Patent Publication Number: US-7218380-B2

Title: Lithographic apparatus and device manufacturing method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is a continuation of U.S. Non-Provisional application Ser. No. 10/994,185, filed Nov. 22, 2004, now U.S. Pat. No. 7,061,581, issued Jun. 13, 2006. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a lithographic apparatus and a device manufacturing method. 
   2. Related Art 
   A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. The lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs), flat panel displays, and other devices involving fine structures. In a conventional lithographic apparatus, a patterning means, which is alternatively referred to as a mask or a reticle, can be used to generate a circuit pattern corresponding to an individual layer of the IC (or other device), and this pattern can be imaged onto a target portion (e.g., comprising part of one or several dies) on a substrate (e.g., a silicon wafer or glass plate) that has a layer of radiation-sensitive material (e.g., resist). Instead of a mask, the patterning means can comprise an array of individually controllable elements that generate the circuit pattern. 
   In general, a single substrate will contain a network of adjacent target portions that are successively exposed. Known lithographic apparatus include steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion in one go, and scanners, in which each target portion is irradiated by scanning the pattern through the beam in a given direction (the “scanning” direction), while synchronously scanning the substrate parallel or anti-parallel to this direction. 
   A lithographic apparatus is known in which a pattern is imparted to a beam by an array of individually controllable elements. Rather than relying upon a preformed mask (also referred to as a reticle) to impart a pattern to a beam, control signals are delivered to the array of controllable elements to control the state of those elements to pattern the beam. This is generally referred to as “maskless” given that it relies upon individually controllable elements rather than a mask to impart the necessary pattern to the beam. A maskless lithographic apparatus can be used to expose relatively large area substrates, for example substrates to be used as flat panel displays. The panels are exposed in a single pass beneath an array of projection systems, each of which is provided with its own patterning system incorporating an array of individually controllable elements. As the substrate is displaced relative to the projection systems, it is necessary to change the state of individual elements in the arrays of controllable elements so as to change the projected patterns. The rate at which the state of the individual elements can be changed, generally referred to as the update rate, is limited and this imposes an upper limit on the maximum speed at which a substrate can be displaced relative to the projection systems. The speed of displacement determines the maximum throughput of the apparatus, and therefore it is desirable to be able to increase the speed of displacement. 
   It is possible to increase the substrate displacement speed by increasing the number of projection systems devoted to the exposure of a single track of pixels in the substrate scanning direction. For example, a substrate displacement speed can be doubled if two projection systems are arranged in series in the scanning direction. With such an arrangement each adjacent pair of pixels in the scanning direction can be exposed by a respective one of the two projection systems. 
   The substrate displacement speed can be further improved by adding further rows of projection systems. Three rows of projection systems trebling the maximum speed and four rows quadrupling the maximum speed. Increasing the substrate speed brings with it its own problems however in terms of maintaining appropriate speed control and achieving the necessary acceleration and deceleration of the substrate before and after scanning of the substrate. 
   Furthermore, adding extra rows of projection systems increases the overall distance that a substrate has to be displaced to achieve a full scan. For example, a row of projection systems capable of exposing the full width (perpendicular to the scanning direction) of the substrate is typically of the order of 100 millimeters deep in the scanning direction and therefore, given a single row of projection systems and a substrate 2 meters long in the scanning direction, a total scan range of 2.1 meters is required. Adding a second row of projection systems increases the scan range to 2.2 meters and so on. 
   However, adding additional rows of projection systems does not result in a proportionate increase in throughput. This is because as the total area that has to be exposed is also larger, adding one projection system increases the total area by the area of that projection system. In addition, adding rows of projection systems also increases the physical footprint of the apparatus. 
   Therefore, what is needed is a system and method that increases throughput in a maskless lithography system. 
   SUMMARY OF THE INVENTION 
   According to an embodiment of the present invention, there is provided a lithographic apparatus comprising an illumination system, an array of individually controllable elements, projection systems, a displacement system. The illumination system supplies a plurality of beams of radiation. The array of individually controllable elements imparting to each beam a pattern in its cross section. The projection systems projecting the patterned beams onto a substrate. The displacement system causes relative displacement between the substrate and the projection systems, such that the beams are scanned across the substrate in a predetermined scanning direction. Each projection system comprises an array of lenses arranged such that each lens in the array directs a respective part of the respective beam towards a respective target area on the substrate. The projection systems are arranged in groups, such that lenses in the arrays of different groups direct parts of different beams to different target areas of the substrate that are aligned in the scanning direction. The groups of projection systems are spaced apart in the scanning direction, such that each group scans beams across a respective area of the substrate as the substrate and projection systems are displaced relative to each other. The respective areas scanned by beams from groups that are adjacent to each other in the scanning direction being contiguous. 
