Classifications

• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N—ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N10/00—Thermoelectric devices comprising a junction of dissimilar materials, i.e. devices exhibiting Seebeck or Peltier effects
  • H10N10/80—Constructional details
  • H10N10/85—Thermoelectric active materials
  • H10N10/857—Thermoelectric active materials comprising compositions changing continuously or discontinuously inside the material
• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N—ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N10/00—Thermoelectric devices comprising a junction of dissimilar materials, i.e. devices exhibiting Seebeck or Peltier effects
  • H10N10/10—Thermoelectric devices comprising a junction of dissimilar materials, i.e. devices exhibiting Seebeck or Peltier effects operating with only the Peltier or Seebeck effects
  • H10N10/17—Thermoelectric devices comprising a junction of dissimilar materials, i.e. devices exhibiting Seebeck or Peltier effects operating with only the Peltier or Seebeck effects characterised by the structure or configuration of the cell or thermocouple forming the device
• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N—ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N10/00—Thermoelectric devices comprising a junction of dissimilar materials, i.e. devices exhibiting Seebeck or Peltier effects
  • H10N10/80—Constructional details
  • H10N10/85—Thermoelectric active materials
  • H10N10/851—Thermoelectric active materials comprising inorganic compositions
  • H10N10/855—Thermoelectric active materials comprising inorganic compositions comprising compounds containing boron, carbon, oxygen or nitrogen
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B82—NANOTECHNOLOGY
  • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
  • B82Y20/00—Nanooptics, e.g. quantum optics or photonic crystals

Definitions

• the present application discloses a number of methods, materials and devices that relate to reducing group velocities of phonons traveling within an at least partially crystalline base material.
• One purpose for group velocity reductions may be to reduce thermal conductivity; another may be to improve the thermoelectric energy conversion figure of merit.
• thermoelectric effect refers to the ability to generate an electric current from a temperature difference between one side of a material and another. Conversely, applying an electric voltage to a thermoelectric material can cause one side of the material to heat while the other side stays cool, or, alternatively, one side to cool down while the other stays hot.
• Devices that incorporate thermoelectric materials have been used in both ways: to create electricity from a heat source or to provide cooling or heating by consuming electricity. To date, thermoelectric devices have been limited to niche or small-scale applications, such as providing power for the Mars Curiosity Rover or the cooling of precision instruments. [0004] The widespread use of thermoelectric materials has been hindered by the problem that materials that are good electrical conductors also tend to be good conductors of heat.
• thermoelectric materials such as introducing holes, inclusions, particles, interfaces and/or grains of other materials into a thermoelectric material.
• thermoelectric material in order to scatter the phonons (carriers of heat), but these tend to reduce the transport of electric current as well (because they scatter the electrons), which negated the
• metamaterial generally involves the inclusion of local resonators (i.e., mechanical oscillators) which enable unique subwavelength properties to emerge. While periodicity is advantageous in some implementations, it is not necessary in a metamateriai.
• periodic locally resonant metamaterials have been considered in various forms, such as by having heavy inclusions coated with a compliant material (e.g., rubber-coated lead spheres) and hosted in a relatively lighter and less stiff matrix (e g., epoxy) Z. Y. Liu, X. X. Zhang, Y.W. Mao, Y. Y. Zhu, Z. Y. Yang, C. T. Chan, and P. Sheng, Science 289, 1734 (2000), or by the presence of pillars on a plate Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O.
• the periodic material can be realized in a variety of ways such as by the layering of multiple constituents, also known as a layered superlattice M. N. Luckyanova, J. Garg, K. Esfarjani, A. Jandl, M. T. Bulsara, A. J Schmidt, A. J. Minnich, S. Chen, M. S. Dresselhaus, Z. F. Ren, E. A. Fitzgerald, and G. Chen, Science 338, 936 (2012), or the introduction of inclusions and/or holes, as in a nanophononic crystal (NPC) J. Tang, H.-T.
• NPC nanophononic crystal
• Manipulation of heat carrying phonons or elastic waves that propagate and scatter can yield beneficial thermal properties.
• One application relates to thermoelectric materials, or the concept of converting energy in the form of heat into electricity and vice versa.
• manipulation of heat carrying phonons or elastic waves that propagate and scatter may be performed at scales such as, but not limited to, nanoscale, microscale, milliscale and centiscale.
• nanoscale refers to a scale on the order of 1 nm to hundreds of nanometers, but less than one micrometer.
• microscale refers to a scale on the order of 1 pm to hundreds of micrometers, but less than one millimeter.
• milliscale refers to a scale on the order of 1 mm to several millimeters, but less than one centimeter.
• centiscale refers to a scale on the order of 1 cm to tens of centimeters, but less than one meter.
• the present application discloses a number of methods, materials and devices that relate to reducing group velocities of phonons traveling within an at least partially crystalline base material.
• One purpose for group velocity reductions, for example, may be to reduce thermal conductivity; another may be to improve the thermoelectric energy conversion figure of merit.
• group velocities of phonons traveling within an at least partially crystalline base material may be reduced by interacting one or more vibration modes generated by at least one locally resonant oscillator and/or atomically disordered material with one or more of the phonons, including, but not limited to, vibration modes associated with the motion of atoms within the locally resonant oscillator and/or atomically disordered material.
• example implementations of phononic metamaterials may be include one or more inclusions disposed within an at least partially crystalline base material.
• the inclusion(s) may be at least partially surrounded by a relatively compliant/soft material (such as graphite, rubber, or polymer) within the at least partially crystalline base material.
• a relatively compliant/soft material such as graphite, rubber, or polymer
• the inclusion and surrounding may operate as a resonator mass.
• the relatively compliant/soft material e.g., graphite
• at least partially surrounding the inclusion may operate as a resonator spring.
• Graphite provides a relatively effective“spring” soft/compliant material that surrounds or at least partially surrounds an inclusion because (1) it is crystalline and can allow vibrations to transmit to the surrounding base material effectively and, (2) it has a relatively high melting temperature and allows for high temperature (e.g., above 400 degrees C) thermoelectric conversion.
• graphite provides a particularly effective soft/compliant material, it is merely an example and other compliant/soft materials may be used.
• a bulk phononic metamaterial may be provided that is relatively easy to fabricate than a one-dimension (e.g., rod shaped) or two-dimension (e.g., plate or sheet shaped) phononic metamaterial base material with many individual layers/pillars/walls disposed adjacent to and extending away from the base material.
• a one-dimension e.g., rod shaped
• two-dimension e.g., plate or sheet shaped
• the inclusions in these variations may include atomically ordered and/or atomically disordered material disposed within an at least partially crystalline base material (e.g., in bulk form) and/or layers/pillars/walls of atomically ordered and/or disordered materials disposed near, adjacent, or juxtaposed to an at least partially crystalline base material.
• the inclusions within the at least partially crystalline base material may be further disposed at least partially within (e.g., at least partially surrounded by) one or more layer of a compliant and/or slippable material, such as graphite, where one or more layer of atoms within the overall layer can vibrate or slip with respect to each other (e.g., with relatively low force) and thus enhance the resonace(s) of the inclusion and their transmission to the least partially crystalline base material.
• a compliant and/or slippable material such as graphite
• an at least partially crystalline base material provides a transport region for electron and phonon flow.
• At least one substructure such as a pillar, wall, ring, plate or the like, extends from a surface of the base material and causes resonance hybridizations in the base material through movement of atoms of the extending substructure(s).
• the extending substructure may comprise an at least partially atomically ordered material (e.g., an at least partially crystalline material) and/or an atomically disordered (e.g., amorphous) material.
• the base material may comprise a reduced-dimension base material, such as a thin film base material (e.g., a film or membrane base material).
• a plurality of substructures may extend from one or more surface of the reduced-dimension base material. Resonance hybridizations caused by atomic movements within the extended substructures, for example, may extend into a reduced dimension of the base material and interact with phonons flowing through a transport region of the base material.
• the interaction of the hybridizing resonances with the phonons traveling through the transport region of the base material may reduce the group velocities of the phonons, which, in some implementations, may further increase the effectiveness of reducing thermal conductivity in the base transport material.
• an at least partially crystalline base material includes one or more inclusions disposed within the at least partially crystalline base material.
• the inclusion(s) are disposed within the base material adjacent to, juxtaposed and/or near a transport region that provides for electron and phonon flow through the base material. Movement of atoms within the inclusion(s) causes resonance
• hybridizations interact with phonons flowing through the transport region of the base material.
• the interaction of the hybridizing resonances with the phonons traveling through the transport region of the base material may reduce the group velocities of the phonons, which, in some implementations, may further increase the effectiveness of reducing thermal conductivity in the base transport material.
• a bulk or discrete thermoelectric material may be produced.
• one or more resonance hybridization generated by atomic movement within an extending structure or inclusion local oscillator may be altered by including another material with a local oscillator.
• a different e.g., relatively heavier or lighter material, relatively stiffer or softer material, etc.
• the different material may alter one or more hybridizing resonance by affecting the atomic motions within the local oscillator(s).
• a relatively heavy or dense material added to the local oscillator for example, may lower a frequency of one or frequencies of more hybridizing resonances and thus alter the interaction between the hybridizing resonances and phonons passing through the base material.
• a material having reduced-dimension base material may be included in a bulk thermoelectric material.
• the reduced-dimension base material structure, with or without extending substructures may be disposed within an outer matrix.
• the outer matrix may comprise a relatively soft matrix material compared to the at least partially crystalline base material and/or the extending local oscillator substructures.
• the surrounding matrix in some implementations, may comprise an atomically disordered material that may also provide hybridizing resonances in addition to those provided from an extending substructure and/or an atomically disordered inclusion disposed within the base material.
• a phononic metamaterial comprises at least one locally resonant pillar (e.g., nanoscale, microscale or milliscale pillar) extending from a surface of the at least partially crystalline base material.
• the extension of the one or more pillars from the base material may improve the thermoelectric energy conversion figure of merit, ZT, by freeing the at least partially crystalline base material from local resonators (or at least added local resonators) acting as internal scatterers that may hinder the motion of electrons and cause a reduction in electrical conductivity of the base material.
• a method for reducing thermal conductivity through an at least partially crystalline base material comprises: generating a plurality of local vibration modes, such as modes of atomic vibration, within the at least partially crystalline base material by the oscillation of at least one locally resonant oscillator (e.g., a nanoscale, microscale or milliscale locally resonant oscillator) coupled to the base material; and interacting at least one of the local vibration modes created by the at least one locally resonant oscillator with a plurality of phonons moving within the base material slowing group velocities of at least a portion of the interacting phonons.
• at least one locally resonant oscillator e.g., a nanoscale, microscale or milliscale locally resonant oscillator
• a phononic metamaterial structure in this implementation includes: an at least partially crystalline base material configured to allow thermal conduction via a plurality of phonons moving through the base material; and at least one locally resonant oscillator coupled to the at least partially crystalline base material.
• the at least one locally resonant oscillator is configured to generate at least one vibration mode, such as a mode of atomic vibration, to interact with the plurality of phonons moving within the base material and slowing group velocities of at least a portion of the interacting phonons and reduce thermal conductivity through the base material
• Fig. 1 shows a comparison of the phonon dispersion and thermal conductivity of a pillared silicon thin film with a corresponding uniform thin film.
• the dispersion curves are colored to represent the modal contribution to the cumulative thermal conductivity, normalized with respect to the highest modal contribution in either configuration.
• the full spectrum is shown in (a) and the 0 ⁇ co ⁇ 2.5 THz portion is shown in (b).
• Phonon DOS and the thermal conductivity, in both differential and cumulative forms, are also shown.
• the gray regions represent the difference in quantity of interest between the two configurations. The introduction of the pillar in the unit cell causes striking changes to all these quantities.
• Fig. 2 depicts a variety of example configurations of 2D phononic metamaterials with 1D locally resonant oscillators extending from a base material.
• Fig. 3 depicts a variety of 1D locally resonant oscillator geometries/shapes of the type that extends from a base material.
• FIGs 5 A and 5B show images of unit cells of example implementations of a locally resonant NPM comprising a pillar extending on top of a thin film base material (e.g., a suspended membrane thin film base material).
• a thin film base material e.g., a suspended membrane thin film base material
• Each image shows an atomic-scale model of a unit cell where the thin film base material (e.g., a suspended membrane thin film base material) and the pillar are made out of single crystal silicon.
• Fig. 6 shows (a) Thermal conductivity as a function of T for various thin film base materials (e.g., suspended membrane thin film base materials). The squares are measurements (K.
• the unit cell dimensions of the FE model are equivalent to a corresponding atomic-scale LD model (dashed line) to enable a direct comparison.
• the steady but slow rate of convergence observed indicates that upon further increase in FE resolution, the relative thermal conductivity, ⁇ P llare d ⁇ un form, is expected to decrease substantially.
• Fig. 9 depicts an additional variety of example configurations of 2D phononic metamaterials with 1D locally resonant oscillators extending from a base material.
• Fig. 10 depicts a variety of example configurations of 2D phononic metamaterials with embedded resonant oscillators.
• Fig. 11 depicts a variety of example configurations of 2D phononic metamaterials with 2D locally resonant oscillators extending from a base material.
• Fig. 12 depicts a variety of example configurations of 1D phononic metamaterials with 1D locally resonant oscillators extending from a base material.
• Fig. 13 depicts a variety of example configurations of 1D phononic metamaterials with 2D locally resonant oscillators extending from a base material.
• Fig. 14 depicts a variety of example configurations of 3D phononic metamaterials with embedded resonant oscillators.
• Figures 15A-15C show an example implementation of a three-dimensional (3D) unit cell including an atomically disordered inclusion (such as an amorphous material) disposed within an at least partially crystalline base material.
• the unit cell for example, may be used within a bulk or other material such as a two- or one-dimensional material like a membrane or a wire,
• Figures 16A and 16B show another example implementation of a three-dimensional (3D) unit cell including an atomically disordered layer disposed adjacent to, juxtaposed and/or
• Figure 17 shows an example of yet another example implementation of one or more unit cell(s) of a material including a plurality of crystalline thermoelectric material layers
• Figure 18 shows another implementation of one or more unit cell(s) of a material including a plurality of at least partially crystalline base material layers each further including a plurality of atomically disordered inclusions.
• Figure 19 shows an example implementation of a composite material comprising a thin film at least partially crystalline base material (e.g., membrane thin film base material) including a plurality of atomically disordered inclusions disposed within the base material and a plurality of pillar extending substructures extending from the base material.
• a thin film at least partially crystalline base material e.g., membrane thin film base material
• Figures 20A and 20B show another example implementation of a composite material comprising a one-dimensional at least partially crystalline base material (e.g., a wire or rod base material) including plurality of atomically disordered inclusions disposed within the base material and a plurality of pillar extending substructures extending from the base material.
• a base material e.g., a wire or rod base material
• Figure 21 shows an example implementation of a thermoelectric device using a bulk phononic metamaterial.
• Figures 22A and 22B show an example implementation of a composite material comprising a thin film at least partially crystalline base material (e.g., membrane thin film base material) including at least one continuous atomically disordered inclusion disposed within the base material and a plurality of pillar extending substructures extending from the base material.
• a thin film at least partially crystalline base material e.g., membrane thin film base material
• Figures 23 A and 23B show an example implementation of a composite material comprising a one-dimensional at least partially crystalline base material (e.g., a wire or rod base material) including at least one continuous atomically disordered inclusion disposed within the base material and a plurality of pillar extending substructures extending from the base material.
• a base material e.g., a wire or rod base material
• Figure 24 depicts yet another example implementation of a bulk composite material comprising an at least partially crystalline base material including at least one continuous atomically disordered inclusion disposed within the base material and a plurality of extending substructures extending from the base material.
• the base material and extending substructures are embedded in an outer matrix material to provide a bulk composite material.
• Figures 25, 26A and 26B depict another example implementation of a three
• the unit cell including an atomically disordered inclusion disposed within an at least partially crystalline base material and an internal inclusion further disposed within the atomically disordered inclusion.
• the unit cell may be used within a bulk or other composite material such as a two- or one-dimensional composite material such as a membrane or a wire, respectively.
