Abstract:
A microelectromechanical system (MEMS)-based electrical switch. The electrical switch includes a moveable electrode, a dielectric layer positioned adjacent the moveable electrode on a first side of the dielectric layer and spaced apart from the moveable electrode when the moveable electrode is in an inactivated position and in contact with the moveable electrode when the moveable electrode is in an activated position, and a substrate attached to the dielectric layer on a second side opposite to the first side, the moveable electrode is configured to brake prior to coming in contact with the dielectric layer when the moveable electrode is switched between the inactivated state and the activated state.

Description:
[0001]    This invention was made with government support under DE-FC52-08NA28617 awarded by the Department of Energy. The government has certain rights in the invention. 
     
    
     TECHNICAL FIELD 
       [0002]    This invention relates to capacitive microelectromechanical switches, and particularly to the problem of electromechanical dielectric degradation associated with the hard landing of a movable electrode. 
       BACKGROUND 
       [0003]    Radio frequency-microelectromechanical systems (RF-MEMS) capacitive switch (CS) based systems have attracted a significant interest in recent years. These RF-MEMS CS systems provide excellent RF characteristics (such as high linearity and low losses), as well as low power consumption. 
         [0004]    A typical RF-MEMS CS system 10 found in the prior art is depicted in  FIG. 10 . Such an RF-MEMS CS may find diverse applications in radar systems, wireless communication, instrumentation, etc. Compared to solid state switches, RF-MEMS switches offer the advantages of low power consumption, low insertion and return loss, extremely high linearity, and excellent isolation. Several disadvantages have been well documented in the prior art including but not limited to reaching and maintain a high level of reliability. One source of degradation of RF-MEMS CSs is the result of dielectric charging by virtue of a built-in charge that causes a shift in the capacitance-voltage characteristics. Additionally, poor reliability related to mechanical creep, and fatigue amongst other issues, continue to hinder the large scale deployment of RF-MEMS switches. Another key reliability concern is the impact velocity—the velocity with which a movable electrode  12  (see  FIG. 10 ) impacts a dielectric layer  14  in an electrostatically actuated (voltage source  16 ) RF-MEMS CS. This impact damages the dielectric layer  14  and increases the adhesion forces which may eventually lead to malfunction of the switch due to stiction. 
         [0005]    To address the challenges in reliability of a CS, novel approaches are needed to address the above-described dielectric degradation caused by impacting of a moveable electrode against a dielectric layer. 
       SUMMARY 
       [0006]    The present disclosure provides a microelectromechanical system (MEMS)-based electrical switch system. The electrical switch system includes at least one electrical switch. The switch includes a moveable electrode. The switch further includes a dielectric layer positioned adjacent the moveable electrode on a first side of the dielectric layer and spaced apart from the moveable electrode when the switch is in an inactivated position and in contact with the moveable electrode when the switch is in an activated position. The switch also includes a substrate attached to the dielectric layer on a second side opposite to the first side. The system also includes at least one voltage source coupled to the switch. The electrical switch system further includes at least one resistive element positioned in series between the switch and the voltage source. The resistive element is configured to brake movement of the moveable electrode prior to coming in contact with the dielectric layer when the voltage source causes the switch to be switched between the inactivated state and the activated state. 
