J Electroceram (2006) 17:247–253 DOI 10.1007/s10832-006-5548-5 I-V relations in semiconductors with ionic motion * I. Riess Received: 1 August 2005 / Revised: 11 October 2005 / Accepted: 17 October 2005 C  Springer Science + Business Media, LLC 2006 Abstract Semiconductors with mobile donors and accep- tors are mixed-ionic-electronic-conductors, MIECs, which exhibit peculiar electronic (electron/hole), I e , current-voltage relations. This is a result of the redistribution of the ions under the applied electrical potential. MIECs are usually ionic ma- terials which exhibit relative low electron/hole mobilities as compared to the materials used in the semiconductor indus- try. However, thin layers of MIECs exhibit a low resistance and fast response and become of increasing interest. The I e −V relations are discussed for a few typical exam- ples. It is shown that they depend on the energy band gap as when it is large, the semiconductor is either p-type or n-type. The I e −V relations depend also on the nature of the electrodes, whether blocking for ion exchange or not. Exper- imental results for Cu 2 O are presented and analyzed using one of the models discussed. Keywords I-V relations . MIEC . Semiconductor . PLEC . Cu 2 O 1 Introduction I−V relations in semiconductors with mobile donors and/or acceptors are quite different form those with frozen ionic de- fects. Under an applied voltage the ionic defects redistribute in the bulk. This may occur when the electrodes exchange freely ions with the bulk and it must occur when they block ion exchange. I e , the electronic (electron/hole) part of the I. Riess Physics Department, Technion-IIT, Haifa 32000, Israel e-mail: riess@tx.technion.ac.il ∗ ICE-2005, KIST, Seoul, Korea, (Invited) current, is affected by the redistribution of the ionic defects. The I e −V relations are, in many cases, non linear. We empha- size that the non linearity originates from the redistribution of the ions in the bulk and is not due to a space charge at the boundaries. The materials that conduct both electrons/holes and ions are known as mixed-ionic-electronic-conductors, MIECs. Most MIECs are ionic solids which exhibit electron/hole small polaron, hopping, conduction and thus have relatively low mobility and conductivity as compared to materials used in the semiconductor industry. However, thin films of these materials, that can now be prepared routinely, exhibit a low resistance and allow for high current densities and fast re- sponse in electronic circuits. It is this and the fact that their defect distribution and I e −V relations can be tuned, that their electronic properties become of interest. In addition to the effect on bulk properties, MIECs may exhibit different contact properties. In the presence of a high concentration of ionic defects any space charge region at the boundaries is thin and may allow for electron tunneling. In this case the electrodes are ohmic with respect to electron exchange. In other cases, with lower concentrations of the mobile charge carriers, one has to examine the effect of the mo- tion of the ions on the work function and the Debye length and thus on the interface properties. The discussion has also to consider the boundary conditions whether the electrodes are inert or chemically active, as well as the nature and rel- ative concentrations of the defects whether due to doping or deviation from stoichiometry or whether due to ion pair production. Last, one has to examine the diffusion length for recombi- nation of electrons/holes and compare it with the scattering length and the Debye length. In ionic crystals electron hole propagate with relatively low mobility. There may be states Springer