### Abstract

The capacitances in the crossover regions of orthogonal transmission lines of finite thickness, fabricated on structures of the approximate dimensions of an integrated circuit, are evaluated in this paper by means of a combined finite difference and analytic expression method. The three-dimensional (3-D) finite difference method (FDM), using very fine mesh grids, is applied to an artificially defined region only a few microns in thickness, where orthogonal transmission lines on different metal layers of an integrated circuit cross one another. In the 600-μm thick dielectric region above the ground plane on the lower surface of an integrated circuit, analytic expressions of the solution to the Laplace equation are formulated. An artificial boundary is assumed to separate the substrate of the 600-μm thick integrated circuit from the thin active region on its uppermost surface where the active circuits and interconnects are actually fabricated, creating two separate regions which are treated using different approaches. An iterative procedure is employed to create a continuous interface between solutions across the boundary of the two regions generated by the two methods. The algorithm converges rapidly to very accurate solutions. The errors between this simulation method and laboratory measurements are within 8% for very small absolute values in the femtoFarad (fF) range. The field solutions are then converted into the equivalent circuit parameters. Finally, the waveshapes of propagating signal pulses are simulated by a networking program in a general electromagnetic modeling tool suite referred to as the Mayo Graphical Integrated Computer Aided Design Suite, or MagiCAD [1], in which the equivalent circuit model and capacitance values of the crossover problem are integrated.

Original language | English (US) |
---|---|

Pages (from-to) | 615-620 |

Number of pages | 6 |

Journal | IEEE Transactions on Components Packaging and Manufacturing Technology Part B |

Volume | 19 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1996 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*IEEE Transactions on Components Packaging and Manufacturing Technology Part B*,

*19*(3), 615-620. https://doi.org/10.1109/96.533904

**A combined finite difference and analytic expression approach to crossover capacitance in a multilayer dielectric environment.** / Pan, Guang Wen; Toupikov, Mikhail; Gilbert, Barry Kent.

Research output: Contribution to journal › Article

*IEEE Transactions on Components Packaging and Manufacturing Technology Part B*, vol. 19, no. 3, pp. 615-620. https://doi.org/10.1109/96.533904

}

TY - JOUR

T1 - A combined finite difference and analytic expression approach to crossover capacitance in a multilayer dielectric environment

AU - Pan, Guang Wen

AU - Toupikov, Mikhail

AU - Gilbert, Barry Kent

PY - 1996/8

Y1 - 1996/8

N2 - The capacitances in the crossover regions of orthogonal transmission lines of finite thickness, fabricated on structures of the approximate dimensions of an integrated circuit, are evaluated in this paper by means of a combined finite difference and analytic expression method. The three-dimensional (3-D) finite difference method (FDM), using very fine mesh grids, is applied to an artificially defined region only a few microns in thickness, where orthogonal transmission lines on different metal layers of an integrated circuit cross one another. In the 600-μm thick dielectric region above the ground plane on the lower surface of an integrated circuit, analytic expressions of the solution to the Laplace equation are formulated. An artificial boundary is assumed to separate the substrate of the 600-μm thick integrated circuit from the thin active region on its uppermost surface where the active circuits and interconnects are actually fabricated, creating two separate regions which are treated using different approaches. An iterative procedure is employed to create a continuous interface between solutions across the boundary of the two regions generated by the two methods. The algorithm converges rapidly to very accurate solutions. The errors between this simulation method and laboratory measurements are within 8% for very small absolute values in the femtoFarad (fF) range. The field solutions are then converted into the equivalent circuit parameters. Finally, the waveshapes of propagating signal pulses are simulated by a networking program in a general electromagnetic modeling tool suite referred to as the Mayo Graphical Integrated Computer Aided Design Suite, or MagiCAD [1], in which the equivalent circuit model and capacitance values of the crossover problem are integrated.

AB - The capacitances in the crossover regions of orthogonal transmission lines of finite thickness, fabricated on structures of the approximate dimensions of an integrated circuit, are evaluated in this paper by means of a combined finite difference and analytic expression method. The three-dimensional (3-D) finite difference method (FDM), using very fine mesh grids, is applied to an artificially defined region only a few microns in thickness, where orthogonal transmission lines on different metal layers of an integrated circuit cross one another. In the 600-μm thick dielectric region above the ground plane on the lower surface of an integrated circuit, analytic expressions of the solution to the Laplace equation are formulated. An artificial boundary is assumed to separate the substrate of the 600-μm thick integrated circuit from the thin active region on its uppermost surface where the active circuits and interconnects are actually fabricated, creating two separate regions which are treated using different approaches. An iterative procedure is employed to create a continuous interface between solutions across the boundary of the two regions generated by the two methods. The algorithm converges rapidly to very accurate solutions. The errors between this simulation method and laboratory measurements are within 8% for very small absolute values in the femtoFarad (fF) range. The field solutions are then converted into the equivalent circuit parameters. Finally, the waveshapes of propagating signal pulses are simulated by a networking program in a general electromagnetic modeling tool suite referred to as the Mayo Graphical Integrated Computer Aided Design Suite, or MagiCAD [1], in which the equivalent circuit model and capacitance values of the crossover problem are integrated.

UR - http://www.scopus.com/inward/record.url?scp=0030214755&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030214755&partnerID=8YFLogxK

U2 - 10.1109/96.533904

DO - 10.1109/96.533904

M3 - Article

AN - SCOPUS:0030214755

VL - 19

SP - 615

EP - 620

JO - IEEE Transactions on Components Packaging and Manufacturing Technology Part B

JF - IEEE Transactions on Components Packaging and Manufacturing Technology Part B

SN - 1070-9894

IS - 3

ER -