Method and system for estimating context offsets for run-to-run control in a semiconductor fabrication facility

A computer-implemented method for run-to-run control, the method comprising:

• causing a pilot run to be performed for a first thread in a process;
• estimating individual context offsets for the first thread based on the pilot run using a state-space model that describes an evolution of the process, wherein the evolution of the process is described using a set of input-output equations, in which a thread offset is expressed as a summation of individual context offsets, wherein each individual context offset is estimated based on a moving horizontal state estimation;
• for a next thread in the process, determining whether the next thread involves a new context not involved in any of previous threads;
• if the next thread involves the new context, causing a pilot run to be performed for the next thread to estimate individual context offsets for the new context using the state-space model;
• and
• if the next thread does not involve the new context, refraining from causing the pilot run to be performed for the next thread.

A system for run-to-run control, the system comprising:

• a memory;
• and
• a processor, coupled to the memory, to:
• identify contexts associated with a fabrication process, the fabrication process having one or more threads, and each thread involving one or more contexts;
• define a set of input-output equations describing the fabrication process, wherein each input-output equation corresponds to a thread and includes a thread offset expressed as a summation of individual context offsets, wherein each individual context offset is estimated based on a moving horizontal state estimation;
• and
• create a state-space model that describes an evolution of the fabrication process using the set of input-output equations, the state-space model allowing to estimate individual context offsets, wherein the thread offset is unbiased even if the individual context offsets are biased when the corresponding thread corresponds to a combination of the one or more contexts.

A system for run-to-run control, the system comprising:

• a memory;
• and
• a processor, coupled to the memory, to:
• cause a pilot run to be performed for a first thread in a process;
• estimate individual context offsets for the first thread based on the pilot run using a state-space model that describes an evolution of the process, wherein the evolution of the process is described using a set of input-output equations, in which a thread offset is expressed as a summation of individual context offsets, wherein each individual context offset is estimated based on a moving horizontal state estimation;
• for a next thread in the process, determine whether the next thread involves a new context not involved in any of previous threads;
• if the next thread involves the new context, cause a pilot run to be performed for the next thread to estimate individual context offset for the new context using the state-space model;
• and
• if the next thread does not involve the new context, refrain from causing the pilot run to be performed for the next thread.

A non-transitory computer-readable storage medium storing instructions that when executed by a computer, cause the computer to perform a method for run-to-run control, the method comprising:

• causing a pilot run to be performed for a first thread in a process;
• estimating individual context offsets for the first thread based on the pilot run using a state-space model that describes an evolution of the process, wherein the evolution of the process is described using a set of input-output equations, in which a thread offset is expressed as a summation of individual context offsets, wherein each individual context offset is estimated based on a moving horizontal state estimation;
• for a next thread in the process, determining whether the next thread involves a new context not involved in any of previous threads;
• if the next thread involves the new context, causing a pilot run to be performed for the next thread to estimate individual context offset for the new context using the state-space model;
• and
• if the next thread does not involve the new context, refraining from causing the pilot run to be performed for the next thread.