WO2022125187A2 - Low temperature sintered thermoelectric material being highly strained nano structures with a secondary nano coating of a conductive metal able to conduct electrons but block phonons - Google Patents

Abstract

A sintered thermoelectric pellet with a nano thick electrically conductive metallic coating constructed so as to decouple and manage optimal performance in thermal conductivity, Seebeck coefficient and electrical conductivity. A porous structure of a doped silicon thermoelectric material optimally is doped to establish a negative (N) and positive (P) type semiconductor bias so to provide the ability to make a P/N semiconductor junction. The porous structure includes angular shaped particulate bodies and smaller necks, which necks are created by sintering or joining the particles below the melting point of the material; the smaller necks are from 8 to 200 nanometers in average diameter. The N type dopants are typically phosphorous or arsenic; the P type are often from column IIIA, such as boron or gallium. To provide an electrical contact between the P and N elements to make a function P/N junction and to provide an electrical path to ground for the electrons converted from phonons by the thermoelectric effects in the grains the entire surface of the pellet both on the outside and the entire reticulated porosity inside is coated by a conductive metallic nano layer of a metal such as silver or nickel or other is deposited by decomposition of silver oxide or in the case of nickel tetracarbonylnickel(0) (Ni(CO)4), said layer of silver or nickel or other metallic coating having a thickness between 8 and 80 nanometers.

Description

TITLE OF INVENTION

Low Temperature Sintered Thermoelectric Material being highly strained nano structures with a secondary nano coating of a conductive metal able to conduct electrons but block phonons

CROSS-REFERENCE TO RELATED APPLICATIONS

This Application claims the benefit of the filing date of U.S. Provisional Patent Application Serial No. 63/091,479, filed October 14, 2020, the entire content of which is herein incorporated.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

BACKGROUND OF THE INVENTION

1. Field of Invention

[0001] The present invention pertains generally to thermoelectric semiconductive materials and, more particularly, to thermoelectric semiconductive materials with high silicon content.

2. Description of the Related Art

[0002] Thermoelectric semiconductive materials generate electricity from thermal flux through confinement of phonons in the presence of the semiconductor thermoelectric effects, or generate temperature differences from electricity by moving phonons in the same way from the cold side to the hot side. Unlike in metals where electrical conductivity increases with decreases in temperature, in pure semiconductors electrical conductivity increases with increases in temperature.

[0003] Thermoelectric materials exhibiting the Seebeck effect in the presence of a thermal flux are useful for the production of electricity from heat. Semiconductive materials that move heat from one side to the other in response to an electrical charge are useful for cooling or heating. Such materials exhibit the Peltier effect.

[0004] The amount of electricity generated in relation to a thermal flux or the amount of heating or cooling provided in relation to the electricity consumed is expressed as conversion efficiency and is a primary consideration for a thermoelectric material. The factors controlling conversion efficiency include the Seebeck voltage, the microvolts per degree kelvin, the electrical conductivity, the thermal conductivity which is an artifact of creating and building thermal flux, the temperature stability over a large range of temperature, and the coefficient of thermal expansion.

[0005] Another primary consideration for a commercially useful thermoelectric material is the longevity of a device incorporating the thermoelectric material. For example, some conventional thermoelectric materials have alternating P-type and N-type thermoelectric semiconductor elements connected by metallic connectors. If the metallic connectors separate from the thermoelectric elements during use, the conversion efficiency of the underlying thermoelectric material loses relevancy as electrical and potentially thermal conductivity are lost from the physical separation of the connectors from the elements.

[0006] Desirable Seebeck thermoelectric materials may be constructed into both planar and complex shaped objects that can be adapted to diverse locations for the conversion of waste heat into electricity. Such a thermoelectric material should have a cross section with properties to maintain a sufficiently high temperature differential between two opposing sides in order to generate voltage efficiently. A very low coefficient of thermal expansion can enable the construction of much larger “legs” of thermoelectric elements, thus providing thermal transfer from the complete cross-section of the legs as compared to trying to move the heat through a very low thermal conductivity material from one side to the other.

[0007] A desirable Seebeck thermoelectric material also has high tensile strength, resistance to thermal shock as waste heat is generally in the 200 to 800 degrees Celsius temperature range, and be formable into layers. The ability to be formed into layers allows the thermoelectric material to serve as the basis for a range of thermoelectric devices. However, conventional thermoelectric materials are often limited to a deposition thickness of about 1 mm due to the competing considerations of thermal and electrical conductivity. For instance, a very high coefficient of thermal expansion and low strength combine to limit the size of a “leg” to a size that can resist the thermomechanical stress imposed by a large delta temperature from the cold side to the hot side.

[0008] Optimally, a thermoelectric material having a high conversion efficiency should have a high Seebeck Coefficient, high electrical conductivity, low thermal conductivity, a low CTE, high strength, and be able to operate at high temperature differences. For a thermoelectric material to operate at high temperature differences from one side of the material to the other, the material desirably has a low coefficient of thermal expansion, low Poisson ratio, and high mechanical strength. See, e.g., Ci et al., Materials Letters 65, 1618- 1620 (2011).

[0009] To achieve high conversion efficiency of electricity into the desired level of heating and/or cooling, or conversely, to achieve a high level of electricity generation from a given temperature difference across the thermoelectric material, a thermoelectric material (TEMat) preferably has a high ZT in combination with the ability to effectively operate at high or low temperatures and at a large temperature difference without thermomechanical failures.

[0010] In view of these considerations, it is desirable to have a TEMat with a high Seebeck Coefficient, high electrical conductivity, and low thermal conductivity to provide a desirable ZT, while simultaneously providing a low coefficient of thermal expansion, and high thermomechanical strength. Thus, an improved TEMat would be able to sustain a large temperature difference (DT) and not degrade when operated at temperature extremes for extended periods of time.

[0011] Present attempts at making commercially useful TEMats have been unsuccessful at making low cost TEMats having attractive conversion efficiencies at sufficient thickness to operate at high temperatures with large DTs. Conventional thermoelectric materials intended for use in thermoelectric generators, which produce electricity from heat, or as thermoelectric coolers, which produce colder temperatures from electricity, have been unable to provide the desired combination of cost, ZT, DT of operation, coefficients of thermal expansion (CTE), and thermomechanical strength. Development in the field of TEMats often has focused on forming nanowires and MEMS from the TEMats. The resulting nanowires and MEMS have provided expectations of high efficiencies (ZT) in converting heat to electricity which have not been achieved due to the phenomena of “ballistic transport” or “ballistic tunneling” which can occur in nano structures in the range of 10 to 30 nanometers which is below the quantum size effect for blocking phonons, but if the Z axis aspect ratio is very high, then the electrons and phonons can stretch out and become thermally conductive. A high Z axis aspect ratio can be seen in a wire that is free of bends, or a thin film surface that is very flat in the x and y axis. However, these structures include tellurium or expensive rare earth metals and cannot be practically made in the thick cross sections needed to maintain a large unaided or largely unaided DT. For many of these materials, aggressive heat exchange apparatus are necessary to limit the DT to prevent catastrophic thermomechanical failure of the TEMat or the device in which the TEMat is used.

[0012] Thus, a commercially useful TEMat requires more than just a high ZT. As conventional TEMats are generally very brittle, an improved TEMat would not be too brittle to be processed using existing processing practices. Such a TEMat also will preferably withstand a large DT in continuous use. To withstand a large DT, the TEMat also requires a low CTE and a high tensile strength. Lastly, from a perspective of size, a larger TEMat component will promote the ability to achieve a larger DT (presuming it does not mechanically fail).

[0013] As can be seen from the above description, there is an ongoing need for TEMats having high conversion efficiencies that can tolerate temperatures extremes, whether high or low, and operate effectively over large temperature differences in continuous use. The TEMats and methods of the present invention overcome at least one of the disadvantages associated with conventional thermoelectric materials, devices, and production methods. There is a lot of context in the approach we are taking and the understanding of the physics we are modeling:

[0014] We are not making a heat engine. We are working with elements where the Camot rules apply, such as moving heat into and out of the system on both sides.

[0015] The thermoelectric system is solid state, similar to a solar cell and semiconductor, but so very different. A TEMat does not suffer the same or as many of the losses of a solar cell, which losses are also outside of Camot laws. Such as reflection, recombination’s, losses of photons to conversion to heat etc. Carnot efficiency models by themselves do not profile losses in the solar cell or the limits of its efficiency.

[0016] We do better in the generator with high temp, but not with high delta T. We do better with a cooler when we limit Delta T with high flux, and that means moving things out quickly and sooner than later. So if you apply the Delta T based model of the Camot, you will not find a helpful model.

[0017] We are not contending with Camot, Fairbanks or S.W. Angrist. We are describing phenomena in a way that perhaps they did not see at the time of their work. We complement them:

[0018] Here are our differences:

[0019] Camot: the inner workings of our thermoelectric device are not optimized by Delta T, or engage in the physics of gas laws and thermodynamics of Delta T

[0020] Fairbanks: The ZT efficiency is not a function of Delta T, but of heat flux

[0021] Angrist: The inflection point for efficiency is thermal flux, not Delta T. As Delta T goes up, flux goes down and efficiency goes down as well.

[0022] Let’s start with a review of Camot and what he described. It is part of our system, but not part of the actual thermoelectric physics. Carnot’s models addressed the efficiency of thermodynamic conversions into mechanical work. So Delta T is the theme, as well as gas laws, PV = NRT etc.

[0023] We really need to look at this both from the perspective of Camot, and I would say Plank from a quantum mechanics physics point of view and look to see the differences in the models we are addressing. So lets start with a simple model Camot would feel comfortable modeling:

THE AUTOMOBILE

[0024] We can agree that the Camot Efficiency is the theoretical maximum efficiency in a heat engine which is operating between two temperatures: [0025] The temperature at which the high temperature reservoir operates (T Hot ).

[0026] The temperature at which the low temperature reservoir operates (T Cold ).

[0027] In the case of an automobile, the two temperatures are:

[0028] The temperature of the combustion gases inside the engine (T Hot ).

[0029] The temperature at which the gases are exhausted from the engine (T Cold ).

[0030] The energy that is put into the engine has to come out either as work or waste heat, with work being output mechanically as well as friction and noise.

[0031] How does this work model wise?

[0032] Peltier at first was a watchmaker amateur physicist playing with the Seebeck effect, published his work in Paris in 1834, 13 years after Seebeck in 1821. He used dissimilar metal parts, bismuth and copper, and until the Russians substituted semiconductors capable of producing a much larger thermal gradient, they were very inefficient.

[0033] In 1821 Thomas Seebeck discovered that electric current will flow through a circuit comprising two dissimilar conductors, provided the junctions where these conductors join are maintained at different temperatures. But we should note that Seebeck could not explain the actual scientific reason behind this phenomenon, at that time we did not have the knowledge or vocabulary to do so. So he wrongly concluded that flowing heat produced the same effect as flowing electricity.

[0034] Later, in 1834, Jean Peltier notes that heat could be moved by the Seebeck effect, but again, he did not understand nor could describe the physics. In the 1850s William Thomson (Lord Kelvin) scientifically explained both, the Seebeck and Peltier effects, and he prove the relationship between them, that the Seebeck Effect was reversable.

[0035] The Peltier effect is the inverse of the Seebeck effect.

THE SEEBECK EFFECT

[0036] The Seebeck effect is a phenomenon wherein a temperature gradient occurring between the two junctions formed by two dissimilar electric conductors or semiconductors causes a potential difference to be developed between them. This potential difference allows electric current to flow through the circuit. Thus, the Seebeck effect states that, a temperature gradient will cause electric current to flow through a circuit.

[0037] Mathematically, if (T1 - T2) is the temperature difference between the two junctions of dissimilar metals, then, according to the Seebeck effect, it will produce an Electromotive Force (Voltage) given by the following:

E = a (T1 - T2)

[0038] The Seebeck Coefficient, a, is the differential Seebeck coefficient or (thermo electric power coefficient) between the two conductors/semiconductors. It is positive when the direction of electric current is the same as the direction of thermal current. And it is temperature dependent. But it is wrong: it is not the temperature differential; it is the concentration of phonons which in a way requires a temperature differential as the phonons flow in and get trapped. And at different temps, as temps rise in silicon a rises.

[0039] But you have to get the electrons created by cascading phonon waves, they are wave packets, as the intersect out without carrying phonons.

[0040] So you want a structure where you trap phonons, so very low kappa among the grains, very low electrical conductivity between the physical grains, but very high electrical conductivity out of the grains to ground without conducting phonons. Hence our thin silver, 25 nanometers enjoys a quantum size effect to conduct electrons, which are fermions, but too thin and rough to conduct phonons, bosons.

[0041] In the case of a generator, the thermal flow and the path to ground are managed such that the N and P have the same path to ground so all heat and electricity flow in the same direction.

[0042] If sigma is high enough, the pipe for conducting electrons without generating heat is larger than the flow of phonons and becomes a non-factor, a prerequisite.

