Patent Publication Number: US-2023144778-A1

Title: Geometrically stable nanohenry inductor

Description:
STATEMENT OF GOVERNMENTAL SUPPORT 
     This invention was made with government support under DE-NA0002839 awarded by the United States Department of Energy/National Nuclear Security Administration. The government has certain rights in the invention. 
    
    
     BACKGROUND 
     1. Field 
     Embodiments of the invention relate to inductors. More specifically, embodiments of the invention relate to inductors configured to produce low value inductances at high frequencies. 
     2. Related Art 
     Inductors typically consist of a wire wrapped into a coil that resists change in current flowing through the wire. However, these traditional inductors are not suitable for providing stable high precision inductance standards for low inductance values. 
     As such, inductance is typically measured using an LCR (inductance, capacitance, resistance) meter that is calibrated using capacitance standards in which complex impedance values are converted into inductance. This method of calibration may be suitable for some ranges of inductance values but becomes inaccurate for inductances in the nanohenry range at high frequencies. Further, the extrapolation and conversion of such methods increases uncertainty in measured values. Further still, capacitors take too long to charge at high frequencies such that it becomes difficult to determine impedance using capacitor calibrated techniques for said frequencies. Specifically, high-value capacitors take a substantial amount of time to charge, therefore requiring lower frequencies to fully charge. As such, it becomes difficult to determine impedance using capacitor calibrated techniques at higher frequencies. Accordingly, what is needed is an inductor and calibration technique capable of producing and measuring inductances accurately at this range. 
     SUMMARY 
     Embodiments of the invention solve the above-mentioned problems by providing a low-value inductor that is stable at high frequencies. In some embodiments, the inductor includes a plurality of radial spokes extending between a first ring and a second concentric ring. Here, the inductance may be selected based on the number and dimensions of the plurality of spokes. In some embodiments, the inductor is a thin film network produced using a thin-film deposition technique. 
     A first embodiment of the invention is directed to an inductor comprising an inner ring, an outer concentric ring forming an outer perimeter, and a plurality of spokes extending radially from the inner ring to the outer ring, each of the plurality of spokes secured to the inner ring at a first end and secured to the outer ring at a second end, wherein the plurality of spokes provides an electrical resistance and a stable electrical inductance based at least in part on a number of spokes in the plurality of spokes, and wherein the inductor is configured to provide a nanohenry inductance value at a frequency equal to or greater than about 100 kilohertz. 
     A second embodiment of the invention is directed to a low value inductor system comprising a non-conductive base portion, and a conductive inductor portion disposed on a surface of the base portion comprising an inner ring, an outer concentric ring, and a plurality of equidistantly spaced spokes extending radially from the inner ring to the outer ring, each of the plurality of spokes secured to the inner ring at a first end and secured to the outer ring at a second end, the plurality of spokes providing an electrical resistance and a stable electrical inductance based at least in part on a number of spokes in the plurality of spokes. 
     A third embodiment of the invention is directed to a method for providing a low value inductor comprising determining one or more materials for the inductor based at least in part on an electrical conductivity, determining a number and one or more dimensions of a plurality of spokes to achieve a desired inductance for the inductor based at least in part on the one or more materials, depositing a first layer of the inductor onto a substrate surface, depositing a second layer of the inductor onto the first layer, and depositing a third layer of the inductor onto the second layer, wherein the inductor comprises an inner ring, a concentric outer ring, and a plurality of spokes extending radially from the inner ring to the outer ring, each of the plurality of spokes secured to the inner ring at a first end and secured to the outer ring at a second end, the plurality of spokes providing an electrical resistance and a stable electrical inductance based at least in part on the number of spokes in the plurality of spokes. 
     Additional embodiments of the invention are directed to methods of manufacturing a low value inductor including using a circuit tracing technique or thin film deposition technique to apply the inductor onto a substrate surface. In some such embodiments, the inductor may be applied as a plurality of material layers stacked upon each other. 
     Further, embodiments of the invention are directed to a method of manufacturing a low value inductor, the method comprising determining dimensions and a number of spokes in a plurality of spokes for the inductor based at least in part on a desired inductance for the inductor, depositing a first layer of the inductor onto a substrate surface, depositing a second layer of the inductor onto the first layer, and depositing a third layer of the inductor onto the second layer, wherein each layer comprises a predetermined thickness and a material for each layer is selected based on one of an electrical conductivity of the material or a connection property of the material. 
