Machine Learning Deciphers Heat Conduction via Phonon Tunneling

Researchers at the Institute of Solid State Physics at Graz University of Technology (TU Graz), in collaboration with colleagues from TU Vienna and the University of Cambridge, have discovered how organic semiconductors transport thermal energy. Their findings present new opportunities for designing materials with customized thermal properties.

Complex materials such as organic semiconductors and microporous metal-organic frameworks (MOFs) are used in applications like OLED displays, solar cells, gas storage, and water extraction. However, certain properties, including the detailed understanding of how they transport thermal energy, remain unclear.

Egbert Zojer led this study.

Little Attention Given to Heat Transport Up to Now

Scientists have been conducting research on charge transport in organic semiconductors for around 40 years, but no one has ever really looked at the detailed mechanisms relevant to heat transport. However, the fundamental properties of materials are very interesting for us and the insights we have gained into heat transport in organic semiconductors are also directly relevant for many other complex materials.

Egbert Zojer, Institute of Solid State Physics, Graz University of Technology

Egbert Zojer adds, “This applies both to materials in which low thermal conductivity is intended to achieve a large thermoelectric effect and to materials that are intended to efficiently supply or dissipate thermal energy through a high thermal conductivity. The fact that we can now determine and understand heat transport so precisely is unparalleled.”

The research team achieved this breakthrough by applying machine learning in an unconventional context for artificial intelligence. Instead of identifying correlations in empirical data, they focused on uncovering causal relationships using strategies previously developed for highly efficient machine-learned potentials. Their goal was to understand how and why heat is distributed within a material.

Traditionally, heat transport in complex crystalline materials like organic semiconductors was explained through the particle-like movement of phonons—energy packets associated with lattice vibrations, typically described in a manner similar to gas particle transport. However, the new findings indicate that an additional mechanism is crucial: the tunneling transport of phonons.

Molecular Length is a Decisive Factor

Tunneling transport relies on the wave-like nature of atomic vibrations in solids and plays a significant role in complex materials with low thermal conductivity. Research indicates that this mechanism becomes increasingly important as the size of the molecules forming an organic semiconductor crystal grows.

“You can imagine that heat transport is not only determined by the collisions of the vibrational quanta, but also by a ‘tunneling effect’ that couples two separate vibrational states with each other,” says Lukas Legenstein, author of the publication.

This finding not only explains why certain organic semiconductors exhibit an unusually low temperature dependence of their thermal conductivity, but also enables a more targeted design of materials with specific thermal properties. We can now influence heat conduction by specifically designing the molecular structure.

Lukas Legenstein, Institute of Solid State Physics, Graz University of Technology

As a result, the researchers aim to apply this new understanding to versatile MOFs, where heat transport is a critical factor in nearly all potential applications, even more so than in organic semiconductors.

Journal Reference:

Legenstein, L., et al. (2025). Heat transport in crystalline organic semiconductors: coexistence of phonon propagation and tunneling. npj Computational Materials. doi.org/10.1038/s41524-025-01514-8.