Prognostic methodology for remaining useful life estimation of retention loss in nanoscale resistive switching memory

Microelectronics Reliability 54 (2014) 1729–1734

Contents lists available at ScienceDirect

Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel

Prognostic methodology for remaining useful life estimation of retention loss in nanoscale resistive switching memory Nagarajan Raghavan a,⇑, Daniel D. Frey b, Kin Leong Pey a a b

Engineering Product Development Pillar, Singapore University of Technology and Design, Singapore 138 682, Singapore Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

a r t i c l e

i n f o

Article history: Received 1 July 2014 Accepted 8 July 2014 Available online 4 August 2014 Keywords: Diffusion Ion migration Noise Power spectral density Resistance switching Retention loss

a b s t r a c t Noise is a key indicator of the physical phenomenon underlying device operation, defect density and degradation trends. The analysis of noise in the frequency domain and the exponent (value of slope, a on logarithmic scale) of the power spectral density (PSD) can provide useful insight on the operating and failure mechanism of any device/system. We shall use this noise as a prognostic indicator to detect the instant at which the retention loss of a non-volatile memory device begins to occur. A qualitative perspective to prognostic management of a resistive random access memory (RRAM) device is provided in this work. Our method of detecting retention loss involves the unique observation of a slope of a = 3/2, which arises due to diffusion or ionic migration phenomenon. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Prognostic principles along with various diagnostic methods are being applied in diverse fields of engineering to predict the remaining useful life (RUL) distribution for a degrading device or system [1]. There exist a wide variety of degradation indices and corresponding property sensors that enable real-time tracking of these parameters [2]. Also, a number of different data-driven, physics-of-failure driven and fusion-driven statistical methods have been developed that enable quantitative determination of the RUL distribution along with its uncertainty which reduces as the system ages due to increasing sample data available for more accurate prediction through feedback [2,3]. While prognostics as a field has shown far-fledged advancements in its application to large scale macro electro-mechanical systems, its application to the nano-regime is still in its incipient stages [4]. The difficulty of applying conventional prognostic techniques for nanoscale devices is the atomic complexity, sensitivity to very small thermal and other perturbations, large noise fluctuations in leakage current, difficulty in directly sensing the degradation parameters in-situ, extrinsic process induced variability and limited knowledge on the operating mechanism and physics of failure in new material based devices. Nevertheless, application ⇑ Corresponding author. Address: 20 Dover Drive, SUTD, Singapore 138 682, Singapore. Tel.: +65 9862 1185; fax: +65 6779 5161. E-mail address: [email protected] (N. Raghavan). http://dx.doi.org/10.1016/j.microrel.2014.07.072 0026-2714/Ó 2014 Elsevier Ltd. All rights reserved.

of prognostics to nanodevices will have a big impact in the future considering that accelerated stresses in aggressively downscaled devices may not really test the intrinsic failure, but rather cause new unforeseen failure mechanisms to come up due to the high stress and short duration constraint for time-efficient reliability assessment. Prognostics is the best alternative to conventional high temperature operating life (HTOL) tests and accelerated stress tests as it helps study the intrinsic kinetics of degradation provided the degradation index we consider (such as threshold voltage, sub-threshold slope, saturation current, etc.) has some functional correlation to the data electrically measured. Considering that the operation of nanodevices (currently the logic and memory technology is advancing towards the 10–22 nm node) is governed by a few charge carriers (electrons/ holes) and/or atoms/ions [5], the current/voltage noise can be a significant factor that can provide in-depth insight into the underlying mechanism. This suggests that noise in the time and frequency domains can serve as a very good diagnostic tool [6]. In this study, we will take advantage of the noise power spectrum and its frequency domain slope to infer qualitatively on the state of degradation of a non-volatile memory device in terms of retention, which refers to the ability of the device to store a binary digital bit (0 or 1) for prolonged time without loss of data during the read phase. The technology considered for demonstration here is the resistive random access memory (RRAM) [7]. The flow of this work is as follows. In Section 2, the structure and operating mechanism of RRAM will be introduced and the

