Patent Publication Number: US-2015068218-A1

Title: Device and method for forming a temperature gradient

Description:
The invention relates to a device for forming a temperature gradient, comprising at least one gastight working space having a cathode and an anode, wherein an inhomogeneous electric field can be produced when an electric voltage is applied between the cathode and the anode in the working space, as well as a working gas located between the cathode and the anode. 
     Furthermore, the invention relates to a method for producing a device for forming a temperature gradient, wherein the device is formed with at least one gastight working space having a cover plate with a cathode and a base plate having an anode and having a working gas located therebetween so that an inhomogeneous electric field can be produced when an electric voltage is applied between the anode and the cathode in the working space. 
     In addition, the invention relates to a method for forming a temperature gradient between a cathode and an anode in a working space by means of a working gas located in the working space, to which working gas an inhomogeneous electric field is applied. 
     A device for forming a temperature gradient which is based on the application of an inhomogeneous electric field is known from DE 10 2008 021 086 A1 as an electrostatic heat pump. A method with which a temperature gradient is formed by means of an inhomogeneous electric field is also theoretically known from the same document. However, it has been shown that, when the teaching from the aforementioned document is applied, a temperature gradient cannot be formed as theoretically predicted and also that no heat can be transferred according to the teaching. 
     It is therefore the object of the invention to disclose a device of the type named at the outset with which a temperature gradient can be achieved and heat can be transferred. 
     Furthermore, it is an object of the invention to disclose a method for producing a device of the type named at the outset with which a device can be produced with which a temperature gradient can be formed in an electrostatic manner. 
     A further object is to disclose a method for forming a temperature gradient of the type named at the outset, which method produces a temperature gradient between the anode and the cathode. 
     The first object is attained according to the invention in that, for a device of the type named at the outset, a distance between the cathode and the anode is less than 5000 nm to enable a heat transport from the anode to the cathode with the working gas. 
     Since a force acts on the molecules or atoms (molecules and atoms are hereinafter used synonymously, since atoms can also be used in place of molecules and vice versa) of the working gas in the inhomogeneous electric field, which force effects an acceleration of the molecules in the direction of the cathode, a kinetic (thermal) energy of the molecules increases with increasing displacement in the direction of the cathode. During an impact with the cathode, the molecules release a part of their kinetic energy to the cathode, which is thus heated. The molecules are subsequently reflected by the cathode and move away from the cathode in an opposing direction, in the direction of the anode. During a movement of the molecules from the cathode in the direction of the anode, the molecules are slowed down by the electric field and lose kinetic energy. An energy difference of the molecules between the cathode and the anode is equal to that energy which is necessary to displace the molecules against the electric field by the distance between the anode and the cathode. The molecules thus cool down before they impact the anode, for which reason thermal energy is released to the molecules from the anode during a contact of the molecules with the anode. At the same time, the anode is cooled in this manner. The molecules are subsequently reflected from the anode in the direction of the cathode, wherein they once again absorb energy on the path to the cathode via the electric field. The inventors have recognized that a temperature gradient can only be formed when molecules of the working gas oscillate between the anode and the cathode in an inhomogeneous electric field as a result of a molecular motion. Therefore, a distance between the anode and the cathode must be small enough so that the molecules oscillate between the anode and the cathode because of the molecular motion and so that they only interact with few other molecules between the anode and the cathode, wherein energy could be released to other molecules or could be absorbed by these molecules. That means that the molecules of the working gas essentially only interact with the anode and the cathode. Preferably, a gas pressure in the working space is smaller than an ambient pressure in order to be able to reduce an interaction between gas molecules. In this regard, a gas pressure of less than 500 mbar, preferably between 40 mbar and 100 mbar, in particular approximately 60 mbar, has proven to be advantageous. Preferably, a positive electric voltage is applied between the cathode and the anode. However, proper functioning is also ensured if a polarity of the applied voltage is reversed, since the molecules or atoms are always accelerated in the direction of the higher field strength. The terms anode and cathode used to describe the invention therefore do not anticipate the polarity of the applied voltage. A strength of the electric voltage, that is, a potential difference between the cathode and the anode, results from the dimensions of the working space used as well as from the desired field strengths. Anode and cathode refer to those surfaces or regions of the working space at which electrons or an electric field enter or exit the working space from a solid body, for example a metal or a dielectric. 
     It is advantageous that a distance between the cathode and the anode is less than five times, preferably less than double, a free path length of the molecules or atoms of the working gas. The interaction between molecules can thus be further reduced. 
