Abstract:
The present invention relates to electron beam lithography, and is directed to a method of compensating for pattern dimension variation caused by a re-scattered electron beam when an electron beam resist is exposed to the electron beam. The method of compensating for pattern dimension variation caused by a re-scattered electron beam comprises the steps of: dividing original exposure pattens into square sections; obtaining a dose of supplemental exposure to the re-scattered electron beam; and compensation-exposing the electron beam resist so that the supplemental exposure dose may be the same for all sections. According to the present invention, the pattern dimension variation can be compensated for a re-scattering effect of the electron beam, thereby uniformly forming a fine pattern width of a more highly-integrated circuit.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention relates to electron beam lithography, and more particularly, to a method of compensating for pattern dimension variation caused by a re-scattering effect of the electron beam occurring when a resist is exposed to the electron beam.  
           [0003]    2. Description of the Related Art  
           [0004]    Electron beam lithography is a technique used in patterning a material layer formed on a substrate in a desired pattern. This entails the process of coating an electron beam resist on a material layer; writing a desired pattern with an electron beam (referred to in the art as an “exposure”); developing the electron beam resist; and etching the material layer by using the electron beam resist pattern formed using the desired pattern as a mask. Electron beam lithography can be used to form a predetermined material layer pattern directly forming an integrated circuit on the substrate, however, in general, electron beam lithography is used to fabricate a photomask for use in photolithography.  
           [0005]    Referring to FIG. 1, the process for fabricating the photomask will be described in greater detail. The process comprises the steps of: coating an electron beam resist  130  on an opaque film  120  (in the case of a phase shift mask, a phase shifting layer is available, hereinafter described simply as an opaque film) formed on a transparent substrate  110 ; writing a desired pattern with an electron beam  150 ; developing the electron beam resist  130  by using a difference of solubility depending on writing of the electron beam; and etching the opaque film  120  by using the formed resist pattern as a mask.  
           [0006]    However, the electron beam  150  does not only expose the desired portion of the electron beam resist  130 , as the electron beam  150  is reflected on the surface of the opaque film  120  or scattered by collisions with atoms of a resist material in the electron beam resist  130  as marked  170  in FIG. 1. Also, the electron beam  150  is reflected in the electron beam resist  130  or on the surface of the electron beam resist  130  and at the lower plane of an objective lens  140  of an electron beam writer and, as a consequence, the electron beam  150  exposes an undesired portion of the electron beam resist  130  as marked  160  in FIG. 1.  
           [0007]    A quantity (a dose) by which the electron beam resist  130  is exposed an extra amount by scattering of the electron beam  150  as described above, is shown in FIG. 2. As shown in FIG. 2, the electron beam resist can be additionally exposed from a region in which a pattern is written with the electron beam, that is, from an edge of the pattern to a maximum distance of 10 cm. Close to the edge of the pattern, the dose can be as high as 25% of the original exposure dose. In FIG. 2, an additional exposure  210  affecting from the region in which a pattern is written with the electron beam, to approximately 10 μm, is caused by forward scattering and backward scattering of the electron beam indicated by reference numeral  170  in FIG. 1, and an additional exposure  220  affecting to approximately 10 cm is caused by re-scattering of the electron beam indicated by reference numeral  160  in FIG. 1. In conclusion, these additional exposures deteriorate the accuracy of the opaque film pattern, and cause a critical dimension (CD) error. The pattern dimension variation caused by the former additional exposure  210  is referred to as a proximity effect, and the pattern dimension variation caused by the latter additional exposure  220  is referred to as a re-scattering effect (multiple scattering effect or a fogging effect) of the electron beam.  
           [0008]    The re-scattering effect of the electron beam affects a wide range (Considering the integration of a current integrated circuit, 10 cm is a very wide range.), and since a dose caused by the additional exposure  220  is relatively small, the effect has not been ascertained, and no compensation method is well-known. However, the pattern dimension variation of the photomask caused by the re-scattering effect of the electron beam is estimated to be about 10˜20 nm when an electron beam dose is 8 μ C/cm 2  at an accelerating voltage of 10 keV, and the pattern dimension variation of the photomask greatly affects the manufacture of more highly-integrated circuits.  
