Patent Publication Number: US-2022238303-A1

Title: Proximity effect correcting method, master plate manufacturing method, and drawing apparatus

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2021-10415, filed on Jan. 26, 2021, the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments of the present invention relate to a proximity effect correcting method, a master plate manufacturing method, and a drawing apparatus. 
     BACKGROUND 
     A master plate for a semiconductor process is sometimes created using an electron beam lithography apparatus. In this case, it may be difficult to appropriately correct the proximity effect due to backscattering of an electron beam in a substrate for the master plate depending on surface profiles of the substrate. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a diagram illustrating an example of a drawing apparatus according to an embodiment; 
         FIG. 1B  is a diagram illustrating another example of the drawing apparatus according to the embodiment; 
         FIG. 2A  is a sectional view illustrating an example of a mask blank to which the drawing apparatus according to the embodiment is applicable; 
         FIG. 2B  is a sectional view illustrating an example of a template blank to which the drawing apparatus according to the embodiment is applicable; 
         FIG. 2C  is a sectional view illustrating another example of the mask blank to which the drawing apparatus according to the embodiment is applicable; 
         FIG. 3  is a flowchart illustrating an example of a proximity effect correcting method according to the embodiment; 
         FIG. 4  is an explanatory diagram for explaining an example of an acquiring process of drawing data illustrated in the flowchart of  FIG. 3 ; 
         FIG. 5  is an explanatory diagram for explaining an example of an acquiring process of surface profile data illustrated in the flowchart of  FIG. 3 ; 
         FIG. 6  is an explanatory diagram for explaining an example of a process of dividing the drawing data into meshes illustrated in the flowchart of  FIG. 3 ; 
         FIG. 7  is an explanatory diagram for explaining an example of inclination angle information and inclination direction information illustrated in the flowchart of  FIG. 3 ; 
         FIG. 8  is an explanatory diagram for explaining an example of a calculating process of an energy distribution of a backscattered beam in a slope portion illustrated in the flowchart of  FIG. 3 ; 
         FIG. 9  is an explanatory diagram for explaining the example of the calculating process of the energy distribution of the backscattered beam in the slope portion in more detail than in  FIG. 8 ; 
         FIG. 10  is an explanatory diagram for explaining an example of the calculating process of the energy distribution of the backscattered beam in the slope portion, in continuation from  FIG. 9 ; 
         FIG. 11  is an explanatory diagram for explaining an example of a calculating process of an integrated energy distribution in the slope portion illustrated in the flowchart of  FIG. 3 , 
         FIG. 12  is an explanatory diagram for explaining an example of a calculating process of a required energy amount illustrated in the flowchart of  FIG. 3 ; 
         FIG. 13  is an explanatory diagram for explaining an example of a calculating process of an inclination angle and an inclination direction of the slope portion illustrated in the flowchart of  FIG. 3 ; 
         FIG. 14  is an explanatory diagram for explaining an example of a calculating process of the energy distribution of the backscattered beam in a boundary portion between flat portions illustrated in the flowchart of  FIG. 3 ; 
         FIG. 15  is an explanatory diagram for explaining an example of a calculating process of the integrated energy distribution in the flat portion illustrated in the flowchart of  FIG. 3 , 
         FIG. 16A  is a sectional view illustrating a manufacturing method of a photomask according to the embodiment; 
         FIG. 16B  is a sectional view illustrating the manufacturing method of a photomask according to the embodiment, in continuation from  FIG. 16A ; 
         FIG. 16C  is a sectional view illustrating the manufacturing method of a photomask according to the embodiment, in continuation from  FIG. 16B ; 
         FIG. 16D  is a sectional view illustrating the manufacturing method of a photomask according to the embodiment, in continuation from  FIG. 16C ; 
         FIG. 16E  is a sectional view illustrating the manufacturing method of a photomask according to the embodiment, in continuation from  FIG. 16D ; 
         FIG. 17A  is a sectional view illustrating a manufacturing method of a template according to the embodiment; 
         FIG. 17B  is a sectional view illustrating the manufacturing method of a template according to the embodiment, in continuation from  FIG. 17A ; 
         FIG. 17C  is a sectional view illustrating the manufacturing method of a template according to the embodiment, in continuation from  FIG. 17B ; 
         FIG. 17D  is a sectional view illustrating the manufacturing method of a template according to the embodiment, in continuation from  FIG. 17C ; and 
         FIG. 17E  is a sectional view illustrating the manufacturing method of a template according to the embodiment, in continuation from  FIG. 17D . 
     
    
    
     DETAILED DESCRIPTION 
     According to one embodiment, a proximity effect correcting method includes acquiring drawing information for drawing a pattern on a substrate with irradiation of an electron beam. The method further includes acquiring surface profile information related to a surface profile of the substrate. The method further includes calculating an energy distribution of a backscattered beam to be produced by backscattering of the electron beam in the substrate on a basis of the acquired drawing information and surface profile information. The method further includes calculating a required energy amount of the electron beam on a basis of the calculated energy distribution. 
     Embodiments of the present invention will be explained below with reference to the drawings. In  FIG. 1A to 17E , same or identical constituent elements are denoted by like reference characters and redundant explanations thereof are omitted. 
     (Drawing Apparatus) 
       FIG. 1A  is a diagram illustrating an example of a drawing apparatus  1  according to an embodiment.  FIG. 1B  is a diagram illustrating another example of the drawing apparatus  1  according to the embodiment. The drawing apparatuses  1  illustrated in  FIGS. 1A and 1B  can be used, for example, to draw a pattern on a substrate  6  described later (that is, a resist film  9  on the substrate  6 ) with irradiation of an electron beam EB at the time of manufacturing a master plate to be used in a semiconductor process. Specific modes of the substrate  6  are not particularly limited as long as the substrate  6  is applicable to manufacturing of a master plate with irradiation of the electron beam EB. For example, the substrate  6  may be a mask blank  6 A or  6 C or a template blank  6 B as will be described later with reference to  FIGS. 2A to 2C . More specifically, the drawing apparatuses  1  illustrated in  FIGS. 1A and 1B  can be used to appropriately correct the proximity effect produced by backscattering in consideration of the fact that the accumulated energy distribution in the resist film  9  due to a backscattered beam (hereinafter, “energy distribution of backscattered beam”) differs depending on differences in the surface profile of the substrate  6 . 
     The drawing apparatus  1  illustrated in  FIG. 1A  includes a computer  2 , a control device  3 , an electron irradiation unit  4 , and a stage  5 . The computer  2  performs various types of computing processing (for example, calculation of an energy distribution of the backscattered beam and calculation of a required energy amount described later) in proximity effect correction. In  FIG. 1A , the computer  2  may further perform computing processing for drawing other than the proximity effect correction. 
     In the drawing apparatus  1  illustrated in  FIG. 1B , the computer  2  is placed outside the drawing apparatus  1 . In  FIG. 1B , the computer  2  outside the drawing apparatus  1  performs various types of computing processing in the proximity effect correction and the drawing apparatus  1  may separately include a computer (not illustrated) that performs computing processing for drawing other than the proximity effect correction. 
     The following explanations of the drawing apparatus  1  are explanations common to the drawing apparatuses  1  illustrated in  FIGS. 1A and 1B  unless otherwise specified. The electron irradiation unit  4  is placed in an electron optical lens barrel (not illustrated). The substrate  6  is mounted on the stage  5  in a vacuum chamber communicated with the electron optical lens barrel. The stage  5  can be moved by a driving device such as a motor, for example, in a horizontal direction (an X direction and a Y direction) and a vertical direction (a Z direction). The irradiation location of the election beam EB with respect to the substrate  6  on the stage  5  can be changed with movement of the stage  5 . 
     Before the constituent parts of the drawing apparatus  1  are described in more detail, examples of the substrate  6  to which the drawing apparatus  1  is applicable are explained below.  FIG. 2A  is a sectional view illustrating an example of the mask blank  6 A to which the drawing apparatus  1  according to the embodiment is applicable.  FIG. 2B  is a sectional view illustrating an example of the template blank  6 B to which the drawing apparatus  1  according to the embodiment is applicable.  FIG. 2C  is a sectional view illustrating another example of the mask blank  6 C to which the drawing apparatus  1  according to the embodiment is applicable. The mask blanks  6 A and  6 C are examples of the substrate  6  used in manufacturing of a photomask being a master plate for photolithography. The template blank  6 B is an example of the substrate  6  used in manufacturing of a template being a master plate for nanoimprint lithography. 
     As illustrated in  FIGS. 2A and 2C , each of the mask blanks  6 A and  6 C as the substrate  6  includes a translucent substrate  61 , and a light shielding film  62  formed on the translucent substrate  61 . The translucent substrate  61  may include, for example, quartz as a principal component. The light shielding film  62  may include, for example, a metal such as chrome (Cr) as a principal component. Meanwhile, the template blank  6 B as the substrate  6  includes, for example, quartz as a principal component, thereby having a translucency as a whole as illustrated in  FIG. 2B . 
     When there is a level difference or a slope on the surface of a processing target film formed on a device substrate (a wafer) for a semiconductor device, it is difficult to process the processing target film with a high accuracy in a case in which a photomask or a template having a uniformly flat surface is used. Specifically, in the case of photolithography using a photomask, it is difficult to focus exposure light onto a resist film on the processing target film, so that appropriately exposing the resist film on the processing target film to light becomes difficult. In the case of nanoimprint lithography using a template, it is difficult to transfer a pattern to a resist on a device substrate being a processing target film while appropriately pressing the template against the resist. As a result, formation of a circuit pattern on the processing target film with a desired accuracy becomes difficult. Therefore, with an objective of processing a processing target film including a level difference or a slope with a high accuracy, each of the surfaces of the substrates  6 A to  6 C for a photomask or a template has a surface profile matching the surface profile of the processing target film. Specifically, the surface of the mask blank  6 A illustrated in  FIG. 2A  has a flat portion  6   a  parallel to an in-plane direction d 1 , a flat portion  6   c  formed to be higher than the flat portion  6   a  by a level difference zd, and a slope portion  6   b  connecting the flat portions  6   a  and  6   c . When the mask blank  6 A is mounted on the stage  5 , the in-plane direction d 1  corresponds to the horizontal direction. While the slope portion  6   b  illustrated in  FIG. 2A  is a linearly inclined plane, a slope portion  6   b ′ may be an inclined curved plane as indicated by sign  6   b ′ in  FIG. 2A . Each of the surfaces of the template blank  6 B illustrated in  FIG. 2B  and the mask blank  6 C illustrated in  FIG. 2C  has flat portions  6   a  and  6   c  adjacent to each other and formed to have different heights by the level difference zd. The template blank  6 B may have a slope portion. 
