Patent Publication Number: US-9899187-B2

Title: Charged particle beam writing apparatus and charged particle beam writing method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2015-087042 filed on Apr. 21, 2015 in Japan, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     Embodiments of the present invention relate generally to a charged particle beam writing apparatus and a charged particle beam writing method, and more specifically, relate to a writing apparatus and method that perform proximity effect correction in the case, for example, where a dose is modulated (or adjusted) due to a prescribed effect other than the proximity effect. 
     Description of Related Art 
     The lithography technique that advances miniaturization of semiconductor devices is extremely important as a unique process whereby patterns are formed in semiconductor manufacturing. In recent years, with high integration of LSI, the line width (critical dimension) required for semiconductor device circuits is decreasing year by year. For forming a desired circuit pattern on such semiconductor devices, a master or “original” pattern (also called a mask or a reticle) of high accuracy is needed. Thus, the electron beam (EB) writing technique, which intrinsically has excellent resolution, is used for producing such a high-precision master pattern. 
     For example, a writing apparatus using a single beam is known, and further, there can be cited a writing apparatus employing the raster method. In the writing apparatus employing the raster method, for example, an electron beam emitted from the electron gun passes through a mask with one hole to be shaped, and the shaped beam is deflected by a deflector to move in a tracing manner on the target object or “sample” in order to irradiate a necessary point by blanking control. 
     Further, for example, a writing apparatus using multiple beams is known. When compared to the case of writing or “drawing” a pattern with a single electron beam, since it is possible to irradiate many beams at a time in multi-beam writing, the throughput can be greatly increased. For example, in the writing apparatus employing the multi-beam system, multi-beams are formed by letting portions of an electron beam emitted from an electron gun pass through a corresponding hole of a plurality of holes in the mask, and each beam is blanking-controlled such that each unblocked beam is reduced by an optical system and deflected by a deflector so as to irradiate a desired position on the target object. 
     Moreover, besides the writing apparatus employing the raster method described above, as the writing apparatus using a single beam, there can be cited, for example, a variable-shaped beam (VSB) writing apparatus. In the writing apparatus of the VSB system, while forming a shot beam by a blanking control, the relative position of two-stage shaping apertures through which the beam passes is variably controlled, thereby variably shaping a beam of each shot. Then, the variably shaped beam is deflected by a deflector so as to irradiate a desired position on the target object. 
     In the various writing systems described above, there is a problem with respect to writing by the raster method or writing method with the multi-beam system in that, when a pattern edge or corner is written, if the pattern edge (boundary) is deviated from the pixel boundary, a desired shape of the pattern edge or corner cannot be formed with a design irradiation dose thereon. Accordingly, it has been examined to perform correction by adjusting the dose thereto. 
     With recent development of the optical lithography technology and shorter wavelengths due to EUV (extreme ultraviolet), the number of electron beam shots required for mask writing is increasing acceleratingly. On the other hand, for ensuring the line width accuracy needed for micropatterning, it is aimed to diminish shot noise and pattern edge roughness by making resist less sensitive and increasing the dose. Thus, since the number of shots and the amount of dose increase limitlessly, the pattern writing time also increases limitlessly. Therefore, in the writing apparatuses of various writing systems described above, it is now examined to reduce the writing time by increasing the current density. 
     However, if the target is irradiated with an increased amount of energy as a higher density electron beam in a short time, another problem occurs in that the substrate overheats resulting in a phenomenon called “resist heating” of changing the resist sensitivity and degrading the line width accuracy. To solve this problem, it is suggested to calculate, for each minimum deflection region in the deflection region, a representative temperature of the minimum deflection region concerned based on heat transfer from other minimum deflection regions written prior to the current one, and to modulate the dose by using the representative temperature (refer to Japanese Patent Application Laid-open (JP-A) No. 2012-069675). 
     On the other hand, in the electron beam writing, a phenomenon called a “proximity effect” occurs when electron beams irradiate a mask covered with resist to write a circuit pattern thereon. The proximity effect occurs by backscattering of electron beams penetrating the resist film, reaching the layer thereunder to be reflected, and entering the resist film again. As a result, a dimensional variation occurs, that is, a written pattern is deviated from a desired dimension. In order to avoid this phenomenon, a proximity effect correction operation that suppresses such dimensional variation by, for example, modulating the dose is performed in the writing apparatus. 
     However, even when the dose is adjusted by performing proximity effect correction calculation, if subsequently performing dose modulation for correcting various effects other than the proximity effect, such as pattern edge/corner correction, resist heating correction described above, etc., there arises another problem in that correction residual error occurs regarding proximity effect correction. 
     As described above, since correction residual error arises in proximity effect correction, it is necessary to again perform proximity effect correction calculation after dose modulation calculation for correcting various effects. However, even in such a case, there is still a problem in that since the calculation amount of proximity effect correction is large, rather sufficient computer resource and processing time are needed, thereby resulting in a problem of difficulty of real time correction calculation. Accordingly, it is necessary to efficiently perform the processing. 
     BRIEF SUMMARY OF THE INVENTION 
     According to one aspect of the present invention, a charged particle beam writing apparatus includes a first correction-irradiation-coefficient-term calculation processing circuitry configured to calculate correction irradiation coefficient terms of from a first order term to an n-th order term, n being an integer of 1 or more, in a case of calculating a first proximity effect correction irradiation coefficient which does not take account of a predetermined effect in order to correct proximity effect of a charged particle beam; a second correction-irradiation-coefficient-term calculation processing circuitry configured to calculate at least one correction irradiation coefficient term up to a k-th order term, k being an integer from 1 to n, in a case of calculating a second proximity effect correction irradiation coefficient which takes account of the predetermined effect in order to correct the proximity effect of the charged particle beam; a 
     proximity-effect-correction-irradiation-coefficient calculation processing circuitry configured to calculate a third proximity effect correction irradiation coefficient where at least one correction irradiation coefficient term up to the k-th order term, in the correction irradiation coefficient terms of from the first order term to the n-th order term for the first proximity effect correction irradiation coefficient which does not take account of the predetermined effect, are replaced by the at least one correction irradiation coefficient term up to the k-th order term, for the second proximity effect correction irradiation coefficient which takes account of the predetermined effect; a dose calculation processing circuitry configured to calculate a dose by using the third proximity effect correction irradiation coefficient; and a writing mechanism including a stage on which a target object is placed, a charged particle beam source, and a deflector, the writing mechanism configured to write a pattern on the target object by using a charged particle beam based on the dose calculated. 
     According to another aspect of the present invention, a charged particle beam writing method includes calculating sequentially correction irradiation coefficient terms of from a first order term to an n-th order term, n being an integer of 1 or more, in a case of calculating a first proximity effect correction irradiation coefficient which does not take account of a predetermined effect in order to correct proximity effect of a charged particle beam; calculating at least one correction irradiation coefficient term up to a k-th order term, k being an integer from 1 to n, in a case of calculating a second proximity effect correction irradiation coefficient which takes account of the predetermined effect in order to correct the proximity effect of the charged particle beam; calculating a third proximity effect correction irradiation coefficient where at least one correction irradiation coefficient term up to the k-th order term, in the correction irradiation coefficient terms of from the first order term to the n-th order term for the first proximity effect correction irradiation coefficient which does not take account of the predetermined effect, are replaced by the at least one correction irradiation coefficient term up to the k-th order term, for the second proximity effect correction irradiation coefficient which takes account of the predetermined effect; calculating a dose by using the third proximity effect correction irradiation coefficient; and writing a pattern on a target object by using a charged particle beam based on the dose calculated. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram showing a configuration of a writing apparatus according to a first embodiment; 
         FIGS. 2A and 2B  are conceptual diagrams each showing a configuration of a multi-beam forming member according to the first embodiment; 
         FIG. 3  is a sectional view showing a configuration of a blanking plate according to the first embodiment; 
         FIG. 4  is a flowchart showing main steps of a writing method according to the first embodiment; 
         FIG. 5  shows an example of an evaluation pattern for evaluating an effect of the first embodiment; 
         FIGS. 6A and 6B  show examples of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions of comparative examples 1 and 2 of the first embodiment; 
         FIG. 7  shows an example of the result of dimensional deviation in the case of writing an evaluation pattern according to the first embodiment; 
         FIG. 8  is a schematic diagram showing a configuration of a writing apparatus according to a third embodiment; 
         FIG. 9  is a conceptual diagram for explaining each region according to the third embodiment; 
         FIG. 10  is a flowchart showing main steps of a writing method according to the third embodiment; 
         FIG. 11  shows an example of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions of a comparative example of the third embodiment; 
         FIG. 12  shows an example of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions according to the third embodiment; and 
