Characterization and modeling of trap number and creation time distributions under negative-bias-temperature stress

(1)

Characterization and modeling of trap number and creation time distributions under

negative-bias-temperature stress

Jung-Piao Chiu, Chi-Wei Li, and Tahui Wang

Citation: Applied Physics Letters 101, 082906 (2012); doi: 10.1063/1.4748108

View online: http://dx.doi.org/10.1063/1.4748108

View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/101/8?ver=pdfcov Published by the AIP Publishing

Articles you may be interested in

Temperature dependence of the emission and capture times of SiON individual traps after positive bias temperature stress

J. Vac. Sci. Technol. B 29, 01AA04 (2011); 10.1116/1.3532947

Bias stress voltage dependence for fast and slow traps resulting in negative bias temperature instability J. Appl. Phys. 107, 024511 (2010); 10.1063/1.3283923

Influence of hydrogen dispersive diffusion in nitrided gate oxide on negative bias temperature instability Appl. Phys. Lett. 93, 013501 (2008); 10.1063/1.2956388

Critical analysis of short-term negative bias temperature instability measurements: Explaining the effect of time-zero delay for on-the-fly measurements

Appl. Phys. Lett. 90, 083505 (2007); 10.1063/1.2695998

Impact of Hf content on negative bias temperature instabilities in HfSiON-based gate stacks Appl. Phys. Lett. 86, 173509 (2005); 10.1063/1.1915513

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 140.113.38.11 On: Thu, 01 May 2014 08:36:44

(2)

Characterization and modeling of trap number and creation time

distributions under negative-bias-temperature stress

Jung-Piao Chiu, Chi-Wei Li, and Tahui Wanga)

Department of Electronics Engineering and Institute of Electronics, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 300, Taiwan

(Received 22 July 2012; accepted 13 August 2012; published online 24 August 2012)

Individual trapped charge creations and a trap number in p-type metal-oxide-semiconductor field effect transistors (pMOSFETs) under negative bias temperature instability (NBTI) stress are investigated. We find that the characteristic times of a trapped charge creation scatter over several decades of time in small area pMOSFETs, which is attributed to an activation energy distribution in the reaction-diffusion (RD) model of NBTI. We develop a statistical model by combining the RD model with an extracted activation energy distribution to calculate a threshold voltage shift distribution at different NBTI stress times. Our model agrees with measured results very well.

VC _{2012 American Institute of Physics. [}_{http://dx.doi.org/10.1063/1.4748108}_]

Negative bias temperature instability has been recog-nized as a major concern in scaled high-permittivity (high-k) gate dielectric p-type metal-oxide-semiconductor field effect transistors (pMOSFETs) because of its significant impact on circuit performance and reliability.1–5 As MOSFET dimen-sions shrink, large variation in negative bias temperature instability (NBTI) induced threshold voltage shifts (DVt) is

observed from a device to a device. In device NBTI qualifi-cation, since it is the tail part of a DVtdistribution to

deter-mine a qualification pass/failure, an accurate model of an overall DVt distribution and its stress time evolutions is

urgently needed in an NBTI qualification method. While the mean of an NBTI DVtdistribution can be well predicted by

the reaction-diffusion (RD) model, the RD model alone is insufficient to describe an entire DVtdistribution. A total Vt

shift in an NBTI stressed device can be expressed as the sum of each individual trapped charge induced Dvt, i.e.,

DVt¼P N

i¼1Dvt;i, whereN is a total number of stress created

trapped charges in a device and Dvtdenotes a single trapped

charge caused Vtshift. Two factors are found to affect a DVt

distribution. One is the dispersion of Dvt and the other is

fluctuations in number of trapsN in stressed devices. The or-igin and the distribution of Dvthave been investigated

thor-oughly.3,4 Previous characterization and 3D atomistic simulation show that the Dvt exhibits an exponential

distri-bution approximately, f(jDvtj) ¼ exp(jDvtj/r)/r, due to a

random substrate dopant induced current-path percolation effect. To derive a DVtdistribution, we still need a

distribu-tion model for a trapped charge number N. In literature, a Poisson distribution was usually assumed forN.4,5The Pois-son model is based on a notion that individual trapped charge creations during NBTI stress are independent. In other words, each new trap creation in a device has the same prob-ability regardless of how many traps have been created. Nevertheless, the RD model and measurement result show that NBTI trap growth rate obeys a power-law dependence on stress time, i.e.,t1/n(n 6),6_{implying that a new trap}

cre-ation rate decreases with an increasing trapped charge

num-ber. Therefore, the use of a Poisson model is contradictory to the RD model and may exaggerate N and a DVtdistribution

tail. In this work, we intend to develop a physics-based dis-tribution model for N with an extracted activation energy distribution.