     At the time of drawing a pattern on the substrate  6  to form a master plate (a photomask or a template), the resist film  9  is formed on the substrate  6 . In  FIG. 16A , the resist film  9  is formed on the mask blank  6 A as an example of the substrate  6 . In  FIG. 17A , the resist film  9  is formed on the template blank  6 B as an example of the substrate  6 . The substrate  6  having the resist film  9  formed thereon is irradiated with the electron beam EB to draw a pattern on the resist film  9 . The electron beam EB irradiated to the substrate  6  backscatters in the substrate  6 . The resist film  9  on the substrate  6  is exposed again to the backscattered beam generated by the backscattering. The proximity effect in which the dimension of the pattern changes from the design value is produced due to re-exposure of the resist film  9 . Specifically, at a place where the pattern density is high, the amount of re-exposure of the resist film  9  due to backscattering from the peripheral part is large and therefore the dimension of the pattern becomes larger than the design value. On the other hand, at a place where the pattern density is low, the amount of re-exposure is small and the dimension of the pattern becomes smaller than the design value. The proximity effect needs to be corrected to ensure the dimension accuracy of the pattern. In correcting the proximity effect, the amount of irradiation of the electron beam EB is controlled on the basis of an energy distribution of the backscattered beam. A Gaussian distribution is often used as the energy distribution of the backscattered beam. However, when a pattern is drawn on the substrate  6  including a level difference or a slope on the surface as the substrates  6 A to  6 C illustrated in  FIGS. 2A to 2C , the energy distribution of the backscattered beam is not uniform. That is, the energy distribution of the backscattered beam differs among flat portions, slope portions, and a boundary portion between adjacent flat portions. In this case, the proximity effect cannot be appropriately corrected if the Gaussian distribution is always used as the energy distribution of the backscattered beam. In contrast thereto, the drawing apparatus  1  according to the embodiment is configured to appropriately correct the proximity effect irrespective of the surface profile of the substrate  6 . 
     Specifically, drawing data  7  is input to the computer  2  as illustrated in  FIGS. 1A and 1B . The drawing data  7  is data for drawing a pattern on the substrate  6  with irradiation of the electron beam EB. The drawing data  7  is, for example, data created by a computer different from the computer  2  on the basis of design data of the master plate. As illustrated in  FIGS. 1A and 1B , surface profile data  8  is input to the computer  2 . The surface profile data  8  is data related to the surface profile of the substrate  6 . The surface profile data  8  is, for example, data created by a computer different from the computer  2  on the basis of the design data of the master plate. The method of inputting the drawing data  7  and the surface profile data  8  to the computer  2  is not particularly limited and can be, for example, input through data communication or input through a storage medium. More details of the drawing data  7  and the surface profile data  8  are explained in an embodiment of a proximity effect correcting method, which will be described later. 
     The computer  2  calculates an energy distribution of a backscattered beam to be produced by backscattering of the electron beam EB in the substrate  6  on the basis of the drawing data  7  and the surface profile data  8  acquired through the inputting. The computer  2  calculates a required energy amount of the electron beam EB to be irradiated to the substrate  6  on the basis of the calculated energy distribution. The required energy amount is an energy amount of the electron beam EB required to appropriately correct the proximity effect irrespective of the surface profile of the substrate  6 . The computer  2  outputs data indicating the calculated required energy amount to the control device  3 . An example of the calculation of the required energy amount by the computer  2  is explained in the embodiment of the proximity effect correcting method described later. 
     The control device  3  controls the irradiation amount of the electron beam EB to be irradiated onto the substrate  6  on the basis of the data indicating the required energy amount (that is, the calculated required energy amount) and input from the computer  2 . That is, the control device  3  adjusts the irradiation amount of the electron beam EB to supply the required energy amount of energy of the electron beam EB to the resist film  9  on the substrate  6 . 
     The electron irradiation unit  4  irradiates the substrate  6  with the electron beam EB of the irradiation amount controlled by the control device  3  to draw a pattern on the resist film  9  on the substrate  6 . The electron irradiation unit  4  includes, for example, an electron gun that emits the electron beam EB, and an electron optical system (a deflector, an electromagnetic lens, or the like) that controls the trajectory of the emitted electron beam EB. 
