Abstract:
A semiconductor device geometrical pattern correction process, semiconductor device manufacturing process and geometrical pattern extraction process are provided, which make it possible to eliminate the adverse effect of corner rounding accompanying miniaturization, that is, a decrease in the projection amount of a gate, while avoiding increased chip area. The correction process comprises a step  102  of detecting a concave diffusion layer corresponding portion and a step  103  of correcting either the concave diffusion layer corresponding portion or a transistor gate corresponding portion which projects from the concave diffusion layer corresponding portion in order to ensure the projection of the gate from the concave diffusion layer corresponding portion against possible corner rounding.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a semiconductor device geometrical pattern correction process for making advance changes, in a mask geometrical pattern for use in the manufacture of semiconductor devices or the like in order to obtain a transferred image that is close to a desired design pattern. The invention also relates to a semiconductor device manufacturing process and a geometrical pattern extraction process adapted for use in the above correction process. 
     2. Prior Art 
     Current techniques for manufacturing semiconductor devices and the like essentially require a photographic step in which a mask geometrical pattern for semiconductor devices is transferred to a resist material on a semiconductor substrate by use of an exposure light source. 
     In recent years, miniaturization in semiconductor device manufacturing processes is advancing at a pace faster than that of reduction in the wavelengths of exposure light sources. This has brought about a strong need for a photographic step in which transferring is carried out with a pattern having a size equivalent to or less than the wavelength of an exposure light source. As a result, there often arises the problem of the difference between a geometrical pattern obtained after transferring and its associated mask geometrical pattern initially designed. 
     One of the causes of such a difference in pattern is “corner rounding” which causes, after transferring, depressions in irregular geometry designed as a mask geometrical pattern. If a depression occurs in a convex gate portion of a transistor or in a concave diffusion layer portion which receives the projection of a gate, a desired amount of projection of the gate from the diffusion layer can be no longer ensured. This leads to electrical continuity between the source and drain of the transistor, resulting in increases in the current of the power source and even a failure in operation in the worst case, where a semiconductor device formed from such a pattern is used. As a matter of course, it is necessary to devise a measure to prevent such problematic depressions in semiconductor devices. 
     With reference to the accompanying drawings, there will be explained one attempt that has been previously made to eliminate the adverse effect of corner rounding on the projection amount of a gate. 
     FIGS. 21 and 22 show one example in which no measure is taken to ensure a satisfactory gate projection amount. 
     In the mask geometrical pattern shown in FIG. 21, a transistor gate  511  projects from a diffusion layer  513 . In this pattern, a measure to compensate for a decrease in the projection amount of the gate is not taken, and therefore another pattern  512  can be made. However, the gate of the mask geometrical pattern shown in FIG. 22 obtained after transferring stands back because of corner rounding so that the source and drain of the diffusion layer are short-circuited. 
     FIGS. 23 and 24 show one example of conventional techniques for preventing a decrease in the projection amount of a gate. 
     According to the conventional technique depicted in FIG. 23, a portion which is likely to decrease in projection amount after transferring because of corner rounding is detected at the stage of designing a mask geometrical pattern and the mask geometrical pattern is modified to compensate for possible decreases. Therefore, the mask geometrical pattern obtained after transferring has an appropriate gate projection amount in spite of a depression in the gate atributable owing to corner rounding. 
     The above conventional technique, however, reveals the problem that since the projection amount of the gate in the mask geometrical pattern is increased, there is no space to accommodate another pattern  512  because of the occupation of the increased gate portion. More specifically, the mask geometrical pattern shown in FIG. 23 which has been modified to compensate for a decrease in gate projection amount does not have a space for the placement of the pattern  512 , while the mask geometrical pattern shown in FIG. 21 which has not undergone such modification can include the pattern  512 . This is a disadvantage to the conventional technique in view of effective space utilization and reduction in chip area. 
     The area of chips is the most critical factor in determining the cost of chips as well as in developing economically competitive chips. 
     The present invention is directed to overcoming the above problems presented by the prior art and one of the objects of the invention is therefore to provide a semiconductor device geometrical pattern correction process, semiconductor device manufacturing process and geometrical pattern extraction process, which are capable of compensating for a decrease in the projection amount of a gate due to corner rounding which accompanies miniaturization, while avoiding increased chip area. 
