Patent Publication Number: US-7220521-B2

Title: Fabrication method of semiconductor device

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application is based on Japanese priority applications No. 2004-230834 and No. 2004-377038 respectively filed on Aug. 6, 2004 and Dec. 27, 2004, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     The present invention generally relates to fabrication of semiconductor devices and more particularly to the technology of alignment of exposure apparatus. 
     With increasing speed and functional diversity of semiconductor devices, extremely miniaturized patterns are formed nowadays on the surface of semiconductor wafers. Associated with this, there exists an increasing demand for more accurate alignment in the photolithographic process, particularly in the exposure step of semiconductor wafers conducted by using an exposure apparatus. 
     In the fabrication process of semiconductor devices, it has been practiced to achieve alignment of semiconductor patterns with regard to an underlying semiconductor pattern at the time of exposure process by measuring the coordinate of alignment marks formed in each of the chip regions arranged in rows and columns on a semiconductor wafer. 
     REFERENCES 
     
         
         Japanese Unexamined Patent Publication 2002-231596 
         Japanese Unexamined Patent Publication 2002-64046 
         Japanese Unexamined Patent Publication 2004-71622 
       
    
     SUMMARY OF THE INVENTION 
       FIGS. 1A and 1B  are respectively a plan view and a cross-sectional view showing an example of alignment of upper and lower layers on such a semiconductor substrate. 
     Referring to  FIGS. 1A and 1B , there is formed a first interlayer insulation film  11  on a silicon substrate (not shown) formed with active devices such as a MOS transistor, wherein the first interlayer insulation film  11  includes contact plugs  11 A and  11 D, an alignment verification pattern  11 C and an alignment mark  11 D, wherein the interlayer insulation film  11  carries thereon a second interlayer insulation film  12  including therein an interconnection pattern  12 A contacting with the contact plugs  11 A and  11 B, an alignment verification  12 B corresponding to the alignment verification pattern  11 C, and an alignment mark  12 C. 
     Thus, in the case of forming the interconnection patterns  12 A,  12 B and  12 C in the interlayer insulation film  12 , alignment is achieved with reference to the alignment mark  11 D in the interlayer insulation film  11 , and the alignment result is confirmed by a microscope (alignment error detection device equipped with an optical microscope) by examining the relationship between the alignment verification pattern  11 C and the alignment verification pattern  12 B. 
     In many cases, the alignment verification patterns  11 C and  12 B or the alignment marks  11 D and  12 C are formed of a pattern having a step, and thus, detection thereof is possible even after the upper layer is formed. Further, it should be noted that the alignment between the contact plug  11 A or  11 B and the interconnection pattern  12 A is achieved with regard to the contact plug  11 A or  11 B and the resist pattern formed on the interlayer insulation film  12  in correspondence to the interconnection pattern  12 A. 
     Further, the alignment of the next interlayer insulation film is achieved by using the alignment mark  12 C included in the interlayer insulation film  12 . 
       FIG. 2  is a diagram showing the exposure of semiconductor chip patterns on a semiconductor wafer. 
     Referring to  FIG. 2 , there are formed semiconductor chip regions  20 C 1 ,  20 C 2 ,  20 C 3 , . . . on a semiconductor wafer  10  in rows and columns, and in correspondence to each of the semiconductor chip regions, there are formed an alignment mark  20 X for the alignment in the X direction and an alignment mark  20 Y for the alignment in the Y direction in the scribe region of the semiconductor wafer  20  in correspondence to the alignment mark  11 D or  12 C noted before. 
     For such alignment, it is first necessary to control the alignment error of the patterns within the wafer, wherein the alignment error occurring in such wafer alignment includes: translational error in the X and Y directions (ShiftX, ShiftY); magnification error in the X and Y directions (WaferMagX, WaferMagY); and rotational error in the X and Y directions (WaferRotX, WaferRotY), wherein the wafer alignment is conducted for the patterns on the wafer to be aligned with reference to the patterns on the wafer to which the alignment is to be achieved. Thereby, the alignment is achieved in terms of the “alignment lattice”, which is defined on the semiconductor wafer such that each chip on the semiconductor wafer is represented by the center of each cell defined by the alignment lattice. Further, it is necessary to control the alignment error of the patterns within each chip (chip alignment), wherein the alignment error occurring in the chip alignment includes: magnification error in the X and Y directions (ChipMagX, ChipMagY); and rotational error in the X and Y directions (ChpRotX, ChipRotY). 
       FIGS. 3 and 4  show the deformation of patterns caused on a semiconductor wafer and on a chip and corresponding to the foregoing corrections. 
     Conventionally, it has been practiced, in order to achieve such positional alignment at the time of exposure of semiconductor wafers of product lot, to process a pilot wafer at first, and feedback the result of the alignment error detection achieved for such a pilot wafer, to the processing of the wafers of the product lot. Alternatively, it has been practiced to refer to the processing lot history of the past and predict the optimum alignment correction parameters. Particularly, the former is used frequently in the processing line for the purpose of development, while the use thereof in the production line is not common in view of severe deterioration of productivity in the exposure process. 
     Because of these reasons, it is currently practiced in the production line of semiconductor devices to achieve the positional alignment by using the history data of the past. In this case, however, there arises a problem of how to predict the alignment error, which tends to increase with time or with the lot number. 
     As mentioned previously, positional alignment includes: wafer alignment achieved for the overall wafer and hence for the chip center of gravity, conducted by using the parameters (ShiftX, ShiftY, WaferMagX, WaferMagY); and chip alignment achieved for each chip conducted by using the parameters (ChipMagX, ChipMagY, ChipRotX, ChipRotY). 
     In order to achieve the chip alignment with high precision, it has been required to provide plural alignment marks within each chip for detecting the alignment error in the X and Y directions, while there arise problems such as limited area available on the scribe lines for formation of such alignment marks, or decrease of throughput of exposure caused by increase of the measuring time of the alignment marks. It is not possible to increase the number of the alignment marks arbitrarily. 
     It should be noted that alignment with regard to the chip center of gravity, and thus, the alignment with regard to the parameters ShiftX, ShiftY, WaferMagX, WaferMagY, WaferRotX and WaferRotY, are dependent on various factors such as: exposure apparatus and exposure condition (optical parameters such as numerical aperture NA, illumination condition, lens distortion, etc.); precision of mask pattern arrangement; exposure apparatus and exposure condition (optical parameters such as numerical aperture NA, illumination condition, lens distortion, etc.) used for exposure of the upper pattern, which is to be aligned with reference to the lower pattern; the precision of the mask pattern arrangement, an the like. 
     Thereby, it has been possible to predict the alignment correction parameters with sufficient precision by using the alignment technology of the exposure apparatus itself. Generally, this has been achieved by extrapolating the optimum alignment parameters of the past that could successfully achieve the alignment of the upper pattern to the lower pattern, under the condition in which all the alignment error factors are identical, more specifically according to a simple moving average of the equation:
 