     Preferably, a distance between the cathode and the anode is less than a free path length of the molecules or atoms of the working gas. This makes it possible for the movement of the molecules between the cathode and the anode to be achieved purely as a result of the molecular motion of the molecules and for molecules to oscillate independently in order to transfer energy. A Knudsen number of the working space, which number indicates a ratio of the free path length of the working gas to the distance between the anode and the cathode, is then approximately one or greater than one. 
     Expediently, the distance between the cathode and the anode is smaller than 2000 nm, preferably smaller than 1000 nm, in particular approximately 500 nm. An effect for forming a temperature gradient can thus, as described above, also be achieved in the case of gas pressures that are achievable with a low design cost of the working space. For this purpose, a distance between 200 nm and 800 nm in particular has proven to be especially advantageous. 
     Advantageously, the working space is delimited by a cover plate and a base plate which are at least partially composed of a dielectric. Since high electric field strengths are applied to the working space, typically between 10 7  V/m and 10 9  V/m, in particular approximately 10 8  V/m, at the anode and between 10 8  V/m and 10 10  V/m, in particular approximately 10 9  V/m, at the cathode, dielectrics have proven especially successful. 
     To facilitate a production, it is advantageous that the dielectric comprises a polymer, in particular a Parylene and/or a photoresist. These materials have proven to be especially advantageous for satisfying the requirements in both electrical terms and also in mechanical terms. Especially the SU-8, a negative resist used in microsystems engineering, has proven to be advantageous for forming structures of the indicated dimensions. 
     For the embodiment of the electric field, it is advantageous that the cover plate is coated at least partially with an electrically conductive material, preferably a metal, in particular gold, at a contact surface to the working space. This has also proven to be advantageous in respect of a heat transfer from the working space to the cover plate. 
     However, it can also be provided that the cover plate is not gold-plated, in order to save cost in the production. In this case, electric voltage is transferred to the anode via an essentially planar metal electrode which is worked into the cover plate. In an embodiment of this type, the anode is designed as a dielectric which connects the metal electrode with the working space. This especially has advantages in respect of production imprecisions that could lead to a direct contact between the anode and the cathode. If the anode is designed as a dielectric, a direct contact between the anode and the cathode does not result in any impermissibly large current flows. Furthermore, an undesired distortion of the electric field is avoided. 
     Advantageously, the base plate and the cover plate respectively comprise a substrate, preferably a silicon substrate, which is connected to the dielectric via an electrically conductive planar electrode. This material is particularly well-suited to conducting a heat transferred via the temperature gradient, so that the device can in particular be used as an electrostatic heat pump. 
     It has proven successful that the cathode is formed as a wire electrode which in particular is formed from gold. By means of a cathode that is formed as a wire electrode and an anode embodied in a planar manner, an inhomogeneous electric field can be formed in a particularly simple manner, which field is necessary for the effect described above. 
     Preferably, the at least one working space has a roughly semicircular cross section. An inhomogeneous field can thus be formed between an anode having a roughly semicircular cross section and a cathode that is preferably arranged equidistant to the anode as a wire electrode. Because of the equal distance of the anode to the cathode, an electric field of this type is particularly well-suited to forming a temperature gradient according to the method described above and to transferring heat. 
     It is advantageous if the at least one working space is embodied in a hemispherical shape or in a roughly pyramidal shape. Calculations and trials have shown that this geometry enables an improved method because of paths on which the molecules or atoms move. Advantageously, the wire electrode which forms the cathode then leads, on a planar boundary area of the hemispherical working space or the roughly pyramidal working space, roughly diagonally across this boundary area of the working space. Of course, other geometric forms of the working space are also possible, such as for example truncated cones or truncated pyramids. 
     For a particularly beneficial design of the electric field, it is advantageous that a cross section of the cathode is less than 3%, preferably less than 1%, in particular less than 0.5%, of a cross section of the working space. This enables, in the case of a planar embodiment of the anode and a positioning of the cathode, which is preferably embodied as a wire electrode, equidistant to the anode, an inhomogeneous field which completely fills the working space. The working space is thus utilized particularly efficiently. 