   According to another embodiment of the present invention, there is provided a device manufacturing method comprising the following steps. Providing beams of radiation using an illumination system. Using arrays of individually controllable elements to impart to each beam a pattern in its cross section. Projecting the patterned beams onto a substrate. Displacing the substrate relative to the patterned beams, such that the beams are scanned across the substrate in a predetermined scanning direction. Each beam is directed towards a substrate by a respective array of lenses arranged such that each lens in the array directs a respective part of the respective beam towards a respective target area on the substrate. The projection systems are arranged in groups, such that lenses in the arrays of different groups direct parts of different beams to different areas of the substrate that are aligned in the scanning direction. The groups are spaced apart in the scanning direction, such that each group scans beams across areas of the substrate as the substrate and projection systems are displaced relative to each other. The respective areas scanned by beams from groups that are adjacent to each other in the scanning direction being contiguous. 
   In one example, it is possible to increase the throughput of lithographic apparatus without increasing the substrate displacement speed and with a reduction in scan range. This can be achieved because essentially contiguous sections of the substrate in the scanning direction are exposed by different arrays of projection devices. 
   As discussed above, to expose a two meter long substrate using a single array of projection devices that is 100 mm deep in the scanning direction would require a scan length of 2.1 meters. Simply adding a second array of projection devices would increase the scan range to 2.2 meters. In contrast, in one example of the present invention a second row of projection devices spaced apart with a pitch of one meter enables the full two meter length of the substrate to be exposed with a scan range of as little as 1.05 meters. 
   In other examples, more than two rows of projection devices can be provided. For example, three rows of projection devices could be provided equally spaced apart in the scanning direction. Alternatively, four rows of projection devices could be provided, either equally spaced apart, or in two groups of two rows with the two groups spaced apart in the scan direction. As a result relatively compact apparatus can achieve very high throughputs without requiring high speed substrate displacement. 
   In one example, each group can be arranged to expose a generally rectangular area of the substrate with the groups spaced apart with a pitch of L/N, where L is the length of the substrate to be exposed and N is the number of groups. Alternatively, each of the contiguous areas can have a generally rectangular main portion and at least one end portion extending in the scanning direction from the main portion, the end portions of contiguous areas having a saw-toothed shape with the teeth of one end section overlapping the teeth of the contiguous end section. The end sections can have a length in the scanning direction equal to the length in the scanning direction of each group of projection systems. With such an arrangement, N groups of projection systems can be distributed in the scanning direction with a pitch of (L+1)/N, where l is the length in the scanning direction of one group. 
   In one example, the substrate is displaced relative to stationary projection systems. Each lens array can project spots of light that are capable of exposing tracks on the surface of the substrate, the tracks exposed by one array being contiguous so that the full width (perpendicular to the scanning direction) of the substrate can be exposed in a single pass. 
   Further embodiments, features, and advantages of the present inventions, as well as the structure and operation of the various embodiments of the present invention, are described in detail below with reference to the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES 
     The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate the present invention and, together with the description, further serve to explain the principles of the invention and to enable a person skilled in the pertinent art to make and use the invention. 
       FIG. 1  depicts a lithographic apparatus, according to one embodiment of the present invention. 
       FIGS. 2 and 3  show components of lithographic projection apparatus incorporating arrays of lenses, each of which is arranged to project a spot of radiation onto the substrate, according to various embodiments of the present invention. 
       FIGS. 4 and 5  show disposition of spots of radiation projected by a lens arrays, according to various embodiments of the present invention. 
       FIG. 6  schematically represents an apparatus for exposing a substrate in a single pass of the substrate beneath an array of optical columns each of which comprises components as illustrated in  FIGS. 2 and 3 , according to one embodiment of the present invention. 
       FIG. 7  schematically represents the different areas of the substrate which can be illuminated by each of the optical columns shown in  FIG. 6 , according to one embodiment of the present invention. 
       FIG. 8  schematically represents a pattern which it can be desired to expose on a substrate using the apparatus of  FIG. 6 , according to one embodiment of the present invention. 
       FIG. 9  schematically represents a position of two arrays of optical columns each of the type shown in  FIG. 6 , according to one embodiment of the present invention. 
       FIG. 10  schematically represents a scan range to expose a full substrate using the apparatus of  FIG. 9 , according to one embodiment of the present invention. 
       FIG. 11  schematically represents one embodiment of the present invention incorporating two groups of optical columns with the groups of optical columns being spaced apart in the scanning direction. 
       FIG. 12  schematically represents a scan range required to expose a full substrate using the apparatus of  FIG. 11 , according to one embodiment of the present invention. 
       FIG. 13  schematically represents a scan range required to expose a full substrate using three groups of optical columns that are juxtaposed, according to one embodiment of the present invention. 
       FIG. 14  schematically represents a scan range required to expose the full substrate using three groups of optical columns with the three groups being spaced apart in the scan direction, according to one embodiment of the present invention. 
       FIG. 15  schematically represents a scan range required to expose a full substrate using four groups of optical columns, according to one embodiment of the present invention. 
       FIG. 16  schematically represents a scan range required to expose a full substrate using an apparatus in which four groups of optical columns are provided, the four groups being arranged in two pairs spaced apart in the scan direction, according to one embodiment of the present invention. 
       FIG. 17  illustrates a saw-toothed boundary between areas of a substrate exposed by adjacent projection systems, according to one embodiment of the present invention. 
       FIGS. 18 and 19  illustrate adopting a boundary as illustrated in  FIG. 17 , according to embodiments of the present invention. 
   

