Toward quantitative modeling of silicon phononic thermocrystals

Abstract

The wealth of technological patterning technologies of deca-nanometer resolution brings opportunities to artificially modulate thermal transport properties. A promising example is given by the recent concepts of "thermocrystals" or "nanophononic crystals" that introduce regular nano-scale inclusions using a pitch scale in between the thermal phonons mean free path and the electron mean free path. In such structures, the lattice thermal conductivity is reduced down to two orders of magnitude with respect to its bulk value. Beyond the promise held by these materials to overcome the well-known “electron crystal-phonon glass” dilemma faced in thermoelectrics, the quantitative prediction of their thermal conductivity poses a challenge. This work paves the way toward understanding and designing silicon nanophononic membranes by means of molecular dynamics simulation. Several systems are studied in order to distinguish the shape contribution from bulk, ultra-thin membranes (8 to 15 nm), 2D phononic crystals, and finally 2D phononic membranes. After having discussed the equilibrium properties of these structures from 300 K to 400 K, the Green-Kubo methodology is used to quantify the thermal conductivity. The results account for several experimental trends and models. It is confirmed that the thin-film geometry as well as the phononic structure act towards a reduction of the thermal conductivity. The further decrease in the phononic engineered membrane clearly demonstrates that both phenomena are cumulative. Finally, limitations of the model and further perspectives are discussed.

Heat transport in phononic-like membranes: Modeling and comparison with modulated nano-wires

“…The reduc- 30 2 tion of the thermal transport was also observed in thin films [20,21,22,23] and nano-wires [24,25,26,27,28,29]. In the recent years, several studies are devoted to thermal behavior of bulk nano-porous systems [30,31,32,33], or nano-porous membranes [34,35,36,37,38].…”

“…Recently, a new method has been proposed to reduce thermal transport in 35 periodic nano-structures. By analogy to the photonic crystals, which are also known as photonic band gap materials as there are forbidden photon propagation frequencies [39,40], an artificially and periodically structured material could remove phonons of certain frequencies [41,36,42,43,44].…”

Complete Band Gaps in Nano-Piezoelectric Phononic Crystals

“…Furthermore, researches have used PCs on the scale µm 10,17,64,65 and mm, resulting in band gaps ranging from GHz and kHz to MHz, respectively. More recently, with the advance of nanomaterials fabrication, nanophononic crystals have been studied and it is possible to control wave propagation in a frequency range from hypersonic [3][4][5][6][66][67][68][69][70][71][72][73][74][75] to thermal [33][34][35][36][37][38][39] . However, nano-piezoelectric PCs have not been investigated yet even though studies about nano-piezoelectric materials have been reported [76][77][78][79] .…”

“…The physical origin of phononic and photonic band gaps can be understood at micro-scale using the classical wave theory to describe the Bragg and Mie resonances, respectively, based on the scattering of mechanical and electromagnetic waves propagating within the crystal 17 . PCs have many applications, such as vibration isolation technology [18][19][20][21][22] , acoustic barriers/filters [23][24][25] , noise suppression devices [26][27] , surface acoustic devices 28 , architectural design 29 , sound shields 30 , acoustic diodes 31 , elastic metamaterials [21][22]25,27,32 and thermal metamaterials [33][34][35][36][37][38][39] . There are also smart PCs that have been studied, such as piezoelectric [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] , piezomagnetic [55][56][57][58] an...…”

Band Structure in Carbon Nanostructure Phononic Crystals

“…The physical origin of phononic and photonic band gaps can be understood at micro-scale using the classical wave theory to describe Bragg and Mie resonances, respectively, based on the scattering of mechanical and electromagnetic waves propagating within the crystal 17 . PCs have many applications, such as vibration isolation technology [18][19][20][21][22] , acoustic barriers/ filters [23][24][25] , noise suppression devices 26,27 , surface acoustic devices 28 , architectural design 29 , sound shields 30 , acoustic diodes 31 , elastic/acoustic metamaterials 21,22,25,27,32 (EM/AM), also known as locally resonant phononic crystals (LRPC), and thermal metamaterials [33][34][35][36][37][38][39] (TM), also known as phononic thermocrystals or locally resonant phononic thermocrystals.…”