Abstract:
A method of forming a photoresist pattern by a photolithography technique is composed of:  
     providing a photoresist layer;  
     exposing the photoresist layer to a first pattern-defining light using a first mask; and  
     exposing the photoresist layer to a second pattern-defining light using a second mask. The first mask includes a shielding region shielding the first pattern-defining light. The second mask includes a phase-shifting region having a phase shifter edge and a non-phase-shifting region adjacent to the phase-shifting region on the phase shifter edge. A first light portion of the second pattern-defining light passes through the phase-shifting region. A second light portion of the second pattern-defining light passes through the non-phase-shifting region. A first phase of the first light portion differs from a second phase of the second light portion. The first and second masks are aligned such that the phase shifter edge overlaps on the shielding region.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    This invention relates to an exposure method for use in photolithography and a mask for use in photolithography. More particularly, the invention relates to a phase-shift mask and an exposure method using the phase-shift mask.  
           [0003]    2. Description of the Related Art  
           [0004]    To form patterns of semiconductor elements, a photolithography technique is commonly employed. A pattern of a mask is transferred to a photosensitive resin layer provided on a semiconductor substrate by the photolithography technique. The photosensitive resin is also known as “resist.” A resist is classified into two type, i.e., negative type and positive type. The negative-type resist is of the type; any part of which that has been exposed to the light applied through a mask will remain on the semiconductor substrate. The positive-type resist is of the type; any part of which that has been exposed to the light applied through a mask will be removed from the semiconductor substrate.  
           [0005]    In recent years, it has been demanded that an image be formed on a resist layer in higher resolution to provide fine patterns of semiconductor elements. Fine semiconductor element patterns increase integration density of a semiconductor integrated circuit.  
           [0006]    To enhance the resolution of an image formed on a resist, a phase shift exposure method is proposed in 1982. In the phase shift exposure method, the phase difference between light beams applied is utilized to improve the resolution of the image focused on a resist layer. The principle of the phase shift exposure will be described, with reference to FIGS. 1A to  1 D and FIGS. 2A to  2 D.  
           [0007]    In the ordinary exposure, the light applied perpendicularly to a mask  106  passes through the transparent regions  150  and  151  of the mask as illustrated in FIG. 1A. Chromium mask patterns  121  are provided on the mask  106 . The mask  106  has transparent regions  150  and  151 . The light beams passing through the transparent regions  150  and  151  have the same phase. The light beams emanate from the transparent regions  150  and  151  and pass through the projection lens of a reducing projection exposure apparatus. The two beams are then focused on the surface of a resist layer, which is on an image-forming surface.  
           [0008]    The distance between the transparent regions  150  and  151  cannot be reduced to an infinitesimal value, for the following reason. If the distance is extremely short, the two beams passing the regions  150  and  151  overlaps at the image-forming surface as indicated by the broken lines in FIG. 1C. The light beams, which have a same phase, intensify each other at the image-forming surface. As a result, the light-intensity distribution on the surface of the resist has one peak as illustrated in solid line in FIG. 1D. Consequently, the chromium mask patterns  121  are not correctly transferred to the resist layer. Thus, the interval between the transparent regions  150  and  151  cannot be decreased over a certain limit. The limit R of resolution for any image formed on a resist is given as follows:  
             R=K   1   ×λ/NA   (1)  
           [0009]    where K 1  is the constant that depends on the properties of the photosensitive resin, λ is the wavelength of the light applied to the mask  106 , and NA is the numerical aperture of the projection lens that is incorporated in the reducing projection exposure apparatus. Here, the limit R is known as “Reyleigh resolution”.  
