Abstract:
A normal incidence rotating compensator ellipsometer includes an illumination source that produces a broadband probe beam. The probe beam is redirected by a beam splitter to be normally incident on a sample under test. Before reaching the sample, the probe beam is passed through a rotating compensator. The probe beam is reflected by the sample and passes through the rotating compensator a second time before reaching a detector. The detector converts the reflected probe beam into equivalent signals for analysis.

Description:
TECHNICAL FIELD 
   The subject invention relates to optical devices used to non-destructively evaluate semiconductor wafers. In particular, the present invention relates to increasing the accuracy of normal incidence metrology systems. 
   BACKGROUND OF THE INVENTION 
   As semiconductor geometries continue to shrink, manufacturers have increasingly turned to optical techniques to perform non-destructive inspection and analysis of semiconductor wafers. Techniques of this type, known generally as optical metrology, operate by illuminating a sample with an incident field (typically referred to as a probe beam) and then detecting and analyzing the reflected energy. Ellipsometry and reflectometry are two examples of commonly used optical techniques. For the specific case of ellipsometry, changes in the polarization state of the probe beam are analyzed. Reflectometry is similar, except that changes in intensity are analyzed. Ellipsometry and reflectometry are effective methods for measuring a wide range of attributes including information about thickness, crystallinity, composition and refractive index. The structural details of ellipsometers are more fully described in U.S. Pat. Nos. 6,449,043, 5,910,842 and 5,798,837 each of which are incorporated in this document by reference. 
   Scatterometry is a specific type of optical metrology that is used when the structural geometry of a subject creates diffraction (optical scattering) of the incoming probe beam. Scatterometry systems analyze diffraction to deduce details of the structures that cause the diffraction to occur. Various optical techniques have been used to perform optical scatterometry. These include broadband spectroscopy (U.S. Pat. Nos. 5,607,800; 5,867,276 and 5,963,329), spectral ellipsometry (U.S. Pat. No. 5,739,909) single-wavelength optical scattering (U.S. Pat. No. 5,889,593), and spectral and single-wavelength beam profile reflectance and beam profile ellipsometry (U.S. Pat. No. 6,429,943). Scatterometry, in these cases generally refers to optical responses in the form of diffraction orders produced by periodic structures, that is, gratings on the wafer. In addition it may be possible to employ any of these measurement technologies, e.g., single-wavelength laser BPR or BPE, to obtain critical dimension (CD) measurements on non-periodic structures, such as isolated lines or isolated vias and mesas. The above cited patents and patent applications, along with PCT Application WO 03/009063, US Application 2002/0158193, US Application 2003/0147086, US Application 2001/0051856 A1, PCT Application WO 01/55669 and PCT Application WO 01/97280 are all incorporated herein by reference. 
   Normal incidence ellipsometry is a widely used type of optical metrology, both for thin film measurements as well as scatterometry applications. As shown in  FIG. 1 , an instrument of this type includes an illumination source that typically produces a broadband polychromatic probe beam. The probe beam is directed by one or more refractive or reflective components (represented as a lens in this example) to a beam splitter. The beam splitter redirects the probe beam through a rotating polarizer and objective lens (which is typically composed of a series of reflective and/or refractive components) before reaching a sample under test. The sample reflects the probe beam and a portion of the reflected probe beam is captured by the objective. The reflected probe beam then passes through the rotating polarizer and beam splitter and is directed by one or more refractive or reflective components (represented, again, as a lens) to a spectrometer. The spectrometer converts the probe beam into equivalent signals for analysis by a processor. 
   For the situation where a grating is being measured by normal-incidence reflectance, the grating is typically oriented so the rulings (grooves) are either parallel or perpendicular to the electric field emerging from the polarizer. These are the two normal modes of the system, where linearly polarized light incident on the grating is reflected as linearly polarized light. The mode where the incident/reflected electric field is parallel to the rulings is conventionally denoted as the transverse magnetic (TM) mode. The other normal mode, where the electric field vector is perpendicular to the rulings, is conventionally denoted the transverse electric (TE) mode. Reflectance measurements using these two modes allow the absolute squares R a  =|r a  | 2  and R b =|r b | 2  of the complex reflectances r a  and r b  for electric fields parallel and perpendicular, respectively, to the rulings to be determined. 
   More general normal-incidence reflectance measurements are also possible. The field vector does not need to be oriented as described above, but can assume any azimuth angle P relative to the rulings. Typically, this angle is varied by rotating the polarizer, although it can be varied by rotating either the polarizer or the grating, either at a fixed angular velocity or as a series of discrete steps. At intermediate angles 
             P   ≠     n   ⁢     π   2         ,         
where n is an integer, the two modes are mixed. This allows the relative amplitude and phase of r a  and r b  to be determined. Specifically, the intensity of the reflected probe beam as a general function of P can be written
   I ( P )=a 0 +a 2  cos(2 P )+a 4  cos(4 P ) 
where the Fourier coefficients a 0 , a 2 , and a 4  are given by
 
