### pptx - UCSD VLSI CAD Laboratory

```Post-Routing BEOL Layout
Optimization for Improved TimeDependent Dielectric Breakdown
(TDDB) Reliability
Tuck-Boon Chan and Andrew B. Kahng
VLSI CAD LABORATORY, UC San Diego
VLSI CAD Laboratory, UC San Diego
-1-
Outline
TDDB Reliability
 Our work: reducing TDDB Margin

– Signal-aware TDDB Analysis
– Post-routing Layout Optimization

Experimental Results and Conclusions
-2-
Motivation

Time-dependent dielectric breakdown (TDDB)
– A dielectric forms a conductive path between the
interconnects due to electrical stress  chip functional error!

Breakdown time, tf α exp (-γEm) [Zhao11]

Electric field (E) across dielectric is increasing [ITRS2011]
E increases linearly 
tf reduces, TDDB risk
TDDB reliability limits (1) wire
density and/or (2) max. voltage
-3-
Via-to-Wire Spacing is Critical

Dielectric btw. via and wire is most susceptible to TDDB

Small spacing is further reduced by mask misalignment
between via and wire

Smaller spacing  higher electric field  shorter lifetime
-4-
Our Work (1)

A chip-level TDDB reliability model
– Enable signal-aware TDDB analysis
-5-
TDDB Model

Dielectric breakdown time is modeled as a Weibull
distribution [Bashir10]
Failure probability
Fij(t) = 1 – ( exp(-t/nij )β )
Weibull shape factor
nij = A  exp(-γ(V/Sij)m )
Supply voltage
Spacing
-6-
Chip Level TDDB Reliability

Apply Poisson area-scaling law to estimate chip failure rate
Fchip(t) = 1 – ( exp(-t  H-1  G)β )
[Bashir10]
G = Σij [ αij  exp(-t  γ(V/Sij)m) (Lij)1/β ]
Stress factor: probability of
interconnects being stressed
viai
Sij
wirej
Lij
-7-
Signal-Aware Analysis



Typical TDDB analysis assumes interconnects are under “DC
stress”  too pessimistic!
Obtain stress factors by running cycle-accurate logic
simulation  too slow
Proposed method: Use state probability from vector-less
logic simulation  much faster
-8-
Our Work (2)

Post-route layout optimization
– Shift wire edges around vias to increase via-towire spacing
– Negligible effect on circuit timing
 Does not require additional design iterations
 Applicable at post-route or mask writing
-9-
Post-Routing Layout Optimization
Inputs
TDDB analysis
and layout
optimization
flow
Design
Netlists
State
probability
Signal-aware
analysis
(optional)
Original
Layout
Calculate
TDDB
reliability
Layout
optimization
Alternative
layout
implementation
Original layout
+ Marker
layers
Modified
layout
-10-
Defining Segments for Perturbation
via
Define movable
edges for layout
optimization
wire
TDDB critical
region
Shift this edge to
increase spacing
Shift this edge to
preserve wire width
Overlapped
region
-11-
Shifting Wire Edges

Shift wire edge to increase via-to-wire spacing

Shifting is not applied if it violates via enclosure rule
-12-
Experiment Setup




4 Benchmark circuits
Synopsys 32nm library
160nm metal pitch
Analyze TDDB on M2, M3 & M4
Layout Parameters
Values
TDDB Model
Parameters
Values
Min. wire spacing
80nm
β
1.0
Min. wire width
80nm
ɣ
49 (nm/V)0.5
Min. via-to-wire spacing
80nm
m
0.5
Via width
70nm
V
1.0V
Via-to-wire spacing variation
5nm
H
1.6 х 1019 snm
Max. wire edge shift
4nm (5%)
Wire segment width
95nm
-13-
Layout Optimization Results

Layout optimization

Signal-aware analysis
-14-
Timing Impact of Layout Optimization



40% of nets are modified
ΔR per net < 0.3 Ω, ΔC per net < 0.1 fF,
Average gate-worst Δdelay = 0.012ps,
– Add total ΔC at driver’s output pin

Average wire-worst Δdelay = 0.012ps
– Add total ΔR at driver’s output pin
Δ Res.
(Ω)
Δ Cap.
(fF)
Max.
Max.
Max.
Avg.
Max.
Avg.
8.0k
0.088
0.046
0.793
0.017
0.969
0.018
29k
9.4k
0.143
0.083
0.615
0.007
0.600
0.007
MPEG2
10k
3.4k
0.144
0.056
1.578
0.012
1.580
0.012
SPARC_ECU
15k
7.0k
0.246
0.076
0.649
0.011
1.090
0.011
Average
17k
7k
0.155
0.065
0.909
0.012
1.060
0.012
Total
nets
Opt.
nets
AES
14k
JPEG
Gate-wost
Δ Delay (ps)
Wire-worst
Δ Delay (ps)
-15-
Conclusions

TDDB is a reliability issue for BEOL
– Limits pitch scaling and/or supply voltage

Signal-aware TDDB analysis  2X chip lifetime

Post-routing layout optimization  +10% chip
lifetime with negligible impact on timing
-16-
Thank you!
-17-
References

[Achanta06] R. S. Achanta, J. L. Plawsky and W. N. Gill, "A Time Dependent Dielectric
Breakdown Model for Field Accelerated Low-k Breakdown Due To Copper Ions”, AIP
Applied Physics Letters 91 (23) 2006, pp. 234106-1 - 234106-3.

[Bashir10] M. Bashir and L. Milor, “Towards a Chip Level Reliability Simulator for
Copper/Low-k Backend Processes”, IEEE Design Automation and Test in Europe, 2010,
pp. 279-282.
[Berman81] A. Berman, “Time-Zero Dielectric Reliability Test By a Ramp Method”, IEEE
Intl. Reliability Physics Symposium, 1981, p. 204.





[Chen06] F. Chen, O. Bravo, K. Chanda, P. McLaughlin, T. Sullivam, J. Goill, J. Lloyd, F.
Kontra and J. Aitken, “Comprehensive Study of Low-k SiCOH TDDB Phenomena and Its
Reliability Lifetime Model Development”, IEEE Intl. Reliability Physics Symposium,
2006, p. 46.
[Lee88] J. Lee, I. C. Chen, and C. Hu, “Modeling and Characterization of Gate Oxide
Reliability”, IEEE Intl. Reliability Physics Symposium, 1988, p. 2268-2278.
[Lloyd05] J. R. Lloyd, E. Liniger, and T. M. Shaw, “Simple model for time-dependent
dielectric breakdown in inter- and intralevel low-k dielectrics”, AIP Journal of Applied
Physics 98, (084109) (2005), 084109-1 – 084109-6.
[Zhao11] L. Zhao, Z. Tőkei, K. Croes, C. J. Wilson, M. Baklanov, G. P. Beyer, and C.
Claeys, “Direct Observation of the 1/E Dependence of Time-Dependent Dielectric
Breakdown in the Presence of Copper”, AIP Applied Physics Letters 98 (03) (2011), pp.
032107-1 - 032107-3.
-18-
```