Patent Publication Number: US-2022238290-A1

Title: Mems element and electrical circuit

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2021-008399, filed on Jan. 22, 2021; the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein relate generally to a MEMS element and an electrical circuit. 
     BACKGROUND 
     For example, a MEMS (Micro Electro Mechanical Systems) element is used in a switch or the like. A stable operation of the MEMS element is desirable. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  are schematic views illustrating a MEMS element according to a first embodiment; 
         FIGS. 2A to 2C  are schematic cross-sectional views illustrating the MEMS element according to the first embodiment; 
         FIG. 3  is a schematic plan view illustrating a portion of the MEMS element according to the first embodiment; 
         FIG. 4  is a schematic plan view illustrating a MEMS element according to the first embodiment; 
         FIG. 5  is a schematic plan view illustrating a MEMS element according to the first embodiment; 
         FIGS. 6A to 6C  are schematic plan views illustrating MEMS elements according to the first embodiment; 
         FIG. 7  is a schematic plan view illustrating a MEMS element according to the first embodiment; 
         FIGS. 8A and 8B  are schematic views illustrating a MEMS element according to the first embodiment; 
         FIGS. 9A and 9B  are schematic views illustrating a MEMS element according to the first embodiment; 
         FIGS. 10A to 10C  are schematic cross-sectional views illustrating a MEMS element according to the first embodiment; 
         FIG. 11  is a schematic cross-sectional view illustrating a MEMS element according to the first embodiment; 
         FIG. 12  is a schematic view illustrating a MEMS element according to a second embodiment; 
         FIG. 13  is a schematic view illustrating a control circuit used in the MEMS element according to the embodiment; and 
         FIG. 14  is a schematic view illustrating a control circuit used in the MEMS element according to the embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     According to one embodiment, a MEMS element includes a first member, and an element part. The element part includes a first fixed electrode fixed to the first member, and a first movable electrode facing the first fixed electrode, a first conductive member electrically connected with the first movable electrode, and a second conductive member electrically connected with the first movable electrode. The first movable electrode is supported by the first and second conductive members to be separated from the first fixed electrode in a first state before a first electrical signal is applied between the second conductive member and the first fixed electrode. The first conductive member is separated from the first movable electrode in a second state after the first electrical signal is applied between the second conductive member and the first fixed electrode. The first movable electrode is supported by the second conductive member to be separated from the first fixed electrode in the second state. 
     According to one embodiment, a MEMS element includes a first member, and an element part. The element part includes a first fixed electrode fixed to the first member, a first movable electrode facing the first fixed electrode, a first conductive member electrically connected with the first movable electrode, and a second conductive member electrically connected with the first movable electrode. The first movable electrode includes a first connection part connected with the first conductive member, and a second connection part connected with the second conductive member. A direction from the first connection part toward the second connection part is along a second direction crossing a first direction. The first direction is from the first fixed electrode toward the first movable electrode. The first fixed electrode includes a first fixed end portion and a second fixed end portion. A position in the second direction of the second fixed end portion is between a position in the second direction of the first fixed end portion and a position in the second direction of the second connection part. 
     According to one embodiment, a MEMS element includes a first member, and an element part. The element part includes a first fixed electrode fixed to the first member, a first movable electrode facing the first fixed electrode, a first conductive member electrically connected with the first movable electrode, and a second conductive member electrically connected with the first movable electrode. The first movable electrode is between the first conductive member and the second conductive member in a second direction crossing a first direction. The first direction is from the first fixed electrode toward the first movable electrode. The first movable electrode includes a first connection part connected with the first conductive member, and a second connection part connected with the second conductive member. A width of the first movable electrode along the second direction increases in an orientation from the first connection part toward the second connection part in at least a portion of the first movable electrode. 
     According to one embodiment, a MEMS element includes a first member, and an element part. The element part includes a first fixed electrode fixed to the first member, a first movable electrode facing the first fixed electrode, a first conductive member electrically connected with the first movable electrode, a first supporter supporting the first conductive member, and a second supporter supporting the first movable electrode, the second supporter being electrically connected with the first movable electrode. The first movable electrode is supported by the first conductive member and the second supporter to be separated from the first fixed electrode in a first state before a first electrical signal is applied between the second supporter and the first fixed electrode. The first conductive member is separated from the first movable electrode in a second state after the first electrical signal is applied between the second supporter and the first fixed electrode. The first movable electrode is supported by the second supporter to be separated from the first fixed electrode in the second state. 
     According to one embodiment, an electrical circuit includes the MEMS element described above, and an electrical element electrically connected with the MEMS element. 
     Various embodiments are described below with reference to the accompanying drawings. 
     The drawings are schematic and conceptual; and the relationships between the thickness and width of portions, the proportions of sizes among portions, etc., are not necessarily the same as the actual values. The dimensions and proportions may be illustrated differently among drawings, even for identical portions. 
     In the specification and drawings, components similar to those described previously or illustrated in an antecedent drawing are marked with like reference numerals, and a detailed description is omitted as appropriate. 
     First Embodiment 
       FIGS. 1A and 1B  are schematic views illustrating a MEMS element according to a first embodiment. 
       FIG. 1A  is a plan view as viewed along arrow AR 1  of  FIG. 1B .  FIG. 1B  is a line A 1 -A 2  cross-sectional view of  FIG. 1A . 
     As shown in  FIG. 1B , the MEMS element  110  according to the embodiment includes a first member  41  and an element part  51 . The first member  41  is, for example, a base body. In the example, the first member  41  includes a substrate  41   s  and an insulating layer  41   i . The substrate  41   s  is, for example, a silicon substrate. The substrate  41   s  may include a control element such as a transistor, etc. The insulating layer  41   i  is located on the substrate  41   s . For example, the element part  51  is located on the insulating layer  41   i . According to the embodiment, the first member  41  may include interconnects, etc. (not illustrated). For example, the interconnects electrically connect the element part  51  and the substrate  41   s . The interconnects may include contact vias. 
     As shown in  FIGS. 1A and 1B , the element part  51  includes a first fixed electrode  11 , a first movable electrode  20 E, a first conductive member  21 , and a second conductive member  22 . The first fixed electrode  11  is fixed to the first member  41 . For example, the first fixed electrode  11  is located on the insulating layer  41   i.    
