Abstract:
A model based measurement method is capable of estimating a cross-sectional shape by matching various pre-created cross-sectional shapes with a library of SEM signal waveforms. The present invention provides a function for determining whether or not it is appropriate to create a model of a cross-sectional shape or a function for verifying the accuracy of estimation results to a conventional model based measurement method, wherein a solution space (expected solution space) is obtained by matching library waveforms and is displayed before measuring the real pattern by means of model based measurement. Moreover, after the real pattern is measured by means of model based measurement, the solution space (real solution space) is obtained by matching the real waveforms with the library waveforms and is displayed.

Description:
BACKGROUND 
     The present invention relates to a shape measurement method and its system for measuring the three-dimensional shape of a pattern of a semiconductor device. 
     As described in Semiconductor Equipment Association of Japan (SEAJ) “2005 Semiconductor Manufacturing Technology Road Map Reports No. 5 Measurement” (Non Patent Literature 1), a length measuring SEM for measuring critical dimension (CD-SEM), a scanning electron microscope (hereinbelow abbreviated to “SEM”) specialized for semiconductor measurement, is most widely used as a pattern dimension management tool in semiconductor process.  FIG. 22A  shows the principle of a length measuring SEM  2200 . An electron beam  2202  emitted from an electron gun  2201  is narrowed with a converging lens  2203 , passed through an objective lens  2205  and two-dimensionally scanned on a sample  2206  with a polarizer  2204 . Secondary electrons  2207  generated from the sample  2206  with the electron beam irradiation are captured with a detector  2208 , and processed inside an image processing unit  2209 , thus an electron beam image is obtained. The obtained electron beam image is displayed on a display  2211  of an output unit  2210 . Since more secondary electrons  2207  are generated at a pattern edge, the signal level of a part of the electron beam corresponding to the pattern edge is high as indicated with its output waveform signal  2220  in  FIG. 22B , and the part corresponding to the pattern edge becomes a bright image. In the length measuring SEM, dimension measurement is performed by obtaining an inter-edge distance  1  as shown in  FIG. 22B . Further, the electron gun  2201 , the converging lens  2203 , the polarizer  2204 , the objective lens  2205  and the like are controlled with a control unit  2212 . 
     Various methods have been proposed as a dimension measurement method, however, (a) threshold method and (b) model based measurement method will be described here. 
     The threshold method is disclosed in Japanese Patent Application Laid-Open Publication No. Sho 55-72807 (Patent Literature 1). In the threshold method, as denoted by numeral  2220  in  FIG. 22B , when peak parts with large signal amount corresponding to left and right pattern edges are respectively referred to as a left white band (left WB) and a right white band (right WB), a Max value and a Min value are obtained in the respective left and right WBs, and a threshold level to internally divide these values at a predetermined ratio th (%) is calculated, and a cross position between the threshold and the signal waveform is defined as an edge position. 
       FIGS. 4A and 4B  show the relation between cross-sectional shapes  411 ,  421  and SEM signal waveforms  412 ,  422 . In the threshold method, as shown in  FIGS. 4A and 4B , as the signal waveforms  412  and  422  change in accordance with the cross-sectional shapes  411  and  421 , even when the threshold levels are equal, the relations between the detected edge positions and edge positions of the measurement subject pattern are not always equal. For example, in  FIG. 4A , an edge point of a tapered edge  413  detected with a threshold level of 50% is inner by 0.5 nm from a bottom edge point, however, that of a vertical edge  423  in  FIG. 4B  is outer by 2.5 nm. In this manner, the dimension obtained by the threshold method is an inter-edge distance representative value to the end, and it is impossible to know the height to which the measured dimension corresponds. 
     On the other hand, Japanese Patent Application Laid-Open Publication No. 2009-198339 (Patent Literature 2) discloses, regarding a pattern measuring method based on SEM image utilizing electron beam simulation, high precision pattern measurement by using a simulation image with appropriately-set shape and dimension, having much influence to the accuracy of matching measurement between simulation and real image. 
     In recent years, strict pattern dimensional management is required in accordance with miniaturization of pattern. There is an increasing need for measurement of subject pattern cross-sectional shape, more particularly, a dimension at a predetermined height (a bottom dimension, a middle dimension, a top dimension or the like) in place of the dimension representative value as described above. 