• Figure 27 depicts yet another example implementation of a bulk composite material comprising an at least partially crystalline base material including at least one continuous atomically disordered inclusion disposed within the base material and a plurality of extending substructures extending from the base material.
• the atomically disordered inclusion and the extending substructures further each include an internal inclusion disposed within the atomically disordered inclusion and the extending substructures.
• the base material and extending substructures are embedded at least in part by an outer matrix material.
• Figures 28A and 28B show yet another implementation of an example bulk composite material comprising an at least partially crystalline base material including at least one continuous atomically disordered inclusion disposed within the base material and an internal inclusion disposed within the atomically disordered inclusion.
• the base material is further embedded at least in part by an outer matrix material.
• Figures 29A through 29B show an example implementation of a three-dimensional (3D) unit cell.
• Figure 29C shows an example implementation of a three-dimensional (3D) phononic metamaterial comprising a plurality individual unit cells.
• Figure 29D shows an example implementation of a three-dimensional (3D) unit cell.
• Figures 30A and 30B show another example implementation of a three-dimensional (3D) unit cell.
• Figure 31 shows an example of yet another example implementation of one or more unit cell(s).
• Figure 32 shows another implementation of one or more unit cell(s).
• Figures 33 A and 33B show an example implementation of a composite material adapted to slow a group velocity of one or more phonons flowing through a crystalline material.
• Figures 34A and 34B show another example implementation of a composite material adapted to slow a group velocity of one or more phonons flowing through a crystalline base material.
• Figure 35 shows an example implementation of a thermoelectric device using a bulk phononic metamaterial.
• Figures 36A, 36B, 36C, 36D, 37A and 37B depict other example implementations of composite materials adapted to slow a group velocity of one or more phonons flowing through an at least partially crystalline material.
• Figure 38 depicts yet another example implementation of a bulk composite
• Figures 39, 40 A and 40B depict another example implementation of a bulk composite material including a phononic metamaterial.
• Figure 41 depicts yet another example implementation of a bulk composite material including a phononic metamaterial.
• Figures 42A and 42B show yet another implementation of an example bulk composite material including a phononic metamaterial.
• Phononic metamaterials are provided herein.
• phononic metamaterials may be provided at the nanoscale (also described as a nanophononic metamaterial (NPM)), at the microscale (also described as a microphononic metamaterial (Micro PM), at the milliscale (also described as a milliphononic metamaterial (Mil li PM) as well as at other larger or smaller scales.
• NPM nanophononic metamaterial
• Micro PM microphononic metamaterial
• milliscale also described as a milliphononic metamaterial (Mil li PM) as well as at other larger or smaller scales.
• a phononic metamaterial can be used to significantly reduce thermal conductivity in a structured semiconducting material (e.g., a nano-structured, micro-structured, milli-structured or centi-structured semiconducting material) and, in some implementations, do so without affecting (or at least without significantly affecting) other important factors for a structured semiconducting material (e.g., a nano-structured, micro-structured, milli-structured or centi-structured semiconducting material) and, in some implementations, do so without affecting (or at least without significantly affecting) other important factors for
• thermoelectric energy conversion such as the electrical conductivity and Seebeck coefficient.
• a phononic metamaterial may contain miniature oscillators/resonators (these two terms are used interchangeably herein) that exchange energy with phonons and alter their propagation characteristics.
• a mode of an oscillator of a phononic metamaterial such as a mode of oscillation of one or more atoms of the resonating substructure, a coupling/hybridization/interaction occurs between a vibration mode of the oscillator and the phonon.
• the couplings will be numerous and will span the entire spectrum (e.g., up to THz). This leads to a significant reduction in the overall thermal conductivity of a material.
• introduction of local resonators specifically ones that exhibit numerous and spread out modes with the lowest mode corresponding to a frequency as low as possible
• the idea is a structural concept that is in principle independent of the base material used.
• the proposed concept may be implemented using a wide range of materials (e.g., a semiconducting material).
• the concept may be even applied using a composite, an alloy, or a conventional thermoelectric material that performs well (for thermoelectric energy conversion) in its raw chemical form or that has already been structured (e.g., nano structured) in a different way to improve its performance.
• the better the thermoelectric performance of the base material in its raw form the better the final thermoelectric performance upon the introduction of the local oscillators/resonators.
• a base material of single crystal silicon may be selected due to its low cost, abundance, advanced state-of-the art in analysis and fabrication, excellent industrial infrastructure already available, high resistance to high temperature and for being non-toxic.
• particular examples described herein may include a particular base material, these are merely examples and many other types of materials may also be used.
• the idea is inherently robust, i.e., performance is resistant (insensitive) to variations in the geometry of all features pertaining to the main body of the material and the local oscillators or resonators (the terms oscillator and resonator are used interchangeably herein). This attribute implies, for example, resistance to surface roughness which provides practical benefits since, at least currently, low-cost fabrication (e.g., nanofabrication) of very smooth structures (e.g., nanostructures) continue to be a technological challenge.
• the local resonances associated with the local oscillators/resonators are standing waves (localized vibrations).
• One advantage is that the effects of these standing waves on reducing the thermal conductivity are practically not negatively influenced by the surface roughness. The roughness will only cause small shifts (up or down) in the frequency values of the local resonances, and, as such, the overall effect of the roughness on reducing the thermal conductivity by the hybridization mechanism is low.
• one or more local oscillator/resonator structures comprise one or more structure extending away from a surface of a thermoelectric base material.
• These structures may comprise any crystalline, partially crystalline or atomically disordered (e.g., amorphous) material in which atoms of the structures may create one or more modes of oscillation.
• Atoms of the structures may, for example, exhibit up to three natural frequencies/hybridizing resonances by movement of those atoms within the structure.
• one or more local oscillator structures may comprise one or more atomically disordered (e.g., amorphous) material mechanically coupled to the at least partially crystalline thermoelectric base material transport medium (e.g., provides transport of phonons and electrons).
• the atomically disordered material may comprise, for example one or more inclusions, layers, pillars, walls, grids, lines, curves, dots or other random or patterned structure comprising one or more atomically disordered material.
• the atomically disordered material acts as one or more oscillators. Movement of one or more of the atoms of the atomically disordered material, for example, exhibits up to three natural
• Resonances couple with heat phonons traveling through the thermoelectric base material such that, through coupling, the group velocities of the phonons are decreased and thermal conductivity may be reduced.
• both at least one local oscillator/resonator structure (e.g., crystalline, partially crystalline and/or atomically disordered) is disposed extending from a surface of a thermoelectric base material and/or at least one atomically disordered (e.g., amorphous) inclusion is disposed within the thermoelectric base material are provided.
• the local oscillator/resonator structure(s) extending from a surface of the base material may provide one or more local resonances (e.g., via one or more modes of atomic vibration) extending through the surface of the base material and coupling with one or more phonons traveling through the base material within a range of the local resonance(s).
• the atomically disordered inclusion material may similarly provide one or more local resonances (e.g., via one or more mode of atomic vibration) emanating from the inclusion material into the base material that couple with one or more phonons traveling through the base material within a range of the corresponding local resonance(s).
• thermal conductivity of the base material may be reduced by interferences of phonons traveling through the base material by either or both of the local resonator structures.
• the number of resonances may be increased or decreased, as desired, by the size and/or number of local resonator structures employed.
• one or more distribution of resonances may be tuned or otherwise selected to correspond to or conform with the distribution of phonons traveling through the thermoelectric base material, and possibly add more weight to phonons that carry most of the heat, to further reduce the thermal conductivity of the base material.
• thermoelectric base material may also be designed to include one or more electron transport regions that are relatively free of barriers to electron flow through the base material, yet allow for local resonances created by nearby local oscillators/resonators to couple/hybridize with phonons traveling through the same transport regions. In this manner, electron flow may be relatively unimpeded while phonon group velocities are substantially decreased reducing thermal conductivity of the thermoelectric base material.
• a material comprises an approximately two-dimensional thin-film base material including an array of oscillators configured to provide local resonances, such as resonances associated with modes of vibration of one or more atoms within the oscillating structures.
• Examples of two-dimensional thin-film type base materials include thin films disposed on a substrate, thin films suspended. Further, the terms thin-film and membrane are used interchangeably.
• An array of pillars or other structures, for example, may extend from one or both free surfaces of the thin-film material (see, for example, Figs. 2A and 2B). This type of
• pillar refers to an upstanding and/or downstanding member or part that extends from a surface of a base material, such as a protrusion, extrusion, extension or the like.
• a pillar may comprise any number of shapes, forms, heights, distribution, location, orientation, material composition or the like.
• a pillar may be integrally formed of the same material as a base material, may be joined or otherwise attached (directly or indirectly) to the base material, may include the same or different material as the base material.
• a pillar for example, may comprise a crystalline material, an at least partially crystalline material or an atomically disordered material.
• a pillar in some implementations, may comprise a nanoscale pillar, a microscale pillar, a milliscale pillar or another larger or smaller scale pillar.
• a nanoscale (or other scale) base material for example, may be described as a one-dimensional (1D) base material in the shape of a wire or rod or column that extends, with the exception of other nanoscale (or other scale) dimensions, in a generally single dimension.
• a nanoscale (or other scale) base material such as a nanomaterial thin- film/membrane/sheet or plate-shaped base material may be described as a two-dimensional (2D) structure, with the exception of other nanoscale (or other scale) dimensions, that extends in two dimensions.
• a different base material such as a bulk material, may be described as a three- dimensional (3D) base material.
• local oscillators/resonators such as pillars shown in Fig. 3 may also be described with respect to one, two or three dimensional structures as described below with reference to those figures.
• a two-dimensional (2D) nanomaterial configuration may be described as a thin film or membrane (the terms thin-film and membranes are used interchangeably herein and apply to both thin films/membranes disposed on a substrate and suspended thin- films/membranes), with a thickness roughly less than 10,000 nm.
• a base material structure i.e., a base material structural configuration to which the oscillators/resonators are applied to
• the thermal conductivity gets reduced by a factor of two or more compared to a bulk state of the same material.
• This reduction in the thermal conductivity is due to (1) a reduction in group velocities due to the thin film structure (this effect weakens with rough surfaces) and (2) due to diffusive scattering of the phonons at the surfaces (this effects strengthens with rough surfaces). Either way, the overall reduction in the thermal conductivity is advantageous for the thermoelectric energy conversion.
• local oscillators/resonators in the form of pillars and atoms within the pillars are positioned periodically along one or both free surfaces of a thin-film base material. While the pillars in principle need not be arranged periodically for the hybridization effect to take root (the relaxation of the periodicity requirement is an advantage from the point of view of design/fabrication flexibility and insensitivity to geometric variations), the periodic positioning of the pillars in this particular implementation (1) provides an efficient way to compactly arrange the pillars, (2) allows for a systematic way to theoretically analyze, assess and design the metamaterial (e.g., a nano structured) phononic metamaterial, and (3) the periodicity provides an additional mechanism for reduction of group velocities, namely, by Bragg scattering (like free surfaces, this effect weakens with rough surfaces) and thus reducing the thermal conductivity.
• the periodic positioning of the pillars in this particular implementation (1) provides an efficient way to compactly arrange the pillars, (2) allows for a systematic way to theoretically analyze, assess and design the metamaterial (e.g
• a size scale of a unit cell (or a representative volume element if the configuration is not periodic) of a metamaterial (e.g., a nanophononic metamaterial) such as a thin-film thickness and lattice spacing between pillars in the pillared thin-film case may be selected to be on the order of 1 to 1,000 nm (or moderately lower or higher than that range).
• the unit cell (or representative volume element) may be too large compared to the mean free path of the phonons leading to a deterioration of the coupling/hybridization/interaction effect between the local resonances/oscillations and the base material phonons/dispersion and thus a loss of the favorable effects that are brought about by the presence of the resonating pillars (or other type of
• the unit cell or representative volume element
• the benefit effects that come about from its periodic arrangement i.e., Bragg scattering
• the characteristic length scale of the unit cell or representative volume element
• the number of atoms in the pillars or other type of oscillators/resonators
• the number of local resonances will be lower which would lead to a lower thermal conductivity reduction effect, although this may still be acceptable in some instances/applications.
• the thickness of the thin film, the lattice spacing and the height of the pillars, all relative to each other, can be selected such the largest size and/or number of pillars can be used per unit area (to increase the extent of the thermal conductivity reduction) but without the coupling between the pillars becoming excessive, which can lead to the extent of the thermal conductivity reduction being weakened (this may occur when the coupling between the pillars exceeds a certain level).
• relative dimensions are provided as discussed below and shown in Fig. 4. However, upon optimization studies, other sets of relative dimensions can be obtained.
• multiple pillar local oscillators/resonators are used on one or both free surfaces of a base thin-film material with each including a unique (distinct) height and/or cross-sectional area (see, for example, Figs. 2D and 2E).
• utilization of multiple pillars (above and/or below the thin film), each of which has a distinct geometrical dimension (in terms of the height and/or the cross-sectional area) provides multiple distinct resonance sets associated the with atoms in the pillars and the overall structural features of the pillars, and the more resonant sets the more couplings/hybridizations/interactions that take place across the spectrum and this in turn leads to the reduction in the group velocity for a larger number of phonons, and consequently a larger reduction in the overall thermal conductivity.
• Theoretical/computational prediction/analysis of performance using supercell lattice dynamics and fitting to experimental data for uniform thin films can be used to obtain the optimal dimensions for various implementations.
• the theoretical/computational technique presented herein provide a method for the prediction/analysis of performance to determine optimal dimensions of the unit cell, and also serve as means for demonstration of a proof of concept. This process involves both atomic-scale lattice dynamics calculations and finite-element based lattice dynamics calculations for relatively large models, as well as the use of experimental data for uniform thin films to provide a conservative estimate of the scattering parameters in the thermal conductivity model used.
• the thermal conductivity model used is given in Equation (1) below and is based on the Boltzmann Transport Equation under the time relaxation approximation).
• a phononic metamaterial such as a nanophononic metamaterial, may be fabricated using a number of techniques, such as at least one of the following group: deposition, physical vapor deposition, chemical vapor deposition, electrochemical deposition, molecular beam epitaxy, atomic layer deposition, removal, etching, wet etching, dry etching, chemical-mechanical planarization, patterning, lithography, ion beam lithography, architecturing (e.g., nano- architecturing) lattice structures and using lattices (e.g., nanolattices) as a scaffold on which to pattern thermoelectric materials, and the like.
• deposition physical vapor deposition, chemical vapor deposition, electrochemical deposition, molecular beam epitaxy, atomic layer deposition, removal, etching, wet etching, dry etching, chemical-mechanical planarization, patterning, lithography, ion beam lithography, architecturing (e.g., nano- architecturing) lattice structures
• ion beam lithography or etching techniques may be used for mass production, although other techniques, such as but not limited to the ones listed above, are also possible.
• a phononic (e.g., nanophononic) metamaterial is fabricated using ion beam lithography.
• techniques such as dry etching and metal assisted chemical (wet) etching may be used.
• silicon thin films/membranes are used as a foundation material for the creation of a locally resonant phononic metamaterial (e.g., an NPM), however, other semiconducting materials, composites (e.g., nanocomposites), and other types of structured (e.g , nano structured) materials are not only contemplated but are expected to be used in different implementations.
• a locally resonant phononic metamaterial e.g., an NPM
• other semiconducting materials, composites (e.g., nanocomposites), and other types of structured (e.g , nano structured) materials are not only contemplated but are expected to be used in different implementations.
• a reduced dimension material such as a thin film/membrane already causes a reduction of k of up to an order of magnitude without necessarily impacting S a o, and is also favorable from the point of view of device integration.
• the choice of silicon in these particular implementations is beneficial due to its wide use in the electronics industry and ease of fabrication and non-toxicity; however, other materials may also be used in other implementations as described herein.
• oscillators/resonators take the for of a periodic or non-periodic array of pillars (e.g., nanoscale pillars) that extend/extrude/protrude off the surface of the thin film (on either one side or both sides, in various implementations as practically permitted).
