Patent Publication Number: US-2006019175-A1

Title: Method of manufacturing membrane mask, method of manufacturing semiconductor device, and membrane mask

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
      This Application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2004-212447, filed on Jul. 21, 2004; the entire contents of which are incorporated herein by reference.  
     BACKGROUND OF THE INVENTION  
      The invention relates to a mask for electron beam exposure, and more particularly, to a method of manufacturing a membrane mask, a method of manufacturing a semiconductor device, and a membrane mask.  
      Lithography technology, which supports the advancement of shrinking in semiconductor devices, is a critical process among other semiconductor manufacturing processes in that it is the only process for producing patterns. Conventionally, optical lithography has been used in producing semiconductor devices. In recent years, however, pattern critical dimensions of advanced devices are approaching the limit resolution. It is thus urgent to develop high-resolution lithography.  
      Electron beam lithography has inherently superior resolution property, and has been partly used for developing and for producing most advanced devices typified by SOC (system on chip). However, in the conventional variable shaped beam exposure method, the wafer processing capacity per unit time, or throughput, is low because the pattern is delineated with one stroke. It is thus unsuitable to mass production of devices.  
      Currently, as the next-generation lithography, Electron Projection Lithography (EPL) technology is proposed, which is recently under research and development.  
       FIG. 15  is a conceptual diagram for illustrating the operation of an EPL exposure apparatus.  
      First, masks  340  are arranged on a mask stage in the EPL exposure apparatus. In each mask  340 , subfield masks  350  are formed and aligned in a grid. In each subfield mask  350 , a subfield pattern is formed for projecting and transferring a subfield  320  served as an exposure unit area for one semiconductor chip. The subfield  320  is an area corresponding to one shot of exposure with electron beam  330  (charged particle beam). In the subfield masks  350 , various subfield patterns transmitting the electron beam  330  are formed, respectively. The electron beam  330  emitted from the charged particle source is deflected by a deflector, with which a pattern of a predetermined subfield mask  350  is irradiated. A subfield  320 , served as an exposure unit area in one semiconductor chip area among a plurality of semiconductor chip areas  310  reduced by an electron lens and partitioned on the wafer  300 , is irradiated with the transmitted electron beam  330  to project and transfer the subfield pattern formed in the subfield mask  350 . Next, the electron beam  330  is deflected by the deflector so that the subfield pattern of a subfield mask  350  located in the next line is irradiated with the electron beam  330 . Similarly, the next subfield  320  for the above-mentioned one semiconductor chip is irradiated to project and transfer a subfield pattern formed in the subfield mask  350  to the next subfield  320 . This is sequentially repeated until exposure of subfield patterns of the subfield masks  350  in that line is completed. Then the mask stage and the wafer stage are moved to a position where the head of the subfield masks  350  in the second line can be projected and transferred to the wafer  300 . Various subfield patterns of the subfield masks  350  in the second line are sequentially irradiated. In this way, subfield patterns of the subfield masks  350  in all lines are irradiated, and thus exposure for one semiconductor chip area  310  is completed. This operation is continued for all semiconductor chip areas  310  partitioned on the wafer  300 . Other information about the EPL exposure apparatus is described in the literature (see, e.g., Japanese Laid-Open Patent Application 2001-319872; “Nikon Technologies: EPL”, http://www.nikon.co.jp/main/jpn/profile/technology/epl/ind ex.htm; and “Stencil reticle development for electron beam projection systems”, S. Kawata, N. Katakura, S. Takahashi, and K. Uchikawa, J. Vac. Sci. Technol. B 17, 2864 (1999)).  