N. Raghavan et al. / Microelectronics Reliability 54 (2014) 1729–1734

retention failure mechanism discussed along with supporting electrical test data. Section 3 presents a summary of the different noise models that exist and the physical phenomenon they represent. We will consider the frequency domain plots of the leakage current in the RRAM at different stages of a retention test and use the slope of the power spectrum as a prognostic tool to clearly identify the onset of failure. Finally, in Section 4, we conclude the study highlighting the effectiveness of noise as a prognostic tool and proposing avenues for further exploration on noise from a quantitative perspective so that it can be used to track defect density evolution and calculate the RUL distribution numerically.

10-6

1μA

10-7 10-8

ITE (A)

1730

SET 10

10-9

(a)

10-10 10-11

Oxygen Vacancy Switching

Bipolar 10-10

RESET -2

2. Resistive switching memory and retention

-1

1.5

0

2

VTE (V)

2.5

VTE (V)

2.1. Device structure and operating mechanism

200μA

SET

10-4

ITE (A)

Fig. 1 shows a schematic of the RRAM consisting of a metal– insulator–metal (MIM) stack with a top electrode (TE), bottom electrode (BE) and insulator (high permittivity (j) dielectric). The RRAM device can be operated in two different modes [8]. The first mode is where the compliance (Icomp) is kept low around 1–10 lA. In this case, as shown by Fig. 1(a) and (b), switching occurs due to voltage and temperature stress induced defect (oxygen vacancy) generation in the dielectric caused by thermochemical bond breaking for the high to low resistance state (HRS ? LRS) transition (called ‘SET’) and defect recombination assisted by drift transport of oxygen ions (which were liberated during the bond breaking process) from the metal electrode (which is an effective oxygen reservoir) and their passivation of the immobile vacancies in the dielectric for LRS ? HRS transition (called ‘RESET’). As seen in Fig. 2(a) where a NiSi – HfO2 (3.6 nm) – Si based stack was tested, the resistance switching here is bipolar, which means that opposite polarity voltages are needed to SET and RESET the device. The second mode (Fig. 1(c) and (d)) involves operating the device at Icomp  100 lA–1 mA. In this case, SET and RESET switching is caused by nucleation and rupture of a metallic filament where the nucleation is electric field-induced while the rupture is initiated by Joule Heating. From Fig. 2(b), it turns out that

-8

10-6

Unipolar 10-8

RESET Bipolar

10-10

(b)

RESET -2

-1

0

1

2

3

VTE (V) Fig. 2. (a) Purely bipolar switching in the RRAM stack for low compliance cases where switching involves the reversible drift transport of oxygen (O2) ions. (b) For the high compliance case, we observe non-polar switching, i.e. both unipolar and bipolar schemes of switch back in current are possible because the mechanism here is driven by polarity independent Joule Heating.

switching in this mode is non-polar, i.e. independent of the voltage polarity [9]. The LRS can be considered as binary ‘1’ and HRS as binary ‘0’. The switching mechanism illustrated in Fig. 1 was understood through detailed microscopic studies involving transmission electron microscopy (TEM). For further details on these microscopic investigations, readers are directed to Refs. [9–11]. 2.2. Retention failure trends

Fig. 1. Schematic of the RRAM stack which switches between two different resistance states (a and b) by means of oxygen vacancy and oxygen ions in the low current compliance mode and (c and d) metal atom/ionic migration in the high compliance case. Typical materials for TE and BE include TiN, TaN, Ni and W, while the dielectric is usually HfO2.