   The present invention will now be described with reference to the accompanying drawings. In the drawings, like reference numbers can indicate identical or functionally similar elements. 
   DETAILED DESCRIPTION OF THE EMBODIMENTS 
   Overview and Terminology 
   Although specific reference can be made in this text to the use of lithographic apparatus in the manufacture of integrated circuits (ICs), it should be understood that the lithographic apparatus described herein can have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, thin-film magnetic heads, micro and macro fluidic devices, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein can be considered as synonymous with the more general terms “substrate” or “target portion,” respectively. The substrate referred to herein can be processed, before or after exposure, in for example a track (e.g., a tool that typically applies a layer of resist to a substrate and develops the exposed resist) or a metrology or inspection tool. Where applicable, the disclosure herein can be applied to such and other substrate processing tools. Further, the substrate can be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein can also refer to a substrate that already contains multiple processed layers. 
   The term “array of individually controllable elements” as here employed should be broadly interpreted as referring to any device that can be used to endow an incoming radiation beam with a patterned cross-section, so that a desired pattern can be created in a target portion of the substrate. The terms “light valve” and “Spatial Light Modulator” (SLM) can also be used in this context. Examples of such patterning devices are discussed below. 
   A programmable mirror array can comprise a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such an apparatus is that, for example, addressed areas of the reflective surface reflect incident light as diffracted light, whereas unaddressed areas reflect incident light as undiffracted light. Using an appropriate spatial filter, the undiffracted light can be filtered out of the reflected beam, leaving only the diffracted light to reach the substrate. In this manner, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. 
   It will be appreciated that, as an alternative, the filter can filter out the diffracted light, leaving the undiffracted light to reach the substrate. An array of diffractive optical micro electrical mechanical system (MEMS) devices can also be used in a corresponding manner. Each diffractive optical MEMS device can include a plurality of reflective ribbons that can be deformed relative to one another to form a grating that reflects incident light as diffracted light. 
   A further alternative embodiment can include a programmable mirror array employing a matrix arrangement of tiny mirrors, each of which can be individually tilted about an axis by applying a suitable localized electric field, or by employing piezoelectric actuation means. Once again, the mirrors are matrix-addressable, such that addressed mirrors will reflect an incoming radiation beam in a different direction to unaddressed mirrors; in this manner, the reflected beam is patterned according to the addressing pattern of the matrix-addressable mirrors. The required matrix addressing can be performed using suitable electronic means. 
   In both of the situations described here above, the array of individually controllable elements can comprise one or more programmable mirror arrays. More information on mirror arrays as here referred to can be gleaned, for example, from U.S. Pat. Nos. 5,296,891 and 5,523,193, and PCT patent applications WO 98/38597 and WO 98/33096, which are incorporated herein by reference in their entireties. 
   A programmable LCD array can also be used. An example of such a construction is given in U.S. Pat. No. 5,229,872, which is incorporated herein by reference in its entirety. 
   It should be appreciated that where pre-biasing of features, optical proximity correction features, phase variation techniques and multiple exposure techniques are used, for example, the pattern “displayed” on the array of individually controllable elements can differ substantially from the pattern eventually transferred to a layer of or on the substrate. Similarly, the pattern eventually generated on the substrate can not correspond to the pattern formed at any one instant on the array of individually controllable elements. This can be the case in an arrangement in which the eventual pattern formed on each part of the substrate is built up over a given period of time or a given number of exposures during which the pattern on the array of individually controllable elements and/or the relative position of the substrate changes. 
   Although specific reference can be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein can have other applications, such as, for example, the manufacture of DNA chips, MEMS, MOEMS, integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, thin film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein can be considered as synonymous with the more general terms “substrate” or “target portion”, respectively. The substrate referred to herein can be processed, before or after exposure, in for example a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist) or a metrology or inspection tool. Where applicable, the disclosure herein can be applied to such and other substrate processing tools. Further, the substrate can be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein can also refer to a substrate that already contains multiple processed layers. 
   The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g. having a wavelength of 365, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g., having a wavelength in the range of 5–20 nm), as well as particle beams, such as ion beams or electron beams. 
   The term “projection system” used herein should be broadly interpreted as encompassing various types of projection systems, including refractive optical systems, reflective optical systems, and catadioptric optical systems, as appropriate, for example, for the exposure radiation being used, or for other factors such as the use of an immersion fluid or the use of a vacuum. Any use of the term “lens” herein can be considered as synonymous with the more general term “projection system.” 
   The illumination system can also encompass various types of optical components, including refractive, reflective, and catadioptric optical components for directing, shaping, or controlling the beam of radiation, and such components can also be referred to below, collectively or singularly, as a “lens.” 
   The lithographic apparatus can be of a type having two (e.g., dual stage) or more substrate tables (and/or two or more mask tables). In such “multiple stage” machines the additional tables can be used in parallel, or preparatory steps can be carried out on one or more tables while one or more other tables are being used for exposure. 
   The lithographic apparatus can also be of a type wherein the substrate is immersed in a liquid having a relatively high refractive index (e.g., water), so as to fill a space between the final element of the projection system and the substrate. Immersion liquids can also be applied to other spaces in the lithographic apparatus, for example, between the substrate and the first element of the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems. 
   Further, the apparatus can be provided with a fluid processing cell to allow interactions between a fluid and irradiated parts of the substrate (e.g., to selectively attach chemicals to the substrate or to selectively modify the surface structure of the substrate). 
   Lithographic Projection Apparatus 
     FIG. 1  schematically depicts a lithographic projection apparatus  100  according to an embodiment of the invention. Apparatus  100  includes at least a radiation system  102 , an array of individually controllable elements  104 , an object table  106  (e.g., a substrate table), and a projection system (“lens”)  108 . 
   Radiation system  102  can be used for supplying a beam  110  of radiation (e.g., UV radiation), which in this particular case also comprises a radiation source  112 . 