[0043] But the efficiency of the generator is about the Seebeck Coefficient, the higher this is the more voltage you make, and the flow and capture of phonons. [0044] Our thermal conductivity in the porous silicon structure is very low because of the amorphous physical nature of our necks, but 40% of the mass is air in reticulated structures. So lots of heat can flow through these air spaces. If the air is hotter than the silicon grains, and if the silicon grains are moving a lot of electrons out from phonon wave interaction in the grains, then there will be a large flow of heat from the air to the grains. But the thermal conductivity of the necks is about 1.8 W/mK, so not zero, and the kappa of the grains is 149 W/mK. So about heat capacity:

[0045] Heat capacity is the ratio of heat absorbed by a material to the temperature change. It is usually expressed as calories per degree in terms of the actual amount of material being considered, most commonly a mole (the molecular weight in grams). Specific heat is the heat required to raise the temperature of the unit mass of a given substance by a given amount (usually one degree).

[0046] Heat capacity can be calculated by dividing the amount of heat energy supplied (E) by the corresponding change in temperature (T). The equation is:

Heat Capacity = E / T.

[0047] So the heat capacity of our materials are silicon, silica and air: j/kgxTk

[0048] Air: 1.005

[0049] Silicon: 705

[0050] Glass: 800

[0051] So it will take very little energy to move heat to air and make it hot, and the silicon will have a great capacity to be “cold” and take heat from the air.

[0052] So where does low thermal conductivity play a role here? Millie Dresselhaus and I agreed that if kappa goes to near zero so does thermal flux and heat flow and it is not the delta T that makes this work globally, but the delta T locally, getting heat to the place where the semiconductor thing is happening. So we want a healthy flow of phonons, but we don’t want to have “leakage” of phonons, especially where we are harvesting electrons. [0053] The air itself is a good conductor, but so are the grains and necks. But perhaps 70% or more of the grains are facing into air, are rough and once phonons find residence there there is enormous thermal resistance to keep them trapped in those grains.

[0054] Given that phonons are bosons, they are energy packets, waves, and when the intersect you get a rise in the energy of the combined wave forms and this tends to enable the semiconductor function to harvest an electron. The silver conductor 25 nm on the surface will take this electron to ground and not carry phonons. Quantum Size effects.

[0055] So the Seebeck equation:

ZT + ((a² * o)/ x) * Tt

[0056] What is wrong with this? Much:

[0057] If kappa goes to near zero so does thermal flux. As kappa goes to zero, heat flux follows:

[0058] So if you have very low thermal conductivity then delta T rises and heat flux drops.

[0059] This does not address building heat flux in the phonon traps;

[0060] Kappa and Sigma in our temperature domains are largely insensitive to temperature. Seebeck is highly temperature dependent.

SUMMARY

[0061] In some embodiments of the present general inventive concept, a sintered thermoelectric pellet with a nano thick electrically conductive metallic coating constructed so as to decouple and manage optimal performance in thermal conductivity, Seebeck coefficient and electrical conductivity, includes a porous structure of a doped thermoelectric material made of silicon which is optimally doped to establish a negative (N) and positive (P) type semiconductor bias so to provide the ability to make a P/N semiconductor junction; wherein the porous structure includes angular shaped particulate bodies and smaller necks, which necks are created by sintering or joining the particles below the melting point of the material, the angular shaped particulate bodies have a body diameter D50 by volume of particles from 500 to 5000 nanometers, which will also give a measurement of diameter D50 of particles by number of 300 to 1200 nanometers the smaller necks are from 8 to 200 nanometers in average diameter, and the doped silicon includes from 1015th to 1020th/cc of at least one dopant, said one dopant being either an N type dopant or a P type dopant, said N type dopants selected from the group consisting of phosphorous and arsenic, said P type dopants selected from the group consisting of boron and gallium; wherein the doping is minimized so as to provide the necessary positive or negative bias to make a P/N junction after thermal processing which will provide the optimized Seebeck coefficient of the material which doping diminishes, upon sintering or joining the porosity is reticulated and in the range of 30% to 45% of the theoretical density and the isolated grains surrounded mostly by air and the small necks serve to trap phonons and form phonon wells and traps; and wherein to provide an electrical contact between the P and N elements to make a function P/N junction and to provide an electrical path to ground for the electrons converted from phonons by the thermoelectric effects in the grains the entire surface of the pellet both on the outside and the entire reticulated porosity inside is coated by a conductive metallic nano layer in the range of 8 to 80 nanometers.

[0062] In some embodiments, said metallic layer is a layer of silver deposited by decomposition of silver oxide.

[0063] In some embodiments, the silver oxide is derived from an aqueous solution of silver nitrate which is decomposed to silver oxide at a temperature in excess of 180 C.

[0064] In some embodiments, the aqueous silver nitrate solution is infiltrated into the reticulated porosity of the structure under a vacuum of minus 200 torr or less, wherein the silver nitrate and silver oxide derive metallic silver coating through thermal decomposition at a temperature less than 400 C, and wherein such metallic coatings can be deposited by other decomposition processes from other metallic compounds which decompose to their conductive forms at temperatures less than 700 C

[0065] In some embodiments, the metallic layer is a layer of nickel.

[0066] In some embodiments, the layer of nickel is deposited by decomposition nickel tetracarbonylnickel(O) (Ni(CO)4). [0067] In some embodiments, the larger angular shaped particulate bodies have a number body diameter D50 from 300 to 4000 nanometers and is composed of doped silicon.

[0068] In some embodiments, the larger angular shaped particulate bodies have a body diameter D50 from 350 to 1800 nanometers.

[0069] In some embodiments, the smaller necks are from 10 to 150 nanometers.

[0070] In some embodiments, the smaller necks are from 12 to 180 nanometers.

[0071] In some embodiments, the larger angular shaped particulate bodies are angular shaped.

[0072] In some embodiments, the doped silicon includes from 100 to 1500 parts per million boron or otherwise described as 1015th to 1020th/cc

[0073] In some embodiments, the doped silicon includes from 100 to 2300 parts per million phosphorous or otherwise described as 1015th to 1020th/cc.

[0074] In some embodiments, the porous structure lacks features arising from doped silicon fines having average particulate diameters of 600 nanometers and less.

[0075] In some embodiments, the porous structure lacks features arising from doped silicon fines having average particulate diameters of 1400 nanometers and less.

[0076] In some embodiments, the porous structure lacks features arising from doped silicon fines having average particulate diameters of 1400 nanometers and less.

[0077] In some embodiments, the pellet having a Seebeck voltage from 150 micro Volts to 600 micro Volts at approximately 23 degrees Centigrade.

[0078] In some embodiments, the sintered thermoelectric pellet has a reticulated porosity and a density from 1.2 to 1.7 grams per cubic centimeter. [0079] In some embodiments, the sintered thermoelectric pellet has a thermal conductivity of less than 10 W/mK.

[0080] In some embodiments, the sintered thermoelectric pellet has a coefficient of thermal expansion less than 6 parts per million.

[0081] Some embodiments further include a metal coating two opposing ends of the pellet, the metal selected from the group consisting of molybdenum, manganese, titanium, tungsten, copper, nickel, gold, silver, alloys thereof, or a combinations thereof.

[0082] In some embodiments, the metal coating the two opposing ends of the pellet contacting to a material with low to matching CTE to silicon, such as Invar, Kovar, tungsten aluminum nitride ceramic which are joined to the pellets at temperatures less than the eutectics temperature of the TEMat and the conductive coating.

[0083] In some embodiments, the joining of a silver coating on silicon is performed at less than the sliver silicon eutectic of 835

[0084] In some embodiments, the aluminum nitride ceramic including a wire or a contact.

[0085] In some embodiments, a method of making a sintered thermoelectric pellet includes milling doped silicon or other Thermoelectric material particulates with or without at least one pressing aide in a mill under an alcoholic carrier liquid until the doped silicon particulates reach a volume D50 of 300 to 5000 nanometers, and a number D50 of between 200 and 100 nanometers where the binder is capable of being extracted in a vacuum of less than minus 450 torr.

[0086] Some embodiments further include combining silicon metal particulates purer than 99.99% silicon metal by weight with enough dopant to provide from 100 to 2300 parts per million of at least one dopant in the silicon metal particulates; and heating the mixture to melting and then cooling the mixture in an atmosphere substantially excluding oxygen to produce doped silicon; and breaking the resulting doped silicon into the doped silicon particulates. [0087] In some embodiments, the doped silicon particulates include from 100 to 2300 parts per million boron or otherwise described as 10^15th to 10^20th/cc.

[0088] In some embodiments, the doped silicon particulates include from 100 to 2300 parts per million phosphorous or otherwise described as 10^15th to 10^20th/cc.

[0089] In some embodiments, the doped silicon particulates have average diameters from 0.1 to 5 microns.

[0090] In some embodiments, the alcoholic carrier liquid is acetone.

[0091] In some embodiments, the alcoholic carrier liquid is ethanol.

[0092] Some embodiments further include, after the further heating under the vacuum, heating the pellet under a reducing atmosphere or vacuum from 580 to 1400 degrees Centigrade.

[0093] Some embodiments further include, after the further heating under the vacuum, heating the pellet under a vacuum or reducing atmosphere from 950 to 1400 degrees Centigrade.

[0094] In some embodiments, compressing is performed with 350 to 6000 psi

[0095] In some embodiments, the pressing aide comprises a carbon-based binder.

[0096] In some embodiments, the carbon-based binder comprises from 4% to 38% by weight the weight of the doped silicon particulates.

[0097] In some embodiments, the carbon-based binder is selected from the group consisting of propylene carbonate, polyethylene glycol, waxes, fatty acids, oleic acid, and combinations thereof.

[0098] In some embodiments, the carbon-based binder includes an approximately 1:9 ratio of fatty acid to polyethylene glycol. [0099] Some embodiments further include metallizing two opposing ends of the pellet with a conductive metal.

[00100] In some embodiments, the conductive metal is selected from the group consisting of molybdenum, manganese, titanium, tungsten copper, nickel, gold, silver, alloys thereof, and combinations thereof.

[00101] Some embodiments further include contacting each of the two, opposing metallized pellet ends with different aluminum nitride ceramic substrates, each ceramic substrate including conductors; and heating to form a thermoelectric module.

BRIEF DESCRIPTION OF THE FIGURES

[00102] The invention may be better understood with reference to the following figures and description.

[00103] FIG. 1A represents a thermoelectric pellet.

[00104] FIG. IB provides a SEM image of the larger angular shaped particulate bodies tapering to necks.

[00105] FIG. 2A represents an assembled thermoelectric module.

[00106] FIG. 2B represents an exploded view of an alternate thermoelectric module where in addition to the first and second substrates, intermediate substrates are present.

[00107] FIG. 3 A represents a top view of a thermoelectric module with the intermediate substrates not shown.

[00108] FIG. 3B is the side view of the thermoelectric module along cut line 5.

[00109] FIG. 3C represents one construction of the thermoelectric module having alternating N- and P-type semiconductor pellets.

[00110] FIG. 4A represents a method of making doped silicon metal particulates suitable for forming a thermoelectric pellet. [00111] FIG. 4B represents a settling method of removing undesirable “fines” from the doped silicon metal particulates after milling.

[00112] FIG. 5 A represents a method of forming a thermoelectric pellet with an organic lubricant.

[00113] FIG. 5B represents a method of forming a thermoelectric pellet with a carbonbased binder.

[00114] FIG. 6 represents a cross-section of angular shaped particulate bodies coated with a 15 nm silver coating.

DETAILED DESCRIPTION

[00115] Other than a high thermal conductivity of 149 W/m*K, silicon metal is an attractive material for making thermoelectric materials. By sintering at low temperature under a reducing atmosphere compressed doped silicon metal particulates with the fines removed, thermoelectric materials having structures of increased physical complexity including larger bodies and smaller necks are formed. Smaller average diameter particulates of doped silicon metal may be layered between coarser particulates of doped silicon metal and pressed to form pellets, which are then sintered at low temperature to form a thermoelectric pellet having increased physical complexity. The opposing ends of the resulting thermoelectric pellet may then be metallized and incorporated between substrates to form a thermoelectric module.

[00116] The described thermoelectric materials can provide high electrical conductivity while providing very low thermal conductivity. For instance, when a conductor’s structure has a porous structure where the nano or micron dimensioned structures are “necked” with connection dimensions less than 2n/Ki: where Kr is the fermi wave vector, then Ohm’s law no longer applies, and electrical conduction is nearly eliminated. Connection dimensions above the 2n/Kf threshold provide electrical conductivity. For silicon, this dimension is about 8 nanometers (nm).

[00117] The connection dimensions required for a phonon, and thus thermal conductivity, are much larger, albeit temperature dependent. For silicon at room temperature, connection dimensions of approximately 200 nm are required, while at 500 degrees Centigrade, connection dimensions of approximately 80 nm are required. Thus, between the smallest connection dimension where electrical conductivity begins and the largest connection dimension where photons begin to freely pass, a window exists where a material can effectively “decouple” the electrical and thermal properties. For example, at temperatures of 500 degrees Centigrade and below, silicon can decouple electrical and thermal properties if the silicon includes connection dimensions from approximately 8 to 80 nanometers.

[00118] So we have a system and the factors are:

[00119] Prerequisite is ability to have a large flowing pipeline for fermions out of the phonon traps. For us now this is 25 nm of silver or nickel on the rough equiaxed rough grains. At millions of Siemens/meter we have a far bigger pipe than the phonons going in. So in terms of figure of merit and efficiency, it is not a factor at this level. This is desired.

