Patent Document

CROSS REFERENCE TO RELATED APPLICATIONS 
     Reference is made to U.S. Ser. No. 09/216,202 filed Dec. 18, 1998 entitled Process for Manufacturing an Electro-Mechanical Grating Device; and further reference is made to U.S. Ser. No. 09/215,973 filed Dec. 18, 1998 entitled Method for Producing Co-Planar Surface Structures. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to the field of modulation of an incident light beam by the use of a mechanical grating device. More particularly, this invention discloses a mechanical grating device which has a significant improvement in the output of the diffracted light beam. 
     BACKGROUND OF THE INVENTION 
     Advances in micromachining technology have given rise to a variety of Micro-electromechanical systems (MEMS) including light modulators for low cost display applications. Such modulators provide high-resolution, high operating speeds (KHz frame rates), multiple gray scale levels, color adaptability, high contrast ratio, and compatibility with VLSI technology. One such modulator has been disclosed in U.S. Pat. No. 5,311,360, issued May 10, 1994 to Bloom et al., entitled “Method and Apparatus for Modulating a Light Beam”. This modulator is a micromachined reflective phase grating. It consists of a plurality of equally spaced deformable elements in the form of beams suspended at both ends above a substrate thereby forming a grating. The deformable elements have a metallic layer that serves both as an electrode, and as reflective surface for incident light. The substrate is also reflective and contains a separate electrode. The deformable elements are designed to have a thickness equal to λ/4 where λ is the wavelength of the incident light source. They are supported a distance of λ/4 above, and parallel to, the substrate. When the deformable elements are actuated (for example a sufficient switching voltage is applied), the deformable are pulled down and the incident light is diffracted. Optical systems can intercept the diffracted light. For display applications, a number of deformable elements are grouped for simultaneous activation thereby defining a pixel, and arrays of such pixels are used to form an image. Furthermore, since gratings are inherently dispersive, this modulator can be used for color displays. 
     U.S. Pat. No. 5,677,783, issued Oct. 14, 1997 to Bloom et al., entitled “Method of Making a Deformable Grating Apparatus for Modulating a Light Beam and Including Means for Obviating Stiction Between Grating Elements and Underlying Substrate” discloses a method of making a deformable grating apparatus for modulating a light beam and including means for obviating stiction between grating elements and underlying substrate. Referring to FIG. 1, a perspective cut-away view of a prior art light modulator  10  is shown. An insulating protective layer  24  is deposited on a silicon substrate  22 . This is followed by the deposition of a sacrificial silicon dioxide layer  16 . A silicon nitride layer  26  is next deposited in which is defined the deformable elements  12 . Both the thickness of the sacrificial silicon dioxide layer  16  and the silicon nitride layer  26  are critical in determining the amplitude modulation and thus the efficiency of the grating device. In order to achieve freestanding beams the sacrificial silicon dioxide layer  16  is etched away in the active area. The remaining sacrificial silicon dioxide layer  16  not removed acts as a supporting frame  14  for the deformable elements  12 . The last fabrication step provides an aluminum film  30  in order to enhance the reflectance of the beams and to provide an electrode for application of a voltage between the deformable elements  12  and the substrate  22 . 
     There are many problems with this prior art device. The thickness of both the sacrificial oxide layer  16  and silicon nitride layer  26  have to each be λ/4. Because these thicknesses determine the grating amplitude of the modulator, their dimensions are critical. Variations in either of these thicknesses will result in unwanted diffraction of light in the off state, as well as lower diffraction efficiency in the on state, thus lower contrast ratios. There is no freedom to adjust the thickness of the deformable element  12  for optimization of its mechanical properties. 
     There is no defined etch stop in the device structure during removal of the sacrificial oxide layer  16 . This requires a carefully controlled time-dependent etch to ensure that the remaining sacrificial oxide layer  16  is able act as the supporting frame  14 . The profile left by the wet etch openings between the beams leaves an uneven wall below the deformable elements  12  where they contact the supporting frame  14 . Such effects will cause variations in the electromechanical properties of the devices. The etching process to remove the sacrificial oxide layer is also a wet process. During this wet processing step it has been seen that stiction tends to occur in that the deformable elements tend to adhere and remain adhered to the substrate. Special drying techniques can be used to overcome this problem but complicate the process. Removal of the sacrificial layer using a dry process is preferred. 
     U.S. Pat. No. 5,661,592, issued Oct. 14, 1997 to Bornstein et al., entitled “Method of Making and an Apparatus for a Flat Diffraction Grating Light Valve” discloses a method for making a deformable grating apparatus which attempts to address the problems associated with this prior art device. An insulating layer is deposited on the substrate. A phosphosilicate glass(PSG) sacrificial layer is next deposited. The phosphosilicate glass(PSG) sacrificial layer is selectively patterned removing the phosphosilicate glass(PSG) sacrificial layer except in regions where the deformable grating elements are to be formed. The phosphosilicate glass(PSG) is reflowed at high temperature to lower the angle of its sidewall. Silicon nitride is then deposited conformably over the phosphosilicate glass(PSG) and patterned into deformable elements. The phosphosilicate glass(PSG) sacrificial layer is then removed by wet etching. By selectively patterning the phosphosilicate glass(PSG) sacrificial layer the region under the beams is more uniform relying now on the uniformity of the reflow of the phosphosilicate glass(PSG) sacrificial layer. However the removal of the phosphosilicate glass(PSG) sacrificial layer is still a wet process with the corresponding disadvantages as described above. The conformal deposition of the silicon nitride over the step height formed by the patterned phosphosilicate glass(PSG) sacrificial layer region also has topography determined by the step height. In patterning the deformable elements this topography will limit the minimum spacing between the deformable elements. Increased spacing between elements will cause increased light scattering decreasing the efficiency of the grating. The use of a phosphosilicate glass(PSG) sacrificial layer also requires a high temperature reflow step that would complicate its integration with CMOS circuitry on the same substrate. 
     There is one problem with the prior art devices, which is, not to provide deformable ribbon elements with a constant cross-section along the entire length of the device. According to this drawback the efficiency of the diffraction grating device is lowered. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a mechanical grating device which has equal actuation conditions for the deformable elements in order to improve the diffraction efficiency of the device. 
     The object is achieved with a mechanical grating device comprising: a base having a surface; a spacer layer provided above the base, said spacer layer defining an upper surface and a longitudinal channel is formed in said spacer layer, said channel having a first and second opposing side wall and a bottom, said side walls being substantially vertically disposed with respect to the bottom, and said channel having a constant cross section along the entire length of the mechanical grating device; and a plurality of spaced apart deformable ribbon elements disposed parallel to each other and spanning the channel, said deformable ribbon elements are fixed to the upper surface of the spacer layer on each side of the channel. 
     Another object is to provide a electromechanical grating device which has equal actuation conditions for the deformable elements of the device in order to improve the diffraction efficiency of the device. 
     These objects are achieved with a electromechanical grating device comprising: a base having a surface; a bottom conductive layer provided within said base; a spacer layer provided above the base, said spacer layer defining an upper surface and a longitudinal channel formed in said spacer layer, said channel having a first and second opposing side wall and a bottom, said side walls being substantially vertically disposed with respect to the bottom, and said channel having a constant cross section along the entire length of the mechanical grating device; and a plurality of spaced apart deformable ribbon elements disposed parallel to each other and spanning the channel, said deformable ribbon elements are fixed to the upper surface of the spacer layer on each side of the channel and each deformable ribbon element is provided with a conductive layer. 
     An advantage of the mechanical or the electromechanical grating device of the present invention is that an improved definition of the position of the channel walls beneath the deformable ribbon elements allow reproducible ribbon length. The reproducible length of the deformable ribbon elements affects resonance frequency, speed of actuation, damping affects due to resonance coupling, and air flow restriction beneath continuous areas of the ribbon layer, etc. A further advantage is that the actuation can be carried out for example by heat or mechanical force activation. Actuation is a deformation of the ribbon resulting from an applied force to affect the height of the ribbons above a substrate. 
     An advantage of the electromechanical grating device is that the formation of a ground plane at the surface of the substrate (for example silicon wafer or glass) allows top side access and better charge confinement within the substrate. 
     Additionally, the structure and materials of the device are selected to be compatible with standard CMOS fabrication methods and allow a fabrication process sequence that make the fabrication of the electromechanical grating device compatible with the integration of CMOS circuitry. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The subject matter of the invention is described with reference to the embodiments shown in the drawing. 
     FIG. 1 is a perspective, partially cut-away view of the prior art grating device; 
     FIG. 2 is an illustration of diffraction from a binary reflective phase grating; 
     FIG. 3 is a perspective, partially cut-away view of the mechanical grating device of the present invention; 
     FIG. 4 is a top view of the mechanical grating device of the present invention; 
     FIG. 5 is a cross-sectional view along plane B—B indicated in FIG. 4 of one embodiment without and applied force to the deformable ribbons; 
     FIG. 6 is a cross-sectional view along plane B—B indicated in FIG. 4 of one embodiment with and applied force to the deformable ribbons 
     FIG. 7 is a cross-sectional view along plane A—A indicated in FIG. 4 to illustrate the provision of an interconnection between the ribbon layer and the base; 
     FIG. 8 is a cross-sectional view along plane A—A indicated in FIG. 4 to illustrate the provision of a reflective layer; and 
     FIG. 9 is a cross-sectional view along plane A—A indicated in FIG. 4 to illustrate device after the last process step; 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 2 providing a description of the diffraction of an incident light beam  11 . Periodic corrugations on optical surfaces (i.e. diffraction gratings) are well known to perturb the directionality of incident light beam  11 . Collimated light incident in air upon a grating is diffracted into a number of different orders, as described by the grating equation (1),                      2      π     λ        sin                   θ   m       =           2      π     λ        sin                   θ   0       +       2      m                 π     Λ         ,           (   1   )                                
     where λ is the wavelength of the incident light and m is an integer denoting the diffracted order. FIG. 2 illustrates a reflective grating  10  having an incident beam  11  incident on the grating  10  at an angle θ 0 . The grating surface is defined to have a period Λ, which defines the angles of diffraction according to the relation presented in Equation 1. A diffracted beam  13  corresponding to diffraction order m exits the grating  10  at an angle θ m . 
     The diffraction grating  10  shown in FIG. 2 is a binary or bi-level grating where the grating profile is a square wave. The duty cycle is defined as the ratio of the width of the groove L 1  to the grating period Λ. A binary phase grating will have the maximum diffraction efficiency when the duty cycle is equal to 0.5 and R, the reflectivity, is equal to 1.0. 
     For uniform reflectivity and 0.5 duty cycle, the relation presented for scalar diffraction theory in Equation 2 is appropriate for the calculation of the theoretical efficiency of diffraction (see M. Born and E. Wolf,  Principles of Optics , 6 th  ed., Pergamon Press, Oxford, 1980, pp. 401-405).                  η   m     =     R                     cos   2          (       π   λ          (         q   m        d     -     m                   λ   /   2         )       )                sin   2          (     m                   π   /   2       )           (     m                   π   /   2       )     2           ,           (   2   )                 where                   q   m                   is                 a                 geometrical                 factor     ,                                   q   m     =       cos                   θ   0       +     cos                   θ   m                     =     1   +         1   -       (     m                   λ   /   Λ       )     2                       for                 normal                   incidence   .                       (   3   )                                
     For normally incident illumination, the maximum efficiency in the first order (m=1) occurs when the grating depth, d=λ/4. Such a grating has equal diffraction efficiencies into the +1 and −1 orders of approximately 40% for the gratings of interest (λ/Λ≦0.5), while the remaining light is diffracted into higher odd orders (i.e. ±3, ±5, etc.). 
     FIG. 3 is a perspective, partially cut-away view of a mechanical grating device  100  of the present invention. The mechanically deformable structures of the mechanical grating device  100  are formed on top of a base  50 . The present embodiment as shown in FIG. 3 discloses a mechanical grating device  100  which can be operated with by the application of an electrostatic force. According to the fact, that the actuation force of the mechanical gating device  100  is electrostatic the base  50  comprises the several layers of different materials. The base  50  comprises a substrate  52 . The material of the substrate  52  is chosen from the materials glass, plastic, metal and semiconductor material. The substrate  52  is covered by a bottom conductive layer  56 . In this embodiment the thin bottom conductive layer  56  is necessary since it acts as an electrode for applying the voltage to actuate the mechanical grating device  100 . The thin bottom conductive layer  56  is covered by a protective layer  58 . The bottom conductive layer  56  is selected from the group consisting of aluminum, titanium, gold, silver, tungsten, silicon alloys and indium tinoxide. Above the protective layer  58  a standoff layer  60  is formed which is followed by a spacer layer  65 . On top of the spacer layer  65 , a ribbon layer  70  is formed which is covered by a reflective layer  78 . In the present embodiment the reflective layer  78  has also to be conductive in order to provide electrodes for the actuation of the mechanical grating device  100 . The electrodes are patterned from the reflective and conductive layer  78 . 
     The spacer layer  65  has a longitudinal channel  67  formed therein. The longitudinal channel  67  comprises a first a second side wall  67   a  and  67   b  and a bottom  67   c . The channel  67  is open to the top and covered by a first and a second set of deformable ribbon elements  72   a  and  72   b . Each deformable ribbon element  72   a  and  72   b  spans the channel  67  and is secured to the surface of the spacer layer  65  on either side of the channel  67 . The bottom  67   c  of the channel  67  is covered by a protective layer  58 . As mentioned above, the ribbon layer  70  is covered by the reflective layer  78 . The reflective layer  78  (conductive) is patterned such that there is a first and a second conducting region  78   a  and  78   b . Both, the first and the second conductive region  78   a  and  78   b  have according to the patterning, a comb-like structure and are arranged at the surface of the mechanical grating  100  device in an interdigitated manner. The first and second conductive region  78   a  and  78   b  are mechanically and electrically isolated from one another. According to the pattern of the reflective layer  78  the ribbon layer  70  is patterned in the same manner. As a result there are the first and the second set of deformable ribbon elements  72   a  and  72   b  spanning the channel  67  and in the direction of the channel  67  are arranged such that every other deformable ribbon element belongs to one set. 
     In the embodiment as shown in FIG. 3 a plurality of standoffs  61  are positioned on the bottom  67   c  of the channel  67 . The standoffs  61  are patterned from the standoff layer  60  such that a group of standoffs  61  is associated only with the deformable ribbon elements  72   a  and  72   b  of the first or the second set. In the embodiment shown here, the group of standoffs  61  is associated with the second set of deformable ribbon elements  72   b . The standoffs  61  may also be patterned in the form of a single bar. 
     Referring to FIG. 4, a top view of the mechanical grating device of the present invention is shown. A first view plane A—A, perpendicular to the length of the mechanical grating device  100  provides a cross-sectional view of the mechanical grating device  100  as shown in FIGS. 7 to  9 . A second view plane B—B, perpendicular to the first view plane A—A of the mechanical grating device  100  provides a cross-sectional view of the mechanical grating device  100  as shown in FIGS. 5 and 6. The mechanical grating device  100  as shown is FIG. 4 is a device which can be actuated by the application of an electrostatic force. A first and a second, electrically conducting region  78   a  and  78   b  are formed on the surface of the mechanical grating device  100 . The first and the second electrically conducting region  78   a  and  78   b  are isolated from each other to allow the application of voltage to either the first or the second set of deformable ribbon elements  72   a  and  72   b . The first conducting region  78   a  applies the voltage to the first set of deformable ribbon elements  72   a  and the second conducting region  78   b  provides the voltage to the second set of deformable ribbon elements  72   b . The first conducting region  78   a  is in contact with the bottom conductive layer  56  (see FIG. 8) designated at the base  50 . The thin bottom conducting layer  56  may be formed above any layer which is below the bottom  67   c  of the channel  67 . From the view of FIG. 4, regions of the spacer layer  65  and protective layer  58  are visible because of pattering of first and second conductive region  78   a  and  78   b  to achieve electrical and mechanical isolation of the deformable ribbon elements  72   a  and  72   b . For operation of the mechanical grating device  100  the electrostatic force is produced by a voltage difference between the thin bottom conductive layer  56  and the first or the second conducting layer  78   a  or  78   b  which are formed atop of each deformable ribbon element  72   a  and  72   b . It s easily understood that a conductive layer can also be formed at the bottom surface  70   b  of each deformable ribbon element  72   a  or  72   b . Additionally, the conductive layer can be located within each deformable ribbon element  72   a  and  72   b.    
     FIG. 5, a cross-sectional view along plane B—B, illustrates the mechanical grating device  100  with no applied voltage to the second conductive region  78   b . In case there is no voltage applied between the thin bottom conducting layer  56  and the first or the second conducting layer  78   a  or  78   b , which are formed atop of each deformable ribbon element  72   a  and  72   b , all of the ribbon elements  72   a  and  72   b  are coplanar. In the embodiment shown in FIG. 5 the top layer on the deformable ribbon elements  72   a  and  72   b  is a reflective and conductive layer  78   a  and  78   b  which defines a top surface  70   a  of the coplanar ribbon elements  72   a  and  72   b . The surface of the ribbon elements  72   a  and  72   b  facing the base  50  of the mechanical grating device  100  is designated as a bottom surface  70   b . On the top surface  50   a  of the base  50  a plurality of standoffs  61  are formed. Each standoff  61  defines a top surface  54   a  which faces the bottom surface  70   b  of the of the ribbon elements  72   a  and  72   b . The depth of the channel  67  is defined by the distance between the bottom surface  70   b  of the ribbon elements  72   a  and  72   b  and the top surface  50   a  of the base  50  or the top surface  54   a  of the standoffs  61 . The plurality of standoffs  61  is distributed on the top surface  50   a  of the base  50 , such that every second deformable ribbon element  72   a  or  72   b  is associated with a standoff  61  (here the second set of deformable ribbon elements  72   b ). According to the embodiment shown in FIG. 5 the base  50  is formed by the substrate  52  which has the bottom conductive layer  56  formed thereon. The sandwich of the substrate  52  and the bottom conductive layer  56  is covered with a protective layer  58  which is the top layer of the base  50 . 
