Modelling of hole transport in a small-molecule organic material assuming carrier heating in a Gaussian density of states

A modelling approach for carrier transport in a Gaussin density of states is presented which takes into account that the energetic distribution of carriers moving via Miller-Abrahams rates is affected by an electric field. This reorganisation of the energetic carrier distribution can be described by virtual carrier heating to an effective temperature. We show that combining this approach with an existing percolation model reproduces the field dependence found in computer studies in literature for uncorrelated Gaussian disorder. Comparing to our experimental results, we also demonstrate that the parameterizations from these publications do not hold at low temperatures. We produced samples of 4,4′,4″-tris-(2-methylphenyl phenylamino)triphenylamine (m-MTDATA) doped into N,N'- diphenyl-N,N'-bis(1-naphthylphenyl)-1,1'-biphenyl-4,4'-diamine (NPB) in the ratio 1:1 with four different thicknesses from 50 nm to 400 nm and measured the IV curves in a temperature range from T=77 K to 346 K. We successfully demonstrate a unified simulation of the samples’ IV characteristics over the entire temperature range under the assumption of carrier heating, which is not possible with published models for correlated and uncorrelated Gaussian disorder.