         [0007]    The present disclosure also provides a microelectromechanical system (MEMS)-based electrical switch. The electrical switch includes a moveable electrode, and a dielectric layer positioned adjacent the moveable electrode on a first side of the dielectric layer and spaced apart from the moveable electrode when the moveable electrode is in an inactivated position and in contact with the moveable electrode when the moveable electrode is in an activated position. The electrical switch also includes a substrate attached to the dielectric layer on a second side opposite to the first side, the moveable electrode is configured to brake movement of the moveable electrode prior to coming in contact with the dielectric layer when the moveable electrode is switched between the inactivated state and the activated state. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0008]      FIG. 1  is a schematic of a typical radio frequency-microelectromechanical system (RF-MEMS) capacitive switch (CS) based system, driven with a novel approach, according to the present disclosure. 
           [0009]      FIG. 2(   a ) is a capacitive loading schematic of the input and output RF transmission lines using a typical RF-MEMS CS. 
           [0010]      FIGS. 2(   b ) and  2 ( c ) are capacitive loading schematic of the input and output RF transmission lines using the typical RF-MEMS CS depicted in  FIG. 2(   a ), in a high capacitance (short circuit) configuration,  FIG. 2(   b ), and in a low capacitance (open circuit) configuration,  FIG. 2(   c ). 
           [0011]      FIG. 3  is a schematic view of a typical RF-MEMS CS driven with a novel approach, according to the present disclosure, depicted in an activated state. 
           [0012]      FIG. 4  is a schematic view of a typical RF-MEMS CS driven with the novel approach, according to the present disclosure, depicted in an inactivated state. 
           [0013]      FIG. 5(   a ) is a graph of Energy (E) vs. displacement (y) profile for V&lt;V PI  (bottom curve) and V&gt;V PI  (top curve), wherein E d  is the energy dissipation at a top electrode-dielectric interface during an activation cycle, in a typical RF-MEMS CS. 
           [0014]      FIG. 5(   b ) is a graph of Displacement (y), as designated in the graph, and velocity (v) as a function of time (t), as designated in the graph, during the activation cycle showing pull-in time (t PI ) and impact velocity (v impact ), in a typical RF-MEMS CS. 
           [0015]      FIGS. 6(   a )- 6 ( d ) are graphs of (a) Velocity (v) as a function of displacement (y) during an activation cycle, according to the present disclosure; (b) v impact  and t PI  as a function of resistance (R); (c) Energy as a function of resistance (R); and (d) distribution of v impact  due to process variation for R=0 and R=10 kΩ, for activation of the RF-MEMS CS according to the present disclosure. 
           [0016]      FIG. 7  is a perspective view of various embodiments of RF-MEMS CS, according to the present disclosure, wherein a moveable electrode and a substrate can be (p 2 ) arrays of cylinders encased in an insulator, and (p 3 ) arrays of spheres encased in an insulator. 
           [0017]      FIG. 8  is a collection of perspective views of various embodiments of RF-MEMS CS, according to the present disclosure, wherein the dielectric can be shaped to include (p 4 ) an array of linear slots; and (p 5 ) a fractal of linear slots. 
           [0018]      FIGS. 9(   a )- 9 ( d ) are graphs of Velocity (v) as a function of displacement (y) during an activation cycle for the various embodiments depicted in  FIGS. 7 and 8 ,  FIG. 9(   a ); v impact  as a function of (g) between individual elements of the CS,  FIG. 9(   b ), v impact  and t PI  for fractal dielectric as a function of (g),  FIG. 9(   c ), and as a function of D F ,  FIG. 9(   d ). In each of the  FIGS. 9(   a )- 9 ( d ), p 1  represents a planar electrode configuration found in the prior art. 
           [0019]      FIG. 10  is a schematic of a typical RF-MEMS CS, found in the prior art. 
       
