Patent Publication Number: US-2013252143-A1

Title: Method and system for design of enhanced accuracy patterns for charged particle beam lithography

Description:
RELATED APPLICATIONS 
     This application: 1) is a continuation-in-part of U.S. patent application Ser. No. 13/037,268 filed on Feb. 28, 2011, entitled “Method And System For Design Of Enhanced Accuracy Patterns For Charged Particle Beam Lithography”; and 2) is a continuation-in-part of U.S. patent application Ser. No. 13/650,618 filed on Oct. 12, 2012, entitled “Method And System For Design Of A Reticle To Be Manufactured Using Variable Shaped Beam Lithography”; both of which are hereby incorporated by reference for all purposes. U.S. patent application Ser. No. 13/650,618: 3) is a continuation of U.S. patent application Ser. No. 13/316,564 filed on Dec. 12, 2011 entitled “Method And System For Design Of A Reticle To Be Manufactured Using Variable Shaped Beam Lithography” and issued as U.S. Pat. No. 8,304,148; 4) which is a continuation of U.S. patent application Ser. No. 13/087,334 filed on Apr. 14, 2011 entitled “Method and System For Design of a Reticle To Be Manufactured Using Variable Shaped Beam Lithography” and issued as U.S. Pat. No. 8,202,672; 5) which is a continuation of U.S. patent application Ser. No. 12/987,994 filed on Jan. 10, 2011 entitled “Method For Manufacturing a Surface and Integrated Circuit Using Variable Shaped Beam Lithography” and issued as U.S. Pat. No. 8,017,289; 6) which is a continuation of U.S. patent application Ser. No. 12/473,265 filed on May 27, 2009 entitled “Method and System for Design of a Reticle to Be Manufactured Using Variable Shaped Beam Lithography” and issued as U.S. Pat. No. 7,901,850; all of which are hereby incorporated by reference for all purposes. U.S. Pat. No. 7,901,850: 7) is a continuation-in-part of U.S. patent application Ser. No. 12/202,366 filed Sep. 1, 2008, entitled “Method and System For Design of a Reticle to Be Manufactured Using Character Projection Lithography” and issued as Ser. No. 7,759,027; and 8) claims priority to U.S. Provisional Patent Application Ser. No. 61/172,659, filed on Apr. 24, 2009 and entitled “Method for Manufacturing a Surface and Integrated Circuit Using Variable Shaped Beam Lithography”; both of which are hereby incorporated by reference for all purposes. This application also: 9) is related to Fujimura, U.S. patent application Ser. No. 13/037,263 filed on Feb. 28, 2011, entitled “Method and System For Design Of A Surface To Be Manufactured Using Charged Particle Beam Lithography”; and 10) is related to Fujimura, U.S. patent application Ser. No. 13/037,270 filed on Feb. 28, 2011, entitled “Method and System For Design Of Enhanced Edge Slope Patterns For Charged Particle Beam Lithography”; both 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 (I.C.). Other substrates could include flat panel displays or even other reticles. Conventional optical lithography typically uses radiation of 193 nm wavelength or longer. Extreme ultraviolet (EUV) or X-ray lithography are also considered types of optical lithography, but use wavelengths much shorter than the 193 nm of conventional 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, holograms, 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. Also, some patterns of a given layer may be written using optical lithography, and other patterns written using maskless direct write. 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, holograms, or magnetic recording heads. 
     Two common types of charged particle beam lithography are variable shaped beam (VSB) and character projection (CP). These are both sub-categories of shaped beam charged particle beam lithography, in which 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. In VSB, 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 (i.e. of “manhattan” orientation), and 45 degree right triangles (i.e. triangles with their three internal angles being 45 degrees, 45 degrees, and 90 degrees) of certain minimum and maximum sizes. At predetermined 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 character projection (CP), there is a stencil in the system that has in it a variety of apertures or characters which may be complex shapes such as rectilinear, arbitrary-angled linear, circular, nearly circular, annular, nearly annular, oval, nearly oval, partially circular, partially nearly circular, partially annular, partially nearly annular, partially nearly oval, 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 a character on the stencil to efficiently produce more complex patterns 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-shaped pattern shot with a VSB system takes four shots, but the same E-shaped pattern 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 degree 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-shaped pattern described above can be partially exposed as an F-shaped pattern or an I-shaped pattern, where different parts of the beam are cut off by an aperture. This is the same mechanism as how various sized rectangles can be shot using VSB. In this disclosure, partial projection is used to mean both character projection and VSB projection. 
     As indicated, in optical lithography the lithographic mask or reticle comprises geometric patterns corresponding to the circuit components to be integrated onto a substrate. The patterns used to manufacture the reticle may be generated utilizing computer-aided design (CAD) software or programs. In designing the patterns the CAD program may follow a set of pre-determined design rules in order to create the reticle. These rules are set by processing, design, and end-use limitations. An example of an end-use limitation is defining the geometry of a transistor in a way in which it cannot sufficiently operate at the required supply voltage. In particular, design rules can define the space tolerance between circuit devices or interconnect lines. The design rules are, for example, used to ensure that the circuit devices or lines do not interact with one another in an undesirable manner. For example, the design rules are used so that lines do not get too close to each other in a way that may cause a short circuit. The design rule limitations reflect, among other things, the smallest dimensions that can be reliably fabricated. When referring to these small dimensions, one usually introduces the concept of a critical dimension. These are, for instance, defined as the smallest width of a line or the smallest space between two lines, those dimensions requiring exquisite control. 
     One goal in integrated circuit fabrication by optical lithography is to reproduce the original circuit design on the substrate by use of the reticle. Integrated circuit fabricators are always attempting to use the semiconductor wafer real estate as efficiently as possible. Engineers keep shrinking the size of the circuits to allow the integrated circuits to contain more circuit elements and to use less power. As the size of an integrated circuit critical dimension is reduced and its circuit density increases, the critical dimension of the circuit pattern or physical design approaches the resolution limit of the optical exposure tool used in conventional optical lithography. As the critical dimensions of the circuit pattern become smaller and approach the resolution value of the exposure tool, the accurate transcription of the physical design to the actual circuit pattern developed on the resist layer becomes difficult. To further the use of optical lithography to transfer patterns having features that are smaller than the light wavelength used in the optical lithography process, a process known as optical proximity correction (OPC) has been developed. OPC alters the physical design to compensate for distortions caused by effects such as optical diffraction and the optical interaction of features with proximate features. OPC includes all resolution enhancement technologies performed with a reticle. 