• pillars e.g., nanoscale pillars
• Such structures may be fabricated, for example, using techniques such as dry etching and metal assisted chemical (wet) etching, although other techniques are also contemplated.
• One advantage of an implementation using pillar-shaped protrusions is that the pillars exhibit numerous local resonances associated with structural vibrations of the pillar as a whole and vibrations of one or more atoms in the pillar, that couple, or more specifically, hybridize with an underlying atomic- level phonon dispersion of a thin film and do so across a full range of its spectrum. These couplings drastically lower the group velocities (at locations where the hybridizations take place) and, consequently, the thermal conductivity. This phenomenon is also known as avoided crossing, which has been studied in naturally occurring materials that have guest atoms encapsulated in caged structures such as clathrat.es.
• the hybridizations in these caged- structure systems are limited to the modes of the guest atom and typically take place only across a narrow band within the acoustic range of the spectrum.
• Another important benefit to utilizing pillars is that the feature manipulating the group velocities (i.e., the pillar or other protrusion itself) is physically outside of the primary flow path of the electrons (which resides in the main body of the thin film).
• This provides an advantage compared to thin- film-based NPCs, in which the inclusions or the holes penetrate through the thickness of the thin film and, hence, may undesirably cause an obstruction to electron transport through the film in addition to scattering the phonons.
• a concern about competition between coherent and nanofeature-induced incoherent thermal transport is no longer of critical importance because the local resonances are phase independent. This quality provides yet another practical benefit as it frees the NPM fro restrictions on geometric tolerances.
• an atomic-level unit cell model for a uniform silicon thin film with thickness t is provided.
• a full phonon band structure for a set of suspended uniform silicon thin films is obtained by running atomic-scale lattice dynamics (LD) calculations in which a three-body Tersoff potential is used for the Si-Si bonds with only the first nearest neighboring interactions considered (other types of interatomic potential may be used). All calculations in this implementation are conducted after minimizing the interatomic potential energy at constant pressure.
• LD atomic-scale lattice dynamics
• the Boltzmann transport model can be used (using a Callaway Holland approach for modeling the scattering), which is expressed as along the x-direction-aligned GC path, where L ⁇ l, C, v g , and t denote the phonon wave number, branch index, specific heat, group velocity, and scattering time, respectively.
• L ⁇ l, C, v g , and t denote the phonon wave number, branch index, specific heat, group velocity, and scattering time, respectively.
• the three latter quantities are dependent on the phonon dispersion.
• the specific heat is expressed as C(K, X)—
• Equation (1) is evaluated along the x-direction GC path.
• the parameters A, B, and I) are all obtained empirically.
• ⁇ 4 and B measured data for uniform silicon thin films on a substrate is utilized since temperature- dependent trends are similar to their suspended counterparts.
• the geometrical configuration of both supercells of this example implementation is shown in the insets of Fig.
• Fig. 1 A phonon dispersion along the GC path is presented in the same figure (Fig. 1) for both the uniform thin film and the pillared thin film.
• the umklapp scattering parameters are kept constant between the uniform and pillared cases. This provides a conservative approximation for the latter since it has been shown that avoided crossings cause a slight reduction of phonon lifetimes.
• Boundary scattering parameters are also kept constant since the pillars in this implementation are relatively small in the cross-sectional area and are external to the main cross section of the nominal thin film; and they are, therefore, not expected to cause a significant deviation from the unifor thin-film boundary scattering parameters.
• Fig. 1 shows a comparison of the phonon dispersion and thermal conductivity of a pillared silicon thin film with a corresponding uniform thin film.
• the dispersion curves in this implementation, are colored to represent the modal contribution to the cumulative thermal conductivity, normalized with respect to the highest modal contribution in either configuration.
• the full spectrum is shown in (a) and a close up view of the 0 ⁇ w ⁇ 2.5 THz frequency range portion is shown in 1(b).
• Phonon DOS and the thermal conductivity, in both differential and cumulative forms, are also shown.
• the gray regions represent the difference in quantity of interest between the two configurations. The introduction of the pillar in the unit cell causes striking changes to all these quantities.
• Figure 1 shows results of the proof of concept implementation.
• the lower (acoustic) branches contribute to a significant portion of the thermal conductivity in both the uniform and pillared thin films.
• the higher wave numbers also significantly contribute to the thermal conductivity.
• the boundary scattering term has been set to the thin- film thickness, i.e., L ::: t ------ 2.72 nm.
• the long waves i.e , those near the G point in the band diagram
• the low contribution is obtained at the low wave number end of the acoustic branches
• the presence of the pillars causes a series of flat locally resonant phonon modes to appear across the entire spectrum, i.e., at both subwavelength and superwavelength frequencies. These modes interact with the underlying acoustic and optical thin-iilm phonon modes and form a hybridization of the dispersion curves. This in turn leads to a flattening of the branches at the intersections and hence a reduction in the group velocities and the thermal conductivity.
• the thin film includes a suspended membrane as the thin film base material.
• C-H thermal conductivity prediction Callaway-Holland
• a second level of curve fitting is performed to harness scattering parameters for a wide range of thin-films as shown in Figs. 6b and 6c (see B. L. Davis,
• Figure 8 where a reduction in the thermal conductivity is observed.
• Figure 8 also displays a converging trend as that is shown in Fig. 7 except that the rate of convergence is slower. This in fact suggests that if the n eie / CC resolution is increased further, a substantial additional reduction in the thermal conductivity of the NPM compared to the uniform thin-film case is to be expected. ETpon comparing with bulk silicon, this estimated relative reduction is to be added to a reduction of roughly a factor 3 (attributed to the transitioning from bulk to a thin-film configuration) as suggested by Fig. 6a.
• pillar-shaped protrusions that function as local oscillators/resonators are discussed in various example implementations, many types and shapes of local oscillators/ resonators (e.g., protrusions (with all the vibrating atoms they comprise) extending from a surface of a contiguous solid medium, such as a thin film, or localized oscillators/resonators (with all the vibrating atoms they comprise) embedded within the main body of a contiguous solid medium) are contemplated and may be interchanged, in whole or in part, with other implementations described.
• a contiguous solid medium such as a thin film
• localized oscillators/resonators with all the vibrating atoms they comprise embedded within the main body of a contiguous solid medium
• Figures 2, 3, 5 and 9 through 14, demonstrate a variety of geometrical configurations for a nanophononic metamaterial as described herein.
• a contiguous, solid medium serving as a skeleton in various implementations, for example, the medium may be composed of a semiconducting material or any type of a crystalline or at least partially crystalline material or composite or alloy with relatively good raw thermoelectric properties) and an assembly of substructures that serve as local resonators/oscillators are provided.
• the main body or skeleton takes the form of a 3D (bulk), 2D (thin-film, sheet, membrane or plate) or 1D (wire, rod, column or beam) medium.
• the surfaces of a 3D main body may be straight or curves, and, similarly, the surfaces, or the centerline along the thin sections, of a 2D or a 1D main body may be straight or curved.
• the oscillators/resonators can take a variety of distributions, shapes and sizes as shown in the drawings and could lie within the main body or extrude out of the main body.
• the oscillators/resonators can take a variety of orientations and material compositions.
• the oscillators/resonators (with all the vibrating atoms they comprise) could be distributed in a perfectly periodic fashion, randomly, or in any other manner.
• the geometric dimensions of the oscillators/resonators could be identical, or could vary within a group whereby the entire group repeats in an identical fashion, or could vary in random fashion, or could be arranged in any other pattern or manner.
• thermoelectric energy conversion performance stability, toxicity, ease of fabrication and scalable manufacturing, ease and suitability of integration into a thermoelectric device, cost, among other factors.
• Figure 3 including Figs. 3 A through 3H, show a plurality of example implementations of pillar-shaped protrusions forming local oscillators/resonators (with all the vibrating atoms they comprise) on one or more surfaces of a contiguous solid medium (e.g., a 3D bulk medium, a 2D thin-film, sheet, membrane or plate medium or a 1D wire, rod, column or beam medium).
• Figure 2A shows different perspective views of one implementation of a thin film medium including a generally two-dimensional (2D) uniform, periodic array of equal-sized pillars disposed on a single surface (e.g., a top surface) of the thin-film medium.
• the pillars are shown in Fig. 2A to have a square cross-section, they can have any other cross-sectional shape such as rectangle, circle, oval, triangle, polygon or other regular or irregular cross-sectional shape (see, for example, cross sections depicted in Fig. 3).
• Figure 2B similarly show different perspective views of a second implementation of a generally two-dimensional (2D) thin-film medium including a periodic, uniform array of equal- sized, pillars disposed on two sides/surfaces (e.g., top and bottom surfaces) of the thin-film medium.
• the size of the pillars on a first side of the medium e.g., top pillars
• the pillars are shown in Fig. 2B to have a square cross-section, they can have any other cross-sectional shape such as rectangle, circle, oval, triangle, polygon or other regular or irregular cross-sectional shape (see, for example, cross sections depicted in Fig. 3).
• Figure 2C show different perspective views of a third implementation of a generally two-dimensional (2D) thin-film medium with a periodic array of equal-sized pillars disposed on a first surface of the thin-film medium (e.g., on a top surface) with an empty row appearing every n number of rows (e.g., every third row in the implementation shown in Fig. 2C).
• 2D generally two-dimensional
• Figure 2D show different perspective views of a fourth implementation of a generally two-dimensional thin-film medium with a periodic array based on a multi-pillared unit cell having pillars with different heights.
• each repeated unit cell has multiple pillars each of a different height but the same cross-sectional area and/or shape.
• each repeated unit cell could have multiple pillars of different heights and also different cross-sectional areas. While in this configuration, there are four pillars in each unit cell, other configurations could include a larger or smaller number of pillars per unit cell, distributed on only one side or both sides of the thin film.
• Fig. 2E shows different perspectives of a fifth implementation of a generally two- dimensional thin-film medium with a periodic array based on a multi-pillared unit cell having pillars with different cross-sectional areas.
• each repeated unit cell has multiple pillars each of a different cross-sectional area but the same height and/or shape.
• each repeated unit cell could have multiple pillars of different cross-sectional areas and also different heights and/or shapes. While in this configuration, there are four pillars in each unit cell, other configurations could include a larger or smaller number of pillars per unit cell.
• Fig. 9 includes sub-parts 9A through 9F showing different example implementations of generally two-dimensional (2D) thin-film/membrane implementations.
• Figure 9A shows different perspective views of a sixth implementation of a generally two-dimensional (2D) thin-film medium including a two-dimensional (2D) periodic array of pillars disposed on a first and second surface of the thin-film medium (e.g., on a top surface and a bottom surface of the medium) in which a thickness (e.g., diameter) of the pillars vary randomly across different locations on the surface of the medium.
• the pillars on each side have same height, and the height of each pillar at the top is different than at the bottom.
• the height of each pillar at the top could be the same as at the bottom.
• pillars are shown on two sides in Fig. 9A, another implementation may have a similar configuration of pillars but on a single side only.
• Figure 9B shows different perspective views of a seventh implementation of a generally two-dimensional (2D) thin-film medium including a two-dimensional (2D) periodic array of pillars disposed on a first and second surface of the thin-film medium (e.g., on a top surface and a bottom surface of the medium) in which a height of the pillars vary randomly across different locations on the surface of the medium.
• the pillars on each side have the same thickness (e.g., diameter), and the thickness of each pillar at the top is the same than at the bottom.
• the thickness of each pillar at the top could be different than at the bottom.
• pillars are shown on two sides in Fig. 9A, another implementation may have a similar configuration of pillars but on a single side only.
• Figure 9C shows different perspective views of an eighth implementation of a generally two-dimensional (2D) thin-film medium including pillars disposed on a single surface (e.g., on a top surface) and whose positions and heights are random while their thicknesses are all the same.
• pillars are shown on a single side in Fig. 9C, another implementation may have a similar configuration of pillars but on two surfaces of a thin-film medium.
• Figure 9D shows different perspective views of an ninth implementation of a generally two-dimensional (2D) thin-film medium including pillars disposed on a single surface (e.g., on a top surface) and whose positions and thicknesses are random while their heights are all the same
• pillars are shown on a single side in Fig. 9D, another implementation may have a similar configuration of pillars but on two surfaces of a thin-film medium.
• Figure 9E shows different perspective views of a tenth implementation of a generally two-dimensional thin film medium including a random (i.e., non-periodic) array of pillars on a single surface (e.g., on a top surface) with the thickness (e.g., diameter), shapes and heights of the pillars varying randomly across the different sites.
• pillars are shown on a single side in Fig. 9E, another implementation may have a similar configuration of pillars but on two surfaces of a thin-film medium.
• Figure 9F shows a configuration of an eleventh implementation based on a vertical stacking of the of the pillared thin-film material shown in Fig. 2A.
• the different features shown in other figures such as pillar spacing (see, for example, Fig. 2C), multi-pillar unit cell (see, for example, Figs. 2D and 2E), walled configuration (see, for example, Figs. 11 A and 11B and their corresponding descriptions) and random pillars (see, for example, Figs. 9A and 9D) may also apply to this vertical stacking configuration. While the figure shows, as an example three layers of pillared thin films stacked on top of each other, the number of layers of pillared thin films stacked could vary.
• Figure 10 includes sub-parts 10A and 10B showing different example implementations of generally two-dimensional (2D) thin-film/membrane implementations.
• Figure 10A shows different perspective views of another implementation of a generally two-dimensional thin film medium including a bridged structure having a central cylinder supported by thin arms (e.g., beams).
• the unit cell may be repeated to form a periodic or non-periodic array.
• the central cylinder (which could be of the same material as the main body of the thin film, or a heavier material) acts as a local oscillator/resonator (with all the vibrating atoms it comprises) in this configuration.
• oscillators/resonators with all the vibrating atoms they comprise
• this configuration e.g., square cylinder, sphere, others
• the supporting arms also could have other shapes, number and orientations.
• This configuration concept could also be realized in the form of a 2D thick plate-like material with each oscillator/resonator (with all the vibrating atoms it comprises) taking the shape of a cylinder, or sphere or other shape.
• FIG 10B shows different perspective views of another implementation of a generally two-dimensional thin film medium with a periodic array of circular inclusions comprising a highly complaint material (i.e., a material that is significantly less stiff than the material from which the main body of the thin film is made).
• a compliant material in this configuration may act as an oscillator/resonator (with all the vibrating atoms it comprises) (i.e., similar to each pillar in Fig. 2A).
• Other shapes and sizes for the inclusions may also be adopted.
• the sites of the compliant inclusions may be ordered in a periodic fashion (as shown) or may be randomly distributed (as in Figs. 9C and 9D).
• the size of each inclusion may be uniform or may vary in groups (as in Figs. 2D and 2E) or vary randomly.
• Figure 11 includes subparts 11 A and 11B showing example generally two-dimensional (2D) thin film implementations.
• Figure 11 A shows different perspective views of another implementation of a generally two-dimensional (2D) thin film medium including a one- dimensional (1D) periodic array of equal-sized walls disposed on a first surface of the thin-film medium (e.g., a top surface of the thin-film medium).
• each wall acts as an oscillator/resonator (with all the vibrating atoms it comprises) representing a 2D version of a pillar.
• the walls have a uniform cross section along the length, but other configurations could have a periodically or non-periodically varying cross-section along the length of the wall.
• FIG. 11 A another implementation may have a similar configuration of walls but on two surfaces of a thin-film medium.
• FIG. 11B shows different perspective views of another implementation of a generally two-dimensional (2D) thin film medium including a two-dimensional (2D) periodic array of equal- sized walls disposed on a first surface of the thin-film medium (e.g., a top surface of the thin-film medium).
• each wall acts as an oscillator/resonator (with all the vibrating atoms it comprises) representing a 2D version of a pillar.
• Each wall has a uniform cross section along the length, but other configurations could have a periodically or non-periodically varying cross-section along the length of each wall.
• the thickness of the vertical walls could be different than the thickness of the horizontal walls.
• walls are shown on a single side in Fig. 11B, another implementation may have a similar configuration of walls but on two surfaces of a thin-film medium.
• Figure 12 includes subparts 12A and 12B showing example generally one- dimensional (1D) implementations.
