Patent Publication Number: US-6707355-B1

Title: Gradually-actuating micromechanical device

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention pertains to electrical devices including switches and capacitors, and more particularly to a gradually-actuating device which may be used to form switches and/or variable-valued circuit elements. 
     2. Description of the Related Art 
     The following descriptions and examples are not admitted to be prior art by virtue of their inclusion within this section. 
     Microelectromechanical switches, or switches made using microelectro-mechanical systems (MEMS) technology, are of interest in part because of their potential for allowing integration of high-quality switches with circuits formed using integrated circuit (IC) technology. As compared to transistor switches formed with conventional IC technology, for example, MEMS switches may exhibit lower losses and a higher ratio of off-impedance to on-impedance. A persistent problem with implementation of MEMS switches has been the high voltage required (often about 10V or higher) to actuate the switches, as compared to typical IC operating voltages (about 5V or lower). 
     These relatively high actuation voltages of MEMS switches are caused at least in part by a tradeoff between the closing and opening effectiveness of a given switch design. In the case of a cantilever switch, for example, approaches to lowering the actuation voltage of the switch include reducing the stiffness of the cantilever beam and reducing the gap between the contact element on the beam and the underlying contact pad. Unfortunately, these design changes typically have the effect of making opening of the switch more difficult. MEMS cantilever switch designs generally use an applied voltage to close the switch, and rely on the spring force in the beam to open the switch when the applied voltage is removed. In opening the switch, the spring force, or restoring force, of the beam must typically counteract what is often called “stiction”. Stiction refers to various forces tending to make two surfaces stick together, such as van der Waals forces, surface tension caused by moisture between the surfaces, and/or bonding between the surfaces (e.g., through oxidation). In general, modifications to a switch which act to lower the closing voltage also tend to make the switch harder to open, such that efforts to form a switch with a lowered closing voltage can result in a switch which may not open reliably (or at all). It would therefore be desirable to develop a switch design which relaxes the constraints imposed by the above-described tradeoff between opening and closing effectiveness. 
     SUMMARY OF THE INVENTION 
     The problems outlined above may be in large part addressed by a method for forming a micromechanical device in which a force associated with operation of the device is varied between locations spaced across a conductive element of the device. The variation in one or more forces across the conductive element of the device may advantageously give rise to a “rolling” motion when the conductive element is brought toward the conductive pad, such that one part of the conductive element comes into the proximity of the pad before other parts do. Such a motion may in some embodiments allow a lower applied force to be used in bringing the conductive element toward the conductive pad than is needed to move a conductive element of similar area which moves “all at once.” Alternatively or in addition, the force variation may give rise to a “peeling” motion when the conductive element moves away from the conductive pad, in which one part of the conductive element moves away from the conductive pad before other parts do. This motion may in some embodiments reduce the tendency for the conductive element to become “stuck” in the vicinity of the conductive pad. In some embodiments, the device may be designed such that stable intermediate configurations are obtained in which only a portion of the conductive element is in the vicinity of the conductive pad. Such an embodiment may be used in forming a variable-valued circuit element, as discussed further below. 
     In a preferred embodiment of the method for forming a micromechanical device, the conductive element is attached to an actuating member of the device, and the variation of the force is in a direction not parallel to the longitudinal axis of the actuating member. The conductive element may in some embodiments be integral to or a part of the actuating member. In an embodiment, the force is a required force for movement of the conductive element toward a conductive pad positioned opposite the conductive element. The conductive element may make contact with the conductive pad during operation of the device, or there may be an insulator between the conductive pad and conductive element, such that they form plates of a capacitor. The force which is varied may also include a force applied to the conductive element during operation of the device, a restoring force tending to pull the conductive element away from a conductive pad, and/or a sticking force between the conductive element and the pad. 
     In an embodiment, the method may include patterning a first conductive layer arranged over a substrate to form a conductive pad, and patterning a second conductive layer arranged over the first conductive layer to form a conductive element. The patterning of the first conductive layer may include shaping the conductive pad to provide at least a portion of the variation in force across the conductive element. Patterning of the first conductive layer may also form a control element adapted for inducing movement of the conductive element toward the conductive pad. In such an embodiment, the patterning may include shaping the control element to provide at least a portion of the variation in force. Patterning of the second conductive layer may include shaping the conductive element to provide at least a portion of the variation in force. In an embodiment, patterning of the second conductive layer includes forming the actuating member, such as a cantilever arm, containing the conductive element, and shaping the member to provide at least a portion of the variation in force. The member may be shaped in various ways, including by forming openings within the member, where the density of the openings may vary in a direction transverse to the member, or in another direction across the member. 
     The method may further include forming a sacrificial layer over the first conductive layer and forming the second conductive layer over the sacrificial layer, before patterning the second conductive layer. The sacrificial layer may then be removed after patterning of the second conductive layer. In an embodiment, the upper surface of the sacrificial layer may be contoured before formation of the second conductive layer. Such contouring may allow shaping of a contacting portion of the subsequently-formed conductive element, and the shaping may provide at least a portion of the variation in force across the conductive element. 
