To Study Electrical Properties Of Single Crstal Organic Diodes Using Drift-diffusion Model

Organic semiconductors are the object of intense investigation because of thepromise of low-cost and large-area electronic applications. A major bottleneck towardsthe design and development of new materials is the lack of fundamental understandingof what limits charge transport in organic semiconductors. In films of crystallineorganic semiconductors, the effect of trap states located in the bandgap is commonlyobserved. The energetic distribution of these localized gap states created by disorder,chemical or morphological defects, or impurities affects the performance of organicdevices made with these materials. The accurate characterization of this trapdistribution and its correlation to the nature of defects is crucial to fully understand thefundamental limits of these materials. In this regard, investigations of highly purifiedorganic single crystals are fundamental, as these constitute model systems where theeffect of micro-structural features such as grain-boundaries is suppressed.Single-crystal studies might allow us to predict the upper performance bounds oforganic semiconductors as well as help design materials with ever increasing carriermobility.In this paper, we characterize the space charge limited current in organicsemiconductors by slove the drift-diffusion equation and Possion equation. The organicsemiconductors are treated as non-degenerate based on recent experiment on validity ofclassical Einstein relationship. Though the expression of density of holes is analyticallyderived by using the Boltzmann statistics, the validity of expression have beendemonstrated in later caclulation. The mobility model of Pasveer et al.[Phys. Rev. Lett.94,206601(2005)] and the exponential model of Pai modified by Blom et al.[Phy. Rev.B55, R656(1997)] are combined to solve drift-diffusion equations to extractinformation about the mobility and effective density of state. The results show that themobility model of Pasveer et al. can not well fit the experimental J-V data for a rubrenesingle crystal from Krellner et al.[Phys. Rev. B75,245115(2007)] both at low andhigh voltages, and some of the parameters extracted show inconsistent temperaturedependence which should be constants in the theoretical framework of Pasveer et al. Whereas the exponential model gives satisfactory fit for experimental J-V data at allvoltage ranges, and the extracted parameters show correct temperature dependence. Thetemperature dependence of parameters contained in the exponential model of mobilitycan be well fitted by using simple expressions proposed by Blom et al. And thetemperature dependence of effective density of state derived from the non-degenerateBoltzmann statistics is verified. The distribution of potential, electric field and densityof holes are calculated as analyzed by changing temperature and applied bias. Whileimpose certain applied bias and stationary temperature on the organic semiconductordevice, the J-V relationship will change with the changing of left barrier or right barrier.Specifically, the left barrier will influence the high voltage regions obviously, while theright barrier will influence the low voltage regions.