• Figure 12A shows different perspective views of another implementation of a generally one-dimensional (1D) wire, rod, column or beam medium including a cyclic periodic array of equal-sized pillars disposed along the circumference of the main body medium.
• each pillar acts as an oscillator/resonator (with all the vibrating atoms it comprises).
• the pillars may have other shapes. While in this configuration, eight pillars protrude at each lattice site, other configurations could include a larger or smaller number of pillars per lattice site.
• Figure 12B shows different perspective views of another implementation of a generally one-dimensional (1D) wire, rod, column or beam medium including a cyclic distribution of pillars of different heights disposed along the circumference of the main body medium.
• each pillar acts as an oscillator/resonator (with all the vibrating atoms it
• the pillars may have other shapes. While in this specification, the pillars may have other shapes. While in this specification, the pillars may have other shapes. While in this
• pillars protrude at each lattice site
• other configurations could include a larger or smaller number of pillars per lattice site.
• the radial distribution of the pillars could be random.
• the heights of the pillars and/or shapes and/or thicknesses could be random along both the radial and axial directions.
• Figure 13 includes subparts 13 A and 13B showing example generally one- dimensional (1D) implementations.
• Figure 13A shows different perspective views of another implementation of a generally one-dimensional (1D) wire, rod, column or beam medium including a one-dimensional (1D) periodic array of cylinders disposed along the axis of the main body medium.
• each cylinder acts as an oscillator/resonator (with all the vibrating atoms it comprises).
• the cylinders may have other shapes.
• FIG. 13B shows different perspective views of another implementation of a generally one-dimensional (1D) wire, rod, column or beam medium including a one-dimensional (1D) periodic array where each unit cell consists of multiple cylinders of different diameters and/or thicknesses disposed along the along the axis of the main body medium.
• each cylinder acts as an oscillator/resonator (with all the vibrating atoms it comprises).
• the cylinders may have other shapes. While in this configuration, there are three cylinders in each unit cell, other configurations could include a larger or smaller number of cylinders per unit cell.
• the size, shape and positioning of the cylinders along the axis of the main body may be random.
• Figure 3 show a variety of shapes and designs for a pillar. Any of these designs, or other shapes that would allow the pillar to function as an oscillator/resonator (with all the vibrating atoms it comprises), may be applied in conjunction with the numerous design concepts/features shown Figs. 2, 9 and 12.
• Figure 14 includes subparts 14A and 14B showing example generally three- dimensional (3D) implementations.
• Figure 14A shows different perspective views of another implementation of a 3D material configuration including a bridged structure having a central sphere supported by thin arms (e.g., beams).
• the unit cell may be repeated to form a periodic or non-periodic array.
• the central sphere (which could be of the same material as the main body of the thin film, or a heavier material) acts as a local
• oscillator/resonator (with all the vibrating atoms it comprises) in this configuration.
• Other shapes for oscillators/resonators (with all the vibrating atoms they comprise) in this configuration e.g., cubic sphere, cylinder, others
• the supporting arms also could have other shapes, number and orientations.
• the sites of the local resonators may be ordered in a periodic fashion (as shown) or may be randomly distributed.
• Figure 14B show a 3D material configuration with a periodic array of cubic inclusions comprising a highly complaint material (i.e., a material that is significantly less stiff than the material from which the main body is made).
• the compliant material in this configuration acts as an oscillator/resonator with all the vibrating atoms it comprises (i.e., similar to the pillars in Fig. 2A).
• Other shapes for the inclusions may be adopted.
• the sites of the compliant inclusions may be ordered in a periodic fashion (as shown) or may be randomly distributed.
• the size of each inclusion may be uniform or may vary in groups or vary randomly.
• Figures 15 A through 21 include example implementations of phononic metamaterials that may be scaled at any number of dimensions, such as nanoscale, microscale, milliscale or even larger or smaller scales.
• the various implementations may include atomically disordered inclusions (e.g., amorphous inclusions) disposed within an at least partially crystalline base material and/or layers/pillars/walls of atomically disordered materials (e.g., amorphous materials) disposed near, adjacent or juxtaposed to an at least partially crystalline base material.
• the inclusions and/or layers of atomically disordered (e.g., amorphous) material within or near an at least partially crystalline base material may reduce group velocities of phonons traveling in the at least partially crystalline base material by interacting one or more vibration modes generated by at least one locally resonant oscillator (including those due to atomic vibrations) formed by the inclusions and/or the extending substructures (e.g., layers, pillars, walls, plates, rings) with one or more of the phonons. Further, thermal transport through the material may be reduced while at least substantially allowing electron transport through the base material channel(s).
• atomically disordered (e.g., amorphous) material within or near an at least partially crystalline base material may reduce group velocities of phonons traveling in the at least partially crystalline base material by interacting one or more vibration modes generated by at least one locally resonant oscillator (including those due to atomic vibrations) formed by the inclusions and/or the extending
• the inclusions and/or extending substructures (e.g., layers, pillars, walls, etc.) shown in Figures 15 A through 28 can take a variety of distributions, shapes and sizes as shown in the drawings and could lie within the main body or extrude out of the main body. Furthermore, the inclusions and/or extending substructures may take a variety of orientations and material compositions. The inclusions and/or extending substructures may be distributed in a perfectly periodic fashion, randomly, or in any other manner. The geometric dimensions of the inclusions and/or extending substructures could be identical, or could vary within a group whereby the entire group repeats in an identical fashion, or could vary in random fashion, or could be arranged in any other pattern or manner.
• atomically disordered inclusions and/or extending substructures may be distributed within a metamaterial such that vibration modes generated by the atomically disordered inclusions and/or extending substructures extend generally throughout an at least partially crystalline base material of the metamaterial and, thus, are able to interact with passing phonons within that base material and reduce one or more group velocities of the phonons traveling in the at least partially crystalline thermoelectric base material. Further, thermal transport through the material may be reduced while at least substantially allowing electron transport through the base material channel(s).
• Figures 15A-15C show an example implementation of a three-dimensional (3D) unit cell 10 that may be used, for example, within a bulk or other material such as a two- or one- dimensional material like a membrane or a wire, respectively.
• the unit cell 10 may comprise a unit cell of a bulk material, such as a three-dimensional (3D) bulk material configuration including a periodic array of unit cells each including one or more inclusions 14 (e.g., the cubic inclusions 14 shown in Figure 15 A) disposed within a base material 16.
• Figure 15 A shows, for example, an implementation of a 3D unit cell 10 comprising a crystalline 17 (e.g., single crystal or partially crystalline) base material 16 structure including one or more inclusions 14 disposed within the crystalline 17 base material 16 structure.
• Figure 15A shows a single inclusion 14 the unit cell may include a plurality of inclusions disposed within the crystalline structure.
• Figure 15B shows a side view of the unit cell of Figure 15 A.
• the unit cell 10 may, for example, be repeated in three dimensions to form a three- dimensional (3D) bulk material 12 as shown in Figure 15C. Similarly, the unit cell may be repeated to create two-dimensional (2D) or one-dimensional structures, such as described herein.
• the inclusions 14, in various implementations may fully or partially comprise an atomically disordered
• amorphous material 18 i.e., a material that is fully or partially non-crystalline.
• the inclusion material in this particular configuration may also be made of a polycrystalline material or a single-crystal material.
• the inclusion material may be, for example, the same type of material as the base material or may be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite material(s).
• the inclusion material in this particular configuration may for example be made of a polymer or partially polymeric material.
• a base material of the unit cell may be constructed with single crystal silicon and one or more inclusion(s) may be made out of amorphous silicon or silicon oxide.
• the inclusion material in this configuration acts as one or more oscillators/resonators where each atom in the inclusion portion exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons. Further, thermal transport through the material may be reduced while at least substantially allowing electron transport through one or more base material channel(s) or transport regions 19. Other shapes for the inclusions may also be adapted. In analogy to the configuration shown in Fig.
• the sites of the inclusion material may be ordered in a periodic fashion (as shown) and/or may be randomly distributed.
• the size of each inclusion e.g., within one or more unit cells
• Figures 16A and 16B show another example implementation of a three-dimensional (3D) unit cell 20 that may be used, for example, within a bulk or other material, such as a two- or one-dimensional material like a membrane or a wire, respectively.
• the unit cell may comprise a unit cell 20 of a bulk base material 26, such as a three- dimensional (3D) bulk base material configuration including an attached layer 24 of a material 28 fully or partially comprising an atomically disordered (e.g., amorphous) material (i.e., a material that is fully or partially non-crystalline).
• the attached layer 24 may be of any thickness and may fully or partially cover the base material.
• the attached layer material 28 in this particular configuration may also be made of a polycrystalline material or a single-crystal material.
• the attached layer may be of the same type of material as the base material or can be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite materials.
• the attached layer in this particular configuration may, for example, be made of a polymer or partially polymeric material.
• Figure 16A shows, for example, an implementation of a 3D unit cell comprising a base material 26 comprising a crystalline material (e.g., single crystal or partially crystalline) structure 27 including one or more attached layers disposed adjacent to, juxtaposed or near the crystalline structure 27.
• Figure 16A shows a single attached layer 24 the unit cell may include a plurality of attached layers (e.g., on opposing sides of the unit cell) disposed adjacent to, juxtaposed to or nearby the base material 26 comprising a crystalline structure 27.
• Figure 16B shows a side view of the unit cell of Figure 16A
• the base material 26 may be constructed of single crystal silicon and the attached layer constructed of amorphous silicon or silicon oxide.
• the attached layer 24 in this configuration acts as one or more oscillators/resonators where each atom in the amorphous portion exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons. Further, thermal transport through the material may be reduced while at least substantially allowing electron transport through one or more base material channel(s). Other shapes, sizes, thicknesses or spatial distribution for the attached layer may be adopted.
• the attached layer may be attached to the base material on one side or more than one side.
• the sites of the attached layer material may be ordered in a periodic fashion (as shown) or may be randomly distributed or may continuously cover the surface.
• the size of each attached layer may be uniform or may vary in groups or vary randomly.
• Figure 17 shows an example of yet another example implementation of one or more unit cell(s) 30 of a material including a plurality of crystalline (e.g., single crystal or partially crystalline) thermoelectric material layers 36, such as a silicon or other at least partially crystalline material 37 configured for thermal transport through the material 36 interposed between one or more attached layers 34.
• the material may, for example, comprise a bulk 3D material, a 2D material or a 1D material.
• One or more layers 34 of atomically disordered (e.g., amorphous) material 38 are disposed adjacent to, juxtaposed or near the crystalline thermoelectric base material components 36.
• the atomically disordered (e.g., amorphous) material layers 34 may comprise an atomically disordered (e.g., amorphous) material 38 (i.e., a material that is fully or partially non crystalline).
• the interposed layers material in this particular configuration may also be made of a poly crystalline material or a single-crystal material.
• the attached layer(s) may be of the same type of material as the base material or can be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite materials.
• the interposed layers in this particular configuration may, for example, be made of a polymer or partially polymeric material.
• the unit cell in this particular implementation, for example, comprises a plurality of crystalline thermoelectric material layers configured for thermal transport through the unit cell and a plurality of attached layers disposed adjacent to, juxtaposed or near one or more of the crystalline
• thermoelectric material layers are thermoelectric material layers.
• the base crystalline material layer(s) may be constructed of single crystal silicon and the attached layer(s) constructed of amorphous silicon or silicon oxide.
• the attached layer(s) in this configuration act as one or more
• the oscillators/resonators generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons. Further, thermal transport through the material may be reduced while at least substantially allowing electron transport through one or more base material channel(s). Other shapes, sizes, thicknesses or spatial distribution for the attached layer may be adopted. Also, the attached layer may be attached to the base material on one side or more than one side.
• the sites of the attached layer material may be ordered in a periodic fashion (as shown) or may be randomly distributed within the base crystalline material or may take a continuous form within the base crystalline material.
• the size of each attached layer may be uniform or may vary in groups or vary randomly.
• a plurality of transport“channels” 39 are formed by the plurality of base material crystalline material layers 36 disposed within the unit cell between the attached layers 34 of atomically disordered (e.g., amorphous) material disposed between two or more channels 39 of the base crystalline material 37.
• atomically disordered e.g., amorphous
• the attached layers 34 of atomically disordered (e.g., amorphous) material 38 act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those stemming from atomic vibrations) within the at least partially crystalline base material channel(s) and interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons. In this manner, thermal transport through the material may be reduced while at least substantially allowing electron transport through the base material channel(s).
• atomically disordered (e.g., amorphous) material 38 act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those stemming from atomic vibrations) within the at least partially crystalline base material channel(s) and interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons
• Figure 18 shows another implementation of one or more unit cell(s) 40 of a material including a plurality of crystalline (e.g., single crystal or partially crystalline) thermoelectric base material layer(s) 46, such as a silicon or other material including one or more inclusions 42, such as shown in Figures 15A-15C, and further including one or more attached layer(s) 44 disposed adjacent to, juxtaposed to or near the base material layer(s) 46, such as shown in Figures 16A and 16B.
• the base material layer(s) 46 may comprise a crystalline (e.g., single crystal or partially crystalline) structure including one or more inclusions 42 disposed within the crystalline structure of the base material 46.
• the inclusion(s) 42 and atomically disordered (e.g., amorphous) material layer(s) 44 may comprise one or more amorphous material 48 (i.e., a material that is fully or partially non-crystalline).
• the material may, for example, comprise a bulk 3D material, a 2D material or a 1D material.
• One or more layers 44 of amorphous material 47 attached layers are disposed adjacent to, juxtaposed to or near the crystalline thermoelectric base material 46 having the inclusion(s) 42.
• the inclusion(s) and the attached layer material may also be made of a polycrystalline material or a single-crystal material.
• the inclusion(s) and attached layer(s) may be of the same type of material as the base material or the other amorphous material or can be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite materials.
• the unit cell in this particular implementation, for example, comprises a plurality of crystalline thermoelectric material layers configured for thermal transport through the unit cell.
• One or more inclusion(s) may be disposed within the thermoelectric material layers and one or more attached layer(s) may be disposed adjacent to, juxtaposed or near one or more of the crystalline thermoelectric material layers.
• the base crystalline material layer(s) may be constructed of single crystal silicon and the inclusion(s) and attached layer(s) constructed of amorphous silicon or silicon oxide.
• the inclusion(s) and attached layer(s) in this configuration act as one or more oscillators/resonators where each atom in the amorphous portion exhibits three natural frequencies/hybridizing resonances.
• Other shapes, sizes, thicknesses or spatial distribution for the attached layer may be adopted.
• the attached layer may be attached to the base material on one side or more than one side.
• the sites of the attached layer material may be ordered in a periodic fashion (as shown) or may be randomly distributed within the base crystalline material or may take a continuous form within the base crystalline material.
• the size of each attached layer may be uniform or may vary in groups or vary randomly.
• a plurality of transport“channels” are formed by the plurality of base crystalline material layers disposed within the unit cell.
• the inclusion(s) and the attached layers of amorphous material disposed between two or more channels of the base crystalline material act as one or more oscillators/resonators that generate a plurality of local vibration modes within the at least partially crystalline base material channel(s) and interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons. In this manner, thermal transport through the material may be reduced while at least substantially allowing electron transport through the base material channel(s).
• Figure 19 shows an example implementation of a composite material 50 adapted to slow a group velocity of one or more phonons flowing through a crystalline material.
• a crystalline base material 56 e.g., single crystal or partially crystalline material 57
• the one or more pillars 54 act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those due to atomic vibrations) within the transport region 59 of the at least partially crystalline base material 56 and interact with a plurality of phonons moving through the transport region 59 and slow the group velocities of at least a portion of the interacting phonons. Further, thermal transport through the base material 56 may be reduced while at least substantially allowing electron transport through one or more base material channel(s) 59.
• the composite material 50 further comprises one or more inclusions 52 disposed within the transport region. As described above with respect to
• the inclusions 52 similarly act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those due to atomic vibrations) within the transport region of the at least partially crystalline base material and interact with a plurality of phonons moving through the transport region and slow the group velocities of at least a portion of the interacting phonons.
