Abstract:
An apparatus to calibrate a polarizer in a polarized optical system at any angle of incidence. The apparatus decouples the polarization effect of the system from the polarization effect of the sample. The apparatus includes a substrate with a polarizer disposed on the surface. An indicator on the substrate indicates the polarization orientation of the polarizer, which is in a predetermined orientation with respect to the substrate.

Description:
FIELD 
       [0001]    This application claims rights and priority on prior pending U.S. patent application Ser. No. 13/164,130 filed 2011 Jun. 20. This invention relates to the field of optical metrology. More particularly, this invention relates to characterization, alignment, and calibration of a polarizer in an optical system, such as a spectral reflectometer. 
       INTRODUCTION 
       [0002]    Currently, the calibration of the system polarizer in a polarized reflectometer uses the internal polarizer of the system in a transmission mode. Specifically, system polarization calibration is performed by stepping the internal polarizer of the system over a discrete set of angles while acquiring raw scans on a non-polarized reference sample (such as silicon oxide) at a fixed position. The acquired system-polarization response-curve on the non-polarizing reference sample, as a function of the internal polarizer stepping angle with respect to its home position and wavelength, is stored as a calibration curve for later characterization of polarized samples (such as grating samples). 
         [0003]    In such methods, although the initial polarizer position is known at its home position of the stepper motor, its relative orientation with respect to a polarized sample is a system-fitting parameter that depends on the specific properties of the polarized sample, such as: the optical properties of the grating and films underneath it, period, critical dimension, profiles, and the orientation of the grating on the stage of the instrument. Such methods are generally limited to a broadband polarized reflectometer having a beam that is directed to the sample at an incident angle of zero degrees or less than ten degrees with respect to the perpendicular of the sample surface, in essence normal incidence or near normal incidence. 
         [0004]    What is needed, therefore, is a more versatile polarization calibration method that decouples polarizing effects of the sample and the system polarization states, and can be used with an arbitrary angle of incidence. 
       SUMMARY 
       [0005]    The above and other needs are met by a calibration apparatus with a substrate, a polarizer disposed on the substrate, and an indicator indicating a polarization orientation of the polarizer. In some embodiments the polarizer is a separate element that is attached to the surface of the substrate. In other embodiments the polarizer is a lithographic polarizer formed directly on the substrate. 
     
    
     
       DRAWINGS 
         [0006]    Further advantages of the invention are apparent by reference to the detailed description when considered in conjunction with the figures, which are not to scale so as to more clearly show the details, wherein like reference numbers indicate like elements throughout the several views, and wherein: 
           [0007]      FIG. 1A  is a top plan view of a polarization calibration apparatus according to an embodiment of the present invention. 
           [0008]      FIG. 1B  is a cross-sectional side view of a polarization calibration apparatus according to an embodiment of the present invention. 
           [0009]      FIG. 1C  is a functional block diagram of a system to be calibrated using a polarization calibration apparatus according to an embodiment of the present invention. 
           [0010]      FIG. 2A  is a combined top plan and logical view of a polarization calibration apparatus according to an embodiment of the present invention, depicting references and angles to be determined according to a first embodiment of the present invention. 
           [0011]      FIG. 2B  is a combined top plan and logical view of a polarization calibration apparatus according to an embodiment of the present invention, depicting references and angles to be determined according to a second embodiment of the present invention. 
           [0012]      FIG. 3  is a flow chart of a method according to an embodiment of the present invention. 
           [0013]      FIG. 4  is a chart of intensity as a function of rotating polarizer angle, with first polarizer at P 0  (0 degrees in the graph), and third, fixed polarizer at angle alpha (91 degrees in the graph), according to an embodiment of the present invention. 
           [0014]      FIG. 5  is a calibration curve of a polarized optical system for signal versus rotation angle of a polarization calibration apparatus, according to an embodiment of the present invention. 
       
    
    
     DESCRIPTION 
       [0015]    With reference now to  FIG. 1A ,  1 B, and  1 C, there is depicted a calibration apparatus  100  that is constructed by forming a polarizer  104  with a known polarization orientation and optical properties to a substrate  102 , such as a standard silicon wafer. The polarizer  104  can work either in a transmission mode or in a reflection mode. The polarizer  104  is selected to have good optical qualities in regard to the polarized optical system  108  to be calibrated. These qualities include a high extinction ratio and low absorption over the spectral wavelength range of the system  108 . The preferred operation is in reflection mode, in which the polarizer  104  is made of a metal grating structure on the substrate  102 . The calibration apparatus  100  could be manufactured by patterning a lithographic polarizer  104  on a standard silicon wafer  102 , or simply attaching a commercial polarizer  104  to a standard silicon wafer  102 . 
         [0016]    The calibration apparatus  100  is loaded onto the sample stage  110  of the system  108  in the same way as a polarized sample. With additional reference now to  FIG. 2A , the notch  106  on the calibration apparatus  100  is used to establish the initial angle  208  φ 0  between the orientation  210  of the calibration apparatus  100 , relative to the reference frame  200  of the system  108  (such as the optical back plane or the plane of incidence). This angle  208  φ 0 is further refined by using the built-in pattern recognition camera  118  that is often available in such systems  108 , in combination with the coordinates of the stage  110  of the system  108 . Once the angle  208  φ 0  is accurately determined, a series of spectra I(φ, φ 0 , λ, P 0 ) are acquired from the calibration apparatus  100  by stepping stage  110  through angles  206  φ through a predetermined range of angles and at predetermined angle increments, while taking readings with the sensor  114 . The complete set of data I(φ, φ 0 , λ, P 0 ) is reduced to I(φ′, P 0 ), and plotted versus (φ′, where φ′=φ−φ 0  and P 0  is the angle  202  (between the system reference  200  and the internal polarizer  122  orientation  204 ) to be determined for the system  108 . The polarizer orientation  202  P 0  of the system is extracted from the curve I(φ′, P 0 ) by a nonlinear regression algorithm: 
         [0000]        I ( P   0 , φ′)= A+B  cos 2(φ′− P   0 )+ C  cos(4φ′−2 P   0 )
 
         [0017]    If the value of  202  P 0  falls outside of the specifications of the system  108 , then the polarizer  122  in the system  108  can be adjusted using mechanical means until it meets the specification. 
         [0018]    An alternate embodiment is depicted in  FIG. 2B , in which a crossed analyzer  116  is inserted in the exit beam of the system  108 , to improve the precision of the measurement of  202  P 0 . The simulation depicted in  FIG. 4  indicates that the resulting intensity curve is proportional to cos(4φ′−P 0 ) when the fixed analyzer  116  is placed at about ninety degrees relative to  202  P 0 . As a result, additional minimum  202  P 0  is introduced when the fixed analyzer is used with the calibration apparatus  100 . The simulation depicted in  FIG. 4  also reveals that if the analyzer  116  angle α  212  (between the system reference  200  and the analyzer  116  orientation) is off by as little as one degree (for example), the intensity curve contains a small cos(2φ′−P 0 ) component. This component introduces about a six degree difference between the maxima, yet no change in the extinction angle  202  P 0 . An additional advantage of using a fixed polarizer  122  during calibration is to allow for a more flexible orientation of the calibration apparatus  100  when there is a limited range of stage  110  rotation angles available. 
         [0019]    Systems  108  often include polarizing elements other than a polarizer  122 , such as a grating spectrometer. Those polarizing elements tend to introduce error into  202  P 0  if they are not properly accounted for. For example, the polarizer calibration angle  202  P 0  in a system  108  with only a polarizer  122  but without an analyzer  116  is susceptible to the alignment error of the grating spectrometer, since the spectrometer has a different spectral efficiency in regard to the p and s polarization states. To characterize the grating spectrometer misalignment angle φ, the internal polarizer  122  of the system  108  is removed and the polarization response curve is measured using the calibration apparatus  100 . In this case, 
         [0000]        I (φ s , φ′)= A+B  cos 2(φ′−φ s ),
 
         [0000]    from which the angle φ s  can be extracted from the curve I(φ s , φ′) using a nonlinear regression. This φ s  can be used to improve the accuracy of  202  P 0 . 
         [0020]      FIG. 5  depicts the results from a polarizer calibration procedure using the calibration apparatus  100  and method as described. In this case,  202  P 0  is determined to be 89.84° relative to the optical reference frame  200  of the system  108 . The discrete data points on the chart are integrated signals measured at angle  206  φ using the calibration apparatus  100 . 
         [0021]      FIG. 3  depicts a flow chart of an embodiment of a method  300  according to the present invention. The apparatus  100  is loaded into the system  108 , as given in block  302 . The notch  106  is used to load the polarizer  104  at the desired position  210 . The system  108  is then focused onto the apparatus  100  and otherwise initialed, as given in block  304 . The initial apparatus angle  208  is then determined relative to the system reference  200 . Spectra are then acquired at various angles with predetermine increments starting from that angle, using the sensor  114 , as given in block  308 . The method determines whether that reading is the final angle at which a spectrum is to be collected, as given in block  310 . If it is not, then the apparatus  108  angle  206  is incremented according to a step, as given in block  312 , and another spectrum is acquired, as given in block  308 . 
         [0022]    When all of the spectra have been acquired, then control flows from block  310  to block  314 , and the angle  202  of system polarization  204  of internal polarizer  122  relative to the system reference  200  is determined, such as from the equations presented above, as given in block  314 . If the angle  202  is within specification for the system  108 , as determined in block  316 , then the method concludes, as given in block  318 . If not, then the system polarizer  122  is adjusted as needed, as given in block  320 , and a new set of spectra are acquired, as described above, to verify the proper position of the polarizer  122 . 
         [0023]    The present polarization apparatus  100  and method can be used for calibrating the polarizer element  122  in a polarized reflectometer  108  at any arbitrary angle of incidence, including normal incident angle and any oblique incident angle. The method decouples the internal polarizer calibration from the spectrometer polarization effect. The method also establishes the initial position of the polarizer  122  using the system reference frame  200  (such as the plane of incidence), which is completely independent of the grating sample loading position. The method also characterizes the overall residual polarization of an unpolarized optical system  108 . 
         [0024]    The foregoing description of embodiments for this invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Obvious modifications or variations are possible in light of the above teachings. The embodiments are chosen and described in an effort to provide illustrations of the principles of the invention and its practical application, and to thereby enable one of ordinary skill in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. All such modifications and variations are within the scope of the invention as determined by the appended claims when interpreted in accordance with the breadth to which they are fairly, legally, and equitably entitled.