Abstract:
A block management method for OPC model calibration includes calculating differences in several different optical functions between first patterns of a first mask and patterns of a second mask corresponding to the first patterns but differing therefrom by a predetermined bias, selecting one or more of the optical functions based on the calculated differences, clustering data of variations in the values of the calculated differences in the selected ones of the optical functions, selecting respective ones of the first patterns in consideration of how the data clusters, and designating the selected first patterns as test patterns.

Description:
[0001]    PRIORITY STATEMENT 
         [0002]    This application claims priority from Korean Patent Application No. 10-2012-0003036 filed on Jan. 10, 2012 in the Korean Intellectual Property Office, and all the benefits accruing therefrom under 35 U.S.C. 119, the contents of which are hereby incorporated by reference in their entirety. 
       BACKGROUND 
       [0003]    1. Field of the Inventive Concept 
         [0004]    The present inventive concept relates to lithography. More particularly, the inventive concept relates to optical proximity correction (OPC) of masks used in photolithographic processes. 
         [0005]    2. Description of the Related Art 
         [0006]    Photolithography is a process by which patterns, e.g., circuit patterns, are transcribed onto a substrate such as a semiconductor wafer. In general, in photolithography, a photosensitive film (photoresist) is formed on the wafer, the photoresist is exposed to an image of patterns of a mask (e.g., a photomask), and the photoresist is developed to remove the exposed or unexposed portions thereof. Then, the resulting photoresist pattern is used as a mask to etch a target layer under the photoresist pattern and thereby form the circuit patterns. 
         [0007]    The mask pattern and exposure conditions of the photolithography process must be designed such that the circuit patterns formed on the wafer bear a precise resemblance to the designed layout of the circuit patterns. However, the circuit patterns formed on the wafer may differ from their designed layout due to diffraction of the exposure light transmitted from certain regions of the mask where the mask patterns are complex or from regions of the mask where the size and line width, for example, of adjacent mask patterns have large differences. One technique used to obviate this problem is optical proximity correction (OPC). OPC is a predictive modeling technique in which a region of a mask having patterns whose image will not be transferred to the wafer precisely as desired will be predicted after designing the mask, and the shape of those mask patterns is altered, in their final design, based on the OPC model to compensate for differences between the design layout of the circuit patterns and the circuit patterns otherwise produced using the unaltered mask patterns. 
       SUMMARY 
       [0008]    According to an aspect of the inventive concept, there is provided a test pattern selection method for OPC model calibration, which includes quantifying optical functions of a first mask having mask patterns, quantifying the same optical functions of a second mask having mask patterns that only differ from the mask patterns of the first mask by a predetermined bias, and calculating the differences between the optical functions, respectively, of the first and second masks, then selecting certain ones of the optical functions, from among those quantified, based on the calculated differences in the optical functions, clustering data of the calculated differences in the optical functions for the selected optical functions, and selecting respective ones of the first patterns in consideration of how the data clusters, and designating the selected first patterns as test patterns. 
         [0009]    According to another aspect of the inventive concept, there is provided a method of fabricating a photomask using an OPC model calibrated using a test pattern selection method in which patterns of a first mask (first mask patterns) are sampled in a manner similar to that described above. Specifically, several different optical functions of the first mask are quantified, the same optical functions of a second mask having mask patterns that correspond to those first mask patterns, respectively, but which differ from the first mask patterns by a predetermined bias are quantified, and the differences between the optical functions, respectively, of the first and second masks are calculated. In this respect, the quantifying of the optical functions of the first mask, the quantifying of the same optical functions of the second mask, and the calculating of the differences between the optical functions are preformed for each pair of corresponding patterns of the first and second masks. Then a sensitivity matrix that includes data of values of the calculated differences in optical function for each of the optical functions, is generated. As a result, the sensitivity matrix also contains data of variations among the values of the calculated differences for each of the optical functions. The sensitivity matrix is analyzed to select one or more optical functions from among the several different optical functions. Data pertaining to the selected optical functions is pulled from the sensitivity matrix and respective ones of the first patterns are selected in consideration of how the data clusters. The selected first patterns are designated as test patterns. Then, a layout of mask patterns of a photomask is altered or “transformed” according to the calibrated OPC model, and the mask patterns are fabricated according to the altered layout. 
