Patent Publication Number: US-10784066-B2

Title: Microelectromechanical switch with metamaterial contacts

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of the filing date of U.S. Provisional Patent Application No. 62/469,752 filed Mar. 10, 2017, the disclosure of which is hereby incorporated herein by reference. 
    
    
     FIELD OF TECHNOLOGY 
     The present disclosure relates to radio frequency (RF) switches, or more particularly RF micro electromechanical system (MEMS) switches. 
     BACKGROUND OF THE INVENTION 
     RF MEMS switches have previously been employed in microwave and millimeter-wave communication systems, such as in signal routing for transmit and receive applications, switched-line phase shifters for phased array antennas, and wide-band tuning networks for modern communication systems. MEMS is typically a silicon-based integrated circuit technology with moving mechanical parts that are released by means of etching sacrificial silicon dioxide layers. 
       FIGS. 1A-1C  illustrate an example circuit design of a cantilevered out-of-plane RF MEMS switch  100 .  FIG. 1A  is a top view of the switch,  FIG. 1B  is a cross-sectional view of the switch along axis X, and  FIG. 1C  is another cross-sectional view of the switch along axis Y. 
     The example switch  100  is formed over a coplanar waveguide  101  in which a signal line  110  is formed between ground planes  102 ,  104  of a substrate  105 . The signal line  110  includes an input port  112  and an output port  114  formed on opposing ends of the substrate  105 . The cantilever switch includes a post  120  or anchor affixed to the substrate  105  and includes an extension extending over the substrate in a direction perpendicular to the signal line  110 . The extension of the cantilever includes a bottom layer  125  of dielectric material, such as silicate, and a top layer  130  of conductive material  130 , such as gold. The cantilever further includes a contact bump or dimple  135  positioned underneath the bottom dielectric layer  120  and in alignment with the signal line ports  112 ,  114 . Thus, when the cantilever is bent downward, the dimple  135  contacts the signal line  110 , thereby connecting the input and output ports  112 ,  114 . 
     The switch  100  also includes an electrostatic actuator (not shown) for actuating the cantilever by applying or removing a DC bias voltage between the cantilever and the ground  102 ,  104  of the coplanar waveguide  101 . The cantilever bends downward and upward, in a direction towards and away from the signal line respectively, in response to the applied voltage from the actuator. Other RF MEMS switches may rely on a lateral movement in order to bring the moveable part of a cantilevered switch towards or away from a contact. Each of the moving part and contact may be metal (resistive switch), or one may be metal while the other is dielectric (capacitive switch). 
     RF MEMS switches, compared to their solid state semiconductor counterparts, exhibit several important advantages such as: superior linearity; low insertion loss; and high isolation. In particular, RF MEMS switches at millimeter wave frequencies are suitable for use in modern telecommunication systems, especially for automotive radar systems, 5G wireless communication, short range indoor microwave links, wide-band transceivers, phased array systems and high precision instrumentation applications. 
     Compared with PIN diodes and field-effect transistor (FET) switches, RF MEMS switches have been found to offer lower power consumption, higher isolation, lower insertion loss and higher linearity at a lower cost. 
     RF MEMS switches can encounter several drawbacks, including high actuation voltages, high insertion loss, and poor return loss. These drawbacks are a challenge to designing MEMS switches for operation in the millimeter wave frequency range. 
     Another problem with RF MEMS switch performance is that it is prone to electromechanical failure after several switching cycles, especially under hot switching conditions. For instance, the switch may fail due to static friction (or stiction) buildup. When the moveable part of the switch is pulled into contact with another component of the system (e.g., a signal line), the static friction can cause the switch to become stuck. It may require a high voltage to overcome the stiction force. But at low voltage, the switch can remain “welded” to the component. 
     BRIEF SUMMARY OF THE INVENTION 
     An aspect of the present disclosure is directed to a microelectromechanical switch including: a signal line having each of an input port and an output port, the signal line formed on a substrate between a first ground plane and a second ground plane formed on the substrate; a primary deflectable beam having a first end, a second end, and a deflectable middle portion between the first and second ends, the first end supported by a first post formed over the first ground plane, the second end supported by a second post formed over the second ground plane, and the middle portion of the primary deflectable beam positioned over at least a portion of the input port and at least a portion of the output port, whereby the deflectable middle portion contacts each of the input port and output port when deflected downward; one or more defected ground structures formed in each of the first ground plane and the second ground plane; and for each defected ground structure, a corresponding secondary deflectable beam positioned over the defected ground structure. The switch may further include a first actuator coupled to the primary deflectable beam and configured to apply a first bias voltage to the primary deflectable beam, whereby the first bias voltage causes the primary deflectable beam to deflect downward toward the signal line, and a second actuator coupled to each of the one or more secondary deflectable beams and configured to apply a second bias voltage to each of the secondary deflectable beams, whereby the second bias voltage causes each secondary deflectable beam to deflect downward toward its corresponding defected ground structure. 
     In some examples, each of the defected ground structures may include a plurality of slots etched into the ground plane and forming a spiral. Also, in some examples, each ground plane may include a first defected ground structure and a second defected ground structure, the length and width of the second defected ground structure being shorter than the length and width of the first defected ground structure. Also, in some examples, the input and output ports may be formed along a first axis of the switch, with the primary deflectable beam extending from the first post to the second post along a second axis perpendicular to the first axis, and the secondary deflectable beams extending in a direction parallel to the first axis. 
     In some examples, each of the secondary deflectable beams may have a first end supported by a first secondary post and a second end supported by a second secondary post. A bottom surface of each secondary deflectable beam may be suspended over the ground plane and corresponding defected ground structure by its first and second secondary posts. An upper surface of the primary deflectable beam may be less than 4 microns higher than the surface of the signal line. An upper surface of each secondary deflectable beam may be less than 2.5 microns higher than the surface of the ground plane. 
     In some examples, the middle portion of the primary deflectable beam may have a plurality of perforations forming a lattice structure. The perforations may increase the flexibility of primary deflectable beam. Each corner of the middle portion may extend outward toward the first or second end in a serpentine pattern. The extended corners of one side of the middle portion may meet at the first end, while the extended corners of the other side of the middle portion meet at the second end. In this regard, the primary deflectable beam may be less than 150 μm long and yet sufficiently flexible for the middle portion to deflect 1 μm or more downward. The downward deflection may be in response to application of a bias voltage, such as a voltage of about 17 volts or less. Additionally or alternatively, each secondary deflectable beam may include a plurality of perforations forming a lattice structure. The perforations may increase flexibility of secondary deflectable beam. 
     In some examples, the switch may achieve insertion loss of less than −2 dB and isolation of greater than −20 dB between 75 GHz and 130 GHz. Also, in some examples, actuation of the primary deflectable beam and non-actuation of the secondary deflectable beams may result in isolation between the input and output ports of about −24 dB or better between 75 GHz and 130 GHz. Similarly, actuation of the secondary deflectable beams and non-actuation of the primary deflectable beam may result in insertion loss of −1.5 dB or better between 75 GHz and 130 GHz. 
     Another aspect of the present disclosure is directed to a microelectromechanical switch including: a signal line comprising each of an input port and an output port, the signal line formed on a substrate between a first ground plane and a second ground plane formed on the substrate; a beam positioned above the signal line, the beam being configured to move in an out-of plane direction relative to the signal line and ground planes, and including an upper contact configured to contact the signal line; and a metamaterial structure included in one of the upper contact and the signal line. In some examples, the metamaterial structure may include concentric split rings. Also, in some examples, the metamaterial structure has an effective permittivity of 0.05 or less over a bandwidth of at least 50 GHz. Further, in some examples, the metamaterial structure exhibits each of a primarily-reflective property and a primarily-transmissive property within a bandwidth of less than 100 GHz. Yet further, in some examples, the metamaterial structure may generate a repulsive Casimir force for separating the beam and signal line 
