TECHNICAL FIELD 
     The present invention relates to a surface shape measurement apparatus for acquiring a surface shape. For example, the invention relates to a measurement apparatus of measuring a surface shape using a light scattering method, more particularly, of measuring micro roughness on a wafer surface or the like in a semiconductor device manufacturing process. 
     BACKGROUND ART 
     Since micro roughness of a semiconductor wafer is greatly involved in performance of an apparatus, management thereof is important. In measurement of the micro roughness, it is preferable to inspect entire semiconductor wafers and the entire surface thereof in an in-line manner, which demands high speed measurement. As a related art, the following document is referred to. 
     CITATION LIST 
     Patent Literature 
     PTL 1: JP-A-2006-54358 
     SUMMARY OF INVENTION 
     Technical Problem 
     PTL 1 discloses a technique in which height measurement using an atomic force microscope (AFM) is used as means for measuring micro roughness. However, this technique does not provide consideration for the problem that it takes time for the measurement. 
     Solution to Problem 
     The invention provides a technique capable of estimating micro roughness from a total sum of signals from plural detection systems and a signal ratio using a light scattering method. 
     The invention provides a technique that rotates and translates a wafer at high speed to measure the entire surface of the wafer with high throughput. 
     Further, the relationship between micro roughness and the intensity of scattered light varies according to a material of the wafer or a film thickness thereof. Further, it is also necessary to calibrate an apparatus. In consideration of the problems, the invention provides a technique that has a function of correcting a detection result that is optically acquired using a sample which is substantially the same as a measurement target and makes the optically acquired detection result come close to a result measured by an apparatus (for example, an AFM) using a different measurement principle. 
     Advantageous Effects of Invention 
     According to the invention, it is possible to acquire information necessary for process management of a wafer in a short amount of time. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIGS. 1A-1E  are diagrams illustrating a surface measurement apparatus according to Embodiment 1. 
         FIG. 2  is a diagram illustrating a flow for estimating a spatial frequency spectrum (PSD function) of micro roughness from the intensity of scattered light that is measured. 
         FIGS. 3A-3C  are diagrams illustrating a PSD function. 
         FIG. 4  is a diagram illustrating a relationship between a PSD function and a surface roughness. 
         FIG. 5  is a diagram illustrating a flow for calculating a surface roughness from a PSD function. 
         FIG. 6  is a flowchart illustrating a calculation method of a correction coefficient k used in calibration of an apparatus. 
         FIG. 7  is a diagram illustrating a model parameter output example of a PSD function with respect to a certain intensity of scattered light. 
         FIG. 8  is a diagram illustrating a reason why plural ABC parameters correspond to a set of signal ratios. 
         FIG. 9  is a diagram illustrating a Fourier transform optical system. 
         FIGS. 10A-10D  are diagrams illustrating a unit area for averaging acquired data in Embodiment 2. 
         FIG. 11  is a diagram illustrating a display example of a surface roughness in a desired spatial frequency band. 
         FIGS. 12A-12B  are diagrams illustrating an example in which a surface roughness is displayed using a histogram. 
         FIG. 13  is a diagram illustrating an example in which a surface roughness and a defect inspection result are displayed in association. 
         FIGS. 14A-14C  are diagrams illustrating correspondence between a defect type and a surface roughness. 
         FIGS. 15A-15B  are diagrams illustrating Embodiment 3. 
         FIG. 16  is a conceptual diagram illustrating Embodiment 4. 
         FIGS. 17A-17B  are diagrams illustrating outlines of an AFM, a CD-SEM, and an MP-SEM. 
         FIG. 18  is a flowchart illustrating Embodiment 4. 
         FIG. 19  is a flowchart illustrating Embodiment 5. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, embodiments of the invention will be described with reference to the accompanying drawings. 
     Embodiment 1 
     In the present embodiment, an apparatus configuration and a surface roughness measurement principle will be described. A schematic configuration of a surface measurement apparatus is shown in  FIG. 1( a ) . Main components are a chuck  102  that suctions a wafer  101 , a rotational stage  103  on which the chuck  101  is mounted, a linear stage  104  on which the rotational stage  101  is mounted, a light source  105 , an illumination optical system  106  having a lens, a mirror or the like, detection systems  181  to  186  having a lens, a mirror or the like, a signal processing system  107 , a control system  108 , and an operation system  109 . 
     Arrangement of the detection systems  181  to  186  is shown in  FIG. 1( b ) . As illumination light supplied from the illumination optical system  108  is converged, a beam spot  121  is formed on a surface of the wafer  101 . Scattered light generated from the beam spot  121  is detected by the plural detection systems  181  to  186 . The detection systems  181  to  186  have the same elevation angle, and are arranged with different azimuth angles. Since the illumination light is obliquely supplied to the wafer  101  and the detection systems  181  to  186  detect the scattered light, the surface measurement apparatus of the present embodiment may be expressed as a so-called dark field type apparatus. Further, shapes of openings of the detection systems  181  to  186  are provided to be substantially circular when viewing the wafer  101  in a normal direction thereof, as shown in  FIG. 1( b ) . 
