On the Switching Parameter Variation of Metal-Oxide RRAM—Part I: Physical Modeling and Simulation Methodology
Abstract
The variation of switching parameters is one of the major challenges to both the scaling and volume production of metal-oxide-based resistive random-access memories (RRAMs). In this two-part paper, the source of such parameter variation is analyzed by a physics-based simulator, which is equipped with the capability to simulate a large number ( ~1000) of cyclic SET-RESET operations. By comparing the simulation results with experimental data, it is found that the random current fluctuation experimentally observed in the RESET processes is caused by the competition between trap generation and recombination, whereas the variation of the high resistance states and the tail bits are directly correlated to the randomness of the trap dynamics. A combined strategy with a bilayer dielectric material and a write-verification technique is proposed to minimize the resistance variation. We describe the simulation methodology and discuss the dc results in Part I. The corroboration of the model and the device optimization strategy will be discussed in Part II.
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The intrinsic variation in memristor switching parameters is a major challenge for applications such as non-volatile memory.
“The intrinsic variability of switching behavior in memristors has been a major obstacle to their adoption as the next generation of universal memory.”
From A novel true random number generator based on a stochastic diffusive memristor (2017) · cites this paper as [25]
Random switching behavior in memristors can be helpful in stochastic computing and hardware security applications.
“On the other hand, this natural stochasticity can be valuable for hardware security applications.”
From A novel true random number generator based on a stochastic diffusive memristor (2017) · cites this paper as [27]
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“The simulation domain determines the geometric features of the simulator, 2D [1, 10, 23, 32] or 3D [5, 7, 11] codes have been developed.”
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Sharma, A. A., Noman, M., Abdelmoula, M., Skowroński, M., & Bain, J. A. (2014) · Advanced Functional Materials · doi:10.1002/adfm.201400461 · Cited by 84 · see citing works
Nanoarchitectonics for Controlling the Number of Dopant Atoms in Solid Electrolyte Nanodots
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“this method [6].”
Wang, D.-T., Dai, Y., Xu, J. L., Chen, L., Sun, Q., Zhou, P., Wang, P., Ding, S., & Zhang, D. W. (2016) · IEEE Electron Device Letters · doi:10.1109/led.2016.2570279 · Cited by 80 · see citing works
“Variation in the resistive switching parameters is the critical issue of RRAM hindering its practical application, and similar arguments exist as well when it comes to flexible RRAM [8].”
BackgroundSet Variability and Failure Induced by Complementary Switching in Bipolar RRAM
Balatti, S., Ambrogio, S., Gilmer, D. C., & Ielmini, D. (2013) · IEEE Electron Device Letters · doi:10.1109/led.2013.2261451 · Cited by 79 · see citing works
“Low-power operation, however, leads to inevitable switching variability, due to individual defect generation/migration events affecting the device resistance R [4], [5].”
BackgroundNitrogen-induced improvement of resistive switching uniformity in a HfO2-based RRAM device
Xie, H., Liu, Q., Li, Y., Lv, H., Wang, M., Liu, X., Sun, H., Yang, X., Long, S., Liu, S., et al. (2012) · Semiconductor Science and Technology · doi:10.1088/0268-1242/27/12/125008 · Cited by 78 · see citing works
“In addition, the increase of Vstop will increase RHRS because more oxygen ions are driven back to the bulk oxide and result in a larger ruptured CF length [21, 22].”
BackgroundHighly Uniform Resistive Switching in HfO2 Films Embedded with Ordered Metal Nanoisland Arrays
Wang, J., Li, L., Huyan, H., Pan, X. Q., & Nonnenmann, S. S. (2019) · Advanced Functional Materials · doi:10.1002/adfm.201808430 · Cited by 77 · see citing works
Chen, W., Fang, R., Balaban, M. B., Yu, W., Gonzalez-Velo, Y., Barnaby, H. J., & Kozicki, M. N. (2016) · Nanotechnology · doi:10.1088/0957-4484/27/25/255202 · Cited by 76 · see citing works
“65 g cm) and connects the pre-doped Cu regions to form a conductive network [16, 17].”
BackgroundResistive RAM-Centric Computing: Design and Modeling Methodology
Li, H., Wu, T. F., Mitra, S., & Wong, H. ‐. P. (2017) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2017.2709812 · Cited by 77 · see citing works
“The variability of the gap distance, CF length, and CF radius due to the stochastic nature of the processes of formation/migration/dissolution of the CF results in a statistical distribution of HRS resistance (RH RS) and LRS resistance (RL RS) after the write operations [53]–[55].”