     In some examples, the switch may be a resistive switch. In such examples, the metamaterial structure may be included in the upper contact. An upper surface of the input and output ports of the signal line may be conductive. The beam further may include a bottom conductive layer to contact each of the input and output ports when the beam is actuated. The metamaterial structure may be embedded in the bottom conductive layer. Also, in some examples, the beam may further include a dielectric layer formed above the bottom conductive layer, and a top conductive layer formed above the dielectric layer. The bottom conductive layer may have a permittivity less than that of the dielectric layer. The top conductive layer may have a permittivity greater than that of the dielectric layer. Each of the top and bottom conductive layers may be made of gold. The dielectric layer may be made of one of silicon nitride or silicon mononitride. Also, in some examples, the switch may further include one or a combination of a second metamaterial structure embedded in the top conductive layer, and a top dielectric layer over the top conductive layer having a common composition as the dielectric layer between the top and bottom conductive layers. Each of the top dielectric layer, the top conductive layer, and the dielectric layer may have a length equal to a length of the beam, while the bottom conductive layer has a length equal to a width of the signal line. In some examples, the switch may have an isolation of greater than about −15 dB between 80 GHz and 100 GHz when the switch is off, and an insertion loss of less than about −1 dB between 80 GHz and 100 GHz when the switch is on. 
     In other examples, the switch may be a capacitive shunt switch. The metamaterial structure may be included in the signal line. The switch may further include a deflectable beam having a first end, a second end, and a deflectable middle portion between the first and second ends, the first end supported by a first post formed over the first ground plane. The second end may be supported by a second post formed over the second ground plane, and the middle portion of the deflectable beam may be positioned over the metamaterial structure in the signal line. The deflectable middle portion may contact the signal line when deflected downward. 
     In some examples, the switch may further include a conductive strip extending from the first ground plane towards the signal line. The conductive strip may extend to the opposing end of the signal line such that it is positioned at least partially on top of the metamaterial structure. In some instances, the first conductive strip may extend from the first ground plane to the second ground plane. 
     In some examples, the signal line may include a first metamaterial structure adjacent to the input port and a second metamaterial structure adjacent to the output port. The switch may further include a first conductive strip extending from the first ground plane towards the second ground plane and positioned at least partially on top of the first metamaterial structure, and a second conductive strip extending from the first ground plane towards the second ground plane and positioned at least partially on top of the second metamaterial structure. 
     In some examples, the switch may include each of a bottom dielectric layer formed on the substrate, each of the ground planes and signal line being formed on the bottom dielectric layer, a conductive post extending downward from one of the ground planes into the bottom dielectric layer, and a conductive beam extending outward from the conductive post towards the signal line. The conductive beam may extend to the opposing end of the signal line such that it is positioned at least partially underneath the metamaterial structure. Additionally, in some examples, the switch may have an isolation of greater than about −15 dB between 30 GHz and 100 GHz when the switch is off, and an insertion loss of less than about −1 dB between 30 GHz and 100 GHz when the switch is on. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a top-down view of a prior art RF MEMS switch. 
         FIG. 1B  is a side view of the switch of  FIG. 1A . 
         FIG. 1C  is a front view of the switch of  FIG. 1A . 
         FIG. 2  is a side view of an RF MEMS shunt switch in accordance with an aspect of the present disclosure. 
         FIG. 3  is a plan view of an example RF MEMS shunt switch in accordance with an aspect of the present disclosure. 
         FIG. 4  is a graphical representation of isolation of the switch of  FIG. 3 . 
         FIG. 5  is a plan view of another example RF MEMS shunt switch in accordance with an aspect of the present disclosure. 
         FIG. 6  is a graphical representation of isolation of the switch of  FIG. 5 . 
         FIG. 7  is a plan view of a switch having a defected ground plane structure in accordance with an aspect of the present disclosure. 
         FIG. 8  is a zoomed image of a portion of the plan view of  FIG. 7 . 
         FIG. 9  is a graphical representation of return loss and insertion loss of the switch of  FIG. 7 . 
         FIG. 10  is a graphical representation of isolation of the switch of  FIG. 7 . 
         FIG. 11  is a partial plan view of a switch having a defected ground plane structure and secondary switches in accordance with an aspect of the present disclosure. 
         FIG. 12  is a side view of the switch of  FIG. 11 . 
         FIG. 13  is a graphical representation of the transmission and reflection phase for the coplanar line of a switch without a defected ground plane structure. 
         FIGS. 14 and 15  are graphical representations of the transmission and reflection phase for coplanar lines of switches with a defected ground plane structure. 
         FIG. 16  is a graphical representation of isolation characteristics of the switch of  FIG. 10  having varying air gap heights. 
         FIG. 17  is a plan view of a switch having a defected ground plane structure and secondary switches in accordance with an aspect of the present disclosure. 
         FIG. 18  is a side view of the switch of  FIG. 17 . 
         FIG. 19  is a schematic diagram of the switch of  FIG. 17 . 
         FIG. 20  is another plan view of the switch of  FIG. 17 . 
         FIG. 21  is a graphical representation of return loss and insertion loss of the switch of  FIG. 17  with the secondary switches activated. 
         FIG. 22  is yet another plan view of the switch of  FIG. 17 . 
         FIGS. 23-25  are graphical representations of isolation characteristics of the switch of  FIG. 17  with the secondary switches not activated and having different defected ground plane structures. 
         FIG. 26  is a graphical representation of isolation characteristics of the switch of  FIG. 17  having varying air gap heights. 
         FIG. 27  is a graphical representation of isolation for switches in accordance with the present disclosure. 
         FIG. 28  is a graphical representation of insertion loss for switches in accordance with the present disclosure. 
         FIG. 29  is a perspective view of a metal-metamaterial interface. 
         FIG. 30A  is a side view of a metal-metal contact. 
         FIG. 30B  is a side view of a metal-metamaterial contact. 
         FIG. 31  is a side view of a metal-metamaterial contact in accordance with an aspect of the disclosure. 
         FIG. 32A  is a top down view of an RF MEMS resistive switch having a metamaterial structure in accordance with an aspect of the disclosure 
         FIG. 32B  is a perspective view of the switch of  FIG. 32A . 
         FIG. 32C  is a cross-sectional view of the perspective view of  FIG. 32B . 
         FIG. 32D  is a side view of the switch of  FIG. 32A  in a down state. 
         FIG. 32E  is a side view of the switch of  FIG. 32A  in an up state. 
         FIG. 33  is a plan view of a metamaterial structure in accordance with an aspect of the disclosure. 
         FIGS. 34-36  are graphical representations of transmission and reflection characteristics over a range of frequencies for example RF MEMS resistive switches having different metamaterial structures in accordance with an aspect of the disclosure. 
         FIG. 37  is a graphical representation of reflection characteristics over a range of frequencies for example RF MEMS resistive switches having different metamaterial structure parameters in accordance with an aspect of the disclosure. 
         FIG. 38  is a graphical representation of transmission and reflection characteristics over a range of frequencies for example RF MEMS resistive switches having different metal plate contact thicknesses in accordance with an aspect of disclosure. 
         FIG. 39  is a graphical representation of transmission and reflection characteristics over a range of frequencies for example RF MEMS resistive switches having different dielectric layer thicknesses in accordance with an aspect of the disclosure. 
         FIG. 40  is a graphical representation of transmission and reflection characteristics over a range of frequencies for example RF MEMS resistive switches having different metal plate thicknesses in accordance with an aspect of the disclosure. 
         FIG. 41  is a graphical representation of extracted permittivity and permeability parameters over a range of frequencies of an example RF MEMS resistive switch in accordance with an aspect of the disclosure. 
         FIG. 42  is a graphical representation of transmission and reflection characteristics over a range of frequencies for an example RF MEMS switch in the OFF state, in accordance with an aspect of the disclosure. 
         FIG. 43  is a graphical representation of transmission and reflection characteristics over a range of frequencies for an example RF MEMS switch in the ON state, in accordance with an aspect of the disclosure. 
         FIGS. 44-46  are graphical representations of transmission and reflection characteristics over a range of frequencies for example RF MEMS capacitive switches having different metamaterial structures in accordance with aspects of the disclosure. 
         FIG. 47A  is a top down view of an example RF MEMS capacitive switch having a metamaterial structure in accordance with an aspect of the disclosure. 
         FIG. 47B  is a side view of the switch of  FIG. 47A . 
         FIG. 47C  is a perspective view of the switch of  FIG. 47A . 
         FIG. 48  is a graphical representation of transmission and reflection characteristics over a range of frequencies for the switch of  FIGS. 47A-C . 
         FIG. 49  is a graphical representation of extracted permittivity and permeability parameters over a range of frequencies of the switch of  FIGS. 47A-C . 
         FIG. 50  is a perspective view of an example RF MEMS capacitive switch having a capacitive shunt and a metamaterial structure in accordance with an aspect of the disclosure. 
         FIG. 51  is a graphical representation of transmission and reflection characteristics over a range of frequencies for the switch of  FIG. 50  in a transmission (ON) state. 
         FIG. 52  is a graphical representation of transmission and reflection characteristics over a range of frequencies for the switch of  FIG. 50  in a reflection (OFF) state. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure provides for RF MEMS switches having improved signal characteristics and reduced vulnerability to stiction. 
