Patent Publication Number: US-2009225390-A1

Title: Feedback system and feedback method for controlling power ratio of incident light

Description:
BACKGROUND OF THE INVENTION  
     1. Field of the Invention 
     The present invention is related to a feedback system and a feedback method for controlling power ratio of incident light. 
     2. Description of the Prior Art 
     As the integration of ICs increases the critical dimension of semiconductors becomes smaller. Therefore, it is desirable to increase the resolution limit of optical exposure tools. A conventional method for improving resolution includes the steps of: off-axis illumination, immersion lithography and increasing the numerical aperture of the lens. As the resolution increases, mask induced polarization may occur. 
     In general, a mask is composed of a mask substrate and a patterned metal layer. The mask substrate can be a quartz substrate, and the patterned metal layer covers the quartz substrate. The light can be defined into two modes: transverse-electric (TE) mode and transverse-magnetic (TM) mode. 
     Polarization effects can be a concern with the decreasing device dimensions. Based on physical properties, the patterned metal layer has a higher transmittance with respect to the TE mode of the light compared to the TM mode of the light, especially when the incident angle is large. On the contrary, the quartz substrate has a low transmittance with respect to the TE mode of the light. Therefore, even if the TE mode of light passing through the patterned metal layer is utilized, the TE mode of light will be blocked by the quartz substrate before it reaches the wafer. As a result, the product yield will be deteriorated. 
     It is therefore the primary object of the present invention to provide a feedback system to adjust the polarization power ratio of incident light. By converting the energy of TM mode to TE mode, the energy of the TE mode can be increased when it reaches the wafer. The resolution and yield can thereby be enhanced. 
     SUMMARY OF THE INVENTION  
     From one aspect of the present invention, the present invention provides a feedback method for controlling polarization ratio of incident light. 
     First, a mask having a mark is provided. Thereafter, the mark is illuminated with incident light. Next, reflected light or refracted light from the illuminated mark is detected to get a first parameter. Afterwards, the first parameter is processed to become a second parameter. Finally, polarization ratio of the incident light is adjusted from the second parameter. 
     From another aspect of the present invention, the present invention further provides a feedback controlling system including an incident light used to illuminate a mark on a mask, a polarization converter used to control the polarization power ratio of the incident light, a detector used to detect reflected light or refracted light from the illuminated mark to get a parameter, and a processor used to calculate the parameter and send a feedback signal to the polarization converter to adjust the polarization power ratio of the incident light. 
     The present invention features disposing a mark on the mask substrate. After the energy of the reflected light or the refracted light from the illuminated mark is detected, the TE/TM polarization power ratio of the incident light can be obtained by calculation. Then, the TE/TM polarization power ratio is fed back into the polarization converter used as a base value. After that, the energy of TE mode of the incident light can be increased by the polarization converter. 
     These and other objectives of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram illustrating a feedback controlling system in accordance with the first embodiment of the present invention. 
         FIG. 2  is a schematic diagram illustrating a feedback controlling system in accordance with the second embodiment of the present invention. 
         FIG. 3  is a schematic diagram illustrating the magnified mark. 
         FIG. 4  is a schematic diagram illustrating the side view of the mask. 
         FIG. 5  illustrates the transmittance of the mask with respect to the zero-order incident light in TE mode versus width. 
     
    
    
