1. Negative Bias Temperature Instability
IRPS 2005 Tutorial on
Negative Bias Temperature Instability
Muhammad A. Alam Basic modeling (1:30 - 3:00 pm)
Anand T. Krishnan Process/Circuits (3:30 - 5:00 pm)

2. Broad Outline of the Tutorial
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

3. Negative Bias Temperature Instability
Basics/Modeling
Muhammad A. Alam
Purdue University
West Lafayette, IN

4. Collaboration and References
Experiments: S. Mahapatra, S. Kumar, D. Saha, IIT Bombay
[1] Mahapatra and Alam, IEDM 2002, p. 505.
[2] Mahapatra, Kumar, & Alam, IEDM 2003, p. 337.
[3] Mahapatra et al. IEDM 2004, p. 105.
Theory: M. Alam, H. Kufluoglu, Purdue University
[1] Alam, Weir, & Silverman, IWGI 2001, p. 10.
[2] Alam, IEDM 2003, p. 346.
[3] Kufluoglu & Alam, IEDM 2004, p. 113.
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.

5. Introduction: What is NBTI all about ?
VDD
VDD
GND
NBTI: Negative Bias Temperature Instability
Gate: GND, Drain: VDD, Source: VDD
Gate negative with respect to S/D
Other degradation modes: TDDB, HCI, etc.

6. NBTI Degradation and Parametric FailureS 4 3 2 1
Stress Time (sec)
% degradation 5 10 15
Spec.
Warranty
before stress
ID (mA)
after stress
VD (volts)

7. Rationale of 10% Criterion: Process, Reliability, Design
-5%
-15%
+15%
t=0 ID
t=10 yr
-10%
IC Failure
ID,nom
So we do not have too much margin, especially
during the ramp-up period of manufacturing ….

8. 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.
Now the great thing about being in a industrial lab is that people are actually faced with problems and if you had couple of friends in the reliability group, if you by them lunch, they will tell you about problems …. And I knew the problem, the best way to solve them is to look it up in the literature ….

9. The Need for NBTI Theory and Measurements
Trap Generation
ln (time)
ln (degradation) ?
Saturation
Hard/soft saturation
Extrapolation
Relaxation
Physics of relaxation
Freq. Dependence
ln (time)
ln (degradation)
V=high, f=low
V=low, f=high
ln (time)
ln (degradation)
Vstress
Vop
10 yr
Time Exponent
Voltage Acceleration
Before 1980
After 2000

10. 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

11. 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

12. The Reaction-Diffusion Model
Silicon
Gate oxide
Poly
kF: Si-H dissociation rate const.
Creates broken-bond NIT
kR : Rate of reverse annealing of Si-H
N0: Total number of Si-H bonds Si H Si H Si H Si H H2 Si H Si H NH
distance
NH: Hydrogen density
DH: Hydrogen diffusion coefficient
mH: Hydrogen mobility
People are not saying that that diffusion does not occur or that annealing term is non-existent, they are simply saying that relatively speaking, these are unimportant.
n=1
n=0
n=1/4
n=1/2
log (time)
log (NIT)

13. The meaning of the Parameters
poly
oxide N0
Time-dependence
Temp-dependence
Field-dependence

14. Field Dependent Problem ?
3.2 V p p n
4.2 V
We did not worry about this in 1970s, because for thick oxides it made very little difference. n n p
Indeed it is, therefore at least we are headed in the right direction ….!

15. 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: Detailed analytical solution]
Alam, IWGI 2001; 10 Multi-region analytical/numerical
Alam, IEDM 2003; Freq. Dependence: analytical/numerical
Kufluoglu & Alam, IEDM Geometrical aspects: numerical/analytical
Chakravarthi, IRPS 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. Note2: R-D Model is a phenomenological Model
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, mH to understand the
features of NBTI, ….
... just as we do not need to know the
microscopic physics of Dn, Dp, mn, mp, ks,
etc. to understand the operation of
bipolar transistor and MOSFETs.
(2) All we need, is just a few
detailed-balance relationships
like 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 involving
nature 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 dielectric
response help illuminate the physics
of mobility and diffusion.

17. Note 3: R-D Model applies to Si-H Bonds only
SILC
Si-H bonds
Si-O bonds CP
NIT by charge pumping = Broken Si-H bond
+ broken Si-O bond
Signature of bulk Si-O bonds …… Stress Induced Leakage Current
Only part of NIT (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)

18. Note 4: Relaxation and Time Exponents
102
101
100
10-1
103
109
105
107
Time (sec)
VT Shift (mV)
Apparent
exponent
Real
Exponent
Nit = Atn
ln (Nit) = ln (A)
+ n ln(t)
R-D model predictions to be compared with
“real exponent” which is smaller than “apparent exponent”.

19. A Reformulation of R-D Theory for Analytical ModelingSi H H H
Si sub. Si H
Poly H
If trap generation rate is small,
and if NIT much smaller than N0, then Si H H NH x
(Neutral) NH x
(Charged)

20. Trap Generation with Neutral H Diffusion
Si sub.
Poly NH x
Combining these two, we get
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.

21. Trap Generation with Neutral H2 Diffusion
Si sub. Si H H2
Poly H2 H2 Si H NH x H2
NH2
n ~ 1/6 is a possible signature
of neutral H2 diffusion
Small exponent because
generation is more difficult.
Combining these two, we get
Reproduces results of Chakravarthi, IRPS, 2003.

22. Trap Generation with charge H (Proton) Diffusion
Si sub.
Poly NH x
Combining these two, we get
Did not find any such
NIT vs. time result
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.

23. Trap Generation with charge H2+ Diffusion
NH2 x Si H H+
H2+
Si sub.
Poly
Combining these two, we get
n ~ 1/3 is a possible signature
of charged H2+ diffusion
Exponents above 1/3 seldom
seen in charge-pumping expt.
(uncorrelated to SILC).

24. Dipersive Diffusion: explanation of non-rational nNH x
Shkrob, PRB, 1996; 54:15073 NH NH x x
nideal
ndis H
0.25 H2
0.16
H2+
0.33
R-D model predicts n=
More amorphous oxides for better NBTI
For finite oxides, at very long time all n
must be rational (no problem > 10 yrs)

25. Theory of Standard Diffusion:
Distribution
Real-Space
Energy-Space
Real Distribution NH
NHf NH x
No Temperature Activation

26. Theory of Activated Diffusion:
Standard
Distribution
Real-Space
Energy-Space
Real Distribution
NHf
NHb NH NH x
with

27. Theory of Dispersive Diffusion:
Real-Space
Energy-Space
Moment-Space M ……

28. ln (NIT)
ln (time)
ln (NIT) T1 T2
ln (time)
ln (NIT) T1 T2
ln (time)
ln (NIT) T1 T2
ln (time)

29. 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, 1998

30. Conclusions: Trap Generation Rate
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
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.
ln (time)
ln (degradation)
Vstress
Vop
10 yr

31. 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 (degradation)

32. Hard-Saturation in R-D Model: Stretched Exponential LimitNH x
ln (time)
ln (degradation)
If trap generation rate is small,
and if NIT much smaller than N0, then
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.

33. Stretched Exponential Limit: Additional Points
ln (degradation)
ln (time)
exponents need not
be rational if diffusion
is dispersive.
Reproduces results from
Blat, PRB, Zafar, VLSI, 2004
is rational, i.e.
1/4,1/6,1/2,1/3

34. Soft Saturation: Reflection at Poly Interface
Oxide
Poly Si H H H H
(1) Si H Si H H
(2) NH
(3) x
Combining, at short time, we get
And at long time ….

35. Proof that it is Poly Interface: Enhancement and Lock-in
S. Rangan et al IEDM Proc. Si
oxide NH x
Poly Si
oxide
Poly NH x

36. The Good and the Bad of Soft Saturation Due to InterfaceNH x
ln (time)
ln (degradation) NH x
ln (degradation)
ln (time)
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

37. Aside: The diffusing species is H2
Within reasonable approximation, diffusing species is H2.

38. 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 (degradation)
ln (time)

39. 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
V=high, DC
V=high, f=low
ln (degradation)
V=low, DC
V=low, f=high
ln (time)

40. NIT R-D Model at Very Low Frequencies (0.001 HZ!) H2 density [a.u.]
stress 1
relax 1
stress 2
relax 2
NIT
3000
4000
1000
time (sec)
1017
1002 s
3002 s
2450 s
2 sec
1016
95 sec
H2 density [a.u.]
1450 s
450 sec
2002 s
3450 s
1015
1014
distance into the Oxide (A)

41. Analytical Model: Relaxation PhaseSi
oxide
NH0(0)
1017
1016
H2 concentration [a.u.]
NH0
1015
(Dt0)1/2
1014
Distance [A]

42. Other Approximate Analytical Models
linear plot
log plot 50
VT = a – bt1/4
New model
Numerical 40
abs (VT) Shift (mV) 30
VT = a – bt1/4
New model
Numerical 20 10
0.5x104 1x x104
Time (sec)

43. NBTI Recovery: Frequency Independence35 DC
DC(meas.)
0.5 Hz (meas.) 25
VT Shift [mV]
0.1 Hz 15
1 Hz 5
Time (sec)
G. Chen et al., EDL,
23(12), p. 734, 2002.

44. Frequency Dependence: Simulation vs. Measurement10 20 30 40 50
meas.
simulation
VT Shift [mV]
Frequency [Hz]
Symmetry in R-D model requires
frequency-independent degradation

45. The Physics of Frequency Independence
High Freq
Low Freq
100
104
108
1012
1016
1020
Low Frequency (1 cycle)
High Frequency (1 cycle)
H2 concentration [a.u.]
Distance into the Oxide [A]

46. The Physics of Frequency Independence
High Freq
Low Freq
100
104
108
1012
1016
1020
100/200 cycle
200/400 cycle
H2 concentration [a.u.]
Distance into the Oxide [A]
R-D model anticipates Frequency Independence!

47. NBTI Lifetime Improvement: DC vs. AC
102
TDC
TAC
TAC
~ 4-8
VT Shift [mV]
101
TDC
100
Time (sec)
At least a factor of 4-8 improvement in lifetime is expected

48. At low frequencies, electro-chemical or reaction
diffusion model indicates frequency independent
improvement ….
M. Alam, IEDM Proc

49. Instantaneous Reaction in Standard R-D model
SiH + hole = Si+ + H
dNIT dt
= kF(N0 – NIT) – kR NHNIT
substrate f Si H Si H Si H
kF = kF0 [tcap-1/(f + tcap-1) ]
kR = kR0 [tanneal-1/(f + tanneal-1) ] H
f = tcap-1
Oxide
ln (kF, kR)
f = tanneal-1
Poly
ln(f)
Time delays in kF and kR may introduce freq. dependence in R-D model

50. Frequency Dependence at High Frequencies10 20 30 40 50 DC
Meas.(Chen, IRPS03)
Meas.(Abadeer, IRPS03)
VT Shift [mV]
Frequency [Hz]
Standard R-D model is inconsistent with high frequency data

51. 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 (degradation)
V=high, f=low
V=low, f=high

52. Broad Conclusions: ? ln (degradation) ln (degradation)
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
Relaxation
Trap Generation
Saturation
ln (time)
ln (degradation)
V=high, f=low
V=low, f=high
ln (time)
ln (degradation)
ln (time)
ln (degradation)
Vstress ?
Vop
10 yr
Factor 4-8 improvement
at low frequency.
Freq. independence at
low frequencies
Better lifetime at high
frequencies.
Robust
H2 diffusion
Field dependence
Exponential activation
Soft-saturation interface
related
Vertical scaling improves
lifetime, but one needs
to be careful.

53. What have we covered so far …..
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