Abstract:
In the field of semiconductor device production, a method and system for fracturing or mask data preparation or optical proximity correction are disclosed, in which a target maximum dosage for a surface is input, and where a plurality of variable shaped beam (VSB) shots is determined that will form a pattern on the surface, where at least two of the shots partially overlap, and where the plurality of shots are determined so that the maximum dosage produced on the surface is less than the target dosage. A similar method is disclosed for manufacturing an integrated circuit.

Description:
RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 13/300,601 filed Nov. 20, 2011 entitled “Method For Design And Manufacture Of Diagonal Patterns With Variable Shaped Beam Lithography” and issued as U.S. Pat. No. 8,329,365, which is a continuation of U.S. patent application Ser. No. 12/750,709 filed Mar. 31, 2010 entitled “Method For Design And Manufacture Of A Reticle Using A Two-Dimensional Dosage Map And Charged Particle Beam Lithography” and issued as U.S. Pat. No. 8,062,813, both of which are hereby incorporated by reference for all purposes. U.S. patent application Ser. No. 12/750,709: 1) is a continuation-in-part of U.S. patent application Ser. No. 12/540,328 filed Aug. 12, 2009 entitled “Method For Design and Manufacture of a Reticle Using a Two-Dimensional Dosage Map and Charged Particle Beam Lithography” and issued as U.S. Pat. No. 8,017,286; 2) is a continuation-in-part of U.S. patent application Ser. No. 12/202,364 filed Sep. 1, 2008 entitled “Method and System for Manufacturing a Reticle Using Character Projection Particle Beam Lithography” and issued as U.S. Pat. No. 7,759,026; 3) is a continuation-in-part of U.S. patent application Ser. No. 12/473,241 filed May 27, 2009, entitled “Method for Manufacturing a Surface and Integrated Circuit Using Variable Shaped Beam Lithography” and issued as U.S. Pat. No. 7,754,401; and 4) is related to U.S. patent application Ser. No. 12/540,323 filed Aug. 12, 2009, entitled “Method For Design And Manufacture Of A Reticle Using Variable Shaped Beam Lithography” and issued as U.S. Pat. No. 7,799,489; all of which are hereby incorporated by reference for all purposes. 
    
    
     BACKGROUND OF THE DISCLOSURE 
     The present disclosure is related to lithography, and more particularly to the design and manufacture of a surface which may be a reticle, a wafer, or any other surface, using charged particle beam lithography. 
     In the production or manufacturing of semiconductor devices, such as integrated circuits, optical lithography may be used to fabricate the semiconductor devices. Optical lithography is a printing process in which a lithographic mask or photomask manufactured from a reticle is used to transfer patterns to a substrate such as a semiconductor or silicon wafer to create the integrated circuit. Other substrates could include flat panel displays or even other reticles. Also, extreme ultraviolet (EUV) or X-ray lithography are considered types of optical lithography. The reticle or multiple reticles may contain a circuit pattern corresponding to an individual layer of the integrated circuit and this pattern can be imaged onto a certain area on the substrate that has been coated with a layer of radiation-sensitive material known as photoresist or resist. Once the patterned layer is transferred the layer may undergo various other processes such as etching, ion-implantation (doping), metallization, oxidation, and polishing. These processes are employed to finish an individual layer in the substrate. If several layers are required, then the whole process or variations thereof will be repeated for each new layer. Eventually, a combination of multiples of devices or integrated circuits will be present on the substrate. These integrated circuits may then be separated from one another by dicing or sawing and then may be mounted into individual packages. In the more general case, the patterns on the substrate may be used to define artifacts such as display pixels or magnetic recording heads. 
     In the production or manufacturing of semiconductor devices, such as integrated circuits, maskless direct write may also be used to fabricate the semiconductor devices. Maskless direct write is a printing process in which charged particle beam lithography is used to transfer patterns to a substrate such as a semiconductor or silicon wafer to create the integrated circuit. Other substrates could include flat panel displays, imprint masks for nano-imprinting, or even reticles. Desired patterns of a layer are written directly on the surface, which in this case is also the substrate. Once the patterned layer is transferred the layer may undergo various other processes such as etching, ion-implantation (doping), metallization, oxidation, and polishing. These processes are employed to finish an individual layer in the substrate. If several layers are required, then the whole process or variations thereof will be repeated for each new layer. Some of the layers may be written using optical lithography while others may be written using maskless direct write to fabricate the same substrate. Eventually, a combination of multiples of devices or integrated circuits will be present on the substrate. These integrated circuits are then separated from one another by dicing or sawing and then mounted into individual packages. In the more general case, the patterns on the surface may be used to define artifacts such as display pixels or magnetic recording heads. 
     Two common types of charged particle beam lithography are variable shaped beam (VSB) and character projection (CP). In VSB charged particle beam lithography, a precise electron beam is shaped and steered so as to expose a resist-coated surface, such as the surface of a wafer or the surface of a reticle. These shapes are simple shapes, usually limited to rectangles of certain minimum and maximum sizes and with sides which are parallel to the axes of a Cartesian coordinate plane, and triangles with their three internal angles being 45 degrees, 45 degrees, and 90 degrees of certain minimum and maximum sizes. At pre-determined locations, doses of electrons are shot into the resist with these simple shapes. The total writing time for this type of system increases with the number of shots. In CP charged particle beam lithography, there is a stencil in the system that has in it a variety of shapes which may be rectilinear, arbitrary-angled linear, circular, annular, part circular, part annular, or arbitrary curvilinear shapes, and which may be a connected set of complex shapes or a group of disjointed sets of a connected set of complex shapes. An electron beam can be shot through the stencil to efficiently produce more complex patterns (i.e. characters) on the reticle. In theory, such a system can be faster than a VSB system because it can shoot more complex shapes with each time-consuming shot. Thus, an E shot with a VSB system takes four shots, but the same E can be shot with one shot with a character projection system. Note that VSB systems can be thought of as a special (simple) case of character projection, where the characters are just simple characters, usually rectangles or 45-45-90 triangles. It is also possible to partially expose a character. This can be done by, for instance, blocking part of the particle beam. For example, the E described above can be partially exposed as an F or an I, where different parts of the beam are cut off by an aperture. 
     The photomasks used for optical lithography are manufactured from reticles onto which a pattern has been formed. There are a number of technologies used for forming patterns on a reticle, including optical lithography and charged particle beam lithography. The most commonly-used system is a VSB charged particle beam system. Reticle writing typically involves multiple passes whereby the given shape on the reticle is written and overwritten. Typically, two to four passes are used to write a reticle to average out precision errors in the charged particle beam system, allowing the creation of more accurate photomasks. Conventionally, within a single pass the constituent shapes do not overlap. Multi-pass writing has a disadvantage of increasing the total time required for the charged particle beam system to form the pattern on the reticle. This extra time increases the cost of the reticles and the resulting photomasks. At present, no available CP charged particle beam system is suitable for use in making photomasks. 
     When using charged particle beam lithography either for making reticles or for direct write, individual doses or shots of charged particles are conventionally designed to avoid overlap wherever possible, and for multi-pass writing, to avoid overlap within a single pass. The dosage is assumed to be the same, or “normal,” at all parts of the formed pattern. This greatly simplifies calculation of how the resist on the reticle will register the pattern. Because of the assumed normal dosage, the fracturing programs that assign VSB shots conventionally do not output dosage information. 
     The cost of charged particle beam lithography is directly related to the time required to expose a pattern on a surface, such as a reticle or wafer. The exposure time is related to the number of shots required to produce the pattern. Patterns can often be formed in fewer shots if the shots are allowed to overlap. Additionally, patterns can be formed in fewer shots if the union of shots is allowed to deviate from the target pattern. When these techniques are used, calculation of the pattern that will be registered by the resist is more complicated. Charged particle beam simulation may be used to determine the pattern that will be registered by the resist. Charged particle beam simulation, which may include simulation of various charged particle beam writing and resist effects, is a compute-intensive process, however. It is impractical to simulate the pattern for an entire integrated circuit, and then to re-simulate the pattern every time a proposed charged particle beam shot is changed. 
