Abstract:
An improved technique of exposing a photoresist through a grating mask reduces the occurrence of overlapping gratings and also avoids distortions in the exposed mask when there is a gap between the contact mask and the photoresist layer. The technique is particularly well suited to forming Bragg gratings on semiconductors and other materials that are used for wavelength selection in, for example, optical communications applications. The technique employs a phase grating held close to, but out of contact with, the photoresist layer. Amongst the advantages provided by the present invention is that the requirements of the permissible thickness of the photoresist layer suitable for writing high visibility gratings are relaxed, thus reducing the complexity and costs for processing the substrate.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention is directed to a method an apparatus for microcircuit fabrication, and more particularly to lithographic techniques for exposing a photoresist layer.  
         BACKGROUND  
         [0002]    In optoelectronic and optical devices, an optical grating can be provided by transferring the corresponding grating contained in a phase mask to a substrate for the device. One approach to transferring a mask grating to a substrate is to diffractively transfer light through the mask onto a layer of light sensitive photoresist on the substrate, thus exposing the positive photoresist with the transferred grating. Exposed portions of the photoresist may then be removed to produce a grating replicated in the photoresist. The replicated grating is then transferred to the substrate by a process such as chemical or reactive ion etching.  
           [0003]    Diffractive transfer of a mask grating includes illuminating the mask grating with light of a given wavelength and coherence length, and replicating the mask grating in the photoresist by diffracting self-interfering light from the mask. The mask is positioned in contact with the photoresist whereby the maximum visibility of the transferred grating in the photoresist is obtained for the directly incident diffracting light. Some light is reflected, however, from the photoresist and substrate surfaces. The reflected light interferes with the directly incident light to cause an interference pattern. This generates an overlapping grating in the photoresist whose extent depends on the thickness of the photoresist. Also, the grating written in the photoresist may become distorted where there are gaps between the mask and the photoresist.  
         SUMMARY OF THE INVENTION  
         [0004]    In view of the problems discussed above, there is a need for an improved technique of exposing a photoresist through a grating mask that reduces occurrence of the overlapping grating and also that avoids distortions in the exposed mask when there is a gap between the contact mask and the photoresist layer. Furthermore, the requirement for high visibility features to be written into the photoresist results in strict requirements on the permissible thickness of the photoresist layer, thus increasing the complexity and costs for processing the substrate.  
           [0005]    Generally, the present invention relates to a method and apparatus for near field holography. The technique is particularly well suited to forming Bragg gratings on semiconductors and other materials that are used for wavelength selection in, for example, optical communications applications. The technique employs a phase grating held close to, but out of contact with, the photoresist layer. An advantage provided by the present invention is that the requirements of the permissible thickness of the photoresist layer are relaxed, thus simplifying the process and reducing costs.  
           [0006]    In one embodiment, the invention is directed to a non-contact method for transferring a pattern from a phase mask to a photoresist layer on a substrate. The method includes adjusting a working distance between the phase mask and the photoresist layer so that the phase mask is not in contact with the photoresist layer and that the zero order and minus first order beams produce a primary grating in the photoresist layer and so as to reduce visibility of a secondary grating in the photoresist layer produced by an indirect light beam. The method also includes directing light to expose the photoresist through the phase mask to the photoresist layer so as to produce zero order and minus first order direct light beams, the light being of a wavelength to expose the photoresist.  
           [0007]    In another embodiment, the invention is directed to a device for non-contact transfer of a pattern from a phase mask to a photoresist layer. The device includes means for directing light to expose the photoresist through the phase mask to the photoresist layer so as to produce zero order and minus first order direct light beams, the light being of a wavelength to expose the photoresist. The device also includes means for adjusting a separation distance between the phase mask and the photoresist layer so that the zero order and minus first order beams produce a primary grating in the photoresist layer and so as to reduce visibility of any secondary grating in the photoresist layer produced by one of the direct light beams and an indirect light beam originating from a surface reflection of a direct light beam from a light input surface of the photoresist layer.  
           [0008]    Another embodiment of the invention is directed to a non-contact method for transferring a pattern from a phase mask to a photoresist layer on a substrate. The method includes adjusting a working distance between the phase mask and the photoresist layer so that the phase mask is not in contact with the photoresist layer, and directing light to expose the photoresist through the phase mask to the photoresist layer so as to produce zero order and minus first order direct light beams.  
           [0009]    Another embodiment of the invention is directed to a device for non-contact transfer of a pattern from a phase mask to a photoresist layer on a substrate. The device includes means for adjusting a working distance between the phase mask and the photoresist layer so that the phase mask is not in contact with the photoresist layer, and means for directing light to expose the photoresist through the phase mask to the photoresist layer so as to produce zero order and minus first order direct light beams.  