The term ‘‘retention’’ refers to the time duration for which the binary data (0/1) can be stored reliably without any possible perturbation to the storage due to internal or external effects. Retention is an important reliability metric for RRAM apart from endurance (voltage pulse cycles to failure ? analogous to mechanical–thermal fatigue) [12]. Fig. 3 shows the current level in the LRS and its reduction to lower levels when a nominal voltage is applied to read the stored data for both high and low Icomp cases. For illustration purpose, we chose a higher VTE (0.9–1.7) V here to purposely induce a degradation of the LRS state (typically VREAD = 100 mV). Note the profile of current degradation for high Icomp, which is initially gradual and then shows a sudden jump indicating a rupture of the conductive filament in LRS. After the jump, the current can exhibit a 1/f trend if the defect density is still high or a 1/f2 Lorentzian if there are only a few defects left, as illustrated by the insets of Fig. 3(a). In the case of low Icomp (Fig. 3(b) and (c)), the degradation trend shows a staircase-like pattern which is because the resistance drops in discrete steps as the vacancies are passivated by the oxygen ions oneby-one in a stochastic fashion.

1731

N. Raghavan et al. / Microelectronics Reliability 54 (2014) 1729–1734

LRS

ITE (A)

10-3

9.5 9 8.5 8 7.5

(a)

10-4

x 10

3. Low frequency noise prognostics

x 10-5

3.1. Background of low frequency noise spectra

1/f Noise

Noise spectra in nanodevices can be classified into five types, each originating from a different underlying phenomenon/mechanism. Four out of these five mechanisms are different in the value of the slope of the power spectral density computed (in the logarithmic scale) from the time domain signal. In our study here, since the index of measurement is the current through the dielectric, we will focus on the ‘current noise’, denoted by SI, obtained by Fourier transformation of the time domain current signal, using Eq. (1), where c(s) is the auto-correlation function of the measured current signal, I(t).

-5

2.4

RTN Lorentzian

2 1.6 10-5

0

100

200

Retention Time (sec) x 10-6

SI ð x Þ ¼

12

(b)

cðsÞ  eixs ds; cðsÞ ¼ hIðtÞ  Iðt þ sÞi

ð1Þ

Thermal noise (STH) is due to the agitation of charge carriers in the device and is independent of the applied voltage [13]. It always exists but in general, has a very low magnitude determining the base level of the noise for any device/system. It is independent of the frequency (hence referred to as ‘‘white’’ noise) and can be expressed by Eq. (2).

x 10-5

ITE (A)

1 1

10 8 5 6

4

4

3

(c)

2 2

Z

Time (sec) 100

STH ð f Þ ¼ 4kB TR

Time (sec)

1 0

100

200

Fig. 3. (a) Retention loss trends for many devices in the LRS state for metal filament based switching at high Icomp. Insets show final noise behavior after abrupt jump in the current. (b and c) Similar retention loss trends at LRS for two devices in oxygen vacancy mode switching for low Icomp.

The overall trend of retention loss can be summarized by the schematic in Fig. 4(a). We need to evaluate the power spectrum for these time domain signals and then consider the slope of the spectrum in the logarithmic domain. The numerical value of the slope can give very clear insight to the phenomenon occurring [4] and whether the system is in equilibrium or not. From the data in Fig. 3(a), it is apparent that there could be more than one step jump during retention loss which could either correspond to a multi-stage filament rupture or the rupture of multiple filaments that could have nucleated during the previous SET voltage sweep. Also, comparing Fig. 3(a) with (b) and (c), it is worth noting that the fluctuations are more apparent and noisy for the latter. This is expected because the defect density at lower compliance is lower and therefore the effect of each defect is more revealing in this case. For high Icomp, the number of defects is so large that their perturbation effects tend to average out (noise cancellation) leading to smooth degradation trends.

Shot noise (SS) is caused by the discrete motion of electrons through the device causing random fluctuation of the current in the DC case [13]. The expression for SS can be given by Eq. (3). Again, this noise is also independent of the frequency.

SS ð f Þ ¼ 2ejIj

ð3Þ

An underlying feature of charge carriers in nanodevices is their tendency to get captured into and emitted from defects that are located in a dielectric. In other words, electrons and holes tend to use defect centers in the dielectric as ‘‘stepping stones’’ for trap/detrap assisted tunneling. When a defect traps an electron, its ability to assist in current flow decreases and vice versa. If we consider a stochastic distribution of the trap/detrap time constants for one single defect in the dielectric, we should observe a rectangular irregular pulse like signal, referred to as ‘‘random telegraph noise (RTN)’’ [14]. Considering the time constants to be exponentially distributed and the current step of the measured pulse signal to be DI, the current noise, SRTN, can be derived to be given by Eq. (4), where sl and sh refer to the low and high current level time constants [13]. Note that the RTN trend appears with a slope of a  2, which is called Lorentzian spectrum. As for the shot and thermal noise components, we have a  0. The frequencies at which the RTN trend is exhibited depends on the spatial location as well as the trap depth (energy level below oxide conduction band) of the defect.