     DETAILED DESCRIPTION  
       FIG. 1  is a schematic diagram illustrating a feedback controlling system  100  in accordance with the first embodiment of the present invention. As shown in  FIG. 1 , the a feedback controlling system includes: 
     (1) A light source  10 . Radiant of the light source  10  is focused to become radiant  10   a  after passing through lens  12 . Then, radiant  10   a  passes through an aperture plate  14 . 
     (2) A polarization converter  16 . A TE/TM polarization power ratio of radiant  10   a  is adjusted by the polarization converter  16  to form incident light  11 . A mark  20  on a mask substrate  22  is illuminated by the incident light  11 , and the incident light  11  is refracted to form refracted light  11 ′. The mask substrate  22  can be a quartz substrate, and the mark  20  and the mask substrate  22  form a mask  18 . 
     (3) A detector  24  used to detect the refracted light  11 ′ from the illuminated portion of the mark  20  to get a parameter. According to a preferred embodiment of the present invention, the parameter can be energy of the refracted light  11 ′ in TE mode. 
     (4) A processor  26  used to calculate the parameter. After calculating the parameter, a TE/TM polarization power ratio of the incident light  11  can be obtained. Then the TE/TM polarization power ratio of the incident light  11  will be fed back into the polarization converter  16  to be a feedback signal. In this way, by taking the TE/TM polarization power ratio of the incident light  11  as a base value, the TE/TM polarization power ratio of the radiant  10   a  will be changed by the polarization converter  16 , and then the TE/TM polarization power ratio of the incident light  11  can be adjusted before illuminating the mark  22  again. 
     The mark  20  can be composed of a plurality of grating lines. Any material that can form the grating lines can be used. There is pitch Λ between the grating lines. According to the preferred embodiment of the present invention, the pitch Λ is smaller than the wavelength of the radiant  10   a . In addition, the mask substrate  22  is not limited to the quartz substrate. 
       FIG. 2  is a schematic diagram illustrating a feedback controlling system  200  in accordance with the second embodiment of the present invention. To simplify the illustration, elements with the same function will use the same numerals in  FIG. 1 . As seen in  FIG. 2 , the radiant  10   a  passes through lens  12  and the aperture plate  14 . Then, the incident light  11  illuminates the mark  20  and mask substrate  22  after going through the polarization converter  16 , and a reflected light  11 ″ is then formed. The first embodiment and the second embodiment only differ in the parameter that the detector  24  detects. The detector  24  in the second embodiment is used to detect the energy of the reflected light  11 ″ in TM mode, and the detector  24  in the first embodiment is used to detect the energy of the refracted light  11 ′ in TE mode. Other operations of elements in feedback system  200  are similar with the feedback system  100 , and therefore omitted for brevity. 
     In another embodiment of the present invention, a feedback method for controlling a polarization power ratio of incident light is provided. The feedback method will be described by utilizing the feedback system  100  as an example.  FIG. 3  is a schematic diagram illustrating the magnified mark  20 . Please refer to  FIG. 3  and  FIG. 1 . As shown in  FIG. 1 , the mark  20  of the mask  18  is illuminated by the incident light  11 . As shown in  FIG. 3 , the mark  20  is composed of a plurality of grating lines. Each grating line has a width W and a thickness h. The grating lines further include a pitch Λ between each grating line. The mark  20  can be made from conductors, or any materials that can make grating lines. One feature of the present invention is that the width W, the pitch Λ and the thickness h of the mark  20  are specially designed. The design of the mark  20  must take the wavelength of the light source  10 , the position of the mask  18  in the system, and the position of the detector  24  into consideration and follow three boundary conditions. The method of designing the mark  20  will be described in detail later. According to a preferred embodiment of the present invention, the pitch Λ of the grating lines is smaller than the wavelength of the radiant  10   a.    
     The method for controlling TE/TM polarization power ratio of incident light is started by measuring the experimental value of the transmittance of mask  18  with respect to the incident light  11 . Next, the incident light  11  illuminates the mask  18  and then passes through the mask substrate  22 . The illuminated portion of the mark  20  and the mask substrate  22  forms the refracted light  11 ′. Thereafter, a first parameter such as energy of the refracted light  11 ′ in TE mode is detected by the detector  24 . Subsequently, the energy of the refracted light  11 ′ in TE mode is sent into the processor  26 . Then the second parameter such as the TE/TM polarization power ratio of the incident light  11  can be calculated by the processor  26  by utilizing transmittance of the mask  18  with respect to the incident light  11 , the energy of the refracted light  11 ′ in TE mode, the total energy of the incident light  11  and the reflective index of the mask substrate  22 . As one skilled in the art should know, the total energy of the incident light  11  can be measured by an optical power meter, and the reflective index of the mask substrate  22  is based on the material of the mask substrate  22 . 
     Then, the TE/TM polarization power ratio of the incident light  11  is fed back into the polarization converter  16  as a base value. Afterwards, the energy of the radiant  10   a  in TM mode can be converted to the energy of the radiant  10   a  in TE mode by the polarization converter  16 . Therefore, when the incident light  11  goes into the mask  18  again, the energy of the incident light  11  in TE mode is increased, and the energy of the incident light  11  in TE mode passing through the mask can thereby also be increased. 
     The design method of the mark  20  used in the feedback controlling system  100  is illustrated as follows.  FIG. 4  is a schematic diagram illustrating the side view of the mask  18 . As shown in  FIG. 4 , the mark  18  is composed of the mark  20  and the mask substrate  22 . The incident light  11  illuminates the mask  18  at an incident angle  0 , wherein the incident angle θ is not equal to zero. The region above the top surface of the mark  20  is defined as region  1 , and the medium positioned at the region  1  has a refractive index n 1 . The region between the grating lines of the mark  20  is defined as region  2 , and the medium positioned at the region  2  has a refractive index n 2 . The region at the mask substrate  22  is defined as region  3 , and the mask substrate  22  has a refractive index n 3 . In addition, each grating line of the mark  20  has the width W and the thickness h (not shown in  FIG. 4 ). Moreover, the pitch A is between the grating lines. Furthermore, coordinate axis, X, Y, and Z is shown in the  FIG. 4 . When the pitch Λ satisfies the Eq. (1), only zero-order light (ground state) can pass through the mark  20 . 
     
