Patent Publication Number: US-7710232-B1

Title: Microelectromechanical tunable inductor

Description:
GOVERNMENT RIGHTS 
     This invention was made with Government support under Contract No. DE-AC04-94AL85000 awarded by the U.S. Department of Energy. The Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates in general to microelectromechanical devices, and in particular to a tunable inductor which can be electrostatically tuned to change its inductance. 
     BACKGROUND OF THE INVENTION 
     In the radio frequency (RF) and microwave technology domain there is a need to integrate passive components including inductors, capacitors, switches and filters on an integrated circuit (IC) chip to lower device size and manufacturing cost and to improve performance and reliability. The integration of these passive devices into an RF IC will provide high value for such applications as voltage-controlled-oscillator (VCO), phase-locked-loop (PLL) and other RF functionality required for advanced telecom systems. 
     Efforts have been focused on improving the RF performance of silicon IC technology, in part due to its low cost, dielectric compatibility, and micromachining properties. The on-chip integration of relatively high-Q fixed and variable inductors with silicon IC technology, however, has been problematic due to the parasitic effects of low-conductivity metallization as well as lossy substrate interactions. As a result, the quality factor Q of inductors fabricated using silicon IC technology is less than about 10 at a frequency of 2 GHz. Therefore, to achieve high performance, most RF IC applications still require the use of off-chip inductors. However, drawbacks of the off-chip inductors include significant parasitic effects, prohibitive size, and large losses due to board-level flip-chip and/or surface-mount interconnections. 
     Inductors with disk-shaped coils wound about an axis which is substantially perpendicular to an underlying semiconductor substrate are lossy due to eddy currents induced in the closely underlying substrate, and also due skin effects which restrict an alternating current (AC) in the coil to a small skin depth at the edge of the coil thereby substantially increasing the AC resistance of the coil. Efforts to overcome the drawbacks of disk-shaped coil inductors with the above-cited alignment have sought to raise the inductors off the substrate (see e.g. U.S. Pat. Nos. 6,184,755; 6,621,141; and 6,922,127). 
     The present invention provides an advance over the prior art by providing a tunable inductor having a pair of coils of substantially the same size which are arranged about a central axis which is substantially parallel to the substrate, and with the pair of coils being electrostatically unrolled in tandem to change the inductance. 
     The tunable inductor of the present invention comprises multi-turn coils which can be partially or completely unrolled to provide a wide variation in inductance. 
     The electrical power required to tune the inductor of the present invention is low since tuning is accomplished electrostatically, and not by resistive current heating. 
     The tunable inductor of the present invention can also be digitally tuned by shaping the coils and/or underlying electrodes, or alternately by using a segmented electrode beneath the pair of coils. 
     These and other advantages of the present invention will become evident to those skilled in the art. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a tunable inductor which comprises a pair of coils of substantially the same size arranged side by side and coiled about a central axis which is oriented substantially parallel to a supporting substrate. Each coil comprises a plurality of turns and has a first end anchored to the supporting substrate, and a second end where the pair of coils are connected together by a bridge which is suspended above the substrate. A first electrode extends beneath each coil, and can be formed on the substrate, or from the substrate. A second electrode is located on each coil and forms at least a part of the bridge connecting the pair of coils together. The inductance of the tunable inductor can be changed by applying a voltage between the first and second electrodes. This partially or completely uncoils (i.e. unrolls) the pair of coils with the exact extent of uncoiling depending upon an applied voltage. 
     The coiling in the tunable inductor is due to a layer of a compressively-stressed material (e.g. silicon dioxide) and a layer of a tensile-stressed material (e.g. silicon nitride) which are laminated together to form the coils. In some embodiments of the present invention, each coil in the tunable inductor can have a shape which is tapered or stepped with distance from the first end to the second end. This is useful for forming the coils without tangling, and also to provide an inductance L which varies proportionately to an applied voltage V. In other embodiments of the present invention, the tunable inductor can have coils with a lattice structure, or with a density of etch-release holes that varies with distance from the first end to the second end. 
     The supporting substrate can comprise a semiconductor substrate (e.g. silicon or a silicon IC). The first electrode can be uniform in width, or tapered or stepped. In some embodiments of the present invention, the first electrode can have a zigzag shape. In other embodiments of the present invention, the first electrode can comprise a segmented electrode. The second electrode can comprise a metal selected from the group consisting of aluminum, copper and tungsten. 
     The present invention also relates to a tunable inductor which comprises a substrate, and a pair of elongate members formed side by side on the substrate and connected together at one end thereof and having an in-plane stress gradient which urges the connected end of the pair of elongate members to coil away from the substrate and to form a pair of substantially identically-sized multi-turn coils from the pair of elongate members, with each multi-turn coil being formed about a central axis which is substantially parallel to the substrate. The tunable inductor also comprises a first electrode which extends beneath the pair of elongate members, and a second electrode which is formed on the pair of elongate members. A voltage applied between the first and second electrodes can be used to partially or completely uncoil the pair of substantially identically-sized multi-turn coils, thereby changing the inductance of the tunable inductor. 