[optimum exposure control parameter value of the exposure apparatus at the time of alignment]=[set value of alignment control parameter of the exposure apparatus at the time of alignment]−[alignment error result of the lower pattern parameter and upper pattern parameter].
 
     On the other hand, with regard to the pattern arrangement of individual chips, it is difficult to achieve precise prediction unless there are provided plural alignment marks within the chip for measurement of the alignment errors. Thus, there has been a tendency that magnification errors or rotational errors are caused at the time of the alignment of the chip patterns, resulting in decrease of productivity such as increase of the repair works or decrease of the yield. 
     Further, with regard to the alignment error for the wafer as a whole, there are cases in which the alignment error is deviated significantly over the prediction when the lot number has exceeded a particular lot number. In such a case, alignment by way of extrapolation is not possible. It should be noted that such large deviation is tend to be caused in recent high-performance exposure apparatuses due to the malfunctioning of its complex mechanism or control error caused by environmental disturbance. 
     Thus, there is a demand for efficient alignment method and exposure method capable of improving, when exposing complex semiconductor patterns inside a chip region defined on a semiconductor wafer consecutively in a superimposed relationship, particularly under the circumstances in which there is little room for providing plural alignment marks inside the chip region, the precision of prediction of the correction parameters set to an exposure apparatus for those alignment errors shown in  FIGS. 3 and 4 , except for the translational error of the chip center of gravity (ShiftX, ShiftY). 
     According to a first aspect of the present invention, there is provided a method of fabricating a semiconductor device that includes an exposing process in which a lower pattern is formed by a first exposing process and an upper pattern is formed thereon by a second exposing process, said exposing process comprising: an earlier exposure step of aligning and exposing, in a just-before lot conducted immediately before a current lot, an upper pattern on a substrate of said just-before lot, on which a lower pattern is formed by said first exposing process, by conducting said second exposing process such that said upper pattern is in alignment with said lower pattern; and a latter exposure step of aligning and exposing, in said current lot, an upper pattern on a substrate of said current lot, on which a lower pattern is formed by said first exposing process, by conducting said second exposing process such that said upper pattern is in alignment with said lower pattern on said substrate of said current lot, said exposure process further comprising the steps of: obtaining a first correction value representing a difference of first and second alignment error correction parameter preset values respectively used at the time of said first exposing process of exposing said lower patterns in said current lot and in said just-before lot; obtaining, as a second correction value, an optimum correction amount of a third alignment error correction parameter preset value, which has been needed for proper alignment of said upper pattern in said second exposing process of said just-before lot, said third alignment error correction parameter has been used in said second exposing process of said just-before lot for exposing said upper pattern; obtaining an optimum correction parameter prediction value to be used for exposing said upper pattern in said second exposing process of said current lot, from said first correction value and said second correction value; and exposing said upper pattern of said current lot in said latter exposure step while using said optimum parameter prediction value. 
     In another aspect, the present invention provides a method of fabricating a semiconductor device that includes an exposing process in which a lower pattern is formed by a first exposing process and an upper pattern is formed thereon by a second exposing process, said exposing process comprising: an earlier exposure step of aligning and exposing, in a just-before lot conducted immediately before a current lot, an upper pattern on a substrate of said just-before lot, on which a lower pattern is formed by said first exposing process, by conducting said second exposing process such that said upper pattern is in alignment with said lower pattern; and a latter exposure step of aligning and exposing, in said current lot, an upper pattern on a substrate of said current lot, on which a lower pattern is formed by said first exposing process, by conducting said second exposing process such that said upper pattern is in alignment with said lower pattern on said substrate of said current lot, said exposure process further comprising the steps of: obtaining first and second alignment error correction parameter preset values used respectively for alignment of said lower patterns at the time of said first exposing process of exposing said lower pattern respectively in said current lot and said just-before lot; obtaining an optimum correction amount needed for correcting an alignment error correction parameter preset value used in said second exposing process of said earlier exposure step for exposing said upper pattern in said just-before lot with proper alignment; obtaining an optimum correction parameter preset value used in said second exposing process of said latter exposure step for exposing said upper pattern of said current lot, from said first alignment error correction parameter preset value, said second alignment error correction parameter preset value and said optimum correction amount; and exposing said upper pattern of said current lot in said second exposing process of said latter exposure step, while using said optimum correction parameter preset value. 
