Patent Publication Number: US-7710579-B2

Title: Measuring method and apparatus for measuring depth of trench pattern

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a technique for measuring a depth of a trench pattern formed on a substrate. 
   2. Description of the Background Art 
   A method of nondestructively measuring a depth of a trench pattern (for example, a set of a plurality of trenches extending in a direction) formed on a substrate by using a spectral interference method has been conventionally suggested. For example, Japanese Examined Patent Publication No. 6-65963 discloses a method of measuring a depth of a trench, where light is applied to a substrate having a trench, reflected light from the substrate is spectrally dispersed to obtain a spectrum, and then a cycle of peak in the spectrum caused by an optical path difference between the uppermost face of the substrate and the bottom face of the trench is specified by a maximum entropy method. Japanese Patent Gazette No. 3740079 also discloses a method of obtaining a depth of an etching trench. In the method, when the depth of the etching trench formed by etching a film on a substrate is measured, first, a spectrum which is obtained relatively to the film on the substrate with an original film thickness and a theoretical spectrum in a case where it is supposed that a thinner film than the original film thickness is formed on the substrate are acquired. The thinner film corresponds to the bottom face of the etching trench (that is to say, the depth of the trench is the difference between the original film thickness and a film thickness of the thinner film), and the spectrum of the film with the original film thickness and the spectrum of the thinner film are mixed with a mixture ratio in accordance with an area ratio of the etching trench in design, to acquire a plurality of mixture spectra corresponding to the etching trenches of a plurality of depths, respectively. The actual spectrum obtained from the substrate is compared with the plurality of mixture spectra to obtain the depth of the etching trench. 
   A spectroscope having a diffraction grating is frequently used in acquisition of a spectral reflectance. In the diffraction grating, a diffraction efficiency which is a ratio between an incident intensity and a reflected intensity of light is largely different between p-polarized light and s-polarized light depending on a wavelength of the light. In measurement of the depth of the trench pattern formed on the substrate, an oscillation direction of the reflected light from the substrate is limited by influence of the trench pattern in accordance with various conditions (that is to say, the reflected light from the substrate becomes polarized light). Thus, there are situations where the spectral reflectance cannot be accurately obtained on the basis of the reflected light from the substrate depending on the oscillation direction of the reflected light which enters the diffraction grating, and the depth of the trench pattern cannot be obtained with accuracy. 
   In measurement of the depth of the trench pattern on the substrate having a single layer film or a multilayer film, when a measured spectral reflectance acquired from the reflected light from the substrate and calculated spectral reflectances obtained by a computation are compared, the influence of the film in the calculated spectral reflectances needs to be considered because the measured spectral reflectance is affected by the film. However, in a case where a film on the substrate is extremely thin (for example, a film thickness of 10 nanometer (nm)), if it is tried to compare the measured spectral reflectance with the calculated spectral reflectances where a film thickness of the film is also included in parameters to obtain the film thickness of the film and the depth of the trench pattern, values of the parameters cannot be determined with accuracy. This is the same as in the case where the multilayer film is formed on the substrate. 
   SUMMARY OF THE INVENTION 
   The present invention is intended for a measuring method of measuring a depth of a trench pattern formed on a substrate. It is an object of the present invention to obtain a depth of the trench pattern with accuracy. 
   The measuring method in accordance with the present invention comprises a) applying illumination light to a substrate having a measurement area where a trench pattern extending in a predetermined direction is formed; b) spectrally dispersing reflected light of the illumination light from the substrate by a diffraction grating which is arranged so that an angle formed between a direction on the substrate which corresponds to a grating direction of the diffraction grating and the predetermined direction becomes equal to or greater than 40 degrees and equal to or smaller than 50 degrees; c) receiving light dispersed in the step b) on a detector to acquire a measured spectral reflectance of the measurement area; and d) comparing the measured spectral reflectance with calculated spectral reflectances which are obtained by a computation where at least a depth of the trench pattern and an area ratio of a bottom face of the trench pattern are used as parameters, to determine values of the parameters. According to the present invention, the depth of the trench pattern can be obtained with accuracy. 
   According to a preferred embodiment of the present invention, the illumination light is directed to the substrate through an objective lens having a numerical aperture which is equal to or greater than 0.05 and equal to or smaller than 0.1 in the step a) and it is possible to surely apply the illumination light to the bottom face of the trench pattern. More preferably, an area ratio of an uppermost face in a surface of the substrate is included in the parameters in the step d), and a sum of a value obtained by multiplying a complex amplitude reflectance which is theoretically calculated on the basis of light from the bottom face of the trench pattern by the area ratio of the bottom face and a value obtained by multiplying a complex amplitude reflectance which is theoretically calculated on the basis of light from the uppermost face by the area ratio of the uppermost face, is made to a complex amplitude reflectance in the measurement area, to obtain the calculated spectral reflectances. It is thereby possible to neglect influence of reflected light from side faces of the trench pattern and to easily obtain the depth of the trench pattern, the area ratio of the bottom face, and the area ratio of the uppermost face. 
   Another preferred measuring method comprises a) applying illumination light to a substrate having a measurement area where a trench pattern extending in a predetermined direction is formed; b) spectrally dispersing reflected light of the illumination light from the substrate by a diffraction grating, the reflected light being directed to the diffraction grating through a depolarizer; c) receiving light dispersed in the step b) on a detector to acquire a measured spectral reflectance of the measurement area; and d) comparing the measured spectral reflectance with calculated spectral reflectances which are obtained by a computation where at least a depth of the trench pattern and an area ratio of a bottom face of the trench pattern are used as parameters, to determine values of the parameters. This makes it possible to obtain the depth of the trench pattern with accuracy. 