     The model based measurement method has been made to respond to this need.  FIG. 3  is a principle diagram of the disclosure in J. S. Villarrubia, A. E. Vladar, J. R. Lowney, and M. T. Postek, “Scanning electron microscope analog of scatterometry,” Proc. of the SPIE, Vol. 4689, pp. 304-312 (2002) (Non Patent Literature) 2. As shown in  FIG. 3 , the pattern cross-sectional shape is represented with plural parameters (hereinbelow, “shape parameters”. In  FIG. 3 , a side wall inclination angle and top roundness are shape parameters). SEM signal waveforms of various cross-sectional shapes are obtained by simulation, and a library is created in advance. Upon dimension measurement, the edge shape and edge position of a subject pattern are estimated by selection of a waveform best corresponding with a real waveform in the library and positional shift of the library waveform. When the calculation of SEM signal waveform creation process in the simulation is appropriate and the shape parameters are appropriate, in principle, it is possible to obtain the cross-sectional shape of the subject pattern by the model based measurement method. 
     SUMMARY 
     As described above, in the model based measurement method, as a library waveform which most coincides with a real waveform is selected, a cross-sectional shape not included in the library cannot be handled. For example, when a real cross-sectional shape has different side wall inclination angles on the top side and the bottom side while the library includes only a simple trapezoid (the side wall inclination angles on the top side and the bottom side are equal), a correct cross-sectional shape cannot be obtained. In this case, it is necessary to divide the cross-sectional shape into upper and lower trapezoids. To obtain more correct cross-sectional shape, it is advantageous to have a large number of shape parameters. 
     However, when there are too many shape parameters, another problem may occur. For example, when side wall inclination angle and top roundness as two shape parameters are used, when a pattern dimension is small, in some cases, (a) a signal waveform when the top roundness is large and the side wall inclination angle is small and (b) a signal waveform when the top roundness is small and the wide wall inclination angle is large are approximately equal. In this case, in the model based measurement method, as a library waveform which most coincides with a real waveform is selected, (a) may be the solution or (b) may be the solution by the influence of slight noise. Thus the measurement result is not stable. In this case, to attach importance to the stability, it is necessary to fix the top roundness or the side wall inclination angle sacrificing the “accuracy”. 
     In this manner, in the model based measurement method, the “accuracy” and the “stability” are in trade-off relation, and to fully use the model based measurement method, setting of appropriate shape parameter in correspondence with the purpose of measurement is the problem. 
     However, in the conventional model based measurement method (Non Patent Literature 2), there is no description about the above-described problem, and accordingly, there is no guideline related to the solution to the problem. 
     The present invention has an object to provide a support function to set an appropriate shape parameter in the model based measurement method. 
     Solution to Problem 
     To address the above-described problem, the present invention provides a shape measurement method including: creating a group of calculated waveforms (library) corresponding to various cross-sectional shapes by electron beam simulation; performing image pickup on a pattern formed on a sample with a scanning electron microscope (SEM); performing matching between a real waveform of an image obtained by the image pickup and the created library and selecting a calculated waveform most coinciding with the real waveform; determining a plurality of shape parameters to represent a cross-sectional shape of the pattern formed on the sample based on the selected calculated waveform; and measuring a three-dimensional shape of the pattern, from an image obtained by performing image pickup on the pattern formed on the sample with the SEM using the determined plurality of shape parameters, wherein the determination of the plurality of shape parameters is performed by supporting setting of shape parameter conditions using the created library, or by checking and determining accuracy of the result of measurement of the three-dimensional shape, or by using both. 
     Further, to address the above-described problem, the present invention provides a shape measurement system including: a scanning electron microscope (SEM) unit to perform image pickup on a pattern formed on a sample; a library creating unit to create a group of calculated waveforms (library) corresponding to various cross-sectional shapes by electron beam simulation; a model base calculation unit to perform matching between a real waveform of an image obtained by performing image pickup with the SEM unit and the library created with the library creating unit to select a calculated waveform most coinciding to the real waveform; a shape parameter determination unit to determine a plurality of shape parameters to represent a cross-sectional shape of the pattern formed on the sample based on the calculated waveform selected with the model base calculation unit; a three-dimensional shape measurement unit to measure a three-dimensional shape of the pattern from an image obtained by performing image pickup on the pattern formed on the sample with the SEM using the plurality of shape parameters determined with the shape parameter determination unit; and an output unit to output the result of measurement with the three-dimensional shape measurement unit, wherein the shape parameter determination unit determines the plurality of shape parameters by supporting setting of shape parameter conditions using the created library, or by checking and determining accuracy of the result of measurement of the three-dimensional shape, or by using both. 
     According to an aspect of the present invention, it is possible to, prior to measurement of real pattern, easily set optimum shape parameter conditions. 
     Further, according to an another aspect of the present invention, it is possible to avoid omission of the necessity of change of conditions, and to obtain a guideline for change. 
     Further, according to an another aspect of the present invention, by presentation of predicted solution space under various image pickup conditions, it is possible to, prior to measurement of real pattern, select image pickup conditions advantageous to cross-sectional shape measurement. 
     These features and advantages of the invention will be apparent from the following more particular description of preferred embodiments of the invention illustrated in the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a flowchart showing an entire processing flow of three-dimensional shape measurement processing using a support function for setting shape parameter conditions. 
         FIG. 2  is a block diagram showing a configuration of a length measuring SEM according to an embodiment of the present invention. 
         FIG. 3  is a diagram explaining the principle of model based measurement as a conventional technique. 
         FIG. 4A  is a diagram explaining the relation between SEM signal waveform and a cross-sectional shape having a tapered edge; and  FIG. 4B  is a diagram explaining the relation between SEM signal waveform and a cross-sectional shape having a vertical edge. 
         FIG. 5  is a flowchart of library creation for model based measurement. 
         FIG. 6A  is a schematic diagram of a pattern cross-sectional shape as a premise of library creation;  FIG. 6B , a table to select a shape parameter representing a cross-sectional shape; and  FIG. 6C , a table to input range and pitch of each shape parameter. 
         FIG. 7  is a flowchart showing the flow of predicted solution space calculation. 
         FIG. 8A  is a diagram showing a cross-sectional shape of a pattern representing a nominal shape;  FIG. 8B , a table to input a nominal value;  FIG. 8C , a table to input a noise level;  FIG. 8D , a signal waveform selected from a library; and  FIG. 8E , a noise-added signal waveform. 
         FIG. 9  is a graph showing superimposed signal waveform without noise and noise-added signal waveform. 
         FIG. 10  is a graph showing predicted solution space. 
         FIG. 11A  is a graph of predicted solution space obtained with fixed top roundness;  FIG. 11B , a graph of the predicted solution space obtained with fixed lower side wall inclination angle; and  FIG. 11C , a graph of the predicted solution space obtained with fixed upper side wall inclination angle. 
         FIG. 12  is a flowchart showing the entire processing flow of three-dimensional shape measurement processing using a measurement result accuracy checking function. 
         FIG. 13  is a flowchart showing the processing flow of real solution space calculation. 
         FIG. 14  is a flowchart showing the processing flow of reference solution space calculation. 
         FIG. 15A  is a graph showing the real solution space;  FIG. 15B , a graph showing the reference solution space; and  FIG. 15C , a graph showing superimposed real waveform and library waveform and further showing a cross-sectional shape. 
         FIG. 16  is a flowchart showing the processing flow of accuracy determination. 
         FIG. 17  is a flowchart showing the processing flow of prediction of image pickup conditions appropriate to cross-sectional shape measurement. 
         FIG. 18  is a GUI to input image pickup conditions. 
         FIG. 19A  is a cross-sectional diagram of a sample showing the result of simulation of internal diffusion of electrons when accelerating voltage is 0.8 kV;  FIG. 19B , a cross-sectional diagram of the sample showing the result of simulation of internal diffusion of electrons when the accelerating voltage is 3 kV;  FIG. 19C , a cross-sectional diagram of the sample showing the result of simulation of internal diffusion of electrons when the accelerating voltage is 5 kV; and  FIG. 19D , a graph showing signal waveforms at respective accelerating voltages obtained by simulation. 