       FIG. 16  illustrates the exposure principle of EPL.  
      In  FIG. 16 , for example, a stencil mask  100 , as an example of a scattering mask in which an opening pattern is formed by perforating openings  150 , is irradiated with electrons accelerated at 100 kV. For material of the stencil mask  100 , silicon (Si) is typically used with a thickness of about 2 μm. Electron beam  330  incident on a portion other than the openings  150  of the stencil mask  100  is greatly scattered at the portion other than the openings  150 . Most of the scattered electrons (mask-scattered electrons)  331  are blocked by a limiting aperture  370  placed at the back focal plane of the objective lens  380 . On the other hand, image-forming electrons  332  transmitted through the opening  150  are projected by a projection lens  360  because they freely pass through the opening  150 . Thus most of the image-forming electrons  332  can pass through the limiting aperture  370 . This difference in aperture transmittance creates contrast of the mask image on the wafer  300 . This is referred to as scattering contrast. When the wafer  300  is subsequently developed, the resist image  301  shown in  FIG. 15  will be formed. With respect to a mask, in addition to the stencil mask, a membrane mask is also available, in which the entire surface of a mask pattern is held with a thin membrane. Masks for use in the EPL exposure apparatus are disclosed in the literature (see, e.g., Japanese Laid-Open Patent Applications 2002-75842 and 2003-68616).  
       FIG. 17  shows an example of a stencil mask and a membrane mask manufactured from typical material.  
      In  FIGS. 17A and 17B , the pattern portion is particularly shown and the other portions are omitted.  FIG. 17A  shows an example stencil mask  100  made of Si with a thickness of 2 μm, for example.  FIG. 17B  shows a membrane mask  200  made of diamondlike carbon (DLC) membrane with a thickness of 30 to 50 nm, on which a patterned DLC scattering layer is formed with a thickness of about 600 nm. Here, as described above, since imaging in EPL technology is based on scattering contrast, electron scattering is taken into consideration when the structure of the scattering mask is determined.  
       FIG. 18  illustrates how electron transmits the aperture.  
      As shown in  FIG. 18A , for the stencil mask  100 , electrons incident on the opening  150  are passed without being scattered. Thus all of these electrons can contribute to exposure. On the other hand, as shown in  FIG. 18B , for the membrane mask  200 , even the electrons incident on the opening pattern portion might be scattered by the membrane  210 . The scattered electrons cannot reach the wafer  300 . Only part of the electrons that are not scattered contribute to exposure (see, e.g., “High-performance membrane mask for electron projection lithography”, H. Yamashita, I. Amemiya, E. Nomura, K. Nakajima, and H. Nozue, J. Vac. Sci. Technol. B 18, 3237 (2000)).  
      For example, in  FIG. 18B , since 30 to 70% of the electrons are scattered, only the remaining 70 to 30% contribute to exposure. The small percentage of unscattered electrons that can contribute to exposure is a shortcoming when the membrane mask  200  is used as a mask in the EPL exposure apparatus, although the membrane corresponding to an exposed portion is thin. This decreases beam current density, and hence throughput.  
       FIG. 19  shows examples of complementary division of patterns.  