    
    
     DETAILED DESCRIPTION 
       [0020]    For the purposes of promoting an understanding of the principles of the present disclosure, reference will now be made to the embodiments illustrated in the drawings, and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of this disclosure is thereby intended. 
         [0021]    Novel radio frequency-microelectromechanical systems (RF-MEMS) capacitive switching arrangements are described. In accordance with the present disclosure, various approaches are described to provide resistive and capacitive braking that can reduce impact velocity of a movable electrode in an RF-MEMS CS significantly without compromising other performance characteristics such as pull-in voltage and pull-in time of the moveable electrode. Resistive braking is achieved by inserting a resistance in series with the voltage source. Capacitive braking is achieved by patterning of the electrode or the dielectric in the RF-MEMS CS. 
         [0022]    Referring to  FIG. 1 , an RF-MEMS CS system  100 , according to the present disclosure, is depicted. The system includes an RF-MEMS CS device  101 , a voltage source  116 , a resistor  118 , and a return mechanism depicted as a spring  120  (which is configured to provide a restoring force in opposite direction to an electrostatic force that can deflect the moveable electrode  102 , see below, downward). The device  101  is coupled to the voltage source  116  and the resistor  118 . It is appreciated that the voltage source  116  can be a switched supply (i.e., on and off) or a linear supply (i.e., capable of providing voltages according to a predetermined range). It is also appreciated that the resistor  118  is intended to represent an impedance (i.e., including a real component and an imaginary component). 
         [0023]    The device  101  is defined by a moveable electrode  102 , a dielectric layer  104 , and a substrate  106 . The moveable electrode  102  and the dielectric layer  104  are separated by a gap, e.g., an airgap, represented by the double arrow  108 . The device is depicted in an inactivated state; therefore the gap  108  is the largest. The moveable electrode  102  is defined by a length  110  and a width  112 . Similarly, the dielectric layer  104  is defined by the length  110  and the width  112 , although other variations are also possible. The dielectric layer  104  is also defined by a thickness of  114 . 
         [0024]    Referring to  FIG. 2(   a ), a model  200 _a for an RF-MEMS CS system is depicted (whether a typical, i.e., without braking as in the RF-MEMS CS systems of prior art, or with braking, i.e., based on the arrangements described herein), is depicted. Incoming RF signal identified as “In” sees an input impedance Z 0    202 _a. The output RF signal also sees an output impedance Z 0    204 _a. While, these input and output impedances  202 _a and  204 _a need not be the same, for sake of simplicity these are identified as being the same. In addition, the RF-MEMS CS system  10  or  100  (see  FIG. 10  and  FIG. 1)  is positioned between the input and output impedances  202 _a and  204 _a. The RF-MEMS CS systems  10  or  100  utilize a corresponding RF-MEMS CS device  11  or  101 , respectively, to provide a low or high capacitance. 
         [0025]    Referring to  FIG. 2(   b), a model  200   _b for an RF-MEMS CS system is depicted (whether a typical, i.e., without braking as in the RF-MEMS CS systems of prior art, or with braking, i.e., based on the arrangements described herein), is depicted. Incoming RF signal identified as “In” sees an input impedance Z 0    202 _b. The output RF signal also sees an output impedance Z 0    204 _b. While, these input and output impedances  202 _b and  204 _b need not be the same, for sake of simplicity these are identified as being the same. In addition, the RF-MEMS CS system  10  or  100  (see  FIG. 10  and  FIG. 1)  is positioned between the input and output impedances  202 _b and  204 _b. The RF-MEMS CS systems  10 _b or  100 _b utilize a corresponding RF-MEMS CS device  11  or  101  in an activated state (i.e., with sources  16  or  116  activated), respectively, to provide a high capacitance. The high capacitance results in a short circuit on the input side, causing the input signal to be substantially reflected. Such a reflection is similar to an electronic switch that is placed in line with the input signal being placed in an open position. Therefore, no or very little of the input signal is transmitted. 
         [0026]    Referring to  FIG. 2(   c ), a model  200 _c for an RF-MEMS CS system is depicted (whether a typical, i.e., without braking as in the RF-MEMS CS systems of prior art, or with braking, i.e., based on the arrangements described herein), is depicted. Incoming RF signal identified as “In” sees an input impedance Z 0    202 _c. The output RF signal also sees an output impedance Z 0    204 _c. While, these input and output impedances  202 _c and  204 _c need not be the same, for sake of simplicity these are identified as being the same. In addition, the RF-MEMS CS system  10  or  100  (see  FIG. 10  and  FIG. 1)  is positioned between the input and output impedances  202 _c and  204 _c. The RF-MEMS CS systems  10 _c or  100 _c utilize a corresponding RF-MEMS CS device  11  or  101  in an inactivated state (i.e., with sources  16  or  116  inactivated), respectively, to provide a low capacitance. The low capacitance results in an open circuit on the input side, causing the input signal to be substantially transmitted. Such a transmission is similar to an electronic switch that is placed in line with the input signal and being placed in a closed position. Therefore, substantially the entire input signal is transmitted. 
         [0027]    Two arrangements are described herein to reduce v impact  during pull-in transient of the switch. The first arrangement (resistive braking) which is based on the idea that part of E d  is remotely dissipated in the resistor  118  (see  FIG. 1 ) away from the moveable electrode  102  and the dielectric layer  104  interface. The second arrangement (capacitive braking) includes patterning of the moveable electrode  102  or the substrate  106  and/or the dielectric layer  104  in such a way that the effective capacitor area decreases dynamically as the moveable electrode  102  approaches the dielectric layer  104 . In a third approach both resistive and capacitive braking can be employed. Both the methods reduce v impact , without compromising V PI  and t PI  significantly. Theory of operation of each approach, i.e., first a typical RF-MEMS CS without any braking arrangement (see  FIG. 10 ), next the approaches according to the present disclosure (see, e.g.,  FIG. 1 ) are described. 
       Typical RM MEMS CS—No Braking 
       [0028]    In the absence of a braking mechanism (i.e., resistive braking, e.g., by the resistor  118  or a capacitive braking, described further below) when the voltage source  116  is activated the moveable electrode  102  accelerates toward the dielectric layer  104  with its velocity increasing until it makes contact with the dielectric layer  104  at a maximum velocity of v impact . By using the resistor  118 , the moveable electrode  102  lands on the dielectric layer  104  softly (i.e., with lower v impact ) without compromising other critical parameters such as pull in time t PI  and pull in voltage V PI . 
         [0029]    The pull-in of the device  11  (see  FIG. 10 ) is achieved by applying a step potential V between the moveable electrode  12  and the substrate  15 . Assuming the moving electrode  12  is at rest at the position depicted in  FIG. 10 , without employing the novel resistive braking represented by the resistor  118  in  FIG. 1 , a step voltage of V&lt;V PI  imparts an energy governed by E T1 =½C(y 0 )V 2  to the device  101 , 
         [0000]    wherein E T1  is the imparted energy,
 
