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December 10, 2012

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Resume:

Gate Leakage vs. NBTI in Plasma Nitrided Oxides: Characterization, Physical

Principles, and Optimization

*1A.E. Islam, 2G. Gupta, 2S. Mahapatra, 3A.T. Krishnan, 4K. Ahmed, 4F. Nouri, 5A. Oates, 1M.A. Alam

*Email: *******@******.***, Phone: 765-***-****, Fax: 765-***-****

Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA; 2Department of EE, IIT Bombay, India;

Texas Instruments, Dallas, TX, USA; 4Applied Materials, Inc., Santa Clara, CA, USA; 5Taiwan Semiconductor Manufacturing

Corp., Hsin-Chu, Taiwan.

Abstract

Since nitrided oxides improve gate leakage at the expense of 1

NMOS

PMOS

NBTI, one must optimize nitrogen concentration in oxinitride

samples for reliable performance and reduced power

dissipation. Here, we analyze wide range of NBTI stress data

JG [A/cm ]

to develop a predictive model for gate leakage and first self- -1

consistent model for field acceleration within R-D E OT: 1.3 nm

framework. This model anticipates a novel design diagram S imulation

for co-optimization of leakage and NBTI for arbitrary D ose= 14.5%

D ose= 21.2%

nitrogen concentration and effective oxide thickness. -3

0.5 1.0

- 1.0 -0.5 0.0

1. Introduction V G [Volts]

Fig. 1: Experimental leakage current (JG) vs. gate voltage (VG) curves

Since nitrided oxides (SiON) improve gate leakage (JG) [1-6]

for SiON devices (14.5% and 21.2% N2 dose) in inversion region,

at the expense of NBTI performance ( VT) [7,8], one must fitted using simulation.

necessarily optimize N2 concentration (%N) in gate-oxides for

high-performance ICs. Despite its importance, however, a Quadratic Fit 0.4

quantitative analysis of leakage/NBTI trade-off (as a function di

of %N), has never been reported and the question Is co- mox

optimization of NBTI/leakage possible at any %N? has never

been answered. In this paper, we simultaneously measure gate

0.3

mox

leakage and delay-free NBTI over broad range of stress-fields,

stress-temperatures and %N, model gate leakage current (JG)

and NBTI degradation within a theoretically consistent

framework (hole-assisted thermal generation of interface traps) 4 (a)

0.2

of field-dependent R-D model, and conclude that although *-**-**-**-**-** 60

there is no optimum %N for NBTI/leakage, the reduction in JG Nitrogen concentration (% atomic)

at NBTI-limited %N (~15-25%, depending on failure criterion) Quadratic Fit 10

can be significant and would reduce power dissipation without 3.0

affecting NBTI-margin. Eg

2. Gate Leakage 8

2.5

Eg [eV]

be [eV]

Comprehensive simulation [9] (which includes the effects of

multi-subband electron/hole quantization, poly-depletion, etc.)

of the measured JG-VG for both N- and PMOS (Fig. 1) was 2.0

done to extract the model parameters as a function of %N (Fig.

2). We assume that any variation in the spatial-profile of

1.5 4

nitrogen results only in second-order correction to calculated 0

**-**-**-**-**-**

JG. Contrary to popular belief [2-6, 10], the oxide parameters Nitrogen Concentration (% atomic)

do not scale linearly with %N. All the parameters have Fig. 2: Variation of gate leakage model parameters with %N (0% for

SiO2, 57.1% for Si3N4) (a) relative permittivity for SiON dielectric, di

approximately a quadratic fit with %N. Here, effective oxide

and oxide effective mass, mox ( b) barrier height for electron, be and

thickness (EOT) is obtained from simulation of CV, and bandgap, Eg. For Si3N4, parameters are obtained from references [2-6]

physical thickness (TPHY) and %N are determined by XPS [11]. ( be: 2.1 eV, Eg: 5.1 eV, di: 7.6, mox: 0.23~0.28). The error bars show

These %N-dependent parameters are used to calculate the variation in parameters expected due to 0.5 error in

JG(N,EOT) for arbitrary %N and EOT, as shown in Fig. 10b. measurement of TPHY by XPS.

1-4244-0439-8/06/$20.00 2006 IEEE

The assertion that NBTI degradation is field-driven is well

3. Reliability based on NBTI

known [12, 13] and easily established by Fig. 5 and R-D

NBTI performance for different SiON devices is monitored

analysis of wide variety of stress data (Fig. 6). The explicit

here by calculating safe operating voltage (Vsafe), which is

parameterization of this Eox dependence is discussed below.

defined as the stress voltage at which device can operate up

to its lifetime (tlife) without crossing the failure criteria (e.g.

60mV of VT [1]). As shown in Fig. 3, degradation data taken

at different stress voltages (V1, V2, V3, V4) can be fitted with

analytical expressions, based on the field-dependent R-D

model to be discussed Section 3.1. Such fitting can be used to

extract lifetimes (t1, t2, t3, t4) at stress voltages and Vsafe, based

on failure criteria. The calculated Vsafe(N,EOT) for arbitrary

%N and EOT is plotted in Fig. 10a.

Fig. 4: Hole-assisted, field-enhanced model for Si-H thermal bond

dissociation. kr0 is assumed to field independent to first order.

VT : 0.167

Temp = 125 0C [13]: 0.167

(dec/MV/cm), V (dec/V)

[14]: 0.167

[12]: 0.167

ID(lin): 0.14, 0.155

VT : 0.14

Fig. 3: Procedure for obtaining lifetimes (t1, t2, t3, t4) at different stress

voltages (V1, V2, V3, V4) a nd VSafe using NBTI model, discussed in section

3.1. Proper VG-Eox transformation is used here and Idlin0 was obtained within

1ms of application of stress.

10 20 30 40 50

3.1 Field-Dependent R-D model EOT, A

Fig. 5: and V (voltage acceleration factor) [12] variation with EOT (n is

Since NBTI is field-dependent [12], the Eox (calculated either mentioned for each case). For field-dependent NBTI model, r emains

from direct integration of CV, or approximated using proper almost constant (~0.6 0.05; dashed line) and V ~ 1/EOT ( solid line) [12].

VG-Eox relationship) dependence of NBTI parameters needs to For VT measurements, necessary dela y correction is done.

be established. The R-D model anticipates that [13]

NIT ~(kf0N0/kr0)2/3{D0exp(-ED/kBT)t}1/6 (1)

for neutral-H2 diffusion [13-15], which is supported by delay-

free NBTI measurements [13-16]. Since the diffusion co-

efficient pre-factor, D0=l2 0 (l is lattice constant, 0 is attempt

frequency) is field-independent, NBTI field-dependence must

be encapsulated in the ratio of forward (kf0) and reverse (kr0)

dissociation constants, i.e. kf0/kr0. Such model assumes that

holes [ph Ec; the field due to mobile carriers] at the Si/SiON

interface tunnel into [probability, PT ~exp( TEox)] and is

captured by Si-H bonds [cross-section, ] ~2 away from the

interface, leading to a hole-assisted, field-enhanced, thermal

generation [rate, B exp(-(EF0-aEox)/kBT)] of interface traps

(Fig. 4). Based on these relations, Eqn. (1) transforms to

NIT = A Ec 2/3exp(2 Eox/3)exp(-nED1/kBT)tn (2)

where, = T+a/kBT, nED1= nED+2/3(EF0-ER0); n~1/6.

Fig. 6: Fitting VT vs. t (log-log scale) at different T a nd VG by (2),

Eq. (2) suggests the overall activation energy for NIT will be

validates the universality of the model, which gives A,, n a s fitting

EIT = nEA = nED + 2/3(EF0 ER0 -aEox). (3) parameters for each temperature (effect of ED1 can be included in A). Here

n =0.15~0.16, indicating H2 diffusion and N2 dose: 8%

H- - Electro-negativity:

0% N2

~ Penetration at 2A [a.u.]

Si: 1.8 H: 2.1

0.6 14.5% N2

Si+ - Ionic bond energy:

[dec/MV/cm]

UH-Si =1.3 (xSi - xH)2 = 0.1 eV

21.2% N2

- SiH Bond length: r = 1.5

T ~ 0.18

- Effective charge transferred:

0.4 Ze = (4 0r UH-Si) = 0.1e

N2 dose: 8% - D ipole Moment: p = Ze . r = 0.15 e

= 0.157

T = 0.27 0.05 dec/MV/cm - Local E-field: Eloc = (1+L )Eox = Eox

0.3 T

a = 0.8 0.15 (Lorentz factor, L = 1 for dipole normal to a thin

4 5

6 7 8 9

0.2 slab)

*-**-**-**-**-** Eox [ MV/cm] - Effective Dipole Moment: a = p = 0.6 ~1.2 (

1/k T [eV-1] Fig. 7b: Wavefunction penetration at 2 (from at the interface may be in between 3.9 ~ 8 [20])

B C-V analysis) modeled using A1exp( TEox).

Fig. 7a: vs. 1/kBT plotting. obtained from Fig. 6 is Analytically [19], T~ (mox/ bh) and A1~

Fig. 7c: Polarization properties of SiH bond,

used here. The obtained T = 0.27 0.05 dec/MV/cm exp (mox bh), which are consistent with the

indicating a = 0.6 ~ 1.2 . [21]

and a = 0.8 0.15 obtained variations using parameters of Fig. 2.

3.2 Extraction of T and a 3.3 Parametric dependence on %N

The tunneling coefficient T can either be determined by the The methodologies discussed above have been used to

intercept of measured (extracted from Fig. 6) vs. 1/kBT plot analyze the Eox and T-dependent NBTI data at various %N to

determine (N) [= T(N)+a(N)/kBT] and EA(N) (see Fig. 8, 9).

(Fig. 7a) or estimated by the simulation of PT(Eox) (Fig. 7b,

While T depends weakly on %N (Fig. 7b), a(N)=kBT [ (N) -

based on parameters from Fig. 2). Both approaches provide

T(N)] ~ 0.25 dEA/dEox and EA(N) shows systematic variation

comparable results. Similarly effective dipole moment a can

either be measured from slope of vs. 1/kBT plot (Fig. 7a) with %N (Fig. 8, 9 [18]). Hence, our analysis shows that the

NBTI degradation with %N variation can be attributed to

and/or from EA vs. Eox variations (Fig. 9), or be theoretically

three factors: reduction of over-all barrier height for

estimated by molecular modeling approach (Fig. 7c). The

dissociation nED1, variation in A(N) and modification of

summary in Table 1 shows that theory and measurements

effective dipole moment a, with negligible contributions from

provide remarkably consistent results. Therefore, part of the

induced hole density (ph).

Eox-dependencies of NBTI arises from Eox-dependence of PT

and the other part, from Eox-induced thermal barrier lowering, 4. Optimization

B (Fig. 9). This, we believe, is the first consistent interpretation

The parameters of (N), EA(N), a(N), n(N), derived by fitting

of field-dependence of NBTI degradation within the R-D

the NBTI data and encapsulated within the field-dependent

framework. Previous analysis of delay-contaminated NBTI

R-D model discussed above, can now be used to calculate

data [17] suggested experimental values of a that was 3~4

Vsafe(N,EOT) for any combinations of %N and EOT (Fig.

times larger than theoretically expected values. It appears that

10a). Fig. 11 summarizes the results for JG(N,EOT) and

similar to resolution of puzzles involving time-exponent

Vsafe(N,EOT), indicating that co-optimization for DC-NBTI

(n=0.25 0.16) and temperature dispersion parameter

and ITRS-limited JG [1] may sometimes require reduced

(d=0.6 0) [13], zero-delay measurements and partitioning T

temperature, inclusion of AC effects [23], and NBTI aware

into T+a/kBT (previous work incorrectly assigns =a/kBT [17]

design [24]. The diagram can be used to calculate any pair of

or = T [12] exclusively) hold the key for consistent estimation

the variables (Vsafe, JG, %N, EOT) when the other pair is

of field-acceleration of NBTI degradation.

given. For example, if an IC design requires Vsafe = 1.1V and

0.65

TABLE 1

Temp=125 0C 1.55 V

1.55V

Comparing a determined by various methodologies 0.6

a/kBT 2.1V

2.1 V

a [ ] Obtained from 1.9V

[dec/MV/cm]

0.6 1.9 V

E [eV]

~4a Eox

Fit of = T +a/kBT

0.8 Fig. 7a 0.4

Fig. 8 Expe

a = ( - T )kBT

0.86 (avg.)

0.55

rime ~4a Eox

0.98 (avg.) a = 0.25 dEA/dEox Fig. 9 0.2

a = ( - T )kBT *

1.47 [17]

0.5

0 0 10 20 30

0.6~1.2 Si-H polarizationFig. 7c Calc 0 14.5 21.2

Nitrogen concetration (% atomic)

[22] ulati

0.65 (avg.) First Principle Fig. 9: EA determined for various sample.

on Fig. 8: Variation of with %N, after fitting With change in %N, there is a systematic

* obtained after delay correction and T ~ 0.27. degradation curves for SiON devices, using (2). As variation in EA. There is also slight

In reference, a = 3.2 stated in the text, will have two parts T ~ 0.225, decrease in EA with increase in VG, because

For Equilibrium structure 0.27, 0.27 (from Fig. 7a and 7b) and a/kBT. EA = ED+2/3n(EF0-ER0-aEox).

3.0 Stress Condition

F ailure Criteria:

Safe Condition

V T = 60 mV; tlife = 5 years

Exponential fit

2.5 0

At T=125 C

log 10(tlife)

Power law fit

1 .6 nm 1.4 nm

1 .2 nm 1.0 nm

2.0

Vsafe [V]

1.5

4 6 8 10

1.0 0

A C Derating = 8; T = 85 C

E, MV/cm

%Nmax required for having V safe = Vdd(ITRS)

Fig. 12: Comparison between exponential and power law fit of VT data

0.5

for obtaining safe operating condition using stress data. Procedure in Fig.

0 5 10 15 20

Nitrogen concentration, % atomic 3 used for obtaining safe condition. Exponential fit underestimates and

power law fit overestimates tlife.

Fig. 10a: Vsafe vs. %N at different EOT (Failure criteria: VT = 60

JG = 10A/cm2 (point A, Fig. 11), the design diagram suggests

mV, tlife=5 years[1]). Dotted line for 1.6 nm EOT indicates the

improvement with AC derating = 8 and T = 85 0C.

an EOT = 1.4nm and %N 17%.

5. Conclusion

1000 NMOS

We have analyzed an extensive set of NBTI data to develop

JG [A/cm ] @ VG= Vdd(ITRS)

the first self-consistent model for field acceleration within R-

100

D framework (compared with other empirical formulation in

Fig. 12), constructed a novel design diagram for co-

optimization of JG and NBTI for arbitrary %N and EOT

combinations, and established the DC (AC)-NBTI limited

upper limit of %N ~ 15-20% (20-25%) for core CMOS

technologies. We anticipate that our analysis would have

1.0 nm 1.2 nm

1.4 nm 1.6 nm broad impact for optimization of %N content in sub-2nm gate

0.1

*-**-**-**-**-** 60 dielectrics.

Nitrogen Concentration, %atomic

Acknowledgement

This work was done with financial support from TI, AMAT, TSMC, Renesas

Fig. 10b: JG @ Vdd(ITRS) for NMOS vs. %N for different EOT. The

and SRC. We also acknowledge NCN for providing computational resources.

error bar @1.2 nm indicates JG variation, expected due to 0.5

error in TPHY, which is negligible upto 30% N2 dose.

References

[1] ITRS 2005 version.

VG = 1.2,1.0,0.8 V %N

[2] M.L. Green et al., JAP, 90(5), p. 2057, 2001.

20 15 10 5 0

[3] P.A. Kraus et al., TED, 52(6), p. 1141, 2005.

1.0

10 [4] G. Lucovsky et al., JVST -A, 18(4), p. 1163, 2000.

10 [5] X. Guo et al., EDL, 19(6), p. 207, 1998.

10 [6] H.Y. Yu et al., TED, 49(7), p. 1158, 2002.

1.2

10 [7] S.S. Tan et al., APL, 82(12), p. 1881, 2003.

EOT(nm)

J G [A/cm -2 ]

10 [8] D.K. Schroder et al., JAP, 94(1), p. 1, 2003.

JG [ A /cm ]

10 [9] A. Ghetti et al., SISPAD, p. 239, 1999.

A 1.4

10 [10] D.M. Brown et al., JES, 115(3), p. 311, 1968.

10 [11] J.R. Shallenberger et al., JVST -A, 17(4), p. 1086, 1999.

[12] M.A. Alam et al., Micro. Reliability, 45(1), p. 71, 2005.

1.6

10 [13] D. Varghese et al., IEDM, p. 684, 2005.

10 [14] S. Chakravarthi et al., IRPS, p. 273, 2004.

-1

[15] A.T. Krishnan et al., IEDM, p. 688, 2005.

0.8 1 1.2 1.4 1.6 1.8 2

-1

10 [16] C.L. Chen et al., IRPS, p. 704, 2005.

0.8 1 1.2 1.4 1.6 1.8 2

-1

10 [17] K.O. Jeppson et al., JAP, 48(5), p. 2004, 1977.

0.6 0.8 1 1.2 1.4 1.6 1.8 2

Vsafe [V] [18] J.P. Campbell et al., IRPS, p. 442, 2006.

Vsafe [V]

[19] Register et al., APL, 74(3), p. 457, 1999.

Fig. 11: Design diagram for SiON devices, obtained by using Fig.

[20] Muller et. al. Nature, 399(6738), 1999.

10a and 10b (JG @ VG = 0.8, 1.0, 1.2V are considered). Example:

[21] Mcpherson et. al., JAP, 84(3), p. 1513, 1998.

choose VG= Vsafe from x-axis and JG from VG specific y-axis, then

[22] Ushio et al., JAP, 97(8), 2005.

read off corresponding %N and EOT. Inclusion of AC effects and

[23] M.A. Alam, IEDM, p. 345, 2003.

temperature reduction will right-shift the diagram, thus enabling

[24] B.C. Paul et al., EDL, 26(8), p. 560, 2005.

co-optimization at smaller EOT.

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