           [0010]    Another embodiment of the invention is directed to an apparatus for near field holography. The apparatus includes a phase mask holder holding a phase mask, a substrate holder holding a substrate having a photoresist layer proximate the phase mask, and a light source for delivering light to the phase mask, exposing light from the light source that has passed through the phase mask having a coherence length. At least one of the phase mask holder and the substrate holder is adjustable for selecting a separation distance between the substrate holder and the phase mask holder so that the phase mask is not in contact with the photoresist layer and that a first distance, corresponding to a distance travelled by a direct beam between the phase mask and the photoresist layer, is shorter than a second distance travelled by an indirect beam between the phase mask and the photoresist layer, by more than the coherence length of the indirect beam.  
           [0011]    Another embodiment of the invention is directed to an apparatus for near field holography. The apparatus includes a phase mask holder, a substrate holder for holding a substrate having a photoresist layer proximate the phase mask when the phase mask holder holds a phase mask, and a light source for delivering light to the phase mask when the phase mask holder holds a phase mask. At least one of the phase mask holder and the substrate holder is adjustable for selecting a separation distance between the substrate holder and the phase mask holder so that, when the phase mask holder holds a phase mask and when the substrate holder holds a substrate having a photoresist layer proximate the phase mask, and not in contact with the phase mask, light from the light source directly incident on the photoresist layer through the phase mask produces substantially no overlapping grating in the photoresist layer with light from the light source indirectly incident on the photoresist layer.  
           [0012]    The above summary of the present invention is not intended to describe each illustrated embodiment or every implementation of the present invention. The figures and the detailed description which follow more particularly exemplify these embodiments. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0013]    The invention may be more completely understood in consideration of the following detailed description of various embodiments of the invention in connection with the accompanying drawings, in which:  
         [0014]    [0014]FIG. 1 schematically illustrates an embodiment of an apparatus for diffractive transfer of a grating according to the present invention;  
         [0015]    [0015]FIG. 2 schematically illustrates an embodiment of an apparatus for measuring the optical distance between a phase mask and a substrate according to the present invention;  
         [0016]    FIGS.  3 A- 3 B schematically illustrate different light beams that can give rise to interference in the photoresist layer;  
         [0017]    FIGS.  4 A- 4 D show graphs of fringe visibility of a grating formed by direct light rays as a function of out-of-contact distance and bandwidth of light incident on the photoresist layer, for different values of collimation, without the consideration of indirect beams;  
         [0018]    FIGS.  5 A- 5 D show graphs of fringe visibility of a grating formed by direct and indirect light rays as a function of out-of-contact distance and bandwidth of light incident on the photoresist layer, for different values of light reflection, with consideration of direct beams;  
         [0019]    [0019]FIG. 6 illustrates a graph showing reflectance contours for a phase mask in contact with the photoresist layer, as a function of photoresist layer thickness and antireflection coating layer thickness;  
         [0020]    [0020]FIG. 7 illustrates a graph showing reflectance contours for a phase mask out of contact with the photoresist layer, as a function of photoresist layer thickness and antireflection coating layer thickness; and  
         [0021]    [0021]FIG. 8 schematically illustrates an apparatus used for measuring visibility of interference fringes formed using light from the light source, according to the present invention. 
     
    
       [0022]    While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.  
       DETAILED DESCRIPTION  
       [0023]    The present invention is applicable to near-field holography and is believed to be particularly suited to a method of diffractively transferring a pattern from a phase mask to a photoresist on a substrate, wherein the pattern is illuminated with at least partially coherent light. The pattern exposed in the photoresist layer may be a grating and may be used in a photolithographic method for forming a grating in a semiconductor material, for example a grating used in a distributed Bragg reflector (DBR) laser, a distributed feedback (DFB) laser, or the like. The method may also be useful for forming gratings in glass and other transparent materials for components used in wavelength division multiplexed (WDM) applications in optical communications, and also in electro-optic materials, such as lithium niobate, for forming integrated optical components.  
         [0024]    In near-field holography, the interference grating is formed by interference, not only between direct beams, but also between direct and indirect beams and between indirect beams. A direct beam is one that interacts with the photoresist layer after passing directly from the phase mask to the photoresist layer. An indirect beam interacts with the photoresist layer after being reflected between the substrate layers and the phase mask. Generally, interference between direct and indirect beams reduces the visibility of the grating formed in the photoresist layer by interference between the two direct beams.  
         [0025]    According to the present invention, the phase mask is held sufficiently far from the photoresist layer so that there is no contact, and that the separation distance between the phase mask and the photoresist is sufficiently large as to reduce coherent relationships between the interfering direct and indirect beams. Where the light source produces light that is relatively incoherent, for example the light source may be a lamp, the separation distance may be in the range 5-30 μm, and more preferably in the range 5-20 λm. Where the light source produces more coherent light, for example where the light source is a laser, the separation may be longer and may be, for example, in the range 5-1000 μm. When the phase mask is separated from the photoresist layer, the visibility of the grating formed in the photoresist layer may be higher than when in contact, with the grating being formed primarily from light directly incident on the photoresist layer. The effects of overlapping gratings, formed as a result of indirect beams interacting with direct beams, are reduced. The method allows for optimization of the out-of contact distance to adjust the grating visibility.  
