Non-Wiedemann-Franz Behavior of the Thermal Conductivity of Organic Semiconductors

Organic semiconductors have attracted increasing interest as thermoelectric converters in recent years due to their intrinsically low thermal conductivity compared to inorganic materials. This boom has led to encouraging practical results, in which the thermal conductivity has predominantly been treated as an empirical number. However, in an optimized thermoelectric material, the electronic component can dominate the thermal conductivity in which case the figure of merit $ZT$ becomes a function of thermopower and Lorentz factor only. Hence design of effective organic thermoelectric materials requires understanding the Lorenz number. Here, analytical modeling and kinetic Monte Carlo simulations are combined to study the effect of energetic disorder and length scales on the correlation of electrical and thermal conductivity in organic semiconductor thermoelectrics. We show that a Lorenz factor up to a factor $\sim 5$ below the Sommerfeld value can be obtained for weakly disordered systems, in contrast with what has been observed for materials with band transport. Although the electronic contribution dominates the thermal conductivity within the application-relevant parameter space, reaching ZT>1 would require to minimize both the energetic disorder but also the lattice thermal conductivity to values below $\kappa_\text{lat}<0.2$W/mK.