SRTN ðxÞ ¼ ðsl þ sh Þ 

Fig. 4. (a) Schematic showing the general trend of gradual current evolution during retention loss from LRS. The spectral exponent of a = 3/2 is observed when the filament gradually shrinks in size due to diffusion/migration of defects (vacancies/ ions). (b) Summary of the different a values for different mechanisms in the power spectral density plot.

ð2Þ

4ðDIÞ2  2 2 1 1 ð Þ þ þ 2 p x s s



l

ð4Þ

h

From a practical viewpoint, the dielectric can contain more than just one defect and these defects could be distributed in space and energy (from a quantum physics viewpoint, energy here refers to the defect energy level within the forbidden bandgap of the oxide). The overall noise can now be considered as a summation of multiple RTN signals, each with a different set of time constants depending on the location and energy of the defect. Integrating the RTN spectrum with a continuous uniform distribution of s, the resulting spectral density expression will have a structural form as shown in Eq. (5) [13], where K is a proportionality constant and {s1, s2} are the minimum and maximum time constants and include the

1732

N. Raghavan et al. / Microelectronics Reliability 54 (2014) 1729–1734

effective value combining both {sl, sh}. This overall noise due to multiple defects is commonly referred to as 1/f noise. Note that the exponent of the frequency term here is unity (a  1).

SI ð x Þ ¼ ¼

K ln ðs2 =s1 Þ K ln ðs2 =s1 Þ



Z s2 s1



ds 1 þ x2 s 2

tan1 ðxs2 Þ  tan1 ðxs1 Þ

ð5Þ

x

While all the above noise fluctuations occur at steady-state, it is also essential to examine the change in the spectral density pattern due to dynamic events such as diffusion/drift of carriers, atoms or ions. If we consider a hypothetical closed volume with length dimension L along which an arbitrary species diffuses with diffusivity, D, Boltzmann constant, kB, and temperature, T, the spectral density of current fluctuations should resemble the expression in Eq. (6) [15–18], where the exponent of the frequency term is a 0 unique value of a  3/2. The symbol K is a proportionality constant which includes some material parameters as well. We have presented a very simple approximate form of the expression for the diffusion noise here, as the computation for the exact expression is more complex and unnecessary for this study.

SI ð x Þ I2

1

pffiffiffiffi kB D K 0 L2



1

ð6Þ

x3=2

Based on the above analysis and review of noise theories, Fig. 4(b) presents a summary of the different slope values in the frequency spectra corresponding to the various phenomena. In the next sub-section, we shall evaluate the noise patterns for two signals in Fig. 3(a) and (c) corresponding to low and high Icomp mode LRS states (oxygen vacancy and metallic filaments respectively) as a real-case study and show how the instance of retention loss is detected.

of the three phases, the corresponding noise spectrum (normalized by the square of the current ? SI/I2) is computed using Eq. (1) and plotted in Fig. 6. When the initial phase (4–13 s) of the signal is analyzed (Fig. 5(a)), the trend appears to be 1/f noise with a  0.94 (Fig. 6(a)) implying that the noise originates due to electron capture and emission from the very many vacancy traps distributed in space and energy that exist in the dielectric for LRS. The second long phase is shown in Fig. 5(b) where the retention loss is observed to occur in multiple discrete steps due to the relatively low number of vacancies and ions. When this signal is analyzed in frequency domain (Fig. 6(b)), the value of a has increased significantly to 1.28, which is quite close the theoretical value of 1.5 for diffusion mechanism. Clearly, the value of a  1.28 is indicative of ionic drift in the RRAM device that has initiated the retention degradation process. Therefore, the first instance when a jumps from a value close to 1 towards 1.5, can be taken to be a prognostic indicator of the beginning of retention degradation. The a value does not approach 1.5 too closely at low Icomp because of the background 1/f noise that continues to exist and plays a dominant role. Therefore, the overall noise is in fact a superposition of the 1/f and 1/f3/2 components with respective weights of A and B, as represented by Eq. (7). If the calculated spectrum in Fig. 6(c) were to be fitted numerically with Eq. (7), the values of A and B can be extracted to quantify the relative influence of the two mechanisms. Nevertheless a change of 36% from a  0.94 to a  1.28 is already a clear indicator of a change in mechanism.

