Reliability is becoming a limiting constraint in high-performance nanometer VLSI chip designs due to the high failure rates in deep submicron and nanoscale devices. It was expected that the future chips will show sign of reliability-induced age much faster than the previous generations. Among of many reliability effects, electromigration (EM)-induced reliability has become a major design constraint due to aggressive transistor scaling and increasing power density.
Electromigration (EM) is a physical phenomenon of the oriented migration of metal (Cu) atoms along a direction of applied electrical field due to the momentum exchange between atoms and the conducting electrons. Migration of atoms results in metal density depletion or accumulation, which leads to build-up of hydrostatic stresses across the conductor. EM can degrade both global interconnects such as power grid networks and signal wires when the current densities are sufficiently high (about 1MA/cm^2). However, the power grid networks are more susceptible to EM effects due to the conduction of unidirectional currents. The motivations of this project
The site contains the recently developed physics-based predictable EM models for general multi-branch interconnect trees and structures which can consider varying current and temperature stressing for both normal and stream stressing conditions. The new physics-based EM models and full-chip assessment techniques can perform model validation for accurate, yet efficient EM sign-off analysis at design stage and EM-aware reliability management at run time for nanometer VLSI chips.
It consists of three major parts:
The first part is the new physics-accurate EM model was developed for single wire based on the first-principle based stress evolution physics. The work was published in DAC'14 (dac14em_and_ACM.pdf) and TCAD'15 (tcad15_phy_em.pdf). The model can predict the mean time to failure (MTTF) of single wire stressed by constant current dentistry and temperature.
The second part is the second physics-based EM model was an extension of the first EM models (DAC'14) for considering the time-varying current density and temperature. We call it dynamic EM models. The work has been published in ASPDAC'16 (aspdac16em_dyn.pdf).
The third part of the codes consists of the compact EM models for multl-branch interconnect wires. The detailed descriptions are given in the TCAD'16 (tcad16tree-em.pdf) paper shown below.
- Physics-based EM predictable model, which consists of void nucleation phase and void growth phase.
- Consider the time-varying current (power) density and temperature impacts in EM effects
- Compact physics-based EM for multi-branch interconnect wires for the first time. The model * More predictable over different stressing conditions (normal or extreme conditions).
- Consider wire geometry or topology impacts on the EM in addition to the wire width.
time_to_failure.m
TTF (time_to_failure) = t_nuc (nucleation time) + t_grow (growth time)
t_nuc: eq(5)
t_grow: eq(7)
1. constant.m
Stress evolution model with constant current and temperature.
2. random.m
Stress evolution model wth the arbitrary piecewise constant currents (eq(7)).
3. switch_off.m
Stress relaxation after switching off the electric current.
4. periodic_pulse.m:
Stress evolution model for pulsed or bidirectional current loads (eq(8)-(11)).
NOTE: random.m describes the general case. It gets the same results as model 1, model 2 and model 3 provided the same current and temperature waveforms.
1. gfunction.m
Computing the basis function (eq(16)).
2. stress3terminals.m
Computing the stress evolution for the 3-terminal interconnect tree.
3. stressone3terminals.m
Computing the stress evolution along the segment 1 of the 3-terminal interconnect tree (eq17).
4. stresstwo3terminals.m
Computing the stress evolution along the segment 2 of the 3-terminal interconnect tree (eq18).
5. stress4terminals.m
Computing the stress evolution for the 4-terminal interconnect tree.
6. stressone4terminals.m
Computing the stress evolution along the segment 1 of the 4-terminal interconnect tree (eq23).
7. stresstwo4terminals.m
Computing the stress evolution along the segment 2 of the 4-terminal interconnect tree (eq24).
8. stressthree4terminals.m
Computing the stress evolution along the segment 3 of the 4-terminal interconnect tree (eq25).
9. stress5terminals.m
Computing the stress evolution for the 5-terminal interconnect tree.
10. stressone5terminals.m
Computing the stress evolution along the segment 1 of the 5-terminal interconnect tree (eq26).
11. stresstwo5terminals.m
Computing the stress evolution along the segment 2 of the 5-terminal interconnect tree (eq27).
12. stressthree5terminals.m
Computing the stress evolution along the segment 3 of the 5-terminal interconnect tree (eq28).
13. stressfour4terminals.m
Computing the stress evolution along the segment 4 of the 5-terminal interconnect tree (eq29).
In the COMSOL_SRC directory
14. EM_1D_via_branch.mph: the 1D two segment COMSOL analysis code based on the Korhonen's equation and block matieral boundary conditions.
[1] X. Huang, T. Yu, V. Sukharev and S. X.-D. Tan, “Physics-Based
Electromigration Assessment for Power Grid Networks,” in
Proc. Design Automation Conf. (DAC’14), San Francisco, June 2014. [dac14em_ana_ACM.pdf]
[2] X. Huang, V. Sukharev, T. Kim, H. Chen and S. X.-D. Tan,
“Electromigration Recovery Modeling and Analysis under
Time-Dependent Current and Temperature Stressing," in Proc. Asia
South Pacific Design Automation Conf. (ASP-DAC’16), Macao,
Jan, 2016. [aspdac16em_dyn.pdf]
[3] H. Chen, S. X.-D. Tan, X. Huang, T. Kim, V. Sukharev,
“Analytical modeling and characterization of electromigration effects
for multi-branch interconnect trees”, IEEE Transaction on Computer-Aided
Design of Integrated Circuits and Systems (TCAD), (in press) [tcad16tree-em.pdf]