Unified model for process variations in integrated circuits

A method of developing a statistical model for integrated circuits, the method comprising:

• forming a set of test patterns of test devices on a plurality of identical dies, wherein a plurality of identical groups are created on each of the identical dies, the test devices comprising metal-oxide-semiconductor (MOS) devices, resistors, capacitors, memory cells, wires, or a combination thereof;
• for a parameter, collecting a set of data from each of the identical groups in each of the identical dies, wherein a set of data from a die form a set of intra-die data, and wherein plurality of sets of data from the plurality of identical dies form a total data set;
• generating a total variation sigma (sigma_total) from the total data set;
• for the parameter, determining a median value from the set of intra-data from the die, wherein median values of the parameter for the plurality of identical dies form a set of inter-die data;
• generating a global variation sigma (sigma_global) from the set of inter-die data, the sigma_global being different from the set of inter-die data;
• and
• generating a local variation sigma (sigma_local) by removing the sigma_global from the sigma_total.

A method of developing a statistical model for integrated circuits, the method comprising:

• forming a set of test patterns of test devices on a plurality of identical dies, wherein a plurality of identical groups are created on each of the identical dies, the test devices comprising metal-oxide-semiconductor (MOS) devices, resistors, capacitors, memory cells, wires, or a combination thereof;
• for a parameter, collecting a set of data from each of the identical groups in each of the identical dies, wherein a set of data from a die form a set of intra-die data, and wherein a plurality of sets of data from the plurality of identical dies form a total data set;
• generating a total variation sigma (sigma_total) from the total data set;
• for the parameter, generating a sigma from a set of intra-die from each of the identical dies to form a set of sigmas, the set of sigmas being different from the set of intra-die data;
• determining a local variation sigma (sigma_local) by averaging the set of sigmas;
• and
• generating a global variation sigma (sigma_global) by removing the sigma_local from the sigma_total.