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Physical Models for BEOL Reliability in Nanoelectronic Devices
Jim Lloyd
SUNY Polytechnic Institute
Albany, NY USA
Martin Gall
Fraunhofer IKTS
Dresden, Germany
BEOL Failure Mechanisms
• Electromigration– A lot of history
– 50 years of study
• Stress Voiding– Creep
– Not unrelated to above
• TDDB in ILD– Significant with low-k
dielectrics+
-
Electromigration
• First identified ~1966
– “Cracked Stripe” problem
– Ilan Blech and Jim Black
Black Equation
t AjH
kT50
2
exp
J.R. BlackProc. 6th Ann. Int'l. Reliab. Phys. Symp., 148 (1967)
The most important paper in electromigration technology
Black’s Law
Generalized Black’s Law
kT
HAjt n exp50
Has units problems with fractional n
Often fractional n values are reported in the literature and
stated as a property of the material.
Actually measured n is a function of the material
and geometry and therefore the test structure.
Sequential EventsNucleation then Growth Diffusion
Nucleation
Pure nucleation is n=2 behavior
Growth
Pure growth is n=1 behavior
kT
H
j
AkT
j
TBttt gnuc exp
)(250
0 1 2 3 4 5 6 7
0
100
200
300
400
500
600
700
800
900
1000
A (weak) 143 ±38
B (weak) 61 ±26
A (strong) 453 ±38
B (strong) 56 ±27
Me
dia
n T
ime
to
Fa
ilure
(h
rs)
Current (mA)
Times to nucleation were similar
Weak mode growth times were1/3 that for strong mode
Delamination• The stress gradient in the chemical potential is the gradient in the
hydrostatic (sh) component of the stress
• The criterion for failure is the creation of a delamination which is
dependent on reaching a critical normal stress (sn) and the adhesion
at the interface where the delamination will occur determined by the
energy release rate.
hkT
jezF s
*
hE
Gn
n
2
2s
02
2
hE
G nad
s
46x
s
sh
sn
sdelam
Run 1 (EAA) DUT 19
R/Ro =2%, 302 hr.V1
M1
x
s
sh
sn
sdelam
Strong and Weak Modes
A Simple Extension
h
EGaddelam
2s
For Copper Gad = ~ 1.5 J/m2
For Aluminum Gad= ~ 25 J/m2
The relative jL (Blech) products for Al and Cu will be directly
proportional to the relationship above. If we assume
that the modulus will vary with the moduli of the metals
we get a ratio of the Blech products of ~ 3.
Assuming equal z*
Add Stress Migration to the Equation2
exp)(
jkT
HkTTt n
n
s
)2
0exp)(
j
TTE
kT
HkTTt n
n
s
Korhonen
Korhonen with thermal stress
For growth only when thermal stress provides void
nucleation the “n” value is one.
It is predicted that “n” will be a function of temperature, becoming smaller at lower
temperatures.0,5
1
1,5
2
2,5
150 200 250 300 350 400
T [°C]
Fraunhofer IKTS/GLOBALFOUNDRIESJoint Project Data
Activation Energy• Measured activation energy
• Considering nucleation, growth and thermal stresses
T
tkH
f
app 1
ln
Experimental Needs to Check Inter-Dependencies:Large Temperature and Current Density Matrices
Electron flow
(a) j [mA/um2] (b) j [mA/um2] (c) j [mA/um2]
41.2 27.5 13.7 6.9 3.4 41.2 27.5 13.7 6.9 3.4 41.2 27.5 13.7 6.9 3.4
T [°C
]
350 x
T [°C
]
350 x x x x
T [°C
]
350 x x x x x
300 x x x 300 x x x x x 300 x x x x x
275 275 275 x x x x
250 x 250 x x x x x 250 x x x x
225 225 225 x x x
200 200 x x x x x 200
Single Links WSB pure Cu WSB Cu(Mn)
Downflow testing, nucleationstress under the via critical
Standard testing will notsee any inter-dependencies:Just one activation energyand one current densityexponent.
n = f(T)
H = f(j)
~ 0.25 Mio Vias ~ 0.25 Mio Vias
Monitoring the resistance imbalance R as a function of time
A change in the imbalance correlates with failure void formation in one of many interconnects. The resistance imbalance change is readily detectable and about equally up- and downward.
