Through the increasing complexity and the development of nanoscale devices a better understanding of the heat transport is important. This purpose evokes investigations of new component concepts like thermal sensors based on 2D effects [1], as the heat transport has a significant impact on the electronic and optical properties of these devices. Furthermore, quantization effects induced by 2D effects, particularly occurring in thin layer structures, need to be taken into account and to be investigated through an appropriate modeling of the heat transport [2]. Along with these measures undertaken, it is possible to design energy efficient components [3] by realizing a reduced heat flow and a fast heat dissipation.

This heat transport mainly consists out of the ballistic and the diffusive transport [4]. While the diffusive transport describes the heat flow through interactions between phonons, like the phonon-phonon scattering, the ballistic transport neglects these effects and contains the interaction free transport through a device. Dependent on the mean free path length of the phonons one of the transport mechanisms is dominant. Especially, in devices with thin films, the ballistic transport is of great significance.

Therefore, modelling the ballistic heat transport is necessary from the perspective of circuit design. Such a model can be achieved by introducing a Hamiltonian for phonons, with which a Liouville von Neumann type equation can be set up. Applying the Wigner-Weyl transform, a Wigner formalism for phonons results. Through this formalism the heat transport through nanoscale devices can be modelled by the use of quasi probability distribution functions  in the phase space. Thereby quantum mechanical effects, occurring at interfaces between two different materials can be taken into account. The diffusive heat transport, e.g., through scattering terms like the phonon-phonon scattering, can be integrated straightforward on this basis.

Wigner based algorithms to model the heat transport are developed and will be demonstrated to enable an energy efficient design of nanoscale devices including 2D components under the perspective of circuit design.

References

1.M.S. Dresselhaus, et al., New Directions for Low-Dimensional Thermoelectric Materials, Adv. Mater. 19, 1043-1053 (2007).

2.R. Heiderhoff, A. Makris, T. Riedl, “Thermal microscopy of electronic materials,” Materials Science in Semiconductor Processing 43, 163-176 (2016).

3.W. Kim, R. Wang, and A. Majumdar, “Nanostructuring expands thermal limits,” Nano Today 2, 40-47 (2007).

4.A. Makris, T. Haeger, R. Heiderhoff, T. Riedl, “From diffusive to ballistic Stefan-Boltzmann heat transport in thin non-crystalline films,” RSC Adv. 6, 94193-94199 (2016).