On the Dispersive versus Arrhenius Temperature Activation of NBTI Time
Evolution in Plasma Nitrided Gate Oxides: Measurements, Theory, and
Implications
D. Varghese, D. Saha, S. Mahapatra, K. Ahmed#1, F. Nouri#1, and M. Alam#2
Department of Electrical Engineering, IIT Bombay, Mumbai 400076, India (91-22-25720408 / souvik@ee.iitb.ac.in)
#1
Applied Materials, Inc., Santa Clara, CA; #2 ECE Department, Purdue University, W. Lafayette, IN
Abstract
Negative Bias Temperature Instability (NBTI) is studied
in p-MOSFETs having Decoupled Plasma Nitrided (DPN)
gate oxides (EOT range of 12AO through 22AO). Threshold
voltage shift (∆VT) is shown to be primarily due to interface
trap generation (∆NIT) and significant hole trapping (∆NOT)
has not been observed. ∆VT follows power-law time (t)
dependence and Arrhenius temperature (T) activation.
Introduction
NBTI is a serious reliability concern for p-MOSFETs [1].
Oxynitrides (required for suppressing boron penetration and
gate leakage) show worse NBTI than control oxides and has
attracted much attention [2-5]. It is important to correctly
measure and extrapolate t evolution of ∆VT to accurately
determine device lifetime. However, this extrapolation is
complicated since (i) impact of delay time on measurement
is not fully understood, (ii) ∆VT origin (∆NIT that predicts tn
dependence or ∆NOT that predicts log (t) dependence) is still
unresolved, and (iii) the nature of temperature dependence
(dispersive vs. Arrhenius activated) remains controversial.
It is therefore necessary to resolve these inconsistencies for
correct estimation of device lifetime.
Highlights of this work
It is shown that: (i) in addition to t-delay, measurement
voltage (VG,meas) and T strongly influence n, (ii) t-delay=0
measurements show power law t dependence for various
EOT, N2 dose, stress-VG and T, (iii) recently reported large
NBTI dispersion is an artifact of t-delay, (iv) for t-delay=0,
short and long time degradation respectively are dispersive
and Arrhenius activated (their relation is explained), (v) no
∆NOT is observed, only ∆NIT governs overall ∆VT and hence
can be explained by R-D model [10-12], and (vi) measured
n along with activation energy (EA) of diffusion uniquely
identify neutral molecular H2 as the diffusion species.
Impact of measurement delay
Fig.1 shows ∆VT (t) (= −(∆Idlin/Idlin0) * VGT0) from onthe-fly [6] and normal (with delay) Idlin measurements. tdelay increases n, and is known to be due to ∆VT recovery
during the stress “stopped” phase [6,7,11]. For identical tdelay, n also increases at lower |VG,meas| (Fig.1, LHS) and
higher T (Fig.1, RHS). This is expected as ∆VT recovery,
believed due to passivation of broken Si- bonds [11,12] is
larger at higher T and lower |VG,meas| [1,7,13]. Fig.2
(LHS) shows ∆NIT (t) measured using charge pumping (CP). Increase in n with higher t-delay and higher T is clearly
seen. Fig.2 (RHS) shows ∆NIT (t) simulated using R-D
model with and without t-delay for different T. For tdelay=0, n~1/6 (for all T) as expected for H2 diffusion [11].
For t-delay>0, n increases at higher T, and is consistent
with the measured trends. Fig.3 shows n (from Idlin and CP) versus T for various t-delay. Increase in n at higher T can
be clearly seen, which is more pronounced for larger tdelay. Further, as average VG,meas for C-P (~0, mean value
of pulse) is lower than |VG,meas| for Idlin, n from C-P is
much larger than that from Idlin for a given t-delay and T.
These results are consistent with increased recovery at
larger t-delay, less negative VG,meas and higher T. Since
delay contaminates all measurements and results in
uncertain values of n, only “on-the-fly” Idlin [6] should be
used to quantify and interpret NBTI defect generation, as
has been done below.
NBTI time evolution
Fig.4 shows ∆VT (t) for various T, plotted in log-log and
lin-log scales. It is obvious that NBTI follows power-law
(not log) time dependence. When plotted in log-log scale, n
shows a slight increase with T for short t, indicating weak
dispersive diffusion [7,9]. However, the T-dependence of n
completely disappears for longer t, and n becomes (slightly
less than) 1/6 for all T. Fig.5 shows the T dependence of
∆VT (t) for various EOT, N2 dose, and stress-VG. Long time
degradation clearly shows an universal Arrhenius, powerlaw (n~1/6) behavior. Contrary to [8], the strong power-law
time dependence suggests ∆VT is governed by ∆NIT and not
∆NOT (at least for DPN oxynitrides for these EOT range).
Furthermore, strong dispersion reported in literature [7,9] is
most likely a consequence of measurement delay. Finally,
we believe historically measured n (~1/5 – 1/3) for NBTI
with uncertain t-delay can all be attributed to this universal
n~1/6 behavior (for t-delay=0), which is explained below.
Explanation using “standard” R-D model
The Arrhenius T activated (longer time), power-law time
evolution of ∆VT (~∆NIT) can be explained by R-D model
[1,10-12]:
∆NIT = (kF.N0/2kR)1/2.[D0.exp(-EA/kT)t]n,
where kF, kR are the Si-H dissociation and passivation rate
constants, N0 is total Si-H bond density, and D=D0.exp(EA/kT) is the diffusivity of released H species. Fig. 6 shows
that long t (varying T) data can be uniquely scaled along Xaxis and Y-axis directions to universal relations, which
yields EA for D and ∆VT respectively [1]. Obtained EA (D)
proves neutral H2 as the diffusion species [14]. This is also
consistent with n~1/6 power-law t dependence as predicted
by R-D model for H2 diffusion (Fig.2) [11]. Moreover, R-D
0-7803-9269-8/05/$20.00 (c) 2005 IEEE
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model suggests EA (∆VT) = EA (D) * n if EA (kF) ~ EA (kR)
[1], as also can be seen from Fig.6.
Interface-trap generation dominated NBTI
Fig.7 shows T dependence ∆VT (t) for devices with same
EOT but various N2 dose. ∆VT for both low and high N2
dose (and their difference) show similar EA (~EA (D) * n).
This proves that increase in NBTI due to increased plasma
N2 dose is due to increase in ∆NIT. To show the universality
that ∆NIT dominates ∆VT, a large number of samples with
different EOT and N2 dose (including control oxides) were
stressed at various T and oxide electric field (EOX). ∆VT (t)
was obtained using on-the-fly Idlin. For few cases ∆NIT (t)
was obtained (separately) from C-P on larger EOT samples.
The results are shown in Figs. 8 and 9 (control and plasma
N2 data plotted separately for clarity, and does not signify
actual magnitude).
Fig.8 shows X-axis scaling factors of T dependent ∆VT (t)
and ∆NIT (t) data. Very similar T activation (EA ranges from
0.54eV through 0.62eV) of all data clearly proves that ∆VT
~ ∆NIT, and plasma N2 and control oxides have very similar
T dependent kinetics. Since EA (kF) ~ EA (kR), T dependence
of ∆NIT is primarily due to that of D [1,9]. Moreover, that
the diffusing species is always neutral molecular H2 is also
unequivocally established (consistent EA (D) and n values).
Fig.9 shows EOX dependence of ∆VT and ∆NIT data. Since
diffusion species is neutral H2, EOX dependence is due to
½
½
that of (kF/kR) and has the form A.EOX exp (BEOX) [1,9].
Once again, qualitatively similar slope “B” suggests ∆VT ~
∆NIT, and plasma N2 and control oxides have similar EOX
dependent kinetics. We believe N2 incorporation impacts
“A”, possibly by reducing the Si-H bond dissociation
energy [15]. In short, control oxides and DPN oxides are
governed by very similar reaction and diffusion mechanics.
Dispersion in n
The transition from dispersive (short t) to Arrhenius (long
t) T activation (Fig.4) can be interpreted rigorously, and is
qualitatively explained using Fig.10. In the absence of deep
trapping sites, H2 would diffuse via shallow hopping sites
(standard diffusion) and shows weak T dependence. ∆NIT
equals total released H2 density (NH) and dNIT/dt = dFH/dx
= D0 d2NH/dx2 (FH: H2 flux).
In the presence of deep traps at a single energy level Ea=
EA, trapping and detrapping of H2 (to and from this level)
influences the T dependence of diffusion. If NHF, NHT are
free and trapped H2 density (NH = NHF + NHT), then NHF/N0
= [NHT/NT] exp (-EA/kT), if fast equilibrium is assumed. N0,
NT are the density of shallow hopping sites and deep traps.
Therefore, dFH/dx = D0 d2NHF/dx2 = D1 d2NH/dx2 (as only
free H2 can diffuse). Assuming (N0/NT) exp (-EA/kT)<<1,
and by rearranging terms, D1 = D0 (N0/NT) exp (-EA/kT).
Hence, Arrhenius T activation is obtained. In such a case,
NIT time evolution can be explained by standard R-D model
solution [1, 10-12] and the universal scaling scheme (Fig.6)
will hold good [1,9].
In the presence of trap energy distribution up to infinity,
trapping and detrapping of H2 to and from multiple energy
levels determine T dependence of diffusion. Emission time
constants of these levels are t=1/ν0 exp (E/kT), ν0 being the
attempt to escape frequency. As t increases, more and more
deep traps emit H2 and as a result, the energy centroid of
trapped H2, EM (t), goes down in energy. Using exponential
trap distribution as g(E) = NT/E0 exp(-E/E0) and assuming
fast equilibrium, NHF/N0 = [NHT/E0g(EM)] exp(-EM(t)/kT),
where EM (t) = kT ln (ν0t). Rearranging, NHF = NH [N0/NT]
exp [kT/E0 ln (ν0t)]/(ν0t), and dFH/dx = D0 d2NHF/dx2 = D2
d2NH/dx2, where D2 = D0 (N0/NT) (1/ν0t)^[1 – kT/E0], which
is a signature of dispersive diffusion [7,16].
For a real system with finite distribution of traps up to EA,
diffusion is dispersive till t=t0, as long as EM(t) reduces with
t. This get transformed to Arrhenius activated diffusion for
t>t0 as steady state is attained [EM(t0)~EA]. The transition
time is t0 = 1/ν0 [exp (EA/kT)]^[1/(1-kT/E0)], and reduces at
higher T. For EA = 0.58eV, Fig.4 predicts ν0 ~ 1012 s-1 and
E0 = 80meV, consistent with published values. (Accurate
determination of t0 can be influenced by non-equilibrium H
to H2 conversion, which can also affect short t slope).
Conclusion
NBTI time evolution is studied for plasma N2 oxynitride
p-MOSFETs. NBTI shows power-law time dependence for
a wide range of EOT, N2 dose, stress-VG and T. It is shown
that delay during measurements result in inaccurate powerlaw slope, which depends on delay time, measurement VG
and T. For zero delay measurements, short-time data shows
dispersive but long-time data show Arrhenius T activation.
It is clearly shown that strong long-time dispersion is an
artifact of measurement-delay. A theory for the transition of
dispersive to Arrhenius T activation is provided. NBTI is
governed by interface trap generation, which follows R-D
model. It is shown that DPN and control samples show very
similar T and EOX dependence of NBTI. Obtained n and EA
for diffusion suggests molecular H2 diffusion governs the
long-time evolution of NBTI behavior.
References
[1] S. Mahapatra et al., p.105, IEDM 2004
[2] Y. Mitani et al., p.509, IEDM 2002
[3] Y. Mitani et al., p.117, IEDM 2004
[4] V. Huard et al., p.40, IRPS 2004
[5] H. Aono et al., p.23, IRPS 2004
[6] S. Rangan et al., p.341, IEDM 2003
[7] B. Kaczer et al., p.381, IRPS 2005
[8] M. Dennis et al., p.109, IEDM 2004
[9] M. Alam et al., Micro. Reliability, v.45, p.71, 2005
[10] K. Jeppson et al., JAP, p. 2004, 1977
[11] S. Chakravarthi et al., p.273, IRPS 2004
[12] M. Alam, p.345, IEDM 2003
[13] S. Mahapatra et al., SSDM 2005
[14] M. L. Reed et al., JAP, p.5776, 1988
[15] S. S. Tan et al., p.70, SSDM 2003
[16] D. Monroe, Solid State Comm., p.435, 1986
Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on January 3, 2009 at 00:42 from IEEE Xplore. Restrictions apply.
O
15
EOT=21.4A , Dose=5.54x10 cm
-VG(stress)
O
10
O
t-delay
O
delay=50ms
10
0
10
1
10
2
3
slope:
0.162, 0.189
0.177, 0.211
1
10
2
10
0.24
15
10
-2
VG(stress)=-3V
Idlin
VG(meas)=-1.5V
0.18
Delay=200ms
VG(meas)~VT
IMEC(IRPS'05)
0.16
0.14
0
50
100
150
O
Temperature ( C)
10
slope:
0.221, 0.264
0.232, 0.289
1
10
10
2
Delay / slope
0ms / 0.17 (T1, T2)
250ms / 0.24(T1), 0.256(T2)
3
0
-1
O
15
-2
EOT=12.3A , Dose=2.34x10 cm
stress (-VG)
1.9V
O
T=100 C
2.1V
10
10
15
slopes:
0.174, 0.14
0.19, 0.14
0.237, 0.14
0.07
0.06
O
T( C)
50
100
150
0.05
0.04
0.03
0.02
t0=20-40s
-2
-3
0.00
5x10 -1 0
1
2
3
4
-1
0
1
2
3
4
10 10 10 10 10 10 10 10 10 10 10 10
stress time (s)
Fig.4. T dependence of ∆VT (t) measured using on-the-fly Idlin
technique, showing power-law (not log) time dependence. Short
time (t<t0) data shows higher slope at higher T (dispersive). Long
time data shows identical slope for all T (Arrhenius activation).
-1
10
O
-1
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)
slope=0.14
O
T=27 C
0
10
1
2
10
10
10
stress time (s)
3
O
15
10
O
T=27 C
-2
10
0
0
2x10
-2
O
-2
2
On-the-fly Idlin
VG(stress)=-1.9V
t0=2-4s
T=27 C
10
10
EOT=12.3A , Dose=1.44x10 cm
-1
T=100 C
∆VT (V)
1
10 10
stress time (s)
0.01
200
Fig.3. T dependence of power-law time exponent
from Idlin and C-P measurements. Higher dispersion
(increase in n with T) is seen for higher measurement
delay. C-P slopes are greater than Idlin slopes for
same T and t-delay.
10
O
T=T1 C
O
O
EOT=21.4A , Dose=5.54x10 cm
50ms (delay)
350ms
350ms
C-P
500ms
0.22
0.20
O
T=27 C
∆VT (V)
time exponent
0.26
1
10
Fig.2. (LHS) T dependence of ∆NIT (t) measured using C-P for
different t-delay. Increase in slope at larger T is more pronounced
when delay is high. (RHS) Numerical solution of R-D model with
and without delay. T-dependent slope observed for non-zero delay.
∆VT (V)
0.28
10
1
Delay
350ms
500ms
2x10 0
10
3
Fig.1. ∆VT (t) from Idlin measurements without and with
delay. (LHS) Different measurement bias, (RHS) different
measurement T. Slope increases for higher delay time,
higher T and lower measurement VG.
0.30
O
0
0
10 10
10
stress time (s)
O
T=T2 C
-2
-2
-VG(meas) / n
3.0V/0.138
1.5V/0.162
1.0V/0.189
T2>T1
D: 100X
kF: 3.1X
kR: 3.5X
9
O
T=50 C
2
10
R-D simulation, H2 molecule
CP (f=800kHz)
VG=-3.0V (stress)
T=150 C
9
On-the-fly
10
2
-2
∆NIT (x10 cm )
T=150 C
Delay
50ms
350ms
T=50 C
VG=-3.0V (stress)
15
EOT=21.4A , Dose=5.54x10 cm
Delay Idlin, VG=-3.0V (stress)
VG=-1.5V (measure)
-VG(meas)
∆VT (V)
-2
-2
-1
∆NIT (x10 cm )
10
1
Dose (x10 cm)
1.44
2.34
2
10
10
10
stress time (s)
3
-2
EOT(A ), Dose (cm )
15
10
21.4, 1.44x10
-2
10
15
12.3, 2.34x10
0
1
2
10
10
10
stress time (s)
3
Fig.5. T dependence of ∆VT (t) for various stress-VG, N2 dose and EOT, measured using on-the-fly Idlin technique. Nondispersive power law behavior is universally observed.
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-2
10
O
15
Control, EOT=12.8A
scale factor (a.u.)
scaled along
X axis
VG=-2.1V
O
27 C
O
-2
50 C
10
O
75 C
O
100 C
scaled along
Y axis
O
8x10
O
Plasma N2, EOT=12.3A
-2
Dose=1.44x10 cm
On-the-fly Idlin
∆VT (scaled, a.u.)
4
10
3
10
2
10
1
X-scale
EA=0.58eV
Y-scale
EA=0.085eV
10
-2
O
15
O
15
O
15
O
15
-3
15
IDlin / 21.4A / 5.54x10 / 8.5
15
C-P / 21.4A / 5.54x10 / 8.5
EA ~ 0.58eV
1
10
Control
O
IDlin / 12.8A / - / 8.0
-1
26
C-P / 26A / - / 9.1
28
30
NH
38
40
Ea = EA (single level)
D1 = D01 exp (-EA/kT)
NH
O
time (log scale)
O
C-P / 21.4A / 5.54 / 125 C
10
-2
B=0.4
Control
O
O
IDlin / 13.6A / - / 125 C
T2
T1
(b)
time (log scale)
O
C-P / 26A / - / 125 C
6
7
8
9
Oxide field, EOX (MV/cm)
10
Distance in oxide
Distance in oxide
0 < Ea < ∞
0 < Ea < EA
D2 = D01 (1/ν0t)^ [1 - kT/E0]NH
D = D2 (0 < t < t0)
D = D1 (t > t0)
Ea
∆NIT (log scale)
(a)
∆NIT (log scale)
∆NIT (log scale)
T1
O
IDlin / 21.4A / 5.54 / 125 C
Fig.9. EOX dependence of ∆VT and ∆NIT data, measured
on films having different EOT and N2 dose. Very similar
EOX dependence is observed for all films. Line is best fit
to control oxide data, and can be used as eye-guide for
plasma oxynitride data.
EA
T2
O
O
10 5
Distance in oxide
EA=0
D = D0 = µ. kT/q
O
O
IDlin / 16.4A / 4.29 / 150 C
-3
32 34 36
-1
1/kT (eV )
Distance in oxide
O
IDlin / 16.4A / 4.29 / 100 C
O
Fig.8. X-axis scaling (like Fig.6) factors for T dependent ∆VT
and ∆NIT data, measured on films having different EOT and N2
dose. Very similar T dependence is observed for all films. Line
is best fit to control oxide data, and can be used as eye-guide
for plasma oxynitride data.
NH
10
-1
O
10
O
O
O
IDlin / 12.3A / 2.34 / 125 C Plasma N2
0.5
10
O
IDlin / 12.3A / 1.44 / 125 C
IDlin / 12.3A / 2.34 / 90 C
15
O
O
O
O
∆VT / [A. EOX ] (a.u.)
X-axis scale factor (a.u.)
10
IDlin / 16.4A / 4.29x10 / 7.5
2
-2
IDlin / 12.3A / 1.44 / 100 C
0
IDlin / 12.3A / 2.34x10 / 8.0
O
Fig.7. T activation of ∆VT data for various
N2 dose. Lower and higher N2 dose (and
their difference) show identical EA, similar
to that of control oxide.
15
IDlin / 12.3A / 2.34x10 / 8.9
O
On-the-fly Idlin
stress: VG=-2.1V, t=10s
O
IDlin / 12.3A / 1.44x10 / 8.2
3
10
EA~0.085eV
-2
Probe/EOT/Dose(x10 cm )/T
IDlin / 12.3A / 1.44x10 / 9.1
10
-2
4x1028 30 32 34 36 38 40
-1
1/kT (eV )
1028 30 32 34 36 38 40
-1
1/kT (eV )
Probe/EOT/Dose(cm )/EOX(MV/cm)
Plasma N2
-2
15
2.34x10 cm
Difference
Fig.6. (LHS) Universal scaling scheme: ∆VT (t) data for various T is scaled along X
and Y-axis directions to universal relations. (RHS) T activation of X and Y-axis scale
factors. Obtained EA from X-axis scaling suggests molecular H2 diffusion. EA (Yscale) = EA (X-scale) * n as predicted by R-D model [1].
4
15
1.44x10 cm
0
-3
0
Plasma N2
O
125 C
3x10 0 1
2
3
4
5
6
10 10 10 10 10 10 10
time (s)
10
-2
∞
T2
T1
time (log scale)
(c)
∆NIT (log scale)
EOT=12.3A
∆VT (V)
7x10
t = t0 (T2)
T2
T1
t = t0 (T1) (d)
time (log scale)
Fig.10. Schematic of H2 diffusion process: (a) without trapping, (b) with single energy trap at EA, (c) with distribution (shape factor E0)
of traps up to ∞, and (d) with finite distribution of traps up to EA. Resulting T dependence of ∆NIT: (a) weak (Einstein relationship), (b)
Arrhenius activated (c) dispersive, and (d) dispersive at short time (t< t0), non-dispersive Arrhenius-like at longer time (t>t0).
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