         FIG. 13  shows an example of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions according to the third embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the embodiments below, there will be described an apparatus and method that can perform writing with efficiently suppressing pattern dimensional variation due to various effects while suppressing correction residual error of proximity effect. 
     In the embodiments below, there will be described a configuration in which an electron beam is used as an example of a charged particle beam. The charged particle beam is not limited to the electron beam, and other charged particle beams such as an ion beam may also be used. 
     First Embodiment 
       FIG. 1  is a schematic diagram showing a configuration of a writing or “drawing” apparatus according to the first embodiment. As shown in  FIG. 1 , a writing apparatus  500  includes a writing mechanism  550  and a control unit  560 . The writing apparatus  500  is an example of a multi charged particle beam writing apparatus. The writing mechanism  550  includes an electron optical column  502  and a writing chamber  503 . In the electron optical column  502 , there are arranged an electron gun  601 , an illumination lens  602 , a multi-beam forming member  603 , a blanking plate  604 , a reducing lens  605 , a limiting aperture member  606 , an objective lens  607 , and a deflector  608 . In the writing chamber  503 , an XY stage  505  is arranged. On the XY stage  505 , there is placed a target object or “sample”  101  such as a mask serving as a writing target substrate when writing is performed. For example, the target object  101  is an exposure mask used for manufacturing semiconductor devices, or is a semiconductor substrate (silicon wafer) on which semiconductor elements are formed. The target object  101  may be, for example, a mask blank on which resist has been applied and nothing has yet been written. A mirror  610  for measuring the position of the XY stage  505  is arranged on the XY stage  505 . 
     The control unit  560  includes a control computer  510 , a memory  512 , a deflection control circuit  530 , a stage position detector  539 , and storage devices  540 ,  542 ,  544 ,  546 ,  548 , and  549  such as magnetic disk drives. The control computer  510 , the memory  512 , the deflection control circuit  530 , the stage position detector  539 , and the storage devices  540 ,  542 ,  544 ,  546 ,  548 , and  549  are connected with each other through a bus (not shown). Writing data that defines pattern data of a plurality of figure patterns to be written is input from outside the writing apparatus  500  and stored in the storage device  540  (storage unit). GMC (grid matching correction) data is input from outside the writing apparatus  500  and stored in the storage device  549  (storage unit). 
     In the control computer  510 , there are arranged a dividing-into-proximity-meshes unit  62 , a grid matching correction (GMC) unit  63 , an area density (ρ″) map generation unit  65 , an area density (ρ) calculation unit  66 , a proximity effect density (U) calculation unit  68 , an irradiation correction coefficient (D p ) calculation unit  70 , a dose (D) calculation unit  71 , a D″ calculation unit  72 , an influence coefficient (α′) calculation unit  77 , a U′ calculation unit  79 , an irradiation correction coefficient (D p ′) calculation unit  80 , an irradiation correction coefficient (D p ″) calculation unit  82 , a dose (D′) calculation unit  84 , an irradiation time (t′) calculation unit  85 , and a writing control unit  86 . Each of the “units” such as the dividing-into-proximity-meshes unit  62 , the GMC unit  63 , the area density (ρ″) map generation unit  65 , the area density (ρ) calculation unit  66 , the proximity effect density (U) calculation unit  68 , the irradiation correction coefficient (D p ) calculation unit  70 , the dose (D) calculation unit  71 , the D″ calculation unit  72 , the influence coefficient (α′) calculation unit  77 , the U′ calculation unit  79 , the irradiation correction coefficient (D p ′) calculation unit  80 , the irradiation correction coefficient (D p ″) calculation unit  82 , the dose (D′) calculation unit  84 , the irradiation time (t′) calculation unit  85 , and the writing control unit  86  includes a processing circuitry. As the processing circuitry, for example, an electric circuit, a computer, a processor, a circuit board, a quantum circuit, or a semiconductor device may be used. Each of the “units” may use a common processing circuitry (same processing circuitry), or different processing circuitries (separate processing circuitries). Input data required in the control computer unit  110 , and calculated results are stored in the memory  512  each time. 
       FIG. 1  shows a configuration necessary for explaining the first embodiment. Other configuration elements generally necessary for the writing apparatus  500  may also be included. 
       FIGS. 2A and 2B  are conceptual diagrams each showing a configuration of a multi-beam forming member according to the first embodiment. As shown in  FIG. 2A , holes (openings)  22  of m rows long (y direction) and n columns wide (x direction) (m≧2, n≧2) are formed, like a matrix, at a predetermined arrangement pitch in the multi-beam forming member  603 . In  FIG. 2A , for example, holes  22  of 512 (rows)×8 (columns) are formed. Each of the holes  22  is a quadrangle of the same dimensional shape. Alternatively, each of the holes  22  can be a circle of the same circumference. Here, there is shown an example in which each of the rows arrayed in the y direction has eight holes  22  from A to H in the x direction. Multi-beams  20  are formed by letting portions of an electron beam  600  individually pass through a corresponding hole of a plurality of holes  22 . The case in which the holes  22  of a plurality of rows and columns are arranged in both the x and the y directions is shown here, but the arrangement is not limited thereto. For example, it is also acceptable that a plurality of holes  22  are arranged in only one row (x direction) or in only one column (y direction). That is, in the case of only one row, a plurality of holes  22  are arranged as a plurality of columns, and in the case of only one column, a plurality of holes  22  are arranged as a plurality of rows. The method of arranging the holes  22  is not limited to the case of  FIG. 2A  where holes are arranged like a grid in the length and width directions. For example, as shown in  FIG. 2B , as to the first and second rows arrayed in the length direction (y direction), each hole in the first row and each hole in the second row may be mutually displaced in the width direction (x direction) by a dimension “a”. Similarly, as to the second and third rows arrayed in the length direction (y direction), each hole in the second row and each hole in the third row may be mutually displaced in the width direction (x direction) by a dimension “b”, for example. 
       FIG. 3  is a sectional view showing the configuration of a blanking plate according to the first embodiment. In  FIG. 3 , the positional relations between electrodes  24  and  26 , and a control circuit  41  are not in accordance with each other. With regard to the configuration of the blanking plate  604  (blanking device), as shown in  FIG. 3 , a semiconductor substrate  331  made of silicon, etc. is placed on a support table  333 . The central part of the substrate  331  is shaved from the back side and processed to be a membrane region  330  (first region) having a thin film thickness h. The circumference surrounding the membrane region  330  is a circumference region  332  (second region) having a thick film thickness H. The upper surface of the membrane region  330  and the upper surface of the circumference region  332  are formed to be at the same height position, or substantially at the same height position. At the backside of the circumference region  332 , the substrate  331  is supported to be on the support table  333 . The central part of the support table  333  is open, and the position of the membrane region  330  is located in the opening part of the support table  333 . 
     In the membrane region  330 , there are formed passage holes  25  (openings), through each of which a corresponding one of multi-beams passes, at the positions each corresponding to each hole  22  of the multi-beam forming member  603  shown in  FIGS. 2A and 2B . In other words, in the substrate  331 , a plurality of penetrating passage holes  25  through each of which a corresponding electron beam  20  of multi-beams passes are formed in a two-dimensional array of m rows long (y direction) and n columns wide (x direction) (m≧2, n≧2). A plurality of pairs of electrodes  24  and  26  (blanker: blanking deflector) at opposite sides of a corresponding one of a plurality of passage holes  25  are arranged in the membrane region  330  as shown in  FIG. 3 . Moreover, close to each passage hole  25 , in the substrate  331  of the membrane region  330 , there is arranged a control circuit  41  (logic circuit) which applies a deflection voltage to the electrode  24  for each passage hole  25 . The other one (for example, electrode  26 ) of the two electrodes  24  and  26  for each beam is grounded (earthed). Further, as shown in  FIG. 3 , for example, 10-bit parallel lines for control signals are connected to each control circuit  41 . In addition to the 10-bit parallel lines, for example, lines for power supply, control clock, etc. are connected to each control circuit  41 . A part of the parallel lines may be used as the line for power supply. An individual blanking mechanism  47  composed of the electrodes  24  and  26  and the control circuit  41  is configured for each of multi-beams. Moreover, on the circumference region  332  having a thick film thickness, pads etc. (not shown) each of which transmits a control signal to each control circuit  41  are arranged. 
       FIG. 4  is a flowchart showing main steps of a writing method according to the first embodiment. As shown in  FIG. 4 , the writing method of the first embodiment executes a series of steps of a ρ(x) calculation step (S 104 ), a U(x) calculation step (S 106 ), a D p (x) calculation step (S 108 ), a D(x) calculation step (S 110 ), a GMC step (S 111 ), an influence coefficient calculation step (S 113 ), a U′(x) calculation step (S 115 ), a D p ′(x) calculation step (S 116 ), a D p ″(x) calculation step (S 118 ), a D″(x) calculation step (S 119 ), a ρ″ map generation step (S 120 ), a D′(x) calculation step (S 121 ), a t′(x) calculation step (S 122 ), and a writing step (S 124 ). 
     First, the dividing-into-proximity-meshes unit  62  (second dividing-into-meshes unit) virtually dividing the writing region of the target object  101  into a plurality of proximity meshes (second mesh region) by the size Δ 2  (second mesh size) for correcting a proximity effect. With respect to the proximity mesh, it is preferable to perform dividing by the size about 1/10 of the influence radius of the proximity effect, such as about 0.5 to 2 μm. 
     In the ρ calculation step (S 104 ), the ρ calculation unit  66  reads writing data from the storage device  540 , and calculates, for each proximity mesh, the area density ρ of a figure pattern arranged in the proximity mesh concerned. Then, the ρ calculation unit  66  generates an area density map by using each mesh value. The ρ calculation unit  66  sequentially reads the data file of each frame region, and calculates the area density ρ for each frame region. That is, here, the area density ρ is calculated using writing data before GMC is performed. 
     In the U(x) calculation step (S 106 ), the U calculation unit  68  calculates a proximity effect density U(x) for each proximity mesh region. The proximity effect density U(x) can be defined by the following equation (1) that convolves a distribution function g(x) with an area density ρ. Hereinafter, the position x indicates a vector. A proximity effect density U(x) map is generated using a mesh value of each proximity mesh region. The U(x) map is stored in the storage device  544 .
 