       FIG. 2  shows an RF shunt switch  200  with a doubly-supported cantilever beam  210  formed above a coplanar waveguide formed on a substrate  201 . A first end  212  and second end  214  of the beam  210  are supported by respective ground planes  202  and  204  formed in the coplanar waveguide. The middle of the beam  210  is suspended over a signal line  220  formed in the coplanar waveguide. The beam  210  is connected to an actuator (not shown) configured to apply a direct current (DC) bias voltage across the beam  210  the ground planes  202 ,  204 . The DC bias voltage causes the beam  210  to deflect downward. 
     In the example of  FIG. 2 , the signal line  220  includes a conductive layer  222  covered by a thin dielectric layer  224 , such as silicon nitride. The dielectric layer may be about 0.2 μm thick. When the beam  210  deflects downward and contacts the signal line  220 , a large shunt capacitance is obtained. The large shunt capacitance blocks RF signals from propagating along the signal line  220  of the coplanar waveguide (ON-state). When the DC bias is removed, the beam  220  deflects upward and returns to its original position, the shunt capacitance drops, and the RF signal resumes propagating in un-attenuated form (OFF-state). 
     In the example of  FIG. 2 , the beam  210  is made of molybdenum, and has a length of about 325 μm, a width of about 60 μm, and a thickness of about 1.2 μm. The signal line  220  extends through the coplanar waveguide, and has a width (in the direction of the beam length) of about 60 μm. The beam  210  is suspended about 2.5 μm above the signal line  220 , thereby forming a 2.5 μm air gap. The dielectric layer has a thickness of about 0.2 μm. 
       FIG. 3  shows a top view of the switch  200  of  FIG. 2 . The beam  210  is perforated, having a grid of small perforations  301  in the middle and a large perforation  302 ,  303  at each end. The perforations yield improved downward deflection of the beam  210 .  FIG. 3  further illustrates the vertical displacement of the beam  210  when the DC bias voltage is applied, which is extends from no displacement at the respective ends  212 ,  214  of the beam, to about 0.91 μm in the middle of the beam  210 . The DC bias for the switch of  FIG. 2  has been observed to be about 37 V. 
       FIG. 4  shows isolation characteristics of the switch of  FIG. 2  when the switch is open, across a band of millimeter wave signals from 75 GHz to 130 GHz. Isolation is about −12.4 dB at 75 GHz, and about −19.7 dB at 130 GHz. Insertion loss of the switch when closed is about 0.74 dB, and return loss is about 10.04 dB. 
     The actuation voltage can be further reduced to less than 37V by providing a different perforation arrangement. In the example of  FIG. 5 , switch  500  includes a rectangular beam  510  made of gold and having a perforated structure. The middle portion  516  of the beam  510  forms a perforated grid or lattice. Each corner of the lattice structure then extends in a serpentine pattern toward the first and second ends  512 ,  514  of the beam  510 . The serpentine patterns on either end are then connected to one another, thereby forming first and second serpentine structures on either end of the beam  510 . The serpentine structure permits for deflection of the beam with a lower bias voltage. 
     The dimensions of the switch shown in  FIG. 5  is largely comparable to that of  FIG. 2 , except that the beam of  FIG. 5  is slightly longer (about 345 μm), and slightly wider (about 65 μm). The beam still deflects downward up to 0.9 μm with only a 17 V bias voltage. 
     The switch of  FIG. 5  also has improved isolation characteristics.  FIG. 6  shows isolation characteristics of the switch of  FIG. 5  when the switch is open, across the 75 GHz to 130 GHz band. Isolation is about −22.0 dB at 75 GHz, and about −14.7 dB at 130 GHz, and drops to as little as about −24.8 dB at 86 GHz. Additionally, insertion loss of the switch when closed is only about 0.6 dB, and return loss is only about 15.15 dB. 
     Nonetheless, the isolation characteristics of the shunt switches of  FIGS. 2 and 5  can be further improved upon, particularly in the millimeter wave frequency band of 75 GHz to 130 GHz. The example switch  700  of  FIG. 7  includes a beam  710  having the same structural arrangement as the beam  510  of  FIG. 5  and formed on a ground plane structure  701  measuring about 320 μm long by about 400 μm wide. The ground plane structure  701  includes a signal line  720  between two ground planes  702 ,  704 . A two-dimensional defected ground structure (DGS) is formed in each of the ground planes  702  and  704  of the switch  700 . The DGS essentially behaves as a band stop filter, thereby affecting the transmission characteristics of the switch  700 . In the example of  FIG. 7 , the DGS forms four spiral shaped slots  731 ,  732 ,  733 ,  734  in a two-by-two grid and having mirror symmetry along the lengthwise axis of the signal line  720 . 
     Characteristics of the spiral shaped slots are shown in greater detail in  FIG. 8 . In the example DGS  800  of  FIG. 8 , each of the spiral shaped slots have a common, uniform width W. A first slot  810  extends from the channel  802  separating the signal line from the ground plane. Each subsequent slot connects to the previous slot at a right angle. Hence, in  FIG. 8 , the second slot  820  connects to the first slot  810  at a right angle, and the third slot  830  connects to the second slot at a right angle turning in the same angular direction, thereby forming a spiral. The DGS of  FIG. 8  includes a total of seven slots formed using the above described spiral pattern. 
     The DGS structure also includes an opening connecting the beginning of the first slot to the end of the fourth slot. Thus, the first four slots of the DGS structure of  FIG. 8  also form a rectangular box having a length defined by the second slot and a width defined by the third slot. The length and width of the rectangular box may be defined in terms of distances “a” and “b” in which “a” is the length of the third slot, and “b” is the difference in length between the second slot and third slot (hence the length of the second slot is equal to a+b). 
     The switch of  FIG. 7  has yet further improved attenuation characteristics.  FIG. 9  shows insertion loss and return loss of the switch  700  when the switch is closed. Insertion loss is about −2.2 dB at 75 GHz, about −10.4 dB at 130 GHz, but drops as low as −16.6 dB at 105 GHz. Return loss is about −24.0 dB at 75 GHz, and about −11.2 dB at 130 GHz, but increases to as much as about −9.5 dB at 105 GHz. 
       FIG. 10  shows isolation for the switch  700  when the switch is open. Isolation is about −17.1 dB at 75 GHz and about −11.5 at 130 GHz, and drops as far as about −32.5 dB at 82 GHz. 
     Despite the improved isolation characteristics of the switch of  FIG. 7 ,  FIG. 9  shows that including the DGS in the ground plane of the switch results in higher insertion loss. To overcome the insertion loss, an improvement to the DGS structures of the  FIG. 7  switch is shown in  FIG. 11 . 
     The switch  1100  of  FIG. 11  is largely similar in structure to that of  FIG. 7 . The switch  1100  has two ground planes  1102 ,  1104  bisected by a signal line  1120  and has four DGS structures  1131 ,  1132 ,  1133 ,  1134  formed in the ground planes. The length of the ground planes and signal line are about 340 μm, and the cumulative width of the switch is about 404 μm. Switch  1100  differs from  FIG. 7  in that each of the DGS structures includes a secondary MEMS switch  1141 ,  1142 ,  1143 ,  144  positioned above the DGS structure. The shape of both the secondary switch and DGS may be rectangular, but the secondary switch may be longer while the DGS structure may be wider. In the example of  FIG. 11 , each DGS structure is a perforated lattice, and is about 105 μm in length and about 85 μm in width, and overlaid by a secondary switch that is about 139 μm in length and 65 μm in width. 
     A side view of a single DGS structure of the switch  1100  is shown in  FIG. 12 , although the DGS structure itself is not shown. The switch  1100  includes a substrate  1101  on which the ground plane  1102  is formed. The ground plane  1102  has a thickness or height of about 2 μm. Although not seen, the slots of the DGS structure  1131  are formed in the ground plane, and may have a depth equal to the height of the ground plane  1102 . A secondary switch  1141  is formed above the DGS structure  1131 . The secondary switch  1141  includes a beam  1151  supported by two feet  1162 ,  1164 . The supporting feet have a height of about 1 μm, thereby raising the beam  1151  about 1 μm above the DGS and ground plane. Thus, there is an air gap of about 1 μm between the non-deflected beam and the DGS positioned below. The beam thickness or height of the beam  1151  may be about 1.2 μm. 
     The beam  1151  is connected to an actuator (not shown) to supply a bias voltage, which runs from the beam  1151  to the ground plane  1102  via the feet  1162 ,  1164 . Applying the bias voltage causes the beam  1151  to deflect downward towards the ground plane  1102 , thereby affecting the capacitive characteristics of the DGS structure  1131 . The amount of voltage applied to the switch  1101  may be continuously variable, and thus the capacitive characteristics of the DGS structure (and its effect on the main MEMS switch of the device) can be varied or tuned. 
     It has been found that the switch arrangement of  FIG. 11  behaves like a metamaterial. This can be seen by first analyzing the transmission and reflection phases of a signal line formed in a coplanar waveguide without the DGS structure of  FIG. 11 , and then analyzing the transmission and reflection phases of the same signal line with the DGS structure of  FIG. 11 . 
       FIG. 13  shows transmission and reflection phases of a signal transmitted across a coplanar waveguide without the DGS structure over a band of millimeter wave frequencies from 50 GHz to 140 GHz. As seen in  FIG. 13 , any shift in the transmission phase of the signal is met with a substantially equal (within about 20 degrees) shift in the reflection phase. 
       FIG. 14  shows transmission and reflection phases of a signal over the same band of frequencies for the same coplanar waveguide but with the DGS structure incorporated into the waveguide at a height of 2.2 μm, which is the distance from the top surface of the substrate (the basin of the slots of the DGS structure) to the bottom surface of the secondary switch positioned above the DGS structure. As can be seen in  FIG. 14 , the transmission and reflection phases do not shift equally across the band of frequencies, and even shift in opposite directions, eventually crossing one another at 85 GHz and then crossing back at 96 GHz. 