           [0009]    On the other hand, the re-scattering effect of the electron beam is introduced, and a method for forming the lower plane of the objective lens in which the re-scattered electron beam is reflected, of a material with a low atomic number, as a method for reducing this effect is disclosed in, Norio Saitou et al., “Multiple Scattered E-beam Effect in Electron Beam Lithography”, SPIE Vol. 1465, pp.185 - p.191, 1991. That is, it is reported in the paper that an additional dose caused by the re-scattering effect of the electron beam when the lower plane of the objective lens is formed of copper, aluminum, and carbon, respectively, was measured, and the re-scattering effect of the electron beam was lowest when carbon was adopted. However, it is shown in FIG. 2 that the re-scattering effect is not remarkably reduced even if carbon is adopted. In FIG. 2, the chart of symbol “◯” applies to the case where aluminum is adopted, and the chart of symbol “□” applies to the case where carbon is adopted.  
           [0010]    Also, a method for reducing the re-scattering effect by absorbing the re-scattered electron beam by attaching an absorber plate in which a honeycomb groove is formed at the lower plane of the objective lens, is disclosed in Naoharu Shimomura et al., “Reduction of Fogging Effect caused by Scattered Electron in an Electron Beam System”, SPIE Vol. 3748, pp.125 - p.132, 1999. However, it is also not possible for all re-scattered electrons to be absorbed by this method, and there is a limitation in reducing the re-scattering effect.  
         SUMMARY OF THE INVENTION  
         [0011]    To address the above limitation, it is an object of the present invention to provide a method of compensating for pattern dimension variation caused by a re-scattering effect of an electron beam.  
           [0012]    Accordingly, to achieve the above object, there is provided a method of compensating for pattern dimension variation caused by a re-scattered electron beam, the method comprising the steps of: dividing original exposure patterns into square sections; determining a dose of additional exposure (referred to herein as a “supplemental exposure dose”) to the re-scattered electron beam for each section; and compensating the electron beam resist so that the supplemental exposure dose may be the same for all sections. That is, the method of compensating for pattern dimension variation caused by a re-scattered electron beam comprises the steps of: dividing original exposure pattens into square sections; determining a dose of supplemental exposure to the re-scattered electron beam when adjacent sections are exposed, for each section; determining a compensation exposure dose for each section by deducting supplemental exposure doses of each section from a predetermined reference value; and compensation-exposing the electron beam resist according to the compensation exposure dose of each section.  
           [0013]    The method of compensating for pattern dimension variation caused by a re-scattering effect of an electron beam according to the present invention can be provided in the form of a recording medium on which a program to be read and performed by a commercial computer is recorded. That is, a recording medium on which a program for obtaining compensation exposure data for compensating pattern dimension variation is recorded includes a program module for dividing original exposure patterns into square sections and determining a dose of supplemental exposure to the re-scattered electron beam when adjacent sections are exposed, for each section, a program module for determining a compensation exposure dose for each section by deducting the supplemental exposure dose of each section from a predetermined reference value, and a program module for setting-up compensation exposure patterns for each section with predetermined compensation exposure patterns so as to expose an area proportional to the compensation exposure dose for each section.  