   An array of individually controllable elements  104  (e.g., a programmable mirror array) can be used for applying a pattern to beam  110 . In general, the position of the array of individually controllable elements  104  can be fixed relative to projection system  108 . However, in an alternative arrangement, an array of individually controllable elements  104  can be connected to a positioning device (not shown) for accurately positioning it with respect to projection system  108 . As here depicted, individually controllable elements  104  are of a reflective type (e.g., have a reflective array of individually controllable elements). 
   Object table  106  can be provided with a substrate holder (not specifically shown) for holding a substrate  114  (e.g., a resist coated silicon wafer or glass substrate) and object table  106  can be connected to a positioning device  116  for accurately positioning substrate  114  with respect to projection system  108 . 
   Projection system  108  (e.g., a quartz and/or CaF 2  lens system or a catadioptric system comprising lens elements made from such materials, or a mirror system) can be used for projecting the patterned beam received from a beam splitter  118  onto a target portion  120  (e.g., one or more dies) of substrate  114 . Projection system  108  can project an image of the array of individually controllable elements  104  onto substrate  114 . Alternatively, projection system  108  can project images of secondary sources for which the elements of the array of individually controllable elements  104  act as shutters. Projection system  108  can also comprise a micro lens array (MLA) to form the secondary sources and to project microspots onto substrate  114 . 
   Source  112  (e.g., an excimer laser) can produce a beam of radiation  122 . Beam  122  is fed into an illumination system (illuminator)  124 , either directly or after having traversed conditioning device  126 , such as a beam expander, for example. Illuminator  124  can comprise an adjusting device  128  for setting the outer and/or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in beam  122 . In addition, illuminator  124  will generally include various other components, such as an integrator  130  and a condenser  132 . In this way, beam  110  impinging on the array of individually controllable elements  104  has a desired uniformity and intensity distribution in its cross section. 
   It should be noted, with regard to  FIG. 1 , that source  112  can be within the housing of lithographic projection apparatus  100  (as is often the case when source  112  is a mercury lamp, for example). In alternative embodiments, source  112  can also be remote from lithographic projection apparatus  100 . In this case, radiation beam  122  would be directed into apparatus  100  (e.g., with the aid of suitable directing mirrors). This latter scenario is often the case when source  112  is an excimer laser. It is to be appreciated that both of these scenarios are contemplated within the scope of the present invention. 
   Beam  110  subsequently intercepts the array of individually controllable elements  104  after being directed using beam splitter  118 . Having been reflected by the array of individually controllable elements  104 , beam  110  passes through projection system  108 , which focuses beam  110  onto a target portion  120  of the substrate  114 . 
   With the aid of positioning device  116  (and optionally interferometric measuring device  134  on a base plate  136  that receives interferometric beams  138  via beam splitter  140 ), substrate table  6  can be moved accurately, so as to position different target portions  120  in the path of beam  110 . Where used, the positioning device for the array of individually controllable elements  104  can be used to accurately correct the position of the array of individually controllable elements  104  with respect to the path of beam  110 , e.g., during a scan. In general, movement of object table  106  is realized with the aid of a long-stroke module (course positioning) and a short-stroke module (fine positioning), which are not explicitly depicted in  FIG. 1 . A similar system can also be used to position the array of individually controllable elements  104 . It will be appreciated that beam  110  can alternatively/additionally be moveable, while object table  106  and/or the array of individually controllable elements  104  can have a fixed position to provide the required relative movement. 
   In an alternative configuration of the embodiment, substrate table  106  can be fixed, with substrate  114  being moveable over substrate table  106 . Where this is done, substrate table  106  is provided with a multitude of openings on a flat uppermost surface, gas being fed through the openings to provide a gas cushion which is capable of supporting substrate  114 . This is conventionally referred to as an air bearing arrangement. Substrate  114  is moved over substrate table  106  using one or more actuators (not shown), which are capable of accurately positioning substrate  114  with respect to the path of beam  110 . Alternatively, substrate  114  can be moved over substrate table  106  by selectively starting and stopping the passage of gas through the openings. 
   Although lithography apparatus  100  according to the invention is herein described as being for exposing a resist on a substrate, it will be appreciated that the invention is not limited to this use and apparatus  100  can be used to project a patterned beam  110  for use in resistless lithography. 
   The depicted apparatus  100  can be used in four preferred modes: 
   1. Step mode: the entire pattern on the array of individually controllable elements  104  is projected in one go (i.e., a single “flash”) onto a target portion  120 . Substrate table  106  is then moved in the x and/or y directions to a different position for a different target portion  120  to be irradiated by patterned beam  110 . 
   2. Scan mode: essentially the same as step mode, except that a given target portion  120  is not exposed in a single “flash.” Instead, the array of individually controllable elements  104  is movable in a given direction (the so-called “scan direction”, e.g., the y direction) with a speed v, so that patterned beam  110  is caused to scan over the array of individually controllable elements  104 . Concurrently, substrate table  106  is simultaneously moved in the same or opposite direction at a speed V=Mv, in which M is the magnification of projection system  108 . In this manner, a relatively large target portion  120  can be exposed, without having to compromise on resolution. 
   3. Pulse mode: the array of individually controllable elements  104  is kept essentially stationary and the entire pattern is projected onto a target portion  120  of substrate  114  using pulsed radiation system  102 . Substrate table  106  is moved with an essentially constant speed such that patterned beam  110  is caused to scan a line across substrate  106 . The pattern on the array of individually controllable elements  104  is updated as required between pulses of radiation system  102  and the pulses are timed such that successive target portions  120  are exposed at the required locations on substrate  114 . Consequently, patterned beam  110  can scan across substrate  114  to expose the complete pattern for a strip of substrate  114 . The process is repeated until complete substrate  114  has been exposed line by line. 
   4. Continuous scan mode: essentially the same as pulse mode except that a substantially constant radiation system  102  is used and the pattern on the array of individually controllable elements  104  is updated as patterned beam  110  scans across substrate  114  and exposes it. 
   Combinations and/or variations on the above described modes of use or entirely different modes of use can also be employed. 
     FIGS. 2 and 3  show components of lithographic projection apparatus incorporating arrays of lenses, each of which is arranged to project a spot of radiation onto the substrate, according to various embodiments of the present invention. 
