Creating multi-layer/multi-input/multi-output (MLMIMO) models for metal-gate structures

A method for establishing a Multi-Layer/Multi-Input/Multi-Output (MLMIMO) model for creating a plurality of metal-gate structures on a patterned wafer, the method comprising:

• selecting a first Multi-Layer-Multi-Step (MLMS) processing sequence and a first Multi-Layer-Multi-Input-Multi-Output (MLMIMO) model, the first MLMS processing sequence being configured to create a patterned hard-mask layer on a second set of wafers using a patterned soft-mask layer on a first set of wafers, the patterned hard-mask layer including one or more hard-mask structures, wherein the first MLMIMO model is configured to simulate the first MLMS processing sequence and includes a plurality of first Controlled Variables (CVs), a plurality of first Manipulated Variables (MVs), and a plurality of first Disturbance Variables (DVs);
• selecting a second Multi-Layer-Multi-Step (MLMS) processing sequence and a second Multi-Layer-Multi-Input-Multi-Output (MLMIMO) model a second Multi-Layer-Multi-Step (MLMS) processing sequence, the second MLMS processing sequence being configured to create one or more patterned metal-gate layers on a third set of wafers using the patterned hard-mask layer on the second set of wafers, the patterned metal-gate layers having one or more metal-gate structures, wherein the second MLMIMO model is configured to simulate the second MLMS processing sequence and includes a second number (Lb) of second Controlled Variables (CV1b CV2b, . . . CVLb), a second number (Mb) of second Manipulated Variables (MV1b, MV2b, . . . MVMb), and a second number (Nb) of second Disturbance Variables (DV1b, DV2b, . . . DVNb), wherein (Lb, Mb, and Nb) are integers greater than one;
• determining a first number (Na) of first Disturbance Variables (DV1a, DV2a, . . . DVNa) associated with the first MLMIMO model, wherein Na is an integer greater than one and one or more first measurement procedures are configured to provide one or more of the first (DV1a, DV2a, . . . DVNa), and one or more of the first (DV1a, DV2a, . . . DVNa), are determined by a preceding procedure or layer;
• determining a first number (La) of first (CV1a, CV2a, . . . CVLa), associated with the first MLMIMO model and ranges associated with the first (CV1a, CV2a, . . . CVLa), wherein La is an integer greater than one and the first (CV1a, CV2a, . . . CVLa), include a center feature width, an edge feature width, a center/edge width ratio, a center sidewall angle (SWA), an edge sidewall angle (SWA), a center/edge sidewall angle (SWA) ratio, a center feature thickness, an edge feature thickness, a center/edge thickness ratio, or profile data for other features, or any combination thereof;
• establishing a first number (Ma) of first (MV1a, MV2a, . . . MVMa) associated with the first MLMIMO model using one or more candidate processing chambers, wherein Ma is an integer greater than one and the first (MV1a, MV2a, . . . MVMa), include one or more first Within-Wafer Manipulated Variables (WiW-MVs) configured to change while a wafer is being processed, and one or more first Wafer-to-Wafer-Manipulated Variables (W2W-MVs) configured to change after the wafer has been processed;
• analyzing the first MLMIMO model, wherein one or more first statistical models are selected, one or more first ranges are provided for the first (CV1a, CV2a, . . . CVLa) and the first (MV1a, MV2a, . . . MVMa), and one or more first statistical analysis procedures are performed to establish first Design of Experiments (DOE) data, wherein the first statistical models are configured to associate one or more of the first (MV1a, MV2a, . . . MVMa), with one or more of the first (CV1a, CV2a, . . . CVLa);
• determining one or more first stability conditions for the first MLMIMO model;
• and
• optimizing the first MLMIMO model using performance parameters associated with a first set of processing tools configured to perform the first MLMS processing sequence.