Abstract:
A charged particle beam column for generating a variable shaped (in cross section) charged particle beam. The charged particle beam column includes: a source of a charged particle beam; a first aperture defining a first opening positioned coaxial to the beam and spaced apart from the source; a second aperture defining a second opening positioned coaxial to the beam and spaced apart from the first aperture; a third aperture defining a third opening positioned coaxial to the beam and spaced apart from the second aperture; an imaging device coaxial to the beam, where the imaging device controls focusing of the beam; and at least two deflection devices coaxial to the beam which controls a path of the beam through the openings. The charged particle beam column alternatively includes a source of a charged particle beam; a first aperture defining a first opening positioned coaxial to the beam and spaced apart from the source; a second aperture defining a second opening positioned coaxial to the beam and spaced apart from the first aperture; a solenoid lens which controls focusing of the beam; and at least one deflection device coaxial to the beam which controls a path of the beam through the openings.

Description:
BACKGROUND 
     1. Field of Invention 
     The invention relates to charged particle beam columns and in particular to charged particle beam columns that generate variable shaped beams. 
     2. Related Art 
     It is well known in the field of electron beam pattern generation that it is desirable to increase the throughput of pattern generation systems. The two main applications for such pattern generation systems are mask making for use in photolithography semiconductor fabrication and direct writing of patterns onto wafers to form semiconductor devices. 
     Lithographic systems typically used in electron beam pattern generation generate or expose patterns by controlling the flow of energy from a source to a substrate coated with a layer sensitive to that form of energy. Pattern exposure is controlled and partitioned into discrete units commonly referred to as flashes, wherein a flash is that portion of the pattern exposed during one cycle of an exposure sequence. Flashes are produced by allowing energy from the source, for example light, electron or other particle beams, to reach the coated substrate within selected pattern areas. The details of flash composition, dose and exposure sequence used to produce a pattern, and hence the control of the lithographic system, define what is known as a writing strategy. 
     In a typical vector scan writing strategy, the beam is positioned only over those sites that require exposure and then unblanked to expose the site (“flash”). Positioning is accomplished by a combination of substrate stage and beam movement in what is often referred to as a semi-random scan. Thus, pattern data must be provided that includes both the dose and position of each flash or site exposed. Frequently, vector scan strategies use a variable shaped beam, that is a beam capable of having a different size and/or shape (in terms of cross section) for each flash. The pattern is then composed from these variable shapes, called primitives. A shaped beam is capable of exposing a so called primitive. Where a variable shaped beam is used, the data additionally includes the location, size and shape for each flash. 
     The typical vector scan process decomposes patterns into rectangular shaped primitives. These rectangles are aligned along the x-y axes defining the vector scan. Thus for example in the pattern depicted in FIG. 1, using a typical vector scan process, only five sub-patterns are true rectangles while the other 62 sub-patterns are triangles approximated by multiple small rectangles. As shown in the example, in a conventional vector scan process, while only 17% of the pattern consists of slanted lines, patterning the slanted lines, i.e., sides not parallel to the x-y vector scan grid, using the rectangle approximations takes approximately 90% of the exposure time. 
     Techniques to generate shaped beams using multiple openings defined in a single aperture are described in, e.g., page 3814 of “Multielectron Beam Blanking Aperture Array System SYNAPSE 2000” by Hiroshi Yasuda, Soichiro Arai, Ju-ichi Kai, Yoshihisa Ooae, Tomohiko Abe, Shigeru Maruyama, and Takashi Kiuchi, J. Vac. Sci. Tech. Bulletin 14(6), November/December 1996; and page 185 of “A High Speed EBL Column Designed to Minimize Beam Interactions” by Lee Veneklasen, J. Vac. Sci. Tech. B3(1), January/February 1985. However, use of an opening, among multiple openings in a single aperture plane, requires deflection of an incident charged particle beam by a large angle. The larger the angle of beam deflection, the more errors that are introduced in beam positioning, and the larger the errors in beam shaping. Further, the larger the required deflection angle, the slower the throughput. 
     Thus what is needed is a beam shaping system capable of patterning non-rectangular primitives with a reduced number of flashes and lower deflection angles to increase throughput of patterns having non-orthogonal sides. 