 U ( x )=∫ρ( x ′) g ( x−x ′) dx′   (1)
 
     As one of various effects causing correction residual error of proximity effect, there is effect of modulating the dose for writing at least one of a pattern edge and a pattern corner. Generally, the boundary of a figure pattern and the boundary of a pixel are not coincident with each other. Even in a pattern whose boundary is coincident with the boundary of a pixel, the boundaries may not coincide with each other when the position of the figure pattern is shifted by performing GMC. In such a case, if not modulating the dose of the pixel where the boundaries do not coincide with each other, the shape of at least one of the pattern edge and the pattern corner deviates when the pattern is written. In multi-beam writing, the roundness of the corner becomes large compared to variable-shaped beam (VSB) writing. Therefore, in multi-beam writing, it is particularly necessary to perform correction of the edge corner by modulating the dose. 
     Depending upon a proximity effect correction coefficient, likelihood (dose latitude: ratio of the CD change amount to the dose change amount) varies. Therefore, the correction coefficient of the dose used for corner correction varies. In the first place, the roundness of the corner may vary depending on a proximity effect. 
     Thus, in multi-beam writing, correction residual error of proximity effect is easily generated under the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. Then, according to the first embodiment, there will be described a configuration where suppressed is correction residual error of proximity effect, which is generated under the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. In the first embodiment, a model using a term obtained by multiplying an incident dose by an influence coefficient α′(x) (an example of an influence coefficient), and a term indicating a back scattering dose is used. Then, the correction dose (proximity effect correction irradiation coefficient) is calculated using the model. For reducing the operation time, according to the first embodiment, proximity effect correction calculation is performed without taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. Then, after that, calculation taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner is performed. Now, first, will be described the case where proximity effect correction calculation is performed without taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. 
     In the D p (x) calculation step (S 108 ), the D p  calculation unit  70  calculates a correction irradiation coefficient D p (x) (first proximity effect correction irradiation coefficient) for correcting a proximity effect without taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. The correction irradiation coefficient D p (x) can be obtained by solving the following model equation (2) where an unknown correction irradiation coefficient D p (x) which does not take account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner, and a proximity effect correction coefficient η are used. Here, the dose D(x) is replaced by the correction irradiation coefficient D p (x) by defining (using) a standardized dose. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     In order to obtain an unknown correction irradiation coefficient D p (x) from the equation (2), a repetition calculation up to the n-th order term (n is an integer of 1 or more) is performed. Therefore, when performing the repetition calculation, the D p  calculation unit  70  sequentially calculates the correction irradiation coefficient term of each order term, from the first order term to the n-th order term. The D p  calculation unit  70  serves as an example of a first correction-irradiation-coefficient-term calculation unit. The correction irradiation coefficient term d 1  of the first order term and the correction irradiation coefficient term d n  of the n-th order term are defined by the following equations (3-1) and (3-2). 
     
       
         
           
             
               
                 
                   
                     
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     The correction irradiation coefficient D p (x) (first proximity effect correction irradiation coefficient) is defined by the following equation (4). An obtained correction irradiation coefficient D p (x), and a correction irradiation coefficient term d 1 (x) of at least one of the correction irradiation coefficient term of each order term are stored in the storage device  544 . 
     
       
         
           
             
               
                 
                   
                     
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     In the D(x) calculation step (S 110 ), the D calculation unit  71  (temporary dose calculation unit) calculates, for each pattern, a dose D(x) (temporary dose) by multiplying an obtained correction irradiation coefficient D p (x) by a reference dose D 0 . 
     In the GMC step (S 111 ), the GMC unit  63  (position deviation correction unit) corrects pattern data, based on position deviation of a pattern to be written which which is caused by distortion of at least one of the target object  101  and the mirror  610 . Specifically, the GMC unit  63  reads writing data from the storage device  540 , and performs GMC for a plurality of figure patterns defined in the writing data. As the GMC, in the first embodiment, a pattern position deviation resulting from distortion of the mirror  610  and/or distortion of the target object  101  is corrected. GMC data used as correction data for correcting the position deviation of a pattern resulting from distortion of the mirror  610  and/or distortion of the target object  101  is stored in the storage device  549 . The GMC unit  63  reads GMC data from the storage device  549 , and performs GMC by correcting pattern data on a plurality of figure patterns defined in writing data. A polynomial (e.g., fourth function) obtained by approximating the correction value for correcting the position deviation of a pattern resulting from distortion of the mirror  610  and/or distortion of the target object  101 , and/or a coefficient of the polynomial are included in the GMC data. Further, included is a correction map defining a correction value for correcting position deviation eccentrically located for which it is difficult to perform approximation by the polynomial. The GMC unit  63  corrects the position of each pattern by using the polynomial or the correction map. Thereby, the position of a pattern can be corrected at the stage of writing data before being developed to shot data. 
     Next, proximity effect correction calculation taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner is performed. According to the first embodiment, a model using a term obtained by multiplying the incident dose by an influence coefficient α′(x) (an example of an influence coefficient), and a term of a back scattering dose is used. This model is defined by the following equation (5) using an unknown proximity effect correction irradiation coefficient D p ′(x) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. Here, the dose D′(x) is replaced by the correction irradiation coefficient D p ′(x) by defining (using) a standardized dose.
 
α′( x ) D   p ′( x )+η∫ρ( x ′) D   p ′( x ′) g ( x−x ′) dx′= ½+η  (5)
 
     An unknown proximity effect correction irradiation coefficient D p ′(x) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner can be obtained by solving the equation (5). For this, an influence coefficient α′(x) for incident dose is required. 
     In the influence coefficient calculation step (S 113 ), the a′ calculation unit  77  calculates an influence coefficient α′(x), based on the dose D(x) (temporary dose) of the position x which is equivalent to at least one of the pattern edge and the pattern corner. The influence coefficient α′(x) is a function depending on x and the dose D(x). Here, since the GMC has been performed according to the first embodiment, the position x is a position after the GMC. With respect to the pattern edge and the pattern corner where the pattern edge (boundary) is deviated from the pixel boundary, a desired shape of the pattern edge or corner cannot be formed with a design irradiation beam dose thereon. Accordingly, such a point should be irradiated with an increased dose. Moreover, it is also preferable that surrounding pixels (pixel outside pattern) around the position of the pattern edge and the pattern corner are also irradiated by beams. In other words, it is also preferable that pixels around the position of the pattern edge or the pattern corner are irradiated with beams even if the area density of the pixels around the pattern edge or the pattern corner is 0 (zero). The influence coefficient α′(x) can be obtained in advance by experiment, etc. according to the position (edge position, corner position, or internal position) in an evaluation figure pattern and the dose D at that position. 
     In the U′(x) calculation step (S 115 ), the U′ calculation unit  79  calculates, for each proximity mesh region, a proximity effect density U′(x) taking account of the influence coefficient α′(x). The proximity effect density U′(x) can be defined by the following equation (6-1) that convolves a distribution function g(x) with an area density ρ′(x) taking account of an influence coefficient α′(x). The area density ρ′(x) can be defined by the following equation (6-2) using an area density ρ(x) and an influence coefficient α′(x). Since the influence coefficient α′(x) is a function of the position after GMC, when calculating the area density ρ′(x), it is necessary to shift the influence coefficient α′(x) to the position before the GMC. Then, a proximity effect density U′(x) map is generated using the mesh value of each proximity mesh region. The U′(x) map is stored in the storage device  544 .
 