     OPC may add sub-resolution lithographic features to mask patterns to reduce differences between the original physical design pattern, that is, the design, and the final transferred circuit pattern on the substrate. The sub-resolution lithographic features interact with the original patterns in the physical design and with each other and compensate for proximity effects to improve the final transferred circuit pattern. One feature that is used to improve the transfer of the pattern is a sub-resolution assist feature (SRAF). Another feature that is added to improve pattern transference is referred to as “serifs”. Serifs are small features that can be positioned on a corner of a pattern to sharpen the corner in the final transferred image. It is often the case that the precision demanded of the surface manufacturing process for SRAFs are less than those for patterns that are intended to print on the substrate, often referred to as main features. Serifs are a part of a main feature. As the limits of optical lithography are being extended far into the sub-wavelength regime, the OPC features must be made more and more complex in order to compensate for even more subtle interactions and effects. As imaging systems are pushed closer to their limits, the ability to produce reticles with sufficiently fine OPC features becomes critical. Although adding serifs or other OPC features to a mask pattern is advantageous, it also substantially increases the total feature count in the mask pattern. For example, adding a serif to each of the corners of a square using conventional techniques adds eight more rectangles to a mask or reticle pattern. Adding OPC features is a very laborious task, requires costly computation time, and results in more expensive reticles. Not only are OPC patterns complex, but since optical proximity effects are long range compared to minimum line and space dimensions, the correct OPC patterns in a given location depend significantly on what other geometry is in the neighborhood. Thus, for instance, a line end will have different size serifs depending on what is near it on the reticle. This is even though the objective might be to produce exactly the same shape on the wafer. These slight but critical variations are important and have prevented others from being able to form reticle patterns. It is conventional to discuss the OPC-decorated patterns to be written on a reticle in terms of main features, that is features that reflect the design before OPC decoration, and OPC features, where OPC features might include serifs, jogs, and SRAF. To quantify what is meant by slight variations, a typical slight variation in OPC decoration from neighborhood to neighborhood might be 5% to 80% of a main feature size. Note that for clarity, variations in the design of the OPC are what is being referenced. Manufacturing variations, such as line-edge roughness and corner rounding, will also be present in the actual surface patterns. When these OPC variations produce substantially the same patterns on the wafer, what is meant is that the geometry on the wafer is targeted to be the same within a specified error, which depends on the details of the function that that geometry is designed to perform, e.g., a transistor or a wire. Nevertheless, typical specifications are in the 2%-50% of a main feature range. There are numerous manufacturing factors that also cause variations, but the OPC component of that overall error is often in the range listed. OPC shapes such as sub-resolution assist features are subject to various design rules, such as a rule based on the size of the smallest feature that can be transferred to the wafer using optical lithography. Other design rules may come from the mask manufacturing process or, if a character projection charged particle beam writing system is used to form the pattern on a reticle, from the stencil manufacturing process. It should also be noted that the accuracy requirement of the SRAF features on the mask may be lower than the accuracy requirements for the main features on the mask. 
     There are a number of technologies used for forming patterns on a reticle, including using optical lithography or charged particle beam lithography. The most commonly used system is the variable shaped beam (VSB), where, as described above, doses of electrons with simple shapes such as manhattan rectangles and 45-degree right triangles expose a resist-coated reticle surface. In conventional mask writing, the doses or shots of electrons are conventionally designed to avoid overlap wherever possible, so as to greatly simplify calculation of how the resist on the reticle will register the pattern. Similarly, the set of shots is designed so as to completely cover the pattern area that is to be formed on the reticle. 
     Reticle writing for the most advanced technology nodes typically involves multiple passes of charged particle beam writing, a process called multi-pass exposure, 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 writer, allowing the creation of more accurate photomasks. Also typically, the list of shots, including the dosages, is the same for every pass. In one variation of multi-pass exposure, the lists of shots may vary among exposure passes, but the union of the shots in any exposure pass covers the same area. Multi-pass writing can reduce over-heating of the resist coating the surface. Multi-pass writing also averages out random errors of the charged particle beam writer. Multi-pass writing using different shot lists for different exposure passes can also reduce the effects of certain systemic errors in the writing process. 
     In EUV lithography, OPC features are generally not required. Therefore, the complexity of the pattern to be manufactured on the reticle is less than with conventional 193 nm wavelength optical lithography, and shot count reduction is correspondingly less important. In EUV, however, mask accuracy requirements are very high because the patterns on the mask, which are typically 4× the size of the patterns on the wafer, are sufficiently small that they are challenging to form precisely using charged particle beam technology such as E-beam. 
     There are numerous undesirable short-range and long-range effects associated with charged particle beam exposure. These effects can cause dimensional inaccuracies in the pattern transferred to a surface such as a reticle. These effects can also increase the dimensional changes that normal process variations cause in the transferred pattern. It would be desirable both to increase the accuracy of the transferred pattern, and also to reduce the dimensional changes associated with process variations. 
