor|metal devices Y. Gil, O.M. Umurhan, I. Riess ⁎ Physics Department, Technion-IIT, Haifa 32000, Israel Received 7 August 2006; received in revised form 12 October 2006; accepted 24 October 2006 Abstract The characteristics of solid state devices based on p-type semiconductors with mobile acceptors are discussed. The devices are basic ones of the form: metal|semiconductor|metal. The metal electrodes are assumed to be chemically inert and to block material exchange. The effect of the contact potentials as well as of the space charge are taken into consideration. The distribution of charge carriers (holes and acceptors) and the I–V relations are evaluated. These results are compared with those of a model in which the acceptors are immobile and with two approximations in which neutrality is assumed either at the boundary or throughout the whole semiconductor. The motion of the acceptors is found, in some cases, to introduce only minor changes in the I–V relations. This finding may be of significance for solid state devices of reduced scale. The I–V relations of samples much thicker than the equilibrium Debye length reduce to the ones obtained assuming local neutrality throughout the sample. The results also depend significantly on the reaction constant between the acceptors and holes to form neutral acceptors. © 2006 Published by Elsevier B.V. Keywords: Solid state device; Semiconductor; Mixed ionic electronic conductor; MIEC; I–V relations; Defect distribution 1. Introduction We discuss solid state devices based on p-type semiconduc- tors with mobile acceptors. Semiconductors that also conduct ions are denoted as mixed-ionic-electronic-conductors (MIECs). MIECs have appeared in solid state devices in the past. For example, Cu|Cu 2 O|Pb cells were reported to have rectifying properties by Grondahl and Geiger as early as 1927 [1]. Cu 2 O is known [2,3] to conduct copper ions as well as holes. The tarnishing of Cu, which occurs even at room temperature, is an example of such an ionic motion. Cu 2 O was reported to show a special type of I–V relations due to such motion [4–7]. In modern solid state devices ionic conduction plays an important role. The doping process involves ionic motion, which takes place at elevated temperatures. The aging process of solid state devices, at room temperature, is a direct result of ionic motion. MIECs also play an important role as electrodes in fuel-cells. Usually, a poor ionic conductivity can be neglected in large scale solid state devices. However, in nanometric scale devices this ionic conduction may become significant. Such a motion may result in new I–V relations under a slowly varying applied voltage [7]. The small size has two effects. First, the distance that the ions have to move in order to significantly alter their concentration is small. Second, the gradients in the electro- chemical potentials are high since the potential differences have a typical value of 0.1–1 V but they appear over a distance which is drastically reduced. The gradient in the ion electrochemical potential is the driving force for the ionic motion. Although it is relevant to many fields, the full properties of a simple device consisting of an MIEC placed between two electrodes, were never completely evaluated. Only limited solutions were given. Riess et al. gave an explicit analytic solution for MIECs assuming local neutrality (L.N.) for various cases [7–10]. Riess and Tannhauser [11] solved analytically the I–V relations for a van-der Pauw configuration under the approximation of small perturbation. Under the same Solid State Ionics 178 (2007) 1 – 12 www.elsevier.com/locate/ssi ⁎ Corresponding author. E-mail address: riess@tx.technion.ac.il (I. Riess). 0167-2738/$ - see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.ssi.2006.10.024