           [0014]    According to the present invention, pattern dimension variation caused by a re-scattering effect of an electron beam can be compensated for, thereby uniformly forming a fine pattern of a more highly-integrated circuit.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]    The above object and advantages of the present invention will become more apparent by describing in detail preferred embodiments thereof with reference to the attached drawings in which:  
         [0016]    [0016]FIG. 1 is a sectional view illustrating a scattering phenomenon of an electron beam when the electron beam is incident on an electron beam resist;  
         [0017]    [0017]FIG. 2 is a graph of dose of supplemental exposure to a scattered electron beam versus distance from the edge of a pattern;  
         [0018]    [0018]FIG. 3 is a flow chart illustrating steps of compensating for pattern dimension variation caused by a re-scattered electron beam, according to an embodiment of the present invention;  
         [0019]    [0019]FIG. 4 is a layout diagram illustrating steps of dividing predetermined exposure patterns into sections according to an embodiment of the present invention;  
         [0020]    [0020]FIG. 5 is a graph illustrating the manner in which compensation exposure dose to compensate for pattern dimension variation caused by a re-scattered electron beam is determined, according to an embodiment of the present invention;  
         [0021]    [0021]FIG. 6 and FIG. 7 illustrate examples of compensation exposure patterns according to an embodiment of the present invention;  
         [0022]    [0022]FIG. 8 illustrates the size of an electron beam spot when compensation exposing according to an embodiment of the present invention;  
         [0023]    [0023]FIG. 9 is a layout diagram illustrating exposure patterns used for an experiment in compensating for pattern dimension variation caused by the re-scattered electron beam, according to an embodiment of the present invention;  
         [0024]    [0024]FIG. 10 and FIG. 11 are graphs of a line width before compensating for pattern dimension variation and a line width after compensating for pattern dimension variation according to the present invention, versus distance from the edge of a pattern, respectively.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0025]    [0025]FIG. 3 is a flow chart illustrating steps of compensating for pattern dimension variation caused by a re-scattered electron beam, according to the present invention. First, an electron beam resist is exposed to an electron beam according to predetermined exposure patterns (step  310 ). Referring back to FIG. 1, an electron beam resist  130  is coated on an opaque film  120  formed on a transparent substrate  110 , and a desired pattern is written with the electron beam. In other words, the electron beam exposure of the step  310  corresponds to a general exposure step, and here, a region not to be exposed to the electron beam is additionally exposed. Here, the desired pattern, for example, may be predetermined material layer patterns as shown in FIG. 4, and the layout of the desired pattern is converted into data form suitable for an electron beam exposure, and is supplied to an electron beam writer. In FIG. 4, the material layer patterns to be actually formed by a follow-up photolithographic process correspond to oblique-lined portions, and a portion exposed by the electron beam corresponds to the oblique-lined portions of FIG. 4 when a photoresist to be used in the follow-up photolithographic process is a negative-type photoresist and in case of a positive-type photoresist, the portion corresponds to a portion excluding the oblique-lined portions of FIG. 4. Hereinafter, for convenience of explanation, it is assumed that the resists to be used as the electron beam resist and in the follow-up photolithographic process are both positive-type resists.  
         [0026]    Returning to FIG. 3, during step  320  exposure patterns, such as those shown in FIG. 4, are divided into square sections  410 . In step  330 , a supplemental exposure dose caused by the re-scattered electron beam is calculated when adjacent sections are exposed, for each section  410 . The step of calculating the supplemental exposure dose for each section  410  can be subdivided as described below.  
         [0027]    First, an exposure pattern density is calculated for each section. As described above, in a case where the photoresist to be used in the follow-up photolithographic process is a positive-type photoresist, the portion exposed by the electron beam to actually fabricate the photomask corresponds to a portion excluding the oblique-lined portions of FIG. 4, and in a case where no oblique-lined portions are included in a section  410 , the exposure pattern density of the section is 1, and on the contrary, in a case where a section is formed of the oblique-lined portions, the exposure pattern density of the section is 0. That is, the exposure pattern density of each section is the fraction of the area of a section not occupied by oblique-lined portions.  
         [0028]    The supplemental exposure doses are calculated for each section using the following equation after the exposure pattern density is calculated for each section:  
               δ     i   ,   j       =       ∑     x   =     -   ξ       ξ            ∑     y   =     -   ξ       ξ            D       i   +   x     ,     j   +   y                   -         x   2     +     y   2         ξ   2                         (   1   )                               
 
         [0029]    wherein δ i,j  is a supplemental exposure dose of a section with x-coordinate i and y-coordinate j, ξ is a re-scattering range, and D i,j  is an exposure pattern density of the section with x-coordinate i and y-coordinate j.  
         [0030]    The above equation 1 will be described in detail below. For example, in a case where the re-scattered electron beam affects the edge of a window  420  indicated by a thick solid line when a portion of the most centered section  410  in FIG. 4 is exposed, the re-scattering range ξ is 2, and in order to calculate the supplemental exposure dose of the most centered section  410 , the supplemental exposure doses caused by the re-scattering effect of the electron beam when each section contained in the window  420  is exposed, are added. Also, the supplemental exposure dose of each section caused by the re-scattering effect when exposing are proportional to the exposure pattern density of the section and inversely proportional to the distance from the most centered section  410 .  
         [0031]    Returning to FIG. 3, after obtaining the supplemental exposure doses with respect to all sections, compensation exposure doses are calculated for each section (step  340 ). The compensation exposure doses are doses that compensate such that the supplemental exposure dose caused by the re-scattering effect of the electron beam may be constant with respect to all sections. The supplemental exposure dose of each section are deducted from a predetermined reference value. Here, the predetermined reference value may be a maximum value of the supplemental exposure dose with respect to all sections, calculated in the step  330 , or the predetermined reference value may be otherwise appropriately designated. That is, as shown in FIG. 2, since the supplemental exposure doses caused by the re-scattering effect of the electron beam are approximately less than 6% when carbon is used for the lower plane material of an objective lens, a maximum supplemental exposure dose may be set up as 6% of the original exposure (step  310 ) dose. Meanwhile, in a case where the reference value is the maximum value of the supplemental exposure dose, as shown in FIG. 5, the compensation exposure dose of a section x is obtained by deducting the supplemental exposure doses of the section from the maximum supplemental exposure dose  510 .  
         [0032]    Subsequently, a compensation exposure is performed according to the compensation exposure dose obtained for each section. In detail, a predetermined compensation exposure pattern is selected according to the compensation exposure dose for each section (step  350 ), and compensation exposure data are established by gathering the selected compensation exposure pattern for each section, and the electron beam resist is exposed by the electron beam according to these compensation exposure data (step  360 ).  
         [0033]    In FIGS. 6 and 7, which illustrate examples of compensation exposure patterns which can be selected, oblique-lined portions  603  and  703  of FIGS. 6 and 7 denote portions compensation-exposed by the electron beam. In the compensation exposure patterns, portions exposed according to the compensation exposure dose of each section become stepwise broad, and the compensation exposure patterns of FIG. 6 are classified into 11 stages, and those of FIG. 7 into 10 stages. The selection of the compensation exposure patterns of FIGS. 6 and 7 according to the compensation exposure dose for each section is done according to tables 1 and 2, respectively: In tables 1 and 2, δ′ i,j  is a compensation exposure dose of a section with x-coordinate i and y-coordinate j, and δ max  is the above-mentioned maximum supplemental exposure dose.  