 U ′( x )=∫ρ′( x ′) g ( x−x ′) dx′   (6-1)
 
ρ′( x )=ρ( x )/2α′( x )  (6-2)
 
     In the D p ′(x) calculation step (S 116 ), for correcting a proximity effect by electron beams, the D p ′ calculation unit  80  calculates correction irradiation coefficient terms up to the k-th order term in the case of calculating, by repetition operation, a correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. k indicates one of integers from 1 to n. For example, the correction irradiation coefficient term d 1 ′ of the first order term is calculated. The D p ′ calculation unit  80  is an example of a second correction-irradiation-coefficient-term calculation unit. The correction irradiation coefficient D p ′(x) can be obtained by solving the model equation (5) where an unknown correction irradiation coefficient D p ′(x) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner, and a proximity effect correction coefficient η are used. Here, the dose D(x) is replaced by the correction irradiation coefficient D p ′(x) by defining (using) a standardized dose. 
     In order to obtain an unknown correction irradiation coefficient D p ′(x) from the equation (5), a repetition calculation up to the n-th order term (n is an integer of 1 or more) is usually performed. However, according to the first embodiment, the correction irradiation coefficient term d 1 ′ of the first order term which is affected most by modulation of the dose to write at least one of the pattern edge and the pattern corner is calculated. Therefore, it does not need to calculate the second and subsequent order terms. The correction irradiation coefficient term d 1 ′ of the first order term for the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) is a solution of the first order term in the case of solving the model equation (5) by repetition calculation. Although the proximity effect correction calculation takes time, the calculation time can be greatly reduced by calculating only the first order term. It is most desirable for k to be 1 (k=1), but k is not limited to be 1 and may be 2 or more. However, in the case of setting k to be high order of second order or more, calculation up to the k-th order term is needed. The correction irradiation coefficient term d 1 ′ of the first order term is defined by the following equation (7). 
     
       
         
           
             
               
                 
                   
                     
                       d 
                       1 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       + 
                       η 
                     
                     
                       
                         1 
                         2 
                       
                       + 
                       
                         η 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             U 
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Thus, the correction irradiation coefficient term d 1 ′ of the first order term for the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner can be calculated using a proximity effect density U′(x) which is a convolution value between a distribution function and the area density ρ′(x) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. With respect to the proximity effect density U′(x), the one which has already been calculated can be read from the storage device  544 . The proximity effect density U′(x) is based on the position of the figure pattern before GMC. This is because the correction calculation of a proximity effect should be calculated based on the position on the surface of the target object, and if calculated based on the position after the GMC, since it is shifted from the design position, an error will occur in correction of the proximity effect. Thus, the correction irradiation coefficient term d 1 ′ of the first order term for the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) is calculated using the area density ρ′(x) obtained from pattern data before GMC of the writing data. That is, the area density ρ(x) obtained from the pattern data before GMC is used. 
     In the D p ″(x) calculation step (S 118 ), the D p ″ calculation unit  82  (proximity-effect-correction-irradiation-coefficient calculation unit) calculates a correction irradiation coefficient D p ″(x) (third proximity effect correction irradiation coefficient) where the correction irradiation coefficient terms up to the k-th order term, in the correction irradiation coefficient term of each order term, from the first order term to the n-th order term, for the correction irradiation coefficient D p (x) (first proximity effect correction irradiation coefficient) which does not take account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner are replaced by the correction irradiation coefficient terms up to the k-th order term for the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. Here, the correction irradiation coefficient D p ″(x) (third proximity effect correction irradiation coefficient) is calculated in which, in the correction irradiation coefficient term of each order term, from the first order term to the n-th order term, for the correction irradiation coefficient D p (x) (first proximity effect correction irradiation coefficient) which does not take account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner, the correction irradiation coefficient term d 1  of the first order term is replaced by the correction irradiation coefficient term d 1 ′ of the first order term for the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. The D p ″ calculation unit  82  is an example of a proximity-effect-correction-irradiation-coefficient calculation unit. That is, the correction irradiation coefficient D p ″(x) is defined by the following equation (8).
 
 D   p ″( x )= D   p ( x )− d   1 ( x )+ d   1 ′( x )  (8)
 
     The dose D is needed for calculating an influence coefficient α′(x) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. Therefore, first of all, it is necessary to calculate the dose D as described above. After that, although it is acceptable to calculate, to the high order term, the correction irradiation coefficient D p ′(x) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner by performing a proximity effect correction calculation taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner, the calculation time becomes very long, and therefore, it is difficult to calculate in real time in accordance with the advance of writing processing. Then, according to the first embodiment, calculated is only the correction irradiation coefficient term d 1 ′ of the first order term which is affected most by modulation of the dose to write at least one of the pattern edge and the pattern corner, and then, the correction irradiation coefficient term d 1  of the first order term of the correction irradiation coefficient D p (x) which has already been calculated is replaced by the calculated correction irradiation coefficient term d 1 ′ of the first order term, thereby greatly reducing the calculation time. Moreover, since the correction irradiation coefficient D p ″(x) which has been obtained by this replacement includes the correction irradiation coefficient term d 1 ′ of the first order term which is affected most by modulation of the dose to write at least one of the pattern edge and the pattern corner, it is possible to perform proximity effect correction taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner. 
     As described above, the correction irradiation coefficient term calculated for the correction irradiation coefficient D p ′(x) is not limited to the first order term. In the case of calculating the correction irradiation coefficient term of the second or subsequent order term, in the correction irradiation coefficient terms of from the first order term to the n-th order term for the correction irradiation coefficient D p (x) (first proximity effect correction irradiation coefficient), the correction irradiation coefficient term of a certain order term should be replaced by the correction irradiation coefficient term of the correction irradiation coefficient D p ′(x) whose order term is the same as the certain order term. Although the calculation time becomes longer than that of the case where the correction irradiation coefficient term of the first order term is replaced, the correction residual error of proximity effect correction can be reduced. 
     In the D″(x) calculation step (S 119 ), the D″ calculation unit  72  calculates, for each pattern, a dose D″(x) by multiplying an obtained correction irradiation coefficient D p ″(x) (third proximity effect correction irradiation coefficient) by the reference dose D 0 . 
     In the ρ″ map generation step (S 120 ), the ρ″ map generation unit  65  calculates, for each pixel region of a plurality of mesh regions (pixel regions) obtained by virtually dividing the writing region of the target object  101  or a chip region to be written, an area density ρ″(x) of a pattern arranged in each pixel region, by using a figure pattern for which GMC has been performed and defined in the writing data. For example, first, the writing region of the target object  101  or the chip region to be written is divided into strip-shaped stripe regions by a predetermined width. Then, each stripe region is virtually divided into a plurality of pixel regions. The size of the pixel region is preferably, for example, a beam size, or smaller than the beam size. For example, it is preferable for the size to be about 10 nm. The ρ″ map generation unit  65  assigns, for each stripe region, corresponding figure patterns of a plurality of figure patterns defined in writing data to a pixel region, for example. Then, the area density ρ″(x) of a figure pattern arranged in each pixel region should be calculated. The area density (ρ″) map is generated for each stripe region. 
     In the D′(x) calculation step (S 121 ), the D′ calculation unit  84  calculates a dose for each pixel region. Specifically, the dose D′(x) is calculated by multiplying a dose D″(x) of a figure pattern for which GMC has been performed, an area density ρ″(x) defined in the ρ″ map, and 1/(2α′(x)). Then, a dose D′(x) map is generated using the mesh value of each pixel region. The D′(x) map is stored in the storage device  548 . 
     In the t′(x) calculation step (S 122 ), the t′ calculation unit  85  calculates, for each pixel region, an irradiation time t′(x). The irradiation time t′(x) can be obtained by dividing the dose D′(x) by the current density J. The irradiation time t′(x) having been obtained for each pixel region is defined as shot data, and is temporarily stored in the storage device  542 . 
     In the writing step (S 124 ), the writing control unit  86  controls the writing mechanism  550  through deflection control circuit  530 , and starts writing processing. The writing mechanism  550  writes a pattern on the target object  101 , using the multi-beams  20 , based on the calculated dose D′(x) (irradiation time t′(x)). Specifically, it operates as described below. 
     The electron beam  600  emitted from the electron gun  201  (emitter) almost perpendicularly (e.g., vertically) illuminates the whole of the multi-beam forming member  603  by the illumination lens  502 . A plurality of holes (openings) each being a quadrangle are formed in the multi-beam forming member  603 . The region including all the plurality of holes is irradiated by the electron beam  600 . For example, a plurality of quadrangular electron beams (multi-beams)  20   a  to  20   e  are formed by letting portions of the electron beam  600  which irradiate the positions of a plurality of holes individually pass through a corresponding hole of the plurality of holes of the multi-beam forming member  603 . The multi-beams  20   a  to  20   e  individually pass through a corresponding blanker (first deflector: individual blanking mechanism) of the blanking plate  604 . Each blanker deflects (blanking deflects) the electron beam  20  which is individually passing. 
     The multi-beams  20   a ,  20   b , . . . ,  20   e  having passed through the blanking plate  604  are reduced by the reducing lens  605 , and go toward the hole in the center of the limiting aperture member  606 . At this stage, the electron beam  20  which was deflected by the electrodes  24  and  26  (blanker) of the blanking plate  604  deviates from the hole in the center of the limiting aperture member  606  and is blocked by the limiting aperture member  606 . On the other hand, the electron beam  20  which was not deflected by the electrodes  24  and  26  (blanker) of the blanking plate  604  passes through the hole in the center of the limiting aperture member  606  as shown in  FIG. 1 . Blanking control is performed by ON/OFF of the individual blanking mechanism so as to control ON/OFF of beams. Thus, the limiting aperture member  606  blocks each beam which was deflected to be in a beam OFF state by the individual blanking mechanism. Then, one shot beam is formed by a beam which has been made during a period from becoming a beam ON state to becoming a beam OFF state and has passed through the limiting aperture member  606 . The multi-beams  20  having passed through the limiting aperture member  606  are focused by the objective lens  607  in order to be a pattern image of a desired reduction ratio, and respective beams (the entire multi-beams  20 ) having passed through the limiting aperture member  606  are collectively deflected in the same direction by the deflector  608  in order that respective beam irradiation positions on the target object  101  may be irradiated. While the XY stage  505  is continuously moving, controlling is performed by the deflector  608  so that irradiation positions of beams may follow (track) the movement of the XY stage  505 , for example. The position of the XY stage  505  is measured by way of radiating a laser from the stage position detector  539  to the mirror  610  on the XY stage  505  and using its catoptric light. The multi-beams  20  irradiating at the same time are ideally aligned at pitches obtained by multiplying the arrangement pitch of a plurality of holes of the aperture member  603  by a desired reduction ratio described above. The writing apparatus  500  performs a writing operation by the raster scan method which sequentially irradiates shot beams, and when writing a desired pattern, a beam required according to a pattern is controlled to be ON by blanking control. 
     As described above, the writing region of the target object  101  is virtually divided into a plurality of strip-shaped stripe regions each having a predetermined width in the y direction, for example. Each of the stripe regions serves as a unit region for writing. The XY stage  505  is moved to make an adjustment such that an irradiation region which can be irradiated by one irradiation of the multi-beams  20  is located at the left end of the first stripe region or at a position more left than the left end, and then writing is started. When writing the first stripe region, the writing advances relatively in the x direction by moving the XY stage  505  in the −x direction, for example. The XY stage  505  is continuously moved at a predetermined speed, for example. After writing the first stripe region, the stage position is moved in the −y direction to make an adjustment such that the irradiation region is located at the right end of the second stripe region or at a position more right than the right end to be relatively located in the y direction. Then, similarly, writing advances in the −x direction by moving the XY stage  505  in the x direction, for example. That is, writing is performed while alternately changing the direction, such as performing writing in the x direction in the third stripe region, and in the −x direction in the fourth stripe region, and thus, the writing time can be reduced. However, the writing operation is not limited to the case of performing writing while alternately changing the direction, and it is also acceptable to perform writing in the same direction when writing each stripe region. By one shot, a plurality of shot patterns of the same number as the number of the holes  22  are formed at a time by multi-beams which have been formed by passing through respective corresponding holes  22  of the multi-beam forming member  603 . 
       FIG. 5  shows an example of an evaluation pattern for evaluating an effect of the first embodiment. In  FIG. 5 , the half (60 μm wide) of the evaluation pattern (120 μm wide) serves as a 1:1 line and space pattern (line width of 0.1 μm) whose area density is 50%. The other half (60 μm wide) is a so-called solid pattern whose area density is 100%. The evaluation pattern is written under different conditions. 
       FIGS. 6A and 6B  show examples of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions of comparative examples 1 and 2 of the first embodiment.  FIG. 7  shows an example of the result of dimensional deviation in the case of writing an evaluation pattern according to the first embodiment. In  FIGS. 6A and 6B  and  FIG. 7 , the ordinate axis denotes a dimensional deviation amount ΔCD and the abscissa axis denotes the position x of an evaluation pattern.  FIG. 6A  shows the result of dimensional deviation in the case of writing an evaluation pattern in multi-beam writing without re-executing proximity effect correction calculation after modulation of the dose to write at least one of the pattern edge and the pattern corner.  FIG. 6B  shows the case, in multi-beam writing, where the proximity effect density U′(x) is calculated based on the position of a figure pattern for which GMC has been performed, in re-executing proximity effect correction calculation after modulation of the dose to write at least one of the pattern edge and the pattern corner. It turns out that, as shown in  FIG. 6A , the deviation amount (ΔCD) of the line width critical dimension (CD) of a pattern to be written is large when proximity effect correction calculation is not re-executed after modulation of the dose to write at least one of the pattern edge and the pattern corner. As shown in  FIG. 6B , even when proximity effect correction calculation is re-executed after modulation of the dose to write at least one of the pattern edge and the pattern corner, ΔCD is still large when correction calculation is executed based on the position of the figure pattern for which GMC has been performed, although ΔCD has been improved compared to the case where proximity effect correction calculation is not re-executed. 
     By contrast, according to the first embodiment, the correction irradiation coefficient D p ″(x) is obtained by calculating only the correction irradiation coefficient term d 1 ′ of the first order term for calculating an unknown correction irradiation coefficient D p ′(x), and replacing the correction irradiation coefficient term d 1  of the first order term of the correction irradiation coefficient D p (x), which has already been obtained, by the correction irradiation coefficient term d 1 ′ of the first order term (PEC mode 2 case). The graph B in  FIG. 7  shows the result of the first embodiment. The graph A in  FIG. 7  shows the result of calculating the correction irradiation coefficient D p ′(x) by performing repetition calculation from the first order term to the n-th order term (n is an integer of 1 or more) and adding each correction irradiation coefficient term from the first order term to the n-th order term in order to obtain an unknown correction irradiation coefficient D p ′(x) (PEC mode 1 case). The graph C in  FIG. 7  shows the result of calculating the correction irradiation coefficient D p ″(x) by using the area density ρ′(x) which is not to be convolved, as will be described later, when calculating only the correction irradiation coefficient term d 1 ′ of the first order term in order to obtain an unknown correction irradiation coefficient D p ′(x) (PEC mode 3 case). With respect to the dimensional deviation amount ΔCD at each position x, there is no great difference between the results of the graphs B and C and the result of the graph A. That is, it turns out that correction has been performed successfully. 
     As described above, according to the first embodiment, even in writing processing of a multi-beam system, it is possible to greatly reduce the operation time so that the correction calculation speed may not be slower than the writing speed. Furthermore, it is possible to efficiently suppress pattern dimensional variation due to modulation of the dose to write at least one of the pattern edge and the pattern corner while suppressing correction residual error of proximity effect. Thus, it is possible to efficiently suppress pattern dimensional variation due to various effects while suppressing correction residual error of proximity effect. Therefore, pattern writing can be performed with high dimension accuracy. 
     Although GMC (grid matching correction) is performed in the examples described above, it is not limited thereto. The case without performing GMC is acceptable. 
     Second Embodiment 
     According to the first embodiment, when calculating the correction irradiation coefficient term d 1 ′ of the first order term for obtaining a correction irradiation coefficient D p ′(x) taking account of the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner, a proximity effect density U(x) obtained by convolving the area density ρ with the distribution function g is used, but it is not limited thereto. According to the second embodiment, calculation different from that of the first embodiment will be described. In the second embodiment, the configuration of the writing apparatus is the same as that of  FIG. 1 . The flowchart of the writing method is the same as that of  FIG. 4 . The contents of the second embodiment are the same as those of the first embodiment except for what is specifically described below. 
     The only difference between the first and second embodiments is the equation for calculating the correction irradiation coefficient term d 1 ′ of the first order term in the case of obtaining, by repetition calculation, the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of influence of modulation of the dose to write at least one of the pattern edge and pattern corner described in the D p ′(x) calculation step (S 116 ). The correction irradiation coefficient term d 1 ′ of the first order term according to the second embodiment is defined by the following equation (9). 
     
