Interconnect thermal modeling for accurate simulation of circuittiming and reliability

We apply three-dimensional finite element analysis to study the thermal coupling between nearby interconnects. We find that the temperature rise in current-carrying lines is significantly influenced by a dense array of lines in a nearby metal level. In contrast, thermal coupling between just two neighboring parallel lines is insignificant for most geometries. Design rules for average root-mean-square current density are provided for specific geometries given the requirement that the interconnect temperature be no more than 5/spl deg/C above the substrate temperature. Semi-empirical formulae for coupling effects are presented based on the numerical results. A procedure is proposed to implement the formulae in computer-aided design tools.

[1]  R. V. Andrews.  SOLVING CONDUCTIVE HEAT TRANSFER PROBLEMS WITH ELECTRICAL-ANALOGUE SHAPE FACTORS , 1955 .

[2]  S. Kutateladze,et al.  A concise encyclopedia of heat transfer , 1966 .

[3]  J. Black.  Electromigration failure modes in aluminum metallization for semiconductor devices , 1969 .

[4]  V. A. Sandborn.  Resistance temperature transducers , 1972 .

[5]  A. Bilotti.  Static temperature distribution in IC chips with isothermal heat sources , 1974 .

[6]  J. Vansant.  Conduction heat transfer solutions , 1980 .

[7]  D. Cahill.  Thermal conductivity measurement from 30 to 750 K: the 3ω method , 1990 .

[8]  K. Goodson,et al.  Effect of microscale thermal conduction on the packing limit of silicon-on-insulator electronics , 1992, [1992 Proceedings] Intersociety Conference on Thermal Phenomena in Electronic Systems.

[9]  G. Vradis,et al.  Thermal Conductivity of Thin Metallic Films , 1994 .

[10]  Seungmin Lee,et al.  Heat transport in thin dielectric films , 1997 .

[11]  W. Hunter.  Self-consistent solutions for allowed interconnect current density. II. Application to design guidelines , 1997 .

[12]  Sung-Mo Kang,et al.  iTEM: a temperature-dependent electromigration reliability diagnosis tool , 1997, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[13]  W. Hunter.  Self-consistent solutions for allowed interconnect current density. I. Implications for technology evolution , 1997 .

[14]  Chenming Hu,et al.  Characterization of self-heating in advanced VLSI interconnect lines based on thermal finite element simulation , 1998 .

[15]  Sung-Mo Kang,et al.  Interconnect thermal modeling for determining design limits on current density , 1999, ISPD '99.