# US 10,121,709 B2 · Virtual metrology systems and methods for using feedforward critical dimension data to predict other critical dimensions of a wafer > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,121,709 B2 - Document ID: US10121709B2 - Status: Granted - Kind: B2 - Application number: 15/413,639 - Filed: 2017-01-24 - Published: 2018-07-26 - Granted: 2018-11-06 - Earliest claimed: 2017-01-24 - Assignees: Lam Research Corporation - Applicants: Lam Research Corporation - Inventors: Ramanapathy Veerasingam - Web page: https://patentgrep.com/patent/US10121709B2 ## CPC - H10P 74/23: {characterised by multiple measurements, corrections, marking or sorting processes} - G06F 30/367: Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods - G06F 30/398: Design verification or optimisation, e.g. using design rule check [DRC], layout versus schematics [LVS] or finite element methods [FEM] (optical proximity correction [OPC] design processes G03F1/36) - H10P 74/203: {Structural properties, e.g. testing or measuring thicknesses, line widths, warpage, bond strengths or physical defects} - H10P: GENERIC PROCESSES OR APPARATUS FOR THE MANUFACTURE OR TREATMENT OF DEVICES COVERED BY CLASS H10 - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract A controller includes a memory that stores a first model corresponding to a first critical dimension of a substrate processed by a substrate processing system and a second model corresponding to a second critical dimension of the substrate. The second model includes a predicted relationship between the first critical dimension and the second critical dimension. A critical dimension prediction module calculates a first prediction of the first critical dimension of the substrate using the first model, provides the first prediction of the first critical dimension as an input to the second model, and calculates and outputs a second prediction of the second critical dimension of the substrate using the second model. ## Claims ### Claim 1 A controller, comprising: a memory that stores (i) a first model corresponding to a first critical dimension of a substrate processed by a substrate processing system and (ii) a second model corresponding to a second critical dimension of the substrate, wherein the second model includes a predicted relationship between the first critical dimension and the second critical dimension; and a critical dimension prediction module that (i) calculates a first prediction of the first critical dimension of the substrate using the first model, (ii) provides the first prediction of the first critical dimension as an input to the second model, and (iii) calculates and outputs a second prediction of the second critical dimension of the substrate using the second model. ### Claim 2 (depends on 1) The controller of claim 1, wherein at least one of the first model and the second model corresponds to a virtual metrology model. ### Claim 3 (depends on 1) The controller of claim 1, wherein the first critical dimension and the second critical dimension are associated with a same feature of the substrate. ### Claim 4 (depends on 1) The controller of claim 1, wherein the first critical dimension and the second critical dimension correspond to a height of a high aspect ratio structure on the substrate. ### Claim 5 (depends on 1) The controller of claim 1, wherein the first critical dimension and the second critical dimension correspond to a width between high aspect ratio structures on the substrate. ### Claim 6 (depends on 1) The controller of claim 1, wherein the critical dimension prediction module updates the second model based on a comparison between the first prediction of the first critical dimension and a measurement of the first critical dimension. ### Claim 7 (depends on 1) The controller of claim 1, wherein the predicted relationship is based on respective measurements of the first critical dimension and the second critical dimension on a plurality of substrates. ### Claim 8 (depends on 1) The controller of claim 1, wherein the predicted relationship is based on a ratio of (i) a difference between the first critical dimension and a third critical dimension to (ii) a difference between the first critical dimension and the second critical dimension. ### Claim 9 (depends on 1) The controller of claim 1, wherein the predicted relationship corresponds to a linear or a non-linear relationship between the first critical dimension and the second critical dimension. ### Claim 10 (depends on 1) A system, comprising: the controller of claim 1; and the substrate processing system, wherein the controller is remotely located from the substrate processing system. ### Claim 11 A method, comprising: storing (i) a first model corresponding to a first critical dimension of a substrate processed by a substrate processing system and (ii) a second model corresponding to a second critical dimension of the substrate, wherein the second model includes a predicted relationship between the first critical dimension and the second critical dimension; calculating a first prediction of the first critical dimension of the substrate using the first model; providing the first prediction of the first critical dimension as an input to the second model; and calculating and outputting a second prediction of the second critical dimension of the substrate using the second model. ### Claim 12 (depends on 11) The method of claim 11, wherein at least one of the first model and the second model corresponds to a virtual metrology model. ### Claim 13 (depends on 11) The method of claim 11, wherein the first critical dimension and the second critical dimension are associated with a same feature of the substrate. ### Claim 14 (depends on 11) The method of claim 11, wherein the first critical dimension and the second critical dimension correspond to a height of a high aspect ratio structure on the substrate. ### Claim 15 (depends on 11) The method of claim 11, wherein the first critical dimension and the second critical dimension correspond to a width between high aspect ratio structures on the substrate. ### Claim 16 (depends on 11) The method of claim 11, further comprising updating the second model based on a comparison between the first prediction of the first critical dimension and a measurement of the first critical dimension. ### Claim 17 (depends on 11) The method of claim 11, wherein the predicted relationship is based on respective measurements of the first critical dimension and the second critical dimension on a plurality of substrates. ### Claim 18 (depends on 11) The method of claim 11, wherein the predicted relationship is based on a ratio of (i) a difference between the first critical dimension and a third critical dimension to (ii) a difference between the first critical dimension and the second critical dimension. ### Claim 19 (depends on 11) The method of claim 11, wherein the predicted relationship corresponds to a linear or a non-linear relationship between the first critical dimension and the second critical dimension.