           [0010]    In the phase shift exposure, light is applied to a resist layer through a phase shift mask  107  as is illustrated in FIG. 2A. The phase shift mask  107  has transparent regions  152  and  153 . The region  153  is provided with a phase shifter  120 , while the region  152  has no phase shifters. The light beam passing through the transparent region  153  is delayed as it passes through the phase shifter  120 . Hence, the light beam passing through the transparent region  153  differs in phase from the light beam passing through the transparent region  152 . The thickness D that the phase shifter should have to impart a phase difference of 180° to the light beams is given as follows:  
             D=λ/{ 2×( n− 1)}  (2)  
           [0011]    where λ is the wavelength of the light applied to the phase shift mask  107 , and n is the refractive index of the phase shifter  120 . If the two light beams emanating from the transparent region  152  and the transparent region  153 , respectively, have a phase difference of 180°, their parts overlapping at the image-forming surface will cancel out each other. As a result, as shown in FIG. 2C, the intensity of light is nil at one part of the surface of the resist layer. It follows that the light-intensity distribution on the resist has two peaks as shown in FIG. 2D. The chromium patterns  121  can therefore be transferred to the resist with high accuracy. Thus, the use of the phase shift mask  107  can enhance the resolution of an image focused on the surface of a resist.  
           [0012]    Also, the phase shift exposure technique can increase the depth of focus (DOF). The term “depth of focus” means the range of distance over which the focus may be displaced without causing troubles. The reason is discussed comparing the ordinary exposure technique and the phase exposure technique in the following.  
           [0013]    In the ordinary exposure using no phase shifters, the more the image-forming surface deviates from the focal plane, the more the two beam emanating from the transparent regions  150  and  151  overlap each other at the image-forming surface. This means that the resolution will sharply decrease if the image-forming surface of the resist deviates from the focal plane.  
           [0014]    In the phase shift exposure, the two adjacent beams emanating from the transparent regions  152  and  153  have a phase difference of 180°. Their overlapping parts cancel out each other at the image-forming surface of the resist layer. The intensity of light is therefore zero at one part of the image-forming surface. Hence, even if defocusing occurs, that is, even if the focus deviates from the image-forming surface, the dimensional precision of the pattern, transferred to the resist, will be hardly influenced. Thus, the depth of focus can be increased in the phase shift exposure.  
           [0015]    The phase shift exposure technique, however, cannot successfully apply to two-dimensional random patterns. The layout pattern of a semiconductor integrated circuit includes regular patterns and random patterns. Each regular pattern extends in one direction only, whereas each random pattern randomly extends first in one direction, and then in another direction. Here, examples of regular patterns are the bit lines and word lines of a DRAM (Dynamic Random Access Memory). Examples of random patterns are the wires of logic circuits. The phase shift masks are designed in accordance with the basic rule that a phase difference of 180° is imparted to two beams that have passed through two adjacent transparent regions. This basic rule can be easily applied to the regular patterns, but not to two-dimensional random patterns.  
           [0016]    [0016]FIG. 3A is a plan view of a phase shift mask  108  that may be used to form two-dimensional random patterns by means of the conventional phase shift exposure. The phase-shift mask  108  is designed to transfer a pattern on a positive-type resist. The mask  108  has a shield region  111 , a transparent region  113  and a transparent region  114 . The shield region  111  is identical in shape to the pattern that is to be transferred to a resist. Phase shifters  120  are provided on the transparent region  113 . The beam passing through the transparent region  113  is out of phase with respect to the beam passing through the transparent region  114 . In other words, the phase of the beam differs by 180° from that of the beam passing through the transparent region  114 . FIG. 3C is a sectional view of the Levenson-type mask  108 , taken along line C-C in FIG. 3A. As FIG. 3C shows, the mask  108  is composed of a glass substrate  122 . A chromium film  121  is provided on the shield region  111 , and a phase shifter  120  is provided on the transparent region  113 . No phase shifters are provided on the transparent region  114 .  
           [0017]    Light is applied to the positive-type resist through the phase-shift mask  108 . Light-exposed parts of the positive-type resist are developed and resist patterns  117  are formed as shown in FIG. 3B. The shield region  111  shields the part  115  of the positive-type resist from the light. Thus, the part  115  of the resist, which opposes the shield region  111 , is developed as is intended.  
           [0018]    In addition, the part  116  of the resist layer, which opposes the boundaries between the transparent regions  113  and  114 , is developed. The beams passing through the transparent region  113  (having a phase shifter) and the transparent region  114  (having no phase shifters) have the opposite phases. The intensity of light is therefore almost nil at the boundary between the transparent regions  113  and  114 . The part  116  of the resist, which opposes the boundary between the transparent regions  113  and  114 , is also developed. That is, not only the part  115  that should be developed, but also the parts  116  which should not be developed is developed.  
           [0019]    With the conventional phase shift exposure it is difficult to prevent the part  116  of the resist layer from being developed. Hence, the conventional phase-shift mask  108  cannot be used to transfer two-dimensional random patterns to a positive-type resist.  
           [0020]    It will be described now how two-dimensional random patterns are transferred to a negative-type resist by means of the conventional phase shift exposure technique. FIG. 4 is a plan view of a phase-shift mask  109  that is used to transfer two-dimensional random patterns to a negative-type resist. As shown in FIG. 4, the phase-shift mask  109  has a shield region  111 ′, a transparent region  113 ′ and a transparent region  114 ′. A phase shifter is provided on the shield region  111 ′. The transparent region  113  has phase shifters while the transparent region  114 ′ has no phase shifters. The phase shifter imparts a phase different of 180° to the beam that has passed through the transparent region  113 ′, with respect to the beam that has passed through the transparent region  114 ′.  
           [0021]    The transparent region  113 ′ is an auxiliary pattern for enhancing the resolution of the negative-type resist pattern that will be formed at a position corresponding to the transparent region  114 ′. Nonetheless, the transparent region  113 ′ is required to have a width equal to or less than the value equivalent to the resolution limit. It is difficult to form transparent regions having such a small width at high reliability. Hence, the conventional phase shift exposure technique cannot process resists to form two-dimensional random patterns on negative-type resists.  
           [0022]    As described above, the conventional phase shift exposure cannot be applied to transfer two-dimensional random patterns on positive-type resists or negative-type resists.  
           [0023]    It is desired that images be formed on resists at resolution high enough to form two-dimensional random patterns.  
           [0024]    It is also desired that two-dimensional random patterns of high precision be transferred to resists by means of phase shift exposure technique.  
         SUMMARY OF THE INVENTION  
         [0025]    An object of the present invention is to form high-resolution images on resists in the process of forming two-dimensional random patterns.  
           [0026]    Another object of the invention is to transfer two-dimensional random patterns of high precision to resists by means of phase shift exposure technique.  
           [0027]    In order to achieve an aspect of the present invention, a method of forming a photoresist pattern by a photolithography technique is composed of:  
           [0028]    providing a photoresist layer;  
           [0029]    exposing the photoresist layer to a first pattern-defining light using a first mask; and  
           [0030]    exposing the photoresist layer to a second pattern-defining light using a second mask. The first mask includes a shielding region shielding the first pattern-defining light. The second mask includes a phase-shifting region having a phase shifter edge and a non-phase-shifting region adjacent to the phase-shifting region on the phase shifter edge. A first light portion of the second pattern-defining light passes through the phase-shifting region. A second light portion of the second pattern-defining light passes through the non-phase-shifting region. A first phase of the first light portion differs from a second phase of the second light portion. The first and second masks are aligned such that the phase shifter edge overlaps on the shielding region.  
           [0031]    The shield region may include a line resist shielding portion to form a line resist pattern extending to a first direction. The line shielding portion has a centerline extending to the direction. In this case, it is desirable that the phase shifter edge substantially overlaps on the centerline when the first and second masks are aligned.  
           [0032]    The phase shifter edge may be composed of first and second phase shifter edges parallel to each other and extending to the first direction. In this case, a distance between the first and second phase shifter edges is desirably larger than a width of the line shielding portion in a second direction perpendicular to the first direction.  
           [0033]    The phase-shifting region may be provided with a phase-shifter layer. In this case, a thickness of the phase-shifter layer is desirably determined such that a phase difference between the first phase and the second phase ranges from 175 to 185°.  
