Monte Carlo phonon transport simulations in hierarchically disordered silicon nanostructures

TL;DR

This study uses Monte Carlo simulations to analyze how hierarchical nanostructuring, including nanocrystallinity and nanopores, affects thermal conductivity in silicon, revealing the impact of randomness on thermal transport and improving predictive models.

Contribution

It introduces extended compact models that accurately predict thermal conductivity in randomized nanostructured silicon, surpassing existing models.

Findings

Randomization increases effective porosity and thermal resistance.

Existing models overestimate conductivity in randomized geometries.

New models predict conductivity within 10% accuracy using simple geometrical features.

Abstract

Hierarchical material nanostructuring is considered to be a very promising direction for high performance thermoelectric materials. In this work we investigate thermal transport in hierarchically nanostructured silicon. We consider the combined presence of nanocrystallinity and nanopores, arranged under both ordered and randomized positions and sizes, by solving the Boltzmann transport equation using the Monte Carlo method. We show that nanocrystalline boundaries degrade the thermal conductivity more drastically when the average grain size becomes smaller than the average phonon mean free path. The introduction of pores degrades the thermal conductivity even further. Its effect, however, is significantly more severe when the pore sizes and positions are randomized, as randomization results in regions of higher porosity along the phonon transport direction, which introduce significant thermal resistance. We show that randomization acts as a large increase in the overall effective porosity. Using our simulations, we show that existing compact nanocrystalline and nanoporous theoretical models describe thermal conductivity accurately under uniform nanostructured conditions, but overestimate it in randomized geometries. We propose extensions to these models that accurately predict the thermal conductivity of randomized nanoporous materials based solely on a few geometrical features. Finally, we show that the new compact models introduced can be used within Matthiessens rule to combine scattering from different geometrical features within approximately 10 per cent accuracy.