Variable-range percolation in disordered organic semiconductors

Charge transport in disordered organic semiconductors is determined by charge carriers hopping through a series of molecules in an energetically disordered landscape, which can be viewed as a percolation problem in a three-dimensional network. Using combined three-dimensional kinetic Monte Carlo simulation and fat percolation theory, we systematically investigated the effect of variable-range hopping (VRH) on percolative charge transport in disordered organic semiconductors. Material dilution is a commonly used technique for bulk heterojunction optoelectronic devices, and has recently been proposed as a method for achieving a high-efficiency charge transport layer in light-emitting devices. In diluted materials, competition between energetic disorder--dominated percolation and spatial site disorder--dominated percolation needs to be clarified, which is theoretically identified and discussed in detail in this work. We find that for realistic molecular wave-function decay lengths, VRH plays a significant role in charge transport. At low temperatures or low active material fractions, VRH becomes even more important. Exponentially shaped deep trap states can further enhance VRH especially at low temperatures. With materials becoming more diluted, energetic disorder--dominated percolation gradually transforms into spatial site disorder--dominated percolation.