[00120] We need a high Seebeck Coefficient. So, silicon doped to 10^16thfor phosphorous (negative semiconductor bias) and boron (positive semiconductor bias) will give us about 400 microvolts per degree kelvin. (We would note that most of the literature gives silicon an optimal value of 440 microvolts per degree kelvin. Seebeck Coefficient in silicon is purity dependent. We have measured 1300 microvolts per degree kelvin in 11 nines pure silicon.)

[00121] We need a phonon trap. Our nanometer and micron sized silicon grains are joined by sintered necks of amorphous and disordered silicon, so very low kappa and very low sigma. The silicon itself has a very high kappa, 149 W/mK, so heat will flow into these grains and given 70% or more is facing a rough surface into air and the necks are amorphous and disordered, once phonons take residence in the silicon grains, they are trapped there. We are trapping bosons, which unlike fermions, electrons and protons etc, do not follow the Pauli Exclusion Rule. Flux can grow and intensify and as the waves bounce around in the grain they find each other and experience cresting energy waves and achieve energy levels to make electrons.

[00122] We need a harness to remove electrons, but not phonons. The quantum size effect for electrons is 4-7 nanometers. Once you reach 12 nm, electrons flow freely. Phonons need a mean free path of between 120 and 200 nm dependent upon temperature. At 25 nm silver or nickel on rounded rough surface, Kappa sub e and Kappa sub p are both very limited, probably limited by 97% or more.

[00123] We need pathways to bring heat flux into place, measured by kW/m², so volume is important. So the more volume we have, the more amperage we will make.

[00124] And we need an insulated pathway to move optimal heat flux into the grains. Air in the porosity will do this effectively, as will the porous structure of silicon and amorphous necks. Once the phonon is in the grain, it is in a phonon trap.

[00125] Voltage is to electricity what temperature is to heat. So the more legs we have the more voltage we produce. So we need the proper amount of legs to accumulate in series the voltage we desire. So if we want 12 volts and we are running 400 microvolts, 250 legs will make .1 volts. 120 of these will give 12 volts for each degree. But if we operate at 700 kelvin, then that single 250 leg module at 400 microvolts will provide 250 times (each leg) .0004 (400 microvolts) times 700 (degrees kelvin, so about 400 C), or 70 volts.

[00126] So we have a TEMat, a thermoelectric material, that operates within a thermoelectric system, whose elements include:

[00127] Relatively pure silicon doped to 10^16th with phosphorous and boron respectively.

[00128] Grains of such silicon milled without oxidation to nm and micron size and equiaxed but rough shapes;

[00129] Such grains joined by sintering at temps significantly below the melting point of silicon (1414 to 1417 C) such that the grains are bonded together with amorphous and disordered silicon necks such that the density of the finished sintered object is about 1.35 gram/cc, or about 58% of the specific density of silicon.

[00130] A thin plating of a conductive material such that we form a conductive harness on the structure with very high electrical conductivity but very low thermal conductivity.

This is 15-30 nm now in our case silver or nickel. We like nickel for higher temps since it will not react or diffuse into the silicon as silver will at temps above about 450 C. [00131] A reticulated structure of porosity where air can carry heat to the silicon grains.

[00132] An interposer of tungsten brazed on either side to protect the porous structure from CTE mismatches where the heat sinks on either side are likely to be materials such as aluminum and copper with CTE values much higher than silicon’s CTE of about 3.6 ppm.

[00133] We believe we want to make larger taller legs so to increase the volume, thereby increasing the heat flux capacity which should optimize the amperage we can create and extract.

[00134] So if one has been using the ZT figure of merit formula, one would be “turning the wrong knobs” so to speak. One would be trying to increase the electrical conductivity of the TEMat, which would diminish the Seebeck Coefficient. One would be trying to decrease the thermal conductivity, which would reduce the thermal flux needed. One would be looking at electrical conductivity as a knob to turn and factor with Seebeck and Temperature, on which it has no effect.

THE PELTIER EFFECT

[00135] The Peltier effect states that an electric current flows through a circuit comprising dissimilar conductors will take thermal energy absorbed from one junction, and discharge that thermal energy at the other junction. Thus this flow will make the first cooler and the latter hotter. In this case a thermal gradient develops from the flowing current, making the Peltier effect inverse of the Seebeck effect. However, as in the Seebeck dynamics, a large delta T is not necessarily our friend. Here is an example of what Peltier was playing with in 1834. The Peltier effect can be verified experimentally by using the following setup:

[00136] As shown, two pieces of copper wire are connected to the two terminals of a battery. These two pieces are then interconnected with the help of a bismuth wire, which completes the setup. [00137] It is observed that when the circuit is closed, as described above, temperature gradient as predicted by the Peltier effect develops. At the junction where current passes from copper to bismuth, the temperature rises, while at the junction where current passes from bismuth to copper, the temperature drops.

[00138] So in this case we are cooling one side and heating the other. So if QC is the rate of cooling in watts, and QH is the rate of heating in watts, then I is the current flowing through the closed circuit:

QC or QH = p x I

[00139] Where is the differential Peltier coefficient difference between the two materials A and B in volts.

[00140] The Peltier Coefficient is key to understanding Peltier performance. Q = (Ila - IIB) * I, where Ila and lib are the respective Peltier Coefficients of the two conductors or semiconductors, and I is the current passing from Ila to lib. This is the difference described above, a difference in voltage.

[00141] The Peltier effect occurs due to the fact that, the average energy of the electrons involved in the transfer of electric current is different for different conductors. It is dependent on several factors, including the energy spectrum of the electrons, their concentration in the conductor, and their scattering under the influence of applied voltage.

[00142] At the junction of two dissimilar conductors, the electrons pass from one conductor to another. Depending upon the direction of flow of electric charge, these electrons will either transfer their excess energy to the surrounding atoms or absorb energy from them. As such, in the former, heat is dissipated, while in the latter, it is absorbed.

[00143] The main advantage of the Peltier effect is that it allows us to build cooling/heating devices that don’t have any moving parts, and therefore, are much less likely to fail as compared to conventional coolers and heaters. They also require almost no maintenance.

[00144] Peltier devices are silent in their operation and can theoretically achieve temperatures as low as -80°C (-176°F). [00145] The Peltier effect can be employed effectively at the microscopic level, where conventional cooling methods would not work.

[00146] When a direct current flow through a Peltier device, heat passes from one side of the device to another, allowing it to act as a heater or cooler. All Peltier devices function in this manner, by transferring heat from one side of the device to another

[00147] Peltier thermoelectric performance is a function a number of variables and factors:

[00148] Ambient temperature,

[00149] Efficiency of both the hot and cold side heat exchangers/heat sinks performance,

[00150] The thermal flux created at the junction with respect to the thermal load,

[00151] The design and geometry of the actual TEMat elements, for instance we believe that 5 mm high “blades” as thin as 500 microns and long could be optimal,

[00152] Seebeck Coefficient,

[00153] Electrical resistivity

[00154] Thermal conductivity

[00155] The amount of heat that can be moved is proportional to the current and time.

[00156] How delta T is managed, low delta T limits the bias of heat moving from the hot side to the cold side. Also, low delta T means we are moving heat flux efficiently from one side to the other.

[00157] {\displaystyle Q=PIt}So now to details:

[00158] About the Peltier Coefficient, which is the reverse path of the Seebeck Coefficient for silicon:

[00159] If not doped, silicon has a natural negative bias in terms of the Peltier Coefficient, as shown above. [00160] One can imagine that thermal conductivity will be a factor without current, but not with current.

[00161] So Q will equal P i t, where P is the Peltier coefficient, I is the current, and t is the time. The Peltier coefficient depends on temperature and the materials the cooler is made of. For instance, in the case of silicon higher temperature is not a good thing.

[00162] In the case of higher temperature, the counter flow of hot to cold are going to be a factor of:

[00163] According to Ohm's law, a Peltier module will produce waste heat itself, where R is the resistance. In our case resistance is very low, so this is not a factor. We are running the current to the active material through a harness that has many millions of S/m conductivity, so resistance is again negligible.

[00164] Heat will also move naturally from the hot side to the cool side by thermal conduction, so while we are moving heat flux from the cold side to the hot side, the natural thermal conduction will rise in effect as the temperature difference grows. So we want to keep delta T and T itself as low as possible.

[00165] If we do not control delta T and T itself the result is that the heat we are transferring from the cold to the hot side drops as the temperature difference grows, and the module becomes less efficient. There comes a temperature difference when the waste heat and heat moving back overcomes the moved heat, and the module starts to heat the cool side instead of cooling it further.

[00166] Another issue with performance is a direct consequence of one of their advantages: being small. This means that if the TEMat is very thin, then the hot side and the cool side are very close to each other (as few as one millimeter in current TEMat coolers), making it easier for the heat to go back to the cool side, and harder to insulate the hot and cool side from each other. In our case we aim for 5 mm, with thin blades and we aim to remove the heat from the side of the blades as soon as possible to limit delta T and T itself.

[00167] So it seems that the dynamics of the Peltier device is different from the Seebeck device in that in the phonons move through thermal conduction through the holes and electrons in the doping. In the case of the Peltier device, they are trying to move naturally through thermal conduction from the hot to the cold, but the Peltier function is moving the phonons through the doped holes and electrons towards the bias of the current which is designed to move phonons to one side and cool the other. In both cases low resistivity and high coefficients are key to performance along with device design to optimize moving of thermal flux and minimizing delta T.

THE THOMPSON COEFFICIENT AND EFFECT

[00168] Of course, the Seebeck and Peltier Coefficients are very temperature dependent in most materials, especially silicon. In silicon temperature increases the coefficients in silicon but the natural bias of thermal flux to migrate through thermal conduction from the hot to the cold is in conflict. So through a cross section, one would have to construct a complex differential equation to model the TEMat effect profile through a cross section.

[00169] Since the Seebeck coefficient is temperature dependent, where we have a spatial gradient in temperature, which we will always have with such low kappa, and this will result in a gradient in the Seebeck coefficient. If a current is driven through this gradient, then a continuous version of the Peltier effect will also occur. This is the Thomson effect was predicted and later observed in 1851 by Lord Kelvin (William Thomson). The Thomson effect describes the heating or cooling of a current-carrying conductor with a temperature gradient.

[00170] If a current density J is passed through a homogeneous conductor, the Thomson effect predicts a heat production rate per unit volume as: q = -kJ * Delta T

[00171] where delta t is the temperature gradient, and K is the Thomson coefficient. The Thomson coefficient is related to the Seebeck coefficient as:

K = T(dS/dT){\displaystyle {\mathcal {K}}=T{\tfrac {dS} {dT}}}.

[00172] This equation does not include Joule heating and ordinary thermal conductivity which we design to minimize with high Sigma and low delta T. [00173] Lord Kelvin identified relationships between the three coefficients, implying that the Thomson, Peltier, and Seebeck effects are different manifestations of the same dynamic, most strongly characterized by the Seebeck coefficient).

[00174] The first Thomson relation is

K = (dII/dT)-S

[00175] where T is the absolute temperature, K is the Thomson coefficient, II is the Peltier coefficient, and S is the Seebeck coefficient.

[00176] The second Thomson relation is

II = TS

[00177] where II is the Peltier Coefficient, T is the absolute temperature and S is the Seebeck Coefficient.

[00178] The Thomson coefficient is the only one of the three coefficients, Thomson, Peltier and Seebeck that can be directly measured for individual materials. The Peltier and Seebeck coefficients can only be easily determined for pairs of materials; hence, it is difficult to find values of absolute Seebeck or Peltier coefficients for an individual material.

[00179] As we can see from the Thomson relations, low delta T, low electrical resistivity and high coefficients are important to Peltier performance. Kappa by itself does not seem to be a big factor other than natural thermal conductivity fighting the bias of the semiconductors. In the case of the generator, natural thermal conductivity bias in the devices favor performance, and high temp should be a good thing. In the case of a cooler, natural thermal conductance is fighting the device and low temp and low delta T are important.

[00180] In all three cases, the original equation for performance exemplified by the ZT equation, led us in the wrong direction and had us turning the wrong knobs. Here is a summary of what we have learned:

[00181] Seebeck and Sigma are inversely interdependent.

[00182] Low thermal conductivity results in low thermal flux and loss of performance. [00183] High heat flux produces high cooler COP.

[00184] Kappa is an artifact, if designed right, of efficient phonon trapping in phonon wells with PN junctions at or near the surface.

[00185] The PN junction is highly conductive if undepleted at low doping levels.

[00186] Sigma is about connecting the P and N junctions at the surface of the P and N legs and about harvesting electrons at the event horizon of the functional PN junction.

[00187] So we need a 10^16th doped silicon for optimizing Seebeck with P/N junction functionality, nano structures to provide phonon wells and an electrically conductive surface able to perfect the PN junction while harvesting electrons as well.

[00188] So work is equal to Heat at High temperature minus Heat rejected at Low temperature. Therefore, this expression becomes: (Q Hot = Heat input at high temperature and Q coia= Heat rejected at low temperature.)

Efficiency = (Q Hot - Q Cold Q Hot)/Q Hot

[00189] Where, Q Hot = Heat input at high temperature and Q Cold = Heat rejected at low temperature.

T|'(%) = 1-(Q Cold\Q Hot) x 100

[00190] Camot showed that the ratio of Q High T to Q Low T must be the same as the ratio of temperatures of high temperature heat and the rejected low temperature heat. So this equation, also called Camot Efficiency, can be simplified as: i]'(%) = 1- (T ColdVT Hot) x 100%

[00191] Note: Unlike the earlier equations, the positions of T cold and Thot are reversed.

