Abstract:
An auto focus system includes a stage on which a substrate is mounted, light sources that irradiate the substrate with a plurality of focus beams directed towards the substrate at different angles, sensors that detect the focus beams reflected from the substrate, and a controller that determines the relative location of a surface of the substrate according to the locations at which the focus beams are detected by the sensors and positions the substrate accordingly. To this end, the controller performs calculations that are free from the influence of variations in the refractive index of the medium through which the focus beams propagate to the surface of the substrate. Therefore, the autofocus process is carried out with a high degree of precision.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an exposure apparatus of photolithographic equipment for use in the manufacturing of semiconductor devices or the like. More particularly, the present invention relates to an auto focus system of the exposure apparatus that positions a substrate for exposure in photolithographic equipment. 
   2. Description of the Related Art 
   Generally, the manufacturing of a semiconductor device includes a photolithographic process in which a fine pattern is formed on a wafer (hereinafter, referred to as a “substrate”). The photolithographic process begins with an exposure process in which a beam of light is directed through a reticle and onto the substrate. In this way, a pattern borne by the reticle is transferred to a layer of photoresist on the substrate. The exposure process is thus crucial in forming a fine pattern on the substrate. In particular, the precision under which the beam of light is focused on the substrate is one very important factor in forming a high-quality pattern, especially a fine multi-layered pattern, on the substrate. To this end, an auto focus system is used to position the substrate in the exposure apparatus such that the image of the pattern borne by the reticle is focused precisely on the plane of the photoresist layer during the exposure process. 
   A conventional auto focus system irradiates the substrate with a so-called focus beam and detects the beam reflected from the substrate to discern the state of the focus of the exposure apparatus. More specifically, the focus beam is directed onto the substrate obliquely and the focus beam reflected from the surface of the substrate is received by a sensor. The sensor senses the location at which the light is incident thereon to determine the relative position of the substrate. A substrate stage, on which the substrate is supported, is driven based on data produced from the output of the sensor to position the substrate in a focal plane of the exposure apparatus. 
   Research aimed at improving the resolution of the exposure apparatus is ongoing to meet the demand for more highly integrated semiconductor devices, i.e., devices that have finer circuit patterns. In this respect, it is known that fine patterns can be formed when the exposure light has a relatively small wavelength. Thus, past research has focused on developing and putting into practice light sources that output exposure light having small wavelengths. Typically, a KrF excimer laser emitting light having a wavelength of 248 nm or an ArF excimer laser emitting light having a wavelength of 193 nm is employed as a light source in the exposure apparatus of current photolithographic equipment. Recently, though, an F2 excimer laser has also been employed as a light source. 
   It is has proven technically difficult to develop light sources that output exposure light having shorter wavelengths than those mentioned above. Thus, an immersion exposure technology, that effectively increases the aperture number of the apparatus, has been suggested as a means for increasing the resolution of the exposure apparatus. The immersion exposure technology employs the existing KrF, ArF or F2 excimer lasers as the light source; however, an immersion medium is interposed between the substrate and an optical system of the exposure apparatus to increase the aperture number. Such immersion exposure technology is disclosed in U.S. Pat. Nos. 6,781,670 and 6,809,794. 
   More specifically, in exposure apparatus that employs the immersion exposure technology, a liquid (immersion) medium is provided between the substrate and the optical system. However, there is a problem in that the refractive index of the immersion medium varies locally due to bubbles or temperature changes generated therein by the light directed therethrough. 
   Such local variations in the refractive index of the immersion medium cause a very large problem in the auto focus process. That is, when the focus beam passes through the immersion medium during the auto focus process, the optical path of the beam may assume an unexpected direction if the beam passes through a portion of the immersion medium in which the refractive index varies. In this case, a focus error occurs. This focus error may be also generated by the air or other material through which the focus beam propagates on its way to the substrate. That is, a focus error due to variations in the refractive index of a medium through which the focus beam must pass can be generated in a dry exposure apparatus in addition to an exposure apparatus employing a liquid immersion medium. 
   SUMMARY OF THE INVENTION 
   An object of the present invention is to solve the aforementioned problems of the prior art. 
   More specifically, an object of the present invention is to provide an auto focus system and auto focus method that are not influenced by variations or fluctuations in the index of refraction of the medium through which a focus beam propagates. 
   Likewise, it is an object of the present invention to provide an exposure apparatus having such an auto focus system, whereby a substrate can be positioned optimally for the exposure process. 
   It is yet another object of the present invention to provide an immersion exposure apparatus that employs an immersion medium between its optical system and a substrate stage to enhance the resolution of the apparatus, and which apparatus includes an auto focus system that is not influenced by variations in the index of refraction of the immersion medium, whereby a very fine pattern can be precisely formed on a substrate. 
   According to one aspect of the present invention, there is provided an auto focus system including a stage for supporting a substrate, measuring light sources that emit a plurality of focus beams towards the substrate at different angles, sensors that receive the focus beams reflected from the substrate and output signals indicative of locations at which the reflected focus beams are received, and control means that determines the relative position of the substrate based on the output of the sensors and controls the position of the stage accordingly. To this end, the control means has a calculation unit that calculates a focus changing value of the substrate indicative of the position of a surface of the substrate relative to a reference plane. 
   Preferably, the auto focus system has first and second measuring light sources oriented to emit a first focus beam and a second focus beam to the same fixed location in the system at the surface of the substrate, and first and second sensors positioned in the system to receive the first and second focus beams, respectively. 
   In this case, the calculation unit is configured to execute an algorithm represented by the following equation: 
   