C is the capacitance,
 
y 0  is the gap between the moveable electrode  12  and the dielectric layer  14 , and V is the voltage applied by the source  16 . A graph of the energy (i.e., E TI ) vs. displacement in the vertical direction (designated as y) is depicted in  FIG. 5(   a ). The moveable electrode  12  eventually comes to rest at a minima (point P 1 , identified in  FIG. 5(   a ) based on the total potential energy (E) landscape which is defined by the sum of electrostatic
 
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         [0000]      FIG. 5(   a ), from point D to P 2 ) at the moveable electrode  12  and the dielectric layer  14  interface that results in damages to the dielectric.  FIG. 5(   b ) shows the displacement (y) and velocity (v) of the moveable electrode  12  as a function of time (t) during the pull-in phase, i.e., the activation cycle. 
         [0030]    Various open and closed loop control techniques have been employed in the prior art to reduce v impact  or E d  for individual and ensemble of MEMS switches. These techniques craft the input waveform so that v(t) is reduced below V PI  V as the moveable electrode approaches the dielectric, thereby ensuring softer landing. Recently an innovative self-learning control algorithm was proposed to minimize the impact velocity and contact bounce by correcting the V(t) waveform iteratively. These external circuits add to the cost and the waveform developed for a nominal switch is often not optimal for an ensemble of switches (due to process variations) and the worst-case design inevitably compromise global performance. 
         [0000]    RF-MEMS CS with Braking 
         [0031]    The dynamics of the switch shown in  FIG. 1  is modeled by coupling a simple spring-mass system with a parallel plate capacitor having a movable electrode. The governing equations for the MEMS CS are 
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         [0000]    where, m is the mass of the upper electrode,
 
k is the spring constant,
 
C is the capacitance of the MEMS switch,
 
v c  is the voltage across the capacitor, and
 
I is the transient current flowing through the capacitor. For conventional parallel plate geometry,
 
A/C=y d /E d +y/E 0 , the series capacitance of the dielectric layer  104  and the air gap  108  (A is the electrode area). Eqs. (1)-(3), can be solved numerically.
 