         FIG. 20A  is a graph showing the predicted solution space when the accelerating voltage is 0.8 kV; and  FIG. 20B , a graph showing the predicted solution space when the accelerating voltage is 3 kV. 
         FIG. 21  is a diagram showing the processing flow of scatterometory. 
         FIG. 22A  is a block diagram showing the configuration of a conventional length measuring SEM; and  FIG. 22B , a diagram showing an output waveform signal of the length measuring SEM. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A shape measurement method and its system according to the present invention provides the following functions (1) to (3). 
     (1) Shape Parameter Conditions Setting Support Function 
     The present function is, prior to measurement of real pattern, presenting solution space under set shape parameter conditions (hereinbelow, “expected solution space”) using a library for model based measurement. More particularly, one waveform corresponding to a predetermined shape parameter value is taken from the library, then matching is performed between this waveform and library member waveforms (respective member waveforms are linked to unique shape parameter value). Thus evaluation values representing waveform coincidence degree in respective combinations are obtained. The result of plotting of the relation between the shape parameter values and the evaluation values is presented. 
     (2) Function of Confirming Accuracy of Measurement Result 
     The present function is, after the measurement of real pattern, presenting solution space under the set shape parameter conditions (hereinbelow, “real solution space”) using real waveform and library for model based measurement. Further, it is a function of displaying superimposed real waveform, library waveform and cross-sectional shape as a measurement result for a location specified on the solution space. More particularly, matching is performed between the real waveform and library member waveforms (the respective waveforms are linked to unique shape parameter) to obtain evaluation values representing waveform coincidence degree in the respective combinations. Then the result of plotting the relation between the shape parameter values and the evaluation values is presented. 
     (3) Function of Predicting Image Pickup Conditions Appropriate to Measurement of Cross-Sectional Shape 
     The present function is previously creating libraries under various image pickup conditions (various accelerating voltages, various energy filter conditions and the like), and presenting the result of acquisition of the above-described predicted solution space by library. 
     First, the configuration of the system for measurement of three-dimensional shape according to the present embodiment will be described using  FIG. 2 . 
     A system for measuring a three-dimensional shape according to the present embodiment has an SEM  200 , an image processing unit  209  to receive an output signal from a detector  208  of the SEM  200  which has detected secondary electrons generated from a sample  206  by emission of an electron beam  202  on the sample  206  with the SEM  200 , and to generate an SEM image, an entire controller  212 , a model base calculation processing unit  220 , an input unit  224 , and an output unit  225  having a display screen  226 . Among these elements, as the configuration of the SEM  200 , the image processing unit  209  which receives the output signal from the detector  208  of the SEM  200  and the entire controller  212  are the same as those described in the background of the present specification using  FIG. 22A , the explanation thereof will be omitted. 
     The model base calculation processor  220  has a model base calculation unit  221 , a library unit  222  and an evaluation processing unit  223 . 
     Hereinbelow, the embodiment to realize the above-described respective functions will be described using the drawings. 
     (1) Shape Parameter Conditions Setting Support Function 
     The present function relates to processing to determine shape parameter conditions.  FIG. 1  shows the entire flow of the processing to determine shape parameter conditions. 
     In the present processing flow, first, the library unit  222  creates a library (S 101 ), then the model base calculation unit  221  calculates expected solution space using the created library (S 102 ), and the calculated expected solution space is displayed on the display screen  226  of the output unit  225  (S 103 ). It is checked whether or not the measurement performance is OK (S 104 ). When it is determined that the measurement performance is OK, the parameter conditions are determined (S 105 ). Then using the determined shape parameter conditions, the three-dimensional shape of a pattern formed on the sample  206  using an SEM image obtained by image pickup with the SEM  200  on the sample  206  is measured with the evaluation processing unit  223  (S 106 ). 
     Hereinbelow, the respective steps, the creation of library (S 101 ), the calculation of expected solution space (S 102 ), the display of expected solution space (S 103 ) and the determination as to whether or not the measurement performance has a problem (S 104 ), will be described in detail. 
     First, the step of library creation (S 101 ) will be described. As described above, in the model based measurement method, the cross-sectional shape as a measurement subject is represented with plural shape parameters, and signal waveforms corresponding to the cross-sectional shape are calculated by SEM simulation (Monte Carlo simulation or the like) and stored as a waveform library. 