[00192] So lets start with our understanding of how our TEMat works and how it is different and similar to and from a solar cell: We have observed and concluded that flux is more important than Delta T, that Delta T is an artifact of a system that traps phonons into a phonon well. (From: Kyle Pietrzyk, Brandon Ohara, Thomas Watson, Madison Gee, Daniel Avalos, Hohyun Lee 2016 Thermoelectric module design strategy for solid-state refrigeration. ScienceDirect Energy j oumal http://dx.doi.Org/10.1016/j.energy.2016.08.058)

[00193] We have also showed and have data correlating leg length, flux and COP.

[00194] So we would therefore disagree with the famous Fairbanks Curve in that Delta

T would reduce efficiency, but thermal flux would increase ZT.

[00195] The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.

[00196] The total entropy of a system and its surroundings can remain constant in ideal cases where the system is in thermodynamic equilibrium or is undergoing a (fictive) reversible process. In all processes that occur, including spontaneous processes, the total entropy of the system and its surroundings increases, and the process is irreversible in the thermodynamic sense. The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past.

[00197] Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical mechanics, classical or quantum, explains the microscopic origin of the law.

[00198] The second law has been expressed in many ways. Its first formulation is credited to the French scientist Sadi Camot, who in 1824 showed that there is an upper limit to the efficiency of conversion of heat to work in a heat engine. This aspect of the second law is often named after Camot.

[00199] The Camot cycle and efficiency defines the upper bound of the possible work output and the efficiency of any classical thermodynamic system. Any machine or process that converts heat to work and is claimed to produce an efficiency greater than the Camot efficiency is not viable because it violates the second law of thermodynamics. The efficiency of devices such as photovoltaic cells requires an analysis from the standpoint of quantum mechanics as well as thermodynamics since such a large portion of the light is converted to heat. Carnot's theorem (1824) is a principle that limits the maximum efficiency for any possible engine. The efficiency solely depends on the temperature difference between the hot and cold thermal reservoirs. Carnot's theorem states:

[00200] All irreversible heat engines between two heat reservoirs are less efficient than a Carnot engine operating between the same reservoirs.

[00201] All reversible heat engines between two heat reservoirs are equally efficient with a Camot engine operating between the same reservoirs.

[00202] In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Camot, however, further postulated that some caloric is lost, not being converted to mechanical work. Hence, no real heat engine could realize the Camot cycle's reversibility and was condemned to be less efficient.

[00203] Equilibrium and entropy modeling is based on isolated system where the processes are reversable. That is how they cycle towards equilibrium. Of course, our TEMat is reversable, where we put heat, we can extract and replace it. With efficiency losses.

[00204] Then we have dwell times based on energy:

[00205] Light travels at 300,000 km/sec in a vacuum

[00206] Signals of flowing electrons in copper wire flow at between .64 and .8 this speed

[00207] Phonons travel at 343 meters per second in air, at 8433 m/sec in silicon, where the electrons are flowing out or in at perhaps 240,000 meters per second.

[00208] So we know that the phonons are moving into and through the silicon at about 8433 m/sec, but we are trapping them. How fast are the electrons moving out to ground. This depends a lot on doping level purity and temperature: For example:

[00209] Electron mobility versus temperature for different doping levels shows that electron mobility favors higher purity in silicon. Seebeck voltage and electron mobility are closely related. Seebeck Coefficient rises in silicon as purity rises, just as electron mobility rises with purity. We conclude that Seebeck is independent of sigma:

[00210] High purity Si (Nd< 10-12 cm-3); time-of-flight technique (Canali et al. [1973])

[00211] High purity Si (Nd< 4 10-13 cm-3): Hall effect (Norton et al. [1973])

[00212] Nd= 1.75 1016 cm-3; Na = 1.48 1015 cm-3; Hall effect (Morin and Maita

[1954]).

[00213] Nd= 1.3 1017 cm-3; Na = 2.2 - 1015 cm-3; Hall effect (Morin and Maita [1954]).

[00214] Here we can see why our amorphous silicon necks were so intractable with respect to electrical conductivity.

[00215] Then there is the matter of dimensionality. The solar cell suffers very large losses due to the ratio of minority carriers and recombination’s as it travels through the silicon. Red light goes deeper than blue, blue is lost at the surface. These are yield losses unrelated to Carnot models. So with dimensionality there is density of state and energy levels. Clearly a bulk material has desirable behaviors, as do quantum dots. But quantum dots are typically 20 to about 150 nm in size but very thin, and we are cores of silicon in the hundreds of nm. Wires are usually less than 10 nm and wells are 10 nm thick. So only the bulk material will conduct electrons well. We are a bulk material but we are playing in the domain of dots, wires and wells at the same time. So the solar cell has many loss characteristics such as reflectance at the surface, conversion to heat, wavelength dependent losses, recombination losses. All these limit efficiency, not so much Delta T.

[00216] But at the same time, where are our losses, and what is the limit on efficiency based on Delta T? I have already waded into these waters on efficiency and Carnot by critiquing the Angrist Model. There exist several glaring issues with the Angrist Model (and subsequent models): (1) hot and cold side temperatures do not depend on input current; (2) maximum temperature difference is “achieved” when heat flux is zero; and (3) we care about refrigerator temperature, not cold side temperature. [00217] Clearly, we want a low Delta T and a high flux. And our model and data suggest that COP and Heat Flux suffer from large Delta T.

[00218] For the most part our designs are based on really high levels of insulation, on the generator we are looking to insulate with porous fused silicon which will have a kappa of about .2 W/mK. So thermal losses will be negligible.

[00219] On the Cooler we want to move heat from the cold to the hot side, we are using electrons as carriers to do this, but as soon as we grab a phonon we want to move it out asap, which is why when on the generators side, we want to be thin, on the cooler side we want to be thick, with high “b” factor, leg length and fill factor:

[00220] So a high Delta T indicates an impairment of heat flux. A low Delta T moves towards an equilibrium where the amount of heat moving through is high, the intensity is high, but the delta T is low.

[00221] So what are the factors that limit or control efficiency in a TEMat? Some observations: (a) We have measured the Seebeck Coefficient of silicon at doping levels in each increment between 10^16th and 10^20th doping with boron and phosphorus. We have measured Seebeck Coefficients for silicon from metallic 98.5% pure through 11 nines purity. So at room temp 10^20thwe are in the range of 60 microvolts per degree K. At 1016^th we are at about 400 microvolts/K. At 11 nines purity it is 1400 microvolts per degree K. Here is a chart of some of the direct measurements we have made:

TABLE 1

[00222] So we conclude Seebeck is independent from Sigma. But we also observe that in a solar cell, the efficiency and output of the solar cell is relatively independent of the thickness of the solar cell’s silicon substrate. Typically the wafer is doped with boron and phosphorous is doped in a very thin layer on the surface of the wafer, and the P/N junction is then a thin layer. The P/N junction is highly electrically conductive and it is in this layer that all the quantum physics takes place. So solar cells out put is a function of surface area. We will find that the same is true for a thermoelectric cell. However, we do not have the P and N, in our example the boron and phosphorous doped silicon in direct interface with each other. Therefore, the electrical conductivity between the conductive surface of the two must be at the same level as that found in the P/N junction as in the solar cell, which is in the range of 60,000 to 100,000 S/m, or even much higher in order to complete an effective P/N junction.

[00223] As we all know, the formula is Seebeck squared times sigma/kappa times absolute temperature. We are converting phonons to electrons in this integrated system. Not only is it not isolated, it can be said to be part of the universe. And the entropy of an electron moving through a high conductivity conductor is enormously lower than the phonon bouncing around all over the place. I can have an air conditioner move the entropy of a room down, but of course this is not an isolated system, there are relatively unlimited inputs and outputs possible.

[00224] So are these factors global or local, both or neither:

[00225] Clearly Seebeck is local and independent of sigma. [00226] Temperature plays here in two regards outside of kappa: We multiply the phrase “Seebeck squared times sigma/kappa” by absolute temperature not delta T. And we produce microvolts where the absolute temperature is factored per operating degree kelvin.

[00227] Nano sized crystalline silicon is highly strained. Strained crystalline silicon presents very different thermal conductivity than unstrained crystalline silicon. So the ability to trap phonons with our structures, necks and strained material combine to show low thermal conductivity and highly efficient powerful phonon trapping and hence high thermal flux:

[00228] So low thermal conductivity is dividing the phrase “Seebeck squared times sigma”. What is low thermal conductivity doing? Is it creating a high delta T, or is it trapping phonons? It does both but the active agent here are phonons so trapping them is clearly a good thing.

[00229] The power to trap phonons while conducting electrons enhances the thermal flux in the local grains. In Ab Initio Study of Coupling between Electronic and Phononic Contribution to Stress-Dependent Thermal Conductivity of Au, Si, and SiC Vikas Samvedi and Vikas Tomar DOI: 10.1061/(ASCE)NM.2153-5477.0000046. 2012 American Society of Civil Engineers conclude:

[00230] “The strain dependent thermal conduction data, however, point to an interesting trend. As shown, increased electronic mobility in Au as a function of increase in temperature leads to reduction in electronic thermal conductivity contribution. Straining does not contribute significantly to the corresponding change in thermal conductivity values because diffused electron mobility is not affected by strain. However, in the case of Si and SiC the contribution of strain is significant. Invariably, the straining leads to reduction in electronic component in all materials examined.”

[00231] Phonons are dominant carriers of heat transport in Si and SiC, with such contribution reducing with increase in temperature and increase in strain. So if we separate sigma from Seebeck, and nano structure the conductor with a thin nano sized layer on our silicon, thick enough to conduct electrons, thin enough to block phonons, we can have very high Seebeck and Sigma at the same time. If we nano structure, we can trap phonons. Where in this model is there a factor operating as pressure, volume, Delta T or even entropy to limit efficiency? [00232] We measure losses in transmitting electricity through wires and photons through optical fiber by dividing the value at the destination end by the value at the sending end times 100 to get a percentage. The efficiencies are subject to many variables. For instance, wavelength, type of light (H.E. 1,1) voltage (HDVC) conductor sizes, diameters, types, bends and so on. But these losses are generally very low. Pressure, volume and delta T are not variables for the most part. So what are the losses in a solid state thermoelectric cell?

[00233] We can insulate so that nearly no heat is lost in the generator.

[00234] We can insulate so nearly no heat is lost on the cooler to the cold side.

[00235] We can engineer legs for the cooler that move the heat out very quickly on the hot side.

[00236] We can engineer legs for the generator so that the heat flux is high.

[00237] In our case we can use silicon at perhaps 1000 K in our system. But we are not a heat engine. There is nothing mechanical going on.

[00238] Here is a sample of conversion efficiency in a heat engine based on temperature:

[00239] What would be our losses? Well at 1000 K with 10^17th doping we would have a Seebeck Coefficient of about 700 microvolts per degree kelvin. So square that and multiply it by sigma of 5 million divide that by .4 W/mK and multiply all that by 1000. A number too stunning to seriously contemplate without a lot of doubts. But would it be as efficient as this heat engine described above? The models are different. We are subject to the dynamics of delta T and pressure and volume as we move heat into and out of our heat sinks on either side of the thermoelectric device. But we are not subject to these dynamics within the thermoelectric device itself. Unlike a solar cell, we do not have wavelength dependent losses as we penetrate the active materials. We have losses at the surfaces, but we have more blunt powerful tools to channel the heat. Unlike the photon, in the generator we are aided by entropy: the heat, the phonons want to go from the hot to cold side. In the case of the cooler we are dragging phonons with the most powerful engines, electrons going to ground. [00240] The power of these electrons going to ground is clearly exhibited by the immense leverage thermal flux provides in efficiency and in the flux resistivity curves. (See Kyle Pietrzyk, Brandon Ohara, Thomas Watson, Madison Gee, Daniel Avalos, Hohyun Lee 2016 Thermoelectric module design strategy for solid-state refrigeration. ScienceDirect Energy journal http://dx.doi.Org/10.1016/j.energy.2016.08.058.)

[00241] If we apply the same to a cooler, would the Camot model apply? Well it has to apply to the movement of phonons from one side to the other in conflict with the laws of entropy, moving heat from cold to hot with electrons. But if there is a free flow of phonons in a large space with lots of air flow, it would be very efficient as the Delta T would be extremely high.

[00242] But would it apply to the interaction of the electrons dragging phonons in the solid-state part of this device?

[00243] No pressure, dragging with the enormous power of the electron. No volume, we are actually densifying the system by intensifying the flux, the population of phonons.

[00244] We observe:

[00245] Seebeck and Sigma are independent of each other, one is local, one is a global network and enabling with electrical conductivity the function of the P/N junction. We want to optimize each in its own domain. We have proven this in several perspectives, most dramatically by measuring actual Seebeck micro voltage per degree kelvin in silicon from 11 nines pure to 98.5% pure and at a variety of doping levels. This corresponds to work done in the same regard with electron mobility.

