A Unified Model for the Space Charge Limited Currents in Organic Materials Combining Field Dependent Mobility and Poole-
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A Unified Model for the Space Charge Limited Currents in Organic Materials Combining Field Dependent Mobility and Poole-Frenkel Detrapping S. C. Jain1, W. Geens1, V. Kumar2, A. Kapoor2, A. Mehra1, T. Aernouts1, J. Poortmans1, R. Mertens1, and M. Willander3 1 IMEC, Kapeldreef 75, 3001 Leuven, Belgium, 2 Solid State Physics Laboratory, Delhi 110054, India, 3 Chalmers University of Technology, Department of Physics, S-41296 Göteborg, Sweden ABSTRACT We have calculated J-V characteristics of an organic conducting sample (containing traps) including the Poole-Frenkel Effect (PFE). Both shallow and exponentially distributed traps are considered. We show that our approach is equivalent to combining the effect of trapping and using the field dependent mobility in one unified model. For shallow single level or shallow Gaussian traps, inclusion of PFE or using the (well-known) field dependent mobility gives the same dependence of current on voltage at a given temperature. However the value of zero field mobility µ0 comes out to be different. We have fabricated and measured the J-V curves of the ITO/MEH-OPV5/Al diodes. An extremely fast rise with voltage V is observed at small voltages, which can be interpreted either by the Schottky contact limited Shockley like current or by bulk space charge limited current with PFE. The correct mechanism can be determined by making J-V measurements at different temperatures. INTRODUCTION Currently two models are being used to interpret the experimental J-V characteristics of conducting organic materials [1-5]. In Model (1) it is assumed that the organic sample contains exponentially distributed traps, which control the current. The field F obtained in the organic samples is up to a few times 106 V/cm and the reduction in the ionization energy of the traps due to Poole-Frenkel Effect (PFE) is substantial [6]. So far the PFE has not been included in the calculation of electrical characteristics of the conducting organics. In Model (2), the mobility µ is assumed to vary with electric field F according to the formula [1,4,5],
µ = µ 0 exp( β F / kT ) ,
(1)
− Et , kT
µ 0 = µ 00 exp
(2)
µ00 is a constant for a given material, β is the Frenkel constant, and Et is an activation energy. (A slightly different form of this equation has been used in Ref. [5].) Neither of these two models is able to explain all the experimental results satisfactorily [3]. Over a narrow range of electric fields the behaviour predicted by Eq. (1) can be obtained using the hopping mobility model [7] in a disordered material by assuming a Gaussian distribution of the site energies. By incorporating correlation between the energies of neighbouring sites Eq. (1) is valid for a broader field range [1,8]. Though Eq. (1) has been used C8.12.1
successfully for interpreting experimental results in a large number of other materials and over a wide range of electric fields [9,10], a general, straightforward derivation of this equation does not exist [1,5]. Nevertheless, recently attempts have been made to construct
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