SI ðf Þ I2

¼

A B þ f b f 3=2

ð7Þ

The last phase in Fig. 5(c) is after the retention loss where only a few defects are left leading to the RTN-like random rectangular pulse fluctuation in the time domain for 141 < t < 151 s. This

(a) 1/f Noise 54

52

4

6

10

12

(b) Diffusion Noise

50

I (t), μA

8

40 30 20 10

I (t), μA

20

40

11

60

80

(c)

100

120

RTN

10.5

145

146

147

Retention Time (sec) Fig. 5. Plot of the three different stages of current evolution for the low Icomp switching device in Fig. 3(c). The three stages correspond to (a) initial 1/f noise. (b) Multi-step current drop due to oxygen vacancy defect annihilation by oxygen ion drift and (c) final steady-state RTN fluctuations due to electron trap/detrap from the remaining few active defects.

Normalized PSD (/Hz)

I (t), μA

For the case of low Icomp  1–10 lA, Fig. 5 shows the three different phases of time evolution of current for LRS retention test. The overall current profile is already plotted in Fig. 3(c). For each

Normalized PSD (/Hz) Normalized PSD (/Hz)

3.2. Power spectral density plot and retention prognostics 101 100 10-1 10-2 10-3 10-4

α ~ 0.944

(a) 1/f noise 1 10-1

100

106 104 102 10

α ~ 1.279

(b) Ionic (c)

Diffusion

0

1.5 10-1

100

101 10-1 10-2

101

α ~ 1.924

100

10

101

(c) RTN

-3

10-4

2

10-1

100

101

Frequency (ω), Hz Fig. 6. Power spectral density plot for the three stages of current evolution shown in Fig. 5. The slopes of (a) a  1, (b) a  1.5 and (c) a = 2 correspond to the 1/f noise, ionic diffusion noise and RTN components respectively. The instant at which the a value changes from 1 to 1.5 indicates the beginning of retention degradation. The post retention drop a can be close to 1 or 1.5 depending on the extent of resistance loss and the compliance chosen for switching.

1733

N. Raghavan et al. / Microelectronics Reliability 54 (2014) 1729–1734

α (PSD Exponent)

2

α (PSD Freq Exponent) Polynomial Fit

1.5 1

RETENTION LOSS

0.5 0

50

100

x 10-4

x 10-4 8

I (t)

8

(b) 6

7.8

Retention

7.6

Signal

4

7.4

(a)

7.2 0

10

20

30

(c)

101

0

100

200

Time (sec)

Time (sec)

Normalized SI (/Hz)