Self-citationUnsupervised Learning on Resistive Memory Array Based Spiking Neural Networks
Guo, Y., Wu, H., Gao, B., & Qian, H. (2019) · Frontiers in Neuroscience · doi:10.3389/fnins.2019.00812 · Cited by 76 · see citing works
“…(LeCun et al., 1989), the conductance of memristive devices can be fine-tuned to the desired value during the training process, using write-verification scheme (Guan et al., 2012; Yao et al., 2017), which introduces operation overheads to modulate the device conductance more precisely.”
BackgroundFang, R., Gonzalez Velo, Y., Chen, W., Holbert, K. E., Kozicki, M. N., Barnaby, H., & Yu, S. (2014) · Applied Physics Letters · doi:10.1063/1.4875748 · Cited by 74 · see citing works
Self-citationPhysical Unclonable Function Exploiting Sneak Paths in Resistive Cross-point Array
Gao, L., Chen, P.-Y., Liu, R., & Yu, S. (2016) · IEEE Transactions on Electron Devices · doi:10.1109/ted.2016.2578720 · Cited by 74 · see citing works
“Due to the randomness of the defect generation and annihilation in oxide, the shape of the conductive filament varies from device to device, and even from cycle to cycle within one device [23].”
BackgroundSelf-citationUnderstanding switching variability and random telegraph noise in resistive RAM
Ambrogio, S., Balatti, S., Cubeta, A., Calderoni, A., Ramaswamy, N., & Ielmini, D. (2013) · Technical digest - International Electron Devices Meeting/Technical digest · doi:10.1109/iedm.2013.6724732 · Cited by 71 · see citing works
Technological exploration of RRAM crossbar array for matrix-vector multiplication
Gu, P., Li, B., Tang, T., Yu, S., Cao, Y. K., Wang, Y., & Yang, H. (2015) · Asia and South Pacific Design Automation Conference (ASP-DAC) · doi:10.1109/aspdac.2015.7058989 · Cited by 71 · see citing works
Self-citationGarbin, D., Bichler, O., Vianello, E., Rafhay, Q., Gamrat, C., Perniola, L., Ghibaudo, G., & DeSalvo, B. (2014) · Technical digest - International Electron Devices Meeting/Technical digest · doi:10.1109/iedm.2014.7047126 · Cited by 68 · see citing works
Zhao, L., Clima, S., Magyari‐Köpe, B., Jurczak, M., & Nishi, Y. (2015) · Applied Physics Letters · doi:10.1063/1.4926337 · Cited by 66 · see citing works
Kim, S., Park, J., Kim, T., Hong, K., Hwang, Y., Park, B., & Kim, H. (2022) · Advanced Intelligent Systems · doi:10.1002/aisy.202100273 · Cited by 64 · see citing works
The ultimate switching speed limit of redox-based resistive switching devices
Menzel, S., von Witzleben, M., Havel, V., & Böttger, U. (2018) · Faraday Discussions · doi:10.1039/c8fd00117k · Cited by 61 · see citing works
Phenomenological modeling of memristive devices
Bayat, F. M., Hoskins, B. D., & Strukov, D. B. (2015) · Applied Physics A · doi:10.1007/s00339-015-8993-7 · Cited by 61 · see citing works
A Robust 8-Bit Non-Volatile Computing-in-Memory Core for Low-Power Parallel MAC Operations
Zhang, S., Huang, K., & Shen, H. (2020) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2020.2971642 · Cited by 60 · see citing works
“As reported in RRAM devices, different reading voltages will cause 0% to 40% resistance deviations, and some even exceed 50% in LRS [10], [12], [13], [30], [39].”
BackgroundConductive filament structure in HfO2 resistive switching memory devices
Privitera, S., Bersuker, G. I., Lombardo, S. A., Bongiorno, C., & Gilmer, D. C. (2015) · Solid-State Electronics · doi:10.1016/j.sse.2015.05.044 · Cited by 59 · see citing works
Compact Model of HfOX-Based Electronic Synaptic Devices for Neuromorphic Computing
Huang, P. C., Zhu, D., Chen, S., Zhou, Z., Chen, Z., Gao, B., Liu, L., Liu, X., & Kang, J. (2017) · IEEE Transactions on Electron Devices · doi:10.1109/ted.2016.2643162 · Cited by 57 · see citing works
“Hence, the O2− transportation rate and VO recombination rate decrease rapidly due to their exponential dependence on electrical filed [33], [34].”
BackgroundAldana, S., García‐Fernández, P., Rodriguez-Fernandez, A., Romero‐Zaliz, R., González, M. B., Jiménez-Molinos, F., Campabadal, F., Gómez‐Campos, F. M., & Roldán, J. B. (2017) · Journal of Physics D Applied Physics · doi:10.1088/1361-6463/aa7939 · Cited by 58 · see citing works
Nanometer-Scale ${\rm HfO}_{x}$ RRAM
Zhang, Z., Wu, Y., Wong, H. ‐. P., & Wong, S. S. (2013) · IEEE Electron Device Letters · doi:10.1109/led.2013.2265404 · Cited by 56 · see citing works
Self-citationReliability Improvement and Effective Switching Layer Model of Thin‐Film MoS2 Memristors
Huang, Y., Gu, Y., Mohan, S., Dolocan, A., Ignacio, N. D., Kutagulla, S., Matthews, K. C., Londoño‐Calderón, A., Chang, Y., Chen, Y., et al. (2023) · Advanced Functional Materials · doi:10.1002/adfm.202214250 · Cited by 55 · see citing works
Stress-induced leakage current and trap generation in HfO2thin films
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Field-enhanced route to generating anti-Frenkel pairs in HfO 2
Schie, M., Menzel, S., Robertson, J., Waser, R. M., & Souza, R. A. D. (2018) · Physical Review Materials · doi:10.1103/physrevmaterials.2.035002 · Cited by 53 · see citing works
Crossbar Nanoscale HfO2-Based Electronic Synapses
Matveyev, Y., Kirtaev, R. V., Fetisova, A., Zakharchenko, S., Negrov, D. V., & Zenkevich, A. V. (2016) · Nanoscale Research Letters · doi:10.1186/s11671-016-1360-6 · Cited by 51 · see citing works
“The probability of an oxygen vacancy generation during the time interval dt depends on the local electric field force Feq acting on the oxygen ion and is given by the formula [24]:”
BackgroundDuncan, D. L., Magyari‐Köpe, B., & Nishi, Y. (2016) · IEEE Electron Device Letters · doi:10.1109/led.2016.2524450 · Cited by 51 · see citing works
Ninomiya, T., Muraoka, S., Wei, Z., Yasuhara, R., Katayama, K., & Takagi, T. (2013) · IEEE Electron Device Letters · doi:10.1109/led.2013.2258653 · Cited by 50 · see citing works
“The conductive filament (CF) model is widely accepted as the mechanism of resistive switching [2]–[4].”
Background$${ SIM}^2{ RRAM}$$ S I M 2 R R A M : a physical model for RRAM devices simulation
Villena, M. A., Roldán, J. B., Jiménez-Molinos, F., Miranda, E. A., Suñé, J., & Lanza, M. (2017) · Journal of Computational Electronics · doi:10.1007/s10825-017-1074-8 · Cited by 50 · see citing works
Egorov, K. V., Lebedinskiǐ, Y. Y., Markeev, A. M., & Orlov, O. M. (2015) · Applied Surface Science · doi:10.1016/j.apsusc.2015.07.217 · Cited by 48 · see citing works
Electronic Conduction in Ti/Poly-TiO2/Ti Structures
Hossein-Babaei, F., & Alaei-Sheini, N. (2016) · Scientific Reports · doi:10.1038/srep29624 · Cited by 47 · see citing works
“Assuming electron hopping between IOVs to be the foremost conduction mechanism 54 , the observed reduction in Δ E a is consistent with the IOV motion for filament formation.”
Set statistics in conductive bridge random access memory device with Cu/HfO2/Pt structure
Zhang, M., Long, S., Wang, G., Xu, X., Li, Y., Liu, Q., Lv, H., Lian, X., Miranda, E. A., Suñé, J., et al. (2014) · Applied Physics Letters · doi:10.1063/1.4901530 · Cited by 47 · see citing works
Effects of RESET Current Overshoot and Resistance State on Reliability of RRAM
Song, J., Lee, D., Woo, J., Koo, Y., Cha, E., Lee, S., Park, J., Moon, K., Misha, S. H., Prakash, A., et al. (2014) · IEEE Electron Device Letters · doi:10.1109/led.2014.2316544 · Cited by 46 · see citing works
“It has already been reported that the current overshoot in the SET process has severe effects on the variability of the LRS [11], [12].”
BackgroundWang, G., Long, S., Yu, Z., Zhang, M., Ye, T., Li, Y., Xu, D., Lv, H., Liu, Q., Wang, M., et al. (2015) · Applied Physics Letters · doi:10.1063/1.4907604 · Cited by 46 · see citing works
Recent trends in hardware security exploiting hybrid CMOS-resistive memory circuits
Sahay, S., & Suri, M. (2017) · Semiconductor Science and Technology · doi:10.1088/1361-6641/aa8f07 · Cited by 44 · see citing works
Detection of the insulating gap and conductive filament growth direction in resistive memories
Yalon, E., Karpov, I. V., Karpov, V. G., Riess, I., Kalaev, D., & Ritter, D. (2015) · Nanoscale · doi:10.1039/c5nr03314d · Cited by 43 · see citing works
Complex Learning in Bio-plausible Memristive Networks
Deng, L., Li, G., Deng, N., Wang, D., Zhang, Z., He, W., Li, H., Pei, J., & Shi, L. (2015) · Scientific Reports · doi:10.1038/srep10684 · Cited by 43 · see citing works
Jing, Z., Yan, B., Yang, Y., & Huang, R. (2022) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2022.3186024 · Cited by 40 · see citing works
“The stochastic dynamics of the conductive filament formation and break introduces randomness among the SET-RESET cycles, i.e, the “C-to-C” variation [25], [26].”
BackgroundComprehensive Compact Phenomenological Modeling of Integrated Metal-Oxide Memristors
Nili, H., Vincent, A. F., Prezesio, M., Mahmoodi, M. R., Kataeva, I., & Strukov, D. B. (2020) · IEEE Transactions on Nanotechnology · doi:10.1109/tnano.2020.2982128 · Cited by 38 · see citing works
Zhang, L., Fong, X., Chang, C.-H., Kong, Z. H., & Roy, K. (2015) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2015.2427251 · Cited by 38 · see citing works
“Table IV lists the optimization results of using BCH-[127, 15, 27], BCH-[127, 29, 21] alone, concatenated code of BCH-[127, 29, 21] and repetition code-[3, 1, 3], respectively (for convenience, we denote these three codec as ECC-I, ECC-II, and ECC-III).”
BackgroundMethodSo, H., Ji, H., Kim, S., & Kim, S. (2024) · Advanced Functional Materials · doi:10.1002/adfm.202405544 · Cited by 38 · see citing works
Crystal that remembers: several ways to utilize nanocrystals in resistive switching memory
Banerjee, W., Liu, Q., Long, S., Lv, H., & Liu, M. (2017) · Journal of Physics D Applied Physics · doi:10.1088/1361-6463/aa7572 · Cited by 37 · see citing works
Kopperberg, N., Wiefels, S., Liberda, S., Waser, R. M., & Menzel, S. (2021) · ACS Applied Materials & Interfaces · doi:10.1021/acsami.1c14667 · Cited by 37 · see citing works
Zhao, Y., Huang, P. C., Chen, Z., Liu, C., Li, H., Chen, B., Ma, W., Zhang, F., Gao, B., Liu, X., et al. (2016) · IEEE Transactions on Electron Devices · doi:10.1109/ted.2016.2532470 · Cited by 36 · see citing works
“Under electric field, the generation probability (Pa) of VO can be described as [30] Pa = f · exp(−(E1 − φ1)/kB Tloc) (2) where f is the vibration frequency, E1 is the activation energy of Ta2O5, Tloc is the local temperature, and φ is the barrier height reduction induced by electric field.”
BackgroundPostcycling Degradation in Metal-Oxide Bipolar Resistive Switching Memory
Wang, Z., Ambrogio, S., Balatti, S., Sills, S. E., Calderoni, A., Ramaswamy, N., & Ielmini, D. (2016) · IEEE Transactions on Electron Devices · doi:10.1109/ted.2016.2604370 · Cited by 35 · see citing works
“To explore the applications of RRAM, switching variability [7], [9], [10], resistance fluctuation [11]–[13], and cycling endurance failure [14]–[16] need to be addressed and understood.”
BackgroundEfficient and Robust RRAM-Based Convolutional Weight Mapping With Shifted and Duplicated Kernel
Zhang, Y., He, G., Wang, G., & Li, Y. (2020) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2020.2998728 · Cited by 35 · see citing works
“However, RRAM devices suffer from cycle-to-cycle conductance variation during writing, which is termed as “temporal variation” [19].”
BackgroundCompact Two-State-Variable Second-Order Memristor Model
Kim, S., Kim, H., & Choi, S. (2016) · Small · doi:10.1002/smll.201600088 · Cited by 34 · see citing works
Gradual reset and set characteristics in yttrium oxide based resistive random access memory
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Fu, J., Liao, Z., & Wang, J. (2022) · IEEE Transactions on Electron Devices · doi:10.1109/ted.2022.3146801 · Cited by 34 · see citing works
Gradient-descent-based learning in memristive crossbar arrays
Nair, M. V., & Dudek, P. (2015) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2015.7280658 · Cited by 33 · see citing works
“In addition, stochastic behavior has been observed [7] [15].”
BackgroundSelf-Heating During submicrosecond Current Transients in Pr0.7Ca0.3MnO3-Based RRAM
Panwar, N., Khanna, A., Kumbhare, P., Chakraborty, I., & Ganguly, U. (2016) · IEEE Transactions on Electron Devices · doi:10.1109/ted.2016.2632712 · Cited by 33 · see citing works
Resistive Neural Hardware Accelerators
Smagulova, K., Fouda, M. E., Kurdahi, F. J., Salama, K. N., & Eltawil, A. M. (2023) · Proceedings of the IEEE · doi:10.1109/jproc.2023.3268092 · Cited by 32 · see citing works
“This problem is known as a hard breakdown [77, 78].”
BackgroundResistive memory variability: A simplified trap-assisted tunneling model
Garbin, D., Vianello, E., Rafhay, Q., Azzaz, M., Candelier, P., de Salvo, B., Ghibaudo, G., & Perniola, L. (2015) · Solid-State Electronics · doi:10.1016/j.sse.2015.09.004 · Cited by 31 · see citing works
Nano-Intrinsic True Random Number Generation: A Device to Data Study
Kim, J., Nili, H., Truong, N. D., Ahmed, T., Yang, J., Jeong, D. S., Sriram, S., Ranasinghe, D. C., Ippolito, S. J., Chun, H., et al. (2019) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2019.2895045 · Cited by 31 · see citing works
“Therefore, an extremely rich degree of stochasticity is available to be harvested for ReRAM-based TRNGs [34]–[36].”
BackgroundPetzold, S., Miranda, E. A., Sharath, S. U., Muñoz-Gorriz, J., Vogel, T., Piros, E., Kaiser, N., Eilhardt, R., Zintler, A., Molina‐Luna, L., et al. (2019) · Journal of Applied Physics · doi:10.1063/1.5094864 · Cited by 31 · see citing works
Liu, Z., & Wang, L. (2020) · IEEE Access · doi:10.1109/access.2020.2990536 · Cited by 31 · see citing works
“The cycle-to-cycle variations on the other hand results in the temporal stochasticity induced by the randomness in atomic configurations over a long incubation period [169], [170], as revealed in Figure 25(a), which undoubtedly brings about some adverse effects on neuromorphic applications.”
Background
- Authors
- Guan, X., Yu, S., & Wong, H.-S. P.
- Affiliations
- Stanford SystemX Alliance (US)
- Venue
- IEEE Transactions on Electron Devices
- Published
- 2012-04
- Volume
- 59
- Issue
- 4
- Pages
- 1172-1182
- ISSN
- 0018-9383 (ISSN-L)
- 1557-9646
- OpenAlex
- W2067242107
- Cited by
- 355
- References
- 43
- Citations by year
- 2026: 8 · 2025: 16 · 2024: 19 · 2023: 21 · 2022: 18 · 2021: 18 · 2020: 29 · 2019: 23 · 2018: 26 · 2017: 35 · 2016: 39 · 2015: 35 · 2014: 32 · 2013: 23 · 2012: 13
- FWCI
- 21.06
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Electron Devices (publishedVersion)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Ferroelectric and Negative Capacitance Devices
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Semiconductor materials and devices
- Keywords
- resistive random access memory, current fluctuations, reset operation, high resistance state, bilayer dielectric, physics-based device modeling
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