     The first movable electrode  20 E faces the first fixed electrode  11 . The first conductive member  21  is electrically connected with the first movable electrode  20 E. The second conductive member  22  is electrically connected with the first movable electrode  20 E. 
     As described below, for example, a first electrical signal Sg 1  (referring to  FIG. 1B ) can be applied between the second conductive member  22  and the first fixed electrode  11 . The state before the first electrical signal Sg 1  is applied is taken as a first state (e.g., an initial state).  FIGS. 1A and 1B  illustrate the first state. 
     As shown in  FIG. 18 , the first movable electrode  20 E is supported by the first and second conductive members  21  and  22  to be separated from the first fixed electrode  11  in the first state. For example, a first gap g 1  is between the first fixed electrode  11  and the first movable electrode  20 E in the first state. 
     A first direction from the first fixed electrode  11  toward the first movable electrode  20 E is taken as a Z-axis direction. One direction perpendicular to the Z-axis direction is taken as an X-axis direction. A direction perpendicular to the Z-axis direction and the X-axis direction is taken as a Y-axis direction. 
     For example, the direction from the first conductive member  21  toward the second conductive member  22  is along a second direction. The second direction crosses the first direction (the Z-axis direction). The second direction is, for example, the X-axis direction. The first movable electrode  20 E is between the first conductive member  21  and the second conductive member  22  in the second direction. 
     The first movable electrode  20 E includes a first connection part  21 C and a second connection part  22 C. The first connection part  21 C is connected with the first conductive member  21 . The second connection part  22 C is connected with the second conductive member  22 . The direction from the first connection part  21 C toward the second connection part  22 C is along the second direction (e.g., the X-axis direction). 
     For example, the element part  51  includes a first supporter  21 S and a second supporter  22 S. The first supporter  21 S and the second supporter  22 S are fixed to the first member  41 . For example, the first supporter  21 S and the second supporter  22 S are conductive. 
     In the first state, one end portion of the first conductive member  21  is connected with the first movable electrode  20 E; and another end portion of the first conductive member  21  is connected to the first supporter  21 S. The first conductive member  21  is supported by the first supporter  21 S to be separated from the first member  41 . 
     In the first state, one end portion of the second conductive member  22  is connected with the first movable electrode  20 E; and another end portion of the second conductive member  22  is connected to the second supporter  22 S. The second conductive member  22  is supported by the second supporter  22 S to be separated from the first member  41 . 
     For example, the distance (the length in the Z-axis direction) between the first fixed electrode  11  and the first movable electrode  20 E is changeable according to the potential difference between the first fixed electrode  11  and the first movable electrode  20 E. The first movable electrode  20 E is displaceable when referenced to the first fixed electrode  11 . 
     A first terminal T 1  and a second terminal T 2  may be provided as shown in  FIG. 1B . The first terminal T 1  is electrically connected with the first conductive member  21 . The second terminal T 2  is electrically connected with the second conductive member  22 . For example, a current can flow between the first terminal T 1  and the second terminal T 2  in the first state. At this time, the MEMS element  110  is in a conducting state (e.g., an on-state). As described below, the first conductive member  21  can be broken. In such a case, a current does not flow between the first terminal T 1  and the second terminal T 2 . At this time, the MEMS element  110  is in a nonconducting state (e.g., an off-state). 
     In the on-state, for example, a current can flow in a first current path  21   cp  that includes the first conductive member  21  and the first movable electrode  20 E (referring to  FIG. 1A ). In the on-state, for example, a current can flow in a second current path  22   cp  that includes the second conductive member  22  and the first movable electrode  20 E (referring to  FIG. 1A ). 
     The MEMS element  110  can function as a normally-on switch element. 
     The element part  51  may include a first capacitance element  31  (referring to  FIG. 1B ). For example, the first capacitance element  31  is electrically connected with the first conductive member  21 . In the example, the first capacitance element  31  is electrically connected with the first terminal T 1 . The electrical connection to the first capacitance element  31  can be controlled by controlling the on-state or the off-state of the element part  51 . 
     As shown in  FIG. 1B , for example, a controller  70  may be provided. For example, the controller  70  is electrically connected with a first control terminal Tc 1  and a second terminal T 2 . The first control terminal Tc 1  is electrically connected with the first fixed electrode  11 . The first electrical signal Sg 1  can be applied between the second conductive member  22  and the first fixed electrode  11  by the controller  70 . The first electrical signal Sg 1  includes at least one of a voltage signal or a current signal. 
     For example, the potential of the second conductive member  22  (e.g., the potential of the second terminal T 2 ) is fixed; and the potential of the first fixed electrode  11  is controllable by the controller  70 . According to the embodiment, the potential of the first fixed electrode  11  may be substantially fixed, and the potential of the second conductive member  22  may be controllable by the controller  70 . As one example hereinbelow, a case is described where the potential of the second conductive member  22  (e.g., the potential of the second terminal T 2 ) is fixed. In such a case, the potential of the first fixed electrode  11  is controlled by the controller  70 . The polarity of the potential difference between the second conductive member  22  and the first fixed electrode  11  is arbitrary. 
     As described above, the distance between the first fixed electrode  11  and the first movable electrode  20 E is reduced by applying a voltage between the second conductive member  22  and the first fixed electrode  11 . At this time, according to the embodiment, the distance at the first conductive member  21  side becomes less than the distance at the second conductive member  22  side. For example, such asymmetry is obtained by at least one of the asymmetry of the characteristics of the conductive members, the asymmetry of the position of the first fixed electrode  11 , or the asymmetry of the first movable electrode  20 E. 
     In one example, the rigidity of the first conductive member  21  is less than the rigidity of the second conductive member  22 . For example, the first conductive member  21  deforms more easily than the second conductive member  22 . As described below, such a rigidity difference is obtained by at least one of the material or configuration of the conductive members. 
     In one example, the first fixed electrode  11  is proximate to the first conductive member  21  side. The position of the first fixed electrode  11  is asymmetric. For example, as described above, the first movable electrode  20 E includes the first connection part  21 C that is connected with the first conductive member  21 , and the second connection part  22 C that is connected with the second conductive member  22 . The direction from the first connection part  21 C toward the second connection part  22 C is along the second direction (e.g., the X-axis direction). As shown in  FIG. 1A , the first fixed electrode  11  includes a first fixed end portion  11   a  and a second fixed end portion  11   b . The position in the second direction (the X-axis direction) of the second fixed end portion  11   b  is between the position in the second direction of the first fixed end portion  11   a  and the position in the second direction of the second connection part  22 C. A first distance d 1  along the second direction between the first fixed end portion  11   a  and the first connection part  21 C is less than a second distance d 2  along the second direction between the second fixed end portion  11   b  and the second connection part  22 C. The first fixed electrode  11  may have such positional asymmetry. 