     SUMMARY OF THE DISCLOSURE 
     A method and system for fracturing or mask data preparation are presented in which overlapping shots are generated to increase dosage in selected portions of a pattern, thus improving the fidelity and/or the critical dimension variation of the transferred pattern. In various embodiments, the improvements may affect the ends of paths or lines, or square or nearly-square patterns. The shots may be varied in their amount of overlap, shot size, and dosage with respect to the dosage of another overlapping shot. Simulation is used to determine the pattern that will be produced on the surface. A method for manufacturing a surface is also disclosed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates an example of a character projection charged particle beam system; 
         FIG. 2A  illustrates an example of a single charged particle beam shot and a cross-sectional dosage graph of the shot; 
         FIG. 2B  illustrates an example of a pair of proximate shots and a cross-sectional dosage graph of the shot pair; 
         FIG. 2C  illustrates an example of a pattern formed on a resist-coated surface from the pair of  FIG. 2B  shots; 
         FIG. 3A  illustrates an example of a polygonal pattern; 
         FIG. 3B  illustrates an example of a conventional fracturing of the polygonal pattern of  FIG. 3A ; 
         FIG. 3C  illustrates an example of an alternate fracturing of the polygonal pattern of  FIG. 3A ; 
         FIG. 4A  illustrates an example of a shot outline from a rectangular shot; 
         FIG. 4B  illustrates an example of a longitudinal dosage curve for the shot of  FIG. 4A  using a normal shot dosage; 
         FIG. 4C  illustrates an example of a longitudinal dosage curve similar to  FIG. 4B , with long-range effects included; 
         FIG. 4D  illustrates an example of a longitudinal dosage curve for the shot of  FIG. 4A  using a higher than normal shot dosage; 
         FIG. 4E  illustrates an example of a longitudinal dosage curve similar to  FIG. 4D , with long-range effects included; 
         FIG. 4F  illustrates an example of a longitudinal dosage curve similar to  FIG. 4E , but with a higher background dosage level; 
         FIG. 5A  illustrates an example of how a 100 nm square VSB shot may be registered on a reticle; 
         FIG. 5B  illustrates an example of how a 60 nm square VSB shot may be registered on a reticle; 
         FIG. 6A  illustrates an example of a pattern comprising the end portion of a line; 
         FIG. 6B  illustrates an example of a conventional single-shot method of forming the pattern of  FIG. 6A  on a surface; 
         FIG. 6C  illustrates an example of a method of forming the pattern of  FIG. 6A  on a surface by one embodiment of the current invention; 
         FIG. 6D  illustrates an example of a method of forming the pattern of  FIG. 6A  on a surface by another embodiment of the current invention; 
         FIG. 6E  illustrates an example of a method of forming the pattern of  FIG. 6A  on a surface by yet another embodiment of the current invention; 
         FIG. 7  illustrates a conceptual flow diagram of how to prepare a surface, such as a reticle, for use in fabricating a substrate such as an integrated circuit on a silicon wafer using optical lithography; 
         FIG. 8  illustrates a conceptual flow diagram of how to prepare a surface for use in fabricating a substrate such as an integrated circuit on a silicon wafer; 
         FIG. 9A  illustrates a square pattern to be formed on a surface; 
         FIG. 9B  illustrates a single-shot method of forming the pattern of  FIG. 9A  on a surface; 
         FIG. 9C  illustrates an example of a method of forming the pattern of  FIG. 9A  on a surface by one embodiment of the current invention; 
         FIG. 9D  illustrates an example of a method of forming the pattern of  FIG. 9A  on a surface by another embodiment of the current invention; and 
         FIG. 9E  illustrates an example of a method of forming the pattern of  FIG. 9A  on a surface by yet another embodiment of the current invention. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     The present disclosure describes a method for fracturing patterns into shots for a charged particle beam writer, where overlapping shots are generated to improve the accuracy and/or the edge slope of the pattern written to a surface. The use of overlapping shots in this application typically increases shot count and exposure time. 
     Referring now to the drawings, wherein like numbers refer to like items,  FIG. 1  illustrates an embodiment of a conventional lithography system  100 , such as a charged particle beam writer system, in this case an electron beam writer system, that employs character projection to manufacture a surface  130 . The electron beam writer system  100  has an electron beam source  112  that projects an electron beam  114  toward an aperture plate  116 . The plate  116  has an aperture  118  formed therein which allows the electron beam  114  to pass. Once the electron beam  114  passes through the aperture  118  it is directed or deflected by a system of lenses (not shown) as electron beam  120  toward another rectangular aperture plate or stencil mask  122 . The stencil  122  has formed therein a number of openings or apertures  124  that define various types of characters  126 , which may be complex characters. Each character  126  formed in the stencil  122  may be used to form a pattern  148  on a surface  130  of a substrate  132 , such as a silicon wafer, a reticle or other substrate. In partial exposure, partial projection, partial character projection, or variable character projection, electron beam  120  may be positioned so as to strike or illuminate only a portion of one of the characters  126 , thereby forming a pattern  148  that is a subset of character  126 . For each character  126  that is smaller than the size of the electron beam  120  defined by aperture  118 , a blanking area  136 , containing no aperture, is designed to be adjacent to the character  126 , so as to prevent the electron beam  120  from illuminating an unwanted character on stencil  122 . An electron beam  134  emerges from one of the characters  126  and passes through an electromagnetic or electrostatic reduction lens  138  which reduces the size of the pattern from the character  126 . In commonly available charged particle beam writer systems, the reduction factor is between 10 and 60. The reduced electron beam  140  emerges from the reduction lens  138 , and is directed by a series of deflectors  142  onto the surface  130  as the pattern  148 , which is depicted as being in the shape of the letter “H” corresponding to character  126 A. The pattern  148  is reduced in size compared to the character  126 A because of the reduction lens  138 . The pattern  148  is drawn by using one shot of the electron beam system  100 . This reduces the overall writing time to complete the pattern  148  as compared to using a variable shape beam (VSB) projection system or method. Although one aperture  118  is shown being formed in the plate  116 , it is possible that there may be more than one aperture in the plate  116 . Although two plates  116  and  122  are shown in this example, there may be only one plate or more than two plates, each plate comprising one or more apertures. 
     In conventional charged particle beam writer systems the reduction lens  138  is calibrated to provide a fixed reduction factor. The reduction lens  138  and/or the deflectors  142  also focus the beam on the plane of the surface  130 . The size of the surface  130  may be significantly larger than the maximum beam deflection capability of the deflection plates  142 . Because of this, patterns are normally written on the surface in a series of stripes. Each stripe contains a plurality of sub-fields, where a sub-field is within the beam deflection capability of the deflection plates  142 . The electron beam writer system  100  contains a positioning mechanism  150  to allow positioning the substrate  132  for each of the stripes and sub-fields. In one variation of the conventional charged particle beam writer system, the substrate  132  is held stationary while a sub-field is exposed, after which the positioning mechanism  150  moves the substrate  132  to the next sub-field position. In another variation of the conventional charged particle beam writer system, the substrate  132  moves continuously during the writing process. In this variation involving continuous movement, in addition to deflection plates  142 , there may be another set of deflection plates (not shown) to move the beam at the same speed and direction as the substrate  132  is moved. 