     According to the present invention, it becomes possible to predict the alignment correction parameters with high precision at the time of fabrication of a semiconductor device particularly for the case in which it is not possible to provide sufficient number of alignment marks inside a chip region because of limited space available for formation of the alignment marks or because of the requirement of throughput, for not only the errors for the translation of the chip center of gravity (ShiftX, ShiftY) but also for the errors in the wafer magnification (WaferMagX, WaferMagY) or wafer distortion (WaferRotX, WaferRotY) respectively about the X and Y axes over the entire wafer, and further for the errors in the magnification (ChipMagX, ChipMagY) and distortion (ChipRotX, ChipRotY) respectively about the X and Y-axes for each of the chip regions. Further, according to the present invention, while it is necessary to carry out the processing of a pilot wafer in the first lot, there is no need of processing a pilot wafer in the second lot and the lots thereafter. Thereby, the productivity of exposure process is improved and so is the yield of production of the semiconductor device. 
     Further, it should be noted that the present invention is effective also in the case in which plural alignment marks are disposed inside a chip region. 
     Further, according to the present invention, it becomes possible to carry out the exposure with minimum alignment error at the time of fabricating a semiconductor device according to the fabrication process that includes an exposing process in which a lower pattern is formed by a first exposing process and an upper pattern is formed thereon by a second exposing process, said exposing process comprising: an earlier exposure step of aligning and exposing, in a just-before lot conducted immediately before a current lot, an upper pattern on a substrate of said just-before lot, on which a lower pattern is formed by said first exposing process, by conducting said second exposing process such that said upper pattern is in alignment with said lower pattern; and a latter exposure step of aligning and exposing, in said current lot, an upper pattern on a substrate of said current lot, on which a lower pattern is formed by said first exposing process, by conducting said second exposing process such that said upper pattern is in alignment with said lower pattern on said substrate of said current lot, said exposure process further comprising the steps of: obtaining first and second alignment error correction parameter preset values used respectively for alignment of said lower patterns at the time of said first exposing process of exposing said lower pattern respectively in said current lot and said just-before lot; obtaining an optimum correction amount needed for correcting an alignment error correction parameter preset value used in said second exposing process of said earlier exposure step for exposing said upper pattern in said just-before lot with proper alignment; obtaining an optimum correction parameter preset value used in said second exposing process of said latter exposure step for exposing said upper pattern of said current lot, from said first alignment error correction parameter preset value, said second alignment error correction parameter preset value and said optimum correction amount; and exposing said upper pattern of said current lot in said second exposing process of said latter exposure step, while using said optimum correction parameter preset value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  are respectively a plan view and a cross sectional view showing a part of a semiconductor device in which first and second patterns including an alignment mark and an alignment verification mark are formed; 
         FIG. 2  is a diagram showing an example of a chip pattern formed on a semiconductor wafer; 
         FIGS. 3 and 4  are diagrams showing examples of alignment error occurring in the chip pattern of  FIG. 2 ; 
         FIG. 5  is a diagram showing the construction of an exposure system according to a first embodiment of the present invention; 
         FIG. 6  is a diagram showing an exposure process according to an embodiment of the present invention that uses the exposure system of  FIG. 5 ; 
         FIG. 7  is a diagram showing the method of obtaining a preset value of the alignment error correction parameter used with the exposure process of  FIG. 6 ; 
         FIG. 8  is a flowchart showing an exposure process according to a first embodiment of the present invention; 
         FIGS. 9A–9D  are diagrams showing an exposure example of the first embodiment of the present invention; 
         FIGS. 10A–10D  are diagrams showing an exposure example of a second embodiment of the present invention; 
         FIG. 11  is a diagram showing the construction of an exposure system according to the second embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     [First Embodiment] 
       FIG. 5  is a diagram showing the construction of an exposure system  20  used with the present invention. 
     Referring to  FIG. 5 , the exposure system  20  includes at least two exposure apparatuses S 1  and S 2  respectively having reticles, and a control unit  101  holding exposure data D 0  and D 1  and controlling the exposure apparatuses S 1  and S 2  with the exposure data D 0  and D 1 , wherein there cooperates an examination device M 1  including a microscope with the exposure apparatus S 1 , while an examination device M 2  including a microscope cooperates with the exposure apparatus S 2 . In the example of  FIGS. 1A and 1B , the exposure data D 0  is used for patterning the lower layer  11  and the exposure data D 1  is used for the patterning of the upper layer  12 . 
     It should be noted that the control unit  100  provides, at the time of carrying out exposure by the exposure apparatuses S 1  and S 2 , the preset values P0set and P1set of the alignment error correction parameter to the exposure apparatuses S 1  and S 2  for compensating for the alignment error of the exposure pattern explained before. 