           [0034]    Also, the first pattern-defining light has a first intensity and the second pattern-defining light has a second intensity. In this case, the second intensity is desirably larger than the first intensity.  
           [0035]    In order to achieve another aspect of the present invention, A mask set is composed of a first mask and second mask. The first mask includes a shielding region shielding a pattern-defining light exposed to the first mask. The second mask includes a phase-shifting region having a phase shifter edge and a non-phase-shifting region adjacent to the phase-shifting region in the phase shifter edge. A first phase of a first light passing through the phase-shifting region differs from a second phase of a second light passing through the non-phase-shifting region. The phase shifter edge overlaps on the shield region when the first and second masks are aligned.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0036]    [0036]FIGS. 1A to  1 D are diagrams explaining a conventional exposure technique;  
         [0037]    [0037]FIGS. 2A to  2 D are diagrams for explaining a conventional phase shift exposure technique;  
         [0038]    [0038]FIG. 3A is a plan view of a conventional Levenson-type mask that may be used to form two-dimensional random patterns;  
         [0039]    [0039]FIG. 3B is a diagram showing parts of a positive-type resist which are developed after exposed to light applied through the mask shown in FIG. 3A;  
         [0040]    [0040]FIG. 3C is a sectional view of the conventional phase-shift mask  108 ;  
         [0041]    [0041]FIG. 4 is a plan view of another Levenson-type mask  109  that may be used to transfer two-dimensional random patterns;  
         [0042]    [0042]FIG. 5A is a plan view of a chromium mask  1 (i.e., a photo-mask) used in the first exposure step of the exposure method according to the invention;  
         [0043]    [0043]FIG. 5B is a sectional view of the chromium mask  1 ;  
         [0044]    [0044]FIG. 5C is a plan view of a chromium-less phase shift mask  2  used in the second exposure step of the exposure method according to the invention;  
         [0045]    [0045]FIG. 5D is a sectional view of the chromium-less phase shift mask  2 ;  
         [0046]    [0046]FIG. 6A shows a layout of patterns obtained when the masks  1  and  2  are laid one upon the other;  
         [0047]    [0047]FIG. 6B is a sectional view of the chromium mask  1 ;  
         [0048]    [0048]FIG. 6C is a sectional view of the chromium-less phase shift mask  2 ;  
         [0049]    [0049]FIG. 6D represents the intensity distribution of a laser beam  54  applied to a positive-type resist  56  in the first exposure step;  
         [0050]    [0050]FIG. 6E depicts the intensity distribution of a laser beam  58  applied to a positive-type resist  56  in the second exposure step;  
         [0051]    [0051]FIG. 6F represents half the total distribution of the light beams applied to the positive-type resist  56  in the first and second exposure steps;  
         [0052]    [0052]FIG. 7 shows the intensity distribution of light applied to a resist in the exposure method of the invention and the intensity distribution of light applied to a resist in the conventional exposure method;  
         [0053]    [0053]FIGS. 8A to  8 F are diagrams showing the defocus-dependency of the intensity distribution of light applied to a resist, which is observed in the exposure method according to the invention;  
         [0054]    [0054]FIGS. 9A to  9 F are diagrams showing the defocus-dependency of the intensity distribution of light applied to a resist, which is observed in the conventional exposure method;  
         [0055]    [0055]FIG. 10 is a plan view depicting another type of a chromium mask and another type of a chromium-less phase shift mask;  
         [0056]    [0056]FIG. 11 is a sectional view of a chromium-less phase shift mask  2 ′ designed for printing patterns on substrates; and  
         [0057]    [0057]FIG. 12 shows the reducing projection exposure apparatus that is used to perform the exposure method according to the present invention.  
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0058]    An exposure method according to an embodiment of the present invention will be described below, with reference to the accompanying drawings.  
         [0059]    The exposure method according to the present embodiment includes the first exposure step and the second exposure step. The first exposure step is performed, using a chromium mask  1  shown in FIG. 5A. The second exposure step is performed, using a chromium-less phase shift mask  2  shown in FIG. 5B.  