     The minimum size pattern that can be projected with reasonable accuracy onto a surface  130  is limited by a variety of short-range physical effects associated with the electron beam writer system  100  and with the surface  130 , which normally comprises a resist coating on the substrate  132 . These effects include forward scattering, Coulomb effect, and resist diffusion. Beam blur is a term used to include all of these short-range effects. The most modern electron beam writer systems can achieve an effective beam blur in the range of 20 nm to 30 nm. Forward scattering may constitute one quarter to one half of the total beam blur. Modern electron beam writer systems contain numerous mechanisms to reduce each of the constituent pieces of beam blur to a minimum. Some electron beam writer systems may allow the beam blur to be varied during the writing process, from the minimum value available on an electron beam writing system to one or more larger values. 
     The shot dosage of a charged particle beam writer such as an electron beam writer system is a function of the intensity of the beam source  112  and the exposure time for each shot. Typically the beam intensity remains fixed, and the exposure time is varied to obtain variable shot dosages. The exposure time may be varied to compensate for various long-range effects such as backscatter and fogging in a process called proximity effect correction (PEC). Electron beam writer systems usually allow setting an overall dosage, called a base dosage, that affects all shots in an exposure pass. Some electron beam writer systems perform dosage compensation calculations within the electron beam writer system itself, and do not allow the dosage of each shot to be assigned individually as part of the input shot list, the input shots therefore having unassigned shot dosages. In such electron beam writer systems all shots have the base dosage, before proximity effect correction. Other electron beam writer systems do allow dosage assignment on a shot-by-shot basis. In electron beam writer systems that allow shot-by-shot dosage assignment, the number of available dosage levels may be 64 to 4096 or more, or there may be a relatively few available dosage levels, such as 3 to 8 levels. Some embodiments of the current invention are targeted for use with charged particle beam writing systems which either do not allow dosage assignment on a shot-by-shot basis, or which allow assignment of one of a relatively few dosage levels. 
       FIGS. 2A-B  illustrate how energy is registered on a resist-coated surface from one or more charged particle beam shots. In  FIG. 2A  rectangular pattern  202  illustrates a shot outline, which is a pattern that will be produced on a resist-coated surface from a shot which is not proximate to other shots. The corners of pattern  202  are rounded due to beam blur. In dosage graph  210 , dosage curve  212  illustrates the cross-sectional dosage along a line  204  through shot outline  202 . Line  214  denotes the resist threshold, which is the dosage above which the resist will register a pattern. As can be seen from dosage graph  210 , dosage curve  212  is above the resist threshold between the X-coordinates “a” and “b”. Coordinate “a” corresponds to dashed line  216 , which denotes the left-most extent of the shot outline  202 . Similarly, coordinate “b” corresponds to dashed line  218 , which denotes the right-most extent of the shot outline  202 . The shot dosage for the shot in the example of  FIG. 2A  is a normal dosage, as marked on dosage graph  210 . In conventional mask writing methodology, the normal dosage is set so that a relatively large rectangular shot will register a pattern of the desired size on the resist-coated surface, in the absence of long-range effects. The normal dosage therefore depends on the value of the resist threshold  214 . 
       FIG. 2B  illustrates the shot outlines of two particle beam shots, and the corresponding dosage curve. Shot outline  222  and shot outline  224  result from two proximate particle beam shots. In dosage graph  220 , dosage curve  230  illustrates the dosage along the line  226  through shot outlines  222  and  224 . As shown in dosage curve  230 , the dosage registered by the resist along line  226  is the combination, such as the sum, of the dosages from two particle beam shots, represented by shot outline  222  and shot outline  224 . As can be seen, dosage curve  230  is above the threshold  214  from X-coordinate “a” to X-coordinate “d”. This indicates that the resist will register the two shots as a single shape, extending from coordinate “a” to coordinate “d”.  FIG. 2C  illustrates a pattern  252  that the two shots from the example of  FIG. 2B  may form. The variable width of pattern  252  is the result of the gap between shot outline  222  and shot outline  224 , and illustrates that a gap between the shots  222  and  224  causes dosage to drop below threshold near the corners of the shot outlines closest to the gap. 
     When using conventional non-overlapping shots using a single exposure pass, conventionally all shots are assigned a normal dosage before PEC dosage adjustment. A charged particle beam writer which does not support shot-by-shot dosage assignment can therefore be used by setting the base dosage to a normal dosage. If multiple exposure passes are used with such a charged particle beam writer, the base dosage is conventionally set according to the following equation: 
       base dosage=normal dosage/# of exposure passes 
       FIGS. 3A-C  illustrate two known methods of fracturing a polygonal pattern.  FIG. 3A  illustrates a polygonal pattern  302  that is desired to be formed on a surface.  FIG. 3B  illustrates a conventional method of forming this pattern using non-overlapping or disjoint shots. Shot outline  310 , shot outline  312  and shot outline  314 , which are marked with X&#39;s for clarity, are mutually disjoint. Additionally, the three shots associated with these shot outlines all use a desired normal dosage, before proximity effect correction. An advantage of using the conventional method as shown in  FIG. 3B  is that the response of the resist can be easily predicted. Also, the shots of  FIG. 3B  can be exposed using a charged particle beam system which does not allow dosage assignment on a shot-by-shot basis, by setting the base dosage of the charged particle beam writer to the normal dosage.  FIG. 3C  illustrates an alternate method of forming the pattern  302  on a resist-coated surface using overlapping shots, disclosed in U.S. Pat. No. 7,901,850 issued Mar. 8, 2011, and entitled “Method And System For Design Of A Reticle To Be Manufactured Using Variable Shaped Beam Lithography.” In  FIG. 3C  the constraint that shot outlines cannot overlap has been eliminated, and shot  320  and shot  322  do overlap. In the example of  FIG. 3C , allowing shot outlines to overlap enables forming the pattern  302  in only two shots, compared to the three shots of  FIG. 3B . In  FIG. 3C , however the response of the resist to the overlapping shots is not as easily predicted as in  FIG. 3B . In particular, the interior corners  324 ,  326 ,  328  and  330  may register as excessively rounded because of the large dosage received by overlapping region  332 , shown by horizontal line shading. Charged particle beam simulation may be used to determine the pattern registered by the resist. In one embodiment, charged particle beam simulation may be used to calculate the dosage for each grid location in a two-dimensional (X and Y) grid, creating a grid of calculated dosages called a dosage map. The results of charged particle beam simulation may indicate use of non-normal dosages for shot  320  and shot  322 . Additionally, in  FIG. 3C  the overlapping of shots in area  332  increases the area dosage beyond what it would be without shot overlap. While the overlap of two individual shots will not increase the area dosage significantly, this technique will increase area dosages and total dosage if used throughout a design. 