     A configuration example of the detection system  183  is shown in  FIG. 1( c )  (this is similarly applied to the other detection systems). The detection system  183  has a detection optical system  191  having an optical axis  193 , and a photoelectric converter  192 . The beam spot  121  is formed on the wafer  101  by the illumination light supplied to the wafer  101 , and the light is scattered with each elevation angle and azimuth angle from the beam spot  121 . The scattered light is converged by the detection optical system  191  having a certain numerical aperture, and the detection optical system  191  includes plural lenses (lens group), so that a so-called light condensing optical system or imaging optical system is configured. The converged scattered light passes through a spatial filter or a polarizing filter to cut off undesirable light components, and then, is photoelectrically converted by the photoelectric converter  192 . A signal obtained by the photoelectric conversion is an electric current or a voltage. Then, the signal is AD-converted and is processed by the signal processing system  107 . As an example of the photoelectric converter  192 , a photo multiplier, an avalanche hot diode array, or a photon counting array in which plural photon counting elements are arranged may be used. 
       FIG. 1 ( d )  shows a scanning method of the beam spot  121 . The wafer  101  rotates as indicated by an arrow  131  by the stage  102  while moving straight in a direction of an arrow  132  by the stage  103 . As the beam spot  121  scans the entire surface of the wafer  101  by the linear movement and the rotational movement, locus thereof forms a concentric circular shape or a spiral shape. Coordinates of the beam spot  121  may be managed by a distance from a wafer center and a rotation angle (a so-called polar coordinate system). The rotation angle may be expressed with reference to a virtual reference line  135  (for example, a half straight line that passes a notch  134  and the wafer center) on the wafer. 
       FIG. 1( e )  is a diagram illustrating an output signal from each of the detection systems  181  to  186 . A horizontal axis  141  indicates time or coordinates in the same direction as the rotational direction  131  of the stage, and a vertical axis  142  indicates the size of the output signal. The scattered light due to the micro roughness of the wafer  101  is incident onto the detection systems  181  to  186 , and a waveform indicated by a micro roughness signal  143  is obtained with respect to each of the detection systems  181  to  186 . A value and coordinates thereof are stored for each of the detection systems  181  to  186 . Further, if the beam spot  121  crosses a defect or the like, an especially large signal  144  is detected. The defect signal  144  is separated from the signal  143  by a high pass filter (HPF), for example, in the signal processing system  107 , and a value and coordinates thereof are stored as a defect. 
     Handling of the micro roughness signal  143  and the defect signal  144  will be described. The removal of the defect signal  144  from the micro roughness signal  143  may be performed based on determination using a signal size, instead of the above-described frequency area separation. That is, if the signal size is equal to or smaller than a specific size (threshold value), an acquired signal may be considered as a micro roughness signal. The threshold value may be set as a fixed value in advance, or may be set in real time from a signal capable of being obviously determined as a micro roughness signal. 
     Further, as a method for acquiring the micro roughness signal, a method in which the defect signal  144  is not separated from the micro roughness signal  143  may also be used. For example, a method for averaging (merge) signals from the detection systems  181  to  186  for a certain period of time or in a certain wafer area may be used. As the averaging method, a method for dividing six detection systems  181  to  186  into plural groups to perform averaging for the divided groups may be used. More specifically, the detection system  181  and the detection system  186  may be a first group, the detection system  182  and the detection system  185  may be a second group, and the detection system  183  and the detection system  184  may be a third group, and the averaging may be performed for each group. An operator can arbitrarily set detection systems to be combined, but it is preferable to adopt a combination in which a change due to the micro roughness can be sharply captured. When an acquirement interval of a sensor output due to the scattered light is sufficiently narrow, the frequency of the defect signal with respect to the acquired signal is extremely small. Thus, even though the intensity of the defect signal  144  is stronger than the intensity of the micro roughness signal  143 , a defect signal after averaging may be handled in the same way as the micro roughness signal. Further, if the averaging is performed, it is possible to reduce a processing load of the signal processing system  107 . Hereinabove, the measurement method of the intensity of scattered light incident onto each detection system on the entire surface of the wafer has been described. 
     Next, a procedure of calculating a surface roughness from a measured intensity of scattered light will be described. The procedure is divided into (1) a procedure of estimating a substantial PSD function of a surface from the intensity of scattered light, and (2) a procedure of calculating a substantial roughness of the surface from the PSD function. 