   Still another preferred measuring method comprises a) applying illumination light to an auxiliary area of a substrate which has a measurement area where a trench pattern is formed and the auxiliary area where the trench pattern does not exist, at least one film being formed on both the measurement area and the auxiliary area; b) obtaining each film thickness of one or more films included in the at least one film by acquiring a spectral reflectance of the auxiliary area on the basis of reflected light of the illumination light from the auxiliary area; c) applying illumination light to the measurement area; d) acquiring a measured spectral reflectance of the measurement area on the basis of reflected light of the illumination light from the measurement area; and e) comparing the measured spectral reflectance with calculated spectral reflectances which are obtained, with use of the each film thickness obtained in the step b), by a computation where at least a depth of the trench pattern and an area ratio of a bottom face of the trench pattern are used as parameters, to determine values of the parameters. In the substrate having the at least one film, it is thereby possible to obtain the depth of the trench pattern with high accuracy by obtaining the film thickness in the area where the trench pattern does not exist. 
   The present invention is also intended for a measuring apparatus for measuring a depth of a trench pattern formed on a substrate. 
   These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a view showing a constitution of a trench shape measuring apparatus in accordance with the first preferred embodiment; 
       FIG. 2  is a flowchart showing an operation flow for measuring a shape of a trench pattern; 
       FIG. 3  is a flowchart showing an operation flow of an auxiliary film thickness measurement; 
       FIG. 4  is a view showing a cross section of a substrate perpendicular to a trench direction; 
       FIG. 5  is a view to explain a process for obtaining a complex amplitude reflectance of a bottom face; 
       FIG. 6  is a view to explain the complex amplitude reflectance in the whole area; and 
       FIG. 7  is a view showing a constitution of a trench shape measuring apparatus in accordance with the second preferred embodiment. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1  is a view showing a construction of a trench shape measuring apparatus  1  in accordance with the first preferred embodiment of the present invention. The trench shape measuring apparatus  1  is for acquiring information about a shape of a trench pattern formed on a semiconductor substrate  9  such as a depth of the trench pattern. Actually, a film thickness of a film formed on the substrate  9  is also measured to acquire the information about the shape of the trench pattern in the trench shape measuring apparatus  1 . The trench pattern on the substrate  9  is a set of a plurality of trenches extending in a direction (i.e., the trench pattern is a pattern having diffraction grating shape) in the preferred embodiment. 
   The trench shape measuring apparatus  1  has a holding part  21  for holding a disk-shaped substrate  9  on which the trench pattern is formed, a rotation mechanism  22  for rotating the holding part  21  around an axis in a vertical direction, a holding part moving mechanism  23  for moving the holding part  21  in the X direction and the Y direction which are the horizontal directions with interposing the rotation mechanism  22 , a light emission part  3  for emitting illumination light, an optical system  4  which directs the illumination light from the light emission part  3  to the substrate  9  and receives reflected light from the substrate  9 , a spectroscope  5  for spectrally dispersing the reflected light which is directed by the optical system  4 , a detector  6  for receiving light spectrally dispersed by the spectroscope  5  to obtain a spectral reflectance, and a control part  7  which has an operation part  71  for performing various computations and controls the whole trench shape measuring apparatus  1 . The holding part moving mechanism  23  includes a X direction moving mechanism and a Y direction moving mechanism which are not shown and each moving mechanism is provided with a combination of a motor, a ball screw, and guide rails. 
   The light emission part  3  has a light source  32  connected to a power supply  31  and emits illumination light (white light). The illumination light from the light source  32  is directed to a half mirror  43  through lenses  41 ,  42  which belong to the optical system  4 , and the illumination light reflected on the side of the substrate  9  is applied to the substrate  9  through an objective lens  44 . Since a numerical aperture (NA) of the objective lens  44  is made to be equal to or greater than 0.05 and equal to or smaller than 0.1, the illumination light is applied to the substrate  9  approximately perpendicularly to the substrate  9  as a nearly parallel light. 
   Reflected light of the illumination light from the substrate  9  is captured by the objective lens  44  and enters the spectroscope  5  through the half mirror  43  and the lens  45 . The spectroscope  5  has an opening plate  51  having a pinhole  511 , and the reflected light passing through the pinhole  511  is applied to a diffraction grating  52  in which a plurality of grooves extending in a direction are formed on its surface (areas of the grooves are hatched in  FIG. 1  and hereinafter, the extending direction of the grooves is referred to as “grating direction”). In  FIG. 1 , the number of the grooves in the diffraction grating  52  is extremely smaller than that formed actually. At this time, if linearly polarized light whose oscillation direction is the Y direction at a main surface of the substrate  9  is emitted from the position of the substrate  9 , the linearly polarized light enters the diffraction grating  52  so that its oscillation direction is parallel to or perpendicular to the grating direction of the diffraction grating  52 . In other words, the diffraction grating  52  is arranged so that a direction on the substrate  9  which corresponds to the grating direction of the diffraction grating  52  is parallel to or perpendicular to the Y direction. The diffraction grating  52  spectrally disperses the reflected light passing through the pinhole  511 , and spectrally dispersed light is directed to different positions on a receiving surface of the detector  6  in accordance with wavelengths. Detailed constituent elements in the spectroscope  5  are omitted in  FIG. 1 . 
