irps 2005 tutorial on negative bias temperature instability muhammad a. alam basic modeling (1:30 -...
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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, [email protected]
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 …..