     Further still, embodiments of the invention are directed to methods of using a low value inductor to provide a low value inductance standard for calibrating an LCR meter. 
     This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Other aspects and advantages of the invention will be apparent from the following detailed description of the embodiments and the accompanying drawing figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING FIGURES 
       Embodiments of the invention are described in detail below with reference to the attached drawing figures, wherein: 
         FIG.  1    depicts an inductor system relating to some embodiments of the invention; 
         FIG.  2 A  depicts an inductor with five radial spokes relating to some embodiments of the invention; 
         FIG.  2 B  depicts an inductor with three radial spokes relating to some embodiments of the invention; 
         FIG.  2 C  depicts an inductor with corresponding dimensions relating to some embodiments of the invention; 
         FIG.  3    depicts a side view of an inductor system relating to some embodiments of the invention; 
         FIG.  4    depicts an exemplary measurement system relating to some embodiments of the invention; 
         FIG.  5    depicts an exemplary circuit board relating to some embodiments of the invention; 
         FIG.  6    depicts an impedance nomograph relating to some embodiments of the invention; and 
         FIG.  7    depicts an exemplary method for manufacturing an inductor relating to some embodiments of the invention. 
     
    
    
     The drawing figures do not limit the invention to the specific embodiments disclosed and described herein. The drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the invention. 
     DETAILED DESCRIPTION 
     The following detailed description references the accompanying drawings that illustrate specific embodiments in which the invention can be practiced. The embodiments are intended to describe aspects of the invention in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments can be utilized and changes can be made without departing from the scope of the invention. The following detailed description is, therefore, not to be taken in a limiting sense. The scope of the invention is defined only by the appended claims, along with the full scope of equivalents to which such claims are entitled. 
     In this description, references to “one embodiment,” “an embodiment,” or “embodiments” mean that the feature or features being referred to are included in at least one embodiment of the technology. Separate references to “one embodiment,” “an embodiment,” or “embodiments” in this description do not necessarily refer to the same embodiment and are also not mutually exclusive unless so stated and/or except as will be readily apparent to those skilled in the art from the description. For example, a feature, structure, act, etc. described in one embodiment may also be included in other embodiments, but is not necessarily included. Thus, the technology can include a variety of combinations and/or integrations of the embodiments described herein. 
     Turning first to  FIG.  1   , an inductor system  100  is depicted relating to some embodiments of the invention. In some embodiments, the system  100  includes a base portion  102  and an inductor  104 . In some such embodiments, the base portion  102  may comprise a ceramic or other non-conductive material. Alternatively, in some embodiments, the base portion  102  may comprise a semiconductor material such as silicon. In some embodiments, the inductor  104  may comprise a conductive material such as a metallic material. Further, in some embodiments, the inductor  104  may comprise a variety of different materials, as will be described in further detail below. In some embodiments, the inductor  104  comprises a thin film network including a corresponding sheet resistance based on the geometry of the thin film network. 
     In some embodiments, the inductor  104  provides an electrical inductance that may be used as an inductance standard for a measurement device as will be described in further detail below. Further, the inductor  104  may be used to provide an electrical inductance within various electronic devices and circuits. Accordingly, embodiments are contemplated in which the inductor  104  provides an electrical path while the base portion  102  is non-conductive. Here, the base portion  102  may function as a substrate providing structural support for the inductor  104 . 
     In some embodiments, the inductor  104  comprises an inner ring  106 , as shown. The inner ring  106  may be a circular ring disposed in a central portion of the inductor  104 . The inductor  104  may further comprise an outer ring  108  disposed on an outer portion of the inductor  104 . In some embodiments, the outer ring  108  is a circular ring which is comparatively larger than the inner ring  106  disposed on an outer perimeter of the inductor  104  and is disposed concentrically around the inner ring  106 , as shown. The inductor  104  further comprises a plurality of spokes  110 . In some embodiments, each of the spokes  110  may be radially disposed between the inner ring  106  and the outer ring  108 . Here, the spokes  110  may be secured at a first end  107  to the inner ring  106  and at a second end  109  to the outer ring  108 . 