     If the energy distribution of the backscattered beam calculated only on the basis of the drawing data  7  and the required energy amount based on this energy distribution are used, there are cases in which the proximity effect cannot be appropriately corrected when the surface of the substrate  6  includes a level difference or a slope. This is because the drawing data  7  does not include information on the surface profile of the substrate  6 , such as the level difference or the slope, and therefore the surface profile of the substrate  6  cannot be considered in the energy distribution of the backscattered beam based on only the drawing data  7 . In contrast thereto, the drawing apparatus  1  according to the embodiment uses the energy distribution of the backscattered beam calculated considering both the drawing data  7  and the surface profile data and the required energy amount based on this energy distribution, so that the proximity effect can be appropriately corrected irrespective of the surface profile of the substrate  6 . 
     (Proximity Effect Correcting Method) 
     An embodiment of the proximity effect correcting method to which the drawing apparatus  1  according to the embodiment is applied is explained below.  FIG. 3  is a flowchart illustrating an example of the proximity effect correcting method according to the embodiment. 
     As illustrated in  FIG. 3 , the computer  2  first acquires the drawing data  7  (Step S 1 ).  FIG. 4  is an explanatory diagram for explaining an example of an acquiring process of the drawing data  7  illustrated in the flowchart of  FIG. 3 . As illustrated in  FIG. 4 , the drawing data  7  indicates a two-dimensional region corresponding to the surface of the substrate  6  and has a pattern P defined in the region. The pattern P on the drawing data  7  is drawn at a corresponding location (that is, coordinates) on the surface of the substrate  6 . Since the drawing data  7  is two-dimensional data, the drawing data  7  does not include height direction information, such as a level difference or a slope on the surface of the substrate  6 . 
     As illustrated in  FIG. 3 , the computer  2  also acquires the surface profile data  8  (Step S 2 ). The surface profile data  8  is data related to heights of the substrate  6  having different heights with respect to the irradiation direction of the electron beam EB. The irradiation direction of the electron beam EB is a direction orthogonal to the in-plane direction d 1  of the substrate  6  and is a direction indicated by an arrow EB (that is, a downward direction) in examples illustrated in  FIGS. 1A, 1B, 8, 14, 16B, and 17B . The acquisition of the surface profile data  8  may be performed before the acquisition of the drawing data  7  or may be performed at the same time as the acquisition of the drawing data  7 .  FIG. 5  is an explanatory diagram for explaining an example of an acquiring process of the surface profile data  8  illustrated in the flowchart of  FIG. 3 . As illustrated in  FIG. 5 , the surface profile data  8  includes at least flat portion arrangement information and height information. The flat portion arrangement information is information indicating arrangement states (for example, locations) of a plurality of flat portions arranged on the surface of the substrate  6  so as to have different heights due to level differences, respectively. More specifically, the flat portion arrangement information indicates a two-dimensional region corresponding to the drawing data and has the flat portions defined in the region. The height information is information indicating the heights of the flat portions. The height information is information indicating relative heights with respect to one of the flat portions. As illustrated in  FIG. 5 , the surface profile data  8  may further include slope portion arrangement information described later. The surface profile data  8  may be data in a table format. 
     After acquiring the drawing data  7  and the surface profile data  8 , the computer  2  divides the drawing data  7  into a plurality of meshes as illustrated in  FIG. 3  (Step S 3 ). The meshes are data obtained by dividing the drawing data  7  to correspond to a plurality of regions on the surface of the substrate  6 , respectively.  FIG. 6  is an explanatory diagram for explaining an example of a process of dividing the drawing data into meshes illustrated in the flowchart of  FIG. 3 . More specifically, meshes M are data obtained by dividing the drawing data  7  in a net-like manner as illustrated in  FIG. 6 . Each of the meshes M is used for drawing on the corresponding region on the surface of the substrate  6 . 
     After dividing the drawing data  7  into the meshes M, the computer  2  determines with respect to each of the meshes M whether slope portion arrangement information corresponding to the mesh M is present as the surface profile data  8  as illustrated in  FIG. 3  (Step S 4 ). The slope portion arrangement information is information indicating arrangement states (for example, locations) of slope portions as illustrated in  FIG. 5 . 
     When the slope portion arrangement information corresponding to the mesh M is present (YES at Step S 4 ), the computer  2  determines whether inclination angle information and inclination direction information corresponding to the mesh M are present as the surface profile data  8  as illustrated in  FIG. 3  (Step S 5 ).  FIG. 7  is an explanatory diagram for explaining an example of the inclination angle information and the inclination direction information illustrated in the flowchart of  FIG. 3 . The inclination angle information is information indicating an inclination angle θ of each of the slope portions as illustrated in  FIG. 7 . The inclination direction information is information indicating the direction of each of the slope portions. More specifically, in the example illustrated in  FIG. 7 , the inclination direction information is information representing a direction on two dimensions in which the height of each of the slope portions decreases, using an angle formed with a reference direction d 2  on the two dimensions. For example, since the direction of a slope portion “a” illustrated in  FIG. 7  on the two dimensions in which the height of the slope portion “a” decreases corresponds to the reference direction d 2 , the inclination direction is zero [degrees]. Meanwhile, since the direction of a slope portion “d” illustrated in  FIG. 7  on the two dimensions in which the height of the slope portion “d” decreases is opposite to the reference direction d 2 , the inclination direction is 180 [degrees]. 