     As described below, the first movable electrode  20 E may be asymmetric by changing a width W 20  of the first movable electrode  20 E (referring to  FIG. 1A ) in the X-axis direction. 
     For example, the distance between the first fixed electrode  11  and the first movable electrode  20 E can be asymmetric due to such asymmetry. 
     An example of a transition from the on-state to the off-state in the MEMS element  110  will now be described. The on-state is, for example, the first state. The off-state is, for example, the second state. 
       FIGS. 2A to 2C  are schematic cross-sectional views illustrating the MEMS element according to the first embodiment. 
     These drawings illustrate the change of the element part  51  when the first electrical signal Sg 1  is applied between the second conductive member  22  and the first fixed electrode  11 . As described above, the first electrical signal Sg 1  is supplied by the controller  70 . 
     The first state ST 1  shown in  FIG. 2A  is a state before the first electrical signal Sg 1  is applied between the second conductive member  22  and the first fixed electrode  11 . For example, the second conductive member  22  and the first fixed electrode  11  are in a floating state FLT. At this time, the first movable electrode  20 E is separated from the first fixed electrode  11 . In such a first state ST 1 , a current can flow between the first terminal T 1  and the second terminal T 2 . In the first state ST 1 , the element part  51  is in the conducting state (the on-state). In the first state ST 1 , the potential difference between the second conductive member  22  and the first fixed electrode  11  may be less than a pull-in voltage. The pull-in voltage is, for example, the voltage when at least a portion of the first movable electrode  20 E or at least a portion of the first conductive member  21  contacts the first fixed electrode  11 . 
     As shown in  FIG. 2B , for example, the second terminal T 2  (the second conductive member  22 ) is set to a ground potential V 0 ; and the first electrical signal Sg 1  (a first operating voltage Vact 1 ) is applied to the first fixed electrode  11 . The state in which the first electrical signal Sg 1  is applied is taken as a third state ST 3 . The third state ST 3  is the operating state. In the third state ST 3 , the first movable electrode  20 E approaches the first fixed electrode  11 . For example, the first movable electrode  20 E is easily tilted due to asymmetry such as that described above. For example, compared to an end portion  20 Eq of the first movable electrode  20 E at the second conductive member  22  side, an end portion  20 Ep of the first movable electrode  20 E at the first conductive member  21  side approaches the first fixed electrode  11 . For example, an end portion  21   p  of the first conductive member  21  may contact the first fixed electrode  11 . Thereby, a current i 2  flows between the first movable electrode  20 E and the first fixed electrode  11 . The temperature easily increases locally at the end portion  20 Ep and the end portion  21   p . For example, the increase of the temperature is due to Joule heat. 
     The first conductive member  21  is separated from the first movable electrode  20 E when the temperature of the end portions  20 Ep and  21   p  locally increases. For example, the first conductive member  21  breaks. As shown in  FIG. 2B , a break portion  21 B occurs in the first conductive member  21 . The first conductive member  21  is divided at the break portion  21 B. 
     The second state ST 2  shown in  FIG. 2C  is a state after the first electrical signal Sg 1  is applied between the second conductive member  22  and the first fixed electrode  11 . For example, in the second state ST 2 , the first fixed electrode  11  is in the floating state FLT. In the second state ST 2 , the first movable electrode  20 E is separated from the first fixed electrode  11 . For example, this is due to the restoring force of the second conductive member  22 . In the second state ST 2 , the first movable electrode  20 E is supported by the second conductive member  22  to be separated from the first fixed electrode  11 . In the second state ST 2 , the first gap g 1  is between the first fixed electrode  11  and the first movable electrode  20 E. In the second state ST 2 , the second conductive member  22  is connected with the first movable electrode  20 E. 
     In the second state ST 2 , the breakage of the first conductive member  21  continues even after the application of the first electrical signal Sg 1  has ended. In the second state ST 2 , a current does not flow between the first terminal T 1  and the second terminal T 2 . In the second state ST 2 , the element part  51  is in the nonconducting state (the off-state). For example, in the second state ST 2 , the second conductive member  22  is in the floating state FLT. Or, in the second state ST 2 , the potential of the second conductive member  22  may be the potential of a circuit that is connected to the second conductive member  22 . 
     Thus, in the second state ST 2  according to the embodiment, the first conductive member  21  is separated from the first movable electrode  20 E; and the first movable electrode  20 E is supported by the second conductive member  22  to be separated from the first fixed electrode  11 . The current that flows between the first terminal T 1  and the second terminal T 2  can be stably blocked. For example, the element part  51  of the MEMS element  110  can function as a OTP (One Time Programmable) element. 
     A reference example may be considered in which the second conductive member  22  is broken. For example, in a first reference example, the first conductive member  21  that is connected with the first terminal T 1  remains connected with the first movable electrode  20 E after breaking the second conductive member  22 . In the first reference example, the end portion  21   p  of the first conductive member  21  continues to contact the first fixed electrode  11  after the application of the first electrical signal Sg 1  has ended. For example, when a transistor that controls the application of the first electrical signal Sg 1  to the first fixed electrode  11  or the like is connected with the first fixed electrode  11 , the parasitic capacitance of the transistor remains even after the application of the first electrical signal Sg 1  has ended. The parasitic capacitance of the transistor affects the capacitance of the first terminal T 1 . In the first reference example, such an unnecessary capacitance remains in the element part  51 . The remaining capacitance easily causes unstable electrical characteristics in the off-state of the element part  51  that functions as a switch. For example, when the signal of the circuit in which the element part  51  is embedded has a high frequency, the remaining capacitance makes the characteristics of the element part  51  unstable. 
     According to the embodiment, the first conductive member  21  is in a broken state in the second state ST 2 . Therefore, the first terminal T 1  is separated from the first fixed electrode  11  and the parasitic capacitance of the transistor. The electrical characteristics of the element part  51  in the off-state are stabilized thereby. Stable off-characteristics can be maintained even for high frequency switching. According to the embodiment, a MEMS element can be provided in which stable operations are possible. 
