Reduction in the Thermal Conductivity of Single Crystalline Silicon by Phononic Crystal Patterning

Abstract

Phononic crystals (PnCs) are the acoustic wave equivalent of photonic crystals, where a periodic array of scattering inclusions located in a homogeneous host material causes certain frequencies to be completely reflected by the structure. In conjunction with creating a phononic band gap, anomalous dispersion accompanied by a large reduction in phonon group velocities can lead to a massive reduction in silicon thermal conductivity. We measured the cross plane thermal conductivity of a series of single crystalline silicon PnCs using time domain thermoreflectance. The measured values are over an order of magnitude lower than those obtained for bulk Si (from 148 W m(-1) K(-1) to as low as 6.8 W m(-1) K(-1)). The measured thermal conductivity is much smaller than that predicted by only accounting for boundary scattering at the interfaces of the PnC lattice, indicating that coherent phononic effects are causing an additional reduction to the cross plane thermal conductivity.

Thermal transport in phononic crystals and the observation of coherent phonon scattering at room temperature

“…Dechaumphai et al 18 used an approach where phonons with MFPs longer than the minimum feature size (distance between adjacent holes) were treated coherently as waves and were modelled using a finite-difference time-domain technique, while phonons with MFPs smaller than the minimum feature size were treated as particles and their transport modelled by the Boltzmann transport equation, taking into account only incoherent boundary scattering. Their study found some agreement with recent experimental work on nano-scale PnCs 9 , highlighting the importance of zone folding, however the model failed to reproduce the cross-plane data 7 possibly because of the lack of lattice periodicity in that direction. Conversely, Jain et al 13 argued that a major deficiency in the previous models is their 2D nature, and proposed a full 3D model.…”

“…impurity;j ¼ Do 4 j ðqÞ and t À 1 boundary;j ¼ Ev j ðqÞ=L, respectively, where L is the effective sample length and is a measure of the average distance between boundaries 7,19,21,22 . The constants B, C, D and E measure the fractional influence of these different types of scattering mechanisms in a given sample, and are determined by fitting equation (1) to measured bulk Si data.…”

“…Recently, it has been proposed that coherent boundary scattering in phononic crystals (PnCs) with relatively large feature sizes (Z100 nm) may hold the key to solving this problem by scattering phonons with minimal influence on electrons [7][8][9] . As phonons traverse such a lattice, they can undergo two types of scattering processes: simple particle-like incoherent scattering as a result of encountering a boundary, and wave-like coherent Bragg 10 scattering due to the periodic geometry of the artificial lattice of air holes.…”

“…Experimentally, however, the thermal conductivity (k) of PnC samples has consistently been measured to be significantly lower than that of an unpatterned film 6,7,9,14,15 , even after taking into account the combination of material removal and simple incoherent boundary scattering 7,9,14 . This suggests that another k reduction mechanism, possibly coherent boundary scattering, must be taking place.…”

Phonon dispersion in hypersonic two-dimensional phononic crystal membranes

“…The first experimental studies on PnCs, limited by fabrication capabilities (spacing of mm), were focused on sound (kHz) and ultrasound (MHz) waves propagation and intended for applications in acoustic filtering, sensing, and wave-guiding [13][14][15][16][17][18]. Recent advances in fabrication methods have allowed reduction of the characteristic sizes of PnCs to nm scale, enabling the control of hypersonic (GHz) phonons [2,4,6,19] and heat transport [20,21]. Therefore, such structures have become attractive for optomechanics, radio frequency (RF), and thermoelectric applications [17,22,23].…”