     The substrate can comprise a semiconductor substrate (e.g. silicon). Each elongate member can comprise a compressively-stressed layer (e.g. silicon dioxide), and a tensile-stressed layer (e.g. silicon nitride, or tungsten, or both). Each elongate member can also have a tapered or stepped shape, or alternately can have a plurality of etch-release holes therein which vary in density with distance towards the unanchored end of that elongate member. 
     The first electrode can comprise polycrystalline silicon or metal (e.g. aluminum, copper or tungsten), or can even be formed from the substrate. In some embodiments of the present invention, the first electrode can have a tapered, stepped or zigzag shape. In other embodiments of the present invention, the first electrode can comprise a segmented electrode which further comprises a plurality of electrodes which are addressable independently or in sets to digitally vary the inductance of the tunable inductor. The second electrode generally comprises metal (e.g. aluminum, copper or tungsten). 
     Additional advantages and novel features of the invention will become apparent to those skilled in the art upon examination of the following detailed description thereof when considered in conjunction with the accompanying drawings. The advantages of the invention can be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated into and form a part of the specification, illustrate several aspects of the present invention and, together with the description, serve to explain the principles of the invention. The drawings are only for the purpose of illustrating preferred embodiments of the invention and are not to be construed as limiting the invention. In the drawings: 
         FIG. 1  shows a schematic perspective view of a first example of a tunable inductor according to the present invention. 
         FIG. 2A  shows a schematic side view of the tunable inductor of  FIG. 1  without any applied voltage. 
         FIG. 2B  shows a schematic side view of the tunable inductor of  FIG. 1  with an applied voltage of sufficient magnitude to unroll the coils by about one-quarter turn. 
         FIG. 2C  shows a schematic side view of the tunable inductor of  FIG. 1  with an applied voltage of sufficient magnitude to unroll the coils by about one-half turn. 
         FIG. 3  shows an enlarged schematic side view of one of the coils in  FIG. 1  to show the various layers therein. 
         FIG. 4  shows an enlarged partial side view of the coil in  FIG. 3  to show the tensile stress which is indicated by inward facing arrows, and the compressive stress which is indicated by outward facing arrows. The arrangement of tensile stress located above the compressive stress produces an in-plane stress gradient in the coils and causes the coils to roll up as shown in  FIG. 3 . 
         FIG. 5A  shows a schematic plan view of a tunable inductor with the coils in a flattened state and having a lattice structure. 
         FIG. 5B  shows a schematic plan view of a tunable inductor with the coils in a flattened state and having a structure of etch-release holes which vary in density along the length of the coils. 
         FIG. 5C  shows a schematic plan view of a tunable inductor with the coils in a flattened state and having a tapered shape. 
         FIG. 5D  shows a schematic plan view of a tunable inductor with the coils in a flattened state and having a stepped shape. 
         FIG. 6  shows a schematic perspective view of a second example of a tunable inductor according to the present invention. 
         FIGS. 7A-7C  schematically illustrate in plan view different shapes which can be used for the first electrode in the tunable inductor of  FIG. 6 . Note that the coils and the sacrificial layer have been removed in  FIGS. 7A-7C  to better show the first electrode which is formed from a layer of polysilicon or metal. 
         FIG. 8  shows a schematic perspective view of a third example of a tunable inductor according to the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  shows a schematic perspective view of a first example of a tunable inductor  10  according to the present invention. In  FIG. 1 , the tunable inductor  10  is a microelectromechanical (MEM) device which comprises a pair of coils  12  and  12 ′ that are of substantially the same size and arranged side by side on a supporting substrate  14 . The coils  12  and  12 ′ are also oriented substantially parallel to each other and comprise a plurality of turns. Each coil  12  and  12 ′ is formed from an elongate member (see  FIGS. 5A-5D ) which coils up about a central axis  16  which is oriented substantially parallel to the substrate  14  as shown in  FIG. 1 . A first end of each coil  12  and  12 ′ is anchored to the substrate  14 , and a second end of each coil  12  and  12 ′ is used to connect the pair of coils  12  and  12 ′ together via a bridge  18  which is suspended above the substrate  14 . The second end is also referred to herein as an unanchored end. 
     A first electrode in this example of the present invention is formed by the substrate  14  extending beneath each coil  12  and  12 ′; and a second electrode  22  is located on each coil  12  and  12 ′ and can form at least a part of the bridge  18  to electrically connect the two coils  12  and  12 ′ together. The coils  12  and  12 ′ in  FIG. 1  are electrically isolated from the substrate  14  by an electrically-insulating thermal oxide layer  24  covering the substrate  14  and a layer of a sacrificial material  26  (also termed a sacrificial layer  26 ) which underlies a part of the coils  12  and  12 ′ and defines an extent to which the coils  12  and  12 ′ roll up. 
     Electrical connections can be made to the pair of coils  12  and  12 ′ by contact pads  28  formed on the layer of the sacrificial material  26  which can comprise polycrystalline silicon (also termed polysilicon). This allows a variable inductance L provided by the tunable inductor  10  to be connected to an electronic circuit with which the tunable inductor  10  is to be used. The contact pads  28  are electrically insulated from the polysilicon sacrificial material by a silicon dioxide layer  30  (see  FIG. 3 ) which forms a part of each coil  12  and  12 ′. In some embodiments of the present invention, the electrical connections to the coils  12  and  12 ′ can comprise wiring formed on the substrate  14  (e.g. when the tunable inductor  10  is connected to an IC formed on the same substrate  14 ). In  FIG. 1 , an opening  32  can also be provided through the thermal oxide layer  24  to form a contact pad  34  on the substrate  14 . The contact pad  34  can be optionally metallized with a sputter-deposited layer of metal which is also used to form the second electrode  22  overtop each coil  12  and  12 ′. 