     According to the embodiment, for example, as shown in  FIG. 1A , a portion of the first conductive member  21  may overlap the first fixed electrode  11  in the Z-axis direction. For example, when a portion of the first conductive member  21  overlaps the first fixed electrode  11  in the Z-axis direction, the portion of the first conductive member  21  easily contacts the first fixed electrode  11  when the first movable electrode  20 E approaches the first fixed electrode  11 . For example, a current locally flows between the first fixed electrode  11  and the portion of the first conductive member  21 . The first conductive member  21  is more stably broken by the current concentrating in the portion of the first conductive member  21 . For example, the mechanical rigidity of the first conductive member  21  is less than the mechanical rigidity of the first movable electrode  20 E. Thereby, the end portion  20 Ep of the first movable electrode  20 E or the end portion  21   p  of the first conductive member  21  easily contacts the first fixed electrode  11 . 
     As shown in  FIG. 1A , for example, the width (a first width W 1 ) of the first conductive member  21  is less than the width W 20  of the first movable electrode  20 E. The width W 20  is the length along the Y-axis direction of the first movable electrode  20 E. Thereby, the first conductive member  21  deforms more easily than the first movable electrode  20 E. 
     In the example as shown in  FIG. 1A , the width (the first width W 1 ) of at least a portion of the first conductive member  21  is less than the width (a second width W 2 ) of at least a portion of the second conductive member  22 . The first conductive member  21  deforms more easily than the second conductive member  22 . 
     The first width W 1  is the length of the at least a portion of the first conductive member  21  along a first cross direction Dp 1  that crosses the extension direction of the first conductive member  21  (referring to  FIG. 1A ). The second width W 2  of the second conductive member  22  is the length of the at least a portion of the second conductive member  22  along a second cross direction Dp 2  that crosses the extension direction of the second conductive member  22  (referring to  FIG. 1A ). The first conductive member  21  and the second conductive member  22  are spring members. For example, it is favorable for the first width W 1  to be not more than 0.5 times the second width W 2 . Thereby, the breaking of the first conductive member  21  and the non-breaking of the second conductive member  22  are stable. 
     As shown in  FIG. 1A , the second conductive member  22  has a second length L 22  along the second current path  22   cp  that includes the second conductive member  22  and the first movable electrode  20 E. In the example, the second length L 22  is the length along the X-axis direction of the second conductive member  22 . 
     In the example as shown in  FIG. 1A , the first conductive member  21  has a meandering structure. An example of the length of the first conductive member  21  will now be described. 
       FIG. 3  is a schematic plan view illustrating a portion of the MEMS element according to the first embodiment. 
       FIG. 3  illustrates the first conductive member  21 . The first conductive member  21  has a first length L 21  along the first current path  21   cp  that includes the first conductive member  21  and the first movable electrode  20 E. The first length L 21  corresponds to the sum of the lengths L 21   a  to L 21   g.    
     For example, the second length L 22  (referring to  FIG. 1A ) is less than the first length L 21 . In such a case as well, the rigidity of the first conductive member  21  is less than the rigidity of the second conductive member  22 . Thereby, the characteristics of the first conductive member  21  are asymmetric with the characteristics of the second conductive member  22 . 
       FIG. 4  is a schematic plan view illustrating a MEMS element according to the first embodiment. 
     In the MEMS element  110   a  according to the embodiment as shown in  FIG. 4 , a distance dx 1  along the X-axis direction (the second direction) between the first supporter  21 S and the first movable electrode  20 E is greater than a distance dx 2  along the X-axis direction between the first movable electrode  20 E and the second supporter  22 S. The rigidity of the first conductive member  21  is less than the rigidity of the second conductive member  22 . 
       FIG. 5  is a schematic plan view illustrating a MEMS element according to the first embodiment. 
     In the MEMS element  110   b  according to the embodiment as shown in  FIG. 5 , a first thickness t 1  of the first conductive member  21  is less than a second thickness t 2  of the second conductive member  22 . The first thickness t 1  is the length of the first conductive member  21  along the first direction (the Z-axis direction) in the first state ST 1 . The second thickness t 2  is the length of the second conductive member  22  along the first direction in the first state ST 1 . Such a thickness difference causes the characteristics of the first conductive member  21  to be asymmetric with the characteristics of the second conductive member  22 . 
       FIGS. 6A to 6C  are schematic plan views illustrating MEMS elements according to the first embodiment. 
     As shown in  FIG. 6A , multiple second conductive members  22  are included in a MEMS element  111  according to the embodiment. A hole may be considered to be provided in one second conductive member  22 . 
     As shown in  FIGS. 6B and 6C , the second conductive member  22  includes multiple branching portions in MEMS elements  112  and  113  according to the embodiment. The multiple portions may be connected to the end portion in the Y-axis direction of the first movable electrode  20 E. A stable support is obtained. A hole may be considered to be provided in one second conductive member  22 . The number of multiple portions may be three or more. 
     For example, in the MEMS elements  110 ,  110   a ,  110   b , and  111  to  113  as described above, the first fixed electrode  11  may be located at an asymmetric position in the X-axis direction. For example, as described with reference to  FIG. 1A , the first distance d 1  along the second direction (the X-axis direction) between the first fixed end portion  11   a  and the first connection part  21 C is less than the second distance d 2  along the second direction between the second fixed end portion  11   b  and the second connection part  22 C. Thereby, stable operations are possible. In one example, the first distance d 1  is not less than 0.001 times and not more than 0.5 times the second distance d 2 . The first distance d 1  may be not less than 0.01 times the second distance d 2 . According to the embodiment, the first distance d 1  may be greater than the second distance d 2  when the first fixed electrode  11  is located at an asymmetric position between the first supporter  21 S and the second supporter  22 S. 
     When the first fixed electrode  11  is located at an asymmetric position in the X-axis direction, the first movable electrode  20 E is supported by the first and second conductive members  21  and  22  to be separated from the first fixed electrode  11  in the first state ST 1  before the first electrical signal Sg 1  is applied. When the first fixed electrode  11  is located at an asymmetric position in the X-axis direction, the first conductive member  21  is easily separated from the first movable electrode  20 E in the second state ST 2  after the first electrical signal Sg 1  is applied. In such a case as well, the first movable electrode  20 E is supported by the second conductive member  22  to be separated from the first fixed electrode  11 . 
