Advanced process control system and method utilizing virtual metrology with reliance index

A computer-implemented APC method, comprising:

• obtaining, by a VM module, a plurality of sets of historical process data used by a process tool for processing a plurality of historical workpieces;
• obtaining, by a VM module, a plurality of historical measurement data of the historical workpieces measured by a metrology tool, wherein said historical measurement values are the measurement values of said historical workpieces which are manufactured in accordance with said sets of historical process data, respectively;
• establishing, by a VM module, a conjecture model in accordance with a conjecture algorithm by using said sets of historical process data and said historical measurement values corresponding thereto, and establishing, by a RI module, a reference model in accordance with a reference algorithm by using said sets of historical process data and said historical measurement values corresponding thereto, wherein said conjecture algorithm is different from said reference algorithm;
• and
• controlling, by a run-to-run (R2R) controller, said process tool to perform process runs in accordance with the following relationships;
• uz+1=g(G1,1,G1,2, . . . ,G1,i,yz);
• uk+1=g(G2,1,G2,2, . . . ,G2,i,ŷk);
• G2,i=f(RIk)×G1,i;
• where G2,i=0 or ŷk−1 but not ŷk is adopted for tuning said R2R controller, if RIk<RIT;
• f(RIk)=RIk, if RIk≧RIT and k≦C;
• f(RIk)=1−RIk, if RIk≧RIT and k>C;
• wherein yz represents an actual measurement value of a sampling workpiece which has been processed in the zth process run by said process tool and measured by said metrology tool;
• uz+1 represents the control action of the (z+1)h process run when yz is adopted;
• G1,i, represents the controller gain used in said R2R controller when yz is adopted, wherein i represents the number of the controller gains used in said R2R controller;
• ŷk generated by the VM module represents a virtual metrology value of a workpiece which has been processed in the kth process run by said process tool, and is generated by inputting a set of process data of said workpiece into said conjecture model;
• uk+1 represents the control action of the (k+1)th process run when ŷk is adopted;
• G2,i, represents the controller gain used in said R2R controller when ŷk is adopted;
• RIk generated by the RI module represents a reliance index (RI) of the kth process run, wherein said reliance index corresponding to the kth process run is generated by calculating an overlap area between the statistical distribution of said virtual metrology value of said workpiece and the statistical distribution of a reference prediction value of said workpiece, wherein said reference prediction value of the kth process run is generated by inputting said set of process data of said workpiece into said reference model, wherein said reliance index is higher when said overlap area is larger, representing that said reliance level of said virtual metrology value corresponding to said reliance index is higher;
• RIT represents the RI threshold value based on the maximal tolerable error limit defined by the errors of the virtual metrology values obtained from said conjecture model;
• and
• C stands for a predetermined number of process runs.

A computer program product stored on a non transitory tangible computer readable recording medium, which, when executed, performs an APC method comprising:

• obtaining a plurality of sets of historical process data used by a process tool for processing a plurality of historical workpieces;
• obtaining a plurality of historical measurement data of the historical workpieces measured by a metrology tool, wherein said historical measurement values are the measurement values of said historical workpieces which are manufactured in accordance with said sets of historical process data, respectively;
• establishing a conjecture model in accordance with a conjecture algorithm by using said sets of historical process data and said historical measurement values corresponding thereto, and a reference model in accordance with a reference algorithm by using said sets of historical process data and said historical measurement values corresponding thereto, wherein said conjecture algorithm is different from said reference algorithm;
• and
• enabling a run-to-run (R2R) controller to control said process tool to perform said process runs in accordance with the following relationships:
• uz+1=g(G1,1,G1,2, . . . ,G1,i,yz)
• uk+1=g(G2,1,G2,2, . . . ,G2,i,ŷk)
• G2,i=f(RIk)×G1,i
• where G2,i=0 or ŷk−1 but not ŷk is adopted for tuning said R2R controller, if RIk<RIT;
• f(RIk)=RIk, if RIk≧RIT and k≦C;
• f(RIk)=1−RIk, if RIk≧RIT and k>C;
• wherein yz represents an actual measurement value of a sampling workpiece which has been processed in the zth process run by said process tool and measured by said metrology tool;
• uz+1 represents the control action of the (z+1)th process run when yz is adopted;
• G1,i,represents the controller gain used in said R2R controller when yz is adopted, wherein i represents the number of the controller gains used in said R2R controller;
• ŷk represents a virtual metrology value of a workpiece which has been processed in the kth process run by said process tool, and is generated by inputting a set of process data of said workpiece into said conjecture model;
• uk+1 represents the control action of the (k+1)th process run when ŷk is adopted;
• G2,i, represents the controller gain used in said R2R controller when ŷk is adopted;
• RIk represents a reliance index (RI) of the kth process run, wherein said reliance index corresponding to the kth process run is generated by calculating an overlap area between the statistical distribution of said virtual metrolou value of said workpiece and the statistical distribution of a reference prediction value of said workpiece, wherein said reference prediction value of the kth process run is generated by inputting said set of process data of said workpiece into said reference model, wherein said reliance index is higher when said overlap area is larger, representing that said reliance level of said virtual metrology value corresponding to said reliance index is higher;
• RIT represents a RI threshold value based on a maximal tolerable error limit defined by the errors of the virtual metrology values obtained from said conjecture model;
• and
• C stands for a predetermined number of process runs.