         [0060]    As shown in FIG. 5A, the chromium mask  1  has a shield region  11  and a first transparent region  12 . The shield region  11  defines a two-dimensional random pattern. The term “two-dimensional random pattern” means a pattern composed of lines irregularly arranged, not composed of lines that extend in vertical direction or horizontal direction, or both. In other words, a two-dimensional random pattern is one in which the interval between the constituent lines and/or the length of each constituent line is not regular in the vertical direction and/or the horizontal direction. The shield region  11  defining a two-dimensional random pattern has vertical lines and horizontal lines, each having a centerline  10 . The shape of the shield  11  is determined based on the design values described in the layout data generated by means of CAD (Computer Aided Design).  
         [0061]    As shown in FIG. 5B, the chromium mask  1  includes a transparent substrate  22 . A shield film  21  is provided on a part of the transparent substrate  22  that corresponds to the shield region  11 . The shield film  21  reflects the light applied to the chromium mask  1  in the exposure process, not allowing the light to pass through the chromium mask  1 . No shield film is provided on the first transparent region  12 . Hence, the first transparent region  12  allows passage of the light.  
         [0062]    As shown in FIG. 5C, the chromium-less phase shift mask  2  has a second transparent region  13  and a third transparent region  14 . In the second transparent region  13 , a phase shifter  20  is formed on the transparent substrate  24  as is illustrated in FIG. 5D. In the third transparent region  14 , no phase shifters are provided on the transparent substrate  24 . The phase shifter  20  shifts the phase of the beam passing through the second transparent region  13 , with respect to the phase of the beam passing through the third transparent region  14 . The phase shifter  20  has such a thickness d that the beam output from it differs in phase by 180° from the beam input to it. The thickness d is defined as follows:  
           d=λ/{ 2×( n− 1)}.  (3)  
         [0063]    The second transparent region  13  has a phase shifter edge  16 . The phase shifter edge  16  is a boundary between the second transparent region  13  and the third transparent region  14 .  
         [0064]    The region near the phase shifter edge  16  functions as a shield section. The beams passing through the second transparent region  13  and third transparent region  14 , respectively, are out of phase with respect to each other. The intensity of light is therefore almost nil at position on a resist layer, where the image of the phase shift edge  16  is formed. The chromium-less phase shift mask  2  substantially has a shield region, though no shield films are provided on it.  
         [0065]    [0065]FIG. 6A shows a layout of patterns obtained when the chromium mask  1  and the chromium-less phase shift mask  2  are laid one upon the other. The phase shifter edge  16  has a part  15  aligning with the centerline  10  of the shield region  11  of the chromium mask  1 . When the masks  1  and  2  are laid one upon the other as shown in FIG. 6A, the centerline  10  of the shield region  11  overlaps the part  15  of the phase shifter edge  16  of the second transparent region  13  shown in FIG. 5B. In FIGS. 5A and 6A, the part  15  of the phase shifter edge  16  is indicated in thick line. The thick line does not mean that the boundary line is thick in part.  
         [0066]    When exposure is carried out using the chromium-less phase shift mask  2 , the part of the resist layer which is near the part on which the phase shifter edge  16  is projected will not be exposed to light. That is, a resist pattern may be formed near the part on which the phase shifter edge  16  is projected. However, no resist patterns will be formed in that part of the resist layer which is exposed to light through the chromium mask  1  in the first exposure step. In the exposure method of this invention, a resist pattern is formed in only a part of the resist layer which is near the position where the phase shifter edge  16  of the second transparent region  12  is projected, and is also covered with the shield region  11 .  
         [0067]    As shown in FIGS. 6A to  6 C, the width of the second transparent region  13 , that is, the distance s between the phase shifter edges  16 , is greater than the width w of the shield region  11  of the chromium mask  1 . The distance s is one between the opposing edges of the second transparent region  13  that defines the phase shifter edges  16 . The fact that the distance s is greater than the width w helps to enhance the resolution of the image focused on the resist, as will be described later.  