                     a   0     =         3   8     ⁢     (              r   a          2     +            r   b          2       )       +       1   4     ⁢     Re   (       r   a     ⁢     r   b   *       )           ;                   a   2     =       1   2     ⁢     (              r   a          2     -            r   b          2       )         ;                 a   4     =         1   8     ⁢     (              r   a          2     +            r   b          2       )       -       1   4     ⁢       Re   ⁡     (       r   a     ⁢     r   b   *       )       .                     
This calculation assumes that at P=0 the electric field is parallel to the rulings, and ignores the partial polarization that would be caused by the beam splitter sketched in  FIG. 1 .
 
   As can be seen, rotating the polarizer generates an additional perspective (Re(r a r b *)). However, the rotating polarizer design is unable to measure the complementary quantity, the imaginary component Im(r a r b *). In addition, if the polarizer is rotated, partial polarization of the source or polarization sensitivity of the detector can lead to systematic errors that cannot be distinguished from the signal due to the sample. Finally, the configuration provides no intrinsic way of verifying that the rulings are indeed parallel to the electric field vector when P is nominally equal to zero. 
   The inability to measure Im(r a r b *) is also true of non-normally incident ellipsometers that utilize single rotating compensators. Im(r a r b *) may be obtained by non-normally incident designs that include modulators in both incident and reflected beams. Designs of this type are obviously more complex (since they include multiple photoelastic-modulators or multiple rotating compensators) and are unable to achieve the small spot sizes available to normal incidence designs. Consequently, there are reasons to believe that measurement accuracy may be improved by other designs that do not suffer these limitations. 
   SUMMARY 
   An embodiment of the present invention provides a normal incidence ellipsometer for scatterometry applications. A typical implementation for an ellipsometer of this type includes an illumination source that produces a broadband white-light probe beam. A polarizer is used to impart a known polarization state to the probe beam. The probe beam is then directed through a rotating compensator that introduces a relative phase delay ξ (phase retardation) between a pair of mutually orthogonally polarized components of the probe beam. After leaving the compensator, the probe beam is directed at normal incidence against the surface of the sample. The sample reflects the probe beam back through the compensator and on to a second polarizer (also referred to as an analyzer). A detector measures the intensity of the probe beam leaving the analyzer as a function of rotational angle of the compensator or analyzer. 
   A processor analyzes the output of the detector to obtain the quantities: |r a  | 2 , |r b | 2 , Re(r a r b *), and Im(r a r b *). This surpasses traditional rotating polarizer designs that are unable to measure the imaginary component Im(r a r b *). It should also be noted that the measured quantities are obtained without the need to align gratings within the sample relative to the polarization of the probe beam. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a prior art ellipsometer that includes a rotating polarizer. 
       FIGS. 2 through 4  show different implementations of the normal incidence rotating compensator ellipsometer provided by the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   An embodiment of the present invention provides a normal incidence ellipsometer for scatterometry applications. As shown in  FIG. 2 , a first implementation for the normal incidence ellipsometer  200  includes an illumination source  202 . Illumination source  202  produces a broadband white-light probe beam that is projected through a beam splitter  204 , polarizer  206  and rotating compensator  208  before reaching a subject  210 . As it traverses this path, polarizer  206  imparts a known polarization state to the probe beam. Rotating compensator  208  introduces a relative phase delay ξ (phase retardation) between a pair of mutually orthogonally polarized optical beam components. The amount of phase retardation is a function of the wavelength, the dispersion characteristics of the material used to form compensator  208 , and the thickness of the compensator  208 . Compensator  208  is rotated at an angular velocity ω about an axis substantially parallel to the propagation direction of the probe beam. When used in this document, rotation is intended to include continuous rotation, as well as rotation in increments or steps. Subject  210  returns the probe beam (though polarizer  206  and rotating compensator  208 ) to beam splitter  204 . Beam splitter  204  redirects the returning probe beam to a spectrometer  212 . Spectrometer  212  is typically a monochrometer-CCD detector combination, but other technologies can also be used. 
     FIG. 3  shows a second implementation  300  for the normal incidence ellipsometer. Ellipsometer  300  shares many of the components described for ellipsometer  200  with the main difference being that the beam splitter  204  and polarizer  206  have been replaced by a beam splitting polarizer  304 . Beam splitting polarizer  304  is a Wollaston prism and performs two functions. The first is to impart a known polarization state to the probe beam. The second is to function as a beam splitter/combiner. As the probe beam returns from subject  308 , beam splitting polarizer  304  directs a portion of the returning probe beam to spectrometer  310 . 
   As shown in  FIG. 4 , a third implementation for the normal incidence ellipsometer  400  includes an illumination source  402 . Illumination source  402  produces a broadband white-light probe beam that is projected through a beam splitter  404 , beam splitting polarizer  406  and rotating compensator  408  before reaching a subject  410 . As it traverses this path, polarizer  406  imparts a known polarization state to the probe beam. Rotating compensator  408  introduces a relative phase delay ξ between a pair of mutually orthogonally polarized optical beam components. The amount of phase retardation is a function of the wavelength, the dispersion characteristics of the material used to form compensator  408 , and the thickness of the compensator  408 . Compensator  408  is rotated at an angular velocity ω about an axis substantially parallel to the propagation direction of the probe beam. When used in this document, rotation is intended to include continuous rotation, as well as rotation in increments or steps. Subject  410  returns the probe beam (though polarizer  406  and rotating compensator  408 ) to beam splitter  404 . 
   Beam splitting polarizer  406  is a Wollaston prism and performs two functions. The first is to impart a known polarization state to the probe beam. The second is to function as a beam splitter/combiner. As the probe beam returns from subject  410 , beam splitting polarizer  406  splits the returning probe beam into two components. The first component (referred to as s-polarized) is characterized by having detected polarization is identical with that of the illuminating polarization, and is directed to s-spectrometer  412 . The orthogonally polarized return component is denoted p-polarized, and is directed to p-spectrometer  414 . Spectrometer  412  and  414  are typically monochrometer-CCD detector combinations, but other technologies can also be used. 
   The intensity of the reflected probe beam received by spectrometers  412  and  414  is a function of the azimuth angle of the rotating compensator  408  relative to the electric field vector and the grating rulings. In what follows C is defined to be the azimuth angle locating the fast axis of the compensator relative to the azimuth angle of the polarizer, which is taken as reference, i.e., to define the value C=0°. The second azimuth angle that must be defined is that of the rulings relative to the same reference as C. The second azimuth angle is denoted as G, where G=0° is the condition where the rulings of the grating are parallel to the field emerging from the polarizer. 
   For arbitrary G, I(C) has the general form:
 
 I ( C )=a 0 +a 2  cos(2 C )+ b   2  sin(2 C )+a 4  cos(4 C )+ b   4  sin(4 C ) +a 6  cos(6 C )+ b   6  sin(6 C )+a 8  cos(8 C )+ b   8  sin(8 C ).
 
   However, for G=0° none of the sin(nC) terms are present, and the general coefficients (to be given later below) simplify. For s-spectrometer  412 , this yields: 
                   a   0     (   s   )       =       ⁢                r   a          2     ⁡     [         cos   4     ⁢     ξ   2       +       1   4     ⁢     sin   2     ⁢   ξ     +       3   8     ⁢     sin   4     ⁢     ξ   2         ]       +              r   b          2     ⁡     [       3   8     ⁢     sin   4     ⁢     ξ   2       ]       +                     ⁢       Re   (       r   a     ⁢     r   b   *       )     ⁡     [         1   4     ⁢     sin   4     ⁢     ξ   2       -       1   4     ⁢     sin   2     ⁢   ξ       ]                     a   2     (   s   )       =       ⁢       Im   (       r   a     ⁢     r   b   *       )     ⁡     [       -     1   2       ⁢   sin   ⁢           ⁢     ξsin   2     ⁢     ξ   2       ]                     a   4     (   s   )       =       ⁢                r   a          2     ⁡     [         1   4     ⁢     sin   2     ⁢   ξ     +       1   2     ⁢     sin   4     ⁢     ξ   2         ]       +              r   b          2     ⁡     [       -     1   2       ⁢     sin   4     ⁢     ξ   2       ]       +       Re   (       r   a     ⁢     r   b   *       )     ⁡     [       1   4     ⁢     sin   2     ⁢   ξ     ]                       a   6     (   s   )       =       ⁢       Im   (       r   a     ⁢     r   b   *       )     ⁡     [       1   2     ⁢   sin   ⁢           ⁢   ξ   ⁢           ⁢     sin   2     ⁢     ξ   2       ]                     a   8     (   s   )       =       ⁢         [              r   a          2     +            r   b          2       ]     ⁡     [       1   8     ⁢     sin   4     ⁢     ξ   2       ]       +       Re   (       r   a     ⁢     r   b   *       )     ⁡     [       -     1   4       ⁢     sin   4     ⁢     ξ   2       ]                     
where ξ=2πd(n e −n o )/λ, where d is the effective thickness of the compensator, n o  and n e  are refractive indices of the ordinary and extraordinary polarizations in the compensator, and λ is the wavelength of light. For p-spectrometer  414  the corresponding expressions are:
 
                   a   0     (   p   )       =       ⁢         [              r   a          2     +            r   b          2       ]     ⁡     [         1   8     ⁢     sin   4     ⁢     ξ   2       +       1   8     ⁢     sin   4     ⁢   ξ       ]       +                     ⁢     Re   ⁢       (       r   a     ⁢     r   b   *       )     ⁡     [         -     1   4       ⁢     sin   4     ⁢     ξ   2       +       1   4     ⁢     sin   4     ⁢     ξ   2         ]                       a   2     (   s   )       =       ⁢       Im   (       r   a     ⁢     r   b   *       )     ⁡     [       1   2     ⁢     sin   2     ⁢           ⁢     ξ   2     ⁢   sin   ⁢           ⁢   ξ     ]                     a   4     (   p   )       =       ⁢         [              r   a          2     +            r   b          2       ]     ⁡     [       -     1   8       ⁢     sin   2     ⁢   ξ     ]       +     Re   ⁢       (       r   a     ⁢     r   b   *       )     ⁡     [       -     1   4       ⁢     sin   2     ⁢   ξ     ]                         a   6     (   s   )       =       ⁢       Im   (       r   a     ⁢     r   b   *       )     ⁡     [       -     1   2       ⁢     sin   2     ⁢           ⁢     ξ   2     ⁢   sin   ⁢           ⁢   ξ     ]                     a   8     (   s   )       =       ⁢         [              r   a          2     +            r   b          2       ]     ⁡     [       -     1   8       ⁢     sin   4     ⁢     ξ   2       ]       +     Re   ⁢       (       r   a     ⁢     r   b   *       )     ⁡     [       1   4     ⁢     sin   4     ⁢     ξ   2       ]                       
where again max (a 0   (s) )=½.
 
   This is a total of five distinct nonzero Fourier coefficients for both spectrometers  412  and  414 . Given ξ, for either set of coefficients the sample parameters |r a  | 2 , |r b | 2 , Re(r a r b *)and Im(r a r b *) are overdetermined. However, their most probable values can be obtained by least-squares fitting. Least-squares routines have the added advantages that (a) the coefficients that are most important in determining a given parameter are also given the most weight; and (b) a measure of the capability of the system to determine all parameters is provided by the goodness of fit. In fact unless absolute intensities are measured, which is hardly ever the case, the sample parameters are determined only to within a normalization constant, meaning that only three of the four sample parameters provide relevant sample information. However, this can be compared to the analogous situation without the compensator, where only two of the three parameters provide relevant information. 
   Once obtained, these parameters may be used in turn to estimate other sample parameters such as thickness of the grating, top and bottom line widths, and the thickness of an underlying film. As described previously, ellipsometers  200  and  300  include a single spectrometer ( 212  and  310 , respectively). For the typical case, these spectrometers measure the s-polarized component of the reflected probe beam and are characterized by the first set of Fourier coefficients listed above. Alternately, spectrometers  212  and  310  may be configured to measure the p-polarization component described by the second set of five Fourier coefficients. 
   We now consider the situation where G takes on general values, so the rulings are not aligned either parallel or perpendicular to the electric field vector emerging from the polarizer. In this case the s-spectrometer receives an intensity whose Fourier components are: 
           DC   ⁢           ⁢   terms   ⁢     :                       3   8     ⁡     [              r   a          2     +            r   b          2       ]       ⁢     sin   4     ⁢     ξ   2       +       [                r   a          2     ⁢     cos   4     ⁢   G     +              r   b          2     ⁢     sin   4     ⁢   G       ]     ⁡     [         cos   4     ⁢     ξ   2       +       1   4     ⁢     sin   4     ⁢   ξ       ]       +       Re   ⁡     (       r   a     ⁢     r   b   *       )       ⁡     [         1   4     ⁢     sin   2     ⁢     ξ   2       +       1   2     ⁢     cos   4     ⁢     ξ   2     ⁢     sin   2     ⁢   2   ⁢   G     -       1   4     ⁢     sin   2     ⁢   ξ       ]                   2   ⁢     C   ′     ⁢           ⁢   terms   ⁢     :                     Im   (       r   a     ⁢     r   b   *       )     ⁡     [     sin   ⁢           ⁢     ξ   ⁡     (         -     1   2       ⁢     sin   2     ⁢           ⁢     ξ   2     ⁢     cos   ⁡     (       2   ⁢     C   ′       -   G     )         +       cos   2     ⁢     ξ   2     ⁢   sin   ⁢           ⁢   2   ⁢   G   ⁢           ⁢     sin   ⁡     (       2   ⁢     C   ′       +   G     )           )         ]       ;               4   ⁢     C   ′     ⁢           ⁢   terms   ⁢     :                       {           1   2     ⁡     [              r   a          2     -            r   b          2       ]       ⁢     sin   4     ⁢     ξ   2       +       1   4     ⁢     sin   2     ⁢     ξ   ⁢           [                r   a          2     ⁢     cos   2     ⁢   G     -              r   b          2     ⁢     sin   2     ⁢   G       ]         }     ⁢   cos   ⁢           ⁢   4   ⁢     C   ′       +       1   4     ⁢     Re   (       r   a     ⁢     r   b   *       )     ⁢     sin   2     ⁢     ξ   ⁡     [       cos   ⁢           ⁢   2   ⁢   G   ⁢           ⁢   cos   ⁢           ⁢   4   ⁢           ⁢     C   ′       -     2   ⁢           ⁢   sin   ⁢           ⁢   2   ⁢   G   ⁢           ⁢   sin   ⁢           ⁢   4   ⁢           ⁢     C   ′         ]           ;               6   ⁢     C   ′     ⁢           ⁢     term   ⁢   s     ⁢     :                     1   2     ⁢     Im   (       r   a     ⁢     r   b   *       )     ⁢   sin   ⁢           ⁢   ξ   ⁢           ⁢     sin   2     ⁢     ξ   2     ⁢     cos   ⁡     (       6   ⁢     C   ′       +   G     )         ;               8   ⁢     C   ′     ⁢           ⁢     term   ⁢   s     ⁢     :                         1   8     ⁡     [              r   a          2     +            r   b          2     -     2   ⁢     Re   (       r   a     ⁢     r   b   *       )         ]       ⁢     sin   4     ⁢     ξ   2     ⁢   cos   ⁢           ⁢   8   ⁢     C   ′       ;     ⁢                 
where
 
             C   ′     =     C   -       G   2     .             
The p-spectrometer receives an intensity whose Fourier components are:
 
   
     
       
         
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                     8 
                   
                   ⁡ 
                   
                     [ 
                     
                       
                         
                            
                           
                             r 
                             a 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             r 
                             b 
                           
                            
                         
                         2 
                       
                       - 
                       
                         2 
                         ⁢ 
                         
                           Re 
                           ( 
                           
                             
                               r 
                               a 
                             
                             ⁢ 
                             
                               r 
                               b 
                               * 
                             
                           
                           ) 
                         
                       
                     
                     ] 
                   
                 
                 ⁢ 
                 
                   sin 
                   4 
                 
                 ⁢ 
                 
                   ξ 
                   2 
                 
                 ⁢ 
                 cos 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 8 
                 ⁢ 
                 
                   
                     C 
                     ′ 
                   
                   . 
                   
                     
 
                   
                   ⁢ 
                   where 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   C 
                   ′ 
                 
               
             
             = 
             
               C 
               - 
               
                 
                   G 
                   2 
                 
                 . 
               
             
           
           ⁢ 
           
               
           
         
       
     
   
   It is now seen that there are in general nine coefficients available for analysis. We therefore obtain even further constraints on the sample parameters. In fact these overdetermine the four sample parameters Re(r a r b *), and Im(r a r b *). In addition we have enough information to determine G. Therefore, one of the main advantages of the configuration follows: it is not necessary to position the grating prior to measurement at G=0, but G can be determined from the coefficients themselves. Thus measurements can be made with an arbitrary orientation of the grating. 
   Extracting Reflectance Parameters at Normal Incidence 
   (a) assume a sample with the principal axes a and b in the plane of the surface with field reflectances r a  and r b  for light polarized parallel to a and b respectively. We seek to obtain the four quantities:
 
| r   a  | 2    ,|r   b | 2   , Re ( r   a   r   b ), and  Im ( r   a   r   b *).
 
   For a series of measurements taken as a function of polarizer or compensator angle θ the intensity may be written (as shown above) as:
 
 I   ω   =|r   a  | 2 ƒ 1 (θ)+| r   b | 2 ƒ 2 (θ)+[ Re ( r   a   r   b *)]ƒ 3 (θ)+[ Im ( r   a   r   b *)]ƒ 4 (θ).
 
   The functions ƒ 1  . . . ƒ 4  could be reduced to their Fourier components but this is not necessary. 
   (b) Now calculate the elements m ij  of the correlation matrix M 1  as: 
             m   ij     =       1   N     ⁢       ∑     ω   =   1     N     ⁢           ⁢         f   i     ⁡     (     θ   ω     )       ⁢       f   j     ⁡     (     θ   ω     )                   
and the elements v i  of the weighted-intensity vector V 1  as:
 
             v   i     =       1   N     ⁢       ∑     ω   =   1     N     ⁢           ⁢       I   ω     ⁢       f   i     ⁡     (     θ   ω     )                   
where θ ω  are the azimuth angles where the I ω  are recorded. Then if we make a vector A such that a 1 =|r a  | 2 , a 2 =|r b | 2 , a 3 =Re(r a r b *), and a 4 =Im(r a r b *) it follows that
 V=MA 
and
   A=M   −1   V    
and so we have formally solved the problem of obtaining the four quantities from the intensity measurements. Note that it is not necessary to decompose ƒ 1  . . . ƒ 4  into Fourier components. This approach may yield faster analysis in repetitive measurements.