Modeling space-charge-limited currents in organic semiconductors: Extracting trap density and mobility

We have developed and have applied a mobility edge model that takes drift and diffusion currents to characterize the space-charge-limited current in organic semiconductors into account. The numerical solution of the drift-diffusion equation allows the utilization of asymmetric contacts to describe the built-in potential within the device. The model has been applied to extract information of the distribution of traps from experimental current-voltage measurements of a rubrene single crystal from Krellner et al. [Phys. Rev. B 75, 245115 (2007)] showing excellent agreement across several orders of magnitude in the current. Although the two contacts are made of the same metal, an energy offset of 580 meV between them, ascribed to differences in the deposition techniques (lamination vs evaporation) was essential to correctly interpret the shape of the current-voltage characteristics at low voltage. A band mobility of $0.13\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for holes is estimated, which is consistent with transport along the long axis of the orthorhombic unit cell. The total density of traps deeper than 0.1 eV was $2.2\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The sensitivity analysis and error estimation in the obtained parameters show that it is not possible to accurately resolve the shape of the trap distribution for energies deeper than 0.3 eV or shallower than 0.1 eV above the valence-band edge. The total number of traps deeper than 0.3 eV, however, can be estimated. Contact asymmetry and the diffusion component of the current play an important role in the description of the device at low bias and are required to obtain reliable information about the distribution of deep traps.