on reliability of microelectronic devices

On Reliability of Microelectronic Devices:An Introductory Lecture on

Negative Bias Temperature Instability

M. A. AlamPurdue UniversityWest Lafayette, IN

Sept. 28, 2005

On Reliability of Microelectronic Devices:

Reliability has always been Important!

A 5000 year old example: Stone vs. Copper tools

A modern example: Honda vs. Yugo

“The car is named Yugo, because it doesn’t …”

Reliability has always been Important!

Microelectronics reliability & viable technologies

Kelly (Bell Labs) to recently-hired Shockley in 1936:

“Instead of mechanical devices, which has annoying maintenance problem, we should look for (reliable) solid state switch ….”

Pauli to his student Peierls, in 1932, on unreliability of Cu2S, Ag2S:

“ Do not work on semiconductors, it is a mess (eine schweinerei); who knows if semiconductor exists at all …..”

Landauer on quantum computing (1992):

“ …. this proposal depends on speculative technology, does not in its current form account all possible sources of noise, unreliability, and manufacturing error, and probably will not work.”

Microelectronics reliability & viabletechnologies

Warranty, Product Recall, and Other Facts of Life

A manufacturer bets the company of the physics of reliability …..

… because the ICs operate in incredibly harsh conditions, turningon and off trillions of timeduring its lifetime ….

… because the lines could open, the source/drain can be shorted, the gateoxide can break ….

Warranty, Product Recall, and Other Facts ofLife

Si-H and SiO2 Bonds

Si-H and SiO2 Bonds

Reliability Issues in Modern Transistors

Initially ….

Drain Voltage

Dra

in C

urre

nt

VG2

VG1GS D

.... a few months later

Broken Si-H bonds: Negative Bias Temperature Instability (NBTI) Hot carrier degradation (HCI)

Broken Si-O bonds: Gate dielectric Breakdown (TDDB)

Reliability Issues in Modern Transistors

Introduction: NBTI defined

GNDVDD

NBTI: Negative Bias Temperature Instability

Gate: GND, Drain: VDD, Source: VDDGate negative with respect to S/D

Other degradation modes: TDDB, HCI, etc.

VDD

Introduction: NBTI defined

VD (volts)

I D (m

A)

before stress

after stress

0 1 2 3 4 0

4

3

2

1

NBTI & Parametric Failure

ΔΣ

Stress Time (sec)

% d

egra

datio

n

101 103 105 107 109

5

10

15

Spec.

War

rant

y

NBTI & Parametric Failure

A Brief History of NBTI

Experiments in late 1960s by Deal and Grove at Fairchild

Role of Si-H bonds and BTI vs. NBTI story (J. Electrochem Soc. 1973;114:266) Came out naturally as PMOS was dominant Important in FAMOS and p-MNOS EEPROMS (Solid State Ckts 1971;6:301)

Theory in late 1970s by Jeppson (JAP, 1977;48:2004)

Generalized Reaction-Diffusion Model Discusses the role of relaxation, bulk traps, ….. Comprehensive study of available experiments

Early 1980s

Issue disappears with NMOS technology and buried channel PMOS

Late 1980s and Early 1990s

Begins to become an issue with dual poly gate, but HCI dominates device reliability

Late 1990s/Early 2000 (Kimizuka, IRPS97;282. Yamamoto, TED99;46:921. Mitani, IEDM02;509)

Voltage scaling reduces HCI and TDDB, but increasing field & temperature reintroduce NBTI concerns for both analog and digital circuits Numerical solution is extensively used for theoretical modeling of NBTI.

A Brief History of NBTI

26 28 30 32 34 36 38 40

100

101

102

TPHY

=36A

Ea=0.49eV

1/kT (eV-1)

D (

arb

. u

nit)

10-3

10-2

10-1

RT

VG=-4.1V

VG=-4.5V

VG=-4.9V

125oC

VG=-3.1V

VG=-3.7V

VG=-4.5V

TPHY

=36A D=1

!NIT

/ [

N1 {

COX

(VG

-VT

)}0.5

] (a

rb.

un

it)

10-3

10-1

101

103

105

107

10-3

10-2

10-1

TPHY

=36AV

G=-4.5V

N1=1

D. t (arb. unit)

RT, T=125oC

T=50oC, T=150

oC

T=90oC

/( ) BEa k T n

ITN t Ae t

!=

n ~ 0.25 Ea ~ 0.5

Exponent and Activation

log( ( )) log( ) (log( ) / )IT BN t n t A Ea k T= + !

Exponent and Activation

A 40-year-old Puzzle …

ln (time)

ln (d

egra

datio

n) T1

T2

Trap Generation

n=0.25 (H diffusion ?) EA=0.5 (H2 diffusion ?)

Before 1980

The exponent is soft (nsat = 0.16) ! NBTI depends on frequency.

ln (time)ln

(deg

rada

tion)

?

Saturation

After 2000

Freq. Dependence

ln (time)

ln (d

egra

datio

n) DC AC

A 40-year-old Puzzle …

A Word about Drawings

Silicon Gate oxide PolySi HSi H

Si H

Si H

Si H

Si H H2

NH

distance

A Word about Drawings

The Reaction-Diffusion Model

Silicon Gate oxide PolySi HSi H

Si H

Si H

Si H

Si H H2

0( ) (0)IT

F IT R H IT

dNk N N k N N

dt= ! !

kF: Si-H dissociation rate const. Creates broken-bond NITkR : Rate of reverse annealing of Si-HN0: Total number of Si-H bonds

2

22

H H IT

H H H

dN d N dND N E

dt dt dt

!µ= + +

NH: Hydrogen densityDH: Hydrogen diffusion coefficientµH: Hydrogen mobility

n=1 n=0

n=1/4

n=1/2

log (time)

log

(NIT

)

NH

distance

The Reaction-Diffusion Model

Meaning of the Parameters

N0 [ ]0

0

/ /

( )

ox F

F F ox

E E E kT

k k p E

e e! " "#

= $

% & % &$ ' (' (

/

0

RE kT

R Rk k e

!"# $= % &/

0

HE kT

H HD D e

!"# $= % &

F

R

k

kSiH h Si H

+ ++ +

oxide

poly

Meaning of the Parameters

A Reformulation of R-D Model

2

22

IT H H

H H H

dN d N dND N E

dt dx dt

!µ= + +

0( ) (0)IT

F IT R H IT

dNk N N k N N

dt= ! !

NH

x

( )H

x t D t=

0( ) ( , )

HD t

IT HN t N x t dx= ! (Neutral)

NH

x

( )H ox

x t E tµ=

0( ) ( , )

H oxE t

IT HN t N x t dx

µ

= ! (Charged)

SiSiSi H

HH

H

H H

H

Si s

ub.

Poly

0 (0)F

H IT

R

k NN N

k

! "#$ %

& '

If trap generation rate is small,and if NIT much smaller than N0, then

( ) ( , , )

0( ) ( , )

H Hx t f D t

IT Hx

N t N x t dxµ=

== !

A Reformulation of R-D Model

NIT with Neutral H Diffusion

0 (0)F

H IT

R

k NN N

k

! "#$ %

& '

NH

x

( )H

x t D t=0

( ) ( , )

1(0)

2

HD t

IT H

H H

N t N x t dx

N D t

=

=

!

10-3

10-2

10-1

RT

VG=-4.1V

VG=-4.5V

VG=-4.9V

125oC

VG=-3.1V

VG=-3.7V

VG=-4.5V

TPHY

=36A D=1

!NIT

/ [

N1 {

COX

(VG

-VT

)}0.5

] (a

rb.

un

it)

10-3

10-1

101

103

105

107

10-3

10-2

10-1

TPHY

=36AV

G=-4.5V

N1=1

D. t (arb. unit)

RT, T=125oC

T=50oC, T=150

oC

T=90oC

SiSiSi H

HH

HH

H

H

Si s

ub.

Poly

Combining these two, we get

10 4( ) ( )

2

F

IT H

R

k NN t D t

k=

n=1/4 even with two sided diffusion

n ∼ 1/4 is a possible signatureof neutral H diffusion

Reproduces results of Jeppson, JAP, 1977.

NIT with Neutral H Diffusion

NIT with Neutral H2 Diffusion

0 (0)F

H IT

R

k NN N

k

! "#$ %

& '

2

2 2

0( ) ( , )

1(0)

2

HD t

IT H

H H

N t N x t dx

N D t

=

=

!


2

10 6( ) ( )

2

F

IT H

R

k NN t D t

k!

( )2

2

2

(0). 2

(0)

H

H

Nconst H H

N=

n ~ 1/6 is a possible signature of neutral H2 diffusion

Small exponent because generation is more difficult.

NH

x

2( )

Hx t D t=

H2

NH

2

SiSiSi H

HH

H2 H2H2

H2

Si s

ub.

Poly

H2

Reproduces results of Chakravarthi, IRPS, 2003.

NIT with Neutral H2 Diffusion

NIT with charged H+ Drift

0 (0)F

H IT

R

k NN N

k

! "#$ %

& '

0( ) ( , )

1(0)

2

H oxE t

IT H

H H ox

N t N x t dx

N E t

µ

µ

=

=

!


( )1

0 2( )2

F

IT H ox

R

k NN t E t

kµ=

NH

x

( )H ox

x t E tµ=

SiSiSi H

H+

H+H+

H+

H+

H+

Si s

ub.