         [0026]    The term “substantially no overlapping grating” is intended to mean that an overlapping grating can be present in the photoresist. However, the effect of the overlapping grating is reduced so that it does not influence the function of the primary grating in a specific application.  
         [0027]    One particular embodiment for implementing the present invention is schematically illustrated in FIG. 1, which shows an exemplary near-field holographic apparatus  100  set up for diffractive transfer of a grating  102  in a phase mask  104  to a layer of photoresist  106  on a substrate  108 .  
         [0028]    A light source  110  is used as a source for ultraviolet (UV) light suitable for exposing the photoresist with the desired resolution. The light source  110  may be, for example, an arc lamp such as a mercury arc lamp, or a laser, such as a rare gas-halide laser. The light  112  produced by the light source  110  is preferably partially coherent to control the visibility of the grating when written on the photoresist. The term partially coherent is intended to cover both quasi-monochromatic and partially collimated light.  
         [0029]    The light  112  emitted from the light source  110  may be at least partially collimated by a first lens  114 . Where the light source is a mercury arc, the arc is preferably oriented so that its image is ultimately parallel to the grating grooves  134  formed in the photoresist layer  106 . A mercury lamp having a small/medium arc is particularly advantageous for producing a small image on the phase mask  104 . The mercury arc lamp may be a high pressure, small/medium arc mercury lamp that provides a source of ultraviolet radiation in the spectral region ranging between 180 nm-600 nm . A high pressure lamp typically contains mercury at a pressure in the range 1 to 5 atm. The length of the mercury arc in a small/medium lamp is typically in the range between 0.5 mm and 4 mm, and the arc-length to arc-width ratio is typically greater than 2. An example of a suitable mercury arc lamp is model “HBO 200W/2” manufactured by Osram. This lamp produces ultraviolet radiation in the spectral region between 200 nm-600 nm.  
         [0030]    The first lens  114 , that collimates the light form the lamp  110 , may be any suitable type of collimating lens, such as a plano-convex lens as illustrated. The lens may be formed from quartz or any other material that is transparent to the UV light  112 .  
         [0031]    After passing through the lens  114 , the light is conditioned in the conditioning unit  115 . The conditioning unit  115  operates on the light to select the properties of the light incident on the photoresist layer. The conditioning unit  115  may be used, for example, to adjust the polarization state of the light reaching the photoresist layer  106 , the bandwidth of the light  112 , or the uniformity of illumination. In particular, the light may be filtered to produce substantially quasi-monochromatic light. The conditioning unit  115  may include a white light filter  116  and an interference filter  118 , whereby the bandwidth Δλ of the illuminating light may be tuned to a desired mercury line for exposing the photoresist layer  106 . The bandwidth of the conditioned light  120  transmitted form the conditioning unit  115  is preferably selected according to the desired visibility of the grating to be written in the photoresist layer  106 . The relationship between bandwidth and grating visibility is discussed more fully below. The bandwidth may be less than about 10 nm and may be approximately 2-4 nm for a center wavelength of 365 nm.  
         [0032]    The conditioning unit  115  may also include a polarizer  122  to polarize the light  112 . The use of polarized light may increase the visibility of the interference pattern formed by the phase mask  104 , since the diffraction efficiency of the phase mask  104  may be polarization dependent.  
         [0033]    The conditioned light beam  120  may then be expanded, typically using a beam expansion telescope  124 . The beam expanding telescope  124  may be formed from two lenses  126  and  128 . The negative expanding lens  126  diverges the light  120  towards the collimating lens  128  that re-collimates the light as an expanded beam  130 . It will be appreciated that other types of telescope may be used. The telescope  124  is preferably arranged to reduce aberrations in the expanded beam  130 . For example, where the expanding lens  126  is a plano-concave lens, the concave side may be directed towards the collimating lens  114  to reduce spherical aberration. Likewise, where the collimating lens  128  is plano-convex, the planar side may be directed towards the expanding lens  126  to reduce spherical aberration. In one particular embodiment, the expanding lens  126  is made of quartz, has a diameter of 55 mm, and a radius of curvature of −56.81 mm on the convex side. The collimating lens  128  may also be made from quartz, with a lens diameter of 100 mm, and a convex surface having a radius of curvature of 208.5 mm. In this arrangement, the collimating lens only collimates the center 100 mm of the diverging beam from the expanding lens  126 . The use of the center portion of the diverging beam increases the coherence of the expanded beam  130  emitted from the telescope  124 .  
         [0034]    The degree of collimation of the expanded beam  130  is given by Δθ, and is determined by the divergence angle of the conditioned light beam  120  entering the telescope, and the ratio of the focal lengths of the expanding lens  126  and the collimating lens  128 . A divergence as low as 0.0005 radians may be achieved using the set-up described above.  
