Atomic-Scale Three-Dimensional Phononic Crystals With a Very Low Thermal Conductivity to Design Crystalline Thermoelectric Devices

Abstract

Superlattices with thermal-insulating behaviors have been studied to design thermoelectric materials but affect heat transfer in only one main direction and often show many cracks and dislocations near their layer interfaces. Quantum-dot (QD) self-assembly is an emerging epitaxial technology to design ultradense arrays of germanium QDs in silicon for many promising electronic and photonic applications such as quantum computing, where accurate QD positioning is required. We theoretically demonstrate that high-density three-dimensional (3D) arrays of molecular-size self-assembled Ge QDs in Si can also show very low thermal conductivity in the three spatial directions. This physical property can be considered in designing new silicon-based crystalline thermoelectric devices, which are compatible with the complementary metal-oxide-semiconductor (CMOS) technologies. To obtain a computationally manageable model of these nanomaterials, we investigate their thermal-insulating behavior with atomic-scale 3D phononic crystals: A phononic-crystal period or supercell consists of diamond-cubic (DC) Si cells. At each supercell center, we substitute Si atoms by Ge atoms in a given number of DC unit cells to form a boxlike nanoparticle (i.e., QD). The nanomaterial thermal conductivity can be reduced by several orders of magnitude compared with bulk Si. A part of this reduction is due to the significant decrease in the phonon group velocities derived from the flat dispersion curves, which are computed with classical lattice dynamics. Moreover, according to the wave-particle duality at small scales, another reduction is obtained from multiple scattering of the particlelike phonons in nanoparticle clusters, which breaks their mean free paths (MFPs) in the 3D nanoparticle array. However, we use an incoherent analytical model of this particlelike scattering. This model leads to overestimations of the MFPs and thermal conductivity, which is nevertheless lower than the minimal Einstein limit of bulk Si and is reduced by a factor of at least 165 compared with bulk Si in an example nanomaterial. We expect an even larger decrease in the thermal conductivity than that predicted in this paper owing to multiple scattering, which can lead to a ZT much larger than unity.

Thermal conductivity prediction of nanoscale phononic crystal slabs using a hybrid lattice dynamics-continuum mechanics technique

“…15,19,21 In Ref. 21 the dispersion was incorporated following an approximate expression for the modification of the wavenumber due to scattering, while in Ref.…”

“…12 The design of PnCs for optimal thermal performance (from the viewpoint of thermoelectrics) can be performed qualitatively based on the maximization of the incoherent and coherent phonon scattering mechanisms, while keeping in consideration that the former needs to be done in a manner that does not interfere with the electrical conductivity. Dispersion and thermal conductivity calculations of bulk material properties or simple lattices with periodicities on the order of a few nanometers have been performed, [13][14][15][16][17][18][19][20][21] as well as for non-periodic systems; [22][23][24][25][26] however, accurate quantitative calculation of the thermal conductivity of PnC devices with lattice constants on the order of hundreds of nanometers or more remains challenging. In fact, for such PnCs at room temperature, thermal conductivity has only been roughly estimated.…”

Thermal characterization of nanoscale phononic crystals using supercell lattice dynamics

“…16 The realization that phononic crystals can now be sized at the nanoscale to influence atomic-scale phonons is opening up a new direction in nanoscale heat transfer and material design. [17][18][19][20][21][22][23][24][25][26][27][28] For example, among the configurations considered is the insertion of periodic holes in silicon slabs. [24][25][26]28 Should the conditions of coherent transport exist in such configurations, phonon waves can in principal linearly interfere while simultaneously experience nonlinear scattering events (see Ref.…”

“…In their supercell lattice dynamics calculations they modeled bulk unit cells with a special treatment for the outer atoms to extract the configuration of the reduced dimension structure of interest. Gillet et al 23 also considered dispersion calculations of supercells, specifically in the context of silicon-germanium quantum-dot materials. However no conditions, or convergence analysis, were provided for proper utilization of the supercell model.…”

Effect of Grain Boundaries on the Vibrational Properties of Phononic Crystals

“…It has been shown theoretically [4] and experimentally [5,6] that phononic crystals with periodicity length on the nanometer scale can have reduced thermal conductivities. This makes them candidates for thermoelectric materials with high figures of merit ZT and has raised interest in the properties of thermal phonons in phononic crystals.…”