     When the inclination angle information and the inclination direction information corresponding to the mesh M (YES at Step S 5 ) are present, the computer  2  acquires the inclination angle from the inclination angle information and acquires the inclination direction from the inclination direction information. The computer  2  then calculates an energy distribution of the backscattered beam in the slope portion on the basis of a function according to the inclination angle and the inclination direction as illustrated in  FIG. 3  (Step S 6 ). 
       FIG. 8  is an explanatory diagram for explaining an example of a calculating process of an energy distribution of the backscattered beam in a slope portion illustrated in the flowchart of  FIG. 3 . A region B in which one shot of the electron beam EB irradiated to a slope portion backscatters in the substrate  6 , and an energy distribution D of the backscattered beam produced by the backscattering are illustrated in a sectional view and a plan view in  FIG. 8 . A region A in which one shot of the electron beam EB irradiated to a flat portion backscatters in the substrate  6  and an energy distribution C of the backscattered beam produced by the backscattering are also illustrated in  FIG. 8  for a comparison with the slope portion. In the example illustrated in  FIG. 8 , the energy distribution C of the backscattered beam in the flat portion is a Gaussian distribution. In contrast thereto, the energy distribution D of the backscattered beam in the slope portion is calculated as a distribution different from the Gaussian distribution C as illustrated in  FIG. 8 . More specifically, the energy distribution D of the backscattered beam in the slope portion is calculated as a distribution in which the peak of the energy amount is shifted toward an inclination direction d 3  of the slope portion from the Gaussian distribution C in the example illustrated in  FIG. 8 . 
       FIG. 9  is an explanatory diagram for explaining the example of the calculating process of the energy distribution of the backscattered beam in the slope portion in more detail than in  FIG. 8 . The drawing data  7  illustrated in  FIG. 9  is partial data corresponding to the slope portion in the drawing data  7  illustrated in  FIGS. 4 and 6 . In the calculating process of the energy distribution (Step S 6 ), the computer  2  first calculates a pattern area ratio in each of meshes M corresponding to the slope portion as illustrated in  FIG. 9  (Step S 61 ). The pattern area ratio is a numerical value that is not less than 0 and not more than 1 and that indicates the ratio of the area of the pattern P with respect to the area of the mesh M for each of the meshes M. As illustrated in  FIG. 9 , the pattern area ratio is larger in meshes M where the pattern P occupies a larger region. 
       FIG. 10  is an explanatory diagram for explaining an example of the calculating process of the energy distribution of the backscattered beam in the slope portion, in continuation from  FIG. 9 . After calculating the pattern area ratio, the computer  2  calculates the energy distribution of the backscattered beam in each of the meshes M corresponding to the slope portion as illustrated in  FIG. 10  (Step S 62 ). In other words, the computer  2  calculates an energy distribution of the backscattered beam to be produced when the electron beam EB according to the pattern P included in each of the meshes M is irradiated to a region on the slope portion corresponding to each of the meshes M. The calculation of the energy distribution of the backscattered beam in each of the meshes M follows, for example, a function obtained on the basis of a Monte Carlo simulation of the energy distribution of the backscattered beam targeted at the slope portion or a function approximating (that is, simplifying) the obtained function. The calculation of the energy distribution of the backscattered beam in each of the meshes M may be performed on the basis of a table indicating the energy amount of each of the meshes M obtained on the basis of an experimental result. 
       FIG. 10  illustrates an energy distribution of the backscattered beam to be produced by the electron beam EB to be irradiated to a region on the slope portion corresponding to each of targeted meshes M 1  to M 3  according to the pattern P included in each of the meshes M 1  to M 3 . Numerical values written in the meshes M 1  to M 3  and M in  FIG. 10  indicate energy amounts of the backscattered beam corresponding to the meshes M 1  to M 3  and M, respectively. More specifically, the energy amounts written in the meshes M 1  to M 3  and M in  FIG. 10  are values relative to the maximum value converted into 1. In  FIG. 10 , the energy amounts of the targeted meshes M 1  to M 3  match the pattern area ratios (see  FIG. 9 ) corresponding to the meshes M 1  to M 3 , respectively. In  FIG. 10 , each of the meshes M 1  to M 3  and M is dotted at a density approximately corresponding to the magnitude of the energy amount of the backscattered beam. Further, the slope portion is schematically illustrated in  FIG. 10  to represent the heights of the regions on the slope portion corresponding to each of the meshes M 1  to M 3  and M. As illustrated in  FIG. 10 , the energy amount is zero in the mesh M 1  that does not include the pattern P, that is, where the pattern area ratio is zero and that is away from the meshes M 2  and M 3  including the pattern P. This is because the mesh M 1  not only causes no backscattering due to the electron beam EB to be irradiated according to the pattern P on its own but also is not influenced by the backscattering due to the electron beam EB to be irradiated according to the pattern P in other meshes. Meanwhile, in the mesh M 2  where the pattern area ratio is 0.3, an energy distribution on the mesh M 2  and surrounding meshes M is calculated based on the backscattered beam to be produced by the electron beam EB to be eradicated according to the pattern P included in the mesh M 2 . This is because the backscattering of the electron beam EB according to the pattern P on the mesh M 2  has an impact not only on the mesh M 2  but also on the surrounding meshes M. In the mesh M 3  where the pattern area ratio is the maximum value 1, an energy distribution of the meshes M 3  and M in a wider range is calculated based on the backscattered beam to be produced by the electron beam EB to be irradiated according to the pattern P included in the mesh M 3 . As illustrated in  FIG. 10 , the energy distribution of the backscattered beam in the slope portion is a distribution that is not an isotropic distribution around the targeted meshes M 2  and M 3  but a distribution having an anisotropic property unevenly distributed toward the inclination direction d 3  of the slope portion. 
     After calculating the energy distribution of the backscattered beam in the slope portion, the computer  2  calculates an integrated energy distribution as illustrated in  FIG. 3  (Step S 7 ). The integrated energy distribution is a distribution obtained by integrating the calculated energy distributions of the meshes.  FIG. 11  is an explanatory diagram for explaining an example of a calculating process of the integrated energy distribution in the slope portion illustrated in the flowchart of  FIG. 3 . The integrated energy distribution illustrated in  FIG. 11  is calculated from the drawing data  7  illustrated in  FIGS. 9 and 10 . However, the integrated energy amount written in each of the meshes in  FIG. 11  is a value relative to the maximum value converted into 1. 
     After calculating the integrated energy distribution, the computer  2  calculates a required energy amount on the basis of the calculated integrated energy distribution as illustrated in  FIG. 3  (Step S 8 ).  FIG. 12  is an explanatory diagram for explaining an example of a calculating process of the required energy amount illustrated in the flowchart of  FIG. 3 . In  FIG. 12 , a required energy amount (μC) in the slope portion for each shot is calculated. For sake of explanations, patterns P 1  corresponding to a required energy amount for each shot are illustrated in  FIG. 12 . The resist film  9  on the substrate  6  on which the patterns P 1  are drawn is exposed not only to the electron beam EB but also to the backscattered beam. That is, not only the irradiation energy of the electron beam EB but also energy of the backscattered beam is added to the resist film  9 . Therefore, the required energy amount is required to be calculated in consideration of the energy amount of the backscattered beam. Accordingly, the computer  2  first defines an irradiation energy amount of the electron beam EB for each shot, to which the integrated energy amount according to the integrated energy distribution is added as illustrated in  FIG. 12 . The defined irradiation energy amount is an unadjusted irradiation energy amount to which an adjustment for the proximity effect correction has not been performed yet. 
     Next, the computer  2  sets an energy amount at a predetermined ratio (for example, 50%) to the maximum value of the unadjusted irradiation energy amount as a threshold. The computer  2  then adjusts the irradiation emery amount for each shot in such a manner that distribution widths (lateral widths in  FIG. 12 ) of the irradiation energy amount of the shots are equalized at the threshold. The adjusted irradiation energy amount is calculated as the required energy amount. The calculated required energy amount is used by the control device  3  to adjust the irradiation amount of the electron beam EB. The proximity effect is corrected in this way. If the proximity effect is not corrected, a plurality of patterns P 2  having an equal width on the design data and being adjacent to each other are drawn as patterns having different widths, as indicated by the patterns P 2  represented by broken line portions in  FIG. 12 . On the other hand, when the proximity effect is corrected according to the embodiment, a plurality of patterns P 1  having an equal width on the design data and being adjacent to each other can be appropriately drawn as the patterns P 1  having the same width, as indicated by the patterns P 1  represented by solid line portions in  FIG. 12 . 
     The computer  2  may recalculate the energy distribution of the backscattered beam using the irradiation amount of the electron beam EB adjusted on the basis of the required energy amount. In this case, the computer  2  may recalculate the integrated energy distribution on the basis of the recalculated energy distribution of the backscattered beam and recalculate the required energy amount of each shot on the basis of the recalculated integrated energy distribution. The recalculation of the required energy amount may be repeated as required. 
     When the inclination angle information and the inclination direction information corresponding to the mesh M are not present (NO at Step S 5 ), the computer  2  calculates the inclination angle and the inclination direction of the slope portion as illustrated in  FIG. 3  (Step S 9 ).  FIG. 13  is an explanatory diagram for explaining an example of a calculating process of the inclination angle and the inclination direction of the slope portion illustrated in the flowchart of  FIG. 3 . The inclination angle and the inclination direction of the slope portion may be calculated, for example, using a linear function or a polynomial based on the slope portion arrangement information and the height information. For example, the inclination angle θ and the inclination direction d 3  may be calculated on the basis of the X coordinate (x1) and the Z coordinate (z1) of a lower end of the slope portion, and the X coordinate (x2) and the Z coordinate (z2) of an upper end of the slope portion indicated by the slope portion arrangement information and the height information as illustrated in  FIG. 13 . In the example illustrated in  FIG. 13 , the inclination angle θ is the arctangent (tan −1 ) of the slope (z2−z1)/(x2−x1) of a linear function connecting the coordinates of two points of the lower end (x1, z1) of the slope portion and the upper end (x2, z2) thereof. In the example illustrated in  FIG. 13 , the inclination direction d 3  is a direction from x2 toward x1, in which the Z value of the linear function decreases. After Step S 9 , the processing proceeds to Step S 6 . 