       FIG. 15  shows transmission and reflection phases for the same coplanar waveguide but with the DGS structure at a height of 2.6 μm. In  FIG. 15 , the transmission and reflection phases shift substantially equally until about 110 GHz, but then begin shifting in opposite directions at frequencies above 115 GHz and even cross one another at about 128 GHz. 
     The particular resonance frequency of the DGS structure can vary depending on the height of the air gap between the ground plane and the beam.  FIG. 16  shows a plot of isolation characteristics for five secondary switches positioned over DGS structures at varying heights. The resonant frequency of the structure is shown to shift to higher frequency as the air gap between the ground plane and beam increases. 
     An example MEMS shunt switch with DGS structures and overlaid secondary switches is shown in more complete form in  FIG. 17 . The switch  1700  includes a signal line  1720  positioned between a first ground plane  1702  and a second ground plane  1704 , the signal line separated from each ground plane by first and second spaces  1703 ,  1705 , respectively. A primary shunt switch  1710  is positioned on top of, is connected to, and bridges the first and second ground planes  1702 ,  1704 . The primary shunt switch  1710  runs perpendicular to, and is suspended over, the signal line  1720 . When a bias voltage is applied to the primary shunt switch  1710 , the switch  1710  deflects downward toward the signal line  1720 . When the bias voltage is not applied, the switch  1710  deflects back upward to its original position. 
     A first DGS structure  1731  and a second DGS structure  1732  are formed in the first ground plane  1702 . A third DGS structure  1733  and a fourth DGS structure  1734  are formed in the second ground plane  1704 . The first and third DGS structures  1731 ,  1733  have mirror symmetry along a lengthwise axis X of the primary switch  1710 , and are a similar shape. The second and fourth DGS structures  1732 ,  1734  also have mirror symmetry along a lengthwise axis X of the primary switch  1710 , and are a similar shape. 
     In the example of  FIG. 17 , the first and third DGS structures  1731 ,  1733  are a different size from the second and fourth DGS structures  1732 ,  1734 . In particular, the second slots of the first and third DGS structures  1731 ,  1733  are about 85 μm long, whereas the second slots of the second and fourth DGS structures  1732 ,  1734  are about 100 μm long. The third slots of the first and third DGS structures  1731 ,  1733  are also shorter than those of the second and fourth DGS structures  1732 ,  1734 . This is in contrast to the four DGS structures shown in each of  FIGS. 7 and 11 , which all have the same dimensions 
     In some examples, the dimensions of the different DGS structures can be characterized in terms of lengths “a,” “a1,” and “b,” whereby a is the length of the third slot in one DGS structure, a1 is the length of the third slot in the other DGS structure, and b is the difference in length between the second and third slots in one or both size DGS structures. In some examples, the differently sized DGS structures may be designed to have the same value “b,” such that the difference between the second and third slot lengths is the same for each structure even when the structures are of different sizes. 
     Each DGS structure is overlaid by a respective secondary shunt switch  1741 ,  1742 ,  1743 ,  1744 . Each secondary shunt switch is connected to its respective ground line, and is suspended over its respective DGS structure with an air gap in between. The secondary shunt switches are rectangular, each of the secondary switches positioned lengthwise parallel to the signal line  1720  and perpendicular to the primary shunt switch  1710 . The secondary switches positioned above the first DGS structure  1731  and the third DGS structure  1733  have a mirror symmetry with the secondary switches positioned above the second DGS structure  1732  and the fourth DGS structure  1734  along a lengthwise axis X of the primary switch  1710 . Additionally, the secondary switches positioned above the first DGS structure  1731  and the second DGS structure  1732  have a mirror symmetry with the secondary switches positioned above the third DGS structure  1733  and the fourth DGS structure  1734  along a lengthwise axis Y of the signal line  1720 . The secondary shunt switches  1741 ,  1742 ,  1743 ,  1744  are also perforated. In the example of  FIG. 17 , the switches have a grid-like lattice perforation. 
       FIG. 18  shows a side view of the switch of  FIG. 17  from the viewpoint along either side of  FIG. 17 . The switch  1700  is formed on a substrate  1701 . A ground plane  1702  is formed over the substrate  1701 , and the primary switch  1710  is formed on top of the ground plane  1702 . The primary switch  1710  has two feet  1712  (the second foot is obstructed by foot  1712  in  FIG. 18 ) supporting a beam  1716 . Two secondary switches  1731 ,  1732  are positioned on either side of the primary switch  1710 . Each of the secondary switches also includes two feet  1752 ,  1754  supporting a beam  1756 . DGS structures (not shown) are formed in the ground plane  1702  at respective positions underneath the secondary switches  1731 ,  1732 . 
     In the example of  FIGS. 17 and 18 , the substrate and ground planes have a length of about 404 μm, and a width of about 340 μm. The ground planes have a thickness of about 2 μm. The primary switch  1710  extends the length of the substrate, and the primary switch feet  1712  and beam  1716  have a width of about 65 μm. The feet  1712  have a height of about 2.5 μm, and the beam  1716  has a thickness of about 1.2 μm. The secondary switches  1731  have a length of about 139 μm, and the secondary switch feet  1752 ,  1754  and beam  1756  have a width of about 65 μm. The feet  1752  have a height of about 1 μm, and the beam  1756  has a thickness of about 1.2 μm. Thus, the entire switch  1700  can be formed on top of the substrate  1701  within a 5.7 μm space. 
       FIG. 19  shows an example layout of a switch  1900 , showing the connections between the primary switch  1910  and secondary switches  1941 - 1944 , a first actuator  1962 , and a second actuator  1964 . The first actuator  1962  is connected to the primary switch  1910  and configured to provide a bias voltage to the primary switch. The second actuator  1964  is connected to each of the secondary switches  1941 - 1944  and is configured to provide a bias voltage to the secondary switches. 
     In operation, the primary switch  1910  may be either ON (bias voltage provided from the first actuator  1962 ) or OFF (no bias voltage provided by the first actuator  1964 ). When the primary switch is ON, the primary switch beam deflects downward, resulting in a large shunt capacitance that blocks RF signals from propagating along the signal line  1920 . When the primary switch is OFF, the primary switch beam deflects back upward (at rest), reducing the shunt capacitance and permitting RF signals to propagate along the signal line  1920 . 
     When the primary switch  1910  is OFF, the secondary switches  1941 - 1944  may be turned ON in order to negate the effects of the DGS structures towards insertion and return loss. A bias voltage is applied from the second actuator  1964  to each of the secondary switches  1941 - 1944 , thereby causing the switches to deflect downward toward the DGS structures and create a shunt capacitance blocking the effects of the DGS structure.  FIG. 20  shows the amount of downward deflection at several points of the secondary switches (measured in μm) when the secondary switches are actuated. 
       FIG. 21  shows return loss and insertion loss characteristics for the switch  1900  when the primary switch is OFF and the secondary switches are ON. At 75 GHz, insertion loss is as low as about −0.6 dB and return loss is as low as about −21.1 dB. At 130 GHz, insertion loss is still relatively low at about −1.5 dB, and return loss is also relatively low at −14.5 dB. 
     Returning to  FIG. 19 , when the primary switch  1910  is ON, the secondary switches  1941 - 1944  may be turned OFF in order to get the benefit of the DGS structures towards isolation. No bias voltage is applied from the second actuator to the secondary switches  1941 - 1944 , so the switches remain separated from the DGS structures underneath by the air gap.  FIG. 22  shows the amount of downward deflection at several cross-sections of the primary switches (measured in μm) when the primary switch is actuated. Deflection along the entire width of the primary switch is uniform for any given point along the length of the switch. 
       FIGS. 23-25  show isolation characteristics for the switch  1900  when the primary switch is ON and the secondary switches are OFF. In the example of  FIG. 23 , the same DGS structure is used. This leads to a significant improvement of isolation at a relatively narrow band (e.g., less than about 10 GHz, between 90 GHz and 100 GHz). At 75 GHz, isolation is about −23.1 dB, and at 130 GHz, isolation is about −23.9 dB. But at about 95 GHz, isolation is improved to about −52 dB. 
     In the examples of  FIGS. 24 and 25 , different DGS structures are used. This leads to an overall improvement of isolation over a wider band of frequencies. The structure represented in  FIG. 24  yields improved isolation at about 84 GHz (about −51 dB) and at about 112 GHz (about −59 dB), and is not worse than about −24 dB between 75 and 130 GHz. The structure represented in  FIG. 25  achieves its best isolation at about 98 GHz (about −41.5 dB), but the improved isolation characteristics do not sharply drop off. In this regard, isolation of −30 dB or better can be achieved across a wide band of frequencies, from about 85 GHz to about 110 GHz. 
     As seen from the attenuation characteristics of  FIGS. 21 and 23 , providing DGS structures with capacitive shunt switches above the DGS structures is an effective way of incorporating the benefits of DGS for improved isolation when RF signals are blocked, while at the same time negating the detriments caused by the DGS to insertion loss and return loss when RF signals are propagating. In this respect, incorporation of DGS structures and corresponding shunt switches is an improvement to RF MEMS design and operation. 
     Table 1 below provides a summary of the actuation voltage, isolation and insertion loss characteristics for the above-described switch designs with air gaps (and cantilever beam heights) of about 2.5 μm: 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                 Shunt Switch + 
                 Shunt Switch + 
               