         [0010]    According to another aspect of the inventive concept, there is provided a test pattern selection method for OPC model calibration, which includes providing a first mask having a number of first patterns, and a second mask having a number of second patterns that are the same as the first patterns but altered by a predetermined bias, on a pattern by pattern basis with respect to the first and second patterns, quantifying differences in optical functions of the first and second masks, corresponding to changes that would occur in the optical functions if the first mask were changed to the second mask in a given photolithographic process, producing a sensitivity matrix of data representative of the differences in the optical functions, analyzing values of the data in the sensitivity matrix, using singular value decomposition (SVD), to select one or more of the optical functions from among those whose differences were quantified, generating data representing the selected optical functions using a clustering of large application (CLARA) process, and correlating the data generated using CLARA with respective ones of the first patterns and designating the respective ones of the first patterns as test selection patterns. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]    The above and other aspects and features of the inventive concept will become more apparent from the following detailed description of the preferred embodiments thereof made with reference to the attached drawings, in which: 
           [0012]      FIG. 1  is a flowchart of an embodiment of a test pattern selection method for OPC model calibration in accordance with the inventive concept; 
           [0013]      FIGS. 2 to 7  steps in the test pattern selection method for OPC model calibration in accordance with the inventive concept, wherein: 
           [0014]      FIG. 2  is schematic plan view of a first mask, 
           [0015]      FIG. 3  is a schematic plan view of a second mask, 
           [0016]      FIG. 4  is a graph of the intensity of light transmitted by the first mask from a section of the first mask taken along line line A-A′ in  FIG. 2 , 
           [0017]      FIG. 5  is a graph of the intensity of light transmitted by the second mask from a section of the second mask taken along line line B-B′ in  FIG. 3 , 
           [0018]      FIG. 6  is a diagram of a sensitivity space in which data of optical function differences of important ones of the optical functions is plotted, and 
           [0019]      FIG. 7  is a simplified form of the sensitivity space; 
           [0020]      FIG. 8  is a graph of model prediction error based on the number of test patterns selected in a method according to the inventive concept and in a prior art method; 
           [0021]      FIG. 9  is a flowchart of a lithographic method of forming patterns in accordance with inventive concept; and 
           [0022]      FIG. 10  is a sectional view of a wafer illustrating exposure and developing steps in the lithographic method, and 
           [0023]      FIG. 11  is a sectional view of the wafer illustrating an etching step. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0024]    The inventive concept will be described more fully hereinafter with reference to the accompanying drawings. In some of the drawings, the number, sizes and relative sizes and shapes of patterns and layers shown in section may be simplified or exaggerated for clarity. 
         [0025]    Other terminology used herein for the purpose of describing particular examples or embodiments of the inventive concept is to be taken in context. For example, the terms “comprises” or “comprising” when used in this specification specifies the presence of stated features or processes but does not preclude the presence or additional features or processes. The term “mask pattern” may refer to a group of several geometric features spaced from each other, and which group may be repeated. 
         [0026]    Hereinafter, a test pattern selection (sampling) method for OPC model calibration in accordance with an embodiment of the present invention will be described with reference to  FIGS. 1 to 7 . 
         [0027]    Referring to  FIGS. 1 to 3 , there are provided a first mask M 1  including a number of patterns (first patterns) and a second mask M 2  including a number of patterns different (second patterns) from the first patterns (step S 100 ). 
         [0028]    For simplicity,  FIG. 2  illustrates the first mask M 1  as having several first patterns. However, in actuality, the first mask M 1  has millions or so of the first patterns. For example, the first mask M 1  may be a spider mask having a number of test patterns on the order of several millions. 
         [0029]    The patterns of the second mask M 2  are the same as the patterns of the first mask M 1  but altered by a predetermined bias AM. For example, referring to  FIG. 3 , the second patterns are equivalent to the first patterns of the first mask M 1  expanded by a predetermined bias AM. However, the inventive concept is not so limited. For instance, the second patterns may be equivalent to the patterns of the first mask M 1  contracted by the predetermined bias AM. 
         [0030]    In other words, the patterns of the second mask M 2  may be equivalent to any uniform alteration of the patterns of the first mask M 1 . 
         [0031]    Also, for simplicity,  FIG. 3  illustrates only several second patterns of the second mask M 2 . However, in practice, the second mask M 2 , like the first mask M 1 , has a number of patterns on the order of several millions. 
         [0032]    Next, a sensitivity matrix is generated (step S 110 ). The sensitivity matrix is a matrix of data of differences in optical functions between the first mask M 1  and the second mask M 2  on a pattern by pattern basis. Optical function basically refers to results of a photolithographic process dependent on the geometry of the mask pattern. Therefore, the sensitivity matrix is a matrix of differences in outcome between using the first mask M 1  in a photolithographic process and the second mask M 2  in the same photolithographic process (i.e., under the same process parameters). 
