# US 8,543,967 B2 · Computer system and method for determining a temperature rise in direct current (DC) lines caused by joule heating of nearby alternating current (AC) lines > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 8,543,967 B2 - Document ID: US8543967B2 - Status: Granted - Kind: B2 - Application number: 13/405,059 - Filed: 2012-02-24 - Published: 2013-08-29 - Granted: 2013-09-24 - Earliest claimed: 2012-02-24 - Assignees: Avago Technologies General IP (Singapore) Pte. Ltd. - Applicants: Jason T. Gentry; Brian C. Miller; William S. Burton; M. Jason Welch; Richard A. Krzyzkowski - Inventors: Jason T. Gentry; Brian C. Miller; William S. Burton; M. Jason Welch; Richard A. Krzyzkowski - Web page: https://patentgrep.com/patent/US8543967B2 ## CPC - G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM] - G06F 2119/08: Thermal analysis or thermal optimisation - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract A computer system performs a verification process that quickly and efficiently determines a temperature rise of DC conductor lines of an IC design caused by Joule heating in nearby AC conductor lines of the IC design, and whether the temperature rise is acceptable in terms of an electromigration performance of the IC design. ## Claims ### Claim 1 A computer system for analyzing an integrated circuit (IC) design to determine whether a temperature rise caused by Joule heating in alternating current (AC) conductor lines is acceptable, the system comprising: a user interface; a memory subsystem that stores a representation of at least a portion of the IC design and computer code for performing a verification analysis; and a processor subsystem, the processor subsystem programmed to: select a characteristic finite area in said representation, the selected characteristic finite area corresponding to an area having a particular shape and size and having a particular direct current (DC) conductor line configuration that is repeated throughout said representation; compute a characteristic function for the selected characteristic finite area, the characteristic function characterizing a temperature rise of the selected characteristic finite area as a function of Joule heating power produced by an alternating current (AC) conductor line configuration of the selected characteristic finite area; for each actual finite area in said representation that has a size and shape and a DC conductor line configuration that matches the size and shape and DC conductor line configuration of the selected characteristic finite area: calculate a total Joule heating power of the AC conductor line configuration of the actual finite area, apply the respective total Joule heating power of each respective actual finite area to said characteristic function to calculate a respective temperature rise value for each respective actual finite area, and compare each respective temperature rise value with a predetermined threshold (TH) value to determine whether the respective temperature rise value exceeds the TH value. ### Claim 2 (depends on 1) The computer system of claim 1, wherein if the respective temperature rise value of a respective actual finite area exceeds the TH value, the respective actual finite area is tagged as failing the verification analysis. ### Claim 3 (depends on 1) The computer system of claim 1, wherein if the respective temperature rise value of a respective actual finite area does not exceed the TH value, the respective actual finite area is tagged as passing the verification analysis. ### Claim 4 (depends on 1) The computer system of claim 1, wherein if the respective temperature rise value of a respective actual finite area exceeds the TH value, the respective actual finite area is deemed to have failed the verification analysis. ### Claim 5 (depends on 1) The computer system of claim 1, wherein if the respective temperature rise value of a respective actual finite area exceeds the TH value, the respective actual finite area is further analyzed in a subsequent verification process that more accurately determines the Joule heating power and the temperature rise value of the respective AC conductor configuration and determines whether the more accurately determined temperature rise value exceeds the TH value. ### Claim 6 (depends on 1) The computer system of claim 1, wherein if the respective temperature rise value of a respective actual finite area exceeds the TH value, then the respective actual finite area is deemed a failed actual finite area and a subsequent verification process is performed that obtains an adjusted temperature rise value for the failed actual finite area based on an analysis of sharing of Joule power heating densities among the failed actual finite area and neighboring actual finite areas that border the failed actual finite area and compares the adjusted temperature rise value with the TH value to determine whether the adjusted temperature rise value exceeds the TH value. ### Claim 7 (depends on 1) The computer system of claim 1, further comprises: a user input device connected to the user interface, wherein the selected characteristic finite area is selected at least partly based on a user input that is inputted into the computer system via the user input device. ### Claim 8 (depends on 1) The computer system of claim 1, wherein the computer system further comprises: a display device connected to the user interface, and wherein the determination of whether the respective temperature rise value exceeds the TH value is displayed on the display device. ### Claim 9 (depends on 1) The computer system of claim 1, wherein the characteristic function is a linear function. ### Claim 10 (depends on 1) The computer system of claim 1, wherein the characteristic function is a nonlinear function. ### Claim 11 (depends on 9) The computer system of claim 9, wherein the linear function is a scalar. ### Claim 12 A method for analyzing an integrated circuit (IC) design in a computer system to determine whether a temperature rise caused by Joule heating in alternating current (AC) conductor lines is acceptable, the method comprising: in a memory subsystem of the computer system, storing a representation of at least a portion of the IC design and computer code for performing a verification analysis; and in a processor subsystem of the computer system: selecting a characteristic finite area in said representation, the selected characteristic finite area corresponding to an area having a particular shape and size and having a particular direct current (DC) line conductor configuration that is repeated throughout said representation; computing a characteristic function for the selected characteristic finite area, the characteristic function characterizing a temperature rise of the selected characteristic finite area as a function of Joule heating power produced by an alternating current (AC) conductor line configuration of the selected characteristic finite area; for each actual finite area in said representation that has a size and shape and a DC conductor line configuration that matches the size and shape and DC conductor line structure of the selected characteristic finite area: calculating a total Joule heating power of the AC conductor line configuration of the actual finite area, applying the respective total Joule heating power of the respective actual finite area to said characteristic function to calculate a respective temperature rise value for the respective actual finite area, and comparing the respective temperature rise value with a predetermined threshold (TH) value to determine whether the respective temperature rise value exceeds the TH value. ### Claim 13 (depends on 12) The method of claim 12, further comprising: if the respective temperature rise