     For example, when the first fixed electrode  11  is located at an asymmetric position in the X-axis direction, the first conductive member  21  and the second conductive member  22  may be separated from the first movable electrode  20 E in the second state ST 2  after the first electrical signal Sg 1  is applied. For example, when the first electrical signal Sg 1  is applied for a long period of time in the operating state (the third state ST 3 ), etc., both the first conductive member  21  and the second conductive member  22  may break. In such a case as well, the first terminal T 1  is separated from the first fixed electrode  11  and the parasitic capacitance of the transistor. Thereby, the electrical characteristics of the element part  51  in the off-state are stable. Stable off-characteristics can be maintained even when a high frequency signal is applied. According to the embodiment, a MEMS element can be provided in which stable operations are possible. 
       FIG. 7  is a schematic plan view illustrating a MEMS element according to the first embodiment. 
     In the MEMS element  114  according to the embodiment as shown in  FIG. 7 , the width W 20  of the first movable electrode  20 E changes. As described above, the first movable electrode  20 E includes the first connection part  21 C that is connected with the first conductive member  21 , and the second connection part  22 C that is connected with the second conductive member  22 . The direction from the first connection part  21 C toward the second connection part  22 C is along the second direction (e.g., the X-axis direction) that crosses the first direction (the Z-axis direction) that is from the first fixed electrode  11  toward the first movable electrode  20 E. A direction that crosses a plane including the first and second directions is taken as a third direction. The third direction is, for example, the Y-axis direction. The width W 20  of the first movable electrode  20 E along the third direction increases in the orientation from the first connection part  21 C toward the second connection part  22 C in at least a portion of the first movable electrode  20 E. 
     By such a configuration, for example, in the third state ST 3 , compared to the end portion  20 Eq of the first movable electrode  20 E at the second conductive member  22  side, the end portion  20 Ep of the first movable electrode  20 E at the first conductive member  21  side approaches the first fixed electrode  11  (referring to  FIG. 2B ). For example, the end portion  21   p  of the first conductive member  21  may contact the first fixed electrode  11 . In the third state ST 3 , the end portion  20 Eq is separated from the first fixed electrode  11 . The first conductive member  21  can stably break. For example, in the second state ST 2 , the first movable electrode  20 E is stably supported by the first conductive member  21  to be separated from the first fixed electrode  11 . 
     In the MEMS element  114  as shown in  FIG. 7 , the at least a portion of the first movable electrode  20 E may include a side portion  20 Es that is oblique to the second direction (e.g., the X-axis direction). By providing such a side portion  20 Es, the width W 20  continuously increases in the orientation from the first connection part  21 C toward the second connection part  22 C. For example, the side portion  20 Es described above is located in at least a portion of the region that is connected to the first conductive member  21  in the first state ST 1 . By such a configuration, the temperature of the first connection part  21 C (or the end portion  21   p  of the first conductive member  21 ) can be effectively increased locally. The first conductive member  21  can be stably broken. A MEMS element can be provided in which stable operations are possible. 
       FIGS. 8A and 8B  are schematic views illustrating a MEMS element according to the first embodiment. 
       FIG. 8A  is a plan view as viewed along arrow AR 1  of  FIG. 8B .  FIG. 8B  is a cross-sectional view. 
     As shown in  FIGS. 8A and 88 , the MEMS element  115  according to the embodiment also includes the first member  41  and the element part  51 . In the MEMS element  115 , the element part  51  includes the first fixed electrode  11  that is fixed to the first member  41 , the first movable electrode  20 E that faces the first fixed electrode  11 , the first conductive member  21  that is electrically connected with the first movable electrode  20 E, the first supporter  21 S that supports the first conductive member  21 , and the second supporter  22 S that supports the first movable electrode  20 E and is electrically connected with the first movable electrode  20 E. The second conductive member  22  is omitted from the MEMS element  115 . 
     In the MEMS element  115  as well, an operation similar to that of the MEMS element  110  is possible. For example, the first movable electrode  20 E is supported by the first conductive member  21  and the second supporter  22 S to be separated from the first fixed electrode  11  in the first state ST 1  before the first electrical signal Sg 1  is applied between the second supporter  22 S and the first fixed electrode  11 . In the second state ST 2  after the first electrical signal Sg 1  is applied between the second supporter  22 S and the first fixed electrode  11 , the first conductive member  21  is separated from the first movable electrode  20 E, and the first movable electrode  20 E is supported by the second supporter  22 S to be separated from the first fixed electrode  11 . In the MEMS element  115  as well, a MEMS element can be provided in which stable operations are possible. 
       FIGS. 9A and 9B  are schematic views illustrating a MEMS element according to the first embodiment. 
       FIG. 9A  is a plan view as viewed along arrow AR 1  of  FIG. 9B .  FIG. 9B  is a line A 1 -A 2  cross-sectional view of  FIG. 9A . 
     In the MEMS element  116  according to the embodiment as shown in  FIGS. 9A and 9B , the element part  51  includes a third supporter  23 S. The element part  51  may further include a fourth supporter  24 S. In the example, the element part  51  further includes a second fixed electrode  12 . Otherwise, the configuration of the MEMS element  116  may be similar to that of the MEMS element  110 . 
     The third supporter  23 S is fixed to the first member  41 . The first movable electrode  20 E includes a first electrode region  20 Ea that is connected with the first conductive member  21  in the first state ST 1 , a second electrode region  20 Eb that is connected with the second conductive member  22  in the first state ST 1 , and a first middle region  20 Ec. The position of the first middle region  20 Ec in the second direction (the X-axis direction) is between the position of the first electrode region  20 Ea in the second direction and the position of the second electrode region  20 Eb in the second direction. For example, the first electrode region  20 Ea faces the first fixed electrode  11 . For example, the second electrode region  20 Eb faces the second fixed electrode  12 . 
     The first middle region  20 Ec is supported by the third supporter  23 S to be separated from the first member  41 . For example, the breakage of the first conductive member  21  is stably obtained. 
     The fourth supporter  24 S is fixed to the first member  41 . At least a portion of the first middle region  20 Ec is between the third supporter  23 S and the fourth supporter  24 S in the third direction (a direction that crosses a plane including the first and second directions, e.g., the Y-axis direction). The first middle region  20 Ec is supported by the fourth supporter  24 S to be separated from the first member  41 . 
     The second fixed electrode  12  is fixed to the first member  41 . As described above, the first movable electrode  20 E includes the first electrode region  20 Ea and the second electrode region  20 Eb. The distance between the first electrode region  20 Ea and the first conductive member  21  is less than the distance between the second electrode region  20 Eb and the first conductive member  21 . The distance between the second electrode region  20 Eb and the second conductive member  22  is less than the distance between the first electrode region  20 Ea and the second conductive member  22 . The first movable electrode  20 E is supported by the first and second conductive members  21  and  22  to be separated from the second fixed electrode  12 . 
     For example, the MEMS element  116  may include a second control terminal Tc 2  that is electrically connected with the second fixed electrode  12 . The controller  70  is electrically connectable with the second fixed electrode  12  via the second control terminal Tc 2 . In the example, the controller  70  is electrically connected with the second conductive member  22  via the second terminal T 2 . For example, a second electrical signal Sg 2  can be applied between the second conductive member  22  and the second fixed electrode  12  by the controller  70 . 
     The on-state and the off-state may be more stably obtained by the first and second electrical signals Sg 1  and Sg 2 . 
       FIGS. 10A to 10C  are schematic cross-sectional views illustrating a MEMS element according to the first embodiment. 
     The first state ST 1  shown in  FIG. 10A  is a state before the first electrical signal Sg 1  is applied between the second conductive member  22  and the first fixed electrode  11 . For example, the second conductive member  22 , the first fixed electrode  11 , and the second fixed electrode  12  are in the floating state FLT. In the first state ST 1 , the potential difference between the second conductive member  22  and the first fixed electrode  11  and the potential difference between the second conductive member  22  and the second fixed electrode  12  may be less than the pull-in voltage. 
     In the third state ST 3  as shown in  FIG. 10B , for example, the second terminal T 2  (the second conductive member  22 ) is set to the ground potential V 0 ; and the first electrical signal Sg 1  (the first operating voltage Vact 1 ) is applied to the first fixed electrode  11 . In the example, the second fixed electrode  12  is set to the ground potential V 0 . For example, compared to the end portion  20 Eq of the first movable electrode  20 E at the second conductive member  22  side, the end portion  20 Ep of the first movable electrode  20 E at the first conductive member  21  side approaches the first fixed electrode  11 . For example, the end portion  20 Ep and the end portion  21   p  of the first conductive member  21  contact the first fixed electrode  11 . The first conductive member  21  is separated from the first movable electrode  20 E and is broken. 
     As shown in  FIG. 10C , for example, the first movable electrode  20 E is separated from the first fixed electrode  11  by the restoring force in the second state ST 2  after the first electrical signal Sg 1  is applied between the second conductive member  22  and the first fixed electrode  11 . 
     In the third state ST 3  described above, there are cases where the state of the end portion  20 Ep contacting the first fixed electrode  11  may continue after at least one of the end portion  20 Ep or the end portion  21   p  contacts the first fixed electrode  11 . For example, there is a possibility that such a state may occur when a compound (e.g., an oxide), etc., forms between the end portion  20 Ep and the first fixed electrode  11 . At this time, for example, there are cases where the end portion  20 Ep is more easily separated from the first fixed electrode  11  by controlling the potential of the second fixed electrode  12 . The off-state is more stably obtained thereby. 
     According to the first embodiment, it is favorable for the electrical resistances of the first and second conductive members  21  and  22  each to be, for example, not more than 10Ω. Because the electrical resistance is low, a signal that includes a high frequency can be efficiently transmitted with low loss. 
     According to the first embodiment, for example, at least one of the first conductive member  21  or the second conductive member  22  includes at least one selected from the group consisting of Al, Cu, Au, Ti, Pd, Pt, and W. A low resistance is obtained, and good transmission in the element part  51  is obtained. 
       FIG. 11  is a schematic cross-sectional view illustrating a MEMS element according to the first embodiment. 
       FIG. 11  illustrates the MEMS element  125  according to the first embodiment.  FIG. 11  illustrates the first state ST 1 . As shown in  FIG. 11 , the MEMS element  125  further includes a second member  42  in addition to the first member  41  and the element part  51 . The first fixed electrode  11  and the first movable electrode  20 E are between the first member  41  and the second member  42 . In the first state ST 1 , the first gap g 1  is between the first fixed electrode  11  and the first movable electrode  20 E. In the first state ST 1 , a second gap g 2  is between the first movable electrode  20 E and the second member  42 . The configuration of the element part  51  of the MEMS element  125  may be a configuration described above. 
     The second member  42  is, for example, a cap. Due to the first and second gaps g 1  and g 2 , the first movable electrode  20 E can be displaced along the Z-axis direction. For example, the first gap g 1  and the second gap g 2  may be in a reduced-pressure state (less than 1 atmosphere). For example, an inert gas may be introduced to the first gap g 1 . 
     For example, the first member  41  may include a control circuit part  41   t . The control circuit part  41   t  includes, for example, a switching element such as a transistor, etc. The application of the first electrical signal Sg 1  to the first fixed electrode  11  may be controlled by the control circuit part  41   t.    
     Second Embodiment 
       FIG. 12  is a schematic view illustrating a MEMS element according to a second embodiment. 
     As shown in  FIG. 12 , the MEMS element  130  according to the embodiment includes multiple element parts  51 . For example, the multiple element parts  51  are connected in parallel. A control signal Vpp can be applied independently to each of the multiple element parts  51 . 
     For example, the first conductive member  21  that is included in one of the multiple element parts  51  is breakable independently from the first conductive member  21  that is included in another one of the multiple element parts  51 . 
     Multiple first capacitance elements  31  are provided in the example. One of the multiple first capacitance elements  31  is connected in series to one of the multiple element parts  51 . The MEMS element  130  is a capacitance element array that includes the multiple element parts  51  and the multiple first capacitance elements  31 . Several of the multiple element parts  51  can be set to the off-state. The electrical capacitance of the MEMS element  130  can be modified by setting several of the multiple element parts  51  to the off-state. 
     Third Embodiment 
     A third embodiment relates to an electrical circuit.  FIG. 12 , which is described above, illustrates the configuration of the electrical circuit  210  according to the embodiment. As shown in  FIG. 12 , the electrical circuit  210  includes a MEMS element (e.g., the MEMS element  130 ) according to the embodiment and an electrical element  55 . The electrical element  55  is electrically connected with the MEMS element  130 . The electrical element  55  includes at least one selected from the group consisting of a resistance, a capacitance element, an inductor element, a diode, and a transistor. The capacitance element that is included in the electrical element  55  may include a sensor. For example, the electrical element  55  may include a sensor element. For example, the electrical element  55  may include a capacitive sensor element. 
     In the electrical circuit  210 , the MEMS element (e.g., the MEMS element  130 ) may include multiple element parts  51 . The characteristics of the electrical circuit  210  are controllable by breaking the first conductive member  21  that is included in at least one of the multiple element parts  51 . 
     For example, when the MEMS element  130  includes the first capacitance element  31 , the electrical capacitance of the MEMS element  130  can be controlled by breaking the first conductive member  21  that is included in at least one of the multiple element parts  51 . As a result, the characteristics of the electrical circuit  210  are controllable. 
     For example, the electrical circuit  210  may be used in a voltage-controlled oscillator (VCO). For example, the electrical circuit  210  may be used in an impedance matching circuit of a high frequency circuit such as an antenna, etc. For example, the electrical circuit  210  may be used in a passive RF tag. For example, the characteristics of the electrical circuit  210  can be appropriately adjusted by adjusting an electrical capacitance or an inductor of the electrical circuit  210 . For example, a voltage-controlled oscillator (VCO) that has stable characteristics is obtained. For example, stable characteristics are obtained in the impedance matching circuit of a high frequency circuit such as an antenna, etc. For example, a passive RF tag or the like that has stable characteristics is obtained. 
       FIGS. 13 and 14  are schematic views illustrating control circuits used in the MEMS element according to the embodiment. 
     As shown in  FIG. 13 , a control circuit  310  includes a voltage step-up circuit  321 , a logic circuit  322 , and a switching matrix  323 . A power supply voltage Vcc is supplied to the voltage step-up circuit  321 . The voltage step-up circuit  321  outputs a high voltage Vh to the switching matrix  323 . The switching matrix  323  outputs multiple control signals Vpp according to a signal  322   a  that is supplied from the logic circuit  322  to the switching matrix  323 . One of the multiple control signals Vpp is supplied to one of the multiple element parts  51 . 
     As shown in  FIG. 14 , a control circuit  311  includes a control power supply  324 , the logic circuit  322 , and the switching matrix  323 . The control power supply  324  is, for example, a control voltage source or a control current source. The control power supply  324  outputs, to the switching matrix  323 , the high voltage Vh and a large current Ih. The switching matrix  323  outputs the multiple control signals Vpp according to the signal  322   a  that is supplied from the logic circuit  322  to the switching matrix  323 . One of the multiple control signals Vpp is supplied to one of the multiple element parts  51 . The switching matrix  323  may output multiple control currents Ipp. One of the multiple control currents Ipp is supplied to one of the multiple element parts  51 . 
     For example, at least a portion of the control circuits  310  and  311  is included in, for example, the controller  70 . 
     Embodiments may include the following configurations (e.g., technological proposals). 
     Configuration 1 
     A MEMS element, comprising: 
     a first member; and 
     an element part, 
     the element part including
         a first fixed electrode fixed to the first member,   a first movable electrode facing the first fixed electrode,   a first conductive member electrically connected with the first movable electrode, and   a second conductive member electrically connected with the first movable electrode,       

     the first movable electrode being supported by the first and second conductive members to be separated from the first fixed electrode in a first state before a first electrical signal is applied between the second conductive member and the first fixed electrode, 
     the first conductive member being separated from the first movable electrode in a second state after the first electrical signal is applied between the second conductive member and the first fixed electrode, 
     the first movable electrode being supported by the second conductive member to be separated from the first fixed electrode in the second state. 
     Configuration 2 
     The MEMS element according to Configuration 1, wherein 
     the first movable electrode is between the first conductive member and the second conductive member in a second direction crossing a first direction, and 
     the first direction is from the first fixed electrode toward the first movable electrode. 
     Configuration 3 
     The MEMS element according to Configuration 1, wherein 
     the first movable electrode includes a first connection part connected with the first conductive member, and a second connection part connected with the second conductive member, 
     a direction from the first connection part toward the second connection part is along a second direction crossing a first direction, 
     the first direction is from the first fixed electrode toward the first movable electrode, 
     a width of the first movable electrode along a third direction increases in an orientation from the first connection part toward the second connection part in at least a portion of the first movable electrode, and 
     the third direction crosses a plane including the first and second directions. 
     Configuration 4 
     The MEMS element according to Configuration 1, wherein 
     the first movable electrode includes a first connection part connected with the first conductive member, and a second connection part connected with the second conductive member, 
     a direction from the first connection part toward the second connection part is along a second direction crossing a first direction, 
     the first direction is from the first fixed electrode toward the first movable electrode, 
     the first fixed electrode includes a first fixed end portion and a second fixed end portion, 
     a position in the second direction of the second fixed end portion is between a position in the second direction of the first fixed end portion and a position in the second direction of the second connection part, and 
     a first distance along the second direction between the first fixed end portion and the first connection part is less than a second distance along the second direction between the second fixed end portion and the second connection part. 
     Configuration 5 
     The MEMS element according to any one of Configurations 1 to 4, wherein 
     the element part further includes a first supporter and a second supporter, 
     the first and second supporters are fixed to the first member, 
     in the first state:
         one end portion of the first conductive member is connected with the first movable electrode;   an other end portion of the first conductive member is connected to the first supporter; and   the first conductive member is supported by the first supporter to be separated from the first member, and       

     in the first state:
         one end portion of the second conductive member is connected with the first movable electrode;   an other end portion of the second conductive member is connected to the second supporter; and   the second conductive member is supported by the second supporter to be separated from the first member.       

     Configuration 6 
     The MEMS element according to Configuration 5, wherein 
     the element part further includes a third supporter fixed to the first member, 
     the first movable electrode includes:
         a first electrode region connected with the first conductive member in the first state,   a second electrode region connected with the second conductive member in the first state, and   a first middle region,       

     a position of the first middle region in the second direction is between a position of the first electrode region in the second direction and a position of the second electrode region in the second direction, and 
     the first middle region is supported by the third supporter to be separated from the first member. 
     Configuration 7 
     The MEMS element according to Configuration 6, wherein 
     the element part further includes a fourth supporter fixed to the first member, 
     at least a portion of the first middle region is between the third supporter and the fourth supporter in a third direction, 
     the third direction crosses a plane including the first and second directions, and 
     the first middle region is supported by the fourth supporter to be separated from the first member. 
     Configuration 8 
     The MEMS element according to any one of Configurations 1 to 7, wherein 
     the element part further includes a second fixed electrode fixed to the first member, 
     the first movable electrode includes a first electrode region and a second electrode region, 
     a distance between the first electrode region and the first conductive member is less than a distance between the second electrode region and the first conductive member, 
     the first electrode region faces the first fixed electrode, 
     the second electrode region faces the second fixed electrode, and 
     the first movable electrode is supported by the first and second conductive members to be separated from the second fixed electrode. 
     Configuration 9 
     A MEMS element, comprising: 
     a first member; and 
     an element part, 
     the element part including
         a first fixed electrode fixed to the first member,   a first movable electrode facing the first fixed electrode,   a first conductive member electrically connected with the first movable electrode, and   a second conductive member electrically connected with the first movable electrode,       

     the first movable electrode including a first connection part connected with the first conductive member, and a second connection part connected with the second conductive member,
         a direction from the first connection part toward the second connection part being along a second direction crossing a first direction,   the first direction being from the first fixed electrode toward the first movable electrode,   the first fixed electrode including a first fixed end portion and a second fixed end portion,   a position in the second direction of the second fixed end portion being between a position in the second direction of the first fixed end portion and a position in the second direction of the second connection part.       

     Configuration 10 
     The MEMS element according to Configuration 9, wherein 
     a first distance along the second direction between the first fixed end portion and the first connection part is less than a second distance along the second direction between the second fixed end portion and the second connection part. 
     Configuration 11 
     The MEMS element according to Configuration 9 or 10, wherein 
     the first movable electrode is supported by the first and second conductive members to be separated from the first fixed electrode in a first state before a first electrical signal is applied between the second conductive member and the first fixed electrode, 
     the first conductive member is separated from the first movable electrode in a second state after the first electrical signal is applied between the second conductive member and the first fixed electrode, and 
     the first movable electrode is supported by the second conductive member to be separated from the first fixed electrode in the second state. 
     Configuration 12 
     The MEMS element according to Configuration 9 or 10, wherein 
     the first movable electrode is supported by the first and second conductive members to be separated from the first fixed electrode in a first state before a first electrical signal is applied between the second conductive member and the first fixed electrode, and 
     the first conductive member and the second conductive member are separated from the first movable electrode in a second state after the first electrical signal is applied between the second conductive member and the first fixed electrode. 
     Configuration 13 
     A MEMS element, comprising: 
     a first member; and 
     an element part, 
     the element part including
         a first fixed electrode fixed to the first member,   a first movable electrode facing the first fixed electrode,   a first conductive member electrically connected with the first movable electrode, and   a second conductive member electrically connected with the first movable electrode,       

     the first movable electrode being between the first conductive member and the second conductive member in a second direction crossing a first direction, 
     the first direction being from the first fixed electrode toward the first movable electrode, 
     the first movable electrode including a first connection part connected with the first conductive member, and a second connection part connected with the second conductive member, 
     a width of the first movable electrode along the second direction increasing in an orientation from the first connection part toward the second connection part in at least a portion of the first movable electrode. 
     Configuration 14 
     The MEMS element according to Configuration 13, wherein 
     the at least a portion of the first movable electrode includes a side portion oblique to the second direction. 
     Configuration 15 
     The MEMS element according to any one of Configurations 1 to 14, wherein 
     a rigidity of the first conductive member is less than a rigidity of the second conductive member. 
     Configuration 16 
     The MEMS element according to any one of Configurations 1 to 15, wherein 
     a first width of at least a portion of the first conductive member is less than a second width of at least a portion of the second conductive member. 
     Configuration 17 
     The MEMS element according to Configuration 16, wherein 
     the first width is not more than 0.5 times the second width. 
     Configuration 18 
     The MEMS element according to any one of Configurations 1 to 17, wherein 
     a first thickness of the first conductive member is less than a second thickness of the second conductive member. 
     Configuration 19 
     A MEMS element, comprising: 
     a first member; and 
     an element part, 
     the element part including
         a first fixed electrode fixed to the first member,   a first movable electrode facing the first fixed electrode,   a first conductive member electrically connected with the first movable electrode,   a first supporter supporting the first conductive member, and   a second supporter supporting the first movable electrode, the second supporter being electrically connected with the first movable electrode,       

     the first movable electrode being supported by the first conductive member and the second supporter to be separated from the first fixed electrode in a first state before a first electrical signal is applied between the second supporter and the first fixed electrode, 
     the first conductive member being separated from the first movable electrode in a second state after the first electrical signal is applied between the second supporter and the first fixed electrode, 
     the first movable electrode being supported by the second supporter to be separated from the first fixed electrode in the second state. 
     Configuration 20 
     An electrical circuit, comprising: 
     the MEMS element according to any one of Configurations 1 to 19; and 
     an electrical element electrically connected with the MEMS element. 
     According to embodiments, a MEMS element and an electrical circuit can be provided in which stable operations are possible. 
     Hereinabove, exemplary embodiments of the invention are described with reference to specific examples. However, the embodiments of the invention are not limited to these specific examples. For example, one skilled in the art may similarly practice the invention by appropriately selecting specific configurations of components included in MEMS elements and electrical circuits such as first members, element parts, fixed electrodes, movable electrodes, first conductive members, second conductive members, etc., from known art. Such practice is included in the scope of the invention to the extent that similar effects thereto are obtained. 
     Further, any two or more components of the specific examples may be combined within the extent of technical feasibility and are included in the scope of the invention to the extent that the purport of the invention is included. 
     Moreover, all MEMS elements, and electrical circuits practicable by an appropriate design modification by one skilled in the art based on the MEMS elements, and the electrical circuits described above as embodiments of the invention also are within the scope of the invention to the extent that the purport of the invention is included. 
     Various other variations and modifications can be conceived by those skilled in the art within the spirit of the invention, and it is understood that such variations and modifications are also encompassed within the scope of the invention. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the invention.