     The tunable inductor  10  can be operated to vary the inductance L therein by applying a direct-current (DC) voltage V from a voltage source  100  between the first electrode  20  (i.e. the substrate  14  in this example) and the second electrode  22  as shown in  FIG. 1 . The voltage V produces an electrostatic force of attraction between the electrodes  20  and  22  with the electrostatic force being strongest beneath the coils  12  and  12 ′ where a spacing between the electrodes  20  and  22  is smallest. The electrostatic force of attraction between the electrodes  20  and  22  will then act to unroll (i.e. uncoil) the pair of coils  12  and  12 ′ as shown in the schematic side views of  FIGS. 2A-2C  until the electrostatic force is balanced by a spring force of the coils  12  and  12 ′. 
     The spring force is due to an in-plane stress gradient arising from a layered structure of the coils  12  and  12 ′ which includes a compressively-stressed layer  30 , which can be silicon dioxide, and a tensile-stressed layer  36 , which can be silicon nitride. The term “in-plane stress gradient” as used herein refers to a variation in stress across the thickness of the coils  12  and  12 ′ which is due to a difference in the magnitude or sign of the stress built into two or more stressed layers that are laminated together to form the coils  12  and  12 ′, with the stress in each stressed layer being directed substantially in the plane of that layer. 
     A metal layer  38 , which can comprise aluminum, copper or tungsten is located above the tensile-stressed silicon nitride layer  36  as shown in  FIG. 3  which is an enlarged schematic side view of the coil  12  in the example of  FIG. 1 . This metal layer  38  forms the second electrode  22 . The in-plane stress gradient within the coils  12  and  12 ′ produced by the compressively-stressed silicon dioxide layer  30  and the tensile-stressed silicon nitride layer  36  initially causes the coils  12  and  12 ′ to curl upward away from the substrate  14  and then to coil up as shown in  FIG. 1  when the tunable inductor  10  is fabricated. 
     When tungsten is used for the metal layer  38 , the tungsten layer  38  will be tensile stressed. This additional tensile stress in the tungsten layer  38  can aid in rolling up the coils  12  and  12 ′. In some cases, the tensile stress provided by the tungsten layer  38  can allow the silicon nitride layer  36  to be omitted. The tungsten layer  38  can be deposited by chemical vapor deposition (CVD) at a temperature of about 400° C. When the tungsten layer  38  is to be deposited directly on the compressively-stressed silicon dioxide layer  30  (i.e. without the silicon nitride layer  36 ), a 20-50 nm thick layer of titanium nitride, which is also compressively stressed, can be initially sputter deposited over the silicon dioxide layer  30  to serve as an adhesion layer since tungsten does not stick or nucleate well on silicon dioxide. 
       FIG. 4  shows an enlarged partial side view of the coil  12  in  FIG. 3  to illustrate the compressive stress in the silicon dioxide layer  30 , which is directed in the plane of the layer  30  and is indicated by a pair of outward-facing arrows. The tensile stress in the silicon nitride layer  36  is also directed in the plane of the layer  36 , and is indicated in  FIG. 4  by a pair of inward-facing arrows. The stress in the metal layer  38  is insubstantial when aluminum or copper is used, but can be substantial when tungsten is used as previously described. The compressive stress seeks to expand the silicon dioxide layer  30  in the plane of the layer  30 ; whereas the tensile stress seeks to contract the silicon nitride layer  36  in the plane of the layer  36 . Then net result is an in-plane stress gradient which urges any unsupported portion of the coils  12  and  12 ′ to bend up away from the substrate  14  beginning at the unanchored end thereof, and continuing to roll up the entire unsupported portion of the coils  12  and  12 ′ as shown in  FIGS. 1 and 3 . 
       FIG. 2A  shows a schematic side view corresponding to the perspective view of  FIG. 1  with no applied voltage V (i.e. V=0). In this state, the inductance L of the tunable inductor  10  is largest due to the number of turns in the coils  12  and  12 ′ being at a maximum. The exact number of turns in the coils  12  and  12 ′ in  FIGS. 1 and 2A  will depend upon a length of the coils when completely unwound, and also upon how tightly the coils  12  and  12 ′ are wound due to the in-plane stress gradient therein. 
     In  FIG. 2B , with an applied voltage V&gt;0, the pair of coils  12  and  12 ′ begin to unroll in tandem, linked together by the bridge  18  (see  FIG. 1 ). Since the coils  12  and  12 ′ are substantially identical with the same size and same number of turns and are linked together by the bridge  18 , the coils  12  and  12 ′ will unroll together smoothly without any warping or tangling of adjacent turns of the coils  12  and  12 ′. The coils  12  and  12 ′ in  FIG. 2B  are shown unrolled by about one-quarter turn. The coils  12  and  12 ′ or electrodes therebeneath can be tailored so that the electrostatic force of attraction produced by the applied voltage V does not overwhelm a restoring spring force of the coils  12  and  12 ′ and completely unroll the coils  12  and  12 ′. This tailoring of the coils  12  and  12 ′ or the electrodes therebeneath, which allows the coils  12  and  12 ′ to be unrolled to an extent which depends upon the applied voltage V, will be described in detail hereinafter. Unrolling of the coils  12  and  12 ′ decreases the inductance L of the tunable inductor  10 . 
     As the coils  12  and  12 ′ begin to unroll in  FIG. 2B , the coils  12  and  12 ′ are urged into contact with the thermal oxide layer  24  by the electrostatic force of attraction produced by the applied voltage V between the first and second electrodes  20  and  22 . 
     In  FIG. 2C , a further increase in the applied voltage V is shown to further unroll (i.e. uncoil) the coils  12  and  12 ′ by an additional one-quarter turn, thereby further reducing the inductance L. As the coils  12  and  12 ′ are unrolled to reduce the inductance L, the location of the central axis  16  above the substrate  14  as shown in  FIG. 1  remains about the same so long as there is at least one turn remaining on the coils  12  and  12 ′. 
     Those skilled in the art will understand that the inductance L of the pair of coils  12  and  12 ′ comprises a self inductance due to each coil  12  and  12 ′, and a mutual inductance due to a coupling between the two coils  12  and  12 ′. The self inductance depends upon the number of turns in each coil  12  and  12 ′ while the mutual inductance depends upon the spacing between the coils  12  and  12 ′, and the direction of current flow therein. 
     Further increasing the voltage V beyond that in  FIG. 2C  will result in the coils  12  and  12 ′ continuing to unroll with a corresponding reduction in the inductance L. At a sufficiently large voltage V, the coils  12  and  12 ′ can be completely unrolled at which point the inductance L will be a minimum. Reducing the voltage V to zero will roll up the coils  12  and  12 ′ as shown in  FIGS. 1 and 2A  due to the restoring spring force generated by the in-plane stress gradient. This process of unrolling and rolling up the coils  12  and  12 ′ can be repeated a number of times as needed for a particular electronic circuit such as an oscillator circuit, tunable filter, matching network, etc., to which the tunable inductor  10  is connected. The electronic circuit, which can be connected between the pair of contact pads  28  in  FIG. 1 , can be located external to the substrate  14 , or in some instances can be located on the same substrate  14  with the tunable inductor  10  as an IC. 
     In the tunable inductor  10  of the present invention, the inductance L can be changed electrostatically over a relatively large range which can be up to ten nanoHenries (nH) or more by using a DC voltage V applied between the electrodes  20  and  22  without the need for flowing a relatively large DC current through the tunable inductor  10  as in other types of tunable inductors known to the art. 
     Fabrication of the tunable inductor  10  of  FIG. 1  will now be described in terms of fabrication on a semiconductor substrate comprising silicon. Those skilled in the art will understand that the tunable inductor  10  of the present invention can be fabricated on other types of semiconductor substrates  14 , including substrates formed of germanium or gallium arsenide. Those skilled in the art will also understand that the tunable inductor  10  of the present invention can also be fabricated on dielectric substrates  14 , including glass, ceramic, sapphire, alumina, fused silica, quartz, etc. 
     To fabricate the tunable inductor  10  of  FIG. 1 , a plurality of material layers, which are compatible with semiconductor IC and MEM device fabrication, can be deposited on a silicon substrate  14 . The substrate  14  can be initially prepared by forming the thermal oxide layer  24  which can be, for example, about 0.4 μm thick. The thermal oxide layer  24  can be formed using a conventional wet or dry thermal oxidation process at an elevated temperature (e.g. 1050° C.) whereby silicon at exposed surfaces of a silicon substrate  14  is converted into silicon dioxide (SiO 2 ). In other embodiments of the present invention where a silicon substrate  14  is not used, a layer of deposited silicon dioxide can be substituted for the thermal oxide layer  24 . In some cases, the thermal oxide layer  24  or a silicon dioxide layer can be omitted (e.g. when the substrate  14  comprises an electrically insulating material such as glass upon which a polysilicon sacrificial layer  26  can be directly deposited). 
     After formation of the thermal oxide layer on the substrate  14 , the sacrificial layer  26  comprising polysilicon about 0.4 μm thick can be blanket deposited over the substrate  14  by low-pressure chemical vapor deposition (LPCVD) at a temperature of 580° C. The compressively-stressed silicon dioxide layer  30  can then be blanket deposited over the silicon substrate  14  by chemical vapor deposition (CVD). This layer  30  can be, for example, about 0.4 μm. 
     After deposition of the compressively-stressed silicon dioxide layer  30 , the tensile-stressed silicon nitride layer  36  can be blanket deposited over the silicon substrate  14  to a thickness of, for example, 20 nanometers. The silicon dioxide layer  30  and the silicon nitride layer  36  can also be used to form a part of the bridge  18  together with a subsequently deposited metal layer  38 . The bridge  18 , which connects the unanchored ends of the coils  12  and  12 ′ together, can have a width which is less than or equal to the width of the coils  12  and  12 ′. 