     In exposing, for example, a repeated pattern on a surface using charged particle beam lithography, the size of each pattern instance, as measured on the final manufactured surface, will be slightly different, due to manufacturing variations. The amount of the size variation is an essential manufacturing optimization criterion. In mask masking today, a root mean square (RMS) variation of no more than 1 nm (1 sigma) may be desired. More size variation translates to more variation in circuit performance, leading to higher design margins being required, making it increasingly difficult to design faster, lower-power integrated circuits. This variation is referred to as critical dimension (CD) variation. A low CD variation is desirable, and indicates that manufacturing variations will produce relatively small size variations on the final manufactured surface. In the smaller scale, the effects of a high CD variation may be observed as line edge roughness (LER). LER is caused by each part of a line edge being slightly differently manufactured, leading to some waviness in a line that is intended to have a straight edge. CD variation is inversely related to the slope of the dosage curve at the resist threshold, which is called edge slope. Therefore, edge slope, or dose margin, is a critical optimization factor for particle beam writing of surfaces. 
       FIG. 4A  illustrates an example of an outline of a rectangular shot  402 .  FIG. 4B  illustrates an example of a dosage graph  410  illustrating the dosage along the line  404  through shot outline  402  with a normal shot dosage, with no backscatter, such as would occur if shot  402  was the only shot within the range of backscattering effect, which, as an example, may be 10 microns. Other long-range effects are also assumed to contribute nothing to the background exposure of  FIG. 4B , leading to a zero background exposure level. The total dosage delivered to the resist is illustrated on the y-axis, and is 100% of a normal dosage. Because of the zero background exposure, the total dosage and the shot dosage are the same. Dosage graph  410  also illustrates the resist threshold  414 . The CD variation of the shape represented by dosage graph  410  in the x-direction is inversely related to the slope of the dosage curve  412  at x-coordinates “a” and “b” where it intersects the resist threshold. 
     The  FIG. 4B  condition of zero background exposure is not reflective of actual designs. Actual designs will typically have many other shots within the backscattering distance of shot  402 .  FIG. 4C  illustrates an example of a dosage graph  420  of a shot with a normal dosage with non-zero background exposure  428 . In this example, a background exposure of 20% of a normal dosage is shown. In dosage graph  420 , dosage curve  422  illustrates the cross-sectional dosage of a shot similar to shot  402 . The CD variation of curve  422  is worse than the CD variation of curve  412 , as indicated by the lower edge slope where curve  422  intersects resist threshold  424  at points “a” and “b”, due to the background exposure caused by backscatter. 
     One method of increasing the slope of the dosage curve at the resist threshold is to increase the shot dosage.  FIG. 4D  illustrates an example of a dosage graph  430  with a dosage curve  432  which illustrates a total dosage of 150% of normal dosage, with no background exposure. With no background exposure, the shot dosage equals the total dosage. Threshold  434  in  FIG. 4D  is unchanged from threshold  414  in  FIG. 4B . Increasing shot dosage increases the size of a pattern registered by the resist. Therefore, to maintain the size of the resist pattern, illustrated as the intersection points of dosage curve  432  with threshold  434 , the shot size used for dosage graph  430  is somewhat smaller than shot  402 . As can be seen, the slope of dosage curve  432  is higher where it intersects threshold  434  than is the slope of dosage curve  412  where it intersects threshold  414 , indicating a lower, improved, CD variation for the higher-dosage shot of  FIG. 4D  than for the normal dosage shot of  FIG. 4B . 
     Like dosage graph  410 , however, the zero background exposure condition of dosage graph  430  is not reflective of actual designs.  FIG. 4E  illustrates an example of a dosage graph  440  with the shot dosage adjusted to achieve a total dosage on the resist of 150% of normal dosage with a 20% background exposure, such as would occur if the dosage of only one shot was increased to achieve total dosage of 150% of a normal dosage, and dosage of other shots remained at 100% of normal dosage. The threshold  444  is the same as in  FIGS. 4B-4D . The background exposure is illustrated as line  448 . As can be seen, the slopes of dosage curve  442  at x-coordinates “a” and “b” are less than the slopes of dosage curve  432  at x-coordinates “a” and “b” because of the presence of backscatter. Comparing graphs  420  and  440  for the effect of shot dosage, the slope of dosage curve  442  at x-coordinates “a” and “b” is higher than the slope of dosage curve  422  at the same x-coordinates, indicating that improved edge slope can be obtained for a single shot by increasing dosage, if dosages of other shots remain the same. 
       FIG. 4F  illustrates an example of a dosage graph  450 , illustrating the case where the dosages of all shots have been increased to 150% of normal dose. Two background dosage levels are shown on dosage graph  450 : a 30% background dose  459 , such as may be produced if all shots use 150% of normal dosage, and a 20% background dose  458  shown for comparison, since 20% is the background dosage in the dosage graph  440 . Dosage curve  452  is based on the 30% background dose  459 . As can be seen, the edge slope of dosage curve  452  at x-coordinates “a” and “b” is less than that of dosage curve  442  at the same points. 
     In summary,  FIGS. 4A-F  illustrate that higher-than-normal dosage can be used selectively to lower CD variation for isolated shapes. Increasing dosage has two undesirable effects, however. First, an increase in dose is achieved in modern charged particle beam writers by lengthening exposure time. Thus, an increase in dose increases the writing time, which increases cost. Second, as illustrated in  FIGS. 4E-F , if many shots within the backscatter range of each other use an increased dosage, the increase in backscatter reduces the edge slope of all shots, thereby worsening CD variation for all shots of a certain assigned dosage. The only way for any given shot to avert this problem is to increase dosage and shoot a smaller size. However, doing this increases the backscatter even more. This cycle causes all shots to be at a higher dose, making write times even worse. Therefore, it is better to increase dose only for shots that define the edge. 
