Resistive Random Access Memory: Doping Technology, Pulse Characterization and Scalability

RESISTIVE RANDOM ACCESS MEMORY: DOPING TECHNOLOGY, PULSE CHARACTERIZATION AND SCALABILITY

A DISSERTATION SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

LIANG ZHAO JUNE, 2015

This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/xj620nn2388

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Yoshio Nishi, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

H.S.Philip Wong

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

S Wong

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Zhiping Yu

Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii Abstract

Recently, the rapid development of big data and internet-of-things has fueled a surge of demand for semiconductor memories. As the scaling of NAND flash is hitting its physical limits, several emerging non-volatile memory technologies are being studied intensively to enable higher memory density and better performance. Among them, resistive random access memory (RRAM) has attracted tremendous interests due to its ability to overcome the inherent limitations of flash memory, while also delivering cost-effectiveness, robust performance and small footprint.

Despite its promising features, several challenges remain to be addressed for the future development and commercialization of RRAM technology. First of all, the physical mechanisms behind resistance-change phenomena have not been fully understood, making it difficult to optimize the device performance. Secondly, the reliability of RRAM should be improved in several aspects, such as the variability of switching parameters, the retention/endurance failures caused by the random nature of filament formation, as well as the requirement for a high-voltage forming process.

Moreover, it is also highly desired to stack RRAM devices in a 3D architecture and/or develop multi-level storage capability to reduce the cost-per-bit and compete with

NAND flash. This thesis presents an in-depth analysis of some state-of-the-art techniques to tackle these challenges from three aspects: the materials, the device structure, as well as the characterization methods.

From the material’s perspective, doping technology of RRAM is investigated as an approach to improve RRAM performance. Ab initio modeling and simulations are applied to study the effects of dopant types, dopant concentrations, oxide phases, and oxide stoichiometry on the electronic and thermodynamic properties of oxygen vacancies in HfO2. The physical insights derived from the calculations provide guidelines to achieve desirable RRAM characteristics through doping.

In the aspect of electrical characterization, the pulse-train characterization techniques are developed for the multi-level control and in-depth physical understanding of conductive filament evolution. By adopting pulse-train operation for an RRAM device with 3-bit potential, the relative standard deviations of resistance levels are improved up to 80% compared to the single-pulse scheme. The observed exponential relation between the saturated resistance and the pulse amplitude provides supporting evidence for the gap-formation model during the RESET process of RRAM.

From the device-structure point of view, the feasibility of ultra-thin HfO2 RRAM is investigated, which helps to achieve the forming-free property and low-power operation. The theoretical scaling limit of HfOx thickness is first estimated using density functional theory within the non-equilibrium Green’s function formalism. The feasibility of 2-nm HfOx RRAM is predicted for large-area devices, and verified by fabricating both planar and 3D vertical RRAM devices. The 3D ultra-thin devices demonstrate promising characteristics including ON/OFF ratio (~100), switching speed

(~20 ns), endurance (108 cycles) and data retention (> 10 years at room temperature).

In contributing to these areas, this thesis aims at advancing both the fundamental understanding and practical implementation of RRAM technology, towards the vision of high-density mass-storage applications.

Acknowledgements

This work would not have been possible without the help, support and encouragement of several individuals, to whom I am greatly indebted.

First of all, I wish to thank Prof. Yoshio Nishi for being the principal advisor of my

PhD studies. Prof. Nishi is the most kind and knowledgeable PhD advisor that I can ever dreamed of. Over the years, he has provided generous support and great freedom for me to pursue whatever ideas and opportunities that I am interested in. With his profound experience and constant encouragement, he guided me through the ups and downs of

PhD life to successfully complete three vastly different research projects. And his wisdom about life has always inspired me to strive and become a better person.

I’m deeply indebted to my co-advisor Prof. H.-S. Philip Wong, who has given me very thoughtful and constructive advice and criticism on the experimental projects. I have learned a lot from his wide industry experience and strong technical expertise. I also enjoyed the collaboration and interactions with multiple students from Prof.

Wong’s group. In particular, I wish to express my gratitude to Dr. Hong-Yu (Henry)

Chen for his extensive help and guidance during the training of my experimental skills.

It is my great pleasure to have him as a mentor and close collaborator.

I am especially thankful to Prof. Zhiping Yu who served as my undergraduate advisor at Tsinghua University, and continued to be my mentor and my dissertation committee member at Stanford. I would like to thank Prof. Simon Wong for being my

vii dissertation committee member, who has given me valuable input and continuous help over the course of PhD studies. I would like to thank Prof. Debby Senesky for being my dissertation committee chair and giving me very helpful suggestions and comments.

I feel very fortunate to have worked with many talented people in and out of

Stanford. Specifically, I wish to acknowledge Dr. Blanka Magyari-Köpe and Dr. Seong-

Geon Park for their great help and mentorship in the area of ab initio simulations. I wish to thank Prof. Shimeng Yu of Arizona State University for all the insightful and fruitful discussions on RRAM technology. I would like to express my sincere gratitude to my collaborators all over the world: Dr. Seung-Wook Ryu, Dan Duncan, Aryan Hazeghi from Nishi group, Zizhen Jiang, Joon Sohn and Kye Okabe from Prof. Philip Wong’s group, Max Shulaker, Tony Wu from Prof. Subhasish Mitra’s group, Ashish Pal from

Prof. Saraswat’s group, Dr. Shih-Chieh Wu and Prof. Tuo-Hung Hou from National

Chiao Tung University, Dr. Sergiu Clima, Dr. Andrea Fantini and Dr. Malgorzata

Jurczak from imec, Dr. Katsumasa Kamiya and Dr. Moon Young Yang from University of Tsukuba, Prof. Kenji Shiraishi from Nagoya University, Dr. Onofrio Pirrotta and Prof.

Luca Larcher from University of Modena and Reggio Emilia, and Dr. Bin Gao and Prof.

Jinfeng Kang from Peking University. I would like to thank all staff members from

Stanford Nanofabrication Facility who offered me a lot of help in the experiments. I am grateful to all members of Nishi group who provided me valuable feedback on the group meetings. I would also like to thank our group secretaries: Sandy Eisensee, Jacky

Burleigh and Marie Hamel who helped me with all kinds of administrative issues.

viii

I am very grateful to all my friends who makes the PhD life much more colorful and enjoyable. In particular, I wish to thank Xiang Fu and Chen Liang for providing me a shelter over the last year; Xingze Wang and Hong-Yu (Henry) Chen for lots of fun we shared together; Ze Yuan and Ximeng Guan for the generous sharing of thoughts and experience on academics and life.

Finally, I’d like to express my deepest thanks to my girlfriend Lily Xu and my parents for their continuous love, support and encouragement. This thesis is dedicated to them.

Table of Contents

List of Figures ...... xi List of Tables ...... xvi Chapter 1 : Introduction ...... 1 1.1 Emerging Non-volatile Memory Technologies ...... 1 1.2 Resistive Random Access Memory (RRAM) Technology ...... 6 1.3 Thesis Motivation and Contributions ...... 10 1.4 Thesis Organization ...... 14 References ...... 16

Chapter 2 : Doping Effects on the Resistive Switching of HfO2 and Its Implications to RRAM Device Design ...... 19 2.1 Motivations of Studying Doping Effects on the Resistive Switching Process ... 20

2.2 Ab Initio Modeling of the Resistive Switching Mechanisms of HfO2 ...... 22

2.3 Selection of Dopant Types for HfO2-based RRAM ...... 29 2.4 Effects of Oxide Phases, Stoichiometry and Dopant Concentrations on RRAM Characteristics ...... 36 References ...... 45 Chapter 3 : Pulse-Train Characterization Techniques of RRAM ...... 50 3.1 Introduction to Pulse-Train Characterization of RRAM ...... 51 3.2 Improved Multi-level Control of RRAM Achieved by Pulse-Train Operation .. 57 3.3 Pulse-Train Characterization of the Conductive Filament Evolution during Resistive Switching ...... 65 References ...... 72 Chapter 4 : Ultra-Thin RRAM: Scaling Limit, Stack Engineering and 3D Integration ...... 76 4.1 Motivations for Studying Ultra-Thin RRAM ...... 77

4.2 Thickness Scaling Limit Analysis of HfO2-based RRAM ...... 80 4.3 3D Integration of Ultra-Thin HfO2 Switching Layer ...... 91 References ...... 96 Chapter 5 : Contributions and Outlook ...... 104 5.1 Summary of Contributions ...... 104 5.2 Future Plan ...... 107

List of Figures

Figure 1.1: Scaling trend of 2D Planar flash and 3D-VNAND technologies [4]...... 2 Figure 1.2: Programming energies vs. cell areas of emerging non-volatile memory technologies reported in recent studies [12]...... 4 Figure 1.3: The growth of memory capacities of the emerging NVM technologies, as well as NAND flash [13]...... 5 Figure 1.4: (a) Schematic of MIM structure for metal–oxide RRAM, and schematics of metal-oxide memory’s I-V curves [9], showing two modes of operation: (b) unipolar and (c) bipolar...... 6 Figure 1.5: Summary of the materials used for binary metal–oxide RRAM. Metals of the corresponding binary oxides used for the switching layer are colored in yellow, while metals used for the electrodes are colored in blue [9]...... 7 Figure 1.6: (a) Schematic of the filamentary switching process of metal-oxide RRAM;

(b) TEM images showing the conductive filament in TiO2-based RRAM [18]; (c) TEM image showing the conductive filaments in Ag-based CBRAM [19]...... 11

Figure 2.1: (a) 3×3×2 supercell of monoclinic HfO2. The positions of 3-fold and 4-fold

oxygen vacancies (VO) are outlined. (b) Electron density of states (DOS) of the

supercell in (a), without VO; (c) Electron density of states (DOS) of the

supercell in (a), with one 3-fold VO; (d) Electron density of states (DOS) of the

supercell in (a), with one 4-fold VO...... 25 Figure 2.2: (a) Schematic of the conductive filament, modeled as a chain of oxygen

vacancies in monoclinic HfO2; (b) Site-projected (top) and total electron DOS (bottom) at the presence of the conductive filament. The site projected DOS is calculated for a Hf atom right next to the filament; (c) Partial charge densities of the conductive filament, calculated by taking the integration of electron DOS in the bandgap. The iso-surface corresponds to the electron density of 0.1e/Å3...... 26

Figure 2.3: (a) Schematic of the 3×3×2 supercell of monoclinic HfO2 with the presence of oxygen vacancy and/or dopant; (b) The oxygen-vacancy formation energies of the supercell depicted in (a), calculated with 2 types of oxygen vacancies and 12 different types of dopant...... 30

Figure 2.4: (a) Schematic of the 3×3×2 supercell of monoclinic HfO2 with the conductive filament and one dopant next to it; (b) The oxygen-vacancy formation energies of the supercell depicted in (a), calculated with for 10 different types of dopant...... 32 Figure 2.5: Schematics of the site-projected electron DOS on the dopant (top), as well as the total DOS of the filament with one dopant next to it (bottom), for 6 types of dopants (Al, Si, Zr, Ta, W and Ni)...... 33

Figure 2.6: (a) Atomic models for HfO2 in monoclinic, cubic, orthorhombic and amorphous phases. (b) Formation energies of oxygen vacancy in pristine and

doped HfO2, in three different crystalline phases. (c) Distributions of the

formation energies of oxygen vacancies in amorphous HfO2, either pristine or doped with three types of dopants (Al, Ti and Si)...... 39

Figure 2.7: (a) Atomic models of amorphous Al-doped HfOx under three different stoichiometric conditions. (b) Electron density of states (DOS) of the three

atomic models shown in (a), calculated by DFT. Electron DOS of pristine HfO2 is plotted as a reference. (c) Distributions of oxygen-vacancy formation energies in the three atomic models shown in (a)...... 42

