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This phenomenon can be understood considering a pore not as a simple cylindrical hole, characterized by its base area and height. Actually due to the three-dimensional shape of a small pore it acts as a diffusion barrier for the dissolved ions. Therefore in a small pore the near surface concentration of dissolved iron will be higher than in a wider pore through which the dissolved ions can much easier diffuse away from the surface. But the higher the iron concentration near the surface is, the more is a further dissolution inhibited and the necessary potential to continue the dissolution is shifted to higher anodic values. That means if a metal surface is covered with an insulating coating a high shift of the open circuit potential into anodic direction indicates very small pores in the coating material. This correlation is supported by the results from similar measurements of iron samples that had been coated with different film thicknesses of the insulating polymer poly(p-xylylene) as can be seen in Fig. 4. Again there is a shift of the open circuit potential in anodic direction going along with a decrease in porosity at higher film thicknesses. current density I / A cm -2 1.0E-02 1.0E-05 1.0E-08 1.0E-11 1.0E-14 -1000 -500 0 500 1000 Fig. 4: Iron samples coated with poly(p-xylylene) potential E / mV 140 nm 240 nm 560 nm While the dissolution current density is proportional to the sum of the base areas of all pores in the coating, the potential shift of the open circuit potential is an indicator of the average size of the pores. Thus it is possible to distinguish between a few major flaws in the coating and a widespread micro-porosity which may both show the same current density. - 96 -
Self-consistent theory of unipolar charge-carrier injection in metal/insulator/metal systems F. Neumann, Y.A. Genenko, C. Melzer, H. von Seggern Charge carrier injection is an important factor in many electronic devices, especially in applications with insulators, where virtually all charge carriers have to be injected from the electrodes. Examples that have been the subject of interest are electronic devices built with organic semiconductors such as organic light-emitting diodes (OLEDs). In this work we develop a device model for a metal/insulator/metal system including the description of charge carrier injection at both metal/insulator interfaces. This model takes into account the electrostatic potential generated by the charges injected. The treatment of this issue faces the problem of self consistency, since the amount of injected charges depends on the height of the energy barriers at the contacts, while the electrostatic potential generated by this charge modifies the height of the injection barrier itself. This problem is solved by defining the boundary conditions in the electrode materials far away from the contacts, where the influence of the charge transfer can be ignored. As a result, charge carrier densities and electric field distributions in the respective media are coupled and depend on the conditions of the system. Let us consider an insulator of thickness L sandwiched in between two metal electrodes. The insulator is supposed to be extended over the space with –L/2 < x < L/2, whereas the metal electrodes are extended over the semi spaces with x < -L/2 and x > L/2, respectively. The continuity of the electrical displacement and of the electrochemical potential across the whole system entails, particularly, at the metal/ insulator interface the following boundary conditions: ± ± ⎡ ∆ eε l ⎤ TF ( ± L / 2) = N exp⎢− ± F ( ± L / 2) ⎥ ⎣ kT kT ⎦ ns s where (x) is the electron density in the insulator, n s (1) N is the effective density of ± states in the LUMO band (LUMO – lowest unoccupied molecular orbital), ∆ are the energy barriers between the Fermi-levels of the respective metal electrodes and the ± bottom of the LUMO-band, T is the temperature, lTF is the Thomas-Fermi length in the respective electrodes, ε is the dielectric constant of the insulator, Fs (x) is the electric field in the insulator, k and e are the Boltzmann constant and the elementary charge, respectively. Using the above boundary conditions the onedimensional drift-diffusion equation together with the Poisson equation were solved numerically. Knowledge about the distribution of the electric field allows for the determination of the voltage drop V across the whole system for a given current density j and hence for the calculation of the current-density-voltage (I-V)-characteristics. In Fig. 1 we present I-V-characteristics of a Ca/organic/Mg system. The I-V-curve calculated for vanishing injection barriers represents a limitation of the current flow through the system. The curves at V>1V with ∆ < ∆ ≅ 0. 27 eV coincide with that in the case − crit - 97 -
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ANNUAL REPORT 2 0 0 6 FACULTY OF MA
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Annual Report 2006 Faculty 11 Mater
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Preface The year 2006 of the Depart
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difference of numerical and analyti
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Institute of Materials Science Phys
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Research Projects Bulk Amorphous Al
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el Dsoki, C.; Landersheim, V. ; Kau
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Das, J.; Kim, K. B.; Xu, W.; Wei, B
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Staff Members Head Prof. Dr. Jürge
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Zhou L.; Rixecker G.; Aldinger F.;
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concerned with the synthesis and ch
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Publications Fleissner, A.; Schmid,
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• Surface analysis The UHV-surfac
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T. Mayer, U. Weiler, E. Mankel and
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Thin films The Thin Film division w
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Berky, W.; Gottschalk, S.; Elliman,
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Guest Scientists Research Projects
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Hesse, S.; Zimmermann, J.; von Segg
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Structure Research The research in
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Research Projects Functional Advanc
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Dincer, I.; Elerman, Y.; Elmali, A;
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hexakis(imidazole)nickel(II)bis(for
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Chemical Analytics The chemical ana
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Rift dynamics, uplift and climate c
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Geology, land use change and erosio
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nearly half a century has been perf
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The Effect of LiF Addition on the S
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In case of the undoped sintered B6O
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Microstructures in Omphacite and Ot
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Modelling phase-assemblage diagrams
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As an example, Fig. 2 shows the che
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MATERIALS SCIENCE Physical Metallur
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