Electromagnetic-Thermal Characterization of on On-Chip Coupled (A)Symmetrical Interconnects

Based on several extended formulas to determine all frequency-and temperature-dependent distributed parameters of on-chip coupled asymmetrical and symmetrical interconnects on silicon substrates, the electromagnetic-thermal characteristics of interconnects were investigated in detail, including 1) wideband series impedances and shunt conductances, 2) conductive and dielectric attenuation constants of even(c) and odd (pi)-mode, 3) pulse waveform distortion and crosstalk, and 4) average power handling capability (APHC). In these investigations, a set of modified formulas were proposed to determine the mutual conductance and capacitance of asymmetrical configuration. Appropriate thermal models were employed to evaluate the rise in temperature of metal interconnects, where the lateral heat dissipation was taken into account for different spacings between two interconnects. Parametric calculations were performed to capture the hybrid effects of all geometric and physical parameters of metal interconnects, such as line thickness, line conductivity, and silicon conductivity. All numerical examples are believed to be useful in the design of (a)symmetrical interconnects for digital and radio frequency circuits.

[1]  K. Saraswat,et al.  Analytical thermal model for multilevel VLSI interconnects incorporating via effect , 2002, IEEE Electron Device Letters.

[2]  D. Williams.  Metal-insulator-semiconductor transmission lines , 1999 .

[3]  V. K. Tripathi,et al.  Time-domain characterization and analysis of dispersive dissipative interconnects , 1992 .

[4]  Cheng-Nan Chiu.  Closed‐form expressions for the line‐coupling parameters of coupled on‐chip interconnects on lossy silicon substrate , 2004 .

[5]  F. G. Shi,et al.  New effective dielectric constant model for ultra-high speed microstrip lines on multilayer dielectric substrates: effect of conductor-dielectric interphase , 2002, 52nd Electronic Components and Technology Conference 2002. (Cat. No.02CH37345).

[6]  A. Weisshaar,et al.  Closed-form expressions for the series impedance parameters of on-chip interconnects on multilayer silicon substrates , 2004, IEEE Transactions on Advanced Packaging.

[7]  Y. J. Yoon,et al.  A new formula for effective dielectric constant in multi-dielectric layer microstrip structure , 2000, IEEE 9th Topical Meeting on Electrical Performance of Electronic Packaging (Cat. No.00TH8524).

[8]  R. Jansen,et al.  Accurate Wide-Range Design Equations for the Frequency-Dependent Characteristic of Parallel Coupled Microstrip Lines , 1984 .

[9]  Yvon Savaria,et al.  A practical approach to model long MIS interconnects in VLSI circuits , 2002, IEEE Trans. Very Large Scale Integr. Syst..

[10]  S. Zaage,et al.  Characterization of the broadband transmission behavior of interconnections on silicon substrates , 1993, 1993 Proceedings Fifth Annual IEEE International Conference on Wafer Scale Integration.

[11]  John Michael Golio.  The RF and Microwave Hanbook , 2001 .

[12]  X.T. Dong,et al.  Wide-band characterization of average power handling capabilities of some microstrip interconnects on polyimide and polyimide/GaAs substrates , 2005, IEEE Transactions on Advanced Packaging.

[13]  Robert W. Dutton,et al.  High-frequency characterization of on-chip digital interconnects , 2002, IEEE J. Solid State Circuits.

[14]  Joungho Kim,et al.  An efficient crosstalk parameter extraction method for high-speed interconnection lines , 2000, ECTC 2000.

[15]  Hai Lan,et al.  Accurate closed-form expressions for the frequency-dependent line parameters of on-chip interconnects on lossy silicon substrate , 2001, IMS 2001.

[16]  James D. Meindl,et al.  Compact distributed RLC interconnect models-Part II: Coupled line transient expressions and peak crosstalk in multilevel networks , 2000 .

[17]  Joungho Kim,et al.  Embedded microstrip interconnection lines for gigahertz digital circuits , 2000 .

[18]  Raafat R. Mansour,et al.  Dispersion characteristics of square pulse with finite rise time in single, tapered, and coupled microstrip lines , 1991 .

[19]  Ting-Yen Chiang,et al.  Impact of Joule heating on scaling of deep sub-micron Cu/low-k interconnects , 2002, 2002 Symposium on VLSI Technology. Digest of Technical Papers (Cat. No.01CH37303).

[20]  Keith W. Goossen,et al.  Modeling of picosecond pulse propagation in microstrip interconnections of integrated circuits , 1989 .

[21]  Constantine A. Balanis,et al.  MIS slow-wave structures over a wide range of parameters , 1992 .

[22]  K. Gupta,et al.  Microstrip Lines and Slotlines , 1979 .

[23]  V. K. Tripathi,et al.  Equivalent Circuits and Characteristics of Inhomogeneous Nonsymmetrical Coupled-Iine Two-Port Circuits (Short Papers) , 1977 .

[24]  W. Yin,et al.  Wideband average power handling capability of coupled microstrips on polyimide and polyimide/GaAs substrates , 2004 .

[25]  A. Weisshaar,et al.  CAD-oriented equivalent-circuit modeling of on-chip interconnects on lossy silicon substrate , 2000 .

[26]  Gaofeng Wang,et al.  Device level modeling of metal-insulator-semiconductor interconnects , 2001 .

[27]  Hai Lan,et al.  Accurate closed-form expressions for the frequency-dependent line parameters of on-chip interconnects on lossy silicon substrate , 2001, 2001 IEEE MTT-S International Microwave Sympsoium Digest (Cat. No.01CH37157).

[28]  S. Vandenberghe,et al.  Some measurement results for frequency-dependent inductance of IC interconnects on a lossy silicon substrate , 2002, IEEE Electron Device Letters.

[29]  V. Tripathi.  Asymmetric Coupled Transmission Lines in an Inhomogeneous Medium , 1975 .

[30]  H. Hasegawa,et al.  Properties of Microstrip Line on Si-SiO/sub 2/ System , 1971 .

[31]  N. D. Arora,et al.  MOSFET Models for VLSI Circuit Simulation: Theory and Practice , 1993 .

[32]  Inder J. Bahl,et al.  Average power handling capability of multilayer microstrip lines , 2001 .

[33]  Franco Stellari,et al.  New formulas of interconnect capacitances based on results of conformal mapping method , 2000 .

[34]  S. K. Kim,et al.  Three-dimensional integration: technology, use, and issues for mixed-signal applications , 2003 .

[35]  J. L. Prince,et al.  Crosstalk analysis for high-speed pulse propagation in lossy electrical interconnections , 1993 .

[36]  K. Banerjee,et al.  Global (interconnect) warming , 2001 .