         [0068]    The exposure method according to the present embodiment will now be described in detail. At first, the first exposure step is carried out, using the chromium mask  1  shown in FIG. 5A. FIG. 12 illustrates a reducing projection exposure apparatus  50  that is used to perform the exposure method. The apparatus  50  effects the first exposure step. In the first exposure step, the chromium mask  1  is secured to the mask holder  51  of the reducing projection exposure apparatus  50 . The KrF excimer laser  52  provided in the apparatus  50  emits a laser beam  53 . The wavelength of the laser beam  53  is 248 nm. The laser beam  53  is applied at right angles to the chromium mask  1 . As shown in FIG. 6B, the shield film  21  reflects the laser beam  53  thus applied. The laser beam  53  cannot pass through the shield region  11  and passes through the first transparent region  12  only. The laser beam  54  emerging from the first transparent region  12  passes through the projection lens  55  of the reducing projection exposure apparatus. The laser beam  54  is applied to the positive-type resist  56  provided on a semiconductor substrate  57 .  
         [0069]    [0069]FIG. 6D shows the intensity distribution of the laser beam  54  at the position on the positive-type resist  56 , where the line C-C′ is projected as shown in FIG. 6A. In FIG. 6D, the origin, at which x=0, coincides with the position where the centerline  10  of the shield region  11  is projected at the surface of the positive-type resist  56 . That is, the origin coincides with the position where the part  15  of the phase shifter edge  16  is projected at the surface of the positive-type resist  56 . On the surface of the positive-type resist  56 , the width w of the shield film  21  has such a value that a resist pattern may be formed, which is 120 nm (0.12 μm) wide along the x axis, i.e., the direction in which the image of the C-C′ line extends. The NA value, that is, the numerical aperture of the projection lens  55  is 0.68.  
         [0070]    The laser beam  54  applied to the to the positive-type resist  56  in the first exposure step has the intensity distribution illustrated in FIG. 6D. As shown in FIG. 6D, the beam  54  is least intense at a position where x=0. That is, the first dark section  3  is formed near that position where x=0. The broken line  40  in FIG.  6 D represents the lower limit to the intensity of light that the positive-type resist  56  responds to. The resist  56  is dissolved at any part that has been irradiated with a laser beam having intensity higher than the intensity represented by the broken line  40 . The intensity corresponding to the broken line  40  varies with the conditions of the exposure process.  
         [0071]    Then, the second exposure step is performed, using the chromium-less phase shift mask  2 . As shown in FIG. 12, the chromium mask  1  is removed from the mask holder  51  and the chromium-less phase shift mask  2  is secured to the mask holder  51 . A laser beam  53  is applied to the chromium-less phase shift mask  2 , at right angles as in the first exposure step. The laser beam  53  passes through both the second transparent region  13  and the third transparent region  14  as is illustrated in FIG. 6C. As described above, the phase shifter  20  has the thickness d defined by the equation (3). Hence, the phase shifter  20  imparts a phase difference of 180° to the two laser beams emerging from the second transparent region  13  and the third transparent region  14 . The laser beam  58  which passed through the second transparent region  13  and the third transparent region  14  passes through the projection lens  55  and is applied to the positive-type resist  56 .  
         [0072]    The laser beams  58  applied to the resist  56  in the second exposure step have the intensity distribution of FIG. 6E at the position on the positive-type resist  56 , where the line C-C′ is projected as shown in FIG. 6A. In FIG. 6E, the origin (x=0) is identical to the origin of the graph (FIG. 6D) that represents the light-intensity distribution observed in the first exposure step. The phase shifter  20  has such a width that the image of the phase shift edge  16  is projected on the positive-type resist  56 , at a distance of 0.4 μm in the x axis. The incoherence ratio σ, or the incoherence of the beam emitted from the KrF excimer laser  52 , is 0.3. It is desired that the incoherence ratio σ be as small as possible in the second exposure step.  