       
         
           
             
               
                 
                   
                     
                       d 
                       1 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       + 
                       η 
                     
                     
                       
                         1 
                         2 
                       
                       + 
                       
                         η 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ρ 
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     As shown in the equation (9), the correction irradiation coefficient term d 1 ′ of the first order term for the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of influence of modulation of the dose to write at least one of the pattern edge and pattern corner is calculated using the area density without convolution. In other words, the area density ρ′(x) is used instead of the proximity effect density U′(x). By performing this calculation, the influence of modulation of the dose to write at least one of the pattern edge and the pattern corner can be taken into account. 
     The graph C of  FIG. 7  described above shows an example of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions according to the second embodiment. With respect to the equation (7) described above, in the second embodiment, when calculating only the correction irradiation coefficient term d 1 ′ of the first order term in order to obtain an unknown correction irradiation coefficient D p ′(x), the area density ρ′(x) which is not to be convolved is used instead of the proximity effect density U′(x). The others are the same as those of the first embodiment (PEC mode 2). Then, based on these contents, the correction irradiation coefficient D p ″(x) is calculated (PEC mode 3).  FIG. 7  shows the result of dimensional deviation in the case of writing an evaluation pattern based on the dose calculated by using the correction irradiation coefficient D p ″(x) of the second embodiment. In the second embodiment, when the graph C of  FIG. 7  is compared with the graphs A and B of  FIG. 7 , the accuracy degrades at the position where a line and space pattern and a solid pattern are connected with each other and the position near the end of the evaluation pattern, but, there is no great difference with respect to the dimensional deviation amount ΔCD at each position x in the central part of the line and space pattern and central part of the solid pattern. That is, it turns out that correction has been performed successfully. 
     As described above, according to the second embodiment, it is possible to obtain effects almost equivalent to those of the first embodiment. Furthermore, correction calculation can be simplified more than that of the first embodiment. 
     Although GMC (grid matching correction) is performed in the examples described above, it is not limited thereto. The case without performing GMC is acceptable. 
     Third Embodiment 
     In the first and second embodiments, there has been described a multi-beam writing apparatus. However, correction residual error of proximity effect correction generated by dimensional variation due to various effects, namely residual error of proximity effect correction due to various effects, is not limited to multi-beam writing. It is also generated in a single beam system, such as a raster beam writing system and a variable shaped beam writing system (VSB writing system). For example, when modulating the dose in order to improve the resolution of a small-sized pattern, or when modulating the dose in order to correct an EUV short range proximity effect, residual error of proximity effect correction is also generated in a single beam system as well as multi-beam system. In the third embodiment, there will be described a configuration where suppressed is correction residual error of proximity effect correction, which is generated due to modulation of the dose in order to improve resolution of a small-sized pattern in the variable shaped beam writing apparatus. 
       FIG. 8  is a schematic diagram showing a configuration of a writing apparatus according to the third embodiment. In  FIG. 8 , a writing apparatus  100  includes a writing mechanism  150  and a control unit  160 . The writing apparatus  100  is an example of a charged particle beam writing apparatus, and particularly, an example of a variable shaped beam (VSB) writing apparatus. The writing mechanism  150  includes an electron optical column  102  and a writing chamber  103 . In the electron optical column  102 , there are arranged an electron gun  201 , an illumination lens  202 , a blanking deflector (blanker)  212 , a blanking aperture  214 , a first shaping aperture plate  203 , a projection lens  204 , a deflector  205 , a second shaping aperture plate  206 , an objective lens  207 , a main deflector  208  and a sub deflector  209 . In the writing chamber  103 , there is arranged an XY stage  105  that is movable at least in the x-y direction. On the XY stage  105 , there are placed a mirror  210  for measuring the stage position, and a target object  101  (substrate) serving as a writing target on which resist has been applied. The target object  101  is an exposure mask, a silicon wafer, and the like used for manufacturing semiconductor devices. The mask may be, for example, a mask blank. 
     The control unit  160  includes a control computer unit  110 , a memory  112 , a deflection control circuit  120 , a DAC (digital-analog converter) amplifier units  130 ,  132 , and  134  (deflection amplifiers), a stage position detector  139 , and storage devices  140 ,  142 ,  144 ,  146 ,  148 , and  149  such as magnetic disk drives. The control computer unit  110 , the memory  112 , the deflection control circuit  120 , the stage position detector  139 , and the storage devices  140 ,  142 ,  144 ,  146 ,  148 , and  149  are connected with each other through a bus (not shown). The deflection control circuit  120  is connected to the DAC amplifier units  130 ,  132  and  134 . The DAC amplifier unit  130  is connected to the blanking deflector  212 . The DAC amplifier unit  132  is connected to the sub deflector  209 . The DAC amplifier unit  134  is connected to the main deflector  208 . 
     In the control computer unit  110 , there are arranged a dividing-into-subfield (SF) meshes unit  60 , the dividing-into-proximity-meshes unit  62 , the grid matching correction (GMC) unit  63 , a dividing-into-shot-figures unit  64 , the area density (ρ) calculation unit  66 , the proximity effect density (U) calculation unit  68 , the irradiation correction coefficient (D p ) calculation unit  70 , the dose (D) calculation unit  71 , the influence coefficient (α′) calculation unit  77 , the U′ calculation unit  79 , the irradiation correction coefficient (D p ′) calculation unit  80 , the irradiation correction coefficient (D p ″) calculation unit  82 , the dose (D′) calculation unit  84 , the irradiation time (t′) calculation unit  85 , and the writing control unit  86 . Each of the “units” such as the dividing-into-SF meshes unit  60 , the dividing-into-proximity-meshes unit  62 , the GMC) unit  63 , the dividing-into-shot-figures unit  64 , the ρ calculation unit  66 , the U calculation unit  68 , the D p  calculation unit  70 , the D calculation unit  71 , the influence coefficient (α′) calculation unit  77 , the U′ calculation unit  79 , the D p ′ calculation unit  80 , the D p ″ calculation unit  82 , the D′ calculation unit  84 , the t′ calculation unit  85 , and the writing control unit  86  includes a processing circuitry. As the processing circuitry, for example, an electric circuit, a computer, a processor, a circuit board, a quantum circuit, or a semiconductor device may be used. Each of the “units” may use a common processing circuitry (same processing circuitry), or different processing circuitries (separate processing circuitries). Input data required in the control computer unit  110 , and calculated results are stored in the memory  112  each time. It is preferable that computers such as a plurality of CPUs or a plurality of GPUs are arranged for the “-unit” requiring a large amount of calculation. 
     Writing data is input from the outside of the writing apparatus  100 , and stored in the storage device  140 . GMC data is input from the outside of the writing apparatus  100 , and stored in the storage device  149 . 
       FIG. 8  shows a configuration necessary for explaining the third embodiment. Other configuration elements generally necessary for the writing apparatus  100  may also be included. 
       FIG. 9  is a conceptual diagram for explaining each region according to the third embodiment. In  FIG. 9 , a writing region  10  of the target object  101  is virtually divided into a plurality of stripe regions  20  arrayed, for example, along the y direction, each being in a strip shape and each having a width deflectable by the main deflector  208 . Further, each of the stripe regions  20  is virtually divided into a plurality of mesh-like subfields (SFs)  30  (small regions) each having a size deflectable by the sub deflector  209 . A shot figure is written at a corresponding shot position  42  in each SF  30 . Although, in the example of  FIG. 9 , the SF  30  is the minimum deflection region, it is not limited thereto. For example, each SF may be further divided virtually into a plurality of small mesh-like under subfields (TF: Tertiary Field). In that case, a sub-sub deflector should be further arranged as the third stage deflector in addition to the two-stage deflector composed of the main deflector and the sub deflector. 
     A digital signal for blanking control is output from the deflection control circuit  120  to the DAC amplifier unit  130 . Then, in the DAC amplifier unit  130 , the digital signal is converted to an analog signal and amplified to be applied as a deflection voltage to the blanking deflector  212 . The electron beam  200  is deflected by this deflection voltage, and thereby a beam of each shot is formed. 
     A digital signal for main deflection control is output from the control circuit  120  to the DAC amplifier  134 . Then, in the DAC amplifier  134 , the digital signal is converted to an analog signal and amplified to be applied as a deflection voltage to the main deflector  208 . The electron beam  200  is deflected by this deflection voltage, and thereby each beam shot is deflected to a reference position in a predetermined subfield (SF) in the virtually divided mesh like SFs. 
     A digital signal for sub deflection control is output from the control circuit  120  to the DAC amplifier  132 . Then, in the DAC amplifier  132 , the digital signal is converted to an analog signal and amplified to be applied as a deflection voltage to the sub deflector  209 . The electron beam  200  is deflected by the deflection voltage, and the beam of each shot is deflected to each shot position in a predetermined mesh-like subfield (SF) obtained by virtual division into meshes. 
     The writing apparatus  100  performs writing processing for each stripe region  20  by using a multiple stage deflector. Here, as an example, a two-stage deflector composed of the main deflector  208  and the sub deflector  209  is used. While the XY stage  105  is continuously moving in the −x direction, for example, writing is performed in the x direction in the first stripe region  20 . After the writing has been finished in the first stripe region  20 , writing is carried out in the same direction or in the opposite direction in the second stripe region  20 . Then, in the same way, writing is performed in the third and subsequent stripe regions  20 . The main deflector  208  (first deflector) sequentially deflects the electron beam  200  to a reference position A of the SF  30  such that the movement of the XY stage  105  is followed. The sub deflector  209  (second deflector) deflects the electron beam  200  from the reference position A of each SF  30  to each shot position  42  of an irradiating beam in the SF  30  concerned. Thus, the sizes of the deflection regions of the main deflector  208  and the sub deflector  209  are different from each other. 
       FIG. 10  is a flowchart showing main steps of a writing method according to the third embodiment. As shown in  FIG. 10 , the writing method of the third embodiment executes a series of steps of the ρ(x) calculation step (S 104 ), the U(x) calculation step (S 106 ), the D p (x) calculation step (S 108 ), the D(x) calculation step (S 110 ), the GMC step (S 111 ), a dividing-into-shot-figures step (S 112 ), the influence coefficient calculation step (S 113 ), the U′(x) calculation step (S 115 ), the D p ′(x) calculation step (S 116 ), the D p ″(x) calculation step (S 118 ), the D′(x) calculation step (S 121 ), the t′(x) calculation step (S 122 ) and the writing step (S 124 ). 
     First, the dividing-into-SF meshes unit  60  (first dividing-into-meshes unit) virtually divides the writing region of the target object  101  into a plurality of mesh-like SFs  30  (first mesh region) by the size Δ 1  (first mesh size) which can be deflected by the sub deflector  209 . Here, the stripe region  20  is divided into a plurality of mesh-like SFs  30 . 
     Then, the dividing-into-proximity-meshes unit  62  (second dividing-into-meshes unit) virtually dividing the writing region of the target object  101  into a plurality of proximity meshes (second mesh region) by the size Δ 2  (second mesh size) for correcting a proximity effect. With respect to the proximity mesh, it is preferable to perform dividing by the size about 1/10 of the influence radius of the proximity effect, such as about 0.5 to 2 μm. 
     The contents of each of the steps from the ρ(x) calculation step (S 104 ) to the GMC step (S 111 ) are the same as those of the first embodiment or the second embodiment. However, the storage device  540  should be read as the storage device  140 . The storage device  544  should be read as the storage device  144 . The mirror  610  should be read as the mirror  210 . The storage device  549  should be read as the storage device  149 . 
     In the dividing-into-shot-figures step (S 112 ), the dividing-into-shot-figures unit  64  performs, for writing data which has been GMC corrected, data conversion processing of a plurality of steps so as to generate apparatus-specific shot data for the writing apparatus  100 . The file structure of the writing data is formed, for example, for each frame region obtained by virtually dividing the chip region of a writing target chip into strip-like regions. The dividing-into-shot-figures unit  64  reads the data file for each frame region in sequence to generate shot data. It is preferable that each frame region is corresponding to each stripe region serving as a writing unit region. However, it is not limited thereto. For example, it is also preferable to obtain regions by dividing the stripe region. Moreover, although a plurality of figure patterns are arranged in a chip, the size which can be formed by one beam shot is restricted in the writing apparatus  100 . Therefore, each figure pattern is divided, in the data conversion processing, into shot figures each having a size that can be irradiated by one beam shot. A figure type, figure size, position, and the like of each shot figure are generated as shot data. The shot data is stored in sequence in the storage device  142 . 
     Next, performed is proximity effect correction calculation taking account of influence of modulation of the dose to improve the resolution of a small-sized pattern. Similarly to the first embodiment, a model is used in which the term obtained by multiplying the incident dose by the influence coefficient α′(x) (an example of an influence coefficient) and the term of back scattering dose are used. 
     The contents of the influence coefficient calculation step (S 113 ), the U′(x) calculation step (S 115 ), and the D p ′(x) calculation step (S 116 ) are the same as those of the first embodiment. However, the storage device  544  should be read as the storage device  144 . Moreover, according to the third embodiment, since the influence coefficient α′(x) is not affected by GMC, the influence coefficient α′(x) is calculated at the position before GMC. 
     By the step described above, the correction irradiation coefficient term d 1 ′ of the first order term for the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of the influence of modulation of the dose to improve the resolution of a small-sized pattern is calculated using the proximity effect density U′(x) which is a convolution value between a distribution function and the area density ρ′(x) taking account of the influence of modulation of the dose to improve the resolution of a small-sized pattern. With respect to the proximity effect density U′(x), the one which has already been calculated can be read from the storage device  144 . The proximity effect density U′(x) is based on the position of the figure pattern before GMC. This is because the correction calculation of a proximity effect should be calculated based on the position on the surface of the target object, and if calculated based on the position after the GMC, since it is shifted from the design position, an error will occur in correction of the proximity effect. Thus, the correction irradiation coefficient term d 1 ′ of the first order term for the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) is calculated using the area density ρ′(x) obtained from pattern data before GMC of the writing data. That is, the area density ρ(x) obtained from pattern data before GMC is used. 
     The contents of the D p ″(x) calculation step (S 118 ) are the same as those of the first embodiment. In the third embodiment, similarly to the first embodiment, calculated is only the correction irradiation coefficient term d 1 ′ of the first order term which is affected most by modulation of the dose to improve the resolution of a small-sized pattern, and then, the correction irradiation coefficient term d 1  of the first order term of the correction irradiation coefficient D p (x) which has already been calculated is replaced by the calculated correction irradiation coefficient term d 1 ′ of the first order term, thereby greatly reducing the calculation time. Moreover, since the correction irradiation coefficient D p ″(x) which has been obtained by this replacement includes the correction irradiation coefficient term d 1 ′ of the first order term which is affected most by modulation of the dose to improve the resolution of a small-sized pattern, it is possible to perform proximity effect correction taking account of the influence of modulation of the dose to improve the resolution of a small-sized pattern. 
     As described above, the correction irradiation coefficient term calculated for the correction irradiation coefficient D p ′(x) is not limited to the first order term. In the case of calculating the correction irradiation coefficient term of the second or subsequent order term, in the correction irradiation coefficient terms of from the first order term to the n-th order term for the correction irradiation coefficient D p (x) (first proximity effect correction irradiation coefficient), the correction irradiation coefficient term of a certain order term should be replaced by the correction irradiation coefficient term of the correction irradiation coefficient D p ′(x) whose order term is the same as the certain order term. Although the calculation time becomes longer than that of the case where the correction irradiation coefficient term of the first order term is replaced, the correction residual error of proximity effect correction can be reduced. 
     In the D′(x) calculation step (S 121 ), the D′ calculation unit  84  calculates, for each shot figure for which GMC has been performed, a dose by using the correction irradiation coefficient D p ″(x) (third proximity effect correction irradiation coefficient). Specifically, a dose D′(x) is calculated by multiplying the obtained correction irradiation coefficient D p ″(x) by a reference dose D 0  and 1/(2α′(x)). 
     In the t′(x) calculation step (S 122 ), the t′ calculation unit  85  calculates, for each shot figure, an irradiation time t′(x). The irradiation time t′(x) can be obtained by dividing the dose D′(x) by the current density J. The obtained irradiation time t′(x) is additionally defined in the shot data, for each shot figure. 
     In the writing step (S 124 ), the writing control unit  86  controls the writing mechanism  150  through deflection control circuit  120 , etc., and starts writing processing. The writing mechanism  150  writes a pattern on the target object  101 , using the electron beam  200 , based on the calculated dose D′(x) (irradiation time t′(x)). Specifically, it operates as described below. The deflection control circuit  120  acquires an irradiation time from the shot data stored in the storage device  142 . Then, the deflection control circuit  120  outputs a digital signal which controls the irradiation time of each shot to the DAC amplifier unit  130 . The DAC amplifier unit  130  converts the digital signal to an analog signal and amplifies it to be applied as a deflection voltage to the blanking deflector  212 . 
     With respect to the electron beam  200  emitted from the electron gun  201  (emitter), when passing through the blanking deflector  212 , it is controlled to pass through the blanking aperture plate  214  by the blanking deflector  212  when in the beam ON state, and the whole of it is deflected to be blocked by the blanking aperture plate  214  when in the beam OFF state. The electron beam  200  that has passed through the blanking aperture plate  214  during the period from the time of changing from a beam OFF state to a beam ON state to the time of again changing to a beam OFF state serves as one shot of the electron beam. The blanking deflector  212  controls the direction of the passing electron beam  200  to alternately generate a beam ON state and a beam OFF state. For example, when in a beam ON state, no voltage is applied to the blanking deflector  212 , and, when in a beam OFF state, a voltage should be applied to it. The dose per shot of the electron beam  200  to irradiate the target object  101  is adjusted depending upon an irradiation time of each shot. 
     As described above, each shot of the electron beam  200 , generated by passing through the blanking deflector  212  and the blanking aperture plate  214 , irradiates the whole of the first shaping aperture plate  203  which has a quadrangular opening by the illumination lens  202 . At this stage, the electron beam  200  is first shaped to a quadrangle. Then, after passing through the first shaping aperture plate  203 , the electron beam  200  of the first aperture image is projected onto the second shaping aperture plate  206  by the projection lens  204 . The first aperture image on the second shaping aperture plate  206  is deflection-controlled by the deflector  205  so as to change (variably shape) the shape and size of the beam. Such variable beam shaping is performed for each shot, and, generally, each shot is shaped to have a different shape and size. Then, after passing through the second shaping aperture plate  206 , the electron beam  200  of the second aperture image is focused by the objective lens  207 , and deflected by the main deflector  208  and the sub deflector  209  to reach a desired position on the target object  101  placed on the XY stage  105  which moves continuously. As described above, a plurality of shots of the electron beam  200  are deflected in order, by each deflector, onto the target object  101  serving as a substrate. 
       FIG. 11  shows an example of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions of the comparative example of the third embodiment.  FIG. 12  shows an example of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions according to the third embodiment. In  FIGS. 11 and 12 , the ordinate axis denotes a dimensional deviation amount ΔCD and the abscissa axis denotes the position x of an evaluation pattern. 
     In the comparative example of the third embodiment, with respect to the equation (10) described above, the correction irradiation coefficient D p ′(x) is calculated by performing repetition calculation from the first order term to the n-th order term (n is an integer of 1 or more) and adding each correction irradiation coefficient term from the first order term to the n-th order term in order to obtain an unknown correction irradiation coefficient D p ′(x) (PEC mode 1 case).  FIG. 11  shows the result of dimensional deviation in the case of writing an evaluation pattern based on the dose calculated by using the correction irradiation coefficient D p ′(x). 
     By contrast, according to the third embodiment, with respect to the equation (10) described above, the correction irradiation coefficient D p ″(x) is obtained by calculating only the correction irradiation coefficient term of the first order term for calculating an unknown correction irradiation coefficient D p ′(x), and replacing the correction irradiation coefficient term d 1  of the first order term of the correction irradiation coefficient D p (x), which has already been obtained, by the correction irradiation coefficient term d 1 ′ of the first order term (PEC mode 2 case).  FIG. 12  shows the result of dimensional deviation in the case of writing an evaluation pattern based on the dose calculated by using the correction irradiation coefficient D p ″(x) of the third embodiment. When comparing  FIG. 11  with  FIG. 12 , since there is no great difference in dimensional deviation amount ΔCD at each position x, it turns out that correction has been performed successfully. 
     As described above, according to the third embodiment, it is possible to greatly reduce the operation time so that the correction calculation speed may not be slower than the writing speed. Furthermore, it is possible to efficiently improve the resolution of a small-sized pattern while suppressing correction residual error of proximity effect. Therefore, pattern writing can be performed with high dimension accuracy. 
     Although GMC (grid matching correction) is performed in the examples described above, it is not limited thereto. The case without performing GMC is acceptable. 
     In the example described above, when calculating the correction irradiation coefficient term d 1 ′ of the first order term for obtaining the correction irradiation coefficient D p ′(x) taking account of various effects, the proximity effect density U(x) obtained by convolving the area density ρ with the distribution function g is used, but it is not limited thereto. Similarly to the second embodiment, it is also preferable to perform calculation using the area density without convolution. 
       FIG. 13  shows an example of the result of dimensional deviation in the case of writing an evaluation pattern under the conditions according to the third embodiment. The evaluation pattern is the same as that of  FIG. 5 . In  FIG. 13 , the ordinate axis denotes a dimensional deviation amount ΔCD and the abscissa axis denotes the position x of an evaluation pattern. According to the third embodiment, when calculating only the correction irradiation coefficient term d 1 ′ of the first order term for obtaining an unknown correction irradiation coefficient D p ′(x), the area density ρ(x) obtained without convolution is used. The others are the same as those of the second embodiment (PEC mode 2). Then, based on these contents, the correction irradiation coefficient D p ″(x) is obtained (PEC mode 3).  FIG. 13  shows the result of dimensional deviation in the case of writing an evaluation pattern based on the dose calculated by using the correction irradiation coefficient D p ″(x) of the third embodiment. When comparing  FIG. 13  with  FIGS. 11 and 12 , the accuracy degrades at the position where a line and space pattern and a solid pattern are connected with each other and the position near the end of the evaluation pattern, but, there is no great difference with respect to the dimensional deviation amount ΔCD at each position x in the central part of the line and space pattern and central part of the solid pattern. That is, it turns out that correction has been performed successfully. 
     Moreover, in the third embodiment, although the correction irradiation coefficient term d 1 ′ of the first order term of the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of various effects is calculated, it is not limited thereto. What is necessary is just to calculate correction irradiation coefficient terms up to the k-th order term of the correction irradiation coefficient D p ′(x) (second proximity effect correction irradiation coefficient) taking account of various effects. k denotes one of integers from 1 to n. As described above in the first embodiment, it is most preferable that k=1, but k is not limited to 1 and may be 2 or more. However, in the case of setting k to be high order of second order or more, calculation up to the k-th order term is needed. 
     Embodiments have been explained referring to specific examples described above. However, the present invention is not limited to these specific examples. For example, although the first embodiment describes the case of using multi-beams, the contents of the first embodiment can be similarly applied to a writing apparatus employing the raster method and using a single beam. Moreover, although, as various effects, dose modulation due to pattern edge/corner correction and dose modulation for improvement of the resolution of a small-sized pattern are described, they are not limited thereto. For example, there is included dose modulation for correcting an effect resulting from dimensional variation other than proximity effect, such as resist heating correction. Furthermore, although, as a method of calculating a correction irradiation coefficient, the area density of a figure pattern is used, it is not limited thereto. For example, the correction irradiation coefficient may be calculated using a dose density obtained by multiplying the area density by the dose weight. 
     While the apparatus configuration, control method, and the like not directly necessary for explaining the present invention are not described, some or all of them can be selectively used case-by-case basis. For example, although description of the configuration of the control unit for controlling the writing apparatus  100  is omitted, it should be understood that some or all of the configuration of the control unit can be selected and used appropriately when necessary. 
     In addition, any other charged particle beam writing apparatus and method that include elements of the present invention and that can be appropriately modified by those skilled in the art, and acquisition method of a dose modulation coefficient of a charged particle beam are included within the scope of the present invention. 
     Additional advantages and modification will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.