A Comprehensive Model for PMOS NBTI Degradation: Recent Progress
Authors1 and Authors2
Purdue University, West Lafayette, IN 47906, USA
2
Department of Electrical Engineering, IIT Bombay, Mumbai 400076, India
1
Negative Bias Temperature Instability (NBTI) is a
well-known reliability concern for PMOS
transistors. We review the literature to find seven
key experimental features of NBTI degradation.
These features appear mutually inconsistent and
have often defied easy interpretation. By
reformulating the Reaction-Diffusion model in a
particularly simple form, we show that these seven
apparently contradictory features of NBTI actually
reflect different facets of the same underlying
physical mechanism.
Keywords: CMOS degradation, reliability physics,
bias temperature instability, mathematical model,
universal scaling
1. Background
Design of any digital circuit is based on the
presumption that transistor parameters will remain
bounded by a certain margin (typically ±15%)
during the projected lifetime of the IC. This margin
consists of initial manufacturing tolerance
encapsulated in CPK numbers as well as other timedependent parameter shifts due to various
transistor degradation mechanisms like Hot Carrier
Degradation (HCI), Gate Dielectric Breakdown
(TDDB), Negative Bias Temperature Instability
(NBTI), etc. Among them, NBTI has been a
persistent (and perhaps most significant) reliability
concern for CMOS technology generations below
130 nm node [1-8]. Two factors – increasing oxide
field (to enhance transistor performance without
scaling gate oxide) and the use of oxynitrides (to
prevent Boron penetration and to reduce gate
leakage)[9, 10] – appear to have exacerbated this
PMOS-specific reliability issue. Specifically,
NBTI causes systematic reduction in transistor
parameters (e.g., drain current, transconductance,
threshold voltage, capacitance, etc.) when a
PMOSFET is biased in inversion (VS=VD=VB=VDD
and VG=0). Since this NBTI-specific biasing
condition arises universally in inverting logic,
SRAM cells, I/O system, dynamic logic, etc.[1113], it is not surprising that the concern about
NBTI is pervasive in the semiconductor industry.
10
0
O
25 C (0.23)
O
90 C (0.25)
10
-1
10
-2
VT (V)
Abstract
O
150 C (0.27)
TPHY=36A, VG=-4.5V
10
-3
10
-1
10
0
1
2
3
10 10 10
stress time (s)
10
4
10
5
Fig. 1: Measurement of NBTI degradation at
different temperatures show n~0.25 and ED~0.5 eV.
Since NBTI has been a reliability concern from the
very early days of integrated circuits in mid 1960s
[14, 15], there are many reports on various aspects
of NBTI degradation over the last 40 years [3]. An
extensive review of the state-of-art of the pre-2003
experimental results and the possible theoretical
foundations has been made in our previous article
in Microelectronics Reliability [1]. After correcting
for artifacts arising from incorrect stress condition
leading to spuriously high degradation exponent at
later stages of degradation, resolving controversies
involving oxide field vs. gate voltage dependence,
and addressing process specific NBTI degradation
issues, the essence and consensus regarding NBTI
phenomena until 2002-2003 can be summarized as
follows:
(1) The degradation is field-driven and is related
to interface traps at the Si/SiO2 interface [4].
(2) Threshold voltage degradation due to NBTI is
given by VT ~ A exp(-nED/kT) tn with n~0.25
(see Fig. 1) and ED~0.5 eV [1, 4, 6].
1
(3) Once NBTI stress is removed, a fraction of
interface traps can self-anneal [6, 16-18].
None of the pre-2003 reports, however, seemed to
have realized that the values of n and ED of NBTI
are self-contradictory and mutually inconsistent.
Since 2003, there have been reports about four
additional features of NBTI degradation that have
further complicated the classical understanding of
this degradation phenomenon:
(4) As NBTI became a long term reliability
concern, many research groups looked for and
found long-term reduction (quasi-saturation?) of
NBTI time-exponent n from 0.25 to 0.13-0.16 [5,
8, 17].
(5) A number of groups reported that NBTI is
smaller for AC stress compared to DC stress, and
the ratio of AC to DC NBTI degradation is
frequency independent [6, 9, 18] at least for low
frequencies (< 10-100 KHz).
discussed in Ref. [1], with a straightforward
generalization of the R-D model. And the seven
features represent various aspects of the same
degradation mechanism. Although the four post2003 NBTI features of saturation, frequency
independence, dispersive temperature dependence,
and indistinguishibility between SiO and SiH
bonds appear to have complicated the physical
picture of NBTI, in reality they hold the key to the
puzzle of the pre-2003 NBTI results. In Sec. 2, we
analyze the nature of the puzzle of the three
observations in pre-2003 literature. In Sec. 3, we
show how the post-2003 observations regarding
saturation and frequency independence actually
help resolve the conceptual inconsistencies. This
model then allows us to connect NBTI and HCI
degradation and anticipate the degradation in