     SUMMARY OF THE INVENTION 
     According to the invention, there is provided a semiconductor device geometrical pattern correction process comprising the steps of: 
     detecting a concave diffusion layer corresponding portion; and 
     correcting at least either the concave diffusion layer corresponding portion or a transistor gate corresponding portion which projects from the concave diffusion layer corresponding portion in order to ensure the projection of a gate from the concave diffusion layer corresponding portion against possible corner rounding. 
     The semiconductor device geometrical pattern correction process of the invention is arranged such that, with a view to compensating for a decrease in the projection amount of a gate owing to corner rounding, modification of the diffusion layer by reduction or modification of the transistor gate by enlargement is made in the transistor gate corresponding portion which projects from the concave diffusion layer corresponding portion on the semiconductor device mask geometrical pattern, so that gate depression with a decreased projection amount owing to corner rounding induced after the photographic step can be compensated. 
     In accomplishing the above primary object, the invention does not cause increased chip area, which is a problem presented by conventional techniques, so that the invention can thus contribute to the development of competitive chips. In addition, since the measure is focused on the compensation for a decrease in the projection amount of the gate, the amount of data that accompany the measure can be minimized and mask fabrication problems can be eliminated. 
     In the above arrangement, the step of correcting the concave diffusion layer corresponding portion is designed to make correction by reduction of the base of the concave portion and may include the step of performing geometrical pattern logical operation. 
     The step of correcting the concave diffusion layer corresponding portion is designed to make correction by reduction of the base of the concave portion and reduction of regions of sides which respectively contact the base in the concave portion, the regions being in the vicinity of the ends of the base. This step may include the steps of correcting a geometrical pattern and performing geometrical pattern logical operation. 
     The step of correcting the transistor gate projecting from the concave diffusion layer corresponding portion is designed to make correction by enlargement of regions of sides which respectively contact an end line in the transistor gate, the regions being positioned in the vicinity of both ends of the end line. This step may include the steps of measuring the difference between two geometrical patterns, correcting a geometrical pattern and performing geometrical pattern logical operation. 
     The step of correcting a transistor gate corresponding portion projecting from the concave diffusion layer corresponding portion is designed to make correction by enlargement of an end line of the transistor gate corresponding portion and enlargement of regions of sides which respectively contact the end line in the transistor gate corresponding portion, the regions being positioned in the vicinity of both ends of the end line. This step may include the steps of measuring the difference between two geometrical patterns, moving the sides of a geometrical pattern, correcting a geometrical pattern and performing geometrical pattern logical operation. 
     The step of correcting the concave diffusion layer corresponding portion may include the steps of moving the sides of a geometrical pattern, correcting a geometrical pattern, performing logical operation on the geometrical pattern obtained after the side movement and the geometrical pattern obtained after the correction, and making space measurement in the geometrical pattern obtained after the logical operation. 
     According to the invention, there is provided a semiconductor device manufacturing process including a photographic step with a mask geometrical pattern that has been corrected by correcting at least either a concave diffusion layer corresponding portion or a transistor gate corresponding portion which projects from the concave diffusion layer corresponding portion, by use of the semiconductor device geometrical pattern correction process. 
     The semiconductor device manufacturing process may include a photographic step with a mask geometrical pattern that has been corrected by reduction of the base of a concave portion, by use of the semiconductor device geometrical pattern correction process. 
     The semiconductor device manufacturing process may include a photographic step with a mask geometrical pattern that has been corrected, using the semiconductor device geometrical pattern correction process, by reduction of the base of a concave portion and reduction of regions of sides that respectively contact the base in the concave portion, the regions being positioned in the vicinity of both ends of the base. 
     The semiconductor device manufacturing process may include a photographic step with a mask geometrical pattern that has been corrected, using the semiconductor device geometrical pattern correction process, by enlargement of regions of sides that respectively contact an end line in a transistor corresponding portion projecting from a concave diffusion layer corresponding portion, the regions being positioned in the vicinity of both ends of the end line. 
     The semiconductor device manufacturing process may include a photographic step with a mask geometrical pattern that has been corrected, using the semiconductor device geometrical pattern correction process, by enlargement of an end line of a transistor gate corresponding portion that projects from a concave diffusion layer corresponding portion and enlargement of regions of sides that respectively contact the end line in the transistor corresponding portion, the regions being positioned in the vicinity of both ends of the end line. 
