Probability constrained optimization for electrical fabrication control

A method, comprising:

• defining a model of a process for manufacturing a device, the process including a plurality of steps;
• defining a plurality of inline process targets for at least a subset of the process steps, the model relating the inline process targets to a plurality of process output parameters;
• defining a first set of constraints for the inline process targets;
• defining a second set of constraints for the process output parameters;
• determining a first set of values for the inline process targets that when applied to the model for the plurality of steps result in a probability of the first set of constraints being met being greater than a first probability threshold and a probability of the second set of constraints being met being greater than a second probability threshold;
• performing a first step of the process using the determined value for the inline process target associated with the first step;
• measuring an output parameter associated with the first step;
• updating the model based on the measured output parameter;
• and
• determining a second set of values for the inline process targets that when applied to the model for the remaining steps in the plurality of steps result in the probability of the first set of constraints being met being greater than the first probability threshold and the probability of the second set of constraints being met being greater than a second probability threshold.

A system, comprising:

• a plurality of tools for manufacturing a device over a plurality of steps;
• a plurality of process controllers associated with at least a subset of the tools, each process controller being configured to control the processing of at least one associated tool based on an inline process target;
• and
• a supervisory controller configured to employ a model of the processing steps for manufacturing the device, the model relating the inline process targets to a plurality of process output parameters, define a first set of probabilistic constraints for the inline process targets, define a second set of probabilistic constraints for the process output parameters, define an objective function based on the model and the plurality of process output parameters, and determine a trajectory of the process output parameters by optimizing the objective function subject to the first and second sets of probabilistic constraints for each process step to determine values for the inline process targets at each process step having an associated process controller, the optimization being iterated after completion of each process step for the remaining process steps.

A system, comprising:

• means for manufacturing a device over a plurality of steps;
• means for controlling the processing over the plurality of steps based on an inline process target for at least a subset of the steps;
• means for defining a model of the processing steps for manufacturing the device, the model relating the inline process targets to a plurality of process output parameters;
• means for defining a first set of probabilistic constraints for the inline process targets and a second set of probabilistic constraints for the process output parameters;
• means for defining an objective function based on the model and the plurality of process output parameters;
• and
• means for determining a trajectory of the process output parameters by optimizing the objective function subject to the first and second sets of probabilistic constraints for each process step to determine values for the inline process targets at each process step having an associated process controller, the optimization being iterated after completion of each process step for the remaining process steps.