Billions of microscopic transistors are packed into computer chips, enabling robust computation and generating great heat. However, heat accumulation in a computer processor can reduce its performance and reliability. 

Engineers use heat sinks, sometimes in conjunction with fans or liquid cooling systems, to keep chips cool; however, these methods frequently require a great deal of energy to operate.

The image above shows a digitized nanomaterial. It can be optimized to make heat-conducting nanomaterials.

MIT researchers have taken a unique approach. The researchers developed an algorithm and software system that can automatically design a nanoscale material to conduct heat in a particular way, such as in one direction.

The researchers made their system by adapting computational methods usually used to build large structures to make nanoscale materials with specific thermal properties.

They made a material that can move heat in a preferred direction (called "thermal anisotropy") and another that can turn heat into electricity efficiently. Then, at MIT.nano, they used the second design to make a nanostructured silicon device to recover heat from waste heat.

Scientists usually use a mix of guesswork and trial and error to figure out how to improve the way a nanomaterial conducts heat. Instead, a person could enter the thermal properties they want into software and get a design that can achieve them.

Here, the researchers introduce a method for density-based topology optimization of non-Fourier thermal transport in nanostructures. It is based on adjoint-based sensitivity analysis of the phonon Boltzmann transport equation (BTE), and a new material interpolation method called the "transmission interpolation model" (TIM).

The hardest part of BTE optimization is dealing with how real and momentum-resolved material properties interact. By setting the density of the material with an interfacial transmission coefficient, TIM can get back to the hard wall and no-interface limits while ensuring that the transition between void and solid regions is smooth. The researchers first use their method to tune a periodic nanomaterial's effective thermal conductivity tensor. Then, they maximize classical phonon size effects under constrained diffusive transport to find a promising new design for a thermoelectric material. Their method makes it possible to optimize materials systematically for heat management and conversion and to design devices that don't work with diffusion.

Conclusion

In this work, the researchers create the TIM that can smoothly interpolate material properties in the context of nondiffusive heat transport. The main idea behind TIM is that instead of tying a volume-based quantity, like the bulk thermal conductivity, to the density of the material, it sets up an interfacial transmission coefficient.

TIM gets back the adiabatic hard-wall and no-interface limits by using this method. First, the researchers use our method to customize a nanomaterial's effective thermal conductivity tensor. It could be helpful for thermal management and routing. Then, they maximize classical size effects while keeping diffusive transport above a certain threshold. It gives them a fourfold improvement over commonly studied staggered configurations. As was said in the last section, the second result could affect thermoelectric materials.

Even though we used a model with a single MFP, the developed method and the interpolation material models can be easily used with more complex versions of the BTE. For example, the use of the recently developed anisotropic MFP-BTE is one possible direction for the future. This method would let us model a real material using first-principles calculations while considering the interaction of phonon-focusing effects and, for example, the possible channels that arise during optimization. Optimizing how heat moves through 2D materials described by the full-scattering operator is another possible extension.