value of a respective actual finite area exceeds the TH value, tagging the respective actual finite area as failing the verification analysis. ### Claim 14 (depends on 12) The method of claim 12, further comprising: if the respective temperature rise value of a respective actual finite area does not exceed the TH value, tagging the respective actual finite area as passing the verification analysis. ### Claim 15 (depends on 12) The method of claim 12, wherein if the respective temperature rise value of a respective actual finite area exceeds the TH value, the respective actual finite area is deemed to have failed the verification analysis. ### Claim 16 (depends on 12) The method of claim 12, further comprising: if the respective temperature rise value of a respective actual finite area exceeds the TH value, further analyzing the respective actual finite area in a subsequent verification process that more accurately determines the Joule heating power and the temperature rise value of the respective AC conductor line configuration to determine whether the more accurately determined temperature rise value exceeds the TH value. ### Claim 17 (depends on 12) The method of claim 12, further comprising: if the respective temperature rise value of a respective actual finite area exceeds the TH value, then the respective actual finite area is deemed a failed actual finite area and the respective failed actual finite area is further analyzed in a subsequent verification process that obtains an adjusted temperature rise value for the failed actual finite area based on an analysis of sharing of Joule power heating densities among the failed actual finite area and neighboring actual finite areas that border the failed actual finite area and compares the adjusted temperature rise value with the TH value to determine whether the adjusted temperature rise value exceeds the TH value. ### Claim 18 (depends on 12) The method of claim 12, further comprising: with a user input device connected to a user interface of the computer system, entering a user input to the computer system, wherein the selected characteristic finite area is selected at least partly based on the user input. ### Claim 19 (depends on 12) The method of claim 12, wherein the computer system further comprises: on a display device connected to a user interface of the computer system, displaying the determination of whether the respective temperature rise value exceeds the TH value. ### Claim 20 (depends on 12) The method of claim 12, wherein the characteristic function is a linear function. ### Claim 21 (depends on 12) The method of claim 12, wherein the characteristic function is a nonlinear function. ### Claim 22 (depends on 20) The method of claim 20, wherein the linear function is a scalar. ### Claim 23 A computer program for analyzing an integrated circuit (IC) design in a computer system to determine whether a temperature rise caused by Joule heating in alternating current (AC) conductor lines of the IC design is acceptable, the computer program comprising computer instructions stored on a non-transitory computer-usable medium, the computer instructions comprising: computer instructions for selecting a characteristic finite area in a representation of at least a portion of the IC design to be used as a characteristic finite area in a verification analysis, the selected characteristic finite area corresponding to an area having a particular shape and size and having a particular direct current (DC) conductor line configuration that is repeated throughout said representation; computer instructions for computing a characteristic function for the selected characteristic finite area, the characteristic function characterizing a temperature rise of the selected characteristic finite area as a function of Joule heating power produced by an alternating current (AC) conductor line configuration of the selected characteristic finite area; computer instructions for analyzing each actual finite area in said representation that has a size and shape and a DC conductor line configuration that matches the size and shape and DC conductor line configuration of the selected characteristic finite area by: calculating a total Joule heating power of the AC conductor line configuration of the actual finite area, applying the respective total Joule heating power of the respective actual finite area to said characteristic function to calculate a respective temperature rise value for the respective actual finite area, and comparing the respective temperature rise value with a predetermined threshold (TH) value to determine whether the respective temperature rise value exceeds the TH value. ### Claim 24 (depends on 23) The computer program of claim 23, further comprising: computer instructions for tagging the respective actual finite area as failing the verification analysis if the respective temperature rise value of the respective actual finite area exceeds the TH value. ### Claim 25 (depends on 23) The computer program of claim 23, further comprising: computer instructions for tagging the respective actual finite area as passing the verification analysis if the respective temperature rise value of the respective actual finite area does not exceed the TH value. ### Claim 26 (depends on 23) The computer program of claim 23, further comprising: computer instructions for further analyzing the respective actual finite area in a subsequent verification process if the respective temperature rise value of the respective actual finite area exceeds the TH value, wherein the subsequent verification process more accurately determines the Joule heating power and the temperature rise value of the respective AC conductor line configuration of the respective actual finite area to determine whether the more accurately determined temperature rise value exceeds the TH value. ### Claim 27 (depends on 23) The computer program of claim 23, further comprising: computer instructions for further analyzing the respective actual finite area in a subsequent verification process if the respective temperature rise value of the respective actual finite area exceeds the TH value, wherein if the respective temperature rise value of the respective actual finite area exceeds the TH value, the respective actual finite area is deemed a failed actual finite area, and wherein the subsequent verification process obtains an adjusted temperature rise value for the failed actual finite area based on an analysis of sharing of Joule power heating densities among the failed actual finite area and neighboring actual finite areas that border the failed actual finite area and compares the adjusted temperature rise value with the TH value to determine whether the adjusted temperature rise value exceeds the TH value. ### Claim 28 (depends on 23) The computer program of claim 23, further comprising: computer instructions for processing a user input that has been inputted into the computer system via a user input device connected to a user interface of the computer system, wherein the selected characteristic finite area is selected at least partly based on the user input. ### Claim 29 (depends on 23) The computer program of claim 23, further comprising: computer instructions for causing the determination of whether the respective temperature rise value exceeds the TH value to be displayed on a display device connected to a user interface of the computer system. ### Claim 30 (depends on 23) The computer program of claim 23, wherein the characteristic function is a linear function. ### Claim 31 (depends on 23) The computer program of claim 23, wherein the characteristic function is a nonlinear function. ### Claim 32 (depends on 30) The computer program of claim 30, wherein the linear function is a scalar.