Patent ID: 7302363

Claim:
A method of monitoring a processing system in real-time, comprising: performing a first process on one or more wafers positioned within a processing chamber having a reduced pressure; monitoring the first process using a first set of nonlinear differential equations {dot over (x)} 1 and a first output equation y 1 , wherein {dot over (x)} 1 =ƒ( x 1 ,p 1 ,u 1 )+ w 1 y 1 =g ( x 1 ,p 1 ,u 1 )+ v 1 and x 1 , p 1 , and u 1 are first process parameters in which the first vector x 1 comprises a first state vector, the first vector p 1 comprises one or more modeling parameters for the first process, the vector u 1 comprises one or more inputs applied to the first process, w 1 is a first additive white noise value having a zero mean, and v 1 is a second additive white noise value having a zero mean; determining a first process model for the first process that relates a first rate of change for at least one parameter of a first set of the first process parameters to a second set of the first process parameters as and/or after a first parameter in the second set is changed from a first value to a second value, wherein the second set does not include the at least one parameter of the first set; determining a first measured rate of change for the at least one parameter of the first set in real time as and/or after the first parameter in the second set is changed from the first value to the second value; executing a first inverse process model for the first process that relates the first measured rate of change to a value for a second parameter in the second set of first process parameters to obtain a predicted value for the second parameter in the second set; calculating a first dynamic estimation error for the first process; comparing the first dynamic estimation error to a first operational limit established for the first process; continuing the first process when the first dynamic estimation error is within the first operational limit; and examining the first process when the first dynamic estimation error is not within the first operational limit.