reduced geometry devices, as well as seek
resolution of NBTI challenges through circuit
techniques. Our Conclusions regarding these issues
are summarized in Sec. 4.
(6) Careful analysis of temperature-dependent
NBTI data (see Fig.1) shows characteristics of
dispersive transport [1, 2, 19]. If this is indeed
the case, lifetime projections at various
temperatures would be more difficult than
previously presumed.
(7) Classical NBTI models are based on
dynamics of broken Si-H bonds and these
models are often validated against Chargepumping data, yet charge pumping technique
probes both broken Si-O and Si-H bonds and can
not distinguish between them [7]. This raises
important concerns regarding the validation of
NBTI models. Moreover, the significance of hole
trapping in determining the NBTI degradation
continues to be an important issue.
Since the original R-D analysis of NBTI [1] did
not address these post-2003 issues, there is an
incorrect presumption that these new features are
incompatible with the R-D model and must be
interpreted with new models of NBTI [5, 20, 21].
The goal of this paper is to show that the seven
features of NBTI degradation discussed above (to
be referred to as Issues 1-7 for the rest of the
paper) can be interpreted within the same
intuitively simple framework of NBTI degradation
Fig. 2: (top) Schematic view of hole-assisted
dissociation of Si-H bond at the Si/oxide interface.
The dissociation and passivation of Si-H bonds at
the Si/SiO2 interface is described by (1*) or (1).
The H may diffuse (middle) or drift (bottom) away
from the interface depending on the charge state of
the diffusing species.
2. The R-D Model of NBTI Degradation:
Definition of the Puzzle
In the Reaction-Diffusion (R-D) formulation of
NBTI degradation [1, 8, 22], one assumes that
2
NBTI arises due to hole-assisted breaking of Si-H
bonds at the Si/SiO2 interface (see Fig. 2, top
illustration). The rate of trap generation is given by,
dN IT
 k F ( N 0  N IT )  k R N H (0) N IT
(1*)
dt
where N0 is the initial number of Si-H bond at the
Si/SiO2 interface. NIT is the fraction of these Si-H
bonds broken at time t due to NBTI stress. The
dissociation rate constant kF is proportional to the
number of inversion layer holes that are captured
by Si-H bonds. The two-electron Si-H covalent
bond is weakened once a hole is captured and this
weakened bond (assisted by the electric field) is
easily broken at relatively moderate temperature.
The broken Si bonds acts as a donor trap [23, 24]
and contributes to the shift in threshold voltage and
reduction in transconductance. The H atoms
released in the process can anneal the broken
bonds, as described by the second term of the right
hand side of (1*) (NH (0) is the H concentration at
the interface, x=0), or the H atoms may diffuse (or
drift) away from the interface, i.e.,
dN IT
d 2 NH
 dN H (0)
 DH
 N H  H Eox 
. (2*)
2
dt
dx
2 dt
The last term in (2*) is negligible. The H atoms
may diffuse with diffusion constant (DH) if the
atoms are neutral, or drift with mobility H if they
are charged.
hand side of (2) can be interpreted as the area
under the triangle (sometimes referred to as
‘Triangle Method’) so that
D t
1
N IT (t )  
N H ( x, t )dx  N H (0) DH t .
0
2
Inserting this expression for NIT into (1), we find
Since the rate of trap generation in (1*) is usually
small compared to the dissociation and annealing
rates and since NIT << N0 ~ 5x1012 cm-2, therefore
 kF N 0 
(1)
 k   N H (0) N IT .
 R 
Also, (2*) may be restated as a conservation
equation which requires that the number of broken
Si-H bonds equal that of total H concentration in
the gate stack, i.e.,
diffusion of neutral H2 requires
N IT (t )  
x ( t )  f ( DH ,H ,t )
x 0
N H ( x, t )dx .
(2)
Here x=0 is defined at the Si/SiO2 interface and
x(t) defines the tip of the diffusion or drift-front
(Fig. 2, middle and bottom figures). Eqs. (1) and
(2) are sufficient to highlight the conceptual
inconsistency of the pre-2003 NBTI literature [15]:
Consider diffusion of neutral atomic H as shown in
Fig. 2 (middle figure). The diffusion distance at a
given time t is x(t) ~ (DHt)1/2, therefore the right
H
N IT (t ) 
kF N 0
1
( DH t ) 4 .
(3)
2k R
This reproduces the classic exponent of n=1/4
which has been the signature of NBTI degradation
based on wide variety of experimental results. The
success of the R-D model in interpreting the NBTI
exponent (see Fig. 1) led to prevailing view that
NBTI degradation is characterized by diffusion of
atomic H in gate dielectrics.
Based on this analysis, it is easy to see why pre2003 NBTI literature generally did not support
interpretation based on diffusion of molecular H2
or drift of H+ (proton). For example, if H-specie is
released as atomic H from Si-H bonds and then
convert to and diffuse as molecular H2, then the
‘Triangle Method’ would predict
D t
1
N IT (t )  
N H ( x , t )dx ~ N H (0) DH t .
0
2
In addition, the conversion between H and H2
would be given by the Law of Mass Action, i.e.,
N H (0) 2 / N H (0)  const. Together with Eq. (1),
H2
2
2
2
 k f N0 
N IT (t )  

 2k R 
2/3
( DH 2 t )
1
6
.
(4)
The exponent n=1/6 reflects the bottleneck of H-H2
conversion which results in higher H concentration
at the Si/SiO2 interface [3]. This allows faster
annealing of broken Si-H bonds and reduced trap
generation rate. Since there had been no
experimental evidence in pre-2003 literature of
NBTI degradation characterized by n=1/6
exponent, a general consensus was that NBTI
degradation by diffusion of molecular H2 is
unlikely.
Similarly, if H drifted away from the interface as
proton, we must retain the drift term in Eq. (2*),
then rewrite the conservation equation 2 (in
analogy to the Triangle Method) as
3
N IT (t ) 

 H Eox t
0
N H ( x, t )dx  N H (0)  H Eox t .
Here Eox is the velocity with which the H+ driftfront moves away from the interface as shown in
Fig. 2 (bottom figure). Together with Eq. (1), we
find [11]
N IT (t ) 
kF N 0
 H Eox t 
1
2.
(5)
kR
The n=1/2 regime has also never been seen in
NBTI measurements, leading one to conclude that
NBTI degradation through proton transport is
unlikely.
The above analysis shows that the time exponent n
is dictated by and is a sensitive measure of the
diffusing specie, as also shown by numerical
solution of R-D model [8, 25-27]. Among the
various exponents (n=1/2 for proton, n=1/6 for
molecular H2, n=1/4 for atomic H), only diffusion
of atomic H appeared to be consistent with
experimental results, therefore the pre-2003
literature assigned atomic H diffusion at the root
cause for NBTI degradation.
have significant implications for projected IC
lifetime, one must reexamine the assumptions of
classical NBTI analysis.
3. The R-D Model for NBTI Degradation:
Resolution of the puzzle
As mentioned in Sec.1, post-2003 NBTI
experiments are characterized by four additional
features: saturation of degradation at long stress
times, independence of NBTI degradation with
frequency, dispersive vs. Arrhenius activation, and
difficulty in distinguishing between dissociation
kinetics of SiO and SiH bonds. Since all these
features have significant implications for lifetime
projection, they mandate a reconsideration of the
R-D model [5, 20, 21, 30, 31].
In addition to time exponents, the activation energy
of NBTI is also extensively studied in pre-2003
literature and various report suggest that EA~0.120.15 eV. If we assume that kF=kF0exp(-EF/kBT),
kR=kR0exp(-ER/kBT) and DH=D0exp(-ED/kBT), then
by Eq. 3,
k N 
N IT (t )   F 0 0 
 kR 0 
0.5
0.25
0
D

e
0.5( EF  ER )  0.25 ED
k BT
0.25
t
so that the net temperature
activation is
EA=0.5(EF-ER) + 0.25ED. Since the specific values
of activation energies of forward dissociation, EF,
reverse annealing, ER, and diffusion coefficient, ED,
were unknown, the inconsistency between time
exponent n and temperature activation EA was
initially not highlighted. However, generalized
scaling arguments consistently showed that EA ~
ED/n [1, 4], with EF~ER [1, 2, 4, 28]. The measured
EA therefore provided a direct measure of ED~0.50.6 eV, which in turn implicated H2 diffusion [29]!
This is the core dilemma of pre-2003 NBTI
literature: the time-exponent in Eq. (3) suggests
atomic H diffusion, while temperature activation
suggests H2 diffusion. Since both these parameters
Fig. 3: Although reflection at the poly-oxide
interface does reduce NIT generation initially (at
time t1), at longer times diffusion in poly dictates
NIT generation, restoring the original exponent.
The saturation characteristics of NBTI was the first
indication that the pre-2003 R-D analysis of NBTI
may not be sufficient and one must somehow
generalize the classical view by introducing new
features like reflection at poly-oxide interface,
depletion of Si-H bonds at the Si/SiO2 interface [5],
the prevalence of hole trapping [32], etc. However,
it is shown below that such modifications have
significant limitations.
3.1 Analysis of Quasi-Saturation
4
3.1.1 Hypothesis of ‘Reflection at Poly/Oxide
Boundary’
If the saturation were caused by reflection at the
poly-oxide interface, one can use Fig. 3 to
compute integrated H concentration for Eq. (2) by
the ‘Triangle Method’
T
1
N IT (t )  N H (Tox ) DH( poly )t  ox  N H (Tox )  N H (0)
2
2
where NH(Tox) is the concentration of H at the
SiO2/poly interface. In addition, the flux continuity
at the interface requires
N H (Tox )
 N (0)  N H (Tox ) 
DH ( poly )
 DH ( ox )  H
.
( poly )
Tox
DH
t


N IT
N0

N IT 
kF

N0 
kR
 ln  1 

t 
t
 2  

 
 2 
2
2
DH 
which, by Taylor expansion, can be simplified to
t

 
 1  e   
N0 

N IT


.


(6)
where =0.25. This Stretched-exponential model
do predict NBTI saturation [5, 8], but it makes the
unrealistic assumption that NBTI stress breaks all
Si-H bonds and predicts that voltage-dependent
NBTI saturation occurs at same NIT concentration,
which is not supported by experiments.
Taken together with Eq. 1, the solution [16]

T 2
N IT (t )   DH( poly )t  2Tox  ox( ox )

DH

DH ( poly ) 
t
1
2



does show onset of saturation as H diffusion front
crosses the oxide-poly interface (Fig. 3, middleleft), however at long times as the H atoms stored
in oxide becomes a negligible part of the total H
stored in oxide and poly (Fig. 3, lower-left), the
trap generation at reverts to
kF N 0
N IT (t ) 
D
( poly )
H
t

1/ 4
2k R
which restores the original pre-saturation exponent.
In other words, the poly-reflection does not result
in saturation in trap generation (unless one makes
the unrealistic assumption that H does not diffuse
in poly, i.e., DH (poly) = 0.)
3.1.2: Hypothesis of ‘Depletion of Si-H Bonds’
Consider the second possibility of NIT-saturation
caused by depletion of all Si-H bonds [5]. Since
NIT may approach N0, therefore (1*) may be
simplified as
 k F ( N 0  N IT ) 

  N H (0) N IT .
kR


Using this relation in (2*), we find
dN IT
 DH
N H (0)

DH  k F   N 0  N IT 


t  kR  
DH t
A simple integration results in
dt
N IT
.

Fig. 4: (Top) Experimental results [9,18] show
that VT shift due to AC NBTI stress is
independent of frequency. (Bottom) The
frequency independence arises from the fact
that if the total duration of stress is the same,
the R-D model predicts generation of equal
amount of H [6].
3.1.3 Hypothesis of
Measurement Delay’
‘Saturation
due
to
It is well known that NIT generated during the
stress phase of the degradation begins to recover as
soon as the stress is removed [6, 8, 17, 18]. Since
each measurement of NIT using conventional stress-
5
It was reported in Ref. [14] that the AC response in
SiO2 films is frequency independent (see Fig. 4
(top)). Ref. [7] interprets this phenomenon as a
delicate interplay between forward dissociation
and reverse annealing rates during the stress and
relaxation phases of AC degradation. Although the
NIT generation/per cycle is very different at low
frequency vs. high frequency, however the total NIT
generated for the same duration of stress is actually
the same (Fig. 4, bottom). Therefore, the
integrated degradation is frequency independent,
consistent with experiment. The corollary to this
statement is that the ratio of the relaxation period
to stress period, S, dictates the net NBTI
degradation. For DC stress, S=0 and for AC stress
(with 50% duty-cycle), S=1. In contrast, during
NBTI measurement, the stress periods increases
geometrically with time while the measurement
window remains the same (Fig. 5), thus S
transitions from 1 to 0: in other words, the effect of
NBTI relaxation during unstressed period is more
significant at early stages of stress compared to
later times. The black line in Fig. 6 (top) shows
that the delay-induced measurement associated
with “molecular-hydrogen” diffusion anticipates a
Degradation (%)
VT
Ref. (8)
On-the-fly (0.138)
50 ms delay (0.189)
1
10
sat
Fig. 5: Measurements are made at regular
intervals to monitor degradation during NBTI
stress: Pre-2003 literature assumed that
measurements have negligible impact on the
degradation itself (top). In reality, however,
measurement window (e.g., 5 sec) allows
significant self-annealing of NIT (bottom).
saturation behavior that is consistent with
measurement. Once the delay is accounted for,
however, the quasi-saturation disappears and the
underlying zero-delay exponent is given by n~0.16.
VT [mV]; ID
measure-stress sequence requires a certain
measurement window, one must necessarily
consider the effect of such interruption of stress on
the measured values themselves. In order to
understand the effect of measurement delay, it is
easier to begin the discussion with analysis of AC
response (50% duty cycle) on NBTI degradation
(Issue 5).
Ref. (17)
0.4s delay (0.20)
3.0s delay (0.21)
10 s delay (0.22)
100s delay (0.24)
IDSAT
0
10
1
10
2
10
Stress Time (sec)
3
10
Fig. 6: (Top) The black dashed-dot curve
resembles typical experimental data showing
systematic saturation of NIT characteristics at
longer time. However, once the measurement
delay is accounted for (red lines), the resulting
curve (blue line) shows no saturation and n~1/6.
(Bottom) Measurement with variable delay
[8,17,18] support the theoretical interpretation.
6
-1
10
-1
O
15
-2
EOT=12.3A , Dose=2.34x10 cm
stress (-VG)
1.9V
O
T=100 C
2.1V
-1
10
10
O
EOT=12.3A
stress VG=-2.1V
stress VG=-2.1V
slope=0.14
slope=0.14
O
O
T=100 C
VT (V)
VT (V)
VT (V)
T=100 C
O
T=27 C
O
T=27 C
15
slope=0.14
-2
10
0
10
1
2
3
10
10
10
stress time (s)
O
T=27 C
-2
10
0
10
1
Dose (x10 cm)
1.44
2.34
2
3
10
10
10
stress time (s)
O
-2
EOT(A ), Dose (cm )
-2
10
0
10
1
21.4, 1.44x10
15
12.3, 2.34x10
15
2
3
10
10
10
stress time (s)
Fig.7. Time evolution of NBTI VT shift obtained from on-the-fly IDLIN measurements for different
stress bias, temperature, film thickness and N2 dose. Universal power-law slope of n~0.16 is obtained.
This is highlighted in Fig. 7, which shows delay
free measurement results obtained for various
stress VG, temperature and on films having
different EOT and N2 dose. The n~0.16 time
exponent is found to be robust. Indeed, recent zerodelay on-the-fly measurements from a number of
research groups have also supported this
conclusion [8,36].
This simple reinterpretation of the NBTI saturation
being an artifact of measurement delay
immediately resolves the pre-2003 controversy
regarding the nature of diffusing species: the
exponent n~0.25 implicated H diffusion, while
activation ED~0.5 eV suggested H2 diffusion. In
fact, n~0.25 is not robust exponent, as indicated by
the saturation of NBTI degradation observed by
experiments (see Fig. 6(top)). Therefore
identification of NBTI with H-diffusion is actually
accidental and reflects measurement-delay induced
relaxation of underlying degradation generated by
H2 diffusion. The diffusing specie is H2 with
consistent values of n ~ 0.16 and ED ~ 0.5 eV.
3.2 Dispersive vs. Activated Transport (Issue 6)
Our discussion above, based on careful analysis of
the absolute value of time-exponent n, resolved
that diffusion of H2 molecule would consistently
interpret experimental data regarding quasisaturation, frequency-insensitive degradation and
n=1/6 exponent with “no-delay” measurements.
Yet, instead of absolute values of n, the groups
who focused on variation of n as a function of
temperature (determined by standard delay-based
measurement, Fig. 8) reached an entirely different
conclusion: that the transport of H-specie is
dispersive and most likely specie is H+(proton),
not H2!
Consider the arguments for dispersive transport:
Historically, NBTI has always been associated
with Arrhenius-like activated transport. This is
because if one assumes that kF=kF0exp(-EF/kBT),
kR=kR0exp(-ER/kBT) and DH=D0exp(-ED/kBT), then
m

k N 
N IT (t )   F 0 0  D0n e
 kR 0 
m ( EF  ER )  nED
k BT
n
t
(the diffusing specie determine m and n, see Eq. 24). For Arrhenius transport, therefore, the
degradation curves ( ln(NIT) vs. ln(t) ) measured at
various temperatures as a function of time should
be parallel to each other.
Over the years, some authors have questioned this
presumption of Arrhenius-like activation, because
H transport in amorphous SiO2 is known to be
dispersive [2]. This dispersive diffusion coefficient
is given by DH ~ DH0 (t)-a [33-35] where a is the
dispersion parameter. Therefore, Eq. (2-4) should
be rewritten as
m
n
k N  D  
N IT (t )   F 0 0   H 0  e
 kR0   v 
m ( EF  ER )
k BT
 vt 
n (1 a )
Assuming that EF-ER ~ 0 and with 1-a=kBT/E0 (E0
measures of the energy-distribution of the trapstates), one finds
7
N IT (t )  At n '
m
n
k N  D 
with A   F 0 0   H 0  v n ' and n=nKBT/E0.
 kR0   v 
For dispersive transport, therefore, both the timeexponent n as well as the prefactor, ln(A) [2],
should scale linearly with T. Indeed, classical (with
delay) measurement of NBTI degradation do show
that n (Fig. 8) scales linearly with temperature,
with dispersion parameter a=0.7 (25C)-0.57
(200C) for H+ transport (i.e., n=0.5), and a=0.4
(25C)-0.1(200C) for diffusion of atomic H
(n=0.25) [1, 2]. Moreover, dispersive-drift of H+
(proton) anticipates that log(t) recovery of NIT once
the stress is removed and such “log(t)” recovery
has been observed in experiments [20]. Therefore,
one concludes that both NBTI time-exponent as
well as temperature activation are dictated by
dispersive transport of H+. This conclusion of H+
transport contradicts the analysis in Sec. 3.1 which
resolved that only H2 diffusion can consistently
interpret NBTI experiments.
0.30
0.28
time exponent
0.26
0.05s (delay)
0.35s
1s
0.24
0.22
0.20
0.18
0.16
0.14
0
50
100
150
O
Temperature ( C)
200
Fig. 8: Temperature dependence of measured
NBTI time exponents obtained by conventional
measurements with different delays.
The view of H+ dispersive transport dictates NBTI,
however, raises a conceptual problem. Oxides used
in modern CMOS technology are so thin that the
diffusion specie reaches the SiO2-poly interface
within seconds [36] and the long term NBTI
degradation is controlled by diffusion (or drift) in
poly-silicon. The distribution of trap levels ET in
poly-silicon is more localized (in energy) than
oxides [E0 ~ kBT] so that a  1, therefore polysilicon is known to be less dispersive than oxides.
Yet, the dispersion parameter needed to fit the
NBTI data (i.e., a ~ 0.7-0.57) is actually greater
than those needed for oxides a=0.1-0.2. How can
poly-silicon be more dispersive than amorphousoxides?
A closer inspection of the measurement technique,
once again, resolves the puzzle. The conclusion of
dispersive transport has been based on classical
measurement technique with measurement delays
of ~200 [2,20] - 500 [1] msec. As shown in Fig. 6
(bottom), such delays lead to significant error in
determining the true NBTI exponents (see Fig. 8)
and therefore any temperature-dependent variation
of these parameters can not be used reach specific
conclusions regarding the mechanics of NBTI
degradation. Once the “zero-delay”, on-the-fly
measurements are used, the temperature dependent
degradation curves becomes parallel to each other
(see Fig. 7) and dispersion parameter a  0,
consistent with nearly nondispersive H-transport in
polysilicon. With a  0 or equivalently n’ n=0.5,
the presumption of H+ transport is no longer viable
because the time exponent of 0.5 for H+ transport
in not observed in experiments and simple
nondispersive diffusion of neutral H2 in polysilicon, with ED=0.5 eV and n=1/6, is sufficient to
explain experimental data.
Finally, we conclude this section with a few
observations regarding sub-100 sec (see Fig. 9)
time-exponents. All the on-the-fly measurements
show that the initial (t < 100 sec) slopes are not
exactly n=1/6 as would be indicated pure H2
diffusion as discussed in Sec. 3.1. Although the
short-time time-exponents does not affect longterm reliability projection and therefore have not
received much attention, in practice this region
provides another opportunity to test consistency of
the theoretical models in a systematic manner.
Currently, there are four interpretations for this
short-time slope: H-capture by bulk oxides [37],
hole trapping [38], short-term non-equilibrium
dispersion in poly-silicon [19], the conversion
from H to H2 conversion at the initial stages of
8
10
O
50 C, 0.174, 0.14
11
-2
10
O
9
2x10
10
-1
0
10
1
2
3
2x10
4
10
10
10
stress time (s)
10
1
5x10 stress V (V)
B
-3
5x10 -1
0
1
2
3
4
5
10 10 10 10 10 10 10
stress time (s)
Fig.9. Measurement of NBTI degradation using
On-the-Fly IDLIN. Short-time data show
temperature dependent time exponent. Long time
curves are parallel to each other.
3.3 SiO and SiH bonds
While “zero-delay” On-the-Fly measurements
helped resolve a number of puzzles (Issues 1-6)
from post-2003 literature, it also highlighted our
general inability to distinguish between SiH and
near-interface SiO bonds by standard measurement
techniques (e.g., Charge-Pumping [41], VT-shift
measurement, etc.). This makes it difficult to
compare predictions of R-D theory (Si-H alone)
with results from standard measurements
(combination of Si-H and Si-O). Indeed, while it is
generally presumed that broken Si-H bonds are the
main source of degradation for most NBTI-like
stress, it is certainly possible that under certain
-2
9
On-the-fly Idlin
VG(stress)=-1.9V
O
T=27 C
0.0
1.5
2.0
2.5
t0=20-40s
NIT (x10 cm )
VT (V)
10
VB=0V
VB=2V
Difference
SILC
O
-2
0
TPHY=26A
VG=-3.1V
O
t0=2-4s
10
10
100 C, 0.19, 0.14
150 C, 0.237, 0.14
1
10
NIT (cm )
-1
circumstances Si-O bonds are also broken,
especially in the presence of hot holes when high
gate or reverse body bias is applied during stress
[4]. Figure 10 (top) shows the time evolution of
interface traps for stress without and with reverse
VB. NIT was directly measured using charge
pumping.
SILC = JG/JG(t=0)
degradation [27]. Among them, the H-capture
model appears to an artifact of measurement delay.
Among the remaining three, it appears that the
model based on H-H2 transition provides the
simplest explanation of this phenomenon (while
remaining consistent with other observations),
specifically because this model anticipates a robust
n~1/3 region consistent with wide variety of
experiments. In this model, there is time-delay of
generation of H by dissociation of Si-H bonds and
subsequent formation of H2 bonds. During the
early stages, generation of H (with higher n)
dictates the NIT generation; later, diffusion of H2
(with lower n) controls the NIT dynamics.
10
2x10
TPHY=22A
O
1
Generated at 1000s
Recovered at next 1000s
0
2.4
2.5
2.6
stress -VG (V)
2.7
Fig.10. (Top) Increased NBTI degradation
in the presence of stress VB. VB>0 induced
additional NIT correlates with SILC and is
due to SiO bonds. (Bottom) NIT recovery
after stress. VB>0 induced additional NIT
due to SiO bonds does not recover.
For VB=0 stress, NIT shows a power law time
dependence with n~0.2 as expected for
measurement with small but finite delay. For VB>0
stress, NIT increases at longer time and shows a
power law but higher n (~0.3). The VB>0V
induced additional NIT shows a power law of n~0.5,
and is identical to that of SILC. Note that hot holes
generated in the presence of reverse VB breaks SiO bonds. Broken Si-O bonds at the oxide bulk
gives rise to SILC [39, 40], and those near the
9
We wish to further highlight that even for stress
leading to negligible broken SiO bonds, Charge
Pumping and On-the-Fly measurements would
produce quite different results (Fig.11). The
apparently large difference (~10X) of as measured
characteristics can mislead one to invoke hole
trapping to account for the difference [42].
However as shown in [43], the difference is
actually due to the following three reasons. First,
Charge Pumping measurements have finite delay,
which causes larger time exponent and lower
magnitude as shown above. Also, the energy zone
in the band gap scanned by Charge Pumping is
quite less compared to On-the-Fly IDLIN. Once
these differences are taken into account, the
difference becomes much less than 2X. Finally,
any non-uniform increased trap generation close to
the conduction band edge [44] (beyond the Charge
Pumping zone) can account for such small
difference between corrected Charge Pumping and
On-the-Fly IDLIN results.
4. Conclusions and Outlook
NBTI has been persistent reliability concern
for Silicon ICs since mid 1960s. A large number of
studies of various aspects of NBTI degradation
have been reported in the literature. However, a
close review of the literature shows that the pre2003 view of NBTI degradation anticipates a timeexponent and temperature-activation that are not
mutually consistent. The post-2003 studies
demonstrating NBTI saturation and frequency
independence, which although appeared to have
complicated the picture, actually holds the key to
resolution of previous inconsistencies leading to a
very simple view of NBTI degradation: NBTI is an
interface trap driven phenomena associated with
breaking of Si-H bonds. Although the H is released
as atomic H, then they convert to and diffuse as
molecular H2. The activation and time exponent of
NBTI are defined by this diffusion of molecular
neutral H2 at long times (> 100 sec). Sub-100s NIT
characteristics are characterized by dynamics of HH2 conversion. This mechanism should be used as
the basis of any lifetime extrapolation protocols for
NBTI degradation.
-2
7x10
On-the-fly Idlin
VT & q.NIT/COX (V)
Si/SiO2 interface show up as additional NIT. As a
further proof, Figure 10 (bottom) shows the recovery
of NIT after stress without and with VB. Identical
recovery following VB=0 and VB>0 stress suggests
that additional NIT created during VB>0 stress does
not recover after stress. This is consistent with the
above picture as no known mechanism exists for
recovery of broken Si-O bonds. It is very important
to choose proper NBTI stress condition to avoid
generation of hot holes and additional NIT due to
broken Si-O bonds, so that R-D model can be used
for reliable prediction of device lifetime. This is an
important prerequisite for any comparison with
experimental data and theoretical model.
delay
corrected
10
-2
E corrected
As measured C-P
O
VG=-3.0V; T=150 C
PNO (2.14nm)
10
-3
0
10
1
2
10
10
stress time (s)
3
10
Fig.11. Comparison of VT shift obtained from
On-the-Fly IDLIN and Charge Pumping. For
fair comparison, Charge Pumping data
corrected for differences in energy zone [41]
and measurement delay.
The ability of R-D model to resolve long-standing
puzzle of NBTI time exponent (n=1/6) for planar
transistors, as discussed in Sec. 3, raises an
intriguing possibility: It is well known that HCI
degradation (for VG ~ VD/2) involves kinetic
dissociation of Si-H bonds and the rate of HCI
degradation also shows a fractional time exponent
(n~0.5), the mechanics of which has never been
explained. Would the R-D theory offer an
explanation of this time-exponent? Indeed, as
shown in Ref. [26] that a very simple analysis
based on solution of Eqs. (1) and (2), that
recognizes the fact that uniform gate stress during
NBTI involves 1D diffusion of H, while the
localized degradation during HCI involves 2D
diffusion of H, can interpret HCI exponents within
the classical R-D framework. Moreover, it is
generally believed that for continued scaling, one
must adopt reduced cross-section transistors (e.g.,
10
FINFET, Fully depleted SOI, etc.). It is natural to
ask if NBTI degradation in planar transistors (as
discussed above) would be modified with
reduction
is
transistor
geometry.
Since
electrostatics is determined by inside Laplace
equation for potential (i.e., 2=0,  is the
potential and  is the dielectric constant) while NIT
is dictated by outside Laplace equation for
hydrogen
concentration
(i.e.,
DH2NH=0,
generalization of (2*)), therefore any device
geometry that improves electrostatics must
necessarily degrade NBTI time-exponent n. Still,
an overall optimization for power-performance is
possible, because better electrostatic control allows
reduction in supply voltage, which in turn reduces
kF in Eq. (3-5). This reduction in kF may easily
compensate for enhanced n associated transistors
with reduced cross-section, so that the overall
performance as well as the reliability are optimized.
One may wish to consult Ref. [25] for additional
details.
The conclusions reached in this paper are broadly
applicable to nitrided and non-nitrided films.
Based on extensive measurement and theoretical
analysis of NBTI degradation in nitrided films, one
we conclude that for moderate nitradation (<15%),
although the parameters of kF, kr, and DH do
change, but the general physics of NBTI
degradation – as encapsulated in R-D framework –
does not. Details of this analysis, involving
optimization of NBTI reliability and the leakage
current as a function of Nitrogen concentration,
will be published elsewhere.
Acknowledgement
We acknowledge contributions from our graduate
students H. Kufluoglu, D. Varghese, and Ahmed E.
Islam. Financial support from National Science
Foundation, Applied Materials and Renesas
Technologies are gratefully acknowledged.
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13