# US 10,482,200 B2 · Modeling random dopant fluctuations in semiconductor devices > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,482,200 B2 - Document ID: US10482200B2 - Status: Granted - Kind: B2 - Application number: 14/146,114 - Filed: 2014-01-02 - Published: 2015-07-02 - Granted: 2019-11-19 - Earliest claimed: 2014-01-02 - Assignees: Globalfoundries Inc. - Applicants: Globalfoundries Inc. - Inventors: Samarth Agarwal; Abhisek Dixit; Jeffrey B. Johnson - Web page: https://patentgrep.com/patent/US10482200B2 ## CPC - G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM] - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract In one embodiment, the invention comprises: defining a first volume in a layer of a semiconductor device; calculating a probability of finding at least one dopant atom in the first volume, based on a dopant distribution of the layer; in the case that the calculated probability is equal to or greater than a pre-determined threshold, defining at least one additional volume in the layer substantially equal to the first volume; and in the case that the calculated probability is less than the pre-determined threshold: aggregating the first volume with a second volume adjacent the first volume, the second volume being substantially equal to the first volume; and recalculating a probability of finding at least one dopant atom in the aggregated first and second volumes, based on the dopant distribution of the layer. ## Claims ### Claim 1 A method of modeling random dopant fluctuations (RDF) in a semiconductor device, the method comprising: executing a computer program product stored on a non-transitory machine-readable storage medium, which, once executed, performs the following steps: overlaying a finite element mesh atop a model of a layer of a semiconductor device; defining a first volume in the layer of the semiconductor device as a node of the finite element mesh; calculating a probability of finding at least one dopant atom in the first volume, based on a dopant distribution of the layer; in the case that the calculated probability is equal to or greater than a pre-determined threshold, defining at least one additional volume in the layer substantially equal to the first volume; and in the case that the calculated probability is less than the pre-determined threshold: aggregating the first volume with a second volume adjacent the first volume, the second volume being substantially equal to the first volume; and recalculating a probability of finding at least one dopant atom in the aggregated first and second volumes, based on the dopant distribution of the layer, wherein the machine-readable storage medium includes at least one medium selected from a group consisting of: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disc read-only memory, an optical storage device, and a magnetic storage device; and employing the calculated probability to control a dopant distribution fluctuation in a manufactured semiconductor device. ### Claim 2 (depends on 1) The method of claim 1, further comprising: in the case that the recalculated probability is equal to or greater than the pre-determined threshold, defining at least one additional volume in the layer substantially equal to the aggregated first and second volumes. ### Claim 3 (depends on 2) The method of claim 2, further comprising: determining a revised dopant distribution for the layer based on the recalculated probability using a Poisson distribution; and applying the revised dopant distribution to each of the first and second volumes. ### Claim 4 (depends on 1) The method of claim 1, further comprising: in the case that the recalculated probability is less than the pre-determined threshold: reaggregating an additional volume with the previously aggregated volumes, the additional volume being adjacent to at least one of the volumes making up the previously aggregated volumes; and further recalculating a probability of finding at least one dopant atom in the aggregated additional volume and the previously aggregated volumes based on the dopant distribution of the layer. ### Claim 5 (depends on 4) The method of claim 4, wherein the additional volume is substantially equal to at least one of the already aggregated volumes. ### Claim 6 (depends on 4) The method of claim 4, further comprising: in the case that the further recalculated probability is less than the pre-determined threshold: iteratively looping the reaggregating and further recalculating steps until the further recalculated probability is equal to or greater than the pre-determined threshold; and defining at least one additional volume in the layer substantially equal to the reaggregated volumes. ### Claim 7 (depends on 6) The method of claim 6, further comprising: determining a revised dopant distribution for the layer based on the further recalculated probability using a Poisson distribution; and applying the revised dopant distribution to each volume making up the reaggregated volumes. ### Claim 8 (depends on 1) The method of claim 1, wherein the node is expected to have a lowest dopant concentration of the layer, based on the dopant distribution. ### Claim 9 (depends on 8) The method of claim 8, wherein the second volume has a dopant concentration greater than or equal to the dopant concentration of the first volume. ### Claim 10 (depends on 7) The method of claim 7, wherein applying the revised dopant distribution includes recalculating a probability of finding at least one dopant atom in the first volume, based on the revised dopant distribution. ### Claim 11 A computer program product for modeling random dopant fluctuations (RDF) in a semiconductor device, the computer program product comprising a non-transitory machine-readable storage medium having program code embodied therewith, the program code being executable by a processor of a computing device to perform a method comprising: overlaying a finite element mesh atop a model of a layer of a semiconductor device; defining a first volume in the layer of the semiconductor device as a node of the finite element mesh; calculating a probability of finding at least one dopant atom in the first volume, based on a dopant distribution of the layer; in the case that the calculated probability is equal to or greater than a pre-determined threshold, defining at least one additional volume in the layer substantially equal to the first volume; and in the case that the calculated probability is less than the pre-determined threshold: aggregating the first volume with a second volume adjacent the first volume, the second volume being substantially equal to the first volume; and recalculating a probability of finding at least one dopant atom in the aggregated first and second volumes, based on the dopant distribution of the layer, wherein the machine-readable storage medium includes at least one medium selected from a group consisting of: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disc read-only memory, an optical storage device, and a magnetic storage device; and employing the calculated probability to control a dopant distribution fluctuation in a manufactured semiconductor device. ### Claim 12 (depends on 11) The computer program product of claim 11, wherein the method further comprises: in the case that the recalculated probability is equal to or greater than the pre-determined threshold, defining at least one additional volume in the layer substantially equal to the aggregated first and second volumes. ### Claim 13 (depends on 12) The computer program product of claim 12, wherein the method further comprises: determining a revised dopant distribution for the layer based on the recalculated probability using a Poisson distribution; and applying the revised dopant distribution to each of the first and second volumes. ### Claim 14 (depends on 11) The computer program product of claim 11, wherein the method further comprises: in the case that the recalculated probability is less than the pre-determined threshold: reaggregating an additional volume with the previously aggregated volumes, the additional volume being adjacent to at least one of the volumes making up the previously aggregated volumes; and further recalculating a probability of finding at least one dopant atom in the aggregated additional volume and the previously aggregated volumes based on the dopant distribution of the layer. ### Claim 15 (depends on 14) The computer program product of claim 14, wherein the additional volume is substantially equal to at least one of the already aggregated volumes. ### Claim 16 (depends on 14) The computer program product of claim 14, wherein the method further comprises: in the case that the further recalculated probability is less than the pre-determined threshold: iteratively looping the reaggregating and further recalculating steps until the further recalculated probability is equal to or greater than the pre-determined threshold; and defining at least one additional volume in the layer substantially equal to the reaggregated volumes. ### Claim 17 (depends on 16) The computer program product of claim 16, wherein the method further comprises: determining a revised dopant distribution for the layer based on the further recalculated probability using a Poisson distribution; and applying the revised dopant distribution to each volume making up the reaggregated volumes. ### Claim 18 (depends on 11) The computer program product of claim 11, wherein the second volume has a dopant concentration greater than or equal to the dopant concentration of the first volume.