     In some embodiments, the plurality of spokes  110  may be equidistantly spaced radially around the inner ring  106 . In some embodiments, the plurality of spokes may be unevenly spaced. In some embodiments, the equidistant spacing of the spokes provides increased stability and reduces variability in the inductor  104  because the signal flow through the inductor  104  is distributed evenly through each of the spokes  110 . For example, in some embodiments, a resonant frequency of the inductor  104  may be maintained by equidistantly spacing the spokes  110 . In some embodiments, each of the spokes  110  provides an electrical connection between the inner ring  106  and the outer ring  108 . 
     In some embodiments, the inductor  104  may be secured to the base portion  102  using a thin film deposition technique, such as sputtering. For example, in some embodiments, the inductor  104  may be sputtered onto a surface of the base portion  102 . Here, a sputtering stencil may be used to control the geometry of the inductor  104 . Accordingly, the sputtering stencil may include a cutout portion representing the final size and shape of the inductor  104  including the inner ring  106 , the outer ring  108 , and the plurality of spokes  110 . Accordingly, each of the inner ring  106 , the outer ring  108 , and the plurality of spokes  110  may be part of a thin film network of the inductor  104 . However, it should be understood that a variety of different processes may be used depending on the size of the inductor and the types of materials used for each of the inductor  104  and the base portion  102 . For example, in some embodiments, the inductor  104  may comprise a copper material and may be produced as a circuit trace on a circuit board, as will be described in further detail below. 
     Turning now to  FIG.  2 A , the inductor  104  is depicted relating to some embodiments of the invention. In some embodiments, the inductor  104  may include five spokes, as shown, extending radially outward from the inner ring  106  to the outer ring  108 . In some embodiments, the number of spokes may be selected to achieve a specific resistance and inductance for the inductor  104 . Here, the electrical resistance may be comparatively decreased by increasing the number of spokes and the electrical resistance may be increased by decreasing the number of spokes. Further, in some embodiments, the resistance and inductance of the inductor  104  may be further affected by the length and width of the spokes  110 . In some embodiments, the spokes  110  may be cylindrical, rectangular, or another suitable shape. For example, embodiments are contemplated in which the spokes  110  may be conical. Further, in some embodiments, the shape of the spokes  110  may be selected based on the type of manufacturing process used to produce the spokes. 
     In some embodiments, each of the inner ring  106  and the outer ring  108  may comprise electrical nodes of the inductor  104 . For example, in some embodiments, the inner ring  106  may provide a first node of the inductor  104  while the outer ring  108  provides a second node of the inductor  104 . Accordingly, a signal path may be provided within the inductor  104  from the inner ring  106  through the plurality of spokes  110  into the outer ring  108 . Here, the plurality of spokes  110  provide a plurality of parallel electrical paths between the nodes of the inductor  104 . Accordingly, the electrical resistances of the plurality of spokes  110  are electrically parallel such that the overall electrical resistance and electrical inductance of the inductor  104  decreases as the number of spokes  110  increases. Further, embodiments are contemplated in which the signal path may be reversed such that the signal path starts at the outer ring  108  and travels through the spokes  110  to the inner ring  106 . Accordingly, a signal may be provided as either of a current or voltage to the inductor  104 . 
     In some embodiments, each of the plurality of spokes  110  may include specific dimensions. In some embodiments, the spokes  110  may be about 0.001 to about 0.003 inches wide. In some embodiments, the spokes  110  may be about 0.05 to about 0.2 inches long. In one embodiment, the spokes  110  are approximately 0.002 inches wide and approximately 0.102 inches long. In some such embodiments, the thickness and length of the spokes may affect the overall resistance and inductance of the inductor  104 . For example, the resistance of the inductor  104  may increase as the thickness of the spokes  110  is decreased. In some embodiments, the spokes  110  may be cylindrical or rectangular. In some embodiments, the shape and specific dimensions of the spokes  110  may vary based on the material and the manufacturing process used to produce the spokes  110 . Further, in some embodiments, the dimensions of the inductor  104  may be outside of the ranges described above. For example, the inductor  104  may be much smaller such that the inductor  104  can be disposed on a circuit board. 