Figure 2.8: (a) Atomic models of amorphous HfOx, undoped or doped with three different dopant concentrations. The Hf, O and dopant atoms are labeled in the same way as Figure 2.7(a). (b-d) Distributions of the oxygen-vacancy

formation energies in (b) Al-doped HfOx, (c) Ti-doped HfO2 and (d) Si-doped

HfO2, calculated at three different dopant concentrations (3%, 18% and 45%)...... 44 Figure 3.1: Two typical configurations of pulsed I-V measurements using Keithley 4200-SCS parameter analyzer: (a) Keithley 4200-SCS controls a switch matrix to allow both the SMU and external pulse generator (Agilent 81150A) to

xii

connect to DUT; (b) Both SMU and a built-in pulse generator are connected to a remote switch (Keithley 4225-RPM) to select between DC and pulse operations...... 52 Figure 3.2: (a) Schematics of both gradual and abrupt RESET processes, obtained from DC sweep. (b) Resistance-change characteristics of an RRAM device upon the application of 100 identical pulses at various amplitudes. Gradual increase of resistance is observed with increasing number of pulses; (c) Resistance-change characteristics of another RRAM device upon the application of 100 identical pulses at various amplitudes. An abrupt switching event occurs and the intermediate states are not accessible. The switching probability depends on the pulse amplitude...... 56

Figure 3.3: (a) Cross-sectional TEM image of the fabricated TiN/HfOx/Pt RRAM device. (b) Elemental compositions throughout the device, obtained by energy- dispersive X-ray spectroscopy (EDX)...... 57 Figure 3.4: DC sweep characteristics of the fabricated RRAM device. 8 resistance levels are achieved with the maximum ON/OFF ratio of ~ 106...... 58 Figure 3.5: (a) Resistance distributions obtained from 100 consecutive DC sweep cycles, at different RESET voltages. (b) Retention characteristics of 8 different resistance levels, measured up to 104 seconds at 125˚C. Retention can be extrapolated to 10 years...... 59 Figure 3.6: (a) Distributions of HRS resistances in 30 switching cycles, obtained by the single-pulse scheme. (b) Distributions of HRS resistances in 100 DC sweep cycles. 7 different HRS states are studied to evaluate MLC capability...... 61 Figure 3.7: Double log plot of the resistance changes upon the applications of 100 identical pulses with different amplitudes. Both measurement data and compact-model simulation results are shown...... 63 Figure 3.8: Distributions of HRS resistances in 30 switching cycles, obtained by the pulse-train scheme with 7 different pulse amplitudes...... 64 Figure 3.9: Relationship between the pulse amplitudes and the mean values of HRS resistance by the pulse-train scheme...... 65

xiii

Figure 3.10: (a) Ion drift velocity in HfO2 RRAM as a function of gap thickness, at fixed temperature and various applied voltages. (b) Measured transient current

of HfO2 RRAM device during a RESET pulse. (c) Ion drift velocity in HfO2 RRAM as a function of the gap thickness, at fixed applied voltage and various different temperatures...... 67 Figure 3.11: (a) DC RESET I-V characteristics with different filament strengths of the ON state, achieved by varying the SET pulse amplitude. (b) Resistance changes during the pulse-train reset scheme, again with different filament strengths of the ON state. (Inset: (a) DC RESET current vs. SET pulse amplitude. (b) Length of subthreshold regime vs. SET pulse amplitude.) .... 70 Figure 3.12: Schematic of the pulse-train characteristics of RRAM, divided into three regions. The corresponding physical processes and applications are outlined and discussed in the framework of filamentary resistive switching...... 71

Figure 4.1: (a) Schematic of the filamentary switching process of HfOx-based RRAM.

(b) Atomic configurations of the TiN/HfOx/TiN RRAM device in both ON and OFF states. (c) The band-decomposed charge density of the RRAM devices,

obtained by taking the integration of electron densities in the bandgap of HfO2. The iso-surface corresponds to the electron density of 0.1e/Å3. The ON-state device demonstrates a delocalized conductive path connecting the two electrodes...... 81 Figure 4.2: Detailed procedures of the two-step approach to simulating I-V characteristics from the initial atomic coordinates of the device...... 83 Figure 4.3: (a) I-V characteristics of the HfOx RRAM devices in ON and OFF states, calculated by NEGF-DFT. (b) Schematic of device-area scaling and its effects on the cell resistance. (c) Estimation of the ON/OFF ratios for different device areas, assuming the CF diameter to be 10nm. (d) Thickness scaling limit of HfOx RRAM as a function of device area...... 84

Figure 4.4: Schematics of the two scenarios to achieve 2-nm HfOx switching layer: remove the excess oxide completely, or replace it with a layer of alternative materials...... 86

xiv

Figure 4.5: (a) Cross-sectional TEM image of the planar RRAM device with 2-nm HfOx 2 2 and 1 x 1 μm device area. (b) Forming voltages of 1 x 1 μm HfOx RRAM devices, plotted as a function of oxide thickness...... 87

Figure 4.6: (a) DC sweep characteristics of the 2-nm and 5-nm HfOx RRAM devices

in 10 DC cycles. (b) Resistance distributions of the 2-nm and 5-nm HfOx devices, obtained from (a). (c) Comparison of DC sweep characteristics of “2-

nm AlOx + 2-nm HfOx” and “2-nm TiOx + 2-nm HfOx” bilayer devices with

the 5-nm HfOx. 20 DC cycles are plotted for each device. (d) Comparison of the resistance distributions of the bilayer devices wtih that of the single-layer

(5nm-HfOx) device...... 88

List of Tables

Table 1.1: Summary of Best Performances Achieved by Metal-oxide RRAM [12] ..... 8

Table 2.1: Lattice Constants and Bandgap of HfO2 by DFT Calculations and Experiments ...... 24

xvi

Chapter 1 : Introduction

1.1 Emerging Non-volatile Memory Technologies

Semiconductor memory has always been an indispensable component of the modern-day electronic systems. With rapid developments of big data infrastructures and the Internet of Things (IoT) in recent years, the demand for bigger, faster, cheaper, and more reliable non-volatile memories (NVM) is ever-increasing. Looking back at the history of flash memory’s success, the exponential growth in its demand driven by cell phones and other consumer electronics was met thanks to the relentless scaling of

NAND flash, which even exceeds the pace of Moore’s law for transistors [1].

However, following the aggressive scaling of NAND flash in the past 30 years, the feature size of flash memory device is also hitting its physical limits. A major obstacle for further scaling is the difficulty to shrink tunneling-oxide and interpoly dielectric

(IPD) thicknesses due to reliability issues [2]. The flash memory cell is more vulnerable to charge leakage and dielectric breakdown when the tunneling oxide or IPD thicknesses become too thin. The degradation of bit-error rate and endurance caused by scaling can be compensated by improved error-correction mechanisms, but only to a limited extent.

Further increase of flash memory density will be driven by pursuing 3-D stackable architectures, or further improving the multi-level cell (MLC) capability.

In 2013, Samsung announced the mass-production of the first 3D vertical NAND flash memory, or V-NAND [3]. Other manufacturers are on the similar path to release

3D NAND flash products. However, the introduction of 3D vertical NAND and MLC operation is also accompanied by increased design/manufacturing cost and degradation of performances.

Figure 1.1: Scaling trend of 2D Planar flash and 3D-VNAND technologies [4].

Moreover, the ever-changing world of electronic products keeps pushing for even better NVM characteristics. An ultimate goal is to achieve the switching speed of SRAM, the cost/endurance of DRAM, while still maintaining the same storage density as

NAND flash [5]. This so-called “universal memory” goes beyond the physical limits of

2 flash, and drives for the development of a new generation of NVM technologies. Among the emerging NVM technologies, three are considered as the most promising candidates:

(1) Phase-change Memory (PCM): PCM utilizes the large resistivity contrast

between crystalline (low resistivity) and amorphous (high resistivity) phases of

the some chalcogenide materials to store information [6]. The operation of PCM

relies on the current-induced Joule heating which either brings the phase-change

material above the melting temperature to become amorphous, or between the

crystallization and melting temperatures to get crystallized.

(2) Spin-transfer-torque RAM (STTRAM): STTRAM stores information based

on the magnetization orientation of two ferromagnetic layers in a magnetic

tunnel junction (MTJ). The MTJ exhibits lower resistance when the two layers

have parallel magnetization, while anti-parallel magnetization leads to higher

resistance. The magnetization of one ferromagnetic layer (called the ‘free layer’)

can be switched by electron current which is spin-polarized by the other layer

(called the ‘fixed layer’) [7]. The switching direction is determined by the flow

direction of the spin-polarized current.

(3) Resistive RAM (RRAM) / Conductive-bridge RAM (CBRAM): Both RRAM

and CBRAM share the relatively simple device structure of metal-insulator-

metal (MIM). The resistance of the insulating layer can be switched by applying

electric field to move certain conductive species, such as oxygen vacancies in

oxide-based RRAM or metal ions in the case of CBRAM. The migration of these

conductive species either causes formation/rupture of conductive filaments or

modifies the interface barrier heights, resulting in the resistance change [8-11].

These three NVM technologies are based on the different physical mechanisms and all have the potential to deliver faster speed, lower power consumption, better endurance and larger storage density compared to NAND flash. The programming energy vs. cell area of these emerging NVMs reported in recent studies are summarized in Figure 1.2

(compiled by Wong et al. [12]). Compared to PCM, RRAM and STTRAM generally have lower programming energy and smaller programming currents. On the other hand,

RRAM has simple processing steps and better scalability compared to STTRAM, less vulnerable to the interface effects. Thus, RRAM technology has its unique advantages in terms of memory density and power consumption.

Equivalent Contact Diameter (nm) 1 4 11 36 113 357 1128 3568 107

106 RRAM CBRAM 5 PCM 10 STT RAM

104

103

102

101

100 Programming Energy (pJ) Energy Programming

10-1

10-2 100 101 102 103 104 105 106 107 2 Cell Area (nm )

Figure 1.2: Programming energies vs. cell areas of emerging non-volatile memory technologies reported in recent studies [12].

Figure 1.3 summarizes the growth of storage capacity in recent years for the emerging NVM technologies as well as NAND flash. Compared to other technologies, the rapid increase of RRAM’s capacity is a proof that it is a suitable candidate for mass- storage applications.

Figure 1.3: The growth of memory capacities of the emerging NVM technologies, as well as NAND flash [13].

1.2 Resistive Random Access Memory (RRAM) Technology

In this thesis, we will focus on the RRAM technology. Figure 1.4(a) shows the basic structure of this type of devices, while Figure 1.4(b) and Figure 1.4(c) depict the

I-V characteristics of two different operation modes [9]. The transition from a high- resistance state (HRS) to a low-resistance state (LRS) is called SET, while the opposite transition (from LRS to HRS) is called RESET. The switching mode is called unipolar when the SET and RESET voltages have the same polarity. Similarly, the switching mode is bipolar when they have opposite polarities. The RESET of unipolar switching is dominated by the Joule heating effects, while that of bipolar switching is a combined effort of both Joule heating and electric field. The former usually requires higher currents and causes larger cycle-to-cycle variations. Thus, the bipolar switching mode is more popular due to the lower power consumption and better endurance.

Figure 1.4: (a) Schematic of MIM structure for metal–oxide RRAM, and schematics of metal-oxide memory’s I-V curves [9], showing two modes of operation: (b) unipolar and (c) bipolar.

As shown in Figure 1.5, a wide variety of metal oxides exhibit resistive switching behaviors. Among various resistive-switching materials, certain metal oxides such as

HfO2 and TaOx (x≤2.5) demonstrate very attractive device performances, including fast switching speed (< 10 ns), low operation current (< 50 μA), long endurance (up to 1012 cycles) and data retention (10 years @ 85°C) [12]. In this thesis, we focus on HfO2- based RRAM due to its promising switching characteristics and CMOS compatibility.

Figure 1.5: Summary of the materials used for binary metal–oxide RRAM. Metals of the corresponding binary oxides used for the switching layer are colored in yellow, while metals used for the electrodes are colored in blue [9].

Currently, the research and development activities of RRAM technologies are very active. Table 1.1 shows a selection of recently-published results which demonstrate the highest performances achieved so far in one or more aspects of device characteristics.

These parameters reflect the current boundaries of RRAM technology, and if combined together, would make a unique and promising candidate for the universal memory [4].

Table 1.1: Summary of Best Performances Achieved by Metal-oxide RRAM [12]

Finally, we would like to point out some potential applications of RRAM technology. As mentioned above, RRAM has been considered as a replacement of

NAND flash for non-volatile mass-storage. This application is currently pursued by several companies such as Crossbar Inc. [14], Micron Technology [15] and SanDisk

[16]. A major challenge for the mass-storage application of RRAM is the sneak-path current issue, which limits the maximum array size and integration density. In order to

8 achieve large arrays, selector devices are required to suppress the leakage currents and read/write disturbance to unselected devices [14]. Another important application of

RRAM is for embedded memory in micro-controllers, caches and internet-of-things

(IoT) devices. These embedded applications emphasize the power-consumption, access speed and reliability as important performance indicators. Compared to conventional technologies, RRAM has big advantages in these aspects. Another potential application of RRAM is fueled by the recent revival of interests in the field of neuromorphic computing [17]. In neuromorphic computing, hardware systems are built to mimic the structure and behaviors of human brain, which consists of neurons and synapses. The neurons process information and the synapses connect different neurons with different strength to achieve the memory functionality. The compact dimension and low-power operation of RRAM makes it an ideal candidate of artificial synaptic devices.

1.3 Thesis Motivation and Contributions

One of the most interesting and controversial aspects of RRAM is the physical mechanisms behind the resistive-switching phenomena. Several different models have been proposed for various switching materials, such as the valency-change mechanism, the thermo-chemical mechanism, the electronic mechanism, etc [10]. A lot of efforts have been dedicated to the classification and experimental verification of these mechanisms. Today, it is widely accepted that the resistive switching of HfO2 is realized by the formation/rupture of a conductive filament consisting of oxygen vacancies. The switching process is demonstrated in Figure 1.6(a). Initially, the pristine HfO2 layer contains few vacancies and exhibits high resistance. After applying a forming voltage, enough oxygen vacancies are created to connect the top and bottom electrodes (TE and

BE) to form a conductive filament. Now the device is said to be in LRS, or ON state.

During the subsequent RESET operation, the RESET voltage is applied to rupture the filament partially or completely, so that the device returns to HRS, or OFF state. The

SET operation is similar to forming as it switches the device from HRS to LRS again, but it typically requires smaller voltage since part of the filament still remains in the switching layer.

Figure 1.6: (a) Schematic of the filamentary switching process of metal-oxide RRAM;

(b) TEM images showing the conductive filament in TiO2-based RRAM [18]; (c) TEM image showing the conductive filaments in Ag-based CBRAM [19].

Since the conductive filament plays a central role in the resistive switching process, it is highly desired that their shapes and evolution can be observed directly. However, this is extremely difficult because of their small dimension (<10 nm in diameter [18]), fast switching transition (< 1 ns [12]) and the complicated nature of the filament. So far, researchers have successfully observe the conductive filaments in TiO2-based RRAM

[18] and Ag-based CBRAM [19]. In TiO2, the oxygen vacancies will arrange periodically to induce a transition into the sub-stoichiometric Magnéli phases [18],

11 which is clearly seen in X-ray diffraction patterns. In Ag-based CBRAM, the Ag ions have good contrast under TEM with the background dielectric. In the case of HfO2, neither of these conditions is satisfied so the observation of conductive filaments remains an unresolved challenge.

Apart from the fundamental physical understanding, the commercial application of

RRAM technology also faces a series of challenges including the variability of switching parameters, the retention/endurance failures caused by the random nature of filament formation, as well as the requirement for a high-voltage forming process and high-current RESET process. In order to compete with NAND flash technology, it is also highly desired to stack RRAM devices in a 3D architecture and develop MLC capability to reduce the cost-per-bit. This thesis presents in-depth analysis of state-of- the-art methods to tackle these challenges from three aspects: the materials, the device structure, as well as the characterization techniques.

From the material’s perspective, doping technology of RRAM is investigated as an approach to improve the performance of RRAM. Ab initio modeling and simulations are applied to study the effects of dopant types, dopant concentrations, oxide phases, and oxide stoichiometry on the electronic and thermodynamic properties of HfO2. The physical insights derived from the calculations provide guidelines to achieve desirable

RRAM characteristics through doping.

In the aspect of characterization techniques, we present a systematic investigation on the pulse-train characterization techniques for the multi-level control and in-depth physical understanding of conductive filament evolution. By applying the pulse-train

RESET scheme to a HfO2 RRAM with 3-bit potential, the relative standard deviations of resistance levels are improved up to 80% compared to the single-pulse scheme. The observed exponential relation between the saturated resistance and the pulse amplitude provides evidence for the gap-formation model of the filament-rupture process.

From the device-structure point of view, we investigate the feasibility of ultra-thin

HfO2 RRAM, which helps to achieve the desirable forming-free property and low- power operations. The theoretical scaling limit of HfOx thickness is first estimated using density functional theory within the non-equilibrium Green’s function formalism. The feasibility of 2-nm HfOx RRAM is predicted for large-area devices, and verified by fabricating both planar and 3D vertical RRAM devices. The 3D ultra-thin devices demonstrate promising characteristics including ON/OFF ratio (~100), switching speed

(~20 ns), endurance (108 cycles) and data retention (> 10 years at room temperature).

1.4 Thesis Organization

This thesis addresses the key challenges of RRAM technology from the perspectives of materials, device structure, characterization and architecture. It is organized as follows:

Chapter 1 gives an overview of the background of this thesis, including a brief introduction of the emerging non-volatile memory technologies, the basics of RRAM and its physical mechanisms, the current status and challenges of RRAM technology, as well as the broad motivations of the work presented in this thesis.

Chapter 2 discusses the doping technology is an important technique to improve the performance of RRAM. Ab initio modeling is applied to thoroughly investigate the effects of dopant types, dopant concentrations, oxide phases and oxide stoichiometry on the electronic and thermodynamic properties of HfOx (x≈2). The physical insights derived from the calculations provide guidelines to achieve desirable RRAM characteristics through doping. Especially, the inconsistent observations regarding the doping effects on forming voltages are explained by the variation of oxygen stoichiometry.

Chapter 3 explores the pulse-train characterization techniques for RRAM, which is capable of achieving more accurate control of conductive-filament evolution. By applying the pulse-train technique to a potential 3-bit RRAM, the relative standard deviations of resistance levels are significantly improved compared to the single-pulse

14 scheme. The observed exponential relationship between the saturated resistance and the pulse amplitude provides a more comprehensive understanding of the switching process.

Chapter 4 demonstrates the combination of ultra-thin HfOx (~2 nm) switching layer and 3D vertical RRAM architecture as a promising strategy to achieve ultrahigh-density

RRAM array. The theoretical scaling limit of HfOx thickness is estimated for the first time using density functional theory within the non-equilibrium Green’s function formalism (NEGF-DFT). The feasibility of 2-nm HfOx RRAM predicted by the calculations is then verified by fabricating both planar and 3D vertical RRAM devices with 2-nm switching layers. The 3D ultra-thin RRAM demonstrates promising device characteristics including sufficient ON/OFF ratio, fast switching speed, good endurance and data retention.

Chapter 5 summarizes the major contributions of this thesis. The potential research topics in the future are also discussed in this chapter.

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Chapter 2 : Doping Effects on the Resistive Switching of HfO2 and Its Implications to RRAM Device Design

Doping technology is an important class of techniques to improve the performance of RRAM. The physical mechanisms behind the doping effects in hafnium oxide are yet to be fully understood. In this chapter, we apply ab initio modeling to study the effects of dopant types, dopant concentrations, oxide phases and oxide stoichiometry on the electronic and thermodynamic properties of HfOx (x ≈ 2). The physical insights derived from the calculations provide guidelines to achieve desirable RRAM characteristics through doping. Especially, the inconsistent observations regarding the doping effects on forming voltages are explained by the variation of oxygen stoichiometry. In the case of Al dopants, only non-stoichiometric oxide will activate the doping effects and result in significant reduction of forming voltages.

2.1 Motivations of Studying Doping Effects on the Resistive Switching Process

Depending on the application, today’s RRAM technology is facing a series of challenges including the requirements for high endurance, good retention, sufficient memory window and low power consumption [1]. Moreover, it is highly desirable to have flexible control of device characteristics to provide large design space and advanced functionality such as gradual switching and multi-level switching capability.

These requirements are often contradictive in nature, and highly dependent on the intrinsic properties of the switching material.

Although a large variety of materials exhibited resistive switching phenomena [1], the performance gap between their switching characteristics are often significant. Over time, research and development efforts have gradually converged to a few materials that show promising performances without significant drawbacks, such as HfO2 and TaOx

(x ≤ 2) [2]. It is often impractical to keep trying new material systems for better performance (except for multi-layer structures in which one might consider additional layers for better oxygen-gettering and/or improved quality of the oxide-electrode interfaces).

On the other hand, the potential to improve intrinsic switching properties is limited, subject to trade-offs and process restrictions. For example, trade-offs have been observed between the retention and the endurance of oxide-based RRAM [3], as well as between the retention and power consumption [4]. With popular deposition methods such as ALD and reactive sputtering, it is often difficult to modulate the stoichiometry

20 of the deposited film, requiring a lot of calibration and fine-tuning to improve the switching characteristics.

Under these premises, doping technology emerged as an attractive approach to further improve RRAM performances. As described in Chapter 1, the resistive switching phenomena of HfO2 can be attributed to the growth and rupture of nanoscale filaments which consist of oxygen vacancies. Since dopants strongly affect the thermodynamic stabilities of these defects, they have the potential to significantly modulate the switching characteristics. Many experiments have shown that doping the metal-oxide switching layer can improve RRAM characteristics [5-9]. For example,

Gao et al. [5] and Zhang et al. [6] found that doping Al or Gd into HfO2 can improve the uniformity of switching parameters. Chen et al. [7] found that the switching voltages, endurance and retention characteristics of HfO2 RRAM can all be tailored by adding dopants such as Al, Ti and Si. A very desirable property of RRAM devices is the elimination of the high-voltage forming process which poses challenge to device testing and circuit design. As shown by Fang et al. [8] and Wang et al. [9], this can also be achieved by doping.

In contrast to the adoption of a new material, adding dopants to the switching layer allows finer control and greater flexibility through the selection of dopant type and concentration. When the dopant concentration approaches zero, the device characteristics return to the original state of the pristine materials. This kind of fine- tuning capability is highly desired, because it preserves the favorable properties of the host material while searching for even better performances.

2.2 Ab Initio Modeling of the Resistive Switching Mechanisms of HfO2

Depending on the fabrication processes, a wide variety of elements can be incorporated into HfO2 as dopants [5-9]. The doping effects on RRAM characteristics are even more complicated, affected by many parameters including the dopant concentration as well as the phase and stoichiometry of HfO2. It is impractical to experiment with each conditions to search for the best scenario. Alternatively, ab initio modeling is used as a computational tool to provide physical insights and speed up the optimization of doping conditions.

The major advantages of ab initio modeling include:

(1) Direct reflection of the above-mentioned parameters (dopant type and

concentration, phase and stoichiometry of HfO2) in the atomistic model;

(2) Accurate prediction of the electronic structures and thermodynamic stability of

the systems with defects (i.e. oxygen vacancies).

Nowadays, the rapidly-increasing computing power allows efficient ab initio simulations of reasonably large systems, enabling us to do ‘virtual experiments’ on many doping conditions without actually fabricating those materials. In particular, density functional theory (DFT) calculations are applied which is a computationally- manageable approach to solving the Schrödinger equation of many-body systems.

In this chapter, all DFT calculations presented are based on the local-density approximation (LDA) and the projector-augmented wave (PAW) methods,

22 implemented by the Vienna Ab initio Simulation Package (VASP) [10-13]. Due to the limitations of LDA [14], on-site Coulomb corrections are applied to both the d-orbital of Hf (Ud) and p-orbital of O (Up). The Ud and Up parameters were derived using a similar approach as in the previous study of TiO2 [15]. As summarized in Table 2.1, this set of parameters accurately reproduced the lattice constants and electronic bandgaps of HfO2 in three different phases.

During the simulations, 2×2×2 Monkhorst-Pack grid were selected for each supercell. PAW-based pseudopotentials were selected to explicitly calculate O 2s22p4 and Hf 5p66s25d2 states as valence electrons, with an energy cutoff of 353eV. The electronic self-consistency was achieved with an energy convergence tolerance of 10-6 eV. And the ground states were obtained by minimizing the net forces on each atom to be smaller than 0.005 eV/Å.

For the studies of resistive switching phenomena, we are particularly interested in the electronic and thermodynamic properties of oxygen vacancies which act as the building blocks of conductive filaments [16]. The electronic densities of states (DOS) reflect the conduction behaviors of the system. As shown in Figure 2.1, the electron

DOS of the pristine HfO2 in the monoclinic phase and HfO2 with a single oxygen vacancy is calculated and compared. When the oxygen vacancy is present, defect states are formed both at the conduction band edge and in the midgap. These defects are localized in nature but can contribute excess electrons to the conduction band.

Table 2.1: Lattice Constants and Bandgap of HfO2 by DFT Calculations and

Experiments

Figure 2.1: (a) 3×3×2 supercell of monoclinic HfO2. The positions of 3-fold and 4-fold oxygen vacancies (VO) are outlined. (b) Electron density of states (DOS) of the supercell in (a), without VO; (c) Electron density of states (DOS) of the supercell in (a), with one

3-fold VO; (d) Electron density of states (DOS) of the supercell in (a), with one 4-fold

VO.

On the other hand, when a chain of oxygen vacancies are introduced into monoclinic HfO2 (Figure 2.2(a)), the defect states are delocalized to form a conduction band in the bandgap (Figure 2.2(b)). Spatially, the electronic wavefunction of the defect states forms a delocalized path along the vacancy chain, which corresponds to the conductive filament (Figure 2.2(c)).

Figure 2.2: (a) Schematic of the conductive filament, modeled as a chain of oxygen vacancies in monoclinic HfO2; (b) Site-projected (top) and total electron DOS (bottom) at the presence of the conductive filament. The site projected DOS is calculated for a Hf atom right next to the filament; (c) Partial charge densities of the conductive filament, calculated by taking the integration of electron DOS in the bandgap. The iso-surface corresponds to the electron density of 0.1e/Å3.

The thermodynamic stabilities of oxygen vacancies are closely related to RRAM characteristics such as forming voltage and retention time. For example, we can associate the macroscopic forming voltage with the microscopic formation energy (Eform) of the oxygen vacancy (VO) [17]:

Eform = Etot,Vo - Etot,0 + µO (2-1)

Here Etot,0 and Etot,Vo represent the total energies of the relaxed supercell before and after the introduction of an oxygen vacancy. µO is the oxygen chemical potential, which has been calculated to be -5.16 eV at atmospheric pressure and room temperature [18].

At thermal equilibrium, the concentration of defects has an exponential dependence on the formation energy:

E c N exp(  form ) (2-2) site kT

Here Nsite is number of possible sites per unit volume that an oxygen vacancy can form. In order to create a stable conductive path that has certain vacancy concentration, the electric field must reduce the formation energy so that the equilibrium vacancy concentration is increased:

E qFd c N exp(  f ) (2-3) CF site kT

Here F is the electric field and d is the average distance of oxygen migration during the forming process. Take 5-nm HfO2 as an example, we can assume d = 2.5 nm. If the forming voltage is 5 V, then the formation energy reduction is about 2.5 eV. Although

27 this equation only holds at quasi-equilibrium condition, it provides an order-of- magnitude estimation for the relationship between the forming voltage and formation energy.

Based on these physical insights, we may conclude that the electron DOS and formation energies bridge the conduction/switching characteristics of RRAM devices with the atomistic-level details of the switching materials. In the next sections, their combinations are consistently applied to evaluate different doping conditions.

2.3 Selection of Dopant Types for HfO2-based RRAM

So far, a wide variety of dopants have been investigated experimentally for HfO2- based RRAM, including Al, Ti, Si, Zr, Gd, Mg, etc [5-9,19]. Most studies have focused on a single type of dopant, making it hard to compare with other studies due to the unique device configuration and fabrication processes. There is a lot of ambiguity regarding the choice of dopant types for better RRAM characteristics.

In this part, we use DFT calculations to study and compare the effects of 12 different dopants from various columns of the periodic table. All the simulations are carried out in a 3×3×2 supercell of monoclinic HfO2 with 216 atoms, in which dopants and oxygen vacancies can be introduced. Simulated under the same conditions, their impact on the electronic and thermodynamic properties of HfO2 can be compared on a fair basis.

First of all, the effects of all dopants on a single oxygen vacancy were studied by placing one dopant atom next to the oxygen vacancy, substituting one of the nearest- neighbor Hf atom (Figure 2.3(a)). Figure 2.3(b) shows the resulting formation energies by each dopant. Depending on their valence electron numbers, the dopants can be classified into Hf-like (Zr, Si, Ti), P-type (Sr, Al, Y, La, Gd) and N-type (Ta, W, Ni, Cu) dopants.

Hf-like dopants has the same valence electron numbers as Hf (6s25d2, or valence electrons). Similar to the doping of MOSEFTs, P-type dopants have less valence electrons than Hf and N-type dopants have more valence electrons Hf.

The calculation results show that Hf-like dopants slightly decrease the vacancy formation energy due to lattice distortion. Interestingly, both P- and N-type dopants decrease the formation energy considerably as compared to Hf-like dopants. To the first order, the trend of formation-energy change can be summarized by a valence-electron- based rule: larger difference between the valence electron numbers of the dopant and

Hf atoms leads to larger reduction in VO formation energy. This rule is a reflection of the Coulomb effects of the excess carriers contributed by the dopants. An exception of the valence-electron-based rule is the Ti dopant, which lowers the vacancy formation energy even more than Ta and W. We attribute this phenomenon to the fact that Ti4+ can be easily reduced to Ti3+ in an oxide environment, making Ti dopants similar to a

P-type dopant. On the other hand, TaO2 and WO2 exist very commonly, suggesting stable Ta4+/W4+ which is similar to a Hf-like dopant.

Secondly, the effects of dopants on the thermodynamic stability of conductive filaments are studied. The conductive filament is modeled as chain of oxygen vacancies, in the same way as described in section 2.2. One or two dopants are introduced near the filament, again as substitution of nearest-neighbor Hf atoms. Figure 2.4 shows the formation energy of oxygen vacancies in a filament with one dopant, with the undoped case as a reference. The same trend as the single-vacancy model is observed, which can also be accounted for by the valence-electron-based rule.

Figure 2.5: Schematics of the site-projected electron DOS on the dopant (top), as well as the total DOS of the filament with one dopant next to it (bottom), for 6 types of dopants (Al, Si, Zr, Ta, W and Ni).

Next, the effects of dopants on the electronic structures of the conductive filaments are further investigated. Figure 2.5 shows the total and dopant-projected electron DOS, as well as partial charge densities of the filament with 5 selected dopants. The projected

DOS of Zr, Ta, W and Ni show a consistent trend: the induced defect states are shifted to lower energy when valence electron number is increased. Zr, Ta and W do not disrupt the filament conduction, but Si and Ni do, which is the consequence of defect state localization at the dopant site. P-type dopants (Al) also disrupt the filament by charge transfer, but the excess electrons are now delocalized into lower bands and with energies

33 not in the bandgap. Therefore, we may conclude that dopants either shift excess electrons to lower levels in the bandgap, or transfer them into lower electronic bands.

In summary, we have identified the valence electron number and the ionic radius as important factors governing the doping effects on RRAM. Based on these observations, some guidelines can be provided to achieve effective doping:

(1) Hf-like dopants (such as Zr, Si, Ta, W, etc.) cause moderate reduction of

formation energies without significantly changing the film’s electronic

properties. Thus, these dopants are ideal candidates for fine-tuning the switching

characteristics while avoiding the degradation of already-optimized pristine

HfO2. Applications of these dopants may include reducing the forming voltage

and increasing the amorphization temperature of HfO2 [20]. The latter is

desirable because it will keep the switching layer in the amorphous state for

better uniformity and reliability. Moreover, these dopants can be incorporated

into HfO2 up to a high concentration, since their corresponding oxides also

exhibit switching behaviors.

(2) Weak P- and N-type dopants (such as Al, La, Gd, Y, etc.) induce larger reduction

of formation energy compared to Hf-like dopants, which helps to achieve

forming-free devices. These dopants are very likely to preserve the switching

capability of HfO2, as shown in the cases of Al- and La-doped HfO2 [5]. The

dopants act as ‘anchors’ of the oxygen vacancies which lead to more stable

filaments and better retention [5-7]. Also, the growth/rupture of the filament is

more likely to occur near the dopants. This kind of spatial confinement makes

the switching process more reproducible and the switching endurance may be

improved. The drawback is that the ON/OFF ratio may be compromised due to

higher carrier concentration and larger leakage current in the OFF state.

(3) Strong P- and N-type dopants (such as Sr, Ni, Cu, etc) are more likely to induce

substantial change of switching parameters and even the collapse of memory

functionality. Because these dopants generate large amounts of charge carriers

as well as oxygen vacancies. At high doping concentrations, the switching layers

are likely to become too conductive to switch. Even at lower concentrations, the

random distributions of these dopants may result in large device-to-device

variations due to their significant impact on the vacancies. Thus, these dopants

are not recommended for the commercial application of RRAM technology.

2.4 Effects of Oxide Phases, Stoichiometry and Dopant Concentrations on RRAM Characteristics

The previous section addressed the effects of dopant types on RRAM characteristics. However, according to various experiments on doped-HfOx RRAM, contradicting results regarding the doping effects have been observed, even for the same type of dopants [5,7,21-24]. For example, when Al were doped into HfOx through various fabrication processes (such as co-oxidation [5], co-sputtering [21] and ion implantation [22]), significant reduction of forming voltages were observed. However, in the case of ALD-based processes, the forming voltage was unchanged/increased, even at similar doping concentration of Al [7,24]. Since forming plays a crucial role in

RRAM characteristics, it is highly desired that such discrepancies can be understood in order to achieve better performances through doping.

Previous analyses have not arrived at a clear explanation, partly due to the fact that the direct observation of conductive filaments in HfOx is extremely difficult. On the other hand, theoretical studies of the doping effects have mostly focused on a single crystalline phase with a particular type of dopant [21,24-25], which cannot explain the contradicting results either. In this section, we propose three factors that potentially cause the observed discrepancy in terms of forming voltages, and apply DFT calculations to examine these factors one by one:

(1) The phase of HfO2: A variety of HfO2 phases can be stabilized under different

process conditions, such as monoclinic, orthorhombic, cubic as well as

amorphous [20,26-28].

(2) The stoichiometry of HfO2: Different fabrication methods often lead to different

stoichiometry of HfO2. Non-stoichiometry causes significant change of material

properties such as bandgap and resistivity [29].

(3) Dopant concentration: In most cases, the doping process has the ability to

continuously modify the dopant concentration. This is a very useful feature for

controlling of doping effects. Moreover, varying doping concentration also

facilitates changes in the phase and stoichiometry of HfO2 [20,26-29].

In the previous section, dopants with similar valence-electron numbers as Hf were predicted to have more controllable doping effects. Following this criteria, three types of dopants (Al, Ti and Si) were selected for the study of above-mentioned factors and their effects on forming.

2.4.1 Effects of Oxide Phases

Both crystalline (monoclinic, orthorhombic and cubic) and amorphous phases of

HfO2 are investigated for a comprehensive understanding (Figure 2.6(a)). The initial lattice parameters of the three crystalline phases were obtained from X-ray diffraction data [30] and relaxed by DFT calculations. As for the amorphous model, the atomic positions are obtained by a melt-and-quench technique that employed classical molecular dynamics, MD, annealing followed by DFT relaxation of the classical model

[31]. Each model of pristine HfO2 has a supercell containing 96 atoms (32 Hf atoms and

64 O atoms). After relaxing the pristine models, dopants were then added by replacing

Hf atoms, followed by the removal of oxygen atoms to create vacancies. Finally, the formation energies of oxygen vacancies are calculated which shed light on the corresponding forming characteristics. For monoclinic and orthorhombic HfO2, oxygen vacancies at two non-equivalent sites are created to calculate their formation energies.

For cubic HfO2, all oxygen atoms are equivalent so we only need to study one of them.

Figure 2.6(b) compares the formation energies in the three crystalline phases. In terms of formation-energy reduction, the dopants’ effects are quantitatively similar in monoclinic and orthorhombic HfO2, which can be sorted as: Al > Ti > Si. On the other hand, the formation-energy reduction by Al and Si in cubic HfO2 is notably larger than its counterparts in other phases. This observation can be explained by the denser atomic arrangement in the cubic phase compared to monoclinic and orthorhombic phases, which amplifies the doping effects through larger lattice distortion.

Amorphous HfO2 is a quite different story compared to crystalline phases. The oxygen atoms are no longer equivalent to each other. Thus, the vacancy formation energies have a continuous distribution instead of showing discrete values. As shown in

Figure 2.6(c), the Si dopant slightly decreases the vacancy formation energies compared to the pristine HfO2. The Ti dopant has a stronger impact on the formation energy, with 40% of all oxygen sites showing a formation-energy reduction of more than 1 eV. The Al dopant reduces the vacancy formation energies in amorphous HfO2 even further. This trend of formation-energy reduction (Al > Ti > Si) is consistent with the calculation results of the crystalline models.

Figure 2.6: (a) Atomic models for HfO2 in monoclinic, cubic, orthorhombic and amorphous phases. (b) Formation energies of oxygen vacancy in pristine and doped

HfO2, in three different crystalline phases. (c) Distributions of the formation energies of oxygen vacancies in amorphous HfO2, either pristine or doped with three types of dopants (Al, Ti and Si).

From these results, we can confirm that phase transitions of HfO2 strongly affect the lowering of the vacancy-formation energy by dopants. However, it still cannot explain the contradicting observations regarding forming voltages.

2.4.2 Effects of Oxide Stoichiometry

Next, we investigate the effects of oxygen stoichiometry on vacancy-formation, using the amorphous HfO2 model and the Al dopant as an example. We focus on the amorphous model because doping can facilitate the amorphization of HfO2. And unlike

TiO2 which can transform into sub-stoichiometric Magnéli phases [32], HfO2 typically stays amorphous at significant non-stoichiometry [29]. In addition, Al is chosen for two reasons:

(1) It has been reported to induce inconsistent effects on forming voltages;

(2) Among the 3 types of dopants studied in the previous section, Al is the only one

that has a different valence electron number from Hf. This will change the oxide

stoichiometry since Al can only be oxidized to 3+ instead of 4+ in the case of

Hf. Replacing one Hf atom by one Al atom will add 0.5 excess oxygen to the

system as compared to the pristine state.

Figure 2.7(a) depicts three supercells created from the amorphous HfO2 model, each representing a different stoichiometry: (1) Oxygen-excess: 1 Al, 0 VO; (2)

Stoichiometric: 2 Al, 1 VO; (3) Oxygen-deficient: 1 Al, 1 VO. Here the numbers before

Al and VO correspond to the difference of each species from the amorphous HfO2 model

(undoped). The electron density of states (DOS) of the three atomic models is presented in Figure 2.7(b), along with the DOS of pristine HfO2. When non-stoichiometry is present in the system, defect states can be observed in the bandgap, regardless of whether it’s oxygen-excess or oxygen-deficient. On the other hand, defect state is not

40 observed in the bandgap of the stoichiometric model. These results agree well with the observed bandgap reduction of HfO2 induced by non-stoichiometry [29].

The formation-energy distributions of oxygen vacancies under different stoichiometric conditions are calculated by DFT and shown in Figure 2.7(c). Compared to pristine HfO2, the oxygen vacancy formation energies in both the oxygen-excess and oxygen-deficient models are significantly reduced by Al dopants. This observation helps to explain the considerable decrease of forming voltages in Al-doped HfOx fabricated by co-oxidization, co-sputtering or ion implantation, since non-stoichiometry is very likely to be introduced in these processes. In contrast, the formation energies of the stoichiometric model have a distribution that almost overlaps with the pristine HfO2, which indicates the formation energies are not reduced. In other words, non- stoichiometry activates the dopants to reduce the forming voltages of HfO2 RRAM. This is an important observation because it provides a reasonable explanation to the increase of forming voltages observed in Al-doped HfO2 grown by ALD. Since HfO2 and Al2O3 are grown separately in this kind of layer-by-layer doping processes, the stoichiometry in the oxide is usually well preserved. Since Al dopants in stoichiometric HfO2 do not reduce the vacancy formation energies, it is expected that the forming voltage is not visibly reduced.

In summary, the effects of oxide stoichiometry on the doping effects provide a possible answer to the inconsistent observations regarding the forming voltages of Al- doped HfOx RRAM. Stoichiometry is identified as a critical factor to be monitored during the doping processes of RRAM.

Figure 2.7: (a) Atomic models of amorphous Al-doped HfOx under three different stoichiometric conditions. (b) Electron density of states (DOS) of the three atomic models shown in (a), calculated by DFT. Electron DOS of pristine HfO2 is plotted as a reference. (c) Distributions of oxygen-vacancy formation energies in the three atomic models shown in (a).

2.4.3 Effects of Dopant Concentration

Finally, we study the effects of dopant concentrations by varying the number of dopant atoms in the supercell. Supercells with 1, 6 and 14 dopants are constructed

(Figure 2.8(a)), which corresponds to the dopant concentrations of 3%, 18% and 45%,

42 respectively. In the case of Al dopants, excess oxygen is removed from the system to preserve the stoichiometry, followed by volume/lattice relaxations. Figures 2.8(b-d) show the distributions of oxygen-vacancy formation energies in Al-, Ti- and Si-doped

HfO2, respectively. For Al dopants up to 40% concentration, no significant change of formation energies can be observed. In the case of both Ti-doped and Si-doped HfO2, a larger reduction of formation energy is obtained at higher doping concentration. In addition to formation-energy, both the phase and stoichiometry of HfO2 can be adjusted by changing the dopant concentrations [20,26-29]. The control of dopant concentration is thus identified as a useful vehicle for tuning RRAM characteristics, in addition to the selection of the type of dopant.

(b) Al-doped HfOx, (c) Ti-doped HfO2 and (d) Si-doped HfO2, calculated at three different dopant concentrations (3%, 18% and 45%).

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Chapter 3 : Pulse-Train Characterization Techniques of RRAM

Precise electrical manipulation of nanoscale defects such as vacancy nano-filament is highly desired for the fine control of RRAM. In this chapter, we present a systematic investigation on the pulse-train characterization techniques for the multi-level control of conductive filament evolution. By applying the pulse-train RESET scheme to a potential 3-bit HfO2 RRAM, the relative standard deviations of resistance levels are improved up to 80% compared to the single-pulse scheme. The observed exponential relation between the saturated resistance and the pulse amplitude provides evidence for the gap-formation model of filament-rupture process.

3.1 Introduction to Pulse-Train Characterization of RRAM

3.1.1 Introduction to Electrical Pulse Characterization

Electrical characterization is a crucial component in the research and development of RRAM technology. Traditionally, electrical characterization of semiconductor devices is performed using DC instruments, such as source measure unit (SMU).

Nowadays, standard instrumentation has improved to possess the capability of applying sub-microsecond electrical pulses, while measuring the current and voltage at the same time.

Two typical configurations of pulsed I-V measurements are shown in Figure 3.1, using Keithley 4200-SCS parameter analyzer as the measurement equipment. As shown in Figure 3.1(a), the parameter analyzer controls a switching matrix to allow both the

SMU and external pulse generator to connect to the device-under-test (DUT). During the operation, the pulse generator is first routed to DUT to apply electrical pulses. The result of pulsing is then measured by connecting SMU with DUT to perform DC sweep.

In Figure 3.1(b), both SMU and a built-in pulse generator are connected to a remote switch to select between DC and pulse operations. Since the remote switch can be moved closer to DUT, the parasitics can be minimized. The first configuration is used for endurance test in Chapter 4, while the second configuration is used throughout this chapter. The ability of fast pulsing and dynamic I-V measurements provide more physical insights to the electrical characteristics and switching mechanisms of RRAM devices.

Figure 3.1: Two typical configurations of pulsed I-V measurements using Keithley 4200-SCS parameter analyzer: (a) Keithley 4200-SCS controls a switch matrix to allow both the SMU and external pulse generator (Agilent 81150A) to connect to DUT; (b) Both SMU and a built-in pulse generator are connected to a remote switch (Keithley 4225-RPM) to select between DC and pulse operations.

Apart from physical understanding, an equally-important advantage of pulse characterization is the minimization of the electrical stress imposed on the RRAM device. This helps to achieve stable and reliable operation, which leads to better cycle- to-cycle variability and endurance. Due to these advantages, pulse characterization is investigated in this chapter to improve both the physical understanding and the device performance of RRAM.

3.1.2 Motivations to Study Pulse-Train Characterization

For HfO2 RRAM, the widely-accepted filamentary-switching mechanism attributes the resistance change to the formation/rupture of nanoscale conductive filaments [1].

Since these filaments originate from the change of oxygen stoichiometry, they are extremely difficult to observe experimentally [2-4]. Thus, the ability to precisely monitor and control the shape/size of these nanoscale defects remains a critical challenge. Particularly, RRAM with a large memory window allows the storage of multiple bits in a single device, which leads to multi-level cells (MLC) [5-6]. However, the stochastic nature of filament evolution can cause substantial cycle-to-cycle variability that limits the total number of bits. Various program-and-verify schemes have been proposed to control the filament-rupture process and to reduce variations [6-

8]. However, accurate resistance measurement over a large dynamic range may significantly increase the operation time and complexity of circuit design. In contrast, applying a train of pre-specified pulses without doing read-and-verify may greatly enhance the measurement speed.

In addition to the speed-up of MLC operations, there is another interesting application of pulse-train characterization, which is to induce gradual switching behaviors. Compared to DC and single-pulse switching, pulse-train measurements can access a continuum of resistance states. This kind of analog memory behaviors make

RRAM an ideal candidate of the synaptic devices in neuromorphic computing applications [9-12]. These synaptic devices use the resistance to represent the connectivity between neurons in a neural network. The connectivity (resistance) can be gradually adjusted by external stimuli (electrical pulses in this case).

Finally, pulse-train characterization also provides additional physical insights to the dynamic process of resistive switching. The superiority of pulse-train characterization compared to DC sweep can be demonstrated in the studies of switching abruptness, a new type of RRAM characteristics which reflects the switching speed and the accessibility of intermediate states.

As shown in Figure 3.2(a), the RESET process by DC sweep can be either gradual or abrupt even for the same batch of devices. In previous studies, the gradual/abrupt behaviors are often associated with bipolar/unipolar switching. However, this rough classification does not account for the fact that both behaviors exist in bipolar devices.

Yet there is no systematic understanding on how to control the abruptness via materials engineering and/or different switching schemes. Here we consider the pulse-train technique as an intuitive way to characterize switching abruptness. As shown in Figure

3.2(b-c), when a train of identical RESET pulses were applied to HfOx RRAM devices

54 with different process conditions, two types of resistance change behaviors were observed:

• Type A (Figure 3.2(b)): the resistance increases gradually with the number of

pulses until it saturates at certain high resistance value. The slope of the

resistance curve increases with increasing pulse amplitudes.

• Type B (Figure 3.2(c)): the resistance oscillates around a certain value until an

abrupt switching event occurs. Only two stable resistance states are observed.

The pulse amplitude determines the probability of switching.

For a similar memory window, type A switches more slowly than type B devices, but their intermediate resistance states are much more accessible. Thus, the former is desirable for MLC/neuromorphic applications, while the latter is favored for high-speed single-bit memories. Such insights are not easily captured in DC sweep or single-pulse switching schemes.

In summary, pulse-train characterization goes one-step further than the electrical- pulse characterization. In this chapter, it is demonstrated to be useful for both the fundamental study and practical application of RRAM.

Figure 3.2: (a) Schematics of both gradual and abrupt RESET processes, obtained from DC sweep. (b) Resistance-change characteristics of an RRAM device upon the application of 100 identical pulses at various amplitudes. Gradual increase of resistance is observed with increasing number of pulses; (c) Resistance-change characteristics of another RRAM device upon the application of 100 identical pulses at various amplitudes. An abrupt switching event occurs and the intermediate states are not accessible. The switching probability depends on the pulse amplitude.

3.2 Improved Multi-level Control of RRAM Achieved by Pulse-Train Operation

In this study, TiN/HfO2/Pt devices are fabricated to investigate the multi-level switching capability of RRAM. Bottom electrode of Pt (~90 nm) is first deposited by e- beam evaporation on Si wafer with 2-nm Ti adhesion layer. Then, HfOx and TiN (~200 nm) were deposited by reactive sputtering at room temperature, followed by a lift-off process to form RRAM cells of 100x100 µm2 area. The cross-sectional TEM image

(Figure 3.3(a)) confirms the HfO2 thickness to be around 25nm. According to electron dispersive X-ray (EDX) analysis (Figure 3.3(b)), an interfacial TiOxNy layer is formed to getter oxygen and create substoichiometric HfOx which serves as the switching layer

[13].

Figure 3.3: (a) Cross-sectional TEM image of the fabricated TiN/HfOx/Pt RRAM device. (b) Elemental compositions throughout the device, obtained by energy- dispersive X-ray spectroscopy (EDX).

The device characteristics are measured using Keithley 4200-SCS semiconductor analyzer with DC and pulsed I-V module. The lengths of all applied pulses are 200 ns, with rise/fall time of 20 ns. As shown in Figure 3.4, the DC sweep characteristics of the device exhibit a very large ON/OFF ratio of 106. By varying the RESET stop voltage from -2.0V to -4.3V, a gradual increment of resistivity is observed. 8 discrete resistance levels are achieved with an average separation by a factor of 7.2, implying the potential capability to store 3 bits in each RRAM cell.

Figure 3.4: DC sweep characteristics of the fabricated RRAM device. 8 resistance levels are achieved with the maximum ON/OFF ratio of ~ 106.

Figure 3.5(a) shows the resistance distributions obtained in 100 consecutive DC sweep cycles with different RESET voltages. At smaller voltages, the uniformity of the high resistance state (HRS) is well-controlled, with resistance levels clearly are

58 separated from each other. However, when higher RESET voltages are applied to reach deep HRS states, the variations are noticeably increased. Figure 3.5(b) shows the retention data collected from 8 resistance states measured at 125˚C, which can be extrapolated to 10 years. These results confirm the potential 3-bit capability of the fabricated devices.

Figure 3.5: (a) Resistance distributions obtained from 100 consecutive DC sweep cycles, at different RESET voltages. (b) Retention characteristics of 8 different resistance levels, measured up to 104 seconds at 125˚C. Retention can be extrapolated to 10 years.

Compared to DC sweep, pulse programming is a more desirable approach for practical applications due to high operation speed and energy efficiency. Multiple resistance levels can be achieved by varying either the widths or amplitudes of RESET pulses [5]. However, these single-pulse schemes often result in cycle-to-cycle variations

59 that are worse than DC sweep, which reduces the margins between resistance levels and lowers the storage capacity. In the case of our 3 bit/cell RRAM, controlling multiple levels by single-pulse scheme becomes extremely challenging. Figure 3.6(a) shows the relative standard deviations of 7 HRS states achieved by applying single pulses with various amplitudes. Compared to DC sweep (Figure 3.6(b)), most of the resistance states exhibits larger variations which cause severe overlapping between the adjacent levels. The only exception is the lowest HRS state, which has very small variation due to reset failure. Varying pulse widths is not studied in this work because the required pulse width increases exponentially (which is six orders of magnitude), and the uniformity is unlikely to be improved compared to varying pulse amplitude [5]. The large variations of single-pulse scheme can be partially attributed to the presence of only one rising edge, which causes the random atomic drift/diffusion to be 'quenched' in the device after the pulse. According to the recent studies on pulse rise-time of RRAM [14], the switching voltages can be substantially affected by the rising edge of the pulses.

Thus, applying a pulse-train should not be viewed as an equivalent single pulse with the longer width of the pulse-train’s cumulative time. Overall, the single-pulse operation scheme is not a favorable approach to controlling the filament evolution for this potential 3-bit RRAM due to the uncontrollable variation among the adjacent levels.

Figure 3.6: (a) Distributions of HRS resistances in 30 switching cycles, obtained by the single-pulse scheme. (b) Distributions of HRS resistances in 100 DC sweep cycles. 7 different HRS states are studied to evaluate MLC capability.

On the other hand, pulse-train operation has been suggested to minimize the reset failures of RRAM [15,16]. It also emerges as a natural method to control analog synaptic devices for neuromorphic applications [9-12]. In this study, the possibility of using a train of identical pulses to achieve multi-level switching with better uniformity is

61 investigated. In this way, we hope to improve the control of the filament evolution by suppressing the stochasticity arising from sharp rising edges. Figure 3.7 shows the change of the resistances during the sequential applications of 100 identical pulses with various amplitudes. Three distinct regimes are observed in these characteristic curves: initially, the resistance changes slowly, then begins to rapidly increase at a certain point, and finally becomes saturated with some fluctuation around a certain value. Following the conventions of MOSFET, the three regimes can be denoted as the subthreshold region, linear region and saturation region. The subthreshold region could be responsible for RESET failures at low voltages [17], and it is generally eliminated at higher voltages. The linear region is where the majority of atomic migrations occurs, which in this case is controlled in a continuous manner. After entering the saturation region, the range of resistance fluctuation is comparable or even smaller than the cycle- to-cycle variations during DC sweep. These pulse-trained characteristics, except for the initial random fluctuations, can be well reproduced by RRAM compact modelling [18].

The observations suggest that if the device reaches its saturation regime, the resistances should become more uniform and insusceptible to further identical stimuli.

Figure 3.7: Double log plot of the resistance changes upon the applications of 100 identical pulses with different amplitudes. Both measurement data and compact-model simulation results are shown.

According to this observation, the pulse-train scheme using 100 identical pulses of

200-ns width is applied to program the fabricated HfO2 device to 7 different HRS states.

Each of the resistance state is programmed for 30 switching cycles. As shown in Figure

3.8, the new scheme significantly reduce the variations compared to the single-pulse scheme. The relative standard deviation in the worst case is improved to 51%.

Compared to 131% from the single-pulse scheme, the pulse-train scheme enables much better separation of the resistance levels.

Figure 3.8: Distributions of HRS resistances in 30 switching cycles, obtained by the pulse-train scheme with 7 different pulse amplitudes.

3.3 Pulse-Train Characterization of the Conductive Filament Evolution during Resistive Switching

In addition to the improved multi-level control, pulse-train characterization also provides additional physical insights to the resistive switching mechanisms. For example, Figure 3.9 plots the mean saturated resistances measured during the pulse- train operation, as a function of the pulse amplitude. An exponential relationship between the mean saturated resistance and the pulse amplitude is discovered.

Figure 3.9: Relationship between the pulse amplitudes and the mean values of HRS resistance by the pulse-train scheme.

During RESET process, it is widely accepted that conductive filament(s) is (are) ruptured to form a tunneling gap between the filament(s) and the electrode. According to the Wentzel-Kramers-Brillouin (WKB) approximation, the tunneling current across

65 the gap is exponentially dependent of the gap thickness (tgap) [19]. The abovementioned results thus suggest the existence of a maximum gap thickness (tgap,max), which is linearly dependent on the RESET pulse amplitude. Figure 3.10(a) further explains the formation of such maximized gap by plotting oxygen drift velocity as a function of the gap thickness. The vacancy migration probability is exponentially dependent of the applied electric field, which is reflected in the drift velocity of oxygen ions [20,21]:

v fa exp(  Em / kT )sinh( qFa / 2 kT ) (3-1)

Where f is the frequency of atomic vibration (~1×1013Hz), a is the hopping distance between adjacent potential wells (~2.5Å). Em is the migration barrier of oxygen ion in

HfO2, which is assumed to be 1.0 eV. F is the electric field, which equals to the applied voltage divided by the gap thickness here. In order for a migration event to occur, the velocity should be large enough to move the ion by one inter-atomic distance. As a reference, this threshold velocity is ~0.001 m/s for 200-ns pulses. As shown in Figure

3.10(a), the drift velocity exhibits a significant drop across the threshold as the gap thickness increases. Beyond this threshold, the migration probability becomes so small that the movement of oxygen vacancies can barely be observed within the pulse duration.

Moreover, the corresponding gap thickness at the threshold is linearly dependent on the applied voltage, consistent with experimental results. To sum up, the saturation regime is a manifestation of maximized gap thickness, which is a consequence of the exponential dependence of ion-drift velocity on the applied electric field.

Figure 3.10: (a) Ion drift velocity in HfO2 RRAM as a function of gap thickness, at fixed temperature and various applied voltages. (b) Measured transient current of HfO2

RRAM device during a RESET pulse. (c) Ion drift velocity in HfO2 RRAM as a function of the gap thickness, at fixed applied voltage and various different temperatures.

Next, the difference between a pulse train and a single pulse with the same equivalent duration is further discussed. Figure 3.10(b) shows the transient current of a HfO2 RRAM device during the RESET pulse. Beginning at the rising edge, the RESET

67 process is not initiated until the current reaches the highest level. Then, the current drops quickly for about 100 ns before reaching the steady state with fluctuations. Before and after initiation, the progress of RESET is totally different even if the current levels are the same. This suggests that the initiation of RESET is a thermal-assisted event which can be connected with gap formation, and the first RESET pulse can be divided into two parts. Before initiation, the filament is connected and the voltage drop is rather uniform across the entire film thickness. A significant amount of heat is needed to rupture the filament by ion diffusion at its weakest spot. After initiation, the tunneling gap is formed and the voltage drop is concentrated to the gap. Now the reset process is field-driven and dominated by ionic drift, without the need for high temperature or high current level.

The characteristics of pulse-train operation can be well explained within this picture.

The subthreshold region corresponds to the condition before initiation of RESET. In the linear region, the gap thickness is gradually expanded until the maximum/saturation is reached. Now according to previous simulations [22], only the pulses before gap formation can create high temperatures in the filament, accompanied by larger thermal fluctuations. And according to eq. (1), the temperature fluctuations result in large variations of ion migration speed (Figure 3.10(c)). This explains why the single-pulse scheme leads to larger device variations: the stochasticity caused by the temperature is quenched in the device after the first pulse. On the other hand, the pulse-train scheme allows correction of the stochasticity with subsequent pulses which result in lower temperatures. Since the process is now field-driven, the resistance is monotonically increasing and strictly limited by the maximum gap thickness, thereby providing better uniformity.

Physical insights were also developed for the subthreshold regime. As shown in

Figure 3.11(a-b), a controlled experiment is carried out to compare the DC and pulse- train RESET, starting with different filament strengths. The filament strength is controlled by applying a SET pulse with different amplitudes, and reflected in the current level required in DC sweep to initiate current drop. This change of filament strength is manifested in the pulse-train characteristics as a change of the saturation regime’s length (Figure 3.11(b)). The saturation regime of the same device increases from 0 to over 100 pulses as the filament becomes stronger and stronger. This observation suggests that the subthreshold regime is essentially a gradual reduction of the filament strength until a gap can be formed. Afterwards, the device will enter the linear regime in which the gap size is expanded.

Figure 3.12 summarizes the proposed filament evolution during the course of pulse-train programming. The different natures of the pulse-trained characteristics happen to satisfy the requirements of different applications: the linear region can be utilized in neuromorphic computing, while the saturation region is desired for precise

MLC control. In this study, 10 identical pulses are sufficient to bring the device into saturation for most resistance levels, according to Figure 3.7.

Figure 3.11: (a) DC RESET I-V characteristics with different filament strengths of the ON state, achieved by varying the SET pulse amplitude. (b) Resistance changes during the pulse-train reset scheme, again with different filament strengths of the ON state. (Inset: (a) DC RESET current vs. SET pulse amplitude. (b) Length of subthreshold regime vs. SET pulse amplitude.)

Figure 3.12: Schematic of the pulse-train characteristics of RRAM, divided into three regions. The corresponding physical processes and applications are outlined and discussed in the framework of filamentary resistive switching.

In summary, we systematically investigated the pulse-train operation scheme for reliable and uniform multi-level control of conductive-filament evolution in RRAM. By applying electrical pulse-train to a potential 3-bit HfO2 device, the relative standard deviation of resistance levels is improved up to 80% compared to the single-pulse scheme. Furthermore, the observed exponential relationship between saturated resistance and pulse amplitude are consistent with the gap-formation model for the filament-rupture process.

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Chapter 4 : Ultra-Thin RRAM: Scaling Limit, Stack Engineering and 3D Integration

In this chapter, we demonstrate the combination of ultra-thin HfOx (~2 nm) switching layer and 3D vertical RRAM architecture as a promising strategy to achieve ultrahigh-density RRAM array. The theoretical scaling limit of HfOx thickness is estimated for the first time using density functional theory within the non-equilibrium

Green’s function formalism (NEGF-DFT). Based on the filamentary-switching mechanisms, the scaling limit is calculated as a function of the device area, and the feasibility of 2-nm HfOx RRAM is predicted for large-area devices. We then verify the calculated scaling limit by fabricating both planar and 3D vertical RRAM devices with

2-nm HfOx switching layers. Compared to the reference devices with thicker HfOx, the

2-nm HfOx devices exhibit similar DC characteristics, indicating the effective switching thickness is less than 2 nm. Moreover, the 3D ultra-thin devices demonstrate promising characteristics including ON/OFF ratio (~100), switching speed (~20 ns), endurance

(108 cycles) and data retention (> 10 years at room temperature).

4.1 Motivations for Studying Ultra-Thin RRAM

The commercial application of RRAM still faces several challenges such as the variability of switching parameters and the requirement for a forming process [1-6].

Moreover, despite the potential scalability to below 10 nm [7-8], the cost-per-bit of planar RRAM is not competitive to the 3D vertical NAND flash [9-12]. In order to further reduce the cost-per-bit, 3D-stackable RRAM architectures are highly desired. In this chapter, the study of ultra-thin switching layer for RRAM is driven by two primary motivations:

(1) Reduce the forming voltage of RRAM to achieve forming-free and low-power

operations;

(2) Improve the scalability of vertical RRAM devices for 3D integration.

The first motivation is straight-forward, since the forming process is essentially a soft breakdown of the fabricated dielectric layer (HfO2 in this case). The initiation of dielectric breakdown is usually dictated by a critical electric field, also called the dielectric strength. Thus, when the switching layer gets thinner, the voltage required to form the RRAM device should become smaller accordingly. The forming-free behavior improves the variability and simplifies the circuit design of RRAM [13].

The second motivation requires more detailed explanation. It is widely accepted that one major advantage of RRAM technology is the superior scalability compared to flash memory. The device area of RRAM has been scaled down to 1 nm by 3 nm [8] or as

77 small as a sharp tip [7]. However, since 3D NAND flash is commercially available, the scalability of RRAM should also be considered in a 3D context.

So far, several 3D vertical RRAM (VRRAM) architectures have been proposed and experimentally demonstrated [14-17]. The scalability of 3D RRAM in the vertical direction has been investigated [18-19]. But compared to horizontal scaling which affects the array density quadratically, the vertical scaling which linearly increases the array density is less efficient. On the other hand, the scalability in the horizontal direction, especially that of the oxide and pillar-electrode thicknesses, has not been fully explored. Although 3-nm HfOx RRAM devices have been demonstrated with small

ON/OFF ratio (<10) [20], pulse-train characterizations in the last chapter indicated the effective switching thickness to be around 1 nm. It is still not clear what is the limit of thickness scaling that still preserves the memory functionality.

In this chapter, the combination of ultra-thin HfOx (~2 nm) switching layer with 3D

VRRAM architecture is demonstrated. The theoretical scaling limit of HfOx thickness was first estimated using density functional theory within the non-equilibrium Green’s function formalism (NEGF-DFT) [21]. Based on the filamentary switching mechanisms, the scaling limit was calculated as a function of device area, and the feasibility of 2-nm

2 HfOx RRAM was predicted for 1(µm) devices. In order to verify the theoretical estimations, planar RRAM devices with 2-nm HfOx directly sandwiched between electrodes (TiN and Pt) were fabricated. Compared to the reference devices with thicker oxide, the 2-nm HfOx devices exhibit similar switching characteristics. Moreover, the

2-nm HfOx layer was stacked with either TiO2 or Al2O3 thin layers to retain the same

78 memory window. Finally, the 2-nm HfOx RRAM was integrated into 3D vertical geometry for the first time. The 3D ultra-thin devices demonstrated promising characteristics such as ON/OFF ratio (~100), switching speed (~20ns), endurance (108 cycles) and data retention (> 10 years), paving the way towards ultrahigh-density 3D

RRAM array.

4.2 Thickness Scaling Limit Analysis of HfO2-based RRAM

In order to theoretically evaluate the thickness scaling limit, it is important to identify the factors that cause RRAM to lose its functionality. It is now widely accepted that the resistive switching of HfOx is achieved by the formation/rupture of conductive filaments (CF) [22-24]. Multiple experimental studies suggested that oxygen vacancy is the defect species that contributes to this localized conductivity (Figure 4.1(a)) [25-

27]. In the ON state, the resistance is determined by the conductive filament. While in the OFF state, the resistance is dominated by the gap between the ruptured filaments, or between one ruptured filament and the electrode. Thus, as the switching layer becomes thinner and thinner, the ON-state resistance should not change much due to the presence of the conductive filament. The OFF-state resistance, on the other hand, shall decrease significantly below a certain oxide thickness, due to the rapidly-increasing leakage current. Ultimately, the ratio between the ON-state and OFF-state resistances will shrink to the point that the RRAM device no longer has a sufficient memory window. An analogy of the situation is the scaling of MOSFET gate dielectric. Aggressive scaling of gate-dielectric thickness results in high direct-tunneling currents across the gate, which causes serious problem for its functionality [28-29].

In this work, we followed a two-step simulation approach to study the effects of

HfOx thickness on the ON/OFF ratio of RRAM. In the first step, atomistic models of the RRAM devices were built and optimized using density functional theory with on- site Coulomb corrections (DFT+U) [30-39]. In the second step, DFT calculations within the non-equilibrium Green's functions (NEGF) framework were carried out based on

80 the optimized atomistic model. This method is often abbreviated as “NEGF-DFT” and has emerged as the de-facto standard approach for modeling non-equilibrium quantum transport in nanostructures [40-43].

Figure 4.1: (a) Schematic of the filamentary switching process of HfOx-based RRAM.

(b) Atomic configurations of the TiN/HfOx/TiN RRAM device in both ON and OFF states. (c) The band-decomposed charge density of the RRAM devices, obtained by taking the integration of electron densities in the bandgap of HfO2. The iso-surface corresponds to the electron density of 0.1e/Å3. The ON-state device demonstrates a delocalized conductive path connecting the two electrodes.

The detailed procedure is depicted in Figure 4.2. Starting from the initial atomic model, DFT calculations were first carried out to relax the atomic positions, until the net force on each atom becomes lower than 0.005eV/Å. The DFT calculations were achieved by local density approximation with on-site Coulomb corrections (LDA+U), implemented in the Vienna Ab-initio Simulation Package (VASP) [34-37]. Next, based on the relaxed atomic model, NEGF-DFT calculations were carried out at different bias voltages to obtain the transmission spectrum, from which the electron currents can be calculated by taking integration. The NEGF-DFT calculations of electron transport were carried out with QuantumWise ATK package [41].

The atomistic models for TiN/HfOx/TiN devices are constructed with approximately 10% lattice mismatch between HfOx (cubic) and TiN (cubic). The TiN lattice is stretched to minimize the stress of the HfOx layer. The thickness of HfOx (tOX) is varied between 1 and 3 nm to search for the scaling limit. The conductive filament is modeled as a chain of oxygen vacancies (Fig 4.1(b)), which was confirmed as a valid assumption for order-of-magnitude estimation of ON/OFF-state resistances [43]. From

DFT calculations, the oxygen-vacancy chain creates a delocalized path of electron wavefunction (Fig 4.1(c)), which acts as the conductive filament in the ON state.

Figure 4.2: Detailed procedures of the two-step approach to simulating I-V characteristics from the initial atomic coordinates of the device.

Figure 4.3(a) shows the calculated I-V characteristics of the RRAM devices in both

ON and OFF states. In the ON state, the I-V characteristics are linear, which implies

Ohmic conduction behaviors. In the OFF state, the devices exhibit non-linear I-V characteristics, which is typically seen in tunneling/hopping conduction. As the oxide

83 thickness varies, the ON-state resistance is linearly dependent on tOX, which is consistent with Ohm’s law. The OFF-state resistance, on the other hand, is exponentially dependent on tOX. This exponential behavior can be explained by considering the WKB approximation for hopping/tunneling conduction, which states that the transmission coefficient across an energy barrier has an exponential dependence on the barrier thickness.

Figure 4.3: (a) I-V characteristics of the HfOx RRAM devices in ON and OFF states, calculated by NEGF-DFT. (b) Schematic of device-area scaling and its effects on the cell resistance. (c) Estimation of the ON/OFF ratios for different device areas, assuming the CF diameter to be 10nm. (d) Thickness scaling limit of HfOx RRAM as a function of device area.

When both ON- and OFF-state resistances are obtained, the ON/OFF ratio of these devices can be calculated. However, the effects of device area should also be considered to determine the ON/OFF ratio for real devices. This is because the atomistic model presented above assumed that the entire HfOx is switching. In reality, no matter how large the device area is, only a limited region (the conductive filament) switches. The typical size of the conductive filament has been estimated by high-resolution TEM to be around 10 nm in diameter [25]. Thus, if the device area is equal to or smaller than 10 nm × 10 nm, it is reasonable to assume that the entire area is switching and the ON/OFF ratio is the same as the above calculations. On the other hand, when the device area is larger than 10 nm × 10 nm, only a fraction of the area is switching and the rest part stays in the high resistance state. Now if the device area varies, the ON-state resistance does not change due to the fixed size of the conductive filament. The OFF state resistance, in the worst case, is proportional to the device area since the leakage current is distributed over the entire area (Figure 4.3(b)). Therefore, the ON/OFF ratio in the worst case is inversely proportional to the cell area. Figure 4.3(c) plots the ON/OFF ratios as a function of the oxide thickness, with three different device areas. If 100x ON/OFF ratio is required for RRAM functionality, then the minimum oxide thicknesses for (10nm)2,

(100nm)2 and (1μm)2 devices are predicted to be 0.7 nm, 1.4 nm and 2 nm, respectively.