     A method such as that described above may be used to form a switch contemplated herein. The switch is adapted such that a force associated with actuation of the switch varies between locations spaced across a contact element of the switch. In a preferred embodiment, the contact element is attached to an actuating member of the switch, and the variation of the force is in a direction not parallel to the longitudinal axis of the actuating member. The force may include, for example, a required closing force for the switch, an applied force during actuation of the switch, a restoring force tending to open the switch, and/or a sticking force tending to keep the switch closed. The force may in some cases vary monotonically from one side of the contact element to an opposing side of the contact element. In an embodiment, the switch is a cantilever switch, and the force varies in a direction transverse to the arm of the cantilever. 
     An embodiment of the switch may include the contact element, a contact pad adapted to make electrical contact with at least a portion of the contact element upon closing of the switch, and a control element for inducing movement of the contact element toward the contact pad. The shapes of one or more of these parts of the switch may be adapted to provide at least a portion of the variation in force across the contact element. Such shape adaptation may include asymmetric shapes and/or shapes having openings formed within them. 
     In addition to the switch described above, a variable-valued circuit element is contemplated herein. The circuit element may include a conductive element, a conductive pad, and a control element for inducing movement of the conductive element toward the conductive pad. The circuit element may be adapted such that a fraction of the conductive element which is moved to the proximity of the conductive pad is variable, depending on a total magnitude of a force applied using the control element. In an embodiment for which an insulator is interposed between the conductive pad and the conductive element, the circuit element may be used as a variable capacitance. In another embodiment, the conductive pad may be divided into multiple separate portions, where the number of portions contacted by the conductive element depends on the force applied using the control element. Each of these portions of the conductive pad may be connected to a respective fixed-value circuit element, so that a variable number of the fixed-value elements may be coupled to the conductive element. The fixed-value circuit elements may include, for example, capacitors, resistors and/or inductors. Each fixed-value circuit element may be connected between its respective conductive pad portion and a terminal common to all of the fixed-value circuit elements, such that those fixed-value elements being coupled to the conductive element are connected in parallel to one another. 
     In a manner similar to that for the switch and the method discussed above, the variable-valued circuit element may be adapted such that a quantity associated with motion of the conductive element is varied between locations spaced across the conductive element. In a preferred embodiment, the conductive element is attached to an actuating member of the circuit element, and the variation of the quantity is in a direction not parallel to the longitudinal axis of the actuating member. The quantity may include, for example, a force required to induce movement of the conductive element toward the conductive pad, a force applied using the control element, a restoring force tending to pull the conductive element away from the conductive pad, and/or a sticking force tending to keep the conductive element in contact with the conductive pad. The shapes of one or more parts of the circuit element may be adapted to provide some or all of the variation of the quantity. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other objects and advantages of the invention will become apparent upon reading the following detailed description and upon reference to the accompanying drawings in which: 
     FIG. 1A is a perspective view of a cantilever switch; 
     FIG. 1B is a top view of the switch of FIG. 1A; 
     FIG. 1C is a cross-sectional view of the switch of FIG. 1A; 
     FIG. 2 illustrates trends in opening and closing effectiveness as a function of beam length for the switch of FIG. 1; 
     FIG. 3A is a top view of a device having an asymmetric control element; 
     FIG. 3B is a top view of the control element of FIG. 3A showing division of the element into increments; 
     FIGS. 4A and 4B are top views of devices each having a control element with a varied density of openings; 
     FIG. 5A is a top view of a device with a cantilever arm having its length varied; 
     FIG. 5B is a perspective view of the device of FIG. 5A; 
     FIG. 6 is a top view of a device having an asymmetric cantilever arm and an asymmetric control element; 
     FIG. 7 illustrates exemplary plots of switch closure as a function of applied potential for various electrostatically-actuated switches; 
     FIGS. 8A and 8B are perspective views of partially-closed switches, corresponding to points “A” and “B,” respectively, in the plot of FIG. 7; 
     FIG. 9 is a top view of a device having an asymmetric contact area; 
     FIGS. 10A and 10B are top views of devices having variable densities of recessed contact area; 
     FIG. 11A is a top view of a device having variable-length slots in an actuating member; 
     FIG. 11B is a top view of a device having variably-spaced slots in an actuating member; 
     FIG. 12A is a top view of a device having asymmetric control element and contact areas, as well as a varying arm length and a variable density of slots within the arm; 
     FIG. 12B is a perspective view of the device of FIG. 12A; 
     FIG. 13A is a perspective view of a device having a pre-stressed contact element; 
     FIG. 13B is a cross-section of the contact element of FIG. 13A; 
     FIG. 14 is a top view of a variable capacitor embodiment; 
     FIG. 15 is a top view of a variable capacitor embodiment having multiple contact pad portions and corresponding fixed-value elements; and 
     FIG. 16 is a flow diagram illustrating a method of fabricating the devices described herein. 