       FIG. 5A  illustrates an example of a square VSB shot  502 . In this example square  502  has a dimension  504  of 100 nm. Pattern  506  is an example of how shot  502 , with a normal dose, may register on a resist-coated surface. As can be seen, the corners  508  of pattern  506  are rounded, due to beam blur. If formed on a reticle to be used for EUV optical lithography using 4× reduction printing, pattern  506  could be used to form a pattern on a wafer having a size of approximately 25 nm.  FIG. 5B  illustrates an example of a smaller square VSB shot  512 . In this example, the dimension  514  of shot  512  is 60 nm, suitable for manufacturing a 4× reticle for a pattern intended to be 15 nm on a wafer. Pattern  516  is an example of how shot  512  may register on a resist-coated surface. As can be seen, the corner rounding effects of beam blur have caused the registered pattern to be virtually circular. Additionally, though not illustrated, the edge slope of pattern  516  will be lower than that of pattern  506 , and may be below a minimum pre-determined level to produce acceptable CD variation.  FIGS. 5A&amp;B  illustrate how beam blur effects become more significant as pattern dimensions decrease. 
     As fabrication processes get smaller, short-range beam blur effects become a more significant issue for both direct-write and for reticle/mask fabrication. Small geometries can also have problems with edge slope due to long-range effects. Accurate fabrication of the ends of minimum-width lines—that is the lines having the minimum width permissible in a fabrication process—can become challenging using conventional techniques, as will be shown below. One type of pattern on which these problems may be exhibited is at a line end, which is the region near an end of a path, where the path may be of constant width, such as interconnect lines or where polysilicon crosses and extends beyond diffusion to form a MOS transistor. 
       FIG. 6A  illustrates an example of a portion  602  of a line that is desired to be formed on a reticle. The portion includes line end  604 . In this example the designed width on the wafer is 20 nm. Using a 4× mask, the target width  606  on the reticle is therefore 80 nm.  FIG. 6B  illustrates an example of an outline of a single VSB shot  614  that may be used with normal dosage to conventionally form the pattern on a reticle.  FIG. 6B  also illustrates a pattern  618  formed on the reticle by the shot  614 . As can be seen, the corners of line-end pattern  618  are significantly rounded. A portion  619  of the perimeter of pattern  618  is illustrated with a dashed line, indicating that this portion of the perimeter has an edge slope that is less than a pre-determined minimum.  FIG. 6C  illustrates an example of a method for forming the pattern  602  according to the current invention. In  FIG. 6C , two shots are used to expose the line-end pattern  602 : shot  624  and shot  625  which overlaps shot  624 . Shot  624  uses higher-than-normal dosage. The additional shot  625  provides additional peak dosage near the line end. Shot  625  uses a lower dosage than shot  624 , if assigned shot dosages are allowed. If assigned shot dosages are not allowed, multi-pass exposure may be used with shot  625  being grouped into an exposure pass having a lower base dosage than the exposure pass with shot  624 . The two shots  624  and  625  can produce a pattern  628  on the reticle, where the corners of pattern  628  are less rounded than the corners of pattern  618 . The dashed line portions  629  of the perimeter of pattern  628  is shorter than the dashed line portion  619  of pattern  618 , indicating improved line end edge slope in pattern  628 , due to the higher line-end exposure in pattern  628  compared to pattern  618 . 
       FIG. 6D  illustrates another embodiment of the current invention, using three shots to form the line end  604  of pattern  602 . Shot  634  uses higher-than-normal dosage, like shot  624  of  FIG. 6C . Additionally, shots  635  and shot  636  overlap shot  634  and add additional peak dosage near the line end corners. Shots  635  and  636  may have lower dosage than shot  634 . Shots  635  and  636  may, as illustrated in this example, extend beyond the outline of shot  634  and of the original pattern  602 . Also, the illustrated shapes  635  and  636  may be shot as separate VSB shots, or in a single CP shot if a complex CP character is designed with the two illustrated shapes  635  and  636 . The three VSB shots  634 ,  635  and  636 , or two shots if a CP shot is used to shoot illustrated shapes  635  and  636 , can produce a pattern  638  on a reticle, where pattern  638  corners are less rounded than the corners of pattern  628  which resulted from two shots. Additionally, low edge slope portion  639  of the perimeter of pattern  638  is smaller than perimeter portion  629  of pattern  628 .  FIG. 6D  illustrates how larger numbers of shots may be used to form line end patterns which both more accurately achieve the desired shape and which have a higher edge slope. 
       FIG. 6E  illustrates yet another embodiment of the current invention, using four shots to form the line end  604  of pattern  602 . In addition to main shot  644 , which may have a higher-than-normal dosage, two corner shots  645  and  646  are used, and shot  647  adds exposure to the middle of the line-end. The dosage of shot  647  may be less than the dosage of shots  645  and  646 . Shot  647  allows the dosage in the middle of the line end to be adjusted independently of the dosages for the line end corners. Pattern  648  illustrates a pattern that shots  644 ,  645 ,  646  and  647  can produce on a reticle. In pattern  648  the perimeter portion  649  which has a lower-than-minimum edge slope is slightly smaller than  FIG. 6D  perimeter portion  639 . Additionally, the illustrated shapes  645  and  646  may be shot as a single complex CP character shot, if these shapes are designed and fabricated on a stencil. 
       FIGS. 6C-E  illustrate how a set of shots may be modified with overlapping shots to produce small areas of high peak dosage near line ends, improving both the accuracy and the edge slope of the pattern manufactured on a reticle. Exposure of only a small area with a higher-than-normal dosage produces less increase in backscatter than if the higher-than-normal dosage was used for the entire pattern. The shots are modified with a shot varying technique, which may include varying one or all of: shot dosages, the placement of the overlap, and the size of the overlapping shot. Particle beam simulation may be used to determine the effect that a set of shots and dosages will produce on the reticle surface. 