               
                   
                   
                 Shunt 
                 DGS w/o 
                 DGS w/ 
               
               
                   
                 Shunt Switch 
                 Switch 
                 Switches 
                 Switches 
               
               
                 Parameters 
                 (FIGS. 2-3) 
                 (FIG. 5) 
                 (FIG. 7) 
                 (FIG. 17) 
               
               
                   
               
             
            
               
                 Shunt Switch 
                 37 V 
                 17 V 
                 17 V 
                 17 V 
               
               
                 Actuation 
               
               
                 Voltage 
               
               
                 Isolation 
                 −12 dB 
                 −15 dB 
                 −11 dB 
                 −24 dB 
               
               
                 (75-130 GHz) 
                 to 
                 to 
                 to 
                 to 
               
               
                   
                 −19 dB 
                 −24 dB 
                 −32 dB 
                 −59 dB 
               
               
                 Insertion 
                 0.74 dB 
                 0.6 dB 
                 −2 dB to 
                 0.6 dB 
               
               
                 Loss 
                   
                   
                 −11 dB 
               
               
                 Material 
                 Molybdenum 
                 Gold 
                 Gold 
                 Gold 
               
               
                 Cantilever 
                 2.5 um 
                 2.5 um 
                 2.5 um 
                 2.5 um 
               
               
                 Height 
               
               
                   
               
            
           
         
       
     