• thermal transport through the transport region 59 of the composite material 50 may be reduced by the pillars 54 and/or inclusions 52 while at least substantially allowing electron transport through the transport region 59 of the composite material.
• Figures 20A and 20B show another example implementation of a composite material 60 adapted to slow a group velocity of one or more phonons flowing through a crystalline base material 66.
• crystalline base material e.g., single crystal or partially crystalline material
• the one or more rings or plates or pillars 64 act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those due to atomic vibrations) within the transport region of the at least partially crystalline base material 66 and interact with a plurality of phonons moving through the transport region 69 and slow the group velocities of at least a portion of the interacting phonons.
• the composite material 60 further comprises one or more inclusions 62 disposed within the transport region 69.
• the inclusions 62 similarly act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those due to atomic vibrations) within the transport region 69 of the at least partially crystalline base material 66 and interact with a plurality of phonons moving through the transport region 69 and slow the group velocities of at least a portion of the interacting phonons.
• thermal transport through the transport region 69 of the composite material may be reduced by the plates, rings, pillars 64 and/or inclusions 62 while at least substantially allowing electron transport through the transport region of the composite material.
• Figure 21 shows an example implementation of a thermoelectric device using a bulk phononic (e.g., nanophononic) metamaterial, such as for example a single crystal silicon material with one or more periodic or non-periodic inclusions of an amorphous material such as amorphous silicon or silicon oxide such as shown in Figure 15 and/or with a single crystal silicon material with one or more attached layer(s) of an amorphous material such as amorphous silicon or silicon oxide such as shown in Figure 16 and/or with a single crystal silicon material with one or more embedded layer(s) of an amorphous material such as amorphous silicon or silicon oxide such as shown in Figure 17.
• a bulk phononic metamaterial such as for example a single crystal silicon material with one or more periodic or non-periodic inclusions of an amorphous material such as amorphous silicon or silicon oxide such as shown in Figure 15 and/or with a single crystal silicon material with one or more attached layer(s) of an amorphous material such as amorphous silicon or silicon oxide
• a bulk phononic (e.g., nanophononic) metamaterial may be doped at any level desired to improve the electrical properties forming a p- type semiconducting material and/or an «-type semiconducting material.
• the transport portion of the phononic (e.g., nanophononic) metamaterial may be alloyed with other elements to reduce the thermal conductivity further while having a minimal effect on the electrical properties such as the electrical conductivity and the Seebeck coefficient.
• Figures 22A, 22B, 23 A and 23B depict other example implementations of composite materials 70, 80 adapted to slow a group velocity of one or more phonons flowing through an at least partially crystalline material.
• a composite material 70 includes a two-dimensional thin-film/membrane base material structure 76 with extended substructures 74 (e.g., pillars).
• Figures 23 A and 23B show a composite material 80 including a one-dimensional (e.g., wire) base material structure 86 with extended substructures 84 (e.g., plates or rings).
• the composite material 70, 80 comprises an at least partially crystalline thermoelectric base material.
• thermoelectric base material includes a base material region 76, 86.
• the base material region 76, 86 includes an at least partially crystalline transport region 79, 89 and at least one atomically disordered oscillator/resonator region 72, 82.
• the at least one transport region 79, 89 includes one or more transport paths (shown by arrows) through the at least partially crystalline thermoelectric base material and is configured to allow electrons flow through the thermoelectric base material at least relatively unimpeded by one or more atomically disordered materials of one or more atomically disordered oscillator/resonator regions 72, 82 (e.g., one or more atomically disordered inclusions) disposed within the base material region 76, 86 of the base material juxtaposed the transport region(s) 79, 89.
• the atomically disordered oscillator/resonator region 72, 82 is adapted to provide local resonances through the movement of one or more atoms within the atomically disordered material (e.g., an amorphous material) of the atomically disordered oscillator/resonator region 72, 82 (e.g., one or more atomically disordered inclusions).
• the local resonances travel into the transport region(s) 79, 89 of the at least partially crystalline thermoelectric base material and interact with one or more phonons traveling through the transport region 79, 89 reducing group velocities and the thermal conductivity of the composite material 70, 80.
• the atomically disordered oscillator/resonator region 72, 82 may comprise a continuous inclusion of atomically disordered (e.g., amorphous) material disposed within the at least partially crystalline thermoelectric base material or may include a plurality of individual inclusions of atomically disordered (e.g., amorphous) material.
• Figures 22 and 23 show a single continuous inclusion of atomically disordered material forming the atomically disordered oscillator/resonator region, a plurality of continuous or discontinuous inclusions may also be used to form one or more atomically disordered oscillator/resonator regions disposed within the thermoelectric base material region.
• base material region may be configured to allow electrons to pass through the transport region(s) without being substantially impeded by the inclusion(s) while still allowing the local resonances of the inclusions to interact with one or more phonons passing through the same transport region.
• the composite materials shown in Figures 22A, 22B, 23 A and 23B further include one or more extending substructures 74, 84 extending outwardly away from a surface of the
• thermoelectric base material region 76, 86 e.g., the 2D thin-film/membrane base material of Figure 22 or the 1D wire base material of Figure 23.
• the extending substructures 74, 84 may comprise any structure that extends away from the at least partially crystalline base material region, such as but not limited to pillars, walls, rings, plates, layers or the like.
• a plurality of extending substructures 74, 84 extend away from a surface of the thermoelectric base material region 76, 86 and provide local oscillators/resonators adapted to create local resonances that extend into one or more transport regions 79, 89 of the base material through the movement of one or more atoms of the extending substructures.
• the local resonances of the extending substructures similarly interact with phonons passing through the transport region(s) of the base material region and decrease the group velocities of the phonons and may reduce the thermal conductivity of the composite material.
• Figures 22A, 22B, 23A and 23B show particular types of substructures (e.g.,
• pillars/walls/plates/rings extending away from a surface of the base material region including the transport region being formed of an at least partially crystalline material, which may be the same or a different material as the at least partially crystalline thermoelectric base material, some or all of the extending substructures may likewise be formed of an atomically disordered (e.g., amorphous) material as described herein.
• Figure 24 depicts yet another example implementation of a bulk composite material 90 including a phononic metamaterial.
• the composite material 90 comprises a base material region 96 including an at least partially crystalline thermoelectric transport region 99 and at least one atomically disordered oscillator/resonator region
• the transport region 99 includes one or more transport regions of the base material region 96.
• the at least partially crystalline base material region 96 provides one or more transport regions 99 for electron and phonon flow through the thermoelectric structure via one or more transport paths
• thermoelectric base material (shown by arrows) extending through the at least partially crystalline thermoelectric base material.
• the transport region(s) 99 are configured to allow electrons to flow through the thermoelectric base material at least relatively unimpeded by one or more atomically disordered materials of one or more atomically disordered oscillator/resonator regions 92 (e.g., one or more atomically disordered inclusions) disposed within the base material region 96 of the base material juxtaposed the transport region(s).
• the composite material further comprises at least one extending substructure 94 (e.g., layers, pillars, walls, rings, plates) that extends away from a surface of the base material region 96.
• the composite material 90 includes a plurality of extending substructures 94 extending in at least two directions away from a surface of the base material region 96 including the at least partially crystalline transport region 99 and a continuous inclusion 92 of atomically disordered (e.g., amorphous) material disposed within the transport region 99 adjacent to two opposite transport regions.
• extending substructures 94 may comprise any structure that extends away from the base material region, such as but not limited to pillars, walls, rings, plates, layers or the like.
• the composite material 90 includes a bulk composite structure including the base material region 96 from which the extending substructures 94 extend.
• the at least partially crystalline transport region 99 and the extending substructures 94 may comprise the same or different at least partially crystalline material(s) (e.g., single crystal silicon or other thermoelectric material), such as shown in Figure 24.
• the extending substructures 94 may comprise the same or a different atomically disordered (e.g., amorphous) material as the atomically disordered oscillator/resonator region 92.
• the base material region 96 and the one or more extending substructures 94 are further disposed within a matrix 98 of atomically disordered (e.g., amorphous) material.
• the matrix 98 of amorphous material may comprise a soft amorphous material within which the base material region and the one or more extending substructures are disposed (e.g., encased, surrounded or the like), although other implementations are also
• the base material region 96 and extending substructures 94 may be surrounded in one, two or three-dimensions (e.g., surrounded at least in part or fully surrounded).
• the surrounding matrix 98 material in this configuration may further act as one or more oscillators/resonators where each atom in the atomically disordered (e.g., amorphous) surrounding material exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators formed by the surrounding atomically disordered material may generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons. Further, thermal transport through the base material may be reduced while at least substantially allowing electron transport through one or more base material channel(s).
• the surrounding matrix 98 material may further be used to convert a reduced dimension structure (e.g., a 2D or 1D base material) into a 3D bulk phononic metamaterial that may be used in standard thermoelectric devices, such as the one shown in Figure 21.
• a reduced dimension structure e.g., a 2D or 1D base material
• the surrounding matrix material may comprise a relatively soft, flexible or other material, such as a polymer material for example, adapted to allow those extending substructures to move at least at an atomic scale.
• any of the other structures disclosed herein e.g., Figures 2, 3, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 22, 23
• Figures 2, 3, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 22, 23 may similarly be disposed within one or more matrix of amorphous or soft material.
• the outer matrix(ces) may provide local resonances (stemming from atomic and structural motion) that further interact with phonons passing through the transport region of the base material that may decrease the group velocities of the phonon(s) and reduce the thermal conductivity of the composite material.
• Figures 25, 26A and 26B depict another example implementation of a bulk composite material 100 including a phononic metamaterial.
• the composite material 100 comprises one or more additional internal inclusions 103 (e.g., additional inclusion(s) disposed inside one or more outer inclusion(s) 102).
• the internal inclusions 103 disposed within the outer atomically disordered inclusions 102 may be adapted to alter one or more characteristic of the outer atomically disordered inclusions 102.
• the internal inclusions 103 that are disposed within the one or more atomically disordered outer inclusions 102 may be adapted to alter one or more atomic movements within the atomically disordered outer inclusions 102.
• the internal inclusion(s) 103 may be relatively heavier or denser than the surrounding atomically disordered outer inclusion 102.
• the internal inclusion(s) 103 may be atomically disordered or ordered materials.
• the outer inclusion(s) 103 may be atomically disordered or ordered materials.
• the outer inclusion may be a soft material such as rubber or other polymers.
• the internal and outer inclusions can take any shape such as cubes, spheres, or the like.
• the internal inclusion(s) 103 may alter (e.g., lower or increase) a frequency of resonances stemming from and/or facilitated by the atomically disordered outer inclusions of the composite material 100.
• the internal inclusion may be relatively heavier or denser than the atomically disordered (e.g., amorphous) inclusion 102 in which it is supported and the atomically disordered (e.g., amorphous) inclusion may comprise a material softer than the internal inclusion 103.
• a heavier material suspended within a soft material may lead to a lowering of the frequencies of local resonances.
• the composite structure(s) (internal inclusion(s) 103 within an atomically disordered outer inclusion 102) may be used to alter one or more hybridizing resonances, which in some implementations, may further increase the effectiveness of reducing thermal conductivity in the base transport material by targeting one or more phonons that carry relatively more heat.
• the combination of the internal inclusions and outer inclusions may be optimized to produce a distribution of resonances from the inclusion(s) that are effective to reduce thermal conductivity of the base transport material and the system as a whole by resonance hybridizations.
• Figures 25, 26A and 26B show the internal inclusions 103 disposed within atomically disordered outer inclusions 102
• the internal inclusions 103 may similarly be disposed within one or more at least partially crystalline oscillator/resonator material, such as a substructure extending from a base material 106 including a transport region.
• one or more material may be disposed within an at least partially crystalline layer, pillar, wall, plate, ring or other structure.
• the internal inclusions for example, may be adapted to alter an atomic movement within the at least partially crystalline extending substructure.
• the extending structures can be made entirely from one or more heavy materials.
• FIG. 27 depicts yet another example implementation of a bulk composite material 110 including a phononic metamaterial that illustrates a combination of the surrounding atomically disordered matrix shown in Figure 24 and the internal inclusions shown in Figures 25 and 26 disposed within a continuous atomically disordered outer inclusion in this implementation.
• the composite material 110 includes a base material region 116 comprising an at least partially crystalline transport region 119 defining one or more transport paths (shown by arrows) for carrying electron and phonon flow through the composite material 110.
• One or more atomically disordered inclusions 112 are disposed within the base material region at least generally outside the transport region(s) 119 so as to reduce physical interference with electron flow within the transport region(s) due to the physical interference of the inclusion(s) 112.
• One or more additional internal inclusions 113 e.g., additional inclusion(s) disposed inside one or more outer inclusion(s) are provided.
• the internal inclusions 113 are disposed within a continuous outer atomically disordered inclusion 112 and may be adapted, for example, to alter one or more characteristic of the continuous outer atomically disordered inclusion 112.
• the internal inclusions 113 disposed within the atomically disordered continuous outer inclusion 112 may be adapted to alter one or more atomic movements within the atomically disordered outer inclusions 112.
• the internal inclusion(s) 113 may be relatively heavier or denser than the surrounding atomically disordered outer inclusion 112.
• the internal inclusion(s) 113 may be atomically disordered or ordered materials.
• the outer inclusion(s) 103 may be atomically disordered or ordered materials.
• the outer inclusion may be a soft material such as rubber or other polymers.
• the internal and outer inclusions can take any shape such as cubes, spheres, or the like.
• the internal inclusion(s) 113 may alter (e.g., lower or increase) a frequency of resonances stemming from and/or facilitated by the atomically disordered outer inclusions 112 of the composite material.
• the composite structure(s) (internal inclusion(s) 113 within an atomically disordered outer inclusion 112) may be used to alter one or more hybridizing resonances, which in some implementations, may further increase the
• the internal inclusions 113 may be optimized to produce a distribution of resonances from the atomically disordered outer inclusion(s) that are effective to reduce thermal conductivity of the base transport material and the system as a whole by resonance hybridizations.
• the inclusions 115 disposed within the extending substructures 114 may be optimized to produce a distribution of resonances that are effective to reduce thermal conductivity of the base transport material and the system as a whole by resonance hybridizations.
• the extending structures can be made entirely from one or more heavy materials.
• the base material region 116 and extending substructures 114 are also disposed within a matrix 118 of atomically disordered (e.g., amorphous) material.
• the matrix 118 of atomically disordered material may comprise a soft amorphous material within which the base material region and extending substructures (e.g., pillars/walls) are disposed, although other implementations are also contemplated.
• the surrounding matrix material in this configuration may further act as one or more oscillators/resonators where each atom in the atomically disordered (e.g., amorphous) surrounding material exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators formed by the surrounding atomically disordered material may generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons. Further, thermal transport through the base material may be reduced while at least substantially allowing electron transport through one or more base material channel(s).
• the bulk composite material provides hybridizing resonances from extended substructures, atomically disordered inclusions that may be altered by one or more additional internal inclusions as well as additional hybridizing resonances from the surrounding outer matrix.
• the surrounding matrix material may comprise a crystalline or at least partially crystalline material that adapts a 2D or 1D composite material into a bulk 3D composite material such as described above with respect to Figure 24.
• Figure 28 shows yet another implementation of an example bulk composite
• the bulk composite material 120 includes a base material region 126 comprising an at least partially crystalline transport region 129 defining one or more transport paths (shown by arrows) for carrying electron and phonon flow through the composite material 120.
• One or more atomically disordered inclusions 122 are disposed within the base material region 126 at least generally outside the transport region(s) 129 so as to reduce physical interference with electron flow within the transport region(s) 129 due to the physical interference of the inclusion(s) 122.
• one or more additional internal inclusions 123 are also disposed within the one or more atomically disordered inclusions 122 such as shown in Figure 27.
• the internal inclusions 123 and/or atomically disordered inclusions 122 within which the internal inclusions 123 are disposed may be designed to alter (e.g., lower or increase) a frequency of resonances stemming from and/or facilitated by the atomically disordered inclusions of the composite material 120.
• the outer inclusion(s) 103 may be atomically disordered or ordered materials.
