Heat transport in crystalline organic semiconductors: coexistence of phonon propagation and tunneling

Understanding heat transport in organic semiconductors is of fundamental and practical relevance. Therefore, we study the lattice thermal conductivities of a series of (oligo)acenes, where an increasing number of rings per molecule leads to a systematic increase of the crystals' complexity. Temperature-dependent thermal conductivity experiments in these systems disagree with predictions based on the traditional Peierls-Boltzmann framework, which describes heat transport in terms of particle-like phonon propagation. We demonstrate that accounting for additional phonon-tunneling conduction mechanisms through the Wigner Transport Equation resolves this disagreement and quantitatively rationalizes experiments. The pronounced increase of tunneling transport with temperature explains several unusual experimental observations, such as a weak temperature dependence in naphthalene's conductivity and an essentially temperature-invariant conductivity in pentacene. While the anisotropic conductivities within the acene planes are essentially material-independent, the tunneling contributions (and hence the total conductivities) significantly increase with molecular length in the molecular backbone direction, which for pentacene results in a surprising minimum of the thermal conductivity at 300K.