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Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices
MR-12162; No of Pages 5 Microelectronics Reliability xxx (2016) xxx–xxx
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Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices Nagarajan Raghavan ⁎ Engineering Product Development (EPD) Pillar, Singapore University of Technology and Design, 487 372, Singapore
a r t i c l e
i n f o
Article history: Received 14 July 2016 Accepted 14 July 2016 Available online xxxx Keywords: Clustering model Forming Resistive switching Voltage distribution Conducting filament
a b s t r a c t The choice of the right statistical model to describe the distribution of switching parameters (forming, SET and RESET voltages) is a critical requirement for RRAM, as it is used to analyze the worst case scenarios of operation that have to be accounted for while designing the cross-bar array structures, so as to ensure a robust design of the circuit and reliable data storage unit. Several models have been proposed in the recent past to characterize the voltage variations in VFORM, VSET and VRESET using the percolation framework. However, most of these models assume defect generation to be a Poisson process and apply the standard Weibull distribution for parameter extraction and lifetime extrapolation. Recent dielectric breakdown studies both at the front-end as well as back-end have shown that the Weibull statistics does not describe the stochastic trends well enough, more so in downscaled structures at the low and high percentile regions given the possibility of defect clustering which is either physics-driven or process quality-driven. This phenomenon of defect clustering is all the more applicable in the context of resistive random access memory (RRAM) devices, as switching occurs repeatedly at ruptured filament locations where defect clusters pre-exist. This study examines the validity of the clustering model for RRAM switching parameter statistics (time/voltage to FORM, SET and RESET) and presents a physical picture to explain the origin of clustering in RRAM. A large set of data from various published studies has been used here to test the suitability and need for a clustering model based reliability assessment. Dependence of the clustering factor on temperature, voltage, device area, dielectric microstructure and resistance state has also been examined. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Spatial and temporal patterns of defect nucleation, transport and growth during electrical/thermal stresses on dielectric thin films play a critical role in determining the lifetime of many nanoelectronic devices, one of which is the resistive random access memory (RRAM). As a potential non-volatile memory (NVM) technology for the future, RRAM operates as a binary storage device through repetitive breakdown and recovery of the dielectric, depending on the applied voltage stress magnitude and polarity. The role of oxygen vacancy/metal ion defects is crucial in the functioning of RRAM as they influence the stochastics of forming, SET and RESET events in the stack. In the past, defect nucleation was by default assumed to follow the Poisson process [1] wherein there is no spatial preference for the evolution of defects and eventual percolation occurs when a cluster of closely spaced defects forms a chain shorting the two electrodes on either side of the oxide layer [2,3]. This led to the widespread use of the Weibull distribution to model the time to breakdown trends in logic devices [4] as well as switching statistics in NVM technology [5].
⁎ 8 Somapah Road, Singapore University of Technology and Design, 487 372, Singapore. E-mail address: [email protected].
However, recent studies on time-dependent dielectric breakdown (TDDB) by Wu et al. [6,7], Yokogawa et al. [8] and Shimizu et al. [9] reveal that the Weibull model fails to describe the failure data well especially at the extreme percentile regions. The existence of process-induced defects as well as intrinsic dimensional (geometric) variations in the patterned features of highly downscaled devices was proposed to be the origin of the non-Weibullian trends observed. Taking cue from yield models that talk about non-homogeneous defect density distributions in space and time [10,11], a failure model was developed in Ref. [6] that accounted for the spatial distribution of defects and its impact on the mean and variation in breakdown lifetime. This is referred to as the clustering model and its validity for FEOL, MEOL and BEOL technologies has been adequately demonstrated [7]. However, in spite of its relevance to the switching stochastics and the commonalities between dielectric breakdown (SBD, HBD) and resistance switching (oxygen vacancies, metal filaments), the cluster model has yet to be advocated for better representation of the distributions of forming voltage (VFORM), SET (VSET) and RESET (VRESET) voltages. The aim of this study is to do just that. There are multiple reasons why the clustering model might be a suitable one for modeling the statistics of switching in RRAM. In recent times, first principle studies by Bradley et al. [12,13] have suggested that the presence of a vacancy defect at a certain location makes it favorable for additional defects to nucleate in its neighborhood with lower
http://dx.doi.org/10.1016/j.microrel.2016.07.139 0026-2714/© 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139
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N. Raghavan / Microelectronics Reliability xxx (2016) xxx–xxx
activation energy. The nucleation of additional defects in the vicinity becomes increasingly thermodynamically favored when the existing defect cluster tends to grow in size as the collection of vacancies has a stronger binding energy per vacancy [13]. It is also possible for vacancies to diffuse/drift and segregate/aggregate along fault lines such as grain boundaries/dislocations in polycrystalline dielectric stacks (microstructure in the post-anneal stage) [14,15]. These non-idealities have not been captured by recent statistical models and as a result, the fit to the forming and SET voltage distributions tend to be inaccurate when the standard Weibull model is used [16,17]. In this study, we will use the clustering model to fit a wide variety of data extracted from various literature reports pertaining to VFORM, VSET and VRESET at different voltage and temperature stress conditions. The dependence of the clustering effect on the above stress factors as well as device area, dielectric microstructure and resistance state level will be examined and the physical mechanism underlying the clustering trends shall be qualitatively explained. This work is organized as follows. Section 2 introduces the clustering model (CM) and its underlying formulation. In Section 3, CM is used to fit the VFORM distribution for both amorphous and polycrystalline microstructure dielectrics. Section 4 analyzes the validity of CM for SET at different temperature and voltage stress conditions as well as device areas. The RESET process is examined in Section 5 and CM is used to fit two very different low resistance states (LRS) with thin and thick filaments to observe the differences in the optimum model parameter values. Finally, Section 6 concludes with a summary of the results and presents key ideas worth investigating further. 2. Defect clustering model The cumulative density function for failure (yield loss) using the clustering model can be expressed by Eq. (1), where λ is the average number of defects and α is the clustering factor. The value of α ranges between (0, ∞) with α → ∞ implying perfectly random defect generation, taking us back to the Poisson process. Low values of α closer to zero are indicative of high clustering effect. In the case of constant and ramped voltage stress, from a reliability standpoint, the expression for λ may be given by Eqs. (2) and (3) in the form of a power law, where η and β represent the mean time (voltage) to failure and the Weibull shape parameter, respectively, while RR is the ramp rate. The parameter λ, in the reliability context with time dependency, can be interpreted as the probability of defect generation which can be assumed to follow power law for the low percentile/early failure scenarios, as is usually the case in percolation models [18,19]. λ −α F CLUS ¼ 1− 1 þ α λ¼
βCVS
ηCVS
λ¼
t
V ηRVS
βRVS
; λ≪1
¼
RR t βRVS ; λ≪1 ηRVS
Fig. 1. Weibull plot of the forming voltage (VFORM) distribution with a cluster model fitting to the data for both amorphous and polycrystalline dielectric thin films. The value of α is lower for polycrystalline stack indicative of more preferential clustering effect in and around the grain boundaries.
This is in line with theoretical [14,15] and experimental [15] studies that point to the grain boundaries (GB) acting as a sink for oxygen vacancies. The overall system free energy is lowered when the vacancies in the grain region migrate and segregate along the GB contours. Fig. 2 illustrates this scenario comparing the two different microstructures.
4. Statistics of SET events for different conditions The SET process occurs in partially ruptured filaments with one or many defect clusters or at least a certain localized arrangement of
ð1Þ
ð2Þ
ð3Þ
3. Statistics of forming voltage (VFORM) Fig. 1 shows the results of a fit of the cluster model to forming voltage measurements on a 5 nm HfOx MIM stack with device area of 40 × 40 nm2. The data was extracted from the work of Govoreanu et al. [20]. Two different microstructures were considered – one amorphous and the other polycrystalline. When the two sets of data are fit using the maximum likelihood estimate (MLE) algorithm, the value of αPOLY = 0.4 b αAMOR = 0.6. This suggests that the clustering effect could be more pronounced in the case of polycrystalline thin films.
Fig. 2. Illustration showing the defect clustering process for polycrystalline and amorphous dielectric RRAM stacks. There is a higher probability for clustering to be dominant in polycrystalline thin films as the grain boundaries serve as a thermodynamic sink for vacancies to segregate to. The shaded squares represent preexisting defects while the dark squares denote the new forming-stress induced defects. Red arrows represent the preferred vacancy migration direction. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139
N. Raghavan / Microelectronics Reliability xxx (2016) xxx–xxx
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defects that are close to each other. Therefore, it is logically expected that the clustering effect will be dominant in the SET stage as well.
4.1. Dependence on switching voltage/ramp speed Constant voltage stress (CVS) measurements of the time to SET were carried out on a 7 nm TaOx stack (patterned area of 25 × 25 μm2) by Nishi et al. [21] for different high stress conditions ranging from 3.0 V to 3.4 V, where the SET event occurred within a few nanoseconds to microseconds. A fit of the cluster model revealed a lower value of α for higher voltages (α = 0.7 for 3.4 V and α = 0.85 for 3.0 V), as shown in Fig. 3. This implies that the tendency to cluster increases with voltage stress. At higher voltages, the local fields in and around vacancy constrictions are significantly enhanced (considering a local chain/collection of slightly dispersed vacancies to be represented by a Quantum Point Contact). These high local fields cause very localized defect generation around the constrictions leading to more and more clustering. This could possibly explain the trends we observe. Further first principle investigations are needed to confirm this speculation here. A higher voltage in the CVS mode corresponds to a higher ramp rate in the standard voltage sweep mode. The results here reveal that slower ramp rates may result in a more controlled variation of the switching voltages, though at the expense of lower operating speeds (frequency) of the device.
Fig. 4. Weibull plot of the time to SET, in nanoseconds, for high voltage CVS stress on a 90 nm GeSe stack, measured at three different temperatures of 50 °C, 70 °C and 90 °C. With increasing temperature, the value of α consistently decreases (more clustering of defects).
4.2. Dependence on temperature Similar intensification of clustering is observed (Fig. 4) when the model is used to fit SET CVS data for different temperature stress conditions ranging from 50 to 90 °C. In this case, the data pertains to a conducting bridge memory stack (50 × 50 μm2 in size) with Cu-doped Ge0·3Se0.7 (90 nm) as the active layer [22]. The value of α decreases from 1.3 to 0.8 as the temperature is increased from 50 ° C to 90 °C. This trend may be due to the higher thermal gradients for vacancy migration as well as joule heating effects because the trap-assisted tunneling leakage currents through the defects are temperature sensitive.
Fig. 3. Fitting the clustering model (solid and dotted red lines) to CVS SET measurement data on 7 nm TaOx for 3.0 V and 3.4 V. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
4.3. Dependence on device area When applying CM to SET data for different area devices, we observe negligible changes in α value, as shown in Fig. 5. The value of α remains close to 2 for all four device areas considered, ranging from 50 × 50 μm2 to 400 × 400 μm2. This intuitively looks reasonable because clustering is predominantly expected to happen only in the vicinity of the major filament that is governing the switching process. If switching at any single cycle is only due to one single “major” filament, then the clustering
Fig. 5. Investigation of the clustering effect in the SET data, corresponding to RRAM devices of different areas, ranging from 50 × 50 μm2 to 400 × 400 μm2. No change in the cluster behavior is observed, implying it is area-independent.
Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139
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N. Raghavan / Microelectronics Reliability xxx (2016) xxx–xxx
effects should be the same in all area devices because filamentation in RRAM is area-independent, except for the forming process. 5. Statistics of RESET events 5.1. Filament size dependence To study the impact (if any) of clustering on the stochastics of RESET, we modeled the VRESET data, collected on a bipolar switching Cu/HfO2/Pt stack with a dielectric thickness of 20 nm, for two different low resistance state (RLRS) values → 50Ω and 2 kΩ [23]. These two RLRS values correspond to a wide and narrow filament nucleation scenario. Fig. 6 shows the fitting results for these two cases and it can be deduced that the value of α is much smaller for the 50Ω stack (α = 0.6) than for the 2 kΩ one (α = 0.8). This is possibly because the localized joule heating effects are quite intense in the thicker filament and therefore the defects close to the top electrode are passivated more preferentially before any of the other defects along the filament. However, for the narrower filament, since the percolation current is not very high, the defects all along the filament may be equally passivated due to negligible joule heating. Therefore, the results of our cluster model fit are in very good agreement with the physical insights that we can use to qualitatively explain the dynamic switching process in filamentation. 6. Conclusions and recommendations In this study, we proved the validity of the clustering model for various phases of the resistive switching process including forming, SET and RESET in a wide variety of material stacks, some of which involve oxygen vacancy based switching, while others are based more on metal filamentation. The dependence of the cluster factor on voltage, temperature, filament size (compliance setting) and device area was examined. Our analysis showed that the clustering effects tend to be more intense at higher voltage and temperature stress conditions as well as for larger filaments (higher compliance setting). Our qualitative explanations of the observed trends are well supported and justified by the statistical likelihood fittings obtained. It may appear that the fitting of the cluster model here is still not that ideally representative of the
Fig. 6. Cluster fit to RESET data on a Weibull scale for thick and thin filaments, corresponding to RLRS = 50Ω and RLRS = 2000Ω.
pattern of data plotted. This is due to the small sample size of available data, more so at the extreme percentile regions. While the clustering model is derived from the binomial yield model, it still does not have a proper physical intuition and background. It is necessary to make use of the fundamental physics governing defect generation to derive the clustering model so that is has a more physical foundation rather than a purely phenomenological one. Furthermore, it would be interesting to apply the model to see how well it describes the read disturb phenomenon and also examine the statistical nature (further possible reduction in α due to possible gradual filament dilation resulting in enhanced localization of subsequent defect generation) of SET and RESET after endurance or retention degradation. The fitting of the model in this study was carried out on very different material stacks for the different stages of switching due to lack of availability of a complete set of data for one particular device. To further confirm our observed trends of clustering and its behavior and technological impact on switching variability trends, additional experimentation using a single material stack becomes necessary.
Acknowledgement This work is funded by the SUTD Start-Up Research Grant No. SRGEPD-2015-108 and the SUTD-ZJU Collaboration Research Grant No. SUTD-ZJU/RES/03/2015. The author would like to thank the International Design Centre (IDC) at SUTD for logistical and technical support during the course of this work.
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Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139
N. Raghavan / Microelectronics Reliability xxx (2016) xxx–xxx [19] J. Suňé, S. Tous, E.Y. Wu, Analytical cell-based model for the breakdown statistics of multilayer insulator stacks, IEEE Electron Device Lett. 30 (12) (2009) 1359–1361. [20] B. Govoreanu, G.S. Kar, Y.Y. Chen, V. Paraschiv, S. Kubicek, A. Fantini, I.P. Radu, et al., 10 × 10nm2 Hf/HfOx crossbar resistive RAM with excellent performance, reliability and low-energy operation, Electron Devices Meeting (IEDM), 2011 IEEE International, IEEE, 2011, pp. 729–732. [21] Y. Nishi, S. Schmelzer, U. Böttger, et al., Weibull analysis of the kinetics of resistive switches based on tantalum oxide thin films, Proc. ESSDERC 2013, pp. 174–177.
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[22] R. Soni, P. Meuffels, G. Staikov, R. Weng, C. Kügeler, A. Petraru, M. Hambe, R. Waser, H. Kohlstedt, On the stochastic nature of resistive switching in Cu doped Ge0·3Se0.7 based memory devices, J. Appl. Phys. 110 (5) (2011), 054509. [23] X. Yang, S. Long, K. Zhang, X. Liu, G. Wang, X. Lian, Q. Liu, H. Lv, M. Wang, H. Xie, H. Sun, Investigation on the RESET switching mechanism of bipolar Cu/HfO2/Pt RRAM devices with a statistical methodology, J. Phys. D. Appl. Phys. 46 (24) (2013) 245107.
Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/mr
Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices Nagarajan Raghavan ⁎ Engineering Product Development (EPD) Pillar, Singapore University of Technology and Design, 487 372, Singapore
a r t i c l e
i n f o
Article history: Received 14 July 2016 Accepted 14 July 2016 Available online xxxx Keywords: Clustering model Forming Resistive switching Voltage distribution Conducting filament
a b s t r a c t The choice of the right statistical model to describe the distribution of switching parameters (forming, SET and RESET voltages) is a critical requirement for RRAM, as it is used to analyze the worst case scenarios of operation that have to be accounted for while designing the cross-bar array structures, so as to ensure a robust design of the circuit and reliable data storage unit. Several models have been proposed in the recent past to characterize the voltage variations in VFORM, VSET and VRESET using the percolation framework. However, most of these models assume defect generation to be a Poisson process and apply the standard Weibull distribution for parameter extraction and lifetime extrapolation. Recent dielectric breakdown studies both at the front-end as well as back-end have shown that the Weibull statistics does not describe the stochastic trends well enough, more so in downscaled structures at the low and high percentile regions given the possibility of defect clustering which is either physics-driven or process quality-driven. This phenomenon of defect clustering is all the more applicable in the context of resistive random access memory (RRAM) devices, as switching occurs repeatedly at ruptured filament locations where defect clusters pre-exist. This study examines the validity of the clustering model for RRAM switching parameter statistics (time/voltage to FORM, SET and RESET) and presents a physical picture to explain the origin of clustering in RRAM. A large set of data from various published studies has been used here to test the suitability and need for a clustering model based reliability assessment. Dependence of the clustering factor on temperature, voltage, device area, dielectric microstructure and resistance state has also been examined. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Spatial and temporal patterns of defect nucleation, transport and growth during electrical/thermal stresses on dielectric thin films play a critical role in determining the lifetime of many nanoelectronic devices, one of which is the resistive random access memory (RRAM). As a potential non-volatile memory (NVM) technology for the future, RRAM operates as a binary storage device through repetitive breakdown and recovery of the dielectric, depending on the applied voltage stress magnitude and polarity. The role of oxygen vacancy/metal ion defects is crucial in the functioning of RRAM as they influence the stochastics of forming, SET and RESET events in the stack. In the past, defect nucleation was by default assumed to follow the Poisson process [1] wherein there is no spatial preference for the evolution of defects and eventual percolation occurs when a cluster of closely spaced defects forms a chain shorting the two electrodes on either side of the oxide layer [2,3]. This led to the widespread use of the Weibull distribution to model the time to breakdown trends in logic devices [4] as well as switching statistics in NVM technology [5].
⁎ 8 Somapah Road, Singapore University of Technology and Design, 487 372, Singapore. E-mail address: [email protected].
However, recent studies on time-dependent dielectric breakdown (TDDB) by Wu et al. [6,7], Yokogawa et al. [8] and Shimizu et al. [9] reveal that the Weibull model fails to describe the failure data well especially at the extreme percentile regions. The existence of process-induced defects as well as intrinsic dimensional (geometric) variations in the patterned features of highly downscaled devices was proposed to be the origin of the non-Weibullian trends observed. Taking cue from yield models that talk about non-homogeneous defect density distributions in space and time [10,11], a failure model was developed in Ref. [6] that accounted for the spatial distribution of defects and its impact on the mean and variation in breakdown lifetime. This is referred to as the clustering model and its validity for FEOL, MEOL and BEOL technologies has been adequately demonstrated [7]. However, in spite of its relevance to the switching stochastics and the commonalities between dielectric breakdown (SBD, HBD) and resistance switching (oxygen vacancies, metal filaments), the cluster model has yet to be advocated for better representation of the distributions of forming voltage (VFORM), SET (VSET) and RESET (VRESET) voltages. The aim of this study is to do just that. There are multiple reasons why the clustering model might be a suitable one for modeling the statistics of switching in RRAM. In recent times, first principle studies by Bradley et al. [12,13] have suggested that the presence of a vacancy defect at a certain location makes it favorable for additional defects to nucleate in its neighborhood with lower
http://dx.doi.org/10.1016/j.microrel.2016.07.139 0026-2714/© 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139
2
N. Raghavan / Microelectronics Reliability xxx (2016) xxx–xxx
activation energy. The nucleation of additional defects in the vicinity becomes increasingly thermodynamically favored when the existing defect cluster tends to grow in size as the collection of vacancies has a stronger binding energy per vacancy [13]. It is also possible for vacancies to diffuse/drift and segregate/aggregate along fault lines such as grain boundaries/dislocations in polycrystalline dielectric stacks (microstructure in the post-anneal stage) [14,15]. These non-idealities have not been captured by recent statistical models and as a result, the fit to the forming and SET voltage distributions tend to be inaccurate when the standard Weibull model is used [16,17]. In this study, we will use the clustering model to fit a wide variety of data extracted from various literature reports pertaining to VFORM, VSET and VRESET at different voltage and temperature stress conditions. The dependence of the clustering effect on the above stress factors as well as device area, dielectric microstructure and resistance state level will be examined and the physical mechanism underlying the clustering trends shall be qualitatively explained. This work is organized as follows. Section 2 introduces the clustering model (CM) and its underlying formulation. In Section 3, CM is used to fit the VFORM distribution for both amorphous and polycrystalline microstructure dielectrics. Section 4 analyzes the validity of CM for SET at different temperature and voltage stress conditions as well as device areas. The RESET process is examined in Section 5 and CM is used to fit two very different low resistance states (LRS) with thin and thick filaments to observe the differences in the optimum model parameter values. Finally, Section 6 concludes with a summary of the results and presents key ideas worth investigating further. 2. Defect clustering model The cumulative density function for failure (yield loss) using the clustering model can be expressed by Eq. (1), where λ is the average number of defects and α is the clustering factor. The value of α ranges between (0, ∞) with α → ∞ implying perfectly random defect generation, taking us back to the Poisson process. Low values of α closer to zero are indicative of high clustering effect. In the case of constant and ramped voltage stress, from a reliability standpoint, the expression for λ may be given by Eqs. (2) and (3) in the form of a power law, where η and β represent the mean time (voltage) to failure and the Weibull shape parameter, respectively, while RR is the ramp rate. The parameter λ, in the reliability context with time dependency, can be interpreted as the probability of defect generation which can be assumed to follow power law for the low percentile/early failure scenarios, as is usually the case in percolation models [18,19]. λ −α F CLUS ¼ 1− 1 þ α λ¼
βCVS
ηCVS
λ¼
t
V ηRVS
βRVS
; λ≪1
¼
RR t βRVS ; λ≪1 ηRVS
Fig. 1. Weibull plot of the forming voltage (VFORM) distribution with a cluster model fitting to the data for both amorphous and polycrystalline dielectric thin films. The value of α is lower for polycrystalline stack indicative of more preferential clustering effect in and around the grain boundaries.
This is in line with theoretical [14,15] and experimental [15] studies that point to the grain boundaries (GB) acting as a sink for oxygen vacancies. The overall system free energy is lowered when the vacancies in the grain region migrate and segregate along the GB contours. Fig. 2 illustrates this scenario comparing the two different microstructures.
4. Statistics of SET events for different conditions The SET process occurs in partially ruptured filaments with one or many defect clusters or at least a certain localized arrangement of
ð1Þ
ð2Þ
ð3Þ
3. Statistics of forming voltage (VFORM) Fig. 1 shows the results of a fit of the cluster model to forming voltage measurements on a 5 nm HfOx MIM stack with device area of 40 × 40 nm2. The data was extracted from the work of Govoreanu et al. [20]. Two different microstructures were considered – one amorphous and the other polycrystalline. When the two sets of data are fit using the maximum likelihood estimate (MLE) algorithm, the value of αPOLY = 0.4 b αAMOR = 0.6. This suggests that the clustering effect could be more pronounced in the case of polycrystalline thin films.
Fig. 2. Illustration showing the defect clustering process for polycrystalline and amorphous dielectric RRAM stacks. There is a higher probability for clustering to be dominant in polycrystalline thin films as the grain boundaries serve as a thermodynamic sink for vacancies to segregate to. The shaded squares represent preexisting defects while the dark squares denote the new forming-stress induced defects. Red arrows represent the preferred vacancy migration direction. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139
N. Raghavan / Microelectronics Reliability xxx (2016) xxx–xxx
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defects that are close to each other. Therefore, it is logically expected that the clustering effect will be dominant in the SET stage as well.
4.1. Dependence on switching voltage/ramp speed Constant voltage stress (CVS) measurements of the time to SET were carried out on a 7 nm TaOx stack (patterned area of 25 × 25 μm2) by Nishi et al. [21] for different high stress conditions ranging from 3.0 V to 3.4 V, where the SET event occurred within a few nanoseconds to microseconds. A fit of the cluster model revealed a lower value of α for higher voltages (α = 0.7 for 3.4 V and α = 0.85 for 3.0 V), as shown in Fig. 3. This implies that the tendency to cluster increases with voltage stress. At higher voltages, the local fields in and around vacancy constrictions are significantly enhanced (considering a local chain/collection of slightly dispersed vacancies to be represented by a Quantum Point Contact). These high local fields cause very localized defect generation around the constrictions leading to more and more clustering. This could possibly explain the trends we observe. Further first principle investigations are needed to confirm this speculation here. A higher voltage in the CVS mode corresponds to a higher ramp rate in the standard voltage sweep mode. The results here reveal that slower ramp rates may result in a more controlled variation of the switching voltages, though at the expense of lower operating speeds (frequency) of the device.
Fig. 4. Weibull plot of the time to SET, in nanoseconds, for high voltage CVS stress on a 90 nm GeSe stack, measured at three different temperatures of 50 °C, 70 °C and 90 °C. With increasing temperature, the value of α consistently decreases (more clustering of defects).
4.2. Dependence on temperature Similar intensification of clustering is observed (Fig. 4) when the model is used to fit SET CVS data for different temperature stress conditions ranging from 50 to 90 °C. In this case, the data pertains to a conducting bridge memory stack (50 × 50 μm2 in size) with Cu-doped Ge0·3Se0.7 (90 nm) as the active layer [22]. The value of α decreases from 1.3 to 0.8 as the temperature is increased from 50 ° C to 90 °C. This trend may be due to the higher thermal gradients for vacancy migration as well as joule heating effects because the trap-assisted tunneling leakage currents through the defects are temperature sensitive.
Fig. 3. Fitting the clustering model (solid and dotted red lines) to CVS SET measurement data on 7 nm TaOx for 3.0 V and 3.4 V. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
4.3. Dependence on device area When applying CM to SET data for different area devices, we observe negligible changes in α value, as shown in Fig. 5. The value of α remains close to 2 for all four device areas considered, ranging from 50 × 50 μm2 to 400 × 400 μm2. This intuitively looks reasonable because clustering is predominantly expected to happen only in the vicinity of the major filament that is governing the switching process. If switching at any single cycle is only due to one single “major” filament, then the clustering
Fig. 5. Investigation of the clustering effect in the SET data, corresponding to RRAM devices of different areas, ranging from 50 × 50 μm2 to 400 × 400 μm2. No change in the cluster behavior is observed, implying it is area-independent.
Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139
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N. Raghavan / Microelectronics Reliability xxx (2016) xxx–xxx
effects should be the same in all area devices because filamentation in RRAM is area-independent, except for the forming process. 5. Statistics of RESET events 5.1. Filament size dependence To study the impact (if any) of clustering on the stochastics of RESET, we modeled the VRESET data, collected on a bipolar switching Cu/HfO2/Pt stack with a dielectric thickness of 20 nm, for two different low resistance state (RLRS) values → 50Ω and 2 kΩ [23]. These two RLRS values correspond to a wide and narrow filament nucleation scenario. Fig. 6 shows the fitting results for these two cases and it can be deduced that the value of α is much smaller for the 50Ω stack (α = 0.6) than for the 2 kΩ one (α = 0.8). This is possibly because the localized joule heating effects are quite intense in the thicker filament and therefore the defects close to the top electrode are passivated more preferentially before any of the other defects along the filament. However, for the narrower filament, since the percolation current is not very high, the defects all along the filament may be equally passivated due to negligible joule heating. Therefore, the results of our cluster model fit are in very good agreement with the physical insights that we can use to qualitatively explain the dynamic switching process in filamentation. 6. Conclusions and recommendations In this study, we proved the validity of the clustering model for various phases of the resistive switching process including forming, SET and RESET in a wide variety of material stacks, some of which involve oxygen vacancy based switching, while others are based more on metal filamentation. The dependence of the cluster factor on voltage, temperature, filament size (compliance setting) and device area was examined. Our analysis showed that the clustering effects tend to be more intense at higher voltage and temperature stress conditions as well as for larger filaments (higher compliance setting). Our qualitative explanations of the observed trends are well supported and justified by the statistical likelihood fittings obtained. It may appear that the fitting of the cluster model here is still not that ideally representative of the
Fig. 6. Cluster fit to RESET data on a Weibull scale for thick and thin filaments, corresponding to RLRS = 50Ω and RLRS = 2000Ω.
pattern of data plotted. This is due to the small sample size of available data, more so at the extreme percentile regions. While the clustering model is derived from the binomial yield model, it still does not have a proper physical intuition and background. It is necessary to make use of the fundamental physics governing defect generation to derive the clustering model so that is has a more physical foundation rather than a purely phenomenological one. Furthermore, it would be interesting to apply the model to see how well it describes the read disturb phenomenon and also examine the statistical nature (further possible reduction in α due to possible gradual filament dilation resulting in enhanced localization of subsequent defect generation) of SET and RESET after endurance or retention degradation. The fitting of the model in this study was carried out on very different material stacks for the different stages of switching due to lack of availability of a complete set of data for one particular device. To further confirm our observed trends of clustering and its behavior and technological impact on switching variability trends, additional experimentation using a single material stack becomes necessary.
Acknowledgement This work is funded by the SUTD Start-Up Research Grant No. SRGEPD-2015-108 and the SUTD-ZJU Collaboration Research Grant No. SUTD-ZJU/RES/03/2015. The author would like to thank the International Design Centre (IDC) at SUTD for logistical and technical support during the course of this work.
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Please cite this article as: N. Raghavan, Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.139