[00246] If one tries to optimize sigma and Seebeck in the same domain, for instance in the active material, increasing Sigma will decrease Seebeck and vice versa. The only way to optimize the tremendous capacity of silicon in terms of Seebeck voltage is to handle Sigma separately. We have the fact that the electron mobility of silicon at higher purity, enough doping to give a P and N bias, but not enough to materially reduce Silicon’s Seebeck potential, along with the fact that an electrically conductive nano layer on the rough surface of our silicon nano particles if more than 8 nm and less than about 40 nm, will conduct electrons but phonons will be a drag on electrons and will not easily conduct. So a thin conductive layer, thick enough for electrons, too thin for phonons, will give the full power of the electronic portion of conductivity but the phononic portion will be a drag.

[00247] Heat flux means high intensity of phonons, which results in higher efficiency, demonstrated by higher COP. High density of phonons is accomplished in several regards, including temperature and heat flow rates and locations.

[00248] The Seebeck conversion of phonons to electrons is a semiconductor function and is not driven by delta T, pressure or volume. It does not fit into the Carnot models. This means kappa is a way of thinking of a measurement that can help create high heat flux, but does not mean that Delta T is desirable, it is not, low delta T is desirable as that is necessary for high heat flux. Kappa is readily controlled by dimensionality, which we have demonstrated. Sigma is a way of harvesting electrons from our quantum wells, where the nano sizes of our quantum wells is so small that the mean electron free path gets those electrons to ground quickly in short distances with small losses

[00249] FIG. 1 A represents a sintered thermoelectric pellet 100. The pellet 100 includes a thermoelectric material 110 having increased physical 15 complexity. Above and below the thermoelectric material 110 is a top layer 120 and a bottom layer 130, respectively. The top layer 120 forms a top end 125, while the bottom layer 130 forms a bottom end 135.

[00250] The thermoelectric material 110 having increased physical complexity is formed by low temperature sintering with substantially reduced oxygen contamination. The thermoelectric material 110 includes doped silicon metal particulates having larger “bodies” and smaller “necks” protruding from and connecting the larger bodies after sintering.

[00251] The larger bodies are generally angular in shape providing larger angular shaped particulate bodies and have a D50 by volume in the range of 3 microns and a D50 by number in the range of 700 nm. Thus, body diameter D50 may be 500 nm to 900 nanometers, preferably 600 nm to 850 nanometers, and more preferably 650 nm to 800 nanometers. In view of these D50’s, the particulate average diameter distribution may be from 200 nm to 4.5 microns. The larger angular shaped particulate bodies preferably have a surface area of 30 to 40, more preferably 33 to 37, square meters per gram. The larger angular shaped particulate bodies taper or “neck” down to form protrusions extending from one larger body to another larger body. The smallest diameter of the necks is from 8 nm to 200 nm, preferably from 10 nm to 150 nm, and more preferably from 12 nm to 80 nm. This framework of larger angular shaped particulate bodies connected by smaller necks provides increased physical complexity to the sintered thermoelectric material 110.

[00252] FIG. IB provides a SEM image of the larger angular shaped particulate bodies tapering to necks having smallest diameter necks from 8 nm to 200 nm. The image establishes the angular shape of the larger particulate bodies and shows necks ranging from approximately 98 nm to 376 nm formed between the larger angular shaped particulate bodies. The image also reveals the porosity of the thermoelectric material 110.

[00253] FIG. 1C provides a SEM image of the larger angular shaped particulate bodies tapering to necks having smallest diameter necks from 8 nm to 200 nm. The image establishes the angular shape of the larger particulate bodies and shows necks ranging from approximately 48 nm to 106 nm formed between the larger angular shaped particulate bodies. The image also reveals the porosity of the thermoelectric material 110.

[00254] The preferred neck diameters between adjacent larger angular shaped particulate bodies are believed to create phonon drag sites within the thermoelectric material that allow electrons to pass but slow down the movement of phonons. By slowing the phonons in relation to the electrons, more phonons may be converted to electrons. In this way, electrical conductivity is believed enhanced, while thermal conductivity is believed reduced.

[00255] The reduction in thermal conductivity is temperature dependent and is believed attributable to the temperature dependency of phonon wavelengths. A phonon at 23° C has a wavelength of about 200 nm, while a phonon at 500° C has a wavelength of about 80 nm. A 100 nm neck between larger angular shaped particulate bodies would significantly slow phonon transfer at 23 degrees Centigrade as the wavelength of the phonon is nearly twice as large as can pass through the physical constraints imposed by the neck. Conversely, the same 100 nm neck would lose most of the ability to slow phonons at 500° C because the neck is now physically larger than the wavelength of the phonons (80 nm) at the higher 500° C temperature. In addition the large ratio of silicon porosity exposed to air creates nearly perfect phonon confinement. [00256] An insight into the thermal conductivity in a porous object includes the idea that a phonon will tend to reflect at the intersection of silicon and air rather than launch from the silicon into the air. This means that the degree of porosity can have a very powerful effect on thermal conductivity as important as the neck size although smaller neck size and higher porosity are interacting variables.

[00257] Thermal and electrical conductivity are global properties of the thermoelectric material. Thermal conductivity is a measure of how well the material transfers the heat that brings phonons to the phonon drag sites, and electrical conductivity is a measure of how well the material transfers electrons away from the phonon drag sites. The thermal and electrical conductivity of the thermoelectric material is the same whether the thermoelectric material is converting electricity to a temperature differential or a temperature differential into electricity. The more phonon drag sites per unit volume of the thermoelectric material, the more efficient the thermoelectric material should be at interconverting heat and electricity. However, the thermoelectric material also must be able to efficiently transfer heat and electricity from its exterior surfaces to and from the phonon drag sites to function in a useful thermoelectric device. This means that an optimal thermoelectric device should be able to decouple the process parameters in constructing the structures so to optimize all three properties at the same time. If doping the silicon is engineered not to conduct electrons but to create the negative and positive semiconductor device so to make N and P junctions, then a lower doping level will also allow much higher Seebeck Coefficients.

[00258] In FIG. 1A, the sintered thermoelectric material 110 is formed from silicon metal particulates doped to increase electrical conductivity through the particulates. N- or fltype dopants may be used to dope the silicon metal, with P-type dopants from column III of the periodic table being preferred, and boron being the presently preferred P-type dopant. Preferred N-type dopants from column V of the periodic table are phosphorous and arsenic. Preferably, the silicon metal particulates may be doped at a level from 10^15th to 10^19th/cm³. When the P-type dopant boron is used, from 100 parts-per-million (ppm) to 1000 ppm dopant may be preferred. When the N-type dopant phosphorous is used, from 100 ppm to 1200 ppm dopant may be preferred.

[00259] This doping is believed to contribute to providing the N and P type electrical semiconductor bias and conductivity through the electron mean path to the surface of the porous silicon so to allow the electrons generated by the Seebeck or Peltier effect to reach the boundary conditions where the porosity interfaces with air.

[00260] Then we put a nano sized metal coating on the surface of the porosity by thermal and or chemical decomposition from a gas or liquid. Examples would include decomposition of silver from silver nitrate, or decomposition of nickel from tetracarbonylnickel(O) (Ni(CO)4. There are many metals and metal alloys that can be applied in these and other means to lay down an electrically conductive layer, which due to the roughness of the silicon surfaces and the thinness of the layer will not conduct phonons.

[00261] So for instance have formed a thin silver layer, in the range of 10 to 30 nanometers, upon the surface of our silicon nano structured thermoelectric pellets by decomposition of silver nitrate. Our intention was to create a secondary structure upon the surface that would convey electrons but not phonons.

[00262] In doing so we have measured pellets thermoelectric properties as follows:

[00263] Sigma: 120,000 Siemens per meter up to 20,000,000 Siemens per meter while maintainin the intrinsic pre plating Seebeck in the range of 180 to 220 microvolts per degree Kelvin

[00264] Inferred thermal conductivity in the range of .5 Watts/meter squared.

[00265] Porosity before silver plating at 1.35 grams/cubic centimeter 42% Porosity after silver plating 40%.

[00266] In the world of thermoelectric it has been an accepted almost biblical truth that electrical, thermal and Seebeck conductivity cannot be disassociated or independently manipulated. Based on much physics, much of it fairly recently published, we have observed that Seebeck was an atomically local function, based on phonon trapping which relates to thermal conductivity but which is not the same thing, that Sigma was global, based on moving electrons out but not phonons, and that in this way we could have very large sigma, very low kappa and high Seebeck at the same time. [00267] At the lowest values we have measured, after four trials so far, the ZT is (Seebeck squared) 0.00018 squared times (Sigma) 120,000 divided by (Kappa) .5 times (Temperature Kelvin) 350 for a ZT Value of 2.66 at room temperature.

[00268] Silicon brings some powerful advantages as a Thermoelectric Material (TEMat) in that somewhat uniquely, it can operate at high temperatures and as temperature rises Seebeck rises, kappa falls and sigma is flat. So at 400 C, about 700 kelvin our silicon has a Seebeck value twice that at room temperature, and of course the fractionated phrase in the Seebeck Equation is factored by the temperature kelvin, which is there 700 C at 400 C instead of 330 at room temperature. So based on these values and data we would see a ZT value of 23.33 at 400 C.

[00269] Our lab has been built and staffed for material science, not module building, though we have built up a competence for metalization, brazing, assembly, and module characterization. We believe we now understand the science we have teased out in this development, and there are two tasks ahead of us: Develop a deep and broad understanding of the silver plating process and perfect it as we modestly recognize it is unlikely we got it near to best practices in four tries.

[00270] We have put typically 14 nanometers of silver on 1.25 square meters of sintered porous silicon and the porosity dropped from 42% to 40%. This 14-nanometer silver is great at conducting electrons since it is more than 8 nm, but terrible at phonons that need 180 nm. Silver nitrate has a melting point 209.7 C and decomposes when heated above its melting point:

2 AgNO₃(l) 2 Ag(s) + O₂(g) + 2 NO₂(g)

[00271] Qualitatively, its decomposition below the melting point is negligible, but progresses quickly from around 250 °C and is totally decomposed at 440 °C. Most metal nitrates thermally decompose to the respective oxides, but silver oxide decomposes at a lower temperature than silver nitrate. Silver oxide decomposes at temperatures above 250 to 280 °C.

[00272] So at about 250 C the silver nitrate decomposes to NO₂ and AG₂O. Then above 280 C the Ag₂O decomposes to 02 and AG: the decomposition of silver nitrate in this case yields elemental silver instead of the nitrate. The thermal decomposition of silver nitrate to produce silver, nitrogen dioxide and oxygen. This reaction takes place at a temperature of 300-500 C

[00273] Solubility of Silver Nitrate in water: (Atherton Seidell, Ph.D, Solubilities of Organic and Inorganic Compounds, D. Van Nostrand Company, 1919 New York):

[00274] 122 g/100 mL (0 °C)

[00275] 170 g/100 mL (10 °C)

[00276] 256 g/100 mL (25 °C)

[00277] 373 g/100 mL (40 °C)

[00278] 912 g/100 mL (100 °C)

[00279] We have calculated that we want about 10 to 30 nm, which will conduct electrons but not phonons. Ballistic tunneling will not occur in this nano structure since the morphology of the silicon in the porous structure is tortuously complex, with enormous angles and roughness. To do so we will make a solution at the limit of about 35 C, at 80 C, and infiltrate the porous materials in minus 700 torr vacuum at 80 C for an hour, and then evacuate the remaining liquid. This we will then sinter at a few temperatures, including 300, 400 and 500 C to investigate effect of this temperature upon the performance of the silver plating.

[00280] The Bohr Radius of silicon is 4.5 nm, and quantum size effects in silicon crystalline material are widely reported in the literature to be powerful starting at about 7.5 nm and fully active below 3 nm. So, we know that if we are more than 8 nm we will conduct electrons.

[00281] Quantum effects are based on quantum confinement, and confinement in silicon with respect to the phonon as measured by thermal conductivity are reported to be very powerful starting at several hundred nanometers, very large under 200 nanometers and nearly total below about 40 nm. See page seven of J Mao et al in their article Size effect in thermoelectric materials npj Quantum Materials (2016) 1, 16028; doi:10.1038/npjquantmats.2016.28; published online 9 December 2016 published well after we started this work. Please note the recent publication date.

[00282] The use of silver oxide to bond to silicon at low temperature has been reported and is used in the semiconductor industry. Tomoki Matsuda, Kota Inami, Keita Motoyama, Tomokazu Sano & Akio Hirose Silver oxide decomposition mediated direct bonding of silicon-based materials Scientific Reports | (2018) 8:10472 | D01:10.1038/s41598-018- 28788-x. Please note the recent publication date.

[00283] Having introduced a new structure into our TEMat design and structure, a diligent due diligence must include a review of silver’s TEMat behavior to assure we are not observing an artifact of silver in terms of the 25 steady Seebeck Coefficient we are measuring.

[00284] We are finding a range of Seebeck Coefficient between 180 and 200 microvolts with sigma values as low as 80,000 S/m and 1 million S/m, something never observed or reported before.

[00285] The recent literature reports silver nano structures, less than 20 nanometers have been reported to generate 1-3 microvolts per degree kelvin. So, the 200 microvolts per degree kelvin is surely rising from the silicon. This literature survey offers these two references as evidence the Seebeck is rising from the silicon, not the silver.

