Abstract:
A MEMS device such as a grating light valve™ light modulator is athermalized such that the force required to deflect the movable portion of the MEMS device remains constant over a range of temperatures. In MEMS embodiments directed to a grating light valve™ light modulator, a ribbon is suspended over a substrate, and the ribbon tension is kept constant over a temperature range by adjusting the aggregate thermal coefficient of expansion of the ribbon to match the aggregate thermal coefficient of expansion of the substrate. Various opposition materials have an opposite thermal coefficient of expansion as the aluminum layer of a grating light valve™ light modulator ribbon, using the thermal coefficient of expansion of the substrate as a zero coefficient reference. The adjustment of the thermal coefficient of expansion of the ribbon can be performed variously by thickening existing layers of opposition material or adding additional layers of new opposition material to the ribbon, or reducing the aluminum in aluminum layer. The aluminum layer may be reduced variously by reducing the thickness of the aluminum layer, or reducing the surface area that the aluminum covers, or reducing both the surface area and the thickness. Embodiments may combine the reduction of aluminum with the use of opposition materials.

Description:
FIELD OF THE INVENTION 
   The present invention relates to the field of leveling thermal stress and tension variations which develop in MEMS devices comprised of different materials. More particularly, the present invention relates to leveling thermal stress variations within a MEMS device by manipulating the effective thermal coefficient of expansion related stress variations over temperature in a first layered member to approximate the effective thermal coefficient of expansion related stress variations over temperature of a second layered member. 
   BACKGROUND OF THE INVENTION 
   MEMS technology involves the process of designing and building micro-sized mechanical and/or electrical structures with technology generally developed for 5V CMOS processes common to IC fabrication. In one area of MEMS device fabrication, typically referred to as surface micro-machining, layers of semiconductor, metal, and insulator materials are utilized to build structures which can be activated by electrostatic, electromagnetic, thermal, or pneumatic means, among others. A balancing force to these externally imposed forces is often provided by the mechanical properties of the structures, such as the spring force in deflected beams, bridges, or membrances. Such MEMS devices are projected to be used in areas of biomedical engineering, aerospace, automotive, data storage, or optical telecommunications, where they are used as dispensers, sensors, actuators, read/write heads, or optical signal processing. 
     FIGS. 1 and 2  illustrate cross sectional views of an embodiment of a grating light valve™ light modulator with movable ribbons. The substrate  119  comprises a silicon layer  120  and a passivating layer  122 , such as silicon dioxide. A conducting layer  124  is configured to receive a charge or to be held at ground potential.  FIG. 1  illustrates the ribbon  134  in an undeflected state.  FIG. 2  illustrates a ribbon  134  in a deflected state. Deflection is typically induced in a ribbon layer  134  by applying a voltage potential to the ribbon  134  with respect to the conducting layer  124 , typically by means of a controller circuit. 
   According to the embodiment illustrated in  FIG. 1 , the conducting layer  124  is formed on top of the passivating layer  122 . The ribbon  134  bridges the conducting layer  124 , with an air gap  132  separating the ribbon  134  from the conducting layer  124 . Referring to  FIGS. 1 and 2 , the ribbon  134  comprising a resilient layer  126  which lends tension, flexibility and elasticity to the ribbon structure  134 , allowing the ribbon  134  to return to its original position when a deflecting force is removed. The resilient layer  126 , also known as the ribbon layer, is typically a stoichiometric silicon nitride layer such as Si 3 N 4 . Tension inherent in the silicon nitride film provides the restoring force to the applied potential force. The resilient layer  126  is typically on the order of about 50-150 nanometers thick in conventional embodiments. The second layer in the ribbon  134 , layer  128 , is a layer which balances the lateral stress between the nitride layer  126  and the aluminum layer  130 , such that in the case of wide ribbons, the curvature after ribbon release is minimized. This layer  128  typically consists of silicon di-oxide, and will be absent for narrow ribbons. Typical oxide layer thicknesses are on the order of about 800 to 2000 nm. The third layer of the ribbon  134  is the aluminum reflecting layer  130 , which is deposited against the surface of the silicon oxide  128 , or with the absence of the oxide, against the surface of the ribbon nitride  126 . The aluminum reflecting layer  130  functions to reflect light for various applications of the grating light valve™ light modulator. The aluminum layer  130  also functions as the complementary capacitor plate, and thus is the electrode that forms one half of the structure across which the field is applied. The aluminum layer  130  is typicaly between about 650 and 1500 nm thick in the conventional embodiments. As noted, an air gap  132  separates the substrate  119  from the ribbon  134 . As can be seen in  FIGS. 3 and 4 , the ribbon layer  126  is bonded to the substrate  122  at an end connection point  135  and/or at a center anchor  136 . 
   The deformable ribbons  134  of grating light valve™ light modulators are representative of a feature common to some MEMS devices. Because most MEMS devices are partly mechanical in nature, they typically involve an electrically or thermally induced mechanical motion of some sort. Moreover, mechanical motion within MEMS devices typically causes elastic material deformation, as illustrated by the ribbons in  FIGS. 1 and 2 . 
   The ribbon  134  is fabricated to exhibit an inherent tension defining a natural resonant frequency, and requiring a specific force necessary to deflect the ribbon  134  relative to the substrate surface  119 , as illustrated in FIG.  2 . Static equilibrium is maintained as the electrostatic force between ribbon  134  and substrate  124  is balanced by the tensile force in ribbon  134 . The force between the ribbon  134  and the substrate  119  is transmitted through the end connection point  135  and the center anchor  136  according to the embodiment shown in FIG.  1 . 
   The voltage required to fully deflect the ribbon, known as the switching voltage or pull-down voltage, is typically on the order of about 15-25 volts in certain conventional embodiments. However, the tension within the ribbon across the substrate does not remain constant over a range of temperatures. It typically reduces when the temperature increases and increases as the temperatures decreases. This has a variety of undesirable effects, one of which is that the changing tension causes the pull-down voltage required to fully deflect the ribbon to change as the temperature changes. The fundamental resonance frequency which depends on ribbon characteristics also changes as the tension changes over a range of temperatures. Because damping time is largely a function of the ribbon mass, the damping time remains largely constant in spite of temperature changes, and is typically in the range of about 0-10 μsec in conventional approaches. There is therefore a desire for a method and apparatus for athermalizing a MEMS design to achieve a constancy of operation over an operational temperature range. More specifically, a desire exists for a method and apparatus for athermalizing the ribbon of a grating light valve™ light modulator to maintain a constancy of tension over an operational temperature range. There is further a desire for a method and apparatus for leveling the deflection voltage of a MEMS device over an operational temperature range. Additionally, there is a desire for leveling the resonant frequency of a MEMS device over an operational temperature range. 
   SUMMARY OF THE INVENTION 
   The present invention is directed to a method and apparatus for leveling the aggregate forces within a MEMS structure over an operational temperature range. The present invention is also directed to a method and apparatus for athermalizing a MEMS component to achieve a constancy of operation over an operational temperature range. The present invention is particularly adapted to athermalizing a ribbon in a grating light valve™ light modulator such that it maintains a constancy of tension over an operational temperature range. The present invention is also directed to a method and apparatus for reducing the variations in the deflection force required to deflect a movable MEMS member. The present invention is particularly adapted to reducing the variation in pull-down voltage of a ribbon in a grating light valve™ light modulator over an operational temperature range. The present invention is further directed to reducing variation in the resonant frequency of a movable MEMS member over an operational temperature range. 
   A MEMS device comprises a first member coupled to a second member, the first member having a first aggregate thermal coefficient of expansion represented by a first value and a second member having a second aggregate thermal coefficient of expansion represented by a second value. A method of athermalizing the MEMS device over an operational temperature range, comprises the step of reducing a difference between the value representing the first aggregate thermal expansion and the second value representing the second aggregate thermal expansion by adjusting the first member to exhibit a third value for its thermal expansion. As an aspect of the present invention, the thermal expansion of the second member is established as a zero coefficient reference value, such that thermal expansion greater than the reference are distinguished by a positive sign, and thermal expansion less than the reference are distinguished by a negative sign. According to one embodiment of the present invention, an athermalization layer comprising a thermal coefficient of expansion whose value has a sign opposite the sign of the first value is added to the first member during a fabrication process. According to an alternative embodiment, a material already present within the first member having a thermal coefficient of expansion with the same sign as the first member is reduced in quantity. The steps of adding an athermalization layer and reducing an amount of an existing material may be used in conjunction. 

   
     BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS 
       FIG. 1  illustrates a cross sectional view of a grating light valve™ light modulator with ribbons in an undeflected position. 
       FIG. 2  illustrates a cross sectional view of one embodiment of a grating light valve™ light modulator with ribbons in a deflected position. 
       FIG. 3  illustrates a side view of two surfaces of differing thermal coefficients of expansion coupled together. 
       FIG. 4  illustrates a side view of two surfaces of differing thermal coefficients of expansion coupled together and bowing as a result of cross boundary thermal stress. 
       FIG. 5  illustrates a side view of two surfaces of differing thermal coefficients of expansion coupled together wherein one surface is experiencing fissures and fractures as a result of cross-boundary thermal stress. 
       FIG. 6  illustrates a side view of two surfaces of differing thermal coefficients of expansion originally coupled together which have undergone delamination as a result of cross-boundary thermal stress. 
       FIG. 7  is a cross sectional illustration of compressive and tensile forces simultaneously present in a single ribbon of a grating light valve™ light modulator. 
       FIG. 8  illustrates a perspective view of a grating light valve™ light modulator comprising reduced thickness of the aluminum layer and increased thickness of the resilient layer. 
       FIG. 9  graphically illustrates aluminum thickness as a function of resilient layer thickness at athermalization. 
       FIG. 10  graphically illustrates the pull-down voltage as a function of aluminum thickness at athermalization according to FIG.  9 . 
       FIG. 11  graphically illustrates the damping time constant as a function of aluminum thickness at athermalization according to FIG.  9 . 
       FIG. 12  graphically illustrates the resonance frequency of the ribbon as a function of aluminum thickness at athermalization according to FIG.  9 . 
       FIG. 13  is a perspective view illustrating a grating light valve™ light modulator comprising a ribbon with a PECVD layer disposed between the resilient layer and the reflective layer. 
       FIG. 14  graphically illustrates the PECVD thickness required for athermalization as a function of aluminum thickness at five different resilient layer thicknesses. 
       FIG. 15  is a perspective view illustrating a grating light valve™ light modulator comprising a ribbon with a silicon dioxide layer disposed between the resilient layer and the aluminum layer. 
       FIG. 16  graphically illustrates silicon dioxide thickness required for athermalization as a function of aluminum thickness at five different resilient layer thicknesses. 
       FIG. 17  is a perspective view illustrating a grating light valve™ light modulator with an aluminum layer comprising less surface area than the surface area of the ribbon. 
       FIG. 18  graphically illustrates the fraction of aluminum coverage over the surface area of a ribbon required for athermalization as a function of aluminum thickness, for three different resilient layer thicknesses. 
       FIG. 19  graphically illustrates ribbon resonance frequency and damping time as a function of the percent of ribbon surface area covered by aluminum. 
       FIG. 20  graphically illustrates pull down voltage as a function of aluminum coverage, normalized at 22 volts for full aluminum coverage. 
       FIG. 21  is a perspective view illustrating a grating light valve™ light modulator with a reduced surface area aluminum layer and a poly-silicon layer covering the entire ribbon surface to increase the capacitance of the ribbon. 
       FIG. 22  illustrates a perspective view of a grating light valve™ light modulator with a reduced surface area aluminum layer, a poly-silicon layer, and a thin-coat silicon nitride layer protecting areas of the poly-silicon layer not covered by the aluminum. 
       FIG. 23  illustrates a cross sectional view of a ribbon of a grating light valve™ light modulator with a poly-silicon layer sandwiched between equal thickness silicon nitride layers, and vias coupling the poly-silicon layer to the aluminum. 
       FIG. 24  illustrates a perspective view of a grating light valve™ light modulator with a reduced surface area aluminum layer, a poly-silicon layer, and a “candy-coat” oxidation layer on the upper and side surface of the conductive poly-silicon layer. 
       FIG. 25  illustrates a cross sectional view of a ribbon of a grating light valve™ light modulator having an oxidized upper surface of a conductive a poly-silicon layer with vias coupling the non-oxidized portion of the conductive poly-silicon layer to the aluminum layer. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   U.S. Pat. No. 5,311,360 entitled “METHOD AND APPARATUS FOR MODULATING A LIGHT BEAM” and U.S. Pat. No. 5,841,579 entitled “FLAT DIFFRACTION GRATING LIGHT VALVE to Bloom et al. and U.S. Pat. No. 5,661,592 entitled “METHOD OF MAKING AN APPARATUS FOR A FLAT DIFFRACTION GRATING LIGHT VALVE” to Bornstein et al., and U.S. Pat. No. 5,808,797 entitled “Method and Apparatus for Modulating a Light Beam” to Bloom, et al. are herein incorporated by reference. 
   Reference will now be made in detail to the preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings. 
     FIG. 7  is a cross sectional view of a ribbon  134 . Arrows present in the layers  126 ,  128  illustrate that there can be distinct tensile and compressive forces present within the layers  126 ,  128  of the ribbon  134 . Rather, the tension of the ribbon is equal to the sum of the tensions and compressions of the various layers, as illustrated in equation 1:
   F   ribbon =Σ(σ Al +σ Si3N4 +σ Ox )   1 )  
In equation 1 above, the tension within the ribbon is seen to be equal to the tension within the aluminum layer  128  plus the tension within the resilient layer  126 , also known as the ribbon layer, and typically comprised of silicon nitride. In some cases there can be an oxide layer  130  ( FIG. 1 ) whose inherent tension is also added. Those skilled in the art will recognize that the equation is exemplary, and could be adapted for a MEMS structure comprising any number of layers. As applied to grating light valve™ light modulators, the curing and fabrication of the various layers is performed with a view toward ensuring that the sum of the forces in the ribbon yield a predetermined aggregate tension at the reference temperature. Initially, the tension will be examined in terms of the aluminum layer  128  and the resilient layer  126  for purposes of simplicity. As with the aggregation of forces within the ribbon, the multiple layers  120  and  122 , of the substrate  119  may be thought of as exerting a single compressive force in resistance to the tensile force of the ribbon. Because most MEMS structures are built on bulk silicon (about 500 μm), the aggregate force is substantially determined by the silicon thermal coefficient of expansion.
 
   In addition to the opposing forces of the ribbon and the substrate, those skilled in the art will recognize that stress exists between each layer  126 ,  128  of the ribbon  134 , and between each layer  120 ,  122  of the substrate  119 . Because the various layers have distinct coefficients of thermal expansion, the stress varies as temperature varies.  FIG. 3  illustrates two surfaces,  150  and  151  bound together at an optimal temperature selected such that the inter-surface stress is minimized.  FIG. 4  illustrates the same surfaces  150  and  151  after the temperature has increased. According to the illustration of  FIG. 4 , layer  151  has a higher coefficient of thermal expansion than layer  150  and, as the temperature increases, warpage of the layers is seen to occur as layer  151  expands more rapidly than layer  150 .  FIGS. 5 and 6  illustrate various forms of catastrophic material failure resulting from excessive cross-boundary thermal stress.  FIG. 6  illustrates fracture of laminate layer  150  as a result of cross-boundary thermal stress exceeding operational range tolerances. As laminate layer  151  expanded faster than layer  150 , the boundary forces create fissures  152  or fractures  152  in the layer expanding more slowly, thus expanding its boundary edge to the same size as the more rapidly expanding edge.  FIG. 6  is an exaggerated illustration of delamination, wherein the contact between the surfaces  150  and  151  is broken, forming a gap  152  between the surfaces. 
   As discussed above, the component layers have different thermal coefficients of expansion. However, when the laminate boundaries of the ribbon  134  and substrate  119  remain intact, it is possible to represent or model the ribbon  134  and the substrate  119  as having a single thermal coefficient of expansion. The process of aggregating the various degrees of thermal expansion comprising the substrate layers  120  and  122 , for example, ( FIG. 7 ) takes into account not only the thermal coefficient of expansion of each layer, but the thickness, density, and modulus of elasticity of each of those layers. Therefore, some layers will have a greater contributory effect in determining the “average” or aggregate thermal coefficient of expansion. 
   This aggregate value is respectively represented by the value α sub  for the substrate  119 , and by the value α ribbon  for the ribbon  134 . 
   As discussed above, the ribbon  134  can be represented as having a single thermal coefficient of expansion, α ribbon , which can be determined by weighted averaging of thermal coefficients of expansion of the respective layers α Si3N4 , α Al  and/or α SiO2  referring to the thermal coefficients of expansion of the resilient  126 , aluminum  128  and/or oxide  130  layers ( FIG. 1 ) of the ribbon  134 , respectively. As with the substrate, it is understood that the “averaging” process requires weighing various factors, such as the thickness, modulus, density and tension of various component layers. 
   Although the relationship of the ribbon  134  to the substrate  119  may advantageously be modeled by representing a single coefficient of expansion for the substrate  119  and the ribbon  134  respectively, some calculations and analyses are advantageously performed by representing the forces and coefficients of expansion in the ribbon layer independently. As noted in equation 1 above, the ribbon tension σ ribbon  can be represented as a sum of the individual tensions of the component layers, Σ(σ Al +α Si3N4 +σ Ox ). Although the present invention includes alternative embodiments of normalizing the aggregate thermal coefficient of expansion α sub  of the substrate  119  to the thermal coefficient of expansion α ribbon  of the ribbon  134 , the preferred embodiment involves normalizing the thermal coefficient of expansion α ribbon  of the ribbon  134  to the substrate α sub . In performing analysis according to the preferred embodiment, it is advantageous to normalize the thermal coefficient of expansion of the substrate α sub  at the reference value of zero, with thermal coefficient expansions of individual ribbon layers such as α Si3N4  and α Al  by positive numbers and negative numbers depending on whether their thermal coefficient of expansion is greater or less than α sub . 
   Because the thermal coefficient of expansion α Al  of aluminum is greater than the reference α sub , being designated by a positive number, as the temperature increases, the aluminum will expand more than the substrate, increasing the compressive component of stress σ Al  contributed by the aluminum layer  128  within the ribbon  134 . By itself, the increasing compressive stress σ Al  of the aluminum, averaged against the overall tension of the ribbon  134  would have the effect of reducing the tension in the ribbon  134 . The resilient layer  126  or ribbon layer, being made of silicon nitride, typically comprises a thermal coefficient of expansion α Si3N4  having a negative coefficient with respect to the reference coefficient α SUB  of the substrate  119 . Accordingly, as the temperature increases, the substrate  119  will expand more than the resilient layer  126 . Although the resilient layer  126  is technically expanding, it may therefore be thought of as contracting relative to the substrate, thereby increasing the tensile component of stress σ Si3N4  within the ribbon  134 . As discussed above, however, as long as the surface connection between the aluminum  128  and resilient  126  layers remains intact, the relative expansion of the aluminum layer  128  is partially balanced against the relative contraction of the resilient layer  126 . Accordingly, just as the individual tensions could be aggregated according to equation 1, the relative coefficient of thermal expansion can be averaged into a representative coefficient, defining the coefficient of thermal expansion of the ribbon  134  relative to the substrate  119 . As discussed above, a representative coefficient of thermal expansion α ribbon  of the ribbon  134  must take into consideration not only the component thermal expansion coefficients α Si3N4 , α Al  of the component resilient  126  and aluminum  128  layers of the ribbon  134 , but other factors such as the thickness, modulus, and tension of the component layers. Limiting the ribbon to two layers for purposes of simplicity of illustration, a representative or aggregate thermal coefficient of expansion α ribbon  of the ribbon  134  can only be given in relation to the variable that is affected, i.e., tension, ribbon resonance frequency, or damping time. 
     FIG. 7  uses arrows to illustrate the compressive forces in the aluminum layer  128  and the tensile forces in the ribbon layer  126 . As discussed above, as long as the boundary between the layers  126  and  128  remains intact, these forces can be aggregated, as illustrated in equation 1 above. As the temperature rises, the ribbon layer  126  is increasing in tension, and the aluminum layer  128  is increasing in compression. Without an athermalization layer according to the present invention, the relative expansion and contraction of the component layers do not average out. Recalling that the thermal coefficient of expansion α Al  of the aluminum layer is positive with respect to the substrate and the thermal coefficient of expansion α ribbon  of the silicon resilient layer  126  is negative with respect to the substrate, the absolute value of the aluminum coefficient α Al  is substantially larger that the absolute value of the silicon nitride coefficient α ribbon  of the resilient layer  126 . As a result, because layer thicknesses are substantially the same order of magnitude, the relatively high thermal coefficient of expansion α Al  of aluminum gives the aluminum layer  128  a disproportionate effect compared with the resilient layer  126 . As a consequence, without an athermalization layer, when the temperature increases, the disproportionate growth of the compressive force from the aluminum layer  128  reduces the tension in the ribbon. However, as a ribbon decreases in tension, it exhibits a lower resonant frequency. It also requires less force to deflect, which means that the pull-down voltage is lower. The pull-down voltage is determined by the potential difference between the ribbon and the substrate, required to deflect the ribbon to a fully deflected position, which in this case is about 30% of the full space between the undeflected ribbon and the substrate. Accordingly, the difference in the thermal coefficients of expansion of the substrate α sub  and the ribbon α ribbon  results in a ribbon that exhibits a constantly changing resonant frequency and a constantly changing pull-down voltage over a range of temperatures. However, with many MEMS devices, operational consistency over a wide range of temperatures is often desirable. This is particularly true with respect to the control of the ribbons in a grating light valve™ light modulator. Other MEMS devices similarly depend on a constancy of behavior. 
     FIG. 8  illustrates an athermalization layer comprising a decreased-aluminum/increased-resilient-layer embodiment of a grating light valve™ light modulator ribbon according to the present invention. The aluminum layer of a grating light valve™ light modulator functions to reflect the incident electromagnetic waves, specifically in the visible and near IR region or the preferred embodiment. According to this embodiment, the aluminum layer is reduced to a thickness in the range of about 40 to 65 nanometers. Because the thickness of a layer is proportional to the effect it has on the aggregate thermal coefficient of expansion of the ribbon α ribbon , by reducing the thickness of the aluminum layer  206 , the aggregate thermal coefficient of expansion of the ribbon α rib  is reduced, thereby normalizing the aggregate thermal coefficient of expansion of the ribbon α rib  to the thermal coefficient of expansion α sub  of the substrate  208 . 
   The lower limit of Aluminum thickness is determined mostly by process conditions. Thin aluminum often suffers from voiding (sections of aluminum disappear) or hillocking (aluminum tends to bunch up at specific locations). At the same time, reflectivity will reduce at low aluminum thickness, resulting in unacceptable device performance. However, thicknesses below 40 nanometers are not likely to serve most purposes, and a thickness of about 45 to 60 nanometers is generally preferred. 
   As discussed above, using the thermal coefficient of expansion α sub  of the substrate  208  as a reference of zero, the thermal coefficient of expansion of the aluminum layer  206  is positive, and the thermal coefficient of expansion α Si3N4  of the resilient layer  204  is negative. Accordingly, athermalization may be achieved by thinning the aluminum layer  206 , increasing the thickness of the resilient layer  204 , or both. Because a reduction of the thickness of the aluminum layer sufficient to reach athermalization between the ribbon and substrate would leave the aluminum layer  206  too thin for many applications, to athermalize the ribbon  202  with respect to the substrate, in conjunction with the thinning of the aluminum layer  206 , the thickness of the resilient layer  204  can be adjusted to assure maximum aluminum reflectivity. At the proper relative values, the combination of thinning the aluminum layer and thickening the silicon nitride layer has the effect of athermalizating the ribbon  202 . Although either the aluminum thickness or the silicon nitride thickness may be considered as the independent variable, for purposes of uniformity and simplicity, the aluminum thickness is herein presented as an independent variable, and the silicon nitride thickness is presented as a “compensating” thickness or dependent variable. 
   The contributory effect of the resilient layer  204  on the aggregate thermal expansion of the ribbon  202  is roughly proportional to the thickness of the resilient layer  204 . Accordingly, by increasing the thickness of the resilient layer  204  to a thickness in the range of about 150 to 250 nanometer range, in conjunction with the thinning of the aluminum layer  206 , the aggregate thermal coefficient of expansion α ribbon  of the ribbon is athermalized with respect to the thermal coefficient of expansion α sub  of the substrate  208 . Again, however, there are practical limits to the thickness which is sustainable by the resilient layer  204 . The resilient layer  204  is comprised of a resilient material such as Low Pressure Chemical Vapor Deposited Silicon Nitride (LPCVD), which exhibits an elasticity and resiliency, such that it seeks to restore the ribbon to an undeflected position when the pull-down voltage is turned off. Accordingly, the process of thickening the resilient layer  204  makes the ribbon  202  more difficult to deflect, and a higher pull down voltage is required. In most applications, the requirement of a higher voltage to achieve full deflection is a disadvantage. 
     FIG. 9  graphically illustrates the athermalization curve for various thickness of the silicon nitride layer in comparison to the aluminum layer. As illustrated by the graph, at an aluminum thickness of approximately 55 nm, the silicon nitride layer configured to athermalize the ribbon  202  with respect to the substrate  208  is approximately 175 nm thick.  FIG. 9  shows that the thickness of the aluminum layer and the resilient layer can vary according to circumstances. The advantages of reducing the thickness of the aluminum layer can be seen by examining the behavioral characteristics of this embodiment illustrated in  FIGS. 10-12 . The pull-down voltage, damping time and resonance frequency are illustrated as a function of aluminum thickness. No silicon nitride thickness is illustrated in these graphs, but the graphs represent behavioral characteristics at athermalization, the athermalized relationship between the aluminum  206  and resilient silicon nitride  204  layers being illustrated in FIG.  9 . Accordingly, the relationship of aluminum to silicon nitride illustrated in  FIG. 9  is operational for  FIGS. 10-12 . 
   According to  FIG. 10 , at an aluminum thickness of 55 nm the required pull down voltage is approximately 35 volts. This appears to be a result that the tensile strength of the ribbon  202  is increased by thickening the resilient layer  204  sufficient to athermalize the ribbon  202 . As  FIG. 10  illustrates, the pull down voltage according to this embodiment traverses a voltage range from about 32 volts to 42 volts corresponding to a respective range of aluminum thickness of about 45 nanometers to 85 nanometers. For comparative purposes, these values can be contrasted to ribbons which are not athermalized, which exhibit a pull-down voltage typically on the order of about 20 volts. 
   Another effect of the decreased-aluminum/increased-resilient-layer embodiment is that, by increasing the thickness of the resilient layer, the mass of the ribbon is increased, making it more resistant to the damping effects of the air or gas it engages during oscillation. Depending on the aluminum thickness and corollary resilient layer thickness, the damping time increases by approximately 50%. 
     FIG. 11  graphically illustrates the relationship between damping time and aluminum thickness at athermalization. At approximately 55 nm aluminum thickness, damping time is roughly 3 microseconds. As the aluminum thickness increases, the silicon nitride thickness is also increased. As graphically illustrated, the increased mass resulting from a thicker resilient layer is seen to have a corollary increase in damping times. At an aluminum thickness of about 70 nm, damping time is approximately 4 microseconds. 
     FIG. 12  graphically illustrates a level resonance frequency at approximately 1.14 MHz over the range of aluminum thicknesses illustrated within the graph, independent of the layer thickness. 
   The athermalization layer of the decreased-aluminum/increased-resilient-layer embodiment discussed above comprises an increase in the thickness of the resilient layer to athermalize the ribbon with respect to the substrate. The resilient layer is advantageously comprised of an LPCVD silcon nitride described earlier. According to one embodiment of the present invention illustrated in  FIG. 13 , an athermalization layer  150  of Plasma Enhanced Chemical Vapor Deposited “PECVD” silicon nitride is incorporated in the ribbon  144 , preferably between the resilient layer  148  and the aluminum layer  146  (FIG.  13 ). Although the PECVD silicon nitride layer  150  and the low pressure chemical vapor deposited LPCVD silicon nitride layer  148  are both expressed by the chemical formula Si 3 N 4 , the LPCVD silicon nitride used in the ribbon layer  148  has a greater tensile stress and resiliency than the PECVD silicon nitride  150 . By using a PECVD silicon nitride layer for athermalization, the PECVD embodiment is capable of athermalizing the ribbon  144  with respect to the substrate  142  without increasing the tension of the ribbon  144  as much as using LPCVD silicon nitride of the increased-resilient-layer embodiment. By using PECVD silicon nitride, the pull down voltage is held to the 28 volts range. 
     FIG. 14  graphically illustrates the thickness of an athermalizing PECVD layer required to athermalize a ribbon at various thicknesses of the resilient layer of 80 nm, 90 nm, 100 nm, 110 nm and 120 nm over a range of aluminum thicknesses from about 45 nm to 85 nm. Using for exemplary purposes a resilient layer thickness of about 90 nm and an aluminum layer thickness of about 75 nm,  FIG. 14  shows that a PECVD layer of about 160 nm is required for athermalization. As a result of the extra mass of the PECVD layer, the resonance frequency drops from about 1140 kHz to approximately 775 kHz. Although a ribbon athermalized with a PECVD silicon nitride layer is more supple than a layer formed by simply increasing the thickness of the LPCVD silicon nitride of the resilient layer, the pull down voltage of a ribbon with an athermalizing PECVD silicon nitride layer nevertheless increases to about 28 volts, roughly a forty percent increase. 
     FIG. 15  illustrates a cross sectional view of a grating light valve™ light modulator and ribbon according to the silicon dioxide athermalization embodiment of the present invention. A layer of silicon dioxide SiO 2  is disposed between the aluminum and silicon nitride layers. Again using the thermal coefficient of expansion α sub , of the substrate as a reference of zero, the aluminum layer  218  has a positive thermal coefficient of expansion α Al , and the silicon dioxide  220  has a negative thermal coefficient of expansion α SiO2 , thereby opposing the influence of the aluminum layer  218 . By incorporating a silicon dioxide layer  220  of the proper thickness between the aluminum  218  and resilient  222  layers, the ribbon  217  is athermalized in relation to the substrate  216 . 
     FIG. 16  graphically illustrates five separate curves representing resilient layer thicknesses of 80 mm, 90 nm, 100 nm, 110 nm and 120 nm respectively. Any one of these curves can be used to determine the required thickness of the silicon dioxide layer shown on the vertical axis to athermalize the ribbon  217  over the range of aluminum thicknesses shown on the horizontal axis. An asterisk  234  indicates a silicon nitride resilient layer thickness of approximately 93 nm and an aluminum thickness of roughly 76 nm, values commonly found in conventional approaches. At these values, the graph indicates that a “compensating silicon dioxide” layer would have to be approximately 560 nm thick. Because the silicon nitride layer also has a negative coefficient of expansion α Si3N4  with respect to the reference substrate value α SUB , the thicker silicon nitride layer also works to counteract the effects of the aluminum layer. Accordingly, at any given thickness for the aluminum layer, the thicker the silicon nitride layer, the thinner the silicon dioxide layer is required to athermalize the ribbon  217  of FIG.  15 . For example, referring to  FIG. 16 , at an aluminum thickness of about 70 nm, athermalization of the ribbon in  FIG. 15  is achieved with a silicon nitride layer  222  that is about 80 nm thick by a silicon dioxide layer approximately 520 nm thick. When the silicon nitride layer  222  is increased to about 120 nm thickness at the same aluminum thickness of about 70 nm, the thickness of the silicon dioxide layer necessary to achieve athermalization is reduced to approximately 400 nm. 
   An advantage of the silicon dioxide layer embodiment is that its tension and elasticity are lower than that of the resilient silicon nitride layer, and accordingly, it does not raise the pull down voltage. In fact, experimental evidence indicates that the suppleness of the ribbon achieved by the silicon dioxide technique actually decreases the pull-down voltage by 35%. Because of the greater mass resulting from the silicon dioxide layer, however, the resonance frequency is slowed from about 1140 kHz to 275 kHz. Whether or not the slower frequency is a disadvantage depends on a particular application. In the fabrication process, individual ribbons are “cut” from a continuous sheet, typically by chemically etching a series of parallel gaps in the sheet, thereby defining a series of elongated ribbons separated by gaps. Increased ribbon thickness puts more demands on the ribbon gap lithographic process and etch chemistry, causing the gaps to be wider with increasing ribbon thickness. As the size of the gap between the ribbons increases, the higher gap-to-ribbon aspect ratio allows for a greater loss of incoming radiation through the gaps. 
     FIG. 17  shows a reduced aluminum embodiment  230  of the present invention wherein the athermalization layer includes an embodiment of the aluminum layer  234 ,  236  itself. The surface area of the aluminum layer  234 ,  236  is reduced by reducing the width of the aluminum layer to a narrow conduit  234  from the end  238  of the ribbon and extending longitudinally along the ribbon up to the optically interactive portion of the aluminum surface  236 , which functions to reflect or diffract incoming electromagnetic waves. The aluminum widens, preferably to a width identical to the ribbon at the active area of the ribbon  237 . The conduit  234  allows the aluminum to maintain electrical continuity with a voltage source, and the wider reflective surface  236  is disposed on the active area of the ribbon configured to reflect incoming light. Accordingly, the narrow conduit has little negative effect on the efficiency of the reflective surface since it does not extend to the active area of the ribbon surface. The reduction in surface area of aluminum reduces the effect which the aluminum has on the aggregate thermal expansion of the ribbon, thereby athermalizing or partially athermalizing the ribbon  230  with respect to the substrate  232 . The effective ribbon tension can be represented by equation 2 below: 
         S   ⁡     (   p   )       =             w   ·       t   Si3N4     (         E   Si3N4     ·     t   Si3N4     ·     σ   Si3N4       +                       p   ·     E   Si3N4     ·     t   Al     ·     σ   Al       +       (     1   -   p     )     ·     E   Al     ·     t   Al     ·     σ   Al         )             (         E   Si3N4     ·     t   Si3N4       +       (     1   -   p     )     ⁢       E   al     ·     t   Al           )             
Wherein S(p) is tension as a function of the percent “p” of the ribbon surface covered by aluminum, w is the width of the ribbon, t is the thickness of the layer, E is Young&#39;s modulus of elasticity, and σ represents stress in pascals.
 
   The effective linear mass of the ribbon can be determined according to equation 3:
 
 M ( p )=(3/8  p   5 −15/8  p   4 +5/2  p   3 )ρ Al   ·w·t   Al ρ Si3N4   ·w·t   Si3N4   3) 
 
wherein M(p) is the effective mass as a function of the percent of the ribbon surface covered by aluminum and ρ is the density of a material referenced by the subscript. Using the equations of effective linear mass and effective ribbon tension, the resonant frequency can be represented in equation 4:
 
ν( p )={3.162/(2 ·π·L )}· sqrt (( S ( p )/( M ( p ))  4) 
 
wherein 3.162 is selected as the square root of ten, ν(p) is the frequency as a function of the percent of the ribbon surface covered by aluminum and L is the ribbon length. Using the equation of effective linear mass, the damping time is represented by equation 5:
 
τ( p )=(π 3   ·d   3   ·M ( p )/(48·η eff   ·w )  5) 
 
wherein τ(p) is the damping constant as a function of the percent “p” of the ribbon surface covered with aluminum, d is the distance from the substrate electrode to the resilient layer in the ribbon, and η eff  is the dynamic viscosity of the gas damping the ribbon, usually measured in micro poise.
 
     FIG. 18  graphically illustrates the aluminum coverage required for athermalization as a function of aluminum thickness. Three separate curves illustrate this function for three different thicknesses of the resilient layer  230  of silicon nitride. To achieve athermalization at an exemplary aluminum thickness of 75 nm and an exemplary silicon nitride thickness of about 90 nm, according to  FIG. 18 , the surface area of the aluminum would have to be reduced to roughly 41 percent of the surface area of the ribbon. Again, the asterisk illustrates thicknesses for the aluminum layer and the resilient layer commonly found in conventional embodiments. 
     FIG. 19  illustrates frequency and damping as a function of the fraction of the surface covered with aluminum, ranging from zero aluminum to total aluminum coverage. The frequency, read against the left hand vertical axis, ranges from approximately 1 MHZ when the aluminum layer covers 100% of the ribbon surface, to a resonant frequency of about 1.28 MHz when no aluminum is present. The right hand vertical axis shows the gradations for damping in seconds. By reducing the percent coverage of aluminum, the mass of the ribbon is reduced. As the mass of the ribbon is reduced, the air or other damping gas between the ribbon and the substrate has a greater damping effect. Accordingly, damping occurs in approximately 1.2 micro seconds with no aluminum, but is slowed to approximately 2 micro seconds with 100% aluminum coverage. 
     FIG. 20  is a graphical illustration of the pull down voltage as a function of the ratio of the aluminum surface area to the ribbon surface area. Because the amount of charge accumulated on the aluminum is dependant upon the surface area of the aluminum, at 100% coverage, the pull down voltage is only about 22 volts. As the percent of surface area is decreased, the pull down voltage must be increased to compensate for the smaller surface area of aluminum available for collecting charge. 
     FIG. 21  illustrates an embodiment of the reduced aluminum embodiment combined with a poly-silicon layer preferably disposed between the aluminum  248  and the silicon nitride (resilient) layer  246 . It was observed in conjunction with  FIG. 20  that a reduction in aluminum surface area requires a progressively greater pull down voltage. An advantage of the reduced aluminum/poly-silicon embodiment therefore is that the poly-silicon  244  is capable of sustaining a potential that aids in the pull down of the ribbon. By extending the poly-silicon layer across the entire surface area of the ribbon, the pull down voltage is roughly the same voltage requirement as for those embodiments wherein the surface area of the aluminum had never been reduced. The reduced-aluminum/poly-silicon embodiment produces a slight increase in resonance frequency of approximately 28% and will lower the damping constant by approximately 45%. Because the poly-silicon is subject to etching in many manufacturing processes, it is preferable that any exposed poly-silicon is protected by a layer of silicon nitride, preferably LPCVD silicon nitride. In addition, in order to provide sufficient conductivity of the poly-silicon, the poly-silicon needs to be doped such as with phosphorous (P), increasing the conductivity. In embodiments utilizing a conductive poly-silicon layer such as a phosphorous doped embodiment, the aluminum conduits  253  depicted in  FIGS. 21 and 22  and discussed further herein are optional provided the conductive poly-silicon layer is grounded to the same anchor as the aluminum layer in the previous embodiments, and provided the conductive poly-silicon layer is conductively coupled with the aluminum layer. 
   Within the reduced aluminum/poly silicon embodiment, two embodiments are envisioned for protecting the poly silicon from etching. According to the thin-coat embodiment, the resilient layer of a standard thickness, such as 100 nm, is beneath poly-silicon. The poly-silicon rests on top of the resilient layer. The aluminum layer rests on top of the poly-silicon layer. The exposed portions of the poly-silicon layer  244  adjacent the narrow aluminum conduit are then coated with a very thin coating of silicon nitride  250 . Because it is important that the aluminum layer  242  and the poly-silicon layer  244  are the same potential, the thin coating  250  of silicon nitride should not extend under the aluminum, but only on the exposed areas of the poly-silicon layer  244 . Because the thin coating of silicon nitride  250  may be much thinner than the actual resilient layer  246 , the thin-coat layer  250  serves to protect the poly-silicon  244  from chemical etching, but has little effect on adding to the resilience of the ribbon. 
     FIG. 22  is an illustration of a thin-coat silicon nitride/reduced aluminum ribbon. The resilient layer  246  and the thin-coat layer  250  are preferably both a silicon nitride. Though not necessarily to scale,  FIG. 22  nevertheless illustrates that the thin-coat layer  250  of silicon nitride is substantially thinner than the resilient layer  246  of silicon nitride. As discussed above, the poly-silicon  244 , which acts to increase the surface area through which the field operates, thereby lowering the required pull down voltage. However, the poly-silicon layer  244  does little to contribute to the tension of the ribbon. Because of its inherent properties, silicon nitride is responsible for a disproportionate amount of the tensile force of the ribbon relative to its thickness. However, because the silicon nitride thin-coat layer  250  is so thin compared to the resilient layer  246 , the tensile force is directed or distributed primarily through the resilient layer, along the dotted lines, with lateral forces indicated by FL and tangential forces indicated by FT. 
   As an alternative to the thin-coat embodiment,  FIG. 23  illustrates a cross sectional view of a poly-silicon sandwich embodiment. The poly-silicon layer  256  is embedded within the resilient silicon nitride layer  254 , with half the mass of the resilient layer  254  above the poly-silicon layer  256  and half the mass of the resilient layer  254  below the poly-silicon layer  256 . This symmetry serves to minimize ribbon warpage, whether the warpage would be due to tensile forces distributed through the ribbon, or thermal expansion and contraction of the component layers of the ribbon. 
   To fully protect the poly-silicon  256  from etching, the preferred embodiment of  FIG. 23  further illustrates that the silicon nitride encompasses the poly-silicon on the sides as well as the top and bottom. Because the main purpose of the poly-silicon is to sustain an electrical field, it can be appreciated that if the poly-silicon layer  256  were electrically insulated within the silicon nitride layer  256 , the aluminum layer would be floating with respect to the ground potential. Accordingly,  FIG. 23  illustrates conductive poly-silicon vias  258  which extend from the poly-silicon layer  256  to the aluminum layer  252 , extending through the resilient silicon nitride layer  254 . The vias  258  allow charge to be evenly distributed from the aluminum layer to the poly-silicon layer, and bring the aluminum to the poly-Si potential. 
     FIGS. 24 and 25  illustrate a final embodiment incorporates the resilient layer as a silicon nitride. A poly-Silicon layer  244  is deposited on top of the resilient layer  246 , and doped with Phosphorous to increase conductivity. The poly-Si is oxidized such that the outside layer (top and sides) of the poly-Si is “candy coated” with oxide  257 . Because the preferred embodiment envisions the oxidation process performed before the aluminum is laid down, the oxidation layer  257  will act to insulate the aluminum  242  from the conductive poly-silicon  244 . Vias  258  function to conduct charge between the poly-Si layer and the aluminum. 
   While the invention was described in conjunction with the preferred embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the invention as defined by the appended claims. Accordingly, the figures and detailed description recited herein are not intended to limit the present invention, but are merely intended to illustrate a particular implementation of the present invention, and to enable those skilled in the art to utilize the principles of the invention set forth herein. 
   Although the present invention is applicable to any MEMS device, application of the present invention to a grating light valve™ light modulator will be used for exemplary purposes throughout much of this description. Those skilled in the art will recognize that the invention discussed herein and the appended claims are applicable to many MEMS devices wherein motion, range of motion, tension, compression, angles of orientation, and other physical properties are affected by members comprising disparate thermal coefficients of expansion.