     
       
         
           f 
           = 
           
             
               1 
               2 
             
             ⁢ 
             
               ( 
               
                 
                   
                     - 
                     
                       
                         θ 
                         0 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             y 
                             0 
                             
                               ( 
                               1 
                               ) 
                             
                           
                           + 
                           
                             y 
                             L 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                   
                   + 
                   
                     
                       θ 
                       0 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           y 
                           0 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         - 
                         
                           y 
                           L 
                           
                             ( 
                             2 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
                 
                   ( 
                   
                     
                       θ 
                       0 
                       
                         ( 
                         1 
                         ) 
                       
                     
                     - 
                     
                       θ 
                       0 
                       
                         ( 
                         2 
                         ) 
                       
                     
                   
                   ) 
                 
               
               ) 
             
           
         
       
     
   
   based on an x, y coordinate system in which the x axis is parallel to the stage and the y axis is perpendicular to the stage, and wherein f is the focus changing value, y 0   (1)  is a value representing the y coordinate of the location from which the first focus beam emanates from the first measuring light source, y 0   (2)  is a value representing the y coordinate of the location from which the second focus beam emanates from the second measuring light source, θ 0   (1)  is an angle of incidence of the first focus beam corresponding to the angle subtended between the first focus beam emanating from the first measuring light source and the x axis, θ 0   (2)  is an angle of incidence of the second focus beam corresponding to the angle subtended between the second focus beam emanating from the second measuring light source and the x axis, y L   (1)  is a value representing the y coordinate of the location at which the reflected first focus beam is received by the first sensor, and y L   (2)  is a value representing the y coordinate of the location at which the reflected second focus beam is received by the second sensor. 
   In addition to a calculation unit, the control means includes a unit that will adjust the position of the stage relative to the optical system of the exposure unit so as to reposition the substrate in preparation for the exposure process. This unit may include a stage controller, and a stage driving unit connected to the stage so as to drive the stage under the command of the stage controller. The stage controller compares the focus changing value calculated by the calculation unit with a focus reference value of the substrate and outputs a control signal representative of the difference between the focus changing value and the reference value. The stage driving unit receives the control signal from the stage controller and drives the stage by an amount based on the control signal. 
   According to another aspect of the present invention, there is provided an auto focus method including steps of irradiating a substrate with a plurality of focus beams at different angles relative to a plane extending parallel to the substrate, detecting locations to which the focus beams are reflected from the substrate, assigning values to the locations, and controlling the position of the substrate according to the assigned values. Preferably, the substrate is simultaneously irradiated by the focus beams. 
   Again, these beams may consist of a first focus beam and a second focus beam. In this case, a focus changing value of the substrate indicative of the height of a surface of the substrate relative to a reference plane is calculated, and the position of the substrate is adjusted on the basis of the focus changing value. The above-mentioned equation may be used for calculating the focus changing value of the substrate. 
   According to still another aspect of the present invention, there is provided an exposure apparatus including the auto focus system described above, an exposure light source, and an optical system interposed between the stage and the exposure light source so as to project light emitted by the exposure light source onto a substrate mounted to the stage. 
   According to still another aspect of the present invention, the exposure apparatus may be an immersion exposure apparatus having an immersion medium occupying a gap between the optical system and the stage. The immersion medium may be a liquid. Also, the immersion medium may be provided in a container or may be fed by a supply system so as to flow through the gap between the optical system and the stage. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and other features and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments thereof made with reference to the attached drawings in which: 
       FIG. 1  is a schematic diagram of an immersion exposure apparatus including an auto focus system according to the present invention; 
       FIG. 2  is an enlarged view of a portion of the auto focus system shown in  FIG. 1 , illustrating a state in which a substrate is irradiated with focus beams of the system according to the present invention; 
       FIG. 3  is a conceptual diagram of the irradiation of a substrate by a focus beam, illustrating a principal behind a method of focusing an exposure apparatus according to the present invention; 
       FIG. 4  is a flowchart of a method of focusing an exposure apparatus according to the present invention; and 
       FIG. 5  is a schematic diagram of a dry exposure apparatus including an auto focus system according to the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Exposure apparatus including an auto focus system of the present invention will now be described in detail with reference to the accompanying drawings. 
   Referring first to  FIG. 1 , an immersion exposure apparatus having an auto focus system according to the present invention includes a light source  10 , a reticle stage  12  for supporting a reticle  11  thereon, an optical system  13 , a substrate stage  15  that is located under the optical system  13  and supports a substrate  14  thereon, an immersion medium  16  that is interposed between the substrate stage  15  and the optical system  13 , and a stage driving unit  22  for aligning the substrate stage  15  with the optical system  13 . 
   An excimer laser is used as the light source  10 . The excimer laser may be a KrF excimer laser or an ArF excimer laser. In the present embodiment, an ArF excimer laser emitting a beam of light having a wavelength shorter than that of the beam emitted by a KrF excimer laser is used. However, a light source that emits light having an even smaller wavelength, such as an F2 excimer laser, may be used. 
   The reticle  11  is located in the optical path of the light output by the light source  10 . The reticle  11  is formed of a quartz plate that bears a pattern corresponding to a circuit pattern to be formed on the substrate  14 . The reticle  11  is mounted on the reticle stage  12 . The reticle stage  12  is aligned with the optical system  13 , etc., by a separate driving device (not shown). 
   The optical system  13  includes a plurality of lenses having the same optical axis and providing a reducing projection magnification. That is, when the reticle is illuminated with light emitted by the light source  10 , the image of the pattern of the reticle  11  is reduced by the optical system  13  and projected onto a layer of photoresist on the substrate  14 . Also, the optical system  13  is supported so that it can be moved along the optical axis to adjust the position of the lenses relative to the light source  10  and reticle stage  15 . 
   The substrate  14  on which a pattern will be formed is mounted on the substrate stage  15 . The immersion medium  16  is supplied from a medium supplying unit  17  to flow through a region of the exposure apparatus located between the optical system  13  and the substrate  14 . Alternatively, a container filled with the immersion medium may be interposed between the optical system  13  and the substrate  14 . 
   The auto focus system is provided at one side of the substrate stage  15 . The auto focus system of the present invention employs a non-TTL (through the lens) method. 
   The auto focus system of the present invention includes a first measuring light source  30  for irradiating the substrate  14  with a first focus beam B 1  and a second measuring light source  31  for irradiating the substrate  14  with a second focus beam B 2 , as shown in  FIGS. 1 and 2 . 
   The first measuring light source  30  and the second measuring light source  31  direct the first focus beam B 1  and the second focus beam B 2  toward the same location on the substrate  14  but at different angles. Preferably, the focus beams B 1  and B 2  are directed onto the substrate  14  at the same time because the refractive index of the immersion medium  16  through which the focus beams B 1  and B 2  pass may change over time as external conditions, such as temperature, change. 
   Also, the auto focus system includes first and second sensors  40  and  41  at a side of the stage  15  opposite that at which the first measuring light source  30  and the second measuring light source  31  are provided. The first sensor  40  is positioned to receive the first focus beam B 1 , and the second sensor  41  is positioned to receive the second focus beam B 2 . A calculation unit  20  calculates a value, representative of the relative position of the stage  15  along the optical axis, using measurements obtained by the sensors  40  and  41 . The auto focus system also includes a stage controller  21  for controlling the stage driving unit  22  of the substrate stage  15  according to the value calculated in the calculation unit  20 . 
   Now, if the refractive index n of the immersion medium  16  is not uniform, the focus beams B 1  and B 2  refract (bend) as they pass through the boundary/boundaries of portions of the immersion medium having the different indices of refraction. In this case, the locations to which the focus beams B 1  and B 2  are reflected from the substrate  14  differ from the locations to which the focus beams B 1  and B 2  would have been reflected had the refractive index of the immersion medium  16  been uniform. Accordingly, the output of the sensors  40 ,  41  is affected by the non-uniformity of the refractive index of the immersion medium. 
   Nonetheless, the auto focus system can determine the proper location of the substrate  14  because the operations performed by the calculation unit  20  to calculate a focus changing value representative of the true location of the stage  15  take into account the variations of the refractive index of the immersion medium  16  and the degree to which the variations in the refractive index of the immersion medium  16  affect the locations on the sensors  40 ,  41  to which the beams B 1  and B 2  are reflected. Therefore, an accurate auto focus process can be performed even though the refractive index of the immersion medium  26  varies. 
   In order to perform the calculation of the present invention, first, the paths of the beams B 1  and B 2  are each expressed by Equation 1 according to  Born  &amp;  Wolf&#39;s  Principles of Optics (p. 130). 
   
     
       
         
           
             
               
                 
                   
                     ⅆ 
                     
                       ⅆ 
                       s 
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       n 
                       ⁢ 
                       
                         
                           ⅆ 
                           
                             r 
                             _ 
                           
                         
                         
                           ⅆ 
                           s 
                         
                       
                     
                     ) 
                   
                 
                 = 
                 
                   ∇ 
                   n 
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 ] 
               
             
           
         
       
     
   
   Here, r=(x, y) is a vector representing the path of a focus beam B 1 , B 2 , s is the distance the focus beam B 1 , B 2  traverses between the light source  30 ,  31  and the sensor  40 ,  41 , and n is the refractive index of the medium through which the beam B 1 , B 2  passes. If the direction parallel to the substrate  14  is x and the direction perpendicular to the substrate  14  is y in  FIG. 2 , Equation 1 can be rewritten as Equations 2 for the components x and y. 
   
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       
                         ⅆ 
                         s 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         n 
                         ⁢ 
                         
                           
                             ⅆ 
                             x 
                           
                           
                             ⅆ 
                             s 
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∂ 
                       n 
                     
                     
                       ∂ 
                       x 
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       ⅆ 
                       
                         ⅆ 
                         s 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         n 
                         ⁢ 
                         
                           
                             ⅆ 
                             y 
                           
                           
                             ⅆ 
                             s 
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∂ 
                       n 
                     
                     
                       ∂ 
                       y 
                     
                   
                 
               
             
             
               
                 [ 
                 
                   Equations 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 ] 
               
             
           
         
       
     
   
   However, the distance between the optical system  13  and the substrate  14  in the exposure apparatus is only several mm, i.e., is very small. On the contrary, the distances between the measuring light sources  30  and  31  and the sensors  40  and  41  are relatively large. That is, the distance in the y direction is much shorter than that in the x direction. Accordingly, variations in the refractive index n in the y direction can be ignored and the value n can be considered as only a function of x. That is, the refractive index of the immersion medium  16  can be expressed as n=n(x). 
   The angle of incidence θ at which a focus beam is directed relative to the normal of the immersion medium (see  FIG. 2 ) can be expressed by Equations 3 and 4. 
   
     
       
         
           
             
               
                 θ 
                 = 
                 
                   
                     ⅆ 
                     y 
                   
                   
                     ⅆ 
                     x 
                   
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
                 ] 
               
             
           
           
             
               
                 
                   ⅆ 
                   
                     ⅆ 
                     s 
                   
                 
                 = 
                 
                   
                     ∂ 
                     
                       ∂ 
                       x 
                     
                   
                   + 
                   
                     
                       ∂ 
                       
                         ∂ 
                         y 
                       
                     
                     ⁢ 
                     
                       
                         ⅆ 
                         y 
                       
                       
                         ⅆ 
                         x 
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
                 ] 
               
             
           
         
       
     
   
   Accordingly, if n=n(x) and Equation 4 are substituted into Equation 2, Equation 5 is obtained. 
   
     
       
         
           
             
               
                 
                   
                     ⅆ 
                     
                       ⅆ 
                       s 
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       n 
                       ⁢ 
                       
                         
                           ⅆ 
                           y 
                         
                         
                           ⅆ 
                           x 
                         
                       
                     
                     ) 
                   
                 
                 = 
                 
                   
                     
                       ∂ 
                       n 
                     
                     
                       ∂ 
                       y 
                     
                   
                   = 
                   0 
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
                 ] 
               
             
           
         
       
     
   
   The result nθ=const from Equation 3 or n(dy/dx)=const according to Equation 5 is obtained. An equation for calculating a focus changing value f using two focus beams can now be induced from these results. 
   First, if the angles at which the focus beams emanate from the measuring light sources  30  and  31  relative to the normal of the immersion medium are θ 0 , values representing the locations of the measuring light sources  30  and  31  are y 0 , and the index of refraction of the medium through which the beam travels is n 0 , Equation 6 and Equation 7 are obtained by integrating Equation 6 when nθ=const or n(dy/dx)=const. 
   
     
       
         
           
             
               
                 dy 
                 = 
                 
                   
                     
                       n 
                       0 
                     
                     
                       n 
                       ⁡ 
                       
                         ( 
                         x 
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     θ 
                     0 
                   
                   ⁢ 
                   dx 
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
                 ] 
               
             
           
           
             
               
                 
                   y 
                   ⁡ 
                   
                     ( 
                     x 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       θ 
                       0 
                     
                     ⁢ 
                     
                       
                         ∫ 
                         0 
                         x 
                       
                       ⁢ 
                       
                         
                           
                             n 
                             0 
                           
                           
                             n 
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ⅆ 
                           x 
                         
                       
                     
                   
                   + 
                   
                     y 
                     ⁡ 
                     
                       ( 
                       0 
                       ) 
                     
                   
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
                 ] 
               
             
           
         
       
     
   
   As shown in  FIG. 3 , the actual focus beams B 1  and B 2  are incident on the immersion medium  16  along the path of the solid line and are reflected at a location on the surface of the substrate  14  at a predetermined height f above a reference plane at y=0. The predetermined height f is the focus changing value which is sought by and obtained according to the present invention. The plane at y=0 is the focal plane of the optical system  13  and is used as a reference plane, the location of which is calculated by a separate method. As mentioned above, θ 0  denotes the angles at which the focus beams B 1  and B 2  are output from the measuring light sources  30  and  31  relative to the normal of the immersion medium  16 . 
   However, calculating the focus changing value f is complicated due to the reflection of the focus beams B 1  and B 2  at the surface of the substrate  14 . Accordingly, mirror images of those portions of the focus beams B 1  and B 2  reflecting from the substrate at the predetermined height f are used to simplify the calculation. That is, a focus beam deflected due to the variations in the refractive index of the immersion medium arrives at the location y L , as shown in  FIG. 3 . This location y L  becomes i L  for a mirror image of that portion of the beam reflecting from the surface at y=f. Accordingly, Equation 8 is obtained.
 
 y   L   +i   L =2 f   [Equation 8]
 
   Next, the location of i L  is expressed by Equation 9 employing Equation 7. Here, L is the distance along the x axis from the measuring light sources  30  and  31  to the sensors  40  and  41 . 
   
     
       
         
           
             
               
                 
                   y 
                   L 
                 
                 = 
                 
                   
                     
                       θ 
                       0 
                     
                     ⁢ 
                     
                       
                         ∫ 
                         0 
                         L 
                       
                       ⁢ 
                       
                         
                           
                             n 
                             0 
                           
                           
                             n 
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ⅆ 
                           x 
                         
                       
                     
                   
                   + 
                   
                     y 
                     0 
                   
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                 
                 ] 
               
             
           
         
       
     
   
   The integral component in Equation 9 is expressed by “C” in Equation 10. 
   
     
       
         
           
             
               
                 C 
                 = 
                 
                   
                     ∫ 
                     0 
                     L 
                   
                   ⁢ 
                   
                     
                       
                         n 
                         0 
                       
                       
                         n 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ⅆ 
                       x 
                     
                   
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   10 
                 
                 ] 
               
             
           
         
       
     
   
   Next, referring back to  FIG. 2 , if the first measuring light source  30  is represented by “(1)” and the second measuring light source  31  is represented by “(2)”, Equation 8 and Equation 9 can be rewritten as Equations 11.
 
 i   L   (1)   =Cθ   0   (1)   +y   0   (1)  
 
 i   L   (2)   =Cθ   0   (2)   +y   0   (2)  
 
 i   L   (1)   +y   L   (1) =2 f  
 
 i   L   (2)   +y   L   (2) =2 f   [Equations 11]
 
   The equations can be solved simultaneously to produce Equation 12. 
   
     
       
         
           
             
               
                 C 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           y 
                           L 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         - 
                         
                           y 
                           L 
                           
                             ( 
                             2 
                             ) 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           y 
                           0 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         - 
                         
                           y 
                           0 
                           
                             ( 
                             2 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   
                     ( 
                     
                       
                         θ 
                         0 
                         
                           ( 
                           2 
                           ) 
                         
                       
                       - 
                       
                         θ 
                         0 
                         
                           ( 
                           1 
                           ) 
                         
                       
                     
                     ) 
                   
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   12 
                 
                 ] 
               
             
           
         
       
     
   
   Therefore, the predetermined height f, which is the focus changing value representing the actual relative position of the substrate  14 , can be expressed by Equation 13. 
   
     
       
         
           
             
               
                 f 
                 = 
                 
                   
                     1 
                     2 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           - 
                           
                             
                               θ 
                               0 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   y 
                                   0 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   y 
                                   L 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           
                             θ 
                             0 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 y 
                                 0 
                                 
                                   ( 
                                   2 
                                   ) 
                                 
                               
                               - 
                               
                                 y 
                                 L 
                                 
                                   ( 
                                   2 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         ( 
                         
                           
                             θ 
                             0 
                             
                               ( 
                               1 
                               ) 
                             
                           
                           - 
                           
                             θ 
                             0 
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 [ 
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   13 
                 
                 ] 
               
             
           
         
       
     
   
   In Equation 13, y 0   (1)  and y 0   (2)  are values representing the y coordinates of the locations from which the beams emanate from the measuring light sources  30  and  31 , and θ 0   (1)  and θ 0   (2)  are angles of incidence of the focus beams B 1  and B 2  on the immersion medium  16  and are thus, predetermined values. On the other hand, y L   (1)  and y L   (2)  are the values of the output of the sensors  40  and  41 , representing the y coordinates of the locations at which the focus beams B 1  and B 2  impinge the sensors  40  and  41 . Hence, all of these values can be substituted into Equation 13 to solve for f. 
   A method of focusing an exposure apparatus according to the present invention will now be described with reference to  FIG. 4 . 
   The focus measuring method of the auto focus system according to the present invention basically includes a focus beam irradiating step (S 100 ), a focus beam detecting step (S 200 ), and a focus location controlling step (S 300  and S 400 ). 
   In the focus beam irradiating step (S 100 ), the first measuring light source  30  and the second measuring light source  31  simultaneously emit the first focus beam B 1  and the second focus beam B 2  toward the same portion of the substrate  14  from different locations and at different angles, respectively. 
   In the detecting step (S 200 ), the first sensor  40  and the second sensor  41  detect the first focus beam B 1  and the second focus beam B 2  reflected from the substrate  14  and output signals whose values are indicative of the locations at which the beams B 1  and B 2  are received, respectively. 
   The controlling step includes a calculating step (S 300 ) of receiving the values representing the locations of the first focus beam B 1  and the second focus beam B 2  on the first sensor  40  and the second sensor  41 , of calculating from these values the focus changing value f of the substrate  14 , and an adjusting step (S 400 ) of adjusting the position of the substrate  14  according to the focus changing value f calculated in the calculating step (S 300 ). 
   In this calculating step (S 300 ), values representing the locations y 0   (1)  and y 0   (2)  from which the first focus beam B 1  and the second beam B 2  emanate, the angles of incidence θ 0   (1)  and θ 0   (2)  of the first focus beam B 1  and the second beam B 2 , and the values y L   (1)  and y L   (2)  produced from the output of the sensors  40  and  41  are received, and calculations are performed according to algorithms corresponding to the above-mentioned equations. Accordingly, the focus changing value f is obtained. 
   According to this method, the calculation of the focus changing value f removes any factor pertaining to variations in the refractive index of the immersion medium  16 . Thus, the auto focus process can be performed accurately even if external conditions and the like create changes in the immersion medium that affect its index of refraction. 
   In the adjusting step S 400 , the stage controller  21  compares the focus changing value f obtained in the calculating step (S 300 ) with the reference value (y=0). Based on the comparison, the stage controller  21  provides the stage driving unit  22  with information on the location of the substrate  14 . Then, the stage driving unit  22  adjusts the stage  15  in the direction of the optical axis to place the substrate  14  at a location where the photoresist layer on the substrate  14  lies in the focal plane of the optical system  13 , whereby a focused image of the pattern of the reticle  11  will be projected onto the photoresist layer. 
     FIG. 5  shows another embodiment of the present invention, in which the auto focus system and the auto focus method are applied to a dry exposure apparatus. In the embodiment of  FIG. 5 , components that are the same as those employed in the embodiment of  FIG. 1  are represented by the same reference numerals and thus, a detailed description thereof will be omitted. 
   An immersion medium is not used in the dry exposure apparatus. However, a gap is present between the substrate  14  and the optical system  13 . Nonetheless, the refractive index of the air/gas in the gap G may vary. Accordingly, the auto focus system and method allow for an accurate auto focus process to be performed similar to that described above in connection with the immersion exposure apparatus. 
   According to the auto focus system, the auto focus method and the exposure apparatus of the present invention, two focus beams are emitted at different angles to measure the state of focus of the substrate. Accordingly, the auto focus process factors out variations in the medium, e.g., air, liquid, or transmission solid, through which the focus beams pass, that affect the refractive index of the medium. Accordingly, the auto focus process is performed with a high degree of precision. Thus, the overall productivity of the semiconductor device manufacturing process is enhanced. 
   Finally, although the present invention has been described above in connection with the preferred embodiments thereof, the invention is not so limited. For example, more than two measuring light sources may be used to irradiate the substrate at a given location, or pairs of the measuring light sources may irradiate the substrate at a plurality of locations. Such modifications can be mathematically modeled rather easily by those skilled in the art by appropriately modifying the above-mentioned equations. Accordingly, such changes and modifications are within the true spirit and scope of the invention as defined by the appended claims.