Abstract—NBTI trapped charge characteristics and recovery
mechanisms are examined by a statistical study of individual trapped charge emissions in nanoscale HfSiON/metal gate pMOS-FETs. We measure individual trapped charge emission times in NBTI recovery in a large number of devices. The characteristic time distributions of the first three emitted holes are obtained. The distributions can be well modeled by using a thermally-assisted tunnel (ThAT) detrapping model. NBTI trapped charge energy and spatial distributions and its activation energy distribution in the ThAT model are discussed and extracted. Based on the ThAT model and measured result of single-charge induced Vt shifts,
we develop a statistical NBTI recovery ΔVt evolution model.
Our model can well reproduce the temporal evolutions of a ΔVt
distribution in a number of NBTI stressed nanometer MOSFETs in relaxation.
Index Terms—Activation energy, charge emission time, negative
bias temperature instability, recovery, statistical model.
I. INTRODUCTION
N
EGATIVE Bias Temperature Instability (NBTI) has been recognized as one of the most important reliability issues in ultra-thin gate oxide CMOS devices [1]–[4]. The use of a high-k gate dielectric even expedites NBTI degradation [3], [4]. Unlike most reliability effects, NBTI Vt degradation recoverspartly after the removal of stress [5]. Several circuit techniques exploiting NBTI recovery have been proposed to alleviate NBTI severity in memory and logic circuits [6], [7]. To improve a design window that is tightened by several variability sources, the integration of NBTI degradation and recovery character-istics into a circuit simulation is called for in modern CMOS circuit design [8]. Hence, underlying degradation and recovery
Manuscript received August 22, 2012; revised January 6, 2013 and January 8, 2013; accepted January 10, 2013. Date of publication February 8, 2013; date of current version February 20, 2013. The authors would like to acknowledge financial support from National Science Council, Taiwan, under contract NSC 99-2221-E-009-169-MY3 and from Ministry of Education in Taiwan under ATU Program. The review of this paper was arranged by Editor B. Kaczer.
J.-P. Chiu, Y.-H. Liu, H.-D. Hsieh, C.-W. Li, and T. Wang are with the De-partment of Electronics Engineering, National Chiao Tung University, Hsinchu 300, Taiwan (e-mail: twang@cc.nctu.edu.tw).
M.-C. Chen is with National Nano Device Laboratories, Hsinchu 30078, Taiwan.
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TED.2013.2240390
mechanisms of NBTI must be understood in order to make a meaningful projection of a device/circuit lifetime. While the reaction-diffusion (RD) model [2], [9]–[11] and a charge trap-ping model [12]–[17] are commonly adopted for NBTI degra-dation, no consensus regarding NBTI recovery mechanisms has been reached. Hydrogen back-diffusion in the framework of the RD model was first proposed to explain a NBTI recovery phenomenon [11]. A ΔVtrelaxation of the form of ΔVt(t) = Vt(0)(1−t/2t0/
1 + t/t0) is anticipated from the back
diffusion theory. Wang et al. used a fast transient technique to characterize NBTI recovery and found a log(t) dependence of ΔVton relaxation time in a time span from 10−3s to 102s [18].
Moreover, they characterized individual trapped hole emissions in small-area devices and proposed a thermally assisted charge tunnel detrapping (ThAT) model for a recoverable component in relaxation [18], [19]. A log(t) dependence was also reported in [20] where the authors proposed a dispersive transport model within the RD framework to overcome the apparent deficiency of the RD model with respect to relaxation time dependence. Alam et al. ascribed a log(t) recovery transient to a fast charge detrapping process on top of slower Nit re-passivation
as encapsulated by the RD model [21], [22]. More recently, Grasser et al. used a time dependent defect spectroscopy method to investigate NBTI recovery and concluded that NBTI recovery is due to thermally-assisted discharging of traps and no diffusion process is involved [17]. Their conclusions are consistent with [18].
In most of earlier works, NBTI behavior was characterized in large-area devices [20], [23] and studies were based on an average and continuous Vt evolution [20]–[23]. In contrast,
NBTI degradation/recovery proceeds in discrete steps in small area devices [18], [24]. Due to the discrete nature of a Vt
evolution, we are able to measure individual trapped charge emission times and each single trapped charge induced Vtshift.
Statistical characterization of NBTI degradation/recovery in small area devices therefore provides important information to help understand a responsible mechanism as well as trapped charge characteristics such as trapped charge energy and spatial distributions and its activation energy distribution. Moreover, a NBTI model accounting for an entire ΔVt distribution is
required in a worst-case circuit simulation. In this paper, a statistical model based on a ThAT model and an extracted activation energy distribution will be developed for a NBTI recovery ΔVtdistribution and its temporal evolutions.
Fig. 1. Example ΔIdand Vttraces in NBTI relaxation. τ1, τ2and τ3 are
the 1st, the 2nd and the 3rd trapped hole emission times, respectively. Δvt,i
(i = 1, 2, 3) represents a single emitted charge induced threshold voltage shift. II. STATISTICALCHARACTERIZATION
OFNBTI RECOVERY
We characterize NBTI recovery in high-k (HfSiON) gate di-electric and metal gate pMOSFETs. The devices have a nominal gate length of 35 nm, a gate width of 70 nm and an effective oxide thickness of ∼1.0 nm. The devices are first stressed at Vg=−1.8 V for 100 sec. The recovery characterization
scheme is similar to [13], i.e., in a relaxation-measurement-relaxation sequence. Both stress and recovery characterizations are performed at room temperature. In measurement phase, the drain voltage is−0.05 V and the gate voltage is chosen such that the pre-stress drain current is ∼500 nA. Drain current variations are recorded using Agilent B1500. The cumulative relaxation time in each device measurement is 1000 s. A corre-sponding ΔVttrace is obtained from a measured ΔIddivided
by a transconductance [25]. Fig. 1 shows example ΔId and
Vt traces in NBTI relaxation. Each abrupt Vt change (Δvt,i)
in the trace is due to a single trapped hole emission, where i denotes a charge detrapping sequence number. Any identifiable RTN signals are not counted. We collect all Δvt,i in ∼170
devices. The magnitude distributions of Δvt,1, Δvt,2 and all
collected Δvt are plotted in Fig. 2. Emitted trapped charges
have a similar Δvtdistribution, characterized by an exponential
function f (|Δvt|) = exp(−|Δvt|/σ)/σ with a σ of 3.3 mV.
The origins and the distribution of the Δvt have been studied
thoroughly and the exponential distribution is realized due to a random substrate dopant induced current path percolation effect [24], [26].
A. Trapped Charge Emission Times
Individual trapped charge emission times, for example, τ1,
τ2 and τ3 in Fig. 1, are clearly defined. We collect the first
three emitted charge characteristic times (τi, i = 1, 2, 3). The
emission characteristic times scatter over several decades of time. The probability density functions (PDFs) of the log(τi),
i = 1, 2, 3, are shown in Fig. 3. The mean (log(τi)) and the
standard deviation (σi) of the distributions are indicated in the
figure. The relationship between thelog(τi) (i = 1, 2, 3) is
easily identified. The mean increases by the same amount with a sequence number, i.e.,log(τi+1) − log(τi) ≈ 1.04. On the
other side, the standard deviation σiincreases with i from σ1=
Fig. 2. Magnitude distributions of Δvt,1, Δvt,2and all collected Δvt,ifrom
NBTI recovery traces in 170 high-k/metal gate pMOSFETs.
Fig. 3. Probability density distributions of a trapped charge (hole) emission time in a log(τ ) scale. τ1, τ2and τ3are the 1st, the 2nd and the 3rd trapped
hole emission times, respectively. The mean (log(τi)) and the standard
deviation (σi) of the distributions are indicated in the figure. The symbols are
measurement result and the solid lines are from Monte Carlo simulation. 1.070 to σ3= 1.285, but its dependence on a sequence number
i is more subtle and requires consideration of trapped charge spatial and energetic distributions and its activation energy. We collect all the charge emission times in about 170 devices and plot their occurrence number distribution in a log(τ ) scale in Fig. 4. A rather uniform distribution from 10−2 s to 103 s in Fig. 4 is obtained, implying a log(t) dependence of a recovery ΔVtin a large area device.
Fig. 4. Histogram of all trapped charge emission times in a log(τ ) scale collected from 170 devices. The occurrence number distribution is rather uniform in a period from 10−2s to 103s.
B. Trapped Charge Spatial and Energy Distributions
According to the ThAT model [19], a trapped charge tunnel emission time in a high-k MOSFET can be expressed as
τi= τ0exp
Ea kT
exp(αILTIL) exp(αkxi) (1)
αIL= 22m∗ILq(Et+ φB) (1a) αk=2 2m∗HKqEt (1b)
where the pre-factor τ0is a lumped parameter, Eais activation energy, TIL is an interfacial layer thickness, xi denotes a trapped charge distance to the HK/IL interface and Et is a trapped charge energy. Other variables have their usual def-initions in [19]. The hole tunneling mass used in this work is m∗IL= 0.41m0 [27] and m∗HK= 0.18m0 [28]. According
to (1), a tunneling front moves in a speed of d = 2.3/αk per decade of time. A removable trapped charge density (Nt) in relaxation therefore can be extracted from the emission occur-rence number versus log(τ ) in Fig. 4 as follows:
Nt=no. of emitted charges/device/decade W× L × d
=αk× (no. of emitted charges/device/decade)
2.3× W × L . (2)
Since the number of emitted charges exhibits a uniform distribution approximately in each decade of time in Fig. 4, we obtain a constant removable trapped charge density Nt in space. With respect to a trapped charge energy distribution, we calculated a voltage drop across an interfacial oxide in NBTI stress by a 2-D numerical device simulation [29]. Quantum corrections are not included in the simulation. The calculated voltage drop is about 0.8 V at a stress Vg of −1.8 V. We
therefore assume that removable trapped holes are uniformly distributed in an energy range of 0 to 0.8 eV above the Si valence band-edge, corresponding to an Etvalue of 2.7 eV to 3.5 eV with respect to the valence band-edge of the HfSiON. This assumption is also adopted in [30] and is supported partly
Fig. 5. Schematic representation of a band diagram of a high-k/metal gate pMOSFET in relaxation. xiand Et represent a trapped charge position and
energy.
by a charge pumping measurement result [31]. Fig. 5 illustrates a removable trapped charge distribution and a band diagram in recovery. The calculated value of αk is from 7.2 to 8.1 nm−1. For simplification, we used an average αk(= 7.65 nm−1) in (2) and obtain a Ntof 1.3× 1018cm−3. An average distance (Δx) between two adjacent trapped charges in the gate-to-substrate direction is about Δx = 1/W LNt∼ 0.32 nm. In addition, the ratio of the emission times of two consecutive emitted trapped charges is
log(τi+1) − log(τi) = 1
2.3× [αk· (xi+1 − xi)]
≡ 1
2.3× (αk· Δx) . (3)
Equation (3) shows that the mean of the log(τi) increases
with i by the same amount, i.e., αkΔx/2.3 = 1.06, without regard to activation energy. Equation (3) is consistent with the measurement result in Fig. 3.
C. Activation Energy Distribution
Note that our NBTI emission time model (1), unlike a RTN model, does not have explicit electric field dependence. In contrary, an NBTI emission time model in [17] shows an exponential electric field dependence. The difference is in that a removable trapped hole in our model is assumed in an energy range above the valence band-edge in relaxation (Fig. 5). This assumption is reasonable because of a large voltage drop (0.8 V) across the interfacial oxide in NBTI stress. The mea-surement results in literature [17], [19] also do not support an exponential field dependence in NBTI recovery. Since an electric field is a secondary effect in NBTI recovery, the wide spread of the trapped charge emission times in NBTI recovery is believed mainly due to an activation energy distribution caused by local chemistry.
From (1), Eacan be expressed as
Fig. 6. Relative activation energy (Ea− Ea) distributions extracted from
the τ1, τ2and τ3, respectively. τ0in (4) is chosen such that theEa is about
0.5 eV. The solid line is a Gaussian-distribution fit.
To extract an Ea distribution from the measured τi, average
values of αk and xi are used in (4) for simplification. The average distance between two consecutive emitted charges is 0.32 nm. The extracted Ea distributions from τ1, τ2, and τ3,
respectively, are shown in Fig. 6. A good match between them is obtained. It should be remarked that the distortion of the Ea distribution of i = 1 is understood because our recovery measurement starts with a time delay of 5 ms. Thus, some emitted charges with very short τ (< 5 ms) are not counted. In Fig. 6, an appropriate τ0 is chosen such that the mean of an
Ea distribution is about 0.5 eV [33]. The solid line in Fig. 6 represents a Gaussian distribution fit with a mean of 0.5 eV and a standard deviation of 0.07 eV. To examine the validity of the Eaextraction, we re-calculate the τ ’s distributions based on an extracted Ea distribution by a Monte Carlo method. In the Monte Carlo procedure, the number of removable trapped charges in each device is selected according to a Poisson distribution [24] with an average number of NtW LTHK, where
THKis the thickness of a high-k dielectric. The use of a Poisson
distribution here is an approximation and its correctness has been discussed in [32]. Then, removable trapped charges are randomly placed in the HK layer. For each trapped charge, an Etis selected in a range from 2.7 eV to 3.5 eV and an Ea is selected according to the distribution in Fig. 6. With a trapped charge location, energy and activation energy, an emission time is calculated according to (1). An emission sequence number is then assigned to each trapped charge according to its calculated emission time. A trapped charge with the shortest τ has i = 1, and the second shortest one has i = 2 and so on. The Monte-Carlo simulated τi (i = 1, 2, 3) distributions (solid lines) are
plotted in Fig. 3. A reasonable agreement between simulation and measurement is obtained. The broadening of the log(τi)
with a sequence number i in Fig. 3 can be partly explained as follows. We re-arrange the terms in (4) and obtain the following equation: log(τi) = 1 2.3 Ea kT + 2.3 log(τ0) + αILTIL+ αkxi . (5)
As i increases, the tunneling distance xi is larger and the variance of the term (αkxi) in the right hand side increases and so does the variance of log(τi).
Fig. 7. Dependence ofτ1 on recovery temperature. The extracted activation
energy is about 0.53 eV. Each data point is an average of ten readings.
The dependence of a hole emission time on recovery temper-ature is investigated. The tempertemper-ature characterization is some-what difficult because some of NBTI traps might be annealed at high temperatures. For this reason, we chose a single-NBTI trap device. We take an average of τ1 from ten measurements
on the same device by repeatedly re-filling a NBTI trap, i.e., a refilling-recovery-refilling sequence. The result in Fig. 7 shows a linear relationship between a hole emission timelog(τ) and 1/kT, suggesting a thermally- assisted process and Arrhenius activation energy.
III. MODELING OF ARECOVERYΔVtDISTRIBUTION
We measure threshold voltage shifts in a large number of devices at different recovery times. The number of emitted holes and a total threshold voltage shift (ΔVt) in each device
are recorded. Fig. 8 shows the measurement results at a re-covery time of 0.1 sec, 10 sec and 1000 sec. The y-axis is a total ΔVtand the x-axis is the number of emitted holes. Each
data point represents a device. A straight line with a slope of 3.3 mV, i.e., an average single-charge induced Vt shift, is
drawn in the figure as a reference. The measurement results scatter along the line. The ΔVtand the emitted charge number
distributions broaden with recovery time in the measurement period. An average of recovery Vt traces in 170 devices is
plotted in Fig. 9, which reflects an observed recovery charac-teristic in a large-area device. A Monte Carlo ΔVtdistribution
model based on the ThAT and extracted trapped charge spa-tial, energetic and activation energy distributions is developed. The simulation flowchart is shown in Fig. 10. For a recovery time tr, the number of emitted charges (N ) is computed by counting all the charges with τi less than tr. For each emitted charge, a Δvt is randomly selected based on the
dis-tribution f (|Δvt|) = exp(−|Δvt|/σ)/σ with σ = 3.3 mV. A
total ΔVt is then calculated as ΔVt=
N
i=1Δvt,i. In total, 5× 105 devices are simulated. The simulated and measured ΔVtdistributions are shown in Fig. 11 at a recovery time of
tr= 0.1 s, 10 s and 1000 s. Our model is in good agree-ment with measureagree-ment. The mean and the variance of the ΔVt distributions versus recovery time are shown in Figs. 9
Fig. 8. Total Vt shift (ΔVt) versus number of emitted trapped holes in a
device at a recovery time of 0.1 s, 10 s and 1000 s. Each data point represents a device. A straight line with a slope of 3.3 mV is drawn as a reference.
Fig. 9. Evolution of ΔVtwith a recovery time. The solid line represents an
average of measured ΔVttraces in 170 devices. The symbols are the mean of
Monte Carlo simulated ΔVtdistributions. A logarithmic time dependence of
ΔVtis obtained.
dependence in a large-area device as well as an overall ΔVt
distribution and its temporal evolution in small-area devices. In short, the log(t) behavior is a result of a uniform spatial distri-bution of trapped charges while Eaand Etdistributions affect a ΔVt distribution and its temporal evolution in small-area
devices.
Fig. 10. Simulation flowchart of a Monte Carlo based ΔVtdistribution model
for NBTI relaxation.
Fig. 11. Probability density distributions of NBTI recovery ΔVtin 70 nm×
35 nm pMOSFETs from measurement and from a Monte Carlo simulation. The recovery time is 0.1 s, 10 s, and 1000 s.
Fig. 12. Variance of a recovery ΔVtdistribution versus a recovery time in
70 nm× 35 nm pMOSFETs from measurement and from a Monte Carlo simulation.
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Jung-Piao Chiu received the B.S. degree in
elec-tronics engineering from National Chiao Tung Uni-versity, Taiwan, in 2007, and is currently working toward the Ph.D. degree.
His research interests are reliability analysis in advanced CMOS and Flash memory devices.
Taiwan, in 2012.
His research interests include electric characteri-zation and reliability study of high-k CMOS devices.
Chi-Wei Li is currently working toward the M.S.
de-gree with the Department of Electronics Engineering and the Institute of Electronics from NCTU, Taiwan. His research interests are reliability analysis in high-k devices and RTN.
Taiwan University and the PhD degree from the University of Illinois, Urbana-Champaign.
Currently, he is a Professor at National Chiao-Tung University, and an Editor of IEEE ELECTRON