     When the slope portion arrangement information corresponding to the mesh M is not present (NO at Step S 4 ), the computer  2  determines whether the mesh corresponds to a boundary between flat portions that are adjacent without a slope portion interposed therebetween as illustrated in  FIG. 3  (Step S 10 ). When the mesh corresponds to the boundary between flat portions (YES at Step S 10 ), the computer  2  calculates an energy distribution of the backscattered beam in the boundary portion between the flat portions on the basis of a function according to the magnitude of a level difference located at the boundary and the distance from the boundary (Step S 11 ). 
       FIG. 14  is an explanatory diagram for explaining an example of a calculating process of the energy distribution of the backscattered beam in a boundary portion between flat portions illustrated in the flowchart of  FIG. 3 . In  FIG. 14 , a region B in which one shot of the electron beam EB irradiated to a boundary portion between flat portions  6 L and  6 H backscatters in the substrate  6 , and an energy distribution D of the backscattered beam produced by the backscattering are illustrated in a sectional view and a plan view.  FIG. 14  also illustrated a region A in which one shot of the electron beam EB irradiated to a completely flat portion including no level differences backscatters in the substrate  6 , and an energy distribution C of the backscattered beam produced by the backscattering, for a comparison with the boundary portion between the flat portions  6 L and  6 H. In the example illustrated in  FIG. 14 , the energy distribution C of the backscattered beam in the completely flat portion is a Gaussian distribution. In contrast thereto, the energy distribution D of the backscattered beam in the boundary portion between the flat portions  6 L and  6 H is calculated as a distribution different from the Gaussian distribution C as illustrated in  FIG. 14 . More specifically, in the example illustrated in  FIG. 14 , the energy distribution D of the backscattered beam in the boundary portion between the flat portions  6 L and  6 H is calculated as a distribution in which the energy amount is concentrated on the side of the flat portion  6 H that is higher in the level relative to the Gaussian distribution C.  FIG. 14  illustrates an example in which the electron beam EB is irradiated to position the beam center on the flat portion  6 H that is higher in the level. When the electron beam EB is irradiated to position the beam center on the flat portion  6 L that is lower in the level, an energy distribution in which the energy amount is concentrated on the side of the flat portion  6 L that is lower in the level is calculated, unlike  FIG. 14 . 
     The calculation of the energy distribution of the backscattered beam in the boundary portion between the flat portions  6 L and  6 H is performed for each of the meshes M similarly in the examples illustrated in  FIGS. 9 and 10 . The calculation of the energy distribution of the backscattered beam in each mesh M is, for example, based on a function according to the magnitude of the level difference zd located at the boundary between the flat portion  6 L and  6 H and the distance in a two-dimensional direction from the boundary. More specifically, the calculation of the energy distribution of the backscattered beam in each mesh M may follow a function obtained on the basis of the Monte Carlo simulation targeted at the boundary portion between the flat portions  6 L and  6 H, or a function approximating (that is, simplifying) the obtained function. Alternatively, the calculation of the energy distribution of the backscattered beam in each mesh M may be performed on the basis of a table indicating the energy amount of each mesh M obtained on the basis of an experimental result. After Step S 11 , the processing proceeds to Step S 7 . 
     When the mesh does not correspond to a boundary between flat portions (NO at Step S 10 ), the computer  2  determines that the mesh corresponds to a completely flat portion including no level difference. In this case, the computer  2  calculates the energy distribution of the backscattered beam in the flat portion on the basis of the Gaussian distribution (Step S 12 ). The energy distribution according to the Gaussian distribution is represented by, for example, the following expression. 
         g ( x )=η× D ( x ′)×(1/ nσ   2 )×exp{−( x−x ′) 2 /σ 2 }
 
     where g(x) is the energy amount, that is, the energy distribution of the backscattered beam at a coordinate x, η is a backscattering coefficient, D(x′) is the irradiation amount of the electron beam EB at an irradiation coordinate x′ of the electron beam EB, and a is the backscattering radius of the backscattered beam. 
     The calculation of the energy distribution of the backscattered beam in the flat portion according to the Gaussian distribution is performed for each mesh M similarly in the examples illustrated in  FIGS. 9 and 10 . After Step S 12 , the processing proceeds to Step S 7 .  FIG. 15  is an explanatory diagram for explaining an example of a calculating process of the integrated energy distribution in the flat portion illustrated in the flowchart of  FIG. 3 .  FIG. 15  illustrates an example of the integrated energy distribution calculated at Step S 7  on the basis of the energy distribution of the backscattered beam according to the Gaussian distribution. 
     The calculation of the energy distribution of the backscattered beam is not limited to the mode illustrated in  FIG. 3 . For example, the energy distribution may be calculated according to a function based on the Monte Carlo simulation described above or an experimental result in a boundary portion between a flat portion and a slope portion. 