     In some embodiments, the geometry of the inductor  104  acts as a simple transmission line providing an electrical path from the inner ring  106 , through the plurality of spokes  110 , and into the outer ring  108 , such that impedance mismatch and de-embedding issues are avoided. In some embodiments, the inductor  104  is a thin film with a uniform thickness which provides a sheet resistance. In some embodiments, the sheet resistance of the inductor  104  corresponds to a desired inductance at a certain frequency. Here, the sheet resistance may be controlled at least in part by the number and dimensions of the spokes  110 , as described herein. 
     Turning now to  FIG.  2 B , the inductor  104  is depicted relating to some embodiments of the invention. In some embodiments, the inductor  104  comprises a different number of spokes. For example, in some embodiments, the inductor  104  comprises three spokes  110 , as shown. Further, embodiments are contemplated in which the inductor  104  comprises more or fewer spokes. For example, twenty-four spokes may be used to reduce the electrical resistance of the inductor  104 . Further, in some embodiments, the electrical resistance and inductance may be varied by altering the size and/or shape of the spokes, as described above. Further, embodiments are contemplated in which the size and/or shape of the inner ring  106  and outer ring  108  may be altered. 
     Embodiments are contemplated in which the inductor  104  comprises a single spoke. Here, the single spoke does not provide a parallel electrical connection and thus will provide a comparatively higher resistance. In some such embodiments, if a single spoke is used, the overall shape of the inductor may be modified. For example, in some such embodiments, the outer and inner rings may be replaced with an electrical node disposed at each end of the single spoke. In some embodiments, the coaxial circular shape associated with the inductor  104  may be desirable to provide stability and reduce variability. 
     Turning now to  FIG.  2 C , the inductor  104  is depicted showing various dimensions of the inductor  104  relating to some embodiments of the invention. In some embodiments, an outer diameter, D, of the outer ring  108  may be approximately 0.6150 inches. Alternatively, in some embodiments, the diameter, D, may be between about 0.5 inches and about 0.7 inches. An inner diameter, d, of the inner ring  106  may be approximately 0.1700 inches. Alternatively, in some embodiments, the diameter, d, may be between about 0.1 inches and about 0.2 inches. A length, L, between the inner surface of the inner ring  106  and the inner surface of the outer ring  108  may be approximately 0.1670 inches. In some embodiments, the length, L, may be between about 0.1 inches and about 0.2 inches. A width, w, of the inner ring  106  may be approximately 0.0700 inches. In some embodiments, the width, w, may be between about 0.05 inches and about 0.1 inches. Further, in some embodiments, the length, l, of the plurality of spokes  110  may be approximately 0.1020 inches. In some embodiments, the length, l, may be between about 0.05 inches and about 0.15 inches. The thickness, t, of each of the plurality of spokes  110  may be approximately 0.0020 inches. Alternatively, in some embodiments, the thickness, t, may be between about 0.001 inches and about 0.003 inches. In some embodiments, the diameter of the inner ring  106  may be about half the diameter of the outer ring  108 . 
     In some embodiments, the dimensions of the inductor  104  may be similar to the values described above or at least within a given range such as within 0.0005 inches of the above-mentioned values. However, in some embodiments, it should be understood that the dimensions described above may be altered. For example, in some embodiments, the dimensions may be reduced such that the inductor is small enough to fit within a microchip or on a circuit board. Further, in other embodiments, the size of the inductor  104  may be increased. Further still, the ratios of the dimensions may be altered in some embodiments. For example, in some embodiments, the thickness, t, of the plurality of spokes  110  may be decreased to increase the electrical resistance of the inductor  104 . 
     In some embodiments, each spoke of the plurality of spokes  110  may have a specific electrical resistance. For example, in some embodiments, each spoke may have an electrical resistance of about 0.502314 ohms such that the overall resistance is about 0.100463 ohms for an inductor  104  with five radially spaced parallel spokes. Accordingly, such an inductor  104  would have an inductance of about 15.989 nanohenrys at a frequency of 1 megahertz. In some embodiments, each spoke may have a resistance of about 0.4 ohms to about 0.6 ohms. In some embodiments, the overall resistance for the inductor may be about 0.05 ohms to about 0.3 ohms. In some embodiments, the inductance may be about 10 nanohenry to about 20 nanohenry at a frequency of about 0.5 MHz to about 1.5 MHz. 