[00286] Vikash Sharma and Gunadhor Singh Okram Electrical transport 10 and thermoelectric properties of silver nanoparticles 2019 :

[00287] https://www.researchgate.net/publication/335290845

[00288] Kockert, M., Kojda, D., Mitdank, R. et al. Nanometrology:

[00289] Absolute Seebeck coefficient of individual silver nanowires. Sci Rep 9, 20265

[00290] (2019). https://doi.org/10.1038/s41598-019-56602-9

[00291] The thermal conductivity of silver is 429 W/mK, but not at 14 nm or in nano structures. The electrical conductivity of silver is 63 million S/m, so long as cross section is more than 8 nm. It is. Our calculations on weight gain indicate we have a layer of about 14 to 24 nm, but “only” one million S/m, which is 1.5% of the theoretical electrical conductivity of silver. It is thought in this system that Kappa sub e is 1.5% of the total and Kappa sub P is the balance. In this case we believe the thin layer of silver is a phonon blocker and that the phonon blocking is holding up 98.5% of the electrons.

[00292] When we make nano structures, we achieve sigma in the range of 5000 S/m and ranging up to 25 to 35,000 measured at low microvolts, but not at volts or hundreds of volts we are measuring the neck conductivity not the grains themselves. We have been able to confirm the different voltage dependent domains of resistance, particularly in silicon. We believe we have been creating an amorphous oxygen rich silicon alloy in the necks which is why we have not been able to tease out higher sigma values. When we remove the oxygen, the necks do not grow, and we are too small to conduct. We have concluded it is not possible to achieve the intrinsic electrical conductivities indicated and measured by doping before milling and sintering the porous object and this is why we pivoted to this idea of a non phonon conducting highly electrically conductive thin coating.

[00293] We have measured between 400,000 and 20,000,000 S/M with the 14- nanometer silver coating, but still 200-350 microvolts per degree kelvin at doping levels of 10^19th. We believe when we reduce the doping to 10^16th we will double the Seebeck micro voltage per degree kelvin. Once the coating on the surface, a white residue of the nitrate, is removed, we believe it is consistent side to side, end to end and through the cross section. A silicon oxide layer is virtually always formed on the surface of Si-materials as a native oxide film. The decomposition of Ag2O facilitates the bonding of Ag to the Si surface creating a strong bond between the silicon and the silver.

[00294] To my knowledge of the art, the literature, and the history, it has been an accepted truth that you cannot disassociate sigma from Seebeck, not kappa from sigma. I believe we have done this, and it argues to my thesis on the local/global phenomena in thermoelectric devices.

[00295] Many metallic nanoparticles, including silicon and silver, thinner than 30 nm or smaller than 10 nm show an apparent melting-point depression where the high surface to volume ratio makes them dramatically more reactive. [00296] After sintering at about 500 C after effective infiltration by the aqueous silver nitrate we get a very small white deposit on the surfaces which we machined off but we have uniform infiltration. We are near the saturation temp, we infiltrate at about 80 C, so when we dry at lower temperature it precipitates locally uniformly and quickly.

[00297] The cross section of the bar appears to be 100% uniform. All measurements on cleaned surfaces are consistent and repeatable.

[00298] Seebeck is in the range of 180 to 210 microvolts per degree kelvin

[00299] The silver will conduct electricity and take along heat rapidly, but only kappa sub e, which is normally much smaller than kappa sub p.

[00300] So thermal conductivity will be limited. The fact we got 1 million S/m instead of 64 million S/m means there is significant electron drag from the phonons unable to transit 14 nm. So, the surface of the silicon is highly conductive of electrons and not so much for phonons. But only Kappa sub

[00301] The 14-nanometer nano structure is too small to conduct Kappa sub P.

[00302] As a result we believe we have structured a wiring harness to and from all the grains to bring in heat, create phonon wells in the silicon by phonon trapping and a highly efficient route out on this wiring harness of silver to harvest phonons processed by the Seebeck Peltier process into electrons or vice versa. The silver will heat up rapidly and the silicon will lag, so phonons will be dumped into the silicon grains.

[00303] While we measure and factor thermal conductivity in the Seebeck Equation, we perceive that the thermoelectric effect is about phonons concentrating and interacting and finding a route to ground as quanta in one way or the other, as phonons or electrons, it is about entropy.

[00304] So while the First Law of Thermodynamics teaches energy is neither created nor destroyed, it also teaches it can be transformed between forms of energy. This is sometimes known as conservation of energy.

[00305] However, heat which is traditionally considered a low-quality form of energy, because it is not readily transformed into other forms of energy. This in particular supports the Second Law of Thermodynamics which teaches that total entropy (a way of measuring unusable waste heat) is always increasing. However, the Thermoelectric effect violates the second law in this case in that the conversion of a phonon to an electron is more efficient and moves entropy down. So while the second law of thermodynamics says that entropy always increases with time, in the case of the experience of the thermoelectric effect, entropy falls. But the second law addresses isolated systems, and this is not an isolated system so we are in fact not violating the second law.

[00306] By concentrating phonons, by trapping them in the silicon grains we increase entropy as phonons which will lead to a decrease in entropy as they find a route out as electrons. As the boundaries of the silicon grains facing into silver and space powerfully contain and confine those phonons they will bounce around, encounter each other, creating energy peaks during these wave like encounters so that an electron is harvested with lower entropy and efficiently travels to ground through the silver conductive network.

[00307] When the phonons convert to electrons, within such a phonon trap, then the electrons will exit to ground on the silver surfaces and the temp will go down so there will be a flow of phonons from the hot, the silver, to the cold, the silicon, continuously.

[00308] With 40% porosity and nano structures I believe the phonon free mean pathway among the silicon grains will be too small to conduct silicon to silicon making the silicon grains phonon traps. We did see that the delta T in the Linseis dropped from 7 to 5.5 degrees K. So, it is conducting more.

[00309] That kappa is not about thermal flow, thermal flow is good, it is about phonon trapping. This system is a good phonon trap which is why we have high Seebeck and high sigma in the same object. The 40% porosity can be increased and silicon to silicon conductivity of electrons and phonons is very poor. But we have a wiring harness from side to ground, among all grains that conducts phonons in, and takes electrons out in the context of a thermo electric device which should have very high efficiency.

[00310] In addition to the increased physical complexity arising from the larger body/smaller neck connections of the doped silicon metal, forming the thermoelectric material 110, low temperature sintering is believed to allow for formation of an external conductivity network surrounding the larger body and neck connections and occupying the “pores” resulting from larger angular shaped particulate bodies being separated by the neck connections. The external conductivity network is believed to provide enhanced global electrical conductivity to the thermoelectric pellet 100.

[00311] After low temperature sintering, the necks of the doped silicon metal particulates are believed to provide local electrical conductivity, while the external conductivity network, as provided by a conductive form of the silver coating, is believed to provide enhanced global electrical conductivity to the thermoelectric material 110. The external conductivity network is believed electrically accessible to the silicon metal particulates and to the surfaces of the sintered thermoelectric material 110. Thus, the enhanced global electrical conductivity provided by the external electrical conductivity network may provide an improvement in electrical conductivity at the upper and lower interfaces, 112, 114, respectively, of the thermoelectric material 110.

[00312] Pressing is preferably performed with 2 to 18 tons of force, preferably from 4 to 15 tons of force, and more preferably from 7 to 9 tons of force. These relatively high pressing pressures are believed to assist in providing the desired electrical conductivity in the sintered thermoelectric material 110.

[00313] An organic lubricant and/or a carbon-based binder may be used as a pressing aide to provide the desired compaction of the doped silicon metal parti culates/conductive form of carbon and to prevent disintegration and/or delamination of the pressed pellet. The organic lubricant and/or carbon-based binder are preferably relatively easy to remove before low temperature sintering the resulting pellet to form the thermoelectric material 110. With appropriate tooling pressing can also be performed without binders and lubricants.

[00314] The sintered thermoelectric pellet 100 preferably has a density from 1.2 to 1.7 grams per cubic centimeter (g/cc). The density of approximately 1.4 g/cc provides a porosity of about 40% to the sintered thermoelectric pellet 100 and provides a thermal conductivity in the range of less than 0.2 W/mK. In comparison, when the sintered thermoelectric pellet 100 has a density in excess of 1.6 g/cc the thermal conductivity is in the range of 0.6 W/mK.

[00315] After sintering the silver coating is applied as described above, before metalization. From this point on the thermal processing limits will be less than the silver silicon eutectic as described above, less than 835 C. [00316] A conductive metal may then be applied to metalize the two opposing ends 125, 135 of the resulting sintered thermoelectric pellet 100. If the pellet 100 lacks the top and bottom layers 120, 130, the upper and lower interfaces 112, 114 become the opposing ends 125, 135 of the thermoelectric material 110 and may be metallized. The applied conductive metal is believed to addresses the issue of “contact resistance” that otherwise would occur due to the angular shape of the sintered silicon metal particulates at the ends of the pellets in comparison to the relatively flat surfaces of the wires, conductive traces, metal plates, and the like. Thus, the applied conductive metal is believed to provide an enhanced electrically conductive interface between the sintered thermoelectric material and the wires, conductive traces, metal plates, and the like that may be used to incorporate the sintered thermoelectric pellets into a useful thermoelectric device.

[00317] The applied conductive metal may include copper, nickel, gold, silver, alloys thereof, and combinations thereof. The conductive metal applied on the two opposing ends 125, 135 or the interfaces of the sintered thermoelectric pellet 100 may have a thickness from 200 nm to 400 nm, for example. Other thicknesses of conductive metal may be used depending on the thermoelectric device being constructed. The conductive metal may be applied to the two opposing ends 125, 135 of the sintered pellets before the pellets are incorporated into a module, or the conductive metal may be present in the substrates between which the non-metallized pellets are placed before the module assembly is fired to bond the sintered thermoelectric pellets 100 to the substrates. Preferably the thermoelectric pellets 100 are bonded to the substrates under inert atmosphere at a temperature from 120 to 780 degrees Celsius, preferably at a temperature from 230 to 420 degrees Celsius.

[00318] The conductive metal may be applied to metalize the two opposing ends 125, 135 of the sintered thermoelectric pellet 100 through electroplating, screen printing, and other methods consistent will applying a conductive metal to the silicon metal.

[00319] Instead of metallizing the two opposing ends 125, 135 of the sintered thermoelectric pellets 100 directly, the opposing metallized ends of the pellets may be formed with metalized porous glass (a “frit”). Preferably, the porous glass includes a high weight percent of the conductive metal.

[00320] For example, a glass frit that is approximately 95% by weight silver metal may be used. Such a pellet may be formed by placing a first frit in the bottom of the press, loading the thermoelectric material on the first frit, and then placing a second frit on the top of the loaded thermoelectric material before applying the pressing force. The pellet with the glass frit ends may then be low temperature sintered to join the frits to the thermoelectric material. The frits also may be applied as a wafer or preform, through screen printing, and the like. Alternatively, the pellet may be formed and sintered, the frits attached, and then fired again to adhere the frits to the two opposing ends 125, 135 of the pellet. Preferably, firing for the purpose of frit adhesion is conducted from 80 to 900 degrees Centigrade, thus lower than the final temperature at which the silicon metal is sintered to prevent disruption of the increased physical complexity structures present in the thermoelectric material 110.

[00321] Using these techniques, a silicon based thermoelectric material 110 may be produced that can stably operate to produce electricity at temperatures exceeding 900 degrees Celsius. This is a substantial and unexpected improvement in relation to conventional bismuth telluride materials that are limited to approximately 200 degrees Celsius.

[00322] FIG. 2A represents an assembled thermoelectric module 200. The thermoelectric module 200 includes a first substrate 210, a second substrate 220, and multiple pellets 100. An individual pellet may be a N-doped pellet 230 or a P-doped pellet 240. The first and second substrates 210, 220 preferably are formed of an aluminum nitride (AIN) ceramic. AIN ceramics have a thermal conductivity of approximately 170180 W/m*K and an electrical resistivity approaching 10¹⁴ power Ohms/cm. Commonly used aluminum oxide ceramics are not favored as they lack the desired thermal conductivity, having a substantially lower thermal conductivity of approximately 18 W/m*K.

[00323] FIG. 2B represents an exploded view of an alternate thermoelectric module 260 where in addition to the first and second substrates 270, 280, intermediate substrates 275 and 285 are present. In relation to FIG. 2A where the sides of the pellets 100 are surrounding by an open space, in FIG. 2B the sides of the pellets 100 are surrounding by the intermediate substrates 275 and 285. While two intermediate substrates are depicted, fewer of more intermediate substrates may be present to isolate the sides of the pellets 100 from exposure. The holes in the intermediate substrates 275 and 285 are sized to correspond to the external diameter of the pellets 100.

[00324] [0096] In addition to the intermediate substrates, the thermodynamic module

260 of FIG. 2B also includes cut-outs in the first and second substrates 270, 280 where the pellets 100 reside. As previously discussed, if the ends of the pellets 100 are not metalized, the cut-outs of the first and second substrates 270, 280 may be metalized. Alternatively, the conductive metal used for metallization may be placed in the cut-outs before the pellets 100 and then the assembled module fired to metalize the ends of the pellets 100 with the cut-outs of the first and second substrates 270, 280.

[00325] The first substrate 270 includes a first external conductor 272 that allows connection of the module 260 to a wire, contact, and the like. Similarly, the second substrate 280 includes a second external conductor 282 that allows connection of the module to a wire, contact, and the like. In combinations, the first and second external conductors 272, 282 establish electrical communication between external devices and the thermoelectric module 260.