       FIG. 19A  shows an example of an opening pattern closed like a donut. Here, when a stencil mask  100  is used as a mask in the EPL exposure apparatus, the portion that electrons pass is completely perforated. As a result, when the opening pattern is shaped like a donut, the mask member inside it will be dropped off. To avoid this, the pattern must be divided into two or more complementary masks. For example, for a donut-shaped pattern, as shown in  FIG. 19A , the mask is divided into a first complementary pattern  111  and a second complementary pattern  112  to prepare first and second complementary masks. Each of the complementary masks is placed in the EPL exposure apparatus. The first and second complementary masks are each exposed once, that is, exposure is performed in two iterations, to complete a pattern on the wafer. Moreover, a pattern having insufficient mechanical strength in which a large mask member is supported by a small supporting portion must also be divided. For example,  FIG. 19B  shows an example of a leaf-shaped opening pattern.  FIG. 19C  shows an L-shaped opening pattern. When a stencil mask  100  is used as a mask in the EPL exposure apparatus, mask division doubles the number of exposure iterations, which decreases throughput.  
      On the other hand, when a membrane mask  200  is used as a mask in the EPL exposure apparatus, the portion that electrons pass is closed by the membrane and not perforated. As a result, even when the opening pattern is shaped like a donut, the mask member inside it will not be dropped off. Consequently, it is not necessary to divide the mask, and thus the number of exposure iterations is not doubled. A pattern is completed on the wafer in one time of exposure. However, if the transmittance of unscattered electrons is low, the exposure time of electron beam is extended all the longer. This decreases beam current density, and hence throughput, as described above.  
      To avoid the decrease of throughput when a membrane mask  200  is used as a mask in the EPL exposure apparatus, it is effective to improve the transmittance of unscattered electrons. Thus, recently, thinning of membranes is advanced for improving the transmittance of unscattered electrons. As described above, a membrane mask using DLC material is developed.  
       FIG. 20  shows the cross-sectional structure of a membrane mask.  
      DLC has a high Young&#39;s modulus, and provides high film strength even when it is subjected to thinning. Moreover, thin film of good quality can be obtained because of its film growth. Currently, a DLC membrane mask  200  with a thickness of 15 to 50 nm is fabricated. For example, a DLC membrane  210  with a thickness of 44 nm yields a transmittance of unscattered electrons of 41%. In this membrane mask  200 , its scattering layer  230  is also made of DLC. However, since it requires to scatter electrons, it has a thickness of about 600 nm, which is thicker than the membrane  210  (see, e.g., “Fabrication of a continuous diamondlike carbon membrane mask for electron lithography”, I. Amemiya, H. Yamashita, S. Nakatsuka, M. Tsukahara, and O. Nagarekawa, J. Vac. Sci. Technol. B 21, 3032 (2003)). In addition, in a mask made of DLC, there may be an etching stopper between the scattering layer and the membrane (see, e.g., Japanese Laid-Open Patent Application 2001-77013).  
      As the thinning of membranes is advanced, membranes with a transmittance of unscattered electrons of 50% or more (70% in  FIG. 17B ) are manufactured.  
      In another technology disclosed in the literature (see, e.g., Japanese Laid-Open Patent Application 2000-319543), instead of further thinning the membrane, a beam current measuring area provided on the membrane mask is irradiated with electron beam, with the membrane mask being installed in the exposure apparatus. The current that reaches the wafer surface is measured. The exposure condition is determined from the measured current value and a set amount of exposure, thereby avoiding the decrease of throughput due to a membrane mask regardless of the membrane thickness of the membrane mask.  
      As described above, in contrast to the stencil mask, the membrane mask requires no complementary division, and the number of exposure iterations is half of that for the stencil mask. However, if the transmittance is half or less, the membrane mask may have exposure throughput lower than the stencil mask.  
      For this reason, further thinning of membranes is continued. However, the mechanical strength of the mask decreases due to the thinning of membrane, which increases the possibility of decrease in yield and breakage in use. Thus undue thinning is not reasonable. Hence an optimum value should exist for the membrane thickness. However, no investigation has been made on the optimum value so far.  
     SUMMARY OF THE INVENTION  
      According to an aspect of the invention, there is provided a method of manufacturing a membrane mask for use in an electron beam exposure apparatus that exposes resist material, comprising: manufacturing the membrane mask with a membrane thickness determined so that an operation time that the electron beam exposure apparatus spends in exposing the resist material to form a predetermined pattern using the membrane mask is comparable to or less than an operation time that the electron beam exposure apparatus spends in exposing the resist material to form the predetermined pattern using complementary masks.  
      According to other aspect of the invention, there is provided a method of manufacturing a semiconductor device comprising the step of exposing resist material using a membrane mask by an electron beam exposure apparatus, wherein the membrane mask with a membrane thickness is used, the membrane thickness being determined so that an operation time that the electron beam exposure apparatus spends in exposing the resist material to form a predetermined pattern using the membrane mask is comparable to or less than an operation time that the electron beam exposure apparatus spends in exposing the resist material to form the predetermined pattern using complementary masks.  
      According to other aspect of the invention, there is provided a membrane mask used for exposing resist material by an electron beam exposure apparatus, the membrane mask having a membrane thickness determined so that an operation time that the electron beam exposure apparatus spends in exposing the resist material to form a predetermined pattern using the membrane mask is comparable to or less than an operation time that the electron beam exposure apparatus spends in exposing the resist material to form the predetermined pattern using complementary masks. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The present invention will be understood more fully from the detailed description given herebelow and from the accompanying drawings of the embodiments of the invention. However, the drawings are not intended to imply limitation of the invention to a specific embodiment, but are for explanation and understanding only.  
      In the drawings:  
       FIGS. 1A and 1B  illustrate the operation time for complementary stencil masks and a membrane mask in the first embodiment;  
       FIG. 2  shows an example of complementary division of a stencil mask;  
       FIG. 3  shows an example of a membrane mask;  
       FIG. 4  shows an example of the relationship between the unscattered electron transmittance and the membrane thickness;  
       FIGS. 5A through 5F  show a technique for determining the optimum membrane thickness from a shot cycle;  
       FIG. 6  shows an example of an apparatus for measuring the unscattered electron transmittance;  
       FIGS. 7A and 7B  show the relationship between the detector signal intensity and the energy loss;  
       FIGS. 8A through 8C  illustrate exposure accuracy for exposure with complementary stencil masks and for exposure with a membrane mask;  
       FIG. 9  illustrates the relationship between the mean free path and the beam acceleration voltage;  
       FIG. 10  illustrates the relationship between the mean free path and the film density of membrane;  
       FIG. 11  shows the example of complementary division of device patterns;  
       FIG. 12  shows the example of complementary division of device patterns;  
       FIG. 13  shows the example of complementary division of device patterns;  
       FIG. 14  shows the example of complementary division of device patterns;  
       FIG. 15  is a conceptual diagram for illustrating the operation of an EPL exposure apparatus;  
       FIG. 16  illustrates the exposure principle of EPL;  
       FIGS. 17A and 17B  show examples of a stencil mask and a membrane mask manufactured from typical material;  
       FIGS. 18A and 18B  illustrate how electron transmits the aperture;  
       FIGS. 19A through 19C  show examples of complementary division of patterns; and  
       FIG. 20  shows the cross-sectional structure of a membrane mask. 
    
    
     DETAILED DESCRIPTION  
      Embodiments of the invention will now be described with reference to the drawings.  
     FIRST EMBODIMENT  
      When a membrane mask is used, the higher the transmittance of unscattered electrons, the higher the throughput. Thus thinning of membranes is advanced. However, at the same time, the mechanical strength decreases, which increases the possibility of decrease in yield and breakage in use. The overall exposure performance of EPL is improved by using a membrane mask with a membrane thickness optimized from parameters of the exposure apparatus in use and electron scattering parameters in the membrane. In the first embodiment, the membrane thickness is optimized by comparison with the throughput of the exposure apparatus obtained when a stencil mask is used.  
       FIG. 1  illustrates the operation time for complementary stencil masks and a membrane mask in the first embodiment.  
      Factors determining the throughput in an electron beam exposure apparatus include resist exposure time and beam settling time. The membrane thickness may be determined so that the sum of these times, that is, shot cycle time served as operation time for which one subfield corresponding to an exposure unit is exposed to a predetermined pattern, is comparable to or less than that for the stencil mask.  
      The term “beam settling time” is defined as a time to be needed to stabilize the electron beam position after deflecting the beam (for example, to the adjacent subfield). The settling time may be defined as a time to be consumed until a current in a beam deflection coil becomes steady state after the beam deflection.  
       FIG. 1A  shows, on the left, a shot cycle for complementary stencil masks, and on the right, a shot cycle for a membrane mask with a transmittance Tm of unscattered electrons of 50%.  
      When complementary stencil masks are used, a first settling time ts for waiting until the electron beam stabilizes after deflecting the electron beam to an desired subfield of the first complementary mask is required. Then, a first exposure time tes for exposing resist to the first complementary pattern formed in the first complementary mask is required. Next, a second settling time ts for exposing the second complementary mask to electron beam is required. Then, a second exposure time tes for exposing resist to the remaining second complementary pattern formed in the second complementary mask is required. Therefore, the shot cycle tcs is the sum of the first settling time ts, the first exposure time tes, the second settling time ts, and the second exposure time tes.  
      On the other hand, when the membrane mask with a transmittance Tm of unscattered electrons of 50% is used, an exposure time tem for exposing resist to a desired, predetermined pattern formed in the membrane mask is required. Here, since the transmittance Tm of unscattered electrons is 50%, the exposure time tem is twice the exposure time tes of the stencil mask that has a transmittance Tm of 100%. In other words, the exposure time tem is the sum of the first the exposure time tes and the second the exposure time tes. Then, a settling time ts for exposing the membrane mask to electron beam is required. One settling time ts remains unchanged for membrane and stencil masks. Therefore, the membrane mask with a transmittance Tm of unscattered electrons of 50% has a shot cycle shorter than the complementary stencil masks by one settling time ts. In other words, in order for the shot cycle to be comparable to or less than that for the stencil mask, the transmittance Tm is not required to be 50% as shown in  FIG. 1A . The transmittance may be even lower.  
       FIG. 1B  shows, on the left, a shot cycle for complementary stencil masks, and on the right, a shot cycle for a membrane mask with a transmittance Tm of unscattered electrons that makes the shot cycle comparable to that for the complementary stencil masks. The shot cycle for the complementary stencil masks is similar to that shown in  FIG. 1A . The shot cycle for the membrane mask is decreased so that the transmittance Tm is lower than 50%, and made comparable to that for the complementary stencil masks. That is, the transmittance Tm can be decreased below 50% so that a longer exposure time tem is required corresponding to one settling time ts. Thus the membrane thickness can be made greater corresponding to the decreased transmittance Tm. Since the membrane thickness can be made greater, the mechanical strength can be made all the greater.  
       FIG. 2  shows an example of complementary division of a stencil mask. Such a mask is normally made from a silicon wafer of an 8-inch diameter.  
      As shown in  FIG. 2 , the stencil mask  100  comprises a first complementary mask  101  and a second complementary mask  102 . First, the first complementary mask  101  is used to expose resist to a first complementary pattern formed in the first complementary mask  101 . Next, a remaining second complementary pattern formed in the second complementary mask  102  is exposed to the resist. Although not shown, a plurality of subfield patterns  350  are formed in the first complementary mask  101  and the second complementary mask  102 . The shot cycle in  FIG. 1  indicates a cycle for completing a predetermined pattern  320  in one subfield.  
       FIG. 3  shows an example of a membrane mask.  
      As shown in  FIG. 3 , two pattern portions  201  are formed in the membrane mask  200 . In contrast to the stencil mask, the membrane mask  200  does not need complementary division. It is thus sufficient to use either of the two pattern portions  201 .  
      In this case, the another of the pattern portions  201  may be used for another chip pattern. Alternatively, same patterns may be formed on both of the two pattern portions  201 . In this case, a die-to-die inspection can be easily performed at the mask defect inspection process.  
      Although not shown, a plurality of subfield patterns  350  are formed in the pattern portion  201 . The shot cycle in  FIG. 1  indicates a cycle for completing a predetermined pattern  320  in one subfield.  
       FIG. 4  shows an example of the relationship between the unscattered electron transmittance and the membrane thickness.  
      As an example,  FIG. 4  shows the case where DLC is used for membrane material. As shown in  FIG. 4 , the unscattered electron transmittance Tm depends on the membrane thickness. It can be seen that the membrane thickness must be reduced in order to decrease the unscattered electron transmittance Tm and increase the throughput.  
       FIG. 5  shows a technique for determining the optimum membrane thickness from a shot cycle.  
      The mean free path Λ of electrons in the membrane of the membrane mask, the sensitivity S of the resist material, the current density J of electron beam applied by the electron beam exposure apparatus, and the settling time ts of electron beam applied by the electron beam exposure apparatus are used to determine the membrane thickness d so that the shot cycle time tcm that the electron beam exposure apparatus spends in exposing the resist material to form a predetermined pattern using the membrane mask has an operation time comparable to or less than the shot cycle time tcs that the electron beam exposure apparatus spends in exposing the resist material to form the predetermined pattern using the complementary masks.  
      The current density J is defined as a current density of the electron beam on a wafer in the case where stencil mask is used (e.g. membrane is not used).  
      In  FIG. 5A , the resist exposure time te is expressed as: 
 
 te=S/J    (1) 
 
 where S is the resist sensitivity and J is the beam current density. 
 
      In  FIG. 5B , given the beam settling time ts, the shot cycle tc is the sum of the beam settling time ts and the resist exposure time te, and thus expressed as: 
 
 tc=ts+te=ts+S/J    (2) 
 
      In  FIG. 5C , first, for the stencil mask, which requires complementary exposure, the net shot cycle tcs is twice the shot cycle tc, because the original pattern is formed by two iterations of exposure: 
 
 tcs= 2( ts+te )=2( ts+S/J )   (3) 
 
      On the other hand, for the membrane mask, the beam current density decreases by the amount associated with the transmittance Tm of unscattered electrons. Thus the shot cycle tcm for the membrane mask is given by: 
 
 tcm=ts+te/Tm=ts+S/ ( J·Tm )   (4) 
 
 Here, for the shot cycle of the membrane mask to be comparable to or less than that for the stencil mask, it is sufficient that tcs≧tcm is satisfied. 
 
      In  FIG. 5D , since it is sufficient that tcs≧tcm, that is, 
 
2( ts+S/J )≧ ts+S /( J·Tm ) 
 
 is satisfied as described above, the transmittance of unscattered electrons for which the shot cycle for the stencil mask is comparable to or less than that for the membrane mask is given by: 
 
 Tm≧te /( ts+ 2 te )   (5) 
 
 Since the resist exposure time is S/J, Equation 5 is written as: 
 
 Tm≧S /( J·ts+ 2 S )   (6) 
 
      In  FIG. 5E , first, the unscattered electron transmittance Tm can be analytically determined from the mean free path Λ of electron scattering in the membrane, expressed as: 
 
 Tm =exp(− d /Λ)   (7) 
 
 where d is the membrane thickness. The mean free path Λ can be determined experimentally by measuring the transmittance of unscattered electrons. Therefore, the following relation is obtained from Equations 6 and 7: 
 
exp(− d /Λ)≧ S /( J·ts+ 2 S )   (8) 
 
      In  FIG. 5F , from Equation 8, the optimum membrane thickness is given by: 
 
 d ≦−Λlog{ S /( J·ts+ 2 S )}  (9) 
 
      Thus the upper limit of the optimum membrane thickness is given by: 
 
 d ≈−Λlog{ S /( J·ts+ 2 S )}  (10) 
 
      Considering that membranes with smaller thickness require careful formation and handling, it is desirable to adopt the thickness given by Equation 10.  
       FIG. 6  shows an example of an apparatus for measuring the unscattered electron transmittance.  
      The unscattered electron transmittance is measured by EADAM (Energy and Angular Distribution Analysis for Membranes) technique. In  FIG. 6 , first, without the membrane mask  200 , an aperture  410  is vertically exposed to electron beam  401  of 100 keV collimated to 1 nm. Here, for example, transmitted electron detection angle (aperture diameter) is set to semi angle 5.5 mrad. Then, the electron beam transmitted through the aperture  410  is analyzed by an energy analyzer  420  and separated according to the energy loss, and the signal intensity is measured by a detector  430 . Subsequently, with the membrane mask  200  being installed, the same operation is performed.  
       FIG. 7  shows the relationship between the detector signal intensity and the energy loss.  
       FIG. 7A  shows an example result measured without the membrane mask  200 . The center (100 keV) peak (maximum) value of the detector signal intensity is assumed as unity.  FIG. 7B  shows an example result measured with the membrane mask  200  being installed. The peak value of the detector signal intensity for unscattered electrons without energy loss due to inelastic scattering is represented by a value relative to the peak value without the membrane mask  200 .  FIG. 7B  shows the peak value of the detector signal intensity of about 41%. That is, the membrane thickness d of the membrane mask  200  used here provides an unscattered electron transmittance Tm of 41%. Substituting these values of the membrane thickness d and the unscattered electron transmittance Tm into Equation 7 described above, the mean free path Λ for the membrane material can be determined experimentally.  
       FIG. 8  illustrates exposure accuracy for exposure with complementary stencil masks and for exposure with a membrane mask.  
      As shown on the left of  FIG. 8A , when the complementary stencil masks are used for exposure, a pattern exposed with the first complementary mask may be misaligned with a pattern exposed with the second complementary mask to result in breaking of circuit. That is, dividing the exposure into two iterations is prone to misalignment which may depend on the accuracy and stability of the exposure system. On the contrary, in the figure on the right, when the membrane mask is used for exposure, such misalignment can be dispensed with because only one iteration of exposure is required. As shown on the left of  FIG. 8B , when the complementary stencil masks are used for exposure, a pattern exposed with the first complementary mask may partially overlap with a pattern exposed with the second complementary mask to swell the line width, thereby being connected with the adjacent wiring to cause short circuit. On the contrary, in the figure on the right, when the membrane mask is used for exposure, such overlapping pattern can be dispensed with because only one iteration of exposure is required. As shown on the left of  FIG. 8C , when the complementary stencil masks are used for exposure, there is a gap between a pattern exposed with the first complementary mask and a pattern exposed with the second complementary mask. Thereby, a pattern exposed with the first complementary mask disconnects with a pattern exposed with the second complementary mask. On the contrary, in the figure on the right, when the membrane mask is used for exposure, such disconnection pattern can be dispensed with because only one iteration of exposure is required. Consequently, for comparable throughput, the membrane mask provides higher yield in exposure than the complementary stencil masks for the overall exposure process.  
      For example, assume that the resist sensitivity is 5 μC/cm 2 , the beam current density is 160 mA/cm 2 , the beam settling time is 25 μs, and the mean free path is 50 nm. From Equation 9, the optimum membrane thickness is 55 nm. This film thickness provides throughput comparable to the stencil mask. Below this film thickness, the membrane mask has higher throughput.  
      As described above, from the viewpoint of throughput, the transmittance Tm of the membrane mask that maximizes its mechanical strength is determined from the parameters of the exposure apparatus (beam current density J and beam settling time ts) and the process parameter (resist sensitivity S) and the electron scattering parameter (mean free path Λ) depending on the membrane material. The technique for optimizing the membrane thickness d to give this membrane transmittance Tm has been described. When a membrane mask is manufactured with the above-described membrane thickness d, for which the throughput is not lower relative to stencil masks with complementary division, the membrane mask can replace the stencil masks without unduly reducing the membrane thickness. Since the membrane thickness is not unduly reduced, the membrane mask can be manufactured without decreasing its mechanical strength more than necessary.  
     SECOND EMBODIMENT  
       FIG. 9  illustrates the relationship between the mean free path and the beam acceleration voltage.  
      As shown in  FIG. 9 , as the beam acceleration voltage V increases, the mean free path Λ also increases. That is, the mean free path Λ is proportional to the beam acceleration voltage V. Therefore, when a mean free path at a certain acceleration voltage is known, an optimum membrane thickness at an arbitrary acceleration voltage can be determined by using Equation 9.  
     THIRD EMBODIMENT  
       FIG. 10  illustrates the relationship between the mean free path and the film density of membrane.  
      As shown in  FIG. 10 , as the film density of membrane ρ increases, the mean free path Λ decreases. That is, the mean free path Λ is inversely proportional to the film density of membrane ρ. Therefore, when a mean free path at a certain film density of membrane ρ is known, an optimum membrane thickness at an arbitrary film density of membrane ρ can be determined by using Equation 9.  
     FOURTH EMBODIMENT  
       FIGS. 11 through 14  show the examples of complementary division of device patterns.  
       FIG. 11  shows patterns formed in an active area of a memory cell part of SRAM (static random access memory). As shown in the figure, many doughnut-shape patterns are formed. Each of these patterns are divided and assigned to either of two masks. In the figure, the hatched parts  111  and the dotted parts  112  are divided and assigned to separate mask, respectively.  
       FIG. 12  shows patterns formed in a gate layer of a logic device. In the figure, the hatched patterns  111  and the dotted patterns  112  are assigned to separate mask, respectively.  
       FIG. 13  shows patterns formed in a peripheral circuit of DRAM (dynamic random access memory). In this case, the doughnut-shape patterns are included. The hatched parts  111  and the dotted parts  112  are assigned to separate mask, respectively.  
       FIG. 14  shows patterns formed in a memory cell part of DRAM. In this case, elongated line-and-space patterns are formed. In such a case, the hatched parts  111  and the dotted parts  112  are assigned to separate mask, respectively, in order to prevent the sticking of the patterns.  
      As described above, according to each of the embodiments, the membrane mask having the optimized membrane thickness is balanced from the viewpoint of throughput and mechanical strength. In addition, the optimum membrane thickness can be determined using the values of beam acceleration voltage, beam current density, and beam settling time of the exposure apparatus, resist sensitivity, and mean free path and density of the membrane. In this way, the parameters of the exposure apparatus and the like can be used to determine the transmittance of the membrane mask that maximizes its mechanical strength from the viewpoint of throughput. The membrane thickness that gives this membrane transmittance is the optimum thickness.  
      As described above, according to each of the embodiments, assuming the comparison with the complementary stencil masks, the transmittance of the membrane can be decreased (i.e., the membrane thickness can be increased) by an amount corresponding to one iteration of the above-described settling time. That is, the transmittance does not need to be 50% or more. Conventionally, no discussions have been made about how the membrane thickness is determined from the viewpoint of throughput comparable to that of the stencil mask. Unnecessary thinning of membrane may increase performance, but decreases mechanical strength by that amount. This decreases mask yield and increases cost, thus compromising the advantage over the stencil mask. In addition, as seen from Equation 2, there is a good balance when the beam settling time is equal to the resist exposure time. Even if the membrane is thinned and the resist exposure time is further reduced, the effect of throughput improvement gradually decreases.  
      In the above description, DLC is mentioned as membrane material. However, it is understood that other materials may be applicable. For example, the membrane may be made of various materials such as amorphous carbon, diamond, amorphous silicon, SiN x , SiC x , Si, and SiO 2 , in addition to DLC.  
      While the present invention has been disclosed in terms of the embodiment in order to facilitate better understanding thereof, it should be appreciated that the invention can be embodied in various ways without departing from the principle of the invention. Therefore, the invention should be understood to include all possible embodiments and modification to the shown embodiments which can be embodied without departing from the principle of the invention as set forth in the appended claims.