       FIG. 5  shows the flow of library creation, and  FIGS. 6A to 6C  show related input items. First, the method of representation of cross-sectional shape, i.e., a shape parameter to represent the cross-sectional shape is determined (S 501 , and  602  in  FIG. 6B ). In this example, as shown in  601  in  FIG. 6A , the cross-sectional shape is represented as a two-step trapezoid having a round top. As the method of representation of cross-sectional shape, it is desirably representation not so different from an actual cross-sectional shape based on the result of observation of cross-section using an SEM or the result of measurement with an atomic force microscope (AFM). Next, the range and pitch of each parameter (in the example of  FIG. 6C , the top roundness (r), an upper side wall inclination angle (θ 1 ), a lower side wall inclination angle (θ 2 ) are inputted (S 502 , and  603  in  FIG. 6C ). It is necessary for the variation range of shape parameter to cover the change range of a measurement subject shape. Based on the above input information, the signal waveforms corresponding to the respective cross-sectional shapes are calculated by SEM simulation (S 503 ). 
     Next, the calculation of expected solution space (S 102 ) will be described.  FIG. 7  shows the flow of the calculation of expected solution space, and  FIGS. 8A to 8E  show related input items and display items. First, the nominal value of the shape parameter is inputted (S 701 , and  802  in  FIG. 8B ). Note that in  FIG. 6A , the cross-sectional shape is represented with a two steps of trapezoid having a round top, however, for the sake of simplification of explanation, it is one step trapezoid having a round top here ( 801 ). Next, a signal waveform for a shape parameter corresponding to the input nominal value is selected from the library (S 702 ). Next, a noise level to be added to the signal waveform as percentage is inputted (S 703 , and  803  in  FIG. 8C ). To visually check the change of waveform by noise, the signal waveform before addition of noise ( 804  in  FIG. 8D ) and the signal waveform after the addition of noise ( 805  in  FIG. 8E ) are displayed. It is desirable that the noise level is set to about the same level of a real signal waveform by referring to the SEM image. 
     Next, as shown in  FIG. 9 , a signal waveform  901  without noise and a noise-added signal waveform  902  are superimposed, and it is estimated to which extent an evaluation value indicating the degree of coincidence between these signal waveforms varies (S 704 ). As the evaluation value, e.g., a chi-square value shown in (Expression 1) is used. 
     
       
         
           
             
               
                 
                   
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     The chi-square value becomes smaller as the both waveforms coincide with each other. Note that as other evaluation value than the chi-square value, a correlation value, a phase-limited correlation value or the like is applicable. 
     At S 704 , more particularly, noise generation using a random number is performed plural times (e.g., about 30 times), then the variation of the chi-square value is obtained. Next, matching is performed between the signal waveform of the nominal shape (signal waveform selected at S 702 ) and the library member waveforms (S 705 ), to calculate the chi-square values in the respective combinations. Based on the variation of the qui-square value previously obtained at S 704 , the range of variation of the measurement value of the respective shape parameters are calculated (S 706 ), and displayed together with the distribution of the chi-square value (S 707 ). 
       FIG. 10  shows an example of the expected solution space. The horizontal axis indicates the side wall inclination angle, and the vertical axis, the top roundness. The chi-square value is indicated with a contour line. Assuming that the variation of the chi-square value obtained at S 704  is 5, a long slender region is a possible range of variation of the result of measurement of cross-sectional shape by model based measurement. The stability of the measurement is high when this region is narrow. In the figure, r min  to r max  is a possible range of the variation of the top roundness, and θ min  to θ max , a possible range of variation of the side wall inclination angle. 
     Note that when the number of shape parameters to be varied is two, as shown in  FIG. 10 , one shape is represented using the axis x while the other shape is represented using the axis y, and the chi-square value is represented with the contour line. As shown in  FIG. 6 , when the number of shape parameters to be varied is three (top roundness, upper side wall inclination angle and lower side wall inclination angle), three types of expected solution spaces where one of the shape parameters is fixed are presented as shown in  FIGS. 11A to 11C . 
     In  FIG. 11A, 111  shows expected solution space with a fixed top roundness; in  FIG. 11B, 112  shows expected solution space with a fixed lower side wall inclination angle; and in  FIG. 11C, 113  shows expected solution space with a fixed upper side wall inclination angle. Note that  FIGS. 11A to 11C  only show a region corresponding to the region in  FIG. 10  where the chi-square value is equal to or less than 5. 
     As the expected solution spaces as shown in  FIGS. 10, 11A to 11C  are presented, it is possible to determine whether or not the shape parameter conditions are appropriate. For example, in  FIG. 11B , it is understood from the expected solution space  112  that the variation range of the both top roundness and upper side wall inclination angle are wide and that the solution is not stable when these are variable parameters. On the other hand, in  FIG. 11A , the expected solution space  111  is localized, and the upper side wall inclination angle and the lower side wall inclination angle are independent to each other. It is understood that even when both of them are used as variable parameters, the solution is not unstable. The same is in the case of expected solution space  113  in  FIG. 11C . In this case, it is understood as a guideline that to obtain stable solution, it is effective to fix the top roundness. 
     On the other hand, when the result that the solution is not unstable even though all the shape parameters are varied is obtained, it is understood as a guideline that there is a possibility to increase the shape parameters to be varied. In this case, it may be arranged such that the shape parameters to be varied are increased, and again, expected solution space is obtained and checked. 
     According to the present embodiment, it is possible to, prior to measurement of real pattern, set optimum shape parameter conditions (conditions such that the number of shape parameters to be varied which is not too large or too small). With these parameters, it is possible to realize model based measurement with higher precision. 
     As described above, it is possible to instantly grasp the distribution of high-coincidence region by presentation of expected solution space with the shape parameter conditions setting support function. Accordingly, it is possible to easily determine whether or not the set shape parameter conditions are appropriate. For example, when there is a wide spread of high-coincidence region or an enclave of high-coincidence region, it is understood that the number of shape parameters is too large and it is not possible to perform measurement with high stability. Further, since it is possible to grasp a shape parameter which expands the high-coincidence region, it is possible to effectively determine a shape parameter to be fixed. When the expected solution space is presented again after the change of shape parameter conditions, it is possible to check the effect. On the other hand, when the high-coincidence region is sufficiently narrow, it is understood that there is a possibility to increase the number of shape parameters. When the number of shape parameters is increased and the expected solution space is presented again, it is possible to determine whether or not the degradation of the stability of measurement by increment of the number of shape parameters is within an allowable range. 
     (2) Function of Confirming Accuracy of Measurement Result 
     The function of confirming the accuracy of measurement result will be described. The shape parameter conditions setting support function described in (1) is to provide a function of supporting setting conditions for shape parameters applied to measurement of real pattern prior to measurement of real pattern. On the other hand, the present function provides a function of judging to confirm the accuracy of measurement result after measurement of real pattern. 
     As the function of judging to confirm the accuracy of measurement result, real solution space is calculated and presented using real waveforms, and for the sake of the above-described judgment, solution space as a comparative subject (hereinbelow, “reference solution space”) is calculated and also presented. 
       FIG. 12  shows the entire processing flow of the function of judging to confirm the accuracy of measurement result. First, the SEM  200  performs image pickup on the sample  206  to obtain an SEM image (S 1201 ), and obtains real solution space from the SEM image (S 1202 ). On the other hand, the library unit  222  creates a library (S 1203 ), and obtains reference solution space using the created library (S 1204 ). Next, the evaluation processing unit compares the real solution space with the reference solution space and judging the accuracy of the solution (S 1205 ), to determine conditions for shape parameters (S 1206 ). Using the determined conditions for shape parameters, three-dimensional measurement is performed on the pattern shape of the sample  206  subjected to image pickup with the SEM (S 1207 ). 
       FIG. 13  shows the flow of calculation of the real solution space at S 1202 . First, the SEM  200  performs image pickup on the sample  206  and obtains a waveform from a real image generated with the image processing unit  209  (S 131 ). The model base calculation unit  221  performs matching between this waveform and library member waveforms registered in the library unit  222 . The evaluation processing unit  223  calculates matching evaluation values in the respective combinations (S 132 ). The calculated values are displayed on the display screen  226  of the output unit  225  (S 133 ). As the matching evaluation value, e.g., a chi-square value as shown in  FIG. 9  is used. 
       FIG. 14  shows the flow of calculating the reference solution space at S 1204 . A library waveform corresponding to a cross-sectional shape outputted as a result of model based measurement is selected from the library (S 141 ). Noise equivalent to the real waveform obtained at S 131  in  FIG. 13  is added to the selected waveform (S 143 ). Next, matching is performed between the waveform to which the noise has been added at S 143  and the library member waveform, and the evaluation values in the respective combinations are calculated (S 144 ), and displayed as the reference solution space (S 145 ). As the matching evaluation value, e.g., a chi-square value as shown in  FIG. 9  is used. 
     To compare the real solution space with the reference solution space, it is desirable to display them together on the screen  226  of the output display unit  225  as shown in  FIGS. 15A to 15C . In  FIG. 15B , reference solution space  152  is, so to speak, solution space which is obtained when model based measurement is performed under ideal conditions. Accordingly, when the difference between the real solution space  151  in  FIG. 15A  and the reference solution space  152  in  FIG. 15B  is small, it is judged that model based measurement has been performed as expected. When the alienation is large, it is judged that model based measurement has not been performed as expected. 
       FIG. 16  shows an example of specific flow at S 1205 . First, minimum values of the both solution spaces are compared (S 161 ). When a chi-square vale is used as an evaluation value, the chi-square value of the real solution space is often greater than the chi-square value of the reference solution space (generally, the coincidence between a real waveform and a library waveform is lower than the coincidence between library waveforms). Accordingly, for example, when the chi-square value of the real solution space is several times greater than that of the reference solution space, it is determined that the accuracy of the result of model based measurement is low, and the processing is terminated (S 162 ). On the other hand, when the difference between the evaluation values is within a supposed range, the shapes of the contour-surrounded regions and the intervals between the contour lines are compared (S 163 ). For example, when the size of the contour-surrounded region of the real solution space is several times greater than that of the reference solution space, it is determined that the accuracy of model based measurement is low, and the processing is terminated (S 164 ). It is determined, passed through these judgments, that the accuracy of measurement result is high (S 165 ). 
     In case that the measurement result is determined not correct (S 162  and S 164 ), it means that the cross-sectional shape of the real pattern is not correctly represented under the set shape parameter conditions. In the present embodiment, as a support function for efficient change of shape parameter conditions, the real waveform, the library waveform and the cross-sectional shape as the solution of model based measurement are superimposed and displayed on the screen  226 . In the real solution space  151  in  FIG. 15A , a cursor  153  as crossed vertical and horizontal lines is placed in desired coordinates then a predetermined button (not shown) is clicked, a real waveform  154 , a library waveform  155  and a cross-sectional shape  153 , in superimposed status, are displayed as shown in  FIG. 15C . With this display, it is possible to determine a part of the cross-sectional shape corresponding to the match/mismatch between the real waveform and the library waveform. With the result displayed on the display, it is possible to obtain a guideline for changing the fixed value of the shape parameter or fixing another shape parameter. 
     According to the above-described function to confirm the certainty of measurement result, as the certainty of measurement result is indicated, it is possible to avoid overlook of the necessity of review of the shape parameter conditions. Further, as the guideline as to how change the shape parameter conditions is displayed, it is possible to efficiently change the shape parameters. Further, with these arrangements, it is possible to realize model based measurement with higher precision. 
     As described above, as real solution space is displayed with the function of confirming the certainty of measurement result, it is possible to instantly grasp the distribution of high-coincidence region. Accordingly, it is possible to easily judge the degree of certainty of the result of model based measurement. For example, by checking whether or not the spread of high-coincidence region is equivalent to the above-described expected solution space, it is determined whether or not the measurement result has accuracy as expected. When it is different from the expected solution space, it is understood that the cross-sectional shape of the real pattern cannot be correctly represented under the set shape parameter conditions and the certainty of measurement result is low. 
     Further, as the real waveform, the library waveform and the cross-sectional shape as a measurement result are superimposed and displayed, it is possible to determine a part of the cross-sectional shape corresponding to the match/mismatch between the real waveform and the library waveform. With the result displayed on the display, it is possible to efficiently change conditions for changing a fixed value of the shape parameter or fixing another shape parameter. 
     Since it is conventionally impossible to indicate the accuracy of measurement result, it is impossible to even notice the necessity of change of conditions. However, according to the present embodiment, it is possible to avoid overlooking the necessity of change of conditions, and to obtain a guideline for change. 
     (3) Function of Predicting Image Pickup Conditions Appropriate to Measurement of Cross-Sectional Shape 
     Next, the function of predicting image pickup conditions appropriate to measurement of cross-sectional shape will be described. This function of predicting image pickup conditions appropriate to measurement of cross-sectional shape is, prior to measurement of real pattern, applying the method of shape parameter conditions setting support explained in (1) to plural imaging conditions and predicting image pickup conditions advantageous to model based measurement. 
       FIG. 17  shows the entire flow of the function of predicting image pickup conditions appropriate to measurement of cross-sectional shape. The input of shape model (S 171 ) and the input of range and pitch of each shape parameter (S 172 ) are the same as those in the case of (1). In the present function, variation of image pickup conditions is inputted (S 173 ), and a signal waveform is calculated by SEM simulation (S 174 ).  FIG. 18  shows an example of a GUI  1800  for input of variation of image pickup conditions. On the GUI  1800 , a number of image pickup conditions  1801  and variation of image pickup conditions are inputted. The variation of image pickup conditions desirably covers the variation of image pickup conditions of an image pickup device (CD-SEM) to be used such as accelerating voltage variation  1801 , energy filter (1) presence/absence  1802  and energy filter (2) presence/absence  1803 . 
       FIGS. 19A to 19C  are diagrams explaining change of signal waveform in accordance with different accelerating voltages. In  FIG. 19A, 191  shows the result of simulation of internal electron diffusion when the accelerating voltage is 0.8 kV;  FIG. 19B, 192  shows the result of simulation when the accelerating voltage is 3 kV; and  FIG. 19C, 193  shows the result of simulation when the accelerating voltage is 5 kV. It is understood that in accordance with increment of accelerating voltage, the incoming depth of the primary electrons is deeper, and the internal diffusion spreads in a wider range. In  FIG. 19D, 194  shows signal waveforms at respective accelerating voltages also obtained by simulation. As a result of difference in internal diffusion, the signal waveforms are different. 
     In the present function, the expected solution space ( FIG. 10 ) indicated in (1) is obtained by the image pickup condition and is presented. The difference in accelerating voltage causes difference in expected solution space as shown in  FIG. 19 . Assuming that  201  in  FIG. 20A  shows expected solution space when the accelerating voltage is 0.8 kV and  202  in  FIG. 20B  shows expected solution space when the accelerating voltage is 3 kV, it is understood that measurement with higher stability can be realized with  201  in  FIG. 20A  where the possible range of diffusion of result of measurement of cross-sectional shape by model based measurement (gray region) is narrower. The image pickup conditions for real pattern measurement may be determined based on this result. 
     According to the present function, it is possible to, prior to measurement of real pattern, predict image pickup conditions more advantageous to model based measurement on a computer. With this arrangement, as the process of determining image pickup conditions in a trial and error manner using an actual sample is not necessary, the efficiency is improved. As a result, it is possible to realize model based measurement with higher precision. 
     The measurement system may be provided with all the respective functions explained in the above-described (1) to (3) or the combination of any two of them. Otherwise, only one of them is employed. 
     Note that the respective functions explained in the above-described (1) to (3) have been described regarding a case where the model based measurement method is applied to a SEM signal waveform, however, they are applicable to scatterometry shown in  FIG. 21 . 
     When the present invention is applied to the scatterometry, the same effects as those described in the above-described embodiments can be obtained. 
     The invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiment is therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims, rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. 
     REFERENCE SIGNS LIST 
     
         
         
           
               200  . . . SEM 
               206  . . . sample 
               209  . . . image processing unit 
               212  . . . entire controller 
               220  . . . model base calculation processing unit 
               221  . . . model base calculation unit 
               222  . . . library unit 
               223  . . . evaluation processing unit 
               224  . . . input unit 
               225  . . . output unit 
               226  . . . display screen