     It would therefore be advantageous to be able to easily determine how resist on a surface such as a wafer or reticle will register a pattern formed by a plurality of charged particle beam shots. This would enable the use of overlapping shots and variable shot dosages. With overlapping shots and variable dosages, patterns can be formed on a surface with fewer shots, thus reducing the cost of forming the pattern on a surface such as a reticle or a wafer, and consequently reducing the cost of manufacturing photomasks and semiconductor devices. 
     SUMMARY OF THE DISCLOSURE 
     A method and system for fracturing or mask data preparation or optical proximity correction is disclosed, in which a target maximum dosage for a surface is input, and where a plurality of variable shaped beam (VSB) shots is determined that will form a pattern on the surface, where at least two of the shots partially overlap, and where the plurality of shots is determined so that the maximum dosage produced on the surface is less than the target dosage. 
     A method for manufacturing an integrated circuit is also disclosed, in which a target maximum dosage for a reticle is input, and where a plurality of variable shaped beam (VSB) shots is determined that will form a pattern on the reticle, where at least two of the shots partially overlap, where the plurality of shots is determined so that the maximum dosage produced on the reticle is less than the target dosage, and where the pattern is formed on the reticle with the plurality of VSB shots. 
     These and other advantages of the present disclosure will become apparent after considering the following detailed specification in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a conceptual flow diagram of a conventional method for manufacturing a reticle and photomask; 
         FIG. 2  illustrates a conceptual flow diagram of manufacturing a reticle and photomask using an exemplary method of the current disclosure; 
         FIG. 3  illustrates a circular pattern, and an example of a dosage map for a circular shot; 
         FIG. 4  illustrates a portion of a 200 nm diameter circular pattern and dosage map, using a 4 nm grid; 
         FIG. 5  illustrates an exemplary dosage map for a rectangular shot; 
         FIG. 6  illustrates a dosage map for a set of six overlapping rectangular shots of the type of  FIG. 5 ; 
         FIG. 7A  illustrates a circular pattern; 
         FIG. 7B  illustrates the dosage map of a rectangular shot; 
         FIG. 7C  illustrates the dosage map of a square shot; 
         FIG. 7D  illustrates the dosage map of three overlapping shots of  FIGS. 7B and 7C  that can form the circular pattern of  FIG. 7A ; 
         FIG. 8A  illustrates a parameterized glyph dosage map; 
         FIG. 8B  illustrates another dosage map for the parameterized glyph of  FIG. 8A ; and 
         FIG. 9  illustrates a dosage graph of a glyph resulting from a circular CP character shot. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       FIG. 1  illustrates a conceptual flow diagram  100  of a conventional method for making a photomask. The input to the process is a computer representation  102  of a desired pattern that is to be formed on a reticle from which the photomask can be manufactured. In step  104  the pattern is fractured into a set of non-overlapping shapes, such as rectangles and triangles, for exposure using a VSB charged particle beam system. The result of step  104  is a shot list  106 , in which the shots are non-overlapping. All shots are assumed to have a normal dosage, and no dosage information is contained in shot list  106 . In step  108  proximity effect correction (PEC) is performed, which assigns a dosage to each shot in the shot list, and which may also slightly adjust the placement of the shots. Step  108  may also include other corrections which perform dosage adjustments. The output of step  108  is a final shot list  110  which includes dosage information. In step  112  a charged particle beam system uses the shot list  110  to expose resist with which the reticle has been coated, thereby forming a pattern  114  on the resist. In step  116  the resist is developed. Through further processing steps  118  the reticle is transformed into a photomask  120 . 
     Variations of the  FIG. 1  method exist. In one variation of this process, called multi-pass exposure, the entire pattern is exposed once, and then exposed a second time, called two-pass exposure. More than two passes may also be used. Multi-pass writing may be used to reduce non-ideal writing effects such as resist heating, resist charging and field-to-field misalignment. In multi-pass writing, the dosage for each pass is proportionately lower than for single-pass writing, the goal being that the sum of the doses for all passes will be a normal dose for all parts of the pattern. Conventionally, therefore, shot overlap within a pass is avoided. In another variation of the  FIG. 1  method, PEC step  108  is performed by the charged particle beam system itself, so PEC step  108  and the expose resist step  112  are combined. 