     With the proximity effect correcting method according to the embodiment, the energy distribution of the backscattered beam can be calculated on the basis of the drawing data  7  and the surface profile data  8 , and the required energy amount of the electron beam can be calculated on the basis of the calculated energy distribution. Accordingly, the proximity effect can be appropriately corrected irrespective of the surface profile of the substrate  6 . 
     With the proximity effect correcting method according to the embodiment, the energy distribution of the backscattered beam in each slope portion can be appropriately calculated on the basis of the drawing data  7 , the flat portion arrangement information, the height information, and the slope portion arrangement information as the surface profile data  8 , the inclination angle of the slope portion, and the inclination direction of the slope portion. 
     With the proximity effect correcting method according to the embodiment, the required energy amount can be appropriately calculated on the basis of the integrated energy distribution obtained by integrating the energy distribution of the backscattered beam for each mesh. 
     With the proximity effect correcting method according to the embodiment, an appropriate correction of the proximity effect according to the surface profile of the substrate  6  can be performed by calculating the energy distribution of the backscattered beam by an appropriate calculation method depending on a boundary portion between a slope portion and a flat portion, or a completely flat portion. 
     (Master Plate Manufacturing Method) 
     The proximity effect correcting method according to the embodiment explained with reference to  FIGS. 3 to 15  can be used for manufacturing of a master plate. An embodiment of a manufacturing method of a photomask, and an embodiment of a manufacturing method of a template are sequentially explained below as master plate manufacturing methods to which the proximity effect correcting method according to the embodiment is applied. 
       FIG. 16A  is a sectional view illustrating a manufacturing method of a photomask according to the embodiment. As illustrated in  FIG. 16A , in manufacturing of a photomask, the resist film  9  is first formed on the mask blank  6 A explained with reference to  FIG. 2A . The formation of the resist film  9  includes coating of the resist film  9  and pre-baking after the coating. In the example illustrated in  FIG. 16A , the resist film  9  is a positive film. The resist film  9  may be a negative film. 
       FIG. 16B  is a sectional view illustrating the manufacturing method of a photomask according to the embodiment, in continuation from  FIG. 16A . After the resist film  9  is formed, the electron beam EB of an irradiation amount adjusted using the proximity effect correcting method according to the embodiment is irradiated by the drawing apparatus  1  as illustrated in  FIG. 16B . Accordingly, the resist film  9  at portions to which the electron beam EB is irradiated is exposed to light. 
       FIG. 16C  is a sectional view illustrating the manufacturing method of a photomask according to the embodiment, in continuation from  FIG. 16B . After the resist film  9  is exposed to light and the exposed resist film  9  is post-baked, the resist film  9  is developed as illustrated in  FIG. 16C . The development of the resist film  9  is performed by a wet process using a chemical. The portions of the resist film  9  exposed to light are removed by the development and the light shielding film  62  is partially exposed at locations where the resist film  9  has been removed. 
       FIG. 16D  is a sectional view illustrating the manufacturing method of a photomask according to the embodiment, in continuation from  FIG. 16C . After the resist film  9  is developed, the light shielding film  62  is etched (that is, processed) using the developed resist film  9  as a mask. The etching is performed by a dry process. 
       FIG. 16E  is a sectional view illustrating the manufacturing method of a photomask according to the embodiment, in continuation from  FIG. 16D . After the light shielding film  62  is etched, the resist film  9  is removed as illustrated in  FIG. 16E . Accordingly, a photomask  60 A is obtained. 
       FIGS. 17A to 17E  are sectional views illustrating a manufacturing method of a template  60 B according to the embodiment. As illustrated in  FIGS. 17A to 17E , the manufacturing method of the template  60 B is basically the same as the manufacturing method of the photomask  60 A. The manufacturing method of the template  60 B is different from the manufacturing method of the photomask  60 A in that a target processed by etching is not the light shielding film  62  but the template blank  6 B. 
     With the manufacturing method of the photomask  60 A or the template  60 B according to the embodiment, the mask blank  6 A or the template blank  6 B can be exposed to light using the electron beam EB of an irradiation amount adjusted using the proximity effect correcting method according to the embodiment. Accordingly, the photomask  60 A or the template  60 B having a pattern with a high dimensional accuracy where the proximity effect has been appropriately corrected irrespective of the surface profile can be obtained. With application of the photomask  60 A or the template  60 B to a semiconductor process, a pattern of an accurate dimension can be formed on a device substrate having a level difference or a slope on the surface, and a semiconductor device can be appropriately manufactured. 
     At least a part of the computers  2  illustrated in  FIGS. 1A and 1B  can be constituted by hardware or software. When it is constituted by software, the computer  2  can be configured such that a program for realizing at least a part of the functions of the computer  2  is stored in a recording medium such as a flexible disk or a CD-ROM, and the program is read and executed by a computer. The recording medium is not limited to a detachable device such as a magnetic disk or an optical disk, and can be a fixed recording medium such as a hard disk device or a memory. Further, a program for realizing at least a part of the functions of the computer  2  can be distributed via a communication line (including wireless communication) such as the Internet. Furthermore, the program can be distributed in an encrypted, modulated, or compressed state via a wired communication line or a wireless communication line such as the Internet, or the program is distributed as it is stored in a recording medium. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel methods and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the methods and systems described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.