   Referring now to  FIG. 2 , the apparatus shown comprises a contrast device  1 , an underside surface of which supports a two dimensional array of elements  2 . Each element  2  in the array can be selectively controlled to act either as an absorber or reflector of radiation. A beam splitter  3  is positioned beneath contrast device  1 . An illumination source  4  directs a beam of radiation  5  towards beam splitter  3 . Beam of radiation  5  is reflected onto the lower surface of contrast device  1 . One of elements  2  of contrast device  1  is shown as reflecting a component part of beam  5  back through beam splitter  3  and projection optics defined by lenses  6 ,  7 , and  8 . A lowermost lens  8  is a field lens that produces a substantially telecentric beam, which is directed towards a microlens array  9 . Microlens array  9  comprises a two dimensional array of small lenses each of which is arranged so as to focus light incident upon it onto an upper surface of a substrate  10 . Thus, for each of elements  2  in contrast device  1  that acts as a mirror, a respective one of the lenses in microlens array  9  is illuminated, and a respective spot of light is projected by that lens in microlens array  9  onto the upper surface of substrate  10 . 
   Referring to  FIG. 3 , this is an alternative representation of components show in  FIG. 2 . In  FIG. 3 , substrate  10  is shown supported on a substrate table  11  beneath microlens array  9 . Projection optics are represented by a simple rectangle  12 . Three contrast elements  2  of contrast device  1  of  FIG. 2  are shown above projection optics  12 . In this embodiment, substrate table  11  is moved in a linear manner in a direction of arrow  13  beneath microlens array  9 . In an alternative arrangement, substrate  10  can be moved in a linear manner on a stationary table  11 . 
     FIGS. 4 and 5  show disposition of spots of radiation projected by a lens arrays, according to various embodiments of the present invention. 
   Referring to  FIG. 4 , this drawing is illustrative of the relationship between the disposition of individual lenses in microlens array  9  of  FIGS. 2 and 3  and a direction of displacement of substrate table  11  of  FIG. 3 . Again, the direction of displacement is represented in  FIG. 4  by arrow  13 . That direction is parallel to a line  14  which is inclined to a further line  15 , which extends parallel to a row of the lenses in microlens array  9 . Each lens projects light onto a different one of a rectangular array of spots one of which is identified by numeral  16 . The lenses are arranged in a regular two dimensional array that is slightly inclined to direction  13  of substrate table movement, as shown such that the entire surface of substrate  10  can be exposed by appropriate control of the illumination beams delivered to the respective lenses by the respective elements  2  of contrast device  1 . Each lens can in effect “write” a continuous line on the surface of substrate  10  and, given the disposition of the lenses relative to the direction of substrate movement, those lines are sufficiently close together to overlap. 
   In one example, to expose a selected two dimensional area of substrate  10 , substrate  10  is advanced beneath microlens array  9  and the individual lenses beneath which the area to be exposed is positioned at any one time are illuminated by rendering the associated elements  2  of contrast device  1  reflective. 
   In  FIG. 4 , the continuous lines that can be written by individual lenses of microlens array  9  overlap to a significant extent in the direction perpendicular to the scan direction represented by arrow  13 . In one example, such overlap is not necessary, and the full surface area of a substrate could be exposed using an arrangement in which projected spots that are adjacent in the direction perpendicular to the scan direction just touch, but do not overlap. Such an arrangement, which minimizes the total number of spots required to expose a given area, is desirable when, as is often the case, the production rate is limited by the rate at which the intensity of individual spots  16  can be changed. 
   In one example, individual spots are generally circular, but when used to expose pixels that are square some overlap between adjacent spots is required. With reference now to  FIG. 5 , a disposition of four spots  17 ,  18 ,  19  and  20  are arranged so that the continuous lines that can be written by each of the spots just touch, but do not overlap. Spots  17 – 20  have a pitch P and a diameter d. The scan direction is represented by the lines between which the four spots  17 – 20  are located. Thus spots  17  and  20  are projected by adjacent lenses in a row of lenses extending transverse to the scan direction, whereas the spots  17  and  18  are projected by adjacent lenses  8  in a column of lenses of microlens array  9 . The column is inclined by a small angle to the scan direction. Spots  17  and  20  are separated by a distance equal to six times the diameter d of each spot. Thus, in order to fully expose substrate  10 , each column of microlens array  9  has seven lenses. 
   It is to be appreciated that  FIG. 5  is schematic, and is not representative of the scale of an actual apparatus. For example, microlens array  9  would typically have a lens pitch P of the order of about 150 micrometers, with each of the lenses projecting a spot (for example spot  17 ) with a diameter d equal to about 1.25 microns. The spot diameter d would typically be greater than the pixel track width to provide limited overlap between adjacent tracks, but for the purposes of illustration it is assumed that the spot diameter d is equal to the pixel track width. Assuming such dimensions apply, microlens array  9  has 120 rows of lenses spaced apart in the scan direction so as to ensure coverage of the full width of substrate  10  between spots that are adjacent in a common row extending transverse to the scan direction (for example spots  17  and  20  in  FIG. 5 ). 
   In one example, to achieve appropriate resolution (spot size) at substrate  10 , an appropriate numerical aperture is used. For example, this can be about 0.15. If the spacing between microlens array  9  (see  FIG. 3 ) and substrate  10  is about 500 micrometers, the pitch P of the lenses in microlens array  9  will be at least about 150 micrometers. If a free working distance is, for example, about 1000 micrometers, the lens pitch P has to be greater, for example about 300 micrometers. A pitch P of 150 micrometers requires 120 lenses assuming a spot diameter d of about 1.25 micrometers at substrate  10 . An array of lenses with a dimension of about 18000 micrometers in the scan direction (120×150). With a pitch P of about 300 micrometers, 240 rows of lenses extending transverse to the scan direction are used to fully cover the about 300 micrometer gap between adjacent lenses in each row. Thus, the number of rows of lenses is doubled as is their spacing, and therefore the length in the scan direction of micolens array  9  is quadrupled to about 720,00 micrometers (300×240). 
   If all the lenses in microlens array  9  were arranged in a single row extending transverse to the scan direction, exposure of the full length of substrate  10  would require transport of substrate  10  by that full length plus a very small distance corresponding to the scan-direction dimension of the row of spots. Given the number of rows of lenses required to expose the full width of substrate  10 , the minimum scan direction is a function of the dimension in the scan direction of microlens array  9 . 
   In addition, although the “footprint” of an individual array of lenses is relatively limited (for example 18,000 micrometers in the case of a free working distance of 500 micrometers, a pitch of 150 micrometers, and a spot diameter of 1.25 micrometers), in practice the footprint of an optical column, of which a lens array forms part, is larger than the footprint of the array itself given the presence of lenses and other components above the lens array itself, for example the components  6 ,  7  and  8  in  FIG. 2 . 
     FIG. 6  schematically represents an apparatus for exposing a substrate in a single pass of the substrate beneath an array of optical columns each of which comprises components as illustrated in  FIGS. 2 and 3 , according to one embodiment of the present invention. This embodiment illustrate an additional demand for space. A substrate  22  is displaced across a substrate table  21  in the direction indicated by arrow  23  beneath an array  24  of six optical columns  25 . Each optical column  25  is illustrated as having a circular periphery representing the overall footprint of that column  25 , within which there is an area  26  that is shaded that corresponds to an actual optical footprint of that column  25  upon substrate  22  as it is advanced beneath that column  25 . It is to be appreciated that, although for the purposes of illustration only six optical columns  25  are shown in  FIG. 6 , in practice it can be the case that there are, for example, twenty five optical columns  25  arranged across the table  21 . 
     FIG. 7  schematically represents the different areas of the substrate which can be illuminated by each of the optical columns shown in  FIG. 6 , according to one embodiment of the present invention. The optical footprints of the optical columns  25  are contiguous, such that the six optical columns  25  together can expose the full width of substrate  22 . Broken lines represent the boundaries between the optical footprints of adjacent columns  25 . Thus, each optical column  25  exposes a respective track  27  extending between a respective pair of broken lines  28 , the tracks  27  covering the full width of substrate  22  between boundaries represented by full lines adjacent side edges  29  of substrate  22 . 
   Within each track  27  the surface of substrate  22  can be considered as being made up of a series of pixels, each of which may or may not be exposed during scanning of substrate  22 . 
     FIG. 8  schematically represents a pattern that can be desired to expose on a substrate using the apparatus of  FIG. 6 , according to one embodiment of the present invention. A row  30  of pixels are shown with alternate pixels shaded. Each row  30  of pixels corresponds to a track traversed by a single lens of one of optical columns  25 . For example, pixel  31  is to be fully exposed (“white”), pixel  32  receives no radiation (“black”), and pixel  33  is fully exposed (“white”). A frequency at which the individually controllable contrast elements  2  ( FIGS. 2 and 3 ) can change their state determines a rate at which the patterned beam projected onto substrate  22  can be changed. This sets a limit on a speed at which substrate  22  can be transported past optical column  25 . If substrate  22  is traveling too fast, the contrast elements  2  cannot switch states sufficiently quickly to deliver the appropriate exposure to individual pixels. For example, assuming an update of 50 kilohertz (the number of times that the state of an individual contrast element  2  can be switched per second), and a pixel dimension of about 1.25 micrometers, then the maximum speed at which substrate  22  can be displaced is about 62,500 micrometers per second. This assumes that each pixel is exposed for a duration which is very short as compared with the speed at which substrate  22  is being transported, such that each exposure is delivered to a given pixel over a period during which substrate  22  is not displaced significantly. 
   In another example, when the contrast device  1  can only be updated at about 25 kilohertz, individual contrast devices cannot be updated sufficiently quickly to change their state as between adjacent pixels in a particular pixel track  30 , and therefore one optical engine can only expose alternate pixels in a particular track  30 . Therefore, either the scanning speed of substrate  22  has to be reduced to only about 31,250 micrometers per second or alternative arrangements must be made. 
     FIG. 9  schematically represents the position of two arrays of optical columns  25  each of the type shown in  FIG. 6 , according to one embodiment of the present invention. In this embodiment two arrays  24  of optical columns  25  each substantially identical to single array  24  shown in  FIG. 6 . Each array  24  is allocated to the exposure of alternate rows of pixels, such that for example in  FIG. 8  one array would be responsible for the exposure of pixels  31  and  33 , while the other array would be responsible for exposure of pixel  32  and the two pixels, other than pixel  32  which are adjacent to pixels  31  and  33 . In this embodiment, a total scan range required to expose the full surface of substrate  22  is increased by a length in the substrate scanning direction of one of the optical column arrays  24 . 
   In one example, a free working distance of about 500 micrometers and a pitch of about 150 micrometers, a microlens array dimension in the direction of scanning will be about 18,000 micrometers. In this example, to accommodate optical components other than the microlens array  9 , adjacent optical columns  25  have to be offset in the scanning direction as represented in  FIGS. 6 and 9 . As a result, each optical column  25  can occupy a relatively large distance in the scanning direction, for example, about 100,000 micrometers. Thus, with the arrangement shown in  FIG. 6 , and substrate  22  with a dimension in the scanning direction of about 2 meters, the total scan range required to expose the full substrate will be about 2.1 meters. With the arrangement shown in  FIG. 9 , the total scan range will be 2.2 meters. Thus with each additional optical column array  24  an additional 0.1 meters is added to the scan range. 
   In this embodiment, an increase in the size of the substrate table and the overall footprint of the apparatus can result. With increasing size comes increasing cost and difficulty with regard to maintaining stable process conditions across the scan range. In some circumstances, it can be impossible to upgrade an existing apparatus to accommodate an increased scanning range simply by adding extra arrays of optical columns. 
     FIG. 10  schematically represents a scan range to expose a full substrate  34  using the apparatus of  FIG. 9 , according to one embodiment of the present invention. This embodiment shows the effect of adding an extra array of optical engines  36 , 37  to increase the required scan range. In this embodiment, substrate  34  has a length L as represented by arrow  35  and two arrays of optical columns  36  and  37  are provided, each with a length l represented by arrows  38  and  39 . Substrate  34  has to be moved from the position shown in the upper half of  FIG. 10  to the position shown in the lower half of  FIG. 10 . The total displacement is therefore L+2l. If substrate  34  only had to move beneath a single array of optical columns, for example array  36 , the distance that substrate  34  would have to be displaced would be L+1. Thus, in order to double the speed at which substrate  34  can be displaced, it is necessary to increase the scan range from L+1 to L+2l. Therefore, the throughput is not doubled by doubling the number of optical columns and doubling the speed of displacement of substrate  34 . 
     FIG. 11  schematically represents one embodiment of the present invention incorporating two groups of optical columns  36 ,  37  with the groups of optical columns  36 ,  37  being spaced apart in a scanning direction. The two arrays of optical columns  36  and  37  are provided to expose substrate  34 , each of the columns  36  and  37  exposing a respective generally rectangular area of substrate  34  with the two generally rectangular areas being contiguous. 
     FIG. 12  represents a total scan range that substrate  34  has to move in order to expose the whole substrate, according to one embodiment of the present invention. Again, arrow  35  represents the length L of the substrate  34  and arrows  38  and  39  represents lengths, in the scan direction, of the arrays of optical columns  36  and  37 . The upper half of  FIG. 12  shows substrate  34  at the beginning of a scan, and the lower half of  FIG. 12  shows substrate  34  at the end of the scan. It is to be appreciated that, in order for each of the generally rectangular areas of the substrate  34  to move beneath one of the arrays of optical columns  36 ,  37 , substrate  34  is be displaced by a distance represented by arrow  40 , that is by a distance equal to (L+2l)/2. Thus, as compared with the arrangement of  FIG. 9 , the speed of substrate displacement is halved, as is the displacement distance. 
