Experimental study of the series resistance effect and its impact on the compact modeling of the conduction characteristics of HfO2-based resistive switching memories

J. Appl. Phys. 130, 054503 (2021); https://doi.org/10.1063/5.0055982 130, 054503 © 2021 Author(s). Experimental study of the series resistance effect and its impact on the compact modeling of the conduction characteristics of HfO2-based resistive switching memories Cite as: J. Appl. Phys. 130, 054503 (2021); https://doi.org/10.1063/5.0055982 Submitted: 05 May 2021 . Accepted: 21 July 2021 . Published Online: 06 August 2021 D. Maldonado, F. Aguirre, G. González-Cordero, A. M. Roldán, M. B. González, F. Jiménez-Molinos, F. Campabadal, E. Miranda, J. B. Roldán, et al. 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Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 View Online Export Citation CrossMar k Submitted: 5 May 2021 · Accepted: 21 July 2021 · Published Online: 6 August 2021 D. Maldonado, 1 F. Aguirre, 2,3,4 G. González-Cordero, 1 A. M. Roldán, 1 M. B. González, 5 F. Jiménez-Molinos, 1 F. Campabadal, 5 E. Miranda, 4 and J. B. Roldán 1,a) AFFILIATIONS 1 Departamento de Electrónica y Tecnología de Computadores, Universidad de Granada, Facultad de Ciencias, Avd. Fuentenueva s/n, 18071 Granada, Spain 2 Unidad de Investigación y Desarrollo de las Ingenierías (UIDI), Facultad Regional Buenos Aires, Universidad Tecnológica Nacional, Medrano 951 (C1179AAQ), Buenos Aires, Argentina 3 Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Godoy Cruz 2290 (C1425FQB), Buenos Aires, Argentina 4 Deparment d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Edifici Q. 08193 Bellaterra, Spain 5 Institut de Microelectrònica de Barcelona, IMB-CNM (CSIC), Carrer dels Til⋅lers, s/n. Campus UAB, 08193 Bellaterra, Spain a) Author to whom correspondence should be addressed: jr[email protected] ABSTRACT The relevance of the intrinsic series resistance effect in the context of resistive random access memory (RRAM) compact modeling is investigated. This resistance notably affects the conduction characteristic of resistive switching memories so that it becomes an essential factor to consider when fitting experimental data, especially those coming from devices exhibiting the so-called snapback and snapforward effects. A thorough description of the resistance value extraction procedure and an analysis of the connection of this value with the set and reset transition voltages in HfO 2 -based valence change memories are presented. Furthermore, in order to illustrate the importance of this feature in the shape of the I–Vcurve, the Stanford model for RRAM devices is enhanced by incorporating the series resistance as an additional parameter in the Verilog-A model script. Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0055982 I. INTRODUCTION Resistive Random Access Memories (RRAMs) are nowadays under study worldwide for their outstanding potential in the development of non-volatile memory-based applications. 1,2 Because of their tunable conduction properties, resistive switching devices are also gaining momentum in the neuromorphic circuit landscape since they can mimic biological synapses. 3–7 Their use in a fully compatible CMOS technology context can unleash an overwhelming development of these applications to advance in neuromorphic computing and neural network hardware implementation. 3–7 Moreover, due to their inherent stochastic nature, these devices can be used as entropy sources for cryptographic circuits, such as physical unclonable functions and random number generators. 8–10 RRAMs features allow us to stack cells in 3D and scale to very small process nodes. The cells typically employ a switching material (usually a transition metal oxide) sandwiched in between two metal electrodes. 1,2 One of the most important physical mechanisms associated with resistive switching (RS) is the formation and rupture of nanofilaments across the dielectric film. From a technology point of view, there is substantial flexibility to optimize the performance through an appropriate selection of switching materials and memory cell organization. However, although RRAMs have demonstrated some advantages over flash devices and other Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 130, 054503-1 Published under an exclusive license by AIP Publishing emerging structures (phase change memories and ferroelectric memories) such as short read/write times, high endurance, low power operation, radiation hardness, CMOS compatibility, they are not exempt from serious drawbacks. 2,11 It is worth mentioning that massive industrial production still faces several challenges such as a high variability and the lack of reliable electronic design automation EDA tools. In this regard, compact models are essential tools to tackle these latter concerns. RRAM compact modeling has been addressed in the last years at different levels. The Stanford model (STFM) 12–15 has been employed by many research groups. Other models have also been introduced. 16–20 In the general modeling context, both analytical expressions to describe device operation and parameter extraction techniques need to be developed as a whole. 21 Even well-established models are unable to reproduce certain observable phenomena and, therefore, they must be continuously improved to account for new physical and technological features associated with particular materials or devices. This is precisely the focus of our work. In particular, we take the intrinsic series resistance effect in RRAM operation analysis into consideration and report a systematic approach to extract this series resistance from the experimental results. As it will be shown in Secs. II–V, the role played by the series resistance is of utmost importance for understanding the RRAM electrical behavior, an issue which has been already recognized by several authors. 22–25 The study of the role played by the series resistance within RRAM models is particularly performed for the STFM since its use is extended and its algebraic formulation is both compact as well as intuitive. The enhanced STFM flexibility to reproduce valence change memories (VCM) experimental data is assessed in depth. For the sake of completeness, it is worth pointing out that in the last few years, VCM devices modeling has been addressed following a variety of approaches; 12,14,16–18 in particular, different types of filament shapes have been considered (cylindrical, truncated cone, and hourglass 26 ). In addition, from the analytical formulation viewpoint, the state variable has been assumed from a different perspective: the width of the gap between the conductive filament tip and the electrode, 12,13 the CF volume or radius, 17,18 and as a generalized memory variable. 27 The device current calculation has been performed also under different considerations including tunneling, Schottky, Poole–Frenkel, and ohmic conduction regimes. 12,14,20,26 Some of the modeling implementations also account for variability 28 and noise; in the latter case, Random Telegraph Noise (RTN) has been found appropriate for cryptographic purposes such as random number generation circuits. 9,29 The paper is organized as follows, in Sec. II, we introduce the device fabrication and measurement details. Section III is devoted to the series resistance extraction procedures, while the modeling developments are tackled in Sec. IV, and finally, we wrap up with the main conclusions in Sec. V. II. DEVICE DESCRIPTION AND MEASUREMENT The RRAMs were fabricated using a highly doped N-type (ρ=4mΩcm) silicon wafer. The top metal electrode consists of a 200 nm TiN/10 nm Ti bi-layer while the bottom metal, a 50 nm-thick W layer, was deposited on the silicon substrate with a 20 nm Ti adhesion layer, see Fig. 1(a). The back of the wafers was metalized with aluminum for electrically contacting the bottom electrode through the silicon substrate. The dielectric layer consists of a 10 nm-thick HfO 2 film deposited by ALD. The area of the devices is 15 × 15 μm 2 . It is worth mentioning that the fabricated RRAMs are valence change mechanism-based devices. FIG. 1. (a) Layer stack scheme of the devices under study and (b) experimental I–Vcurves for 1000 set/reset cycles. The inset in (b) shows the set and reset voltages for two of the curves measured. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 130, 054503-2 Published under an exclusive license by AIP Publishing The electrical characterization of the devices was performed applying a ramped voltage (0.08 V/s) to the TiN/Ti top electrode with a voltage step of 0.01 V and with the W bottom electrode grounded. A forming process was performed with current compliance I CC = 0.1 mA and subsequently a sequence of 1000 RS cycles was measured, see Fig. 1(b). These cycles consist of consecutive set and reset transitions. In particular, for positive voltages, a set process leads to the formation of a conductive filament (CF) that shorts the electrodes 30 and the device switches to the low resistance state (LRS). The reset process occurs at negative voltages, in this case, the CF is ruptured and the device switches back to the high resistance state (HRS). 30 See the set and reset voltages indicated in the inset of Fig. 1(b). III. SERIES RESISTANCE AND TRANSITION VOLTAGES EXTRACTION In order to calculate the intrinsic series resistance, R series , for compact modeling purposes, a numerical procedure similar to that used in previous publications 22–24 is considered here. The method consists in using a redefined voltage scale, V N =V Applied –I Measured ×R series , where V Applied is the external applied voltage and I Measured the measured current. We replot the experimental I–Vcurves (as the ones shown in Fig. 1)by changing the variable in the Xaxis to V N instead of the experimental V Applied .BysweepingR series , we obtain different modified I Measured –V N curves (see Fig. 2). Among them, we select the one with the steepest slope (close to a vertical line) in the region after the curve knee; in doing so, we make sure the set process is visualized properly as long as the current rises while the voltage is constant as shown in Fig. 2. This behavior is a clear sign of a sustained conductive filament growth that leads to a current rise even if the device voltage is fixed. The slope of the curve is computed by a linear regression scheme along its straightest part. Based on the obtained R series value, a comparison between V set and the transition voltage for the set process (V TS ) is performed to assess the influence of R series on the I–Vcurves. Notice that V set is obtained from the original I–Vcurve (first point where the FIG. 2. Modified I–Vcurves (measured current vs V N ) for a set process making use of different series resistances. For the sake of clarity, only four curves corresponding to different series resistances are included. The black-dashed lines are the result of the linear regression performed to choose the curve with the highest slope in the methodology proposed. FIG. 3. Experimental current vs applied voltage for one cycle in a long RS series for one of the devices under study. The new transition voltage V TS is obtained from the I–V N curve. (a) Linear and (b) logarithmic scale. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 130, 054503-3 Published under an exclusive license by AIP Publishing maximum current slope along the I–Vcurve is found) and V TS from the modified one (I Measured –V N )aftertheR series calculation. In this latter case, the projection in the X axis of the vertical line obtained in thenewcurve(I Measured –V N ) is assumed as V TS (see Fig. 3). The above described methodology can lead to erroneous values for the series resistance in some particular I–V N curves (because of the snapback effect). In order to improve the parameter extraction method, only a region of the vertical section of the modified I–Vcurve is fitted when searching for the steepest slope. As indicated in Fig. 4(a), the fitting region is selected to be in between a current value of 0.9 × I max and a current resulting from the average of the current (I S ) (obtained at the point where the set voltage is determined in the original experimental curve) and the maximum current I max , as shown in Fig. 4(a).This FIG. 4. (a) Modified I–Vcurve in a set process for a series resistance = 22.1 Ω. This value was obtained with the improved methodology. (b) Application of this methodology to the 1000 RS set cycles measured (for each I–Vcurve one series resistance value is obtained). The red line indicates the average curve (calculated as the mean) of all the RS cycles, while the black curve corresponds to the median curve of all the RS cycles considered. FIG. 5. (a) Experimental and modified reset I–Vcurves. (b) Modified I–Vreset curves for the 1000 cycles measured. The red line corresponds to the average curve (calculated as the mean) of all the RS cycles and the black curve corresponds to the median. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 130, 054503-4 Published under an exclusive license by AIP Publishing methodology has been found to be more appropriate when snapback effects [Fig. 4(a)] take place in the lower part of the “intrinsic”I–Vcurve. 22–24 By doing this, the snapback is avoided since this region represents the starting phase of the conductive filament formation (the weight of the series resistance with respect to the overall resistance, device plus series resistance, changes fast here). The proper set process takes place in the vertical section of the I–V N curve, as already stated. While the highest region of the curve cannot be considered because of a different reason. When the filament can no longer expand, the process slows down, which can be regarded as the appearance of an additional series resistance. FIG. 6. Transition voltage for reset vs transition voltage for set for the data under study (1000 cycles). (a) The correlation of the variables plotted is shown and the corresponding series resistances are given in a color code. (b) 3D plot of the series resistance vs set transition voltage and reset transition voltage for the whole RS series. FIG. 7. Cumulative distribution functions for the studied parameters in the whole RS series: (a) series resistance and (b) transition voltages for the set (V TS ) and for the reset processes (V TR ). The mean values for the series resistance, V TS , and V TR are 22.80 Ω, 0.418 V, and −0.384 V, respectively. The standard deviation for the latter parameters is 2.26 Ω, 0.042 V, and 0.043 V in each case. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 130, 054503-5 Published under an exclusive license by AIP Publishing FIG. 8. (a) Calculated series resistance vs cycle number in the whole RS series for the data under study and (b) set transition voltage (V TS ) and reset transition voltage (V TR ) vs cycle number in the whole RS series for the data under study. FIG. 9. (a) Three-dimensional view of the STFM modeling structure with an indication of different device regions [top electrode (TE), dielectric, conductive filament, and bottom electrode (BE)] and (b) schematic representation of the main model geometrical parameters. The gap (g) between the TE and the filament tip is one of the state variables, the other one is the temperature (T), (c) subcircuit for the STFM implementation, and (d) proposed modification of STFM implementation with cylindrical CF including the series resistance. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 130, 054503-6 Published under an exclusive license by AIP Publishing Figure 4(b) shows the proposed fitting methodology applied to the measured 1000 RS cycles as well as the median and average I–Vcurve. As it can be seen, the snapback effect is clear for some of the curves plotted. Once R series is determined after obtaining the steepest slope, the reset curves are corrected accordingly as illustrated in Fig. 5. In addition, the reset and reset transition (V TR ) voltages are calculated from the measured and corrected reset curves, respectively. They are obtained as the voltages corresponding to the maximum current values, see Fig. 5(a). Notice that the values of the set and reset transition voltages are quite similar, suggesting a clear electric field dependence of the resistive switching mechanisms. They are the minimum voltages required to induce the vacancy movements in opposite directions. Nevertheless, temperature effects are also known to be involved in resistive switching due to the thermally activated nature of the diffusive transport mechanism. 12,30–35 It is interesting to notice the axes scale in Fig. 6(a), the transition voltages are located in relatively narrow intervals; i.e., cycle-to-cycle variability is low (within a few tenths of a volt). In addition, see that the higher the transition voltages absolute value, the lower the series resistance, Fig. 6(b). Figure 7(a) illustrates the cumulative distribution function (CDF) for the series resistances extracted from the 1000 cycles measured. The corresponding transition voltages CDFs are shown in Fig. 7(b). Notice that V TS and V TR are described by the same CDF except for the voltage sign (they are parallel). The variability of the series resistance and the transition voltages as a function of the cycle number is illustrated in Figs. 8(a) and 8(b), respectively. A reasonable modeling of these numerical series can be performed by means of time series analysis for circuit simulation purposes. 36 Notice that cycle-to-cycle (C2C) autocorrelation effects cannot be disregarded. In addition, the results seem to be consistent, at least in the medium term, with a mean-reverting stochastic process. In the case of V TR and V TS , the cross-correlation is more than evident: as V TS increases, V TR decreases in a symmetrical fashion. Again, this is a clear evidence that the same physical mechanism activates the switching process. Once the intrinsic series resistance parameter is extracted, the C2C variability and the statistical distribution of the results can be analyzed and quantified; in Sec. IV, we introduce the observed parameter variation in the compact modeling approach. It is important to highlight that the methodology introduced here, although presented for VCM devices could also be employed with other RRAM technologies. IV. SERIES RESISTANCE INFLUENCE ON RRAM COMPACT MODELING In this section, the role played by the series resistance in the RRAM electrical behavior is investigated by means of the Stanford FIG. 10. Experimental (black symbols) and modified current (red symbols) vs voltage. Modeled data employing the STFM are shown for the modified (red line) and original (black line, in this case, it is included an external resistance to account for the role of the series resistance, see the schematic). (a) Linear and (b) logarithmic scales. TABLE I. Stanford model parameters employed for the fitting of the experimental devices under study, in particular, for the cycle selected in Fig. 10. Stanford model parameters Device parameters Unit Resistive switching Set Reset V o V 0.45 I 0 mA 48 g 0 nm 0.35 ν 0 m/s 5 × 10 6 Α…1 1.1 Β…115 γ 0 …20 Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 130, 054503-7 Published under an exclusive license by AIP Publishing FIG. 11. Current vs voltage for the modeled curves obtained with the Stanford model isolating some parameter variations. (a) I 0 , (b) ν 0 , (c) V 0 , (d) β, (e) g 0 , and (f) γ 0 . Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 130, 054503 (2021); doi: 10.1063/5.0055982 130, 054503-8 Published under an exclusive license by AIP Publishing