• the outer inclusion may be a soft material such as rubber or other polymers.
• the internal and outer inclusions can take any shape such as cubes, spheres, or the like.
• the composite structure may be used to alter one or more hybridizing resonances to reduce the group velocities of phonons traveling through the transport region of the composite material, which in some implementations, may further increase the effectiveness of reducing thermal conductivity in the base transport material by targeting one or more phonons that carry relatively more heat.
• the base material region is disposed within (e.g., between or surrounded by) a matrix 128 of an atomically disordered material that forms a matrix of atomically disordered (e.g., amorphous) material surrounding the base material region.
• the matrix 128 of atomically disordered material may comprise a soft amorphous material within which the base material region is disposed, although other implementations are also contemplated.
• the outer matrix material may further act as one or more oscillators/resonators where each atom in the atomically disordered (e.g., amorphous) surrounding material exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators formed by the surrounding atomically disordered material may generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons. Further, thermal transport through the base material may be reduced while at least substantially allowing electron transport through one or more base material channel(s).
• the surrounding matrix material is shown as an atomically disordered material in the particular implementation shown in Figure 28, for example, the surrounding matrix material may comprise a crystalline or at least partially crystalline material that adapts a 2D or 1D composite material into a bulk 3D composite material such as described above with respect to Figures 24 and 27.
• the bulk composite material may comprise a plurality of repeated cells (e.g., unit cells), such as having the structures shown in Figure 28.
• a one, two or three-dimensional composite material structure may be formed by individual unit cells repeated in one, two or three dimensions.
• Figures 29 A through 42 include further example implementations of phononic metamaterials that may be scaled at any number of dimensions, such as nanoscale, microscale, milliscale or even larger or smaller scales.
• the phononic metamaterials may include one or more inclusions disposed within an at least partially crystalline base material.
• the inclusion(s) may be at least partially surrounded by a relatively compliant/soft material (such as graphite) within the at least partially crystalline base material.
• the inclusion may be fully or partially surrounded by the layer(s) of relatively compliant or soft material.
• voids may be disposed between the inclusion and the base material in one or more openings where the layer(s) of relatively compliant or soft material are not disposed between the inclusion and the base material.
• the voids in various example implementations may include air, gas, vacuum, liquid, and/or solid and may provide room for the inclusion to move as it vibrates within the base material.
• the inclusion where not surrounded by the layer(s) of relatively compliant or soft material, may be disposed directly adjacent to the base material.
• the inclusion and surrounding layer(s) and/or void(s) may operate as a resonator mass (similar to the pillars described above with respect to
• the relatively compliant/soft material e.g., graphite
• the relatively compliant/soft material at least partially surrounding the inclusion may operate as a resonator spring.
• Graphite provides a relatively effective“spring” soft/compliant material that surrounds or at least partially surrounds an inclusion because (1) it is crystalline and can allow vibrations to transmit to the surrounding base material effectively and, (2) it has a relatively high melting temperature and allows for high temperature (e.g., above 400 degrees C) thermoelectric conversion.
• graphite provides a particularly effective soft/compliant material, it is merely an example and other compliant/soft materials may be used.
• a bulk phononic metamaterial may be provided that is relatively easy to fabricate than a one-dimension (e.g., rod shaped) or two-dimension (e.g., plate or sheet shaped) phononic metamaterial base material with many individual layers/pillars/walls disposed adjacent to and extending away from the base material.
• a one-dimension e.g., rod shaped
• two-dimension e.g., plate or sheet shaped
• the inclusions in these variations may include atomically ordered and/or atomically disordered material disposed within an at least partially crystalline base material (e.g., in bulk form) and/or layers/pillars/walls of atomically ordered and/or disordered materials disposed near, adjacent, or juxtaposed to an at least partially crystalline base material.
• the inclusions within the at least partially crystalline base material may be further disposed at least partially within (e.g., at least partially surrounded by) one or more layer of a compliant and/or slippable material, such as graphite, where one or more layer of atoms within the overall layer can vibrate or slip with respect to each other (e.g., with relatively low force) and thus enhance the resonace(s) of the inclusion and their transmission to the least partially crystalline base material.
• a compliant and/or slippable material such as graphite
• Graphite for example, comprises atoms strongly bonded together in one or more direction and weakly bonded (e.g., by van der Waal bonds) in one or more other direction.
• This combination of bonding features gives the graphite layer a relatively high melting temperature (e.g., higher than polymers) while also high compliance or softness along certain directions due to the weak, e.g., van der Waal, bonds.
• the weak bonds enable individual atomic-scale layer(s) of the overall layer to vibrate normal to the layer(s) and/or slip parallel to the layer(s) with respect to other atomic-scale layer(s) of the layer via vibration or slippage between layers of atoms which give rise to high compliance or softness.
• a graphite layer has these characteristics because it comprises a stack of electrically conducting graphene layers held together by weak van der Waals bonds. These properties allow the graphite layer to act as a spring holding the inclusion(s) which act as a one or more mass.
• Such a configuration may give rise to one or more internal resonances within the host (matrix/base) material of the composite. In principle, the number of resonances may be as many as the number of atoms in the inclusion multiplied by three (i.e., the number of degrees of freedom per atom).
• the layer(s) within which the inclusion(s) are disposed may be adapted to alter one or more characteristic of the inner inclusion(s). For example, one or more atomic movements within the inclusion(s) and/or outer layer(s) may be altered by the outer layer(s) or inclusion(s) or the interaction therebetween.
• the inclusion(s) may be relatively heavier or denser than the surrounding layer(s) and, possibly, also heavier or denser than the surrounding at least partially crystalline base material.
• the inclusion(s) may be atomically ordered or disordered materials.
• the outer layer(s) may be atomically ordered or disordered materials.
• the outer layer(s) may be a soft and/or compliant material such as rubber or other polymers.
• the inclusion(s) and outer layer(s) can take any shape, such as but not limited to cubes, spheres, or the like.
• the inclusion(s) and outer layer(s) may alter (e.g., lower or increase) a frequency of resonances stemming from and/or facilitated by the effective spring-mass effect due to the combination of inclusion(s) and outer layer(s).
• the inclusion(s) may be relatively heavier or denser than the outer layer(s) in which it is supported and the outer layer(s) may comprise a material softer or more compliant than the inclusion(s).
• a heavier material suspended within a soft or compliant material e.g., partially or fully surrounded by a soft or compliant material
• the composite structure(s) may be used to alter one or more hybridizing resonances, which in some implementations, may further increase the effectiveness of reducing thermal conductivity in the surrounding (matrix/base) transport material by targeting one or more phonons that carry relatively more heat.
• the combination of the inclusion(s) and the outer layer(s) may be optimized to produce a distribution of resonances from the inclusion(s) that are effective to reduce thermal conductivity of the surrounding (matrix) transport material and the system as a whole by resonance hybridizations.
• the inclusions disposed at least partially within one or more layer of compliant and/or slippable material within the at least partially crystalline base material and/or extending substructures may reduce group velocities of phonons traveling in the at least partially crystalline base material (transport region) by interacting one or more vibration modes generated by at least one locally resonant oscillator (including those due to atomic vibrations) formed by the inclusions and/or the extending substructures (e.g., layers, pillars, walls, plates, rings) with one or more of the phonons.
• thermal transport through the material may be reduced while at least
• reduction in thermal conductivity due to resonances may involve one or more of the following: (1) group velocity reduction of passing phonons, (2) mode localization within the resonating region that leads to localizing heat rather than transporting it, and (3) reduction of phonon lifetimes near resonance coupling regions in the phonon band structure.
• Figures 29A through 42B can take a variety of distributions, shapes and sizes as shown in the drawings and could lie within the main body or extend away from and/or extrude out of the main body including the at least partially crystalline base material.
• the inclusions and/or extending substructures may have a variety of orientations and material compositions.
• the inclusions and/or extending substructures may be distributed in a perfectly periodic fashion, randomly, or in any other manner.
• the geometric dimensions of the inclusions and/or extending substructures could be identical, or could vary within a group whereby the entire group repeats in an identical fashion, or could vary in random fashion, or could be arranged in any other pattern or manner, random or periodic.
• inclusions and/or extending substructures may be distributed within a metamaterial such that vibration modes generated by the inclusions and/or extending substructures extend generally throughout an at least partially crystalline base material of the metamaterial and, thus, are able to reduce thermal conductivity through the at least partially crystalline base material.
• the reduction in thermal conductivity is believed to be caused by one or more of the following: (1) group velocity reduction of passing phonons, (2) mode localization within the resonating region that leads to localizing heat rather than transporting it, and (3) reduction of phonon lifetimes near resonance coupling regions in the phonon band structure.
• thermal transport through the material may be reduced while at least substantially allowing electron transport through the base material channel(s).
• Figures 29 A through 29B show an example implementation of a three-dimensional (3D) unit cell 210 that may be used, for example, within a bulk or other material such as a two- or one- dimensional material like a membrane or a wire, respectively.
• the unit cell 210 may comprise a unit cell of a bulk material.
• a three-dimensional (3D) bulk material configuration may include a periodic array of unit cells 210 each including one or more inclusions 214 (e.g., the cubic inclusions 214 shown in Figure 29A) disposed within a base material 216.
• Figure 29A shows, for example, an implementation of a 3D unit cell 210 comprising a crystalline 217 (e.g., single crystal or partially crystalline) base material 216 structure including one or more inclusions 214 disposed within the crystalline 217 base material 216 structure.
• the inclusion 214 is further at least partially disposed within (e.g., partially or fully surrounded by) one or more layer 215 of a compliant and/or slippable material, such as graphite, rubber or polymer.
• the compliant and/or slippable material includes a plurality of individual sub-layers (e.g., atomic-scale layers) adapted to vibrate normal to the layers or slip or vibrate parallel to the layers and with respect to one another.
• Figure 29A shows a single inclusion 214
• the unit cell may include a plurality of inclusions disposed within the crystalline structure. Further, the inclusion(s) 214 may be disposed at least partially within a plurality of layers of compliant and/or slippable material (e.g., partially or fully surrounded by the compliant and/or slippable material).
• Figure 29B shows a side view of the unit cell of Figure 29 A.
• the unit cell 210 may, for example, be repeated, periodically or randomly, in three dimensions to form a three-dimensional (3D) bulk material 212 as shown in Figure 29C. Similarly, the unit cell may be repeated to create two-dimensional (2D) or one-dimensional structures, such as described herein.
• the inclusions 214 in various implementations may comprise an atomically ordered and/or disordered (e.g., amorphous) material.
• the inclusion material in one particular configuration for example, may be made of a polycrystalline material or a single-crystal material.
• the inclusion material may be, for example, the same type of material as the base material or may be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite material(s).
• the inclusion material in this particular configuration may for example be made of a polymer or partially polymeric material.
• a base material of the unit cell may be constructed with single crystal silicon and one or more inclusion(s) may be made out of crystalline silicon or amorphous silicon or silicon oxide or any crystalline material such as germanium or gallium nitride or any other semiconducting materials or ceramic or metal or a composite comprising a combination of these materials.
• the inclusion material disposed at least partially within one or more outer layer 215 of compliant and/or slippable material in this configuration acts as one or more oscillators/resonators where each atom in the inclusion portion exhibits three natural frequencies/hybridizing resonances.
• oscillators/resonators generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and may slow the group velocities of at least a portion of the interacting phonons, cause mode localization and/or increased phonon scattering. Further, thermal transport through the material may be reduced while at least substantially allowing electron transport through one or more base material channel(s) or transport regions 219. Other shapes for the inclusions may also be adapted. In analogy to the configuration shown in Fig. 10B (which is a two-dimensional version), the sites of the inclusion material may be ordered in a periodic fashion (as shown) and/or may be randomly or otherwise distributed. Similarly, the size of each inclusion (e.g., within one or more unit cells) may be uniform or may vary in groups or vary randomly or otherwise.
• Figure 29D shows a side view of another example implementation of a three- dimensional (3D) unit cell 250 that may be used, for example, within a bulk or other material such as a two- or one-dimensional material like a membrane or a wire, respectively, such as described above with respect to Figs. 29A through 29C.
• the unit cell 250 may comprise a unit cell of a bulk material.
• a three-dimensional (3D) bulk material configuration may include a periodic array of unit cells 250 each including one or more
• FIG. 29B shows, for example, an implementation of a 3D unit cell 250 comprising a crystalline (e.g., single crystal or partially crystalline) base material 256 structure including one or more inclusions 254 disposed within the crystalline base material 256 structure.
• a crystalline (e.g., single crystal or partially crystalline) base material 256 structure including one or more inclusions 254 disposed within the crystalline base material 256 structure.
• the inclusion 254 is further partially disposed within one or more layer 255 of a compliant and/or slippable material, such as graphite, rubber or polymer.
• a compliant and/or slippable material such as graphite, rubber or polymer.
• the compliant and/or slippable material includes a plurality of individual sub-layers (e.g., atomic-scale layers) adapted to vibrate normal to the layers or slip or vibrate parallel to the layers and with respect to one another such as described above.
• Figure 29D shows a single inclusion 254, the unit cell may include a plurality of inclusions disposed within the crystalline structure. Further, the inclusion(s) 254 may be disposed partially within a plurality of layers of compliant and/or slippable material (e.g., partially or fully surrounded by the compliant and/or slippable material).
• the inclusion is partially surrounded by the layer(s) of relatively compliant, slippable, or soft material and further one or more voids 257 are also disposed between the inclusion and the base material in one or more openings where the layer(s) of relatively compliant or soft material are not disposed between the inclusion and the base material.
• the voids in various example implementations may include air, gas, vacuum, liquid, and/or solid and may provide room for the inclusion to move as it vibrates within the base material.
• the inclusion, where not surrounded by the layer(s) of relatively compliant or soft material may be disposed directly adjacent to the base material 256.
• the unit cell 250 may, for example, be repeated, periodically or randomly, in three dimensions to form a three- dimensional (3D) bulk material. Similarly, the unit cell may be repeated to create two-dimensional
• the inclusions 254, in various implementations may comprise an atomically ordered and/or disordered (e.g., amorphous) material.
• the inclusion material in one particular configuration may be made of a
• the inclusion material may be, for example, the same type of material as the base material or may be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite material(s).
• the inclusion material in this particular configuration may for example be made of a polymer or partially polymeric material.
• a base material of the unit cell may be constructed with single crystal silicon and one or more inclusion(s) may be made out of crystalline silicon or amorphous silicon or silicon oxide or any crystalline material such as germanium or gallium nitride or any other semiconducting materials or ceramic or metal or a composite comprising a combination of these materials.
• the inclusion material disposed partially within one or more outer layer 255 of compliant and/or slippable material in this configuration acts as one or more oscillators/resonators where each atom in the inclusion portion exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and may slow the group velocities of at least a portion of the interacting phonons, cause mode localization and/or increased phonon scattering. Further, thermal transport through the material may be reduced while at least substantially allowing electron transport through one or more base material channel(s) or transport regions 259. Other shapes for the inclusions may also be adapted.
• the sites of the inclusion material may be ordered in a periodic fashion (as shown) and/or may be randomly or otherwise distributed.
• the size of each inclusion e.g., within one or more unit cells
• Figures 30A and 30B show another example implementation of a three-dimensional
• the unit cell 320 may be used, for example, within a bulk or other material, such as a two- or one-dimensional material like a membrane or a wire, respectively.
• the unit cell 320 may comprise a unit cell of a bulk base material 326, such as a three- dimensional (3D) bulk base material configuration including an attached layer 324 of a material 328 either disposed directly adjacent to the bulk base material or disposed with one or more layers (e.g., layer(s) of soft/compliant material) disposed between the layer and the bulk base material.
• the attached layer 324 of material 328 for example, may comprise an atomically ordered and/or atomically disordered material (e.g., amorphous material).
• the attached layer 324 may be of any thickness and may fully or partially cover the base material 326.
• the attached layer material 328 in one particular configuration may be made of a polycrystalline material or a single-crystal material.
• the attached layer may be of the same type of material as the base material or can be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite materials.
• the attached layer in this particular configuration may, for example, be made of a polymer or partially polymeric material.
• Figure 30 A shows, for example, an implementation of a
• 3D unit cell comprising a base material 326 comprising a crystalline material (e.g., single crystal or partially crystalline) structure ill including one or more attached layers 324 disposed adjacent to, juxtaposed or near the crystalline structure 327.
• Figure 30A shows a single attached layer 324 the unit cell may include a plurality of attached layers (e.g., on opposing sides of the unit cell) disposed adjacent to, juxtaposed or nearby the base material 326 comprising a crystalline structure 327.
• a layer 325 of slippable material is disposed at least partially between the attached layer 324 and the base material 326.
• the layer 325 of a compliant or slippable material for example, may comprise a plurality of atomic-scale sub-layers adapted to vibrate or slip with respect to one another.
• Figure 30B shows a side view of the unit cell of Figure 30 A.
• the base material 326 may be any material 326 .
• the attached layer 324 and interposed layer 325 of a compliant or slippable material in this configuration acts as one or more oscillators/resonators where each atom in the attached layer 324 exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering.
• thermal transport through the material may be reduced while at least substantially allowing electron transport through one or more base material channel(s).
• Other shapes, sizes, thicknesses or spatial distribution for the attached layer may be adopted.
• the attached layer 324 and the interposed layer 325 of a compliant or slippable material disposed at least partially between the layer 324 and the base material 326 may be attached to the base material 326 on one side or more than one side.
• the sites of the attached layer 324 and the interposed layer 325 of a compliant or slippable material may be ordered in a periodic fashion (as shown) or may be randomly distributed or may continuously cover the surface.
• the size of each attached layer 324 and interposed layer 325 may be uniform or may vary in groups or vary randomly.
• Figure 31 shows an example of yet another example implementation of one or more unit cell(s) 330 of a material including a plurality of crystalline (e.g., single crystal or partially crystalline) thermoelectric base material layers 336, such as a silicon or other at least partially crystalline material 337 configured for thermal transport through the base material 336 interposed between one or more attached layers 334 and layers 325 of a compliant or slippable material, such as graphite.
• the base material 336 may, for example, comprise a bulk 3D material, a 2D material or a 1D material.
• One or more layers 334 of atomically ordered and/or atomically disordered (e.g., amorphous) material 338 are disposed adjacent to, juxtaposed or near the crystalline thermoelectric base material components 336.
• the layer 334 is disposed directly adjacent to an interposed layer 335 of a compliant or slippable material, such as described above with reference to Figures 30A and 30B.
• the layer(s) 334 may comprise an atomically ordered and/or atomically disordered (e.g., amorphous) material 338.
• the layer(s) in this particular configuration may, for example, be made of a poly crystalline material or a single-crystal material.
• the attached layer(s) 334 may be of the same type of material as the base material or can be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite materials.
• the attached material layers 334 in this particular configuration may, for example, be made of a polymer or partially polymeric material.
• the unit cell in this particular implementation, for example, comprises a plurality of crystalline thermoelectric material layers 336 configured for thermal transport through the unit cell and a plurality of attached layers 334 disposed adjacent to, juxtaposed or near one or more of the crystalline thermoelectric base material layers 336, and one or more interposed layer of a compliant or slippable material 335 disposed at least partially between the attached layer(s) 334 and the base material layer(s) 336.
• the base crystalline material layer(s) 336 may be constructed of single crystal silicon, the attached layer(s) or pillars or walls 334 constructed of atomically ordered or disordered material (e.g., crystalline silicon, polycrystalline silicon or other crystalline or polycrystalline material, amorphous silicon or silicon oxide, or ceramic or metal), and the interposed layer 335 constructed of graphite or other compliant material.
• the attached layer(s) 334 and the interposed layer 335 in this configuration act as one or more
• oscillators/resonators where each atom in the attached layer 334 portion exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material 336 channel(s) and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering.
• thermal transport through the base material 336 may be reduced while at least substantially allowing electron transport through one or more base material channel(s).
• Other shapes, sizes, thicknesses or spatial distribution for the attached layer 334 and interposed layer 335 may be adopted.
• the attached layer 334 and the interposed layer 335 may be attached to the base material on one side or more than one side.
• the sites of the attached layer 334 and interposed layer 335 materials may be ordered in a periodic fashion (as shown) or may be randomly distributed within the base crystalline material or may take a continuous form within the base crystalline material.
• the size of each attached layer may be uniform or may vary in groups or vary randomly.
• a plurality of transport“channels” 339 are formed by the plurality of base material crystalline material layers 336 disposed within the unit cell between the attached layers 334 and interposed layers 335 of material disposed between two or more channels 339 of the base crystalline material 337.
• the attached layers 334 of material 338 and interposed layers 335 act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those stemming from atomic vibrations) within the at least partially crystalline base material channel(s) and interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering. In this manner, thermal transport through the material may be reduced while at least substantially allowing electron transport through the base material channel(s).
• Figure 32 shows another implementation of one or more unit cell(s) 340 of a material including a plurality of at least partially crystalline (e.g., single crystal or partially crystalline) thermoelectric base material layer(s) 346, such as a silicon or other material including one or more inclusions 342.
• the inclusions 342 are disposed at least partially within a non-transport region of the base material 346, leaving relatively open transport regions 349 for easier electron flow through the base material 346.
• inclusions 342, in this implementation, are at least partially surrounded by a compliant or slippable material 343, such as shown in Figures 29A-29C, and further include one or more attached layer(s) 344 and interposed layers 345 disposed adjacent to, juxtaposed to or near the base material layer(s) 46, such as shown in Figures 30A and 3 OB.
• the base material region(s) 346 may comprise a crystalline (e.g., single crystal or partially crystalline) structure including one or more inclusions 342 disposed within the crystalline structure of the base material 346 and disposed at least partially within (e.g., fully or partially surrounded by) the layer 343 of a compliant or slippable material.
• the base material 346 may, for example, comprise a bulk 3D material, a 2D material or a 1D material.
• One or more attached layer 344 and interposed layer 345 are disposed adjacent to, juxtaposed to or near the crystalline thermoelectric base material 346 having the inclusion(s) 342 and an at least partially surrounding layer 343 of a compliant or slippable material.
• the inclusion(s) 342 and the attached layer 344 material may also be made of a polycrystalline material or a single-crystal material.
• the inclusion(s) 342 and attached layer(s) 344 may be of the same type of material as the base material 346 or can be made of any other material, such as but not limited to semiconductor, metal, ceramic, polymer and/or composite materials.
• the unit cell in this particular implementation, for example, comprises a plurality of at least partially crystalline thermoelectric material layers configured for thermal transport through the unit cell.
• One or more inclusion(s) 342 may be disposed within the thermoelectric base material layers 346 and at least partially within the layer 343 of a compliant or slippable material and one or more attached layer(s) 344 and interposed layer 345 may be disposed adjacent to, juxtaposed or near one or more of the crystalline thermoelectric base material layers 346.
• the base crystalline material layer(s) 346 may be constructed of single crystal silicon and the inclusion(s) 342 and attached layer(s) 344 constructed of an atomically ordered or disordered material (e.g., single-crystal silicon,
• the inclusion(s) 342 and attached layer(s) 344 along with the layers 342 and 345, respectively, in this configuration act as one or more
• the attached layer 344 and interposed layer 345 may be attached to the base material 346 on one side or more than one side.
• the sites of the attached layer material may be ordered in a periodic fashion (as shown) or may be randomly or otherwise distributed within the base crystalline material or may take a continuous form within the base crystalline material.
• the size of each attached layer may be uniform or may vary in groups or vary randomly or otherwise.
• a plurality of transport“channels” 349 are formed by the plurality of base crystalline material layers 346 disposed within the unit cell.
• the inclusion(s) 342, layer(s) 343 of compliant or slippable material, attached layer(s) 344 and interposed layer(s) 345 of compliant or slippable material act as one or more oscillators/resonators that generate a plurality of local vibration modes within the at least partially crystalline base material channel(s) and interact with a plurality of phonons moving through the base material transport channel(s) and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering.
• thermal transport through the material may be reduced while at least substantially allowing electron transport through the base material channel(s).
• Figures 33A and 33B show an example implementation of a composite material 350 adapted to slow a group velocity of one or more phonons flowing through a crystalline material, and, possibly, cause mode localization and/or increased phonon scattering.
• a crystalline base material 356 e.g., single crystal or partially crystalline material 357 defines at least one transport region 359 along with one or more pillars 354 disposed adjacent to, juxtaposed to or near the transport region 359 of the composite material 350, such as described above with respect to Figures 2, 3, 9, 11, 12 and 13.
• An interposed layer 355 of compliant or slippable material is disposed at least partially between the base material 356 and the one or more pillars 354.
• the one or more pillars 354 and layers 355 act as one or more
• the composite material 350 further comprises one or more inclusions 352 disposed at least partially within (e.g., fully or partially surrounded by) a compliant or slippable material 353 within the transport region 359. As described above with respect to Figures 15A-15C, 18, 29A,
• the inclusions 352 similarly act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those due to atomic vibrations) within the transport region 359 of the at least partially crystalline base material and interact with a plurality of phonons moving through the transport region and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering.
• thermal transport through the transport region 359 of the composite material 350 may be reduced by the pillars 354 and/or inclusions 352 along with the compliant or slippable material layers 353 and 355 while at least substantially allowing electron transport through the transport region 359 of the composite material 350.
• Figures 34A and 34B show another example implementation of a composite
• crystalline base material e.g., single crystal or partially crystalline material
• An interposed layer 365 of compliant or slippable material is disposed at least partially between the base material 366 and the one or more pillars 364.
• the one or more rings or plates or pillars 364 and interposed layers 365 of compliant or slippable material act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those due to atomic vibrations) within the transport region of the at least partially crystalline base material 366 and interact with a plurality of phonons moving through the transport region 369 and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering.
• the composite material 360 further comprises one or more inclusions 362 disposed at least partially within a layer 363 of compliant or slippable material within the transport region 369.
• the inclusions 362 and layers 363 similarly act as one or more oscillators/resonators that generate a plurality of local vibration modes (including those due to atomic vibrations) within the transport region 369 of the at least partially crystalline base material 366 and interact with a plurality of phonons moving through the transport region 369 and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering.
• thermal transport through the transport region 369 of the composite material 360 may be reduced by the plates, rings, pillars 364 and/or inclusions 362 while at least substantially allowing electron transport through the transport region of the composite material.
• Figure 35 shows an example implementation of a thermoelectric device using a bulk phononic (e.g., nanophononic) metamaterial, such as for example a single crystal silicon material with one or more periodic or non-periodic inclusions of an atomically ordered or disordered material (e.g., crystalline silicon, polycrystalline silicon, other crystalline or polycrystalline material, silicon or silicon oxide, or ceramic or metal) disposed at least partially within a layer of compliant or slippable material such as shown in Figure 29 A, 29B and/or with a single crystal silicon material with one or more attached layer(s) of an atomically ordered or disordered material
• a bulk phononic metamaterial such as for example a single crystal silicon material with one or more periodic or non-periodic inclusions of an atomically ordered or disordered material (e.g., crystalline silicon, polycrystalline silicon, other crystalline or polycrystalline material, silicon or silicon oxide, or ceramic or metal) disposed at least partially within a layer of compliant or slippable material such as shown in Figure 29
• crystalline silicon, polycrystalline silicon, other crystalline or polycrystalline material, silicon or silicon oxide, or ceramic or metal disposed at least partially within a layer of compliant or slippable material such as shown in Figure 30 and/or with a single crystal silicon material with one or more embedded layer(s) of an atomically ordered or disordered material (e.g., crystalline silicon, polycrystalline silicon, other crystalline or polycrystalline material, silicon or silicon oxide, or ceramic or metal) disposed at least partially within a layer of compliant or slippable material such as shown in Figure 31.
• an atomically ordered or disordered material e.g., crystalline silicon, polycrystalline silicon, other crystalline or polycrystalline material, silicon or silicon oxide, or ceramic or metal
• a bulk phononic (e.g., phononic or nanophononic) metamaterial may be doped at any level desired to improve the electrical properties forming a p- type semiconducting material and/or an «-type semiconducting material.
• the transport portion of the phononic (e.g., nanophononic) metamaterial may be alloyed with other elements to reduce the thermal conductivity further while having a minimal effect on the electrical properties such as the electrical conductivity and the Seebeck coefficient.
• Figures 36A, 36B, 37A and 37B depict other example implementations of composite materials 370, 380 adapted to slow a group velocity of one or more phonons flowing through an at least partially crystalline material, and, possibly, cause mode localization and/or increased phonon scattering.
• a composite material 370 includes a two- dimensional thin-film/membrane base material structure 376 with extended substructures 374 (e.g., pillars) and an interposed layer 375 of a compliant or slippable material disposed at least partially between the base material structure 376 and the extended substructures 374.
• Figures 37A and 37B show a composite material 380 including a one-dimensional (e.g., wire) base material structure 386 with extended substructures 384 (e.g., plates or rings) and an interposed layer 385 of a compliant or slippable material disposed at least partially between the base material structure 386 and the extended substructures 384.
• the composite material 370, 380 comprises an at least partially crystalline thermoelectric base material.
• a thermoelectric base material includes a base material region 376, 386.
• the base material region 376, 386 includes an at least partially crystalline transport region 379, 389 and at least one atomically ordered or disordered oscillator/resonator region 372, 382 disposed at least partially within a layer 373, 383 of compliant or slippable material.
• the resonator region/inclusion 372 is partially surrounded by the layer 373 of compliant, slippable, or soft material
• the resonator region/inclusion 382 is wholly surrounded by the layer 383 of compliant, slippable, or soft material.
• the inclusion may be fully or partially surrounded by the layer(s) of relatively compliant, slippable, or soft material.
• voids 377 such as shown in
• Figures 36A and 36B may optionally be disposed between the inclusion and the base material in one or more openings where the layer(s) of relatively compliant or soft material are not disposed between the inclusion and the base material.
• the voids in various example implementations may include air, gas, vacuum, liquid, and/or solid and may provide room for the inclusion to move as it vibrates within the base material.
• the inclusion, where not surrounded by the layer(s) of relatively compliant or soft material may be disposed directly adjacent to the base material 376, such as shown in the example implementation of Figures 36C and 36D.
• the at least one transport region 379, 389 includes one or more transport paths (shown by arrows) through the at least partially crystalline thermoelectric base material and is configured to allow electrons flow through the thermoelectric base material at least relatively unimpeded by one or more atomically ordered or disordered materials of one or more oscillator/resonator regions 372,
• the atomically ordered or disordered oscillator/resonator region 372, 382 and respective layers of compliant or slippable material 373, 383 are adapted to provide local resonances through the movement of one or more atoms within the atomically ordered or disordered material of the oscillator/resonator region 372, 382 (e.g., one or more inclusions) and the layers 373, 383 of compliant or slippable material.
• the local resonances travel into the transport region(s)
• the atomically ordered or disordered oscillator/resonator region 372, 382 may comprise a continuous inclusion of atomically ordered or disordered material disposed within the at least partially crystalline thermoelectric base material or may include a plurality of individual inclusions of atomically ordered or disordered material.
• the inclusion(s) may also be disposed at least partially within one or more layer of compliant or slippable material within the at least partially crystalline base material.
• Figures 36A, 36B, 37A and 37B show a single continuous inclusion forming the oscillator/resonator region
• a plurality of continuous or discontinuous inclusions may also be used to form one or more atomically ordered or disordered oscillator/resonator regions disposed at least partially within a layer of compliant or slippable material within the thermoelectric base material region.
• local resonances of atoms within the inclusion(s) and layer(s) of compliant or slippable material extend into the transport region(s) and interact with phonons passing through the region.
• the base material region may be configured to allow electrons to pass through the transport region(s) without being substantially impeded by the inclusion(s) while still allowing the local resonances of the inclusions and layer(s) of compliant or slippable material to interact with one or more phonons passing through the same transport region.
• thermoelectric base material region 376, 386 e.g., the 2D thin-film/membrane base material of
• the extending substructures 374, 384 may comprise any structure that extends away from the at least partially crystalline base material region, such as but not limited to pillars, walls, rings, plates, layers or the like.