                                     TABLE 1                           Open ratio of   Compensation           compensation exposure   exposure       Compensation exposure dose   pattern (%)   pattern                                δ′ i,j  &lt; 0.05 δ max     0   610       0.05 δ max   ≦ δ′ i,j  &lt; 0.15 δ max     10   615       0.15 δ max   ≦ δ′ i,j  &lt; 0.25 δ max     20   620       0.25 δ max   ≦ δ′ i,j  &lt; 0.35 δ max     30   625       0.35 δ max   ≦ δ′ i,j  &lt; 0.45 δ max     40   630       0.45 δ max   ≦ δ′ i,j  &lt; 0.55 δ max     50   635       0.55 δ max   ≦ δ′ i,j  &lt; 0.65 δ max     60   640       0.65 δ max   ≦ δ′ i,j  &lt; 0.75 δ max     70   645       0.75 δ max   ≦ δ′ i,j  &lt; 0.85 δ max     80   650       0.85 δ max   ≦ δ′ i,j  &lt; 0.95 δ max     90   655       0.95 δ max   ≦ δ′ i,j  &lt; 1.0 δ max     100   660                  
 
         [0034]    [0034]                                     TABLE 2                           Open ratio of   Compensation           compensation exposure   exposure       Compensation exposure dose   pattern   pattern                                δ′ i,j  &lt; 0.5    0   710       0.05 δ max  ≦ δ′ i,j  &lt; 0.16 δ max     1/9   715       0.16 δ max  ≦ δ′ i,j  &lt; 0.27 δ max     2/9   720       0.27 δ max  ≦ δ′ i,j  &lt; 0.38 δ max     3/9   725       0.38 δ max  ≦ δ′ i,j  &lt; 0.49 δ max     4/9   730       0.49 δ max  ≦ δ′ i,j  &lt; 0.60 δ max     5/9   735       0.60 δ max  ≦ δ′ i,j  &lt; 0.71 δ max     6/9   740       0.71 δ max  ≦ δ′ i,j  &lt; 0.82 δ max     7/9   745       0.82 δ max  ≦ δ′ i,j  &lt; 0.93 δ max     8/9   750       0.93 δ max  ≦ δ′ i,j  &lt; 1.0 δ max     1   755                    
         [0035]    The maximum dose during compensation-exposing (step  360 ) is preferably a sufficiently small value (for example, less than 6%) compared to that at the original exposure (step  310 ), preferably, however, the compensation exposure time is comparatively short, for example less than 30 minutes (exposure time at the original exposure is generally several hours.), so that the compensation exposure patterns of FIGS. 6 and 7 are not actually formed on the photomask.  
         [0036]    Also, as shown in FIG. 8, preferably, a spot size  810  of the electron beam when compensation-exposing is several times greater than a line width of the compensation exposure patterns  603  so that the spot  810  overlaps unexposed portions  605 .  
         [0037]    When the compensation exposure is performed in this way, the supplemental exposure dose caused by the re-scattering effect of the electron beam at each section becomes constant, thereby the pattern dimension variation of the photomask is prevented.  
         [0038]    In the above-mentioned embodiment, the method according to the present invention is applied to the fabrication of the photomask. However, in alternative embodiments, the method of the present invention can be applied to the patterning of a predetermined material layer formed on a substrate so as to construct an integrated circuit.  
         [0039]    Hereinafter, experimental examples in which the pattern line width variation when the compensation exposure is performed according to the method of the present invention will be described, in comparison to an example in which the compensation exposure is not performed.  
         [0040]    First, as shown in FIG. 9, an exposure pattern  910  of a 70 mm×70 mm size in which a test pattern  940 , in which linear patterns  950  having a predetermined line width are arranged is formed, is provided. In FIG. 9, oblique-lined regions  930  and  950  correspond to an opaque film pattern, and a blank region  920  corresponds to a portion exposed to the electron beam.  
         [0041]    [0041]FIG. 10 is a graph in which a line width of the test pattern  910  (see FIG. 9) is measured, following a general exposure to the electron beam (step  310 ). In the graph of FIG. 10, the horizontal axis denotes distance to an unexposed area  930  from a boundary between a 100% exposed area (the non-oblique-lined area  920  of FIG. 9) and the unexposed area (the oblique-lined area  930 ), and the vertical axis denotes a measured line width of the test pattern. Reference numeral  1010  denotes a line width when exposing at an accelerating voltage of 50 keV and a dose of 32 μ C/cm 2 , and reference numeral  1020  denotes a line width when exposing at an accelerating voltage of 10 keV and a dose of 8 μ C/cm 2 . Also, reference numeral  1030  denotes a line width when exposing at an accelerating voltage of 10 keV and a dose of 8 μ C/cm 2  and converting the 100% exposed area  920  of FIG. 9 into an area having an average exposure pattern density of 70% with a similar level to that of a conventional integrated circuit device.  
         [0042]    Referring to FIG. 10, variation widths of line widths, that is, differences in a maximum line width and a minimum line width are 53 nm( 1010 ), 15 nm( 1020 ), and 10 nm( 1030 ), respectively. Also, the variation of the line widths including the variation of the line widths at the test pattern  940  of the 100% exposed area  920 , are measured as 87 nm( 1010 ), 22 nm( 1020 ), and 15 nm( 1030 ), respectively.  
         [0043]    Following this, the compensation exposure was performed according to the method of compensating for pattern dimension variation caused by the re-scattered electron beam of the present invention. That is, the exposure pattern  910  of, for example, 70 nm×70 nm of FIG. 9 is divided into the sections of, for example, 1 mm×1 mm, and the exposure pattern density and the supplemental exposure dose with respect to each section are determined.  
         [0044]    Here, the re-scattering range ξ is set up as 8 mm, and the maximum supplemental exposure dose value δ max  is set up as 3.5% of the original exposure dose. After obtaining the compensation exposure dose for each section, the line widths of the test pattern formed by the compensation exposure according to the compensation exposure doses are measured.  
         [0045]    Referring to FIG. 11, a graph illustrating the above measured results, the horizontal and vertical axes are the same as those of FIG. 10, and reference numerals  1110 ,  1120 , and  1130  denote measured line widths corresponding to  1010 , 1020 , and  1030  of FIG. 10, respectively. In FIG. 11, in the cases of  1110 ,  1120 , and  1130 , the variation widths of the line widths are remarkably reduced compared to those of FIG. 10. The variation widths of the line width including the variation of the line widths at the test pattern  940  of the 100% exposed area  920 , are measured as 23 nm( 1110 ), 6 nm( 1120 ), and 4 nm( 1130 ), respectively.  
         [0046]    Meanwhile, the method of compensating for a pattern dimension variation caused by the re-scattered electron beam of the present invention may be realized by a software program, and the program may be provided on computer readable media. Therefore, the method of compensating for pattern dimension variation of the present invention can be performed by a general-purpose digital computer. The media can include storage media such as magnetic media (for example, a read-only memory (ROM), a floppy disk, and a hard disk etc.), optical media (for example, CD-ROM and a digital versatile-disc (DVD) etc.), and carrier waves (for example, transfer via Internet).  
         [0047]    In general, the exposure patterns as shown in FIG. 4 are converted into exposure data for writing with an electron beam and supplied to the electron beam writer, the compensation exposure patterns of FIGS.  6  or  7  obtained by the method of the present invention are also supplied to the electron beam writer as the compensation exposure data. In particular, all steps of the method of the present invention, that is, the steps of: dividing original exposure patterns (FIG. 4) into predetermined-size sections and determining a dose of supplemental exposure by the re-scattered electron beam for each section; obtaining a compensation exposure dose for each section; and selecting predetermined compensation exposure patterns according to the compensation exposure dose for each section and establishing compensation exposure data with respect to entire exposure patterns, can be essentially realized by modules of a computer program, and it is also preferable for the steps to be realized by the computer program. Here, codes and code segments of a functional program, in which each program module is actually coded, can be readily implemented by a skilled computer programmer.  
         [0048]    As described above, according to the present invention, the exposure patterns are preferably divided into square sections, and the supplemental exposure dose caused by the re-scattering effect of the electron beam and the compensation exposure dose are determined for each section. The electron beam resist is compensation-exposed according to predetermined compensation exposure patterns according to the compensation exposure dose for each section, thereby minimizing the pattern dimension variation caused by the re-scattering effect of the electron beam.  
         [0049]    The method of compensating for pattern dimension variation caused by the re-scattering effect of the electron beam of the present invention can be realized by a computer program and performed in a general-purpose digital computer, thereby minimizing the pattern dimension variation caused by the re-scattered electron beam in an electron beam exposure system.