   In one example, given an update rate for the pattern imparting contrast devices of about 12.5 kilohertz, a pixel size of about 1.25 microns, a substrate with about a 1 meter length in the scan direction, and an optical column array with a length in the scan direction of about 100,000 microns, then the maximum speed at which a substrate can be moved past the structure shown in  FIG. 9  would be (1,000,000+100,000)/(1.25×12500)=about 70.4 seconds. If a second row of optical columns is added as shown in  FIG. 9 , the time taken to scan the substrate will be (1,000,000+200,000)/(2×1.25×12500)=about 38.4 seconds. 
   To achieve a full scan in 38.4 seconds, the velocity of the substrate assuming a constant speed over the full exposure process will be 0.03125 meters per second. 
   In contrast, with two arrays of optical columns  36 ,  37  arranged as shown in  FIG. 11 , the time taken to expose the full substrate will be (500,000+100,000)/1.25×12500 which equals about 38.4 seconds. Thus, the time taken for a single scan is exactly the same as in the case of  FIG. 9 . However, the total displacement of substrate  34  during the scanning process is halved, as is the substrate velocity. 
     FIG. 13  schematically represents a scan range required to expose a full substrate using three groups of optical columns that are juxtaposed, according to one embodiment of the present invention. Three arrays of optical columns  41 , 42  and  43  arranged to expose a substrate  44 , a dimension  45  indicating the total scan range. 
     FIG. 14  schematically represents the scan range required to expose a full substrate using three groups of optical columns with the three groups being spaced apart in a scan direction, according to one embodiment of the present invention. 
   In  FIG. 13 , optical column array  41  exposes every third pixel along the length of substrate  44 , while in  FIG. 14  optical column  41  exposes each pixel of a generally rectangular area occupying a left hand third of substrate  44 . Thus, for an identical scan duration in  FIG. 14 , the substrate scan speed and substrate displacement are reduced by a factor of three as compared with  FIG. 13 . 
   In the examples of the invention represented in  FIGS. 12 and 14 , individual arrays of optical columns are equally spaced apart along the length of the scan range with a pitch equal to L/N, where L is the length of the substrate to be exposed and N is the number of groups of optical columns. It is possible, however, to have groups of arrays of optical columns arranged along the direction of scan. 
     FIG. 15  schematically represents a scan range required to expose a full substrate using four groups of optical columns, according to one embodiment of the present invention. In this embodiment, the four optical column arrays arranged adjacent each other so as to be able to scan a substrate  50 . An upper half of  FIG. 15  shows substrate  50  as its leading edge just reaches an optical column array  46 , and a lower half shows a trailing edge of substrate  50  as it just leaves the trailing end of an optical column array  49 . 
     FIG. 16  schematically represents a scan range required to expose a full substrate using an apparatus in which four groups of optical columns are provided, the four groups being arranged in two pairs spaced apart in the scan direction, according to one embodiment of the present invention. This in contrast to  FIG. 15 , in  FIG. 16 , equivalent optical column arrays  46 ,  47 ,  48  and  49  are arranged in two pairs, a upper half of  FIG. 16  showing substrate  50  just before the beginning of a scan, and a lower half of  FIG. 16  showing substrate  50  immediately after the scan. 
   Whereas in  FIG. 16  the scan range as represented by arrow  51  is equal to the overall length in the scan direction of substrate  50  plus four times the length in the scan direction of each of the optical column arrays, in  FIG. 16  the scan range is indicated by arrow  52  and is equal to half the length of the scan range  51  in  FIG. 15 . Once again, for a given throughput, the scan range and speed is halved in the case illustrated in  FIG. 16  as compared with the case illustrated in  FIG. 15 . 
     FIGS. 12 ,  14  and  16  assume that each of the spaced-apart groups of optical columns exposes a respective one of a series of contiguous generally rectangular areas on the substrate, the contiguous areas having mutual boundaries defined by straight lines extending parallel to the leading and trailing edges of the lens arrays such as the lens array shown in  FIG. 4 . With such an arrangement, each of the generally rectangular areas is displaced relative to the optical columns by a distance equal to the length of the rectangle in the scan direction plus the width of the optical column group in the scan direction. An alternative approach is possible in which the boundaries between adjacent contiguous areas to be exposed by adjacent groups of optical columns have a saw-tooth shape. This is possible because of the distribution of lenses in the optical columns, as schematically represented in  FIG. 4 , and as further described below with reference to  FIG. 17 . 
     FIG. 17  illustrates a saw-toothed boundary between areas of a substrate exposed by adjacent projection systems, according to one embodiment of the present invention. Assuming that a portion of substrate is being transported in the direction of arrow  53  beneath an array of lenses, such as schematically represented in  FIG. 4 , but having many more lenses than are depicted in  FIG. 4 , then line  54  represents the track of the lens at the top left hand corner of the array and line  55  represents the track of the lens at the bottom right hand corner of the array. Line  56  represents the position in the scan direction of the bottom left hand lens of the array, and line  57  represents the position in the scan direction of the top right hand lens of the array. The shaded area  55  represents an area of the substrate that is exposed by one group of optical columns, and the unshaded area  59  represents an area of the substrate that is exposed by the adjacent group of optical columns. The boundary between these two areas is saw-tooth shaped. Thus, the areas exposed by adjacent groups of optical columns overlap in the scan direction, with each area having a main generally rectangular area and an end portion with a saw-tooth edge, the end section having a length in the scanning direction equal to the length in the scanning direction of each group of projection systems. 
     FIGS. 18 and 19  illustrate adopting a boundary as illustrated in  FIG. 17 , according to embodiments of the present invention. This can result in desired number of groups of optical columns required to achieve a particular throughput. 
     FIG. 18  corresponds to  FIGS. 11 and 12 , in which two groups of optical columns are used to expose respective generally rectangular areas of the substrate. In  FIG. 18 , optical column group  60  is used to expose generally rectangular shaded area  61  extending from the left hand side of the group  60 , and optical column group  62  is used to expose generally rectangular shaded area  63  extending from the left hand side of group  60  to the left hand side of group  62 . 
     FIG. 19  represents the case as explained with reference to  FIG. 17 , in which a section of the substrate extending in the scan direction is exposed by both of optical column groups  60  and  62 . Optical column group  60  is used to expose part of the substrate areas  64  beneath group  60  and substrate areas  65  extending to the left of group  60 . Optical column group  62  is used to expose part of substrate are  64  beneath group  60  and substrate area  66  extending to the right of group  60 . 
   In the case illustrated in  FIG. 18 , in some circumstances the number of optical column groups required to achieve a given throughput can be greater than the number required in the case illustrated in  FIG. 19 . This difference is explained further below. 
   If there is only one group of optical columns, as in the case illustrated for example in  FIG. 10 , the number of optical columns required in the scan direction can be expressed as follows: 
   