     Measurements are provided for the above example switches and designs. However, it will be readily appreciated that the particular dimensions of the RF MEMS switches, structures, and waveguide components may be altered without deviating from the core concepts of the present disclosure. For instance, the substrate, ground plane and signal line may be made longer or shorter, wider or narrower, and thicker or thinner Additionally, the primary and secondary switches may be designed in different shapes having different lengths, different widths, or different patterns, such as to enable a desired amount of deflection. Similarly, the air gap between switches and the components positioned underneath may be altered. And the shape and size of the DGS structures may also be altered. 
     The switch operations described above contemplate actuating either the primary switch but not the secondary switches, or actuating the secondary switches but not the primary switch. However, it will be readily appreciated that other forms of operation are possible. For example, in some cases, improved isolation characteristics may be achieved by providing a bias voltage to all of the primary and secondary switches.  FIG. 26  shows isolation characteristics for several switches having different DGS and secondary switch arrangements, in which both switches are actuated. Actuating the secondary switch results in improved isolation characteristics over a narrow band of frequencies. The particular band at which the improved isolation occurs varies depending on the air gap height between the switches and DGS structures. As the air gap increases, the frequency band at which the best isolation for the switch occurs shifts upward. In particular, for an air gap of 2.2 μm isolation of about −52 dB is achieved at about 85 GHz, for an air gap of 2.3 μm isolation of about −52 dB is achieved at about 85 GHz, for an air gap of 2.4 μm isolation of about −52 dB is achieved at about 85 GHz, for an air gap of 2.5 μm isolation of about −52 dB is achieved at about 85 GHz, for an air gap of 2.6 μm isolation of about −52 dB is achieved at about 85 GHz, for an air gap of 2.7 μm isolation of about −52 dB is achieved at about 85 GHz, for an air gap of 3.0 μm isolation of about −52 dB is achieved at about 85 GHz. This demonstrates the relative flexibility of the proposed combination of DGS structures with secondary switches for providing improved isolation across a wide range of high frequencies. 
     Overall, it is shown that providing both the DGS structures and secondary switches can achieve improvements in both insertion loss and isolation. These dual improvements are in contrast to the tradeoffs conventionally seen when using either only a shunt switch (good insertion loss, poor isolation) or only a DGS structure (improved isolation, but worse insertion loss). These findings are further summarized in the charts of  FIGS. 27 and 28 , which show the isolation and insertion loss characteristics of the respective structures discussed above. 
     As noted above, the proposed combination of a primary shunt switch, DGS structures and secondary shunt switches, is shown to behave like a metamaterial. In addition to this solution, it is also proposed to improve stiction of the MEMS switch using metamaterial layers within the design of the switch contacts, as described in greater detail herein. 
     It is possible to reduce the likelihood of stiction by increasing the bias voltage applied to the switch. Alternatively, instead of increasing bias voltage, the electric field of the switch can be increased by distancing the top electrode from ground. This can be accomplished, for example, by sandwiching the conductive layer (e.g., gold) between two dielectric layers (e.g., silicon oxynitride). 
     As a further alternative, the beam can be modified to maximize its restoring force without having to increase the bias voltage. Improved restoring force is influenced by such parameters as increased plate size, shortened beam length, or increased dielectric thickness. 
     In addition to controlling the distance between the electrode and ground and controlling the structural parameters of the switch contacts, it is also contemplated in the present disclosure to weaken or reverse the forces applied to the switch contacts due to their proximity. These forces are described in greater detail using the arrangements illustrated in  FIGS. 29 and 30 . 
       FIG. 29  is a force diagram illustration of an experimental setup  2900 , in which a plane of metal  2910  is positioned in parallel to a metamaterial  2920 . The metal and metamaterial are positioned apart from one another at a distance “d.” The forces illustrated in the setup  2900  are shown using arrows  2930 . A first force applied to the metal  2910  and metamaterial  2920  brings the two planes closer to one another. However, application of this first force has been observed under the specific conditions of the experimental setup  2900  to result in a second and opposite force “F” that causes the two planes to separate from one another. 
     In the case of two uncharged metal plates positioned closely to one another and in parallel, a force causing the two plates to move towards one another has been observed. This force is referred to as the Casimir force. The Casimir force originates from the interaction of the surfaces with the surrounding electromagnetic spectrum, and exhibits a dependence on the dielectric properties of the surfaces and the medium between the surfaces. Casimir forces between macroscopic surfaces have the same physical origin as atom-surface interactions and those between two atoms or molecules (van de Waals forces), because they originate from quantum fluctuations. 
     The Casimir force is known to be proportional to the effective permittivity of metal plates. Therefore, by decreasing the effective permittivity on the metal planes, the Casimir force too can be decreased. This can result in reduced forces preventing the plates from separating from one another, thus at least partially mitigating the stiction problem observed in MEMS switches. 
     However, aside from reducing the Casimir force by reducing permittivity between plates, a repulsive force can actually be generated between the planes if the effective permittivity is sufficiently decreased, such as by using metamaterials. This repulsive force is sometimes referred to as the “repulsive Casimir force,” and in the present application can further be used to resolve the stiction issue by repelling the contacts from one another. Thus, generating a repulsive Casimir force can result in even less of a liability for the contacts to effectively become “welded” together due to stiction. 
     Casimir interactions (both attractive and repulsive forces) may be realized in engineered materials such as silicon crystals, which can be used for levitation, microwave switches, MEMS oscillators and gyroscopes. Casimir interaction is attractive in magnetic Metamaterials made of nonmagnetic meta-atoms. In contrast, intrinsically magnetic meta-atoms could potentially lead to Casimir repulsion. Chiral Metamaterials made of metallic and dielectric metaatoms are good candidates for Casimir repulsion. One approach is to engineer the material combinations that give rise to Casimir repulsive forces. For example, Casimir repulsive forces have been observed between multilayer walls made of alternating layers of a topological insulator (TI) and a normal insulator. The Casimir repulsion under the influence of the magnetization orientation in the magnetic coatings on TI layer surfaces, the layer thicknesses, and the topological magnetoelectric polarizability, has been demonstrated. For the multilayer structures with parallel magnetization on the TI layer surfaces, it is feasible to enhance the repulsion by increasing the TI layer number, which is due to the accumulation of the contribution to the repulsion from the polarization rotation effect occurring on each TI layer surface. Generally, in the distance region where there is Casimir attraction between semi-infinite TIs, the force may turn into repulsion in the TI multilayer structure, and in the region of repulsion for semi-infinite TI, the repulsive force can be enhanced in magnitude, the enhancement tends to a maximum while the structure contains sufficiently many layers. 
     In general, Casimir forces between macroscopic surfaces entail separations typically &gt;0.1 um where retardation plays an essential role, while van der Waals forces refer to separations &lt;0.01 um where retardation is insignificant. Advances in theoretical studies and experimental techniques have enabled examination of the Casimir force beyond the configuration of two parallel perfect metal plates. Novel materials and shapes of the interacting bodies enable new opportunities for applications and, at the same time, pose new open questions. On the theoretical side, MTM-Inspired structures can produce a powerful Casimir Effect, which will allow transportation of matter; this implies, in principle, that the effect can be used to attract or push away physical matter. A further complexity of the Casimir force potentially allows greater opportunity for neutralization or for use of Casimir forces to partially cancel Van Der Waals forces. It is to note that polaritonic involvement causes a repulsive Casimir force between Metal and MTM structures. For example, binding TM polaritons govern at shorter distance, inundated by joint repulsion due to anti-binding TM and TE polaritons. Thus, in the case of a hybrid arrangement, surface plasmons can be indicative of the strength and sign of the Casimir force. 
       FIGS. 30A and 30B  show a typical example of a levitating mirror. The repulsive Casimir force of the metamaterial may balance the weight of one of the mirrors, letting it levitate on zero-point fluctuation. 
       FIG. 30A  shows a first metal plate  3010  or mirror separated from a second metal plate  3040  or mirror by a distance d. The two metal plates may be thought of as opposing contacts in a MEMS switch, and may be liable to become permanently stuck to one another at distances “d” that are sufficiently small. By contrast,  FIG. 30B  shows a thin layer of metamaterial  3020  affixed to a surface of the first metal plate  3010  and positioned in between the metal plates  3010 ,  3040 . A Casimir force  3030  is produced at the boundary between the metamaterial  3020  and the second metal plate  3040 , thereby causing the second metal plate to further separate from the first metal plate  3010  by a distance d′. This additional separation may even counteract gravitational forces, and thus cause the second metal plate  3040  to levitate. In some cases, the metamaterial may be made from gold foil. 
     In the application of an RF MEMS switch structure, the switch may include a deflectable beam having a shorting bar positioned on a surface of the beam and aligned with the contact of the signal line. The shorting bar may be made of metal, such as a thin layer of gold foil located. When the shorting bar touches the signal line, the metal-to-metal contact surfaces may stick to one another in the form of strong adhesion. This adhesion causes undesirable stiction problems, which in turn may cause the switch to be electrically shorted, and it may take a considerable amount of force to separate the shorting bar from the signal line. The RF MEMS switch generally relies on stresses accumulating in the beam as a result of the beam&#39;s deflection in order to counteract the adhesive forces and to return the beam back to its at-rest or equilibrium position. This counteractive force, which is the sum of the stresses in the beam, is referred to as the restoring force that “restores” the beam to its at-rest position. However, this force is not always sufficient to counteract adhesive forces between the metal contacts. By providing a metamaterial structure between the metal contacts, the restoring force of the beam can be supplemented using the repulsive Casimir force generated when the shortening bar touches or comes within proximity to the signal line. 
     The Casimir force can be controlled by providing a permittivity gradient in the contact of the deflectable beam. The permittivity gradient can be provided by interfacing three layers of media in either decreasing or increasing order of permittivity. In  FIG. 31 , three layers of media are provided: a first layer  3110  having permittivity ε 1 , a second layer  3120  having permittivity ε 2 , and a third layer  3130  having permittivity ε 3 . The first and third layers may be metal layers, and the second layer may be a dielectric layer. The layers may be interfaced such that either ε 1 &lt;ε 2 &lt;ε 3  or ε 1 &gt;ε 2 &gt;ε 3 . This may be possible by providing one metal layer with positive permittivity, and another metal layer with negative permittivity. For instance, the first layer  3110  may be made of gold and have an infinite permittivity, the second layer  3120  may be made of a dielectric (e.g., silicon mononitride (SiN)) and have a small but positive permittivity (e.g., 7) and the third layer  3130  may include a metamaterial unit cell  3135  and may have a zero or even negative permittivity. In other examples, the first layer  3110  can also include a metamaterial unit cell  3115  in order to acquire the desired permittivity. 
       FIGS. 32A-E  are illustrations of an example RF MEMS switch  3200  incorporating metamaterial cells in order to provide a repulsive Casimir force between contacts of the switch.  FIG. 32A  is a top-down view of the switch,  FIG. 32B  is a perspective view of the switch,  FIG. 32C  is a bisected cross-sectional perspective view of the switch,  FIG. 32D  is a side view of the switch in a closed position, and  FIG. 32E  is a side view of the switch in an open position. 
     The switch is formed in a coplanar waveguide  3201  positioned having two ground planes  3202  and  3204  formed above a substrate  3205 . The ground planes are separated by a channel and a signal line  3210  is formed lengthwise in the channel. The signal line  3210  includes each of an input port  3212  through which a signal is received (arrow in) and an output port through which the signal is transmitted (arrow out). 
     The switch includes a cantilevered beam that moves in and out of the plane of the coplanar waveguide in order to move in and out of contact with the signal line  3210 . The beam includes multiple layers. In the example of  FIG. 32 , from top to bottom, the layers include: a top layer  3420  of dielectric material, a first metal layer  3210 , a dielectric layer  3220 , and a second metal layer  3230 . Each of the first and second metal layers  3210 ,  3220  may include a metamaterial device  3215 ,  3235  encased within, as shown in the cross-sectional view of  FIG. 32C . The top layer  3210  and first mater layer  3220  may be adapted to extend across the entire length of the beam, whereas the length of the sandwiched dielectric layer  3220  and second metal layer  3230  may be limited to the area above the signal line  3210 . Alternatively, the dielectric layer  3220  may extend the entire length of the beam while only the second metal layer  3230  may be limited to the area above the signal line  3210 . 
     The ground planes  3202 ,  3204  and signal line ports  3212 ,  3214  may be separated from the substrate  3205  by a thin layer of dielectric  3250 , such as SiN or SiO 2 . 
     Operation of the switch may be controlled by moving an anchor  3270  to which the beam is attached in and out of the plane of the coplanar waveguide  3201 . In this case, the ground line  3202  may include a hole  3260  though which a post or anchor  3270  of the beam is positioned. Moving the post  3270  up and down can result in the contacts of the switch separating or contacting one another, respectively.  FIG. 32D  shows the switch closed, with the contacts contacting one another.  FIG. 32E  shows the switch open, with the dielectric and metal layers of the beam elevated above the signal line ports  3214 , thereby forming a gap  3275  of a given height H. 
     In the example of  FIGS. 32A-E , the section of the coplanar waveguide shown may be about 100 μm, and the beam may have a width of about 75 μm. The anchor  3270  to which the beam is attached may have a length (in the direction of the beam length) of about 11.25 μm and a width of about 75 μm. The opening  3260  into which the beam is anchored may have a greater length and width, such as about 80 μm by 30 μm. The overall length of the waveguide (in the direction of the beam length) may be about 330 μm, whereby the ground planes and the signal lines may each have a width (also in the direction of the beam length) of about 75 μm, with 38 μm channels in between. The beam may have a length of about 140 μm (not including the length of the anchor  3270 ). 
     The overall height of the beam when in the closed position may be about 5 μm, relative to the dielectric surface on which the ground planes and signal line are formed. Each of the ground planes and signal line may be 2 μm thick. The beam may then contribute an additional 3 μm to the height of the switch, whereby each of the metal layers  3210 ,  3230  is about 1 μm thick and the dielectric layer  3220  sandwiched in between may also be about 1 μm. The top layer  3440  may add about an additional 0.2 μm to the height of the switch. The height of the switch may increase by H when open, as shown in  FIG. 32E . 
     The metamaterial unit cells included in the second metal layer  3230 , and optionally in the first metal layer  3210  as well, may have the shape of a split ring resonator. The split rings may be square-shaped.  FIG. 33  illustrates an example metal layer  3310  having each of a first split ring  3322  having width L, and a second split ring  3324 , formed in the layer, whereby forming the rings may involve cutting out the rings from the layer. Each of the rings may be concentric, and may be aligned so that the splits  3330  in the respective rings are positioned on opposing sides of the layer  3310 . Each of the rings may have a uniform width W, and the splits  3330  may have a uniform width G. The rings may further be separated from one another by a uniform separation  3332  having width S. 
     Different unit cell structures may provide different metamaterial characteristics at the relevant band of frequencies for the RF MEMS switch (e.g., between 60 to 130 GHz). Each of  FIGS. 34-36  provides simulated test results for transmission and reflection characteristics for a respective unit cell structure. In the particular examples provided herein, the simulated test results were collected using Matlab code, although other programs could be used to run simulations in other cases. 
     The metamaterial structure  3401  of  FIG. 34  is included in a metal layer having a width equal to the width of the beam  3402 . In this example, the unit cell is of transmission type at low frequencies, at about 300 GHz and again at about 470 GHz. The unit cell is of reflection type, with attenuation of the transmission exceeding that of the reflection, at about 150 GHz, and again at about 300 GHz. Thus, the structure of  FIG. 34  is shown to exhibit metamaterial properties. 
     The metamaterial structure  3501  of  FIG. 35  is included in a metal layer having a length equal to the width of the signal line, and further attached to a beam  3502  having a width much smaller than the width of the metal layer. In this example, the unit cell is shown to have transmission properties at about 54 GHz and reflection properties at about 150 GHz. Therefore, the structure of  FIG. 35  is also shown to exhibit metamaterial properties. 
     The metamaterial structure  3601  of  FIG. 36  is included in a metal layer having a length equal to the width of the signal line, and further attached to a U-shaped beam  3602  having two branches each having width much smaller than the width of the metal layer. In this example, the unit cell is shown to have transmission properties at about 80 GHz and reflection properties at about 163 GHz. Therefore, the structure of  FIG. 36  is also shown to exhibit metamaterial properties, and these properties can be exhibited over a relatively narrow bandwidth of about 83 GHz. 
     Additionally, the parameters of the metamaterial cell structures may be varied to produce different transmission and reflection characteristics. For example,  FIG. 37  provides a graph plotting reflection characteristics for a metamaterial cell having different parameters G, S and W (as defined in connection with  FIG. 33  above). In the particular example of  FIG. 37 , it can be seen that the frequency at which reflection is most greatly attenuated varied from about 80 GHz to about 90 GHz depending on G, S and W. For instance, where G is 2 μm, S is 3 μm, and W is 9 μm, insertion loss drops to about −74 dB at 80 GHz. By comparison, other parameters of G, S, and W yield a reflection of about −60 dB at about 90 GHz. 
     In addition to the use of different metamaterial cell structures and cell structure parameters, the metal layers of the MEMS switch may also be formed with different parameters and dimensions as compared to those parameters and dimensions described above.  FIG. 38  is a plot of both transmission and reflection properties of a switch for which the thickness of the second metal layer “d” (e.g.,  3230  of  FIGS. 32A-E ) varies between 0.5 μm through 2 μm.  FIG. 39  is a plot of transmission and reflection properties of a switch for which the thickness of the sandwiched dielectric layer (e.g.,  3220  of  FIGS. 32A-E ) varies between 1.5 μm through 5 μm.  FIG. 40  is a plot of transmission and reflection properties of a switch for which the thickness of the first metal layer “d1” (e.g.,  3210  of  FIGS. 32A-E ) varies between 0.5 μm through 2 μm. The transmission properties of the various MEMS switches are largely similar in each of these conditions, although the frequency at which the transmission attenuates varies between about 160 GHz and about 180 GHz, and the reflection properties of the switch vary mainly between 60 GHz and 150 GHz. 
     Using the transmission and reflection data described above, permeability and permittivity of the metamaterial cells can be extracted using parameter extraction procedures known in the art. The parameter extraction is shown in  FIG. 41 . As can be seen from  FIG. 41 , the metamaterial structure exhibits near zero permittivity as well as permeability at a band of frequencies centered around 80 GHz. Therefore, it is clear from  FIG. 41  that these structures would produce a repulsive Casimir force around the band of frequencies ranging from about 60 GHz to about 130 GHz. 
       FIGS. 42 and 43  further demonstrate the overall response of the RF MEMS switch in each of its ON and OFF states, respectively. In  FIG. 42 , when the switch is OFF, and thus not passing the transmitted signal between input and output ports, the reflection characteristics are shown to be just slightly less than 0 dB even at frequencies of up to 130 GHz, and the transmission characteristics are between about −20 dB and −15 dB between operating frequencies of about 60 GHz to about 130 GHz. In  FIG. 43 , when the switch is ON, and thus passing the transmitted signal between input and output ports, the reflection characteristics are as low as about −73.5 dB at 80 GHz with the transmission characteristics as high as −0.33 dB while the reflection and transmission characteristics at 163 GHz are both about −6.75 dB. 