     For a practical application of the device in which a heat flow of several watts is transferred, it has proven successful that multiple working spaces are arranged next to one another, wherein the individual working spaces are spatially connected to one another by bridges. Since only a small amount of energy can be transferred due to the dimensions of each working space, advantageously multiple working spaces are arranged next to one another to also be able to transfer larger amounts of energy. The bridges, which are hollow spaces filled with working gas, also prevent a temperature difference between the anode and the cathode from leading to a heat flow from the cathode to the anode via the base plate and the cover plate. If the working spaces are embodied in a hemispherical shape or in a roughly pyramidal shape, it is advantageous to arrange the working spaces next to one another on two planes so that these planes are arranged in multiple rows and columns in the form of a grid. Particularly in the case of pyramidal working spaces, there thus results a high utilization of the available space on a plane. 
     Expediently, the working spaces arranged next to one another comprise a shared anode. Potential differences between working spaces positioned next to one another which could lead to undesired current flows can thus be avoided. Even if the anodes of the individual working spaces are formed separately, it is advantageous if the anodes of the individual working spaces are electrically connected to one another. 
     Preferably, the cathodes of the working spaces arranged next to one another are electrically connected to one another. On the one hand, this is advantageous in respect of a production; on the other hand, an electric field with a gradient between the cathodes is thus avoided, so that the temperature gradient is only generated between the anode and the cathode. Provided that working spaces embodied in a hemispheric shape or in a roughly pyramidal shape are used, this can be achieved particularly easily in that the cathodes are embodied as wire electrodes which are arranged roughly diagonally on a planar area through the individual working spaces. Thus, one wire electrode forms the cathode of multiple working spaces in a particularly simple manner. 
     To achieve large temperature differences, it is advantageous that multiple working spaces are arranged serially above one another in multiple layers, wherein heat can be transferred between the layers. As a result, temperature differences of the individual layers are added and a total temperature difference of the entire device can be configured via the number of layers. Since, with one layer, only a small temperature difference is achievable as a function of a selected field strength, a working gas used, and the dimensions of the working space, multiple layers must be placed on top of one another such that the temperature differences are added. To transfer heat between the individual layers, the layers are preferably connected via a thermally conductive material, in particular a silicon substrate. 
     With multiple layers arranged on top of one another, it is advantageous that the cathodes of the individual layers and the anodes of the individual layers are electrically connected to one another respectively. Exceedingly high direct current voltages in the device are thus avoided which, for example, could lead to an arcing. 
     The second object is achieved according to the invention in that, in a method for producing a device of the type named at the outset, the cover plate is arranged at a distance of less than 5000 nm to the base plate. 
     As described above, the effect according to the invention is only achieved and a temperature gradient is only formed in a method according to the invention if the molecules or atoms of the working gas essentially do not transfer heat to other molecules of the working gas, but rather transport heat from the anode to the cathode. This is enabled with a small distance of the base plate to the cover plate, wherein preferably a pressure of the working gas is small enough so that only little interaction can occur between individual molecules. In this respect, a pressure that is lower than an ambient pressure, preferably less than 500 mbar, in particular preferably between 40 mbar and 100 mbar, particularly 60 mbar, has proven to be advantageous. 
     Preferably, the cover plate is produced using a stamping die produced in a galvanizing process. Since the cover plate preferably comprises a structuring with dimensions within a nanometer range so that the inhomogeneous electric field can be formed, a high-precision production method is necessary to be able to produce corresponding structures. In this respect, a method has proven to be useful in which a stamping die comprising a negative mold of the structures that are to be produced is produced in the galvanizing process. The cover plate is then stamped using the produced stamping die so that the structures are formed in the cover plate. To stamp the cover plate with the stamping die, a hot stamping method is preferably used in which the cover plate is brought to a deformation temperature and the stamping die is then pressed into the cover plate in a power-controlled manner and/or a path-controlled manner, wherein the cover plate is stamped. The cover plate is subsequently cooled until it has solidified, and the stamping die is removed from the cover plate. 
     To form an advantageous inhomogeneous electric field, the stamping die which is used preferably comprises a galvanic structure with a roughly semicircular cross section, wherein a radius of the roughly semicircular cross section is less than 5000 nm, preferably less than 1000 nm, in particular preferably between 100 nm and 800 nm, particularly roughly 350 nm. The stamping die preferably comprises a polymer layer applied to a base plate, in particular a layer which is composed of Parylene or photoresist. To form the galvanic structure, at least one wire electrode is arranged on a surface of the stamping die, preferably on the polymer layer, in a first step. In a further step metal, preferably gold, is deposited on the wire electrode in a galvanic process by application of an electric voltage. In this manner, a galvanic structure is formed around the at least one wire electrode, which structure comprises the roughly semicircular cross section starting from the wire electrode as a central point. The cross section of the structure, which determines dimensions of the working space via the stamping of the cover plate, can be influenced via the amount of metal that is deposited on the wire electrode. 
     Advantageously, the stamping die that is used comprises a metallization layer having a metallization layer thickness of less than 1000 nm, preferably less than 500 nm, in particular preferably between 50 nm and 300 nm, particularly approximately 100 nm. Particularly if multiple working spaces are produced next to one another, it is advantageous to also provide the galvanic structure with a full-area metallization layer before the stamping of the cover plate. Bridges between the individual working spaces are thus formed during the stamping of the cover plate, which bridges prevent or at least reduce a heat backflow from the cathode to the anode. The metallization layer is preferably composed of gold or potassium. 
     To form the base plate and the cover plate, an electrically conductive planar electrode is preferably applied to a substrate. This has proven to be particularly advantageous for the electric field required in the method according to the invention. 
     Expediently, a dielectric is applied to the planar electrode. Because of the high electric field strengths, this is advantageous for achieving the desired formation of the electric field. 
     To achieve a particularly suitable contacting, a contact surface between the cover plate and the working space is coated with a metal, in particular gold. A thusly produced planar metallization of the contact surface then forms the anode, which is embodied as a planar electrode. If multiple working spaces are arranged next to one another, the anodes of the individual working spaces are connected via the planar metallization. Gold exhibits favorable properties in respect of electrical conductivity, chemical resistance and thermal conduction, for which reason gold is preferably used on the anode. 
     However, it can also be provided that the contact surface between the working space and the cover panel, which forms the anode, is designed as a dielectric. This has advantages in the event of a direct contact between the anode and the cathode occurring due to imprecisions during the production. If the anode is designed as a dielectric, high currents and field distortions are avoided in the case of a direct contact. The production can also be simplified by this measure, in which the face of the anode is not coated. 
     To form a device which comprises multiple working spaces arranged next to one another and on top of one another to be able to produce large temperature differences, multiple base plates and cover plates are stacked on top of one another. It can thereby be provided that one plate can be embodied on a top side as a base plate and one plate on a bottom side as a cover plate in order to design a production process in a simpler manner and to improve a heat transfer from one layer to a next layer. 
     To simplify the production, it is advantageous if roughly flat planar electrodes are applied to an essentially plate-shaped substrate layer on two sides, which electrodes form electrodes of working spaces positioned on top of one another. Those parts via which an electric voltage is conducted from outside the device into the region of the working space are thereby referred to as electrodes. However, these electrodes do not need to lead directly into the working space, since the electric field is also formed when the electrodes lead to a region bordering the working space, for example to a dielectric. Preferably the electric voltage that generates the electric field is applied to these electrodes in the method. This simplifies the production and reduces costs in the production. The substrate layer is thereby advantageously composed of a dielectric, whereby high currents inside the substrate layer from an electrode of a layer to the electrode of the layer positioned thereabove are prevented. A thickness of the substrate layer which defines a distance between the cathode and the anode is thereby determined as a function of a desired maximum current inside the plate and of a conductance of the dielectric selected. Typically, currents inside the substrate layer are less than 10 −5  A, in particular less than 10 −10  A, preferably smaller than 10 −15  A. Because the substrate layer in this embodiment assumes both a structural function concerning a gastight separation of working spaces positioned on top of one another and also an electric function concerning the supply of an electric potential to working spaces positioned on top of one another, the production can occur in a particularly cost-effective manner. 
     It can also be preferred that the cathode is formed by a wire electrode produced in a lift-off process. The lift-off process has proven successful for producing structures within the nanometer range. A sacrificial layer, usually a photoresist, is thereby deposited on a substrate in a first step. The sacrificial layer is then structured using an inverse pattern of the eventual structure. This preferably occurs in a hot-stamping process or by means of photolithography. 
     After the structuring, metal, preferably gold, is deposited across the entire area on the structured surface, wherein the metal is deposited on the substrate in the region of the structuring. In a final step, the sacrificial layer is removed in a wet-chemical manner, for example using a solvent, wherein the metal that was deposited on a top side of the sacrificial layer is lifted and removed. Thus, only the metal in the regions of the structuring remains, where metal is in direct contact with the substrate. In this manner, the wire electrodes within the nanometer range can be produced particularly precisely and cost-effectively. 
     The third object is attained in that, in a method for forming a temperature gradient of the type named at the outset, molecules or atoms of the working gas carry out a molecular motion and thereby oscillate between the cathode and the anode, wherein these molecules or atoms absorb energy at the anode and release energy at the cathode. 
     Because the molecules or atoms oscillate independently between the anode and the cathode due to the molecular motion, energy can be inputted into the molecules through the electric field during a movement in the direction of the cathode, whereby a kinetic (thermal) energy of the molecules is increased. At the cathode, the molecules release energy to the cathode, whereby the cathode is heated. The molecules are then reflected in the direction of the anode. In a subsequent motion in the direction of the anode, the kinetic (thermal) energy of the molecules decreases, since these molecules are moved against the electric field, whereby the molecules can absorb energy at the anode before they are once again reflected in the direction of the cathode. Only by means of an independent oscillation of the molecules as the result of the molecular motion does the method become effective and lead to the formation of a temperature gradient between the anode and the cathode, whereby heat is transferred by means of an electrostatic process. 
     Preferably, molecules or atoms of the working gas essentially only interact with the anode and the cathode of the working space. This prevents an undesired heat transfer between molecules among one another, whereby the effect described above would appear to a considerably lesser extent, since molecules could already be cooled before arriving at the cathode. Preferably, the dimensions of the working space and the thermodynamic states of the working gas are chosen such that a molecule on the path between the anode and the cathode only strikes another molecule with a very low probability. This can be influenced particularly easily by a distance from the anode to the cathode in the working space and a pressure of the working gas. 
     Advantageously, a working space is used which comprises a distance between the anode and the cathode which is less than five times, preferably less than double, a free path length of the molecules or the atoms of the working gas. With an embodiment of this type of the working space, the method for forming the temperature gradient can be achieved particularly advantageously, since little interaction takes place between molecules. 
     Particularly preferably, a working space is used which comprises a distance between the anode and the cathode which is less than the free path length of the molecules or the atoms of the working gas. In this manner, a movement of the molecules between the anode and the cathode is guaranteed as a result of the molecular motion. A Knudsen number of the working space, which indicates a ratio of the free path length of the working gas to the distance between the anode and the cathode, is then approximately one or slightly greater than one. 
     It has proven successful that the molecules or atoms of the working gas are accelerated from the anode in the direction of the cathode by the electric field. Energy is thus inputted into the molecules, which release this energy to the cathode to transfer heat and to form the temperature gradient. 
     It is advantageous that molecules or atoms of the working gas are decelerated at the cathode, wherein energy is released from the molecules or the atoms to the cathode. A temperature gradient between the anode and the cathode is thereby formed which enables a heat flow. 
     It is advantageous if a working gas is used which does not comprise a dipole moment. Due to the electric field, a working gas without a dipole moment is polarized and the molecules of the working gas are aligned according to the electric field and are accelerated by the electric field. Because the dipole moment of the working gas is induced by the electric field, a polarization of the molecules is retained even after an impact of the molecules with the anode or the cathode. In contrast to a working gas which comprises a dipole moment, an alignment of the molecules as in the case of a working gas with a static dipole moment does not occur. Preferably, a working gas is used which has a high polarizability and a high mass in order to maximize a transferable heat flow per volume. In this regard, particularly gases or molecules that can be brought into the gas phase, such as argon, xenon, C 60 , C 60 F 60 , iodine, SF 6 , and UF 6  have proven successful. 
     Expediently, corresponding processes take place in multiple working spaces positioned on top of one another, wherein a temperature difference between a bottommost working space and a topmost working space is formed which is larger than the temperature difference that can be produced with a single working space. In this manner, a greater temperature difference is formed than that which would be possible with a single layer, whereby heat flows of several megawatts can be transferred. 
    
    
     
       Additional features, advantages and effects of the invention follow from the exemplary embodiment illustrated below. The drawings which are thereby referenced show the following: 
         FIG. 1  through  FIG. 5  show devices according to the invention for forming a temperature gradient; 
         FIG. 6  shows a stamping die for producing a device according to  FIG. 1  in a first production step; 
         FIGS. 7 and 8  show the stamping die according to  FIG. 6  in additional process steps. 
         FIG. 1  shows a device  1  according to the invention for forming a temperature gradient, wherein a base plate  2  and a cover plate  3  are visible. In the present exemplary embodiment, the base plate  2  and the cover plate  3  are respectively formed from a substrate layer  5 , preferably composed of a silicon substrate, onto which respectively one planar electrode  6  is applied. A layer composed of a dielectric  4  is applied respectively to the planar electrodes  6 . The planar electrodes  6 , which are arranged between the layer of the dielectric  4  and the substrate respectively in the base plate  2  and cover plate  3 , are composed preferably of gold, in particular to be able to conduct a heat especially well which is transported in a method according to the invention. As can be seen in  FIG. 1 , the base plate  2  comprises an essentially planar surface on which cathodes  8  formed as wire electrodes are arranged. The cover plate  3  comprises a structuring on that side which opposes the base plate  2 . The surface of the structured side is covered by a metallization which is preferably formed from gold and forms anodes  7 . Because of the structuring of the cover plate  3 , the planar embodiment of the anodes  7  and a line-shaped embodiment of the cathodes  8 , an inhomogeneous electric field forms when an electric voltage is applied between the anodes  7  and the cathodes  8 , which field is essential for the formation of a temperature gradient. In the present exemplary embodiment, the structuring of the cover plate  3  is embodied in a roughly semicircular shape in order to allow a uniform distance from the planar anode  7  to the line-shaped cathode  8 . This enables an electric field, which is particularly advantageous for the formation of a temperature gradient. The device  1  comprises an extension in a direction perpendicular to an illustrated drawing plane so that the structuring in the cover plate  3  essentially comprises semicylindrical surfaces. A working space  9  which is formed between respectively a cathode  8  and the semicircular anode  7  across from the cathode  8  is filled by a working gas. In  FIG. 1 , three working spaces  9  are fully depicted in cross section, wherein the individual working spaces  9  are connected among one another by bridges  13 . The bridges  13  prevent a heat flow from the cathode  8  to the anode  7  via the layer which is formed from a dielectric  4 . A minimum distance  11  between the base plate  2  and the cover plate  3 , which distance exists because of the bridges  13 , is approximately 100 nm in the exemplary embodiment illustrated. A polymer, in particular a Parylene, or a photoresist is used, preferably the commercially available SU-8, as a dielectric  4 . To accurately position the cover plate  3  and the base plate  2 , spacers which are not depicted are arranged between the base plate  2  and the cover plate  3 , which spacers have the dimensions of the minimum distance  11  between the base plate  2  and the cover plate  3  to ensure the minimum distance  11 . To enable a method for forming a temperature gradient with the device  1 , the dimensions of the working space  9  and the space between the base plate  2  and the cover plate  3  are to be chosen such that the distance between the cathode  8  and the anode  7  is roughly equal to a free path length of molecules or atoms of the working gas. This is dependent upon the working gas used and a pressure in the working space  9 . In the present exemplary embodiment, the minimum distance between the cathode  8  and the anode  7  is respectively approximately 500 nm; the cathode  8  has a circular cross section with a diameter of approximately 50 nm. The minimum distance  11  between the base plate  2  and the cover plate  3  in the region of the bridges  13  is approximately 100 nm. The dielectric  4  of the base plate  2  has a dielectric thickness  12  of approximately 350 nm. The anodes  7  of the individual working spaces  9  are connected among one another in the region of the bridges  13  in an electrically conductive manner by the metallization which covers the entire structured surface of the cover plate  3 . To prevent current flows between the individual cathodes  8 , the individual cathodes  8  are also electrically connected among one another. Since only small temperature differences and transferable heat flows are achievable with a single working space  9  due to the small dimensions, multiple working spaces  9 , as indicated in  FIG. 1 , are arranged next to one another. In addition, multiple working spaces  9  are also positioned on top of one another so that the temperature differences of the individual layers can be added and so that large heat flows can also be transferred. To avoid high potential differences between the individual layers, it has proven successful to electrically connect all of the anodes  7  among one another and to electrically connect the cathodes  8  among one another. An inert gas without a dipole moment is used as a working gas. The working space  9  can be embodied as schematically illustrated in  FIG. 1 . Preferably, sharp edges, in particular in the region of the bridges  13 , can also be rounded to avoid peak discharges. However, it can also be preferably provided that the anodes  7  of the working spaces  9  are not coated, so that the anodes  7  are formed from the dielectric  4  and so that no metallization is provided on the anodes  7 . This has proven to be expedient in a direct contact between the anode  7  and the cathode  8  and therefore for avoiding current flows and field distortions. In addition, a production is thus also simplified. Because of the dimensions within the nanometer range, a direct contact cannot be ruled out in particular due to production imprecisions. 
         FIGS. 2 and 3  show a further device  1  according to the invention in a side view and top view, which device in contrast to the device  1  according to  FIG. 1 , however, does not have any significant extension in a direction perpendicular to an illustrated drawing plane, but rather comprises roughly pyramidal working spaces  9  which are again connected via bridges  13 . In particular, this has the advantage that atoms or molecules cannot be deflected in the direction of the extension and that an efficiency is increased. Further, the device  1  according to  FIGS. 2 and 3  does not comprise any metallized anodes  7  in order to avoid an undesired current flow and a field distortion in the event of production imprecisions which could lead to a contact between the anode  7  and the cathode  8 . 
     
    
    
     The anode  7  at which electrons enter or exit the working space  9  depending on a polarization of the applied voltage is formed by the dielectric  4  in the device  1 , which is illustrated in  FIGS. 2 and 3 . The voltage is applied to the planar electrodes  6  which are arranged on the substrate layer  5 . In  FIG. 3 , it can be recognized in the top view that multiple working spaces  9  are arranged next to one another in multiple rows and columns in order to transfer larger current flows. Preferably, multiple layers are arranged on top of one another, wherein it is advantageous to apply two planar electrodes  6  to a roughly plate-shaped substrate layer  5 , which electrodes are used as voltage supplies for the working spaces  9  arranged below and above the substrate layer  5 . Thus, the base plate  2 , the substrate layer  5  and the cover plate  3  with worked-in planar electrodes  6  can be pre-produced as a single element. For an assembly of the device  1 , the pre-produced elements can then only be positioned above one another. The base plate  2  of a working space  9  positioned above the base plate  2  is then a part of the same element which forms the cover plate  3  of a working space  9  positioned therebeneath. A distance of the planar electrodes  6  that are arranged on a substrate layer  5  is preferably chosen such that a flow from a planar electrode  6  through the substrate layer  5  onto the second planar electrode  6  arranged on the substrate layer  5  is less than 10 −5  A, preferably 10 −10  A, in particular 10 −15  A. Along with the distance, this flow is dependent upon the conductance of the material of the substrate layer  5  and upon the selected voltage between the anode  7  and the cathode  8 . The device  1  according to  FIGS. 2 and 3  essentially has similar main dimensions to the device  1  shown in  FIG. 1 , wherein the working space  9  has a maximum height of approximately 450 nm. An electrode distance  21  of the planar electrode  6 , which is arranged above the anode  7 , to the cathode  8  is approximately 800 nm so that a distance between two planar electrodes  6  of a working space  9  is approximately 1150 nm. A distance from a wire electrode  15  to a wire electrode preferably positioned parallel next to it is approximately 1100 nm. Between the working spaces  9 , bridges  13  are once again provided which ensure a minimum distance  11  of approximately 100 nm. 
       FIGS. 4 and 5  show a further device  1  according to the invention in a side view and top view, which device only differs from the device  1  depicted in  FIGS. 2 and 3  in that the working space  9  is not embodied as a full pyramid, but rather as a truncated pyramid. The essential dimensions are embodied analogously to the devices  1  according to  FIGS. 1 through 3 . A maximum height of the working space in the shape of a truncated pyramid is approximately 550 nm. 