     First, the PSD function will be described. When a surface shape is expressed using three-dimensional coordinates (X, Y, Z), a height Z may be two-dimensionally Fourier transformed with respect to (X, Y), and a value obtained by squaring amplitude thereof may be expressed as a spatial frequency spectrum. The spatial frequency spectrum becomes a function P(fx, fy) in which (fx, fy) which are reciprocals of (X, Y) are used as variables. P(fr) obtained by expressing the function P using fr=√(fx×fx+fy×fy) indicates a power spectral density (PSD) function. The PSD function has the size of a surface roughness and cycle information. That is, the PSD function may be expressed as an example of a function that expresses the spatial frequency spectrum. Further, acquirement of the PSD function and acquirement of information about the surface shape are substantially equivalent to each other. 
     Next, the procedure of estimating the PSD function from the intensity of scattered light will be described with reference to  FIG. 2 . First, the operator inputs a material and a film thickness of a measurement target through the operation system  109  (step  201  in  FIG. 2 ). This information is used for a measurement condition of scattered light or a correction coefficient k. 
     Next, the intensity of scattered light is measured by the detection systems  181  to  186  using the method described with reference to  FIG. 1  (step  202  in  FIG. 2 ). As the intensity of scattered light, a value measured in advance may be stored in the signal processing system  107 , and the value may be read. 
     Then, the signal processing system  107  calculates a total sum Σ of detection signals (step  203  in  FIG. 2 ), and divides each signal of the detection systems  181  to  186  by the total sum Σ (step  204  in  FIG. 2 ). This means that the ratio of each detection system to the total sum of the signals is obtained. 
     In parallel with steps  202  to  204 , the signal processing system  107  refers to a predetermined correction coefficient K that is stored in advance based on the originally input material and film thickness (step  207  in  FIG. 2 ), and multiplies the correction coefficient K by the ratio of each detection system calculated in step  204  (step  205  in  FIG. 2 ). 
     The signal processing system  107  estimates the PSD function from the signal ratio and the total sum Σ acquired in this way (step  206  in  FIG. 2 ). The estimation of the PSD function is performed by the signal processing system  107  using a library recorded in memory thereof. In the library, the relationship between the PSD function and the detection signal in the optical condition is recorded with respect to a variety of known micro roughnesses. The signal processing system  107  compares the detected signal with the library to estimate the PSD function. The estimated PSD function and a surface roughness (which will be described later) are associated with coordinates on the wafer to be stored in the memory of the signal processing system  107 . 
     Next, the PSD function estimated in the present embodiment will be described with reference to  FIG. 3 . A horizontal axis  301  indicates the above-described f=fr, and a vertical axis  302  indicates the size of the spatial frequency spectrum, which represents a double-logarithmic graph. 
       FIG. 3( a )  shows a first PSD function, which is referred to as an ABC model hereinafter. The ABC model is expressed as PSD(f)=A/(1+Bf 2 ) c/2  using parameters A, B, and C, with respect to the spatial frequency f of the surface roughness. On a low frequency side, the PSD maintains a constant value, and on a high frequency side, the PSD becomes small. The constant value on the low frequency side is represented as A, an inclination on the high frequency side is represented as −C/2, and a spatial frequency at a branch point is represented as 1/B. 
       FIG. 3( b )  shows a second PSD function, which is referred to as a fractal ABC model hereinafter. This model is expressed as PSD(f)=A/(1+Bf 2 ) c2 +K/f M  using parameters A, B, C, K, and M. The fractal ABC model has a feature that the value is larger with a segment of K and a inclination of −M on a low frequency side, compared with the ABC model. 
       FIG. 3( c )  shows a third PSD function, which is referred to as a Double ABC model hereinafter. This model is expressed as PSD(f)=A 1 /(1+B 1 f 2 ) c1/2 +A 2 /(1+B 2 f 2 ) c2/2  using parameters A 1 , B 1 , C 1 , A 2 , B 2 , and C 2 . Addition of two different ABC models is performed. Hereinabove, the procedure of calculating the PSD function from the intensity of scattered light has been described, but the present embodiment may define PSD functions having different waveforms. As shown in  FIG. 3 , the PSD functions become continuous smooth functions. 
     Next, the procedure of calculating the surface roughness from the PSD function will be described.  FIG. 4  is a diagram illustrating the relationship between the PSD function and the surface roughness (RMS roughness). The RMS roughness becomes a value obtained by integrating a product of a PSD function  401  and a spatial, frequency f in a certain spatial frequency band (band f 1  to f 2  in  FIG. 4 ). When an integration interval f 1  to f 2  is arbitrarily selected and the RMS roughness in the interval is set as RMS(f 1 , f 2 ), RMS(f 1 , f 2 )=√(2π∫ f2   f1 PSD(f)×fdf). 
       FIG. 5  shows the procedure of calculating the RMS roughness. First, the arbitrary spatial frequency band f 1  to f 2  is selected ( 501  in  FIG. 5 ). Then, the RMS roughness is calculated from RMS(f 1 , f 2 )=√(2π∫ f2   f1 PSD(f)×fdf). The RMS roughness can be acquired by this procedure. Hereinbefore, the procedure of calculating the surface roughness from the PSD function has been described. 