     Turning now to  FIG.  3   , a side view of the inductor system  100  is depicted relating to some embodiments of the invention. It should be understood that the illustration shown in  FIG.  3    may include any combination of the inner ring  106 , the outer ring  108 , or the plurality of spokes  110 . For example, in some embodiments, only the outer ring  108  may be visible from the side. In some embodiments, the inductor  104  may comprise a plurality of layers disposed on the base portion  102 . For example, a first layer  112  may be disposed directly onto the base portion  102 , as shown. Further, a second layer  114  may be disposed on the first layer  112 . Further still, a third layer  116  may be disposed on the second layer  114 . It should be understood that in some embodiments, more or fewer layers may be included. Further, various different materials may be used for each layer, as will be described in further detail below to achieve specific properties of the inductor  104 . 
     In some embodiments, the first layer  112  may include a first material which may be selected based on a connection property of the first material to a material of the base portion. Accordingly, embodiments are contemplated in which a material of one or more of the layers of the inductor  104  are selected such that they adequately connect to the base portion  102  or to another layer of the inductor  104 . Accordingly, in some embodiments, the first layer  112  may comprise a titanium tungsten material such that it adheres to the base portion  102  material, such as a ceramic material. Alternatively, in some embodiments, the base portion  102  may comprise a Flame Retardant 4 (FR4) material. In some embodiments, the second layer  114  may comprise a nickel material such that it adheres to the material of the first layer, such as a titanium tungsten material. In some embodiments, the third layer  116  may comprise a gold material such that it adheres to the material of the second layer, such as a nickel material. However, it should be understood that other materials may be used based on the material of the base portion  102 , such as aluminum, copper, magnesium, tin, and other materials not explicitly described herein. Further, in some embodiments, the material of the layers may be selected based on a desired electrical conductivity for the inductor  104 . For example, in some embodiments, it may be desirable to use a material comprising gold for at least one of the layers to provide electrical conductivity to the inductor  104 . Alternatively, in some embodiments, other materials may be used to provide electrical conductivity such as copper or aluminum. 
     In some embodiments, gold may be used in the top-most layer (the third layer  116 ) to prevent rust from forming on the surface of the inductor  104 . In some embodiments, other suitable rust preventative materials may be selected for the top-most layer. Further, in some embodiments, materials for the layers may be selected based on an atomical roughness of the materials. For example, chromium or titanium may be used to improve the film adhesion which provides increased contact area between the layers and the substrate surface. However, it should be understood that other materials may be used to improve the film adhesion. Additionally, in some embodiments, the combination of materials for the layers may be selected to improve the electrical properties of the inductor  104 . For example, a layer comprising nickel may improve the electrical resistance and inductance of an adjacent layer comprising gold. 
     In some embodiments, the thickness of each layer may be selected to provide a specific electrical resistance. Further, in some embodiments, the thickness may be selected based on the type of material of the layer. In some embodiments, the first layer  112  may have a thickness of about 1 nm (0.03937 microinches) to about 100 nm (3.937 microinches). In some embodiments, the second layer  114  may have a thickness of about 4 microinches to about 12 microinches. In some embodiments, the third layer may have a thickness of about 50 microinches to about 100 microinches. In some embodiments, the second layer  114  is thicker than the first layer  112  and the third layer  116  is thicker than the second layer  114 . For example, in some embodiments, the second layer  114  may be about 4 times thicker than the first layer  112  and the third layer  116  may be about 10 times thicker than the second layer  114 . However, it should be understood that, in some embodiments, the thicknesses of the layers may be varied based on the specific materials used and the overall size and shape of the inductor  104 . 
     For example, in some embodiments, the first layer  112  may include a titanium-tungsten alloy material having a thickness of around 50 nanometers (1.97 microinches), the second layer  114  may include a nickel material having a thickness of around 8 microinches, and the third layer  116  may include a gold material having thickness of around 80 microinches. However, embodiments are contemplated in which different thicknesses and materials may be used. Further, in some embodiments, more or fewer layers may be included. In some embodiments, the inductor  104  may include only a single layer. For example, embodiments are contemplated in which the inductor  104  includes a single conductive layer comprising a copper material. 