     The metal layer  38 , which can comprise aluminum about 0.4 μm thick, can then be deposited over the substrate  14  by evaporation or sputtering. The aluminum layer  38  has relatively low stress compared to the underlying silicon nitride and silicon dioxide layers  36  and  30 , respectively. The metal layer  38  forms the second electrode  22  on the coils  12  and  12 ′ and also forms a part of the bridge  18 . Additionally, the metal layer  38  forms the contact pads  28  and can also be deposited overtop the contact pad  34  when the opening  32  has been formed prior to depositing the metal layer  38 . 
     After deposition of the plurality of material layers as described above, reactive ion etching using a photolithographically-defined etch mask (not shown) can be used to etch down to the sacrificial material  26  and define the shape of the various elements of the tunable inductor  10 , including the coils  12  and  12 ′, the bridge  18 , and the contact pads  28 . At this point in the fabrication process, the coils  12  and  12 ′ will be in a flattened state since they are still attached to the underlying sacrificial material  26 . 
     A plurality of micron-sized or larger etch-release holes  40  can be etched through the various material layers (i.e. the layers  30 ,  36  and  38 ) forming the coils  12  and  12 ′ in the reactive ion etching step used to define the shape of the coils  12  and  12 ′. These etch-release holes  40  are useful to expose the underlying sacrificial material  26  so that a subsequent selective etching step can remove the sacrificial material  26  faster and more thoroughly. The etch-release holes  40  can be circular, square, rectangular, or of any arbitrary shape. 
       FIG. 5A  shows an embodiment of the device  10  of  FIG. 1  where a plurality of rectangular etch-release holes  40  have been provided in the coils  12  and  12 ′. In this schematic plan view of the device  10  after etching down to define the shape of the coils  12  and  12 ′ and removal of the etch mask, the rectangular etch-release holes  40  form a lattice structure for the coils  12  and  12 ′ which can aid in removing the sacrificial material beneath the coils  12  and  12 ′. The lattice structure in  FIG. 5A  can also extend downward through the thermal oxide layer  24 , if desired, to reduce the voltage required for actuation of the tunable inductor  10 . In other embodiments of the present invention, the first electrode  20  can have this same lattice structure (e.g. when a single reactive ion etch step is used to define the shapes of both the first electrode  20  and the coils  12  and  12 ′ and bridge  18 ). 
     To control the extent of unrolling of the coils  12  and  12 ′, the density (i.e. number per unit area) of the etch-release holes  40  can be varied along the length of the coils  12  and  12 ′. This is schematically illustrated in  FIG. 5B  which shows a schematic plan view of an embodiment of the tunable inductor  10  with the coils  12  and  12 ′ in a completely unrolled state. As the density of the etch-release holes  40  increases along the length of each coil  12  and  12 ′ towards the unanchored end thereof as shown in  FIG. 5B , this decreases the area of electrically conductive material in the coils  12  and  12 ′ due to the increasing area taken up by the etch-release holes  40 . As a result, the electrostatic force of attraction between the coils  12  and  12 ′ and the underlying electrode  20  will be reduced as the coils  12  and  12 ′ unwind to a larger extent so that a larger voltage V will be needed to further unroll the coils  12  and  12 ′. In this way, the extent of unrolling the coils can be made proportional to the applied voltage V so that the inductance L provided by the coils  12  and  12 ′ will vary inversely proportional to the applied voltage V. 
     The density of the etch-release holes  40  in  FIG. 5B  can be made to vary linearly or non-linearly with distance along the coils  12  and  12 ′ to control exactly how the inductance L in the tunable inductor  10  varies with the applied voltage V. Alternately, the variation in density of the etch-release holes  40  can be stepped along the length of the coils  12  and  12 ′ to allow the inductance L to be changed in discrete steps with the applied voltage V which can also be stepped. 
     Other ways are possible to make the extent of unrolling of the coils  12  and  12 ′ proportional to the applied voltage V for control of the inductance L of the tunable inductor  10 . For example, the coils  12  and  12 ′ can have a tapered shape as shown in the schematic plan view of  FIG. 5C , or a stepped shape as shown in  FIG. 5D . In each case, the area of the coils  12  and  12 ′ upon which the electrostatic force of attraction will act will then decrease with distance towards the unanchored end of the coils  12  and  12 ′. This tapered or stepped shape is also useful to assist the flattened coils  12  and  12 ′ in coiling up smoothly from the unanchored end thereof (i.e. the end nearest the bridge  18 ) without tangling. Although both sides of each coil  12  and  12 ′ in  FIGS. 5C and 5D  are shown tapered or stepped inward on both sides of each coil  12  and  12 ′, those skilled in the art will understand that the tapering or stepping can be located on only one side of each coil  12  and  12 ′. Although not shown in  FIGS. 5C and 5D , a plurality of etch-release holes  40  can also be provided in the coils  12  and  12 ′. 
     The length of the flattened coils  12  and  12 ′ in  FIGS. 5A-5D  can be, for example, a few millimeters (mm) or more, with the width of the flattened coils  12  and  12 ′ being, for example, 0.1-1 mm. When the coils  12  and  12 ′ are formed as shown in  FIGS. 5A-5D , with a first electrode  20  being formed on the substrate  12 , as will be described hereinafter, the first electrode  20  can be optionally formed with the same structure as the coils  12  and  12 ′ (i.e. having a lattice structure as shown in  FIG. 5A , having a varying density of etch release holes  40  as shown in  FIG. 5B , having a tapered shape as showing in  FIG. 5C , or having a stepped shape as shown in  FIG. 5D .) 