     Next, the correction coefficient k described in step  207  in  FIG. 2  will be described. The correction coefficient k functions to correct the surface roughness calculated from the intensity of scattered light to the surface roughness measured by the AFM. In other words, it can be said that the surface roughness that is optically obtained by the correction coefficient k comes close to an actual roughness. Further, it can be said that the correction coefficient k is defined by a result obtained by measuring a sample which is substantially the same as a sample by an optical method and a result obtained by measuring the sample by a method different from the optical method. Further, it can be said that the different method refers to a method with high resolution (for example, measurement using an AFM) compared with the optical method. A value of the correction coefficient k is prepared with respect to each of the detection systems  181  to  186  according to wafer information (for example, according to each material that forms the wafer, or each film type on the wafer). That is, it can be said that the correction coefficient k is changed according to the material that forms the sample and the film type on the sample. 
       FIG. 6  shows a procedure of calculating the correction coefficient k. In this procedure, in addition to the surface measurement apparatus (which may be expressed as a first apparatus or an optical apparatus) described in  FIG. 1 , an apparatus (which may be expressed as a second apparatus that measures the surface by a measurement principle different from that of the first apparatus) capable of directly measuring height information of the surface is prepared. Here, as the second apparatus, an AFM with high resolution compared with the surface measurement apparatus will be described as an example. First, a wafer which is substantially the same as a measurement target (hereinafter, referred to as the same wafer) is prepared (step  601  in  FIG. 6 ). 
     Height data is acquired using the AFM with respect to the same wafer (step  602  in  FIG. 6 ). 
     Next, a PSD function is calculated using two-dimensional Fourier transform from the acquired height data (step  603  in  FIG. 6 ). 
     The intensity of scattered light incident onto the detection systems  181  to  186  of the surface measurement apparatus is calculated using the PSD function (step  604  in  FIG. 6 ). The calculation of the intensity of scattered light is performed using the PSD function, a refractive index of a material of the wafer surface, and an illumination condition as input data, and using a bidirectional reflectance distribution function (BRDF). 
     Next, the total sum Σ of the intensity of scattered light incident onto the respective detection systems acquired in step  604  is calculated (step  605  in  FIG. 6 ), and the intensity of scattered light of each detection system is divided by the total sum Σ to calculate a signal ratio of each detection system (step  606  in  FIG. 6 ). This signal ratio indicates a signal ratio calculated from AFM data. 
     In parallel with step  602  to step  606 , the intensity of scattered light is acquired using the surface measurement apparatus with respect to the same wafer ( 607  in  FIG. 6 ). 
     A total sum Σ of the detection signals acquired in step  607  is calculated ( 608  in  FIG. 6 ), and the detection signal of each of the detection systems  181  to  186  is divided by the total sum Σ to calculate a signal ratio of each of the detection systems  181  to  186  ( 609  in  FIG. 6 ). This signal ratio indicates a signal ratio which is optically measured. 
     Next, the correction coefficient k is calculated from the following expression with respect to the detection systems  181  to  186 . k=(signal ratio acquired from AFM)/(signal ratio acquired from measurement of the intensity of scattered light) (step  610  in  FIG. 6 ). In this way, the correction coefficient k with respect to one material and one film type is calculated. When calculating a correction coefficient of another wafer, the procedure returns to flow  601 , and in other cases, the procedure is terminated (step  611  in  FIG. 6 ). The acquired correction coefficient k is used in step  205  in  FIG. 2 . 
     Here, an output example of model parameters of a PSD function for a certain intensity of scattered light will be described with reference to  FIG. 7 . The PSD function uses an ABC model as an example. When a signal of each detection system measured by the surface measurement apparatus and multiplied by the correction coefficient k is a signal  701 , ABC parameters corresponding thereto include plural sets of parameters  702 . When the signal is a signal  703 , the ABC parameters include plural sets of parameters  704 . In the present embodiment, plural ABC parameters correspond to one set of signal ratios. 
     A reason why the plural ABC parameters correspond to one set of signal ratios will be described with reference to  FIG. 8 . Reference numerals  802 ,  803 , and  804  indicate PSD functions having different B parameters. A spatial frequency band capable of being measured by the surface measurement apparatus is determined by an angle of incident light with respect to a wafer and a wavelength of the light. When the band corresponds to  801 , it is difficult to separate the PSD functions  802  to  804  from the measured value. Thus, as shown in  FIG. 7 , plural sets of ABC parameters correspond to one set of signal ratios. Further, the RMS roughness may be calculated with respect to each of the ABC parameters. Accordingly, plural pieces of RMS roughness correspond to one set of signal ratios. The RMS roughness may employ values calculated in the following (1) and (2). (1) Average values Avg(Ai), Avg(Bi), and Avg(Ci) of plural ABC parameters Ai, Bi, and Ci which are candidates are calculated. The RMS roughness is calculated using the values and an arbitrary spatial frequency area f 1  to f 2 . That is, the RMS roughness is expressed as RMS=Function (Avg(Ai), Avg(Bi), Avg(Ci), f 1 , f 2 ). (2) The RMS roughness is calculated using the plural ABC parameters Ai, Bi, and Ci which are the candidates and the arbitrary spatial frequency areas f 1  to f 2 . That is, the RMS roughness is expressed as RMSi=Function (Ai, Bi, Ci, f 1 , f 2 ). An average value of the RMS roughness is used as the RMS roughness. That is, the RMS roughness is expressed as RMS=Avg(RMSi). An operator may arbitrarily select (1) or (2). 
     Hereinabove, an example in which the detection systems  181  to  186  include the light condensing optical system or the imaging optical system has been described, but the detection system  183  also includes a Fourier transform optical system as shown in  FIG. 9  (this is similarly applied to the other detection systems). When the detection system  183  is the Fourier transform optical system, scattered light from the wafer  101  is collimated by a detection optical system  901  to become parallel light which is substantially parallel to the optical axis  193 . The parallel light is photoelectrically converted by a sensor  902  in which plural photoelectric converters are arranged. If the Fourier transform optical system is employed in the detection systems  181  to  186 , it is possible to measure spatial distribution of the scattered light with higher resolution, and to improve estimation accuracy of the PSD function. Further, the same effect can also be acquired by increasing the number of detection systems. 
     According to the present embodiment, it is possible to acquire information relating to a wafer surface at a relatively high speed. Further, according to the present embodiment, it is possible to estimate information other than a spatial frequency band capable of being measured. 
     Embodiment 2 
     In Embodiment 1, the method for measuring the intensity of scattered light from one beam spot on the wafer to calculate the surface roughness has been described. In the present embodiment, a data handling method for the entire surface of a wafer, a roughness display method, and a comparison analysis example with respect to a defect detection function will be described. 
     An area where data is merged will be described with reference to  FIG. 10 .  FIG. 10( a )  shows a state where data (the intensity of scattered light, and PSD related parameters) on respective beam spots  1012  (in which the size of one spot is several μ 2 ) is all managed. Here, the management includes storing data acquired for each certain unit area in the signal processing system  107  and the control system  108 , and displaying the data on a display or the like in the operation system  109 . If a wafer surface  1001  is scanned in a concentric circular shape or a spiral shape, boundary lines  1011  may be defined in a radius direction. An interval between the boundary lines  1011  substantially corresponds to the length of the beam spot in the radius direction. Further, an area between two boundary lines  1011  is divided in a circumferential direction to manage a value for each beam spot  1012 . That is, it can be said that  FIG. 10( a )  shows a state where data acquired for each area of the beam spot  1012  is substantially managed. 
     Further, it is also possible to manage data acquired for each unit area larger than the size of the beam spot. For example, in the present embodiment, as shown in  FIG. 10( b ) , data may be averaged in a boundary divided by radial boundary lines  1021  and  1022  and circumferential boundary lines  1023 ,  1024 , and  1025  to manage a value thereof. In the case of  FIG. 10 , an interval between the boundary lines  1021  and  1022  is longer than the length of the beam spot in the radius direction, and the area of a unit area defined by the boundary lines  1021 ,  1022 ,  1023 ,  1024 , and  1025  is larger than the area of the beam spot. 
     Further, as shown in  FIG. 10( c ) , it is also possible to manage data according to design data (for example, die division pattern) of a predetermined pattern to be formed on a wafer. In the case of  FIG. 10( c ) , a unit area  1031  is formed by referring to data of a die manufactured on a wafer (for example, coordinates and dimensions). The data is averaged in the unit area  1031 , and the averaged value is managed. The design data may be stored in advance in the memory of the signal processing system  107 , or may be downloaded from an external processing device through a network. 
     Further, as shown in  FIG. 10( d ) , it is also possible to manage data in an arbitrary area designated by an operator. In  FIG. 10( d ) , the operator designates an area  1042  of an arbitrary shape on a wafer map by a mouse pointer  1041  in the operation system  109 . Then, data is averaged in the area, and the averaged value is managed. In the case of  FIG. 10( d ) , the area  1042  designated by the operator becomes a unit area. The operator may arbitrarily select which management method among  FIG. 10( a )  to  FIG. 10( d )  is employed. 
     Next, a display method of the acquired RMS roughness  FIG. 11  will be described with reference to  FIG. 11 .  FIG. 11  is a diagram illustrating a case where data is managed by the method shown in  FIG. 10( a )  and the RMS roughness is displayed. As described with reference to  FIG. 4 , the value of the RMS roughness is determined in the spatial frequency band. 
     First, a display section in the operation system  109  includes a mechanism for designating the spatial frequency band. As a designation method, there is a method performed by input of numerical values. A lower limit f 1  of a band is input into a box  1103 , and an upper limit f 2  is input into a box  1104 . Further, a scale bar  1105  is prepared, and a lower limit value  1106  and an upper limit value  1107  of a spatial frequency in consideration of the performance of the apparatus are set at opposite ends. Here, a lower limit value  1108  and an upper limit value  1109  of the spatial frequency band where the RMS roughness is calculated are set between the lower limit value  1106  and the upper limit value  1107 , and a mechanism capable of continuously changing the lower limit value  1108  and the upper limit value  1109  using a mouse pointer or the like is provided. Values corresponding to the positions of the limit values  1108  and  1109  are displayed in the boxes  1103  and  1104 , respectively. With respect to the spatial frequency band determined in this way, the RMS roughness is calculated from the expression in  FIG. 4 , and is displayed on a wafer map  1001 . As a display example of the RMS roughness, a contour display is used. Contour lines  1101  and representative values  1102  are displayed by the RMS roughness. A gradation display including color bars or a pattern display may be employed, instead of the contour display. 
     As an example in which quantitative display is performed, a histogram display may be used instead of the figure display on the wafer map  1101 . The histogram display will be described with reference to  FIG. 12 . A procedure for designating a spatial frequency band to calculate the RMS roughness is the same as in  FIG. 11 . In  FIG. 12( a ) , an area having a certain RMS roughness (range) is counted to form a histogram. Further, a cumulative histogram obtained by sequentially accumulating the RMS roughness from a small RMS roughness side of the histogram in  FIG. 12( a )  is shown in  FIG. 12( b ) . The vertical axis may be the frequency or ratio. 
     Next, a comparison analysis example of data on PSD parameters and RMS roughness and data on defect inspection will be described with reference to  FIG. 13 .  FIG. 13  is an example in which data on obtained surface roughnesses and defects is displayed on the wafer map  1001 . The defect data (for example, coordinates or type) may be obtained using the surface measurement apparatus of the present embodiment, or other optical type inspection apparatuses, or may be obtained using other apparatuses (for example, an apparatus that detects or classifies defects using an electron beam). In  FIG. 13 , the RMS roughness is expressed by the contours  1101  on the wafer map  1001 , and the defects are expressed by marks  1301 . Further, the types of the defects are divided by different shape signs as indicated by reference numeral  1302 , and are displayed so that an operator can easily recognize the difference between the defect types. According to such a display, it is possible to visually recognize the relationship between the defect and the surface roughness. In  FIG. 13 , the data on the defect and the surface roughness is displayed on substantially the same wafer map  1001 , but may be respectively displayed on different wafer maps  1001 . 
     Further, in the present embodiment, an operator may select an arbitrary type or an arbitrary defect from the wafer map  1001  in  FIG. 13 , and an average PSD function in an area corresponding to the selected defect may be displayed. A display example indicating the relationship between a defect type and a PSD function will be described with reference to  FIG. 14 .  FIG. 14  shows a function of displaying an average PSD function in an area corresponding to a defect for each defect type in  FIG. 13 . The operator selects an arbitrary type defect from reference numeral  1302  using a predetermined input device.  FIG. 14( a )  shows an average PSD function  1303  in an area corresponding to a defect A.  FIG. 14( b )  shows an average PSD function  1304  in an area corresponding to a defect B.  FIG. 14( c )  shows an average PSD function  1305  in an area corresponding to a defect other than the defects A and B. Thus, it is possible to recognize the relationship between reasons why each defect occurs and the PSD function. The operator selects a specific defect from the wafer map  1001  instead of reference numeral  1302 , and may display a PSD function with respect to the selected specific defect. 
     Embodiment 3 
     Next, Embodiment 3 will be described. In the present embodiment, the contents described in Embodiments 1 and 2 are applied as a system (so-called process monitor) that monitors an abnormality in a wafer processing process. 
       FIG. 15  is a diagram illustrating the present embodiment.  FIG. 15( a )  shows a procedure of process monitoring in the present embodiment. A wafer is transported to a manufacturing device (step  1401 ). Predetermined processes are performed for the transported wafer (step  1402 ). Here, the processes include polishing, washing, deposition, and etching for the wafer. 
     Surface measurement is performed for the wafer for which the predetermined processes are performed, according to the contents described in Embodiments 1 and 2 (step  1403 ). 
     If there is an abnormality in the measurement result, the result is fed back to the manufacturing device (step  1405 ). The feedback includes a change in polishing conditions, a change in washing conditions, a change in deposition conditions, or a change in etching conditions. If there is no abnormality, the process monitoring is terminated. 
       FIG. 15( b )  is a diagram illustrating step  1404 . It is assumed that a PSD function acquired at a certain time point  1409  on a time axis  1408  is a function  1410 . On the other hand, it is assumed that a PSD function measured at a different time point  1411  (more specifically, later in time) is a function  1412 . When comparing the function  1408  with the function  1410 , it is understood that a low frequency portion  1413  of the PSD function increases at the time point  1411  compared with the time point  1409 . This indicates that roughness at a low frequency, that is, at a long cycle increases. That is, this indicates that the surface state is changed according to a certain change in the manufacturing device. In this way, by comparing the shapes of the PSD functions acquired at different time points in the signal processing system  107 , it is possible to recognize the change in the surface state. In  FIG. 15( b ) , two PSD functions that are actually acquired at different time points are compared, but it is not necessary to actually measure a reference PSD function in the determination of step  1404 , and the operator may arbitrarily define the reference PSD function using the signal processing system  107 . Further, it is possible to change the reference PSD function in the determination of step  1404  according to the contents of the processes performed for the wafer. Further, focusing on which band of the PSD function to determine an abnormality for may be arbitrarily changed according to the contents of the processes. 
     According to the present embodiment, it is possible to understand the degree of change in a specific spatial frequency band with respect to the entire surface of a wafer and all the wafers. Thus, it is possible to provide significant information for narrowing down abnormalities of the respective processes and the respective manufacturing devices, and to provide a rapid feedback with respect to the wafer processing process. 
     Embodiment 4 
     Next, Embodiment 4 will be described. The present embodiment shows an example in which a surface of a wafer is measured using a measurement apparatus capable of inspecting and measuring the surface with a resolution higher than that of the surface measurement apparatus and the surface measurement apparatus according to Embodiments 1 to 3. 
       FIG. 16  is a conceptual diagram illustrating the present embodiment. A system of the present embodiment includes the surface measurement apparatus (first measurement apparatus) according to Embodiments 1 to 3 and a measurement apparatus (second measurement apparatus) capable of measuring a surface with a resolution higher than that of the surface measurement apparatus. As an example of the second measurement apparatus, the above-described atomic force microscope (AFM), a multi purpose scanning electron microscope (MP-SEM) capable of measuring defects and performing detection and classification, or a critical dimension scanning electron microscope (CD-SEM) that measures a line width of a pattern formed on a wafer may be used. 
     The AFM or SEM can measure and observe a high resolution surface shape, but has a weak point in that visual field thereof is relatively narrow. Further, it is necessary to determine measurement conditions according to a measuring object. 
     The present embodiment is based on these considerations. 
     An operation principle of the AFM will be described with reference to  FIG. 17( a ) . A probe  1603  of which tip thereof has a size of several 10 nm comes close to a wafer  101  on a moving stage  1607  in a range where an interatomic force acts. Here, a laser  1602  emitted from a light source  1601  is reflected from an upper portion of a probe tip, and a reflected light  1604  is detected by a light detection system  1605  in which areas are divided and is recorded by a signal processing system  1608 . If the stage  1607  moves by a control system  1606 , the probe  1603  is displaced up and down along a surface shape of the wafer  101 . Thus, the light  1604  reflected from the upper portion of the probe tip is displaced, and the intensity of received light in each divided area of the light detection system  1605  is changed. The change is converted into the displacement of the probe by the signal processing system  1608  and is associated with the coordinates of the wafer  101 , and thus, it is possible to measure the surface shape of the wafer. 
     The AFM includes a mode in which the probe  1603  is substantially in contact with a sample in the atmosphere for scanning (so-called contact mode), a mode in which the probe  1603  is not in contact with the sample in the vacuum and is vibrated with a predetermined resonance frequency to measure a shift of the frequency (so-called non-contact mode), or other measurement modes (for example, a mode in which a distance between the sample and the probe is changed so that the probe leaps, when the sample is scanned by the non-contact mode). 
     Next, an operation principle of the MP-SEM will be described with reference to  FIG. 17( b ) . An electron beam  1612  emitted from an electron gun  1611  is focused by a focusing lens  1613 . Then, the beam passes through polarizing coils  1614  and  1615  controlled by a control section  1620  and is narrowed by an objective lens to illuminate the wafer  101 . A reflected electron, a secondary electron or the like  1617  at the moment is detected by a detection system, and is recorded in a signal processing system  1619 . The wafer is scanned with the electron beam by the control system  1620 , and the surface shape of the wafer can be observed from the position at that time and the size of the detection signal. With respect to the CD-SEM, by performing pattern matching between a predetermined area observed by the MP-SEM and a predetermined reference image, it is possible to perform measurement of the line width. 
       FIG. 18  shows a flow of measurement of the present embodiment. First, surface measurement of the entire surface of a wafer is performed by the surface measurement apparatus (first apparatus) (step  1701 ). Here, an operator records coordinates to be specifically measured into the signal processing system  107 , for example, as coordinates relating to a notch ( 134  in  FIG. 1( d ) ) of the wafer, for example. In step  1701 , estimation of the surface roughness is also performed. 
     Thereafter, measurement conditions of the second apparatus are determined from the surface roughness estimated in step  1701  (step  1702 ). In the determination, the signal processing system  107  may be used, or instead, an external processing system may be used. Here, the measurement conditions include the above-described plural measurement modes for the AFM, and an acceleration voltage for the SEM. 
     Then, the second apparatus performs inspection in the measurement conditions determined in step  1702  for at least the coordinates designated by the operator in step  1701  (step  1703 ). 
     The result of step  1701  and the result of step  1703  are combined on the same wafer map (step  1704 ). Thus, it is possible to compare and analyze two measurement results. That is, it is possible to compare an entire surface state of the wafer with a partial state of the wafer. 
     Embodiment 5 
     Next, Embodiment 5 will be described. The present embodiment is characterized in that at least one of a PSD function and a surface roughness of a wafer on which a certain film (for example, particularly, a transparent film) is formed on a surface thereof (hereinafter, referred to as a transparent film wafer) is obtained. 
     First, with respect to a wafer with an insufficient non-transparent film with respect to a wavelength, that is, a film that does not generate scattered light from a lower layer with reference to a surface of the film, the PSD function and the surface roughness may be measured by at least one of the methods according to Embodiments 1 to 4. 
     On the other hand, with respect to a wafer with a transparent film such as SiO 2  or Si 3 N 4 , it is preferable to acquire information relating to a surface thereof before the transparent film is deposited. The reason is because, in the case of the transparent film, scattered light from the wafer with the transparent film is measured as the sum of scattered light from a film surface and scattered light from an interface between an under film layer and the wafer surface. 
     Thus, in the present embodiment, at least one of the PSD function and the surface roughness of the transparent film surface of the transparent film wafer is acquired by a flow shown in  FIG. 19 . First, data on scattered light with respect to a wafer with no transparent film is acquired (step  1901 ). The process of step  1901  includes at least one of measurement of data on scattered light using the surface measurement apparatus according to Embodiment 1 and acquirement of data on scattered light by performing a predetermined process for measurement data of the AFM. The process of step  1901  is performed with respect to each of the detection systems  181  to  186 . Data acquired in step  1901  is stored in the signal processing system  107 . 
     In measurement of the transparent film wafer, the data acquired in step  1901  is loaded from the signal processing system  107  (step  1902 ). 
     Next, measurement of scattered light is performed for the transparent film wafer using at least one of the surface measurement apparatuses according to Embodiments 1 to 4 (step  1903 ). 
     Since the data acquired in step  1901  is handled so as to be substantially equivalent to the scattered light from the interface, the signal processing system  107  removes the result obtained in step  1901  from the result obtained in step  1903  (step  1904 ). The process of step  1904  is performed for each of the detection systems  181  to  186 . Through the process of step  1904 , data used for subsequent calculations becomes data indicating the scattered light from the transparent film surface. 
     At least one of the methods according to Embodiment 1 to 4 is applied to the result obtained in step  1904 , to thereby acquire the PSD function and the surface roughness for the transparent film surface (step  1905 ). 
     According to the present embodiment, even when measuring a wafer on which a certain film (for example, particularly, a transparent film) is formed, it is possible to correctly obtain a PSD function and a surface roughness. If the surface roughness of the wafer before deposition is sufficiently constant, it is not necessary to measure the surface roughness with respect to all the wafers before deposition. That is, the data acquired in step  1901  may be used in calculation for a different wafer on which substantially the same type of film is formed. 
     Hereinbefore, the embodiments of the invention have been described, but the invention is not limited to the embodiments. Here, the wafer refers to a wafer in a broad sense, such as a silicon wafer, a substrate made of a material other than silicon, or other samples. The contents described in this specification may be applied to a defect inspection device that detects a defect such as a scar or a foreign material on a sample. Further, the contents described in the respective embodiments may be partially removed, or may be mutually exchanged or combined. 
     REFERENCE SIGNS LIST 
       101  WAFER 
       102  CHUCK 
       103  ROTATIONAL STAGE 
       104  LINEAR STAGE 
       105  LIGHT SOURCE 
       106  ILLUMINATION OPTICAL SYSTEM 
       107  SIGNAL PROCESSING SYSTEM 
       108  CONTROL SYSTEM 
       109  OPERATION SYSTEM 
       181  DETECTION SYSTEM 
       182  DETECTION SYSTEM 
       183  DETECTION SYSTEM 
       184  DETECTION SYSTEM 
       185  DETECTION SYSTEM 
       186  DETECTION SYSTEM
The invention discloses a technique that estimates micro roughness from a total sum of detection signals from plural detection systems and signal ratios, using a light scattering method. The technique rotates and translates a wafer at high speed to measure the entire surface of the wafer with high throughput. The relationship between the micro roughness and the intensity of scattered light varies according to a material of the wafer and a film thickness thereof. Moreover, calibration of an apparatus is also necessary. Thus, for instance, the invention provides a technique that has a function of correcting an optically acquired detection result using a sample which is substantially the same as a measurement target and makes the optically acquired detection result come close to a result measured by an apparatus, such as an AFM, using a different measurement principle.