     SUMMARY 
     An embodiment of the present invention includes a charged particle beam column for generating a variable shaped charged particle beam, the charged particle beam column including: a source of the charged particle beam; a first aperture defining a first opening positioned coaxial to the beam and spaced apart from the source; a second aperture defining a second opening positioned coaxial to the beam and spaced apart from the first aperture; a third aperture defining a third opening positioned coaxial to the beam and spaced apart from the second aperture; an imaging device coaxial to the beam, where the imaging device controls focusing of the beam; and at least two deflection devices coaxial to the beam which controls a path of the beam through the openings. 
     Thereby an embodiment of the present invention includes a method for shaping a charged particle beam, the method including the acts of: generating a charged particle beam; shaping the charged particle beam through a first opening; shaping the charged particle beam through a second opening; and shaping the charged particle beam through a third opening. 
     The present invention will be more fully understood in light of the following detailed description taken together with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS 
     FIG. 1 depicts a pattern represented as rectangular shaped primitives in a conventional vector scan writing strategy. 
     FIGS. 2A to  2 C depict schematically respective beam columns  200 A to  200 C in accordance with embodiments of the present invention. 
     FIG. 2D depicts a solenoid lens suitable for use in an embodiment of the present invention. 
     FIG. 3A depicts a planar view of aperture  300  that defines opening  302 . 
     FIG. 3B depicts a cross sectional view of first aperture  300  along line A—A of FIG.  3 A. 
     FIG. 4A depicts a relationship between a length, L, of a desired line, a radius, R, of a circular opening, and a tolerable error, Δ. 
     FIG. 4B depicts a relationship between distance, R, from the center of an opening to a corner Z, and length, L, of a side of an opening. 
     FIG. 5 depicts an example of a shaping of the image of beam  202  by a combination of first aperture  206 . 1 , second aperture  206 . 2 , third aperture  206 . 3 , and fourth aperture  206 . 4 . 
     FIG. 6 depicts a patterns  902  and  904  consisting of primitives generated by either of beam columns  200 A to  200 C. 
     FIG. 7A depicts a planar view of aperture  500  that defines opening  502 . 
     FIG. 7B depicts a cross sectional view of first aperture  500  along line B—B of FIG.  5 A. 
     FIG. 8A depicts a planar view of aperture  600  that defines opening  602 . 
     FIG. 8B depicts a cross sectional view of first aperture  600  along line C—C of FIG.  8 A. 
     FIG. 9A depicts in plan view the sequence of aperture openings that shape the image of beam  202  in accordance with an embodiment of the present invention. 
     FIG. 9B depicts a sample of beam images shapes created by shaping a beam with the four apertures of FIG. 9A, in accordance with an embodiment of the present invention. 
    
    
     Note that use of the same reference numbers in different figures indicates the same or like elements. 
     DETAILED DESCRIPTION 
     Beam Column 
     An embodiment of the present invention includes an electron beam column  200 A (shown schematically in a side view in FIG. 2A) that uses shaping apertures to generate electron (or other charged particle) beam cross sections having at least 3 approximately straight sides. In this embodiment, each shaping aperture defines a circular opening. In other embodiments, as discussed in more detail below, each aperture defines an opening having at least 3 straight sides. 
     Electron beam column  200  includes a conventional electron beam source  201  that outputs an electron beam  202  having a circular shaped cross section, whereby the combination of the first aperture  206 . 1 , a second aperture  206 . 2 , a third aperture  206 . 3 , and a fourth aperture  206 . 4  shapes the cross section of electron beam  202 . The direction of the electron beam  202  through the shaping apertures is controlled by a combination of: a conventional first deflector  210 . 1 , a conventional second deflector  210 . 2 , and a conventional third deflector  210 . 3 . The following components control the focusing of the cross section of electron beam  202 : a conventional first field lens  204 . 1 , a conventional first transfer lens  208 . 1 , a conventional second field lens  204 . 2 , a conventional second transfer lens  208 . 2 , a conventional third field lens  204 . 3 , a conventional third transfer lens  208 . 3 , and a conventional fourth field lens  204 . 4 . 
     The electron beam source  201  outputs electron beam  202  having a circular cross section. Crossover point  203 . 1  represents the gun crossover point of electron beam  202 . 
     First aperture  206 . 1  is positioned below electron beam source  201 . (Herein “below” means downstream with regard to the electron beam direction from beam source  201 .) An implementation of first aperture  206 . 1  is depicted in FIG. 3A as aperture  300 , which defines a circular opening  302 . FIG. 3B depicts a cross sectional view of aperture  300  along line A—A of FIG.  3 A. An equation describing a size of opening  302  is provided later. 
     Referring to FIG. 3A, a suitable conventional technique to fabricate the first aperture  206 . 1  is as follows. A top surface of a silicon wafer is covered with resist except for an exposed circular region defined by lithography. The top surface is etched to define a corresponding circular opening in the top surface. A bottom surface of the wafer, opposite the top surface is then covered with resist except for a circular region opposite the etched circular opening and having a same diameter. The bottom surface is etched to define a corresponding circular opening in the bottom surface. Thereby a circular opening, that corresponds to circular opening  302 , is etched entirely through the silicon wafer. 
     The conventional first field lens  204 . 1  is positioned within the same plane as first aperture  206 . 1 . First field lens  204 . 1  focuses the gun crossover point  203 . 1  onto crossover plane  203 . 2  and axially aligned with ray  212  that extends between the center of the openings defined in first aperture  206 . 1  and second aperture  206 . 2 . Crossover plane  203 . 2  is midway between the planes of first aperture  206 . 1  and second aperture  206 . 2 . A suitable implementation of first field lens  204 . 1  is an electron or non-beam lens. 
     The conventional first deflector  210 . 1  is positioned within the plane of crossover plane  203 . 2  and below first field lens  208 . 1 . When a voltage or current is applied to first deflector  210 . 1 , first deflector  210 . 1  generates a two dimensional field which deflects the path of electron beam  202  towards second aperture  206 . 2  and controls where electron beam  202  impinges second aperture  206 . 2 . 
     The conventional first transfer lens  208 . 1  is positioned within the plane of crossover plane  203 . 2 . First transfer lens  208 . 1  focuses the beam cross section as shaped by first aperture  206 . 1  onto the plane of second aperture  206 . 2 . A suitable implementation of first transfer lens  208 . 1  is an electron or non-beam lens. 
     Second aperture  206 . 2  is positioned below first transfer lens  208 . 1 . Second aperture  206 . 2  is similar to first aperture  206 . 1 . 
     The conventional second field lens  204 . 2  is positioned within the same plane as second aperture  206 . 2 . Second field lens  204 . 2  focuses the image from crossover plane  203 . 2  onto crossover plane  203 . 3  and axially aligned with ray  212  that extends between the center of the openings defined in second aperture  206 . 2  and third aperture  206 . 3 . Crossover plane  203 . 3  is midway between the planes of second aperture  206 . 2  and third aperture  206 . 3 . A suitable implementation of second field lens  204 . 2  is similar to first field lens  204 . 1 . 
     The conventional second deflector  210 . 2  is positioned within the plane of crossover plane  203 . 3  and below second field lens  204 . 2 . When a voltage or current is applied to second deflector  210 . 2 , second deflector  210 . 2  generates a two dimensional field which deflects the path of electron beam  202  towards third aperture  206 . 3  and controls where electron beam  202  impinges third aperture  206 . 3 . 
     The conventional second transfer lens  208 . 2  is positioned within the plane of crossover plane  203 . 3 . Second transfer lens  208 . 2  focuses the cross section of beam  202 , shaped by first aperture  206 . 1  and optionally by second aperture  206 . 2 , onto the plane of third aperture  206 . 3 . A suitable implementation of second transfer lens  208 . 2  is similar to first transfer lens  208 . 1 . 
     Third aperture  206 . 3  is positioned below second transfer lens  208 . 2 . Third aperture  206 . 3  is similar to first aperture  206 . 1 . 
     The conventional third field lens  204 . 3  is positioned within the same plane as third aperture  206 . 3 . Third field lens  204 . 3  focuses the image from crossover plane  203 . 3  onto crossover plane  203 . 4  and axially aligned with ray  212  that extends between the center of the openings defined in third aperture  206 . 3  and fourth aperture  206 . 4 . Crossover plane  203 . 4  is midway between the planes of third aperture  206 . 3  and fourth aperture  206 . 4 . A suitable implementation of third field lens  204 . 3  is similar to first field lens  204 . 1 . 
     The conventional third deflector  210 . 3  is positioned within the plane of crossover plane  203 . 4  and below third field lens  204 . 3 . When a voltage or current is applied to third deflector  210 . 3 , third deflector  210 . 3  generates a two dimensional field which controls the path of electron beam  202  towards fourth aperture  206 . 4  and controls where electron beam  202  impinges fourth aperture  206 . 4 . 
     The conventional third transfer lens  208 . 3  is positioned within the plane of crossover plane  203 . 4 . Third transfer lens  208 . 3  focuses the cross section of beam  202 , shaped by first aperture  206 . 1 , optionally by second aperture  206 . 2 , and optionally by third aperture  206 . 3 , onto the plane of fourth aperture  206 . 4 . A suitable implementation of third transfer lens  208 . 3  is similar to first transfer lens  208 . 1 . 
     Fourth aperture  206 . 4  is positioned below third transfer lens  208 . 3 . Fourth aperture  206 . 4  is similar to first aperture  206 . 1 . 
     The conventional fourth field lens  206 . 4  is positioned within the same plane as fourth aperture  206 . 4 . Fourth field lens  206 . 4  focuses the image from crossover plane  203 . 4  onto crossover plane  203 . 5 , which coincides with a surface of substrate  214 , and along a ray  212  that extends between through the centers of the openings defined in first aperture  206 . 1  to fourth aperture  206 . 4 . A suitable implementation of third field lens  204 . 3  is similar to first field lens  204 . 1 . 
     In this embodiment, the centers of the openings (point C shown in FIG. 3A) of first aperture  206 . 1 , second aperture  206 . 2 , third aperture  206 . 3 , and fourth aperture  206 . 4  are aligned along axis  212  descending from electron beam source  201 . 
     Second Beam Column 
     FIG. 2B schematically depicts a side view of beam column  200 B, in accordance with a second embodiment of the present invention. Like beam column  200 A, beam column  200 B includes a conventional electron beam source  201  that outputs an electron (or other charged particle) beam  202  having a circular shaped cross section, whereby first aperture  206 . 1 , a second aperture  206 . 2 , a third aperture  206 . 3 , and a fourth aperture  206 . 4  shape the cross section of electron beam  202 . The direction of the electron beam  202  through the shaping apertures is controlled by the combination of conventional first deflector  222 . 1 , a conventional second deflector  222 . 2 , and a conventional third deflector  222 . 3 . Solenoid lens  220 , which controls the focusing of the cross section of electron beam  202 , surrounds both the shaping apertures and the deflectors  222 . 1  to  222 . 3 . 
     First aperture  206 . 1 , second aperture  206 . 2 , third aperture  206 . 3 , and fourth aperture  206 . 4  are similar to the apertures having the same reference numbers as described above with respect to beam column  200 A. First deflector  222 . 1 , second deflector  222 . 2 , and third deflector  222 . 3  are similar to respective first deflector  210 . 1 , second deflector  210 . 2 , and third deflector  210 . 3  described above. The apertures and the deflectors of the beam column  200 B are arranged similarly as within beam column  200 A. 
     In this embodiment, the solenoid lens  220  performs similar functions as the combination of first field lens  204 . 1 , first transfer lens  208 . 1 , second field lens  204 . 2 , second transfer lens  208 . 2 , third field lens  204 . 3 , third transfer lens  208 . 3 , and fourth field lens  204 . 4 , described earlier with respect to beam column  200 A of FIG.  2 A. Thus solenoid lens  220  focuses the image from gun crossover point  203 . 1  onto crossover point  224 . 1  (located midway between first aperture  206 . 1  and second aperture  206 . 2 ), focuses the image at crossover point  224 . 1  onto crossover point  224 . 2  (located midway between second aperture  206 . 2  and third aperture  206 . 3 ), focuses the image at crossover point  224 . 2  onto crossover point  224 . 3  (located midway between third aperture  206 . 3  and fourth aperture  206 . 4 ), and focuses the image at crossover point  224 . 3  on crossover point  224 . 4 , the surface of substrate  214 . Solenoid lens  220  also focuses the image shaped by first aperture  206 . 1  onto the plane of second aperture  206 . 2 , focuses the image shaped by second aperture  206 . 2  onto the plane of third aperture  206 . 3 , and focuses the image shaped by the third aperture  206 . 3  onto the plane of fourth aperture  206 . 4 . 
     A suitable implementation of solenoid lens  220  is a conventional solenoid coil, such as depicted in FIG.  2 D. In one embodiment, the solenoid coil is enclosed by a cylindrical pipe (shown in cross section as  280 ), positioned coaxial with the beam  202 , to confine the solenoid coil&#39;s magnetic field. A suitable material of cylindrical pipe  280  is, e.g., iron. When a constant (D.C.) current is applied to the coils of the solenoid lens  220 , solenoid lens  220  generates a uniform magnetic field (not depicted), according to the principles of the well known Bio-Savart Law, which effectively deflects any electrons which stray from ray  212  to travel along ray  212 . The current level through the solenoid is set to achieve beam focusing at crossover point  224 . 4 . Such a current further focuses the beam throughout beam column  200 B as specified above. Thus beam column  200 B allows for convenient beam image focusing without the use of separate lens elements. 
     The separate lens elements of beam column  200 A are less compact than solenoid lens  220 , and thus solenoid lens  220  allows for beam column  200 B to be more compact than beam column  200 A. Consequently, beam column  200 B incurs less image distortion caused by electron-electron interactions. Beam column  200 B is also likely to be of lower cost than the combination of lenses of beam column  200 A. 
     Third Beam Column 
     FIG. 2C schematically depicts a side view of beam column  200 C, in accordance with a third embodiment of the present invention. Similar to beam columns  200 A and  200 B, beam column  200 C includes a conventional electron beam source  201  that outputs an electron beam  202  having a circular shaped cross section, whereby first aperture  206 . 1 , a second aperture  206 . 2 , a third aperture  206 . 3 , and a fourth aperture  206 . 4  shape the cross section of electron beam  202 . The direction of the electron beam  202  through the shaping apertures is controlled by a combination of conventional deflectors  254 . 1  to  254 . 5 . The focusing of the beam image, i.e., cross section, of electron beam  202  is controlled by a combination of field lenses  250 . 1  to  250 . 4  and transfer lens  260 . 
     Both the first field lens  250 . 1  and first aperture  206 . 1  are positioned below source  201 . Deflectors  254 . 1  and  254 . 2 , both positioned below first field lens  250 . 1  and first aperture  206 . 1 , separately deflect the direction of beam  202  from first aperture  206 . 1  and thereby control a location on second aperture  206 . 2  that beam  202  impinges. The second field lens  250 . 2  and second aperture  206 . 2  are positioned below deflector  254 . 2 . The combination of first field lens  250 . 1  and second field lens  250 . 2  focus an image of the gun crossover point  203 . 1  onto the plane of the transfer lens  260 . The arrangement of first field lens  250 . 1 , second field lens  250 . 2 , and deflectors  254 . 1  and  254 . 2 , relative to two shaping apertures, is conventional. 
     Transfer lens  260  focuses a cross section of beam  202  defined by the openings of the apertures  206 . 1  and  206 . 2 , located within the object plane  262 , onto plane  264 . Object plane  262  is located midway between the planes of first aperture  206 . 1  and  206 . 2 . Plane  264  is located midway between the planes of third aperture  206 . 3  and fourth aperture  206 . 4 . 
     Deflector  254 . 3 , positioned within the same plane as transfer lens  260 , controls the direction of beam  202  from second aperture  206 . 2  and thereby controls a location on third aperture  206 . 3  that beam  202  impinges. 
     Third field lens  250 . 3  and third aperture  206 . 3  are positioned below transfer lens  260 . Deflectors  254 . 4  and  254 . 5 , both positioned below third field lens  250 . 3  and third aperture  206 . 3 , separately deflect the direction of beam  202  from third aperture  206 . 3  and thereby control a location on fourth aperture  206 . 4  that beam  202  impinges. The fourth field lens  250 . 4  and fourth aperture  206 . 4  are positioned below deflector  254 . 5 . The combination of third field lens  250 . 3  and fourth field lens  250 . 4  focus an image of beam  202 , located at crossover plane  252 . 1 , onto crossover plane  252 . 2 , the surface of substrate  214 . 
     The final cross sectional shape of beam  202  at crossover plane  252 . 2  is effectively a shadow formed by overlap of openings of apertures  206 . 1 ,  206 . 2 ,  206 . 3 , and  206 . 4 . 
     First aperture  206 . 1 , second aperture  206 . 2 , third aperture  206 . 3 , and fourth aperture  206 . 4  are aligned by axis  212  descending from electron beam source  201  through crossover point C shown in FIG.  3 A. 
     Comparison of Beam Columns 
     By comparison, in beam column  200 C, electron beam  202  is not focused within the plane of any aperture. Thus, the cross section of electron beam  202  within each aperture plane of beam column  200 C is likely blurred. Consequently, each aperture of beam column  200 C creates a shadow projection with a blurred cross section. In beam columns  200 A and  200 B, the beam  202  is focused within at least the planes of apertures  206 . 2  to  206 . 4 . Consequently, beam columns  200 A and  200 B more accurately shape beam images than does beam column  200 C. However, beam column  200 A is longer than beam column  200 C and consequently incurs more electron-electron interactions, which blur the shaped electron beam on a target substrate. Beam column  200 B is more compact than beam column  200 A and thereby incurs less image blur due to electron-electron interactions than beam column  200 A because single solenoid lens  220  is more compact than separate field and transfer lenses of beam column  200 A. 
     Size of Circular Shaped Aperture Openings 
     A description of an equation describing a radius of the circular openings defined in apertures  206 . 1  to  206 . 4  follows. The following geometric equation, whose variables are illustrated in FIG. 4A, describes a relationship between a length, L, of a desired line, a radius, R, of a circular opening, and a tolerable error, Δ, measured in terms of a farthest distance between the line having length L that intersects two points (P 1  and P 2 ) of the circular opening:        R   ≥       M        (       4        Δ   2       +     L   2       )         8      Δ                              
     where M is the magnification factor, which is the ratio of the size of the image at crossover plane  203 . 5  to the size at gun crossover point  203 . 1 . 
     Example Shaping Sequence 
     The following describes an exemplary operation of beam columns  200 A to  200 C . FIG. 5 depicts in a plan view an example of shaping of the image of beam  202  by a combination of first aperture  206 . 1 , second aperture  206 . 2 , third aperture  206 . 3 , and fourth aperture  206 . 4 . Electron beam source  201  outputs circular shaped electron beam  202 . Electron beam intersects first aperture  206 . 1 , as shown at  402 , to shape the image of beam  202 , as shown at  404 . At  402 , the large circle is the aperture and the smaller circle is the image of beam  202 . 
     Next, first deflector  210 . 1 ,  222 . 1 , or  254 . 1  and  254 . 2  together, located above second aperture  206 . 2 , changes the direction of electron beam  202  so that electron beam intersects second aperture  206 . 2  as shown at  406  to shape the image of beam  202  as shown at  408 . 
     Next, second deflector  210 . 2 ,  222 . 2 , or  254 . 3 , located above third aperture  206 . 3 , changes the direction of electron beam  202  so that the image of beam  202  intersects third aperture  206 . 3  as shown at  410  to shape the image of beam  202  as shown at  412 . 
     Next, third deflector  210 . 3 ,  222 . 3 , or  254 . 4  and  254 . 5  together, located above fourth aperture  206 . 4 , changes the direction of electron beam  202  so that the image of beam  202  intersects fourth aperture  206 . 4 , shown at  414 , to shape the image of beam  202 , shown at  416 . In this example, the final shape of the image of beam  202  is shown at  416 . 
     Thus beam columns  200 A to  200 C generate variable shaped electron beams with a cross section having at least 3 approximately linear sides, shown as  416 A and  416 B for example. The sides are only approximately linear because the circular openings shape the electron beam  202 . A shaped side becomes more linear the larger the diameter of the circular opening is relative to the diameter of the electron beam  202  cross section. 
     FIG. 6 depicts patterns  902  and  904  consisting of primitives generated by either of beam columns  200 A to  200 C . By comparison, for pattern  902 , 5 flashes are required by use of either of beam columns  200 A to  200 C as opposed to 62 flashes required by use of the prior art variable shape beam system (FIG.  1 ). Pattern  904  requires 8 flashes. 
     Other Opening Shapes Defined By the Apertures 
     For aperture openings having at least 3 straight sides of equal length, the following equation, whose variables are illustrated in FIG. 4B, represents a relationship between distance R, measured from the center of an aperture opening to a corner Z, and length, L, of a side of an aperture opening.        R   =       M                 L       2        sin        (     180        °   /   N       )                                  
     where 
     N is a number of sides of the opening, i.e., 360°/2β; 
     β is half the angle between two adjacent corners Z—Z with respect to the center of the opening, Y; and 
     M is the magnification described earlier with respect to FIG.  4 A. 
     The length L is greater than or equal to a maximum desired cross sectional side length of beam  202 . 
     For example, for a square shaped opening, 2β=90° and thus R must be greater than or equal to 0.41 ML. 
     Note that the angle between adjacent sides of a beam cross section depends on the number of shaping apertures, a number of straight sides of an opening defined within an aperture, and any angular rotation of between openings. Thus increasing the number of straight sides of each aperture opening decreases possible angles between adjacent sides of a beam cross section. Rotating the aperture openings relative to each other further decreases possible angles between adjacent sides of a beam cross section. 
     Square Shaped Openings 
     In an embodiment of the present invention, first aperture  206 . 1  and second aperture  206 . 2  each define a square opening shown as opening  502  of aperture  500  (FIGS. 7A and 7B) and third aperture  206 . 3  and fourth aperture  206 . 4  each define an opening shown as opening  602  of aperture  600  (FIGS.  8 A and  8 B). Third aperture  206 . 3  and fourth aperture  206 . 4  each define square shaped openings of the same size as the square shaped openings defined by each of first aperture  206 . 1  and second aperture  206 . 2  except that the openings defined by third aperture  206 . 3  and fourth aperture  206 . 4  are rotated by 45 degrees about crossover point C shown in FIG. 7A relative to the opening  502  of aperture  500 . The center crossover points of first aperture  206 . 1 , second aperture  206 . 2 , third aperture  206 . 3 , and fourth aperture  206 . 4  (shown as C in FIGS. 7A and 8A) are aligned along an axis descending from the electron source  201 . 
     FIG. 9A depicts in plan view the sequence of aperture openings that shape the image of beam  202  in accordance with this embodiment of the present invention. 
     In accordance with this embodiment, FIG. 9B depicts a sample of beam images shapes created by shaping a beam with the aperture openings of FIG.  9 A. Thereby this embodiment generates electron beam  202  having a cross section having sides with angles of 0, 45, 90, or 135 degrees to one another, the sides being within the plane of the target. 
     By contrast, the circular shaped openings allow for more angles between adjacent sides of a beam cross section than the square shaped openings. The square shaped openings allow for limited angles between sides of a beam cross section and therefore introduce errors between desired angles and generated angles. However, the circular shaped openings do not shape beam sides as straight as the square shaped openings. 
     The above-described embodiments of the present invention are illustrative and not limiting. It will thus be obvious to those skilled in the art that various changes and modifications may be made without departing from this invention in its broader aspects. For example, the number of shaping apertures used can vary, with of course additional or less imaging and deflectors used. The openings defined by each shaping aperture can have three or more sides and can be rotated relative to each other. The openings defined by each shaping aperture need not have symmetrical side lengths. Each shaping aperture need not define the same opening shape. Therefore, the appended claims encompass all such changes and modifications as fall within the true scope of this invention.