Bi-directional thermoelectric gas compressor amenable to nanofabrication

Abstract

An apparatus for creating pressure gradients in gas, includes a thermoelectric stack that includes a plurality of thin films of thermoelectric material separated by a thermal and electrical insulator, wherein each thin film, of the plurality of thin films, is in communication with a gas in which a pressure gradient is created. The apparatus further includes at least one aperture connecting two volumes of the gas at opposite sides of the thermoelectric stack, at least one electrical conductor connecting the plurality of thin films, where the at least one electrical conductor includes walls of the aperture or a separate element, and an electric current supply to supply electrical current to the plurality of thin film.

Description

BI-DIRECTIONAL THERMOELECTRIC GAS COMPRESSOR AMENABLE TO NANOFABRICATIONCROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims benefit of U.S. Provisional Patent Application No. 63 / 662,052 filed on June 20, 2024, the contents of which provisional application are hereby incorporated by reference for all purposes.FIELD

[0002] The present disclosure relates to micropumps intended for providing gas flow, gas rarefaction, gas compression and maintaining a specified pressure or pressure difference, as well as methods of using and manufacturing such micropumps.BACKGROUND

[0003] Dynamic control of gas flow, which includes optimized regulation of time-varying systems, is desired for a wide range of applications. This includes applications where the flow of gas is used or applied directly, such as propulsion systems, gas analyzers, and mass flow controllers, and indirectly, such as fluidic micropumps, lab-on-a-chip, and other pneumatically driven systems.

[0004] Dynamic control of large-scale gas flows and systems is an established field with dominating technologies being rotary vane, screw, scroll, turbofan, turbomolecular, diffusion, and cryogenic pumps. Such pumps are either used directly, as in the case of propulsion, vacuum, and HVAC systems, or indirectly where the gas is compressed or rarefied in a separate volume and then introduced using valves, such as in pneumatic tools, pneumatic actuators, micro fluidics, nano fluidics and mass flow controllers.

[0005] Dynamic control of small-scale gas systems in volumes ranging from cubic nanometers to cubic millimeters is relatively new technology demanded by medical, pharmaceutical, and micro propulsion fields, with examples such as electronically controlled drug delivery patches, lab-on-a-chip systems, and microdrones. It requires miniaturization of various systems that enable the dynamic control of gas flows, and demands low power, high precision, in a small footprint and at a low price. Such challenges have been partially addressed over the last 20 years through various concepts, largely varying in efficiency and applicability. Most of these concepts can be placed into the following four categories with detailed examples given by E. Philip Muntz and Stephen E. Vargo in a chapter on Microscale Gas Pumps in The MEMs Handbook by CRC in 2002 (see, e.g., https: / / worldcat.orQ / title / 925742962).

[0006] The first category of microscale gas pumps is that of positive-displacement pumps, driven by vanes, scrolls, roots, claws, screws, diaphragms, membranes, or pistons. The primary principle of operation is the compression and expansion of the displacement volume through consecutive displacement of the diaphragm, membrane or piston. The frequency and amplitude of the membrane motion determine the performance of the pump. These pumps are often used directly to decrease the pressure of a volume for vacuum applications, inject gas for analysis, pressurize a volume for displacement of fluid, or pneumatic control of a mechanical system. One of the earlier versions of such a device was described in U.S. Patent No. 5,529,465 toZengerle, et al., which pertains to a micro-miniaturized, electrostatically driven diaphragm micropump. Several commercial micro displacement pumps are availablefrom various manufacturers such as TCS Micropumps Ltd, Binaca Pumps, Takasago Fluidic Systems and others.

[0007] The second category of microscale gas pumps is that of kinetic pumps such as vapor jet, diffusion, molecular drag, regenerative drag or turbomolecular. Like their larger analog, a turbomolecular pump, these pumps drive gas molecules by repeated collisions with a rapidly moving solid surface. A rapidly spinning rotor pushes gas molecules from the inlet of the pump toward the exhaust, thus creating a pressure difference. Such pumps are capable of creating a pressure differential of at least an order of magnitude, and performance per square centimeter of pump operating area can exceed 100 mL / min. Rotary pumps are difficult to miniaturize, not only because of the need to use precise micromachining, but also because their performance drops roughly as the radius cubed. An example of a miniaturized rotary pump was developed by the Honeywell Corporation and consists of about 2,000 blades squeezed into a 25 mm diameter, 2.5 mm thick plate. This is described in more detail in “Multi-objective optimization design of a pump-turbine impeller based on an inverse design using a combination optimization strategy” by Wei Yang and Ruofu Xiao, published by Journal of Fluids Engineering in 2014 (see, e.g., https: / / doi.orq / 10.1115 / 1 .4025454).

[0008] The third category of microscale gas pumps is that of capture pumps, such as cryopumps, getters, and ionization pumps, such as sputter ion and orbitron ion. These pumps operate by ionizing gas molecules and then using electric fields to accelerate the ions toward a surface where they become trapped, thereby removing the ions from the evacuated volume. Such micropumps are still at their early development stages. Examples of such micropumps include, e.g., “Carbon nanotube-based field ionizationvacuum”, by D. Jang, M. Eng Thesis, MIT, 2012 (see, e.g., http: / / hdl.handle.net / l721 .1 / 77022) and “Miniaturized electron-impact-ionization pumps using double-gated isolated vertically aligned carbon nanotube arrays”, by V. Jayanty, M. S. Thesis, MIT, 2012 (see, e.g., http: / / hdl.handle.net / 1721 .1 / 75659).

[0009] The fourth category of microscale gas pumps are thermal diffusion pumps which contain no moving components and no moving auxiliary fluid or gas species. The thermal diffusion driving such pumps is an effect, sometimes synergistic, of thermal transpiration and thermal creep. Originally the thermal transpiration phenomenon was associated with gas effusion through small holes and long channels and described as gas motion between two chambers connected by a porous material with a pore size smaller than the gas mean free path by E. H. Kennard, in Kinetic Theory of Gases, McGraw Hill, 1938. More recently, transpiration has sometimes been understood in terms of thermal diffusion (i.e., the existence of a thermal force on a gas initiated only by temperature differences) and in the absence of any noticeable pressure difference in that gas. Thermal creep, first theoretically explained by physicist James Clerk Maxwell and originally called thermal transpiration by physicist Osborne Reynolds, is the phenomenon of gas motion initiated by the temperature gradients along a wall wherein the gas creeps in the direction from cold to hot.

[0010] The discovery of transpiration and thermal creep phenomena has led to the theoretical development and practical implementation of the Knudsen Compressor, a device drafted over a hundred years ago by Martin Knudsen and described in “Eine Revision der Gleichgewichtsbedingung der Gase Thermische Molekularstromungund”, published in 1910 in Annalen der Physik (see, e.g.,https: / / doi.Org / 10.1002 / andp.19093360110). Knudsen studied differentially heated and cooled capillaries to produce a staged compressor, and much later this was adapted to microscale by G. Pham-Van-Diep, P. Keeley, E. P Muntz, D. P. Weaver, in “A Micromechanical Knudsen Compressor” in Rarefied Gas Dynamics in 1995 by Oxford University Press (see, e.g., https: / / www.worldcat.org / title / 60281623).

[0011] Muntz outlined a micro-electromechanical molecular-transpiration Knudsen compressor capable of generating large changes in pressure by utilizing a cascade of multiple stages. Each stage is composed of a capillary and connector section. A temperature increase across the capillaries results in a pressure increase driven by thermal transpiration. The capillary section is followed by a connector section where the pressure is approximately constant while the temperature drops toward its original value entering the stage. The manufacturing details were described in U.S. Pat. No. 6,533,554 by Vargo, et al., for thermal transpiration pump. Later, some modifications to the concept were made and described in U.S. Patent No. 7,367,781 by Gianchandani, et al. for a packaged micromachined device such as a vacuum micropump, device having a micromachined sealed electrical interconnect and device having a suspended micromachined bonding pad.

[0012] U.S. Pat. No. 8,235,675 to Gianchandani, et al. also describes a system and a method for providing a thermal transpiration gas pump using a nanoporous ceramic material. A micropump made of porous ceramic materials, such as zeolite, was proposed to constrain the flow of gas molecules to the free molecular or transitional flow regime. An alternative design of a multi-staged micropump described in U.S. Patent No. 9,695,807 to Kloss, et al. Kloss et al. describes a configuration that includes continuouscylindrical separating pipes having at least two alternating stages of pipes of small radius and large radius connected in succession. One end of the pipes constitutes a hot zone, and the opposite end constitutes a cold zone. Such pipes alternate straight pipes with a large radius and U-shaped curved pipes with a small radius.

[0013] Another configuration for thermal transpiration micropumps is described in U.S. Patent No. 7,572,110 to Bernard et al., which discloses a pumping apparatus using thermal transpiration micropumps. Therein, each micropump included at least one cavity with an inlet connected to an inlet channel of a small cross-section and an outlet connected to an outlet channel. Each micropump also included a heater element for heating the segment of the inlet channel that is adjacent to the cavity, and a plurality of such micropumps were connected in series. Another micro-electromechanical pump is described in U.S. Patent No. 7,980,828 to Lantz et al. entitled Microelectromechanical Pump Utilizing Porous Silicon. The design included a porous silicon region sandwiched between an inlet chamber and an outlet chamber. The porous silicon region was formed in a silicon substrate and contains pores extending between the inlet and outlet chambers, with each pore having a cross-sectional dimension approximately equal to or smaller than the mean free path of a gas being pumped. Another machined thermal diffusion pump was presented by Q. Cheng, Y. Qin and Y. B. Gianchandani from the University of Michigan at the 2017 IEEE 30.sup.th international conference on MEMS in Las Vegas, NV where they used mixed cellulose-ester membranes as the core of a micro-machined pump which reduced power requirements, titled “A bidirectional Knudsen pump with superior thermal management for micro-gas chromatography applications” (https: / / doi.orq / 10.1109 / MEMSYS.2017.7863367). Other micro thermaldiffusion pumps have been proposed and demonstrated, however as of 2024, there does not appear to be any thermal diffusion pumps on the market.

[0014] Two major challenges for commercializing thermal diffusion pumps are the power requirements and manufacturing complexity. With respect to the first major challenge for commercialization of thermal diffusion pumps (i.e., power requirements), the primary bottleneck of earlier designs, which drastically reduces energy efficiency, are narrow tubes or channels for gas passage that connect the heated and unheated chambers. Such channels, either micro-machined or inherently present in porous materials separating the chambers, while driving the pressure difference, greatly reduce the mass flow rate and drive manufacturing complexity. This is because at microscale, the dimensions of the channels in the direction perpendicular to the gas flow become comparable to the gas mean free path. Hagen-Poiseuille law, which governs gas flows in the continuum regime, is not applicable in this case, and the friction on the channel walls becomes prohibitively large. To reduce such friction, and to a large extent overcome the long-tube constraint, U.S. Patent No. 11 ,885,320 by Garbuz, et al. describes a novel configuration which makes use of the ability of thermoelectric elements to impose temperature gradients in gas on nano and microscale (i.e., the scale of the gas mean free path where thermal diffusion effect is maximum).Thermoelectric elements, and in particular, PNP configuration (i.e. p-type I n-type I p- type sequencing) applied to maintain temperature gradients along short apertures, disclosed therein, provides an opportunity to effectively create pressure differences in gas at nano and microscale.

[0015] The second major challenge for commercialization of thermal diffusion pumps (i.e., manufacturing complexity) is related to the scaling of the production of thermal diffusion micropumps. This is largely related to the availability of commercially available systems and processes that can create precise nanostructures at commercially viable costs. The main culprit is the use of non-standard materials that are not available commercially.

[0016] Therefore, dynamic control of gas pressure in small volumes is a field of active research with a wide range of applications, and one of the most promising technologies is a thermal diffusion gas pump, that until now has been limited by manufacturing complexity.SUMMARY

[0017] The present disclosure provides a description of systems and methods aimed to alleviate the mass production challenge of the previously proposed thermal diffusion heat engines.

[0018] A primary objective of exemplary embodiments of the disclosed technology is the effective designs of a thermoelectric gas compressor that are amenable to straightforward nano and microfabrication using standard semiconductor materials and processes. Improvements are also disclosed that further increase the power efficiency of thermoelectric gas compressors as compared to the state of the art.

[0019] Disclosed herein are methods and exemplary embodiments of an apparatus for creating gas flow and gas compression at nano and microscale. In an exemplary embodiment, an apparatus includes two volumes of gas separated by a thermoelectricstack containing two parallel thermoelectric thin-f ilm plates, with at least one aperture through the thermoelectric stack that fluidical ly connects the two volumes for gas, aperture walls serving as an electric conductor between the parallel (or nearly parallel) thin-film plates. In preferred embodiments, the thermoelectric films are of the same type (e.g., both either p-type or n-type thermoelectric, with the choice based on the availability of materials and their thermoelectric figure of merit). Sufficient electrical conductivity of aperture walls is a necessary condition of gas compressor operation, and they may be either conductive metals or thermoelectric materials. If the aperture walls are thermoelectric, they are of opposite type to the thin film type (e.g., if thin films are p- type, aperture walls are n-type, and vice versa). This is used to amplify the thermoelectric effect and increase temperature difference between the thin films. While using aperture walls is a straightforward way to electrically connect the parallel thermoelectric thin films, manufacturing and / or optimization considerations may dictate a different layout, where the aperture walls are made of a dielectric material, and the electric connection between the thermoelectric films is provided by a separate, dedicated element or elements, which may be of a cylindrical, rectangular, or other shape.

[0020] The electric current supplied to the thermoelectric thin films establishes thermal (temperature) gradients across the aperture connecting the two volumes, and a temperature difference between the two films. The thermal gradient, which induces thermal creep, and temperature difference, which induces thermal transpiration, results in a flow of gas from one volume, through the aperture and into the other volume in the general direction of the temperature gradient (cold to hot).

[0021] Performance improvements are also disclosed herein. First, to minimize heat losses due to energy transfer between the hot and the cold thin film, a gap between them is filled with air, which is achieved by a successive deposition and removal of an oxide layer. Second, to increase energy efficiency, more than one aperture is used such that some of the apertures have electrically conductive walls, and the rest of the apertures have electrically and thermally insulating walls. Third, to improve thermal uniformity of thermoelectric thin films and provide high electrical conductivity through the thermoelectric stack, thin-film layers or coatings with high thermal and electrical conductivity, such as metals, are added on the top or bottom of each thermoelectric thin film. Coatings may also be used for protection from changes in material properties of thermoelectric thin films over time due to external factors, such as oxidation. Fourth, the thickness of thermoelectric films may be reduced in the components that electrically connect the thermoelectric stack to the circuit.

[0022] The operation of the thermoelectric or Peltier films herein is based on the reverse phenomenon of the Seebeck effect - the electrical current flowing through the junction connecting two materials with different Seebeck coefficients will emit or absorb phonons proportional to the current at the junction to balance the difference in the chemical potential of the two materials. Therefore, there are many pairs of electrically conductive or semiconductive materials with different chemical potentials that are chemically stable in a surrounding gas to be pumped that can be used to build thermoelectric elements pertinent to present disclosure. When scaling down the gas pumps, electric contact resistance becomes one of the main sources of inefficiency. Therefore, materials and processes that have been developed to minimize electrical contact resistances at thenano scale are advantageous even if the thermoelectric efficiency of the material pair is lower than other material choices. Examples of material pairs that have been optimized for mass production include, e.g., p-type silicon, n-type silicon and p-type silicon germanium, n-type silicon germanium (SiGe). In the exemplary embodiments shown below, p-type and n-type SiGe are used.

[0023] Exemplary embodiments of the disclosed apparatus include a sequence of fluidically connected volumes (chambers), with thermoelectric stacks serving as separating barriers between the chambers, and apertures serving as passages for gas between the adjacent chambers. A resulting gas pressure difference between the first and the last chamber is nearly proportional to the number of chambers between them. The exemplary embodiments disclosed herein also include an array of sequences operating in parallel. The total gas mass flow increases proportionally to the number of sequences.

[0024] An apparatus for creating pressure gradients in gas, including a thermoelectric stack that includes a plurality of thin films of thermoelectric material separated by a thermal and electrical insulator, wherein each thin film, of the plurality of thin films, is in communication with a gas in which a pressure gradient is created. The apparatus further includes (i) at least one aperture connecting two volumes of the gas at opposite sides of the thermoelectric stack, (ii) at least one electrical conductor connecting the plurality of thin films, wherein said at least one electrical conductor includes walls of the aperture or a separate element, and (iii) means to supply electric current to the plurality of thin films.

[0025] The present disclosure describes a method of creating a gas compressor, including: providing a thermoelectric stack including a plurality of thin films of thermoelectric material; separating each thin film of the plurality of thin films by a thermal and electrical insulator, wherein each thin film, of the plurality of thin films, is in communication with a gas in which a pressure gradient is created; defining at least one aperture connecting two volumes of gas at opposite sides of the thermoelectric stack, connecting, using at least one electrical conductor, the plurality of thin films, wherein said at least one electrical conductor includes walls of the at least one aperture or a separate element, and supplying electric current to the plurality of films.

[0026] The present disclosure further describes an apparatus for creating pressure gradients in gas, including: a resistive stack including a thin electrically conductive material and a passively cooled material separated by a thermal insulator, wherein the thin electrically conductive material and the passively cooled material are in communication with a gas in which a pressure gradient is created; at least one aperture connecting two volumes of the gas at opposite sides of the resistive stack; and means to supply an electric current to the thin electrically conductive material.

[0027] The present disclosure also describes a method of creating a gas compressor, including: providing a resistive stack including a thin electrically conductive material and a passively cooled material separated by a thermal insulator, wherein the thin electrically conductive material and the passively cooled material are in communication with a gas in which a pressure gradient is created; connecting, via at least one aperture, two volumes of gas at opposite sides of the resistive stack; and supplying an electric current to the thin electrically conductive material.BRIEF DESCRIPTION OF THE DRAWING FIGURES

[0028] The scope of the present disclosure is best understood from the following detailed description of exemplary embodiments when read in conjunction with the accompanying drawings. Included in the drawings are the following figures:

[0029] FIG. 1 schematically illustrates a conventional PN (p-type and n-type) thermoelectric cooler.

[0030] FIG. 2 schematically illustrates a PNP thermoelectric heat pump in accordance with exemplary embodiments.

[0031] FIG. 3A illustrates a thermoelectric stack represented by two PNP thermoelectric heat pumps connected sequentially and fitted with apertures to create gas bulk flow and pressure differences in gas, in accordance with exemplary embodiments.

[0032] FIGS. 3B and 3C depict examples of alternative configurations of a thermoelectric heat pump, in accordance with exemplary embodiments.

[0033] FIG. 4 schematically illustrates a cross-section of a multiple-stage nanofabrication layout of the disclosed gas compressor, in accordance with exemplary embodiments.

[0034] FIG. 5 illustrates a cross-section single stage of the gas compressor of FIG. 4, in accordance with exemplary embodiments.

[0035] FIG. 6 illustrates deposited material layers around a single aperture, in accordance with exemplary embodiments.

[0036] FIG. 7 illustrates a top-down view of an upper part of a thermoelectric island depicted in FIG. 5, in accordance with exemplary embodiments.

[0037] FIG. 8 illustrates a side view of an upper part of the thermoelectric island depicted in FIG. 5 with the etched thermoelectric film, in accordance with exemplary embodiments.

[0038] FIG. 9 illustrates an exemplary manufacturing process flow of the disclosed gas compressor, in accordance with exemplary embodiments.

[0039] FIG. 10 schematically illustrates a battery-operated island that creates air compression through by resistive heating of its bottom side, in accordance with exemplary embodiments.

[0040] FIG. 11 schematically illustrates a resistively heated island with wall-less apertures, in accordance with exemplary embodiments.

[0041] FIG. 12 illustrates a multi-aperture conducting part of an island with a resistively heated moat, in accordance with exemplary embodiments.

[0042] FIG. 13 schematically illustrates a nanofabrication layout of a resistively driven uni-directional gas compressor, in accordance with exemplary embodiments.

[0043] FIG. 14 illustrates an exemplary nanofabrication and electric connection layout of a bi-directional resistively driven gas compressor, in accordance with exemplary embodiments.

[0044] Further areas of applicability of the present disclosure will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description of exemplary embodiments is intended for illustration purposes only and is, therefore, not intended to necessarily limit the scope of the disclosure.DETAILED DESCRIPTION

[0045] A gas compressor, as disclosed herein, uses two physical effects which define its ultimate performance. The first effect, thermal diffusion, relates to ideal gases, such as atmospheric air, whose behavior changes qualitatively when it acts on heated objects comparable to the molecular mean free path of about 67 nm. The second effect, thermoelectric Peltier effect, provides means to maintain significant temperature gradients in thermoelectric materials over distances as small as tens of nanometers. These two effects are explained below.Gas compressor principle of operation: thermal diffusion effect

[0046] Gas behaves like a fluid when forces that act on a gas do so at large scales. When forces that act on a gas do so at scales on the order of the mean free path of the gas, the gas can no longer be treated at a macroscopic level as a fluid and instead needs to be treated at a microscopic level as individual particles, exhibiting unique behaviors. For ambient gas with a number density n, the mean free path A may be approximated as 2 ~ >1, where d is the molecular diameter. At standard 2Ttd2n atmospheric conditions, the molecular mean free path is approximately 67 nm, and any flow with characteristic scales less than a few micrometers at standard atmospheric conditions needs to be treated at microscopic level.

[0047] When thermal gradients are imposed on a gas flow at microscale, there are several phenomena at play. These phenomena are (i) thermal transpiration, (ii) radiometric flow, and (iii) thermal creep. All these phenomena define the effect ofthermal diffusion that determines the pressure differential and flow rate through apertures of the disclosed gas compressor (discussed in more detail herein).Thermal transpiration

[0048] Suppose there are two vessels containing the same kind of gas, and these vessels are connected through a porous plug, such that the pore sizes are much smaller than the gas mean free path. According to kinetic theory, a rate Z at which the molecules enter the pores of the plug are written as Z = is theaverage thermal speed of the gas, T is the gas temperature, k is the Boltzmann constant, and m is the molecular mass. Therefore, Z may be presented as Z = .p,- 2kT / m where p is gas pressure. The important proportionality here is Z oc ^=. If the pores were small holes in an infinitely thin sheet, differential flow is expected to continue until the gas densities become so adjusted that the quantityhad the same value on the twosides, i.e. until — = — between the two vessels. Absent some special circumstances, P2 ^2 such as the pore size comparable to the molecule size, the above condition is valid for a plug of a finite thickness. While the plug thickness impacts the time which the flow needs to reach this condition - the thicker the plug the longer that time, it will not change the pressure ratio in the two vessels, which is totally defined by the corresponding temperature ratio.Radiometric phenomenon

[0049] Radiometric phenomenon is traditionally associated with, and attributed to, so- called radiometric forces. Radiometric forces are forces that act on a thin vaneimmersed in rarefied gas when a temperature gradient is imposed along or across the vane. The impact of radiometric forces on gas flows through heated apertures, and thus on the performance of the gas compressor (as disclosed herein), is through the third Newton's law - the force (or the rate of momentum transfer) imposed by the gas to the heated surface is equal, and opposite in sign, to the force from that surface to the gas. Importantly, radiometric forces are observed only in the free molecular and transitional flow regimes.

[0050] It is directly relevant to the gas compressor (as disclosed herein) that the dependence of the radiometric force on the Knudsen number, has a bell-shaped profile. The Knudsen number is the ratio of the gas mean free path to the characteristic flow scale, which in this case is the aperture diameter. For a fixed pressure, the radiometric force and thus the opposite force from the vane to the gas that is being used in the disclosed gas compressors tends to zero at Kn>10 (too few molecules to impact), and at Kn<0.01 (thermal stresses in gas diminish in the continuum flow regime).Thermal creep

[0051] Thermal creep is a steady streaming motion induced by a temperature gradient parallel to a fluid boundary, in the absence of gravity. Thermal creep has been explained as using ideas from the kinetic gas theory (see, e.g., J.C. Maxwell, "On stresses in rarified gases arising from inequalities of temperature," Philosophical Transactions of the Royal Society of London, 1879, Vol. 170, pp. 231 -256). Consider a gas with a temperature gradient parallel to a confining wall. Because hotter particles impart more parallel momentum to the wall than do colder, a shear stress is exerted on the wall, with the gas flowing from colder to hotter as a reaction force. The resultingstationary velocity of the gas is the "thermal creep" velocity and is parallel to the wall.The flow velocity is directly proportional to the temperature gradient. The cold-to-hot thermal creep directly relates to the development of the disclosed compressor technology.Gas thermal diffusion

[0052] Operation of the gas compressor (as disclosed herein) is driven by all of the above effects - thermal transpiration, radiometric forces, and thermal creep. The combination of these phenomena is called thermal diffusion, because their combined effect is to promote the diffusion of gas molecules in the direction from cold to hot, and induce thermal drift of gas in that direction, and thus cause gas compression. Such a cold-to-hot thermal gradient, set in the gas flow direction, should be imposed by some means, of which thermoelectric is the most efficient, as will be explained below, across a plate that separates gas volumes on which pressure gradients need to be imposed.Note that such a plate must have apertures of some shape for gas flow passage.Gas compressor principle of operation: thermoelectric Peltier effect

[0053] The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa via a thermocouple. The term "thermoelectric effect" encompasses three separately identified effects: the Seebeck effect, Peltier effect, and Thomson effect. The Seebeck effect is the conversion of heat directly into electricity at the junction of different types of wire. This effect translates into an electromotive field equal to —aAT, where a is the Seebeck coefficient, a property of the local material, and AT is the temperature gradient. The Peltier effect, which is the presence of heating or cooling at an electrified junction of two different conductors, is of the most relevance tothe gas compressor technology (as disclosed herein) and, thus, is discussed in more detail below. When a current is made to flow through a junction between two conductors, A and B, heat may be generated or removed at the junction. The Peltier heat generated at the junction per unit time isQ = (nA- nBwhere nAand nBare the Peltier coefficients of semiconductors A and B, and I is the electric current from A to B. The total heat generated is not determined by the Peltier effect alone, as it is also influenced by Joule heating and thermal-gradient Thompson effects. Joule heating is the heat that is generated whenever a current is passed through a resistive material. From a device efficiency perspective, Joule heating always indicates a heat loss and thus needs to be minimized. Thompson effect is a second- order effect which arises due to changes in material properties (Seebeck coefficient introduced below); it usually may be neglected in practical applications.

[0054] The Peltier coefficients represent how much heat is carried per unit charge.Since charge current must be continuous across a junction, the associated heat flow will develop a discontinuity if nAand nBare different. The Peltier effect can be considered as the back-action counterpart to the Seebeck effect: if a simple thermoelectric circuit is closed, then the Seebeck effect will drive a current, which in turn (by the Peltier effect) will always transfer heat from a hot junction to a cold junction. The close relationship between Peltier and Seebeck effects can be seen in the direct connection between their coefficients, n = Ta.

[0055] The Peltier effect is the driving mechanism of Peltier coolers, and it is also the effect used in the disclosed gas compressors. The main idea behind a simpleconventional thermoelectric cooler is illustrated in FIG 1 . The device 100 has two sides, upper 101 and lower 104. Both sides are made of electric conductors, typically metals. Electrically connecting these sides are thermoelectric elements of p-type 102 and n-type 103. The device 100, thus, effectively has three horizontal layers: two conduction layers and one thermoelectric layer in the middle. When a DC electric current, I, flows through the device 100, as illustrated by I arrows, it brings heat from one side (upper 101 ) to the other (lower 104), so that the top side (upper 101 ) becomes cooler while the bottom (lower 104) side becomes hotter. The heat transfer is promoted by excess electrons (negative charges denoted “-”) of the n-type thermoelectric element migrating in the direction opposite to the electric current, and excess holes (positive charges denoted “+”) of the p-type thermoelectric element migrating in the direction of the electric current. In usual electronics applications, the hot side is attached to a heat sink so that it remains at ambient temperature, while the cool side goes below room temperature, and cools the load. Note that if the current were to flow in the opposite direction, the cold and the hot side would be reversed.

[0056] Two unique semiconductors, one n-type and one p-type, are used in the core of a conventional thermoelectric cooler, because they need to have different electron densities. The semiconductors are placed thermally, in parallel, to each other and electrically, in series, and then joined with a thermally conducting plate on each side. When a voltage is applied to the free ends of the two semiconductors, there is a flow of DC current across the junction of the semiconductors causing a temperature difference.The side with the cooling plate absorbs heat from the load, which is then moved to theother side of the device where the heat sink is attached. Elementary Peltier coolers may be connected in series to increase the dissipated (transferred) heat.

[0057] For the gas compressors (as disclosed herein), there is no load that needs to be cooled, and the Peltier effect is used as a heat pump, not a cooler. This is because the purpose of a thermoelectric cooler is to move heat from the cooled side, while the purpose of a thermoelectric element in the gas compressor is to maintain a temperature gradient between the cold and the hot side. In the latter case, heat is transferred from one end of a thermoelectric element to the other and then dissipated to the gas adjacent to it. The cold side in this case is kept at a temperature nearly equal, or slightly higher, than the surrounding (ambient) temperature. The difference between thermoelectric elements in conventional coolers and in a nano-compressor is therefore manifested most in the thickness of the elements in the direction perpendicular to the direction of the current: to maximize efficiency, the thickness must be relatively wide in coolers and narrow in gas compressors.

[0058] The cooling efficiency of a thermoelectric device is determined by the ability of a given material to efficiently produce thermoelectric power, and is related to its dimensionless figure of merit ZT given bywhich depends on the Seebeck coefficient a, thermal conductivity K, electrical conductivity a, and temperature T. Higher ZT values generally indicate better performance; the value of ZT on the order of 1 or higher is often considered as necessary for widespread use of thermoelectric devices. A high figure of merit requiresthe use of a material with a large power factor oa2and a low thermal conductivity. Just as with thermoelectric coolers, the gas compressor (as disclosed herein) also benefits from higher ZT, as its energy efficiency E is approximately proportional to it, E = pVZT. Here, p is gas pressure, and V is the volumetric gas flow.

[0059] Importantly, the application of the thermoelectric effect to a heat pump, unlike a cooler, may be fairly efficient even for relatively low ZE materials, such as silicon germanium SiGe. For thermoelectric coolers, as explained in detail by H.J. Goldsmid in Section 2 of his Introduction to Thermoelectricity (Springer 2010), the expression for the cooling power iswhere the subscripts p and n refer to p-type and n-type thermoelectric elements, and 1 and 2, to the source (load) and sink, respectively. The rate of expenditure of electrical power is

[0060] The coefficient of performance is then given by the ratio <p =On the other hand, for thermoelectric heat pumps, such as the disclosed gas compressor, what matters is the heat delivered to the sink, and not the cooling power at the source. The rate at which the sink is heated is<72= <?1 + w = w(cf) + 1).Therefore, the rate of heat delivery can, and usually is, greater than the spent electrical power, because < > is normally positive.

[0061] As previously mentioned, a key feature of the gas compressor (as disclosed herein) is a thermoelectric heat pump, which maintains temperature gradients in gas and promotes its thermal diffusion (bulk motion) driving pressure differences. An exemplary embodiment of such a heat pump 200 is shown in FIG. 2. Electric current is supported by a potential difference established by power source 208, such as a direct current (DC) battery. The electric current flows through a conductor 206 and enters the heat pump 200 through a p-type thermoelectric element 205. Because positive charges (holes) of 206 move with the electric current, a thermal heat is transferred through the p- type thermoelectric element 205 by the Peltier effect in the direction from left to right. For better temperature uniformity, there is a metal layer (film) 207 that provides efficient current and heat transfer. The metal layers of FIG. 2 may be made of, for example, tungsten, and the thermoelectric layers may be made of, for example, silicongermanium (SiGe). However, other semiconductor fabrication friendly materials may be used instead. It is important that metals have sufficiently high electrical and thermal conductivities, and thermoelectric materials have sufficiently high figures of merit ZT. Conducted through the p-type thermoelectric element 205 and then the metal layer (film) 207, the electric current then passes through an n-type thermoelectric element 204, which, due to the downward motion of electrons, results in heat transfer by the Peltier effect from the top layers of heat-spreading metal film 201 and a p-type thermoelectric film 203 to the bottom films (i.e., the p-type thermoelectric element 205 and then the metal layer (film) 207). Subsequently, the electric current leaves the heat pump 200 through the thermoelectric element 203 to a conductor 202, which connects the heat pump 200 to the power source 208. As the current passes from thethermoelectric element 203 to the conductor 202, heat is again transferred by the Peltier effect in the direction from left to right, and thus away from the thermoelectric element 203. The result of this current propagation is an efficient heating of the bottom film (i.e. , metal layer (film) 207) and cooling of the top film (i.e., heat-spreading metal film 201 ). The configuration shown in FIG. 2 is a PNP type configuration (i.e. the electric current passes sequentially p-type thermoelectric element, then n-type element, and finally, another p-type element).

[0062] When the metal layer (film) 207 and the p-type thermoelectric element 205 become hot, and the heat-spreading metal film 201 and the thermoelectric element 203 become cold, heat will flow back from the metal layer (film) 207 and the p-type thermoelectric element 205 to the heat-spreading metal film 201 and the thermoelectric element 203, reducing the temperature difference and, thus, the efficiency of the heat pump 200. To minimize this heat flow, it is beneficial to have a dielectric material with low thermal conductivity separating the thermoelectric element 203 and the p-type thermoelectric element 205. That material may be gas, such as air, or airgel, or other very low thermal conductivity material. In this case, the main route of the heat backflow will be through the n-type thermoelectric element 204, although the heat conduction through air (or similar material) cannot be fully discounted. The radiation losses are negligibly small at temperatures less than 400 K. Note that if the direction of the electric current is reversed, then the heat-spreading metal film 201 becomes hot and the metal layer (film) 207 becomes cold.

[0063] For sufficiently thin thermoelectric and conduction layers 1 and 2, the actual sequence of these layers may be dictated by manufacturing considerations andoptimization. It is only necessary that there is one conduction and one thermoelectric layer as the top two and the bottom two layers. For example, the illustrated apparatus may use, from top to bottom, Conduction 1 -Thermoelectric 1 -Air-Conduction 2- Thermoelectric 2 sequence. While the embodiment of FIG. 2 is presented as planar, it may also be axially symmetric with the n-type thermoelectric element 204 at the center or have another three-dimensional shape. The parallel or nearly parallel alignment of the five layers is convenient for manufacturing in standard semiconductor fabrication facilities. These five layers effectively define a thermoelectric stack upon which the disclosed gas compressor is based.

[0064] Additional changes may be made to the PNP configuration. First, an NPN configuration may be used instead. Second, the second thermoelectric material may be replaced by a highly conductive material with low or negligible thermoelectric properties, such as for example platinum. In this case, the n-type thermoelectric element 204 needs to be extremely thin to minimize heat backflow. The configuration then becomes PP, or NN if n-type thermoelectric elements are used instead of p-type.

[0065] The heat pump 200 shown in FIG. 2 may be easily adapted to operate as a gas compressor 300. Such an adaptation is schematically illustrated in FIG. 3A. Here, two thermoelectric heat pumps 300A and 300B are connected in series. The left heat pump (300A) is similar to the heat pump 200 described above with respect to FIG. 2. The electric current I supplied by source 316 flows through a metal conductor 310 and enters the left heat pump 300A through a p-type thermoelectric element 308. The electric current is then conducted primarily through metal film 311 , which also promotes uniform temperature distribution. The electric current then passes throughthermoelectric element 306, which defines an aperture 314 therein. Subsequently, the electric current passes through metal film 301 and leaves the left heat pump 300A through p-type thermoelectric element 304. The Peltier effect will result in cooling of the metal film 301 , heating of metal film 311 , and a thermal gradient in the direction from bottom to top through the thermoelectric element 306. As a result, there will be a thermal diffusion of gas (such as air) surrounding the left heat pump 300A (as shown in Figg. 3A) through aperture 314 in the direction from metal film 301 to metal film 311 . As a result, gas pressure above metal film 301 will be lower than gas pressure below metal film 311 , and the left heat pump 300A becomes a gas compressor.

[0066] After the electric current leaves the left heat pump 300A / gas compressor via a conducting film 302, the electric current immediately enters the right heat pump 300B / gas compressor. It does so through p-type thermoelectric element 305. After the electric current passes through metal film 303, it then flows through n-type thermoelectric element 307. Subsequently, the electric current passes through metal film 312 and leaves the right heat pump 300B through p-type thermoelectric element 309. It then concludes the loop to power supply 316 through metal conductor 313. A result of the electric current passing through the right heat pump 300B is heating the plate 303 and cooling the plate 312. Because there is an aperture 315 defined in element 307, the gas above metal film 303 will be pressurized, and the gas below metal film312 will be rarefied. The two heat pumps 300A and 300B, shown in FIG. 3A, schematically represent two stages of the disclosed gas compressor. An air layer in the middle of the thermoelectric stack serves a purpose of reducing heat backflow. In the two stages of the gas compressor 300 illustrated in FIG. 3A, the bulk flow of gas is created whichmoves the gas first through aperture 314 in the downward direction and then through aperture 315 in the upward direction.

[0067] In the exemplary embodiment of FIG. 3A, the metal films / layers 301 , 303, 311 and 312may be made of, for example, tungsten (W), and the thermoelectric layers may be made of, for example, silicon-germanium (SiGe), and the gas may be air. These materials are given for illustration purposes only, as tungsten (W) can be replaced by other electrically and thermally conductive materials, silicon germanium may be replaced by other thermoelectric materials amenable to semiconductor processing, and gas can be any gaseous medium. The apertures 314, 315 are shown as circular in the direction perpendicular to the air flow, but they may have other shapes. The order of Conduction 1 and Thermoelectric 1 layers may be reversed. The order of Conduction 2 and Thermoelectric 2 layers may also be reversed. The electric current may flow in the opposite direction, thus making cold plates hot, and hot plates cold. Finally, other thermoelectric configurations may be used instead of the PNP-PNP configuration shown in FIG. 3A, such as a NPN-NPN configuration (so that 304, 305, 308,309 would be n- type thermoelectric materials and 306, 307 would be p-type thermoelectric materials), a PP-PP configuration (so that 304, 305, 308,309 would be p-type thermoelectric materials and 306, 307 would be non-thermoelectric electrically conductive materials), and a NN-NN configuration (so that 304, 305, 308,309 would be n-type thermoelectric materials and 306, 307 would be non-thermoelectric electrically conductive materials).

[0068] If the gas being compressed is atmospheric air, dimensions of key elements of the disclosed heat pump would be in tens of nanometers to single microns. This refers to the thickness of conduction, thermoelectric, and air layers, as well as the diameter ofthe apertures (or their minimum dimension in the direction perpendicular to the gas flow if apertures are not circular tubes). This is because the thermal diffusion effect is maximum at dimensions comparable to the gas mean free path (67 nm in air at 1 atm). More specifically, these dimensions need to be reduced, with the optimum diameter and thickness of the thermoelectric stack on the order of 100 nm. Because decreasing dimensions also increase heat backflow, key dimensions should be determined through multi-parametric optimization, which should be tailored to a specific application.

[0069] As known in the art, electric current passing through any material, even that with very low electrical resistivity, heats that material. This effect is called Joule heating, and the heat release is proportional to l2R, where R is the electrical resistance of the material. Joule heating will increase temperatures of all elements of the gas compressor. Because the thermal diffusion driven bulk flow velocity through apertures 314 and 315 of FIG. 3A in the direction from cold to hot is proportional to the temperature difference between the corresponding hot and cold plates (311 -301 and 303-312), Joule heating itself will not significantly impact the pressure gradients across the apertures. However, whereas the Peltier effect produces the useful work of creating pressure differences in gas, Joule heating does not; to a large extent Joule energy is a part of electrical energy that is wasted. In an energy efficient gas compressor, the electric current will be optimized so that the temperature of the cold side is close to the surrounding (room) temperature.

[0070] The exemplary embodiment shown in FIG. 3A, and discussed above, illustrates a configuration where n-type thermoelectric material is in direct contact with both p-type thermoelectric material and a metal. Direct contact between n-type and p-typethermoelectric materials effectively form a diode. Other types of embodiments are possible, such as a diode-free embodiment illustrated in FIG. 3B where, due to the symmetry of thermoelectric pumps (FIG. 3A), only one heat pump is shown. In the embodiment of FIG. 3B, there is no direct contact between n-type and p-type thermoelectric materials. Yet another embodiment is given in FIG. 3B where the diode effect is amplified. Here, two additional pairs of n-type elements are added in order to change thermoelectric properties of the heat pump and potentially improve its performance. Other diode embodiments may be implemented, such as adding only one n-type element per W-Metal / p-SiGe I W-metal connection. Here again, the order of Conduction and Thermoelectric layers may be reversed, as well as may be reversed p- type and n-type elements in FIGS. 3B and FIG. 3C. P-SiGe in FIG. 3C may be detached from vertical n-SiGe in the manner shown in FIG. 3B. As previously discussed, the materials SiGe and W, shown in FIGS. 3A-3C, are for illustration only, and, thus, other suitable thermoelectric and conducting materials may be used.

[0071] The layered architecture of the thermoelectric stack containing two serially connected heat pumps 300A and 300B, as illustrated in FIG. 3A, is amenable to micro and nanofabrication at standard semiconductor facilities. Applying consecutively standard semiconductor etching and deposition processes, this architecture may be followed to manufacture a gas compressor which includes multiple compression stages, each defined by a single heat pump and two gas volumes adjacent to it. An exemplary embodiment of such a gas compressor 400 is illustrated in FIG. 4.

[0072] FIG. 4 illustrates a four-stage gas compressor 400, which uses atmospheric air as an example of an ideal gas, and compresses it by applying electric current to fourthermoelectric stacks connected in series. All four stacks are made using the same layered Conduction 1 - Thermoelectric 1 - Air - Thermoelectric 2 - Conduction 2 architecture, and all four use the same thin films. Four stages are shown in this example, but any other suitable number may, limited only by the size of a single stage as it relates to the size of the wafer being processed. The thin films depicted in FIG. 4, similar to those in FIG. 3A, are electric and heat conductors (such as tungsten) 403 and 407, and same-type (either p-type or n-type SiGe) thermoelectric films 404 and 406. White color indicates air, so that there is air gap between the thermoelectric layers. An air gap is obtained by etching out an oxide layer using a process such as HP vapor etching, which is performed through special holes 413, as will be discussed in more detail below. Apertures 412 have walls 408, which are made of either a very thin electrically conducting film or a thin thermoelectric film of the type opposite to the thermoelectric films 404, 406 (i.e. if 404, 406 are p-type, 408 is n-type, and vice versa). While six apertures are shown in FIG. 4, such a number is one of the key subjects of optimization and, thus, may be greater or lesser than 6. It is important that the aperture diameter is comparable to the local gas mean free path; for atmospheric air the diameter should be chosen between 10 nm less than 5 micron.

[0073] The electrons, driven by the potential difference of the power supply terminals 415 (negative), 416 (positive), flow left-to-right through heat conductor 407, and then enter the first stage through thermoelectric film 406. The electrons then travel again through heat conductor 407 due to its much higher electric conductivity than thermoelectric films 406. Subsequently, the electrons move up through aperture walls 408 and flow through conductor film 403. Finally, the electrons leave the first stagethrough thermoelectric film 404 and then enter the second stage similar to the first one.Note, a thin layer of a dielectric film 405 (black line) electrically separates thermoelectric layers 404 and 406. Such a flow of electrons is identical to the flow of electric current through the left thermoelectric heat pump 300A of FIG. 3A. Because the direction of the electric current is opposite to the flow of electrons, then, if thermoelectric films 404, 406 are p-type and aperture walls 408 are n-type thermoelectric, the effect of such electron flow in FIG. 4 is high temperature at conductor film 403 and low temperature at heat conductor 407. The temperature gradient induces bulk flow of air through apertures 412, as a result of thermal diffusion.

[0074] For the bulk flow of gas to create noticeable gas pressure gradients, the volumes of air to be compressed by impermeable walls must be bound. As shown in FIG 4, this is achieved by (i) silicon substrate 410, and (ii) two silicon films 410 and 401 which cap and separate different stages. The air volumes (chambers) are also bounded by walls in the in-plane direction of FIG. 4. The resultant bulk air flow is illustrated by vertical gray arrows. Air enters the gas compressor 400 through Air In / Out aperture, moves left-to- right through gas chamber 411 , flows upward through first-stage apertures 412, etc., and leaves the gas compressor 400 via Air Out / ln aperture. Importantly, the electric potentials at terminals 415 and 416 may be reversed, reversing the direction of the electron flow, and causing the air to flow in the opposite direction (thus “Air In / out notation in this figure). This results in the gas compressor 400 being fully bi-directional. As illustrated in FIG. 4, the air inlet and outlet are located at the top side of the silicon substrate (wafer) 410. One or both of the air inlet / outlet may also be built at the bottom,with manufacturing techniques such as deep reactive ion etch used to create channel(s) for the air passage.