• a plurality of extending substructures 374, 384 extend away from a surface of the thermoelectric base material region 376, 386 along with one or more interposed layers 375, 385 of a compliant or slippable material and provide local oscillators/resonators adapted to create local resonances that extend into one or more transport regions 379, 389 of the base material through the movement of one or more atoms of the extending substructures.
• the local resonances of the extending substructures and interposed layers similarly interact with phonons passing through the transport region(s) of the base material region and decrease the group velocities of the phonons and may reduce the thermal conductivity of the composite material, and, possibly, cause mode localization and/or increased phonon scattering.
• Figures 36A, 36B, 37A and 37B show particular types of substructures (e.g., pillars/walls/plates/rings) and interposed layers extending away from a surface of the base material region including the transport region being formed of an at least partially crystalline material, which may be the same or a different material as the at least partially crystalline thermoelectric base material, some or all of the extending substructures may likewise be formed of an atomically ordered or disordered material as described herein.
• substructures e.g., pillars/walls/plates/rings
• Figure 38 depicts yet another example implementation of a bulk composite material 390 including a phononic metamaterial.
• the composite material 390 comprises a base material region 396 including an at least partially crystalline thermoelectric transport region 399 and at least one atomically ordered or disordered
• the transport region 399 includes one or more transport regions of the base material region 396.
• the at least partially crystalline base material region 396 provides one or more transport regions 399 for electron and phonon flow through the thermoelectric structure via one or more transport paths (shown by arrows) extending through the at least partially crystalline thermoelectric base material.
• the transport region(s) 399 are configured to allow electrons to flow through the thermoelectric base material at least relatively unimpeded by one or more atomically ordered or disordered materials of one or more oscillator/resonator regions 392 (e.g., one or more inclusions) disposed at least partially within a layer of compliant or slippable material 393 disposed within the base material region 396 of the base material juxtaposed the transport region(s).
• the composite material further comprises at least one extending substructure 394 (e.g., layers, pillars, walls, rings, plates) and an interposed layer 395 that extend away from a surface of the base material region 396.
• the composite material 390 includes a plurality of extending substructures 394 and interposed layers
• extending substructures 394 may comprise any structure that extends away from the base material region, such as but not limited to pillars, walls, rings, plates, layers or the like.
• the composite material 390 in this particular implementation, includes a bulk composite structure including the base material region 396 from which the extending substructures
• the at least partially crystalline transport region 399 and the extending substructures 394/layers 395 of compliant or slippable material may comprise the same or different at least partially crystalline material(s)
• the extending substructures 394 395 may comprise the same or a different atomically ordered or disordered material as the atomically ordered or disordered oscillator/resonator region 392.
• the base material region 396 and the one or more extending substructures 394 may be further disposed within a matrix 398 of atomically ordered or disordered material (e.g., an amorphous matrix)
• a matrix 398 of amorphous material may comprise a soft amorphous material within which the base material region and the one or more extending substructures are disposed (e.g., encased, surrounded or the like), although other implementations are also contemplated.
• the base material region 396 and extending substructures 394 may be surrounded in one, two or three-dimensions (e.g., surrounded at least in part or fully surrounded).
• the surrounding matrix 398 material in this configuration may further act as one or more oscillators/resonators where each atom in the atomically disordered (e.g., amorphous) surrounding material exhibits three natural frequencies/hybridizing resonances.
• oscillators/resonators formed by the surrounding atomically disordered material may generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering. Further, thermal transport through the base material may be reduced while at least substantially allowing electron transport through one or more base material channel(s).
• the surrounding matrix 398 material may further be used to convert a reduced dimension structure (e.g., a 2D or 1D base material) into a 3D bulk phononic metamaterial that may be used in standard thermoelectric devices, such as the one shown in Figure 35.
• a reduced dimension structure e.g., a 2D or 1D base material
• the surrounding matrix material may comprise a relatively soft, flexible or other material, such as a polymer material for example, adapted to allow those extending substructures to move at least at an atomic scale.
• any of the other structures disclosed herein e.g., Figures 2, 3, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 22, 23
• Figures 2, 3, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 22, 23 may similarly be disposed within one or more matrix of amorphous or soft material.
• the outer matrix(ces) may provide local resonances (stemming from atomic and structural motion) that further interact with phonons passing through the transport region of the base material that may decrease the group velocities of the phonon(s) and reduce the thermal conductivity of the composite material, and, possibly, cause mode localization and/or increased phonon scattering.
• Figures 39, 40 A and 40B depict another example implementation of a bulk composite material 400 including a phononic metamaterial.
• the composite material 400 comprises an at least partially crystalline base material 406 and one or more complex inclusion 401 disposed within the base material 406.
• the complex inclusion 401 comprises an inner inclusion 402 and an outer inclusion 403, although any number of materials, configurations, layers, etc. are possible.
• the complex inclusion 401, comprising inner and outer components 402, 403, is at least partially surrounded by one or more outer layer 405 or disposed at least partially surrounding the complex inclusion 403.
• an additional layer(s) may be disposed between two or more layers or materials of the complex inclusion 403.
• the complex inclusion may comprise a plurality of inclusion materials that together form the equivalent of a mass in a spring resonator as described herein.
• the outer inclusion e.g., rubber or polymer
• the outer inclusion may assist an outer layer 405 to perform the role of a spring in a spring resonator.
• the outer layer(s) 405 may include graphite or a similar compliant or slippable material where one or more layer of atoms can slip with respect to each other (e.g., with relatively low force).
• Graphite for example, comprises atoms strongly bonded together in one or more direction and weakly bonded (e.g., by van der Waal bonds) in one or more other direction.
• This combination of bonding features gives the graphite outer layer or inclusion a relatively high melting temperature (e.g., higher than polymers) while also high compliance or softness along certain directions due to the weak, e.g., van der Waal, bonds.
• the weak bonds enable individual atomic-scale layer(s) of the outer
• graphite has these characteristics because it comprises a stack of electrically conducting graphene layers held together by weak van der Waals bonds. These properties allow the outer layer(s)/inclusion(s) to act as a spring holding the complex inclusion 401 which act as a one or more mass. Such a configuration, for example, may give rise to one or more internal resonances within the host (matrix) material of the composite 400.
• the number of resonances may be as many as the number of atoms in the inner inclusion(s) multiplied by three (i.e., the number of degrees of freedom per atom).
• the outer layer(s) 405 and outer inclusion(s) 403 within which the internal inclusion(s) 402 are disposed, for example, may be adapted to alter one or more
• the inner inclusion(s) 402. For example, one or more atomic movements within the complex inclusion 401 and/or outer layer(s)/coating(s)/, which comprises one or more internal inclusion(s) 402 and one or more outer inclusion(s) 403.
• the complex inclusion may be altered by the inner component inclusion(s) 402 and the outer component inclusion(s) 403 or the interaction therebetween.
• the internal inclusion(s) 402 may be relatively heavier or denser than the surrounding outer layer(s)/inclusion(s) 403.
• the outer inclusion(s) and the internal inclusion(s) 402 may be atomically ordered or disordered materials.
• the complex inclusion may further be at least partially surrounded by a layer 405 of compbant/sbppable material, such as graphite, rubber or polymer.
• a layer 405 of compbant/sbppable material such as graphite, rubber or polymer.
• the outer layer(s) 405 and/or outer inclusion(s) 403 may be a soft material such as rubber or other polymers.
• the internal inclusion(s) 402 and outer layer(s) 405 and outer inclusion(s) 405 can take any shape, such as but not limited to cubes, spheres, or the like.
• the internal inclusion(s) 402 and outer layer(s) 405 and outer inclusion(s) 403 may alter (e.g., lower or increase) a frequency of resonances stemming from and/or facilitated by the effective spring-mass effect due to the combination of internal inclusion(s) 402 and outer layer(s) 405 and outer inclusion(s) 403.
• the internal inclusion(s) 402 may be relatively heavier or denser than the outer layer(s) 405 and outer inclusion(s) 403 in which it is supported and the outer layer(s) 405 and outer inclusion(s) 403 may comprise a material softer than the internal inclusion(s) 402.
• the composite structure(s) may be used to alter one or more hybridizing resonances, which in some implementations, may further increase the effectiveness of reducing thermal conductivity in the surrounding (matrix) transport material by targeting one or more phonons that carry relatively more heat. Further, in some
• the combination of the internal inclusion(s) 402, outer inclusion(s) 403 and outer layer(s) 405 may be optimized to produce a distribution of resonances from the internal inclusion(s) 402 and, sometimes, outer inclusion(s) 403 that are effective to reduce thermal conductivity of the surrounding (matrix) transport material and the system as a whole by resonance hybridizations.
• one or more material may be disposed within an at least partially crystalline layer, pillar, wall, plate, ring or other structure.
• the internal inclusions may be adapted to alter an atomic movement within the at least partially crystalline extending substructure.
• the extending structures can be made entirely from one or more heavy materials.
• a relatively heavy or dense material such as a metal material, for example, may be used to lower a frequency of one or more atomic motion within the extending substructure and, thus, alter hybridizing resonance(s) produced.
• Figure 41 depicts yet another example implementation of a bulk composite material 410 including a phononic metamaterial that illustrates a combination of a surrounding atomically ordered or disordered matrix shown in Figure 38 and the internal inclusions shown in Figures 39 and 40 disposed within a continuous atomically ordered or disordered outer inclusion in this implementation.
• the inclusion(s) are disposed at least partially within a layer 415 of compliant or slippable material.
• the composite material 410 includes a base material region 416 comprising an at least partially crystalline transport region 419 defining one or more transport paths (shown by arrows) for carrying electron and phonon flow through the composite material 410.
• One or more inclusions 412 are disposed at least partially within a layer 415 of compliant or slippable material within the base material region at least generally outside the transport region(s) 419 so as to reduce physical interference with electron flow within the transport region(s) due to the physical interference of the inclusion(s) 412 and layers 415, 417.
• One or more additional internal inclusions 413 e.g., additional inclusion(s) disposed inside one or more outer inclusion(s) are provided.
• the internal inclusions 413 are disposed within a continuous outer inclusion 412 and may be adapted, for example, to alter one or more characteristic of the continuous outer inclusion 412.
• the internal inclusions 413 disposed within the continuous outer inclusion 112 and a corresponding layer 415 of compliant or slippable material may be adapted to alter one or more atomic movements within the outer inclusions 412.
• the internal inclusion(s) 413 may be relatively heavier or denser than the surrounding outer inclusion 412.
• the internal inclusion(s) 413 may be atomically ordered or disordered materials.
• the outer inclusion(s) 403 may be atomically disordered or ordered materials.
• the outer inclusion may be a soft material such as rubber or other polymers.
• the internal and outer inclusions can take any shape such as cubes, spheres, or the like.
• the internal inclusion(s) 413 may alter (e.g., lower or increase) a frequency of resonances stemming from and/or facilitated by the outer inclusions 412 of the composite material.
• the composite structure(s) (internal inclusion(s) 413 within an outer inclusion 412) may be used to alter one or more hybridizing resonances, which in some implementations, may further increase the effectiveness of reducing thermal conductivity in the base transport material by targeting one or more phonons that carry relatively more heat.
• the internal inclusions 413 may be optimized to produce a distribution of resonances from the outer inclusion(s) that are effective to reduce thermal conductivity of the base transport material and the system as a whole by resonance hybridizations.
• the inclusions 411 disposed within the extending substructures 414 may be optimized along with one or more respective layers of compliant or slippable material to produce a distribution of resonances that are effective to reduce thermal conductivity of the base transport material and the system as a whole by resonance hybridizations.
• the extending structures can be made entirely from one or more heavy materials.
• the base material region 416 and extending substructures 414 are also disposed within a matrix 418 of atomically ordered or disordered material
• the matrix 418 of atomically ordered or disordered material may comprise a crystalline, poly crystalline or soft amorphous material within which the base material region and extending substructures (e.g., pillars/walls) are disposed, although other implementations are also contemplated.
• the surrounding matrix material in this configuration may further act as one or more oscillators/resonators where each atom in the atomically ordered or disordered surrounding material exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators formed by the surrounding atomically ordered or disordered material may generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering. Further, thermal transport through the base material may be reduced while at least substantially allowing electron transport through one or more base material channel(s).
• the bulk composite material provides hybridizing resonances from extended substructures, atomically ordered or disordered inclusions that may be altered by one or more additional internal inclusions with a layer of compliant and/or slippable material as well as additional hybridizing resonances from the surrounding outer matrix.
• Figure 42 shows yet another implementation of an example bulk composite
• the bulk composite material 420 includes a base material region 426 comprising an at least partially crystalline transport region 429 defining one or more transport paths (shown by arrows) for carrying electron and phonon flow through the composite material 420.
• One or more atomically ordered or disordered inclusions 422 are disposed at least partially within a layer 425 of a compliant or slippable material and within the base material region 426 at least generally outside the transport region(s) 449 so as to reduce physical interference with electron flow within the transport region(s) 429 due to the physical interference of the inclusion(s) 422 and the layer 425.
• a complex inclusion comprises one or more additional internal inclusions 423 (e.g., a relatively dense or heavy material such as metal, ceramic, nonmetal, etc.) are also disposed within the one or more outer inclusions 422 such as shown in Figure 41.
• the internal inclusions 423 and/or inclusions 422 within which the internal inclusions 423 are disposed may be designed to alter (e.g., lower or increase) a frequency of resonances stemming from and/or facilitated by the atomically disordered inclusions of the composite material 420.
• the outer inclusion(s) 403 may be atomically ordered or disordered materials.
• the outer inclusion may be a soft material such as rubber or other polymers.
• the internal and outer inclusions can take any shape such as cubes, spheres, or the like.
• the composite structure may be used to alter one or more hybridizing resonances to reduce the group velocities of phonons traveling through the transport region of the composite material, and, possibly, cause mode localization and/or increased phonon scattering, which in some
• implementations may further increase the effectiveness of reducing thermal conductivity in the base transport material by targeting one or more phonons that carry relatively transport heat.
• the base material region is disposed within (e.g., between or surrounded by) a matrix 428 of an atomically ordered or disordered material that forms a matrix of atomically ordered or disordered material surrounding the base material region.
• the matrix 428 may comprise a soft material within which the base material region is disposed, although other implementations are also contemplated.
• the outer matrix material may further act as one or more oscillators/resonators where each atom in the atomically ordered or disordered surrounding material exhibits three natural frequencies/hybridizing resonances.
• the oscillators/resonators formed by the surrounding atomically ordered or disordered material may generate a plurality of local vibration modes that interact with a plurality of phonons moving through the base material channel(s) and slow the group velocities of at least a portion of the interacting phonons, and, possibly, cause mode localization and/or increased phonon scattering.
• thermal transport through the base material may be reduced while at least substantially allowing electron transport through one or more base material channel(s).
• the surrounding matrix material may comprises an atomically disordered material
• the surrounding matrix material may comprise a crystalline or at least partially crystalline material that adapts a 2D or 1D composite material into a bulk 3D composite material such as described above with respect to Figures 38 and 41.
• the bulk composite material may comprise a plurality of repeated cells (e.g., unit cells), such as having the structures shown in Figure 42.
• a one, two or three-dimensional composite material structure may be formed by individual unit cells repeated in one, two or three dimensions.
• phononic metamaterials are described with respect to reducing thermal transport through a base material are described in detail herein, the phononic metamaterials can be used in many other applications.
• such phononic metamaterials may be used in applications such as, but not limited to applied for thermoelectric energy conversion and other possible applications that utilize the effects induced by the local resonances.
• additional applications includes sensors, heat concentrators, heat dissipaters, thermal emitters, semiconductors, superconductors, photovoltaic materials, optomechanical materials, antennas, photonic materials, optical absorbers, lasers, infrared materials, quantum computing, among others.
• joinder references do not necessarily infer that two elements are directly connected and in fixed relation to each other. It is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative only and not limiting. Changes in detail or structure may be made without departing from the spirit of the invention as defined in the appended claims.

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• 2019
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