   The receiving surface of the detector  6  has an array of a plurality of light receiving elements, and light of each wavelength included in a predetermined wavelength band (hereinafter, referred to as “measurement wavelength band”) is received by the corresponding light receiving element to acquire an intensity of the light. In the trench shape measuring apparatus  1 , an intensity of light is obtained in advance in the case that the holding part  21  is provided with a mirror irradiated with the illumination light and reflected light from the mirror is applied to each light receiving element of the detector  6  through the spectroscope  5 . Thus, each light receiving element obtains a ratio between the intensity of light acquired from the substrate  9  and the intensity of light acquired with the mirror as a (relative) reflectance. As a result, a set of a plurality of reflectances which respectively correspond to a plurality of wavelengths included in the measurement wavelength band is obtained as the spectral reflectance. The spectral reflectance obtained in the detector  6  is referred to as a “measured spectral reflectance” in the following description. A computation for obtaining the ratio between the intensity of the light acquired from the substrate  9  and that acquired with the mirror may be performed outside the detector  6 . 
   Next discussion will be made on an operation flow for measuring the shape of the trench pattern in the trench shape measuring apparatus  1 , with reference to  FIG. 2 . In measurement of the trench pattern shape, first, the substrate  9  to be measured is loaded into the trench shape measuring apparatus  1  by a carrier device which is located outside the trench shape measuring apparatus  1 , and it is placed and held on the holding part  21  (Step S 10 ). At this time, in a predetermined measurement area  93  on the substrate  9 , the trench pattern is formed so as to extend in a direction predetermined relatively to a reference portion formed on the substrate  9  (i.e., the portion is formed for determining a direction of the substrate  9  and for example, it is a notch, an orientation flat, or the like). In the trench shape measuring apparatus  1 , the substrate  9  is held on the holding part  21  with the reference portion contacting positioning pins provided in the holding part  21  so that the substrate  9  is oriented in a predetermined direction. Therefore, the orientation of the trench pattern within the measurement area  93  of the substrate  9  which is held on the holding part  21  is made to any angle in the range of 45 degrees ±5 degrees (from 40 to 50 degrees) with respect to the Y direction (preferably, the trench pattern is tilted by 45 degrees with respect to the Y direction). In other words, an angle formed between a direction on the substrate  9  which corresponds to the grating direction of the diffraction grating  52  and the extending direction of the trench pattern is made to be equal to or greater than 40 degrees and equal to or smaller than 50 degrees (preferably, it is made to 45 degrees). In the following discussion, the extending direction of the trench pattern is also referred to as a “trench direction”. 
   Subsequently, it is confirmed whether or not a process for accessorily measuring the film thickness of the film formed on the substrate  9  (hereinafter, referred to as “auxiliary film thickness measurement”) is performed before acquisition of the information relating to the shape of the trench pattern (the information includes the depth of the trench pattern and the like, and hereinafter referred to as “trench pattern information”) (Step S 11 ). Necessity of the auxiliary film thickness measurement is determined in accordance with a film structure of the substrate  9 . For example, when an extremely thin single layer film or a multilayer film is formed on the substrate  9 , the auxiliary film thickness measurement is performed to improve measurement accuracy of the trench pattern information. In the following description, the extremely thin single layer film shall be formed on the substrate  9  and the auxiliary film thickness measurement is performed (Step S 12 ). 
     FIG. 3  is a flowchart showing an operation flow of the auxiliary film thickness measurement.  FIG. 4  is a view showing a cross section of the substrate  9  which is perpendicular to the trench direction. Hatching of the cross section of the substrate  9  is not shown in  FIG. 4  (same as in  FIG. 5  which is later discussed). 
   As shown in  FIG. 4 , a thin film  91  of silicon oxide (SiO 2 ) (A film thickness of the film is, for example, 10 nanometer (nm), and the film thickness of the film  91  in  FIG. 4  is thicker than that of the actual film. The same is applied to  FIG. 5  later discussed) is formed on the surface of the substrate  9 , and a plurality of trenches  92  which are arranged at a regular pitch P 1  in a direction perpendicular to the trench direction is formed by etching a main body  90  of the substrate  9  which is made of the film  91  and silicon (Si). Actually, an area  94  where the trench pattern does not exist (the area  94  is a so-called solid area, for acquiring information for assisting measurement of the trench pattern shape, and it is hereinafter referred to as “auxiliary area  94 ”) is formed on the main surface of the substrate  9 , other than the measurement area  93  having the trench pattern which is an object area to be measured. In the auxiliary film thickness measurement, after the auxiliary area  94  is arranged at an irradiation position of the illumination light by the holding part moving mechanism  23 , the illumination light is emitted from the light emission part  3  and applied to the auxiliary area  94  (Step S 121 ). The optical system  4  directs reflected light from the auxiliary area  94  to the spectroscope  5 , it spectrally disperses the reflected light (Step S 122 ), and spectrally dispersed light is received on the detector  6  to acquire a measured spectral reflectance of the auxiliary area  94  (Step S 123 ). 
   In the trench shape measuring apparatus  1 , calculated spectral reflectances for the auxiliary film thickness measurement are obtained and prepared in advance, and discussion will be made on the calculated spectral reflectances used in the auxiliary film thickness measurement. In acquisition of the calculated spectral reflectances, first, given that the film  91  has a certain film thickness d, a reflectance R relative to light with a wavelength λ is obtained by substituting each of the following values into the equation 1, where N is a refractive index of the film  91 , θ is an incident angle of the light (illumination light) to the film  91 , λ is the wavelength of the light, r 01  is an amplitude reflectance in an interface between an air  99  and the film  91 , and r 12  is an amplitude reflectance in an interface between the film  91  and the main body  90  of the substrate  9 . The incident angle θ of the light to the film  91  is 0 degree in the preferred embodiment (same as in the equations 3 and 4 which are later discussed). Further, r without a numerical subscript in the equation 1 represents a complex amplitude reflectance and β represents a film phase thickness (which is the same as in the equations 3 and 4 discussed later). 
   
     
       
         
           
             
               
                 
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   Actually, the reflectance R is obtained for each of the plurality of wavelengths included in the measurement wavelength band, and a set of a plurality of reflectances R with respect to the plurality of wavelengths is obtained as the calculated spectral reflectance. In the trench shape measuring apparatus  1 , a plurality of calculated spectral reflectances relative to a plurality of film thicknesses are acquired by repeating the above computation with changing an assumed film thickness of the film  91 . 
   The measured spectral reflectance of the auxiliary area  94  which is obtained in Step S 123  is compared with the plurality of calculated spectral reflectances, and a calculated spectral reflectance approximating to the measured spectral reflectance is specified from these calculated spectral reflectances to obtain the film thickness of the film  91  (Step S 124 ). Specifically, a degree of similarity Err is obtained by the equation 2 where, with respect to a certain wavelength, Rc is a reflectance represented by the calculated spectral reflectance and Rm is a reflectance represented by the measured spectral reflectance. In the equation 2, mean (A) is an average of a plurality of A which are obtained relatively to the plurality of wavelengths included in the measurement wavelength band.
 
 Err =mean(( Rc−Rm ) 2 )  Eq. 2
 
   In the trench shape measuring apparatus  1 , the calculated spectral reflectance where the degree of similarity Err is minimum is specified, and a film thickness relative to the above calculated spectral reflectance is made to the film thickness of the film  91  in the auxiliary area  94  of the substrate  9 . In a case where the degree of similarity Err is equal to or smaller than a predetermined value or the like, there may be a case where the nonlinear optimization method such as the Gauss-Newton method or the Levenberg-Marquardt method is used as necessary, and the calculated spectral reflectance where the degree of similarity Err becomes greater than the predetermined value is acquired while converging the degree of similarity Err, to obtain the film thickness of the film  91 . 
   As discussed above, after obtaining the film thickness of the film  91  of the substrate  9 , setting of parameters (so-called generation of a measurement recipe) in a computation of calculated spectral reflectances in acquisition of the trench pattern information is performed (these calculated spectral reflectances are different from those in the auxiliary film thickness measurement) ( FIG. 2 : Step S 13 ). Specifically, the depth of the trench pattern (i.e., the depth of a trench  92 ), an area ratio of a set of bottom faces  921  which are formed in a plurality of trenches  92  in the measurement area  93 , and an area ratio of a set of a plurality of uppermost faces (which are areas having the same height as the surface of the auxiliary area  94 )  931  are used as parameters, and an initial value and a plurality of values of changes (i.e., the differences from the initial value) in each of the parameters are set in the operation part  71  and the film thickness of the film  91  which is obtained in Step S 12  is also set in the operation part  71 . Since a plurality of values are set to each parameter, the degree of similarity is suppressed to fall into a local optimum in calculation of the degree of similarity which is later discussed. In the following description, the area ratio of the set of the plurality of bottom faces  921  and the area ratio of the set of the plurality of uppermost faces  931  are simply referred to as “the area ratio of the bottom face  921 ” and “the area ratio of the uppermost face  931 ”. 
   Subsequently, the calculated spectral reflectances in acquisition of the trench pattern information are obtained (Step S 14 ). Specifically, a complex amplitude reflectance r I  of the uppermost face  931  relative to light with a wavelength λ is obtained by substituting each of the following values into the equation 3, where d is a value to which the film thickness of the film  91  is set, N is a refractive index of the film  91 , θ is an incident angle of the light (illumination light) to the film  91 , λ is the wavelength of the light, r 01  is an amplitude reflectance in an interface between the air  99  and the film  91 , and r 12  is an amplitude reflectance in an interface between the film  91  and the main body  90  of the substrate  9 . 
   
     
       
         
           
             
               
                 
                   
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   With respect to the bottom face  921 , assuming that the trench  92  is a film  99   a  of air having the film thickness t which is equal to the initial value of the depth of the trench  92 , as shown by hatching in  FIG. 5 , a complex amplitude reflectance r II  of the bottom face  921  relative to light with a wavelength λ is obtained by substituting each of the following values into the equation 4, where N is a refractive index of the film  99   a , θ is an incident angle of the light (illumination light) to the film  99   a , λ is the wavelength of the light, r 01  is an amplitude reflectance in an interface between the air  99  and the film  99   a , and  r   12  is an amplitude reflectance in an interface between the film  99   a  and the main body  90  of the substrate  9 . Actually, in the equation 4, the refractive index N is 1 and the amplitude reflectance r 01  in an interface between the air  99  and the film  99   a  is 0. 
   
     
       
         
           
             
               
                 
                   
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   As abstractly shown by arrows  81 ,  82 , interference occurs by an optical path difference between lights from areas V 1 , V 2  which are differently hatched in  FIG. 6 . A complex amplitude reflectance r v  relative to light with a certain wavelength in the whole of the areas V 1 , V 2  is obtained by the equation 5, where A v1  and A v2  are area ratios of the areas V 1 , V 2 , respectively, and r v1  and r v2  are complex amplitude reflectances relative to the light with the wavelength in the areas V 1 , V 2 , respectively.
 
 rv=rv   1   ×Av   1   +rv   2   ×Av   2   Eq. 5
 
   Actually, inclining side faces  922  of the trench  92  exist in the measurement area  93  on the right side of  FIG. 4 , in addition to the uppermost faces  931  and the bottom faces  921 . Referring to areas of the side faces  922  seen along a direction perpendicular to the substrate  9  as side areas, a complex amplitude reflectance r sample  relative to light with a certain wavelength in the measurement area  93  is obtained by the equation 6, where A I , A II  and A III  are an area ratio of the uppermost face  931  in the measurement area  93 , an area ratio of the bottom face  921  in the trench  92 , and an area ratio of the side areas in the trench  92 , respectively (accurately, an area ratio of the set of the plurality of uppermost faces  931  in the measurement area  93 , an area ratio of the set of the plurality of bottom faces  921  in the plurality of trenches  92 , and an area ratio of a set of side areas in the plurality of trenches  92 ) (the sum of the area ratios A I , A II  and A III  is 1) and r I , r II  and r III  are a complex amplitude reflectance of the uppermost face  931  relative to the light with the wavelength, a complex amplitude reflectance of the bottom face  921  in the trench  92 , and a complex amplitude reflectance of the side areas, respectively.
 
 r   sample   =r   I   ×A   I   +r   II   ×A   II   +r   III   ×A   III   Eq. 6
 
   In the preferred embodiment, as discussed later, since the illumination light is applied to the substrate  9  through the objective lens  44  with the small numerical aperture and the reflected light from the substrate  9  enters the optical system  4  through the objective lens  44 , it is possible to neglect light reflected from the side faces  922  (that is to say, the light hardly enters the optical system  4 ), and make the complex amplitude reflectance r III  in the side areas to 0. Therefore, by substituting initial values into the area ratio A I  of the uppermost face  931  and the area ratio All of the bottom face  921  in the equation 6, and also substituting the complex amplitude reflectance r I  of the uppermost face  931  and the complex amplitude reflectance r II  of the bottom face  921 , which are relative to the light with the wavelength λ and obtained by the equations 3 and 4, into the equation 6, obtained is the complex amplitude reflectance r sample  of the measurement area  93  relative to the light with the wavelength λ in a case where the depth of the trench  92 , the area ratio of the bottom face  921 , and the area ratio of the uppermost face  931  in the parameters are made to the initial values, respectively. Then, as shown in the equation 7, a reflectance R sample  of the measurement area  93  relative to the light with the wavelength λ when each parameter is made to the initial value, is obtained by acquiring a square value of the absolute value of the complex amplitude reflectance r sample .
 
 R   sample   =|r   sample | 2   Eq. 7
 
   Actually, the reflectance R sample  is obtained for each of the plurality of wavelengths included in the measurement wavelength band and a set of a plurality of reflectances R sample  with respect to the plurality of wavelengths is acquired as the calculated spectral reflectance when each parameter is made to the initial value. In the trench shape measuring apparatus  1 , the above computation is repeated while sequentially changing a value of each parameter to the initial value and values which are away from the initial value by the values of changes (hereinafter, collectively referred to as “set values”), to acquire the plurality of calculated spectral reflectances which respectively correspond to all combinations of the set values with respect to the depth of the trench  92 , the area ratio of the bottom face  921 , and the area ratio of the uppermost face  931 . 
   After obtaining the plurality of calculated spectral reflectances, the irradiation position of the illumination light on the substrate  9  is arranged within the measurement area  93  by the holding part moving mechanism  23 , the illumination light is emitted from the light emission part  3  and applied to the measurement area  93  on the substrate  9  (Step S 15 ). At this time, since the illumination light is directed to the substrate  9  through the objective lens  44  with the small numerical aperture as discussed above, it is possible to surely perform application of the illumination light to the bottom faces  921  of the trench pattern. Also, since the reflected light from the measurement area  93  of the substrate  9  is received into the optical system  4  through the objective lens  44 , light reflected from the side faces  922  of the trench  92  and first and higher order diffracted light from the trench pattern are not received into the optical system  4  and normally reflected light (zeroth order light) from the bottom face  921  only enters the optical system  4 . The reflected light is directed to the spectroscope  5  by the optical system  4  and it is spectrally dispersed by the diffraction grating  52  (Step S 16 ). Then, spectrally dispersed light is received on the detector  6  to acquire the measured spectral reflectance of the measurement area  93  (Step S 17 ). 
   Subsequently, the degree of similarity Err between the measured spectral reflectance and each of the plurality of calculated spectral reflectances which are obtained in Step S 14  is obtained by the above equation 2. The calculated spectral reflectance where the degree of similarity Err is minimum is specified, and values of the parameters relative to the calculated spectral reflectance are acquired as the depth of the trench  92 , the area ratio of the bottom face  921 , and the area ratio of the uppermost face  931  in the measurement area  93  on the substrate  9  (Step S 18 ). As discussed above, values of the plurality of parameters are determined by comparing the measured spectral reflectance of the measurement area  93  and the calculated spectral reflectances, to acquire the trench pattern information. In a case where the degree of similarity Err is equal to or smaller than a predetermined value or the like, there may be a case where the nonlinear optimization method such as the Gauss-Newton method or the Levenberg-Marquardt method is used as necessary, and the calculated spectral reflectance where the degree of similarity Err becomes greater than the predetermined value is acquired while converging the degree of similarity Err, to obtain the depth of the trench  92 , the area ratio of the bottom face  921 , and the area ratio of the uppermost face  931  in the measurement area  93 . 
   Other information about the shape of the trench pattern is also acquired in the operation part  71  (Step S 19 ). For example, a value where the area ratio of the bottom face  921  and the area ratio of the uppermost face  931  are subtracted from the value 1 is obtained as the area ratio of the side areas, and a width of one side face  922  in the direction perpendicular to the trench direction (the width indicated by the reference sign W 1  in  FIG. 4 ) is acquired with use of the known pitch P 1 , to obtain a tilt angle of the side face  922  on the cross section of the substrate  9  which is perpendicular to the trench direction (the tilt angle indicated by the reference sign γ in  FIG. 4 ). A width of one uppermost face  931  (the width is indicated by the reference sign W 2  in  FIG. 4  and considered as a line width) and a width of one bottom face  921  (the width indicated by the reference sign W 3  in  FIG. 4 ) with respect to the direction perpendicular to the trench direction can be also acquired with use of the pitch P 1 . When the area of the measurement area  93  is known, it is possible to obtain the total area of each of the bottom faces  921 , the uppermost faces  931 , and the side areas. 
   In a case where the film  91  on the substrate  9  is relatively thick or the like, the trench pattern information can be acquired without the auxiliary film thickness measurement in the trench shape measuring apparatus  1  (Step S 11 ). In this case, the film thickness of the film  91  is also used as a parameter in addition to the depth of the trench pattern, the area ratio of the bottom face  921  in the trench  92  and the area ratio of the uppermost face  931 , and set values of each parameter are set in the operation part  71  (Step S 13 ). Subsequently, a plurality of calculated spectral reflectances which respectively correspond to all combinations of the set values with respect to the depth of the trench  92 , the area ratio of the bottom face  921 , the area ratio of the uppermost face  931 , and the film thickness of the film  91  are acquired by the computation (Step S 14 ). Then, the illumination light is applied to the measurement area  93  by the light emission part  3 , a measured spectral reflectance of the measurement area  93  is acquired on the basis of the reflected light of the illumination light from the measurement area  93  (Steps S 15  to S 17 ), and then a value of each parameter is determined by comparing the measured spectral reflectance and the plurality of calculated spectral reflectances. In consequence, the depth of the trench  92  on the substrate  9 , the area ratio of the bottom face  921 , the area ratio of the uppermost face  931 , and the film thickness of the film  91  are obtained (Step S 18 ). Other information about the shape of the trench pattern is also acquired as necessary (Step S 19 ). 
   In the diffraction grating of the spectroscope, a diffraction efficiency which is a ratio between an incident intensity and the reflected intensity of light is largely different between polarized light having the oscillation direction parallel to the grating direction and that having the oscillation direction perpendicular to the grating direction, depending on a wavelength of the light. In measurement of the trench pattern shape, the oscillation direction of the reflected light from the substrate is limited by influence of the trench pattern (for example, the reflected light from the substrate  9  includes much linearly polarized light which oscillates in a direction parallel to the trench direction on the substrate  9  and much ellipsoidal polarized light which oscillates approximately along the direction). In this case, if there is a (significant) difference between an angle formed between the grating direction and an oscillation surface of the reflected light incident on the diffraction grating and an angle formed between the direction perpendicular to the grating direction and the oscillation surface, a spectrum of the reflected light from the substrate cannot be accurately acquired (that is to say, an accurate spectral reflectance of the substrate cannot be acquired), and it is not possible to obtain the depth of the trench pattern with accuracy. 
   On the other hand, in the trench shape measuring apparatus  1 , since the diffraction grating  52  to which the reflected light of the illumination light from the substrate  9  is directed is arranged so that the angle formed between the direction on the substrate  9  which corresponds to the grating direction of the diffraction grating  52  and the trench direction becomes equal to or greater than 40 degrees and equal to or smaller than 50 degrees (preferably, it becomes 45 degrees), it is possible to accurately obtain the spectral reflectance of the substrate without influence of polarization of the reflected light by the trench pattern on the substrate  9  and accurately obtain the depth of the trench pattern in a nondestructive method. 
   In the trench shape measuring apparatus  1 , since the numerical aperture of the objective lens  44  is made to be equal to or greater than 0.05 and equal to or smaller than 0.1, even if an aspect ratio (a length-to-width ratio of the shape of the cross section) of the trench pattern formed on the substrate  9  is large, it is possible to surely perform application of the illumination light to the bottom face  921  of the trench pattern and receive the reflected light from the bottom face  921  by the diffraction grating  52 . In acquisition of the trench pattern information, with respect to each wavelength included in the measurement wavelength band, the sum of a value obtained by multiplying the complex amplitude reflectance which is theoretically calculated on the basis of the light from the bottom face  921  by the area ratio of the bottom face  921  and a value obtained by multiplying the complex amplitude reflectance which is theoretically calculated on the basis of the light from the uppermost face  931  by the area ratio of the uppermost face  931  is used as the complex amplitude reflectance in the measurement area  93 , and the calculated spectral reflectances can be appropriately obtained with neglecting influence of the reflected light from the side faces  922  of the trench pattern. As a result, it is possible to easily and accurately obtain the depth of the trench pattern, the area ratio of the bottom face  921 , and the area ratio of the uppermost face  931 . 
   In the auxiliary film thickness measurement, the illumination light is applied to the auxiliary area  94  and the spectral reflectance of the auxiliary area  94  is acquired by the detector  6 , to obtain the film thickness of the film  91  on the substrate  9 . Then, the calculated spectral reflectances in acquisition of the trench pattern information are acquired with use of the film thickness which is obtained in the auxiliary film thickness measurement. In this manner, it is possible to obtain the depth of the trench pattern with high accuracy by obtaining the film thickness with respect to the area where the trench pattern does not exist on the substrate  9  having the film  91 . Further, even if the auxiliary film thickness measurement is not performed, since the film thickness of the film  91  is included in the parameters for the computation of the calculated spectral reflectances in acquisition of the trench pattern information, it is possible to accurately obtain the depth of the trench pattern in consideration of the film  91  formed on the substrate  9 . 
   In the trench shape measuring apparatus  1 , measurement of the shape of the trench pattern on the substrate  9 , where a plurality of films (i.e., multilayer film) are formed, may be performed. For example, when the auxiliary film thickness measurement is performed (Step S 11 ), the illumination light is applied to the auxiliary area  94  on the substrate  9  and the spectral reflectance of the auxiliary area  94  is acquired on the basis of the reflected light by the detector  6 , to obtain each film thickness of one or more films, which are not all of the plurality of films, included in the plurality of films (for example, each of the one or more films is a film with a low measurement sensitivity where it is difficult to accurately obtain its film thickness when the film thickness is included in the parameters together with the depth of the trench pattern in acquisition of the trench pattern information) (Step S 12 ). Subsequently, each film thickness of rest of the plurality of films is included in the parameters, in addition to the depth of the trench pattern, the area ratio of the bottom face  921  in the trench  92  of the measurement area  93 , and the area ratio of the uppermost face  931 , and set values of each parameter are set in the operation part  71  (Step S 13 ). With use of film thickness(es) of the one or more films which is acquired in the auxiliary film thickness measurement, the plurality of calculated spectral reflectances which respectively correspond to all combinations of the set values with respect to the depth of the trench  92 , the area ratio of the bottom face  921 , the area ratio of the uppermost face  931 , and film thickness(es) of the other film(s) (the rest of the plurality of films) is obtained by the computation (Step S 14 ). The plurality of calculated spectral reflectances are compared with the measured spectral reflectance which is acquired by application of the illumination light to the measurement area  93 , to determine a value of each parameter (Steps S 15  to S 18 ). As described above, since each film thickness of a film(s) other than one or more films measured in the auxiliary film thickness measurement is included in the parameters for the computation in acquisition of the trench pattern information, it is also possible to accurately obtain the each film thickness of the film(s) which is not measured in the auxiliary film thickness measurement. 
   All film thicknesses of the plurality of films may be obtained in the auxiliary film thickness measurement. Further, the film thickness of the film measured in the auxiliary film thickness measurement may be included in the parameters for the computation in acquisition of the trench pattern information and in this case, it is preferable the measured value obtained in the auxiliary film thickness measurement is made to the initial value. 
   As discussed above, in the trench shape measuring apparatus  1 , in a case where at least one film is formed on both the measurement area  93  and the auxiliary area  94  of the substrate  9  where the trench pattern does not exist, in the auxiliary film thickness measurement, the illumination light is applied to the auxiliary area  94  and the spectral reflectance of the auxiliary area  94  is acquired on the basis of the reflected light, to obtain each film thickness of one or more films included in the at least one film. Subsequently, the calculated spectral reflectances are acquired with use of the each film thickness in acquisition of the trench pattern information and it is therefore possible to obtain the depth of the trench pattern on the substrate  9  having the at least one film with high accuracy. 
   When measurement of the shape of the trench pattern on the substrate  9  on which a plurality of films are formed is performed, a film thickness of each of the plurality of films may be included in the parameters for the computation in acquisition of the trench pattern information without performing the auxiliary film thickness measurement, depending on a film structure on the substrate  9 . That is to say, when at least one film is formed on the measurement area  93  of the substrate  9 , since the film thickness of each of the at least one film is included in the parameters for the computation in acquisition of the trench pattern information, it is possible to accurately obtain the depth of the trench pattern in consideration of the film(s) formed on the substrate  9 . 
     FIG. 7  is a view showing a construction of a trench shape measuring apparatus  1   a  in accordance with the second preferred embodiment of the present invention. The trench shape measuring apparatus  1   a  in  FIG. 7  is different from the trench shape measuring apparatus  1  in  FIG. 1 , in that a depolarizer  46  for converting polarized light included in incident light into unpolarized light is provided between the half mirror  43  and the lens  45 . Other constituent elements in  FIG. 7  are the same as those in  FIG. 1  and represented by the same reference signs in the following discussion. 
   In a measurement operation of the shape of the trench pattern in the trench shape measuring apparatus  1   a  shown in  FIG. 7 , the orientation of the substrate  9  is not adjusted in holding the substrate  9  on the holding part  21  ( FIG. 2 : Step S 10 ), and the following processes after Step S 10  are performed in the same manner as the trench shape measuring apparatus  1  in  FIG. 1 . In the trench shape measuring apparatus  1   a , since the depolarizer  46  is arranged on the optical path between the substrate  9  and the diffraction grating  52 , it is possible to eliminate influence of polarization of the reflected light by the trench pattern with using the depolarizer  46  and precisely acquire the spectral reflectance, to obtain the depth of the trench pattern with accuracy. The depolarizer  46  may be arranged at any position on the optical path between the substrate  9  and the diffraction grating  52 . 
   Though the preferred embodiments of the present invention have been discussed above, the present invention is not limited to the above-discussed preferred embodiments, but allows various variations. 
   In the first preferred embodiment, though the orientation of the substrate  9  is adjusted relatively to the diffraction grating  52  in holding the substrate  9  on the holding part  21 , there may be a case where, for example, a mechanism which rotates the spectroscope  5  and the detector  6  as a unit around the central axis of the diffraction grating  52  is provided, and the spectroscope  5  and the detector  6  are rotated so that the angle formed between the direction on the substrate  9  which corresponds to the grating direction of the diffraction grating  52  and the trench direction becomes equal to or greater than 40 degrees and equal to or smaller than 50 degrees (preferably, it becomes 45 degrees) in acquisition of the measured spectral reflectance. 
   In the trench shape measuring apparatus  1   a  in  FIG. 7 , the reflected light of the illumination light from the substrate  9  is directed to the diffraction grating  52  through the depolarizer  46  and the influence of polarization of the reflected light by the trench pattern can be easily eliminated. In the trench shape measuring apparatus  1  in  FIG. 1 , the depolarizer may be added on the optical path between the substrate  9  and the diffraction grating  52  to eliminate the influence of polarization of the reflected light more reliably. 
   Although the depth of the trench pattern, the area ratio of the bottom face  921  and the area ratio of the uppermost face  931  are surely included in the parameters for the computation in acquisition of the trench pattern information in the above first and second preferred embodiments, the depth of the trench pattern and the area ratio of the bottom face  921  (the area ratio may be a value obtained by subtracting the area ratio of the uppermost face  931  from 1) may be only used as parameters in a case where the area of the side areas is considered as 0, such as a case where the side areas  922  of the trench  92  are perpendicular to the substrate  9 . That is to say, the calculated spectral reflectances are obtained by a computation where at least the depth of the trench pattern and the area ratio of the bottom face  921  in the trench pattern are made to parameters. 
   In the trench shape measuring apparatuses  1  and  1   a , the holding part moving mechanism  23  moves the substrate  9  as an irradiation position changing part, to change the irradiation position on the substrate  9  of the illumination light from the light emission part  3 . The irradiation position changing part can be composed of a mechanism which moves the light emission part  3 , the optical system  4 , the spectroscope  5 , and the detector  6  relatively to the substrate  9 . 
   Each process in the operation flow shown in  FIG. 2  may be appropriately changed within a range where the operation can be performed and for example, the calculated spectral reflectances may be obtained after acquisition of the measured spectral reflectance. 
   The method of eliminating the influence of polarization of the reflected light in the trench shape measuring apparatuses  1  and  1   a  is used in a case where the influence of polarization by the trench pattern occurs in the reflected light from a substrate such as a substrate on which only one trench is formed, a substrate where a plurality of trenches extending in two directions orthogonal to each other are formed, or a substrate where a set of a plurality of holes arranged in a direction is practically considered as one trench, other than the substrate  9  on which the plurality of trenches extending in a direction (trenches in line and space) are formed. In other words, a substrate where the trench pattern substantially extending in a predetermined direction is formed in a measurement area is made to an object. 
   The method of accurately acquiring the trench pattern information by performing the auxiliary film thickness measurement can be applied to a substrate having trench patterns with various shapes. In this case, the measured spectral reflectance may be obtained by spectrally dispersing the reflected light with use of an optical element other than the diffraction grating  52 . 
   A substrate which is to be measured in the trench shape measuring apparatuses  1  and  1   a  may be a printed circuit board, a glass substrate or the like, other than a semiconductor substrate. 
   While the invention has been shown and described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is therefore understood that numerous modifications and variations can be devised without departing from the scope of the invention. 
   This application claims priority benefit under 35 U.S.C. Section 119 of Japanese Patent Application No. 2006-228597 filed in the Japan Patent Office on Aug. 25, 2006 and Japanese Patent Application No. 2007-101307 filed in the Japan Patent Office on Apr. 9, 2007, the entire disclosures of which are incorporated herein by reference.