       FIG. 3  illustrates an example of how a dosage map  304  can be used to show the dosage of a CP shot used to form a circular pattern  302  on a resist-coasted surface. The area in the vicinity of the circle has been divided into a grid of squares, where each square represents a point or sample point in the Cartesian plane where the dosage will be calculated. The size of the grid relative to the circle in this example is larger than would be typical, and is used for illustration. This grid becomes a dosage map by calculating and recording the charged particle dosage for each sample point. Charged particle beam simulation may be used to calculate the dosage in each grid square. The nominal dosage of the CP shot in this example is 1.0, meaning 1.0 times a normal dosage. The blur of the charged particle beam caused by forward scattering of the charged particles, Coulomb effect and other physical, chemical and electromagnetic effects causes a gradual falloff of dosage around the edges of the circular CP shot. The resist threshold is that dosage level above which the resist will register a pattern. If a resist with a threshold of approximately 0.6 is used, a pattern similar to the target pattern will be registered by the resist. In the example of  FIG. 3 , the grid is too coarse to precisely determine the shape of the pattern that will be registered by the resist. The use of a finer grid allows a more accurate calculation of the registered pattern, but also requires more computational effort to calculate. Additionally, since the dosage across a single grid square varies, any of a variety of conventions can be used in calculating the grid dosage value. The calculated dosage for each grid may, for example, represent the average dosage over the area of the grid, or may represent the dosage in the lower-left corner of the grid square, or may represent the dosage in the center of the grid square. Some other convention may also be used. The shot information, including shot dosage, shot shape if VSB, shot location on the stencil if CP, partial character exposure information if CP, and the dosage map information can be stored in a glyph library, so that the dosage map for other shots which match this shot&#39;s shape and dosage can be quickly accessed. Glyph creation is, in fact, the process of calculating a dosage map for a shot or group of shots and storing the shot information and calculated dosage map for future use. The calculated dosage map may be stored either as a two-dimensional matrix of dosage values as shown in  FIG. 3 , or in a different format, such as a set of instructions for creating a two-dimensional set of dosage values. 
       FIG. 4  illustrates a grid map  402  showing an open arc  404 . The arc  404  represents a portion of a 200 nm circular pattern, and the grid map  402  is a portion of a grid map for the circular pattern using a 4 nm grid. The nominal shot dosage is 1.0. A resist threshold of 0.5 is used in this example. This illustrates the large number of grid calculations that a fine grid can require even for a small pattern. Grid sizes between 1 nm and 40 nm, in the scale of a surface, may be useful for calculating dosages for patterns for modern semiconductor processes. Larger grid sizes, such between 50 nm and 1 micron, may be used for calculation of longer-range exposure effects such as backscatter and fogging, and may also be more appropriate for manufacturing patterns for other products. 
       FIG. 5  and  FIG. 6  illustrate how dosages for multiple shots may be combined as an embodiment of the present disclosure.  FIG. 5  shows a two-dimensional dosage map  502  for a single rectangular VSB shot. The calculation of the shot dosage map  502  may be accomplished using charged particle beam simulation. The nominal shot dosage is 1.0 in this example. Use of a resist with a threshold of 0.6 will cause a pattern similar to the rectangle to be registered on the resist.  FIG. 6  illustrates a dosage map  602  which may result from a set of six overlapping shots onto a resist-coated target surface, such as a reticle or a semiconductor wafer substrate. Dosage map  602  is a combination of six dosage maps of the type  502 . The nominal outlines of the six shots are shown. The combination of dosage maps can be done by creating a dosage map  602  for the target surface, and then combining each shot dosage map into the target surface dosage map. The combination process involves aligning each shot dosage map within the Cartesian coordinate space of the target surface dosage map, then applying a mathematical operation or set of operations, such as addition, to combine the dosage value for each grid position of the shot dosage map into the dosage value for the corresponding grid position in the target surface dosage map. In this example the outlines from each of the six rectangular shots indicate how each of the six shot dosage maps are aligned within the Cartesian coordinate space of the target surface dosage map  602 . In this example, the mathematical operation used is simple addition. Dosage maps may also be combined using more complex sets of mathematical operations. For example, the combination operation could incorporate calculation of resist charging, which can cause translation and deformation of a shot due to the negative charge which has accumulated on the resist from temporally recent and geometrically nearby shots. In one embodiment the created target surface dosage map  602  may initially contain no shot information. The target dosage map  602  may be empty, with all entries having zero dosage, or the target dosage map  602  may be initialized with an estimate for the long range dosage effects, such as back scatter and fogging. In another embodiment the target dosage map  602  may be initialized with dosages from one or more shots determined without use of a dosage map. As can be seen from the target surface dosage map  602 , with a resist threshold of 0.6, the pattern that the resist registers will be smoother than the union of the outline of the individual shots. For example, the interior corners of the unioned shot pattern will be substantially filled in, since the dosages in these grid positions is either 0.6 or 1.0. This dosage map  602  illustrates that the pattern registered on the resist from this set of six shots will approximate, in the middle portion, a constant width line angled 45 degrees with respect to the Cartesian axes. Creation of the one-shot dosage map  502 , such as by using charged particle beam simulation, allows calculation of the dosage map  602  by combining each of six copies or instances of the dosage map  502  into the initial target surface dosage map  602 . This may be computationally faster than simulating the collection of six VSB shots using charged particle beam simulation. 
       FIGS. 7A-D  illustrate another example of combining dosage maps as an embodiment of the present disclosure.  FIG. 7A  shows a desired circular pattern  702 .  FIG. 7B  shows a dosage map  704  of a rectangular shot that can be used in a plurality of shots to create the pattern  702 . The nominal shot dosage for the shot represented in the dosage map  704  is 0.7, meaning 0.7 times a normal dose.  FIG. 7C  shows a dosage map  706  for a square shot with a nominal shot dosage of 0.6.  FIG. 7D  shows a combined dosage map  710  resulting from the combination of three dosages maps from three overlapping shots: a) the dosage map  704  of the rectangular shot, b) a 90 degree rotated version of dosage map  704 , and c) dosage map  706  of the square shot. If a resist with a threshold of 0.7 is used, a pattern similar to the desired circular pattern  702  will be registered on the resist per the combined dosage map  710 . In this example the shots represented by dosage maps  704  and  706  use a dosage less than 1.0, so as to limit the maximum dosage to 2.0 in the area where all three shots overlap, as shown in dosage map  710 . Some photomask production processes limit the maximum combined dosage to values such as 2.0 times the normal dosage.  FIG. 7D  also illustrates how the length of the two non-square rectangular shots has been made larger than the diameter of the desired circular pattern  702 . The “oversizing” of these rectangles compensates for corner rounding that may occur on these shots because of the dosage of 0.7. As shown in dosage map  704 , the dosage is less near the edges and in the corners of the shot, due to the Gaussian dosage fall-off near the edges of the shot. Overall,  FIGS. 7A-D  illustrate how a circular pattern can be calculated using a small number of shot dosage maps—in this case only two. Although  FIGS. 7A-D  illustrate the combination of dosage maps for a circular pattern, this method is applicable to any rectilinear or curvilinear shape or set of shapes. 