     After patterning the various elements of the tunable inductor  10  by reactive ion etching, the polysilicon sacrificial material  26  can be removed using a selective etchant which can be a dry fluorine-based etchant (e.g. gaseous xenon difluoride vapor, or sulfur hexafluoride in a downstream plasma etching system). The use of a dry selective etchant reduces the possibility of stiction (i.e. adhesion) of the flattened coils  12  and  12 ′ to the thermal oxide layer  24 , or to the underlying substrate  14 . The use of a dry selective etchant also prevents exposure the coils  12  and  12 ′ to fluid forces which are present with a wet etchant and the possibility of deforming or tangling the coils  12  and  12 ′ due to such fluid forces. 
     The dry fluorine-based etchant removes exposed portions of the polysilicon sacrificial material  26  while not substantially chemically attacking the other material layers including the thermal oxide layer  24 , the silicon dioxide layer  30 , the silicon nitride layer  36 , and the metal layer  38 . As the sacrificial material  26  is removed from beneath the flattened coils  12  and  12 ′, the coils will begin to roll up beginning at the unanchored end of the coils  12  and  12 ′ until the coils  12  and  12 ′ are completely rolled up as shown in  FIG. 1 . The diameter of the rolled-up coils  12  and  12 ′ will depend upon the length and thickness of the silicon nitride and metal layers  36  and  38 , respectively, and how tightly they are coiled due to the in-plane stress gradient. As an example, the rolled up coils  12  and  12 ′ can have a diameter of about 1 millimeter or less when the length of the coils.  12  and  12 ′ is 4-5 mm and the thicknesses of the layers  30 ,  36  and  38  are as previously described. In the rolled up coils  12  and  12 ′, adjacent turns of the coils are electrically isolated from each other by the silicon dioxide and silicon nitride layers  30  and  36 , respectively, which are both electrically insulating. 
     In some embodiments of the present invention, the tunable inductor  10  can be fabricated on a semiconductor substrate  14  (e.g. comprising silicon, germanium, gallium arsenide, etc.) which also includes an IC comprising a plurality of interconnected circuit elements such as transistors, resistors, capacitors, or a combination thereof. These embodiments of the present invention can be formed by first fabricating the IC on the substrate  14  using a series of well-known semiconductor IC processing steps. One or more tunable inductors  10  can then be fabricated on the semiconductor substrate  14  alongside the IC, or above the IC and subsequently packaged together with the IC in a hermetically-sealed package. 
     To prevent any damage to the IC, the process steps used to fabricate one or more tunable inductors  10  on the same substrate  14  as the IC can be carried out at a relatively low temperature of about 400° C. or less. This can entail the use of plasma-enhanced chemical vapor deposition (PECVD) to deposit the polysilicon sacrificial material  26 , the silicon dioxide layer  30  and the silicon nitride layer  36  rather than the use of LPCVD and CVD as described previously. Additionally, when one or more tunable inductors  10  are to be fabricated above the IC, in some cases, a layer of an interconnect metallization for the IC can be used to form the first electrode  20 . The interconnect metallization can comprise, for example, aluminum, copper or tungsten. 
     A schematic perspective view of a second example of the tunable inductor  10  of the present invention is shown in  FIG. 6 . In this second example, the first electrode  20  can comprise polysilicon or a metal such as aluminum, copper or tungsten, which can be optionally overcoated with a thin (e.g. 0.1-0.5 μm) electrically-insulating layer of silicon dioxide or silicon nitride. When the first electrode  20  is formed from a blanket-deposited layer  42  of polysilicon or metal, a portion of the layer  42  can be left in place beneath the sacrificial layer  26  as shown in  FIGS. 7A-7C  to connect each elongate portion of the electrode  20  together and also to form the contact pad  34  which is electrically connected to the electrode  20  through the layer  42 . When the first electrode  20  in the example of  FIG. 6  is formed from polysilicon, the polysilicon can be doped during deposition with boron or phosphorous for electrical conductivity. As previously described, the first electrode  20  can also be formed from an interconnect metallization used for an IC formed beneath the tunable inductor  10 , or alternately form a deposited metal layer. 
     In the example of  FIG. 6 , the substrate  14  can comprise an electrically-insulating substrate  14  (e.g. an undoped semiconductor substrate such as undoped silicon, or a glass, ceramic, sapphire, alumina, quartz or fused silica substrate). When a semiconductor substrate is used, layer of a thermal oxide, silicon dioxide or silicon nitride can be provided over the semiconductor substrate  14  prior to depositing the metal layer  42 , if needed, to electrically isolate the first electrode  20  from the semiconductor substrate  14 . 
     In the example of  FIG. 6 , the remaining layers used for the structure of the tunable inductor  10  can be as previously described (i.e. a polysilicon sacrificial layer  26 , a compressively-stressed silicon dioxide layer  30 , a tensile-stressed silicon nitride layer  36 , and a metal layer  38 , which can comprise aluminum, copper or tungsten). 