         [0073]    In the second exposure step, the laser beam  58  applied to the positive-type resist  56  has least intense at two positions, x=0 (μm) and x=0.4 (μm), as shown in FIG. 6E. That is, the beam is most weak at two positions where the image of the phase shift edge  16  is projected on the resist  56 . Two second dark sections  4   1  and  4   2  are formed, respectively, near that position where x=0 (μm) and near the position where x=0.4 (μm).  
         [0074]    The second transparent region  13  and the third transparent region  14 , through which two beams output of phase pass, sharply change the light-intensity distribution at a position which is close to the position where the image of the phase shift edge  16  is projected on the positive-type resist  56 . The intensities of the laser beams  58  much change at the boundary of the second dark sections  4   1  and  4   2 . This means that the widths of both dark sections  4   1  and  4   2  can be decreased.  
         [0075]    [0075]FIG. 6F represents half the total distribution of the light beams applied to the positive-type resist  56  in the first and second exposure steps. As FIG. 6F shows, a third dark section  5  is formed on the positive-type resist  56 . The third dark section  5  is located near a position that corresponds to the origin (x=0) of the graph (FIG. 6F). That is, the third dark section  5  is formed at a position where the first dark section  3  and one of the second dark sections  4   1  overlap each other. Namely, the third dark section  5  is provided at the position where a pattern is to be formed.  
         [0076]    Also, no resist patterns should not be formed at the position where the other second dark section  4   2  is provided. However, no resist patterns will be formed at the position where the other second dark section  4   2  is provided. This is because a light beam having more intense than is represented by the broken line  40  is applied at the position where the other second dark section  4   2  is provided in the first exposure step.  
         [0077]    Thus, the phase shift exposure technique according to the present embodiment can be utilized to form two-dimensional random patterns.  
         [0078]    In the second exposure step, the distance s between the phase shifter edges  16  is desirably greater than the width w of the shield region  11  of the chromium mask  1 . This results in that the phase shifter edges  16  of the phase shifter  20  reliably function as shield sections. The shorter the distance s between the edges  16 , the shorter the distance between the two dark sections formed in the second exposure step. If the distance s is too short, no dark sections will be formed on the positive-type resist  56 . Hence, it is required that the distance s between the phase shifter edges be sufficiently long. The distance s greater than the width w of the shield region  11  enhances the resolution of the image focused on the positive-type resist  56 . In addition, two-dimensional random patterns can be formed in high dimensional precision on the positive-type resist  56 .  
         [0079]    The exposure method according to the present embodiment can form images on the positive-type resist  56  at higher resolution than is possible with the conventional exposure method. FIG. 7 is a magnified representation of that part of FIG. 6F which shows the light-intensity distribution (solid line) at the third dark section  5 , and illustrates the light-intensity distribution (broken lines) observed in the conventional exposure method using a chromium mask  1  only. The exposure method of the invention increases the contrast about twice the value achieved by the conventional exposure method. The word “contrast” used here is concerned with the light applied to the positive-type resist. It means the ratio of the most intense part of the beam to the least intense part thereof in terms of brightness.  
         [0080]    Moreover, the exposure method of the invention can increase the depth of focus more than is possible with the conventional exposure method described above. FIGS. 8A to  8 F are diagrams showing the defocus-dependency of light-intensity distribution, which is observed in the exposure method according to the invention. FIGS.  9 A to  9 F are diagrams illustrating the defocus-dependency of light-intensity distribution, which is observed in the conventional exposure method. “Defocus” here represents a difference in vertical directions from the surface of the resist whose focal position is the image field. As seen from FIGS. 8A to  8 F and FIGS. 9A to  9 F, the depth of focus achieved in the method of the invention is greater than that obtained in the conventional method. Thanks to the great depth of focus, two-dimensional random patterns can be formed on the resist in the exposure method according to the present invention.  