       FIG. 9  illustrates in graphical form an example of a glyph. A glyph is a dosage map calculated from one or more CP and/or VSB shots, with each shot comprising a position and a shot dosage. The glyph illustrated in  FIG. 9  may be, for example, calculated from a shot of a circular CP character. The glyph&#39;s two-dimensional dosage map is displayed in  FIG. 9  as a dosage graph  900 . The dosage graph  900  is shown in three-dimensional isometric view, with the “Z” dimension representing the dosage at each X, Y location. The center of the CP shot is point  902 , which is also the point of highest calculated dosage. As can be seen, the dosage falls off in any X, Y direction from point  902 . Also shown on dosage graph  900  is a resist threshold  904 , which is the dosage above which resist coating a surface would register a pattern if the resist were to be exposed with only this shot. The portion of the dosage graph which is above the resist threshold  904  is marked as graph portion  906 . The portion of glyph  900  which will result in a registered pattern area on a resist-coated surface is thus the projection of graph portion  906  onto the X-Y plane. As can be seen from  FIG. 9 , the registered pattern area created by flattening graph portion  906  is circular or nearly circular. The glyph calculated from the circular CP character and represented by the dosage graph  900  is therefore circularly symmetric or nearly circularly symmetric, and will produce a circular or nearly circular registered pattern area on the resist-coated surface. 
       FIG. 2  illustrates an exemplary conceptual flow diagram  200  of a method for manufacturing a photomask according to the current disclosure. There are three types of input data to the process: stencil information  218 , which is information about the CP characters on the stencil of the charged particle beam system; process information  236 , which includes information such as the resist dosage threshold above which the resist will register a pattern; and a computer representation of the desired pattern  216  to be formed on the reticle. In addition, initial optional steps shown by steps  202 - 212  involve the creation of a library of glyphs. The first step in the optional creation of a library of glyphs is VSB/CP shot selection  202 , in which one or more VSB or CP shots, each shot with a specific dosage, are combined to create a set of shots  204 . The set of shots  204  may include overlapping VSB shots and/or overlapping CP shots. The VSB/CP shot selection step uses the stencil information  218 , which includes information about the CP characters that are available on the stencil. The set of shots  204  is simulated in step  206  using charged particle beam simulation to create a dosage map  208  of the set of shots. Step  206  may include simulation of various physical phenomena including forward scattering, resist diffusion, Coulomb effect and etching. The result of step  206  is a two-dimensional dosage map  208  which represents the combined dosage from the sets of shots  204  at each of the grid positions in the map. The dosage map  208  is called a glyph. In step  210  the information about each of the shots in the set of shots, and the dosage map  208  of this additional glyph is stored a library of glyphs  212 . In one embodiment, a set of glyphs may be combined into a type of glyph called a parameterized glyph. 
     The required portion of the flow  200  involves creation of a photomask. In step  220  a combined dosage map for the reticle or reticle portion is calculated. Step  220  uses as input the desired pattern  216  to be formed on the reticle, the process information  236 , the stencil information  218 , and the glyph library  212  if a glyph library has been created. In step  220  a reticle dosage map may be created, into which shot dosage information, for example a shot dosage map, will be combined. In one embodiment the reticle dosage map may be initialized to zeros. In another embodiment, the grid squares of the reticle dosage map may be initialized with an estimated correction for long-range effects such as backscattering, fogging, or loading, a term which refers to the effects of localized resist developer depletion. In another embodiment, the reticle dosage map may be initialized with dosage information from one or more glyphs, or from one or more shots which have been determined without use of a dosage map. Step  220  may involve VSB/CP shot selection  222  or glyph selection  234 , or both of these. If a VSB or CP shot is selected, the shot is simulated using charged particle beam simulation in step  224  and a dosage map  226  of the shot may be created. The charged particle beam simulation may comprise convolving a shape with a Gaussian. The convolution may be with a binary function of the shape, where the binary function determines whether a point is inside or outside the shape. The shape may be an aperture shape or multiple aperture shapes, or a slight modification thereof. In one embodiment, this simulation may include looking up the results of a previous simulation of the same shot, such as when using a temporary shot dosage map cache. In another embodiment, the shot dosage information may be represented in some way other than a dosage map, where this other representation allows the shot dosage information to be combined into the reticle dosage map. Both VSB and CP shots may be allowed to overlap, and may have varying dosages with respect to each other. If a glyph is selected, the dosage map of the glyph is input from the glyph library. In step  220 , the various glyph dosage maps and the shot information such as shot dosage maps are combined into the reticle dosage map. In one embodiment, the combination is done by adding the dosages. Using the resulting combined dosage map and the resist information  236 , a reticle pattern may be calculated. If the reticle image matches the desired pattern  216  within a pre-determined tolerance, then a combined shot list  238  is output, containing the determined VSB/CP shots and the shots constituting the selected glyphs. If the calculated reticle image does not match the target image  216  within a predetermined tolerance as calculated in step  220 , the set of selected CP shots, VSB shots and/or glyphs is revised, the dosage maps are recalculated, and the reticle pattern is recalculated. In one embodiment, the initial set of shots and/or glyphs may be determined in a correct-by-construction method, so that no shot or glyph modifications are required. In another embodiment, step  220  includes an optimization technique so as to minimize either the total number of shots represented by the selected VSB/CP shots and glyphs, or the total charged particle beam writing time, or some other parameter. In yet another embodiment, VSB/CP shot selection  222  and glyph selection  234  are performed so as to generate multiple sets of shots, each of which can form a reticle image that matches the desired pattern  216 , but at a lower-than-normal dosage, to support multi-pass writing. 