     Turning now to  FIG.  4   , an exemplary measurement system  120  is depicted relating to some embodiments of the invention. In some such embodiments, the inductor  104  may be included within an adapter  122 , as shown. Here, the adapter  122  may be a high-frequency, precision electrical adapter which may interface with the inductor  104  and include a first electrical node  124  and a second electrical node  126 , as shown. In some embodiments, the first electrical node  124  may be electrically coupled, for example, to the inner ring  106  of the inductor  104 , while the second electrical node  126  may be electrically coupled to the outer ring  108  of the inductor  104 . In some embodiments, the inductor  104  may be soldered onto the adapter  122 . Accordingly, a sufficient electrical connection may be made between the inductor  104  and the adapter  122 . 
     In some embodiments, the measurement system  120  may further include an LCR meter  128  for measuring an electrical inductance value. In some embodiments, the LCR meter  128  may be calibrated using the inductor  104 . For example, the LCR meter  128  may be coupled to the adapter  122  at each of the first electrical node  124  and the second electrical node  126  such that an electrical signal path is provided through the inductor  104 . Accordingly, the low value inductance of the inductor  104  may be used as a low-value inductance standard to calibrate the LCR meter  128 . 
     In some embodiments, calibration of the LCR meter  128  with the inductor  104  allows inductance to be measured directly. Accordingly, the inductance can be measured without first measuring capacitance and converting to impedance. As such, the uncertainty in the measured value may be significantly reduced compared to methods in which an inductance value is determined by converting a capacitance value. Further, in some embodiments, radio frequency de-embedding may be avoided when using the inductor  104 . In some embodiments, the use of the inductor  104  to calibrate the LCR meter  128  further improves the uncertainty since the inductance values can be measured directly and error is not propagated through calculation such as with capacitance calibration techniques. 
     Turning now to  FIG.  5   , an exemplary circuit board  150  is depicted relating to some embodiments of the invention. In some embodiments, the circuit board  150  may be a printed circuit board such as an integrated circuit of a microprocessor or a microchip. In some embodiments, the circuit board  150  may comprise a silicon base structure with a plurality of circuit components. In some embodiments, the inductor  104  is disposed onto a top surface of the circuit board  150 , as shown. Accordingly, the inductor  104  may comprise a conductive metal trace. For example, the inductor  104  may be mounted onto the top surface of the circuit board  150  as a copper circuit trace. 
     In some embodiments, the inductor  104  may be applied using a thin film deposition technique such as a sputtering process. Alternatively, the inductor  104  may be applied using any other known technique suitable to mount the inductor  104  to the circuit board  150 . In some embodiments, the inductor  104  may be produced as a circuit trace on the circuit board  150  using a subtractive process, such as etching, to remove excess copper and leave the copper trace of the inductor  104 . It should be understood that a variety of different methods of applying the circuit trace are also contemplated, as well as a variety of other materials. 
     In some embodiments, the circuit board  150  further comprises one or more additional circuit components  152 , as shown. The additional circuit components  152  may be any of a variety of electrical components, such as electrical sources, electrical loads, resistors, capacitors, additional inductors, and/or transistors. In some embodiments, the circuit components  152  may interface with additional circuit traces on the circuit board  150 . Accordingly, embodiments are contemplated in which the same circuit trace material is used to produce both the inductor  104  and other circuit trace paths on the circuit board  150 . In some such embodiments, the inductor  104  may be generated as part of the circuit tracing process. 
     It should be understood that the inductor  104  is not limited to use with printed circuit boards and that embodiments are contemplated in which the inductor  104  may be used in any other type of circuit or electronic device. For example, the inductor  104  may be wired into a circuit of an electronic device to provide a stable low value inductance within said electronic device. In some embodiments, the inductor  104  may be used as an energy storage device within an electrical circuit. 
     Turning now to  FIG.  6   , an impedance nomograph  160  is depicted relating to some embodiments of the invention. As shown, the impedance nomograph  160  shows the relationship between various electrical parameters including frequency, impedance, and inductance. In some embodiments, the nomograph  160  may include a logarithmic scale for one or more of the parameters, as shown. The impedance nomograph  160  includes a highlighted region  162  denoting a range of values for which it becomes difficult to accurately measure inductance using standard capacitance measurement techniques. Specifically, it may become difficult to measure low inductances such as in the nanohenry range below 100 nanohenrys at high frequencies such as at or over 100 kilohertz. 
     In some embodiments, the inductor  104  may be configured to produce an inductance value within the highlighted region  162 . Accordingly, the inductor  104  may be used as an inductance standard to calibrate various measurement devices, as described above. In some embodiments, the nomograph  160  further includes an indication of the uncertainty of the impedance for a given value. In some embodiments, the uncertainty may be shown as a percentage value of the measured value. 
     Turning now to  FIG.  7   , an exemplary method  700  for producing the inductor  104  is depicted relating to some embodiments of the invention. At step  702 , the material of the inductor  104  (including each of the layers), a number of spokes and the dimensions of the plurality of spokes  110  is determined based on a desired inductance value. Accordingly, the number of spokes and the dimensions of the spokes may be selected to produce the desired inductance. In some embodiments, each of the plurality of spokes  110  has the same or substantially similar dimensions. Alternatively, embodiments are contemplated in which one or more of the spokes have different dimensions. 
     At step  704 , the first layer  112  is deposited onto a substrate surface. In some embodiments, the substrate surface may be an upper surface of the base portion  102  which, in some embodiments, may be a ceramic. Alternatively, in some embodiments, the base portion  102  may comprise silicon or another suitable semiconductor material or insulator material. For example, printed circuit board substrates may include materials such as epoxy laminates, resin, reinforced fiberglass, or FR4, as described above. In some embodiments, quartz substrates are also contemplated. Accordingly, embodiments are contemplated in which the first layer  112  comprises a titanium tungsten material such that the first layer  112  adheres to the material of the base portion  102 , as shown in  FIG.  3   . In some embodiments, the first layer  112  may be deposited onto the substrate surface via a sputtering process or any other suitable thin film deposition technique. 
     At step  706 , the second layer  114  is deposited onto a top surface of the first layer  112 . Here, the second layer  114  may comprise a nickel material such that it adequately adheres to the first layer  112 . Similar to the first layer  112 , the second layer  114  may be deposited via sputtering. At step  708 , the third layer  116  is deposited onto a top surface of the second layer  114 . In some embodiments, the third layer  116  is deposited using sputtering and the third layer  116  may comprise a gold material such that the third layer  116  adequately adheres to the material of the second layer  114 . 
     It should be understood that, in some embodiments, various other techniques may be used to deposit the layers of the inductor  104 . Further, embodiments are contemplated in which a plurality of different deposition techniques are used. For example, the first layer  112  may be deposited using a first process while the second layer  114  is deposited using a second process, and the third layer  116  may be deposited using a third process. Further still, the layers may be manufactured using subtractive methods such as etching, as described above. 
     In some embodiments, each of the layers may be deposited with a specific thickness. For example, embodiments are contemplated in which the first layer  112  has a first thickness, the second layer  114  has a second thickness distinct from the first thickness, and the third layer  116  has a third thickness distinct from the first and second thicknesses. In some embodiments, the thickness of each layer may be selected based on the type of materials used and the desired inductance value for the inductor  104 . For example, in some embodiments, the first layer  112  may have a minimum thickness of about 50 nanometers such that the nickel material of the second layer  114  is able to adhere to the titanium tungsten material of the first layer  112 . However, it should be understood that various other materials may be used. 
     In some embodiments, the inductor  104  produces a low value inductance in the nanohenry range (i.e., at or below 100 nanohenrys) for a corresponding high frequency (i.e., at or above 100 kilohertz). In some embodiments, the low value inductance is associated with the electrical resistance from the plurality of spokes  110 . Accordingly, the inductance of the inductor  104  may be controlled by varying any combination of the number of spokes in the plurality of spokes  110 , the length and width of the spokes, or the material of the inductor  104 . 
     It should be understood that the inductor  104 , as described herein, may be used in a variety of different applications such in metrology labs to provide a high stability precision low value inductance standard for calibration and measurement techniques, in various industries including military, automotive, and aerospace to provide a low value inductor, and in microelectronics to provide a small-scale inductor, for example, placed on a circuit board or within a microchip, as described above. Further, the inductor  104  may be used in any suitable application that requires an accurate surface-mounted inductor. 
     Although the invention has been described with reference to the embodiments illustrated in the attached drawing figures, it is noted that equivalents may be employed and substitutions made herein without departing from the scope of the invention as recited in the claims.