We characterize NBTI trapped charge creation in high-k (HfO2) gate dielectric and metal gate pMOSFETs. The

devi-ces have a drawn gate length of 30 nm, a gate width of 80 nm and an effective oxide thickness of 0.8 nm. Our characteriza-tion consists of two alternating phases. In NBTI stress phase, Vgs¼ 1.8 V and Vd¼ 0 V. In measurement phase, the drain

voltage is0.05 V and the gate voltage is adjusted to have a drain current of 500 nA in a fresh device. Drain current variations in NBTI stress are traced with a switch delay time less than 1 ls using Agilent B1500. A corresponding DVt

trace is obtained from a measured DIddivided by a

transcon-ductance. Fig.1shows representative Vttraces in two

devi-ces during NBTI stress. Each sudden Vtchange (Dvt) in the

traces is due to a single trapped hole creation. We collect about 900 Dvt in 130 devices. The extracted r is about

3.3 mV. In addition, individual trapped charge creation times are clearly defined in the figure. We collect the first three charge creation times in about 130 devices. The trap creation characteristic times scatter over several decades of time.

FIG. 1. Vttraces during NBTI stress in two high-k (HfO2) gate dielectric

and metal gate pMOSFETs. s1, s2, and s3are the 1st, the 2nd, and the 3rd

trapped hole creation times. Dvtis a single trapped charge induced threshold

voltage shift.

a)

Electronic address: [email protected].

0003-6951/2012/101(8)/082906/3/$30.00 101, 082906-1 VC2012 American Institute of Physics

APPLIED PHYSICS LETTERS 101, 082906 (2012)

(3)

Their probability density functions (PDF) are shown in Fig.2. The wide spread of the characteristic times is attrib-uted to an activation energy distribution in the RD model due to local chemistry because other processes or variables in the RD model are unlikely to cause such wide distribu-tions. In the following, we will extract an activation energy distribution from the measured trap characteristic time distributions.

According to the RD model, an NBTI trap creation rate is formulated as N¼ At1n_exp Ea kBT ; n 6; (1) where A WLD01=6 KF0½SiH½hþ pKR0 2=3 : (2)

W is a gate width, L is a gate length, and other variables have their usual definitions as in Ref.6. Three activation energies (EF,ER,Ediffusion) associated with KF,KR, andD in the RD

model are lumped together and effective activation energy (Ea) in Eq.(1)is defined as6 Ea¼ 1 6Edif f usionþ 2 3ðEF ERÞ: (3) By re-arranging the terms in Eq. (1), the relationship between effective activation energy and the ith trapped charge creation time (si) is shown below

Ea ¼

2:3kBT

n ½nlogðAÞ þ logðsiÞ nlogðiÞ: (4) Thus, we can extract a relative activation energy distribution from the measured log(si) by subtracting nlog(i) from it.

According to our measurement data,n is about 5.6 in the ini-tial stress stage, which is slightly different fromn¼ 6 in the RD model. The log(si)-nlog(i) and corresponding activation

energy distributions from the s1, s2, and s3, respectively, are

shown in Fig.3. The top X-axis in Fig.3denotes extracted Eaaccording to Eq.(4). The pre-factorA is chosen such that

the mean of the Ea is consistent with a published result in

Ref. 7. A reasonably good match of the activation energy distributions from the s1, s2, and s3 is obtained. The solid

line in Fig. 3 represents a Gaussian-distribution fit. The mean of the Gaussian distribution is l(Ea)¼ 0.12 eV and the

standard deviation is r(Ea)¼ 0.015 eV.

A statistical model based on a Monte Carlo (MC) approach is developed to calculate N and DVtdistributions.

In our MC simulation, a sequence number (i) is assigned to each precursor in a device. The number of precursors is set equal to M¼ 24 in a 80 nm 30 nm device, which corre-sponds to a precursor density of 1012cm2.8 Each trapped charge creation time (si) is then calculated according to

Eq.(4)by randomly selecting anEafrom the Gaussian

distri-bution. In this approach, we can reproduce the same si

distri-butions as in Fig. 2. For a stress time t, N is computed by counting all the precursors with si(i¼ 1,2,…,24) less than t.

For each counted precursor, a Dvtis randomly selected based

on the distribution f(jDvtj) ¼ exp(jDvtj/r)/r with

r¼ 3.3 mV. In total, 5 105 _{devices are simulated in the}

MC simulation. The simulated and measured DVt

distribu-tions are shown in Fig.4at a stress time oft¼ 1 s and 100 s. Good agreement between the Monte Carlo simulation and measurement is obtained. Finally, we compare this model with the Poisson distribution model at a stress time of 100 s. To highlight the difference between the two models, only the tail part of a complementary cumulative distribution function (1-CDF) of the DVt is shown in Fig.5. A DVt distribution

based on the Poisson model is also shown in Fig.5for com-parison. In addition, trap number distributions from the two models are plotted in the inset. The Poisson model appa-rently yields a broader distribution inN and thus a larger DVt

FIG. 2. The probability distribution of a trapped charge (hole) creation time in NBTI stress. s1, s2, and s3are the 1st, the 2nd, and the 3rd trapped hole

creation times, respectively, in a device. The three log(s) distributions have a similar shape but are shifted by an amountnlog(i).

FIG. 3. The probability distributions of log(si)-nlog(i) (bottom X-axis) and

corresponding activation energy (Ea) (top X-axis). The pre-factorA in Eq. (4)is chosen such that the mean of theEais about 0.12 eV. The solid line

represents a Gaussian-distribution fit.

082906-2 Chiu, Li, and Wang Appl. Phys. Lett. 101, 082906 (2012)

(4)

tail, as explained earlier. The difference between the two models increases as more trapped charges are created.

In summary, we characterize NBTI trap creation in a large number of high-k dielectric pMOSFETs. An activation energy distribution in the RD model is extracted. We pro-pose a statistical model for a trap number distribution. Our model can be used to predict an NBTI DVtdistribution and

its stress time evolutions.

The authors would like to acknowledge financial support from National Science Council, Taiwan, under Contract No. NSC 99-2221-E-009-169-MY3 and from Ministry of Educa-tion in Taiwan under ATU Program.

1

S. Pae, J. Maiz, C. Prasad, and B. Woolery,IEEE Trans. Device Mater. Reliab.8, 519 (2008).

2

S. E. Rauch,IEEE Trans. Device Mater. Reliab.7, 524 (2007).

3

B. Kaczer, Ph. J. Roussel, T. Grasser, and G. Groeseneken,IEEE Electron Device Lett.31, 411 (2010).

4_{B. Kaczer, T. Grasser, Ph. J. Rousse, J. Franco, R. Degraeve, L.-A.}

Rag-narsson, E. Simoen, G. Groeseneken, and H. Reisinger, inProceedings of the International Reliab. Physics Symposium (IEEE Anaheim, CA, 2010), p. 26.

5_{T. Grasser, H. Reisinger, P.-J. Wagner, F. Schanovsky, W. Goes, and B.}

Kaczer, in Proceedings of the International Reliab. Physics Symposium (IEEE Anaheim, CA, 2010), p. 16.

6

A. T. Krishnan, S. Chakravarthi, P. Nicollian, V. Reddy, and S. Krishnan,

Appl. Phys. Lett.88, 153518 (2006).

7

S. Rangan, N. Mielke, and E. C. C. Yeh, Tech. Dig. – Int. Electron Devices Meet. 2003, 341.

8

A. Stesmans,Phys. Rev. B61, 8393 (2000).

FIG. 5. Comparison of NBTI induced DVtdistributions (1-CDF) calculated

from this model and from the Poisson model. The dots are measurement data points. Only the tail part of the 1-CDF is drawn to highlight the differ-ence between these two models. The inset shows trapped charge number dis-tributions from the two models. The stress time is 100 s.

FIG. 4. NBTI induced DVtdistributions from measurement and from a

Monte Carlo simulation. The stress time is 1 s (a) and 100 s (b), respectively.

082906-3 Chiu, Li, and Wang Appl. Phys. Lett. 101, 082906 (2012)