     The combined shot list  238  comprises the determined list of selected VSB shots, selected CP shots and shots constituting the selected glyphs. All the shots in the final shot list  238  include dosage information. In step  240 , proximity effect correction (PEC) and/or other corrections may be performed or corrections may be refined from earlier estimates. Step  240  uses the combined shot list  238  as input and produces a final shot list  242  in which the shot dosages have been adjusted. The final shot list  242  is used by the charged particle beam system in step  244  to expose resist with which the reticle has been coated, thereby forming a pattern  246  on the resist. In step  248  the resist is developed. Through further processing steps  250  the reticle is transformed into a photomask  252 . 
       FIGS. 8A  &amp; B illustrate an example of a parameterized glyph. The dosage map  802  illustrated in  FIG. 8A  is for a rectangular shot  804  of width  812 , or eight grid units in this example. The two vertical lines  806  and  808  define a region of the dosage map which is of width  810 , or four grid units in this example. Within this region  810  of the dosage map  802 , all grid squares in each row have identical dosage values.  FIG. 8B  illustrates a dosage map  820  for a rectangular shot  824  of width  832 , or twelve grid units in this example. The dosage map  820  is similar to the dosage map  802 , including the dosage values of the grid squares, except that between vertical lines  826  and  828 , dosage map  820  contains four more grid columns than the dosage map  802  contains between lines  806  and  808 . This “stretchable” portion of the dosage map  820  is of width  830 , or eight grid units in this example. By identifying a stretchable or parameterizable region where the dosages are identical along the stretchable dimension, such as the region between lines  806  and  808  of  FIG. 8A  or between lines  826  and  828  of  FIG. 8B , a dosage map for a rectangular shot of the same height as shots  804  and  824  can be generated for shots with any width greater than  812 . Limitations of the charged particle beam system may further restrict the size of the rectangular shots for which this method can be used to generate a dosage map. In other embodiments, a repeated dosage pattern in the dosage map may allow dosage maps to be generated for single shots or groups of shots of only discrete lengths, rather than of a continuous length such as the example of  FIGS. 8A  &amp; B. This example shows how a dosage map for a parameterized glyph may be generated. In other embodiments, other dimensions may be parameterized, such as height or diameter. 
     While the specification has been described in detail with respect to specific embodiments, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing, may readily conceive of alterations to, variations of, and equivalents to these embodiments. These and other modifications and variations to the present methods for fracturing, creating glyphs and manufacturing a surface may be practiced by those of ordinary skill in the art, without departing from the spirit and scope of the present subject matter, which is more particularly set forth in the appended claims. Furthermore, those of ordinary skill in the art will appreciate that the foregoing description is by way of example only, and is not intended to be limiting. Steps can be added to, taken from or modified from the steps in this specification without deviating from the scope of the invention. In general, any flowcharts presented are only intended to indicate one possible sequence of basic operations to achieve a function, and many variations are possible. Thus, it is intended that the present subject matter covers such modifications and variations as come within the scope of the appended claims and their equivalents.