Monte Carlo phonon transport simulations in hierarchically disordered silicon nanostructures

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 Matthiessen's rule to combine scattering from different geometrical features within ~10% accuracy. . 3.7 Wm −1 K −1 for an average pore size of ~ 30 nm and grain sizes between 50 and 80 nm. 21 By reducing both pore and grain sizes, however, Basu et al. reported κ = 1.2 Wm −1 K −1 at 40% porosity in p-type silicon. 22 A recent work in SiGe nanomeshes, reported ultralow κ of 0.55 ± 0.10 Wm −1 K −1 for SiGe nanocrystalline nanoporous structures, a value well below the amorphous limit. 23 A significant amount of work can be found in the literature attempting to clarify these experimental observations. However, theoretical investigations of thermal conductivity in highly/hierarchically disordered nanostructures (which include not only crystalline boundaries, but also pores of random sizes placed at random positions) are very limited. Understanding the qualitative and quantitative details of such geometries on the thermal conductivity would allow the design of more efficient thermoelectrics and heat management materials in general. In this work, we solve the Boltzmann transport equation for phonons in disordered Si nanostructures using the Monte Carlo (MC) method. Monte Carlo, which can capture the details of geometry with relative accuracy, is widely employed to understand phonon transport in various nanostructures such as nanowires, 24,25,26 thin films, 27,28 nanoporous materials, 29,30,31,32,33 polycrystalline materials, 10,15,34,35,36 nanocomposites, 37,38 corrugated structures, 39,40,41,42 silicon-on-insulator devices, 43 etc. We consider geometries that include grai...

Large-scale molecular dynamics investigation of geometrical features in nanoporous Si

“…In the case of fully randomized void geometries, in terms of void position and size, we find that having more (and smaller) randomized voids lowers the thermal conductivity compared to the uniform system. The strength of this effect seems to increase with porosity, in agreement with macroscale Monte Carlo works as well [24], although the details of the size and position distributions seem to have a weaker effect at high porosities. Finally, we also show that transport along the pores, i.e.…”

“…In disordered nanoporous materials clustering happens in a statistical fashion, and increases local resistance, which reduces the overall κ. This is a well-defined effect that we have investigated using ray-tracing Monte Carlo simulations in the past for much larger pore sizes and geometries [24,28]. Here, as a first step, in Fig.…”

“…1 we observe that the simulated systems approach a 10-fold decrease in thermal conductivity at porosities as low as 2%. This is a large decrease, but it is well known that the thermal conductivity in nanoporous materials deviates significantly from macroscale porous materials, which follow the Eucken model in which κ is reduced linearly with porosity [24,29]. We note, however, that in our simulations, in most cases pores/voids are closely packed perpendicular to the transport direction, clearly forming planes/surfaces of high thermal resistance where the pores/voids are concentrated (through periodic boundary conditions in the y-direction), which will have a more drastic effect on κ along the x-direction.…”

“…Several computational studies have addressed various geometrical aspects of porosity, e.g. variations in pore surface area [21][22][23][24], pore numbers [23,25], sizes [21,23,25,26], shapes [23,27], distances [21,22,26], boundary roughness [24,25,27,28], and amorphicity [22,29].…”

“…Molecular dynamics (MD) [21,22,25,[29][30][31], often coupled with lattice dynamics [22,32], and Monte Carlo (MC) Boltzmann transport equation (BTE) solvers [12,23,24,33] are the most commonly used computational approaches to investigate thermal transport on nanoporous materials.…”