       FIGS. 9A-E  illustrate the use of overlapping shots with square patterns, such as are commonly used for contact and via patterns in integrated circuit design.  FIG. 9A  illustrates an example of a desired pattern  902  to be formed on a reticle.  FIG. 9B  illustrates a single VSB shot  912  which may be used to form pattern  902  conventionally. For small patterns, however, use of single VSB shot  912  may cause corner rounding similar to the corner rounding illustrated in  FIG. 6B  pattern  618 . Also like pattern  618 , use of single shot  912  may cause edge slope to be undesirably low.  FIG. 9C  illustrates an example of one embodiment of the present invention for forming a square or nearly-square pattern. Five VSB shots may be used, including shot  922 , which is cross-hatched for identification, and four VSB corner shots  924  which overlap the corners of shot  922 . Alternatively, all four illustrated corner shapes  924  may be designed into a single complex CP character on a stencil, allowing the example of  FIG. 9C  to be shot with one VSB shot  922  and one CP shot  924 . As with the  FIG. 6D  line-end shot configuration, the addition of corner shots to increase peak dosage near the corners of the pattern may improve the fidelity of the transferred pattern, and may also improve the edge slope near the corners of the transferred pattern, so as to reduce CD variation. 
       FIG. 9D  illustrates an example of another embodiment of the present invention. Like the  FIG. 9C  shot configuration,  FIG. 9D  may be shot using five VSB shots, including shot  932 , which is cross-hatched, and four additional shots  934  around the perimeter areas of the original pattern  902 . Also like  FIG. 9C , a CP character may be designed to expose the pattern illustrated by the four rectangles  934  in a single CP shot, allowing  FIG. 9D  to be exposed in one VSB shot  932  and one CP shot for all shapes  934 . The use of the perimeter CP shot or VSB shots can increase the edge slope of the entire perimeter of the transferred pattern by increasing peak dosage near the perimeter. The small perimeter CP shot or VSB shots do not increase the area dosage as much as if a higher dosage was used for shot  912 , reducing the backscatter compared to if a higher dosage shot  912  was used alone. 
       FIG. 9E  illustrates an example of another embodiment of the present invention. Nine regions are illustrated in  FIG. 9E : a) a large region  942 , b) four side regions  944 , and c) four corner regions  948 . As can be seen, all regions  944  and  948  overlap region  942 . These regions may be exposed by any of the following methods:
         Nine separate VSB shots, including one for region  942 , four shots for the four regions  944 , and four shots for the four corner regions  948 .   Five VSB shots. Region  942  is exposed by one shot. For the remaining four VSB shots, each shot includes the union of one side region  944  and two corner regions  948  adjacent to the side regions. This provides a higher dosage at the corners than along the side perimeters. The additional peak exposure near the corner may provide improved accuracy and/or edge slope.   One VSB shot for region  942  and two CP shots—one shot each of two CP characters. One CP character may be designed, for example to include the four side regions  944  and a second CP character may be designed to include the four corner regions  948 . This solution allows independent dosage control of the corner regions and non-corner side regions.
 
The method using one VSB shot with two CP shots should require less exposure time than either the nine-shot VSB or the five-shot VSB methods. Additionally, the size of shot  942  may be modified to be smaller than the desired pattern  902 .
       

     The methods of this invention may also be employed with fabrication processes that use rectangular contacts and/or vias. For rectangular patterns with an aspect ratio of about 1:1.5 or less, the method illustrated in  FIG. 9D  may be used. For rectangular patterns with greater aspect ratios, each end of the longer axes of the rectangular pattern may be treated as a line end. 
     The solution described above with  FIG. 9C  may be implemented even using a charged particle beam system that does not allow dosage assignment for individual shots. In one embodiment of the present invention, a small number of dosages may be selected, for example two dosages such as 1.0× normal and 0.6× normal, and shots for each of these two dosages may be separated and exposed in two separate exposures passes, where the base dosage for one exposure pass is 1.0× normal and the base dosage for the other exposure pass is 0.6× normal. In the example of  FIG. 9C , shot  922  may be assigned to a first exposure pass which uses a base dosage of 1.0× normal dosage before PEC correction. The four shots  924  may be assigned to a second exposure pass which uses a base dosage of 0.6× normal dosage before PEC correction. Thus, overlapping shots can create pattern dosages greater than 100% of normal, even with charged particle beam writers which do not support dosage assignment for individual shots. 
     The dosage that would be received by a surface can be calculated and stored as a two-dimensional (X and Y) dosage map called a glyph. A two-dimensional dosage map or glyph is a two-dimensional grid of calculated dosage values for the vicinity of the shots comprising the glyph. This dosage map or glyph can be stored in a library of glyphs. The glyph library can be used as input during fracturing of the patterns in a design. For example, referring again to  FIG. 9D , a dosage map may be calculated for the combination of shots  932  and the four shots  934  and stored in the glyph library. If during fracturing, one of the input patterns is a square pattern of the same size as pattern  902 , the glyph for pattern  902  and the five shots comprising the glyph may be retrieved from the library, avoiding the computational effort of determining an appropriate set of shots to form the square input pattern. Glyphs may also contain CP shots, and may contain dragged CP or VSB shots. A series of glyphs may also be combined to create a parameterized glyph. Parameters may be discrete or may be continuous. For example, the shots and dosage maps for forming square patterns such as square pattern  902  may be calculated for a plurality of pattern sizes, and the plurality of resulting glyphs may be combined to form a discrete parameterized glyph. In another example, a pattern width may be parameterized as a function of dragged shot velocity. 
       FIG. 7  is a conceptual flow diagram  750  of how to prepare a reticle for use in fabricating a surface such as an integrated circuit on a silicon wafer. In a first step  752 , a physical design, such as a physical design of an integrated circuit, is designed. This can include determining the logic gates, transistors, metal layers, and other items that are required to be found in a physical design such as that in an integrated circuit. Next, in a step  754 , optical proximity correction is determined. In an embodiment of this disclosure this can include taking as input a library of pre-calculated glyphs or parameterized glyphs  776 . This can also alternatively, or in addition, include taking as input a library of pre-designed characters  770  including complex characters that are to be available on a stencil  760  in a step  762 . In an embodiment of this disclosure, an OPC step  754  may also include simultaneous optimization of shot count or write times, and may also include a fracturing operation, a shot placement operation, a dose assignment operation, or may also include a shot sequence optimization operation, or other mask data preparation operations, with some or all of these operations being simultaneous or combined in a single step. Once optical proximity correction is completed a mask design is developed in a step  756 . 
     In a step  758 , a mask data preparation operation which may include a fracturing operation, a shot placement operation, a dose assignment operation, or a shot sequence optimization may take place. Either of the steps of the OPC step  754  or of the MDP step  758 , or a separate program independent of these two steps  754  or  758  can include a program for determining a limited number of stencil characters that need to be present on a stencil or a large number of glyphs or parameterized glyphs that can be shot on the surface with a small number of shots by combining characters that need to be present on a stencil with varying dose, position, and degree of partial exposure to write all or a large part of the required patterns on a reticle. Combining OPC and any or all of the various operations of mask data preparation in one step is contemplated in this disclosure. Mask data preparation step  758 , which may include a fracturing operation, may also comprise a pattern matching operation to match glyphs to create a mask that matches closely to the mask design. In some embodiments of this disclosure, mask data preparation step  758  may include generating overlapping shots so as to produce a higher peak dosage near line ends or near perimeters of square or nearly-square patterns. Mask data preparation may also comprise inputting patterns to be formed on a surface with the patterns being slightly different, selecting a set of characters to be used to form the number of patterns, the set of characters fitting on a stencil mask, the set of characters possibly including both complex and VSB characters, and the set of characters based on varying character dose or varying character position or applying partial exposure of a character within the set of characters or dragging a character to reduce the shot count or total write time. A set of slightly different patterns on the surface may be designed to produce substantially the same pattern on a substrate. Also, the set of characters may be selected from a predetermined set of characters. In one embodiment of this disclosure, a set of characters available on a stencil in a step  770  that may be selected quickly during the mask writing step  762  may be prepared for a specific mask design. In that embodiment, once the mask data preparation step  758  is completed, a stencil is prepared in a step  760 . In another embodiment of this disclosure, a stencil is prepared in the step  760  prior to or simultaneous with the MDP step  758  and may be independent of the particular mask design. In this embodiment, the characters available in the step  770  and the stencil layout are designed in step  772  to output generically for many potential mask designs  756  to incorporate slightly different patterns that are likely to be output by a particular OPC program  754  or a particular MDP program  758  or particular types of designs that characterizes the physical design  752  such as memories, flash memories, system on chip designs, or particular process technology being designed to in physical design  752 , or a particular cell library used in physical design  752 , or any other common characteristics that may form different sets of slightly different patterns in mask design  756 . The stencil can include a set of characters, such as a limited number of characters that was determined in the step  758 , including a set of adjustment characters. 
     Once the stencil is completed the stencil is used to generate a surface in a mask writer machine, such as an electron beam writer system. This particular step is identified as a step  762 . The electron beam writer system projects a beam of electrons through the stencil onto a surface to form patterns in a surface, as shown in a step  764 . The completed surface may then be used in an optical lithography machine, which is shown in a step  766 . Finally, in a step  768 , a substrate such as a silicon wafer is produced. As has been previously described, in step  770  characters may be provided to the OPC step  754  or the MDP step  758 . The step  770  also provides characters to a character and stencil design step  772  or a glyph generation step  774 . The character and stencil design step  772  provides input to the stencil step  760  and to the characters step  770 . The glyph generation step  774  provides information to a glyphs or parameterized glyphs step  776 . Also, as has been discussed, the glyphs or parameterized glyphs step  776  provides information to the OPC step  754  or the MDP step  758 . 
     Referring now to  FIG. 8 , another exemplary conceptual flow diagram  800  of how to prepare a surface which is directly written on a substrate such as a silicon wafer is shown. In a first step  802 , a physical design, such as a physical design of an integrated circuit is designed. This may be an ideal pattern that the designer wants transferred onto a substrate. Next, in a step  804 , various data preparation (DP) steps, including fracturing and PEC, are performed to prepare input data to a substrate writing device. Step  804  may include fracturing of the patterns into a set of complex CP and/or VSB shots, where some of the shots may overlap each other. The step  804  may also comprise inputting possible glyphs or parameterized glyphs from step  824 , the glyphs being based on predetermined characters from step  818 , and the glyphs being determined using a calculation of varying a character dose or varying a character position or applying partial exposure of a character in glyph generation step  822 . The step  804  may also comprise pattern matching to match glyphs to create a wafer image that matches closely to the physical design created in the step  802 . Iterations, potentially including only one iteration where a correct-by-construction “deterministic” calculation is performed, of pattern matching, dose assignment, and equivalence checking may also be performed. In some embodiments of this disclosure, data preparation step  804  may include generating overlapping shots near the line ends or near the perimeters of square or nearly-square patterns. A stencil is prepared in a step  808  and is then provided to a wafer writer in a step  810 . Once the stencil is completed the stencil is used to prepare a wafer in a wafer writer machine, such as an electron beam writer system. This step is identified as the step  810 . The electron beam writer system projects a beam of electrons through the stencil onto a surface to form patterns in a surface. The surface is completed in a step  812 . 
     Further, in a step  818  characters may be provided to the data preparation and PEC step  804 . The step  818  also provides characters to a glyph generation step  822 . The character and stencil design step  820  provides input to the stencil step  808  or to a character step  818 . The character step  818  may provide input to the character and stencil design step  820 . The glyph generation step  822  provides information to a glyphs or parameterized glyphs step  824 . The glyphs or parameterized glyphs step  824  provides information to the Data Prep and PEC step  804 . The step  810  may include repeated application as required for each layer of processing, potentially with some processed using the methods described in association with  FIG. 7 , and others processed using the methods outlined above with respect to  FIG. 8 , or others produced using any other wafer writing method to produce integrated circuits on the silicon wafer. 
     The fracturing, mask data preparation, proximity effect correction and glyph creation flows described in this disclosure may be implemented using general-purpose computers with appropriate computer software as computation devices. Due to the large amount of calculations required, multiple computers or processor cores may also be used in parallel. In one embodiment, the computations may be subdivided into a plurality of 2-dimensional geometric regions for one or more computation-intensive steps in the flow, to support parallel processing. In another embodiment, a special-purpose hardware device, either used singly or in multiples, may be used to perform the computations of one or more steps with greater speed than using general-purpose computers or processor cores. In one embodiment, the special-purpose hardware device may be a graphics processing unit (GPU). In another embodiment, the optimization and simulation processes described in this disclosure may include iterative processes of revising and recalculating possible solutions, so as to minimize either the total number of shots, or the total charged particle beam writing time, or some other parameter. In yet another embodiment, an initial set of shots may be determined in a correct-by-construction method, so that no shot modifications are required. 
     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, mask data preparation, and proximity effect correction 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.