Dependence of general Einstein relation on density of state for organic semiconductors

• The ζ in the GER (D/μ = ζkT/q) is calculated based on Gaussian and CCIE DOSs.
• The ζ is a gradually decreasing function with temperature for both DOSs.
• The ζ is a gradually increasing function of carrier density p for the Gaussian DOS.
• The ζ – p curves have a platform in the typical range of density for the CCIE DOS.
• The ideality factor of diodes can be explained based on the GER from the CCIE DOS.

The Einstein relation (ER) about the diffusion coefficient D and mobility μ of charge carriers has been suspected for disordered organic semiconductors. The general Einstein relation (GER) is popular in recent years, and usually been calculated based on the Gaussian DOS. A clearly cutting inverse-exponential (CCIE) DOS [Org. Elect. 30 (2016) 60–66] is proposed. The mobility is obtained by solving variable range hopping (VRH) equations. The results show that the experimental mobility-density data can be well fitted by using single CCIE DOS in the wide ranges of density, but cannot be fitted by using single Gaussian or un-cutting exponential-type DOS. In this work, the coefficient ζ in the GER (D/μ = ζkT/q) is calculated based on the Gaussian and CCIE DOSs. The variations of coefficient ζ with temperature and density are analyzed. It is shown that the ζ are a gradually decreasing function with temperature and similar for both DOSs. But variations of ζ with density are very different for both DOSs. The ζ is a gradually increasing function of density for the Gaussian DOS, but a non-monotonously increasing function of density for the CCIE DOS with a platform located in the typical range of density. The ζ is assumed as a constant to analyze the data of ideality factor for two organic diodes based on rr-P3HT and OC1C10-PPV in literature, the theoretical results are in agreement with experimental data.

Figure optionsDownload as PowerPoint slide