Abstract:
An estimation apparatus for estimating a formation of a plurality of wiring layers for an integrated circuit to be manufactured by laminating the wiring layers each formed through a deposition process of a wiring material on a substrate and subsequently polishing the deposited wiring material, the apparatus includes a deposition estimator, a polishing estimator, and an adjuster. The apparatus includes an optimizer configured to optimize distribution of the height of the wiring material for each of the wiring layers within an acceptable range by controlling the adjuster to generate various combinations of adjusted patterns of the wiring layers and by controlling the deposition estimator and the polishing estimator to perform estimation of distribution of deposition height of the wiring material and distribution of the wiring material to be remained after polishing for each of the wiring layers, respectively, for each of the combinations of the adjusted patterns.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2008-316175, filed on Dec. 11, 2008, the entire contents of which are incorporated herein by reference. 
       FIELD 
       [0002]    The embodiments discussed herein are related to an estimation technique for estimating a formation of a plurality of wiring layers for an integrated circuit. 
       BACKGROUND 
       [0003]    In a manufacturing process of a semiconductor integrated circuit, light exposure, etching, deposition (plating) and polishing are repeated on a wafer to construct a laminate structure, thereby forming a desired circuit. At this time, productivity is enhanced by simultaneously forming plural semiconductor integrated circuits on one wafer. 
         [0004]    Particularly, it has been recently needed to increase the wafer diameter and thus increase the number of circuits to be formed in a lump. However, as the large-size design of the wafer progresses, it is harder to execute uniform processing on both the center portion and the peripheral portion of a wafer. In addition, miniaturization of circuits also progresses, and thus high-precision processing has been needed. 
         [0005]    For example, with respect to recently mainstream copper wires, ECP (Electro-Chemical Plating) of generating a wire groove on an insulating material and executing copper plating on the wire groove to fill the wire groove with copper is executed. However, not only the wire groove, but also the overall insulating material is covered by copper plating at the same time, and thus CMP (Chemical Mechanical Polishing) is used as polishing for exposing a wire pattern. 
         [0006]    Here, when a large height difference exists on the wafer as a result of CMP, dispersion in height of copper wires or wiring short-circuiting caused by residue of copper occurs. In each case, deterioration of performance or reduction in yield occurs. 
         [0007]    Furthermore, there is a case where a problem occurs in case of a lamination layer although no problem occurs in case of a monolayer. Particularly, such a problem is liable to occur in a case where a lower layer is positionally lower than the surrounding and an upper layer is positionally higher than the surrounding. 
         [0008]    It has been hitherto general to actually manufacture a semiconductor integrated circuit and correct the layout thereof after an error occurs in the thus-manufactured semiconductor integrated circuit. This process is very low in efficiency from the viewpoint of the manufacturing cost and the time cost because a wafer is actually created. Therefore, a method of simulating CMP and perform prediction and correction before the actual manufacturing has been proposed. There is Japanese Laid-open Patent Publication No. 2003-224098 as a reference document. 
         [0009]    However, when a chip is actually created and then corrected, the manufacturing cost and the time cost are caused to increase. Furthermore, when chips are manufactured with containing risky portions therein, the yield is reduced by about ten percentages. 
         [0010]    When the CMP simulation is used, it is unnecessary to actually manufacture chips. Therefore, it contributes to some degree of reduction in cost. However, the simulation needs several hours to about one day in accordance with the size of chips. When a risk portion is corrected, the CMP simulation is needed to be executed many times, and thus the total simulation time is equal to several days to several weeks in some cases. 
         [0011]    That is, the conventional technique has a problem that much time is taken to obtain a CMP result, and thus huge amounts of time are needed to determine an optimum circuit layout. 
       SUMMARY 
       [0012]    According to an aspect of the embodiment an estimation apparatus for estimating a formation of a plurality of wiring layers for an integrated circuit to be manufactured by laminating the wiring layers each formed through a deposition process of a wiring material on a substrate and subsequently polishing the deposited wiring material, the apparatus includes a deposition estimator configured to estimate distribution of a deposition height of the wiring material for each of the wiring layers, a polishing estimator configured to estimate distribution of a height of the wiring material to be remained after polishing for each of the wiring layers on the basis of the estimated distribution of the deposition height of the wiring material of each of the wiring layers and the estimated distribution of the height of the wiring material to be remained after polishing for any underlying wiring layer, an adjuster configured to adjust the pattern of at least one of the wiring layers without affecting the electrical function of the at least one of the wiring layers, and an optimizer configured to optimize distribution of the height of the wiring material for each of the wiring layers within an acceptable range by controlling the adjuster to generate various combinations of adjusted patterns of the wiring layers and by controlling the deposition estimator and the polishing estimator to perform estimation of distribution of deposition height of the wiring material and distribution of the wiring material to be remained after polishing for each of the wiring layers, respectively, for each of the combinations of the adjusted patterns. 
         [0013]    The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
         [0014]    It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention, as claimed. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0015]      FIG. 1  is a diagram illustrating the construction of an LSI manufacturing system according to an embodiment. 
           [0016]      FIG. 2  is a diagram illustrating CMP estimation and a risk degree. 
           [0017]      FIGS. 3A ,  3 B and  3 C are diagrams illustrating a scrape amount of CMP. 
           [0018]      FIG. 4  is a diagram illustrating risk degree estimation based on ECP. 
           [0019]      FIGS. 5A and 5B  are diagrams illustrating risk estimation executed in consideration of a lamination layer. 
           [0020]      FIG. 6  is a diagram illustrating creation of maximum risk degree data. 
           [0021]      FIG. 7  is a flowchart illustrating the processing operation of an LSI manufacturing system. 
           [0022]      FIG. 8  is a flowchart illustrating the processing operation based on a mesh divider  21 , an ECP calculator  22  and a risk degree estimator  23 . 
           [0023]      FIG. 9  is a flowchart illustrating the processing operation of an each-mesh maximum risk degree extractor  24 , each-layer adjustment range calculator  25 , an optimizing processor  26  and a dummy metal arranging unit  27 . 
           [0024]      FIG. 10  is a diagram illustrating calculation of a risk degree and an adjustment range. 
           [0025]      FIG. 11  is a diagram illustrating a specific example of each-layer mesh data. 
           [0026]      FIG. 12  is a diagram illustrating creation of a deposition height ecp (nm) and a monolayer risk degree F 1 . 
           [0027]      FIG. 13  is a diagram illustrating a specific example of maximum risk degree data. 
           [0028]      FIG. 14  is a diagram illustrating a specific example of corrected candidate mesh data. 
           [0029]      FIG. 15  is a diagram illustrating each-layer mesh data representing a risk degree adjustment range of each layer. 
           [0030]      FIG. 16  is a diagram illustrating each-layer mesh data representing an optimum monolayer risk degree F 2  of each layer. 
           [0031]      FIG. 17  is a diagram illustrating a dummy copper density Bdens in the optimum monolayer risk degree F 2  and each-layer mesh data representing a dummy wire circumferential length Bedge. 
           [0032]      FIG. 18  is a diagram illustrating each-layer mesh data obtained by updating the dummy-based copper density Ddens (%), the dummy-based wire circumferential length Dedge (nm), the deposition height ecp (nm) and the monolayer risk degree F 1 . 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0033]    Embodiments of an estimation apparatus, an estimation method and an estimation program will be described hereunder in detail with reference to the drawings. 
         [0034]      FIG. 1  is a diagram illustrating the construction of an LSI (large-scale integrated circuit) manufacturing system according to an embodiment. As illustrated in  FIG. 1 , the LSI manufacturing system  10  includes a layout design device  11 , a manufacturing device  12 , a CMP error check device  13  and an estimation apparatus  20 . 
         [0035]    The layout design device  11  is a device for designing a circuit layout of LSI, and first outputs a designed circuit layout to the estimation device  20 . The estimation device  20  predicts and estimates an execution result of CMP from the circuit layout, and returns an estimation result to the layout design device  11 . 
         [0036]    When the estimation result of the estimation apparatus  20  is insufficient, the layout design device  11  corrects the layout, and outputs the corrected layout to the estimation apparatus  20 . The circuit layout whose prediction and estimation result is excellent is output to the manufacturing device  12 . 
         [0037]    The manufacturing device  12  manufactures LSI on the basis of the circuit layout obtained from the layout design device  11 . In this case, the manufacturing device  12  estimates the state after execution of actual polishing by a CMP error check device  13  every layer (one cycle of exposure, etching, deposition (plating) and polishing), and returns the estimation result to the layout design device  11 . 
         [0038]    The layout design device  11  reflects the estimation result of the CMP error check device  13  to the circuit layout, determines a final layout and delivers the final layout to a mass production line, for example. 
         [0039]    The estimation apparatus  20  includes an input/output potion  31 , a data base  32 , a mesh divider  21 , an ECP calculator  22  for a deposition estimator, a risk degree estimator  23  for a polishing estimator, an each-mesh maximum risk degree extractor  24 , an each-layer adjustment range calculator  25 , an optimizing processor  26  and a dummy metal arranging unit  27 . 
         [0040]    The input/output processor  31  is an interface for registering the circuit layout received from the layout design device  11  into the data base  32 , reading out the data updated/created through the processing in the estimation apparatus  20  and delivering the updated/created data to the layout design device  11 . 
         [0041]    The mesh divider  21  subjects the circuit layout registered in the data base  32  to mesh division. Here, the circuit layout corresponds to a laminate of plural wiring layers (monolayer circuit layouts) each of which is formed through one cycle of exposure, etching, deposition (plating) and polishing described above. The mesh divider  21  divides each of the plural wiring layers into meshes as partial areas, and registers them in the data base as mesh data of each layer (each-layer mesh data). When the mesh divider  21  divides the plural wiring layers, the division is performed so that the position and size of the meshes are identical among the respective wiring layers, and also the meshes are overlapped with each other between the upper and lower layers when the upper and lower layers are laminated. 
         [0042]    The ECP calculator  22  uses an ECP model  41  to calculate the deposition height after ECP is executed on each divisional mesh. A model for calculating a deposition height on the basis of a wire density and a wire circumferential length is known as the ECP model for calculating the deposition height after execution of ECP. 
         [0043]    The risk degree estimator  23  compares a prediction value of the deposition height of a mesh with prediction values of the deposition heights of surrounding meshes by using a risk degree calculation expression  42  to calculate an estimation value for the CMP process, and determines the risk degree of CMP from the calculation result. 
         [0044]    The CMP estimation and the risk degree will be further described with reference to  FIG. 2 . In  FIG. 2 , unevenness occurs on the surface as a result of CMP. A convex portion  51   a  occurs because wiring materials (for example, copper) deposited (plated) by ECP remains. The convex portion  51   a  remaining on oxide  52  (for example, silicon oxide) for insulating copper wires  51  from each other causes wire short-circuit. Furthermore, a concave portion  51   b  occurs because copper deposited (plated) by ECP is excessively scraped. The wire resistance of the concave portion  51   b  increases, and causes deterioration of the circuit performance. 
         [0045]    The scrape amount based on CMP varies in accordance with not only the wire density, but also the wire width. Even when the wire density is equal to 50%, the wire portion would be greatly scraped if the wire width is large as illustrated in  FIG. 3A . This happens because copper is more easily scraped than oxide. Even when the wire density is equal to 50% and the wire width is small as illustrated in  FIG. 3C , the wire portion is more easily scraped as a whole because the width of the oxide is also reduced. On the other hand, when the wire density is equal to 50% and the wire width is middle as illustrated in  FIG. 3B , the width of the oxide is sufficiently stout to CMP and also the oxide portions are arranged at proper intervals, so that the scrape amount is small. 
         [0046]    Therefore, by utilizing the fact that the height of ECP (plating) or the deposition amount of copper propagates and it affects the height after polishing based on CMP, the estimation apparatus  20  obtains the height difference between the deposition height of copper and the height of the surrounding portion as an estimation value, that is, it estimates the result of CMP and obtains it as a value representing a risk degree at which wiring short-circuiting or deterioration of circuit performance occurs. 
         [0047]    Specifically, when a target place is high and the surrounding portion around the target place is low as illustrated in  FIG. 4 , it is determined that the risk degree is high. When the deposition height of the target place is high and the surrounding portion is also high, it is determined that the risk degree is low, and also when the deposition height of the target place is low and the surrounding portion is also low, it is likewise determined that the risk degree is low. 
         [0048]    Furthermore, in consideration of the fact that the unevenness after CMP is amplified by the lamination, the height difference between the upper and lower layers is also estimated. For example, as illustrated in  FIG. 5B , in a case where the lower layer is low and the upper layer is high, copper is more liable to remain at a portion where copper is originally liable to remain because the bottom surface of the portion concerned is lower than the surrounding portion around the portion concerned. Therefore, a trouble caused by wire short-circuit may occur at this portion. 
         [0049]    In a case where the lower layer is high and the upper layer is low, copper is more easily scraped at a portion where copper is originally easily scraped because the bottom surface of the portion concerned is higher than the surrounding portion around the portion concerned. Therefore, the wire height is reduced, and thus the deterioration of performance may occur. 
         [0050]    On the other hand, as illustrated in  FIG. 5A , in a case where both the lower layer and the upper layer are high and also in a case where both the lower layer and the upper layer are low, the wiring short-circuiting and the deterioration performance relatively hardly occur. Therefore, in the estimation apparatus  20 , the estimation value of the mesh is compared with the estimation values of the upper and lower layers, whereby a lamination-layer estimation value is calculated in consideration of the lamination layer. 
         [0051]    The each-mesh maximum risk degree extractor  24  creates maximum risk degree data obtained by extracting the maximum risk degree as the maximum estimation value representing highest necessity of improvement from estimation values of plural meshes laminated at the same position on a deposition plane. 
         [0052]    The creation of the maximum risk degree data will be described with reference to  FIG. 6 . When the risk degrees of meshes at the coordinate (x,y)=(3,1) are compared with one another, the risk degree on a second layer (layer L 2 ) is highest, and thus the maximum risk degree of the mesh (3, 1) of the maximum risk degree data Lcx is set to the same value as the risk degree of the mesh (3, 1) of the layer L 2 . 
         [0053]    Likewise, when the risk degrees of the meshes at the coordinate (x,y)=(5, 4) are compared with one another, the risk degree on the second layer (layer L 2 ) is highest, and thus the maximum risk degree of the mesh (5, 4) of the maximum risk degree data Lcx is set to the same value as the risk degree of the mesh (5, 4) of the layer L 2 . 
         [0054]    Furthermore, when the risk degrees of the meshes at the coordinate (x,y)=(7, 5) are compared with one another, the risk degree of a layer (layer L 1 ) which is first formed on the deposition plane is highest, and thus the maximum risk degree of the mesh (7, 5) of the maximum risk degree data Lcx is set to the same value as the risk degree of the mesh (7, 5) of the layer L 2 . 
         [0055]    When the risk degrees of the meshes at the coordinate (x,y)=(2, 6) are compared with one another, the risk degree of a layer (layer Lmax) which is finally formed on the deposition plane is highest, and thus the maximum risk degree of the mesh (2, 6) of the maximum risk degree data Lcx is set to the same value as the mesh (2, 6) of the layer Lmax. 
         [0056]    The each-layer adjustment range calculator  25  registers mesh coordinates providing the maximum risk degrees exceeding a threshold value in the maximum risk degree data into the corrected candidate mesh data. 
         [0057]    With respect to each of the mesh coordinates registered in the corrected candidate mesh data, the each-layer adjustment range calculator  25  calculates a risk-degree changeable range of each of the meshes of the respective layers to be laminated on the mesh coordinate concerned. Here, a case where the adjustment range of the risk degree is determined will be described. The risk degree is a value determined on the basis of the deposition height, and thus the adjustment range of the deposition height may be determined. 
         [0058]    Specifically, the adjustment of the risk degree or the deposition height is executed by changing the layout (patterns) of dummy metal as a wire which does not affect the electrical characteristic of the circuit. 
         [0059]    The optimizing processor  26  optimizes the distribution of the risk degree (or the deposition height when the deposition height is used) of each mesh in the adjustment range calculated by the each-layer adjustment range calculator  25 . 
         [0060]    The dummy metal arranging unit  27  calculates the arrangement of the dummy metal of each mesh so that the mesh concerned has the risk degree (or the deposition height when the deposition height is used) calculated by the optimizing processor  26 . 
         [0061]    Next, the overall processing operation of the LSI manufacturing system will be described with reference to the flowchart of  FIG. 7 . As illustrated in  FIG. 7 , the layout design device  11  first designs a layout (operation S 101 ), and then the estimation apparatus  20  executes risk degree determination processing (operation S 102 ). 
         [0062]    As a result, when a risk degree which is not less than a threshold value is output, the estimation apparatus  20  outputs a risk degree error (operation S 103 , Yes), and the layout design device  11  which receives the risk degree error executes layout design again (operation S 101 ). 
         [0063]    On the other hand, when the risk degree is less than the threshold value (operation S 103 , No), the manufacturing device  12  executes the manufacturing (operation S 104 ), and the CMP error check device  13  executes the CMP error check (operation S 105 ). 
         [0064]    As a result, when the CMP error check device  13  outputs the CMP error (operation S 105 , Yes), the layout design device  11  executes the layout design again (operation S 101 ). When the CMP error check device  13  does not output any CMP error (operation  5105 , No), it is determined that a proper circuit layout is obtained, and thus the processing is finished. 
         [0065]    Next, a specific processing operation of the risk degree determination processing of the estimation apparatus  20  will be described.  FIG. 8  is a flowchart illustrating the processing operation based on the mesh divider  21 , the ECP calculator  22  and the risk degree estimator  23 . 
         [0066]    The mesh divider  21  first selects the lowermost layer, that is, a circuit layout to be first formed on the deposition plane from the each-layer mesh data (operation S 201 ), and subjects the selected layer to mesh division (i.e., divides the selected layer into plural meshed areas) (operation S 202 ). 
         [0067]    Subsequently, the ECP calculator  22  selects a mesh as a processing target (operation S 203 ), and calculates the deposition height of the target mesh by ECP simulation (operation S 204 ). 
         [0068]    Thereafter, the ECP calculator  22  determines whether the calculation of the deposition height on all the meshes is finished or not (operation S 205 ). If the calculation is not finished (operation S 205 , No), the processing returns to the mesh selection (operation S 203 ). 
         [0069]    When the calculation of the deposition height on all the meshes is finished (operation S 205 , Yes), the risk degree estimator  23  selects a next processing target mesh (operation S 206 ), and executes the risk degree calculation on the target mesh concerned (operation S 207 ). 
         [0070]    Thereafter, the risk degree estimator  23  determines whether the risk degree calculation on all the meshes is finished or not (operation S 208 ). If the calculation is not finished (operation S 208 , No), the processing returns to the mesh selection (operation S 206 ). 
         [0071]    When the calculation of the risk degree on all the meshes is finished (operation S 208 , Yes), it is determined whether the processing on all the layers is finished or not (operation S 209 ). When the processing is not finished (operation S 209 , No), the processing returns to the selection of the determination target layer, and a just-above layer is selected (operation S 201 ). 
         [0072]    When the determination on all the layers is finished (operation S 209 , Yes), a calculation result is output (operation S 210 ), and the processing is finished. 
         [0073]      FIG. 9  is a flowchart illustrating the processing operation of the each-mesh maximum risk degree extractor  24 , the each-layer adjustment range calculator  25 , the optimizing processor  26  and the dummy metal arranging unit  27 . 
         [0074]    First, the each-mesh maximum risk degree extractor  24  records, as the maximum risk degree, the maximum value of the risk degrees of all the meshes to be laminated on each mesh coordinate in association with the mesh coordinate (operation S 301 ). Furthermore, it registers, in the corrected candidate mesh data, mesh coordinates at which the maximum risk degrees are not less than a threshold value (operation S 302 ). 
         [0075]    When there exists some mesh coordinate registered in the corrected candidate mesh data (operation S 303 , Yes), the each-layer adjustment range calculator  25  selects the mesh coordinate at which the value of the registered mesh coordinate, and the maximum risk degree is highest (operation S 304 ). 
         [0076]    With respect to the mesh of each layer formed on the selected mesh coordinate, the each-layer adjustment range calculator  25  calculates a risk-degree range adjustable by changing the layout (patterns) of the dummy metal (operation S 305 ). 
         [0077]    The optimizing processor  26  derives an optimum risk degree of each mesh in the adjustable range calculated by the each-layer adjustment range calculator  25  (operation S 306 ), updates the data of the wire density and the wire circumference length so that each mesh has the thus-derived optimum risk degree and updates the risk degree on the basis of the thus-updated wire density and wire circumference length (operation S 307 ). Thereafter, the selected mesh coordinate is removed from the corrected candidate mesh data (operation S 308 ), and then the processing returns to the operation S 303 . 
         [0078]    When the corrected candidate mesh data is under the state that no mesh coordinate is registered in the corrected candidate mesh data (operation S 303 , No), it is determined whether the processing may be finished or not (operation S 309 ). This is because when the temporarily registered corrected candidate mesh data are updated by optimizing the risk degree, the updated new risk degree may exceed the threshold value. Specifically, in the finishing determining process, when all the maximum risk degrees are less than the threshold value or when the repetitive frequency of the processing from the extraction of the maximum risk degree till the optimization of the risk degree reaches a predetermined one, it is determined that the processing may be finished. 
         [0079]    When the processing is not finished (operation S 309 , No), the processing returns to the operation S 301 . When the processing is finished (operation S 309 , Yes), the arrangement of the dummy metal is calculated in conformity with the risk degree updated by the dummy metal arranging unit  27  (operation S 310 ), and then the processing is finished. 
         [0080]    Next, the calculation of the risk degree and the adjustment range will be described with reference to  FIG. 10 . The estimation apparatus  20  sections an LSI chip in a mesh form, and a mesh having a sharp plating (deposition) height difference from surrounding meshes around the mesh is set as a risk place. Various manners such as the difference from the average value of several surrounding meshes, the deviation, etc. may be applied. 
         [0081]    For example, the absolute value of the difference between the deposition (plating) height of a target mesh and the average deposition (plating) height of the surrounding meshes is set as the value of the risk degree (estimation value), and “risk degree error” is output when the estimation value is equal to 200 nm or more. In this case, when the deposition height of a target mesh (center mesh) is equal to +100 nm from a reference plane, the deposition height of the adjacent meshes is equal to −50 nm and the deposition height of the surrounding meshes around the adjacent meshes is equal to −80 nm as illustrated in  FIG. 10 , the simple average value of the deposition height is equal to (−50*8+−80*16+100)/25=−63.2(nm), and the mono-layer risk degree of the target mesh is equal to 100−(−63.2)=163.2. 
         [0082]    Furthermore, when the averaging is executed while the first surrounding meshes (the meshes which are just adjacent to the target mesh) are weighted by (×1.0) and the second surrounding meshes (the meshes which surround the target mesh through the first surrounding meshes) are weighted by (×0.5), the average value of the deposition height is calculated by (−50*8+(−80)*16*0.5+100)/(1+8+16*0.5)=−55.3, and thus the monolayer risk degree of the target mesh is equal to 100−(−55.2)=155.3. 
         [0083]    Furthermore, when an index of a lamination layer is derived on the basis of the difference in numerical value between the upper and lower layers, the difference between the monolayer risk degree of the target mesh and the monolayer risk degree of the lower layer may be calculated. For example, when the monolayer risk degree of the target mesh is equal to 163.2 and the monolayer risk degree of the lower layer is equal to −70, the risk degree of the lamination layer is equal to 163.2−(−70)=233.2 (nm). 
         [0084]    The adjustment range of the risk degree of the center mesh will be considered by applying to a case where the risk degree of the mesh at the center is calculated from the simple average value, that is, the monolayer risk degree of the center mesh is equal to 163.2 as described. 
         [0085]    When the dummy metal is arranged in the mesh, a dummy metal insertable area is determined every mesh by an original circuit layout, and the changeable wire density is restricted by insertion of a dummy. Furthermore, in the case of the same wire density, the deposition height is increased as the size of the dummy metal is reduced and the number of the dummy metal pieces is increased. On the other hand, the deposition height is reduced as the size is increased and the number is reduced. 
         [0086]    In the example of  FIG. 10 , the upper limit of the deposition height is equal to +140 nm by changing the layout (patterns) of the dummy inserted into the dummy insertable area. Accordingly, the average deposition height is equal to (−50*8+−80*16+140)/25=−61.6(nm), and the upper limit of the monolayer risk degree of the target mesh is equal to 140−(−61.6)=201.2. 
         [0087]    The deposition height when no dummy is inserted is equal to +90 nm. Accordingly, the average deposition height is equal to (−50*8+−80*16+90)/25=−63.6(nm), and thus the monolayer risk degree of the target mesh is equal to 90−(−63.6)=153.6. 
         [0088]    The lower limit of the deposition height when the layout (patterns) of the dummy inserted into the dummy insertable area is equal to +70 nm. Accordingly, the average deposition height is equal to (−50*8+−80*16+70)/25=−64.4(nm), and the lower limit of the monolayer risk degree of the target mesh is equal to 70−(−61.6)=134.4. 
         [0089]    Next, the optimization of the risk degree will be further described. When the risk degree is optimized, specifically, the difference in risk degree between layers, that is, the sum of squares of the risk degrees of the lamination layer may be minimized. Furthermore, the risk degree in the monolayer may be considered, or any function may be used to weight the risk degree or the like. 
         [0090]    With respect to the optimization itself, all the layers may be optimized at once by using a gradient method, a steepest descent method or the like, or the optimization may be performed every two layers. 
         [0091]    As an example, when the uppermost plane is set to an n-th layer and the initial risk degree of an i-th layer is set to x i   (0) , the risk degree may be optimized by the calculation expression below: 
         [0000]    
       