     Fabrication of this example of the present invention can proceed substantially the same as that described previously except that the first electrode  20  can be patterned using the same reactive ion etching step used to pattern the of the coils  12  and  12 ′, or in some cases the first electrode  20  can be patterned using a separate reactive ion etching step when the shape of the first electrode  20  is different from the shape of the coils  12  and  12 ′. Although not shown in FIGS.  6  and  7 A- 7 C, the electrode  20  can also comprise a region which is initially beneath the bridge  18  when the coils  12  and  12 ′ are in a flattened state when a single reactive ion etching step is used to form both the first electrode  20  and the coils  12  and  12 ′. Alternately, the metal or polysilicon used to form the first electrode  20  can be deposited and patterned separately by reactive ion etching prior to depositing and patterning the remaining layers. This will generally be the case if the first electrode  20  comprises polysilicon since the polysilicon first electrode  20  will need to be overcoated with a thin (e.g. 0.1-0.5 μm) layer of silicon dioxide or silicon nitride to protect them from being etched away during removal of the overlying polysilicon sacrificial material  26 . 
     Those skilled in the art will understand that the first electrode  20  and the coils  12  and  12 ′ can, in some instances, have different lengths. As an example, the length of the elongate portions of the first electrode  20  can be less than the length of the coils  12  and  12 ′. This can be useful to limit a minimum value of the inductance L, or to prevent the coils  12  and  12 ′ from unrolling completely. 
     The first electrode  20  can have a uniform width as shown in  FIG. 6 . Alternately, the first electrode  20  can be tapered as shown in the schematic plan view of  FIG. 7A  which has omitted the coils  12  and  12 ′ and the sacrificial material  26  to better show the shape of the first electrode  20 . The first electrode  20  can also be stepped as shown in  FIG. 7B . When the first electrode  20  is tapered or stepped, the coils  12  and  12 ′ can also be tapered or stepped, or alternately the coils  12  and  12 ′ can have a substantially uniform width. In any case, the tapered or stepped first electrode  20  provides a way of making the inductance L of the tunable inductor  10  to vary proportionately with the applied voltage V since the tapered or stepped shape of the first electrode  20  will decrease the electrostatic force of attraction with distance so that an increasing voltage V will be needed to further unroll the coils  12  and  12 ′. 
     Another way of forming the first electrode  20  is shown in the schematic plan view of  FIG. 7C  which again omits the coils  12  and  12 ′ and the sacrificial material  26  to better show the shape of the first electrode  20 . In  FIG. 7C , each elongate portion of the first electrode  20  has a zigzag shape (also termed a serpentine shape). This zigzag shape is useful to provide an increased resistance for the first electrode  20  which can reduce RF losses in the tunable inductor  10 . The zigzag shape of the first electrode  20  can also be slanted as shown in  FIG. 7C . This is useful to provide a more uniform electrostatic force of attraction between the electrode  20  and the coils  12  and  12 ′ as the coils  12  and  12 ′ unroll and thereby eliminate the possibility of any local minima in the electrostatic force of attraction which might otherwise exist and impede the unrolling of the coils  12  and  12 ′ as the inductance L is changed. 
     With the first electrode  20  being formed of metal or polysilicon and patterned as described above, the polysilicon sacrificial material  26  after deposition will generally not be planar over the first electrode  20 . A chemical-mechanical polishing (CMP) step can be used after deposition of the polysilicon sacrificial material  26  to provide a planar surface for the deposition of the remaining layers used to form the tunable inductor  10  in  FIG. 6 . 
     After the various layers have been deposited and patterned, the polysilicon sacrificial material can be removed as described previously to release the flattened coils  12  and  12 ′ to roll up due to the in-plane stress gradient. Operation of this device  10  is similar to that described previously with reference to FIGS.  1  and  2 A- 2 C. 
       FIG. 8  shows a schematic perspective view of a third example of a tunable inductor  10  according to the present invention. In  FIG. 8 , the tunable inductor  10  comprises first electrode  20  which is formed as a segmented electrode to control and vary the inductance L of the tunable inductor  10 . The segmented first electrode  20  in  FIG. 8  comprises a plurality of electrodes  44  which are spaced apart in a side by side arrangement. The electrodes  44 , which can be, for example 0.1-0.5 mm wide and spaced apart by up to a few microns, can be electrically isolated from each other so that they can be independently addressed, or addressed in sets. 
     Addressing of the segmented first electrode  20  in  FIG. 8  to provide a digitally selected predetermined value of the inductance L can be accomplished using one or more DC programming voltages. As a particular set of electrodes  44  extending outward away from the rolled up coils  12  and  12 ′ is addressed with the DC programming voltage, which can be the same or different for each electrode  44  in the set, the pair of coils  12  and  12 ′ will be urged electrostatically to unroll to an extent corresponding to the number of electrodes  44  in that particular set (i.e. the coils  12  and  12 ′ will unroll a distance which is approximately equal the combined width of the electrodes  44  in that set). This can provide discrete stepped values of the inductance L which can be digitally selected to allow a discrete tuning of an electronic circuit to which the tunable inductor  10  is connected. The term “digitally selected” as used herein refers to the ability to address particular sets of the electrodes  44  in the tunable inductor  10  and thereby select a number of discrete values of the inductance L between a maximum inductance L Max  and a minimum inductance L Min . 
     When different DC programming voltages are used to address the individual electrodes  44  in the segmented first electrode  20 , the DC programming voltages can be the same or different depending upon the exact shape of the coils  12  and  12 ′. The different DC programming voltages can be applied in a stepped sequence to unroll the coils  12  and  12 ′ as needed to select a particular value of the inductance L, and then removed in the same stepped sequence to smoothly roll up the coils  12  and  12 ′ when the inductance L is to be increased. 
     When a single DC programming voltage is used, the single DC programming voltage can be set to the maximum voltage V Max  that is required to unroll the coils  12  and  12 ′ to an extent needed to provide a predetermined variation in the inductance L. This maximum voltage V Max  can be up to a few tens of volts or more, and will depend upon the exact thickness of the layers  30  and  36  between the electrodes  20  and  22 , and will also depend upon the thickness of any electrically-insulating layer that may be provided overtop the segmented first electrode  20 . The single DC programming voltage can be applied to and removed from the individual electrodes  44  with a predetermined time constant so that the coils  12  and  12 ′ will smoothly unroll or roll up to change the inductance L of the tunable inductor  10 . 
     Fabrication of the tunable inductor  10  of  FIG. 8  can be performed using the same material layers previously described with reference to the second example of  FIG. 6 . After deposition of the polysilicon or metal layer (e.g. aluminum, copper or tungsten) used to form the segmented first electrode  20 , the individual electrodes  44  can be defined by a reactive ion etching step. The segmented first electrode  20  can then be optionally coated with a layer of an electrically-insulating material (e.g. silicon dioxide or silicon nitride), with the electrically-insulating material being planarized using a CMP step. A layer of the polysilicon sacrificial material  26  can then be blanket deposited over the substrate  14  and planarized by CMP, if needed, to provide a flat surface for subsequent deposition of the various layers  30 ,  36  and  38  used to form the coils  12  and  12 ′. 
     A second reactive ion etch step can then be used to pattern the layers  30 ,  36  and  38  to define the shapes of the flattened coils  12  and  12 ′ and the bridge  18 . In this case, the reactive ion etching step needs only to etch down to expose the polysilicon sacrificial material  26  beneath the coils  12  and  12 ′. The coils  12  and  12 ′ and bridge  18  can then be released using the dry selective etchant to selectively remove the polysilicon sacrificial material  26  and allow the coils  12  and  12 ′ to roll up in tandem beginning at the unanchored end thereof. 
     In other embodiments of the present invention, the bridge  18  can extend between the coils  12  and  12 ′ along a portion or the entire length thereof. In these embodiments, a metal portion of the bridge  18  formed from the metal layer  38  will generally have a width that is less than or equal to the width of each coil  12  or  12 ′. The remainder of the bridge  18 , which can be formed from the silicon dioxide and silicon nitride layers  30  and  36 , can extend outward from the bridge  18  toward the anchored end of the coils  12  and  12 ′ for a predetermined distance which, in some cases, can be up to the entire length of the coils  12  and  12 ′. A plurality of etch-release holes  40  can be formed through the layers  30  and  36  in the bridge  18  as needed to aid in removing the underlying polysilicon sacrificial material  26  using the selective etchant. In these embodiments of the present invention where the bridge  18  extends between the coils  12  and  12 ′ up to the entire length thereof, a spacing between the coils  12  and  12 ′ will generally be smaller than the length of the coils  12  and  12 ′ so that the in-plane stress gradient will cause the coils  12  and  12 ′ to roll up while the bridge  18  remains substantially flat in a direction parallel to the central axis  16  about which the coils  12  and  12 ′ wind. As an example, the coils can be spaced apart by a distance of 0.5-1 millimeter while the length of the coils  12  and  12 ′ can be 4-5 millimeters or more. 
     In yet other embodiments of the present invention the first electrode  20  in  FIG. 6  can be provided as a flat plate which can act as a ground plane to electrically isolate the tunable inductor  10  from the substrate  14 , or from an IC formed on the substrate  14  beneath the tunable inductor  10 , thereby minimizing capacitive and magnetic coupling to the substrate  14  or to the IC. Such a single plate first electrode  20  can be formed by separately patterning the metal layer  42  used to form the first electrode  20  in  FIG. 6 , or alternately by not etching through the metal layer  42  when the shapes of the flattened coils  12  and  12 ′ and bridge  18  are defined by reactive ion etching. 
     Although the metal layer  38  on the coils  12  and  12 ′, which is used for each second electrode  22 , has been described herein as being located above the compressively-stressed silicon dioxide layer  30  and the tensile-stressed silicon nitride layer  36  (see  FIGS. 3 and 4 ), in other embodiments of the present invention, the metal layer  38  can be located beneath the layers  30  and  36 . When this is done, a thin (0.1-0.5 μm) electrically-insulating layer (e.g. silicon dioxide or silicon nitride) can be provided overtop the first electrode  20  to prevent the possibility of short circuiting the electrodes  20  and  22  during operation of the tunable inductor  10 . 
     The matter set forth in the foregoing description and accompanying drawings is offered by way of illustration only and not as a limitation. The actual scope of the invention is intended to be defined in the following claims when viewed in their proper perspective based on the prior art.