     Here, it should be noted that the preset value P0set is an alignment error correction parameter used for correcting the alignment error of the first exposure apparatus S 1  at the time of exposure of the lower layer  11  and includes in fact ten alignment error correction parameters: ShiftX; ShiftY; WaferMagX; WaferMagY; WaferRotX; WaferRotY; ChipMagX; ChipMagY; ChipRotX; and ChipRotY explained before. 
     Similarly, the foregoing preset value P1set is an alignment error correction parameter used for correcting the alignment error in the second exposure apparatus S 2  at the time of exposure of the upper layer  12  and includes in fact ten alignment error correction parameters: ShiftX; ShiftY; WaferMagX; WaferMagY; WaferRotX; WaferRotY; ChipMagX; ChipMagY; ChipRotX; and ChipRotY explained before. 
     In each of the exposure apparatuses S 1  and S 2 , the patterns shown in  FIGS. 1A and 1B  are processed repeatedly from the Lot # 1  to Lot #j. 
     It should be noted that these correction parameters change with each lot, and thus, it is needed, with such exposure technology in which plural patterns are superimposed, to provide a correction algorithm for obtaining an optimum correction parameter that minimizes the alignment error between the exposed patterns formed as a result of the exposure. 
       FIG. 6  shows the initial values P0set and P1set respectively used for exposing the upper pattern (formed by process P1) on the lower pattern (formed by process P0) while using the exposure system  20  of  FIG. 5  in terms of ppm, and further the alignment error result parameters P0result and P1result respectively representing the alignment error result for the case of using the foregoing initial values P0set and P1set also in terms of ppm. 
     In  FIG. 6 , it should be noted that the parameter P1truevalue represents the true value of P1 and is defined as P1truevalue=P1set−P1result. Thus, the parameter P1result should become zero in the case there holds the relationship P1truevalue=P1 (optimum value) and the parameter P1truevalue has been used for the preset value in place of P1setvalue. The same applies also to P0truevalue. 
     It should be noted that the foregoing alignment error result parameters P0result and P1result, or the true value corresponding to these, are obtained from the exposure patterns of the past including the Lot# 1 –Lot#j by means of the foregoing examination devices M 1  and M 2 , and are held in a memory unit  102  provided in a part of the control unit  101  of  FIG. 5 . Here, it should be noted that the alignment error result parameters P0result and P1result are observed values obtained from the alignment verification patterns  11 C and  11 D shown in  FIGS. 1A and 1B . 
     Referring to  FIG. 6 , the preset values P0set and P1set, and the alignment error result parameters P0result and P1result are defined for each of ShiftX, ShiftY, WaferMagX, WaferMagY, WaferRotX, WaferRotY, ChipMagX, ChipMagY, ChipRotX, ChipRotY (P0set(ShiftX); P0set(ShiftY); P0set(WaferMagX); P0set(WaferMagY); P0set(WaferRotX); P0set(WaferRotY); P0set(ChipMagX); P0set(ChipMagY); P0set(ChipRotX); P0set(ChipRotY); P1set(ShiftX); P1set(ShiftY); P1set(WaferMagX); P1set(WaferMagY); P1set(WaferRotX); P1set(WaferRotY); P1set(ChipMagX); P1set(ChipMagY); P1set(ChipRotX); P1set(ChipRotY)). Thereby, it should be noted that each parameter is obtained for each of the Lot# 1 –Lot#j. In the illustrated example, it should be noted that Lot# 1  is the oldest and Lot# 5  is the newest. 
     In the present embodiment, it should be noted that the control unit  101  determines the preset values P0set and P1set of the exposure apparatuses S 1  and S 2  for those parameters other than the parameters ChipMagX and ChipMagY, from the moving average of the past trend of the true values such as the one shown in  FIG. 7 , or alternatively by the polynomial approximation representing the variation of the true value with the exposure processing time. 
     From  FIG. 6 , it can be seen that, in the case the foregoing preset values are obtained from the past trend as such, the errors resulting from the use of the preset values P0result and P1result do not exceed 0.50 ppm in any of the cases of aligning the contact plugs  11 A and  11 B in the layer  11  or the interconnection pattern  12 A in the layer  12  in the model structure of  FIGS. 1A and 1B  apart from the translational error (ShiftX, ShiftY), except for the foregoing parameter ChipMagX. Thus,  FIG. 6  indicates that a satisfactory prediction is achieved for the alignment error correction parameters, except for the parameter ChipMagX. 
     On the other hand, in the case of aligning the interconnection pattern  12 A, it can be seen in  FIG. 6  that there are cases in which the alignment error result parameter, P1result, takes a value exceeding 0.5 ppm (lot# 2  and lot# 3 ) with regard to the foregoing parameter ChipMagX. 
     In such a case, it is not possible to sufficiently compensate for the distortion of the actual exposure pattern, as long as the preset value P1set obtained from the past trend is used. Further, with regard to the parameter ChipMgY, too, there are cases in which the alignment error result parameter P1result takes a value close to 0.5 ppm (0.47 for lot# 4 ; and 0.42 for lot# 3 ). 
     In view of the foregoing situation, the present embodiment obtains the corrected value Estimate(ChipMagX,L 5 ) of the alignment error correction parameter ChipMagX of the lot# 5  from the quantity (P0set(ChipMagX,L 5 )−P0set(ChipMagX,L 4 )) representing a difference of the preset values set to the first exposure apparatus S 1  for aligning and exposing the lower patterns  11 A and  11 B (process P0) between the current lot (lot# 5 ) and the just-before lot (lot# 4 ), and further from the quantity (P1set(ChipMagX,L 4 )−P1result(ChipMagX,L 4 ) representing a difference between the preset value (P1set(ChipMagX,L 4 )) for aligning and exposing the interconnection pattern  12 A (process P1) for the foregoing just-before lot (lot# 4 ) and the result of the alignment error measurement (P1result(ChipMagX,L 4 ) for the same just-before lot (lot# 4 ), according to the relationship 
     
       
         
           
             
               
                 
                   
                     Estimate 
                     ⁡ 
                     
                       ( 
                       
                         ChipMagX 
                         , 
                         
                           L 
                           5 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       { 
                       
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             set 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagX 
                                 , 
                                 
                                   L 
                                   5 
                                 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             set 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagX 
                                 , 
                                 
                                   L 
                                   4 
                                 
                               
                               ) 
                             
                           
                         
                       
                       } 
                     
                     + 
                     
                       { 
                       
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             set 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagX 
                                 , 
                                 
                                   L 
                                   4 
                                 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             result 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagX 
                                 , 
                                 
                                   L 
                                   4 
                                 
                               
                               ) 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In the present example, the corrected alignment error correction parameter Estimate(ChipMagX,L 5 ) takes the value of (1.03−0.16)+(1.79−0.4)=2.26(ppm), while it should be noted that this value is offset only by 0.21 ppm (ΔX in  FIG. 6 ) from the true value 2.47 of ChipMagX for the lot # 5  (=P1set(ChipMagX,L 5 )−P1result(ChipMagX,L 5 )=2.25−(−0.22)=2.47). 
     Similarly, the corrected alignment error correction parameter Estimate(ChipMagY,L 5 ) for the parameter ChipMagY is obtained according to the relationship 
     
       
         
           
             
               
                 
                   
                     Estimate 
                     ⁡ 
                     
                       ( 
                       
                         ChipMagY 
                         , 
                         
                           L 
                           5 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       { 
                       
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             set 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagY 
                                 , 
                                 
                                   L 
                                   5 
                                 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             set 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagY 
                                 , 
                                 
                                   L 
                                   4 
                                 
                               
                               ) 
                             
                           
                         
                       
                       } 
                     
                     + 
                     
                       { 
                       
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             set 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagY 
                                 , 
                                 
                                   L 
                                   4 
                                 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             result 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagY 
                                 , 
                                 
                                   L 
                                   4 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In this case, the corrected alignment error correction parameter Estimate(ChipMagY,L 5 ) takes the value (1.24−0.94)+(0.96−0.47)=0.79(ppm), while this value is offset only by 0.1 ppm (ΔY in  FIG. 6 ) from the true value 0.89 of ChipMagY for the lot # 5  (=P1set(ChipMagY,L 5 )−P1result(ChipMaY,L 5 )=0.94−0.05=0.89. 
     Generalizing the foregoing equations (1) and (2), the present embodiment obtains the corrected alignment error correction parameter Estimate(ChipMagX,Y, Lj) for the j-th lot (Lj) according to the relationship 
     
       
         
           
             
               
                 
                   
                     Estimate 
                     ⁡ 
                     
                       ( 
                       
                         ChipMagX 
                         , 
                         Y 
                         , 
                         
                           L 
                           j 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       { 
                       
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
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                             set 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagX 
                                 , 
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                                 , 
                                 
                                   L 
                                   j 
                                 
                               
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                         - 
                         
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                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             set 
                             ⁡ 
                             
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                                 ChipMagX 
                                 , 
                                 Y 
                                 , 
                                 
                                   L 
                                   
                                     j 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       } 
                     
                     + 
                     
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                           P 
                           ⁢ 
                           
                               
                           
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                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             set 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagX 
                                 , 
                                 Y 
                                 , 
                                 
                                   L 
                                   
                                     j 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           P 
                           ⁢ 
                           
                               
                           
                           ⁢ 
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                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             result 
                             ⁡ 
                             
                               ( 
                               
                                 ChipMagX 
                                 , 
                                 Y 
                                 , 
                                 
                                   L 
                                   
                                     j 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     According to the foregoing method, it becomes possible to expose, in the current lot, an upper pattern  12 A on a substrate, on which lower patterns  11 A and  11 B of the current lot are formed already by using the first exposure apparatus S 1 , by using the second exposure apparatus S 2  such that the upper pattern  12 A is in alignment with the lower patterns  11 A and  11 B while setting an optimum correction parameter preset value to the second exposure apparatus S 2 . The process is summarized in the flowchart of  FIG. 8 . 
     Referring to  FIG. 8 , a first correction value [P0set(ChipMagX,Y, L j )−P0set(ChipMagX,Y, L j-1 )], indicative of a difference between first and second alignment error correction parameters given to the first exposure apparatus S 1  respectively for the exposure of the current lot and for the exposure of the just-before lot for alignment of the lower patterns  11 A and  11 B, is obtained in the first step  1 . 
     Next, as shown in the second step  2 , a second correction value P1result(ChipMagX,Y, L j-1 ), representing the actual alignment error observed at the time exposing the upper pattern  12 A in the just-before lot by using the second exposure apparatus S 2 , is obtained. 
     Further, in the step  3 , a correction preset value (true value) that has been needed for the third alignment error correction parameter preset value P1set(ChipMagX,Y, L j-1 ), which is given to the second exposure apparatus S 2  at the time of exposure of the upper pattern  12 A in the just-before lot, for proper alignment of the upper pattern  12 A, is obtained as P1set(ChipMagX,Y, L j-1 )−P1result(ChipMagX,Y, L j-1 ). 
     Further, in the step  4  of  FIG. 8 , the preset value of the alignment error correction parameter P0set(ChipMagX,Y, L j ), which is set to the first exposure apparatus S 1  at the time of exposing the lower patterns  11 A and  11 B in the current lot by using the exposure apparatus S 1 , is corrected by the foregoing first and second correction values as [{P0set(ChipMagX,Y, L j )−P0set(ChipMagX,Y, L j-1 )}+{P1set(ChipMagX,Y, L j-1 )−P1result(ChipMagX,Y, L j-1 )}], and with this, the optimum correction parameter preset value Estimate(ChipMagX,Y, L j ), which is set to the second exposure apparatus S 2  at the time of exposure of the current lot, is obtained. 
     Further, in the step  5  of  FIG. 8 , the foregoing optimum correction parameter preset value is set to the second exposure apparatus S 2  and the exposure for the pattern  12 A of the current lot is carried out. 
     In the foregoing procedure, it should be noted that the actual error amount P1result(ChipMagX,Y, L j-1 ) caused in the correction parameter set to the exposure apparatus S 2  at the time of exposure of the lower patterns  11 A and  11 B in the just-before lot due to the causes attributed to the substrate is obtained from the actual measurement of the alignment verification pattern of the layer  11  shown in  FIGS. 1A and 1B , and from this, the foregoing corrected preset value of the third alignment error correction parameter is obtained. 
     Although the foregoing embodiment has been explained for the case of obtaining the corrected alignment error correction parameter Estimate for the parameters ChipMagX and ChipMagy, it should be noted that the method of the present invention is applicable also to any of the items shown in  FIG. 6 . 