     The examples of  FIGS. 32 through 43  demonstrate the possibility of incorporating metamaterials into a high frequency resistive MEMS switch in order to reduce the effects of stiction. However, it will also be appreciated that the above principles can be similarly applied to capacitive MEMS switches. As with the resistive switch, a sandwich of metal and dielectric layers may be used to achieve the desired permittivity interface, such as having a gold layer with infinite permittivity, a dielectric layer with positive but low permittivity, and a metamaterial layer with a permittivity in the range of about zero or less. Unlike the example switches above, in the capacitive switch, the metamaterial layer may be provided as part of the signal line contact instead of as part of the beam contact. 
     Different unit cell structures may provide different metamaterial characteristics at the relevant band of frequencies for the RF MEMS switch (e.g., between 60 to 130 GHz). Each of  FIGS. 44-46  provides simulated test results for transmission and reflection characteristics for a respective unit cell structure. In the particular examples provided herein, the simulated test results were collected using Matlab code, although other programs could be used to run simulations in other cases. 
     The metamaterial structure  4401  of  FIG. 44  is included in a metal layer (e.g., of a signal line contact) and interfaces beam  4402 . In this example, the beam is thinner than the metamaterial structure, and is supported by a single support extending from one of the ground planes adjacent the signal line. The unit cell is of transmission type at about 34 GHz (having reflection characteristics of −88.75 dB and transmission characteristics of −0.29 dB). The unit cell is of reflection type at about 120 GHz. Thus, the structure of  FIG. 44  is shown to exhibit metamaterial properties. 
     The metamaterial structure  4501  of  FIG. 45  is included in a metal layer (e.g., of a signal line contact) and interfaces beam  4502 . In this example, the beam is thinner than the metamaterial structure, and is doubly supported by posts on either side of the signal line. The unit cell is of transmission type at about 40 GHz (having reflection characteristics of −54 dB and transmission characteristics of −0.5 dB). The unit cell is of reflection type at about 140 GHz. Thus, the structure of  FIG. 45  is shown to exhibit metamaterial properties. 
       FIG. 46  includes two metamaterial structures  4601  and  4603  positioned at opposing input and output sides of the signal line. Each metamaterial structure  4601 ,  4603  is included in a metal layer (e.g., of the signal line contact). Further, a respective doubly-supported beam  4602 ,  4604  is positioned above each of the metamaterial structures  4601 ,  4602 . As in the example of  FIG. 45 , the beams are thinner than the metamaterial structures. The unit cell is of transmission type at about 8 GHz (having reflection characteristics of −60 dB and transmission characteristics of −0.01 dB). The unit cell is of reflection type at about 160 GHz. Thus, the structure of  FIG. 45  is shown to exhibit metamaterial properties. 
     Another example switch  4700  is shown in  FIGS. 47A-C .  FIG. 47  is a top-down view of the switch.  FIG. 47B  is a side view of the switch.  FIG. 47C  is a perspective view of the switch. 
     The switch includes a structure formed over a signal line having an input side  4712  and an output side  4714 . A metamaterial structure having an outer split ring  4722  and inner split ring  4724  is formed in the signal line contact between the input side  4712  and output side  4714 , through which a signal is received (arrow in) and an output port through which the signal is transmitted (arrow out). 
     As with the previously described split ring structures, the structure of  FIG. 47A-C  has a width W, a split width of G, and the space between the rings has a width S. The signal line has a width L, and the channel separating the signal line from the respective ground planes has a width C. 
     Each of the ground planes  4702 ,  4704  and the signal line are formed from a conductive material such as gold, and are formed on top of a dielectric material  4740  such as silicon nitride (Si 3 N 4 ), which itself is formed on top of a substrate  4705 . One of the ground planes  4702  includes a post  4770  extending downward from the ground plane  4702  into the dielectric material  4740 , and a beam  4780  extending from the post  4770  in the direction of the signal line  4714 . The edge of the beam  4780  is aligned with the opposing edge of the signal line  4712 ,  4714 , such that the end of beam  4780  is positioned underneath the metamaterial structures  4722 ,  4724 , of the signal line  4712 ,  4714 . In  FIGS. 47A and 47C , the post  4770  can be seen through an opening  4760  in the ground plane  4702 . 
     In the example of  FIGS. 47A-C , the ground planes and the signal line may each have a width (in the direction of the beam  4780  length) of about 73 μm and the beam may have a length of about 168 μm. The metamaterial structure formed on the signal line contact may have a ring width W of about 15 μm, a split width G of about 8 μm, and a spacing between rings S of about 5 μm. 
     Transmission and reflection characteristics of the switch  4700  over a range of frequencies are shown in  FIG. 48 . As can be seen from  FIG. 48 , the metamaterial is most reflective at about 175 GHz and most transmissive at about 80 GHz. 
     Based on these results, a material parameter extraction can be performed in order to determine the permittivity and permeability of the metamaterial structure. The extraction is shown over a range of frequencies in  FIG. 49 . As seen in  FIG. 49 , the metamaterial structure exhibits near zero permittivity and permeability between about 50 GHz and 150 GHz. This indicates that the structure of  FIG. 48  is suitable for reducing Casimir forces (or even generating repulsive Casimir forces) in the desired frequency band of the present disclosure. 
       FIG. 50  shows a perspective view of a capacitive shunt RF MEMS switch  5000  utilizing a metamaterial signal line contact in order to reduce stiction in the switch. Much of the features of switch  5000  may be compared to those of switch  4700  in  FIGS. 47A-C  (ground planes  5002  and  5004  and substrate  5005  compare to planes  4702  and  4704  and substrate  4705 ; signal line input and outputs  5012  and  5014  compare to  4712  and  4714 ; split ring metamaterial structure  5022  and  5024  compares to structure  4722  and  4724 ; dielectric layers  4740  and  5040  are comparable; openings  4760  and  5060  are comparable; posts  4770  and  5070  are comparable; and beams  4780  and  5080  are comparable). The switch  5000  further includes a deflectable beam  5050 . The beam  5050  may be comparable to the rectangular beam  510  described in connection with  FIG. 5  (e.g., may be made from gold, may have a perforated grid structure, may extend in a serpentine pattern). The deflectable beam  5050  is supported by a pair of posts formed on top of the ground planes  5002  and  5004 , respectively, and is configured to deflect downward towards the signal line when actuated by a bias voltage. 
     In operation, the bias voltage causes a midpoint of the beam  5050  to deflect downward until it comes in contact with the signal line contact, thereby causing the signal line to turn off (or in other cases to turn on). When the bias voltage is removed, the midpoint of the beam  5050  deflects back upward. Because the midpoint of the beam is aligned with the metamaterial structure  5022 ,  5024  of the signal line contact, the Casimir effect at the interface between the beam and the signal line contact is diminished or even repulsive, thereby reducing the liability of stiction between the beam  5050  and the signal line. 
     Although not shown in  FIG. 50 , the signal line contact may further include a later of dielectric material above the metal layer including the metamaterial structure. The dielectric layer may be made of SiN, and may function as an isolation layer in order to achieve the desired permittivity gradient, as discussed above in connection with  FIG. 31 . Stated another way, the beam  5050  may have an infinite permittivity, the isolation layer may have a positive but smaller permittivity, and the metal layer including the metamaterial structure in the signal line contact may have a near zero, zero or even negative permittivity, thereby satisfying the ε 1 &lt;ε 2 &lt;ε 3  condition (or vice versa). 
     Performance of the switch  500  is shown in  FIGS. 51 and 52 , which are plots of both reflection and transmission characteristics of the switch across a range of high RF frequencies.  FIG. 51  demonstrates operation of the switch in the ON state (transmitting signals) and  FIG. 52  demonstrates operation of the switch in the OFF state (cutting off transmission of signals) 
     In  FIG. 51 , most notably, at 10.3 GHz, return loss is as high as −29.8 dB while insertion loss is as low as about −0.07 dB. Even at 100.2 GHz, return loss is as high as −8.9 dB while insertion loss is only about −1.23 dB. This demonstrates good operation of the switch in the ON state across a wide range of high frequencies, from 10 GHz to 100 GHz. 
     In  FIG. 52 , the switch is off, thus changing to being reflective instead of transmissive. At 29.3 GHz, insertion loss is as high as about −22.2 dB while return loss is as low as about −0.26 dB. Even at 100.2 GHz, insertion loss is as high as −14.9 dB while return loss is only about −0.82 dB. This demonstrates good operation of the switch in its OFF state across nearly the same wide range of high frequencies, from about 20 GHz to 100 GHz. 
     Altogether, good insertion loss and return loss characteristics of the RF MEMS Switch in the ON and OFF states are achieved over 30-100 GHz frequency band. This makes the presently described switch a good candidate for high frequency switching operations over a wide bandwidth of frequencies. Accordingly, the switches described in the present disclosure can improve operation and performance of applications requiring high frequencies (e.g., 10 GHz or greater) over a wide bandwidth. Such technologies may include, but are not limited to, 5G communications, switching networks, phase shifters (e.g., in electronically scanned phase array antennas) and Internet of Things (IoT) applications. 
     In the present disclosure, the metamaterial structures described are split rings. However, those skilled in the art should recognize that other metamaterial structures may be used, provided that those structures provide similar permittivity and permeability characteristics within the desired range of frequencies. For instance, a topology inspired Möbius transformation MTM (metamaterial) structures (meaning a structure that forms a continuous closed path that maps onto itself, or stated another way, the structure may have a topology in which a closed path extends two or more revolutions around an axis (e.g., at or close to the center of the structure) before the closed path is completed) may be considered advantageous for generating repulsive Casimir forces. 
     Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims.