Abstract:
A method for defining a full phase layout for defining a layer of material in an integrated circuit is described. The method can be used to define, arrange, and refine phase shifters to substantially define the layer using phase shifting. Through the process, computer readable definitions of an alternating aperture, dark field phase shift mask and of a complimentary mask are generated. Masks can be made from the definitions and then used to fabricate a layer of material in an integrated circuit. The separations between phase shifters, or cuts, are designed for easy mask manufacturability while also maximizing the amount of each feature defined by the phase shifting mask. Cost functions are used to describe the relative quality of phase assignments and to select higher quality phase assignments and reduce phase conflicts.

Description:
RELATED APPLICATIONS  
       [0001]     This application is a divisional of U.S. Application No. 10/809,650 filed 25 Mar. 2004, entitled “Design and Layout of Phase Shifting Photolithographic Masks,” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention, which application is a divisional of U.S. Application No. 10/085,759, filed 28 Feb. 2002, entitled “Design and Layout of Phase Shifting Photolithographic Masks,” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention, which application is a continuation-in-part of, and incorporates by reference, U.S. Patent Application Ser. No. 09/669,359 filed 26 Sep. 2000 entitled “Phase Shift Masking for Complex Patterns” having inventor Christophe Pierrat and assigned to the assignee of the present invention, which is a non-provisional of U.S. Provisional Patent Application Ser. No. 60/215,938 filed 05 Jul. 2000 entitled “Phase Shift Masking For Complex Layouts” having inventor Christophe Pierrat and assigned to the assignee of the present invention.  
         [0002]     This application is a divisional of U.S. Application No. 10/809,650 filed 25 Mar. 2004, entitled “Design and Layout of Phase Shifting Photolithographic Masks,” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention, which application is a divisional of U.S. Application No. 10/085,759, filed 28 Feb. 2002, entitled “Design and Layout of Phase Shifting Photolithographic Masks,” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention, which application is related to, claims the benefit of priority of, and incorporates by reference, the U.S. Provisional Patent Application Ser. No. 60/296,788 filed 08 Jun. 2001 entitled “Phase Conflict Resolution for Photolithographic Masks” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention.  
         [0003]     This application is a divisional of U.S. Application No. 10/809,650 filed 25 Mar. 2004, entitled “Design and Layout of Phase Shifting Photolithographic Masks,” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention, which application is a divisional of U.S. Application No. 10/085,759, filed 28 Feb. 2002, entitled “Design and Layout of Phase Shifting Photolithographic Masks,” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention, which application is related to, claims the benefit of priority of, and incorporates by reference, the U.S. Provisional Patent Application Ser. No. 60/304,142 filed 10 Jul. 2001 entitled “Phase Conflict Resolution for Photolithographic Masks” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention.  
         [0004]     This application is a divisional of U.S. Application No. 10/809,650 filed 25 Mar. 2004, entitled “Design and Layout of Phase Shifting Photolithographic Masks,” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention, which application is a divisional of U.S. Application No. 10/085,759, filed 28 Feb. 2002, entitled “Design and Layout of Phase Shifting Photolithographic Masks,” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention, which application is related to, claims the benefit of priority of, and incorporates by reference, the U.S. Provisional Patent Application Ser. No. 60/325,689 filed 28 Sep. 2001 entitled “Cost Functions And Gate CD Reduction In Phase Shifting Photolithographic Masks” having inventors Christophe Pierrat and Michel Côté and assigned to the assignee of the present invention. 
     
    
     BACKGROUND OF THE INVENTION  
       [0005]     1. Field of the Invention  
         [0006]     The present invention relates to manufacturing small dimension features of objects, such as integrated circuits, using photolithographic masks. More particularly, the present invention relates to phase shift masking of complex layouts for integrated circuits and similar objects.  
         [0007]     2. Description of Related Art  
         [0008]     Phase shift masking has been applied to create small dimension features in integrated circuits. Typically the features have been limited to selected elements of the design, which have a small, critical dimension. See, for example, U.S. Pat. No. 5,766,806.  
         [0009]     Although manufacturing of small dimension features in integrated circuits has resulted in improved speed and performance, it is desirable to apply phase shift masking more extensively in the manufacturing of such devices. However, the extension of phase shift masking to more complex designs results in a large increase in the complexity of the mask layout problem. For example, when laying out phase shift windows on dense designs, phase conflicts will occur. One type of phase conflict is a location in the layout at which two phase shift windows having the same phase are laid out in proximity to a feature to be exposed by the masks, such as by overlapping of the phase shift windows intended for implementation of adjacent lines in the exposure pattern. If the phase shift windows have the same phase, then they do not result in the optical interference necessary to create the desired feature. Thus, it is necessary to prevent inadvertent layout of phase shift windows in phase conflict near features to be formed in the layer defined by the mask.  
         [0010]     In the design of a single integrated circuit, millions of features may be laid out. The burden on data processing resources for iterative operations over such large numbers of features can be huge, and in some cases makes the iterative operation impractical. The layout of phase shift windows and the assignment phase shift values to such windows, for circuits in which a significant amount of the layout is accomplished by phase shifting, is one such iterative operation which has been impractical using prior art techniques.  
         [0011]     Because of these and other complexities, implementation of a phase shift masking technology for complex designs will require improvements in the approach to the design of phase shift masks.  
       SUMMARY OF THE INVENTION  
       [0012]     A method for defining a full phase layout for defining a layer of material in an integrated circuit (IC) is described. In a full phase layout substantially all features of a layer of material, e.g. the polysilicon layer, are defined using phase shifting. By defining features using phase shifting, the majority of the layer can be composed of sub-wavelength features. For example if a λ=193 nm stepper is used then the a feature significantly less than λ in size is difficult to manufacture on the final IC without using phase shifting. By providing a systematic approach to placing, shaping, and assigning phase to the phase shifters, the method can produce high quality layouts that can be produced as photolithographic masks. Those masks can in turn be used in the production of a layer of an IC.  
         [0013]     For a given pattern, e.g. the polysilicon (or gate) layer of an integrated circuit, the features can be identified. By growing a region around the features—except for end caps of features—a maximum shifter area can be defined. The maximum shifter area corresponds to the space where the shifters are desirably placed to define the features. Shifter shapes can then be placed against the edges of the feature. The shifter shapes are spaced apart from one another to leave open spaces where cuts, or openings, between different shifters may be necessary. The spacing requirement is related to the design rules for minimum spacing and edge length and may be different for different types of situations, e.g. outer and inner corner.  
         [0014]     In some embodiments, the shifter shapes are a trapezoid stacked on top of a rectangle. This shape is designed to admit a cut that has a square notch at the top. Thus avoiding pointed corners which may be difficult to manufacture in a mask.  
         [0015]     In some embodiments, the shifter shapes are then refined to fill certain open areas within the maximum shifter area.  
         [0016]     Next, phase dependencies between the different shifter shapes are determined along with costs. This is important because there are certain requirements for an alternating aperture phase shifting mask, e.g. shifter on opposite sides of a feature should have opposite phase. However, there may be additional considerations beyond phase conflicts that should be considered. For example, how desirable, or undesirable, is it to have two shifters be the same phase on an inside corner, outside corner, along three edges, etc. Other criterion may include multiple-layer dependencies, e.g. positioning based on contacts, diffusion areas, etc. As well as cost functions for small shifters. Overall, the cost functions describe the relative quality of a given arrangement, e.g. shifter shape A and shifter shape B given same phase.  
         [0017]     Phase can then be assigned to the shifter shapes according to the dependencies and the cost functions. After that, same phase shifters can be merged together filling some of the previously open cut spaces. Additional refinements are provided by some embodiments of the invention including removal of small shifters, squaring of corners, and filling open spaces with the dominant or subordinate phase.  
         [0018]     After the phase shifters are defined, the trim shapes can be defined using the phase shifter shapes and the original pattern. In some embodiments, the logical or of the finished phase shifter shapes and the original layout are combined, down-sized to account for mask misalignment errors and then another logical or is performed with the original layout. The trim layout may include attenuated phase shifting shapes, e.g. tri-tone mask, etc.  
         [0019]     In some embodiments, the input is a file containing the layout in a format such as GDS-II stream format and the output may be one or more files. In one embodiment, the output is a single GDS-II stream format file containing both the trim and phase layers. In other embodiments, the output is two mask data files, one for each mask, suitable for use by mask fabrication machines.  
         [0020]     Embodiments of the invention include photolithographic masks. The photolithographic masks include a phase mask and a complimentary mask. The phase mask comprises a dark field, alternating aperture phase mask where the phase windows have been arranged to define the target pattern as described above. The complimentary mask comprises a mask designed to clear artifact left by the phase mask and define and remaining edges or edge segments not defined by the phase mask.  
         [0021]     Embodiments of the invention include methods for manufacturing integrated circuits. The method includes exposing a layer of material in an IC using masks prepared and defined as described above. 
     
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0022]      FIG. 1  illustrates exemplary inner corner cuts used to shape phase and trim layers.  
         [0023]      FIG. 2  illustrates exemplary outer corner cuts used to shape phase and trim layers.  
         [0024]      FIG. 3  illustrates the cut shape in greater detail.  
         [0025]      FIG. 4  illustrates a shifter boundary after endcap identification.  
         [0026]      FIG. 5  illustrates an endcap cutting protection area.  
         [0027]      FIG. 6  illustrates an initial shifter shape.  
         [0028]      FIG. 7  illustrates the minimum shifter separation for merging.  
         [0029]      FIG. 8  illustrates the shifters of  FIG. 7  after merging.  
         [0030]      FIG. 9  illustrates notches to be filled between proximate shifters.  
         [0031]      FIG. 10  illustrates how the shifter shape of  FIG. 6  leaves open cuts on outer corners.  
         [0032]      FIG. 11  illustrates an initial shifter placement on a contact landing area.  
         [0033]      FIG. 12  illustrates the layout of  FIG. 11  after the shifter has been extended to the boundary.  
         [0034]      FIG. 13  illustrates the layout of  FIG. 12  after the open spaces are further filled by the shifter.  
         [0035]      FIG. 14  illustrates the measurements used in a cost function for a straight line phase conflict.  
         [0036]      FIG. 15  illustrates the measurements used in a cost function for an inner corner.  
         [0037]      FIG. 16  illustrates the measurements used in a cost function for an outer corner.  
         [0038]      FIG. 17  illustrates the measurements used in a cost function for a three-edge case.  
         [0039]      FIG. 18  illustrates the measurements used in a cost function for the small shifter area case.  
         [0040]      FIG. 19  illustrates cost function sensitivity to features on other layers.  
         [0041]      FIG. 20  is a process flow diagram for preparing a layout.  
         [0042]      FIG. 21  illustrates an example layout after endcap identification.  
         [0043]      FIG. 22  illustrates the layout of  FIG. 21  after shifter boundaries are defined.  
         [0044]      FIG. 23  illustrates the field cuts for the layout of  FIG. 22 .  
         [0045]      FIG. 24  illustrates the corner cut shapes for the layout  FIG. 22 .  
         [0046]      FIG. 25  is a process flow diagram for designing a phase layer and a trim layer to substantially define a pattern of a layout using phase shifting.  
         [0047]      FIG. 26  illustrates the layout of  FIG. 21  after placement of shifters according to the process of  FIG. 25 .  
         [0048]      FIG. 27  illustrates the layout of  FIG. 26  after some open spaces have been filled according to the process of  FIG. 25 .  
         [0049]      FIG. 28  illustrates the layout of  FIG. 27  after additional refinement of the shifter shapes according to the process of  FIG. 25 .  
         [0050]      FIG. 29  illustrates the layout of  FIG. 28  after initial phase assignment as occurred according to the process of  FIG. 25 .  
         [0051]      FIG. 30  illustrates a phase layer for the layout of  FIG. 29  after enlargement of shifters according to the process of  FIG. 25 .  
         [0052]      FIG. 31  illustrates the refinement of phase shifters through flood filling using the dominant phase.  
         [0053]      FIG. 32  illustrates the refinement of phase shifters through flood filling using the dominant phase.  
         [0054]      FIG. 33  illustrates the refinement of phase shifters through flood filling using the subordinate phase.  
         [0055]      FIG. 34  illustrates the refinement of phase shifters through squaring off and flood filling using the dominant phase.  
         [0056]      FIG. 35  illustrates the phase layer for the layout of  FIG. 30  after refinement of the shifters according the process of  FIG. 25 .  
         [0057]      FIG. 36  illustrates the trim layer superimposed on the phase layer of the layout of  FIG. 34 .  
         [0058]      FIG. 37  illustrates the completed phase shifting layout for the layout of  FIG. 34 .  
         [0059]      FIG. 38  illustrates the trim layer for use in conjunction with the layout of  FIG. 35 . 
     
    
     DETAILED DESCRIPTION  
       [0060]     Overview  
         [0061]     Methods and apparatuses for defining phase, and corresponding trim, layouts for defining a layer of material in an integrated circuit are described. Embodiments of the invention include mask data preparation (MDP) data created according to and by the methods and apparatuses described herein. Other embodiments include masks, or reticles, and integrated circuit products produced from the layouts defined by the methods and apparatuses described herein.  
         [0062]     According to one embodiment of the invention an input layout, e.g. in GDS-II stream format, is received for a layer of material. Embodiments of the invention, e.g. by the process of  FIG. 25  described below, produce one or more output layouts to define substantially all portions of the pattern of the layout using phase shifting. For example, the output layout may include a GDS-II stream file having one or more phase layers and a trim layer. In some embodiments, the 0 and 180 degree phase shifters are separated into different layers to assist in the mask manufacturing process. This is in part a limitation of the current GDS-II stream format, as the file format does not provide a standard way of designating phase on polygons within a layer. For convenience of illustration and discussion, the singular term phase layer as used herein will refer to all of the relevant phase layers in a given output file format designed for use in creating the phase mask. Thus the output is what is sometimes referred to as a “full phase” layout, or mask/reticle. Additionally, the output can include a corresponding layout for the complementary mask, sometimes referred to as a “trim mask”, for use in conjunction with the full phase mask. As with the phase data, the trim data can be in the same file and/or a separate file.  
         [0063]     The invention will be described in greater detail as follows. A variety of setup information including parameters, cutting shapes, shifter shapes, and the like will be considered first. Then the process used by some embodiments of the invention will be discussed with reference to an example layout.  
         [0064]     Setup  
         [0065]     The process whereby the phase layers and trim layers are defined is best understood with respect to the setup of the problem and several parameters used in working with the original layout. First, cut shapes and the arrangement of inner and outer corner cuts will be described. Then, the manner in which the boundary of the phase region is created will be considered. Next, the initial shifter shapes and sizes will be described. Then the process of gradually growing shifter shapes will be considered. Finally, cost functions used to determine placement and shaping of phase shifters and cuts will be considered.  
         [0066]     Cut Shapes and Inner and Outer Corners  
         [0067]     Turning first to  FIGS. 1-3 , exemplary inner and out corner cuts for a layout are shown as well as a more detailed view of a cut shape used by one embodiment of the invention. Turning first to  FIG. 1 , inner corner cuts  100  are examined with respect to a phase layer  102  and a trim layer  104  for an exemplary inner corner. In the phase layer  102 , a feature  110  is defined by a shifter  112  and a shifter  114  is shown (the feature  110  is actually not a part of the phase layer  102  itself). Similarly, the trim layer  104  includes a trim  118  to protect the areas defined by the shifters and define the corner. The boundary of the feature  110  is indicated by a dashed line in the trim layer  104 . Of particular interest is the cut shape used, see discussion of  FIG. 3 , below for more detail. The cut shape comprises a substantially square shaped notch with a straight line neck at a 45 degree angle coming out of the corner of the notch. The shape is designed to comply with design rules—and more importantly—facilitate mask manufacturability.  
         [0068]     Similarly,  FIG. 2  shows outer corner cuts  200  including a phase layer  202  and a trim layer  204 . In the phase layer  202 , a feature  210  is defined by a shifter  212  and a shifter  214  (the feature  210  is not a part of the phase layer  202  itself but is shown for clarity of illustration). In the trim layer  204 , a trim  218  to protect areas defined by the shifters and define the corner is shown. Dashed lines are used to show the boundary of the feature  210  in the trim layer  204 . Additionally, a dotted and dashed line shows an alternative corner shape  222  that can be employed on the trim layer  204 . The alternative corner is designed to be completely design rule clean. In comparison, the original corner might create a design rule violation due to the close proximity of the edges of the corner to the angled edges of the cut. As in  FIG. 2 , the similar cut shape is used to provide a design rule compliant—and more importantly—easy to manufacture mask for the layouts.  
         [0069]     Turning to  FIG. 3 , an exemplary cut  300  is shown as a dotted outline. The cut  300  is shaped like the cuts used in  FIG. 1  and  FIG. 2  to separate shifter pairs. The shape includes a substantially square notch at the top that is intersected at an offset on a 45 degree angle by a straight neck that ends in a squared off form. Note that an angle  306  between the square notch and the neck. In one embodiment the angle is 135 degrees. The sizes of the various edges of the cut  300  will be process and design rule dependent. For example, the edge length  302  will be related to the minimum edge length for the process—accounting for mask manufacturing requirements. In one embodiment the edge length  302  is a multiple, r&gt;0.0, of the minimum edge length. In this example, r=1.0. Similarly, the edge length  304  will be similarly dependent on the minimum edge length, e.g. a multiple r′&gt;0.0 of the minimum edge length. In this example, r′={square root}{square root over (2)}/2. The width  308  of the neck will be dependent on the minimum edge separation as well as the lithographic properties of the process, e.g. by a multiple r″&gt;0.0. More specifically, the width  308  must be sufficient to allow the trim to clear phase artifacts left between the alternate phase shifters adjacent to the cut.  
         [0070]     Boundaries  
         [0071]     Continuing to  FIG. 4  the desired phase boundary is shown for a feature  400  having an endcap  404 . A boundary  402  is shown as a heavy dashed line. As seen, the boundary can be created by a grow operation on the feature shape—except where the endcap  404  is present. It should be noted that the height of the endcap  404  should be related to the minimum edge length, e.g. 0.8X, 1.0X, 1.1X, and more generally rX, r&gt;=0.0. In some embodiments, the endcap area is a straight line resulting in a flat boundary across the top edge of the feature  400 . This reflects a difference in whether or not the phase shifters or the trim will be used to define the end cap and how much the phase area on adjacent features will need to be reduced. More specifically, looking at a feature  410  adjacent to the endcap  404  of the feature  400 , with the shifters for the feature  400  contained within the boundary  402 , the need to reduce the boundary around the feature  410  will be less than if the shifters for the feature  400  extended all the way to the top of the endcap  404 . Thus, the handling of endcaps represents a layout design tradeoff. In one embodiment, it is preferred to use the phase shifters to define the end cap and so the boundary is flat at the end caps.  
         [0072]     In another embodiment, the endcap handling is determined on a case-by-case basis with reference to one or more rules describing how certain endcap cases should be handled. For example a rule might specify that if no feature is in close proximity to the endcap use a flat boundary. However, in situations where there is a close feature, e.g. as with the feature  410  in  FIG. 4 , then the area around the endcap should be defined using the trim layer. In still other embodiments, a simulation is performed on the area of the layout using both possibilities and the configuration resulting in better results is selected.  
         [0073]     The boundary  402  should be set at the preferred shifter width for reproducing the feature  400 . For example if the feature  400  has a critical dimension (CD) of X nm and the preferred shifter width is Y nm for a critical dimension of X nm with a given lithographic process (e.g. a specific wavelength of light, coherency, resist characteristics, etc.) then the boundary can be placed Y nm from the edges of the feature  400 . For example, for a 248 nm wavelength lithographic process a preferred shifter width may be 150 nm-300 nm. The preferred width can be determined from test pattern simulations and measurements under a variety of conditions.  
         [0074]     Additional ways of handling the boundary vis-à-vis adjacent features and endcaps should be considered with reference to  FIG. 5 . Specifically,  FIG. 5  shows a feature  500  and a feature  510  with boundary  502  and boundary  512 , respectively. An endcap  504  on the feature  500  is shown. As can be seen the areas within the boundary  502  and the boundary  512  overlap. Also shown is a portion of the minimum boundary  514  associated with the feature  510  (heavy dotted and dashed line). The minimum boundary  514  represents a minimum shifter width for use in defining the feature  510 . A cutting protection region  520  is shown (checkered pattern) on either side of the endcap  504 . This region includes a minimum separation away from the top edge of the boundary  502  (e.g. the vertical direction in  FIG. 5 ). It is also sufficiently wide in the other direction (e.g. horizontal direction in  FIG. 5 ) to admit cuts, e.g. width of boundary  502 . However, any area that must be included in accordance with the minimum boundary  514  is taken out of the cutting protection area as seen by the end of the cutting protection  520  at the minimum boundary  514  to ensure that there will be adequate shifter width to define the feature  510 . Thus, the cutting protection  520  ensures that there is adequate room to admit a straight line cut to the right (or left) of the endcap  504  while also allowing the definition of the feature  510  using phase shifting.  
         [0075]     Shifter Sizes and Shapes  
         [0076]     Turning to  FIG. 6 , the basic shifter shape will be considered. Specifically, a feature  600  is shown with an associated shifter  610  placed adjacent to the feature. The shifter  610  has, at this point, not yet been assigned phase. At this point, shifter  610  is a rectangular shape with a trapezoid sitting on “top” of the rectangle. The edges of the trapezoidal portion are at 45 degrees to accommodate a cut. However, more generally any design rule compliant angle can be used. Another aspect of the shifter shape is it permits an adjacent cut to remain open even when the shifter directly abuts the base of the cut (see discussion of  FIG. 22 ). The direction from the base of the shifter  610  abutting the feature  600  to the top of the shifter will be referred to as the (shifter) width as it is the relevant dimension for controlling the critical dimension (CD) of the feature  600 . Additionally, for smaller shifters, the trapezoidal portion can be omitted provided the shifter meets the minimum width requirements.  
         [0077]     The shifter  610  has been positioned along the edge that abuts the feature  600  so that a minimum distance d 1  has been maintained between the ends of the shifter and the next corner or, in this case, edge. The minimum distance d 1  should be of adequate size to admit a cut. In one embodiment, this distance is different for an inner versus an outer corner general form of Equation 1. 
 
Inner Corner (1+{square root}{square root over (2)}/2) dim  
 
Outer Corner ({square root}{square root over (2)}/2) dim    (1) 
 
 where dim is the minimum dimension permitted. More generally the form is a multiple r&gt;0.0 of the minimum dimension. 
 
         [0079]     Similarly, the shifter  610  is first placed with the rectangular portion at the minimum allowed shifter width, d 2 . (This is the vertical direction in  FIG. 6  along the axis from the base of the shifter towards the base of the trapezoidal region.) This minimum shifter width is derived from design rule parameters, e.g. minimum dimension. From a lithographic perspective, this may not be of a size sufficient to define the feature (e.g. the feature  600 ) in conjunction with the other shifters (not shown in  FIG. 6 ) and the trim layer (also not shown). In one λ=248 nm process, d 2  is 0.06 μm.  
         [0080]     Also, as seen in  FIG. 6  it may be useful to maximize shifter length, d 3 , as the starting length for the shifter  610 , shown as the length along the top edge of the shifter  610  in  FIG. 6 . When the minimum width d 2  is used but d 3  is maximized, the trapezoidal portion of the shifter will generally predominate as seen in  FIG. 6 . Further, this shifter placement sets up the desired cutting positions. On an inner corner, only the single cut seen in  FIG. 1  is available. On an outside corner, the shape of the shifter  610  allows the cut to come from any angle, including the forty-five degree angle shown in  FIG. 2 . More specifically, turning briefly to  FIG. 10 , where the outer corner of a feature  1000  is shown with shifter  1002  and shifter  1004  the arrows show that the outer corner cut can be placed at any angle based on the shifter positioning. Note also that the shifter  610  has been maximized in overall width to touch the boundary (heavy dashed lines). In some situations it may not be possible to expand the shifter to reach the boundary while maintaining a trapezoidal shape in which case the shifter shapes shown in  FIGS. 11-13  can be used as appropriate.  
         [0081]     Turning to  FIG. 7 , a feature  720  and a feature  700  that are part of a layout are now visible in the figure along with a shifter  730  and a shifter  710 , respectively. The shifter  710  and the shifter  730  are in close proximity. Here, the separation between the respective shifters is less than the minimum separation, d 4 . In some embodiments, d 4  corresponds to a minimum separation design rule and/or one or more lithographic parameters relating to minimum separation. In some embodiments of the invention, shifters are merged as shown in  FIG. 8  with the shifter  710  and the shifter  730  merged into a shifter  810 , shaped as shown. In some embodiments, notch filling may also need to be performed as described in conjunction with  FIG. 9 , e.g. to remain design rule compliant.  
         [0082]      FIG. 9  illustrates a similar configuration to that found in  FIG. 7  however here, the two original shifters, the shifter  920  and the shifter  910  adjacent to the feature  720  and the feature  900 , respectively, are abutting one another leaving notches, the notch  930  and the notch  932 . Some embodiments of the invention merge the shifters and fill such notches, as shown by the dashed lines. The width of the filled notch corresponds to the length over which the two shifters are less than, or equal to, d 4  apart in some embodiments.  
         [0083]     Reshaping of Shifters  
         [0084]     Turning to  FIGS. 11-13 , the reshaping of a shifter placed as described in  FIG. 6  during the processing of the layout according to embodiments of the invention will be considered.  FIG. 11  shows a feature  1100 , a contact landing pad, and two of the cuts as dashed lines for the cut  1104  and the cut  1106 . (The other cuts are omitted for clarity of illustration.) The outer edge of the cuts also show where the boundary, or preferred shifter width, would fall. (Emphasized by the heavy dashed line in  FIG. 11  only.) As can be seen in  FIG. 11  the shifter  1102  is placed at the minimum width, and length, with enough room to accommodate the cut  1104  and the cut  1106 . However, if the sides of the trapezoids are maintained at a forty-five degree angle then the shifter cannot fill the entire shifter width to the boundary while maintaining the shapes shown in  FIGS. 6-9 .  
         [0085]     During the processing of the layout, as will be described more fully in connection with  FIG. 25 , the shifter can be increased in size to the maximum width, as seen in  FIG. 12 . Here, the shifter  1202  is shown. In one embodiment, the reshaping of  FIG. 12  is only performed if the boundary abuts the field of the layout. Further, as appropriate one or both of the surrounding areas between the shifter and the cuts can be incorporated into the shifter. The circumstances where this would be appropriate will be described in greater detail in conjunction with  FIG. 25 .  FIG. 13  shows the expanded shifter as three separate shifters, the shifter  1302 , the shifter  1304 , and the shifter  1306 . In the final output layout these will have the same phase and can, if appropriate, be merged into a single polygon representing the entire shifter. It should also be noted that the combined shape of the three shifters is similar to the shape of the shifter in  FIG. 6  rotated so that the trapezoidal portion is adjacent to the original feature.  
         [0086]     Cost Functions  
         [0087]     Turning to  FIGS. 14-17  cost functions used by embodiments of the invention will now be considered in greater detail. The cost functions can be used to describe the relative “badness” (or “goodness” depending on how the function is formulated) of accepting a particular configuration. For purposes of cost functions, a conflict is an arrangement of shifters on a phase layer of a layout that will cause a (desired) feature to either fully or partially fail to resolve. In addition to reducing conflicts, cost functions can be used to cause embodiments of the invention to prefer one configuration over another based on the relative cost of two choices. The use of the cost functions in designing the phase layer will be described in greater detail in connection with  FIG. 25 .  
         [0088]      FIG. 14  illustrates a conflict caused by overlapping same phase shifters. Specifically, in  FIG. 14 a  feature  1400  is surrounded in part by a shifter  1402  and a shifter  1404 , both the same phase. The two shifters are separated by distance  1420 , e.g. the width of the feature  1400 . The region the two shifters overlap in is the overlap  1410 . One way to express the cost of allowing this phase conflict is a formula of the general form of Equation 2.  
             r   ⁢     overlap       (     distance   -   dim     )     +   ɛ               (   2   )               
 Where overlap is the measurement of the phase conflict length (e.g. overlap  1410 ), distance is how far apart the shifters are (e.g. distance  1420 ), dim is the minimum feature width for the design, ε is the minimum grid size, and r&gt;0.0 is an implementation dependent ratio, according to one embodiment r=1.0 for a straight line shifter conflict. Thus, if the shifter  1402  and the shifter  1404  are the same phase and the length over which they overlap is large, the cost of permitting the conflict to remain in the layout is high. 
 
         [0090]     The two-edge case has two basic forms: inner corner,  FIG. 15 , and outer corner,  FIG. 16 , and refers to an inner or outer corner. In the two-edge case some embodiments of the invention prefer to avoid cutting the phase region. Thus, in such embodiments, the cost function is designed to associate a greater cost with dividing the shifter  1502  and the shifter  1504  (that partially define the feature  1500 ) as opposed to having a single large (same-phase) shifter. The same goal is true with respect to  FIG. 16  and the shifter  1602  and the shifter  1604  (that partially define the feature  1600 ).  
         [0091]     More specifically, equations of the general form of Equation 3 can be used:  
             r   ⁢     1     min   ⁡     (       d   01     ,     d   12       )                 (   3   )             
 
 For either inner or outer corner computations where d 01  is the length of one of the two edges and d 12  is the length of the other and r&gt;0.0. Returning to  FIG. 15 , the distance  1520  and the distance  1530  would correspond to d 01  and d 12 , respectively. Similarly, in  FIG. 16 , the distance  1620  and the distance  1630  would correspond to d 01  and d 12 , respectively. The ratio r used is implementation dependent. According to one embodiment, r=16.0 for outer corners and 6.0 for inner corners. 
 
         [0093]     The three-edge case is illustrated by  FIG. 17  and occurs when there are an inner and an outer corner in close proximity to one another, e.g. a “staircase” step. The feature  1700  has an edge with a distance  1720  that is insufficient to admit placement of a shifter shape according to the parameters described above in connection with  FIG. 6 . The preference is to assign all three edges the same phase, e.g. have a single contiguous shifter. Cost equations of the general form of Equation 4 can be used:  
             r   ⁢     1     d   12               (   4   )             
 
 where r&gt;0.0 and d 12  corresponds to the length of the short edge, e.g. the distance  1720  in  FIG. 17 . The ratio r used is implementation dependent. According to one embodiment, r=5.0. 
 
         [0095]     Additionally, some embodiments of the invention proscribe a cost function for small shifter areas. Take for example the situation of  FIG. 18  where two small shifters, e.g. the shifter  1800  and the shifter  1810 , are in close proximity. Such small shifters may be difficult to manufacture in the mask and it may be desirable to encourage them to be joined into a single, larger shifter. Such a cost function can be of the general form of Equation 5:  
             r   ⁡     (       1   a1     +     1   a2       )             (   5   )             
 
 where “a1” is the geometrical area of a first shifter within a given distance, e.g. n nanometers, of the current shifter and “a2” is the area of the current (small) shifter. For example, if the shifter  1800  is the current shifter, its area would be given by a2 while the area of the shifter  1810  would be given by a1. In one embodiment, r=0.07. As noted, the cost for all shifters within a given distance can be computed and/or the value of r can also be varied over distance, e.g. further away shifters use a lower r value. 
 
         [0097]     Further, although the cost functions are shown as relating to a single ratio, r, in fact multiple ratios can be used. For example, in one embodiment, the value of r can be selected based on the other elements of the equation, e.g. if distance&gt;120 nm, r=8.0 for an outer corner, but if distance&gt;240 nm, r=4.0, etc. This can be used if no particular distance/area cutoffs are used when computing costs and/or to further modulate the relative costs based on the declining penalty for conflicts at greater distances. In other embodiments, the size of adjacent feature regions is relevant to the value of r. For example, if a cut will touch a relatively large region, e.g. a contact landing pad, it may be more desirable to allow a cut in that location than if the cut touches a smaller region, e.g. the T intersection. For example, consider the cut location  1840  in  FIG. 18  adjacent to a large polysilicon region versus the cut location  1940  adjacent to a smaller polysilicon region. Thus in some embodiments, the value of r for large regions may be less than the value of r used for smaller adjacent regions because a phase conflict can be more easily corrected with OPC in larger regions.  
         [0098]     Other embodiments of the invention use information from multiple layers in defining and selecting appropriate cost functions. Turning briefly to  FIG. 21  which shows a layout  2100 , if a small rectangular area (e.g. the ends of the feature  2110  or the end of the feature  2120 ) was determined to be a contact landing pad, a different cost function could be selected. According to one embodiment of the invention, when contact landing pads are detected, there is a preference as expressed by the formulation of the cost function to use the maximum number of cuts to improve printing of the region. Other examples include avoiding cuts adjacent to the diffusion regions that define transistors, e.g. at a T-junction, etc. (see  FIG. 19  where diffusion  1910  forms a gate with feature  1900  and a cutting location  1940  is indicated). Some other rule types might include via layer-metal layer interaction detection to ensure electrical connectivity as well as for local interconnect-polysilicon interactions.  
         [0099]     Ultimately, the cost functions may be used by embodiments of the invention during the process of  FIG. 25  and more particularly during steps  2540  and  2545 , which will be described in greater detail below.  
         [0100]     Branch and Bound  
         [0101]     A brief discussion of branch and bound algorithms will be provided as some embodiments of the invention make use of the same for solving the phase assignment problem. There are a number of varieties of branch and bound algorithms that are well known. In one embodiment, the branch and bound algorithm in the abraCAD(TM) software from Cadabra Design Automation, a Numerical Technologies Company, San Jose, Calif., is used.  
         [0102]     The phase assignment problem can be set up for branch and bound by viewing the problem as selecting a single path from 2 n  possible paths in a tree (representing the search space) where n is the number of phase shifters in a given layout, or layout region, being processed for phase assignment. Initial phase assignments can be provided for one or more phase shifters to start the process and provide initial costs. The solver searches the solution space while simultaneously bounding the search space, e.g. by eliminating paths that appear to result in high costs. This allows the continued branching (search) of portions of the solution space that result in lower costs.  
         [0103]     The stopping point can be user selected: run until minimum reached, phase assignment cost below a threshold value, for a given period of time and then select lowest cost found at that point, etc. Additionally, advantageously, branch and bound can generally be performed in parallel if sufficient computing resources are available.  
         [0104]     Alternatively, graph based algorithms can be used to solve the phase assignment problem as appropriate using weighted graph edges and graph coloring algorithms.  
         [0105]     Now, the process of defining the phase layers and complimentary trim layer will be considered in greater detail.  
         [0106]     Process Flow  
         [0107]     Turning to  FIG. 20 , a process flow for preparing a layout is shown. The process of  FIG. 20  can be used in conjunction with the process of  FIG. 25  to design a phase layer and trim layer to substantially define a pattern of a layout using phase shifting. The resultant layouts can be used to define phase shifting masks, and corresponding trim masks, that can in turn be used in lithographic processes to define integrated circuits.  
         [0108]     The process starts at step  2000  as the maximum shifter area is determined. This is simply the preferred shifter sizes, e.g. a given distance n nm from the structures to be defined. As described in conjunction with  FIG. 4-5 , this can be computed after identification of endcaps. For one sample k=248 nm process, the preferred shifter area is 150-300 nm. The particular value of n can be determined from simulations and/or test mask exposures and will be lithography process, design, and layout dependent.  
         [0109]     Turning to  FIG. 21 , a layout  2100  is shown including two features, a feature  2110  and a feature  2120 .  FIG. 21  shows the layout after the endcaps, endcap  2112  and endcap  2122 , have been identified. Then, in  FIG. 22 , the layout  2200  is shown that includes the layout  2100  and a boundary  2230  defining the maximum, or preferred, shifter width to use in defining the features as a heavy dashed line.  
         [0110]     Next, at step  2005 , several intermediate values and/or shapes can be computed for later use. In some embodiments, these values and/or shapes are computed only as needed. The following values and/or shapes are pre-computed according to one embodiment: 
            non-field=shifter shapes+original layout         field=area within the boundary−non-field        
 
         [0113]     These values and/or shapes can then be more easily used in subsequent steps. Similarly, the locations of non-critical areas can be identified. For example, all minimum size regions such as wire bends (corner of L), intersections of wires (T), and other non-minimum width features can be identified; all of which can be considered non-critical.  
         [0114]     Next, at step  2010 , the locations of cuts from the field are determined. This is easy understand with respect to  FIG. 23  where the layout  2300  is shown including cuts from the boundary  2230  inward towards the field in a predefined cut shape (see  FIG. 3 ) at each corner of the boundary  2230 . As can be seen, some of the locations of the cuts would overlap the features, e.g. near endcaps. Other cuts, e.g. the cut  2310 , are notable as the cut only exists because of how the line ends are handled and the cut is not generated by step  2015 . Other similar examples include the cut  2312  and the cut  2314 . In contrast a number of the other cuts, e.g. the cut  2316 , occur both at a corner of the boundary and a corner of a feature. Thus, the cut  2316  is also found at step  2015 .  
         [0115]     The process continues at step  2015 , with the identification of corner cut shapes, e.g. from the corners features to the boundaries. This is shown in  FIG. 24 , including the layout  2400 . In  FIG. 24 , the boundary edge has been made thinner to emphasize that the cut locations are determined by the corners of the features. Again, as compared to  FIG. 23 , several additional cut locations are found, e.g. the cut  2410 . Again, as in step  2010 , the cut shape is in accordance with the shape seen in  FIG. 3 . The step  2010  and step  2015  can be done in parallel, out of order with respect to one another, and/or combined into a single step.  
         [0116]     Additionally, in some embodiments, possible cuts are computed along non-critical portions of features, e.g. the back of the T in  FIG. 19  (not shown). In one embodiment, these cutting locations can be computed in conjunction with the determination of non-critical regions at step  2005  of the process of  FIG. 20 . If that option is selected, then for each edge, cuts of the minimum width centered about the middle of the non-critical region can be computed for later use as an additional step of  FIG. 20  (not shown).  
         [0117]     As noted the process of  FIG. 20  is preparatory in nature. In some embodiments, the entire process is omitted with values computed during the process of  FIG. 25  on an as needed basis. Upon completion of the process of  FIG. 20 , the process of  FIG. 25  is then commenced. From a conceptual point of view, at the start of process  FIG. 25 , the layout being operated on is the layout shown in  FIG. 21  and all of the values computed during the process of  FIG. 20  are preserved, e.g. in extra layers of the layout, memory, etc.  
         [0118]     The process of  FIG. 25  starts at step  2520  with initial placement of shifter shapes. For illustration purposes, several cutting locations are shown as dotted outlines. In one embodiment, the shifters are placed according to the basic shape shown in  FIG. 6 . The shifter shapes are placed along each edge of the layout, e.g. the layout  2600  in  FIG. 26 . Turning first to the shifter  2610 , it was placed abutting the edge of the adjacent feature. The shifter size is maximized while obeying the distance to edge constraint d 1  (see  FIG. 6 ). As can be seen if the shifter, e.g. the shifter  2610 , cannot be extended to the preferred width, the extension approach shown in  FIGS. 11-13  can be used. Additionally, if there are two cuts in region (e.g. left hand side of shifter  2614 ) then the shifter will ensure that both remain open (this effect may be implicit in the value of d, for inner and outer corners.).  
         [0119]     Also, note that  FIG. 26  does not show merger of shifters, e.g. the shifter  2612  and the shifter  2614 . Which can happen as part of step  2520  and/or step  2525 . Additionally, as noted, the shifter shapes are designed to admit a cut. This is shown in  FIG. 26  by the shifter  2620 , for example. Here, the shifter comes quite close to the adjacent shifter as shown in the region  2625  (shown as a dashed circle), but the angles of the trapezoidal portion of the shifter  2620  admit the cut. Similarly outer corners admit cuts as shown in  FIG. 10  from all angles.  
         [0120]     The process then continues at step  2525  with the filling open spaces and shifter mergers. Shifter merging and notch fill was described above with respect to  FIGS. 7-9  and that process can occur at this step (or it could have been performed as part of step  2520 ). For example, the shifter  2612  and the shifter  2614  can be merged and notch filled at this step to form the shifter  2714  shown in the layout  2700  of  FIG. 27 . Additionally, open spaces such as corners near endcaps can be removed as seen in  FIG. 27  where the formerly open space adjacent to the shifter  2620  is now filled (e.g. filled open space  2725 ). More generally, the process can be best understood if the cuts are removed from view as seen in  FIG. 27  and each open space is considered. Take for example the open space  2730 . As can be seen the open space touches three distinct phase shifters. This makes that open space an unsuitable candidate for filling at this step. The requirement is that the space touch only one shifter or only one non-critical shape.  
         [0121]     Other open spaces adjacent to shifters have been filled in  FIG. 27  as well (reference numerals omitted). Additionally, although the filled open spaces are shown as distinct triangular polygons in  FIG. 27 , the shifter shape can be formed as single or multiple polygons depending on the formats supported by the layout description format (see, e.g., the single polygon used for the shifter  2620  and the filled open space  2725  in  FIG. 28 ).  
         [0122]     At step  2530 , the process continues with filling making use of forty-five degree cuts. This involves filling shifters, e.g. as seen in  FIG. 12 . However, it is undesirable to simply fill all corners. In one embodiment, the test to determine whether or not the space is filled is: (i) will the filled area remain design rule compliant, (ii) will the expanded shifter touch two non-critical areas (field or non-critical features). The relevant non-critical features can easily be computed at this step. The non-critical features comprise those portions of the original layout not abutting a shifter and field. The cleanup provided at step  2530  can be seen in layout  2800  of  FIG. 28  where a number of the forty-five degree shifters have been filled, e.g. fill  2810 , fill  2812 , and fill  2814 . But, note that region  2820 , region  2822 , and region  2824  did not get filled. In the case of the region  2822  and the region  2824 , a shifter merger would have occurred. In the case of the region  2820 , the region abuts two cuts and so it is kept open. More specifically in some embodiments, the shifters are expanded if the area touches one cut, at most one shifter, the field, and at most two corners of the original layout.  
         [0123]     Next, at step  2535  the process loops on the above steps ( 2525 - 2530 ) until the process is complete and then continues at step  2540 . The stopping criteria can include whether or not changes were made to the shifter shapes during the previous pass through the loop, a fixed number of iterations, other stopping criteria and/or combinations of the above, e.g. loop at most 5 times but stop as soon as no changes are made.  
         [0124]     The specific breakdown and components of the steps  2520 - 2535  can be altered; however, at the time step  2540  has begun the shifter shapes should be established and to the extent practical at a maximal size (width, length, filled open spaces, etc.). That is because steps  2540 - 2565  primarily assign phase rather than reshape and/or redefine shifters.  
         [0125]     The process continues at step  2540  with the determinations of phase dependencies and computations of cost functions. As described above in connections with  FIGS. 14-19 , cost functions describe the relative badness (or goodness depending on the formulation) of permitting a particular type of phase assignment to different shifters. As noted, the cost functions can be layer sensitive, have different formulations for different distances of interaction, etc. Note, that to provide a useful reduction in processing costs, the layout can be grouped into small regions, or clusters, for processing throughout the process of  FIG. 25 . The benefits of clustering though are most apparent during step  2545 , e.g. if branch and bound is used then the value of n will be smaller for a portion of a layout than for the entire layout. In one embodiment, a cluster comprises a region of layout within a single boundary polygon, thus a single layout might have hundreds, or thousands, of clusters.  
         [0126]     At step  2545 , phase assignment is performed. According to one embodiment, a branch and bound type algorithm is used, see above. In the process, the specific cuts that will actually be used are determined. For example if two shifters are separated by a cut, but are assigned the same phase, they can eventually be merged. Turning to  FIG. 29 , the layout of  FIG. 28  is shown as the layout  2900  with initial phase assignments.  
         [0127]     Next, at step  2550 , shifters can be enlarged and cuts filled. In one embodiment, this is performed by growing the original layout towards the boundary and then computing the open spaces. If a given open region touches shifters of all one phase then that region can be filled with that phase. Contrast, for example, the region  2910  (touching two different phased shifters) with the region  2912  (touching two same phased shifters). If appropriate other algorithms can be used to identify the open regions, or spaces, which can be filled according to this step.  
         [0128]     The results of step  2550  are shown in  FIG. 30  where the layout  3000  shows that the shifters have been enlarged to fill the cut spaces. As noted, the region  2910  is not filled by this step because the phase of the adjacent shifters are different.  
         [0129]     The process continues at step  2560  with the removal of small shifters. This can be based on a predetermined sizing criteria. For some layouts this will result in open spaces that can be filled with the dominant, or subordinate, phase when the process continues at steps  2570  and  2580 , respectively. The example layout does not have any shifters to be removed at step  2560  and so the layout is not modified by step  2560 .  
         [0130]     Next, at step  2570 , further refinement of the shifters occurs. This includes flood filling cuts with the dominant phase of the adjoining areas. Turning briefly to the layout  3100  of  FIG. 31 , a shifter  3110  and a shifter  3120  define a feature  3160  similar to the feature  2120  seen in the other layouts; however due to the absence of feature  2110  in the layout  3100  there are shifters all around the large region of the feature  3160  in  FIG. 31 . The layout  3100  has been processed according to the process of  FIG. 20  and the process of  FIG. 25 . After step  2550 , the shifter shapes shown of the shifter  3120  and the shifter  3110  have been established. At step  2560 , the flood fill  3130  and will be converted from open space to shifters. The decision to make the phase of shifter  3110  the dominant phase in the cutting region of the cut  3150  can be based upon a number of factors: the total area and phase of surrounding phase shifters, relative edge length of shifters abutting the open space, etc. Here, the phase of the shifter  3110  was determined to be dominant, e.g. from edge length abutting the formerly open space.  
         [0131]     As can be seen in  FIG. 31 , one effect of selecting the dominant phase can be to determine the position of the resulting cut, e.g. the cut  3150 . In  FIG. 31 , the cut  3150  is vertically oriented and abuts the shifter  3120 . If however the shifter  3120  had been found to have the dominant phase, then the resulting cut would have been horizontally oriented and adjacent to the shifter  3110 .  
         [0132]     As part of step  2570 , any minimum spacing or minimum edge length violations created during the flood fill of step  2570  can be corrected (not shown in  FIG. 31 ). Turning to  FIG. 32 a  portion of a simple layout processed in a similar fashion to the layout of  FIG. 31  is shown. In  FIG. 32 , a feature  3200  and a feature  3210  have the shifter  3220 , the shifter  3230  and the shifter  3240  placed around the features to define the features. At step  2570 , the shifter  3250  and the shifter  3260  were added during the flood fill with the dominant phase. This leaves a sharp corner that is not design rule compliant on the shifter  3250  where it abuts the cut. During step  2560 , that corner can be removed as shown by the shifter  3330  of  FIG. 33 . However, this removal in turn makes the opening larger than is absolutely necessary at the top, e.g. larger than the minimum separation between shifters.  
         [0133]     During step  2580 , the subordinate phase can be used to make the cut opening between the shifter  3330  and the shifter  3340  the minimum allowed separation throughout by filling open spaces using the subordinate phase, thus adding a shifter  3350  as seen in  FIG. 33 . As in step  2570 , spacing and edge length violations can be corrected after the fill.  
         [0134]     Looking at  FIGS. 31-33  it can be seen that the cut shapes, while design rule compliant, are relatively complex and may present slight difficulties for mask manufacturing, inspection, etc. Accordingly, some embodiments of the invention include a step in the process of  FIG. 25  (not shown) to square off shifter shapes. This will result in straighter cuts as seen in  FIG. 34  where the layout of  FIG. 32  has been squared (square off  3410  and square off  3420 ) and then step  2470  was applied resulting in flood fill  3430  and flood fill  3440 . Note also that step  2580  will not result in any changes to the layout of  FIG. 34  as there will be no additional open space to fill. Note also that the resulting cut is easy to manufacture.  
         [0135]     More specifically, the square off step can occur any time after phase assignment and in one embodiment occurs between step  2560  and step  2570 . In one embodiment the criterion for squaring off a shifter is that the square off section to be added back is neither (i) touching or adjacent within a predetermined separation to a shifter of a different phase nor (ii) overlaps with any other square off sections. Also the square off can include two possible square off for shifters of the type shown in  FIG. 12 , e.g. shifter  1202 . Specifically, one square off could make the trapezoidal region rectangular while leaving the top unchanged. Also, the top portion could then be separately squared with the filled in formerly trapezoidal section. This type of double square off can be seen in  FIG. 35  just above the cut  3510  where the squared off portion is shown as a separate shifter shape for illustrative purposes.  
         [0136]     The results of step  2560  and step  2570  for the layout of  FIG. 30  are shown as layout  3500  in  FIG. 35  (note that the square off procedure described above was used.). Note the square off of the shifters around the cut  3510 , e.g. square off  3520 , followed by the fill with the dominant phase, e.g. fill dominant  3530 . The process then continues to step  2580  where the flood fill is repeated; however, this time the subordinate, rather than dominant phase is used in deciding which regions to fill. In other respects, step  2580  is identical to step  2570 . In the example layout shown, there is no additional filling to occur at step  2580 .  
         [0137]     At this point, according to some embodiments of the invention, processing of the layout is complete.  
         [0138]     The trim layout, or layer, can be derived from the phase layer. This is shown for the layout of  FIG. 35  in  FIG. 36  as shown by the trim  3610  in layout  3600  (note the outline of the original features are shown with a dotted outline and the phase layers shown in the background for reference). In one embodiment this can be a simple geometric computation based on the shifter shapes+original layout shrunk by a slight shrink, e.g. 0.02 μ, with the original layout then added back in. The amount of the shrink can be determined based on the given process including sufficient tolerances for mask misalignment, exposure conditions, etc. For example, by using different doses for the phase and trim layer, the size of the openings in the trim layer can be smaller than might otherwise be acceptable to clear phase artifacts. See, e.g. U.S. Patent Application No. 09/972,428 entitled “Exposure Control For Phase Shifting Photolithographic Masks” having inventors Christophe Pierrat, et. al., filed 5 Oct. 2001.  
         [0139]     Turning to  FIG. 37  the complete layout  3700  for the phase shifting mask is shown with the phase shifters as light transmissive regions (shifter  3710 , shifter  3720 , and shifter  3730 ) and opaque protective material (e.g. chrome) elsewhere on the mask. For illustrative purposes the outlines of the original features are shown as a dotted outline. As noted the shifter  3710  may be in one layer of the GDS-II output file containing the mask description while the shifter  3720  and the shifter  3730  are in another (e.g. 0 in one layer, 180 in the other). Additionally, but not shown, the cuts could be continuous phase and/or multiphase light transmissive regions, e.g. 0-180 gradually, 90 in cuts, 60 and 120 in cuts, and/or some other combinations.  FIG. 38  illustrates the complete trim layout  3800  for the complementary trim mask showing the trim  3610 . Additionally, as was originally noted in conjunction with  FIG. 2 , it is possible to use a diagonal rather than notched opening on the outer corner, shown as a dotted line for alternate corner  3810 .  
         [0140]     Also, some additional post processing may be required and/or desirable to for compliance of the layouts with design and mask manufacturing rules. For example, turning to the layouts of  FIG. 37  and  FIG. 38 , there is an extremely short edge in both the shifter and trim layers adjacent to the region of the cut  3510  (see  FIG. 35 ). This edge may be removed by extending the width of the trim and shifter along the edge perpendicular to that short edge to eliminate the short edge, shown only on trim layer in  FIG. 38  as a dashed line for post processed edge  3820 .  
         [0141]     Representative Alternative Embodiments  
         [0142]     Additionally, although the description has primarily focused on examples of defining a polysilicon, or “poly”, layer within an IC, phase shifting can be used to define other layers of material, e.g. interconnects, metal, etc.  
         [0143]     In some embodiments, different shapes created by intermediate and final processing steps are maintained in different layers of a single data file. For example, if the GDS-II stream format is used, the original layout could be maintained in a first layer, the zero degree shifters in a second layer, the 180-degree shifters in a third layer, and the trim layer in a fourth layer. In other embodiments, multiple data files are used for separating relevant information. Additionally, as seen in the figures, the results of intermediate processing steps can be output and viewed to better understand the shifter shaping and assignment process for a given layout.  
         [0144]     In some embodiments, the resultant layout comprises a layout where at least one of: 
        eighty percent (80%) of non-memory portions in one layer of material in the layout;     eighty percent (80%) of a part of the floorplan in one layer of material;     eighty percent (80%) of cells in a given area;     ninety percent (90%) of a layer of material;     ninety five percent (95%) of a layer of material;     ninety nine percent (99%) of a layer of material;     one hundred percent (100%) of a layer of material;     one hundred percent (100%) of a in a functional unit of the chip (e.g. ALU) in one layer of material;     one hundred percent (100%) of features in a layer of material that are in the critical path of the design;     one hundred percent (100%) of features in a layer of material above or below certain dimensions, e.g. all features with a critical dimension 50 μm&lt;CD&lt;100 μm;     everything in a layer of material except those features that cannot be phase shifted due to phase conflicts that cannot be resolved;     everything in a layer of material except test structures; and     one hundred percent (100%) of all non-dummy features, e.g. features providing structural support for processing purposes, and non-electrically functional features in a layer of material 
 
