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