         [0035]    The quality of the grating transferred to the photoresist layer  106  depends on its visibility. Generally, for two interfering beams of equal intensity, the visibility depends on the degree of mutual coherence which is determined by both temporal and spatial coherence. The beam expanding telescope  124  and the conditioning unit  115  permit tuning the degree of mutual coherence to an optimum for a given separation distance between the photoresist layer  106  and the phase mask  104 .  
         [0036]    The expanded beam  130  transmitted from the beam expanding telescope  124  therefore has a coherence length that is dependent upon the type of light source used, the conditioning that takes place in the conditioning unit  115  and the beam expanding telescope  124 .  
         [0037]    The expanded beam  130  is directed, at an angle θ i , to the phase mask  104  via a beam steering mirror  132 . It will be appreciated, however, that the expanded beam  130  may be directly incident on the mask  106  from the beam expanding telescope  124 . The steering mirror  132  is advantageous for adjusting the angle at which the expanded beam  130  is incident on the mask  104 . The incident angle, θ i , may be the Bragg angle for the phase mask  104 .  
         [0038]    The phase mask  104  includes surface relief grooves  134  in the light emitting face  136  of the phase mask  104  opposite the light receiving face  138 . It will be appreciated, however, that the phase mask  104  may also be used in an inverted position, with the light  130  incident on the grooves  134 . The phase mask  104  is typically held in a phase mask holder  144 . The phase mask holder may be movable relative to the photoresist layer  106 .  
         [0039]    The photoresist layer  106  is sensitive to light at the wavelength selected for forming the interference grating using the phase mask  104 . A suitable photoresist is Shipley 1828 photoresist supplied by Micro Resist Technology, Berlin, Germany. The photoresist layer  106  is applied to the substrate  108  using any suitable technique, such as spin coating. The substrate  108  may be supported by any suitable method, for example using a chuck  140 . The chuck  140  may be supported on a micropositioning apparatus  142 , such as a mask aligner. Antireflection (AR) coating layers may be disposed above the photoresist layer  106  as AR layer  107  and/or between the photoresist layer  106  and the substrate  108  as AR layer  109 .  
         [0040]    The mask  104  is separated from the photoresist layer  106  by the out-of-contact distance, d, which, for a mercury lamp source, is typically in the range of 5-30 μm, and may be in the range 5-20 μm. The out-of-contact distance may also be referred to as the working distance. The out-of-contact distance, d, may be varied by adjusting the micropositioning apparatus  142  and/or the mask holder  144 .  
         [0041]    The out-of-contact distance, d, may be measured by interference measurements, for example using the apparatus  200  illustrated in FIG. 2. Light from a broadband light source  202 , for example visible light, is focused simultaneously on the photoresist layer  106  and the light emitting side of the phase mask  104  by a lens  204 . The light may be directed from the light source  202  via a fiber or fiber bundle  206 .  
         [0042]    The light  208  reflected from the photoresist  106  and from the phase mask  104  is collected by a condensing lens  210  and is directed to a spectrometer  212 . The light  208  may be directed to the spectrometer  212  via a fiber  214 . The distance between the phase mask  104  and the photoresist  106  is found from the interference in the reflected light  208 . This interference gives rise to wavelength dependent extrema. The gap distance, d, is determined form the position of these extrema using the following formula: 
           d= ( M   ab λ a λ b )/(2(λ a −λ b )cos(θ)) 
         [0043]    The detector of the spectrometer detects extrema in the light passing through the spectrometer when the spectrometer wavelength is scanned. The extrema are either maxima or minima in intensity. M ab  is the number of extrema detected by the spectrometer, divided by two, when scanning between λ a  and λ b , and λ a  is the wavelength position for the extremum with the longest wavelength, while λ b  is the wavelength position for the extrema with the shortest wavelength. θ is the angle of incidence on the photoresist  106 .  
         [0044]    This measurement may be used to correct for any nonuniformity in the out-of-contact distance, d, and the nonuniformity corrected before the photoresist  106  is exposed to the UV light  130 . The out-of-contact distance, d, is typically measured over a part of the  108  substrate, but may also be measured over the whole substrate  108 .  
         [0045]    The collimated light beam  130  is directed onto the phase mask  104  via the mirror  132 , at an angle of incidence θ i , whereby the phase mask produces diffracting beams. If the wavelength of the light is λ and the period of the grating is Λ, then the grating produces two interfering diffraction beams when the angle of incidence fulfills the condition: 
         ½(1−sinθ i )&lt;λ/Λ&lt;1−sinθ i . 
         [0046]    The first diffraction beam is the zero order beam  146  that passes through the phase mask  104  substantially undeflected and the second beam  148  is diffracted by the phase mask  104  into the minus first order. When the angle of the minus first order beam  148  is −θ i , the phase mask  104  is said to be illuminated under the Bragg condition, or at the Bragg angle. The relative intensities of the two beams  146  and  148  may be made to be approximately equal by adjusting the grating profile and grating depth of the phase mask  104 .  
         [0047]    [0047]FIGS. 3A and 3B illustrate different light beams that propagate between the phase mask  104  and the photoresist layer  106 . Under certain conditions, these different light beams may contribute to the production of an interference grating in the photoresist. The collimated beam  130  is incident on the phase mask  104  at incident angle θ i . The zero order beam  300  corresponds to light that travels directly through the phase mask  104  without angular deviation. The minus first order beam  302  is light that is diffracted into the minus first order by the phase mask. Both the zero order and the minus first order beams  300  and  302  are direct beams (shown with solid lines). Direct beams are beams that pass directly from the phase mask  104  to the photoresist layer  106 .  
         [0048]    A beam that is reflected to the phase mask  104  and then redirected by the phase mask  104  to the photoresist layer  106 , is referred to as an indirect beam. Indirect beams are illustrated in FIGS. 3A and 3B with dashed lines. Light beam  304  is initially directed in the same direction as the zero order direct beam  300 , but is reflected off the substrate  108 , photoresist layer  106  or antireflection coating  107  or  109 , back to the phase mask  104  and is then redirected back to the photoresist layer  106  by the phase mask  104 . Light beam  306  initially is directed in the same direction as the minus first order direct beam  302  but is reflected off the substrate  108 , photoresist layer  106  or antireflection coating  107  or  109 , back to the phase mask  104  and is reflected back to the photoresist layer  106  by the phase mask  104 .  
         [0049]    Another type of indirect beam  308  initially starts off in the same direction as the zero order direct beam  300 , but reflects off the substrate  108 , photoresist layer  106  or antireflection coating  107  or  109 , back to the phase mask  104 . The beam  308  is diffracted back to the photoresist layer  106  in a direction approximately antiparallel to the direction incident on the phase mask  104 . Another type of indirect beam  310  initially starts off in the same direction as the minus first order direct beam  302 , but reflects off the substrate  108 , photoresist layer  106  or antireflection coating  107  or  109 , back to the phase mask  104 . The beam  310  is diffracted back to the photoresist layer  106  in a direction approximately antiparallel to the direction incident on the phase mask  104 . Each of the beams  300 - 310  interacts with the others. The interactions involving one or more indirect beams may be divided into two groups. The first group shows little variation in the x-direction, but demonstrates a periodic variation of (λ cos(θ i ))/2 along the z-direction due to the phase differences between interacting beams. This introduces a variation in the visibility of the grating along the x-direction due to gap variation. It is, therefore, important to reduce the contribution from the indirect beams. Examples of interactions that fall into this first group include interactions between beams  300  and  304 , and between beams  302  and  306 . A second group of interactions has a periodical variation in the x-direction which has a period approximately the same as the period of the interaction between the two direct beams  300  and  302 . This second group has the same variation in the z-direction as the first group. Examples of interactions in this second group include interactions between beams  300  and  308 , and between beams  302  and  310 .  
         [0050]    The first group of interactions typically give rise to different d.c. contributions to the irradiance in the photoresist layer  106 , the magnitude of these contributions being dependent on the magnitude of d. The second group of interactions typically gives rise to spatially varying contributions to the irradiance in the photoresist layer  106 , which also depend on the magnitude of d. interference grating formed by the interaction between the two direct beams  300  and  302  is referred to as a primary grating. All other interference gratings, whether or not formed by the direct beams  300  and  302 , are referred to as secondary gratings.  
         [0051]    There are typically imperfections in the setup, however, for example small variations in the thickness of the phase mask  104  and in the out-of-contact distance between the phase mask  104  and the photoresist layer  106 . Variations in the out-of-contact distance may result from variations in the thickness of the phase mask  104 , substrate  108 , photoresist layer  106  or the antireflection layers  107  or  109 . The indirect beams give rise to overlapping gratings because of these imperfections. Both the overlapping gratings and the d.c. contributions reduce the visibility of the desired periodic grating structure induced in the photoresist layer  106 . Therefore, it is an important goal to reduce, if not eliminate, the interference of various indirect beams that produces the DC contributions and the overlapping gratings.  
         [0052]    The out-of-contact distance is preferably adjusted to be within ±1 μm from a desired value for the out-of-contact distance. Preferably, the visibility of the fringes in the primary grating produced by the direct zero and minus first order beams  300  and  302  is greater than 80%, and more preferably greater than 90%. High quality exposure of the photoresist layer  106  is obtained by careful selection of the out-of-contact distance, d.  
         [0053]    Consider a phase mask with period Λ, illuminated at the first Bragg angle using partially coherent light with a center wavelength λ fulfilling the condition: ⅔Λ≦λ≦2Λ. The incident light diffracts into the zero and minus first orders, as discussed above. The relative intensity of the diffraction orders depends on the depth and shape of the grating. A properly optimized grating has almost identical intensity in the two orders. Here we calculate the sharpness of the interference fringes, also known as the visibility, due to interference between the indirect and direct beams as illustrated in FIGS. 3A and 3B. It is assumed in the calculations that the two diffracted beams are of equal intensity.  
         [0054]    When considering temporal coherence we compare a light wave, E(t), with itself at different times, t and t+τ. When considering spatial coherence we compare light waves, E(r,t), at different points r 1 , and r 2  in space. In the more general case of spatiotemporal coherence we consider both different times and different spatial points.  
         [0055]    The total electrical field arising due to the light in the photoresist layer  106  is found by first performing coherent addition of the direct and indirect fields between the phase mask  104  and the photoresist layer  106 , taking into account the reflection from the substrate  108 , the photoresist layer  106  and antireflection layer either above or below the photoresist layer  106 , the diffraction from the phase mask  104 , the time delay of the indirect fields, angular dispersion and collimation. Second, an integration is performed over divergence angle and wavenumber. An analysis of the incoherent addition of intensities is provided in “Analysis of grating formation with excimer lasers irradiated phase mask”, published by P. E. Dyer, R. J. Farley and R. Giedl in Optics Communications vol. 115, 1995, pp. 327-334, incorporated herein by reference.  
         [0056]    Having obtained the total electrical field, the total intensity can be calculated and the visibility of the interference fringes is determined as a function of out-of-contact distance, d, as 
           V ( d )=( I   max ( d )−I min ( d ))/( I   max ( d )+I min ( d ))  (1) 
         [0057]    where I max  is the maximum intensity on the interference grating and I min  is the minimum intensity. The visibility for a given distance, d, may be found by finding the maximum and minimum intensity at that distance.  
         [0058]    The field contributions, E 0  and E 1,  for the zero order and minus first order beams  300  and  302  respectively, immediately following the phase mask  104  are given by: 
           E   0 =η 0   e   ik(x sin(θ)+z cos(θ))   (2) 
         and  E   1 =η −1 e ik(x sin(θ1)+z cos(θ1)+φ1)   (3) 
         [0059]    where η i  is the diffraction intensity into the ith diffraction order, (i=0, −1), φ1 is the phase difference due to oblique wavefront between interfering waves, k is the wavenumber, θ is the incident angle on the phase mask  104  and θ1 is the diffraction angle of the minus first order. The presence of the photoresist layer  106 , substrate  108  and the optional antireflection layers  107  and/or  109  means that multiple interference has to be considered. The lowest order contributing fields are: 
           E   2   =r   12 η 0   e   ik(x sin(θ)+z cos(θ)+φ2 )  (4) 
           E   3   =r   12 η 0   e   ik(x sin(θ1)+z cos(θ1)+φ3)   (5) 
           E   4   =r   12 η −1   e   ik(x sin(θ1)+z cos(θ1)+φ4)   (6) 
           E   5   =r   12 η −1   e   ik(x sin(θ)+z cos(θ)+φ5)   (7) 
         [0060]    where r 12 =(R pm .R sub ) ½  and R pm  is the diffraction efficiency from the phase mask  104  and R sub  is the reflectance of the substrate  108  and the thin film layers, including the photoresist layer  106  and any antireflection layer. The phase angles φ 2 , . . . , φ 5 , represent the phase terms due to reflection and due to the oblique wavefront. E 2  corresponds to beam  304 , E 3  corresponds to beam  308 , E 4  corresponds to beam  306  and E 5  corresponds to beam  310 , shown in FIGS. 3A and 3B. The total irradiance, I tot , produced by light having different wavevectors and incident angles is thus given by:  
               I   tot     =     ∫     ∫       D   k          D   θ            ∑     i   ,     j   =   0       5            E   i          E   j   *             θ             k                       (   8   )                               
 
         [0061]    where D k  and D θ  are the distribution functions for wavenumber and incident angle respectively.  
         [0062]    The visibility of the grating induced in the photoresist layer  106  is shown in FIGS.  4 A-  4 D for gratings formed by the direct beams (E 0  and E 1 ) only. The visibility curves are plotted as a function of out-of-contact distance, d, in μm, along the x-axis and bandwidth of the illuminating light  130 , Δλ, in nanometers, along the y-axis. For each of these curves, the assumed wavelength was 365 nm, the incident angle, θ i , was 49.5°, and the expanded light beam  130  was assumed to have a Gaussian intensity distribution. In FIG. 4A, the assumed full width, half maximum (FWHM) divergence, Δθ, was zero radians. The area to the left of curve  402  has a visibility of 1 and the area between curves  402  and  404  has a visibility of 0.9 or more. Therefore, curve  402  may be referred to as the 90% contour and curve  404  referred to as the 80% contour. Curves  406 ,  408 ,  410 ,  412 ,  414 ,  416  and  418  are the 70%, 60%, 50%, 40%, 30%, 20%, and 10% contours respectively. In FIG. 4B, the assumed divergence was 0.001 radians and curves  422 ,  424 ,  426 ,  428 ,  430 ,  432 ,  434 ,  436  and  438  are the 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 10% contours respectively, In FIG. 4C, the assumed divergence was 0.002 radians and curves  442 ,  444 ,  446 ,  448 ,  450 ,  452 ,  454 ,  456  and  458  are the 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 10% contours respectively. In FIG. 4D, the assumed divergence was 0.003 radians and curves  462 ,  464 ,  466 ,  468 ,  470 ,  472 ,  474 ,  476  and  478  are the 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 10% contours respectively. It is apparent from FIGS.  4 A- 4 D that the visibility, in general, increases with reduced bandwidth, in other words with increasingly coherent light. Also, the visibility generally falls with increased out-of-contact distance, d.  
         [0063]    The visibility is also shown in FIGS.  5 A- 5 D calculated for both direct and indirect beams, for a beam divergence of 0.001 radians. The same values for wavelength and incident angle were used as were used to generate the curves in FIGS.  4 A- 4 D. In FIG. 5A, the reflectivity factor, r 12 , was 0.05. Curves  502 ,  504 ,  506 ,  508 ,  510 ,  512 ,  514 ,  516  and  518  are the 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 10% contours respectively. In FIG. 5B, the reflectivity factor was 0.1 and curves  522 ,  524 ,  526 ,  528 ,  530 ,  532 ,  534 ,  536  and  538  are the 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 10% contours respectively. In FIG. 5C, the reflectivity factor was 0.015 and curves  542 ,  544 ,  546 ,  548 ,  550 ,  552 ,  554 ,  556  and  558  are the 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 10% contours respectively. In FIG. 5D the reflectivity factor was 0.2 and curves  562 ,  564 ,  566 ,  568 ,  570 ,  572 ,  574 ,  576  and  578  are the 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 10% contours respectively. The boundaries between the regions of different visibility are less well defined than for the cases illustrated in FIGS.  4 A- 4 D, particularly for higher reflectivity. This is a result of considering interference from the indirect beams.  
         [0064]    FIGS.  5 A- 5 D show that the oscillation amplitude due to the phase difference of the reflected beams, resulting in the “fuzzier” contours than are seen in FIGS.  4 A- 4 D, is greater for smaller values of d than for larger values. It is also apparent that it is possible to simultaneously achieve low oscillation amplitude and high visibility by selecting optimal bandwidth and optimal distance, d. A preferred set of operating parameters is that r 12  is less than 0.1, the bandwidth Δλ is less than 4 nm and the visibility is around 85%, corresponding to a separation distance of about 6 μm.  
         [0065]    This parameter range may be used to provide a larger process window than is available using contact near-field holography. One of the limits of contact near-field holography is that the thicknesses of the photoresist layer  106 , and any antireflection layers  107  and  109 , need to be controlled within tight limits in order to reduce the effect of indirect beams on the grating visibility.  
         [0066]    [0066]FIG. 6 illustrates three reflectance contours for reflectance of 1%, 2% and 3% from the substrate and thin film layers as a function of the thickness, t 1 , of the photoresist layer, and the thickness, t 2 , of the antireflection coating layer, when the phase mask is in contact with the photoresist layer. The thickness of the photoresist layer is required to be within a window of around 6 nm in order to obtain a reflectance of less than 1%. This is difficult to obtain using inexpensive techniques, such as spin coating, and requires that the spin coating machine should be calibrated each time in order to achieve a photoresist or antireflection coating layer of correct thickness.  
         [0067]    In contrast, the non-contact case provides more relaxed restrictions on the photoresist layer thickness. For non-contact processing, the tolerance for the photoresist thickness is the condition r 12 &lt;0.01. Using a typical value of 7% diffraction efficiency for R pm  in the equation for r 12 , this corresponds to a value of R sub  for the non-contact case of about 14%. FIG. 7 illustrates contours of R sub  as a function of the thickness of the photoresist layer, t 1 , and the thickness of the antireflection coating layer, t 2 , when the phase mask is out of contact with the photoresist layer. The contours are illustrated in 1% steps, with 1%, 3%, 5%, 10% and 15% contours labeled. The relatively large permitted variation in R sub  results in a photoresist layer thickness range of about 30 nm. Non-contact exposure therefore enlarges the process window for the photoresist layer  106  from about 6 nm to about 30 nm. It is significantly easier to deposit the photoresist layer  106  to a thickness tolerance of about 30 nm as compared to a tolerance of 6 nm in the contact case. Therefore, the non-contact approach eases process restrictions imposed in the contact approach.  
         [0068]    In addition to selecting the spacing, d, on the basis of theoretical considerations, the spacing, d, may also be selected using experimental measurements of the visibility of transferred direct and overlapping gratings in the photoresist layer  106  for a given configuration of the optical set up. The coherence length of the exposing light that interacts with the photoresist layer  106  may be measured by measuring the fringe visibility induced in the photoresist layer  106  for a number of different separations between the phase mask  104  and the photoresist layer  106 . The coherence length of the exposing light is defined as that separation distance between the phase mask  104  and the photoresist layer  106  at which the visibility has fallen to 1/e of the maximum fringe visibility value of all interacting beams.  
         [0069]    The exposing light is formed from two components, direct beams and indirect beams. The direct beams, taken alone, have a longer coherence length than the indirect beams, so the overall coherence length of the exposing light typically has a coherence length that is less than the coherence length of the direct beams alone. The coherence length of an indirect beam, defined as the distance at which the visibility of an interference pattern formed between a direct beam and the indirect beam falls to 1/e of the maximum of all intersecting beams, is inherently dependent on the value of r 12 . Typically, for a given bandwidth of exposing light, the visibility is higher for smaller separations between the photoresist layer and the phase mask. However, by separating the photoresist layer from the phase mask according to the principles set forth herein, the deleterious effects of direct beams are reduced.  
         [0070]    The interference fringes for the direct propagating beams may be also be measured to a high accuracy using, for example, a Michelson interferometer equipped with a 50/50-beam splitter at the appropriate wavelength, for example as discussed in “Principles of Optics” by Max Born and Emil Wolf, Pergamon Press, Oxford, 6 th  edition, 1980, pages 300-323, and 499-518, incorporated herein by reference.  
         [0071]    One method of measuring the fringe visibility is discussed with reference to FIG. 8. The method uses a Michelson interferometer  800 , having a 50/50 beamsplitter  802 , and two reflectors  804  and  806 . A compensating plate  808  may be positioned between one of the reflectors  804  and the beamsplitter  802  to compensate for the other beam travelling through the beamsplitter  802 . One of the direct beams  300  or  302  is directed into the beamsplitter  802 , which directs beams of equal intensity towards the two mirrors  804  and  806 . The two mirrors reflect beams  810  and  812  that are combined at the beamsplitter  802  and form an interference pattern at the detector  814 . It will be appreciated that the Michelson interferometer  800  may be different from that illustrated, for example it may not include a compensating plate  808 , or the mirrors may be replaced by retroreflecting prisms.  
         [0072]    First, the mirror positions are optimized for spatial and temporal coherence by setting the lengths of the different arms to be equal, and for the two reflected beams  810  and  812  to completely overlap at the detector  814 . This condition, with no path length difference, produces white light fringes.  
         [0073]    Second, the position for the temporal coherence is moved away from the optimal position in appropriate steps by translating one or more of the mirrors  804  and  806  in the directions of arrows  816  and  818 . At each translation step, data is acquired using the detector  814  which may be, for example, a CCD or photodiode array that is sensitive to the wavelength of light being used. The visibility is calculated from equation (1), with the modification that d represents the movement of the temporal coherence mirror/prism away from the optimal position.  
         [0074]    The alignment of the mirrors  804  and  806  may also be adjusted by rotating one or both of the mirrors  804  and  806  in the directions of arrows  820  and  822  so that one part of the wavefront of the first beam  810  interferes with a different part of the wavefront of the second beam  812 . In other words, the beams  810  and  812  are sheared with respect to each other. If the amount of shear corresponds to the relative shift of the wavefronts between the zero order and minus first order beams, then an accurate measurement of the visibility of the grating due to the direct beams may be made. By calculating the fringe visibility for various combinations of path length difference and shear, the fringe visibility corresponding to various values of d may be mapped out. The coherence length of the direct beams may be measured using the Michelson interferometer  800 .  
         [0075]    The visibility information for the direct interfering beams can be used to choose an exposure window for test exposures. The transferred grating in test wafers may subsequently be measured for period variation, duty cycle variation and height variation over several areas using an atomic force microscope (AFM) or a scanning electron microscope (SEM). An optimal out-of-contact window may be determined from a statistical analysis of the experimental results.  
         [0076]    It will be appreciated that the experimental technique for measuring the visibility of the fringes produced by the light need not be restricted to the use of a Michelson interferometer. Other experimental approaches to measuring the fringe visibility include using a Mach Zehnder interferometer and other suitable interferometric techniques.  
         [0077]    As noted above, the present invention is applicable to photolithographic methods of transferring a pattern from a phase mask to a substrate. It is believed to be particularly useful for reducing the precision in the thickness of the photoresist and antireflection layers that is needed to obtain high exposures of high contrast. The present invention should not be considered limited to the particular examples described above, but rather should be understood to cover all aspects of the invention as fairly set out in the attached claims. Various modifications, equivalent processes, as well as numerous structures to which the present invention may be applicable will be readily apparent to those of skill in the art to which the present invention is directed upon review of the present specification. The claims are intended to cover such modifications and devices.