Abstract:
Method for computing an exposure pattern for exposing a desired pattern on a target in a charged-particle lithography apparatus, in which a particle beam is directed to and illuminates a pattern definition device comprising an aperture array composed of a plurality of blanking apertures through which said particle beam penetrates for writing said desired pattern by exposing a multitude of pixels within an exposure area on the target, said method taking into account a spatially dependent distortion of the target within the exposure area, with respect to dislocations transversal to the direction of the particle beam.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application No. 62/046,643 filed on Sep. 5, 2014, the disclosure of which is hereby incorporated by reference in its entirety. 
    
    
     FIELD OF THE INVENTION AND DESCRIPTION OF PRIOR ART 
     Embodiments of the invention relate to the field of charged-particle multi-beam processing apparatuses for the exposure of a target by means of a structured beam of electrically charged particles, and in particular to a method for computing an exposure pattern for exposing a desired pattern on a target in a charged-particle lithography apparatus. In such an apparatus a particle beam is generated in an illumination system, is directed to and illuminates a pattern definition device comprising an aperture array composed of a plurality of blanking apertures through which said particle beam penetrates and is then imaged by a projection optics system onto a target, for writing said desired pattern by exposing a multitude of pixels within an exposure area on the target. 
     The applicant has realized charged-particle multi-beam tools of the mentioned type and developed corresponding charged-particle optics, pattern definition (PD) device, and multi-beam writing method, in particular a 50 keV electron multi-beam writer to realize leading-edge complex photomasks for 193 nm immersion lithography, of masks for EUV lithography and of templates (1× masks) for imprint lithography. The system is called eMET (electron Mask Exposure Tool) or MBMW (multi-beam mask writer) for exposing 6″ mask blank substrates. The multi-beam system has been called PML2 (Projection Mask-Less Lithography) for electron beam direct writer (EBDW) applications on Silicon wafer substrates. The multi-beam column and writing method can also be used for multi-beam inspection applications. 
     The schematics of the multi-beam writer are shown in  FIG. 1 . Such a lithographic apparatus is well known in prior art, such as U.S. Pat. No. 6,768,125, EP 2 187 427 A1 (=U.S. Pat. No. 8,222,621) and EP 2 363 875 A1 (=U.S. Pat. No. 8,378,320). In the following, only those details are given as needed to disclose certain embodiments of the invention such that one of ordinary skill in the art can practice the various embodiments of the invention; for the sake of clarity, the components are not shown to size in  FIG. 1 . The main components of the lithography apparatus  1  are—corresponding to the direction of the lithography beam lb, pb which in this example runs vertically downward in  FIG. 1 —an illumination system  3 , a pattern definition (PD) system  4 , a projecting system  5 , and a target station  6  with the substrate  16 . The whole apparatus  1  is contained in a vacuum housing  2  held at high vacuum to ensure an unimpeded propagation of the beam lb, pb along the optical axis cx of the apparatus. The charged-particle optical systems  3 ,  5  are realized using electrostatic and/or magnetic lenses. 
     The illumination system  3  comprises, for instance, an electron gun  7 , an extraction system  8  as well as a condenser lens system  9 . It should, however, be noted that in place of electrons, in general, other electrically charged particles can be used as well. Apart from electrons these can be, for instance, hydrogen ions or heavier ions, charged atom clusters, or charged molecules. 
     The extraction system  8  accelerates the particles to a defined energy of typically several keV, e.g. 5 keV. By means of a condenser lens system  9 , the particles emitted from the source  7  are formed into a wide, substantially telecentric particle beam  50  serving as lithography beam lb. The lithography beam lb then irradiates a PD system  4  which comprises a number of plates with a plurality of openings or apertures  24  ( FIG. 2 ). The PD system  4  is held at a specific position in the path of the lithography beam lb, which thus irradiates the plurality of apertures and is split up into a number of beamlets. 
     Referring to  FIG. 2 , some of the apertures  24  of the PD system  4  are “switched on” or “open” so as to be transparent to the incident beam in the sense that they allow the portion of the beam (beamlets  51 ) that is transmitted through it to reach the target; the other apertures are “switched off” or “closed”, i.e. the corresponding beamlets  52  cannot reach the target, and thus effectively these apertures and/or openings are non-transparent (opaque) to the beam. Thus, the lithography beam lb is structured into a patterned beam pb, emerging from the PD system  4 . The pattern of switched on apertures—the only portions of the PD system  4  which are transparent to the lithography beam lb—is chosen according to a pattern which is to be exposed on the target  16 . It has to be noted that the “switching on/off” of the beamlets usually is realized by some sort of deflection means provided in one of the plates of the PD system  4 : “Switched off”-beamlets are deflected off their path (by very small angles) so they cannot reach the target but are merely absorbed somewhere in the lithography apparatus, e.g. by an absorbing plate  11 . 
     The pattern as represented by the patterned beam pb is then projected by means of an electro-magneto-optical projection system  5  onto the substrate  16  where it forms an image of the “switched-on” apertures and/or openings. The projection system  5  implements a demagnification of, for instance, 200:1 with two crossovers c 1  and c 2 . The target or “substrate”  16  is, for instance, a 6″ mask blank or a silicon wafer covered with a particle sensitive resist layer  17 . The substrate is held by a chuck  15  and positioned by a substrate stage  14  of the target station  6 . 
     The information regarding the pattern to be exposed is supplied to the PD system  4  by a data path realized by means of an electronic pattern information processing system  18 . (Also see discussion of  FIGS. 14A and 14B  below.) 
     In the embodiment shown in  FIG. 1 , the projection system  5  is composed of a number of consecutive electro-magneto-optical projector stages  10   a ,  10   b ,  10   c , consisting of electrostatic and/or magnetic lenses and other deflection means. These lenses and means are shown in symbolic form only, since their application is well known in the prior art. The projection system  5  employs a demagnifying imaging through crossovers c 1 , c 2 . The demagnification factor for both stages is chosen such that an overall demagnification of several hundred results, e.g. 200:1. A demagnification of this order is in particular suitable with a lithography setup, in order to alleviate problems of miniaturization in the PD device. 
     In the whole projection system  5 , provisions are made to extensively compensate chromatic and geometric aberrations. As a means to shift the image laterally as a whole, i.e. along a direction perpendicular to the optical axis cx, deflection means  12   a ,  12   b  and  12   c  are provided in the condenser  3  and projection system  5 . The deflection means can be realized as, for instance, a multipole electrode system which is positioned near the source extraction system ( 12   a ), near the first crossover, as shown in  FIG. 1  with the deflection means  12   b , and/or after the final lens  10   c  of the respective projector, as in the case with the stage deflection means  12   c  in  FIG. 1 . In this apparatus, a multipole electrode arrangement is used as deflection means both for shifting the image in relation to the stage motion and for correction of the imaging system in conjunction with the charged-particle optics alignment system. These deflection means  10   a ,  10   b ,  10   c  are not to be confused with the deflection array means of the PD system  4  which, in conjunction with the stopping plate  11 , are used to switch selected beamlets of the patterned beam pd to “on” or “off” state, since the former only deal with the particle beam as a whole. There is also the possibility to rotate the ensemble of programmable beams using a solenoid  13  providing an axial magnetic field. 
     As can be seen in the sectional detail of  FIG. 2 , the PD system  4  preferably comprises three plates stacked in a consecutive configuration: An “Aperture Array Plate” (AAP)  20 , a “Deflection Array Plate” (DAP)  30  and a “Field-boundary Array Plate” (FAP)  40 . It is worthwhile to note that the term ‘plate’ refers to an overall shape of the respective device, but does not necessarily indicate that a plate is realized as a single plate component even though the latter is usually the preferred way of implementation; still, in certain embodiments, a ‘plate’, such as the aperture array plate, may be composed of a number of sub-plates. The plates are preferably arranged parallel to each other, at mutual distances along the Z direction. 
     The flat upper surface of AAP  20  forms a defined potential interface to the condenser optics/illumination system  11 . The AAP may, e.g. be made from a square or rectangular piece of a silicon wafer (approx. 1 mm thickness)  21  with a thinned center part  22 . The plate may be covered by an electrically conductive protective layer  23  which will be particularly advantageous when using hydrogen or helium ions (line in U.S. Pat. No. 6,858,118). When using electrons or heavy ions (e.g. argon or xenon), the layer  23  may also be of silicon provided by the surface section of  21  and  22 , respectively, so that there is no interface between layer  23  and bulk parts  21 / 22 , respectively. 
     The AAP  20  is provided with a plurality of apertures  24  realized as openings traversing the thinned part  22 . In the embodiment shown the apertures  24  are realized having a straight profile fabricated into the layer  23  and a “retrograde” profile in the bulk layer of the AAP  20  such that the downward outlets  25  of the openings are wider than in the main part of the apertures  24 . Both the straight and retrograde profiles can be fabricated with state-of-the-art structuring techniques such as reactive ion etching. The retrograde profile strongly reduces mirror charging effects of the beam passing through the opening. 
     The DAP  30  is a plate provided with a plurality of openings  33 , whose positions correspond to those of the apertures  24  in the AAP  20 , and which are provided with electrodes  35 ,  38  configured for deflecting the individual sub-beams passing through the openings  33  selectively from their respective paths. The DAP  30  can, for instance, be fabricated by post-processing a CMOS wafer with an ASIC circuitry. The DAP  30  is, for instance, made from a piece of a CMOS wafer having a square or rectangular shape and comprises a thicker part  31  forming a frame holding a center part  32  which has been thinned (but may be suitably thicker as compared to the thickness of  22 ). The aperture openings  33  in the center part  32  are wider compared to the apertures  24  (by approx. 2 μm at each side for instance). CMOS electronics  34  is used to control the electrodes  35 ,  38 , which are provided by means of MEMS techniques. Adjacent to each opening  33 , a “ground” electrode  35  and a deflection electrode  38  are provided. The ground electrodes  35  are electrically interconnected, connected to a common ground potential, and comprise a retrograde part  36  to prevent charging and an isolation section  37  in order to prevent unwanted shortcuts to the CMOS circuitry. The ground electrodes  35  may also be connected to those parts of the CMOS circuitry  34  which are at the same potential as the silicon bulk portions  31  and  32 . 
     The deflection electrodes  38  are configured to be selectively applied an electrostatic potential; when such electrostatic potential is applied to an electrode  38 , this will generate an electric field causing a deflection upon the corresponding sub-beam, deflecting it off its nominal path. The electrodes  38  as well may have a retrograde section  39  in order to avoid charging. Each of the electrodes  38  is connected at its lower part to a respective contact site within the CMOS circuitry  34 . 
     The height of the ground electrodes  35  is higher than the height of the deflection electrodes  38  in order to suppress cross-talk effects between the beams. 
     The arrangement of a PD system  12  with a DAP  30  having electrodes oriented downstream as shown in  FIG. 2  is only one of several possibilities. Further DAP configurations, e.g. with embedded ground and deflection electrodes, can easily be devised by the skilled person (see other patents in the name of the applicant, such as U.S. Pat. No. 8,198,601 B2). 
     The third plate  40  serving as FAP has a flat surface facing to the first lens part of the down-stream demagnifying charged-particle projection optics and thus provides a defined potential interface to the first lens  16   a  of the projection optics. The thicker part  41  of FAP  40  is a square or rectangular frame made from a part of a silicon wafer, with a thinned center section  42 . The FAP  40  is provided with a plurality of openings  43  which correspond to the openings  24 ,  33  of the AAP  20  and DAP  30  but are wider as compared to the latter. 
     The PD system  4 , and in particular the first plate thereof, the AAP  20 , is illuminated by a broad charged particle beam  50  (herein, “broad” beam means that the beam is sufficiently wide to cover the entire area of the aperture array formed in the AAP), which is thus divided into many thousands of micrometer-sized beams  51  when transmitted through the apertures  24 . The beamlets  51  and  52  will traverse the DAP and FAP unhindered. 
     As already mentioned, whenever a deflection electrode  38  is powered through the CMOS electronics, an electric field will be generated between the deflection electrode and the corresponding ground electrode, leading to a small but sufficient deflection of the respective beam  52  passing through ( FIG. 2 ). The deflected beam can traverse the DAP and FAP unhindered as the openings  33  and  43 , respectively, are made sufficiently wide. However, the deflected beam  52  is filtered out at the stopping plate  15  of the sub-column ( FIG. 1 ). Thus, only those beams which are unaffected by the DAP will reach the substrate. 
     The reduction factor of the demagnifying charged-particle optics  16  is chosen suitably in view of the dimensions of the beams and their mutual distance in the PD device  4  and the desired dimensions of the structures at the target. This will allow for micrometer-sized beams at the PD system whereas nanometer-sized beams are projected onto the substrate. 
     The ensemble of (unaffected) beams  51  as formed by AAP is projected to the substrate with a predefined reduction factor R of the projection charged-particle optics. Thus, at the substrate a “beam array field” (BAF) is projected having widths BX=AX/R and BY=AY/R, respectively, where AX and AY denote the sizes of the aperture array field along the X and Y directions, respectively. The beam size of an individual beam at the substrate is given by bX=aX/R and by=aY/R, respectively, where aX and aY denote the sizes of the beam  51  as measured along the X and Y directions, respectively, at the level of the DAP  30 . 
     It is worthwhile to note that the individual beams  51 ,  52  depicted in  FIG. 2  are representative of a much larger number of sub-beams, typically many thousands, arranged in a two-dimensional X-Y array. The applicant has, for instance, realized multi-beam charged-particle optics with a reduction factor of R=200 for ion as well as electron multi-beam columns with many thousands (e.g., 262,144) programmable beams. The applicant has realized such columns with a beam array field of approx. 82 μm×82 μm at the substrate. These examples are stated for illustrative purpose, but are not to be construed as limiting examples. 
     As a typical implementation of an MBMW, the applicant has realized a 50 keV electron MBMW providing 512×512 (262,144) programmable beamlets of 20 nm beam size within a 81.92 μm×81.92 μm beam array field at the substrate. For the realized writer system the substrate is a 6″ mask blank (area: 6″×6″=152.4 mm×152.4 mm, thickness: 1″/4=6.35 mm) covered with an electron beam sensitive resist. Furthermore, in the realized system of the applicant multi-beam writing is possible on resist covered 150 mm Si wafers. 
     The current density of the realized MBMW system of the applicant is ≦1 A/cm 2  when using 20 nm beam size. Thus, when all programmable 262,144 beamlets are “on” the current is ≦1.05 μA. 
     The MBMW column as realized by the applicant has a 1 sigma blur of approx. 5 nm, as verified experimentally and published in “eMET POC: Realization of a proof-of-concept 50 keV electron multibeam Mask Exposure Tool”, by Elmar Platzgummer et al., in Proc. of SPIE Vol. 8166, 816622-1 (2011). 
     There is the possibility to change the beam size from 20 nm to e.g. 10 nm. For a column with 200:1 reduction this is straightforward by using an aperture array plate (AAP) with 2 μm×2 μm opening size of the apertures instead of 4 μm×4 μm opening size. As outlined in U.S. Pat. No. 8,546,767 of the applicant, there is also a possibility of an in-situ change of the beam size. 
     When using 10 nm beam size and providing a current density at the substrate of no higher than 4 A/cm 2  the current of 262,144 programmable beamlets is again 1.05 μA at maximum. Thus, also in this case there is virtually no change of the 1 sigma column blur with current through the column. 
     The first generation MBMW production tools are targeted to use 20 nm and 10 nm beams providing up to approx. 1 μA current for all 262,144 programmable beams “on”. For following generations of MBMW production tools there is the plan to use even smaller beam size of e.g. 8 nm and concurrently to provide e.g. 640×640=409,600 beamlets within the 81.92 μm×81.92 μm beam array field at the substrate. Keeping the maximum current density at 4 A/cm 2  will ensure that the maximum current (with all beamlets “on”) is 1.05 μA. For instance, using a 5 nm beam size there allows providing e.g. 1024×1024=1,048,576 programmable beams within the 81.92 μm×81.92 beam array field at the substrate. again, at a maximum current density of 4 A/cm 2  the maximum current (with all beamlets “on”) is 1.05 μA. 
     The multi-beam writing method proposed by the applicant also includes a method using the same spot size, e.g. 20 nm, with an overlap between the spots, with a selected amount of overlap. In the “Double Grid” multi-beam exposure, the overlap between the spots is half of the beam size in X as well as in Y direction. In the “Quad Grid” multi-beam exposure, the overlap between the spots is a quarter of the beam size in X as well as in Y direction. The spot size at the substrate is aX/R where aX is the opening width of the apertures in the aperture array plate ( FIG. 2 ) and R is the reduction factor of the charged-particle projection optics. Each spot is exposed with discrete dose levels. For instance, when using 4 bits for programming the dose levels, the dose level of each spot can be selected to be 0, 1, 2, . . . 14, or 15 units. 
     In  FIG. 3A , an illustration for the case of a zero blur, the ideal intensity profile  61  is shown for a line with 30 nm width. When using “Quad Grid” multi-beam exposure, the overlap is a quarter of the beam size. Thus, for the case of using 20 nm beam size the physical grid size is 5 nm. A discrete dose level can be assigned to each physical grid area, which is 5 nm×5 nm for the example shown, and in  FIG. 3B  the discrete dose levels  62  applied for generating the 30 nm line are indicated.  FIG. 3C  shows the superposition of the zero blur intensity profile  61  ( FIG. 3A ) and the dose level histogram  62  ( FIG. 3B ). In the general case the dose level histogram will not be symmetrical in order to position the left and right edge at pre-defined positions. In  FIG. 3D  a simulation is shown for a line of 30.0 nm width with the left edge to be positioned at 0.0 nm and the right edge at 30.0 nm. For the simulation, exposure of 20 nm beam spots with a 1 sigma blur of 5.1 nm (12.0 nm FWHM blur) was assumed. The intensity profile  66  is formed by overlapping exposure spots  63 ,  64 , and  65 . The dose level of the leftmost exposure spot  64  is adjusted such that the 30 nm line starts at position  67 , i.e. the desired 0.0 nm position. The dose level of the rightmost exposure spot  65  is adjusted such that exposed line ends at  68  with 30.0 nm width. As shown in  FIG. 3D , the overlap of the 20 nm exposure spots  63 ,  64 ,  65  is a quarter of the beam size, i.e. 5 nm (“Quad Grid”). 
     Using the multi-beam exposure tool with 20 nm beam size and Quad Grid exposure (5 nm physical grid size), the line width can be changed in steps of 0.1 nm. As examples,  FIG. 4A  shows the intensity profile for 31.4 nm line width and  FIG. 4B  for 40.0 nm line width. Because of the integer dose levels there are slight deviations from the 0.1 nm address grid. These deviations are indicated as “edge position error” in the upper parts of  FIG. 4A  and  FIG. 4B , as functions of the desired line width, in 0.1 nm steps between 30.0 nm and 40.0 nm. As can be seen the deviations are within ±0.05 nm. Furthermore, the changes of edge position with 10% change of dose, as shown in the lower parts of  FIG. 4A  and  FIG. 4B , are approx. 1 nm, varying only slightly for different line widths. In other words, since the dose is controlled in a multi-beam writer tool of the applicant to better than 1%, there is only approx. 0.1 nm change of edge position with 1% change of dose. 
       FIG. 5A  illustrates one advantage of the multi-beam writer, namely, that the line width is virtually independent of blur variations at the 50% dose threshold. The edge positions  63  and  64  are where the zero blur intensity profile  61  crosses the “0.5” intensity level ( FIG. 5A  and  FIG. 5B ). The dose level assignments  62  are for using 20 nm beam size with 1 sigma blur of 5 nm and Quad Grid multi-beam exposure, providing a 5 nm physical grid. The intensity profiles  71 ,  72 , and  73  are calculated with 3.5 nm, 5.0 nm, and 7.5 nm 1 sigma blur, respectively. 
     As outlined above, the multi-beam tool column as realized by the applicant has a very low blur of approx. 5 nm 1 sigma. Therefore, the condition that the line width is independent of blur variations holds for a large range of beam size values, including 20 nm and 10 nm beam size. 
     When writing a pattern on a substrate such as a 6″ mask blank or silicon wafer, there are non-ideal situations which have to be taken into account during the multi-beam writing process in order to realize a mask or wafer with desired features and pattern fidelity. Possible problems to be taken into account are e.g. distortions of the substrate due to processing, distortions of the beam array field which cannot be corrected via optical deflection means, “loading effects” in a subsequent etching process, or charge induced influences. These effects can be simulated and/or measured. Corresponding data may be provided beforehand when preparing the data file for the patterns to be printed with the multi-beam writer (“data based correction”), or these effects may be calculated on basis of a model of the effect (“model based correction”). In most cases it turns out that corrections have to be done for substrate segments which are smaller than the size (area) of the beam array field, in order to meet the high demands of modern and future nanolithography technology. 
       FIG. 6  illustrates one example of local distortions in a target realized as a 6″ photomask blank  80  consisting of a 6″×6″×1″/4 quarzglass plate  80  covered with an electrically conducting masking layer and an electron beam sensitive resist. The local distortions may be caused by pattern density variations within the mask pattern field  83  of typically 133 mm×104 mm. Within this mask pattern field there may be areas of different density of exposed spots, for instance high density  84  and low density  85  pattern areas. In addition, usually there are subfields  82  with patterns for alignment purposes. Of course, embodiments of the invention are not restricted to this type of target but can be implemented using a wide range of targets and substrate. 
     SUMMARY OF THE INVENTION 
     Certain embodiments of the invention are described in the independent claims  1  and  15 . Advantageous developments and further aspects are described in the dependent claims. In detail, the method according to certain embodiments of the invention are intended to take into account a spatially dependent distortion of the target within the exposure area, with respect to dislocations transversal to the direction of the particle beam, and it comprises the steps of 
     (i) subdividing the exposure area into a plurality of non-overlapping sub-regions, 
     (ii) determining a subregion dislocation for each of said subregions, said subregion dislocation comprising a set of parameters describing (or, in other words, compensating) the distortion of the target at the location of the respective subregion, 
     (iii) providing the desired pattern as a graphical representation on the exposure area on the target, said graphical representation being composed of a plurality of graphical elements, each graphical element located at a respective position in the exposure area,
 
(iv) modifying the graphical representation in accordance with the plurality of subregion displacements, by dislocating each graphical element according to a subregion dislocation of the subregion which includes the respective position of the graphical element, obtaining a plurality of graphical elements thus dislocated, which compose a corrected graphical representation,
 
(v) calculating, from the corrected graphical representation, an exposure pattern defined on the multitude of pixels, said exposure pattern being suitable to create a nominal dose distribution on the target realizing contour lines representing the desired pattern.
 
     In relation to the distortions discussed above, many embodiments of the present invention aim at correcting distortion errors primarily of short-range; that is, for the case when the dislocations induced by the distortion are not constant over the substrate area, and variations of the displacements can be neglected only within (small) regions of the substrate, i.e., subregions of the exposure area, which are preferably of a comparably small area. In particular, the area of a subregion or segment may be comparable or smaller than e.g. the area of the beam array field. A number of embodiments of the invention suggest that such distortions are taken into account in the data path of the multi-beam writer tool. More specifically, the area to be exposed is divided into a number of non-overlapping subregions, i.e., discrete segments, whose size is customizable and stands in relation to the demanded precision. For instance, in a typical realization of the invention, said area is divided into n×m segments where the area of a segment is smaller than the beam array field, e.g. into rectangular segments of 10.25 μm×10.25 μm size when using a 82 μm×82 μm beam array field. As will be discussed further below in more detail, the distortion on each segment can be predetermined up to a certain precision using state-of-the-art methods; and this allows compensation of the distortions by modifying the pattern to be exposed accordingly, for instance, by altering the shape and placement of regions of said pattern in accordance to their nominal position in relation to the segmentation of the exposure area/substrate. These modifications take place in the data path before the respective part of the pattern is projected onto the substrate. According to preferred implementations of the invention, these corrections may include scaling in both spatial directions X and Y, rotations, angle corrections and X/Y-displacement/shift corrections. Typically, the distortion correction for each segment is small in comparison to the FWHM (full width half maximum) blur of the multi-beam writer column (it is noted that the FWHM blur is equal to 2.355 times the 1 sigma blur). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the following, the present invention is illustrated by several embodiments described below in more detail with reference to the attached drawings. It is emphasized that the embodiments shown here are of illustrative character and are not to be construed as limit the scope of the invention. The drawings schematically show: 
         FIG. 1  a charged-particle multi-beam system of state of the art in a longitudinal sectional view; 
         FIG. 2  a pattern definition system of state of the art in a longitudinal section; 
         FIGS. 3A-3D  illustrate intensity profiles of the multi-beam mask writer tool, namely,  FIG. 3A  shows a zero blur intensity profile for a line with 30 nm width,  FIG. 3B  indicates dose levels of overlapping exposure spots,  FIG. 3C  is a superposition of the previous two figures and  FIG. 3D  shows a simulated intensity profile  66  for a line of 30 nm width; 
         FIGS. 4A-4B  show multi-beam writer intensity profiles and related data as obtained for simulations of lines with a line width of 31.4 nm ( FIG. 4A ) and 40.0 nm ( FIG. 4B ), respectively; 
         FIG. 5A  shows intensity profiles of a 30 nm line as exposed with the multi-beam writer tool of the applicant, and 
         FIG. 5B  shows a detail of  FIG. 5A  at the left-hand flank where the intensity profiles cross the 50% intensity level; 
         FIG. 6  shows a typical example of the layout of a 6″ photomask substrate; 
         FIG. 7  shows a segmentation of an exposure area, assuming zero deviation of the X/Y positions of the segments; 
         FIG. 8A  shows an example where the segments are assigned distortion corrections, indicated by displacement vectors; 
         FIG. 8B  illustrates the distortion corrections as displaced segments; 
         FIG. 8C  shows a general assignment of distortion corrections of a single segment; and 
         FIG. 8D  shows an example of a general distortion correction including correction types shown in  FIG. 8C  affecting the exposure area from  FIG. 7 . 
         FIG. 9  shows an example of a pattern to be exposed being intersected by the segmentation boundaries of four segments. 
         FIG. 10  shows the pattern of  FIG. 9  after distortion correction according to a first variant of the invention. 
         FIGS. 11A-C  illustrate the distortion correction according to a second variant of the invention.  FIG. 11A  illustrates a division of the pattern to be exposed into smaller features according to the second variant.  FIG. 11B  depicts the pattern after distortion correction.  FIG. 11C  shows a modified version where the previously divided features of the pattern are reunited. 
         FIGS. 12A-D  illustrate treatment of critical features crossing a segment boundary.  FIG. 12A  shows a pattern having a critical feature element.  FIG. 12B  shows the modification of segment boundaries, so the whole critical element is allocated to one segment.  FIG. 14C  shows the resulting situation of X/Y shifts.  FIG. 14D  shows the same situation of  FIG. 14C  in more detail and with exaggerated displacements. 
         FIGS. 13A +B illustrate distortion correction according to a third variant.  FIG. 13A  shows an exemplary division of the pattern into smaller features, and  FIG. 13B  depicts the pattern after distortion correction. 
         FIG. 14A  shows a data path flow wherein the corrected vector data file is generated prior to rasterization. 
         FIG. 14B  shows another data path flow wherein the corrected pixel data file is generated after rasterization. 
         FIGS. 15A-E  illustrate interpolating of correction parameters with the example of the X/Y-displacement vectors.  FIG. 15A  shows assignments of displacement vectors to nine neighboring different segments.  FIGS. 15B and 15C  show the same assignments separated into the X- and Y-components, respectively, for each vector and segment.  FIGS. 15D and 15E  show contour-line plots of interpolated values with respect to the X- and Y-components, respectively, of the relative parameter. 
     
    
    
     DETAILED DESCRIPTION 
     Charged-particle multi-beam tools which are suitable for implementing certain embodiments of the invention are described above with reference to  FIGS. 1 to 5B . Further details about multi-beam charged-particle multi-beam tools can be found in U.S. Pat. No. 6,768,125, EP 2 187 427 A1 and EP 2 363 875 A1 and references cited therein, which are all herewith included by reference as part of the disclosure. 
     According to many embodiments of the invention, the exposure area is divided into a plurality of discrete subregions, hereinafter mostly referred to as “segments”.  FIG. 7  shows one example of an exposure area (shown is a part of the area of the substrate pattern field) segmented into segments  91 , with respect to an ideal zero deviation of the X/Y positions of segments. The segmentation may, but need not, be a regular grid and/or correspond to a grid aligned along the mathematical grid  92 . Preferably, the subregions may be realized as rectangular or quadratic segments  91 . It should be noted that many embodiments of the present invention include all finite-element-coverings of said area. Here, the size (or, area) of the segments (which generally is inversely proportional to their number) is related to the available computational power (speed of the datapath) and demanded precision. Apart from this limitation, the segmentation is chosen freely; ideally, however, appropriately with respect the given distortions. In a typical realization of the invention, the computational power should allow for a maximal segment size which is smaller than the beam array field of the multi-beam writer. For instance, for a mask field of 132 mm×104 mm to be exposed with a multi-beam writer possessing a 82 μm×82 μm beam array field with 512×512=262,144 beamlets, the available computational power of a realistic implementation will allow for a division into segments of approximately 10.25 μm×10.25 μm. 
     Each of said segments is assigned an individual distortion-correction, which is obtained from model-based and/or measurement-based analyses of the distortions affecting the multi-beam writer tool and specifically the target. Primarily, these corrections concern placement corrections.  FIG. 8A  shows an example of an assignment of placement correction vectors to the segmentation of  FIG. 7 , resulting in shift corrections as illustrated in  FIG. 8B . In this example, all segments  91 ′ have an X/Y shift with respect to the mathematical grid  92  (with the exception of two segments where the X/Y shift is zero), visualized in  FIG. 8A  with arrows  93  indicating the direction and symbolizing the amount of the segment area shifts, and in  FIG. 8B  as hatched segments  91 ′. Note that these shifts are depicted exaggerated for sake of clarity. In order to allow for higher-order corrections, each of the segments can also be assigned further correction-factors. In many embodiments of the invention and depicted in  FIG. 8C , these corrections may, for instance, include a rotation R 01  around a reference point, scaling in X-direction SX 01 , scaling in Y-direction SY 01  and an angle-correction A 01 , besides the mentioned shift D 01  along X and/or Y directions. Each set of parameters describing a correction of a segment is also called a “dislocation”  93 ′ in the context of the present application.  FIG. 8D  illustrates the influences on the segments in such a scenario with dislocations according to multiple types of corrections of  FIG. 8C . Note that due to angle-correction a rectangular segment may become an arbitrary parallelogram  91 ″. Note further that for the sake of simplicity, all of the following drawings only contain X/Y-placement corrections. However, embodiments of the invention are not limited to this single correction type. 
     As one important aspect of certain embodiments of the invention, the pattern to be exposed is considered for distortion correction. This concerns the way how the corrections assigned to each of the segments, is incorporated in said pattern which is composed of a plurality of graphical elements (e.g., polygons in case of a vector graphics, or pixels in case of a raster graphics). Preferred embodiments of the invention include the following schemes: 
     a) In a usual application, the pattern to be exposed is given as a polygon, like the polygon PG 0  shown in  FIG. 9 . (In general, a pattern will comprise a plurality of polygons and possibly other structures, such as circular dots, etc.) Here, the lines  94 ,  95  denote boundaries between the segments S 01 , S 02 , S 03 , S 04 .  FIG. 10  shows how the polygon PG 0  will look after distortion correction according to this first variant. The vectors D 11 , D 12 , D 13 , D 14  in  FIG. 9A  are vectors corresponding to displacement/shift corrections assigned to the segments S 01 , S 02 , S 03 , S 04 . According to one embodiment of the invention, each of the coordinates of the vertices defining the polygon is corrected according to the segment in which it lies. For instance, in  FIG. 10  all vertices of the original polygon (depicted in dashed lines) in the upper right segment S 03  are collectively shifted by the vector D 13 . In the more general case of corrections beyond shifts (rotation, X/Y-scaling and angle-correction) all vertex coordinates within one segment are transformed according to the correction that has been assigned to this particular segment. 
     b) According to a second variant of the invention, the pattern to be exposed is divided into segments at segment borders identical to the boundaries  94 ,  95  of the segmentation of the exposure area and corrected accordingly. As an illustrating example,  FIG. 11A  shows how the pattern to be exposed of  FIG. 9 , represented by polygon PG 0 , is divided by segment lines  94 ,  95  into four polygons PG 01 , PG 02 , PG 03 , PG 04 . The points where the polygons PG 01 , PG 02 , PG 03  and PG 04  meet at the segment boundaries  94 ,  95  are indicated as “border points” P 1 , P 2 , P 3 , P 4  and P 5  in  FIG. 11A .  FIG. 11B  illustrates the situation after corrections of the segment X/Y positions. It can be seen that the polygons PG 01 ′, PG 02 ′, PG 03 ′ and PG 04 ′ have new positions according to the individual distortion correction of each segment. It should be noted that instead of the border points P 1 , P 2 , P 3 , P 4 , P 5  there are now 12 new border points P 1 S 01 , P 1 S 02 , P 2 S 02 , P 2 S 03 , P 3 S 03 , P 3 S 04 , P 4 S 04 , P 4 S 01 , P 5 S 01 , P 5 S 02 , P 5 S 03 , and P 5 S 04 . Furthermore, each of the polygons PG 01 , PG 02 , PG 03 , PG 04  may also be rotated, resealed and angle-corrected (not shown in  FIG. 11B ) according to the correction assignment of the segments. 
     In a modified version of variant b), the new border points, in the example P 1 S 01 , P 1 S 02 , P 2 S 02 , P 2 S 03 , P 3 S 03 , P 3 S 04 , P 4 S 04 , P 4 S 01 , P 5 S 01 , P 5 S 02 , P 5 S 03 , and P 5 S 04 , which are a consequence of the segmentation, may also be used to reunify the pattern to be exposed. This optional version of variant b) is visualized in  FIG. 11C , where and connections (thick lines  FIG. 11C ) between the pairs P 1 S 01 -P 1 S 02 , P 2 S 02 -P 2 S 03 , P 3 S 03 -P 3 S 04 , and P 4 S 04 -P 4 S 01  enable a reunion of the polygons PG 01 , PG 02 , PG 03 , PG 04  (which were separated due to segmentation) into a single polygon PG 0 S; and the points P 5 S 01 , P 5 S 02 , P 5 S 03 , and P 5 S 04 , which are in the interior of the reunified polygon, vanish. 
     For a further optional version of variant b), it is important to note that the boundaries of the segments may be adapted in order to avoid the segmentation of critical features. As an example  FIG. 12A  shows a pattern PN 0  with a critical feature  142  of such length that the feature extends beyond the segment boundary. Thus, part  143  of the critical feature would belong to the segment with the main part of pattern PN 02 , whereas the part  144  of the critical feature  142  would belong to part PN 03  in the neighboring segment S 03 . In order to avoid the segmentation of such a critical feature there is an automatic feature of the datapath algorithm indicating a critical area between segment boundaries. There is then the decision to allocate the critical feature  152  as a whole to one segment only, in this case segment S 02 , so the critical feature remains part of feature PN 02 , PN 02 ′. The result of this procedure is given in  FIG. 12B  where the pattern PN 02  is generated including the critical feature. In other words, the segment boundary is altered at the region of the critical feature  152 .  FIG. 12C  shows the situation PN 0 ′ after applying a displacement/shift correction. The same is shown in  FIG. 12D  in more detail, where the coordinate displacements are exaggerated for clarity. 
     c) According to a third variant, the pattern to be exposed may be divided into a plurality of smaller features (typically but not necessarily polygons) independently from the segmentation of the exposure area. An arbitrary but reasonable reference point of each feature is used to assign each of them to one of the exposure area segments. A reasonable reference point is typically the center-of-mass, or the center of a bounding box enclosing each feature. Subsequently, each feature is distortion corrected according to its segment assignment. 
     As for the segmentation of the exposure area, the division of the pattern to be exposed into smaller features can be chosen freely. In a preferred embodiment of the invention there is the option to state a maximal size of the features. Typically, said maximal feature size is chosen small in relation to the segmentation of the exposure area. 
       FIG. 13A  and  FIG. 13B  illustrate an example of variant c).  FIG. 13A  shows that the exposure pattern of  FIG. 9  is divided into a plurality of polygons PL 0 , composed of smaller features (polygon portions) PL 01 , . . . , PL 07 , irrespective of the boundaries  94 ,  95  of the segments S 01 , S 02 , S 03  and S 04 . Each of the polygon portions PL 01  . . . PL 07  is assigned a reference point denoted by a B 01 , . . . , B 07 . In a preferred embodiment of the invention, these reference points are chosen to be the center of masses of the portions PL 01  . . . PL 07 , or the center of a rectangular bounding box minimally surrounding the respective portion (i.e., the center of the rectangular hull along X- and Y-directions). The distortion correction is then applied to each feature according to in which segment its reference point lies. For example,  FIG. 13B  illustrates that in the resulting structure PL 0 ′ comprising new portions PL 01 ′ . . . PL 07 ′, the polygon portions PL 02 ′, PL 03 ′ and PL 04 ′ are still connected as their reference points B 02 , B 03  and B 04  lie in the same segment S 02  and, consequently, are shifted in the same way; whereas other portions are shifted with respect to each others: for instance, portion PL 01 ′ is separated from portion PL 02 ′ after distortion correction, since reference point B 01  lies in segment S 01  whose assigned X/Y-placement-correction differs from the X/Y-placement-correction of segment S 02 . 
     Variants a) and c) also allow for applying 2D multivariate interpolation of the distortion correction factors, such as factors D 01 , R 01 , SX 01 , SY 01 , A 01  illustrated in  FIG. 8C , with respect to the center of the segments covering the exposure area. In particular, according to this embodiment of the invention, in variant a) each of the coordinates of the vertices defining the polygon is corrected according to the 2-dimensionally interpolated value (for example, via bilinear interpolation, bicubic interpolation, or spline interpolation). In variant c), every feature is distortion corrected according to the interpolated value at its reference point. 
       FIGS. 15A-E  show an example of the interpolation of the X/Y-displacement vectors D 15  between nine neighboring segments.  FIG. 15A  shows the originally assigned 2D-displacement vectors. In  FIGS. 15B and 15C  these displacement vectors are divided into their respective X- and Y-components for each segment, denoted by D 15 -X and D 15 -Y.  FIG. 15D  shows a contour-line plot of interpolated values D 15 ′-X with respect to the X-components of these vectors, and  FIG. 15E  shows a contour-line plot of interpolated values D 15 ′-Y with respect to the Y-components of these vectors. Hence, in total this interpolation yields a continuous function of displacement vectors defined by the components D 15 ′-X and D 15 ′-Y. 
     Multi-Beam System Datapath with Short-Range Distortion Correction 
       FIGS. 14A and 14B  illustrate how the above distortion corrections are incorporated in the datapath flow, in two respective variant processes. 
     The complete pattern image comprises a vast amount of image data, which is why for efficient processing of this data a high-speed datapath is needed that generates the pixel data to be exposed, preferably in real-time. The pattern to be exposed is typically described in a vector format, e.g. as a collection of geometries like rectangles, trapezoids or general polygons, which typically offers better data compaction and therefore reduces the requirements on data storage. The datapath comprises three major parts: 
     1) a distortion correction processing unit, which may implement one of above variants a), b) or c) 
     2) a rasterization process to translate the vector to pixel data, and 
     3) a buffer to temporarily store the pixel data for the writing process. 
     The distortion correction according to several embodiments of the invention can be done either prior to rasterization ( FIG. 14A ), or after rasterization ( FIG. 14B ). 
       FIG. 14A  shows a flowchart  120  of the datapath for the case when the distortion correction is done prior to rasterization. The datapath starts upon being supplied a pattern to be exposed  121 , presented e.g. as a vector data file. 
     Stage  122 : The exposure area is segmented into smaller areas. In a preferred realization of the invention these areas are small (or of about the same size) in comparison to the area of the beam array field of the multi-bream writer. Corrections that can be applied in the vector domain (e.g. proximity effect correction) may be carried out to all chunks independently, possibly in parallel, and the resulting data is sorted and coded in a way to improve computation speed of the following steps. The output is a collection of chunks where all chunks contain a collection of geometries. 
     Stage  123 : The pattern to be exposed is prepared for distortion corrected according to one of the above variants a), b) or c). Each of the variants comprises a step where particular features or point coordinates of the pattern to be exposed are assigned to a respective segment of the exposure area. In particular, variants b) and c) comprise a step where the pattern to be exposed is divided into smaller features. 
     Stage  124 : Next, the distortion correction is performed separately for each segment. In accordance with certain embodiments of the invention, these corrections may include parameters such as scaling SX 01 , SY 01  in both spatial directions X and Y, a rotation R 01 , an angle correction A 01  and most importantly a X/Y-positioning-correction D 01 , as shown in  FIG. 8C . 
     Stage  125  is Rasterization for the Multi-Beam Tool: The geometries of every feature are converted to a raster graphics array, where the pixel gray level represents the physical dose of the corresponding aperture image. Every pixel that is completely inside a geometry is assigned the gray level (intensity value) of the polygon, whereas the gray level of pixels that cross an edge of a geometry is weighed by the fraction of the area of the pixel that is covered by the geometry. This method implies a linear relation between the area of the geometry and the total dose after the rasterization. The doses are first calculated as floating point numbers; only later they are converted to the discrete set of dose values as supported by the PD device. As a result of rasterization the pixel data will be in the format of floating point numbers representing nominal dose values for the respective pixels. 
     Stage  126  comprises other pixel-based corrections, such as dose corrections and/or defective beam corrections. Details for these corrections can be found elsewhere and are not part of the invention. This step may be skipped if no pixel-based corrections are required. 
     Stage  127  provides Dithering: The dithering process converts the dose value data into gray value data, based on a predetermined gray value scale. This is a position-dependent rounding process that ensures that rounding errors are averaged over nearby pixels which, combined with oversampling, allows for a much finer dose variation than with the discrete set of dose values available for a single aperture (see section “Illustration of the Compensation Method”). This conversion can be realized by means of known algorithms for the conversion of visual image data into pixel graphics. It is possible to apply additional corrections (which are not part of the present invention) at this stage, provided they can be applied in the pixel domain, immediately before or after dithering depending on the actual correction (e.g. defective apertures correction). 
     Stage  128  is Pixel Packaging: The pixel image obtained from stage  127  is sorted according to the placement grid sequence and sent to the pixel buffer  129  of the electronic pattern information processing system  18  ( FIG. 1 ). The pixel data is buffered until a sufficient amount of data, typically at least the length of a stripe to be imaged on the target, is present which triggers the exposure of the stripe. The data is taken out of the buffer during the writing process. After the stripe has been written, the process described above starts anew for the pattern data of the next region, such as the next stripe. 
     As mentioned above and illustrated in the data path flowchart  130  of  FIG. 14B , for variant b) and c) there is also the possibility to implement the stages of the distortion correction  133 ,  134 ,  135  after rasterization  132 , as shown in  FIG. 14B . In other respect, the same considerations apply as discussed above with  FIG. 14A ; in particular, the stages  131  and  136 - 139  are equivalent to the stages  121  and  125 - 129  of data path  120 . To account for the discretized nature of a raster graphics, the dislocation corrections may additionally require a rounding of the dislocated locations to the raster coordinates.