 are defined using phase shifting. Further it should be understood that even when a feature is substantially defined using the phase shifting mask (e.g. the feature  3160  in layout  3100  of  FIG. 31 ) portions of the feature at cut openings and end-caps are defined by the complimentary mask. Therefore, features such as the feature  3160  are considered to be defined using the phase shifting (or using the “phase shifting mask”). 
       
 
         [0159]     Embodiments of the invention can include manufactured masks and/or mask sets fabricated according to the layouts defined according to embodiments of the invention. For example, the layouts of  FIG. 37  and  FIG. 38  could be processed by mask data preparation software such as CATS(TM) from Transcription Enterprises, Inc., a Numerical Technologies company, San Jose, Calif. to produce mask data files in formats suitable for use by mask writing and fabrication machines. Embodiments of the invention include finished integrated circuits including a layer of material defined by masks constructed from layouts defined according to embodiments of the invention.  
         [0160]     Embodiments of the invention include a method of manufacturing a layer of material an integrated circuit. One wafer fabrication process used in such embodiments comprises: applying a photoresist layer to the top surface of a wafer; baking the photoresist layer; positioning the first mask over the photoresist layer; exposing the photoresist layer through the first mask; positions the second mask over the photoresist layer; exposing the photoresist layer through the second mask; baking the wafer; developing the photoresist layer; chemical etching or ion implantation; and removing the photoresist layer. Additional layers of material can be similarly defined. The first and second mask are the phase shifting mask and complimentary mask created from the layouts described above. For example the first mask could be a mask constructed from the layout  3700  of  FIG. 37  and the second mask could be a mask constructed from the layout  3800  of  FIG. 38 . The mask exposure order can be reversed according to one embodiment of the invention, e.g. complimentary mask exposed then phase shifting mask.  
         [0161]     Some embodiments of the invention include computer programs for performing the processes of  FIG. 17 . In one embodiment, the process is implemented using the abraCAD(TM) software produced by Cadabra Design Automation, a Numerical Technologies company, San Jose, Calif. In one embodiment, the process is described using an AL language program inside the abraCAD(TM) software. In some embodiments, the computer programs are stored in computer readable media, e.g. CD-ROM, DVD, etc. In other embodiments, the computer programs are embodied in an electromagnetic carrier wave and/or computer data signal. For example, the electromagnetic carrier wave and/or computer data signal may include the programs being accessed over a network.  
         [0162]     As used herein, the terms lithography and/or optical lithography refer to processes that include the use of visible, ultraviolet, deep ultraviolet, extreme ultraviolet, x-ray, e-beam, and/or other radiation sources for lithography purposes.  
         [0163]     Conclusion  
         [0164]     The foregoing description of embodiments of the invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations will be apparent. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others to understand the invention for various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims.