IRPS 2005 Tutorial onNegative Bias Temperature Instability

Muhammad A. Alam Basic modeling (1:30 - 3:00 pm)

Anand T. Krishnan Process/Circuits (3:30 - 5:00 pm)

Part I: Basics and Models (Muhammad A. Alam)

Introduction: NBTI defined and a brief history of NBTI NBTI degradation kinetics Nature of NBTI precursor and created traps Voltage and temperature acceleration Statistical aspects Recovery and frequency dependence

Part II (Anand T. Krishnan)

Process dependency (a) Nitrogen (b) Fluorine (c) Other  Device impact (GM,VT, ION, IOFF, CGD,mobility etc.) Circuit impact Scaling impact Conclusion 

Broad Outline of the Tutorial

Negative Bias Temperature InstabilityBasics/Modeling

Muhammad A. AlamPurdue UniversityWest Lafayette, INalam@purdue.edu

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, IIT Bombay

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.

Introduction: What is NBTI all about ?

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

VD (volts)

I D (

mA

)

before stress

after stress

0 1 2 3 4 0

4

3

2

1

NBTI Degradation and Parametric Failure

Stress Time (sec)

% d

eg

rad

ati

on

101 103 105 107 109

5

10

15

Spec.

War

rant

y

Rationale of 10% Criterion: Process, Reliability, Design

So we do not have too much margin, especially during the ramp-up period of manufacturing ….

IDID,nom

+15%-15%t=0

-5%

Process

Design

t=10 yr

-10%

IC Failure

A Brief History of NBTI: And it does have a history!

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.

The Need for NBTI Theory and Measurements

ln (time)

ln (

deg

rad

ati

on

) Vstress

Vop

10 yr

Trap Generation

Time Exponent

Voltage Acceleration

ln (time)ln (

deg

rad

ati

on

)

?

Saturation

Hard/soft saturation

Extrapolation

Relaxation

Physics of relaxation

Freq. Dependence

ln (time)ln (

deg

rad

ati

on

) V=high, f=low

V=low, f=high

Before 1980 After 2000

Three Issues of NBTI

Time Dependence

Geometry-dependent NBTI exponents H vs. H2 diffusion Charged or neutral species Temperature-dependent exponents and anomalous diffusion

Saturation Characteristics

Soft saturation due to interfaces/lock-in Hard Saturation and stretched exponentials Frequency Dependence

Low frequency High frequency

Three Issues of NBTI

Time Dependence

Geometry-dependent NBTI exponents H vs. H2 diffusion Charged or neutral species Temperature-dependent exponents and anomalous diffusion

Saturation Characteristics

Soft saturation due to interfaces/Lock-in Hard Saturation and stretched exponentials Frequency Dependence

Low frequency High frequency

The Reaction-Diffusion Model

Silicon Gate oxide PolySi H

Si H

Si H

Si H

Si H

Si H H2

0( ) (0)ITF 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

2 2H H IT

H H H

dN d N dND N E

dt dt dt

NH: Hydrogen densityDH: Hydrogen diffusion coefficientH: Hydrogen mobility

n=1 n=0

n=1/4

n=1/2

log (time)

log

(N

IT)

NH

distance

The meaning of the Parameters

N0 0

0

/ /

( )

ox F

F F ox

E E E kT

k k p E

e e

/0

RE kTR Rk k e

/0

HE kTH HD D e

0/

/ 20 0 00

0

F RH

ox

E En E kTn E En nF F

IT H HR R

k N k NN D t D pe e t

k k

Time-dependenceTemp-dependenceField-dependence

F

R

k

kSiH h Si H

oxide

poly

Field Dependent Problem ?

10-1

100

101

102

103

10410

-4

10-3

10-2

10-1

T=25OC

TPHY

=26A

stress time (s)

No

rma

lize

d I D

sh

ift (

at

VG-V

T=0

.7V

)

PI -3.2V NA -3.2V NA -4.2Vp p

n

3.2 V

n np

4.2 V

0( ) (0)ITF IT R H IT

dNk N N k N N

dt

2

2 2H H IT

H H H

dN d N dND N E

dt dt dt

Indeed it is, therefore at least we are headed in the right direction ….!

Note 1: Many Phenomenological Models: All Approximations to R-D Theory!

Diffusion Limited Reaction-Diffusion Model (R-D)

• Jeppson, JAP 1977; 48: 2004 Single region, simple analytical solution• Ogawa, PRB, 1995; 51: 4218 Detailed analytical solution]• Alam, IWGI 2001; 10 Multi-region analytical/numerical• Alam, IEDM 2003; 346 Freq. Dependence: analytical/numerical• Kufluoglu & Alam, IEDM 2004. Geometrical aspects: numerical/analytical• Chakravarthi, IRPS 2003. H2 exponents

Drift Limited Stretched Exponential Model (S-E)

• Blat, JAP, 1991; 69:1712.Simple exponential• Kakalios, PRL,1987; 1037 Dispersive diffusion• Sufi Zafar (VLSI 2004) Derivation for Stretched Exponential

Bond-dissociation limited Reaction Model (B-D)

Hess (IEDM00), Penzin (TED03) Power-law, multiple exponents

Note2: R-D Model is a phenomenological Model

0( ) (0)ITF IT R H IT

dNk N N k N N

dt

2

2 2H H IT

H H H

dN d N dND N E

dt dt dt

0

oxD A

s

dE qp n N N

dx

2

2p p ox

dp d p dD p E

dt dx dx

2

2n n ox

dn d n dD n E

dt dx dx

R-D model for NBTI is analogous to Drift-diffusion model for devices

(1) We need not know the micro- scopic physics of kF and kR, DH, H to understand the features of NBTI, ….

... just as we do not need to know themicroscopic physics of Dn, Dp, n, p, s, etc. to understand the operation of bipolar transistor and MOSFETs.

(2) All we need, is just a fewdetailed-balance relationshipslike how kF and kR are related, …

….. just as all we need for DD equations is detailed-balance relationship like Einstein relationship.

(3) First principle calculations involvingnature of traps, physics of diffusion, etc. help illuminate the physics of the coefficients and is very useful, ….

…. just as detailed analysis of scattering based on Fermi Golden rule or dielectricresponse help illuminate the physics of mobility and diffusion.

Note 3: R-D Model applies to Si-H Bonds only

NIT by charge pumping = Broken Si-H bond + broken Si-O bond

Signature of bulk Si-O bonds …… Stress Induced Leakage CurrentOnly part of (identified by CP) that is not correlated to SILC should be compared to the predictions of Reaction-Diffusion Model

Total VT shift = contribution from Si-H bonds (R-D Model) + contributions from Si-O bonds at bulk & interface (AHI model)

Si-O bonds Si-H bonds

SILC

CP

Note 4: Relaxation and Time Exponents

102

101

100

10-1

103 109105 107101

Time (sec)

VT

Shi

ft

(mV

) Apparent exponent

Real Exponent

R-D model predictions to be compared with “real exponent” which is smaller than “apparent exponent”.

Nit = Atn

ln (Nit) = ln (A) + n ln(t)

A Reformulation of R-D Theory for Analytical Modeling

2

2 2IT H H

H H H

dN d N dND N E

dt dx dt

0( ) (0)ITF IT R H IT

dNk N N k N N

dt

NH

x

( ) Hx t D t

0( ) ( , )

HD t

IT HN t N x t dx (Neutral)

NH

x

( ) H oxx t E t

0( ) ( , )

H oxE t

IT HN t N x t dx

(Charged)

Si

Si

Si H

H

HH

H H

H

Si s

ub.

Pol

y

0 (0)FH 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 HxN t N x t dx

Trap Generation with Neutral H Diffusion

0 (0)FH IT

R

k NN N

k

NH

x

( ) Hx t D t0

( ) ( , )

1(0)

2

HD t

IT H

H H

N t N x t dx

N D t

10-3

10-2

10-1

RTVG=-4.1VVG=-4.5VVG=-4.9V

125oCVG=-3.1VVG=-3.7VVG=-4.5V

TPHY

=36A D=1

NIT /

[N

1 {C

OX(V

G-V

T)}0.

5 ] (a

rb.

unit)

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=150oC

T=90oC

Si

Si

Si H

H

HH

HH

H

Si s

ub.

Pol

yCombining these two, we get

10 4( ) ( )

2F

IT HR

k NN t D t

k

n=1/4 even with two sided diffusion

n 1/4 is a possible signature of neutral H diffusion

Reproduces results of Jeppson, JAP, 1977.

Trap Generation with Neutral H2 Diffusion

0 (0)FH 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

Combining these two, we get

2

10 6( ) ( )

2F

IT HR

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

Si

Si

Si H

H

HH2 H2

H2

H2

Si s

ub.

Pol

y

H2

Reproduces results of Chakravarthi, IRPS, 2003.

Trap Generation with charge H (Proton) Diffusion

0 (0)FH 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

Combining these two, we get

1

0 2( )2F

IT H oxR

k NN t E t

k

NH

x

( ) H oxx t E t

Did not find any such NIT vs. time result

Si

Si

Si H

H+

H+

H+

H+

H+

H+

Si s

ub.

Pol

y

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.

Trap Generation with charge H2+ Diffusion

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)FH 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

2

2

2

(0).

(0)H

H

Nconst H H H

N

Combining these two, we get

1

0 3( )2F

IT H oxR

k NN t E t

k

NH

2

x

( ) H oxx t E t

Si

Si

Si H

H

H+

H2+

H2+

H2+

H2+

Si s

ub.

Pol

y

Dipersive Diffusion: explanation of non-rational nN

H

x

NH

x

*

0( ) ( )2

nFIT H

R

k NN t D t

k

nideal ndis

H 0.25 0.20-0.25

H2 0.16 0.128-0.144

H2+ 0.33 0.264-0.297

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( ) pHD D t

NH

x

NH

x

(1 )0 0( )2

nn pF

IT pR

k N DN t t

k w

Shkrob, PRB, 1996; 54:15073

Theory of Standard Diffusion: N

H

x

NHf

NH

StandardDistribution

Real-Space Energy-Space Real Distribution

0 0

2

( ) ( ) ( ) ( )f f f fH H H HIT

D N x dx N x D N x dx N xdN

dt x

2 2

0 2 2

fIT H H

H

dN d N d ND D

dt dx dx

0HD D

No Temperature Activation

Theory of Activated Diffusion: N

H

x

0 0* exp( / ) exp( / )BH B

T

ND D Ea kT D Ea k T

N

NHf

NHb

NH

StandardDistribution

Real-Space Energy-Space Real Distribution

2

0 2

fIT HdN d N

Ddt dx

/ /

exp( / )

f bH B H TN N N B N

B Ea kT

/ [ /(1 )]

~ exp( / ) /

fH H B T

H B B T

N N N N B B

N Ea k T N N

2

2IT H

H

dN d ND

dt dx

with

0 exp( / )HD D Ea kT

Theory of Dispersive Diffusion:

Real-Space Energy-Space

( )

( )

/ /

exp( / )

f b iH B H i T

ii a B

N N N B N

B E k T

01 /0 (1/ ) Bk T E

HD D t

……

0/ /( ( )

exp( ( ) / )

f bH B H M M

M M B

N N N B E g E

B E t k T

M

Moment-Space

0

exp( ( ) / )( )

f b HH H M B

M

NN N E t k T

E g E

1/ log( / )M Bt v E k T

0 0( ) ( / ) exp( / )Tg E N E E E

2

0 2

fIT HdN d N

Ddt dx

2

2IT H

H

dN d ND

dt dx

01 /0 (1/ ) Bk T E

HD D t

ln

(N

IT)

ln (time)

ln (

NIT) T1 T2

ln (time)

ln (

NIT)

T1

T2

ln (time)

ln (

NIT) T1

T2

ln (time)

2 exp( / )HA

T

NE kBT

N

0

1

3

1Bk T

E

vt

4 3 0

2 0

(0 )

( )

t t

t t

1H

T

N

N

.AE const

0 aE

0 a AE E

H, H2, (H2+) ?

Ea suggest diffusion of neutral H2

assumption*,

if we can assume EF-ER is small, can we ?

M. L. Reed, JAP, p.5776, 199826 28 30 32 34 36 38 40

100

101

102

TPHY

=36A

Ea=0.49eV

1/kT (eV-1)

D (

arb.

uni

t)

0/

/ 20 0 00

0

F RH

ox

nE EE kTn E E nnF F

IT H HR R

k N k NN D t pe D e t

k k

( )( )

2F R

a H H

E EE D E

n

Conclusions: Trap Generation Rate

ln (time)

ln (

deg

rad

ati

on

) Vstress

Vop

10 yr

Trap generation is well-described by a power-law, consistent with reaction-diffusion model. These are robust power-laws correct for many decades in time.

The analytical methodology presented is universally consistent with numerical solution of R-D model. In fact, this even work for 2D and 3D solutions (Kuflouglu, IEDM 2004).

Reaction-diffusion model predicts generation exponent in the range of 0.3-0.12

However, only rational exponent n=0.33,0.25,0.16 corresponding to H2+, H2, and H are robust. Other n improve IC lifetime, but should be used carefully.

NBTI activation energy of 0.12 eV suggests that the diffusing species may be neutral H2.

The most probable form of field dependence is sqrt(Eox)exp(-Eox/kT). NBTI is field dependent, but does not depend on voltage explicitly.

Three Issues of NBTI

Time Dependence

Geometry-dependent NBTI exponents H vs. H2 diffusion Charged or neutral species

Saturation Characteristics

Soft saturation due to interfaces/Lock-in Hard Saturation and stretched exponentials Frequency Dependence

Low frequency High frequency

ln (time)ln (

deg

rad

ati

on

)

Hard-Saturation in R-D Model: Stretched Exponential Limit

0( ) (0)ITF IT R H IT

dNk N N k N N

dt

0( )(0)F IT

H ITR

k N NN N

k

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

2

2 2IT H H

H H H

dN d N dND N E

dt dx dt

0(0)IT H H F ITH

R ITH

dN N D k N ND

dt t k ND t

22

0 0

ln 1 22

IT IT FH

R

N N k t tD

N N k

0

1 et

ITN

N

R-D solution for hard saturation (all Si-H bonds broken) can be approximated by stretched-exponential function.

Since only lateral shift is allowed, such saturation increase lifetime modestly.

NH

x

( ) Hx t D t

ln (time)ln (

deg

rad

ati

on

)

Stretched Exponential Limit: Additional Points

0( )ITF IT R H IT

dNk N N k N N

dt

ln (time)ln (

deg

rad

ati

on

)

0

1t

ITNe

N

0ITdN

dt

0( ),ITF IT R H IT

dNk N N K N N

dt

0

ITN t

N

0

1t

ITNe

N

is rational, i.e. 1/4,1/6,1/2,1/3

2

0

1 FH

R

kD

k N

0 0( ) pHD D t

H B

H

D k T

q

(1 )

0

1

pt

ITNe

N

exponents need not be rational if diffusionis dispersive.

Reproduces results from Blat, PRB, 1991. Zafar, VLSI, 2004

Soft Saturation: Reflection at Poly Interface

0 (0)FH IT

R

k NN N

k

NH

x( ) ( )

( )

( ) (0) (poly oxH H HH Hpoly

H

N W N N WD D

WD t

(1)

0

( ) ( , )

1( ) ( ) (0)

2 2

HD t

IT H

H ox H H H

N t N x t dx

WN T D t N W N

(2)

(3)

10-1

100

101

102

103

104

105

10-3

10-2

10-1

T=125OC

TPHY

=36A

EOX

(MV/cm)7.48.810.7

VT s

hift

(V

)

stress time (s)

1/ 4( )0( )2

polyFIT H

R

k NN t D t

k

And at long time ….

122 ( )

(0( )

( ) 22

polypolyF ox H

IT ox oxR

k N T DN t D t T

k D t

Combining, at short time, we get

Si

Si

Si H

HH

H

H

Poly

H

H

Oxide

Proof that it is Poly Interface: Enhancement and Lock-in

Si oxide

NH

x

Poly

10-1

100

101

102

103

10410

-4

10-3

10-2

5x10-2

tBREAK

TPHY

=26A

T=125OC

EOX

(MV/cm) 9.1 8.0 6.9 5.7

VT

shift

(V

)

stress time (s)

S. Rangan et al. 2003 IEDM Proc.

Si oxide

NH

x

Poly

NH

x

0ox HT D

ln (time)ln (

deg

rad

ati

on

)

2

0ox

H

T

D

The Good and the Bad of Soft Saturation Due to Interface

NH

x

ln (time)ln (

deg

rad

ati

on

) Good: Vertical scaling is possible, with orders of magnitude in increased lifetime.

Bad: Saturation is not permanent. Initial Exponent would return.

Kufluoglu & Alam, unpublished results

Aside: The diffusing species is H2

10-1

100

101

102

103

10410

-4

10-3

10-2

5x10-2

tBREAK

TPHY

=26A

T=125OC

EOX

(MV/cm) 9.1 8.0 6.9 5.7

VT

shift

(V

)

stress time (s)

26 28 30 32 3410

-4

10-3

10-2

10-1

100

101

102

Ea=0.58

EH=0.53

TPHY

=26AE

OX=6.9MV/cm

1/kT (eV-1)

1/t B

RE

AK; D

(ar

b. u

nit)

1/tBREAK

D

2 2/

0

HE KTox oxbreak

H

T Te

D D

( )( )

2F R

a H H

E EE D E

n

Within reasonable approximation, diffusing species is H2.

Conclusions: Saturation Characteristics

We identified two types of saturation: Hard Saturation: When all Si-H bonds are broken Soft Saturation: When diffusion front reaches poly interface. (Also see Chakravarthi, IRPS 2004).

The stretched exponential form, sometimes taken as an alternative to R-D model, is simply the hard saturation limit of R-D model. Hard saturation requires lateral scaling; lifetime improvement is small.

Soft-saturation, which is in better accord with experiment, is related to interface reflection.

The horizontal shift associated with soft-saturation increases lifetime greatly; but beware that this saturation is not robust and the rate will increase at a later time!

ln (time)

ln (

deg

rad

ati

on

)

Three Issues of NBTI

Time Dependence

Geometry-dependent NBTI exponents H vs. H2 diffusion Charged or neutral species

Saturation Characteristics

Soft saturation due to interfaces/Lock-in Hard Saturation and stretched exponentials Frequency Dependence

Low frequency High frequency

ln (time)ln (

deg

rad

ati

on

) V=high, f=low

V=low, f=high

V=high, DC

V=low, DC

R-D Model at Very Low Frequencies (0.001 HZ!)

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

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)

21

(0)2

IT H H

IT H H

N N D

N N D t

0( ) (0)ITF IT R H IT

dNk N N k N N

dt

(0) (*)0 0

(0) (*)

20 0 0

H H H

IT IT IT

H H

N N N

N N N

AN BN C

(0)

0

11IT IT

x tN N x

x

Other Approximate Analytical Models

Time (sec)

abs

(VT)

Shi

ft (

mV

)

100 101 102 103 104 10510

20

30

40

50

0.5x104 1x104 1.5x104

linear plot log plot

VT = a – bt1/4

New model

Numerical

VT = a – bt1/4

New model

Numerical

G. Chen et al., EDL, 23(12), p. 734, 2002.

NBTI Recovery: Frequency Independence

0 250 500 750 10005

15

25

35

VT S

hift

[m

V]

0.1 Hz

1 Hz

Time (sec)

DCDC(meas.)0.5 Hz (meas.)

Frequency Dependence: Simulation vs. Measurement

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 [

mV

]

The Physics of Frequency Independence

0 20 40 60 80 100

Distance into the Oxide [A]

H2

con

cent

ratio

n [a

.u.]

100

104

108

1012

1016

1020

High Freq

Low Freq

Low Frequency (1 cycle)

High Frequency (1 cycle)

The Physics of Frequency Independence

R-D model anticipates Frequency Independence!

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

H2

con

cen

tra

tion

[a.u

.]

100

104

108

1012

1016

1020

High Freq

Low Freq

100/200 cycle

200/400 cycle

NBTI Lifetime Improvement: DC vs. AC

At least a factor of 4-8 improvement in lifetime is expected

100 101 102 103

Time (sec)

100

101

102

VT S

hift

[m

V] TDC TAC

TAC

TDC

~ 4-8

At low frequencies, electro-chemical or reaction diffusion model indicates frequency independent improvement ….

M. Alam, IEDM Proc. 2003.

Instantaneous Reaction in Standard R-D model

Si

H

Si

H

Si

H

dNIT

dt= kF(N0 – NIT) – kR NHNIT

H

Poly

Oxide

substrate

SiH + hole = Si+ + H

ln (

k F, k R

)

ln(f)

kF = kF0 [cap-1/(f + cap

-1

f

f = cap-1

Time delays in kF and kR may introduce freq. dependence in R-D model

kR = kR0 [anneal-1/(f + anneal

-1

f = anneal-1

Frequency Dependence at High Frequencies

Standard R-D model is inconsistent with high frequency data

Meas.(Abadeer, IRPS03)

Meas.(Chen, IRPS03)

10-1 101 103 105 107

Frequency [Hz]

10

20

30

40

50

0

DCV

T S

hift

[m

V]

Conclusions: Relaxation Characteristics

Solution to R-D model can interpret experimental relaxation data.

At low frequencies, NIT improvement (x2) is frequency dependent. Increase lifetime by a factor of 4 to 8. At higher frequencies, further improvement is possible and is anticipated from R-D model.

ln (time)ln (

deg

rad

ati

on

) V=high, f=low

V=low, f=high

Broad Conclusions:

ln (time)ln (

deg

rad

ati

on

)

ln (time)

ln (

deg

rad

ati

on

)

Vstress

Vop

10 yr

?

Trap Generation Saturation Relaxation

Robust 0.3-0.12 H2 diffusion Field dependence Exponential activation

Soft-saturation interface related Vertical scaling improves lifetime, but one needs to be careful.

Factor 4-8 improvement at low frequency. Freq. independence at low frequencies Better lifetime at high frequencies.

ln (time)ln (

deg

rad

ati

on

) V=high, f=low

V=low, f=high

The analytical reformulation R-D model is a powerful framework for NBTI studies

All NBTI models can be shown to be approximation of R-D model

Part I: Basics and Models (Muhammad A. Alam)

Introduction: NBTI defined and a brief history of NBTI NBTI degradation kinetics Nature of NBTI precursor and created traps I did not go in details. Details can be found in S. Tan, APL, 2003; 82:1881. Ushio, APL, 2002; 81:1818. Schroder, JAP; 2003;94:1; Reddy, IRPS 2002; 248. Voltage and temperature acceleration Statistical aspects I did not have time to cover it, but you can review Hess, IEDM 2000 and Penzin, TED, 2003. Recovery and frequency dependence

Part II (Anand T. Krishnan)

Process dependency (a) Nitrogen (b) Fluorine (c) Other  Device impact (Gm,VT, ION, IOFF, CGD, mobility, etc.) Circuit and Scaling impact Conclusion 

What have we covered so far …..