nbti graphs

8/2/2019 Nbti Graphs

1/47

Negative Bias Temperature InstabilityBasics/Modeling

Muhammad A. AlamPurdue UniversityWest Lafayette, [email protected]


2/47

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 toillustrate difference in opinions or to generalize results.


3/47

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


4/47

Stress Time (sec)

%

degradation

VD

(volts)

ID(mA)

101 103 105 107 109

5

10

15before stress

after stress

0 1 2 3 40

4

3

2

1

Spec.

Warran

ty

NBTI Degradation and Parametr ic Failure

DS


5/47

Rationale of 10% Criter ion: Process, Reliability, Design

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

IDID,nom

+15%-15%t=0

t=10 yr

-5%

-10%

Process

Design

IC Failure


6/47

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

Experiments in late 1960s by Deal and Grove at Fairchild

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

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

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

Early 1980s

m Issue disappears with NMOS technology and buried channel PMOS

Late 1980s and Early 1990s

m 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)

m Voltage scaling reduces HCI and TDDB, but increasing field & temperaturereintroduce NBTI concerns for both analog and digital circuits

m Numerical solution is extensively used for theoretical modeling of NBTI.


7/47

The Need for NBTI Theory and Measurements

ln (time)ln

(degrad

ation)

ln (time)ln

(degrad

ation)

Vstress

Vop

10 yr

?

Trap Generation Saturation Relaxation

m Time Exponent

m Voltage Acceleration

mHard/soft saturation

m Extrapolation

m Physics of relaxation

m Freq. Dependence

ln (time)ln

(degrad

ation)

V=high,f=low

V=low,f=high

Before 1980 After 2000


8/47


9/47

Three Issues of NBTI

q Time Dependence

m Geometry-dependent NBTI exponents

m H vs. H2 diffusion

m Charged or neutral species

m Temperature-dependent exponents and

anomalous diffusion

q Saturation Characteristics

m Soft saturation due to interfaces/Lock-in

m Hard Saturation and stretched exponentials

q Frequency Dependence

m Low frequency

m High frequency


10/47

The Reaction-Diffusion Model

H2

Silicon Gate oxide PolySi H

Si H

Si H

Si H

Si H

Si H

0( ) (0)IT

F IT R H IT

dNk N N k N N

dt=

2

2 2

H H IT H H H

dN d N dN D N E

dt dt dt

= + +

kF: Si-H dissociation rate const.

Creates broken-bond NITkR : Rate of reverse annealing of Si-H

N0: Total number of Si-H bonds

NH: Hydrogen density

DH: Hydrogen diffusion coefficient

H: Hydrogen mobilityn=1 n=0

n=1/4

n=1/2

log (time)

log(NIT

)

NH

distance


11/47

The meaning of Parameters

N0 [ ]0

0

/ /

( )

ox F

F F ox

E E E kT

k k p E

e e

=

/

0R E kT

R Rk k e =

/

0H E kT

H H D D e =

( ) 0/

/ 20 0 00

0

F RH

ox

E En E kT n E En nF F

IT H H

R R

k N k N N D t D pe e t

k k

+ = =

Time-dependenceTemp-dependenceField-dependence

F

R

kk

SiH h Si H + ++ +


12/47

Note1: R-D Model is a phenomenological Model

0( ) (0)IT

F IT R H IT

dNk N N k N N

dt=

2

22

H H IT H H H

dN d N dN D N E

dt dt dt

= + +

( )0

ox

D A

s

dE qp n N N

dx = +

( )2

2 p p ox

dp d p d D p E

dt dx dx=

( )2

2n n ox

dn d n d D 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 thefeatures of NBTI, .

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

(2) All we need, is just a few

detailed-balance relationshipslike how kF and kR are related,

.. just as all we need for DD

equations is detailed-balancerelationship like Einstein relationship.

(3) First principle calculations involving

nature of traps, physics of diffusion,etc. help illuminate the physics ofthe coefficients and is very useful, .

. just as detailed analysis of scatteringbased on Fermi Golden rule or dielectricresponse help illuminate the physicsof mobility and diffusion.


13/47

Note 2: R-D Model applies to Si-H Bonds only

NITby charge pumping = Broken Si-H bond + broken Si-O bondSignature of bulk Si-O bonds Stress Induced Leakage Current

Only part of (identified by CP) that is not correlated to SILC shouldbe compared to the predictions of Reaction-Diffusion Model

Total VTshift = contribution from Si-H bonds (R-D Model)

+ contributions from Si-O bonds at bulk & interface (AHI model)

Si-O bondsSi-H bonds

SILC

CP


14/47

Note 3: Relaxation and Time Exponents

102

101

100

10-1

103 109105 107101Time (sec)

VT

Shift(mV) Apparent

exponent

RealExponent

R-D model predictions to be compared withreal exponent which is smaller than apparent exponent.

Nit = Atn

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


15/47

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


16/47

Field Dependent Problem ?

10-1

100

101

102

103

10410

-4

10-3

10

-2

10-1

T=25OC

TPHY

=26A

stress time (s)

Norma

lize

dIDs

hift(atV

G-V

T=

0.7

V)

PI -3.2V

NA -3.2V

NA -4.2Vp p

n

3.2 V

n np

4.2 V

0( ) (0)IT

F IT R H IT

dNk N N k N N

dt=

2

2

2

H H IT H H H

dN d N dN D N E

dt dt dt

= + +

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


17/47

A Reformulation of R-D Theory for Analytical Modeling

2

22

IT H H H H H

dN d N dN D N E

dt dx dt

= + +

0( ) (0)IT F IT R H IT dN k N N k N N dt =

0 (0)F H IT R

k NN N

k

If trap generation rate is small,and ifNIT much smaller thanN0, then

( ) ( , , )

0( ) ( , )

H Hx t f D t

IT H x

N t N x t dx=

=

=

N

H

x

( ) Hx t D t =

NH

x

( ) H ox x t E t =

0( ) ( , )

HD t

IT H N t N x t dx=

0( ) ( , )

H oxE t

IT H N t N x t dx

=

(Neutral)

(Charged)

Si

Si

Si H

H

HH

HH

H

Sisu

b.

Po

ly


18/47

Trap Generat ion with Neutral H Diffusion

0 (0)F H IT R

k N N Nk

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

=

=

Combining these two, we get

10 4( ) ( )

2

F IT H

R

k N N t D t

k=

n=1/4 even with two sided diffusion

n 1/4 is a possible signatureof neutral H diffusion

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

N

IT/[N

1{C

OX

(VG

-VT

)}0.5](arb.unit)

10-3

10-1

101

103

105

107

10-3

10-2

10-1

TPHY

=36A

VG=-4.5V

N1=1

D. t (arb. unit)

RT, T=125oC

T=50oC, T=150

oC

T=90oC

Si

Si

Si H

H

H

H HH

H

Sisub

.

Poly

Reproduces results of Jeppson, JAP, 1977.


19/47

Trap Generation with Neutral H2 Diffusion

0 (0)F H IT R

k N N Nk

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 N N t D t

k

( )2

2

2

(0). 2

(0)

H

H

Nconst H H

N=

NH

x

2( )

Hx t D t =

m n ~ 1/6 is a possible signature

of neutral H2 diffusionm Small exponent because

generation is more difficult.

H2

NH2

Si

Si

Si H

H

HH

2 H2H2

H2

Sisu

b.

Po

ly

H2

Reproduces results of Chakravarthi, IRPS, 2003.


20/47

Trap Generat ion with charge H (Proton) Diffusion

0 (0)F H IT R

k N N Nk

0( ) ( , )

1(0)

2

H oxE t

IT H

H H ox

N t N x t dx

N E t

=

=


( )1

0 2( )2

F IT H ox

R

k N N t E t

k=

NH

x

( ) H oxx t E t =

mn ~ 1/2 is a possible signatureof charged H diffusion

m Rapid removal ofH+ byEox field increaseNIT gen. rate.

Did not find any suchNIT vs. time result

SiSi

Si H

H+H+ H+

H+

H+

H+

Sisu

b.

Po

ly

Reproduces results of Ogawa, PRB, 1995.


21/47

Trap Generation with charge H2+ Diffusion

m n ~ 1/3 is a possible signatureof charged H2

+ diffusion

m Exponents above 1/3 seldomseen in charge-pumping expt.

(uncorrelated to SILC).

0 (0)F H IT R

k N N Nk

0( ) ( , )

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

+ += +

( )1

0 3( )2

F

IT H ox

R

k N N t E t

k

N

H

x

( ) H ox

x t E t =

Si

Si

Si H

H

H+H2

+

H2+

H2+

H2+

Sisu

b.

Po

ly


22/47

Dipersive Diffusion: explanation of non-rational n

NH

x

NH

x

NH

x

NH

x

*

0( ) ( )2

nF IT H

R

k N N t D t

k

0 0( )

p

H D D t =

(1 )0 0( )2

n

n pFIT p

R

k N D N t t

k w

0.264-0.2970.33H2+

0.128-0.1440.16H2

0.20-0.250.25H

ndis

nidealm R-D model predicts n=0.30-0.12

m More amorphous oxides for better NBTI

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

Shkrob, PRB, 1996; 54:15073


23/47

H, H2, (H2+) ?

Ea suggest diffusion ofneutral H2 assumption*,

ifwe can assume EF-ER is

small, can we ?

M. L. Reed, JAP, p.5776, 1998

26 28 30 32 34 36 38 40

100

101

102

TPHY

=36A

Ea=0.49eV

1/kT (eV-1)

D(arb.

un

it)

( ) 0/

/ 20 0 0

0

0

F RH

ox

nE E E kT n E E nnF F

IT H H

R R

k N k N N D t pe D e t

k k

+ = =

( )( )

2

F Ra H H

E E E D E

n

= +


24/47

Conclusions: Trap Generation Rate

ln (time)ln

(degradation)

Vstress

Vop

10 yr

m

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

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

m Reaction-diffusion model predicts generationexponent in the range of 0.3-0.12

m However, only rational exponent n=0.33,0.25,0.16

corresponding to H2+, H2, and H are robust. Other nimprove IC lifetime, but should be used carefully.

m NBTI activation energy of 0.12 eV suggeststhat the diffusing species may be neutral H2.

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


25/47


q Time Dependence








m Low frequencym High frequency

ln (time)ln

(degradation)


26/47

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

0( ) (0)IT

F IT R H IT

dN

k N N k N N dt =

0( ) (0)F IT H IT

R

k N NN N

k

If trap generation rate is small,and ifNIT much smaller thanN0, then

2

22

IT H H

H H H

dN d N dN D N E

dt dx dt

= + +

0(0)

IT H H F IT H

R IT H

dN N D k N N D

dt t k N D t

=

22

0 0

ln 1 22

IT IT F H

R

N N k t t D

N N k

+ =

0

1 e

t

ITN

N

NH

x

( )H

x t D t =

ln (time)ln

(degradat

ion)

m R-D solution for hard saturation (all Si-Hbonds broken) can be approximated bystretched-exponential function.

m Since only lateral shift is allowed, suchsaturation increase lifetime modestly.


27/47

Stretched Exponential Limit: Additional Points

0( )IT

F IT R H IT

dNk N N k N N

dt=

0

1

t

ITN eN

ln (time)ln

(degradation)

0( ),IT

F IT R H IT

dNk N N K N N

dt


28/47

Soft Saturation: Reflect ion at Poly Interface

0 (0)F H IT R

k NN Nk

NH

x

{ }

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

=

= + +

Combining, at short time, we get

( ) ( )

( )

( ) (0) ( poly ox H H H H Hpoly

H

N W N N W D D

WD t

=

(1)

(2)

(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

shift(

V)

stress time (s)

122 ( )

(0

( )( ) 22

polypolyF ox H

IT oxox

R

k N T D

N t D t T k D t + +

{ }1/4

( )0( )2

polyF IT H

R

k N N t D t

k

And at long time .

Si

Si

Si H

HH

H

H

Poly

H

H

Oxide


29/47

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


30/47

The Good and the Bad of Saturation Due to Inter face

NH

x

0ox HT D =

ln (time)

ln

(degradation

)

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

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

2

0ox

H

T

D =

NH

x

ln (time)ln

(degradation

)

Kufluoglu & Alam, unpublished results


31/47

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

=26A

EOX

=6.9MV/cm

1/kT (eV-1)

1/t

BREAK

;D(arb.

un

it)

1/tBREAK

D

2 2/

0

H E KT ox oxbreak

H

T Te

D D = = ( )( )

2

F Ra H H

E E E D E n

= +

Within reasonable approximation, diffusing species is H2.


32/47

Conclusions: Saturation Character istics

mWe identified two types of saturation:Hard Saturation: When all Si-H bonds are brokenSoft Saturation: When diffusion front reaches polyinterface. (Also see Chakravarthi, IRPS 2004).

m The stretched exponential form, sometimes taken

as an alternative to R-D model, is simply the hardsaturation limit of R-D model.

m Hard saturation requires lateral scaling;lifetime improvement is small.

m Soft-saturation, which is in better accord withexperiment, is related to interface reflection.

m The horizontal shift associated with soft-saturationincreases lifetime greatly; but beware that thissaturation is not robust and the rate will increaseat a later time!

ln (time)

ln

(degradation)


33/47


q Time Dependence








m Low frequencym High frequency

ln (time)ln

(degradat

ion)

V=high,f=low

V=low,f=high

V=high, DC

V=low, DC


34/47

R-D Model at Very Low Frequenc ies (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

density[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


35/47

Analyt ical Model: Relaxation Phase

0 10 20 30 401014

1015

1016

1017

Distance [A]

H2

concentration[a.u.]

Si oxide

NH0

NH0

(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)IT

F IT R H IT

dNk N N k N N

dt=

(0) (*)

0 0

(0) (*)

2

0 00

H H H

IT IT IT

H H

N N N

N N N

AN BN C

=

=

+ + =

(0 )

0

11

IT IT

x t N N x

x

= +


36/47

Other Approximate Analytical Models

Time (sec)

abs(V

T)Sh

ift(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


37/47

G. Chen et al., EDL,

23(12), p. 734, 2002.

NBTI Recovery: Frequency Independence

0 250 500 750 1000

5

15

25

35

VT

Shift

[mV]

0.1 Hz

1 Hz

Time (sec)

DCDC(meas.)0.5 Hz (meas.)


38/47

Frequency Dependence: Simulation vs. Measurement

Symmetry in R-D model requiresfrequency-independent degradation

simulation

meas.

10-1 101 103 105 107

Frequency [Hz]

10

20

30

40

50

0

VT

Shift[mV]


39/47

The Physics of Frequency Independence

0 20 40 60 80 100

Distance into the Oxide [A]

H2co

ncentration[a.u.]

100

104

108

1012

1016

1020

High Freq

Low Freq

Low Frequency (1 cycle)

High Frequency (1 cycle)


40/47

The Physics of Frequency Independence

R-D model anticipates Frequency Independence!

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

H2concentration[a

.u.]

100

104

108

1012

1016

1020

High Freq

Low Freq

100/200 cycle

200/400 cycle


41/47

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

Sh

ift[mV] TDC TAC

TAC

TDC

~ 4-8


42/47

At low frequencies, electro-chemical or reactiondiffusion model indicates frequency independentimprovement .

M. Alam, IEDM Proc. 2003.


43/47

Instantaneous React ion in Standard R-D model

Si

H

Si

H

Si

H

dNITd t

= kF(N0 NIT) kR NHNIT

H

Poly

Oxide

substrate

SiH + hole = Si

+

+ H

ln(kF,

kR

)

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


44/47

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

DC

VT

Shift[mV]


45/47

Conclusions: Relaxation Characteristics

m Solution to R-D model can interpretexperimental relaxation data.

m At low frequencies, N IT improvement (x2)

is frequency dependent. Increase lifetime by afactor of 4 to 8.

m At higher frequencies, further improvementis possible and is anticipated from R-D model. ln (time)

ln

(degra

dation)

V=high, f=low

V=low, f=high


46/47

Broad Conclusions:

ln (time)ln

(degrad

ation)

ln (time)ln

(degradation)

Vstress

Vop

10 yr

?

Trap Generation Saturation Relaxation

m Robust 0.3-0.12m H2 diffusionm Field dependencem Exponential activation

m Soft-saturation interfacerelated

m Vertical scaling improveslifetime, but one needsto be careful.

m Factor 4-8 improvementat low frequency.

m Freq. independence atlow frequencies

m Better lifetime at highfrequencies.

ln (time)ln

(degra

dation)

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


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

q Introduction: NBTI defined and a brief history of NBTI

q NBTI degradation kinetics

q 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.

q Voltage and temperature acceleration

q Statistical aspects

I did not have time to cover it, but you can review

Hess, IEDM 2000 and Penzin, TED, 2003.

q Recovery and frequency dependence

Part II (Anand T. Krishnan)

q Process dependency (a) Nitrogen (b) Fluorine (c) Other

q Device impact (Gm,VT, ION, IOFF, CGD, mobility, etc.)

q Circuit and Scaling impact

q Conclusion

What have we covered so far ..

nbti graphs

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