    
    
     While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The typical tradeoff between opening and closing effectiveness is illustrated for an exemplary electrostatically-actuated MEMS switch using FIGS. 1 and 2. FIGS. 1A,  1 B and  1 C are perspective, top, and cross-sectional views of MEMS cantilever switch  10 . Conductive beam  12  is fixed at one end to contact pad  14 . The other end of beam  12  resides a spaced distance above a second contact pad  16  when the switch is open, as in FIG.  1 . Gate, or control, electrode  18  underlies beam  12  between the two contact pads. In the electrostatic switch of FIG. 1, application of an electrostatic potential difference between gate electrode  18  and beam  12  creates an attractive electrostatic force between them, causing beam  12  to move downward. Contact element  20  at the end of beam  12  is thereby connected to contact pad  16 , so that a signal may be passed between contact pads  14  and  16  along beam  12 . The switch remains closed as long as the potential is applied. Upon removing the applied potential, the spring force of the cantilever beam  12  should pull the beam back up, opening the switch. It is noted that in FIGS. 1A and 1C, as well as in the other perspective and cross-sectional views provided herein, the vertical dimensions are exaggerated for illustrative purposes. Gap  22  between beam  12  and electrode  18 , for example, may be on the order of a micron. The width of cantilever  12  may be on the order of tens of microns, on the other hand, while the length of the cantilever may be on the order of tens to hundreds of microns. 
     Because the electrostatic force is relatively weak, a high field (typically on the order of tens of volts applied across a gap  22  on the order of a micron) is needed to close switch  16 . As noted above, approaches to lowering the applied voltage needed to close the switch include reducing the gap thickness and reducing the stiffness of the beam. As also discussed above, however, these approaches tend to increase stiction, thereby making the switch less likely to open reliably. An illustration of trends in relative opening and closing effectiveness of a cantilever switch such as that of FIG. 1, as a function of length of the cantilever beam, is shown in FIG.  2 . Curve  24  of FIG. 2 indicates that less force is required to close the switch as the beam length is increased, since lengthening the beam is a way of reducing its stiffness and making the unpinned end of the beam easier to pull down. A longer beam may also allow a larger gate electrode to be used, increasing the “electrostatic area” over which the electrostatic force is applied. The reduction in beam stiffness, however, reduces the restoring force of the beam, so that its resistance to opening increases with increasing beam length, as indicated by curve  26 . It is noted that curves  24  and  26  are intended only for qualitative illustration, and that no significance is to be applied to the particular shape of the curves, only to their overall directions. Similar trends are observed if variables other than beam length are considered. For example, increasing beam length in FIG. 2 could be replaced with quantities such as decreasing gap spacing, decreasing beam thickness, decreasing beam stiffness, etc. 
     A top view of an exemplary embodiment of a device having a force varied across its contact element is shown in FIG.  3 A. The device in this case is a cantilever switch similar in some respects to switch  10  of FIG.  1 . As in the case of switch  10 , cantilever beam  12  is pinned at contact pad  14  and connects contact element  20  to contact pad  16  when the switch is closed. Instead of having a rectangular control electrode underlying the beam as in FIG. 1, the switch of FIG. 3A has a control element  28  with length varying in a direction transverse to the beam. In particular, with respect to longitudinal axis  32  of beam  12 , the variation in length (defined in the direction of the longitudinal axis) of control element  28  is in a direction transverse to the longitudinal axis. The length variation of element  28  may also be described as a variation in incremental area of the element. As shown in FIG. 3B, element  28  may be divided into equal-width increments  28 A,  28 B,  28   c,    28   d,  etc. In the case of a rectangular control element, each of these increments would have the same area. Element  28 , on the other hand, has a variation in incremental area in a direction transverse to the longitudinal axis of beam  12 . Similarly defined longitudinal axes and area increments may be applied to all of the devices described herein. 
     Control element  28  is preferably a gate electrode used to apply an electrostatic potential between element  28  and beam  12 . The variation in incremental area of element  28  therefore results in a variation in the incremental electrostatic area between the element and the beam. More electrostatic force is therefore applied to beam  12  near edge  34  of the beam (the upper edge in the orientation of FIG. 3A) than near edge  36  (the lower edge), with a smooth variation in between. Arrow  30  illustrates the direction of increasing electrostatic force across beam  12  and, therefore, contact element  20 . Application of a potential difference between control electrode  28  and beam  12  may consequently result in a rolling motion for closure of the switch, in which edge  38  of contact element  20  makes contact with contact pad  16  before edge  40  of contact element  20  does. In the embodiment of FIG. 3A, such a rolling motion is believed to result from a variation in the applied force across contact element  20 . 
     Although illustrated in FIG.  3 A and other figures herein as applied to a cantilever switch, the methods and structures described herein are applicable to other types of switches and devices. For example, control element  28  of FIG. 3A could underlie a membrane or strap supported at both ends to form a membrane (or strap, or “bridge”) device, or element  28  could be used under a “teeter-totter” beam adapted to rock about a central fulcrum. The force variation structures illustrated by other figures included herein may similarly apply to other switches and devices. Although the variation of the length of control element  28  of FIG. 3, and thereby its incremental area, is in a direction transverse to the longitudinal axis of the element, the direction of variation is not limited to this transverse direction. In a preferred embodiment, for the device of FIG.  3  and the other devices disclosed herein, the direction of force variation is in a direction not parallel to the longitudinal axis. (A force variation directed diagonally across a cantilever arm, for example, could be resolved into components including a component parallel to the longitudinal axis, but the resultant direction of the force variation would not be parallel to the longitudinal axis, and there would also be a component not parallel to the longitudinal axis.) 