         [0032]    Equation (2) indicates that the acceleration of the moveable electrode  102  is directly proportional to the electrostatic force which is given by Eq. (4) 
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         [0000]    As moveable electrode  102  approaches the dielectric layer  104 , v impact  can be dynamically reduced by modulating V c  or C such that either the point D or P 2  in  FIG. 5(   a ) move in a way to reduce E d  and v impact . 
         [0033]    Resistive Braking 
         [0034]    Referring to  FIG. 3 , a schematic view of the RF-MEMS CS system  100 _b, according to the present disclosure using a resistive braking arrangement is depicted. The system  100 _b includes an RF-MEMS CS device  101 _b, a voltage source  116 _b, and a resistor  118 . The device  101 _b is coupled to the voltage source  116 _b and the resistor  118 . It is appreciated that the voltage source  116 _b can be a switched supply (i.e., capable of providing discrete output voltages) or a linear supply (i.e., capable of providing voltages according to a predetermined range). It is also appreciated that the resistor  118  is intended to represent an impedance (i.e., including a real component and an imaginary component). 
         [0035]    The device  101 _b is defined by a moveable electrode  102 _b, a dielectric layer  104 _b, and the substrate  106 . The moveable electrode  102 _b and the dielectric layer  104 _b are depicted in contact with one and other. The device  101 _b is depicted in an activated state. 
         [0036]    Referring to  FIG. 4 , a schematic view of the RF-MEMS CS system  100 _c, according to the present disclosure using a resistive braking arrangement is depicted. The system includes an RF-MEMS CS device  101 _c, a voltage source  116 _c, and a resistor  118 . The device  101 _c is coupled to the voltage source  116 _c and the resistor  118 . It is appreciated that the voltage source  116 _c can be a switched supply (i.e., on and off) or a linear supply (i.e., capable of providing voltages according to a predetermined range). It is also appreciated that the resistor  118  is intended to represent an impedance (i.e., including a real component and an imaginary component). 
         [0037]    The device  101 _c is defined by a moveable electrode  102 _c, a dielectric layer  104 _c, and a substrate  106 . The moveable electrode  102 _c and the dielectric layer  104 _c are separated by a gap, e.g., an airgap. The device  101 _c is depicted in an inactivated state; therefore the gap is the largest. 
         [0038]    Reducing v impact  is accomplished by inserting a resistor  118  in series with the voltage source  116  (see  FIG. 1 ). Initially, there will be large  t=0 +    transient (few ns) to charge the capacitor during which the charging current  I  can be significant. Once this  t=0 +    transient is over and the upper electrode begins to move,  I  is relatively small at the early stages of pull-in such that  V 0 ˜V  and the moveable electrode  102  (or  102 _b,  102 _c) pulls in. For t close to t PI , I increases rapidly, causing significant remote resistive dissipation across the resistor  118 . As a result, the point D moves down closer to P 2  in  FIG. 5(   a ), with corresponding reduction in E d  and v impact . This self-retardation does not require any complex external circuitry to shape V c , but achieves the same effect dynamically through the negative feedback introduced by the resistor  118  in the scheme. 
         [0039]    Dynamic resistive braking by solving Eqs. (1)-(3) numerically for a typical/practical MEMS switch is described (i.e., based on the RF-MEMS CS system  100  depicted in  FIG. 1 ). Referring to  FIG. 6(   a ) shows u as a function of y during pull-in with (i) the resistor  118  having a value of 0 Ω; and (ii) the resistor  118  having a value of 10 kΩ. In both the cases, the moveable electrode  102  (or  102 _b or  102 _c) lands on the dielectric in almost same t PI  (see  FIG. 6(   b )), however, with the resistor  118  having a value of 10 kΩ, v impact  is reduced by almost 50%, so that only 25% of the kinetic energy is dissipated on the moveable electrode  102  (or  102 _b or  102 _c) and the dielectric layer  104  (or  104 _b or  104 _c) interface, while the rest 75% is dissipated in the remote resistance. Since resistive braking is only operative for a short duration close to t˜t PI  when v(t) is high ( FIG. 5(   b )), the resistive braking changes v impact  without affecting t PI  significantly. The upper limit of the resistance  118  is determined by the determination that if the resistance  118  is too high, the increase in t PI  may be unacceptable, as I becomes large enough to reduce v c  and retard the motion of the moveable electrode  102  (or  102 _b or  102 _c) throughout the pull-in process. For the illustrative problem, if the resistance  118 &lt;1 MΩ, large reduction in v impact , without changing t PI  significantly can be achieved (as depicted in  FIG. 6(   b )).  FIG. 6(   c ) shows various components of energy dissipation as a function of the resistance  118 . Total energy 
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         [0000]    decreases with the resistance  118  and energy dissipated through the resistance  118   (E R =∫I 2 Rdt)  increases with the resistance  118 . It should be noted that 
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         [0000]    by energy conservation) is independent of the resistance  118 . This means that the energy dissipation at the surface of the dielectric layer  104  (or  104 _b or  104 _c) decreases because of increase in the (remote) resistive dissipation through the resistance  118  while keeping the energy supplied by the voltage source  116  (or  116 _b or  116 _c) unchanged. 