[0075] The gas compressor 400 illustrated in FIG. 4 further includes a silicon nitride film 409, an oxide layer 414, and a dashed rectangular inset depicting a complete single stage 500 of the disclosed gas compressor 400.

[0076] The single stage 500 of the gas compressor 400 is illustrated in FIG. 5, which represents a zoomed-in view of the dashed rectangular insert of FIG. 4. As depicted in FIG. 5, electrons flowing left-to-right from a negative terminal of a power supply enter the stage 500 through p-type thermoelectric film 504, then go through the conductor (metal) film 504. Subsequently, the electrons travel downwards through the conductor (or n-type thermoelectric) aperture walls 508, left-to-right through the conductor film 507 and finally exit the stage 500 through p-type thermoelectric film 506. Similar to FIG. 4, thermoelectric material of the p-type thermoelectric films 504 and 506 are of the same type, and if thermoelectric material is used in the aperture walls508, it is to be of the opposite type to the p-type thermoelectric films 504 and 506. The gas / air (depicted in white) moves in the direction of the electron flow, through apertures 512, thus increasing pressure in chamber 511 .

[0077] The sequential deposition of thermoelectric and conduction layers of a thermoelectric stack 600 in an island shown in FIG. 5 is illustrated in more detail in FIG. 6 (as an exemplary PNP apparatus). FIG. 6 represents a zoomed-in view of the conduction layers of the thermoelectric stack 600 (marked as a black dashed rectangle) in FIG. 5. As shown in FIG. 6, a first metal layer 601 (e.g., of high-conductivity metal, such as tungsten) is deposited. Then, a first layer of p-type thermoelectric material 602,such as SiGe, is deposited. This is followed by a thin layer 603 of hard oxide, such alumina, for thermoelectric layer isolation (this corresponds to layer 505 in FIG. 5). This layer will not be affected by subsequent HF vapor etch. Next, a layer of oxide 604 is deposited which will then be removed by HF vapor. Subsequently, a second layer of p- type thermoelectric material 605 is deposited on top of the layer of oxide 604. After removal of the layer of oxide 604, a resulting gap will be naturally filled with air, thus reducing thermal conductivity of the thermoelectric stack 600. Then, a second metal layer 606 is deposited. After patterning and etching circular apertures, an n-type thermoelectric material layer 607 is deposited and then etched to the second metal layer 606. As a result, there will be an aperture 608 in the thermoelectric stack 600, with a diameter equal to the initial aperture diameter minus double thickness of the n-type thermoelectric material layer 607.

[0078] Although the p-type thermoelectric film 504 in FIG. 5 is shown as it was broken into three separate parts by apertures 513, in reality these apertures occupy only a small area of the film in the in-plane direction. This is illustrated in more detail in FIG. 7, which represents a zoomed in view of a thermoelectric island 700 (dashed gray rectangle 700) in FIG. 5, but plotted in the top-down view (a plane perpendicular to the plane of FIG. 5). The thermoelectric island 700 (schematically illustrated in FIG. 7 for a PNP exemplary apparatus) defines apertures 701 , which are used for etching and removing the oxide layer between the thin layer 603 of hard oxide and the p-type thermoelectric material 605 of FIG. 6. These apertures 701 occupy only a small fraction of the area of the p-type thermoelectric film 703 and a top metal conducting film 702.While three apertures 701 are shown to the left and to the right of the conductor film 702and are depicted as circular, this number and shape is a subject of design optimization. Note that thermoelectric film 703 effectively defines an island with apertures (thermoelectric stack), so that the electric current enters the island only through the four sides (left-right-top-bottom) of the thermoelectric film 703. In the example shown in FIG. 7, 48 apertures 704 are plotted. That number, however, as well as the aperture shape, are subjects of design optimization. In the shown embodiment, all apertures are walled with an n-type thermoelectric material 705.

[0079] Aperture optimization also needs to take into consideration that there may be two types of apertures, depending on the electric conductivity of their walls: active and passive. In the active apertures, walls are electrically conductive, i.e. made of metals, thermoelectric materials, or a combination thereof. In the passive apertures, walls are made from a dielectric material (it may also be air). Reducing heat conduction through aperture walls is necessary for both active and passive apertures. The number, location, and shape of both active and passive apertures are subjects of design optimization. The thickness of all thermoelectric, conduction, and air layers of thermoelectric stack also are to be found through optimization. An additional optimization parameter may be the thickness of the parts of the thermoelectric films which hold the island.

[0080] Changing the thickness of the thermoelectric film locally is illustrated in FIG. 8, which represents a cross section of a top part of an island 800 indicated by the dashed line in FIG. 7. The plane of FIG. 8 is, therefore, perpendicular to the plane of FIG. 7 and parallel to the planes of FIG. 4-6. Starting with initially uniform thickness of thermoelectric film 801 , selective etching which has negligible impact on the conduction film 802 will remove part of the thermoelectric film 801 which is not covered by theconduction film 802. The etching will not significantly affect the diameters of apertures 804 but may affect the aperture walls 805 if the wall material is a thermoelectric material similar to the material of the thermoelectric film 801 . In this case, the etching needs to be conducted so that it stops short of removing the electric contact between the conduction film 802 and the aperture walls 805. The main result of such a selective etching are indentations 806.Fabrication of an exemplary embodiment of gas compressor

[0081] An exemplary method 900 of fabricating the PNP gas compressor apparatus 400 of FIG. 4 is illustrated in FIG. 9. Starting from a silicon wafer, the process begins with etching a few micron deep trenches that will be subsequently used as lower gas chambers 411 (shown in FIG. 4). A few hundred nanometer thick silicon nitride liner will then be deposited to later serve as an etch stop. An oxide such as SiO2 will then be deposited using high density plasma-enhanced chemical vapor deposition. The oxide layer will then be polished and annealed, followed by deposition of a thin layer of spin- on-glass, and about a 100 nm layer of tungsten (bottom conduction layer 407). Then, a 100 nm layer of a p-type (boron doped) silicon germanium is grown (bottom thermoelectric layer 406). After patterning and etching, a separating thin layer of alumina is deposited. Subsequently, another layer of oxide is deposited, which later will be removed by etching to create an air gap in the thermoelectric stack between thermoelectric layers 404 and 406. After patterning and etching, a layer about 100 nm thick p-type SiGe is deposited (top thermoelectric layer 404). Then, about 100 nm thick layer of tungsten is deposited, followed by patterning and etching. The next step is to make apertures, first by depositing alumina mask, then patterning apertures, and finallyetching through the thermoelectric stack. After that, the alumina layer is removed, and an n-type SiGe layer (phosphorus doped SiGe) is deposited, thus forming aperture walls 408. This n-type thermoelectric material is subsequently etched to open apertures. An oxide layer is then deposited which shapes up upper gas chambers. The first layer of silicon 402 is deposited on top, and then holes are etched in this layer to create access to HF vapor. The application of HF vapor will subsequently remove all oxide, clearing up the upper and lower gas chambers and the space between the p-type thermoelectric layers, all to be filled with atmospheric air. Finally, another layer of silicon 401 is deposited to seal holes, and subsequently patterned and etched to open the air path.

[0082] Optimal carrier concentration for silicon germanium depends on stoichiometry and is generally around 1O20per cubic centimeter. While N. M. Ravindra, B. Jariwala, A. Banobre and A. Maske describe “Thermoelectric properties of silicon germanium alloys” in chapter 4 of SpringerBriefs in Materials, https: / / doi.org / 10.1007 / 978-3-319-96341- 9_4, and it is a good starting point, each commercial lab working with silicon germanium will have their own recipe for p-type silicon germanium transistors and n-type silicon germanium transistors, and the doping will generally need to increase 2 orders of magnitude per cubic centimeter for thermoelectric applications. Therefore, a proper design of experiment needs to be conducted to find the doping level corresponding to the peak thermoelectric figure of merit ZT at room temperature.Gas compressor optimization methods

[0083] The geometry of the disclosed device can be adjusted and fine-tuned using numerical and / or analytical means and is generally the subject of optimization.

[0084] The optimization should be based on key geometric and flow parameters P, such as the dimensions of the electrical and structural components, thermoelectric elements, gas compression chambers, the angles of the mounts, the distance between sequential stages, the number of stages in series and in parallel, the number of apertures per stage, aperture dimensions, materials of all components, etc. A plurality of apparatus can be connected fluidically in parallel and / or in series in a predetermined arrangement yielding a desired flow rate and / or compression ratio. The optimization may also consider factors related to the interconnects between the upper and lower thermoelectric films of the thermoelectric stack, i.e. solid materials which provide electrical and / or thermal connection between these films. Such interconnects may be (i) active apertures with thermoelectric walls, such as doped silicon germanium, (ii) active apertures with electrically conductive walls which have negligibly small Seebeck coefficient, such as platinum, (iii) passive apertures with dielectric walls (either a directly deposited dielectric of an electrically conductive material such as silicon or metal which is subsequently converted to an oxide), and (iv) thermoelectric (semiconductor) elements shaped as cylinders, rectangles, pillars of various forms, etc., and (v) electrical conductors shaped as cylinders, rectangles, pillars of various forms, etc. An optimized gas compressor may contain any combination of these five types of interconnects. A single interconnect may also combine different thermoelectric, dielectric, and conductor materials. When a particular interconnect is an aperture, the thickness of aperture walls and their porosity need to be factored in. The thickness of aperture walls in interconnect types i-iii and the dimensions of interconnect types iv-v are responsible for structural integrity of the thermoelectric stack and electrical continuity for active apertures. Foractive apertures, both these factors benefit from thicker walls. At the same time, any aperture walls need to be thin enough to minimize thermal backflow. Depending on the application and specific requirements, the aperture walls may be as thin as one monolayer, and as thick as 2 microns. The porosity of the aperture walls, on one hand, reduces the undesirable thermal conduction (heat backflow), but at the same time, reduces the performance-improving electrical conductivity and thermoelectric effect, and may induce performance-degrading internal gas flows. The pores in active and passive aperture walls need to be less than 2 mean free paths, preferably less than 1 mean free path, optimally less than 0.25 mean free path, and ideally 0%. The ratio of hole area to sidewall area needs to be less than 50%, preferably less than 25%, optimally less than 10% and ideally 0%.