     Additional approaches to variation of the incremental electrostatic area of a control electrode are shown in FIG.  4 . Control electrode  42  in FIG. 4A includes slots  44 . In an embodiment in which electrode  42  is patterned from a conductive layer, slots  44  can be formed by selectively removing the corresponding portions of the conductive layer. Because the slots are spaced closer together near edge  46  of electrode  42 , and farther apart moving toward edge  48 , the electrostatic area is larger near edge  48  and smaller near edge  46 . The applied force on the beam and contact element therefore varies in a direction transverse to the longitudinal axis of beam  12 , increasing from the lower edge to the upper edge as shown by arrow  30 . FIG. 4B illustrates an approach similar to FIG. 4A, except that the electrostatic area of control electrode  50  is varied using a varied density of openings  52 . The opening shapes shown in FIG. 4 are merely exemplary, and innumerable shapes and/or dimensions achievable through microfabrication techniques could be used. 
     As discussed further above, the embodiments of FIGS. 3 and 4 illustrate exemplary ways to provide a variation in applied force across the contact element of a switch or other device. An example of a way to vary a different force is illustrated by FIG.  5 . FIG. 5A is a top view, and FIG. 5B a perspective view, of a cantilever switch having a variation in beam length. Contact pads  14  and  16 , and control electrode  18  are similar to those of FIG. 1, and are therefore assigned the same respective reference numerals in FIG.  5 . The length, along its longitudinal axis, of beam  54  varies in a direction transverse to the longitudinal axis, from longest along edge  58  to shortest along edge  60 . The shape of contact element  56  is altered in this embodiment to follow the shape of the beam. In particular, the distance between the contact element and the pinned end of the cantilever is varied across the contact element. This variation in length of the beam or distance from the pinned end is believed to cause beam  54  to behave like a longer beam near edge  58 , and a shorter beam near edge  60 . The shorter beam is stiffer and has a stronger restoring force, such that the restoring force varies across contact element  56 , increasing from edge  64  to edge  62 , as shown by dashed-line arrow  66  in FIG.  5 A. This variation in restoring force is believed to result in a peeling motion when a potential between control electrode  18  and beam  54  is removed in order to open the switch. The portion of contact element  56  near edge  62  may pull away from contact pad  16  first upon removal of the potential, followed by adjacent portions in turn, and ending with the portion near edge  64 . 
     In addition to the restoring force variation indicated by arrow  66  in FIG. 5A, the beam length variation of FIG. 5 may also provide a variation across the beam of the force required to pull the end of the beam down when closing the switch. The increased length of the beam near edge  58  may make the end of the beam near this edge easier to pull down with a given applied force. This effect is believed to be more likely in the case of switches having relatively small gaps between the contact element and the underlying contact pad. Such a lower required force near edge  58  as compared to the portion of the beam near edge  60  may result in a rolling motion during closing of the switch, in which the portion of contact element  56  near edge  64  makes contact with pad  16  first. 
     The various techniques and structures described herein for providing variation of force across the contact element of a device can generally be combined with one another, as illustrated by the embodiment of FIG.  6 . Contact pad  14 , asymmetric beam  54  and contact element  56  of the switch of FIG. 6 are similar to those shown in FIG.  5 . The embodiment of FIG. 6 also has an asymmetric control element  68  and contact pad  70 , however. The length variation of beam  56  results in a restoring force variation similar to that of FIG. 5, as indicated by arrow  66 . The variation in electrostatic area provided by the shape of control element  68  gives rise to a variation in applied force similar to that shown in FIG. 3A, as indicated by arrow  30 . The combined variations in applied force and restoring force may result in a switch that closes with a rolling motion from edge  64  of the contact element down to edge  62 , and that opens with a peeling motion from edge  62  up to edge  64 . 
     The gradual actuation, by rolling and/or peeling, of a switch such as that of FIG. 6 is believed to be advantageous by relaxing somewhat the inverse relationship, such as that shown in FIG. 2 above, typically seen between opening and closing effectiveness of such a switch. A switch such as that of FIG. 6 may exhibit a required closing voltage similar to that of a symmetrical switch having a beam as long as the longer side (along edge  58 ) of beam  54 , while exhibiting an opening effectiveness similar to that of a symmetrical switch having a beam as short as the shorter side (along edge  60 ) of beam  54 . The gradually-actuating design may therefore allow a reduction in closing voltage without as much of the reduction in opening effectiveness which generally accompanies such a closing voltage reduction. 