     
       
         
           
             N 
             oc 
           
           = 
           
             
               
                 L 
                 s 
               
               + 
               
                 L 
                 ocg 
               
             
             
               
                 L 
                 p 
               
               · 
               f 
               · 
               ET 
             
           
         
       
     
   
   where:
         N oc =number of optical columns   L s =length of the substrate in the scan direction   L ocg =length of the optical column group in the scan direction   L p =length of each pixel to be exposed in the scan direction   f=maximum frequency at which individual pixels can be addressed   ET=the throughput, that is the time within which a full substrate has to be exposed.
 
 L   ocg   =N   oc   .L   oc 
       

   where L oc  is the length of one optical column in the scan direction, and therefore: 
   
     
       
         
           
             N 
             oc 
           
           = 
           
             
               L 
               s 
             
             
               
                 
                   L 
                   p 
                 
                 · 
                 f 
                 · 
                 ET 
               
               - 
               
                 L 
                 oc 
               
             
           
         
       
     
   
   N oc  is an integer. Assuming a throughput time ET of about 29 seconds, an addressing frequency of about 10 kHz, a substrate length L s  of about 1m, and optical column length L oc  of about 0.1 m, and a pixel length L p  of about 1 μm, then to achieve the target throughput requires about 5.26 optical columns, which in practice requires six optical columns. 
   Separating the optical columns as depicted in  FIG. 18  into two groups of three would result in a substrate length to be exposed by each group of L s =0.5. Thus, each group would require about 2.63 optical columns (half 5.26), that is in practice three optical columns. Thus, for the given throughput, there would still be a need for a total of six optical columns. 
   In the case as illustrated in  FIG. 19 , in which a section of the substrate is exposed by both of the two groups of optical columns, the equation determining the number of optical columns required to achieve a given throughput is different from that above as follows: 
   
     
       
         
           
             N 
             oc 
           
           = 
           
             
               
                 L 
                 s 
               
               + 
               
                 
                   L 
                   ocg 
                 
                 / 
                 N 
               
             
             
               
                 L 
                 p 
               
               · 
               f 
               · 
               ET 
             
           
         
       
     
   
   where N=number of groups of optical engines. The above equation can be simplified to: 
   
     
       
         
           
             N 
             oc 
           
           = 
           
             
               L 
               s 
             
             
               
                 
                   L 
                   p 
                 
                 · 
                 f 
                 · 
                 ET 
               
               - 
               
                 
                   L 
                   oc 
                 
                 / 
                 N 
               
             
           
         
       
     
   
   If two groups of optical engines are provided, then:
 
N oc =4.17
 
   Thus each group would require about 2.09 optical columns, which is substantially less than the 2.63 required with an arrangement, such as that illustrated in  FIG. 18 , but still would, in practice, require three optical columns per group. If, however, the optical columns were arranged in four groups, the above equation indicates:
 
N oc =3.77
 
   Thus, given four optical columns equally spaced apart in the scan direction with adjacent columns exposing overlapping areas of the substrate, a throughput can be achieved which requires six optical columns, if the optical columns are all arranged in a single group, or six optical columns if the optical columns are equally spaced apart, but do not expose overlapping areas of the substrate. This ability to reduce the number of optical columns required to achieve a given throughput is a significant additional result to the reduction in scan distance achieved as described above. 
   It will be appreciated that in an arrangement, such as that illustrated in  FIG. 18 , the groups of optical columns can be spaced apart with a pitch equal to L/N, where L is the length of the substrate to be exposed and N is the number of optical column groups. In contrast, in an arrangement such as that illustrated in  FIG. 19 , the group of optical columns are spaced apart with a pitch of (L+1)/N. 
   CONCLUSION 
   While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. It will be apparent to persons skilled in the relevant art that various changes in form and detail can be made therein without departing from the spirit and scope of the invention. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents. It is to be appreciated that only the Detailed Description section is intended to be used to interpret the appended claims, and not the Summary and Abstract sections of this document.