       
         
           
             
               
                 
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     wherein φ=2/π−θ. In this state, the reflective index and the transmittance of the mark  20  are highly related to the polarization of the incident light  11 . 
     There are two common methods of designing the mark having a specific reflective index and transmittance to certain polarized light. 
     (1) Vector Analysis Method 
     ]Assuming the mark  20  is made from a perfect conductor, the wave function of the electromagnetic wave followed the boundary conditions of the mark  20  can be expressed as follows: 
         {right arrow over (E)}   (1)   =ŷE   y0   (1)   e   i(k     z       (2)     z+k     x       (1)     (x−w/2))    (2) 
         {right arrow over (E)}   (2)   =ŷE   y0   (2) ( e   i(k     z       (2)     z+k     x       (2)     (x+w/2)))   +e   i(k     z       (2)     z−k     x       (2)     (x−w/2))    (3) 
         {right arrow over (E)}   (3)   =ŷE   y0   (3)   e   i(k     z       (2)     z−k     x       (3)     (x+w/2))    (4) 
     Eq. (2), (3), and (4) are equations which describe the electromagnetic wave in region  1 ,  2 , and  3  respectively. {right arrow over (E)} is electric field, k is wave vector. E y0  is wave amplitude. The superscripted number shows the region, and the subscripted number shows the direction. For example, k z   (2)  is wave vector in region  2  and in Z-axis direction, and E y0   (1)  is the wave amplitude in region  1 . 
     Next, k z   (2) ,k x   (1) ,k x   (2) ,k x   (3)  are solved by using Eq. (2), (3) and (4) together with Eq. (5) (eigen function) illustrated as follows. 
         V=ε″   m   k   0   2   +i (√{square root over (( k   z   (2) ) 2 −ε′ m   k   0   2 )}+tan  h ( w /2√{square root over (( k   z   (2) ) 2 −ε 2   k   0   2 )})√{square root over (( k   z   (2) ) 2 −ε 2   k   0   2 )})   (5 
     V is the eigen value and ε 2  is the permittivity of the medium in region  2 . ε′ m  is the real part of the permittivity of the grating lines. ε″ m  is the imaginary part of the permittivity of the grating lines. Therefore, the transmittance can be expressed as follows. 
     
       
         
           
             
               
                 
                   
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     P is the mode number. α p  is the wave vector of the diffraction mode, P, along the X-axis direction. 
     (2) Finite Different Time Domain (FDTD) Method 
     In this method, the electromagnetic wave is expressed as a difference quotient. Next, by taking the boundary conditions into consideration, the FDTD can be used for solving the transmittance of the mask  18  with respect to the zero-order incident light  11  in TE mode. 
     It is assumed that A=500 nm, h=380 nm, θ=0, n 1 =n 2 =n 3 =1, and the wavelength of the incident light  11  is 670 nm. The transmittance of the mask  18  with respect to the zero-order incident light  11  in TE mode versus width W is shown in  FIG. 5 . The bold line in  FIG. 5  illustrates the result calculated by the vector analysis method, when the material of the mark  20  is a perfect conductor. The dotted line in  FIG. 5  illustrates the result calculated by the FDTD method, when the material of the mark  20  is silver. 
     Please refer to  FIG. 5 , assuming the width W of the mark  20  is  350  nm, and the material of the mark  20  is silver. As seen in  FIG. 5 , the theoretical value of the transmittance of the mask  18  with respect to the zero-order incident light  11  in TE mode is 0.92. According to the preferred embodiment of the present invention, 0.92 (transmittance) is high enough to enable the feedback method in the present invention to be carried out. Thereafter, the mark  20  can be made in the scale of A=500 nm, h=380 nm, W=350 nm, which is assumed above. Subsequently, a transmittance test is run to decide the experimental value of the transmittance of the mask  18  with respect to the incident light  11  in TE mode. It is assumed that the experimental transmittance is 0.9 and the energy of the refracted light  11 ′ in TE mode detected by the detector  24  is 9.0 mW. Therefore, the energy of the incident light  11  in TE mode can be calculated as 10 mW. The total energy of the incident light  11  which can be known by the optical power meter is 15 mW in this embodiment. Therefore, the TE/TM polarization power ratio of incident light  11  can be calculated as 2. Next, the TE/TM polarization power ratio of incident light  11  is fed back into the polarization converter  16  as the base value to adjust the radiant  10   a . Then, the TE/TM polarization power ratio of incident light  11  can be adjusted before illuminating the mark  20  again. This feedback method for controlling TE/TM polarization power ratio of incident light can be operated repeatedly until the TE/TM polarization power ratio of incident light  11  is high enough. 
     In another embodiment of the present invention, another feedback method for controlling TE/TM polarization power ratio of incident light is provided. The feedback method will be described by utilizing the feedback system  200  as example. As shown in  FIG. 2 , the detector  24  is used to detect the energy of reflected light  11 ″ in a specific polarized direction, such as the energy of reflected light  11 ″ in TM mode. Therefore, the vector analysis method or the FDTD method can be used to design the mark  20  of the feedback system  200 . The width, the thickness and the pitch of the mark  20  can be determined due to the reflective index of the mask  18  with respect to the specific polarized mode of the incident light  11 . Afterwards, the mark  20  can be made. Then, the mask  18  undergoes a reflective test to get the experimental value of the reflective index of the mask  18  with respect to the incident light  11  in a specific polarized mode. According to the preferred embodiment, the pitch of the mark  20  is smaller than the wavelength of the radiant  10   a . When the feedback method is operated with the feedback system  200 , the energy of reflected light  11 ″ in TM mode is detected by the detector  24 . Based on the experimental value of the reflective index of the mask  18  with respect to the incident light  11  and the energy of reflected light  11 ″ in TM mode, the energy of the incident light  11  in TM mode can be calculated. If the total energy of the incident light  11  is known by the optical power meter, then the TE/TM polarization power ratio of incident light  11  can be calculated. Thereafter, the TE/TM polarization power ratio of incident light  11  is fed into the polarization converter  16  as the base value to adjust the radiant  10   a . Then, the TE/TM polarization power ratio of incident light  11  can be adjusted before illuminating the mark  20  again. This feedback method for controlling TE/TM polarization power ratio of incident light can be operated repeatedly until the TE/TM polarization power ratio of incident light  11  is high enough. 
     Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention.