Alignment method and apparatus therefor

Abstract

A method of aligning each of a plurality of processing areas arranged on a substrate with a predetermined transfer position in a static coordinate system XY for defining a moving position of said substrate, a pattern of a mask being transferred to each of the plurality of processing areas, the method comprising the steps of: wherein each of the plurality of processing areas has a specific point and a plurality of marks for alignment arranged by a predetermined positional relationship with respect to said specific point; measuring coordinate positions of a predetermined number of marks selected from several processing areas of the plurality of processing areas on the static coordinate system XY; calculating a plurality of parameters in a model equation expressing the regularity of arrangement of the plurality of processing areas by performing a statistic calculation by use with the measured plurality of coordinate positions, arrangement coordinate values upon the design of the specific points of the several processing areas and relative arrangement coordinate values upon the design of the selected marks of the several processing areas with respect to corresponding the specific points on the several processing areas; and determining coordinate positions of respective said specific points of the plurality of processing areas on the static coordinate system XY by using the calculated parameters.

What is claimed is:  
     
         1 . A method of aligning each of a plurality of processing areas arranged on a substrate with a predetermined transfer position in a static coordinate system XY for defining a moving position of said substrate, a pattern of a mask being transferred to each of said plurality of processing areas, wherein each of said plurality of processing areas has a plurality of positioning marks arranged by a predetermined positional relationship with respect to a specific point set in each of said plurality of processing areas, said method comprising: 
 (1) with respect to at least one substrate among a first to (K−1)th substrates (integer: 2≦K≦N):    measuring a coordinate position of a positioning mark in said static coordinate system XY in each of several processing areas out of said plurality of processing areas on said substrate by first and second alignment sensors;    calculating parameters of a first model equation expressing the regularity of arrangement of said plurality of processing areas by performing a statistical computation using first coordinate positions measured by said first alignment sensor and second coordinate positions measured by said second alignment sensor, and arrangement coordinates upon a design of said specific point and relative arrangement coordinates upon a design of said positioning mark for said specific point in said several processing areas; and    moving said substrate relative to said mask based on coordinate positions of said plurality of processing areas in said static coordinate system XY, determined in accordance with said calculated parameters; and    (2) with respect to a K-th substrate and subsequent substrates:    measuring coordinate positions of a plurality of positioning marks on said substrate in said static coordinate system XY by one of said first and second alignment sensors;    calculating parameters of a second model equation expressing the regularity of arrangement of said plurality of processing areas based on the coordinate positions measured by said one alignment sensor; and    moving said substrate relative to said mask based on coordinate positions of said plurality of processing areas in said static coordinate system XY, determined in accordance with the parameters of said first model equation and the parameters of said second model equation.    
     
     
         2 . A method according to    claim 1   , wherein (1) with respect to said at least one substrate: 
 calculating and storing differences between said parameters of said first model calculated by a first statistical computation using said first coordinate positions and said parameters of said first model calculated by a second statistical computation using said second coordinate positions,    (2) with respect to said K-th substrate and subsequent substrates:    at least one of said parameters of said second model equation is determined in accordance with said stored differences and said coordinate positions measured by said one alignment sensor, and the others of said parameters of said second model equation are determined in accordance with said coordinate positions measured by said one alignment sensor.    
     
     
         3 . A method according to    claim 1   , further comprising: 
 correcting at least on of a relative rotation error between said mask pattern and each of said processing areas and a relative configuration error between said mask pattern and each of said processing areas based on said stored parameters.    
     
     
         4 . A method according to    claim 1   , further comprising: 
 measuring some of said plurality of positioning marks by the use of only one of said two alignment sensors with respect to the K-th and subsequent substrates, while measuring another some of said plurality of positioning marks by the use of any alignment sensor; and    determining parameters based on results of these measurements.    
     
     
         5 . A method in which each of a plurality of shot areas two-dimensionally arranged on each of N (integer: N≧2) substrates in accordance with an arrangement coordinate upon the design on said substrate is to be aligned with a predetermined reference position in a static coordinate system for defining a moving position of said substrate, a coordinate position of each of said plurality of shot areas in said static coordinate system is calculated by measuring a coordinate position of a shot area selected in advance out of said plurality of shot areas in said static coordinate system and by performing a statistical computation of said plurality of coordinate positions measured, and each of said plurality of shot areas is aligned with said reference position by controlling said moving position of said substrate in accordance with said calculated coordinate positions, wherein: 
 prior to the alignment of each of the plurality of shot areas on a k-th (integer: 2≦k≦N) and subsequent substrates with said reference position in accordance with the coordinate positions calculated by said statistical computation, one-dimensional or two-dimensional position measurement is performed at a plurality of points in each of the shot areas by the use of two alignment sensors with respect to at least one of the first to the (k−1)th substrates, and a difference between results of the statistical computations of the coordinate positions measured by the respective alignment sensors and a result of the statistical computation in a shot area of the coordinate positions measured by said respective alignment sensors is obtained and stored; and  
 one-dimensional or two-dimensional position measurement is performed at one point in each of the shot areas by the use of only one of said two alignment sensors when the k-th substrate or any substrate subsequent thereto is aligned, and the already-stored difference between results of the statistical computations of the coordinate positions measured by said two alignment sensors and the already-stored result of the statistical computation in said shot area of the coordinate positions measured by said respective alignment sensors is corrected, whereby alignment can be effected based on said corrected results.  
 
     
     
         6 . A method according to    claim 5   , comprising: 
 performing one-dimensional or two-dimensional position measurement at one point in a shot area by the use of one of said two alignment sensors when the k-th substrate or any substrate subsequent thereto is aligned, and measuring a one-dimensional coordinate position to a predetermined direction at a different point in said shot area by the use of either of the alignment sensors; and    correcting a result obtained by performing statistical computation of a measurement result at said one point in said shot area and a measurement result at said different point by the use of the already-stored difference between results of the statistical computations of the coordinate positions measured by said two alignment sensors and the already-stored result of the statistical computation of the coordinate positions in said shot area measured by said two alignment sensors, respectively, thereby effecting alignment based on said corrected results.    
     
     
         7 . A method of transferring a pattern of a mask onto each of a plurality of areas on a substrate, comprising: 
 measuring coordinate positions, on a static coordinate system in which said substrate is moved, of first marks on said substrate;    determining parameters in an equation to define arrangement and a formal feature of said plurality of areas in accordance with said measured coordinate positions, said formal feature including at least one of rotation, size and shape of said plurality of areas; and    relatively moving said mask and said substrate in accordance with said parameters to transfer said pattern onto said each area.    
     
     
         8 . A method according to    claim 7   , further comprising: 
 forming an image of said pattern on said substrate through a projection optical system; and    relatively rotating said mask and said substrate based on a rotation error, of said areas relative to said formed image, determined in accordance with a part of said parameters.    
     
     
         9 . A method according to    claim 7   , further comprising: 
 forming an image of said pattern on said substrate through a projection optical system; and    adjusting an optical property of said projection optical system based on a configuration error, of said areas relative to said formed image, determined in accordance with a part of said parameters.    
     
     
         10 . A method according to    claim 7   , further comprising: 
 measuring coordinate positions on said static coordinate system, of a plurality of second marks on said mask; and    determining a parameter in an equation to define arrangement of said plurality of second marks in accordance with the measured coordinate positions,    wherein said mask and said substrate are relatively moved in accordance with the determined parameter and said parameters.    
     
     
         11 . A method according to    claim 7   , wherein 
 said parameters being calculated so that each of deviations between said measured coordinate positions and coordinate positions determined by said equation for each of said first marks is minimized.    
     
     
         12 . A method according to    claim 11   , wherein 
 coordinate positions on said static coordinate system, of said plurality of areas are determined in accordance with said equation of which said parameters are calculated to relatively move said mask and said substrate based on the determined coordinate positions.    
     
     
         13 . A method according to    claim 9   , wherein 
 said configuration error includes a magnification error of said areas relative to said formed image.    
     
     
         14 . A method according to    claim 2   , wherein the others of said parameters of said second model equation includes an offset, a rotation and a rectangular degree of said substrate and a rotation of said processing areas.