Extraction of nitride trap density from stress induced leakage current in silicon-oxide-nitride-oxide-silicon flash memory

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Extraction of nitride trap density from stress induced leakage current in

silicon-oxide-nitride-oxide-silicon flash memory

Shaw-Hung Gu, Tahui Wang, Wen-Pin Lu, Yen-Hui Joseph Ku, and Chih-Yuan Lu

Citation: Applied Physics Letters 89, 163514 (2006); doi: 10.1063/1.2360180 View online: http://dx.doi.org/10.1063/1.2360180

View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/89/16?ver=pdfcov

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Extraction of nitride trap density from stress induced leakage current

in silicon-oxide-nitride-oxide-silicon flash memory

Shaw-Hung Gua兲 and Tahui Wangb兲

Department of Electronics Engineering, National Chiao-Tung University, Hsin-Chu, Taiwan

Wen-Pin Lu, Yen-Hui Joseph Ku, and Chih-Yuan Lu

Technology Development Center, Macronix International Company, Ltd., No. 16, Li-Hsin Road, Science Based Industrial Park, Hsin-Chu 30077, Taiwan

共Received 11 April 2006; accepted 26 August 2006; published online 20 October 2006兲

The authors propose a technique to extract a silicon nitride trap density from stress induced leakage current in a polycrystalline silicon-oxide-nitride-oxide-silicon flash memory cell. An analytical model based on the Frenkel-Poole emission is developed to correlate a nitride trap density with stress induced leakage current. The extracted nitride trap density is 7.0⫻1012 _cm−2_eV−1_{. They find}

Polycrystalline silicon-oxide-nitride-oxide-silicon 共SONOS兲 flash memories have received much interest in re-cent years for their simpler fabrication process and better scalability as compared to conventional floating gate flash memory.1,2 For SONOS cells, programed charges are stored in silicon nitride traps. The cell programming and retention characteristics are intimately related to nitride trap character-istics. Much research effort with respect to silicon nitride process optimization has been conducted to improve nitride trap properties. However, nitride trap characterization tech-niques are still very limited at present. Lundström and Svensson estimated a nitride trap density with a direct tun-neling model.3 Paulsen et al. employed a low-frequency 共⬍1 kHz兲 charge pumping technique to separate nitride traps from interfacial oxide traps by a difference in their time constants.4 Later, they extracted a nitride trap density from reverse modeling of threshold voltage共Vt兲 retention loss by

combining trap-to-band tunneling and thermal excitation of trapped electrons in a nitride.5,6All the above methods, how-ever, are restricted to ultrathin bottom oxides共1.5–2.5 nm兲. For today’s SONOS cells, for example, nitride-read-only-memory共NROM兲共Ref.7兲 or Nitride-based multiple bits/cell

共Nbit兲共Ref.8兲 technology, a thicker bottom oxide is usually

employed to improve data retention. No appropriate nitride trap characterization methods are available for these cells.

In this work, we observe a high-voltage stress induced gate leakage current in a large area SONOS capacitor. An analytical model to extract a nitride trap density from the stress induced leakage current is developed. The effects of programming window共⌬Vt兲 and stress condition on the

ex-traction result are evaluated. The nitride trap energy distribu-tion is also profiled.

The SONOS capacitors used in this work have a 9 nm top oxide, a 6 nm silicon nitride, and a 5 nm bottom oxide. The capacitor area is 500⫻500␮m2. Uniform Fowler-Nordheim共FN兲 injection is employed for programming. The measured program-state gate leakage current versus retention time before and after a FN stress is shown in Fig.1共a兲. The FN stress is performed at Vg= −20 V for 1500 s. The

pro-gram Vtwindow is 3 V. The corresponding Vtretention loss

is shown in Fig. 1共b兲. A significant stress induced leakage current 共SILC兲 is observed in Fig. 1共a兲. Unlike in a metal oxide semiconductor capacitor, the SILC in a SONOS exhib-its a unique two-stage time dependence. In the first stage, the SILC exhibits a dc-like characteristic and in the second stage it follows a 1 / t time dependence. Our numerical simulation has shown that the first stage leakage current is limited by stress created oxide traps and the second stage is determined by the Frenkel-Poole 共FP兲 emission of nitride trapped electrons.9 According to the FP emission model, the nitride trapped charge emission time is

a兲_{Electronic mail: [email protected]} b兲_{Electronic mail: [email protected]}

FIG. 1. 共a兲 Measured gate leakage current in a large area SONOS 共500 ⫻500␮m2_{兲 at V}

g= 0 V. The stress condition is Vg= −20 V for 1500 s. Both

devices are programed to an identical threshold voltage window of 3 V.共b兲 Corresponding Vtretention loss for the two samples.