       FIG. 6  shows a stamping die  14  which is used to produce the cover plate  3  from  FIG. 1  in a first production step. In a process step according to  FIG. 6 , the stamping die  14  is composed of a base plate  17  which, similar to the base plate  2  according to  FIG. 1 , is formed from a substrate and a dielectric  4 . A silicon substrate is preferably used as a substrate; a polymer, in particular Parylene, or a photoresist, in particular the photoresist SU-8, is preferably used as a dielectric  4 . On the surface of the dielectric  4  of the stamping die  14 , which is essentially embodied in a planar manner, wire electrodes  15  are arranged which essentially have a circular cross section. The wire electrodes  15  are preferably formed in a lift-off process, wherein sharp edges are rounded by tempering. It has thereby proven to be advantageous to use a lift-off process based on an electron beam lithography, wherein gold is preferably used as a wire material. Preferably, Parylene on silicon is used as a substrate material for the lift-off process. To round the edges of the wire electrodes  15  produced in the lift-off process, which electrodes have a width of less than 100 nm and wire spacings of approximately 1 μm, the wire electrode  15  is tempered following the lift-off process. In this process step, the surface roughness and the wire shape are optimized at approximately 50° C. to 500° C., preferably 100° C. to 300° C. The stamping die  14  preferably has the same extension in a direction perpendicular to the illustrated sectional plane as the device  1  according to  FIG. 1  in order to be able to design the production in a simple manner. To produce the structure illustrated in  FIG. 1  in the dielectric  4  of the cover plate  3 , which structure essentially comprises semicylindrical recesses in the cover plate  3 , the cover plate  3  is heated until the dielectric  4  has transitioned into a deformable state. A negative mold of the structuring is then pressed into the dielectric  4  so that the desired structuring is formed in the dielectric  4 . The negative mold or stamping die  14  is formed in that, as illustrated in  FIG. 7 , a galvanic structure  18  is applied to the stamping die  14  according to  FIG. 6  in a further process step, which structure has an essentially semicircular cross section for each working space  9 . For this purpose, metal is deposited on the wire electrodes  15  in a galvanizing process, wherein a galvanic structure  18  forms around each wire electrode  15 , which structure has a semicircular cross section. To form the cover plate  3  from  FIG. 1 , which has a working space radius  10  of approximately 500 nm, metal is deposited on the wire electrode  15  until the galvanic structure  18  has a structural radius  16  of approximately 350 nm. If, as illustrated in the exemplary embodiment, a working space  9  with a roughly circular cross section is used, the working space radius  10  is equal to the minimum distance between the anode  7  and the cathode  8 . To stamp the bridges  13  which connect the individual working spaces  9  among one another and enable a minimum distance  11  between the base plate  2  and the cover plate  3 , a metallization layer  19  is applied to the galvanic structure  18 . 
       FIG. 8  shows the stamping die  14  from  FIG. 7 , wherein a full-area metallization layer  19  with a metallization layer thickness  20  of approximately 100 nm is applied to the galvanic structure  18  in a further processing step. The full-area metallization is preferably composed of gold or potassium. These metals have proven particularly successful for stamping the desired structure into the cover plate  3 . The devices  1  according to  FIGS. 2 through 4  are produced in an analogous manner with adapted stamping dies  14 , wherein the application of a metallization to the anode  7  as explained above is not mandatory. 
     To form a temperature gradient and to transfer heat with the device  1  from  FIG. 1 , an electric voltage is applied to the anode  7  and the cathode  8  or to the planar electrodes  6  so that an inhomogeneous electric field is produced in the working space  9 . The electric field thereby has a field strength of approximately 10 8  V/m at the anode and a field strength of approximately 10 9  V/m at the cathode. As a result of the electric field, molecules of the working gas which is preferably free of a dipole moment are polarized and accelerated in the direction of the cathode  8 . Since the minimum distance between the anode  7  and the cathode  8 , the working space radius  10 , is roughly equal to a free path length of the molecules of the working gas, the molecules of the working gas oscillate constantly between the anode  7  and the cathode  8 . A pressure in the working space is typically smaller than an ambient pressure, preferably smaller than 500 mbar, in particular preferably between 40 mbar and 100 mbar, particularly approximately 60 mbar. Because of an acceleration which the molecules experience during a movement from the anode  7  to the cathode  8 , a kinetic and therefore thermal energy of the molecules increases. During the impact of the molecules on the cathode  8 , the molecules release heat to the cathode  8 , whereby a heating of the cathode  8  occurs. The molecules are then reflected by the cathode  8  and move in the direction of the anode  7 . During a movement in this direction, the kinetic and thermal energy of the molecules decrease, since they are moved against the electric field. The molecules are thus cooled until they arrive at the anode  7  and absorb energy from the anode  7  in the form of heat during an impact with the anode  7 . The molecules are then reflected again in the direction of the cathode  8 . Preferably, a working gas without a dipole moment, in particular an inert gas, is used. However, it is also possible to use a working gas which has a dipole moment. Molecules of a working gas of this type are aligned in the direction of the electric field by the electric field. 
     With a method according to the invention, it is possible to form a temperature gradient by means of an electrostatic field. For example, a temperature difference of approximately 1.5 K to 3.5 K can be achieved with a device as illustrated schematically in  FIG. 1 . It is thus possible to omit mechanically moved parts that are used in conventional devices to form a temperature gradient, whereby signs of wear and noises are avoided. Through an arrangement of multiple layers on top of one another, the achievable temperature difference can be increased. With a method according to the invention and a device  1  according to the invention, large temperature differences can also be produced and heat flows of several megawatts can be transferred with a corresponding arrangement of multiple working spaces  9  next to one another and on top of one another.