[0085] The optimization based on the geometrical parameters and materials needs to take into consideration a number of physical effects and phenomena that may be at play in an operating gas compressor. For example, there are two major effects associated with the propagation of the electric current, the Peltier effect in thermoelectric materials and the Joule heating in all electrically conducting materials. Both of these effects contribute to the temperature distribution and heat flow through the solid materials, but for the temperature estimate to be complete, other effects need to be accounted for. These are primarily the heat conduction through the solids, and the heat convection and conduction by gas at the surfaces; there is also photon radiation which affects the temperature distribution for high enough temperatures. Small size of characteristic features, such as aperture diameters and lengths, makes the thermal diffusion of gas being compressed, and the compounding radiometric, transpiration, and thermal creepeffects, the main mechanisms which govern the bulk flow and the compression of gas. Additional layer of complexity is related to potentially time-dependent, bi-directional operation of the gas compressor, when its compression ratio gradually increases and decreases. Finally, the optimization parameters P may need to be connected with or related to external factors. An example here is the application of the gas compressor to operate a peristaltic fluidic pump, where several gas compressors sequentially deflect a membrane to transport a fluid through a capillary. The parameters P in this case may include some time-dependent input from the membrane that is being deflected.

[0086] The complexity of the underlying phenomena that affect the performance of the disclosed gas compressor makes the optimization of the disclosed gas compressor a complex multi-parametric problem. The solution to the problem may include a number of numerical and theoretical tools of different levels of fidelity, from relatively simple onedimensional approximate formulas and techniques to full 3D, time accurate computational methods. For accurate solution of gas transport, due to the microscopic nature of thermal diffusion phenomena, one needs to use kinetic solvers based on the solution of the Boltzmann equation, such as the direct simulation Monte Carlo method or finite volume methods for model kinetic equations. For accurate modeling of heat transfer through solids, one needs to apply thermal, electric, and heat conduction solvers which, in the most general case, solve the Maxwell equations for the propagation of electromagnetic waves combined with the heat transfer equations. Because the solutions for the gas and the solid affect each other through the gas-solid interfaces, corresponding solvers need to be coupled, or integrated.

[0087] The optimization may proceed through iterations and can be represented in the following algorithm:Model Evolution Algorithm Set model constraints C Set search parameters P Set initial approximation of the embodiment M Do While performance criteria K are not met Do While numerical solution accuracy A is not reached Run kinetic gas solver using C Run electromagnetic & heat conduction solver using C Integrated gas-solid solution S End Do Update M using S and P End Do

[0088] The optimization of the gas compressor may be bound by a set of constraints C such as the preferred operating pressure, gas species, input power, costs of materials, manufacturing process, external factors such as integration, environmental conditions, etc. The optimization process may also use the end-of-optimization criteria K such as the desired mass flow and compression ratios, i.e. the ratios of the outlet and inlet pressures. The optimization needs to take into consideration the fact that the mass flow and the compression ratio oppose each other. The higher the mass flow through the device, the lower the pressure difference across it, and vice versa, the higher the pressure difference, the lower the mass flow. Therefore, to optimize the system design, both the minimally acceptable pressure difference and the mass flow may be required. The optimization should start with an initial approximation of the apparatus model M, which may be the examples of a single stage and multi-stage embodiments shown above. After that, the main loop is run until the optimum configuration M is found thatsatisfies the criteria K. In that loop, the model M is adjusted using the search parameters P and the output from the performance-evaluating solution block. The latter one may be represented as a “do” loop that runs until some prescribed numerical accuracy is reached and may include stand-alone or unified solvers for the gas flow inside the apparatus and the heat flow inside the solid blocks of the device. While simple analytical estimates are possible for these solver steps, the best accuracy of numerical solution would be provided by kinetic gas solvers and finite volume of finite element solvers for the heat conduction, electrical and thermoelectric equations that may also include heat transfer mechanisms such as convection and radiation, etc. The computational optimization process may be assisted and amended by experimental means.Resistively operated gas compressor

[0089] An exemplary embodiment of a nanofabrication-ready gas compressor based on thermoelectric heating and described above is not the only method of creating compression in gases at micro and nanoscale. Another method, illustrated by the exemplary embodiment shown below, is resistive (Joule) heating. The principle of operation of a resistively heated gas compressor 1000 is illustrated in FIG. 10. Electric current is supplied by power source 1001 , which may be a DC battery. The current passes through electrically conducting material 1002, then flows through a thin electrically conducting material 1003, which defines one or more openings (apertures) therein, and finally exits through conducting material 1004.

[0090] In FIG. 10, a single circular aperture 1005 is shown on a flat-plate 1003, but the flat-plate 1003 may have more than one aperture, and such apertures may be anysuitable shape (i.e. not necessarily circular). The result of the electric current passing through electrically conducting material 1002 and the thin electrically conducting material 1003 is their resistive. Because the resistive heat release is inversely proportional to the thickness of the material, and the thin electrically conducting material 1003 is thinner than the electrically conducting material 1002 and conducting material 1004, the thin electrically conducting material 1003 will be hotter than both the electrically conducting material 1002 and conducting material 1004. To create a temperature difference across aperture 1005, and separate gas (air in this example) into hot and cold volumes, a material 1006 is placed above the flat-plate 1003. This material 1006 may be a dielectric, conductor, or semiconductor. Ideally, it will be a material with high thermal conductivity, such as aluminum nitride, silicon nitride, or similar. High thermal conductivity will improve passive cooling of the material 1006 and, thus, increase temperature difference between the material 1006 and the thin electrically conducting material 1003. A single or multiple apertures 1005 provides the path for gas transport from the cold region above the material 1006 to the hot (warm) region below the thin electrically conducting material 1003. Walls 1007 of the aperture(s) 1005 should be made from a low thermal conductivity material, such as polyimide, porous silicon dioxide, parylene, etc., and should be thin enough to minimize heat transfer from the thin electrically conducting material 1003 to the material 1006. For the gas transport to be efficient, the dimensions of the apertures 1005 need to be on the order of the local mean free path of gas molecules. Note that aperture(s) 1005 is the only fluidic path that connects the gas volume above the material 1006 with the gas volume below the thin electrically conducting material 1003; the region between the thin electrically conductingmaterial 1003 and the material 1006 is filled with a thermal and electrical insulator, which may be air, another gas, aerogel, etc.

[0091] To reduce manufacturing costs, and increase energy efficiency, the embodiment shown in FIG. 10 may be modified to remove aperture walls 1007. An embodiment of a resistively heated gas compressor 1100, which implements such a modification is shown in FIG. 11. The electric current, supplied by the power source 1101 , flows through a conductor 1102, then a thin conductor 1103, and finally a conductor 1105. Because the thin conductor 113 is thinner than both conductors 1102 and 1105, it becomes hotter due to resistive heating. Above, and in the immediate vicinity of the conductors 1102, 1103, 1105, there is a material 1106 with high conductivity, which may be either dielectric, conductor, and semiconductor. Material 1106 is heated by the thin conducted 103 through the heat conduction in air, and is passively cooled by the air above it and by the surrounding structure to which the material 1106 is attached. The conductor 1103 defines an aperture (or multiple apertures) 1104, and the material 1106 defines an aperture 1107, such that the aperture 1107 defined in the material 1106 is aligned with the aperture 1103 defined in the conductor 1103. While circular apertures are illustrated in FIG. 11 , other aperture shapes, such as rectangular, may also be used. In the embodiment of FIG. 11 , there are no walls connecting the aperture 1104 defined in the conductor and the aperture 1107 defined in the material 1106, but the distance between the conductor 1103 and the material 1106 should be small enough, preferably less than ten gas molecular mean free paths, for the gas to be compressed in the region below the conductor 1103. For this embodiment, a gap between the conductor 1103 and the material 1106 is filled with the carrier gas, such as air.

[0092] A modification of a thin flat conductor 1103 is illustrated in FIG. 12, which may result in a more uniform temperature distribution over the hot surface in the horizontal direction. In this case, electric current enters through a conductor 1201 , passes through a thin conducting film 1202, heating it, then goes through a thicker conductor 1203, which contains aperture(s) 1204, then flows through another thin conducting film 1205, heating it similarly to the thin conducting film 1202, and exits through conductor 1206. The result of the resistive heating from the passing electric current is elevated temperature in the thin conducting film 1202, thicker conductor 1203, and thin conducting film 1205, where the temperature in the thicker conductor 1203, bound by hot thin conducting films 1202 and 1205, is relatively uniform. Thin conducting films 1202 and 1205, thus, form a “moat” which bounds the temperature of the thicker conductor 1203. Similar to FIG. 11 , where there is a cold plate 1106 in close proximity to with an aperture, the thicker conductor 1203 depicted in FIG. 12 will also require a cold plate with apertures aligned with the apertures 1204. Such apertures may be either walled as in FIG. 10, or wall-less as in FIG. 11 .

[0093] Resistively heated compression stacks shown in FIGS. 10-12 may be assembled in series in a manner amenable to nanofabrication, similar to an example of a thermoelectric compressor embodiment shown in FIG. 4. An example of a resistively driven compressor embodiment is illustrated in FIG. 13. As depicted in FIG. 13, a four- stage gas compressor 1300 uses atmospheric air as an example of an ideal gas, and compresses it by applying electric current to four resistive stacks connected in series. All four stages are made using layered Hot surface - Air - Cold Surface architecture, such as one of those shown schematically in FIGS 10-12. Odd stages have the hotconducting surface on the top of the stack and the cold surfaces on the bottom, moving the air upward. Even stages have the hot conducting surfaces at the bottom, moving the air downward. When electric current is supplied by power source 1308, metal surfaces 1307 become hot, prompting cold-to-hot thermal diffusion of air through apertures 1306. The ambient air (or the air from the volume being de-com pressed) is thus pulled through the compressor entrance 1302 in the direction of the arrow and into the first (leftmost) air chamber 1301 . The leftmost stage moves air upward, and further to the right towards the second stage. The second stage moves air through the apertures downward and towards the third stage, etc. The resulting general direction of air compressor is from left to right, although it may be from left to right if the positioning of cold and hot surfaces is reversed. In the exemplary embodiment shown here, the air exits the compressor 1300 through channel 1303 etched in silicon wafer 1304. As shown FIG. 13, the wafer 1304 bounds the air chambers below the resistive stacks. The air chambers above the resistive stack are bounded by a dielectric cap 1305 which may be one of many materials, such as silicon or silicon nitride.

[0094] Whereas only four stages are shown in embodiment of FIG. 13, any other number may also be used, limited only by the size of a single stage as it relates to the size of the silicon wafer being processed. If required by compressor specifications, stages connected sequentially may also be connected in parallel. The number of sequential stages affects the compression ratio, and the number of parallel stages, the volumetric flow through the compressor.

[0095] The exemplary embodiment of a resistive compressor shown in FIG. 13 is onedirectional, i.e. switching the direction of the electric current as in the thermoelectriccompressor, will not change the direction of the air flow. The resistive compressor, however, may be modified to provide bi-directionality of the gas flow. An example of such a modification is shown in FIG. 14, where the hot conductive surfaces of are at the bottom of all four resistive stacks. The bi-directionality of resistive compressor 1400 is achieved by electric means, where odd and even stages of the compressor are powered separately from power source 1401 using electric switches or relays 1402 to provide independent operation of even and odd stages. In the embodiment illustrated in FIG. 14, powering the odd stages will move air from right to left (from opening 1403 to opening 1404), and powering the even stages will move the air in the opposite direction.

[0096] Techniques consistent with the present disclosure provide, among other features, microfluidic pumps and methods of delivering accurate dosage with such pumps. While various exemplary embodiments of the disclosed systems, devices, and methods have been described above it should be understood that they have been presented for purposes of example only, not limitations. It is not exhaustive and does not limit the disclosure to the precise form disclosed. Modifications and variations are possible in light of the above teachings or can be acquired from practicing of the disclosure, without departing from the breadth or scope.

Claims

WHAT IS CLAIMED IS:1 . An apparatus for creating pressure gradients in gas, comprising: a thermoelectric stack that includes a plurality of thin films of thermoelectric material separated by a thermal and electrical insulator, wherein each thin film, of the plurality of thin films, is in contact with a gas in which a pressure gradient is created; at least one aperture connecting two volumes of the gas at opposite sides of the thermoelectric stack; at least one electrical conductor connecting the plurality of thin films, wherein said at least one electrical conductor includes walls of the aperture or a separate element; and means to supply electric current to the plurality of thin films.

2. The apparatus according to claim 1 , wherein the thermoelectric material of the plurality of thin films is p-type.

3. The apparatus according to claim 1 , wherein the thermoelectric material of the plurality of films is n-type.

4. The apparatus according to claim 2, wherein the walls of at least one aperture are of n-type thermoelectric material.

5. The apparatus according to claim 3, wherein the walls of at least one aperture are of p-type thermoelectric material.

6. The apparatus according to claim 2, wherein at least one n-type thermoelectric element electrically connects the plurality of thin films.

7. The apparatus according to claim 3, wherein at least one p-type thermoelectric element electrically connects the plurality of thin films.

8. The apparatus according to claim 1 , wherein a thicknesses of the plurality of thin films is between a single monolayer of the thermoelectric material and 2 microns.

9. The apparatus according to claim 1 , wherein a thickness of said insulator is between 1 nm and 2 microns.

10. The apparatus according to claim 1 , wherein a thickness of aperture walls is between a single monolayer of the thermoelectric material and 2 microns.11 . The apparatus according to claim 1 , wherein at least one aperture with walls is made of electrically and thermally insulating material.

12. The apparatus according to claim 1 , wherein part of at least one of the plurality of thermoelectric films is in contact with an electrically and thermally conducting film.

13. The apparatus according to claim 1 , wherein said thermal and electrical insulator is air.

14. The apparatus according to claim 1 , wherein the supplied electric current is bi-directional.

15. The apparatus according to claim 1 , wherein the thermoelectric stack has a coating.

16. The apparatus according to claim 1 , wherein at least one film of the plurality of thin films in contact with a heat sink.

17. The apparatus according to claim 16, wherein said heat sink is the electrical conductor.

18. The apparatus according to claim 1 , wherein a thermoelectric material of a type opposite to the thermoelectric material of the plurality of thin films is used as a diode.

19. The apparatus according to claim 1 , wherein the two volumes of gas are confined by walls which define two gas chambers separated by the thermoelectric stack.

20. A plurality of apparatus of claim 19 connected fluidically in parallel and / or in series in a predetermined arrangement yielding a flow rate and / or compression ratio.21 . A method of creating a gas compressor, comprising providing a thermoelectric stack including a plurality of thin films of thermoelectric material; separating each thin film of the plurality of thin films by a thermal and electrical insulator, wherein each thin film, of the plurality of thin films, is in communication with a gas in which a pressure gradient is created; defining at least one aperture connecting two volumes of gas at opposite sides of the thermoelectric stack; connecting, using at least one electrical conductor, the plurality of thin films, wherein said at least one electrical conductor includes walls of the at least one aperture or a separate element; and supplying electric current to the plurality of films.

22. The method according to claim 21 , further comprising: increasing gas compressor efficiency by creating an air gap between the plurality of thin films.

23. The method according to claim 21 , further comprising: increasing gas compressor efficiency by changing a thickness of each film of the plurality of thin films with a selective etching.

24. An apparatus for creating pressure gradients in gas, comprising: a resistive stack including a thin electrically conductive material and a passively cooled material separated by a thermal insulator, wherein the thin electrically conductive material and the passively cooled material are in communication with a gas in which a pressure gradient is created; at least one aperture connecting two volumes of the gas at opposite sides of the resistive stack; and means to supply an electric current to the thin electrically conductive material.

25. The apparatus according to claim 24, wherein thicknesses of the thin electrically conductive material and the passively cooled material are films with thicknesses between a single monolayer of the material and 2 microns.

26. The apparatus according to claim 24, wherein at least one aperture with walls is made of thermally insulating material.

27. The apparatus according to claim 26, wherein said thermally insulating material is air.

28. The apparatus according to claim 24, wherein the supplied electric current is bi-directional.

29. The apparatus according to claim 24, wherein the resistive stack has a coating.

30. The apparatus according to claim 24, wherein the passively cooled material is in contact with a heat sink.31 . The apparatus according to claim 24, wherein said thin conductive material bounds a thick thermally conductive material including at least one aperture.

32. The apparatus according to claim 24, wherein the two volumes of gas are confined by walls defining two gas chambers separated by the resistive stack.

33. A plurality of apparatus of claim 32 connected fluidically in parallel and / or in series in a predetermined arrangement yielding a flow rate and / or compression ratio.

34. A method of creating a gas compressor, comprising: providing a resistive stack including a thin electrically conductive material and a passively cooled material separated by a thermal insulator, wherein the thin electrically conductive material and the passively cooled material are in communication with a gas in which a pressure gradient is created; connecting, via at least one aperture, two volumes of gas at opposite sides of the resistive stack; and supplying an electric current to the thin electrically conductive material.

35. A method according to claim 34, further comprising: increasing gas compressor efficiency by creating an air gap between the thin electrically conductive material and the passively cooled material.

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