[00326] In addition to the external conductors 272, 282 establishing electrical communication to external devices, the first substrate 270 includes internal conductors 274 between individual pellets establishing electrical communication from N-doped to P-doped pellets and from P-doped to N-doped pellets, but not between pellets of like doping. While a specific internal conductor pattern is represented in FIG. 2B, other internal conductor patterns may be used than maintain electrical conductivity between pellets of alternating doping.

[00327] Such construction results in multiple pellets 100, each pellet 100 having opposed metalized ends, assembled into a thermoelectric module 200, 260. Thus, a first conductive end of each pellet may contact a first substrate, while a second conductive end of each pellet contacts a second substrate. In this manner, the first conductive end of a pellet is in electrical and thermal communication with the first substrate and the second conductive end of the pellet (opposing end) is in electrical and thermal communication with a second substrate. The sides of each pellet also are in thermal, but not electrical communication with any intermediate substrates.

[00328] FIG. 3 A represents a top view of a thermoelectric module 300, such as the module 200 or the module 260, with the intermediate substrates not shown. The top substrate is represented as 370. Line 5 intersects the approximate middle of TEMat pellets 310, which are shown in dashed lines as the top ends of the pellets would not be visible when viewing the substrate 370. [00329] FIG. 3B is the side view of the thermoelectric module 300 along cut line 5. The interiors of the pellets 310 in the first and second substrates 370, 380 are shown. Thus, it can be seen that the pellets 310 extend into the first and second substrates 370, 380. The pellets may have diameters of approximately 12 mm and heights of approximately 10 mm. Cut-outs 320 in the substrates 370, 380 where the pellets 310 reside may have a depth of approximately 2 mm, with an approximately 2 mm substrate thickness under the cut-outs 320 to provide the first and second substrate with a height of approximately 4 mm. This example construction provides approximately 6 mm of exposed height on the side of each pellet that may be left exposed or covered by one or more intermediate substrate. Other dimensions may be used to form the thermoelectric module. The cut-outs 320 may be formed in the AIN ceramic material in the “green” state before the material is fired to form a ceramic. Preferably, the pellets 310 are sintered and then added to the green AIN material with metallization in the cut-outs 320. The green ceramic is then fired to metalize the opposing ends of the pellets 310 and to harden the AIN into a ceramic state. While not shown in the figure, heat sinks may be placed on the exterior surfaces of the first and second substrates 370, 380 to form the thermoelectric module.

[00330] FIG. 3C represents one construction of the thermoelectric module 300 having alternating N- and P-type semiconductor pellets 310. The figure represents a construction where the bottom substrate 380 provides electrical conductivity between adjacent N- and P- type pellets, while a third adjacent N-type pellet is electrically connected to a rearward P-type pellet through the top substrate 370.

[00331] FIG. 4A represents a method 400 of making doped silicon metal particulates suitable for forming a thermoelectric pellet. In 410, silicon purer than “six-nines” (99.9999%), preferably from nine to eleven nines pure (99.9999999% to 99.999999999%), is heated with dopant to achieve a doping level from 10^20th to 10^22nd/cm³, as previously discussed. Heating is performed under an atmosphere substantially excluding oxygen. In 420, when vacuum is used to assist in excluding oxygen, the vacuum is maintained at less than 10'⁶ Torr, above 950 degrees Centigrade to reduce silicon sublimation. In 430, heating is continued until a preferred melting temperature from 1414 to 1450 degrees Centigrade is reached. Thus, as the temperature is increased, vacuum is reduced in relation to backfilling with an inert gas. At temperatures above 1400 degrees Centigrade, the vacuum is preferably approximately 10-¹ Torr. [00332] In 440, the melted silicon and dopant are cooled under the oxygen excluding atmosphere. In 450, the doped silicon is broken into particulates having a preferred average diameter of 1 millimeter (mm) or less. In 460, the doped silicon particulates are milled under an alcoholic carrier liquid and inert atmosphere in an attrition mill. A preferred milling media is a ceramic, such as zirconia, with an approximately 3 mm average diameter. In 470, milling is continued to reduce the average diameter of the doped silicon metal particulates to the 1 to 5 micron range. This milling procedure is generally as described in U.S. Pat. No. 6,638,491, entitled “Method of Producing Silicon Metal Particulates of Reduced Average Particle Size”.

[00333] In 480, the desired quantity of the 1 to 5 micron average diameter doped silicon metal particulates optionally may be removed from the mill under inert atmosphere. In 490, milling is continued to produce doped silicon metal particulates having the desired D50. This milling process can be continuous with the larger, 1 to 3 micron particulates removed from the mill at an intermediate time, or batch-wise where milling is stopped to remove the larger 1 to 3 micron particulates and then restarted to reduce the remaining 1 to 3 micron particulates to the desired D50 to form the thermoelectric material.

[00334] FIG. 4B represents a settling method 495 of removing undesirable “fines” from the doped silicon metal particulates after milling. An issue that arises in the measurement of any milled material is that while milling produces a relatively large distribution of particulate sizes, the technique or techniques used to determine the diameters, average diameters, D50 and the like may not accurately determine the size or existence of particulates below a threshold. Thus, during the settling method 495, particulates having average diameters of approximately 600 nm and less, preferably 400 nm and less, and more preferably 200 nm and less remain suspended in a carrier liquid while the larger desired particulates are precipitated and collected.

[00335] Particulates having average diameters of 200 nm and less are believed to substantially interfere with neck formation between the larger particulates during low temperature sintering. Such interference in neck formation is believed to adversely reduce electrical conductivity through the sintered thermoelectric material.

[00336] In 492, the milled doped silicon metal particulates having the desired D50 are suspended in an alcoholic carrier liquid. Ethanol is a preferred alcoholic carrier liquid, but other alcoholic carrier liquids, such as acetone, and combinations of alcoholic carrier liquids may be used that suspend, but substantially do not react chemically with the particulates. In 494, the doped silicon metal particulates are cooled in the carrier liquid. Preferably, cooling is continued until a temperature from 2 to 6 degrees Celsius, more preferably from 3 to 5 degrees Celsius is reached.

[00337] In 496, the cooled suspension is allowed to settle the larger particulates for a time period from 4 to 48 hours, preferably from 10 to 36 hours, and more preferably from 20 to 28 hours. For example, to remove fines of 500 nm and below at approximately 4° C, settling may take approximately 12 hours, while at the same temperature, to remove fines of 200 nm and below, settling may take approximately 24 hours. The upper size limit of the larger settled particles may be controlled by the selected cooling temperature and settling time, as may be determined in accord with the principles of Brownian motion. Preferably, settling is continued until an average diameter particle distribution of 400 nm to 2.4 microns is obtained.

[00338] The settling process results in an approximate 5% to 10% increase in the D50 value for the milled doped silicon metal particulates, but the true effect on the milled particulates is not presently known as much of the instrumentation used to routinely measure D50 cannot reliably measure particulate average diameters below 150 nm, which are substantially removed through the settling process.

[00339] In 498, the alcoholic carrier liquid including the remaining fines is decanted from the settled larger particulates. If desired, an optional second settling and decantation may be performed at the same or with a different alcoholic carrier liquid, temperature, and/or time (not shown). The settled particulates are then collected under inert atmosphere and optionally dried (not shown).

[00340] When the doped silicon metal particulates are milled with a conductive form of carbon, the settling procedure can be adjusted so the conductive form of carbon substantially settles with the larger particulates. As previously described, the conductive form of carbon also may be added to the larger particulates after milling through subsequent mixing. [00341] FIG. 5 A represents a method 500 of forming a thermoelectric pellet with an organic lubricant. In 510, the organic lubricant desired for later pressing is added during milling or after the particulates are milled. If appropriate, some of the alcoholic carrier liquid used during milling may be retained for use as the organic lubricant. Spray drying may be used to apply the organic lubricant or additional organic lubricant. In 515, coarser doped silicon metal may optionally be placed in the press above and below the finer doped silicon, as previously discussed. In 520, the doped silicon metal is pressed to form a pellet as previously described. In 530, the organic lubricant is removed from the pellets under vacuum and optionally with heat. In 540, the pellet is sintered at low temperature under a reducing atmosphere, as previously discussed. In 550, the two opposing ends of the pellet are metalized, as previously discussed.

[00342] FIG. 5B represents a method 505 of forming a thermoelectric pellet with a carbon-based binder. In 560, the carbon-based binder desired for later pressing is added during milling or after the particulates are milled. If appropriate, some of the alcoholic carrier liquid used during milling may be retained as an organic lubricant. In 565, coarser doped silicon metal may optionally be placed in the press above and below the finer doped silicon, as previously discussed. In 570, the doped silicon metal is pressed to form a pellet as previously described.

[00343] In 580, the carbon-based binder is removed from the pellet. The carbon-based binder is removed by heating the pellet from approximately 300° C to 400° C under flowing dry air. While inert gasses, vacuum, and other “modified atmospheres” may be used, the pellet is preferably heated in a stream of dry air to remove the carbon-based binder. The gas selected to remove the carbon-based binder is selected on the basis that the gas includes sufficient oxygen to substantially convert the carbon-based binder to carbon dioxide and water vapor. The temperature selected to remove the carbon-based binder is selected on the basis that the temperature is high enough to substantially convert the carbon-based binder into carbon dioxide and water vapor, but low enough to substantially reduce the formation of silicon carbides and oxides, as previously discussed in relation to low temperature sintering. The carbon-based binder removal temperature is preferably lower than the temperature used for sintering the pellet that forms the thermoelectric material and is lower than the temperature at which silicon metal substantially sublimes. Preferably, the gas and temperature are selected to substantially remove the carbon-based binder from the pellet after approximately 1 hour of heating.

[00344] In 585, the pellet is sintered at low temperature under vacuum and then a reducing atmosphere, as previously discussed. In 590, the two opposing ends of the pellet are metalized, as previously discussed.

[00345] FIG. 6 represents a cross-section of angular shaped particulate bodies 605 coated with a 15 nm silver coating 615. The angular shaped particulate bodies are joined by smaller necks, which necks are created by sintering or joining the particles below the melting point of the material. The angular shaped particulate bodies have a body diameter D50 by volume of particles from 500 to 5000 nanometers, which will also give a measurement of diameter D50 of particles by number of 300 to 1200 nanometers. The smaller necks are from 8 to 200 nanometers in average diameter, and the doped silicon includes from 100 to 2300 parts per million of at least one dopant. Upon sintering or joining, the porosity is reticulated and in the range of 30% to 45% of the theoretical density and the isolated grains surrounded mostly by air and the small necks serve to trap phonons and form phonon wells and traps. To provide an electrical path to ground for the electrons converted from phonons by the thermoelectric effects in the grains, the entire surface of the pellet both on the outside and the entire reticulated porosity inside is coated by a conductive metallic nano layer in the range of 8 to 80 nanometers; in the illustrated example embodiment, metallic nano layer is silver and the thickness is 15 nm. A layer of silver is deposited by decomposition of silver oxide, said layer of silver having a thickness between 8 and 80 nanometers, wherein the silver oxide is derived from an aqueous solution of silver nitrate which is decomposed at a temperature in excess of 180 C to silver oxide.

[00346] One of ordinary skill in the art will find a wide range of metals and alloys that can be applied. Some will have better utility than others, for example in the case of a cooler, temperatures are relatively low and diffusion into silicon is less of a concern. In the case of a generator one can anticipate wishing to operate at temperatures as high as 700 C or more and diffusion of the metal into silicon must be addressed.

[00347] The aqueous silver nitrate solution is infiltrated into the reticulated porosity of the structure under a vacuum of minus 200 torr or less, wherein the silver nitrate and silver oxide derive metallic silver coating through thermal decomposition at a temperature less than 400 C, and wherein such metallic coatings can be deposited by other decomposition processes from other metallic compounds which decompose to their conductive forms at temperatures less than 700 C.

[00348] The following examples illustrate one or more embodiments of the invention. Numerous variations may be made to the following examples that he within the scope of the invention.

EXAMPLES

Example 1 : Prophetic Highly Doped Silicon Formation

[00349] Combine silicon metal having from six to nine nines purity in a high temperature ceramic vessel with an amount of dopant to achieve a doping density of 10^16th/cm³ or higher. Fire the mixture under inert atmosphere to form a wafer of highly doped silicon metal. The wafer is then quickly frozen, crushed, and added to the mill to form the desired silicon metal particulate average diameters. The dopant may be from Column Illa of the periodic table to form a P-type semiconductor or from Column VA to form an N-type semiconductor.

Example 2: Thermoelectric Pellet Formation

[00350] Silicon metal having the desired P type dopant was milled under an alcoholic carrier liquid with an optional dispersant-binder until the doped silicon metal particulates had an average diameter of about 350 nm.

[00351] Silicon nitride milling media of about 3 mm in diameter was used in combination with a 300 to 600 revolution per minute paddle speed. Carbon black was added at approximately 5% by weight (6.4% by volume) in relation to the silicon metal to the mill under an alcoholic carrier liquid. The milled material was removed from the mill, processed to remove any undesirable dispersant-binders, and pellets formed by pressing the material to form the thermoelectric material. Pressing was performed with approximately 8 tons of force with the addition of a silver glass frit at the top and bottom of the material. In this manner, at the electrical interfaces the thermoelectric material may provide about 0.6 W/m*K at about 400 microvolts. [00352] The following table lists some relevant properties of thermoelectric material made from this general procedure:

TABLE 2

Example 3: Fine Removal from a Milled Slurry [00353] Smaller than one millimeter silicon particulates doped with phosphorous to 1700 ppm or boron to 1000 ppm are milled to a D50 of about 800 nm by volume as determined with the Leeds and Northrup microtrac (Microtrac, Montgomeryville, PA) or similar instrument. The surface area measured by the microtrac is about 9 meters per gram. Milling is performed in acetone and “settling” continues for about 12 hours in a column of acetone about four or more inches above the base, three times, finally achieving a D50 by volume of 3.2 microns, a surface area less than 3 meters and a D50 by number of about 800- 900 nm. After decanting the fines with the acetone, the resulting silicon metal particulates are then put into a binder, pressed in a dry press tool in a uniaxial press, the binder removed in oxygen at less than 450 C, and then sintered at about 1350 degrees Centigrade under argon or under an argon/hydrogen mixture. An optional conductive form of carbon may be added with the binder if not included when milling the smaller than one millimeter doped silicon particulates.

Example 4: Layered Thermoelectric Pellet Formation

[00354] Smaller than millimeter silicon particulates doped with phosphorous to 1700 ppm or boron to 1000 ppm are milled to a D50 of about 800 nm by volume as determined with the Leeds and Northrup microtrac (Microtrac, Montgomeryville, PA) or similar instrument. The surface area measured by the microtrac is about 9 meters per gram. Milling is performed in acetone and “settling” continues for about 12 hours in a column of acetone about four or more inches above the base, three times, finally achieving a D50 by volume of 3.2 microns, a surface area less than 3 meters and a D50 by number of about 800-900 nm. After decanting the fines with the acetone, the resulting silicon metal particulates are then put into a carbon-based binder. Doped silicon metal particulates of larger average diameter, preferably from 1 to 30 microns are added to a dry press tool in a uniaxial press, the smaller silicon metal particulates are added, and additional larger average diameter particulates are added on top of the smaller particulates. From 7 to 9 tons of pressure is applied and the binder removed in oxygen at less than 450 C. The pellet is then sintered at about 1350 degrees Centigrade under argon or under an argon/hydrogen mixture.

Example 5: Construction of a Thermoelectric Module

[00355] Metallized thermoelectric pellets from Example 2 or 4 with N- or P-type doping are assembled between two plates of aluminum nitride ceramic including the desired arrangement of external conductors and heated from 120 to 780 degrees Centigrade to bond the pellets to the ceramic.

[00356] To provide a clear and more consistent understanding of the specification and claims of this application, the following definitions are provided.

[00357] Thermoelectric effects include the Seebeck effect, the Peltier effect, and the Thomson effect. Each involves the direct conversion of a temperature difference to an electric voltage or vice versa. The Seebeck effect is the conversion of heat into electricity at the junction of different types of material. The Seebeck coefficient (S) describes the magnitude of the voltage produced from a given temperature difference for a material. The Peltier effect is the conversion of electricity into a temperature difference, thus either cooling or heating at an electrified junction of different types of material. The Peltier coefficient describes the heat produced from a given current for a material. The Thomson effect relates to the generation or absorption of heat when a current is passed through a single material having a temperature difference along its length.

[00358] ZT for a thermoelectric material (TEMat) is a measure of the TEMat’s conversion efficiency, whether the material is converting a temperature difference to electricity or electricity to a temperature difference.

[00359] The “Z” of the ZT is calculated by multiplying the Seebeck Coefficient (S) squared by electrical conductivity (Sigma o) and dividing by thermal conductivity (k), thus Z= S²o/k. ZT is then determined by multiplying Z by the absolute temperature (in Kelvins).

[00360] DT for a TEMat is a measure of temperature difference, with larger values representing a larger temperature difference across the material. Thus, the TEMat desirably maintains a large DT at either high or low temperature.

[00361] Silicon metal is in elemental form, thus not in the form of an oxide or ionic salt. In this application, “silicon” and “silicon metal” are used interchangeably.

[00362] P-type semiconductors include “holes” for electrons to enter through the addition of trivalent atoms, such as boron, aluminum, or gallium to the filled valence silicon atoms forming the body of the semiconductive material. [00363] N-type semiconductors include “free” electrons through the addition of pentavalent atoms, such as phosphorus, arsenic, or antimony to the filled valence silicon atoms forming the body of the semiconductive material.

[00364] Thermal Conductivity (TC) may be expressed in terms of Watts per meter Kelvin (W/m*K). The measurement of thermal conductivity for a porous material takes into consideration the equipment being used for the measurement and how the instrument operates with respect to the sending and reading of the sonic signals used for the TC measurement. If the material being measured is a porous material where the porosity is reticulated, (meaning the material includes a continuous or networked pathway from one side to the other around the pores) a signal can sonically 15 travel through the air in the pores of the network at a high rate of speed (approximately 343 meters per second with very low losses). In contrast, if the intrinsic thermal conductivity of the reticulated porous object is in the range of 0.16 W/mK, then the sonic velocity through the silicon is reduced from its 9620 meters/sec to 10.33 meters per second (0.16/149 x 9620). Thus, to properly measure such a reticulated material, an instrument using diffusivity as the thermal transfer measurement technique must measure the material in a vacuum so that all or nearly all the signal is read through the silicon and not the air within the pores.

[00365] Coefficient of Thermal Expansion (CTE) is defined as the fractional increase in the diameter of a particulate per degree Centigrade increase in temperature, and may be expressed in units of um/m/C or ppm/C.

[00366] An angular shaped particulate body is not spherical or substantially spherical, and instead has an aspect ratio between the shortest dimension through the center of the particulate body, thus the “width” of the particulate body, and the longest dimension through the center of the particulate body, thus the “length” of the particulate body. To be angular, a particulate body has an aspect ratio from 1.3 to 1.8 (length/width).

[00367] Sintering is a process of forming a solid phase mass of silicon metal through heating without melting the silicon to the point of liquification. Thus, sintering occurs below the 1,414 to 1,450 degrees Centigrade melting point of silicon metal.

[00368] Reducing atmospheres include a mixture of argon and hydrogen, forming gas (nitrogen and hydrogen), and the like. A preferred reducing atmosphere is a mixture of argon and hydrogen where hydrogen is from 5 % to 10 % (weight hydrogen/weight argon) of the mixture.

[00369] An alcoholic carrier liquid is an alcoholic liquid that solubilizes dispersantbinders, suspends the silicon metal during milling, and reduces exposure of the exposed silicon metal surfaces to oxygen and other contaminants during processing and milling. During milling, fresh silicon metal surfaces are exposed that would be exposed to the atmosphere without the alcoholic carrier liquid. Alcoholic carrier liquids include ethanol, 1,2-propendiol, acetone, and the like. Other alcoholic carrier liquids may be used that form an azeotrope with water where the last few percent of water cannot be distilled from the alcohol. During processing and milling, the alcoholic carrier is substantially maintained at a water content where it traps and holds the water as opposed to being saturated to the point water is released. For example, ethanol will uptake water at concentrations up to about 5% by weight, while at higher water concentrations, the ethanol will release the water. Ethanol is the preferred alcoholic carrier liquid; however, other alcoholic liquids that scavenge water and/or oxygen and that are compatible with the chemistry of the other processing and milling constituents may be used.

[00370] The term “on” is defined as “above” and is relative to the orientation being described. For example, if a first element is deposited over at least a portion of a second element, the first element is said to be “deposited on” the second. In another example, if a first element is present above at least a portion of a second element, the first element is said to be “on” the second. The use of the term “on” does not exclude the presence of substances between the upper and lower elements being described. For example, a first element may have a coating over its top surface, yet a second element over at least a portion of the first element and its top coating can be described as “on” the first element. Thus, the use of the term “on” may or may not mean that the two elements being related are in physical contact with each other.

[00371] Note that spatially relative terms, such as “up,” “down,” “right,” “left,” “beneath,” “below,” “lower,” “above,” “upper” and the like, may be used for ease of description to describe one element or feature's relationship to another element or feature. Spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over or rotated, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

[00372] While various aspects of the invention are described, it will be apparent to those of ordinary skill in the art that other embodiments and implementations are possible within the scope of the invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.

Claims

59

CLAIMS A sintered thermoelectric pellet with a nano thick electrically conductive metallic coating constructed so as to decouple and manage optimal performance in thermal conductivity, Seebeck coefficient and electrical conductivity, comprising: a porous structure of a doped thermoelectric material made of silicon which is optimally doped to establish a negative (N) and positive (P) type semiconductor bias so to provide the ability to make a P/N semiconductor junction; wherein the porous structure includes angular shaped particulate bodies and smaller necks, which necks are created by sintering or joining the particles below the melting point of the material, the angular shaped particulate bodies have a body diameter D50 by volume of particles from 500 to 5000 nanometers, which will also give a measurement of diameter D50 of particles by number of 300 to 1200 nanometers the smaller necks are from 8 to 200 nanometers in average diameter, and the doped silicon includes from 10^15th to 10^20th/cc of at least one dopant, said one dopant being either an N type dopant or a P type dopant, said N type dopants selected from the group consisting of phosphorous and arsenic, said P type dopants selected from the group consisting of boron and gallium; wherein the doping is minimized so as to provide the necessary positive or negative bias to make a P/N junction after thermal processing which will provide the optimized Seebeck coefficient of the material which doping diminishes, upon sintering or joining the porosity is reticulated and in the range of 30% to 45% of the theoretical density and the isolated grains surrounded mostly by air and the small necks serve to trap phonons and form phonon wells and traps; and wherein to provide an electrical contact between the P and N elements to make a function P/N junction and to provide an electrical path to ground for the electrons converted from phonons by the thermoelectric effects in the grains 60 the entire surface of the pellet both on the outside and the entire reticulated porosity inside is coated by a conductive metallic nano layer in the range of 8 to 80 nanometers. The sintered thermoelectric pellet of claim 1, where the larger angular shaped particulate bodies have a number body diameter D50 from 300 to 4000 nanometers and is composed of doped silicon. The sintered thermoelectric pellet of claim 1, where the larger angular shaped particulate bodies have a body diameter D50 from 350 to 1800 nanometers. The sintered thermoelectric pellet of claim 1 , where the smaller necks are from 10 to 150 nanometers. The sintered thermoelectric pellet of claim 1, where the smaller necks are from 12 to 180 nanometers. The sintered thermoelectric pellet of claim 1, where the doped silicon includes from 100 to 1500 parts per million boron or from 100 to 2300 parts per million phosphorous or otherwise described as 10^15th to 10^20th/cc The sintered thermoelectric pellet of claim 1, where the porous structure lacks features arising from doped silicon fines having average particulate diameters of 600 nanometers and less. The sintered thermoelectric pellet of claim 1, where the porous structure lacks features arising from doped silicon fines having average particulate diameters of 1400 nanometers and less. The sintered thermoelectric pellet of claim 1, the pellet having a Seebeck voltage from 150 micro Volts to 600 micro Volts at approximately 23 degrees Centigrade. The sintered thermoelectric pellet of claim 1, where the sintered thermoelectric pellet has a reticulated porosity and a density from 1.2 to 1.7 grams per cubic centimeter. The sintered thermoelectric pellet of claim 1 , where the sintered thermoelectric pellet has a coefficient of thermal expansion less than 6 parts per million. 61 A method of making a sintered thermoelectric pellet, the method comprising: milling doped silicon or other Thermoelectric material particulates with or without at least one pressing aide in a mill under an alcoholic carrier liquid until the doped silicon particulates reach a volume D50 of 300 to 5000 nanometers, and a number D50 of between 200 and 100 nanometers where the binder is capable of being extracted in a vacuum of less than minus 450 torr. The method of claim 12, further comprising: combining silicon metal particulates purer than 99.99% silicon metal by weight with enough dopant to provide from 100 to 2300 parts per million of at least one dopant in the silicon metal particulates; and heating the mixture to melting and then cooling the mixture in an atmosphere substantially excluding oxygen to produce doped silicon; and breaking the resulting doped silicon into the doped silicon particulates. The method of claim 12, where the doped silicon particulates include from 100 to 2300 parts per million boron or from 100 to 2300 parts per million phosphorous or otherwise described as 10^15th to 10^20th/cc. The method of claim 12, where the doped silicon particulates have average diameters from 0.1 to 5 microns. The method of claim 12, further comprising after the further heating under the vacuum, heating the pellet under a reducing atmosphere or vacuum from 580 to 1400 degrees Centigrade. The method of claim 12, further comprising after the further heating under the vacuum, heating the pellet under a vacuum or reducing atmosphere from 950 to 1400 degrees Centigrade. The method of claim 12, where compressing is performed with 350 to 6000 psi The method of claim 12, where the pressing aide comprises a carbon-based binder. 62 The method of claim 19, where the carbon-based binder comprises from 4% to 38% by weight the weight of the doped silicon particulates. The method of claim 19, where the carbon-based binder is selected from the group consisting of propylene carbonate, polyethylene glycol, waxes, fatty acids, oleic acid, and combinations thereof. The method of claim 19, where the carbon-based binder includes an approximately 1:9 ratio of fatty acid to polyethylene glycol. The method of claim 19, further comprising metallizing two opposing ends of the pellet with a conductive metal.