R
M. Gall et al., ADMETA Japan Session 2009; M. Hauschildt et al., J. Appl. Phys. 108, 013523 (2010), and M. Gall et al., J. Appl. Phys. 108, 013524 (2010)
Time [a.u.]
Wheatstone Bridge EM Testing
Simultaneous testing of4 x 270 = 1080 interconnects
1000.0100.010.01.00.1
99
95
80
50
20
5
1
0.01
0.0001
TTF [a.u.]
Pe
rce
nt
Single Link Structures
20-Link Structures
WSB Structures
Probability Plot for TTF V1M1 [h]
Censoring Column in censor V1M1 - ML Estimates
Lognormal
The lifetime distributions of differently sized test structures line up well. An early fail tail is clearly visible which is not easily detectable with single links. The application of WSB devices enables “deep censoring“ in the very early failure
regime. The method is extremely efficient also in terms of testing time, up to 10x faster.
Results and Comparison withStandard Testing
1000.0100.010.01.00.1
99
95
80
50
20
5
1
0.01
0.0001
TTF [a.u.]
Pe
rce
nt
Loc 5.09396
Scale 1.00236
Mean 269.434
StDev 354.506
Median 163.034
IQ R 237.631
Failure 81
C ensor 26468
A D* 40.972
Table of Statistics
Probability Plot for TTF V1M1
Censoring Column in censor V1M1 - ML Estimates
Lognormal
Model Prediction and Experimental Data for n (pure Cu)
Under the assumption that the nucleation term has a square-dependence on the threshold stress,
the temperature range up to
300C can be well-described,
but slight deviation at 350°C.
Best fit to the data suggest a nucleation stress of ~340 MPa. This stress coincides with the thermal stress at about 50°C.
20 ))(
)(exp(j
TTE
kT
HkTt n
n
s
Simulation of Stress under the Via at 50°C
~ 385 MPa
(about 13% off)
Analysis of “Apparent“ ActivationEnergies
Due to longer testing times at lower current densities, the thermal stress effects are also able to influence the measured activation energy.
The energy barrier H is lowered and can be described by an apparent or effective activation energy:
Using this equation, the change in Has a function of current density is well-described.
40nm technology
HH
H
Comparison of 40 and 28nm Technologies
The activation energies for 40nm and 28nm with Cu(Mn) integration are nearly identical and show a very similar decrease at low j (also better confidence levels at 28nm).
40nm technology
HH
H
0,4
0,6
0,8
1
1,2
1,4
0 10 20 30 40 50
Ea, apparent
Cu(Mn)
j [mA/µm2]
28nm technology
H
[eV
]H, app
Impact on Extrapolations: Statistical Distributions and Binning
1
10
100
1000
104
105
106
0 0.2 0.4 0.6 0.8 1
N(S)
S
During chip operation, a wide statistical distribution of current levels across billions of contacts, vias, and interconnects exists: binning is necessary, N(S) = amount of links at stress factor S (maximum design current is S = 1).
Statistical EM Budgeting (SEB) needs to be performed to assess the chip reliability (*M. Gall et al., Stress Workshop 2004), plus binning approach
Stress factordistribution at M1*,
S = Idc/Imax
TDDB in low-k ILD
• Observation
– Low-k Interlevel Dielectrics (ILD) have shorter lifetimes as compared to SiO2 based ILD
– Behavior did not obey traditional extrapolation models
• E model and 1/E model did not fit well
• Configurations all included Cu metallization– Cu diffuses readily even through SiO2, it just zips through low k dielectrics
• Uncertain whether short lifetime due to ILD or Cu or both
To E or not to E
0 1x106
2x106
3x106
4x106
5x106
1E-5
100000
1E15
1E25
1E35M
TF
Field
Impact Model
Square Root Model
E Model
TDDB of Interlevel Dielectrics
• ILD fundamentally different than gate oxides
– Gate dielectrics obey the McPherson E model quite well, especially at low accelerations
– ILD TDDB was shown to deviate significantly from E model
– Root-E model et al.
– Power Law Model and “Lucky Electron” Impact Damage Models appear to fit the data best
• Over testing lasting more than 3 years under stress
Power Law TDDB
• First applied to very thin gate oxides
– Seems to fit the data over large spreads in lifetime
• Several orders of magnitude
tf = AV -n
Impact Damage (Lucky Electron) Model
l Is the distance to where the collision takes place - +
e-
*
If there is enough energy a “trap” or
some type of damage that promotes
failure is created
Note that this type of model implies a threshold. The maximum energy possible to create a “trap” is eV where V is the applied voltage.
Time to Failure
exp
0
A
NNt
f
f
Which basically states that for testing conditions we will obey Root-E kinetics
but at use conditions the kinetics will be All models are indistinguishable at high (test) fields
But better represented by 1/E kinetics at low (use) fields
If this is right, this is very good news
Chasing after the Physical Mechanism:In Situ Observations
Millions of vias and meters of nanoscale Cu lines Difficult to predict and find the failure site for
ex-situ imaging
O. Aubel, IEEE International Reliability
Physics Symposium Tutorial (2011)
Post-breakdown in TEM
Minor information on thedamage mechanism anddegradation kinetics
Tip-to-tip structure
TEM In-situ imaging and chemical
analysis Damage mechanism and
degradation kinetics
(a) SiCN
Cu TaN/Ta
Ultra-low k
SiO2
CoWP
Pad
(b)
a)
M2
V1
M1
OSG
SiCN
Courtesy: Hystron Inc. (TEM holder) and Carl Zeiss Inc. (TEM)
Zeiss LIBRA 200 MC Cs
• 200/80 KV analytical TEM• Cs probe-corrected• Monochromator (corrected)• Omega spectrometer for EELS; EDX• Energy resolution ~ 0.15 eV• STEM resolution (HR) ~ 0.12 nm
b)
c)
d)
e)
PI95 Hysitron TEM holder
Keithley 237f)
Tip-to-tip structure
H-bar sample in SEM
Setup in the TEM
(a) (b) (c)
(d) (e) (f)
PositivePositivePositive
• Intact TaN/Ta barrier is
crucial, otherwise
massive diffusion of Cu
through the dielectric
(Type I).
• Most pristine samples
show degradation of
dielectric until
breakdown occurs
under the M1 SiCN top
layer (Type II).
• Some pristine samples
also show degradation
of SiO2 under M1 and
breakdown at that
location (Type III).
Failure Modes and Damage Mechanisms
Type I Type II Type III
Searching for Cu (EELS after Breakdown)
• No indication of Cu traces in brightfield TEM images
• Si and N maps show the breakdown of OSG occurred below SiCN
• Trace Cu bridge along the SiCN/OSG interface could be seen clearly
Cu signal
50 nm
Tomography in the TEM
• In all tested samples, dissolution effects on the positively charged tip side
were observed: The TaN/Ta barrier “vanishes“ at the bottom corner of M1,
followed by out-diffusion of Cu nanoparticles.
• Unexpected mechanism, pointing to importance of process control at that
critical location.
Summary• Contrary to widely accepted assumptions, the EM current density
exponent n is not a constant, but changes with temperature. Extrapolations to use conditions are therefore complex, and effectivevalues need to be set.
• The same is true for the EM activation energy H. At low currentdensities, a significant drop of about 0.1 to 0.2 eV has beenmeasured, consistent with the proposed model. A binning approachin conjunction with Statistical EM Budgeting (SEB) is proposed forcorrect extrapolations.
• Until today, the correct model for BEOL TDDB is not set and the conservative SQRT(E) model is widely used. Most recent data indictethat the “Lucky Electron“ and Power Law models describe long-term TDDB data the best, indicating a good reliability margin.
• The role of Cu still needs to be accounted for as in situ experimentation indicates various diffusion processes at criticallocations in the BEOL stack. More work needs to be done here toevaluate the sequential processes of dielectric damage and Cu diffusion.
Acknowledgments
Thomas Shaw, Eric Liniger, Bob Rosenberg, C.K. Hu (IBM), Michael Lane (Emory and Henry College), and Brian McGowan(Fairchild Semiconductor)
Matthias Kraatz, Christoph Sander, Zhongquan Liao, Yvonne Standke, Rüdiger Rosenkranz, Uwe Mühle, Jürgen Gluch, andEhrenfried Zschech
Meike Hauschildt, Kong Boon Yeap, Georg Talut, Oliver Aubel, Armand Beyer, Christian Hennesthal, Frank Jentsch, and Rico Kühnel
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