APPLIED PHYSICS LETTERS 89, 163514共2006兲

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␶e共A*T2兲−1exp共共␾− q共qE/␲␧兲1/2兲/kT兲 =␶

⬘

exp共␾/kT兲,

共1兲 where A* _{is the Richardson constant,} _␾ _{is the nitride trap}

energy measured from the conduction band edge, E is the electric field, ␶

⬘

is the proportionality constant, and other variables have their usual definitions. In the FP emission lim-ited condition共second stage兲, the electron occupation factor 共f兲 of a nitride trap state with an energy ␾ has a retention time dependence as follows;5,6

f共␾兲 = exp关− t/␶e共␾兲兴 = exp关共− t/␶

⬘

兲exp共−␾/kT兲兴. 共2兲

Because the above double exponential changes abruptly from 0 to 1 around␾f=共kT兲ln共t/␶

⬘

兲, f共␾兲 can be approximated by

a step function at␾=␾f and thus␾fis referred to as the FP

emission front hereafter. This approximation translates into a “clear-cut” picture; at a certain time t, trap states above the emission front ␾f are completely emptied while the states

below␾f are occupied by electrons. The FP emission front

moves downward in SiN band gap with a speed of d␾f/ dt

= kT / t, or 2.3kT/decade of time. The nitride charge leakage current in the second stage therefore can be expressed as

Ig= AqNt共␾f兲d␾f/dt = AqNt共␾f兲kT/t 共3a兲

and the nitride trap density can be extracted as

Nt共␾f兲 = Igt/AqkT. 共3b兲

Since the emission front stays almost unchanged in the first stage共␾f=␾0兲 and begins to move at the onset time 共ton兲 of

the second stage with a constant speed in a log共t兲 scale, the relationship between␾f and retention time t is readily

ob-tained,

␾f=␾0+ kT ln共t/ton兲, 共4兲

where␾0is the emission front in the first stage and is

deter-mined by the total amount of programed charges. From our numerical simulation, ␾0 is estimated to be 0.8 eV for the

present SONOS structure and programming window.9From Eqs.共3兲 and共4兲, the nitride trap density is characterized, as shown in Fig. 2. The solid line is directly from the SILC 关Fig. 1共a兲兴 and the dashed line is extrapolated from the Vt

shift 关Fig. 1共b兲兴. Notably, Fig. 2 reveals that the trapped charges have a rather uniform distribution over an energy range of measurement共⬃0.2 eV兲.

To further verify our nitride trap profiling technique, we change the FN stress condition and programming window. Figure3shows the SILC for two different FN stresses. The two samples have the same programming window and thus the same ␾0. It can be shown that the effective time for

nitride trapped charges at the emission front to escape from the ONO film9,10

␶eff= ␶e共␾f兲 +␶c共␾f兲 ␶c共␾f兲 ␶ox⬇ ␶e共␾f兲 ␶c共␾f兲 ␶ox, 共5兲

where␶e共␾f兲 and␶c共␾f兲 represent the electron emission time

and capture time between the emission front and the nitride conduction band.␶oxis the conduction band electron

tunnel-ing time via stress induced oxide traps. The lightly stressed sample共B兲 has a lower first-stage dc leakage because of less oxide trap creation and thus a longer␶_ox. It is worth pointing out that the SILC in the two samples共A and B兲 converges in the second stage. The reason is that the␾fof the two samples

at a certain time in the second stage is only shifted by

KT ln共ton共B兲/ton共A兲兲⬃0.06 eV. As mentioned earlier, the

ni-tride trap density Ntis almost a constant in the measurement

range. The leakage current, which is proportional to Nt 关Eq.

3兴, is therefore nearly the same in the second stage regardless of stress conditions.

In addition, the SILC for different program windows is shown in Fig.4. The program window is 3 V for sample A and is 2.5 V for sample C. Sample A has a smaller ␾₀ for more programed charges. According to the

Shockley-Read-FIG. 2. Extracted nitride trap density distribution vs relative nitride trap energy.␾₀is estimated to be 0.8 eV共Ref.9兲.

FIG. 3. Measured SILC in two differently stressed samples. Sample A is stressed at Vg= −20 V for 1500 s and sample B is for 5 s. The programming

window is 3 V.

FIG. 4. Measured SILC for two different programming windows. Samples A and C are stressed under the same condition共Vg= −20 V for 1500 s兲 but

have program windows of 3 and 2.5 V, respectively.

163514-2 Gu et al. Appl. Phys. Lett. 89, 163514共2006兲

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Hall theory,␶e/␶c⬀exp共␾/ kT兲 and the difference in ␾0

be-tween samples A and C can be estimated from the ratio of the SILC in the first stage, i.e.,

SILC共first stage兲 ⬀ 1/␶eff⬀ exp共−␾0/kT兲

and

␾0共A兲 −␾0共C兲 = − kT ln共SILC共A兲/SILC共C兲兲. 共6兲

The␾0difference is still small. Consequently, samples A

and C have almost the same leakage current in the second stage because Nt共␾兲 can be considered as a constant for such

small␾0 difference. The extracted nitride trap density from

samples A–C is listed in TableI. The extracted result is in reasonably good agreement without regard to stress condi-tion and programming window.

In summary, a simple and reliable nitride trap profiling technique for a thicker bottom oxide SONOS is developed.

We find that a SILC in a SONOS exhibits a distinguished two-stage feature. The nearly 1 / t dependence in the second stage suggests that the nitride traps have a uniform energy distribution. The extracted nitride trap density is around 7.0 ⫻1012_cm−2_eV−1

The authors would like to acknowledge financial support from NSC, Taiwan under Contract No. NSC 94-2215-E-009-004. They would also like to thank the Technology Develop-ment Center of MXIC for providing technical support.

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共2004兲. TABLE I. Extracted nitride trap density from samples A, B, and C,

respec-tively, by using our technique.

Sample Nt共cm−2_eV−1_兲

A 7.1⫻1012

B 6.3⫻1012

C 6.2⫻1012

163514-3 Gu et al. Appl. Phys. Lett. 89, 163514共2006兲