The quality and reliability of interconnects in microelectronics is a major challenge considering the increasing level of integration and high current densities. This work studied the problem of transient Joule heating in interconnects in a two-dimensional (2D) inhomogeneous domain using the transmission line matrix (TLM) method. Computational efficiency of the TLM method and its ability to accept non-uniform 2D and 3D mesh and variable time step makes it a good candidate for multi-scale analysis of Joule heating in on-chip interconnects. The TLM method was implemented with link-resistor (LR) and link-line (LL) formulations, and the results were compared with a finite element (FE) model. The overall behavior of the TLM models were in good agreement with the FE model while, near the heat source, the transient TLM solutions developed slower than the FE solution. The steady-state results of the TLM and FE models were identical. The two TLM formulations yielded slightly different transient results, with the LL result growing slower, particularly at the source boundary and becoming unstable at short time-steps. It was concluded that the LR formulation is more accurate for transient thermal analysis.

References

References
1.
Phan
,
T.
,
Dilhaire
,
S.
,
Quintard
,
V.
,
Lewis
,
D.
, and
Claeys
,
W.
, 1997, “
Thermomechanical Study of AlCu Based Interconnect Under Pulsed Thermoelectric Excitation
,”
J. Appl. Phys.
,
81
, pp.
1157
1157
.
2.
Evans
,
J. W.
,
Evans
,
J. Y.
,
Lall
,
P.
,and
Cornford
,
S. L.
, 1998, “
Thermomechanical Failures in Microelectronic Interconnects
,”
Microelectron. Reliab.
,
38
, pp.
523
529
.
3.
Bastawros
,
A. F.
, and
Kim
,
K. S.
, 1998, “
Experimental Study on Electric-Current Induced Damage Evolution at the Crack Tip in Thin Film Conductors
,”
Trans. ASME J. Electron. Packag.
,
120
, pp.
354
359
.
4.
Bilotti
,
A. A.
, 1974, “
Static Temperature Distribution in IC Chips with Isothermal Heat Sources
,”
IEEE Trans. Electron Devices
,
ED-21
, pp.
217
226
.
5.
Teng
,
C. C.
,
Cheng
,
Y.-K.
,
Rosenbaum
,
E.
, and
Kang
,
S.-M.
, 2002, “
iTEM: A Temperature-Dependent Electromigration Reliability Diagnosis Tool
,”
IEEE Trans. Comput.-Aided Des.
,
16
, pp.
882
893
.
6.
Chen
,
D.
Li
,
E.
,
Rosenbaum
,
E.
, and
Kang
,
S.-M.
, 2002, “
Interconnect Thermal Modeling for Accurate Simulation of Circuit Timing and Reliability
,”
IEEE Trans. Comput.-Aided Des.
,
19
, pp.
197
205
.
7.
Stan
,
M. R.
,
Skadron
,
K.
,
Barcella
,
M.
,
Huang
,
W.
,
Sankaranarayana
,
K.
, and
Velusamy
,
S.
, 2003, “
HotSpot: A Dynamic Compact Thermal Model at the Processor-Architecture Level
,”
Microelectron. J.
,
34
, pp.
1153
1165
.
8.
Gurrum
,
S. P.
,
Joshi
,
Y. K.
,
King
,
W. P.
,
Ramakrishna
,
K.
, and
Gall
,
M.
, 2008, “
A Compact Approach to On-Chip Interconnect Heat Conduction Modeling using the Finite Element Method
,”
J. Electron. Packag.
,
130
, p.
031001
.
9.
Smy
,
T.
,
Walkey
,
D.
, and
Dew
,
S. K.
, 2001, “
Transient 3D Heat Flow Analysis for Integrated Circuit Devices using the Transmission Line Matrix Method on a Quad Tree Mesh
,”
Solid-State Electron.
,
45
, pp.
1137
1148
.
10.
Christopoulos
,
C.
, 1995,
The Transmission-Line Modeling Method TLM
,
IEEE Press
,
New York
.
11.
De Cogan
,
D.
,
O’Connor
,
W. J.
, and
Pulko
,
S.
, 2006,
Transmission Line Matrix in Computational Mechanics
,
CRC
,
Boca Raton, FL
.
12.
Ait-sadi
,
R.
, and
Naylor
,
P.
, 1993, “
An Investigation of the Different TLM Configurations used in the Modelling of Diffusion Problems
,”
Int. J. Numer. Model.
,
6
, pp.
253
268
.
13.
Zhang
,
Z. M.
, 2007,
Nano/Microscale Heat Transfer
,
McGraw-Hill Professional
,
New York
.
14.
Johns
,
P. B.
, 1977, “
A Simple Explicit and Unconditionally Stable Numerical Routine for the Solution of the Diffusion Equation
,”
Int. J. Numer. Methods Eng.
,
11
, pp.
1307
1328
.
15.
Gui
,
X.
,
Webb
,
P. W.
, and
De Cogan
,
D.
, 1992, “
An Error Parameter in TLM Diffusion Modelling
,”
Int. J. Numer. Model.
,
5
, pp.
129
137
.
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