appears as a Lorentzian spectrum with a  1.92 in Fig. 6(c). However, RTN trends may not always show up as it depends on the extent of retention loss and the initial Icomp we begin with. In our noise analysis thus far, we intentionally considered a certain time window for the posterior noise analysis in the three phases to illustrate the widely different a values that they give. This was possible because we carried out a post-mortem of the already measured data. However, a true prognostic application is realized only when the noise evolution and a value is tracked real-time by taking a certain window of data and shifting this window by a few units at every instance. As an example, the noise analysis could begin for the first 1000 data points and then we could shift the window from 0:1000 to 5:1005, 10:1010, 15:1015 and so on. We adopt this procedure here for the same signal analyzed in Figs. 5 and 6 with a window width of 1024 points. The interesting trend of dynamic change in a value is shown in Fig. 7. Note that the value of a changes gradually from 1 towards 1.5 and then back towards 1 as the 1/f noise dominates the signal for this low Icomp case. The region where a is closest to 1.5 is the instance at which the most drastic retention loss jumps occur. As shown by the dotted white line in Fig. 7, we may use polynomial or other data fitting models to track the trend of evolution of a towards 1.5 and we may arbitrarily define failure to be the case where a ? 1.4, so that a numerical estimate of RUL can be obtained (though this is a deterministic approach that does not account for the uncertainty in the RUL estimate). Note that the dynamic tracking of a depends on the width of the data window used for analysis. A careful choice of the window width is needed to track the degradation accurately. When compared to Fig. 6(c), we do not observe any Lorentzian trend in Fig. 7 for the later stages of current evolution because the RTN signal gets hidden in the 1/f noise when a long time window is chosen. Finally, to illustrate the retention loss caused by the diffusion or migration of the metal atoms/ions for high Icomp switching, we consider one of the current – time evolution trends in Fig. 3(a), as reproduced in the inset of Fig. 8(b) here. When considering the initial monotonic gradual change in the current (Fig. 8(a)) and plotting the power spectrum for this phase, we end up with very clear trends showing a  1.56, which is very close to the theoretical value. This example further illustrates that the 3/2 slope very uniquely defines the onset of retention loss and helps in diagnosing the stage of degradation of the stored data in the non-volatile memory device. It is worth noting that for switching at high Icomp, noise analysis is much simpler as the 1/f noise components (which always exist for metal filaments as well) appear subdued. This is clearly visible when the spectra in Fig. 8(c) is compared with that in Fig. 6(b). The values of a are more accurately representative of the intrinsic mechanism in the case of high Icomp.

α ~ 1.562 Ionic

100

Diffusion 10-1 10-2 10-3

10-1

100

101

Frequency (ω), Hz Fig. 8. (a) Current decrease with time for the metal filament mode RRAM which was programmed to an LRS with high Icomp  1 mA. The gradual decrease in current is due to the slow migration of metal ions during joule heating prior to filamentary rupture (retention loss). (b) Complete time profile of current decay during the retention loss test. The data presented in (a) and analyzed in frequency domain in (c) corresponds to the first 26 s of measurement when the retention loss occurs ‘‘gradually’’ due to ionic transport. (c) Power spectral density plot of the I–t trend in (a) with the a value being very close to the ideal value of 1.5. The spectrum has much lower fluctuation (higher ‘‘signal-to-noise’’ ratio) for the higher Icomp case, as expected.

4. Conclusions and recommendations In this study, we presented a new low-frequency noise based technique for diagnosing the onset of retention loss failure in RRAM devices. The technique is highly sensitive to the internal atomic and electronic fluctuations and can be used as an effective prognostic tool to estimate the RUL, if good data prediction methods are used. Application of prognostics for nanodevices is a relatively new area of research and this study makes a significant effort in advancing this topic. Low frequency noise is an inherent feature of many nano to macro systems and the power spectral slope-based tracking of degradation state proposed in this work can be applied to all kinds of systems with different dynamics and internal responses. While the technique proposed here may be useful for discrete critical devices in a large circuit, the extension of this method to the circuit or array level is essential because electronic prognostic initiatives are more effective at the circuit/ system level rather than just the device level. Tracking a single device degradation in the circuit can be practically tough in real systems and it would be better to carry out these noise studies at a modular level. The noise analysis and associated theory also deserves further investigation because the magnitude of noise power has a direct correlation to defect density and other material parameters. Therefore, the noise information could be translated to track the degradation of other metrics that govern the reliability of the device.

150

Sense Time (sec) Fig. 7. Dynamic tracking of the a value during the retention test where the a slowly drifts from 1 towards 1.5 and then back to 1 after the unintended resistance jumps occurred. The value of a depends also on the time window chosen for the noise analysis. A very short or very long time window may not yield accurate results and therefore an optimum time window has to be chosen for this purpose to get the clear trends as seen above.

Acknowledgement This work is funded by the SUTD-MIT International Design Centre (IDC) Research Grant # IDG11300103. The authors would like to thank the Interuniversity Microelectronics Centre (IMEC), Belgium for provision of samples for electrical characterization in this study.

1734

N. Raghavan et al. / Microelectronics Reliability 54 (2014) 1729–1734

References [1] Sikorska J, Hodkiewicz M, Ma L. Prognostic modelling options for remaining useful life estimation by industry. Mech Syst Signal Proc 2011;25(5):1803–36. [2] Pecht M. Prognostics and health management of electronics. New Jersey (USA): John Wiley & Sons; 2008. [3] Si XS, Wang W, Hu CH, Zhou DH. Remaining useful life estimation – a review on the statistical data driven approaches. Eur J Oper Res 2011;213(1):1–14. [4] Raghavan N, Pey KL, Frey DD. Noise-based prognostic design for real-time degradation analysis of nanodevice dielectric breakdown. IEEE Annual Reliability Maintainability Symposium (RAMS) 2013:1–7. [5] Hwang CH, Li TY, Han MH, Lee KF, Cheng HW, Li Y, et al. Statistical analysis of metal gate workfunction variability, process variation, and random dopant fluctuation in nano-CMOS circuits. Int Simul Semicond Proc Dev (SIPAD) 2009:1–4. [6] Vandamme LKJ. Noise as a diagnostic tool for quality and reliability of electronic devices. IEEE Trans Electron Dev 1994;41(11):2176–87. [7] Akinaga H, Shima H. Resistive random access memory (ReRAM) based on metal oxides. Proc IEEE 2010;98(12):2237–51. [8] Raghavan N, Pey KL, Liu WH, Wu X, Li X, Bosman M. Evidence for compliance controlled oxygen vacancy and metal filament based resistive switching mechanisms in RRAM. Microelectron Eng 2011;88(7):1124–8. [9] Li X, Liu WH, Raghavan N, Bosman M, Pey KL. Resistive switching in NiSi gate metal–oxide–semiconductor transistors. Appl Phys Lett 2010;97:202904.

[10] Li X, Tung CH., Pey KL, Lo VL. The chemistry of gate dielectric breakdown. In: IEDM 2008. IEEE int electron dev meeting, 15–17 Dec 2008, Piscataway, NJ, USA; 2008. p. 4. [11] Li X, Tung CH, Pey KL. The nature of dielectric breakdown. Appl Phys Lett 2008;93:072903. [12] Gao B, Kang JF, Zhang HW, Sun B, Chen B, Liu LF, Liu XY, Han RQ, Wang YY, Fang Z, Yu HY, Kwong DL. Oxide-based RRAM: physical based retention projection. In: Proceedings of the European solid-state device research conference (ESSDERC); 2010. p. 392–5. [13] von Haartman M, Östling M. Low frequency noise in advanced MOS devices. Netherlands: Springer Publications; 2007. [14] Li X, Tung CH, Pey KL, Lo VL. The physical origin of random telegraph noise after dielectric breakdown. Appl Phys Lett 2009;94:132904-1–4-3. [15] Moktadir Z, van Honschoten JW, Elwenspoek M. Long range diffusion noise in platinum microwires with metallic adhesion layers. Appl Phys Lett 2007;90:233506. [16] Voss RF, Clarke J. Flicker (1/f) noise: equilibrium temperature and resistance fluctuations. Phys Rev B 1976;13(2):556–73. [17] Bora A, Raychaudhuri AK. Evolution of 1/fa noise during electromigration stressing of metal film: spectral signature of electromigration process. J Appl Phys 2006;99(11):113701. [18] Rocha PRF, Gomes HL, Vandamme LKJ, Chen Q, Kiazadeh A, de Leeuw DM, et al. Low-frequency diffusion noise in resistive-switching memories based on metal–oxide polymer structure. IEEE Trans Electron Dev 2012;59(9):2483–7.