         [0081]    In the exposure method described above, more light is desirably applied to the resist in the second exposure step than in the first exposure step. The light-intensity distribution in the second exposure step using the phase shift mask is sharper than the light-intensity distribution in the first exposure step using no phase shift masks. It is desired that light be applied to a part (x=0) of the resist, where a resist pattern will be formed, mainly in the second exposure step. When more light is applied to the resist in the second exposure step than in the first exposure step, the ratio of light applied in the second exposure step to the light applied in the first exposure is greater. This further enhances the resolution of the image focused at the surface of the resist and ultimately increases the dimensional precision of the two-dimensional random patterns formed on the resist. In the first exposure step, on the other hand, it suffices to apply a smaller amount of light to the second dark section  4   2  of the resist. This is because no pattern needs be formed on the second dark section  4   2 .  
         [0082]    The phase shifter edge  16  provided at the second transparent region  13  of the chromium-less phase shift mask  2  can achieve the object of the present invention, only if the overlapping parts of the chromium mask  1  and the phase shift mask  2  lie over the shield region  11 . A resist pattern is formed on only that part of the resist which is near the image of the phase shift edge  16  of the second transparent region  12  projected on the resist and which is protected by the shield region  11 . It is, however, desired that all centerline  10  of the shield region  11  should align with the phase shifter edge  16  provided at the second transparent region  13 . If the centerline  10  aligns with the phase shifter edge  16 , the least intense point in the distribution of the laser beam applied in the first exposure step coincides with the least intense point in the light distribution of the laser beam applied in the second exposure step. This enhances the resolution of any pattern formed on the resist.  
         [0083]    The chromium mask  1  and chromium-less phase shift mask  2 , shown in FIG. 5A and FIG. 5B, respectively, are nothing more than examples. The chromium mask and chromium-less mask that are shown in FIG. 10 may replace them. FIG. 10 is a plan view depicting the alternative chromium mask and chromium-less phase shift mask, which overlap each other. As shown in FIG. 10, the distance s 3  between the phase shifter edges of the chromium-less phase shift mask is equal to the distance between shield regions. The term “distance between shield regions” means the distance between the centerlines of any two opposing shield regions. Like the chromium-less phase shift mask  2  described above, the chromium-less phase shift mask shown in FIG. 10 has phase shifter edges spaced apart by distances (s 1 , s 2 , s 4 , s 5 ) which are longer than the width of the shield region  11  of the chromium mask.  
         [0084]    Also, the two beams that have passed through the second and third transparent regions  13  and  14 , respectively, are allowed to have a phase difference that deviates a little from the desired value of 180°. The experiments the inventor hereof conducted reveal that the light-intensity distributions of the beams applied to the resist in the first and second exposure steps have a desirable contrast so long as the phase difference falls within the range of 175° to 185°.  
         [0085]    [0085]FIG. 11 shows a chromium-less phase shift mask  2 ′ designed for printing patterns on substrates. The mask  2 ′ may be used in place of the chromium-less phase shift film  2 . The chromium-less phase shift mask  2 ′ has a transparent substrate  24 ′. The transparent substrate  24 ′ has a phase shifter  20 ′ that has been etched to a depth d′. The depth d′ is given as follows:  
           d′=/{ 2×( n′− 1)},  (3′)  
         [0086]    where n′ is the refractive index of the transparent substrate  24 ′.  
         [0087]    In the exposure method described above, it is possible to use the chromium-less phase shift mask in the first exposure step and the chromium mask in the second exposure step.  
         [0088]    As has been described above, the exposure method according to the present invention comprises the first exposure step and the second exposure step. A photo-mask having a two-dimensional random pattern is used in the first exposure step. A phase shift mask having a phase shift edge pattern is used in the second exposure step. With the exposure method of the invention, it is possible to form two-dimensional random patterns by the use of phase shift exposure technique. The exposure method of the invention can therefore enhance the resolution of images focused on a resist. Moreover, the exposure method of the invention can form, on resists, two-dimensional random patterns of high dimensional precision.  
         [0089]    Although the invention has been described in its preferred form with a certain degree of particularity, it is understood that the present disclosure of the preferred form has been changed in the details of construction and the combination and arrangement of parts may be resorted to without departing from the spirit and scope of the invention as hereinafter claimed.