     FIG. 6, a cross-sectional view along plane B—B, illustrates the mechanical grating device  100  with an applied voltage to the second conductive region  78   b  in order to demonstrate the actuation of the second set of deformable ribbon elements  72   b . FIG. 6 illustrates the height change, for example of the second set of deformable ribbon elements  72   b , in case a voltage is applied between the conductive layer  78   b  on top of the second set of deformable elements  72   b  and the bottom conductive layer  56 . According to the voltage difference the actuated ribbons (here: the second set of deformable ribbon elements  72   b ) make contact with the standoffs  61 . The separation of the top surface  70   a  of the coplanar not actuated ribbon elements  72   a  and a top surface  54   b  of the coplanar actuated ribbon elements  72   b  is designed to maximize the efficiency of diffraction by control of the depth of the channel  67  and the heights of the standoffs  61 . The thickness D of the ribbon layer  70  is selected to optimize performance by influencing the electrostatic force required for actuation and the returning force affecting the speed and resonance amplitudes of the device attributed to the tensile stress of the ribbon layer  70 . 
     FIG. 7 is a cross-sectional view along plane A—A as indicated in FIG. 4 to illustrate the provision of an interconnection  75  between the ribbon layer  70  and the base  50 . In the illustrated embodiment the base  50  is formed by the substrate  52  which is covered by the bottom conductive layer  56  which defines a surface  56   a . On top of the bottom conductive layer  56  the protective layer  58  is formed. Contact to the bottom conductive layer  56  is accomplished by etching at least one opening  74  through the multilayered device. The multilayered device comprises the base  50  (composition of the base  50  see above) defining a surface  53 . The surface is covered with a standoff layer  60  being patterned in the area of the channel  67 . The patterning process defines the plurality of standoffs  61 . The standoff layer  60  is covered by a spacer layer  65  which has the channel  67  formed therein. The channel  67  is filled with a material  66  different to the material of the spacer layer  65 . The material  66  in the channel  67  and the material of the spacer layer define the coplanar surface  64   a  of the later formed deformable ribbon elements  72   a  and  72   b . Preferably, the coplanar surface  64   a  is precisely optically coplanar over the entire length of the the later formed deformable ribbon elements  72   a  and  72   b  which span channel  67  such that a light beam reflected from this surface or from the bottom surface  70   b  before removal of material  66  in the channel  67  would always be reflected specularly if it were scanned along these surfaces, providing the beam did not impinge on the edges of elements  72   a  or  72   b . As is well known in the practice of optical engineering, this requires a surface planarity of less than about 200 Angstrom units. In this case surface  70   b  remains optically coplanar after removal of the material  66  and the ribbon elements  72   a  and  72   b  remain optically coplanar on both their bottom and top surfaces after removal of the material  66  providing the material of ribbon elements  72   a  and  72   b  was deposited with uniform thickness and uniform tensile stress. In this case ribbon elements  72   a  and  72   b  have no mechanically irregularities at the points at which they contact spacer layer  65 , thereby ensuring the ribbons pull down uniformly and predictably during device operation. On top of the coplanar surface  64   a  a ribbon layer  70  is formed. The opening  74  is filled by a thick conducting layer  76  which is for example an aluminum alloy. The conductive layer  76  is limited by photolithographic processing and etching methods to a small area coated by the thick conducting layer  76 . 
     FIG. 8 is a cross-sectional view along plane A—A indicated in FIG. 4 to illustrate the provision of a reflective layer  78 . Since in the present embodiment the force applied to the deformable ribbon elements  72   a  and  72   b  is an electrostatic force, the reflective layer  78  deposited atop the ribbon layer  70  is also conductive. This is an ideal combination because the conducting layer being reflective improves the efficiency of diffraction. 
     FIG. 9 is a cross-sectional view along plane A—A indicated in FIG. 4 to illustrate the device after the last process step. As illustrated in FIG. 9 the conducting layer  78  and ribbon layer  70  are patterned using photolithographic processing. First the conducting layer  78  is etched followed by the etching of the ribbon layer  70  using the remaining conducting layer  78  as a mask for etching. This etching process defines first and second conducting region  78   a  and  78   b  of the conducting layer  78  to achieve electrical and mechanical isolation. Finally, the sacrificial layer  66  filling the channel  67  is removed by dry etching methods using xenon difluoride to yield the device cross-sectional view illustrated in FIG.  9 . Now the patterned deformable ribbon elements  72   a  and  72   b  are suspended above the channel  67 . Preferably ribbon elements  72   a  and  72   b  precisely optically coplanar over their entire length . 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention. 
     
       
         
               
             
               
               
             
           
               
                   
               
               
                 PARTS LIST 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 10 
                 prior art light modulator 
               
               
                 10 
                 diffraction grating 
               
               
                 11 
                 incident light beam 
               
               
                 12 
                 deformable elements 
               
               
                 13 
                 diffracted beam 
               
               
                 14 
                 frame 
               
               
                 16 
                 spacer layer 
               
               
                 22 
                 substrate 
               
               
                 24 
                 passivating layer 
               
               
                 26 
                 conducting layer 
               
               
                 30 
                 thin layer 
               
               
                 50 
                 base 
               
               
                 50a 
                 top surface of base 
               
               
                 52 
                 substrate 
               
               
                 53 
                 surface of the base 
               
               
                 54a 
                 top surface of standoffs 
               
               
                 54b 
                 top surface of actuated ribbon elements 
               
               
                 56 
                 thin bottom conductive layer 
               
               
                 56b 
                 surface of conductive layer 
               
               
                 58 
                 protective layer 
               
               
                 60 
                 standoff layer 
               
               
                 61 
                 standoff 
               
               
                 64a 
                 coplanar surface 
               
               
                 65 
                 spacer layer 
               
               
                 66 
                 material filled in the channel 67 
               
               
                 67 
                 channel 
               
               
                 70 
                 ribbon layer 
               
               
                 70a 
                 top surface of the coplanar ribbon elements 
               
               
                 70b 
                 bottom surface of the coplanar ribbon elements 
               
               
                 72a 
                 first set of deformable ribbon elements 
               
               
                 72b 
                 second set of deformable ribbon elements 
               
               
                 74 
                 opening 
               
               
                 75 
                 interconnection 
               
               
                 76 
                 thick conducting layer 
               
               
                 78a 
                 first conducting region 
               
               
                 78b 
                 second conducting region 
               
               
                 100 
                 mechanical grating device 
               
               
                 A—A 
                 first view plane 
               
               
                 B—B 
                 second view plane 
               
               
                 θ 0   
                 angle of incident light beam 
               
               
                 m 
                 diffraction order 
               
               
                 θ m   
                 exit angle of the diffracted light beam 
               
               
                 Λ 
                 groove width 
               
               
                 L 1   
                 period of the grating 
               
               
                 d 
                 grating depth 
               
               
                 D 
                 thickness of the ribbon layer

Technology Category: g