Poly

n ~ 1/2 is a possible signature of charged H diffusion

Rapid removal of H+ by Eox field increase NIT gen. rate.

Reproduces results of Ogawa, PRB, 1995.

NIT with charged H+ Drift

NIT with charge H2+ Drift

n ~ 1/3 is a possible signature of charged H2

+ diffusion

Exponents above 1/3 seldom seen in charge-pumping expt. (uncorrelated to SILC).

0 (0)F

H IT

R

k NN N

k

! "#$ %

& '

20

2

( ) ( , )

1(0)

2

H oxE t

IT H

H H ox

N t N x t dx

N E t

µ

µ

=

=

!

( )2

2

2

(0).

(0)

H

H

Nconst H H H

N

+ += +


( )1

0 3( )2

F

IT H ox

R

k NN t E t

kµ!

NH

2

x

( )H ox

x t E tµ=

SiSiSi H

HH+

H2+

H2+

H2+

H2+

Si s

ub.

Poly

NIT with charge H2+ Drift

Dispersive Diffusion & non-rational nN

H

x

NH

x

*

0( ) ( )2

nF

IT H

R

k NN t D t

k!

0.264-0.2970.33H2+

0.128-0.1440.16H2

0.20-0.250.25H

ndisnideal R-D model predicts n=0.30-0.12

More amorphous oxides for better NBTI

For finite oxides, at very long time all n must be rational (no problem > 10 yrs)

0 0( ) p

HD D t! "

=

NH

x

NH

x

(1 )0 0( )2

n

n pFIT p

R

k N DN t t

k w

!" #$ % &

' (

Shkrob, PRB, 1996; 54:15073

Dispersive Diffusion & non-rational n

26 28 30 32 34 36 38 40

100

101

102

TPHY

=36A

Ea=0.49eV

1/kT (eV-1)

D (

arb

. u

nit)

10-3

10-2

10-1

RT

VG=-4.1V

VG=-4.5V

VG=-4.9V

125oC

VG=-3.1V

VG=-3.7V

VG=-4.5V

TPHY

=36A D=1

!NIT

/ [

N1 {

COX

(VG

-VT

)}0.5

] (a

rb.

un

it)

10-3

10-1

101

103

105

107

10-3

10-2

10-1

TPHY

=36AV

G=-4.5V

N1=1

D. t (arb. unit)

RT, T=125oC

T=50oC, T=150

oC

T=90oC

n ~ 0.25 (H or H2+ diffusion?) Ea ~ 0.5 (H2 diffusion ?)

Puzzle: H or H2 or H2+ ?

/0( ) ( )2

BEa k T nF

IT o

R

k NN t D e t

k

!=

Puzzle: H or H2 or H2+ ?

Clue 1: NBTI Saturation

ln (time)

ln (d

egra

datio

n)

Clue 1: NBTI Saturation

Saturation by Poly Reflection

0 (0)F

H IT

R

k NN N

k

! "#$ %

& '

NH

x

(1)

{ }1

( ) ( ) ( ) (0)2 2

IT H ox H H H

WN t N T D t N W N= + +(2)

( ) ( )

( )

( ) (0) (poly oxH H HH Hpoly

H

N W N N WD D

WD t

!" #= $ %

& '(3)

10-1

100

101

102

103

104

105

10-3

10-2

10-1

T=125OC

TPHY

=36A

EOX

(MV/cm)

7.4

8.8

10.7

VT s

hift (V

)

stress time (s)

122 ( )

(0

( )( ) 2

2

polypolyF ox H

IT ox ox

R

k N T DN t D t T

k D t

! "# + +$ %

$ %& '

Combining, at short time, we get

SiSiSi H

HH

H

H

Poly

H

H

Oxide

{ }1/ 4

( )0( )2

polyFIT H

R

k NN t D t

k!

… but alas, at long time ….

Saturation by Poly Reflection

… but the explanation is wrong

ln (time)

ln (d

egra

datio

n)

NH

distanceKufluoglu, unpublished results

NH

distance

SiSiSi H

HH

Poly

H

H

Oxide

at time t1

at time t2

t1

t2

… but the explanation is wrong

Clue 2: Frequency Dependence

ln (time)

ln (d

egra

datio

n) DC AC

Ming-Fu Li, National University of Singapore, EDL, 2002.

Clue 2: Frequency Dependence

R-D Model at Low Frequencies

stress 1 relax 1 stress 2 relax 2

0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 distance into the Oxide (A)

1014

1015

1016

1017

H2

dens

ity [a

.u.]

time (sec)

2 sec

95 sec

1000 3000 4000

450 sec

NIT

1450 s

1002 s

2002 s

3002 s

3450 s

2450 s

R-D Model at Low Frequencies

Analytical Model: Relaxation Phase

0 10 20 30 401014

1015

1016

1017

Distance [A]

H2 c

once

ntra

tion

[a.u

.] Si oxide

NH

0N

H0(0

)

(Dt0)1/2

(0)

0

(*)

1(0)

2

1(0)

2

IT H H

IT H H

N N D

N N D t

!

"

=

=

0( ) (0)IT

F IT R H IT

dNk N N k N N

dt= ! !

(0) (*)

0 0

(0) (*)

2

0 0 0

H H H

IT IT IT

H H

N N N

N N N

AN BN C

= !

= !

+ + =

(0)

0

11

IT IT

x tN N x

x

!

"

# $ # $= % &' ( ' (

+ ) *) *

Analytical Model: Relaxation Phase

Approximate Analytical Models

Time (sec)

abs

(VT)

Shi

ft (m

V)

100 101 102 103 104 10510

20

30

40

50

0.5x104 1x104 1.5x104

linear plotlog plot

VT = a – bt1/4

New modelNumerical

VT = a – bt1/4

New modelNumerical

Approximate Analytical Models

Frequency Dependence Interpreted

Symmetry in R-D model requires frequency-independent degradation

simulationmeas.

10-1 101 103 105 107

Frequency [Hz]

10

20

30

40

50

0

VT

Shi

ft [m

V]

Frequency Dependence Interpreted

Frequency Independence Interpreted

0 20 40 60 80 100Distance into the Oxide [A]

H2

conc

entra

tion

[a.u

.]

100

104

108

1012

1016

1020

High Freq

Low Freq

Low Frequency (1 cycle)

High Frequency (1 cycle)


R-D model anticipates Frequency Independence!

0 20 40 60 80 100Distance into the Oxide [A]

H2 co

ncen

tratio

n [a

.u.]

100

104

108

1012

1016

1020

High Freq

Low Freq

100/200 cycle

200/400 cycle



Measurement: A variable-frequency AC Stress!

1s 10s 100s 1000s Stress time

What we thought we were doing …

S. Rangan, Intel, IEDM 2003.

6s 21s 126s 1031s Stress time

What we were actually doing …

* 5 sec. measurement window (for example).

Measurement: A variable-frequency ACStress!

R-D Simulations for DC NBTI

Actually, n=0.16 at all times (H2 diffusion), measurement delay makes itappear n=0.25 at short times. A 40 year old puzzle finally resolved!

H. Kuflouglu,unpublished results

R-D Simulations for DC NBTI

AC NBTI: Sim. & Measurement

Only DC simulations are fit toexperimental data (VG=2.1V).

AC simulations are inherentlyrelated to DC results

Delay of 6.3 sec is used

AC NBTI: Sim. & Measurement

Conclusive Confirmation

100

101

102

103

10-2

10-1

t-delay

-VG(meas)

-VG(stress)

EOT=21.4AO, Dose=5.54x10

15cm

-2

On-the-fly

delay=50ms

T=50OC

VG=-3.0V (stress)

-VG(meas) / n

3.0V/0.138

1.5V/0.162

1.0V/0.189

stress time (s)

!VT

(V

)

100

101

102

103

Delay

50ms

350ms

Delay Idlin, VG=-3.0V (stress)

VG=-1.5V (measure)

T=150OC

T=50OC

slope:

0.162, 0.189

0.177, 0.211

D. Varghese,IEDM 2005

Conclusive Confirmation

Conclusions

Reliability is, has been, and will be a key consideration for a viable technology.

Over the last fifteen years, reliability engineering (a collection of pragmatic, empirical rules) have gradually evolved into reliability physics (grounded in sound understanding of underlying physics).

In this talk we considered NBTI, similar physical models exist for Hot carrier degradation and Time dependent dielectric breakdown.

The NBTI model provides proper prescription of extrapolating device lifetime. We will consider these extrapolation methods in a separate talk.

Finally, do not underestimate the power of simple models. What we did in 4/5 lines of algebra, is actually equivalent to tens of PRB, JAP, TED, EDL papers over last 30 years.

Conclusions

Collaboration and References

[1] Mahapatra and Alam, IEDM 2002, p. 505.[2] Mahapatra, Kumar, & Alam, IEDM 2003, p. 337.[3] Mahapatra et al. IEDM 2004, p. 105.

[1] Alam, Weir, & Silverman, IWGI 2001, p. 10. [2] Alam, IEDM 2003, p. 346.[3] Kufluoglu & Alam, IEDM 2004, p. 113.

Experiments: S. Mahapatra, S. Kumar, D. Saha, D. Varghese, IIT

Theory: M. Alam, H. Kufluoglu, Purdue University

• For convenience, most of the figures of this talk are taken from these references. I will use other figures to illustrate difference in opinions or to generalize results.

Collaboration and References

Questions & Answers

on reliability of microelectronic devices

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