     Further, it should be noted that the preset values used in the foregoing process for the initial value of the alignment error correction parameters of the exposure apparatuses S 1  and S 2  are not limited to those obtained from the trend of the true value as explained before, but any arbitrary values can be used as long as they fall within the range in which the correction can be made. 
     Further, while the foregoing explanation has been made based on the assumption that the exposure apparatus S 1  and the exposure apparatus S 2  are different exposure apparatuses, it is also possible that these are the same exposure apparatus. 
     Further, while the relationship of Equation (3) has been defined with regard to the current lot #j and the just-before lot #j- 1 , it is also possible to define Equation (3) for the current lot #j and arbitrary lot of the past such as the lot number #j- 1 , #j- 2 , . . . . Thereby, it is also possible to determine the value of the parameter Estimate(ChipMagX,Y, L j ) from a simple average or weighted average of these. 
       FIGS. 9A–9D  show examples of alignment achieved according to the present embodiment. 
     Referring to  FIGS. 9A–9D , it should be noted that  FIG. 9A  represents the lot-to-lot variation of the alignment error correction parameter preset value set to the exposure apparatus S 1  at the time of exposing the lower pattern (process P0) for the parameter ChipMagX, while  FIG. 9B  shows the alignment error trend of the exposure apparatus S 1  used for the exposure of the lower pattern (process P0) for the same parameter ChipMagX. 
     Further,  FIG. 9C  shows the lot-to-lot variation of the true value, in other words the error between the preset value of the alignment error correction parameter set to the exposure apparatus S 2  at the time of the exposure of the upper pattern (process P1) and the observed exposure result, while  FIG. 9D  shows the alignment error trend of the exposure apparatus S 2  used for exposing the upper pattern (process P1). 
     It should be noted that the example of  FIGS. 9A–9D  assumes that the state of the exposure apparatuses S 1  and S 2  are stable as shown in  FIGS. 9B and 9D , and thus, the leap of the alignment correction parameter preset value P0set(ChipMagX, L 7 ) observed for the lower pattern between the lot# 6  and the lot # 7  shown in  FIG. 9A  reflects the change of exposure condition occurred at the time of exposure of a further lower pattern between the lot# 6  and the lot# 7 . In this case, it will be also noted that there is caused a corresponding leap in the exposure true value (=exposure preset value−exposure result) of the upper pattern between the lot# 6  and the lot# 7  as shown in  FIG. 9C . 
     Thus, the present embodiment provides prediction of the exposure preset values causing a leap between the lot# 6  and the lot# 7  at the time of the exposure process (process P1) of the upper pattern, based on the leap of the preset values caused between the lot# 6  and the lot# 7  at the time of the exposure of the lower pattern (process P0) and the leap of the exposure true value observed between the lot# 6  and the lot# 7  at the time of the exposure process P0, for the case in which the exposure apparatuses S 1  and S 2  themselves are in the stable state. 
     [Second Embodiment] 
       FIGS. 10A–10D  are diagrams showing the alignment method according to a second embodiment of the present invention. 
     Referring to  FIGS. 10A–10D ,  FIG. 10A  represents the lot-to-lot variation of the preset value of the alignment error preset parameter provided to the exposure apparatus S 1  at the time of exposing the lower pattern P0 for the parameter ChipMagX, while  FIG. 10B  shows the alignment error trend of the exposure apparatus used for the exposure of the lower pattern (process P0) with regard to the same parameter ChipMagX. 
     Further,  FIG. 10C  shows the lot-to-lot variation of the error between the alignment error correction parameter preset value provided to the exposure apparatus at the time of the exposure of the upper pattern (process P1) and the exposure result, and hence the lot-to-lot variation of the true value, while  FIG. 10D  shows the alignment error trend of the exposure apparatus S 2  used for the exposure of the upper pattern with the process P1. 
     In the example of  FIGS. 10A–10D , the state of the exposure apparatus is stable throughout as shown in  FIG. 10D , while it can be seen that there is caused a leap in the state of the exposure apparatus S 1  between the lot# 6  and the lot# 7  as shown in  FIG. 10B , and in correspondence to this, there is caused a variation in the alignment error correction parameter preset value used at the time of the exposure of the lower pattern in the process P0 between the lot# 6  and the lot# 7  as shown in  FIG. 10A . On the other hand, it can be seen that the exposure true value for the upper pattern shown in  FIG. 10C  takes a value almost zero in correspondence to the stability of the state of the exposure apparatus S 2 . 
     In such a case in which there is caused a variation of state in the exposure apparatus S 1 , it should be noted that the foregoing corrected alignment error correction parameter Estimate(ChipMagX,Y, L j ) is obtained as 
                 Estimate   ⁡     (     ChipMagX   ,   Y   ,     L   j       )       =       {       P   ⁢           ⁢   0   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L   j       )         -     P   ⁢           ⁢   0   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L     j   -   1         )           }     +     {       P   ⁢           ⁢   1   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L     j   -   1         )         -     P   ⁢           ⁢   1   ⁢           ⁢     result   ⁡     (     ChipMagX   ,   Y   ,     L     j   -   1         )           }         ,         
when the relationship of Equation (3) is applied directly, while this equation does not take into consideration the change of state of the exposure apparatus S 1  that has caused the leap of the alignment correction parameter preset value from P0set(ChipMagX,Y, L 6 ) to P0set(ChipMagX,Y, L 7 ) between the lot# 6  and the lot# 7 , and thus, direct application of Equation (3) to such a situation would result in a wrong prediction.
 
     In order to obtain a correct result, is is necessary to modify the foregoing equation to 
                       Estimate   ⁡     (     ChipMagX   ,   Y   ,     L   j       )       =       {       P   ⁢           ⁢   0   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L   ⁢           ⁢   7       )         -     P   ⁢           ⁢   0   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L   ⁢           ⁢   6       )           }     +     {       P   ⁢           ⁢   1   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L     j   -   1         )         -     P   ⁢           ⁢   1   ⁢           ⁢     result   ⁡     (     ChipMagX   ,   Y   ,     L     j   -   1         )           }     -     {       E   ⁢           ⁢   0   ⁢     (     t   =     L   j       )       -     E   ⁢           ⁢   0   ⁢     (     t   =     L     1   -   j         )         }         ,           (   4   )               
wherein it should be noted that E0(t=L j ) represents the variation of the state of the exposure apparatus in the case the exposure processing P0 of the lot #L j  is carried out by using the exposure apparatus S 1 , and thus, the term E0(t=L j )−E0(t=L 1-j ) represents the amount of variation of the state of the exposure apparatus S 1  from the lot #j-1 to the lot #j.
 
     Thus, in the case of the example of  FIGS. 10A–10D , it will be noted that the leap of the alignment error correction parameter preset value {P0set(ChipMagX,Y, L 7 )−P0set(ChipMagX,Y, L 6 )} between the lot # 6  and the lot # 7  is substantially cancelled out by the variation of the state of the exposure apparatus S 1 . 
     Thus, the present embodiment generalizes the foregoing relationship of Equation (3) to the relationship of Equation (4) by taking into consideration the variation of state of the exposure apparatus S 1 , while the equation (4) is further generalized, by taking into consideration the variation of state of the exposure apparatus S 2 , as 
                       Estimate   ⁡     (     ChipMagX   ,   Y   ,     L   j       )       =       {       P   ⁢           ⁢   0   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L   7       )         -     P   ⁢           ⁢   0   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L   6       )           }     -     {       E   ⁢           ⁢   0   ⁢     (     t   =   Lj     )       -     E   ⁢           ⁢   0   ⁢     (     t   =     L     1   -   j         )         }     +     {       P   ⁢           ⁢   1   ⁢           ⁢     set   ⁡     (     ChipMagX   ,   Y   ,     L     j   -   1         )         -     P   ⁢           ⁢   1   ⁢           ⁢     result   ⁡     (     ChipMagX   ,   Y   ,     L     j   -   1         )           }     -     {       E   ⁢           ⁢   1   ⁢     (     t   =     L   j       )       -     E   ⁢           ⁢   1   ⁢     (     t   =     L     1   -   j         )         }         ,           (   5   )               
wherein E1(t=Lj) represents the variation of the exposure apparatus S 2  for the case the exposure processing P1 of the lot #Lj is carried out by the exposure apparatus S 2  and the term E1(t=L j )−E1(t=L 1-j)  represents the amount of state of the exposure apparatus S 2  from the lot #j- 1  to the lot #j.
 
     Thus, with the present embodiment, the corrected preset value of the alignment error correction parameter is obtained by taking into consideration the variation of state of the exposure apparatuses S 1  and S 2 , wherein it should be noted that the foregoing variation of state E0(t=L j ) or E1(t=L j ) of the exposure apparatus S 1  or S 2  is not the quantity that can be obtained for each lot. Thus, these quantities have to be obtained by periodically processing a reference wafer and measuring the trend of alignment error. Alternatively, it is possible to construct a database for the difference between the prediction of Estimate(ChipMagX,Y, Lj) of the current lot #j and the true value ({P1set(ChipMagX,Y, Lj)−P1result(ChipMagX,Y, L j )} while regarding the same as representing the variation of state of the exposure apparatus S 2  in the case the foregoing difference exceeds a predetermined range. In this case, the state of the exposure apparatus S 2  can be defined for an arbitrary time t by integrating the same on the time axis. 
     Thus, in the present embodiment, there are provided databases DB to the exposure apparatuses S 1  and S 2  as shown in  FIG. 11  and the trend of the variation of the state of the respective exposure apparatuses are stored in the respective databases in the form of the date and time in which the change of the state has occurred together with the amount of the change. Thereby, the corrected alignment error correction parameter Estimate (ChipMagX,Y, L j ) is obtained by reading out the state E0(t) and E1(t) of the exposure apparatuses S 1  and S 2  from the database at the time of the exposure process. 
       FIG. 11 , it should be noted that those parts explained previously with reference to  FIG. 5  are designated by the same reference numerals and the description thereof will be omitted. 
     Here, it should be noted that the variation trend of the state of the exposure apparatus held in the database DB is not limited to the one related to the fabrication and production of a specific semiconductor device such as the one explained with reference to  FIGS. 1A and 1B , but it is also possible to include the trend data at the time of fabricating other various semiconductor devices into the trend data held in the database. 
     Further, while the relationship of Equation (5) is defined for the current lot #j and the just-before lot #j- 1 , it is also possible to define the quantity Estimate(ChipMagX,Y, Lj) between the current lot #j and the past lot #j-i (i=1, 2, 3, . . . ) and use the value of the quantity Estimate(ChipMagX,Y, L j ) obtained by a simple average or weighted average of these. 
     Further, the present invention is not limited to the embodiments described heretofore, but various variations and modifications may be made without departing from the scope of the invention.