     An illustration of exemplary switch closure characteristics as a function of applied force for various electrostatically-actuated switch designs is shown in FIG.  7 . The vertical axis indicates percentage closure of the switch, as a function of the applied potential difference, or voltage, along the horizontal axis. The percentage closure refers to the fraction of the contact element which is in contact with a corresponding contact pad (or in some cases with an insulating layer formed over the pad), rather than, for example, the size of a gap between the contact element and the contact pad. Curve  72  is an exemplary characteristic for a symmetric switch, such as that of FIG.  1 . Once a sufficient voltage is applied, the switch closes, with the entire contact element coming into the contact with the corresponding contact pad. Curve  72  therefore indicates an abrupt change from zero percent closure to one hundred percent. The required value  74  of applied voltage is dependent on, for example, the dimensions of the switch and properties of the materials used to fabricate it. Curve  76  is an exemplary characteristic for an embodiment of a gradually-actuating switch as described herein, such as those in FIGS. 3,  4  and  6 . For this switch, a first portion of the contact element makes contact with the contact pad when a voltage  78  is applied. Voltage level  80  causes about 25% of the contact element area to be in contact with the contact pad, as indicated by point “A” on the curve, while level  82  results in about 75% closure, as indicated by point “B.” The switch corresponding to curve  76  becomes completely closed when a potential difference greater than or equal to level  84  is applied. 
     Perspective views of a contact element  86  and corresponding contact pad  88  corresponding to points “A” and “B” of FIG. 7 are shown in FIGS. 8A and 8B, respectively. In FIG. 8A, approximately 25% of contact element  86  is in contact with contact pad  88 , while in FIG. 8B, about 75% of element  86  is in contact with pad  88 . The dashed lines on contact pad  88  show the position of contact element  86  when the switch is fully closed. As in the case of other perspective views included herein, the vertical scale in the views of FIG. 8 is exaggerated to better illustrate the partial contact formation. Contact element  86  is attached to an actuating member  90 , which could be, for example, an arm of a cantilever or teeter-totter switch. The gradual closing shown in FIG. 8 is a result of a variation of one or more forces across contact element  86 . The particular structure providing the force variation is not shown in FIG.  8 . The force variation could be provided, for example, by a variation in incremental area of a control element (not shown) underlying member  90 . Other techniques could also be used instead or in addition, such as variation of the beam length or of the incremental area of the beam (discussed further below). 
     If the device corresponding to curve  76  in FIG. 7 is to be used as a switch, application of a potential difference at or above level  84  would typically be desirable for closing the switch, in order to induce complete closing as rapidly as possible. In such an embodiment, the configurations shown in FIGS. 8A and 8B occur transiently during the closing of the switch. In an alternative embodiment, however, the device may be used as a variable circuit element. In such a case, application of an intermediate voltage to maintain the device in a partially-closed state may be desirable. Variable circuit element structures are discussed further with respect to FIGS. 14 and 15 below. 
     Returning to FIG. 7, curve  92  is an exemplary characteristic for another embodiment of a gradually-actuating switch. The switch corresponding to curve  92  begins to close when a voltage of level  94  is applied, and initially closes gradually with increasing voltage applied. When a voltage of level  96  is applied, however, no further applied voltage is needed to bring the switch to 100% closed. In some embodiments of the device described herein having a variation of force across the contact element, opening or closing may proceed “on its own” after an initial “getting started.” In particular, a portion of the switch already open or closed may “assist” with the opening or closing of an adjacent portion, which may in turn assist with the next adjacent portion, and so on. 
     In the case of closing a switch, for example, consider that some initial gap between the actuating member of the switch and a control element generally exists before any voltage is applied. If a voltage sufficient to pull down a first portion of the actuating member, and therefore a first portion of the contact member, is applied, the size of the gap between the first portion of the actuating member and the control element will be reduced. The gap between the control element and a portion of the actuating member immediately adjacent the first portion will accordingly also be reduced (though to a lesser degree). This reduced gap will cause an increase in electrostatic force for a given potential difference between the control element and the actuating member. This increased force may be sufficient to pull down this adjacent portion of the actuating member. The reduction in gap may then propagate across the actuating member, allowing the switch to close entirely, without any increase in voltage applied. Similarly, a device for which some portions of the contact element are initially “stuck” to the contact pad, even after removal of an applied closing force, may be completely opened through “pulling up” of the stuck portions of the actuating member by adjacent open portions of the member. 
     In the embodiment corresponding to curve  92  of FIG. 7, some increase in applied voltage (the difference between levels  96  and  94 ) is needed after the switch first begins to close and before the above-described “self-closing” mechanism begins. In other embodiments, however, the self-closing behavior might start as soon as any portion of the contact element had made contact, so that a curve showing percentage closure as a function of applied voltage would resemble curve  72 . Without being bound to theory, it is believed that the tendency of a gradually-actuating switch to exhibit the above-described self-closing or self-opening behavior is related to the magnitude of the force variation across the contact element. In particular, designs with more slowly-varying forces are believed to be more likely to exhibit the self-closing or self-opening behavior. Designs in which the force varies more quickly are believed to be more likely to exhibit the stable applied-voltage-dependent closure illustrated by curve  76  of FIG.  7 . The nature of the closing behavior is therefore believed to be controllable by design of the force variation. 
     It is noted that the variations shown in the figures included herein are merely exemplary, and that possibilities for tailoring details of the force variation are limited only by the patterning and other fabrication techniques used to form the devices. Current micromechanical switches, for example, typically have lateral dimensions on the order of tens or hundreds of microns, while patterning techniques common in IC fabrication processes can provide submicron resolution. The capability for tailoring force variations in micromechanical devices is therefore believed to be quite high. For example, the asymmetric shapes for control electrodes, contact pads and/or actuating members described herein need not be formed from straight lines, as shown in the figures. Specific curved shapes could be used instead. Furthermore, the force associated with the device operation does not need to be varied monotonically from one side of the contact element to the other, as shown in the figures, but could be largest or smallest somewhere in the interior of the element, for example. 
     Some additional structures giving rise to variations of force across the contact element of a device are shown in FIGS. 9-11. In the embodiment of FIG. 9, contact pads  14  and  16  and control element  18  are similar to those in the switch of FIG.  1 . Contact element  100 , on the other hand, has an asymmetric shape, with its length varying from longest along edge  102  to shortest along edge  104 . By contrast to the switch shown in FIG. 6, the length of beam  98  between the pinned end (over contact pad  14 ) and contact element  100  is constant. The asymmetry of contact element  100  causes a variation across contact element  100  in the contact area between the contact element and contact pad  16 . This variation in contact area is believed to cause a variation in the sticking force, or stiction between the contact element and contact pad. Opening of the switch of FIG. 9 when potential is removed from control element  18  may therefore proceed with a peeling motion, in which edge  104  of contact element  100  pulls away from contact pad  16  first, followed by intermediate portions of the contact element and finally by edge  102 . The direction of the sticking force variation is illustrated by dotted-line arrow  107 . 
     Another way of varying the contact area and thereby the sticking force is illustrated by FIG.  10 . In FIG. 10A, dimples  108  are formed within contact element  110 . A dimple as used herein is a small recessed portion of the contact element, which extends lower (closer to contact pad  16 ) than the surrounding contact element area. The recessed portions may be formed to a sufficient depth that only the recessed portions actually make contact with the underlying contact pad when the switch is closed. Variation of the density of dimples  108  in FIG. 10A therefore provides a variation in contact area between contact element  110  and contact pad  16 . The increased contact area toward the upper edge of contact element  110  provides an increased sticking force in this direction, as indicated by arrow  107 . FIG. 10B is a top view of an embodiment in which a coarser variation in contact area is used. Recessed portion  116  is formed in the upper part of the contact element, while the lower portion  118  of the contact element is not recessed. The recess of portion  116  is preferably of sufficient depth that portion  118  does not ever contact underlying contact pad  16 , even when the switch is fully closed. Portion  118  can therefore never “stick” to pad  16 , and may help “pull up” recessed portion  116  during opening of the switch. The contact element of FIG. 10B therefore also exhibits a variation in sticking force, albeit a coarse variation, across the contact element. The recessed portions of the contact element shown in FIGS. 10A and 10B may in some embodiments be fabricated through contouring of an underlying sacrificial layer before deposition of a conductive layer subsequently patterned to form the contact element. Fabrication of the devices described herein is discussed further in the description of FIG. 16 below. 
     As with all of the force variation techniques described herein, other ways of varying the sticking force may be apparent to one of ordinary skill in the art of microfabrication in view of this disclosure. For example, the contact area might also be varied through the use of openings similar to those shown for the control element in FIG. 4, where the openings could be made in the contact element and/or the underlying contact pad. As another example, the contact pad shape could be made asymmetric in a manner similar to that discussed with respect to the contact element in the description of FIG.  9 . 
     FIG. 11 illustrates the use of slots within an actuating member, a cantilever beam in this case, to establish a variation in force across the contact element. FIG. 11A is a top view of an embodiment in which variable-length slots are spaced across the actuating member, while FIG. 11B illustrates the use of equal-length slots of varying density. In each case, the reduced stiffness of the member near its upper edge establishes a restoring force variation having a direction indicated by arrow  66 . Although the use of openings near the pinned ends of the cantilever arms of FIGS. 11A and 11B is believed to provide a particularly efficient means of varying the beam stiffness, other opening shapes, dimensions and locations within the actuating member may also be used. 
     A switch embodiment combining multiple of the above-described force variation structures is shown in FIG.  12 . FIG. 12A is a top view, and FIG. 12B a perspective view of the switch. Control element  68  and contact pad  70  are similar to those shown in FIG. 6, while beam  120  includes variable-length slots in the manner of the beam of FIG.  11 A. In addition, contact element  122  has an area variation similar to that of the contact element shown in FIG.  9 . These variations combine to provide an applied force variation in the direction indicated by arrow  30 , a restoring force variation in the direction of arrow  66 , and a sticking force variation in the direction indicated by arrow  107 . For the switches shown in FIG.  6  and FIG. 12, it can be seen that the forces tending to close the switch or keep it closed (e.g., applied force, sticking force) tend to vary in the opposite direction as the forces tending to open the switch or keep it open (e.g., restoring force). This may be a desirable arrangement with regard to preventing the forces from “working against” one another. However, this relationship may not necessarily hold for every device embodiment, particularly when combinations of force variation structures are employed. 
     Still another approach to providing a force variation across the contact element of a device is shown in FIG.  13 . FIG. 13A is a perspective view of a switch including a pre-stressed contact element  126 . Contact element  126  is stressed prior to (and independently of) operation of the switch through the use of stressor lines  128  on the upper surface of element  126 . The stressor lines are made of a material which is tensile stressed with respect to the underlying contact element. This may be achieved in some embodiments by depositing the contact material under conditions that produce lower tensile stresses and then depositing the material that makes the stressor lines under conditions that produce relatively higher tensile stresses. Methods for adjusting film stresses may include, without being limited to, depositing films at different rates, varied temperatures, varied compositions, varied pressures, under various surface conditions such as plasma or ion bombardment, under exposure to various radiations, under exposure to various acoustic energies, and/or with the use of varied reactant mass transport rates. If the contact element is formed from gold, for example, chromium, which can be deposited with a tensile stress magnitude larger than that of gold, may be a suitable choice for the stressor lines. A cross-section of the contact element and underlying contact pad along cut B—B is shown in FIG.  13 B. As can be seen in the cross-section, the tensile stress applied by stressor lines  128  pulls up the outer ends of contact element  126 . When the switch is closed, therefore, the central portion of contact element  126  makes contact with pad  16  first, followed by the outer portions. When the switch is opened, the tensile stress is believed to cause the outer ends of the contact element to pull away from pad  16  first, followed by the central portion. The stressing of the contact portion therefore establishes a variation in restoring force, increasing going from the center to the outer edges of the contact element. Furthermore, a variation in force required to close the switch is varied across the contact element, increasing from the outer edges to the center. 
     The arrangement of stressor lines  128  in FIG. 13A is merely exemplary, and a different configuration of stressor material could be used. In the embodiment of FIG. 13A, an opening  130  is included in beam  124  at the edge of conductive element  126 . Such an opening may help to decouple the contact element from the rest of the beam, allowing the stressor lines to more readily deform the contact element. Such a decoupling could be done differently in some embodiments, for example by leaving the central portion of the beam intact and removing portions at the outer edges of the beam on each side. As with the other force variation structures described herein, the stressed contact element of FIG. 13 could in some embodiments be combined with other force variation structures. For example, the electrostatic area between beam  124  and control element  18  could be varied by tailoring the shape of control element  18 . In a preferred embodiment, such additional variations could be designed to make restoring force stronger at the edges of the contact element, and/or make applied force stronger at the center of the element. 
     The above-described examples have used switch designs to illustrate force variation structures. A device having a variation in force across the contact element may also be used as a variable circuit element, as shown by the embodiments of FIGS. 14 and 15. In FIG. 14, the inclusion of insulating layer  134  between contact pad  16  and contact element  20  forms a variable capacitor  136  from a cantilever switch having force variations across the contact pad. In the embodiment of FIG. 14, the force variations present include a restoring force variation caused by the variable length slots in beam  132 , and an applied force variation resulting from an electrostatic area variation caused by the asymmetric shape of control element  68 . Considering the closure versus applied potential characteristics of FIG. 7, at least a portion of the characteristic for variable capacitor  136  must have a variation such as that of curve  76  in FIG.  7 . In other words, the element must be designed such that one or more intermediate levels of force applied using control element  68  result in corresponding stable, partially-closed configurations of the device. There should therefore be one or more applied force levels for which the self-closing and/or self-opening behavior described above does not occur. As noted above, this behavior is believed to be controllable by tailoring the rate of force variation across the contact element. 
     In the embodiment of FIG. 15, no insulating layer is included between the contact element and underlying contact pad, but the contact pad is divided into multiple electrically isolated portions  138 . Depending on the potential difference applied between control element  68  and beam  132 , a variable number of these pad portions are in contact with contact element  20  (and therefore with each other). Separate fixed-value elements, in this case capacitors C 1  through C 6 , may be connected to the respective pad portions. Opposite ends of the fixed-value elements may be connected together to form a common output terminal  140 . Connection of pad portions  138  to conductive element  20  therefore connects the corresponding fixed-value elements in parallel with each other. In this way, a variable capacitor may be formed having a wider range of values than may be available for the parallel-plate design of FIG.  14 . Other fixed-value elements, such as resistors or inductors, could be used in place of the capacitors of FIG. 15 to form other types of variable circuit element. In some embodiments, different types of fixed value elements could be used within a device (e.g., capacitors connected to some of pad portions  138  while resistors are connected to other pad portions). 
     An exemplary embodiment of a method which may be used to form a device such as the gradually-actuating switches or variable circuit elements described above is shown in FIG.  16 . It is noted that the methods and structures described herein are believed to also be applicable to devices other than switches and variable circuit elements. Other types of micromechanical devices involving motion, such as movable mirrors or flow controllers, may also benefit from variation of a force across a conductive element. In the method shown in the flow diagram of FIG. 16, a first conductive layer is formed (box  142 ), preferably on some sort of insulating substrate. The substrate may include a semiconductor substrate, for example, or an insulating layer formed over a conducting or semiconducting substrate. The conductive layer may be formed using various techniques, including chemical vapor deposition, physical vapor deposition techniques such as evaporation or sputtering, and electrochemical plating, or combinations of such methods. A suitable thickness for the first conductive layer may be approximately a few microns, although thinner or thicker layers could be used depending on the particular materials and process used. 
     The first conductive layer may then be patterned (box  144 ) to form one or more contact pads and control elements. For example, contact pads such as pads  14  and  70  of FIG. 12A may be patterned from such a conductive layer, as well as a control element such as element  68  of FIG.  12 A. The patterning may be achieved using, for example, lithography and etching techniques such as would be apparent to those of ordinary skill in the art of microfabrication in view of this disclosure. Depending on the particular device being formed, the arrangement of contact pads and control elements may vary from that of FIG.  12 A. The control elements shown in the figures are preferably control electrodes for electrostatically actuated movement, but other forms of actuation are possible and contemplated. For example, an actuating member could be made from a magnetic material, and a coil used as a control element in the case of a magnetically-actuated device. In some magnetically-actuated embodiments, a flat coil could be patterned from the first conductive layer of FIG. 16 in place of an electrostatic control electrode. The applied magnetic force generated may vary across the surface of such a flat coil, thereby providing a form of force variation. Other force variation structures described herein, such as adaptations of the shape of the actuating member or the contact pad, may also be suitable for use with magnetic actuation. Other types of actuation, such as thermal actuation in which moving elements include materials of dissimilar thermal expansion coefficient, may also be compatible with at least some of the force variation structures described herein. For example, the structures described for variation of the restoring force of an actuating member may be compatible with thermal actuation. Depending on the form of actuation used, therefore, the patterning of the first conductive layer may or may not include formation of a control element as described in FIG.  16 . 
     The patterning of the first conductive layer described above may be used to implement several of the force variation structures discussed herein. For example, this patterning may control the shape of any conductive pads and/or control elements being formed, and may be used to form openings within such a pad or control element. 
     A sacrificial layer may then be formed over the patterned first conductive layer, as indicated in box  146  of FIG.  6 . Such a sacrificial layer may be used to support elevated portions of the device during fabrication. The layer material may be conductive or insulating, and may be chosen based on criteria such as its ease of patterning or contouring, and/or its ability to be etched away without damage to surrounding structures. The sacrificial layer may then be contoured (box  148 ) prior to formation of overlying layers. “Contouring” as used herein may include forming openings through the sacrificial layer in which interconnection or support structures may be formed, as well as forming shallower depressions in the upper surface of the sacrificial layer. Such shallower depressions may be useful in creating recessed portions such as “dimples” in subsequently-formed overlying elements. Contouring of the sacrificial layer may therefore be used in implementing force variation structures as described herein. For example, a variable density of recessed portions of a conductive element could be formed. The contouring may be done using techniques similar to those used for patterning the first conductive layer, with appropriate adjustments to account for any differences in the materials being patterned and/or removed. A suitable thickness for the sacrificial layer when formed may be on the order of a few microns, although contouring may result in thicknesses of less than one micron in some areas of the device. 
     A second conductive layer may then be formed over the contoured sacrificial layer (box  150 ). The layer may be formed using methods similar to those described above for the first conductive layer formation. Preferred thicknesses of the second conductive layer may range from about 1 micron to about 10 microns, depending on the stiffness of the material used. The second conductive layer may then be patterned (box  152 ) to form one or more contact elements and actuating members (such as a beam or membrane) for the device. In the figures included herein, a conductive element has been illustrated as a recessed portion of a conductive actuating member, such that a signal may be connected from one contact pad to another through the actuating member and conductive element. Such a configuration is not required by the structures and methods described herein, however. In some embodiments, for example, at least a portion of the actuating member could be insulating, and a contact pad such as pad  14  of FIG. 12A could be electrically isolated from a pad such as pad  70  of FIG. 12A, even with each pad in contact with one end of the actuating member. This configuration may be useful in embodiments for which the conductive element itself is positioned to bridge a gap between more than one conductive pad, thereby connecting multiple pads together. In an embodiment such as this, the patterning of the second conductive layer might form the conductive element but not the entire actuating member. An additional layer formation and patterning might then be used to complete the actuating member. Patterning to form a conductive element and/or actuating member may be used to implement various force variations across the conductive element of a device. As noted above, the patterning may be used to control an element&#39;s shape or to form a desired variation of opening density within an element. 
     After formation of the contact element and actuating member, the sacrificial layer may be removed (box  154 ), thereby freeing the actuating member for motion in response to the appropriate applied force. The steps described above may not include all steps used in forming the micromechanical device, and certainly do not include all steps used in forming a typical circuit containing such a device. The above-described steps may be combined with other steps used for, e.g., transistor fabrication in forming a complete circuit. Further steps may include those relating to, e.g., interconnection, passivation, and packaging of a circuit. 
     It will be appreciated to those skilled in the art having the benefit of this disclosure that this invention is believed to provide a device in which a force associated with operation of the device is varied across a contact element of the device, and a method for forming such a device. Further modifications and alternative embodiments of various aspects of the invention will be apparent to those skilled in the art in view of this description. For example, other types of force variation, such as variation in the thickness of an actuating member, may be apparent in view of this disclosure. Such a thickness variation, for example, could be formed by repeated deposition and patterning of portions of the actuating member, and forming a force variation in an actuating member could generally be described in terms of varying an incremental volume of the actuating member. It is intended that the following claims be interpreted to embrace all such modifications and changes and, accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense.