Multiple matching reference spectra for in-situ optical monitoring

Abstract

A method of controlling polishing includes storing a plurality libraries, each library including a plurality of reference spectra, polishing a substrate, measuring a sequence of spectra of light from the substrate during polishing, and for each measured spectrum of the sequence of spectra, finding a best matching first reference spectrum from a first library from the plurality of libraries and finding a best matching second reference spectrum from a different second library from the plurality of libraries, determining a first value associated with the best matching first reference spectrum and determining a second value from the best matching second reference spectrum, and calculating a third value from the first value and the second value to generate a sequence of calculated third values. At least one of a polishing endpoint or an adjustment for a polishing rate can be determined based on the sequence of calculated third values.

1 . A method of controlling polishing, comprising:
 storing a plurality libraries, each library including a plurality of reference spectra;   polishing a substrate;   measuring a sequence of spectra of light from the substrate during polishing;   for each measured spectrum of the sequence of spectra, finding a best matching first reference spectrum from a first library from the plurality of libraries and finding a best matching second reference spectrum from a different second library from the plurality of libraries;   for each measured spectrum of the sequence of spectra, determining a first value associated with the best matching first reference spectrum and determining a second value from the best matching second reference spectrum;   for each measured spectrum of the sequence of spectra, calculating a third value from the first value and the second value to generate a sequence of calculated third values; and   determining at least one of a polishing endpoint or an adjustment for a polishing rate based on the sequence of calculated third values.   
     
     
         2 . The method of  claim 1 , wherein calculating the third value from the first value and the second value comprises interpolating between the first value and the second value. 
     
     
         3 . The method of  claim 2 , wherein calculating the third value from the first value and the second value comprises calculating a weighted average of the first value and the second value. 
     
     
         4 . The method of  claim 3 , wherein calculating the weighted average of the first value and the second value comprises calculating a first goodness of fit between the best matching first reference spectrum and the measured spectrum, calculating a second goodness of fit between the best matching second reference spectrum and the measured spectrum, and calculating weights for the weighted average based on the first goodness of fit and the second goodness of fit. 
     
     
         5 . The method of  claim 4 , wherein the goodness of fit comprises a sum of squared differences, a sum of absolute differences, or a cross-correlation. 
     
     
         6 . The method of  claim 4 , wherein calculating the third value V 3  comprises calculating V 3 =(V 1 *W 1 +V 2 *W 2 )/(W 1 +W 2 ), where V 1  is the first value, V 2  is the second value, W 1  is a first weight, and W 2  is a second weight, and W 1  and W 2  are calculated based on the first goodness of fit and the second goodness of fit. 
     
     
         7 . The method of  claim 6 , wherein W 1 =1−(X 1 /(X 1 +X 2 )) and W 2 =1−(X 2 /(X 1 +X 2 )), where X 1  is the first goodness of fit and X 2  is the second goodness of fit. 
     
     
         8 . The method of  claim 1 , wherein calculating the third value from the first value and the second value comprises extrapolating from the first value and the second value. 
     
     
         9 . The method of  claim 8 , wherein extrapolating from the first value and the second value comprises calculating a first goodness of fit between the best matching first reference spectrum and the measured spectrum, and calculating a second goodness of fit between the best matching second reference spectrum and the measured spectrum, and extrapolating based on the first value, the first goodness of fit, the second value and the second goodness of fit. 
     
     
         10 . The method of  claim 9 , wherein the goodness of fit comprises one or more of a sum of squared differences, a sum of absolute differences, or a cross-correlation. 
     
     
         11 . The method of  claim 9 , wherein calculating the third value V 3  comprises calculating V 3 =V 1 −X 1 *(V 1 −V 2 )/(X 1 −X 2 ), where V 1  is the first value, V 2  is the second value, X 1  is the first goodness of fit and X 2  is the second goodness of fit. 
     
     
         12 . The method of  claim 1 , further comprising determining whether to interpolate or extrapolate in calculating the third value. 
     
     
         13 . The method of  claim 12 , further comprising calculating a first goodness of fit between the best matching first reference spectrum and the measured spectrum, calculating a second goodness of fit between the best matching second reference spectrum and the measured spectrum, and calculating a third goodness of fit between the best matching first reference spectrum and the best matching second reference spectrum, and wherein determining whether to interpolate or extrapolate comprises comparing the third goodness of fit to the first goodness of fit and the second goodness of fit. 
     
     
         14 . The method of  claim 13 , further comprising interpolating between the first value and the second value if the third goodness of fit is worse than the first goodness of fit and the second goodness of fit. 
     
     
         15 . The method of  claim 13 , further comprising extrapolating from the first value and the second value if the third goodness of fit is better than the first goodness of fit or the second goodness of fit. 
     
     
         16 . The method of  claim 1 , wherein finding a first best matching reference spectrum from a first library from the plurality of libraries consists of searching only the first library, and wherein finding the best matching second reference spectrum from a different second library from the plurality of libraries comprises searching only the second library. 
     
     
         17 . The method of  claim 1 , wherein the plurality of libraries comprises three libraries. 
     
     
         18 . The method of  claim 9 , wherein finding a first best matching reference spectrum from a first library from the plurality of libraries comprises searching at least two of the three libraries. 
     
     
         19 . The method of  claim 10 , wherein finding a first best matching reference spectrum from a first library from the plurality of libraries comprises searching the three libraries. 
     
     
         20 . The method of  claim 1 , wherein the first value and the second value are index values. 
     
     
         21 . The method of  claim 1 , wherein the first value and the second value are thickness values. 
     
     
         22 . The method of  claim 1 , further comprising fitting a linear function to the sequence of third values. 
     
     
         23 . The method of  claim 22 , further comprising halting the polishing when the linear function matches or exceeds a target value. 
     
     
         24 . The method of  claim 1 , wherein the substrate includes a second layer overlying a first layer, the first layer having a different composition than the second layer, the second layer being polished in the polishing step. 
     
     
         25 . The method of  claim 14 , wherein the first library comprises spectra for the substrate having the first layer of a first thickness and the second library comprises spectra for a substrate having the first layer of a different second thickness. 
     
     
         26 . The method of  claim 1 , wherein the substrate includes a plurality of zones, and a polishing rate of each zone is independently controllable by an independently variable polishing parameter, and further comprising:
 measuring a sequence of spectra from each zone during polishing;   for each measured spectrum in the sequence of spectra for each zone, finding a first best matching reference spectrum from a first library from the plurality of libraries and finding a best matching second reference spectrum from a different second library from the plurality of libraries;   for each measured spectrum of the sequence of spectra for each zone, determining a first value associated with the best matching first reference spectrum and determining a second value from the best matching second reference spectrum;   for each measured spectrum of the sequence of spectra for each zone, calculating a third value from the first value and the second value to generate a sequence of calculated third values for each zone; and   based on the sequence of calculated third values for each zone adjusting the polishing parameter for at least one zone to adjust the polishing rate of the at least one zone such that the plurality of zones have a smaller difference in thickness at the polishing endpoint than without such adjustment.