         
           
             [ 
             
               
                 f 
                  
                 
                   ( 
                   x 
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         x 
                         n 
                       
                       - 
                       
                         x 
                         
                           n 
                           - 
                           1 
                         
                       
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     
                       ( 
                       
                         
                           x 
                           
                             n 
                             - 
                             1 
                           
                         
                         - 
                         
                           x 
                           
                             n 
                             - 
                             2 
                           
                         
                       
                       ) 
                     
                     2 
                   
                    
                   
                       
                   
                    
                   … 
                    
                   
                       
                   
                    
                   
                     
                       ( 
                       
                         
                           x 
                           2 
                         
                         - 
                         
                           x 
                           1 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
             
             ] 
           
         
       
       
         
           
             
               f 
                
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               
                 
                   ( 
                   
                     
                       x 
                       n 
                     
                     - 
                     
                       x 
                       
                         n 
                         - 
                         1 
                       
                     
                   
                   ) 
                 
                 2 
               
               + 
               
                 
                   
                     ( 
                     
                       
                         x 
                         
                           n 
                           - 
                           1 
                         
                       
                       - 
                       
                         x 
                         
                           n 
                           - 
                           2 
                         
                       
                     
                     ) 
                   
                   2 
                 
                  
                 
                     
                 
                  
                 … 
                  
                 
                     
                 
                  
                 
                   
                     ( 
                     
                       
                         x 
                         2 
                       
                       - 
                       
                         x 
                         1 
                       
                     
                     ) 
                   
                   2 
                 
               
             
           
         
       
       
         
           
             ( 
             
               
                 x 
                 
                   ( 
                   
                     k 
                     + 
                     1 
                   
                   ) 
                 
               
               = 
               
                 
                   x 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 - 
                 
                   α 
                    
                   
                     [ 
                     
                       
                         
                           
                             
                               ∂ 
                               
                                 f 
                                  
                                 
                                   ( 
                                   
                                     x 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                             / 
                             
                               ∂ 
                               
                                 x 
                                 1 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               ∂ 
                               
                                 f 
                                  
                                 
                                   ( 
                                   
                                     x 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                             / 
                             
                               ∂ 
                               
                                 x 
                                 2 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             
                               ∂ 
                               
                                 f 
                                  
                                 
                                   ( 
                                   
                                     x 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                             / 
                             
                               ∂ 
                               
                                 x 
                                 n 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
             
             ) 
           
         
       
       
         
           
             
               x 
               
                 ( 
                 
                   k 
                   + 
                   1 
                 
                 ) 
               
             
             = 
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               - 
               
                 α 
                  
                 
                   [ 
                   
                     
                       
                         
                           
                             ∂ 
                             
                               f 
                                
                               
                                 ( 
                                 
                                   x 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                           / 
                           
                             ∂ 
                             
                               x 
                               1 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             ∂ 
                             
                               f 
                                
                               
                                 ( 
                                 
                                   x 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                           / 
                           
                             ∂ 
                             
                               x 
                               2 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         ⋮ 
                       
                     
                     
                       
                         
                           
                             ∂ 
                             
                               f 
                                
                               
                                 ( 
                                 
                                   x 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                           / 
                           
                             ∂ 
                             
                               x 
                               n 
                               
                                 ( 
                                 x 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
         [0092]      FIG. 11  is a diagram illustrating a specific example of each-layer mesh data as input/output data of the estimation apparatus  20 . The data illustrated in  FIG. 11  include items of the mesh coordinate x, the mesh coordinate y, the layer (Lay), the copper density dens, the wire circumference length edge (nm), the dummy insertable area Darea, the dummy-based copper density Ddens (%), the dummy-based wire circumference length Dedge (nm), the deposition (plating) height ecp (nm), the monolayer risk degree F 1 , the monolayer risk degree upper limit Max, the monolayer risk degree lower limit Min, the optimum monolayer risk degree F 2 , and the dummy copper density Bdens and the dummy wire circumference length Bedge at the optimum monolayer risk degree F 2 . 
         [0093]    The items which have been already input in  FIG. 11  are data which are obtained from the data created by the layout design device  11 , and values have been input in only the mesh coordinate x, the mesh coordinate y, the layer (Lay), the copper density dens, the wire circumference length edge (nm), the dummy insertable area Darea, the dummy copper density Ddens and the dummy wire circumference length Dedge (nm). 
         [0094]    The ECP calculator  22  and the risk degree estimator  23  executes ECP simulation and risk degree check by using the data illustrated in  FIG. 11 , and fills the values of the deposition height ecp (nm) and the monolayer risk degree F 1  into these items ( FIG. 12 ). 
         [0095]    The each-mesh maximum risk degree extractor  24  extracts the maximum risk degree with respect to each mesh coordinate, and creates maximum risk degree data illustrated in  FIG. 13 . The maximum risk degree data illustrated in  FIG. 13  include the items of the mesh coordinates x, y and the maximum risk degree Fworst. In  FIG. 12 , the maximum risk degree is the maximum value of the risk degree at the same mesh coordinate, and it is the maximum value in the monolayer risk degree F 1  and the lamination layer risk degree corresponding to the difference in monolayer risk degree F 1  between the adjacent layers in the up-and-down direction. In these maximum risk degree data, the mesh coordinate at which the maximum risk degree exceeds a predetermined threshold value is a risk place which is needed to be corrected. In  FIG. 13 , the maximum risk degree at (x,y)=(44, 27) exceeds the threshold value. 
         [0096]    The corrected candidate mesh data are data for holding risk places as correction candidates. As illustrated in  FIG. 14 , mesh coordinates at which the maximum risk degree exceeds the threshold value are extracted from the maximum risk degree data, and then sorted in the order of the maximum risk degree. 
         [0097]      FIG. 15  illustrates data obtained by selecting the mesh coordinate providing the largest maximum risk degree, that is, the first mesh coordinate of the corrected candidate data and determining the risk degree adjustment range of each layer. Specifically, with respect to the data illustrated in  FIG. 15 , data are extracted from the each-layer mesh data for (x,y)=(27, 44) which is the head data illustrated in  FIG. 14 , and the monolayer risk degree upper limit Max and the monolayer risk degree lower limit Min of each layer are determined. In  FIG. 15 , the lamination layer risk degree between layer=2 and layer=3 is equal to 320, and thus it is the maximum risk degree. 
         [0098]      FIG. 16  illustrates data obtained by optimizing the distribution of the risk degree between the monolayer risk degree upper limit Max and the monolayer risk degree lower limit Min and determining the optimum monolayer risk degree F 2  of each layer. 
         [0099]      FIG. 17  illustrates a state that the dummy copper density Bdens and the dummy wire circumference length Bedge at the optimum monolayer risk degree F 2  are determined from the optimum monolayer risk degree F 2  of each layer. 
         [0000]    Here, with respect to layer=4, the monolayer risk degree F 1  is equal to the optimum monolayer risk degree F 2 , and thus it is unnecessary to determine anew the dummy copper density Bdens and the dummy wire circumference length Bedge. 
         [0100]      FIG. 18  is a diagram illustrating a state that the dummy-based copper density Ddens (%), the dummy-based wire circumference length Dedge (nm), the deposition height ecp (nm) and the monolayer risk degree F 1  are updated from the dummy copper density Bdens and the dummy wire circumference length Bedge at the optimum monolayer risk degree F 2 . Here, with respect to layer=4, the monolayer risk degree F 1  and the optimum monolayer risk degree F 2  are equal, and the dummy copper density Bdens and the dummy wire circumference length Bedge are not determined. Therefore, these data are not needed to be updated. 
         [0101]    As described above, in the LSI manufacturing system illustrated in the above embodiment, the estimation apparatus  20  subjects the circuit layout to mesh division, and simulates the deposition (plating) height of each mesh and determines the risk degree on the basis of the variation of the ECP deposition (plating) height. Furthermore, it optimizes the distribution of the risk degree in the height direction with respect to the meshes of the respective layers formed at the same mesh coordinate. 
         [0102]    The ECP simulation (or the index of ECP) is determined in a shorter period of time as compared with the CMP simulation. Therefore, the CMP result may be predicted and estimated in a short period of time, and thus the layout correction speed may be increased, so that the yield may be enhanced in a short period of time. 
         [0103]    Specifically, it is considered that the arrangement of the dummy metal is likewise changed by using the CMP simulation. In the case of ECP, the effect of the change of one mesh is closed in the mesh. However, in the case of CMP, the change of one mesh affects the overall chip, and thus the whole surface of the chip has to be simulated every time. Accordingly, assuming that the dummy is changed ten times in an area of 10% of the chip, it is roughly estimated that a calculation time of 8 hours× several thousands times or more is needed. 
         [0104]    Particularly, the optimization is executed in consideration of all the layers in the height direction. Therefore, the layout correction speed may be more increased as compared with the case where the correction is executed in consideration of the horizontal direction of the same layer or only the risk degrees of layers adjacent to each other in the up-and-down direction. 
         [0105]    The estimation apparatus may be constructed to provide an estimation program to a computer (CPU) of an LSI manufacturing system. 
         [0106]    The estimation program may be stored in ROM of a computer, or stored in a “portable physical medium” such as a computer-readable flexible disk (FD), CD-ROM, a magneto-optical disk or the like, or in “another computer (or sever)” or the like connected to the computer through a public line, the Internet, LAN, WAN or the like so that the computer reads out and executes the program. 
         [0107]    According to this embodiment, the estimation of the polishing process is executed in consideration of the lamination layer by using a deposition (plating) process simulation whose processing time is short. Therefore, there may be obtained the estimation apparatus, the estimation method and the storage medium having the estimation program stored therein with which the result of the polishing process may be estimated in a short period of time and thus the layout correction time may be increased, so that the yield may be enhanced in a short period of time. 
         [0108]    All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the principles of the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although the embodiments of the present inventions have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.