     According to the invention, there is provided a geometrical pattern extraction process which includes the steps of moving the sides of a geometrical pattern, correcting a geometrical pattern, performing logical operation on the geometrical pattern obtained after the side movement and the geometrical pattern obtained after the correction, and making space measurement in the geometrical pattern obtained after the logical operation 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a process drawing showing a process of correcting a mask geometrical pattern for semiconductor devices according to a first embodiment of the invention. 
     FIG. 2 is a process drawing showing the details of a concave diffusion layer detecting step  102 . 
     FIG.  3 ( a ) illustrates a diffusion layer geometrical pattern according to the first embodiment, FIG.  3 ( b ) illustrates a geometrical pattern obtained after side movement (reduction), FIG.  3 ( c ) illustrates a geometrical pattern obtained after correction (reduction), FIG.  3 ( d ) illustrates a geometrical pattern obtained after logical operation (subtraction), and FIG.  3 ( e ) illustrates a diffusion layer geometrical pattern as a detection result. 
     FIG. 4 is a process drawing showing the details of the OPC step  103  of the first embodiment shown in FIG.  1 . 
     FIG.  5 ( a ) illustrates a diffusion layer geometrical pattern of the first embodiment, FIG.  5 ( b ) illustrates a geometrical pattern obtained after detection of a concave diffusion layer, and FIG.  5 ( c ) illustrates a geometrical pattern obtained after OPC. 
     FIG. 6 illustrates a geometrical pattern obtained by OPC according to the first embodiment. 
     FIG. 7 illustrates a geometrical pattern obtained after transferring in OPC according to the first embodiment. 
     FIG. 8 is a process drawing showing a part of a process of correcting a semiconductor device mask geometrical pattern according to a second embodiment of the invention. 
     FIG.  9 ( a ) illustrates a diffusion layer geometrical pattern according to the second embodiment, FIG.  9 ( b ) illustrates a geometrical pattern obtained after correction (enlargement), and FIG.  9 ( c ) illustrates a geometrical pattern obtained after OPC. 
     FIG. 10 illustrates a geometrical pattern obtained by OPC according to the second embodiment. 
     FIG. 11 illustrates a geometrical pattern obtained after transferring in OPC according to the second embodiment. 
     FIG. 12 is a process drawing showing a part of a process of correcting a semiconductor device mask geometrical pattern according to a third embodiment of the invention. 
     FIG.  13 ( a ) illustrates a geometrical pattern after displacement measurement according to the third embodiment, FIG.  13 ( b ) illustrates a geometrical pattern after correction (enlargement), FIG.  13 ( c ) illustrates a geometrical pattern after correction (enlargement), FIG.  13 ( d ) illustrates a geometrical pattern after logical operation (multiplication), FIG.  13 ( e ) illustrates a geometrical pattern after logical operation (multiplication), FIG.  13 ( f ) illustrates a geometrical pattern after logical operation (subtraction), FIG.  13 ( g ) illustrates a geometrical pattern after correction (enlargement) and FIG.  13 ( h ) illustrates a geometrical pattern after logical operation (addition). 
     FIG. 14 illustrates a geometrical pattern obtained by OPC according to the third embodiment. 
     FIG. 15 illustrates a geometrical pattern obtained after transferring in OPC according to the third embodiment. 
     FIG. 16 is a process drawing showing a part of a process of correcting a semiconductor device mask geometrical pattern according to a fourth embodiment of the invention. 
     FIG. 17 illustrates a geometrical pattern of a transistor gate according to the fourth embodiment, FIG.  17 ( b ) illustrates a geometrical pattern after side movement (enlargement), FIG.  17 ( c ) illustrates a geometrical pattern after correction (enlargement), FIG.  17 ( d ) illustrates a geometrical pattern after logical operation (subtraction), FIG.  17 ( e ) illustrates a geometrical pattern after correction (enlargement), FIG.  17 ( f ) illustrates a geometrical pattern after logical operation (subtraction), FIG.  17 ( g ) illustrates a geometrical pattern after correction (enlargement) and FIG.  17 ( h ) illustrates a geometrical pattern after logical operation (addition). 
     FIG. 18 illustrates a geometrical pattern obtained by OPC according to the fourth embodiment. 
     FIG. 19 illustrates a geometrical pattern after transferring in OPC according to the fourth embodiment. 
     FIGS.  20 ( a )- 20 ( e ) illustrate a concave geometrical pattern extraction process employed in a detection step corresponding to one shown in FIG. 3, wherein FIG.  20 ( a ) illustrates a convex geometrical pattern, FIG.  20 ( b ) illustrates a geometrical pattern after side movement (enlargement), FIG.  20 ( c ) illustrates a geometrical pattern after correction (enlargement), FIG.  20 ( d ) illustrates a geometrical pattern after logical operation (subtraction), and FIG.  20 ( e ) illustrates a diffusion layer geometrical pattern as a detection result. 
     FIG. 21 illustrates a geometrical pattern prepared according to one example of conventional techniques. 
     FIG. 22 illustrates a geometrical pattern obtained after transferring of the pattern shown in FIG.  21 . 
     FIG. 23 illustrates a geometrical pattern prepared according to another example of conventional techniques, the pattern being modified for ensuring the projection amount of a transistor gate. 
     FIG. 24 illustrates a geometrical pattern obtained after transferring of the pattern with modification shown in FIG.  23 . 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to the accompanying drawings, preferred embodiments of the present invention will be described below. 
     FIG. 1 shows a process of correcting a mask geometrical pattern for semiconductor devices according to a first embodiment of the invention. 
     A mask geometrical pattern  101  shown in FIG. 1 is input for processing at a concave diffusion layer detection step  102  and then subject to processing at an OPC step  103  in which Optical Proximity Correction (hereinafter referred to as OPC) is performed for compensating for the difference between a mask geometrical pattern initially designed and a geometrical pattern after transferring. Thereafter, a mask geometrical pattern  104  after OPC is output. 
     FIG. 2 is a process drawing showing the concave diffusion layer detection step  102  in detail. As seen from FIG. 2, a diffusion layer geometrical pattern undergoes a side movement (reduction) step  201 , a correction (reduction) step  202 , a logical operation (subtraction) step  203  and a space measurement step  204 , whereby a concave diffusion layer is detected. The above series of steps constitutes a concave geometrical pattern extraction process applied to the concave diffusion layer detection step  102 . 
     The diffusion layer geometrical pattern shown in FIG.  3 ( a ) is subject to side movement by a specified amount A in the side movement (reduction) step  201  so that the geometrical pattern shown in FIG.  3 ( b ) is output. The diffusion layer geometrical pattern is also subject to correction (reduction) by the specified amount A in a correction (reduction) step  202  thereby to release the geometrical pattern shown in FIG.  3 ( c ). The geometrical patterns shown in FIGS.  3 ( b ) and  3 ( c ) undergo logical operation (subtraction) in the logical operation (subtraction) step  203  to output the geometrical pattern shown in FIG.  3 ( d ). The geometrical pattern shown in FIG.  3 ( d ) then undergoes space measurement in the space measurement step  204  so that the geometrical pattern shown in FIG.  3 ( e ) is output to areas having spaces equal to or less than a specified amount B. The geometrical pattern shown in FIG.  3 ( e ) is a result of the detection of the concave diffusion layer. 
     FIG. 4 shows a logical operation step  301  that is a detail step of the OPC step  103  according to the first embodiment of the invention. In the logical operation (subtraction) step  301 , the diffusion layer geometrical pattern shown in FIG.  5 ( a ) undergoes logical operation (subtraction) together with the geometrical pattern shown in FIG.  5 ( b ) which is an output from the concave diffusion layer detection step  102 , so that the geometrical pattern shown in FIG.  5 ( c ) is output. 
     The amount of correction carried out in the OPC step  103  can be controlled by altering the specified amount A used in the side movement (reduction) step  201  and in the correction (reduction) step  202 . 
     FIGS. 6 and 7 show geometrical patterns corrected by the semiconductor device mask geometrical pattern correction process according to the first embodiment of the invention. Reference numerals  1 ,  2  and  3  designate a concave diffusion layer corresponding portion, a gate corresponding portion, and another pattern, respectively. 
     The semiconductor device mask geometrical pattern shown in FIG. 6 is such a pattern that can ensure a desired gate projection amount after transferring as seen from FIG. 7 while allowing the placement of another pattern  3 . 
     A decrease in the projection amount of the gate caused by corner rounding induced after the photographic step can be compensated in the semiconductor device produced by photographing with the above corrected semiconductor device mask geometrical pattern. 
     In accomplishing the above primary object, the invention does not cause increased chip area which is a problem imposed by conventional techniques, so that the invention can highly contribute to the development of competitive chips. Further, since the process of the invention is focused on the compensation for a decrease in the projection amount of the gate, the amount of data that accompany the process can be minimized and no problems occur in mask fabrication. 
     FIG. 8 shows a part of a semiconductor device mask geometrical pattern correction process according to a second embodiment of the invention. The process of the second embodiment can be implemented by replacing the OPC step  103  of the first embodiment with the OPC step shown in FIG.  8 . 
     The geometrical pattern shown in FIG.  3 ( d ) which is generated in the concave diffusion layer detection step  102  undergoes correction (enlargement) by a specified amount C in a correction (enlargement) step  401  shown in FIG. 8 so that the geometrical pattern shown in FIG.  9 ( b ) is output. In a logical operation (subtraction) step  402 , logical operation (subtraction) on the geometrical patterns shown in FIGS.  9 ( a ) and  9 ( b ) is performed so that the geometrical pattern shown in FIG.  9 ( c ) is output. 
     It should be noted that the amount of correction in the OPC step  103  can be controlled by altering the specified amount C used in the correction (enlargement) step  401 . 
     FIGS. 10 and 11 show geometrical patterns corrected by the semiconductor device mask geometrical pattern correction process according to the second embodiment. 
     The semiconductor device mask geometrical pattern shown in FIG. 10 is such a pattern that can ensure a desired gate projection amount after transferring as seen from FIGURE11 while allowing the placement of another pattern  3 . 
     FIG. 12 shows a part of a semiconductor device mask geometrical pattern correction process according to a third embodiment of the invention. The process of the third embodiment can be implemented by replacing the OPC step  103  of the first embodiment with the OPC step shown in FIG.  12 . 
     The diffusion layer geometrical pattern and transistor gate geometrical pattern shown in FIG.  13 ( a ) undergo displacement measurement in a displacement measurement step  501  so that the geometrical pattern shown in FIG.  13 ( a ) is output to areas having values less than a specified amount D. Further, the geometrical pattern shown in FIG.  13 ( a ) undergoes correction (enlargement) by a specified amount E in the correction (enlargement) step  502  so that the geometrical pattern shown in FIG.  13 ( b ) is output. The geometrical pattern shown in FIG.  13 ( a ) undergoes correction (enlargement) by a specified amount F in the correction (enlargement) step  502  so that the geometrical pattern shown in FIG.  13 ( c ) is output. 
     In a logical operation (multiplication) step  503 , logical operation (multiplication) on the geometrical pattern shown in FIG.  13 ( b ) and the transistor gate geometrical pattern shown in FIG.  13 ( a ) is performed so that the geometrical pattern shown in FIG.  13 ( d ) is output. Further, in a logical operation (multiplication) step  503 , logical operation (multiplication) on the geometrical pattern shown in FIG.  13 ( c ) and the transistor gate geometrical pattern shown in FIG.  13 ( a ) is performed so that the geometrical pattern shown in FIG.  13 ( e ) is output. Then, in a logical operation (subtraction) step  504 , logical operation (subtraction) on the geometrical patterns shown in FIG.  13 ( d ) and  13 ( e ) is performed so that the geometrical pattern shown in FIG.  13 ( f ) is output. The geometrical pattern shown in FIG.  13 ( f ) undergoes correction (enlargement) by a specified amount G in a correction (enlargement) step  505  so that the geometrical pattern shown in FIG.  13 ( g ) is released. Lastly, in a logical operation (addition) step  506 , logical operation (addition) on the geometrical pattern shown in FIG.  13 ( g ) and the transistor gate geometrical pattern shown in FIG.  13 ( a ) is performed so that the geometrical pattern shown in FIG.  13 ( h ) is released. 
     The amount of correction carried out in the OPC step  103  can be controlled by altering the specified amount D used in the displacement measurement step  501 , the specified amount E used in the correction (enlargement) step  502 , the specified amount F used in the correction (enlargement)  502 , and the specified amount G used in the correction (enlargement) step  505 . 
     FIGS. 14 and 15 show geometrical patterns corrected by the semiconductor device mask geometrical pattern correction process according to the third embodiment of the invention. 
     The semiconductor device mask geometrical pattern shown in FIG. 14 is such a pattern that can ensure a desired gate projection amount after transferring as seen from FIG. 15 while allowing the placement of another pattern  3 . 
     FIG. 16 shows a part of a semiconductor device mask geometrical pattern correction process according to a fourth embodiment of the invention. The process of the fourth embodiment can be implemented by replacing the OPC step  103  of the first embodiment with the OPC step shown in FIG.  16 . The transistor gate geometrical pattern shown in FIG.  17 ( a ) undergoes side movement (enlargement) by a specified amount H in a side movement (enlargement) step  601  to output the geometrical pattern shown in FIG.  17 ( b ). The transistor gate geometrical pattern shown in FIG.  17 ( a ) undergoes correction (enlargement) by a specified amount H in a correction (engagement) step so that the geometrical pattern shown in FIG.  17 ( c ) is output. Subsequently, logical operation (subtraction) on the geometrical patterns shown in FIGS.  17 ( b ) and  17 ( c ) is performed in a logical operation (subtraction) step  603  so that the geometrical pattern shown in FIG.  17 ( d ) is output. In a logical operation (multiplication) step  604 , logical operation (multiplication) is performed on the geometrical patterns shown in FIGS.  17 ( e ) and  17 ( d ) which have been obtained by correction (enlargement) with the specified amount H as a correction amount in a similar manner to the displacement measurement step  501  and correction (enlargement) step  502  shown in FIG. 12, so that the geometrical pattern shown in FIG.  17 ( f ) is output. The geometrical pattern shown in FIG.  17 ( f ) then undergoes correction (enlargement) by a specified amount I in a correction (enlargement) step  605  to release the geometrical pattern shown in FIG.  17 ( g ). Lastly, logical operation (addition) on the geometrical pattern shown in FIG.  17 ( g ) and the transistor gate geometrical pattern shown in FIG.  17 ( a ) is performed in a logical operation (addition) step  606  so that the geometrical pattern shown in FIG.  17 ( h ) is output. 
     The amount of correction in the OPC step  103  can be controlled by altering the specified amount H used in the side movement step  601 , the specified amount H used in the correction (enlargement) step  602 , the specified amount H used in generating the pattern shown in FIG.  17 ( e ) and the specified amount I used in the correction (enlargement) step  605 . 
     FIGS. 18 and 19 show geometrical patterns corrected by the semiconductor device mask geometrical pattern correction process according to the fourth embodiment of the invention. 
     The semiconductor device mask geometrical pattern shown in FIG. 18 is such a pattern that can ensure a desired gate projection amount after transferring as seen from FIG. 19 while allowing the placement of another pattern  3 . 
     In the geometrical pattern extraction process of the invention, the side movement (reduction) step and correction (reduction) step in the concave diffusion layer detection step are changed to a side movement (enlargement) step and correction (enlargement) step, respectively, whereby this process can be utilized as a convex pattern detection step. 
     FIG. 20 corresponds to FIG.  3  and illustrates a process of extracting a convex geometrical pattern. 
     FIGS.  20 ( a ) ,  20 ( b ) ,  20 ( c ) ,  20 ( d ) and  20 ( e ) illustrate (i) a convex geometrical pattern, (ii) a geometrical pattern after undergoing side movement in a side movement (enlargement) step, (iii) a geometrical pattern after undergoing correction in a correction (enlargement) step, (iv) a geometrical pattern obtained from logical operation (subtraction) performed on the geometrical patterns shown in FIGS.  20 ( b ) and  20 ( c ), and ( v ) a geometrical pattern outputted, as a detection result, to areas having spaces equal to or less than a specified amount after undergoing space measurement in a space measurement step. 
     It will be appreciated that the invention is not limited to cases where either the concave diffusion layer corresponding portion or the transistor gate corresponding portion which projects from the concave diffusion layer corresponding portion is corrected, but can be arranged such that both of them are corrected by employing any of the first to fourth embodiments in combination.