Thermal transport size effects in silicon membranes featuring nanopillars as local resonators

Abstract

Silicon membranes patterned by nanometer-scale pillars standing on the surface provide a practical platform for thermal conductivity reduction by resonance hybridization. Using molecular simulations, we investigate the effect of nanopillar size, unit-cell size, and finite-structure size on the net capacity of the local resonators in reducing the thermal conductivity of the base membrane. The results indicate that the thermal conductivity reduction increases as the ratio of the volumetric size of a unit nanopillar to that of the base membrane is increased, and the intensity of this reduction varies with unit-cell size at a rate dependent on the volumetric ratio. Considering sample size, the resonance-induced thermal conductivity drop is shown to increase slightly with the number of unit cells until it would eventually level off.In semiconducting materials, heat is carried mostly by phonons which are quanta of lattice vibrations [1]. This provides an opportunity to introduce significant changes to the thermal transport properties by direct engineering of the phonon characteristics−which are shaped primarily by the phonon band structure and the nature of the underlying scattering mechanisms [2]. Recent reviews survey developments in theory, computation, and experiment pertaining to nanoscale thermal transport in a variety of materials and point to the remarkable possibilities for using nanostructuring as a means for phonon engineering [3].Thermoelectric energy conversion stands to benefit profoundly from the ability to alter the phonon properties by nanostructuring [4], as well as by reducing the material dimensionality [5]. Thermoelectric materials, which generate electricity from heat and vice versa, are characterized by a figure of merit defined as ZT = σT S 2 /k, where S is the Seebeck coefficient, σ is the electrical conductivity, k is the thermal conductivity (consisting of a lattice component and an electrical component), and T is absolute temperature [6]. One strategy to improve the value of ZT , particularly in semiconductors, is to reduce the lattice thermal conductivity and attempt to do so without negatively affecting S and σ. A promising approach for achieving this goal is to introduce nanoscale local resonators as intrinsic substructures within, or attached to, a host crystalline material [7,8]. The emerging system, called nanophononic metamaterial (NPM), exhibits unique properties that are not attainable in conventional nanostructured media such as nanocomposites [9] or nanophononic crystals [10]. The substructure resonances, which could be numerous for relatively large substructures, may be tuned to couple with all or most of the heat-carrying phonon modes of the underlying host medium. This atomic-scale coupling mechanism is essentially a resonance hybridization between the wavenumberdependent wave modes of the host medium (phonons) and the wavenumber-independent vibration modes of the local substructure (vibrons). The outcome is significant reductions in the phonon group velocities across roughly ...

Phonon and heat transport control using pillar-based phononic crystals

“…They confirmed that nanopillars could reduce the thermal conductivity by 50% and demonstrated that this reduction depends on the pillar diameter and the ratio of the pillar volume to that on the membrane within a unit cell [33]. This conclusion was confirmed by Honarvar et al [57]. …”

“…Usually, researchers tentatively attribute the thermal conductivity reduction to the impact of local resonances on the phonon dispersion [32–34,55,57,58]. Indeed, the occurrence of the local resonances was demonstrated by different simulation techniques [30,38,55,58], and since the local resonances flatten the dispersion branches (Figure 1), the average group velocity becomes lower [32,33,57]. Hence, this effect can be linked to the thermal conductivity reduction.…”

Complete Band Gaps in Nano-Piezoelectric Phononic Crystals

“…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...…”

“…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] .…”

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.…”