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Statistical analysis of random telegraph noise in HfO2-based RRAM devices in LRS
Solid-State Electronics 113 (2015) 132–137
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Statistical analysis of random telegraph noise in HfO2-based RRAM devices in LRS Francesco Maria Puglisi a,⇑, Paolo Pavan a, Luca Larcher b, Andrea Padovani b a b
Dipartimento di Ingegneria ‘‘Enzo Ferrari’’, Università di Modena e Reggio Emilia, Via Pietro Vivarelli 10/1, 41125 Modena, Italy Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, Via Amendola 2, 42122 Modena, Italy
a r t i c l e
i n f o
Article history: Available online 2 June 2015 Keywords: RRAM RTN FHMM Cycling Variability Resistive switching
a b s t r a c t In this work, we present a thorough statistical characterization of Random Telegraph Noise (RTN) in HfO2-based Resistive Random Access Memory (RRAM) cells in Low Resistive State (LRS). Devices are tested under a variety of operational conditions. A Factorial Hidden Markov Model (FHMM) analysis is exploited to extrapolate the properties of the traps causing multi-level RTN in LRS. The trapping and de-trapping of charge carriers into/out of defects located in the proximity of the conductive filament results in a shielding effect on a portion of the conductive filament, leading to the observed RTN current fluctuations. It is found that both oxygen vacancies and oxygen ions defects may be responsible for the observed RTN. The variations of the current observed at subsequent set/reset cycles are instead attributed to the stochastic variations in the filament due to oxidation/reduction processes during reset and set operations, respectively. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Resistive random access memories (RRAMs) are currently one of the most promising class of alternative non-volatile memories (NVMs), exhibiting reliable and fast switching [1], low-power operation [2], and high-density [3]. Among different resistive switching devices, RRAM cells based on hafnium oxide show superior performances [4] and excellent compatibility with the standard CMOS back-end of line. Actual understanding of RRAMs switching mechanism relies on the formation and successive partial oxidation of a conductive filament (CF) during set and reset operations, respectively [5]. The formation of a CF sets the device in the low-resistance state (LRS) while its partial oxidation leads to the creation of a dielectric barrier, determining the high-resistance state (HRS) [6–10]. The charge transport in LRS exhibits quasi-ohmic behavior [5], whereas the conduction in HRS is dominated by a multi-phonon trap-assisted tunneling (TAT) process [11] via the traps in the barrier. Unfortunately, stochastic features inborn in this technology, i.e. cycling variability and Random Telegraph Noise (RTN) [12–16], are hampering the device scaling and multi-bit storage implementation, delaying the full scale industrial exploitation of the RRAM concept. In this work we explore RTN characteristics in RRAM devices, focusing on the LRS, which has not been extensively covered in the literature as it ⇑ Corresponding author. Tel.: +39 059 2056324. E-mail address: [email protected] (F.M. Puglisi). http://dx.doi.org/10.1016/j.sse.2015.05.027 0038-1101/Ó 2015 Elsevier Ltd. All rights reserved.
exhibits lower current noise compared to the High Resistive State (HRS) [17,18]. Our previous works [13,14] exploited the color-coded time-lag plots and Hidden Markov Model [19] (HMM) to investigate the characteristics of RTN in RRAMs, showing that multi-level RTN can be seen as a superposition of many two-level RTN signals, each associated with a single trap [13]. We also proposed the factorial hidden Markov Model [20,21] (FHMM), a more refined implementation of the HMM, as a tool to derive the statistical properties of multi-level RTN. In this paper, the current noise in reading conditions is extensively characterized after set operations performed at different current compliances through the FHMM analysis [20,21]. In order to take into account the cycling variability of the LRS, a compact model is exploited to estimate the CF cross-section after each switching cycle [8]. This paper is organized as follows: devices and experiments are described in Section 2; in Section 3 we introduce the tools used for the analysis of the experimental data, i.e., FHMM and Compact Model, respectively; in Section 4 we report on the experimental results of RTN and I–V characterization; in Section 5 we discuss the results, suggesting possible mechanisms responsible for RTN in these devices. Conclusions follow.
2. Devices and experiments Measurements are performed on 20 TiN/Ti/HfOx/TiN 200 200 nm2 cross-bar RRAM devices in 1T1R configuration.
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Devices with 5.6 nm ALD HfO2 and 8 nm Ti layer are analyzed. The Ti layer sputtered on top of the hafnium oxide acts as an oxygen exchange layer, inducing an oxygen deficiency in the oxide film during post-deposition annealing at 400 °C for 30 min. This is required to induce a given degree of oxygen sub-stoichiometry (needed for a reliable switching), which is caused by the interaction between the Ti capping layer and the hafnium oxide layer, as explained in [22,23]. A preliminary forming operation, under current compliance limit, is performed to set the device into the initial condition enabling resistive switching; the use of 1T1R configuration allows minimizing the current overshoot due to parasitic capacitances [22,23]. Set and reset operations drive the device in LRS and HRS, respectively. After forming (occurring at a typical voltage of 3 V in these devices), which sets the device to LRS, one hundred complete switching DC cycles (set-read-reset) are performed. A semiconductor parameter analyzer is used to both acquire I–V curves during switching cycles (see Figs. 1 and 2) and properly bias the device (in reading conditions we consider VREAD = 0.1 V). The maximum absolute value of the voltage during the reset DC sweeps is VRESET = 1.6 V. Current fluctuations (ILRSt data) during the read operation are measured by sampling the current vs. time, collecting 10 k samples (i.e. current measures) with a sampling time of 10 ls, which corresponds to a total measurement time of 0.1 s. This measurement process allows to characterize 1 bit per reading operation. 3. Device structure and RTN analysis Among major concerns for RRAM future scaling and development, RTN disturb is currently limiting the full exploitation of this technology. The RTN current fluctuations, as shown in the inset of Fig. 1, reduce the readout margin of the device and may cause read failures. In this work we focus on the analysis of RTN in LRS, which has not been thoroughly investigated in the literature, compared to HRS [17,18]. Noise data are analyzed by considering also the physical parameters describing the device in LRS (i.e. CF cross-section), which depends on the set conditions (i.e. the current compliance). Estimating this value after every switching cycle allows considering the effect of cycling variability of the LRS while performing RTN analysis and to relate RTN to the physical properties of the CF. 3.1. Device structure in LRS In order to fully understand the dynamics of RTN in LRS, it is mandatory to comprehensively describe the state of the device in
Fig. 1. Schematics of an RRAM structure for different forming/set conditions. (a) The cell prior to forming. (b) A conductive filament (blue cylinder) is formed by applying a positive voltage ramp. (c) Reset operation partially oxidizes the conductive filament creating a dielectric barrier (orange section of the cylinder), with the thickness x. (d and e) The conductive filament cross-section increases with the magnitude of the current compliance. Circles represents the defects in the barrier contributing to charge transport in HRS. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. (a) LRS current measured in reading conditions (V = 0.1 V) and (b) RTN current fluctuations extracted from the multi-level ILRS-time traces through the FHMM technique at each set/read/reset cycle in 8 nm Ti/5.6 nm HfOX RRAM devices: differently colored symbols represent the current fluctuations due to individual traps identified in a given cycle, while the cumulative current fluctuation due to the superposition of the effects of all traps is represented by the black squares with dashed line. The applied reset voltage is 1.6 V. The current compliance is 70 lA. Missing data points in certain cycles in (b) indicate that no RTN signal is detected (only Gaussian noise). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
LRS. This resistive state is reached for the first time when the CF is formed as a result of the preliminary forming operation, which determines the CF properties [5]. Under typical forming conditions (i.e. current compliance), the conductive filament exhibits quasi-ohmic I–V characteristics indicating that it is formed by an Hf-rich (oxygen deficient) region in the dielectric [24]. The CF formation is a two-step process involving the Hf–O bond breakage and the subsequent diffusion of the released oxygen ions out of the forming CF region [5,24,25]. O ions distribution is, in turn, the critical factor controlling the subsequent reset process. The oxygen extraction occurring during the forming transient leads to the increase of the local O vacancy defects density and, eventually, to the formation of defect sub-bands, which are associated with very high defect density [5]. After the CF formation, the dominant charge transport mechanism is the electron drift through the defect sub-band, described in the framework of the Landauer formalism [26], which allows reproducing the LRS quasi-ohmic I–V characteristics. The reset operation is described as a partial re-oxidation of the CF due to the oxygen ions diffusion from the surroundings of the CF and their recombination with the O vacancies at the bottom tip of the CF [6–10,24]. This leads to the creation of a dielectric and O vacancy defect-rich barrier, responsible for the relatively low current observed in HRS. The HRS current is due to the electron TAT transport through the O vacancies in the dielectric barrier [5,11], which is mostly controlled by the barrier thickness, tB, and the distribution of the O vacancy defects within the barrier. It has to be pointed out that, while both the dielectric barrier and the CF are characterized by a high O vacancy density, their electrical behavior is dissimilar. The O vacancy defects density in the CF is indeed much larger than that in the dielectric barrier, leading to different charge transport regimes, TAT through O vacancies in HRS and electrons drift through a defect sub-band in LRS, respectively [5]. The set operation, typically performed by imposing the same current compliance limit adopted in the forming operation, allows the resistance switching from HRS to LRS, which corresponds to the restoration of the CF [7–10]. The set process physics is analogous to that of the forming process [5], and involves breaking the thin dielectric barrier formed during reset. However the voltage at which it occurs is much lower than the forming one,
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because of the reduced thickness of the dielectric barrier. This is due to the relatively high conductivity of the undisrupted CF portion, which makes the most of the voltage applied during set to drop across the oxidized CF tip (dielectric barrier). Thus, voltages as low as 0.5–1 V allow the electric field in the dielectric barrier to approach its intrinsic dielectric strength, thus resulting in a fast Hf–O bond breakage and release of the oxygen ions that restores the characteristics of the CF [24,25]. Since the major properties (e.g. shape, size) of the CF are not affected by switching cycles, which change the characteristics only of a fragment of the CF, the distribution of the LRS resistance is expected to be narrow. The cycling variability observed in LRS is hence due to the modulation of the CF properties (i.e. CF cross-section) in a small region, as a result of the intrinsic randomness in the physics of the set process [9,10]. 3.2. Random telegraph noise analysis Currently, the physical mechanism responsible for RTN current fluctuations in LRS is still unclear. Nevertheless, there are a number of evidences indicating that RTN may results from the trapping and de-trapping of charge carriers at defects located in close proximity to the edge of the CF [27–31]. The defects contributing to RTN are characterized through an FHMM analysis, which we proposed as an effective tool to overcome the limitations of HMM when dealing with multi-level RTN [20,21]. Indeed, HMM [14,19] models the input signal as a Markov chain with K hidden states (i.e. discrete current levels). This approach is suitable to analyze a two-level RTN (associated with the activity of a single trap), whereas it becomes inappropriate with the multi-level RTN, which is generated by many traps. In fact, in the standard case of a two-level RTN, the difference between the current levels corresponds to the amplitude of the RTN fluctuation and the HMM approach can be used to efficiently estimate the hidden states, hence the amplitude of the fluctuation. With multi-level RTN the estimation of the hidden current levels is not sufficient to univocally determine the amplitude of each two-level fluctuation generating the RTN. The FHMM allows overcoming the HMM limits by considering the multi-level RTN as the summation of independent two-level Markov chains [20,21], each corresponding to trapping/de-trapping at an individual defect, instead of representing it as a single Markov chain with many states. This methodology allows to decompose the multi-level RTN into different two-level fluctuations and to retrieve the properties of each defect contributing to the RTN. Further details about the FHMM technique are available in [20,21]. For the characterization of traps contributing to RTN we considered RRAM devices in different operating conditions and for several consecutive switching cycles and reading operations: for each reading operation, the corresponding current time-series is processed with the FHMM method and the statistical properties of each detected trap are collected [13,14,19–21], i.e. the current fluctuation (DI), DI normalized w.r.t. the average DC current (DI/I), capture (sc) and emission time (se).
To this purpose, we reported in Fig. 2 the LRS current measured in reading conditions (VREAD = 0.1 V) and RTN current fluctuation (DI) as extracted from the multi-level RTN ILRS-time traces at each switching cycle using the FHMM technique [20,21]. For each switching cycle, we show the current fluctuations associated with every individual trap detected by the FHMM algorithm and the maximum current variation in the ILRS-time trace, calculated by summing up the individual current fluctuations. The LRS current varies from nearly 2 lA up to 6 lA (for a current compliance of 70 lA), whereas the current fluctuations range from 1 lA to nearly 1 nA for VRESET = 1.6 V. Different DI amplitudes are found for similar LRS read currents and vice versa, see Fig. 2, indicating that the ILRS (or equivalently RLRS) variation during cycling is not straightforwardly correlated to the RTN current fluctuations. Similar results were also obtained on device formed at different current compliances. This trend is confirmed also by the correlation scatter plot in Fig. 3a, which displays the normalized RTN current fluctuation (DI/I) vs. RLRS observed at multiple switching cycles and different current compliances, which are represented by different symbols and colors. The RTN amplitudes do not correlate to RLRS measured at the same current compliance, confirming that RTN and RLRS cycling variability are concurrent but not point-to-point correlated phenomena. Still, statistical correlation can be observed between the non-normalized RTN currents (DI) and RLRS, Fig. 3b, which is due to the fact that a high current compliance leads to the formation of a wider (on average) conductive filament resulting in a higher LRS read current [5,7–10], Fig. 1. In order to fully explore RTN characteristics, we analyzed RTN and I-V data in LRS at different switching cycles for devices formed at different current compliances. For each cycle, we reported the read current from the I–V curve in reading conditions (i.e. VREAD = 0.1 V) and the DI associated with each trap detected by the FHMM method. Results are reported in Fig. 4. The read current is normally distributed over cycling and shows a narrow dispersion around its mean value. This is primarily due to the intrinsic randomness of the set/reset operations, resulting in changes in cross section and/or resistivity of a relatively small portion of the CF [5,7–10]: this reflects in the normal distributions of the read current shown in Fig. 4. On the other hand, DI distributions show a different shape than the reading current distribution; see Fig. 4. However, the DI distribution shifts with the current compliance imposed during forming, due to the variation of the average conductance (i.e. cross section and/or resistivity) of the CF, which affects the average current and its fluctuations [12–14,29–31], Figs. 4 and 5. Indeed, the normalized DI/I distribution is unaffected by the current compliance, Figs. 3 and 4. This trend may be associated with a different mechanism governing the RTN (responsible for the different shapes of ILRS and DI distributions), which is statistically linked
4. RTN analysis results For a complete RTN analysis, we implemented a statistical approach accounting for both cycling variability and RTN. The cycling variability derives from the intrinsic randomness of the set process, which affects the CF properties, i.e. CF cross-section, which in turn affects the charge transport leading to the RLRS, or equivalently ILRS, variability displayed in Fig. 2a. Since RTN appears as an instability in the charge transport mechanism (it emerges as fluctuations of the read current), it is necessary to preliminarily verify the correlation between RTN and RLRS cycling variability.
Fig. 3. Correlation scatter plots between RLRS and the normalized RTN current fluctuations (a) and RTN current fluctuations (b). RLRS is measured at VREAD = 0.1 V on devices formed at different current compliances (different symbols and colors), displaying different LRS resistances. The same legend applies to (a) and (b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 4. Experimental (symbols) and simulated (lines) probability plots of current fluctuation amplitude, DI (left, empty circles), read current extracted from I–V data (middle, empty squares) and normalized current fluctuation amplitude DI/I (right, empty triangles) at different current compliances (different colors). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
to the mechanism governing the reading current variability (in agreement with the same dependence of ILRS and DI distributions on the current compliance and the invariance of the DI/I distribution), see also Fig. 3. This is strengthened by the results in Fig. 5, where the statistical relation between the current compliance and both the average read current and the average current fluctuation DI over cycling is evidenced. Moreover, since the RTN analysis can estimate how many defects are contributing to each RTN trace, we can perform a quantitative evaluation of the statistical RTN current fluctuation complexity defining a figure of merit (FoM): the ‘‘effective number of traps’’ (ENOT), i.e. the average number of traps detected by the FHMM method over multiple switching cycles under the same set/reset/read conditions. This is mandatory to average out the effect of cycle-to-cycle variability. We estimated the ENOT for several devices under different operating conditions. A higher current compliance, which implies a higher average read current, Fig. 5, results in a larger cross-section (on average), which leads to a larger effective numbers of traps (ENOT) contributing to RTN, i.e. higher RTN complexity, Fig. 6. This parameter does not represent a quantitative estimation of all the defects in the surroundings of the CF, but only of a portion of them (i.e. only the defects capturing and emitting charge carriers with characteristic times which fall between the sampling time and the total measurement time). 5. Discussion The results highlighted in Section 4 suggest that the CF size is related to the statistical complexity of RTN and to the (average) number of defects contributing to the RTN. Despite the higher RTN complexity, no point-to-point correlation is found between the read current and RTN fluctuation amplitudes, Figs. 2 and 3.
Fig. 5. The average value (over multiple switching cycles) of current fluctuation amplitudes is reported versus the average value of the read current and the current compliance, showing a linear trend (dashed line).
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Fig. 6. Effective number of traps contributing to RTN (ENOT) vs. average read current and current compliance for devices formed with different current compliances and linear fitting (dashed line).
Nevertheless, the statistical relation between the average current fluctuations and read current emerges over multiple switching cycles and/or by considering different current compliances (i.e. different CF average cross-sections). To devise a model for RTN in LRS (i.e. which mechanism is causing the modulation of the charge transport over time resulting in RTN), we have to discuss the results in a comprehensive framework which includes the properties of the CF and their variability over cycling as well as the physical understanding of the charge transport. The charge-transport through the CF in LRS exhibits quasi-ohmic characteristics, which is due to a conductive sub-band originating from the very high defect density, presumably oxygen vacancies, in the CF [5], see Section 3.1. In this ohmic-like conductive regime, the charge carriers drift along the highly-defective conductive filament in a delocalized fashion. Trap-Assisted Tunneling (TAT) processes [11] through the oxygen vacancy defects, instead, dominate the conduction through the dielectric barrier in HRS, Fig. 1(c and e). RTN in hafnia-based RRAM devices in HRS was attributed to the activation and de-activation of TAT-supporting defects [12,28–31], i.e. oxygen vacancies. The physical mechanisms responsible for defect activation and de-activation have not been unambiguously identified yet. Among the possible options, it has been shown that the TAT charge transport could be affected by charging and discharging of defects not directly involved in the electron transport [28–30], located in the close proximity of TAT-supporting traps and recently identified with the interstitial oxygen [32,33]. The capture/ emission of an electron by one of such defects may cause a Coulomb blockade of the nearby TAT trap, thus changing the capture and emission rates and inducing the RTN current fluctuations [29]. A similar mechanism could also be responsible for RTN fluctuations in LRS, as schematically illustrated in Figs. 7 and 8: trapping/de-trapping of carriers in/from a defect located in the close proximity of the conductive filament may affect the local conductivity properties of the close CF portion because of the local screening of the trapped charge field, affecting the charge transport (i.e. the current in the CF). The effect of the trapped charge on the LRS current is much lower than that observed on the HRS current because of the higher O-deficiency of the CF, which increases its metallic-like character and the immunity to the screening effect of the trapped charge field. The successive charge emission restores the original local properties of the CF portion close to the defect, thus resulting in the observed RTN current traces. Simulations of a 3D RRAM device in LRS using a kinetic Monte-Carlo approach confirm that this scenario is naturally associated with RTN, Fig. 7. These simulations consider the ohmic-like transport in the CF and the multi-phonon trap-assisted tunneling to take into account trapping and detrapping at defect sites around the CF. Moreover, the 3D potential and temperature maps are calculated to include the effect of the trapped charge field and the local temperature gradient due to the charge transport mechanism.
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According to the above description, the read current in LRS should scale with the conductive filament cross-section, which is in turn controlled by the current compliance imposed during forming/set operations. In this scenario, cycling variability is due to the variations of the characteristics of a small portion of the CF during set and reset operations. This agrees with the normal narrow distributions of the read current scaling with the current compliance, as shown in Fig. 4. On the other hand, the shape of the DI distribution should be related to the statistical distribution of the traps (inducing RTN current fluctuations) around the conductive filament. In order to quantitatively explain this trend, we simulated the DI distribution by considering a uniform distribution of traps around the conductive filament. The screening effect of the trapped charge on the CF decreases with the squared distance from the filament, r2, as it is caused by the electric field associated with the trapped charge. Accordingly, the current fluctuation is described through:
DI ¼
Fig. 7. Schematic of the simulated RRAM device in LRS exhibiting the CF without (a) and with (b) an RTN-inducing defect in its surroundings. The O vacancies composing the CF are represented by the red spots while the RTN-inducing defect is the green spot. The distance of the RTN-inducing defect from the closest O vacancy in the CF is 0.8 nm. (c) Kinetic Monte–Carlo simulation of the current evolution over time corresponding to the a and b cases, indicated with a solid blue and a dashed red line, respectively. Trapping and detrapping at the defect in close proximity to the CF (green spot in b) causes RTN fluctuations of the LRS current. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
k r2
ð3Þ
where k is a parameter depending on CF characteristics, i.e. cross section, sub-stoichiometry level and geometry. The DI distributions simulated under the above assumptions allow describing the experimental data, as shown in Fig. 4, confirming that the shape of the RTN current fluctuations distribution is due to the distribution of traps around the CF. The DI distribution shift with the current compliance is due to the variation of the average conductance (i.e. cross section and/or resistivity) of the filament, which affects the average current and its fluctuations, Figs. 4–6. We also simulated the dynamics of the charge trapping and de-trapping at RTN-inducing defects. For this purpose, we considered a delocalized ohmic-like conduction in the CF and employed a multi-phonon TAT description to properly model the capture and emission of charge carriers into/from the defects in the surroundings of the CF [11]:
Fig. 7 shows the result of two kinetic Monte-Carlo simulations, which include and exclude the presence of a defect in the surroundings of the CF, respectively. The presence of a defect in the surroundings of the CF results in RTN due to the screening of the electric field generated by the trapped charge (the defect is supposed to be electrically active thus it can get charged and discharged). Since this mechanism implies the modulation of the ohmic-like charge transport through a quasi-metallic CF, this effect can also be effectively and intuitively seen as a modulation of the effective cross section of the CF, Fig. 8. Indeed, the resistance of the device can be written as:
RLRS ¼
qCF tox S
ð1Þ
where qCF is the CF resistivity, tox is the CF thickness (or, equivalently, the oxide layer thickness) and S is the CF cross-section. The current fluctuation DI at constant VREAD due to the activity of a single defect can also be written as:
V READ V READ DI ¼ ¼ DS DRLRS qCF t ox
ð2Þ
where DS is the equivalent CF cross-section modulation due to trapped charge field.
Fig. 8. Illustration of RTN mechanism in LRS. The orange cylinder represents the conductive filament while tox is the thickness of the HfO2 layer. (a) The empty trap does not affect the electron drift along the conductive filament. (b) The charge trapping into a defect in close proximity of the CF blocks a portion of the conductive filament because of the screening of the trapped charge field. (c) I-time trace in LRS showing RTN current fluctuations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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[3]
[4]
[5] [6]
[7] Fig. 9. Experimental (symbols) and simulated (lines) probability plots of capture, sc, and emission, se, times measured on devices formed at different current compliances (only three compliances are reported for clarity). Both capture and emission times follow a lognormal distribution which is not sensitive to the current compliance, in agreement with a uniform distribution of defects around the conductive filament.
considering a uniform defects distribution around the conductive filament with a relaxation energy EREL = 1.2 ± 0.2 eV (corresponding to O vacancy defects) allows reproducing accurately the average capture, sc, and emission, se, times, as derived using the FHMM analysis [20,21], as shown in Fig. 9. Both sc and se do not depend, as expected, on the current compliance [29,30], which in turns control the filament cross-section, see Fig. 9. Noticeably, in this scenario the charge trapping and detrapping at defect sites in the surroundings of the CF is simulated by considering all possible transitions between defects (i.e. trap-to-trap transitions), which also implies capture and emission of charge carriers from/into the CF itself. Simulations considering the O vacancy defects in the surroundings of the CF nicely reproduce the capture and emission times distributions of experimental RTN times-series, as measured using a 10 ls sampling time and a 0.1 s total measurement time. Nevertheless, some research groups detected RTN fluctuations in LRS also in more relaxed time ranges, e.g. several seconds [12,18,27]. These slower RTN fluctuations can hardly be associated with O vacancy defects due to their relaxation energy (EREL = 1.2 eV) which is too small to determine such slow RTN dynamics. In this framework, slow RTN fluctuations may be associated with trapping and de-trapping at interstitial O ions defects, which are naturally present in the surroundings of the CF, see also Section 3.1, and have been recently associated with the slow RTN fluctuations in HRS, due to their larger relaxation energy (EREL = 2.3–2.65 eV) [32,33].
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6. Conclusions [23]
We investigated the RTN and cycling-induced current variations in RRAM devices formed by imposing different current compliances. RTN was explored employing the FHMM analysis, which helps in revealing the properties of the defects involved in RTN. RTN in LRS was attributed to the screening of a portion of the conductive filament due to charge trapping at defects located in the close proximity of the conductive filament. Conversely, LRS resistance variability during cycling is caused by the modifications of the conductive filament characteristics, due to the stochastic nature of the physical processes governing set and reset operations. The statistical analysis confirms that RTN and cycling variability in LRS are due to concurrent yet point-to-point uncorrelated processes. References [1] Chen, Y.-S, et al. Highly scalable hafnium oxide memory with improvements of resistive distribution and read disturb immunity. In: Proceedings of IEEE Electron Devices Meeting (IEDM), 7–9 Dec. 2009. p. 1–4. [2] Govoreanu B, et al. Vacancy-modulated conductive oxide resistive RAM (VMCO-RRAM): An area-scalable switching current, self-compliant, highly nonlinear and wide on/off-window resistive switching cell. In: Proceedings of
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A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 1989;77(2):257–86. Puglisi FM, Pavan P. RTN analysis with FHMM as a tool for multi-trap characterization in HfOX RRAM. In: Proceedings of IEEE International Conference on Electron Devices and Solid-State Circuits (EDSSC), 3–5 June 2013. p. 1–2. Puglisi FM, Pavan P. Factorial Hidden Markov Model analysis of random telegraph noise in resistive random access memories. ECTI Trans Electr Eng Electron Commun 2014;12(1):24–9. Lee HY, et al. Low power and high speed bipolar switching with a thin reactive Ti buffer layer in robust HfO2 based RRAM. In: Proceedings of IEEE International Electron Devices Meeting (IEDM), 15–17 Dec. 2008. pp. 1–4. Young-Fisher KG et al. Leakage current-forming voltage relation and oxygen gettering in HfOx RRAM devices. IEEE Electron Device Lett 2013;34(6):750–2. Larcher L et al. Progresses in modeling HfOx RRAM operations and variability. ECS Trans 2014;64(14):49–60. McKenna KP. Optimal stoichiometry for nucleation and growth of conductive filaments in HfOx. Modell Simul Mater Sci Eng 2014;22(2):025001. Landauer R. Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J Res Dev 1957;1(3):223–31. Ambrogio S, et al. Understanding switching variability and random telegraph noise in resistive RAM. In: Proceedings of the IEEE International Electron Devices Meeting (IEDM), 9–11 Dec. 2013. p. 3151–54. Puglisi FM, et al. Instability of HfO2 RRAM devices: comparing RTN and cycling variability. In: Proceedings of the IEEE International Reliability Physics Symposium (IRPS), 1–5 June 2014, MY. 5.1–MY. 5.5. Puglisi FM, Pavan P, Padovani A, Larcher L. A study on HfO2 RRAM in HRS based on I–V and RTN analysis. Solid State Electron. 2014;102:69–75. Puglisi FM, Pavan P, Padovani A, Larcher L. Random telegraph noise analysis to investigate the properties of active traps of HfO2-based RRAM in HRS. 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Statistical analysis of random telegraph noise in HfO2-based RRAM devices in LRS Francesco Maria Puglisi a,⇑, Paolo Pavan a, Luca Larcher b, Andrea Padovani b a b
Dipartimento di Ingegneria ‘‘Enzo Ferrari’’, Università di Modena e Reggio Emilia, Via Pietro Vivarelli 10/1, 41125 Modena, Italy Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, Via Amendola 2, 42122 Modena, Italy
a r t i c l e
i n f o
Article history: Available online 2 June 2015 Keywords: RRAM RTN FHMM Cycling Variability Resistive switching
a b s t r a c t In this work, we present a thorough statistical characterization of Random Telegraph Noise (RTN) in HfO2-based Resistive Random Access Memory (RRAM) cells in Low Resistive State (LRS). Devices are tested under a variety of operational conditions. A Factorial Hidden Markov Model (FHMM) analysis is exploited to extrapolate the properties of the traps causing multi-level RTN in LRS. The trapping and de-trapping of charge carriers into/out of defects located in the proximity of the conductive filament results in a shielding effect on a portion of the conductive filament, leading to the observed RTN current fluctuations. It is found that both oxygen vacancies and oxygen ions defects may be responsible for the observed RTN. The variations of the current observed at subsequent set/reset cycles are instead attributed to the stochastic variations in the filament due to oxidation/reduction processes during reset and set operations, respectively. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Resistive random access memories (RRAMs) are currently one of the most promising class of alternative non-volatile memories (NVMs), exhibiting reliable and fast switching [1], low-power operation [2], and high-density [3]. Among different resistive switching devices, RRAM cells based on hafnium oxide show superior performances [4] and excellent compatibility with the standard CMOS back-end of line. Actual understanding of RRAMs switching mechanism relies on the formation and successive partial oxidation of a conductive filament (CF) during set and reset operations, respectively [5]. The formation of a CF sets the device in the low-resistance state (LRS) while its partial oxidation leads to the creation of a dielectric barrier, determining the high-resistance state (HRS) [6–10]. The charge transport in LRS exhibits quasi-ohmic behavior [5], whereas the conduction in HRS is dominated by a multi-phonon trap-assisted tunneling (TAT) process [11] via the traps in the barrier. Unfortunately, stochastic features inborn in this technology, i.e. cycling variability and Random Telegraph Noise (RTN) [12–16], are hampering the device scaling and multi-bit storage implementation, delaying the full scale industrial exploitation of the RRAM concept. In this work we explore RTN characteristics in RRAM devices, focusing on the LRS, which has not been extensively covered in the literature as it ⇑ Corresponding author. Tel.: +39 059 2056324. E-mail address: [email protected] (F.M. Puglisi). http://dx.doi.org/10.1016/j.sse.2015.05.027 0038-1101/Ó 2015 Elsevier Ltd. All rights reserved.
exhibits lower current noise compared to the High Resistive State (HRS) [17,18]. Our previous works [13,14] exploited the color-coded time-lag plots and Hidden Markov Model [19] (HMM) to investigate the characteristics of RTN in RRAMs, showing that multi-level RTN can be seen as a superposition of many two-level RTN signals, each associated with a single trap [13]. We also proposed the factorial hidden Markov Model [20,21] (FHMM), a more refined implementation of the HMM, as a tool to derive the statistical properties of multi-level RTN. In this paper, the current noise in reading conditions is extensively characterized after set operations performed at different current compliances through the FHMM analysis [20,21]. In order to take into account the cycling variability of the LRS, a compact model is exploited to estimate the CF cross-section after each switching cycle [8]. This paper is organized as follows: devices and experiments are described in Section 2; in Section 3 we introduce the tools used for the analysis of the experimental data, i.e., FHMM and Compact Model, respectively; in Section 4 we report on the experimental results of RTN and I–V characterization; in Section 5 we discuss the results, suggesting possible mechanisms responsible for RTN in these devices. Conclusions follow.
2. Devices and experiments Measurements are performed on 20 TiN/Ti/HfOx/TiN 200 200 nm2 cross-bar RRAM devices in 1T1R configuration.
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Devices with 5.6 nm ALD HfO2 and 8 nm Ti layer are analyzed. The Ti layer sputtered on top of the hafnium oxide acts as an oxygen exchange layer, inducing an oxygen deficiency in the oxide film during post-deposition annealing at 400 °C for 30 min. This is required to induce a given degree of oxygen sub-stoichiometry (needed for a reliable switching), which is caused by the interaction between the Ti capping layer and the hafnium oxide layer, as explained in [22,23]. A preliminary forming operation, under current compliance limit, is performed to set the device into the initial condition enabling resistive switching; the use of 1T1R configuration allows minimizing the current overshoot due to parasitic capacitances [22,23]. Set and reset operations drive the device in LRS and HRS, respectively. After forming (occurring at a typical voltage of 3 V in these devices), which sets the device to LRS, one hundred complete switching DC cycles (set-read-reset) are performed. A semiconductor parameter analyzer is used to both acquire I–V curves during switching cycles (see Figs. 1 and 2) and properly bias the device (in reading conditions we consider VREAD = 0.1 V). The maximum absolute value of the voltage during the reset DC sweeps is VRESET = 1.6 V. Current fluctuations (ILRSt data) during the read operation are measured by sampling the current vs. time, collecting 10 k samples (i.e. current measures) with a sampling time of 10 ls, which corresponds to a total measurement time of 0.1 s. This measurement process allows to characterize 1 bit per reading operation. 3. Device structure and RTN analysis Among major concerns for RRAM future scaling and development, RTN disturb is currently limiting the full exploitation of this technology. The RTN current fluctuations, as shown in the inset of Fig. 1, reduce the readout margin of the device and may cause read failures. In this work we focus on the analysis of RTN in LRS, which has not been thoroughly investigated in the literature, compared to HRS [17,18]. Noise data are analyzed by considering also the physical parameters describing the device in LRS (i.e. CF cross-section), which depends on the set conditions (i.e. the current compliance). Estimating this value after every switching cycle allows considering the effect of cycling variability of the LRS while performing RTN analysis and to relate RTN to the physical properties of the CF. 3.1. Device structure in LRS In order to fully understand the dynamics of RTN in LRS, it is mandatory to comprehensively describe the state of the device in
Fig. 1. Schematics of an RRAM structure for different forming/set conditions. (a) The cell prior to forming. (b) A conductive filament (blue cylinder) is formed by applying a positive voltage ramp. (c) Reset operation partially oxidizes the conductive filament creating a dielectric barrier (orange section of the cylinder), with the thickness x. (d and e) The conductive filament cross-section increases with the magnitude of the current compliance. Circles represents the defects in the barrier contributing to charge transport in HRS. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. (a) LRS current measured in reading conditions (V = 0.1 V) and (b) RTN current fluctuations extracted from the multi-level ILRS-time traces through the FHMM technique at each set/read/reset cycle in 8 nm Ti/5.6 nm HfOX RRAM devices: differently colored symbols represent the current fluctuations due to individual traps identified in a given cycle, while the cumulative current fluctuation due to the superposition of the effects of all traps is represented by the black squares with dashed line. The applied reset voltage is 1.6 V. The current compliance is 70 lA. Missing data points in certain cycles in (b) indicate that no RTN signal is detected (only Gaussian noise). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
LRS. This resistive state is reached for the first time when the CF is formed as a result of the preliminary forming operation, which determines the CF properties [5]. Under typical forming conditions (i.e. current compliance), the conductive filament exhibits quasi-ohmic I–V characteristics indicating that it is formed by an Hf-rich (oxygen deficient) region in the dielectric [24]. The CF formation is a two-step process involving the Hf–O bond breakage and the subsequent diffusion of the released oxygen ions out of the forming CF region [5,24,25]. O ions distribution is, in turn, the critical factor controlling the subsequent reset process. The oxygen extraction occurring during the forming transient leads to the increase of the local O vacancy defects density and, eventually, to the formation of defect sub-bands, which are associated with very high defect density [5]. After the CF formation, the dominant charge transport mechanism is the electron drift through the defect sub-band, described in the framework of the Landauer formalism [26], which allows reproducing the LRS quasi-ohmic I–V characteristics. The reset operation is described as a partial re-oxidation of the CF due to the oxygen ions diffusion from the surroundings of the CF and their recombination with the O vacancies at the bottom tip of the CF [6–10,24]. This leads to the creation of a dielectric and O vacancy defect-rich barrier, responsible for the relatively low current observed in HRS. The HRS current is due to the electron TAT transport through the O vacancies in the dielectric barrier [5,11], which is mostly controlled by the barrier thickness, tB, and the distribution of the O vacancy defects within the barrier. It has to be pointed out that, while both the dielectric barrier and the CF are characterized by a high O vacancy density, their electrical behavior is dissimilar. The O vacancy defects density in the CF is indeed much larger than that in the dielectric barrier, leading to different charge transport regimes, TAT through O vacancies in HRS and electrons drift through a defect sub-band in LRS, respectively [5]. The set operation, typically performed by imposing the same current compliance limit adopted in the forming operation, allows the resistance switching from HRS to LRS, which corresponds to the restoration of the CF [7–10]. The set process physics is analogous to that of the forming process [5], and involves breaking the thin dielectric barrier formed during reset. However the voltage at which it occurs is much lower than the forming one,
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because of the reduced thickness of the dielectric barrier. This is due to the relatively high conductivity of the undisrupted CF portion, which makes the most of the voltage applied during set to drop across the oxidized CF tip (dielectric barrier). Thus, voltages as low as 0.5–1 V allow the electric field in the dielectric barrier to approach its intrinsic dielectric strength, thus resulting in a fast Hf–O bond breakage and release of the oxygen ions that restores the characteristics of the CF [24,25]. Since the major properties (e.g. shape, size) of the CF are not affected by switching cycles, which change the characteristics only of a fragment of the CF, the distribution of the LRS resistance is expected to be narrow. The cycling variability observed in LRS is hence due to the modulation of the CF properties (i.e. CF cross-section) in a small region, as a result of the intrinsic randomness in the physics of the set process [9,10]. 3.2. Random telegraph noise analysis Currently, the physical mechanism responsible for RTN current fluctuations in LRS is still unclear. Nevertheless, there are a number of evidences indicating that RTN may results from the trapping and de-trapping of charge carriers at defects located in close proximity to the edge of the CF [27–31]. The defects contributing to RTN are characterized through an FHMM analysis, which we proposed as an effective tool to overcome the limitations of HMM when dealing with multi-level RTN [20,21]. Indeed, HMM [14,19] models the input signal as a Markov chain with K hidden states (i.e. discrete current levels). This approach is suitable to analyze a two-level RTN (associated with the activity of a single trap), whereas it becomes inappropriate with the multi-level RTN, which is generated by many traps. In fact, in the standard case of a two-level RTN, the difference between the current levels corresponds to the amplitude of the RTN fluctuation and the HMM approach can be used to efficiently estimate the hidden states, hence the amplitude of the fluctuation. With multi-level RTN the estimation of the hidden current levels is not sufficient to univocally determine the amplitude of each two-level fluctuation generating the RTN. The FHMM allows overcoming the HMM limits by considering the multi-level RTN as the summation of independent two-level Markov chains [20,21], each corresponding to trapping/de-trapping at an individual defect, instead of representing it as a single Markov chain with many states. This methodology allows to decompose the multi-level RTN into different two-level fluctuations and to retrieve the properties of each defect contributing to the RTN. Further details about the FHMM technique are available in [20,21]. For the characterization of traps contributing to RTN we considered RRAM devices in different operating conditions and for several consecutive switching cycles and reading operations: for each reading operation, the corresponding current time-series is processed with the FHMM method and the statistical properties of each detected trap are collected [13,14,19–21], i.e. the current fluctuation (DI), DI normalized w.r.t. the average DC current (DI/I), capture (sc) and emission time (se).
To this purpose, we reported in Fig. 2 the LRS current measured in reading conditions (VREAD = 0.1 V) and RTN current fluctuation (DI) as extracted from the multi-level RTN ILRS-time traces at each switching cycle using the FHMM technique [20,21]. For each switching cycle, we show the current fluctuations associated with every individual trap detected by the FHMM algorithm and the maximum current variation in the ILRS-time trace, calculated by summing up the individual current fluctuations. The LRS current varies from nearly 2 lA up to 6 lA (for a current compliance of 70 lA), whereas the current fluctuations range from 1 lA to nearly 1 nA for VRESET = 1.6 V. Different DI amplitudes are found for similar LRS read currents and vice versa, see Fig. 2, indicating that the ILRS (or equivalently RLRS) variation during cycling is not straightforwardly correlated to the RTN current fluctuations. Similar results were also obtained on device formed at different current compliances. This trend is confirmed also by the correlation scatter plot in Fig. 3a, which displays the normalized RTN current fluctuation (DI/I) vs. RLRS observed at multiple switching cycles and different current compliances, which are represented by different symbols and colors. The RTN amplitudes do not correlate to RLRS measured at the same current compliance, confirming that RTN and RLRS cycling variability are concurrent but not point-to-point correlated phenomena. Still, statistical correlation can be observed between the non-normalized RTN currents (DI) and RLRS, Fig. 3b, which is due to the fact that a high current compliance leads to the formation of a wider (on average) conductive filament resulting in a higher LRS read current [5,7–10], Fig. 1. In order to fully explore RTN characteristics, we analyzed RTN and I-V data in LRS at different switching cycles for devices formed at different current compliances. For each cycle, we reported the read current from the I–V curve in reading conditions (i.e. VREAD = 0.1 V) and the DI associated with each trap detected by the FHMM method. Results are reported in Fig. 4. The read current is normally distributed over cycling and shows a narrow dispersion around its mean value. This is primarily due to the intrinsic randomness of the set/reset operations, resulting in changes in cross section and/or resistivity of a relatively small portion of the CF [5,7–10]: this reflects in the normal distributions of the read current shown in Fig. 4. On the other hand, DI distributions show a different shape than the reading current distribution; see Fig. 4. However, the DI distribution shifts with the current compliance imposed during forming, due to the variation of the average conductance (i.e. cross section and/or resistivity) of the CF, which affects the average current and its fluctuations [12–14,29–31], Figs. 4 and 5. Indeed, the normalized DI/I distribution is unaffected by the current compliance, Figs. 3 and 4. This trend may be associated with a different mechanism governing the RTN (responsible for the different shapes of ILRS and DI distributions), which is statistically linked
4. RTN analysis results For a complete RTN analysis, we implemented a statistical approach accounting for both cycling variability and RTN. The cycling variability derives from the intrinsic randomness of the set process, which affects the CF properties, i.e. CF cross-section, which in turn affects the charge transport leading to the RLRS, or equivalently ILRS, variability displayed in Fig. 2a. Since RTN appears as an instability in the charge transport mechanism (it emerges as fluctuations of the read current), it is necessary to preliminarily verify the correlation between RTN and RLRS cycling variability.
Fig. 3. Correlation scatter plots between RLRS and the normalized RTN current fluctuations (a) and RTN current fluctuations (b). RLRS is measured at VREAD = 0.1 V on devices formed at different current compliances (different symbols and colors), displaying different LRS resistances. The same legend applies to (a) and (b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 4. Experimental (symbols) and simulated (lines) probability plots of current fluctuation amplitude, DI (left, empty circles), read current extracted from I–V data (middle, empty squares) and normalized current fluctuation amplitude DI/I (right, empty triangles) at different current compliances (different colors). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
to the mechanism governing the reading current variability (in agreement with the same dependence of ILRS and DI distributions on the current compliance and the invariance of the DI/I distribution), see also Fig. 3. This is strengthened by the results in Fig. 5, where the statistical relation between the current compliance and both the average read current and the average current fluctuation DI over cycling is evidenced. Moreover, since the RTN analysis can estimate how many defects are contributing to each RTN trace, we can perform a quantitative evaluation of the statistical RTN current fluctuation complexity defining a figure of merit (FoM): the ‘‘effective number of traps’’ (ENOT), i.e. the average number of traps detected by the FHMM method over multiple switching cycles under the same set/reset/read conditions. This is mandatory to average out the effect of cycle-to-cycle variability. We estimated the ENOT for several devices under different operating conditions. A higher current compliance, which implies a higher average read current, Fig. 5, results in a larger cross-section (on average), which leads to a larger effective numbers of traps (ENOT) contributing to RTN, i.e. higher RTN complexity, Fig. 6. This parameter does not represent a quantitative estimation of all the defects in the surroundings of the CF, but only of a portion of them (i.e. only the defects capturing and emitting charge carriers with characteristic times which fall between the sampling time and the total measurement time). 5. Discussion The results highlighted in Section 4 suggest that the CF size is related to the statistical complexity of RTN and to the (average) number of defects contributing to the RTN. Despite the higher RTN complexity, no point-to-point correlation is found between the read current and RTN fluctuation amplitudes, Figs. 2 and 3.
Fig. 5. The average value (over multiple switching cycles) of current fluctuation amplitudes is reported versus the average value of the read current and the current compliance, showing a linear trend (dashed line).
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Fig. 6. Effective number of traps contributing to RTN (ENOT) vs. average read current and current compliance for devices formed with different current compliances and linear fitting (dashed line).
Nevertheless, the statistical relation between the average current fluctuations and read current emerges over multiple switching cycles and/or by considering different current compliances (i.e. different CF average cross-sections). To devise a model for RTN in LRS (i.e. which mechanism is causing the modulation of the charge transport over time resulting in RTN), we have to discuss the results in a comprehensive framework which includes the properties of the CF and their variability over cycling as well as the physical understanding of the charge transport. The charge-transport through the CF in LRS exhibits quasi-ohmic characteristics, which is due to a conductive sub-band originating from the very high defect density, presumably oxygen vacancies, in the CF [5], see Section 3.1. In this ohmic-like conductive regime, the charge carriers drift along the highly-defective conductive filament in a delocalized fashion. Trap-Assisted Tunneling (TAT) processes [11] through the oxygen vacancy defects, instead, dominate the conduction through the dielectric barrier in HRS, Fig. 1(c and e). RTN in hafnia-based RRAM devices in HRS was attributed to the activation and de-activation of TAT-supporting defects [12,28–31], i.e. oxygen vacancies. The physical mechanisms responsible for defect activation and de-activation have not been unambiguously identified yet. Among the possible options, it has been shown that the TAT charge transport could be affected by charging and discharging of defects not directly involved in the electron transport [28–30], located in the close proximity of TAT-supporting traps and recently identified with the interstitial oxygen [32,33]. The capture/ emission of an electron by one of such defects may cause a Coulomb blockade of the nearby TAT trap, thus changing the capture and emission rates and inducing the RTN current fluctuations [29]. A similar mechanism could also be responsible for RTN fluctuations in LRS, as schematically illustrated in Figs. 7 and 8: trapping/de-trapping of carriers in/from a defect located in the close proximity of the conductive filament may affect the local conductivity properties of the close CF portion because of the local screening of the trapped charge field, affecting the charge transport (i.e. the current in the CF). The effect of the trapped charge on the LRS current is much lower than that observed on the HRS current because of the higher O-deficiency of the CF, which increases its metallic-like character and the immunity to the screening effect of the trapped charge field. The successive charge emission restores the original local properties of the CF portion close to the defect, thus resulting in the observed RTN current traces. Simulations of a 3D RRAM device in LRS using a kinetic Monte-Carlo approach confirm that this scenario is naturally associated with RTN, Fig. 7. These simulations consider the ohmic-like transport in the CF and the multi-phonon trap-assisted tunneling to take into account trapping and detrapping at defect sites around the CF. Moreover, the 3D potential and temperature maps are calculated to include the effect of the trapped charge field and the local temperature gradient due to the charge transport mechanism.
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According to the above description, the read current in LRS should scale with the conductive filament cross-section, which is in turn controlled by the current compliance imposed during forming/set operations. In this scenario, cycling variability is due to the variations of the characteristics of a small portion of the CF during set and reset operations. This agrees with the normal narrow distributions of the read current scaling with the current compliance, as shown in Fig. 4. On the other hand, the shape of the DI distribution should be related to the statistical distribution of the traps (inducing RTN current fluctuations) around the conductive filament. In order to quantitatively explain this trend, we simulated the DI distribution by considering a uniform distribution of traps around the conductive filament. The screening effect of the trapped charge on the CF decreases with the squared distance from the filament, r2, as it is caused by the electric field associated with the trapped charge. Accordingly, the current fluctuation is described through:
DI ¼
Fig. 7. Schematic of the simulated RRAM device in LRS exhibiting the CF without (a) and with (b) an RTN-inducing defect in its surroundings. The O vacancies composing the CF are represented by the red spots while the RTN-inducing defect is the green spot. The distance of the RTN-inducing defect from the closest O vacancy in the CF is 0.8 nm. (c) Kinetic Monte–Carlo simulation of the current evolution over time corresponding to the a and b cases, indicated with a solid blue and a dashed red line, respectively. Trapping and detrapping at the defect in close proximity to the CF (green spot in b) causes RTN fluctuations of the LRS current. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
k r2
ð3Þ
where k is a parameter depending on CF characteristics, i.e. cross section, sub-stoichiometry level and geometry. The DI distributions simulated under the above assumptions allow describing the experimental data, as shown in Fig. 4, confirming that the shape of the RTN current fluctuations distribution is due to the distribution of traps around the CF. The DI distribution shift with the current compliance is due to the variation of the average conductance (i.e. cross section and/or resistivity) of the filament, which affects the average current and its fluctuations, Figs. 4–6. We also simulated the dynamics of the charge trapping and de-trapping at RTN-inducing defects. For this purpose, we considered a delocalized ohmic-like conduction in the CF and employed a multi-phonon TAT description to properly model the capture and emission of charge carriers into/from the defects in the surroundings of the CF [11]:
Fig. 7 shows the result of two kinetic Monte-Carlo simulations, which include and exclude the presence of a defect in the surroundings of the CF, respectively. The presence of a defect in the surroundings of the CF results in RTN due to the screening of the electric field generated by the trapped charge (the defect is supposed to be electrically active thus it can get charged and discharged). Since this mechanism implies the modulation of the ohmic-like charge transport through a quasi-metallic CF, this effect can also be effectively and intuitively seen as a modulation of the effective cross section of the CF, Fig. 8. Indeed, the resistance of the device can be written as:
RLRS ¼
qCF tox S
ð1Þ
where qCF is the CF resistivity, tox is the CF thickness (or, equivalently, the oxide layer thickness) and S is the CF cross-section. The current fluctuation DI at constant VREAD due to the activity of a single defect can also be written as:
V READ V READ DI ¼ ¼ DS DRLRS qCF t ox
ð2Þ
where DS is the equivalent CF cross-section modulation due to trapped charge field.
Fig. 8. Illustration of RTN mechanism in LRS. The orange cylinder represents the conductive filament while tox is the thickness of the HfO2 layer. (a) The empty trap does not affect the electron drift along the conductive filament. (b) The charge trapping into a defect in close proximity of the CF blocks a portion of the conductive filament because of the screening of the trapped charge field. (c) I-time trace in LRS showing RTN current fluctuations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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[3]
[4]
[5] [6]
[7] Fig. 9. Experimental (symbols) and simulated (lines) probability plots of capture, sc, and emission, se, times measured on devices formed at different current compliances (only three compliances are reported for clarity). Both capture and emission times follow a lognormal distribution which is not sensitive to the current compliance, in agreement with a uniform distribution of defects around the conductive filament.
considering a uniform defects distribution around the conductive filament with a relaxation energy EREL = 1.2 ± 0.2 eV (corresponding to O vacancy defects) allows reproducing accurately the average capture, sc, and emission, se, times, as derived using the FHMM analysis [20,21], as shown in Fig. 9. Both sc and se do not depend, as expected, on the current compliance [29,30], which in turns control the filament cross-section, see Fig. 9. Noticeably, in this scenario the charge trapping and detrapping at defect sites in the surroundings of the CF is simulated by considering all possible transitions between defects (i.e. trap-to-trap transitions), which also implies capture and emission of charge carriers from/into the CF itself. Simulations considering the O vacancy defects in the surroundings of the CF nicely reproduce the capture and emission times distributions of experimental RTN times-series, as measured using a 10 ls sampling time and a 0.1 s total measurement time. Nevertheless, some research groups detected RTN fluctuations in LRS also in more relaxed time ranges, e.g. several seconds [12,18,27]. These slower RTN fluctuations can hardly be associated with O vacancy defects due to their relaxation energy (EREL = 1.2 eV) which is too small to determine such slow RTN dynamics. In this framework, slow RTN fluctuations may be associated with trapping and de-trapping at interstitial O ions defects, which are naturally present in the surroundings of the CF, see also Section 3.1, and have been recently associated with the slow RTN fluctuations in HRS, due to their larger relaxation energy (EREL = 2.3–2.65 eV) [32,33].
[8] [9]
[10] [11] [12]
[13]
[14] [15]
[16]
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6. Conclusions [23]
We investigated the RTN and cycling-induced current variations in RRAM devices formed by imposing different current compliances. RTN was explored employing the FHMM analysis, which helps in revealing the properties of the defects involved in RTN. RTN in LRS was attributed to the screening of a portion of the conductive filament due to charge trapping at defects located in the close proximity of the conductive filament. Conversely, LRS resistance variability during cycling is caused by the modifications of the conductive filament characteristics, due to the stochastic nature of the physical processes governing set and reset operations. The statistical analysis confirms that RTN and cycling variability in LRS are due to concurrent yet point-to-point uncorrelated processes. References [1] Chen, Y.-S, et al. Highly scalable hafnium oxide memory with improvements of resistive distribution and read disturb immunity. In: Proceedings of IEEE Electron Devices Meeting (IEDM), 7–9 Dec. 2009. p. 1–4. [2] Govoreanu B, et al. Vacancy-modulated conductive oxide resistive RAM (VMCO-RRAM): An area-scalable switching current, self-compliant, highly nonlinear and wide on/off-window resistive switching cell. In: Proceedings of
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