         [0033]    In this regard, optical results of a photolithography process will change as the geometry of the mask patterns change, in this case by the predetermined geometrical bias ΔM. Examples of the optical results dependent on characteristics of the mask pattern, i.e., examples of the optical functions, are the critical dimension (CD) of the pattern formed as a result of the photolithography process, the contrast of the image transmitted by the mask (onto some focal plane which in practice is within the photoresist), the slope of the sidewalls of the pattern formed, the contour of the pattern formed, and the intensity of the light transmitted by the mask, Imax and Imin. These are but examples and the inventive concept is not limited to them. 
         [0034]    Thus, the sensitivity matrix may be generated by measuring (quantifying) a plurality of optical functions, respectively, of the first and second masks M 1  and M 2  pattern by pattern, calculating the difference between the value of that optical function and the value of the same optical function of the mask M 2  pattern by pattern, and arranging the calculations in a matrix. 
         [0035]    For example, the intensity of light transmitted from the first mask M 1  along line A-A′ in  FIG. 2  (i.e., from one pattern) is illustrated in  FIG. 4 , and the intensity of light transmitted from the second mask M 2  along line B-B′ in  FIG. 3  (i.e., from a corresponding pattern) is illustrated in  FIG. 5 . Referring to these  FIGS. 4 and 5 , it can be seen that the intensity of light changes as the shape of the pattern of the first mask M 1 , through which line A-A′ passes, is geometrically altered by the predetermined bias ΔM. A value of this change may be referred to as an optical function difference. 
         [0036]    An example of the sensitivity matrix S is shown below. 
         [0000]    
       
         
           
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         [0037]    Here, each row of the sensitivity matrix S represents the optical function differences between a respective pair of the corresponding patterns of the masks M 1  and M 2 . Each column of the sensitivity matrix S is thus a representation of variations in the optical function differences for a respective one of the optical functions. Thus, the columns represent the optical differences between masks M 1  and M 2  for each pair of corresponding first and second mask patterns. 
         [0038]    In this example of the sensitivity matrix, the first column shows the variations of the changes in the critical dimensions (CD) of the patterns produced by in effect changing the mask patterns from the first patterns (patterns of the mask M 1 ) to the second patterns (patterns of the second mask M 2 ), the second column shows the variations in the contour, the third column shows the variations in contrast, the fourth column shows the variations in Imax, the fifth column shows the variations of the Imin, and the sixth column shows the variations in slope. 
         [0039]    The sensitivity matrix S may have more columns than in the above-illustrated example because, as mentioned above, various other optical functions of a mask may change with changes in the geometry of the mask patterns by a predetermined bias ΔM. Also, the arrangement of the columns in the matrix S is not limited to that shown above. 
         [0040]    Next, important ones of the functions among the optical functions in the sensitivity matrix S are selected (step S 120 ). More specifically, the optical functions that make a significant impact on the mask performance or “sensitivity” are selected by analyzing (the values in) the sensitivity matrix S using statistics. 
         [0041]    To this end, the sensitivity matrix S is normalized. 
         [0042]    An example in which the sensitivity matrix S is transformed through singular value decomposition (SVD) is shown below. 
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         [0043]    Accordingly, the rank of the sensitivity matrix S may be reduced. Then, the important optical functions are selected based on a comparison of the singular values σ 1  to σ P  in the transformed sensitivity matrix S shown above. 
         [0044]    For example, among the above-mentioned optical functions, i.e., critical dimension (CD), contrast, slope, contour, Imax, and Imin, the critical dimension (CD) and contrast are selected through this process as the important optical functions. 
         [0045]    Then, the values of the optical function differences of the selected (“important”) optical functions, i.e., data from those columns of the sensitivity matrix pertaining to the selected (“important”) optical functions, are clustered (step S 130 ). 
         [0046]    More specifically, for example as shown in  FIG. 6 , first, the values of the differences in optical function between corresponding patterns of the first and second masks M 1  and M 2  due to differences ΔM in the geometrical shapes of the corresponding patterns, for each of the selected optical functions (CD and contour in this example), are plotted in a sensitivity space. In the sensitivity space of  FIG. 6 , the values associated with the critical dimension (CD) are plotted along the X axis, and the values associated with the contrast are plotted along the Y axis. Only some of the very many (approximately millions of) data points that may be obtained this way are shown in  FIG. 6 . 
         [0047]    The load of the system of data can be reduced while maintaining the accuracy of the OPC model if similar optical functions differences, as represented by adjacent points in the sensitivity space, are represented by only one data point. In this case, the corresponding pairs of mask patterns which show similar variations in the values of their optical function differences, with respect to the important optical functions of critical dimension (CD) and contrast, serve as a load in the system. Therefore, the clustering method clusters the similar values of the optical function (critical dimension (CD) and contrast) differences, and assigns to each cluster a value representative of the cluster. 
         [0048]    To this end, various data clustering methods know per se may be used. That is, any well-known clustering method may be used as long as the between-cluster variation (spread among the values assigned to the clusters) is larger than the within-cluster variation (spread of values within each cluster). As an example, an iterative clustering process may be used. 
         [0049]    In an example of this embodiment, a clustering of large application (CLARA) method is used. In this method, by using an objective cost function Q represented by the following equation, a representative value m j  at a minimum of the objective cost function Q is assigned to each cluster c j . 
         [0000]    
       
         
           
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         [0050]    Here, k is a designated number for each cluster, x i  refers to an i-th point among the illustrated points, and c j  refers to a j-th cluster of data represented by the value in m j . 
         [0051]    Thus, a large amount of data can be processed in a short period of time. 
         [0052]    When the above-described clustering process is completed, the sensitivity space is simplified. In the example of this embodiment described above, sensitivity space shown  FIG. 6  may wind up simplified as shown in  FIG. 7 . For example, a first cluster C 1  of data points of the sensitivity space of  FIG. 6  is represented by value m 1  in  FIG. 7 . The representative values shown in  FIG. 7  although minimal are capable of improving the accuracy (predictive power) of the OPC model. These representative values thus correspond to test patterns. 
         [0053]    That is, referring back to  FIG. 1 , test patterns are selected among the first patterns by using the results of the clustering process (step S 140 ). More specifically, the representative values shown in  FIG. 7  are correlated with respective ones of the patterns of the first mask M 1  from which the values were derived, and these first patterns are selected (designated) as the test patterns. 
         [0054]    Then, OPC model calibration is performed (step S 150 ). Specifically, the test patterns SEM are measured using a scanning electron microscope (SEM), and these measurements are used to calibrate an OPC model. Then a photomask subjected to OPC based on the calibrated OPC model, is fabricated. In general, mask patterns in the shape and arrangement of a desired circuit pattern to be formed are laid out, the geometry of the mask patterns is altered based on the calibrated OPC model thereby compensating for aspects of the lithographic process which would otherwise cause the pattern formed using the unaltered mask patterns in a lithographic process to differ from the desired circuit pattern. Because OPC models, and the calibrating of an OPC model using SEM measurements of a sample of mask patterns, are well known per se, the specifics of the OPC model calibration according to the inventive concept will not be described in detail for the sake of brevity. 
         [0055]    However, an effect of the OPC model calibration, in accordance with the inventive concept, i.e., of determining which patterns from among all the patterns of the mask are to be used for OPC model calibration, will be described with reference to the graph of  FIG. 8 . 
         [0056]    The graph of  FIG. 8  illustrates differences in model prediction error with changes in the number of the test patterns. Here, A represents data obtained when an OPC model was calibrated based on measurements of test patterns selected using an image parameter space (IPS) technique, and B represents data obtained when the test patterns were selected according to the inventive concept. 
         [0057]    Referring to  FIG. 8 , it can be seen that the model prediction error is smaller when the OPC model was calibrated according to the inventive concept, regardless of the number of the test patterns that wind up being selected. Furthermore, it can be seen that the range of model prediction errors (difference between maximum and minimum values) is also smaller according to the inventive concept. 
         [0058]    Accordingly, it can be confirmed that the predictive power or accuracy of the OPC model calibrated in accordance with the inventive concept is improved. 
         [0059]    Next, a pattern forming method in accordance with the inventive concept will be described with reference to  FIGS. 9 to 11 . 
         [0060]    Referring to  FIGS. 9 and 10 , a substrate  1100  is provided (step S 500 ). In this example, the substrate  1100  is a semiconductor wafer on which a layer of photoresist has been formed. Then, a mask  1000  is formed on the substrate  1100  (step S 510 ). In one example of this embodiment, the mask  1000  is formed by exposing and developing the photoresist layer, wherein the exposure process uses a photomask which has been designed and fabricated using OPC calibrated in the manner described above according to the inventive concept. 
         [0061]    Then, referring to  FIGS. 9 and 11 , the substrate  1100  is patterned (step S 520 ). Specifically, areas of the substrate  1100  are etched as illustrated using the mask  1000  disposed on the substrate  1100  as an etch mask, thereby forming trenches  1110  in the substrate  1100 . Accordingly, a specific pattern  1120 , as defined by the trenches  1110  formed in the substrate  1100 , is transcribed to the substrate  1100 . 
         [0062]    Finally, an embodiment of the inventive concept and examples thereof have been described above in detail. The inventive concept may, however, be embodied in many different forms and should not be construed as being limited to the embodiments described above. Rather, these embodiments were described so that this disclosure is thorough and complete, and fully conveys the inventive concept to those skilled in the art. Thus, the true spirit and scope of the inventive concept is not limited by the embodiment and examples described above but by the following claims.