         [0040]    Advantageously, resistive braking works well for an ensemble of switches in presence of process variation.  FIG. 6(   d ) shows the distribution of impact velocity with 10% variation in the input parameters (L, W, y 0 , y d , etc.). Both, the mean (μ) and the standard deviation (σ) of the impact velocity are reduced significantly for the resistance  118 =10 kΩ. 
         [0041]    Dynamic Braking by ‘Fractal’ Capacitance 
         [0042]    An alternate scheme for reducing v impact  is to pattern the moveable electrode  102  (or  102 _b or  102 _c) or the substrate  106  or the dielectric layer  104  (or  104 _b or  104 _c) as shown in  FIG. 7  and  FIG. 8  identified as (p 2 )-(p 5 ). For example, the moveable electrode  102  (or  102 _b or  102 _c) and/or the substrate  106  can be an array of electrically connected cylinders, see  FIG. 7 , (p 2 ) or spheres (p 3 ). Alternatively or in addition thereto, the dielectric layer  104  (or  104 _b or  104 _c) can be patterned to have an array/fractal of linear slots, see  FIG. 8  (p 4 ) &amp; (p 5 ). Patterns in  FIG. 7  (i.e., (p 2 ) &amp; p 3 ) can be fabricated using various techniques such as dielectrophoretic directed assembly, contact or transfer printing methods, or liquid-alloy filled microchannels. In general, however, top-down patterning of the dielectric and metal electrodes may be more manufacturable than bottom-up techniques described above. 
         [0043]    Regardless the patterning, in the up-state of the moveable electrode  102  (or  102 _b or  102 _c) the fringing fields between the plates ensure that these patterned capacitors are indistinguishable from unpatterned parallel plate capacitor and therefore C=Ay −1  before pull-in; V PI  is therefore unaffected by patterning. As the moveable electrode  102  (or  102 _b or  102 _c) approaches the dielectric during pull-in, however, the individual field lines associated with the patterned array begins to separate rapidly from each other and elements of the array begins to behave as an isolated capacitors, with dramatic reduction in the effective area of the capacitor and hence the capacitance (C=A(y)y −1 ). This dramatic reduction in the capacitance of a patterned capacitor causes electrostatic potential energy to reduce in magnitude, pushing point P 2  up closer to D (see  FIG. 5(   b )) resulting in reduced E d  and v impact . 
         [0044]    The capacitance C(y) for the patterned structures shown in  FIGS. 7 and 8  ((p 2 )-(p 5 )) can be calculated by solving the Poisson&#39;s equation i.e. ∇ 2 φ(x, y, z)=0 (φbeing the potential at the point (x, y, z), where x and z are parallel to the electrode), numerically for each y and then be used in Eqs. (1)-(3). The results for the pull-in dynamics are summarized in  FIGS. 9(   a )-( d ).  FIG. 9(   a ) shows v as a function of y for patterned electrodes or dielectric. Reduction in v impact  is maximum for an array of spheres.  FIGS. 9(   b )-( c ) show and v impact  and t PI  as a function of separation (g) between individual elements (see  FIGS. 7 and 8)  of the patterned electrode or dielectric. As g increases, v impact  decreases at the cost of increased t PI ,  FIG. 9(   d ) shows v impact  and t PI  as a function of fractal dimension (D F ) of patterned dielectric of FIG.  8 (p 5 ). As D F  of the patterned dielectric increases, the dielectric begins to resemble a classical parallel plate MEMS switch and the advantages of patterning are rapidly diminished. 
         [0045]    It should be appreciated that while the above disclosure has dealt primarily with RF MEMS CS, the soft landing arrangements can be applied to any switches that require two electrodes to move with respect to each other and make contact in order to switch. A large selection of such switches (e.g., MEMS type switches) is seen in applications outside of RF circuits. In any such application, employing the resistive braking and/or the dynamic braking as described above can be used to slow the relative movement and thereby cushion the contact as one electrode comes into contact with another. In general, the above-described arrangements are applicable to systems (e.g., MEMS ohmic switches, nanoelectromechanical system relays) involving contacting of two electrodes actuated by a voltage source. While, only one moveable electrode is shown in the figures in this application where the movement of the moveable electrode is with respect to a fixed dielectric layer, it is well within the scope of this disclosure to also include cases where i) there is a moveable electrode that is moveable with respect to a fixed electrode by application of a voltage, and ii) two moveable electrodes that are moveable with respect to each other by application of voltages to each of the two moveable electrodes. 
         [0046]    Those skilled in the art will recognize that numerous modifications can be made to the specific implementations described above. Therefore, the following claims are not to be limited to the specific embodiments illustrated and described above. The claims, as originally presented and as they may be amended, encompass variations, alternatives, modifications, improvements, equivalents, and substantial equivalents of the embodiments and teachings disclosed herein, including those that are presently unforeseen or unappreciated, and that, for example, may arise from applicants/patentees and others.