Resistive memories simulation based on the kinetic Monte Carlo algorithm

Resumen

Nowadays, there is a demand rise for volatile and non-volatile data storage. This rise comes from the need of these memories for internet of things (IoT) devices, solid-state drives (SSD), 5G circuits, cloud storage, artificial intelligence, data mining or smartphones and laptops [Gupta2019]. The low power consumption is a key factor for these latter applications but also for mimicking biological synapses in neural networks [Prezioso2015, Alibart2013] as they need high density of devices to implement neurons and synapses. It should be noted that a high density of devices with high power consumption is a problem in whatever integrated circuit context in the current nanoelectronics industry [Chen2016, You2014, Munjal2019]. In the non-volatile memory realm, the current dominating technology is the flash due to its high density, reliability and low cost. However, it has some limitations as the low operation speed, the durability and the need of high writing voltages, which means also a high power consumption. In this context, Resistive RAMs (RRAM) technology can face these hurdles and, therefore, it is one of the most promising emerging technologies for substituting flash memories. In this sense, RRAMs offer key features for the former applications as a good scalability, speed and latency, low operation voltage and low power consumption. Furthermore, it has an ease integration in the current CMOS technology in the Back-End-Of-Line (BEOL), in addition to a good data retention, a great endurance and can be vertically stacked in 3D architectures due to its simple structure [Pan2014, Nardi2011, Lim2015, Ielmini2016, Lanza2019, Munjal2019, Gupta2019, Carboni2019, Xie2013, Waser2010, Waser2012, Zahurak2014]. Different kinds of memories as static memories (SRAM), dynamic memories (DRAM) and non-volatile memories (NVM) can be found. The non-volatile ones store information when the power systems are turned off. For these types of memories, different technological alternatives rise such as RRAMs, Phase Change Memories (PCM) or Spin-Transfer Torque RAMs (STT-RAMs), which are attracting high research efforts [Xie2013] due to the key role that plays the information storage in the electronic industry. This key role is based on the need of better devices to handle the high amount of information circulating around the world. The focus on NVM is based on two main reasons: 1. The main problem with the non-volatility is the lower operation speed in comparison with SRAM and DRAM. If this problem were solved the NVMs would displace the two latter ones for many applications [Xie2013]. 2. These types of memories are key components of data storage systems [Xie2013]. NVMs based on flash technology are widely used in smartphones, video games, scientific instrumentation and industrial robotics, but they are finding their technological limit [Gupta2019, Xie2013, Waser2010, Waser2012]. In this situation, RRAMs are one of the best positioned as an emerging technology in comparison to Magnetic RAMs (MRAMs), STT-RAM memories or PCM memories [Lanza2019, Xie2013, Waser2010, Waser2012]. These resistive memories are based on the change of the resistance of the device (process known as resistive switching) with a hysteretic behavior. If RRAMs finally displace the current technology, the electronic landscape would change dramatically, as new electronic applications and computer architectures could develop intensively. For instance, smart distributed systems (out of the classical Von Neumann architecture paradigm) with computation capacities greater than the current ones could be built [Wang2019]. Typically, RRAMs consist of a Metal-Insulator-Metal (MIM) structure, although also Metal-Insulator-Semiconductor structures can be found. Usually the dielectric material is made of an oxide whose resistance can be changed. However, RS phenomena have been also observed in other different materials [Lanza2019, Munjal2019, Gupta2019, Carboni2019, Waser2012]: 1. Transition metal oxides (TMOs). 2. Perovskite family (TMO) with paraelectric, ferroelectric, multiferroelectric and magnetic functionality. 3. Graphene oxides, hexagonal boron nitride and other two-dimensional materials. While good result can be obtained at the device level, the real challenge is fabricating NVM chips and artificial neural networks as they can have billions of cells [Lanza2019]. Some good results have been obtained until now, as integrated circuits based on RRAMs have been fabricated [Zahurak2014, Liu2014b, Kawahara2013]. A 16Gb Non-volatile Cu-based RRAM circuit has been fabricated with the 27nm node, an operation speed of 180MB/s for writing and 900MB/s for reading operation [Zahurak2014]. Also, a 32 Gbits memory using a 24nm CMOS process, based in a MeOx RRAM device reported at [Liu2014b]. These advances allow one being optimistic about the future of this technology. However, before the complete industrial implementation of this technology, some hurdles related with endurance and variability must be faced. Both the variability related to the fabrication process (differences between devices) and the one related to the RS process (differences between cycles in the same device) need to be considered. The latter one is linked to the physics behind the RS process [Lanza2019, Pan2014] and this makes the need of computational tools essential to study it. In the landscape of simulators there can be found different types of models depending on the issues to deal with. Continuum models can be used for the study of the average behavior of the devices [Villena2013, Villena2014, Menzel2015, Ielmini2017], but ab initio techniques (density functional theory and molecular dynamics) are usually preferred for focusing on the atomic characteristics of the dielectric and its interfaces with the electrodes, as they can get more accurate results because they are based on first principles [Zhao2015, Zhao2017, Duncan2016, Duncan2017]. Nevertheless, this work is focused on the development of simulators based on kinetic Monte Carlo algorithms that can combine atomistic and continuum models. This technique has been selected in order to get a microscopic description of the evolution of the conductive filament. Furthermore, it also allows to reproduce in a natural way the stochastic behavior of the system and hence to correctly describe some phenomena linked to it [Menzel2015, Vandelli2013, Vandelli2015, Voter2007, Wong2012, Guy2015]. The efforts in this doctoral thesis have been focused on the development of RRAM physical simulators able to reproduce the resistive switching operation that takes place within the devices. The simulators were designed for the two main types of RRAMs, Conductive Bridge RAMs (both for unipolar and bipolar) and for Valence Change Memories. The work includes four publications in scientific journals indexed in the Journal Citation Report of Science Citation Index, one Proceedings published in IEEE Xplore digital library, four contributions to International Conferences. I have also contributed to other publications, where a book chapter is included, three videos detailing the operation of each simulator. The outline of this work is the following: Chapter 1 exposes the state of the art of RRAM technology, the comparation with flash technology and the flash technology limitations that RRAM devices can overcome. In this sense, the promising future in the field of Non-Volatile Memories and neuromorphic computing is pointed out due to the great electrical and technological features. Different types of RRAM devices as Conductive Bridge RAM and Valence Change Memories have been explained. Furthermore, it has been mentioned the different materials that can be used for fabricate them, in addition to details about the fabrication process, the main physical foundations and the most important characteristics. Furthermore, the main hurdles that must be faced for the complete industrial implementation of this technology have been highlighted and the computational tools that must be used for this task. The different models explained are the microscopic models, in connection to the kinetic Monte Carlo algorithm, Finite Element Methods and compact models. Based on our purpose to study the system physics, the kinetic Monte Carlo algorithm has been selected as a good choice for the kernels of the physical simulators we present. Chapter 2 describes the kinetic Monte Carlo algorithm, the grid used for the simulation domain and the Finite Element Method used for solving the Poisson and heat equations that are included in the simulators. Besides, some techniques for the conductive filament density and compactness calculation are exposed as well as the effect of the virtual electrode evolution versus the electric field. Chapter 3 deals with Conductive Bridge RAMs, both for unipolar and bipolar operation. The resistive switching mechanisms are explained for both types of operation and two different simulators are developed and presented, one for the unipolar case and the other for bipolar devices. The resistive switching process is based on redox processes and on the migration of ions coming from the electrochemically active electrode which form percolation paths (conductive filaments). In this context, the main difference between unipolar and bipolar devices relies on how they carry out the CF rupture process (RESET). The unipolar rupture is due to thermally activated dissolution of the percolation paths, while the reset in the bipolar case is controlled by means of the electric field. Then, once the simulators are fully developed, they are used for analyzing the CF density and compactness and their relation to the device resistance. The chapter includes the following contributions: • [Aldana2017] Aldana, S., García-Fernández, P., Rodríguez-Fernández, A., Romero-Zaliz, R., González, M. B., Jiménez-Molinos, F., ... & Roldán, J. B. (2017). A 3D kinetic Monte Carlo simulation study of resistive switching processes in Ni/HfO2/Si-n+-based RRAMs. Journal of Physics D: Applied Physics, 50(33), 335103. • [Aldana2018] S. Aldana, J. B. Roldán, P. García-Fernández, J. Suñe, R. Romero-Zaliz, F. Jiménez-Molinos, S. Long, F. Gómez-Campos, M. Liu, “An in-depth description of bipolar resistive switching in Cu/HfOx/Pt devices, a 3D kinetic Monte Carlo simulation approach”, Journal of Applied Physics, 123(15), 154501, 2018. • [Aldana2018b] Aldana, S., García-Fernández, P., Romero-Zaliz, R., Jiménez-Molinos, F., Gómez-Campos, F., & Roldán, J. B. (2018). Analysis of conductive filament density in resistive random access memories: a 3D kinetic Monte Carlo approach. Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, 36(6), 062201. • [Aldana2018c] Aldana, S., García-Fernández, P., Romero-Zaliz, R., González, M. B., Jiménez-Molinos, F., Campabadal, F., ... & Roldán, J. B. (2018, November). A Kinetic Monte Carlo Simulator to Characterize Resistive Switching and Charge Conduction in Ni/HfO2/Si RRAMs. In 2018 Spanish Conference on Electron Devices (CDE) (pp. 1-4). IEEE Xplore. Chapter 4 deals with Valence Change Memories. The resistive switching mechanism is explained for these types of devices and a simulator to study the physics behind its operation has been developed and presented. The resistive switching is based on the generation of a Frenkel defect-rich region (oxygen vacancies and oxygen ions) which form the percolation paths. Only bipolar operation it is expected for these devices as one bias is needed for extracting the oxygen ions from the dielectric layer to the storage layer and the opposite bias for injecting them back in the dielectric. After developing the simulator, it has been used to carry out data retention tests in order to analyze experimental results. The chapter includes the following contribution: [Aldana2020] Aldana, S., García-Fernández, P., Romero-Zaliz, R., González, M. B., Jiménez-Molinos, F., Gómez-Campos, F., ... & Roldán, J. B. (2020). Resistive switching in HfO2 based valence change memories, a comprehensive 3D kinetic Monte Carlo approach. Journal of Physics D: Applied Physics, 53(22), 225106. Chapter 5 summarizes the main conclusions of this doctoral thesis. Chapter 6 is an appendix, where the conduction mechanisms through the dielectric (the device in the High Resistance State and during the Low Resistance State are treated). Also, details about the percolation path determination algorithm and explanations of the kinetic Monte Carlo algorithm are given. Besides, it sheds some light about the finite element method used for solving heat and Poisson equation in a 3D domain. Finally, the device fabrication processes used along this work are exposed. 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