Abstract:
Microelectromechanical (MEM) buckling beam thermal actuators are disclosed wherein the buckling direction of a beam is constrained to a desired direction of actuation, which can be in-plane or out-of-plane with respect to a support substrate. The actuators comprise as-fabricated, linear beams of uniform cross section supported above the substrate by supports which rigidly attach a beam to the substrate. The beams can be heated by methods including the passage of an electrical current through them. The buckling direction of an initially straight beam upon heating and expansion is controlled by incorporating one or more directional constraints attached to the substrate and proximal to the mid-point of the beam. In the event that the beam initially buckles in an undesired direction, deformation of the beam induced by contact with a directional constraint generates an opposing force to re-direct the buckling beam into the desired direction. The displacement and force generated by the movement of the buckling beam can be harnessed to perform useful work, such as closing contacts in an electrical switch.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     The United States Government has certain rights in this invention pursuant to Department of Energy Contract No. DE-AC04-94AL85000 with Sandia Corporation. 
    
    
     FIELD OF THE INVENTION 
     The invention generally relates to microelectromechanical (MEM) thermal actuators. The invention additionally relates to MEM thermal actuators comprising beams, mechanically fixed at both ends and heated to induce expansion and eventual buckling of the beam, the buckling motion of the beam producing a force and displacement for the desired actuation. The invention further relates to MEM thermal actuators of the buckling beam type, wherein the buckling direction of the beam is mechanically constrained to the desired direction of actuation, which can be in the plane of, or out of the plane of, a support substrate. 
     BACKGROUND OF THE INVENTION 
     The invention generally relates to thermal actuators of the buckling beam type, fabricated by microelectromechanical (MEM) technologies. Microelectromechanical (MEM) fabrication technologies, including surface micromachining methods based on integrated circuit (IC) manufacturing (e.g. semiconductor device manufacture), bulk micromachining, focused ion beam (FIB) processing, deep reactive ion etching (DRIE), LIGA (an acronym based on the first letters of the German words for lithography, electroplating and molding) and their combination, can be used to form microelectromechanical devices such as microsensors and microactuators, including buckling beam thermal actuators. 
     Dimensions of structures fabricated by MEM technologies can range from on the order of 0.1 μm, to on the order of a few millimeters, and include silicon, polysilicon, glass, dielectric and metallic structures that are either unsupported (i.e. free standing) or alternatively can be adhered to a substrate, or built up upon a substrate during manufacture. Substrates can comprise ceramics, glass-ceramics, low-temperature co-fireable ceramics (LTCC), quartz, glass, printed wiring boards (e.g. manufactured of polymeric materials including polytetrafluoroethylene, polyimide, epoxy, glass filled epoxy), silicon (e.g. silicon wafers), silicon on insulator (e.g. SOD substrates and metals. Dielectric layers for example, polymeric, silicon-oxide, silicon-nitride, glass and ceramic layers can be applied to the surface of conductive substrates (e.g. metallic and silicon substrates) to electrically isolate individual MEM elements within a fabricated structure, or isolate MEM elements from the substrate. 
     An exemplary surface micromachining technology is the Sandia Ultra-planar Multi-level MEMS Technology (SUMMiT™) available at Sandia National Laboratories, Albuquerque, N. Mex., wherein multiple polysilicon and dielectric layers are used to form mechanical structures on a silicon substrate, as described in the commonly owned patents, U.S. Pat. No. 5,804,084 to R. Nasby et al., and U.S. Pat. No. 6,082,208 to M. Rodgers et al., the entirety of their disclosures herein incorporated by reference. Additionally as described in the design guide “SUMMiT V™, Five level Surface Micromachining Technology Design Manual”, Version 3.0, Jan. 18, 2007, [online] [retrieved on Jan. 14, 2008] retrieved from the Internet: &lt;URL:http://www.mems.sandia.gov/sample/doc/SUMMiT_V_Dmanual_V3.0.pdf&gt;, the entirety of the disclosure incorporated herein by reference, structural elements (e.g. buckling beams) can be fabricated utilizing up to five layers (or combinations thereof) of patterned polysilicon with the individual polysilicon layers ranging in thickness from approximately 0.3 μm up to approximately 2.25 μm, and dielectric layers comprising silicon oxides and silicon nitride layers ranging from approximately 0.63 μm up to approximately 2.0 μm per dielectric layer. 
     Structural elements formed from layers that are thicker than typically available in a multi-level polysilicon technology, can comprise single crystal silicon structural elements fabricated using silicon on insulator (SOI) substrates and surface micromachining methods as described in commonly owned patents, U.S. Pat. No. 7,289,009 to T. Christenson et al., and U.S. Pat. No. 7,038,150 to M. Polosky et al., the entirety of their disclosures herein incorporated by reference. SOI substrates can comprise a base layer of up to approximately 500 μm of single crystalline silicon, and a dielectric layer of up to 200 μm silicon oxide (e.g. SiO 2 ) insulating the base layer of silicon from a second layer of single crystal silicon that can be up to approximately 500 μm thick. Thicker structural elements, as for example incorporated into a buckling beam thermal actuator, can provide correspondingly greater actuation forces. Within the context of this disclosure, silicon oxide refers to oxides of silicon that may either be thermally grown or deposited by chemical vapor deposition methods and can comprise the stoichiometric composition (SiO 2 ) as well as non-stoichiometric compositions (SiO x ). 
     MEM buckling beam thermal actuators generally comprise an elongated member, for example a beam formed by patterning one or more layers of polysilicon or a layer of single crystal silicon, which is rigidly attached to a substrate, for example a silicon base, by dielectric supports at each end of the beam. Heating the beam, for example by passing an electrical current through it, causes the beam to expand and eventually buckle. The force generated by the buckling motion of the beam, generally in a direction perpendicular to its length, can be harnessed to perform useful work as an actuator. An issue for buckling beam thermal actuators is controlling (i.e. constraining) the buckling direction of the beam to be in the desired direction of actuation for the actuator. For example, initially straight beams of uniform cross-section along their length can buckle in more than one direction, and measures need be undertaken to insure that such a beam buckles, i.e. provides actuation, in the direction desired. 
     Methods to control the actuation direction of MEM thermal actuators include forming the elongated element in an initial shape such as a “V-beam”, a chevron shape or a curved shape, producing a beam with variable cross-sections, and coupling an array of beams of differing cross-sections. These approaches can add complexity to the processes used to fabricate thermal actuators. Embodiments of the present invention overcome these difficulties by incorporating a directional constraint element which acts as a mechanical stop and/or limiter, to ensure buckling occurs in the desired direction of actuation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and form part of the specification, illustrate several embodiments of the present invention and, together with the description, serve to explain the principles of the invention. The drawings provided herein are not drawn to scale. 
         FIG. 1A  is a plan schematic view of an embodiment of a MEM buckling beam thermal actuator according to the present invention. 
         FIG. 1B  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 1A . 
         FIG. 1C  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 1A , wherein the buckling direction of the beam is in the desired direction of actuation. 
         FIG. 2A  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 1A , wherein the onset of buckling is in a direction not aligned with the desired direction of actuation. 
         FIG. 2B  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 2A , wherein buckling is occurring in a direction not aligned with the desired direction of actuation. 
         FIG. 2C  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 2B , wherein the buckling direction has been constrained to occur in the desired direction of actuation. 
         FIG. 2D  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 2C , in an actuated state wherein the buckling direction is in the desired direction of actuation. 
         FIG. 3A  is a plan schematic view of an embodiment of a MEM buckling beam thermal actuator according to the present invention, coupled to an electrical contactor in an electrically open state. 
         FIG. 3B  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 3A  in an actuated state, wherein the electrical contactor is in a closed state. 
         FIG. 4A  is a plan schematic view of another embodiment of a MEM buckling beam thermal actuator according to the present invention. 
         FIG. 4B  is a schematic cross-sectional view of the embodiment of the MEM thermal actuator according to  FIG. 4A . 
         FIG. 4C  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 4B , wherein the buckling direction of the beam is in the desired direction of actuation. 
         FIG. 5A  is a schematic cross-sectional view of the embodiment of the MEM thermal actuator according to  FIG. 4B , wherein the onset of buckling is in a direction not aligned with the desired direction of actuation. 
         FIG. 5B  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 5A , wherein buckling is occurring in a direction not aligned with the desired direction of actuation. 
         FIG. 5C  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 5B , wherein the buckling direction has been constrained to occur in the desired direction of actuation. 
         FIG. 6A  is a schematic cross-sectional view of a further embodiment of a MEM thermal actuator according to the present invention, wherein the onset of buckling is in a direction not aligned with the desired direction of actuation. 
         FIG. 6B  is a schematic cross-sectional view of the embodiment of the MEM thermal actuator according to  FIG. 6A , wherein buckling is occurring in a direction not aligned with the desired direction of actuation. 
         FIG. 6C  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 6B , wherein the buckling direction has been constrained to occur in the desired direction of actuation. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following examples describe embodiments of the invention as can be fabricated in a surface micromachining technology such as the Sandia Ultra-planar Multi-level MEMS Technology (SUMMiT™) available at Sandia National Laboratories, Albuquerque, N. Mex. and other MEM fabrication technologies including surface micromachining as applied to silicon on insulator (SOI) substrates. Alternative MEM technologies (e.g. as discussed above) can be utilized as well in the practice of the invention. 
       FIG. 1A  is a plan schematic view of an embodiment of a MEM buckling beam thermal actuator according to the present invention. In this exemplary embodiment, MEM buckling beam thermal actuator  100  is presumed to be fabricated in a technology such as the Sandia Ultra-planar Multi-level MEMS Technology (SUMMiT™) technology. MEM buckling beam thermal actuator  100  comprises a silicon substrate  102  upon (and into) the surface of which mechanical structures can be fabricated by the successive deposition and patterning of polysilicon and dielectric layers. Supports  104  are attached to the surface of the substrate and serve to support an elongated element  110  above the surface of the substrate  102 . Elongated element  110  (e.g. a beam) and supports  104  can comprise (e.g. be built up from) successively deposited and patterned layers of polysilicon (doped or un-doped), dielectrics (e.g. silicon nitride, silicon oxide) and metals (e.g. aluminum, copper, nickel). Elongated element  110  can for example, comprise a beam of doped polysilicon that can function as a resistively heated element upon the passage of an electrical current through its length. In this and other embodiments of the invention the elongated element  110  can be as-fabricated in the simple straight form as illustrated (e.g. as a linear beam) of uniform cross-section. As discussed below, a directional constraint element  120  is incorporated to ensure the actuator  100  provides a direction of actuation  130  in a pre-determined, i.e. desired direction. 
       FIG. 1B  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 1A , through the section line A-A. Supports  104  disposed at each end of the elongated element  110  rigidly connect the elongated element  110  to the substrate  102  and provide for a clearance space  108  (e.g. a gap) between the elongated element  110  and the substrate  102 . Supports  104  can comprise built up layers of polysilicon and can be electrically isolated from the substrate  102  by means of a dielectric layer  112  (e.g. comprising silicon oxide and/or silicon nitride). Supports  104  can comprise doped polysilicon and/or metallic materials for the purpose of providing electrical connectivity to the elongated element  110 . A recess  106  (e.g. an etched well or depression) can be incorporated into the substrate  102  adjacent to the elongated element  110  for the purpose of reducing thermal energy losses from the elongated element  110  to the substrate  102 . Comparison of  FIGS. 1A and 1B  illustrate that the cross-section (e.g. given by “w” and “t”) of the elongated element  110  can be arranged so that the greater dimension (“t”) is perpendicular to the direction of actuation  130 , to facilitate flexure and buckling of the elongated element  110  in the desired direction of actuation  130 . 
       FIG. 1C  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 1A , wherein the buckling direction of the beam is in the desired direction of actuation. Applying a voltage (“V”) across the elongated element  110  for example by means of supports  104  (e.g. acting as electrical contact pads) causes an electrical current (“I”) to flow through the elongated element  110  that causes the elongated element  110  to resistively heat and expand. However, as the supports  104  serve to pin the ends of the elongated element  110  to the substrate, the elongated element  110  is forced into a mechanical instability and buckles, moving the center portion of the elongated element  110  outward and in the direction of actuation  130 . As described below, this movement of the center portion of the elongated element  110  produces a force in the actuation direction  130  which can be harnessed to perform useful work. When the voltage (“V”) is removed, resistive heating of the elongated element  110  ceases and the elongated element  110  returns to its initially straight form as illustrated in  FIG. 1A . Elongated element  110  could as well be heated indirectly by application of a separate resistively heated layer (e.g. the elongated element could comprise multiple layers) or by optical energy, for example by illumination from a heating lamp or a laser, or could as well be heated convectively by the flow of a heated gas over its length. 
     The above description illustrates an elongated element  110  that is as-fabricated in a substantially straight form (e.g. a linear beam) of substantially uniform cross-section, expanding and buckling in the desired direction of actuation  130 . However, due to manufacturing tolerances and other environmental factors, the possibility exists that the initially straight elongated element  110  could expand in a direction opposed to the desired direction of actuation  130 . The utility of the directional constraint  120  becomes apparent in the following description of  FIGS. 2A through 2D . 
       FIG. 2A  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 1A , wherein the onset of buckling is in a direction not aligned with the desired direction of actuation. In this example, application of a voltage (“V”, not shown) across the elongated element  110  causes current (“I”) to flow through the elongated element  110  heating the elongated element  110  which expands and buckles, in a direction not aligned to the desired direction of actuation  130 . Due to the pinning constraint of the supports  104 , the elongated element  110  buckles outwardly and contacts the directional constraint  120 . Directional constraint  120  can comprise a block or end stop affixed to the substrate, fabricated of deposited and patterned layers of polysilicon and/or dielectrics such as silicon oxide and silicon nitride, and can comprise a substantially thermally and/or electrically isolated structure from the substrate  102 . In this example, directional constraint  120  is illustrated as a rectangular feature with a curved or pointed surface to minimize the contact area engaging the elongated element  110 . The directional constraint  120  can be positioned proximal to the center along the length of the elongated element  110 , but the precise location is not critical to the practice of the invention. 
       FIG. 2B  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 2A , wherein buckling is occurring in a direction not aligned with the desired direction of actuation. Continued heating and expansion of the elongated element  110  causes the elongated element  110  to deform over the directional constraint  120 . As illustrated, the directional constraint  120  induces a reverse curvature near the center portion of the elongated element  110  thereby producing a force opposing continued motion of the elongated element  110  in the undesired direction. 
       FIG. 2C  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 2B , wherein the buckling direction has been constrained (e.g. re-directed) to occur in the desired direction of actuation. Continued heating and eventual deflection of the elongated element  110  by the constraint  120  forces the beam to “snap”, i.e. to rapidly change direction, and move in the desired direction of actuation  130 . The direction of the forces acting along the length of the elongated member  110  by the curvature induced by the interaction with the directional constraint  120  urge the elongated member to deform and buckle in the desired direction of actuation  130 . 
       FIG. 2D  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 2C , in an actuated state wherein the buckling direction is in the desired direction of actuation. Once the directional constraint  120  has forced the elongated member  110  to buckle into the desired direction of actuation  130 , the elongated member  110  can achieve the desired actuated state. When the voltage (“V”) is removed, resistive heating of the elongated element  110  ceases and the elongated element  110  returns to its initially straight form as illustrated in  FIG. 2A . By incorporation of the directional constraint  120 , MEM thermal actuator  100  is assured to produce a force and displacement, in the desired direction of actuation  130 , regardless of the initial direction the elongated element  110  may buckle towards. 
       FIG. 3A  is a plan schematic view of an embodiment of a MEM buckling beam thermal actuator according to the present invention, coupled to a MEM electrical contactor in an electrically open state. The principles and like numbered elements of MEM actuator  300  are as described above. In this embodiment, an elongated element  110  is mechanically coupled via a coupling device  162  to a MEM moveable electrical contactor  160 . Two MEM electrical circuits  140  and  150  (e.g. conductors) are electrically isolated from each other and positioned near the contactor  162 . Electrical circuits  140  and  150  can comprise conductive structures and contacts fabricated of doped polysilicon and/or metals for example. Coupling device  162  can comprise a push rod or similar movable MEM mechanical element configured to couple the force and displacement created by the movement of the buckling elongated element  110 , to the moveable electrical contacts. Coupling element  162  can be fabricated of deposited and patterned layers of polysilicon and/or dielectrics such as silicon oxide and silicon nitride, and can comprise a substantially thermally and/or electrically isolated structure from the substrate  102 . 
       FIG. 3B  is a plan schematic view of an embodiment of the MEM thermal actuator according to  FIG. 3A  in an actuated state, wherein the MEM electrical contactor is in a closed state. Applying a voltage to and inducing current (“I”) to flow through the elongated element  110  causes the elongated element  110  to expand and eventually buckle in the direction of actuation  130 , either with or without interaction with the directional constraint  120 . Coupling element  162  is engaged by the movement of the buckling elongated element  110  and forces the electrical contactor  160  to electrically interconnect circuit elements  150  and  140 . In this manner, MEM buckling thermal actuator  300  can provide utility in many applications, including as in this example, a MEM electrical switch. 
       FIG. 4A  is a plan schematic view of another embodiment of a MEM buckling beam thermal actuator according to the present invention. In this exemplary embodiment, MEM buckling beam thermal actuator  400  is illustrated as fabricated by surface micromachining methods as applied to a silicon on insulator (SOI) substrate  402 . Thermal actuator  400  comprises a SOI substrate  402  that can comprise two layers of single crystal silicon material separated by a dielectric (e.g. a silicon oxide). Mechanical structures are typically formed of the single crystal silicon layers by successive patterning and etching processes as described above. Supports  404  are attached to the surface of the substrate  402  and serve to support an elongated element  410  above the surface of the substrate  402 . Elongated element  410  (e.g. a beam) and supports  404  can comprise patterned layers of single crystal silicon (doped or un-doped) and silicon oxide dielectric. Elongated element  410  can for example, comprise a beam of doped silicon that can function as a resistively heated element upon the passage of an electrical current through its length. In this exemplary embodiment of the invention, the elongated element  410  can comprise a single crystalline silicon beam as-fabricated in a simple straight form of uniform cross-section, electrically isolated from the substrate  402  by a dielectric layer(s)  412 . As discussed below, a directional constraint element  420  is incorporated to ensure the actuator  400  provides a direction of actuation  430  in a pre-determined, i.e. desired direction. 
       FIG. 4B  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 4A , through the section line A-A. Supports  404  disposed at each end of the elongated element  410  rigidly connect the elongated element  410  to the substrate  402  and provide for a clearance space  408  (e.g. a gap) between the elongated element  410  and the substrate  402 . Supports  404  can be defined in a single crystal silicon layer (in this example, the same layer used to create the elongated element  410 ) and can be electrically isolated from the substrate  402  by means of a dielectric layer  412  (e.g. comprising silicon oxide). A recess  406  (e.g. an etched well or depression) can be incorporated into the substrate  402  adjacent to the elongated element  410  for the purpose of reducing thermal energy losses from the elongated element  410  to the substrate  402 . Recess  406  can as well comprise a through hole or cut-out, etched through the backside of substrate  402 . Comparison of  FIGS. 4A and 4B  illustrate that the cross-section (e.g. given by “w” and “t”) of the elongated element  410  can be arranged so that the greater dimension (“w”) in this embodiment, is perpendicular to the direction of actuation  430 , to facilitate flexure and buckling of the elongated element  410  in the desired direction of actuation  430 , e.g. out of the plane of the substrate  402 . 
       FIG. 4C  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 4B , wherein the buckling direction of the beam is in the desired direction of actuation. Applying a voltage (“V”) across the elongated element  410  for example by means of supports  404  (e.g. acting as electrical contact pads) causes an electrical current (“I”) to flow through the elongated element  410  that causes the elongated element  410  to resistively heat and expand. However, as the supports  404  serve to pin the ends of the elongated element  410  to the substrate, the elongated element  410  is forced into a mechanical instability and buckles, moving the center portion of the elongated element  410  upward and in the direction of actuation  430  (i.e. out of the plane of the substrate  402 ). As described below, this movement of the center portion of the elongated element  410  produces a force in the actuation direction  430  which can be harnessed to perform useful work. When the voltage (“V”) is removed, resistive heating of the elongated element  410  ceases and the elongated element  410  returns to its initially straight form as illustrated in  FIG. 4A . Elongated element  410  could as well be heated indirectly by application of a separate resistively heated layer (e.g. the elongated element could comprise multiple layers) or by optical energy, for example by illumination from a heating lamp or a laser, or could as well be heated convectively by the flow of a heated gas over its length. 
       FIG. 5A  is a schematic cross-sectional view of the embodiment of the MEM thermal actuator according to  FIG. 4B , wherein the onset of buckling is in a direction not aligned with the desired direction of actuation. Application of a voltage (“V”, not shown) across the elongated element  410  causes current (“I”) to flow through the elongated element  410  heating the elongated element  410  which expands and buckles, in a direction not aligned to the desired direction of actuation  430 . Due to the pinning constraint of the supports  404 , the elongated element  410  buckles downwardly and contacts the directional constraint  420 . Directional constraint  420  can comprise a block or end stop affixed to the substrate  402 , and can as in the example of an SOI wafer be etched from the base layer of single crystal silicon. Directional constraint  420  can comprise a substantially thermally and/or electrically isolated structure from the substrate  402 . In this example, directional constraint  420  can comprise a rectangular feature with a curved or pointed surface to minimize the contact area engaging the elongated element  410 . The directional constraint  420  can be positioned proximal to the center along the length of the elongated element  410 , but the precise location is not critical to the practice of the invention. 
       FIG. 5B  is plan schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 5A , wherein buckling is occurring in a direction not aligned with the desired direction of actuation. Continued heating and expansion of the elongated element  410  causes the elongated element  410  to deform over the directional constraint  420 . As illustrated, the directional constraint  420  induces a reverse curvature near the center portion of the elongated element  410  thereby producing a force opposing continued motion of the elongated element  410  in the undesired direction. 
       FIG. 5C  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 5A , wherein the buckling direction has been constrained (e.g. re-directed) to occur in the desired direction of actuation. Continued heating and eventual deflection of the elongated element  410  by the constraint  420  forces the beam to “snap” and move in the desired direction of actuation  430 . The direction of the forces acting along the length of the elongated element  410  by the curvature induced by the interaction with the directional constraint  420  urge the elongated member to deform and buckle in the desired direction of actuation  430 . When the voltage (“V”) is removed, resistive heating of the elongated element  410  ceases and the elongated element  410  returns to its initially straight form as illustrated in  FIG. 5A . By incorporation of the directional constraint  420 , MEM thermal actuator  400  is assured to produce a force and displacement, in the desired direction of actuation  430 , regardless of the initial direction the elongated element  410  expands and moves towards. 
       FIG. 6A  is a schematic cross-sectional view of a further embodiment of a MEM thermal actuator according to the present invention, wherein the onset of buckling is in a direction not aligned with the desired direction of actuation. In the examples presented above, elongated element  410  is illustrated as expanding and bucking in a “first-order” mode, i.e. exhibiting a singular radius of curvature along its length during the initial stage of expansion. However elongated element  410  can expand and buckle in a “higher-order” mode achieving for example, an “S” shape as illustrated. This can be accommodated (i.e. re-directed) by embodiments of the invention incorporating a plurality of directional constraint elements  422 . Passing a current (“I”) through the elongated element  410  heats the elongated element  410  which then expands and buckles, in a direction not aligned to the desired direction of actuation  430 . Directional constraints  422  can comprise a block or end stop affixed to the substrate, fabricated of layers of silicon and/or dielectrics such as silicon oxide and silicon nitride, and can comprise a substantially thermally and/or electrically isolated structure from the substrate  402 . 
       FIG. 6B  is plan schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 6A , wherein buckling is occurring in a direction not aligned with the desired direction of actuation. Continued heating and expansion of the elongated element  410  causes the elongated element  410  to buckle downwardly and contact the directional constraints  422 , which can comprise a plurality of directional constraint elements disposed along the length of, and proximal to, the elongated element  410 . As described above directional constraints  422  can comprise blocks or end stops affixed to the substrate  402 , and can as in the example of an SOI wafer be etched from the base layer of single crystal silicon. As illustrated, the directional constraints  422  induce a reverse curvature in a portion of the elongated element  410  thereby producing a force opposing continued motion of the elongated element  410  in the undesired direction. 
       FIG. 6C  is a schematic cross-sectional view of an embodiment of the MEM thermal actuator according to  FIG. 6A , wherein the buckling direction has been constrained (e.g. re-directed) to occur in the desired direction of actuation. Continued heating and eventual deflection of the elongated element  410  by the constraints  422  forces the beam to “snap” and move in the desired direction of actuation  430 . The direction of the forces acting along the length of the elongated member  410  by the curvature induced by the interaction with the directional constraints  422  urge the elongated member to deform and buckle in the desired direction of actuation  430 . When the voltage (“V”) is removed, resistive heating of the elongated element  410  ceases and the elongated element  410  returns to its initially straight (e.g. un-actuated) form as illustrated in  FIG. 6A . 
     The above described exemplary embodiments present several variants of the invention but do not limit the scope of the invention. Those skilled in the art will appreciate that the present invention can be implemented in other equivalent ways. The actual scope of the invention is intended to be defined in the following claims.