Temperature and Size Effects on the Extremely Low Thermal Conductivity of Self-assembled Germanium Quantum-dot Supercrystals in Silicon

2010 ◽  
Vol 1267 ◽  
Author(s):  
Jean-Numa Gillet
Keyword(s):  
Thermal Conductivity ◽  
Quantum Dot ◽  
Phonon Scattering ◽  
Lattice Mismatch ◽  
Average Distance ◽  
Near Field ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Atomic Scale ◽  
Self Assembled

AbstractDesign of semiconducting nanomaterials with an indirect electronic bandgap is currently one of the major areas of research to obtain a high thermoelectric yield by lowering their lattice thermal conductivity. Intensive investigations on superlattices were performed to achieve this goal. However, like one-dimensional nanowires, they decrease heat transport in only one propagation direction of the phonons. Moreover, they often lead to dislocations since they are composed of layered materials with a lattice mismatch. Design of superlattices with a thermoelectric figure of merit ZT higher than unity is therefore hazardous. Self-assembly of epitaxial layers on silicon has been used for bottom-up synthesis of three-dimensional (3D) Ge quantum-dot (QD) arrays in Si for quantum-device and solar-energy applications. Using the atomic-scale 3D phononic crystal model, it is predicted that high-density 3D arrays of self-assembled Ge QDs in Si can as well show an extreme reduction of the thermal transport. 3D supercrystals of Ge QDs in Si present a thermal conductivity that can be as tiny as that of air. These extremely low values of the thermal conductivity are computed for a number of Ge filling ratios and size parameters of the 3D Si-Ge supercrystal. Owing to incoherent phonon scattering with predominant near-field effects, the same conclusion holds for supercrystals with moderate QD disordering. As a result, design of highly-efficient CMOS-compatible thermoelectric devices with ZT possibly much higher than unity might be possible. In this theoretical study, simultaneous evolution of both temperature and average distance between the Ge QDs is analyzed for a non-variable Ge filling ratio to obtain thermal-conductivity values as low as that of air (+/- 0.025 W/m/K).

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

2008 ◽  
Author(s):  
Jean-Numa Gillet ◽  
Yann Chalopin ◽  
Sebastian Volz
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Phononic Crystals ◽  
Atomic Scale ◽  
Oxide Semiconductor ◽  
Low Thermal Conductivity ◽  
Self Assembled ◽  
Cmos Processes

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.

Atomic-Scale Three-Dimensional Phononic Crystals With a Lower Thermal Conductivity Than the Einstein Limit of Bulk Silicon

2008 ◽  
Author(s):  
Jean-Numa Gillet ◽  
Yann Chalopin ◽  
Sebastian Volz
Keyword(s):  
Thermal Conductivity ◽  
Power Factor ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Phononic Crystals ◽  
Atomic Scale ◽  
Oxide Semiconductor ◽  
Bulk Silicon ◽  
Low Thermal Conductivity ◽  
Self Assembled

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.

Atomic Scale Three-Dimensional Phononic Crystals With Very Low Thermal Conductivities

2008 ◽  
Author(s):  
Jean-Numa Gillet ◽  
Sebastian Volz ◽  
Yann Chalopin
Keyword(s):  
Thermal Conductivity ◽  
Lattice Constant ◽  
Lattice Mismatch ◽  
Bulk Material ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Phononic Crystals ◽  
Atomic Scale ◽  
Phonon Confinement ◽  
Thermal Conductivities

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.

Thermal Design of Highly-Efficient Thermoelectric Materials With Atomic-Scale Three-Dimensional Phononic Crystals

2007 ◽  
Author(s):  
Jean-Numa Gillet ◽  
Yann Chalopin ◽  
Sebastian Volz
Keyword(s):  
Thermal Conductivity ◽  
Bulk Material ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Dispersion Curves ◽  
Phononic Crystals ◽  
Thermal Design ◽  
Atomic Scale ◽  
Thermal Insulating

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.

Atomic-Scale Three-Dimensional Phononic Crystals With a Large Thermoelectric Figure of Merit

2008 ◽  
Author(s):  
Jean-Numa Gillet ◽  
Sebastian Volz
Keyword(s):  
Thermal Conductivity ◽  
Figure Of Merit ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Phononic Crystals ◽  
Atomic Scale ◽  
Thermoelectric Figure Of Merit ◽  
Thermoelectric Figure ◽  
Low Thermal Conductivity ◽  
Cmos Compatible

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.

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

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Jean-Numa Gillet ◽  
Yann Chalopin ◽  
Sebastian Volz
Keyword(s):  
Thermal Conductivity ◽  
Multiple Scattering ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Phononic Crystals ◽  
Atomic Scale ◽  
Thermoelectric Devices ◽  
Low Thermal Conductivity ◽  
Thermal Insulating ◽  
Wave Particle Duality

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.

Size Effects on the Thermal Properties of Self-assembled Ge Quantum Dots in Single-crystal Silicon

2009 ◽  
Vol 1172 ◽  
Author(s):  
Jean-Numa Gillet
Keyword(s):  
Thermal Conductivity ◽  
Phononic Crystal ◽  
Single Crystal Silicon ◽  
Lattice Parameter ◽  
Filling Ratio ◽  
Atomic Scale ◽  
Thermoelectric Devices ◽  
Crystal Silicon ◽  
Low Thermal Conductivity ◽  
Self Assembled

AbstractSuperlattices with an ultra-low thermal conductivity were extensively studied to design thermoelectric materials. However, since they are made up of superposed materials showing lattice mismatches, they often show cracks and dislocations. Therefore, it is challenging to fabricate superlattices with a thermoelectric figure of merit ZT higher than unity. Moreover, like nanowires, they decrease heat transport in only one main direction. Self-assembly from epitaxial layers on a Si substrate is a major bottom-up technology to fabricate 3D Ge quantum-dot (QD) arrays in Si, which have been used for 3D quantum-device applications. Using the model of the atomic-scale 3D phononic crystal, we showed that 3D high-density arrays of self-assembled Ge QDs in Si can also show an ultra-low thermal conductivity in 3D, which can be several orders of magnitude lower than that of bulk Si. As a result, they can be considered to design novel 3D thermoelectric devices showing CMOS compatibility. In an example QD crystal, the thermal conductivity can be decreased below only 0.2 W/m/K. The main objective of this paper is to show the size dependence of the thermal conductivity versus the supercell lattice parameter d. For a constant QD-crystal filling ratio x = 12.5 at%, a decrease of the thermal conductivity is observed for an increasing d. This analysis enables us to predict that the optimal d-value will be of the order of 11 nm for the given filling ratio. At this optimum, the thermal conductivity decreases to the global minimum value of 0.9 W/m/K. The presented results are a first step towards the optimal design of thermoelectric devices with a maximal ZT obtained by global optimization of the size parameters.

Numerical Analysis the Strain Distribution of GaN/AlN Self-Organized Pyramid Quantum Dot

2007 ◽  
Author(s):  
Yumin Liu ◽  
Zhongyuan Yu
Keyword(s):  
Quantum Dot ◽  
Green’S Function ◽  
Green's Function ◽  
Elastic Constants ◽  
Lattice Mismatch ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Self Organized ◽  
Contour Plots ◽  
Three Dimensional Finite Element

Based on the three-dimensional finite element approach, we investigate the strain field distribution of the GaN/AlN self-organized quantum dot. The truncated hexagonal pyramid quantum dot that has been found in experiment is adopted as the physical model in our simulation. The material elastic constants parameters used in this paper are of wurtzite structure, and there are five independent elastic constants. In dealing with the lattice mismatch, we employ a three-dimensional anisotropic pseudo-thermal expansion. We compare the calculated results with that calculated by Green’s function theory, in which many assumptions are made, and prove the correctness of our results. The strain distributions of the equal strain surface three-dimensional contour plots of the six strain components are given. Finally, the anisotropic characteristics of the GaN/AlN quantum dot material are discussed, the results demonstrate that the position of the elastic strain energy density minimum position is just located above the buried quantum dot and have no influence on the thickness of the capping layer. So the anisotropy has no obvious influence on the vertical alignment of post-growth of the next layer of quantum dots. Our model does not adopt the assumptions used in the Green’s function approach, so better reliability and precision of results are expected.

scholarly journals Tunnel-Coupled Quantum Dots: Atomistic Theory of Quantum Dot Molecules and Arrays

2002 ◽  
Vol 737 ◽  
Author(s):  
Garnett W. Bryant ◽  
Javier Aizpurua ◽  
W. Jaskolski ◽  
Michal Zielinski
Keyword(s):  
Quantum Dot ◽  
Tight Binding ◽  
Atomic State ◽  
Atomic Scale ◽  
Binding Theory ◽  
Electron States ◽  
Quantum Dot Molecules ◽  
Artificial Molecule ◽  
Self Assembled ◽  
Envelope Functions

ABSTRACTAn understanding of how dots couple in quantum dot molecules and arrays is needed so that the possibilities for tailored nanooptics in these systems can be explored. The properties of tunnel-coupled dots will be determined by how the dots couple through atomic-scale junctions. We present an atomistic empirical tight-binding theory of coupled, CdS nanocrystal artificial-molecules, vertically and laterally coupled InAs/GaAs self-assembled dots, and arrays of InAs/GaAs self-assembled dots. Electron states follow the artificial molecule analogy. The coupling of hole states is much more complex. There are significant departures from the artificial molecule analogy because the interdot hole coupling is determined by the hole envelope functions, as for the electron states, and by the hole atomic state near interdot interfaces.

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