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Jean-Numa Gillet

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Proceedings Papers

*Proc. ASME*. IMECE2008, Volume 11: Mechanical Systems and Control, 1019-1028, October 31–November 6, 2008

Paper No: IMECE2008-68381

Abstract

The design of thermoelectric materials led to extensive research on superlattices with a low thermal conductivity. Indeed, the thermoelectric figure of merit ZT varies with the inverse of the thermal conductivity but is directly proportional to the power factor. Unfortunately, as nanowires, superlattices cancel heat conduction in only one main direction. Moreover they often show dislocations owing to lattice mismatches, which reduces their electrical conductivity and avoids a ZT larger than unity. Self-assembly is a major epitaxial technology to design ultradense arrays of germanium quantum dots (QDs) in silicon for many promising electronic and photonic applications as quantum computing. Accurate positioning of the self-assembled QD can now be achieved with few dislocations. We theoretically demonstrate that high-density three-dimensional (3-D) arrays of self-assembled Ge QDs, with a size of only some nanometers, in a Si matrix can also show an ultra-low thermal conductivity in the three spatial directions. This property can be considered to design new CMOS-compatible thermoelectric devices. To obtain a realistic and computationally-manageable model of these nanomaterials, we simulate their thermal behavior with atomic-scale 3-D phononic crystals. A phononic-crystal period (supercell) consists of diamond-like Si cells. At each supercell center, we substitute Si atoms by Ge atoms to form a box-like nanoparticle. Since this phononic crystal is periodic, we compute its phonon dispersion curves by classical lattice dynamics. Non-periodicities can be introduced with statistical distributions. From the flat dispersion curves, we obtain very small group velocities; this reduces the thermal conductivity in our phononic crystal compared to bulk Si. However, owing to the wave-particle duality at very small scales in quantum mechanics, another reduction arises from multiple scattering of the particle-like phonons in nanoparticle clusters. At room temperature, the thermal conductivity in an example phononic crystal can be reduced by a factor of at least 165 compared to bulk Si or below 0.95 W/mK. This value, which is lower than the classical Einstein limit of single crystalline Si, is an upper limit of the thermal conductivity since we use an incoherent-scattering approach for the nanoparticles. Because of its very low thermal conductivity, we hope to obtain a much larger ZT than unity in our atomic-scale 3-D phononic crystal. Indeed, this silicon-based nanomaterial is crystalline with a power factor that can be optimized by doping using CMOS-compatible processes. Future research on the phononic-crystal electrical conductivity has to be performed in order to compute the full ZT with a good accuracy.

Proceedings Papers

*Proc. ASME*. HT2008, Heat Transfer: Volume 1, 25-34, August 10–14, 2008

Paper No: HT2008-56403

Abstract

Extensive research about superlattices with a very low thermal conductivity was performed to design thermoelectric materials. Indeed, the thermoelectric figure of merit ZT varies with the inverse of the thermal conductivity but is directly proportional to the power factor. Unfortunately, as nanowires, superlattices reduce heat transfer in only one main direction. Moreover, they often show dislocations owing to lattice mismatches. Therefore, fabrication of nanomaterials with a ZT larger than the alloy limit usually fails with the superlattices. Self-assembly is a major epitaxial technology to fabricate ultradense arrays of germaniums quantum dots (QD) in a silicon matrix for many promising electronic and photonic applications as quantum computing. We theoretically demonstrate that high-density three-dimensional (3-D) periodic arrays of small self-assembled Ge nanoparticles (i.e. the QDs), with a size of some nanometers, in Si can show a very low thermal conductivity in the three spatial directions. This property can be considered to design thermoelectric devices, which are compatible with the complementary metal-oxide-semiconductor (CMOS) technologies. 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 (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 Ge nanoparticle. The phononic-crystal dispersion curves, which are computed by classical lattice dynamics, are flat compared to those of bulk Si. In an example phononic crystal, the thermal conductivity can be reduced below the value of only 0.95 W/mK or by a factor of at least 165 compared to bulk silicon at 300 K. Close to the melting point of silicon, we obtain a larger decrease of the thermal conductivity below the value of 0.5 W/mK, which is twice smaller than the classical Einstein Limit of single crystalline Si. In this paper, we use an incoherent-scattering approach for the nanoparticles. Therefore, we expect an even larger decrease of the phononic-crystal thermal conductivity when multiple-scattering effects, as multiple reflections and diffusions of the phonons between the Ge nanoparticles, will be considered in a more realistic model. As a consequence of our simulations, a large ZT could be achieved in 3-D ultradense self-assembled Ge nanoparticle arrays in Si. Indeed, these nanomaterials with a very small thermal conductivity are crystalline semiconductors with a power factor that can be optimized by doping using CMOS-compatible technologies, which is not possible with other recently-proposed nanomaterials.

Proceedings Papers

*Proc. ASME*. MNHT2008, ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer, Parts A and B, 15-23, June 6–9, 2008

Paper No: MNHT2008-52111

Abstract

Superlattices have been used to design thermoelectric materials with ultra-low thermal conductivities. Indeed, the thermoelectric figure of merit ZT varies as the inverse of the material thermal conductivity. However, the design of a thermoelectric material with ZT superior to the alloy limit usually fails with the superlattices because of two major drawbacks: First, a lattice mismatch can occur between the different layers of a superlattice as in a Si/Ge superlattice. This leads to the formation of defects and dislocations, which reduces the electrical conductivity and therefore avoids the increase of ZT compared to the alloy limit. On the other hand, the superlattices only affect heat transfer in one direction. To cancel heat conduction in the three spatial directions, we propose atomic-scale three-dimensional (3D) phononic crystals. Because the lattice constant of our phononic crystal is of the order of some nanometers, we obtain phonon confinement in the THz range and a nanomaterial with a very low thermal conductivity. This is not possible with the usual phononic crystals, which show band gaps in the sub-MHz range owing to their large lattice constant of the order of 1 mm. A period of our atomic-scale 3D phononic crystal is composed of a given number of diamond-like silicon cells forming a supercell. A periodic Si/Ge heterostructure is obtained since we substitute at each supercell center the Si atoms in a smaller number of cells by Ge atoms. The Ge atoms in the cells located at each supercell center form a box-like nanoparticle with a size that can be varied to obtain different atomic configurations of our nanomaterial. We also propose another design for our phononic crystal where we introduce a small number of diamond-like silicon cells at the center of a periodic supercell of diamond-like germanium cells. In this second design, we form box-like nanoparticles of Si atoms in a germanium matrix instead of boxlike nanoparticles of Ge atoms in a silicon matrix in the first design. With the dispersion curves computed by lattice dynamics and a general equation, we obtain the thermal conductivities of several atomic configurations of our phononic crystal. Compared to a bulk material, the thermal conductivity can be reduced by at least one order of magnitude in our phononic crystal. This reduction is only due to the phonon group velocities, and we expect a further decrease owing to the diminution of the phonon mean free path in our phononic crystal.

Proceedings Papers

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

*Proc. ASME*. ENIC2008, ASME 2008 3rd Energy Nanotechnology International Conference, 61-70, August 10–14, 2008

Paper No: ENIC2008-53052

Abstract

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.

Proceedings Papers

*Proc. ASME*. IMECE2007, Volume 10: Mechanics of Solids and Structures, Parts A and B, 1161-1168, November 11–15, 2007

Paper No: IMECE2007-43538

Abstract

Owing to their thermal insulating properties, superlattices have been extensively studied. A breakthrough in the performance of thermoelectric devices was achieved by using superlattice materials. The problem of those nanostructured materials is that they mainly affect heat transfer in only one direction. In this paper, the concept of canceling heat conduction in the three spatial directions by using atomic-scale three-dimensional (3D) phononic crystals is explored. A period of our atomic-scale 3D phononic crystal is made up of a large number of diamond-like cells of silicon atoms, which form a square supercell. At the center of each supercell, we substitute a smaller number of Si diamond-like cells by other diamond-like cells, which are composed of germanium atoms. This elementary heterostructure is periodically repeated to form a Si/Ge 3D nanostructure. To obtain different atomic configurations of the phononic crystal, the number of Ge diamond-like cells at the center of each supercell can be varied by substitution of Si diamond-like cells. The dispersion curves of those atomic configurations can be computed by lattice dynamics. With a general equation, the thermal conductivity of our atomic-scale 3D phononic crystal can be derived from the dispersion curves. The thermal conductivity can be reduced by at least one order of magnitude in an atomic-scale 3D phononic crystal compared to a bulk material. This reduction is due to the decrease of the phonon group velocities without taking into account that of the phonon average mean free path.

Journal Articles

Journal: Journal of Heat Transfer

Article Type: Micro/Nanoscale Heat Transfer—Part Ii

*. April 2009, 131(4): 043206.*

*J. Heat Transfer*Published Online: February 20, 2009

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 Z T much larger than unity.