Thermal Modeling of Atomic-Scale Three-Dimensional Phononic Crystals for Thermoelectric Applications

Extensive research on semiconducting superlattices with a very low thermal conductivity was performed to fabricate thermoelectric materials. However, as nanowires, superlattices affect heat transfer in only one main direction, and often show dislocations owing to lattice mismatches when they are made up of a periodic repetition of two materials with different lattice constants. This reduces their electrical conductivity. Therefore it is challenging to obtain a thermoelectric figure of merit ZT superior to unity with the superlattices. Self-assembly with lithographic patterning and/or liquid precursors is a major epitaxial technology to fabricate ultradense arrays of germaniums quantum dots (QDs) in silicon for many promising electronic and photonic applications as quantum computing where accurate QD positioning and low degree of dislocations are required. We theoretically demonstrate that high-density three-dimensional (3-D) arrays of self-assembled Ge nanoparticles, with a size of some nanometers, in Si can also show a very low thermal conductivity in the three spatial directions. This property can now be considered to design new thermoelectric devices, which are compatible with new complementary metal-oxide-semiconductor (CMOS) processes. To obtain a computationally manageable model of these nanomaterials, we simulate their thermal behavior with atomic-scale 3-D phononic crystals. A phononic-crystal period or supercell consists of diamond-like Si cells. At each supercell center, we substitute Si atoms by Ge atoms in a given number of cells to form a box-like nanoparticle. According to our model, in an example 3-D phononic crystal, the thermal conductivity can be reduced to a value lower than only 0.2 W/mK or by a factor of at least 750 compared to bulk Si at 300 K. This value is five times smaller than the Einstein Limit of single-crystalline bulk Si. We considered the flat dispersion curves computed by lattice dynamics to obtain this huge decrease. However, we did not consider multiple-scattering effects as multiple reflections and diffusions of the phonons between the Ge nanoparticles. We expect a larger decrease of the real thermal conductivity owing to the reduction of the phonon mean free paths from these collective effects. We hope to obtain a large ZT in these self-assembled Ge nanoparticle arrays in Si. Indeed, they are crystalline with an electrical conductivity that can be also increased by doping using CMOS processes, which is not possible with other recently proposed materials.