The thickness scaling limit of HfOx as a function of the device area is summarized in

Figure 4.3(d). The feasibility of 2-nm HfOx for large-area RRAM devices is confirmed and will be explored experimentally in the next section. In summary, the theoretical results predicted that the oxide thickness has significant scalability beyond the current practices in the experimental studies.

4.3 Experimental Demonstration of Ultra-Thin HfO2 Switching Layer

If the effective switching thickness is less than 2 nm, then the excess oxide thickness can either be removed completely, or be replaced by a layer of alternative materials, without losing the memory functionality. Thus, the feasibility of 2-nm HfOx switching layer is explored following these two scenarios (Figure 4.4).

Figure 4.4: Schematics of the two scenarios to achieve 2-nm HfOx switching layer: remove the excess oxide completely, or replace it with a layer of alternative materials.

Firstly, TiN/HfOx/Pt stacks with 2-nm HfOx were fabricated to form 1 μm x 1 μm cross-point RRAM devices [44]. 50-nm Pt was deposited as bottom electrode by e-beam

86 evaporation on SiO2/Si substrate. Then, HfOx was deposited by atomic layer deposition

(ALD) using TEMA-Hf as precursor at 200 °C. The thickness of HfOx is precisely controlled by the number of ALD cycles, confirmed by cross-sectional TEM analysis

(Figure 4.5(a)). Finally, 200-nm TiN was deposited by reactive sputtering and then was lifted-off.

We first investigated the scaling of forming voltages with the oxide thickness (tOX).

As shown in Figure 4.5(b), the forming voltages of HfOx with 2-10 nm thicknesses indicate a linear dependence on tOX. There is a finite intercept (~ 2.0 V) of the linear extrapolation at zero oxide thickness, which can be attributed to the Schottky barrier height (ΦB) between Pt and HfO2. This also explains why the TiN/HfOx/Pt devices usually exhibit larger forming voltages than TiN/HfOx/TiN devices with similar oxide

87 thickness [45,46]. This linear scaling behavior suggests that thickness scaling is one useful approach to achieve forming-free devices.

Figure 4.6: (a) DC sweep characteristics of the 2-nm and 5-nm HfOx RRAM devices in 10 DC cycles. (b) Resistance distributions of the 2-nm and 5-nm HfOx devices, obtained from (a). (c) Comparison of DC sweep characteristics of “2-nm AlOx + 2-nm

HfOx” and “2-nm TiOx + 2-nm HfOx” bilayer devices with the 5-nm HfOx. 20 DC cycles are plotted for each device. (d) Comparison of the resistance distributions of the bilayer devices wtih that of the single-layer (5nm-HfOx) device.

Figure 4.6(a) compares the DC sweep characteristics of a 2-nm and a 5-nm HfOx devices. Figure 4.6(b) summarizes their resistance distributions in 10 DC cycles. It is shown that the ON- and OFF-state resistance distributions are almost the same in the two cases. This observation suggests that the effective switching thicknesses are comparable in both cases, which is less than 2 nm. This is consistent with the estimation derived from pulse-train measurements of HfOx RRAM that the maximum gap thickness is less than 1 nm under similar operation conditions.

Next, the feasibility of ultra-thin switching layer is further verified by stacking 2- nm HfOx with a 2-nm layer of alternative oxide to make bi-layer devices. Here TiO2 and Al2O3 were chosen to stack with HfO2 due to the maturity of ALD growth processes.

AlOx was deposited by thermal ALD using Trimethylaluminum at 200 °C, and TiOx was deposited by ALD using TDMA-Ti at 200 °C. Figure 4.6(c) compares the DC characteristics and resistance distributions of bilayer devices with the single-layer (5- nm HfOx) device. The DC sweep curves of TiN/HfOx/Al2O3/Pt stack are very similar to that of 5-nm HfOx. The TiN/HfOx/TiO2/Pt stack has higher ON- and OFF-state resistances, but retains a similar memory window. The differences between Al2O3 and

TiO2 may be attributed to the fact that TiO2 thin layers are generally more conductive.

Thus, during the forming process no conductive filament is formed in TiO2 and the device exhibits higher resistance values due to the serial resistance of un-formed TiO2.

On the other hand, the as-grown Al2O3 has higher initial resistance and requires breakdown during the forming process. After forming, the Al2O3 layer remains conductive and does not affect ON-/OFF-state resistances.

These results confirm 2-nm HfOx is sufficient for memory functionality when the

2 device area is smaller than 1 (μm) . In addition, TiO2 layer can be considered as a potential selector to suppress the sneak-path currents in high-density RRAM arrays.

4.3 3D Integration of Ultra-Thin HfO2 Switching Layer

The feasibility of ultra-thin-oxide RRAM suggests a new way to improve the cost- efficiency and performance of 3D memory array. Consider the 3D VRRAM structure shown in Figure 4.7(a) [16], it consists of the horizontal metal-plane electrodes and vertical pillar electrodes. At their intersections, RRAM devices are formed by a metal- oxide layer sandwiched between the metals. The trench size is one of the critical aspects of the horizontal scaling of 3D VRRAM, similar to the case of 3D NAND flash [47].

The mathematical description for trench-size scaling is simply:

F = d + 2 tOX (4-1)

Where F is the trench size, d is the diameter of the vertical pillar electrode and tOX is the thickness of oxide switching layer. In previous studies, the diameter of metal pillars has been identified as a limiting factor for the scaling of 3D VRRAM [18-19].

This is because the small cross-sectional area of the metal pillar leads to large parasitic resistance and voltage drop along the interconnect lines, which degrades the memory window and causes access failures in a large 3D array. To cope with this limitation, a core-shell structure was purposed to achieve better horizontal scalability [19]. From

Equation (4-1), an alternative approach to extend VRRAM’s scaling limit can be derived, which is to use ultra-thin oxide for the switching layer. By doing so, the excess oxide thickness is traded for the benefits of larger electrode and smaller parasitic resistance. This approach is twice as effective as reducing the pillar diameter.

Figure 4.7: (a) Schematic of the device structure and the dimensional parameters of 3D vertical VRRAM. The trench size F is affected by both pillar diameter and tOX. (b)

Comparison of the maximum array sizes achieved by using 5nm, 3nm or 2nm HfOx as the switching layer, obtained by the SPICE simulations.

For a more quantitative view, the trench size of 15 nm is considered. In this case, a reduction of HfOx thickness from 5 nm to 2 nm leads to an increase of the pillar diameter from 5 nm to 11 nm, which reduces the parasitic resistance by more than 4.8 times. To demonstrate the advantages of this change, SPICE circuits were built for 32-layer 3D

VRRAM arrays to simulate the write access voltage (VDD = 3 V) [48]. The array size at which the access voltage drops below 1.8 V is defined as the maximum array size.

Figure 4.7(b) summarizes the simulation results, which shows that 2-nm HfOx significantly improves the array capacity at 15-nm trench size, making it comparable to the capacity of 5nm-HfOx at 20-nm trench size. In other words, 2-nm HfOx enabled the trench size of 3D VRRAM to scale down by one more technology node (from 20 nm to

15 nm).

To realize this capability, 3D vertical RRAM with 2-nm HfOx switching layer is demonstrated. Figure 4.8(a) shows the cross-sectional TEM image of the as-fabricated

VRRAM device. The switching layer is formed on the sidewall of the trench, which has a thickness of about 2 nm. Figure 4.8(b) shows the I-V characteristics of 100 DC cycles of the as-fabricated device. Figure 4.8(c) demonstrates 1000 cycles of pulse switching, using an incremental-step pulse program (ISPP) algorithm [49,50] to achieve the 100x

ON/OFF ratio predicted by simulations. Figure 4.8(d) shows the pulse-cycling

8 endurance of five 2-nm HfOx VRRAM devices which all reach 10 cycles, with an average ON/OFF ratio of 20. Figure 4.8(e) shows the results of temperature-accelerated retention test of the device. The retention time is defined as the time at which the

ON/OFF ratio falls below 10. The retention times measured at elevated temperature can be extrapolated to over 10 years at room temperature (Figure 4.8(f)).

The overall performances of 2-nm HfOx devices integrated into the 3D architecture are superior compared to planar devices. The improvement might be attributed to the smaller device area (13.9 nm × 1 μm vs. 1 μm × 1 μm) and reduced interface roughness due to the vertical configuration (since the roughness in the vertical direction can now be neglected). The promising device performances, together with the much-improved array capacity, suggest a promising solution towards high-density 3D vertical RRAM.

Figure 4.8. (a) Cross-sectional TEM image of the fabricated 3D VRRAM device with

2-nm HfOx as the switching layer. (b) DC sweep characteristics of the 2-nm HfOx VRRAM device. The compliance current of SET operation is 100 µA. The black solid line represents the average values of 100 DC cycles. (c) Pulse switching of the 2-nm

HfOx VRRAM device for 1000 cycles, achieved by an advanced pulse-verify scheme which expands the ON/OFF ratio to 100. (d) Pulse-cycling endurance of five 2-nm 8 HfOx VRRAM devices, measured up to 10 switching cycles. (e) Accelerated retention characteristics at elevated temperatures. (f) Retention times at elevated temperatures, which are defined as the time at which ON/OFF < 10 and obtained from (e). The retention times are extrapolated back to over 10 years at room temperature.

In summary, the combination of ultra-thin HfOx (~2 nm) switching layer and 3D vertical RRAM architecture is demonstrated as a promising strategy to achieve ultrahigh-density RRAM array. The theoretical scaling limit of HfOx thickness was

94 estimated for the first time using density functional theory within the non-equilibrium

Green’s function formalism. Based on the filamentary-switching mechanisms, the scaling limit is calculated as a function of the device area, and the feasibility of 2-nm

HfOx RRAM is predicted for large-area devices. This kind of scalability, according to array simulations, enabled the trench size of 3D vertical RRAM to scale down by one more technology node (from 20 nm to 15 nm). In order to verify the feasibility of the calculated scaling limit, planar devices with 2-nm HfOx directly sandwiched between electrodes were fabricated. Compared to the reference devices with thicker HfOx, the 2- nm HfOx devices exhibit similar DC characteristics, indicating the effective switching thickness is less than 2 nm. Moreover, the 2-nm HfOx layer was stacked with either

TiO2 or Al2O3 thin layers and still retained the memory functionality. Finally, the 2-nm

HfOx RRAM was integrated into 3D vertical geometry for the first time. The 3D ultra- thin devices demonstrated promising characteristics including ON/OFF ratio (~100), switching speed (~20 ns), endurance (108 cycles) and data retention (> 10 years), paving a way towards ultra-high-density 3D vertical RRAM array.

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Chapter 5 : Contributions and Outlook

5.1 Summary of Contributions

The key contributions of this thesis include three aspects:

(1) It advanced the theoretical understanding of the doping effects in the resistive

switching process of metal oxides, especially HfO2;

(2) It developed the pulse-train characterization technique to monitor the dynamic

switching process and to gain better control over filament evolution;

(3) It provided a first principles framework to estimate the scaling limit of

switching-layer thickness, and verified it by experimental demonstration of 2-

nm HfO2 devices.

Firstly, doping the resistive-switching layer is proposed as an important materials- engineering techniques to improve the variability, retention and power consumption of

RRAM. The effects of dopant types, dopant concentrations, oxide phases, and oxide stoichiometry on the electronic and thermodynamic properties of HfO2 are thoroughly investigated using ab initio modeling and simulations. The physical insights derived from the calculations provide guidelines to achieve desirable RRAM characteristics through doping. In particular, a long-standing dilemma regarding the doping effects on

104 the forming voltages of RRAM have been resolved by the identification of the stoichiometry of HfO2 as a critical factor.

Secondly, this thesis presents a systematic investigation on the pulse-train characterization techniques for the multi-level control and in-depth physical understanding of conductive filament evolution. The development of pulse-train technique is inspired by the spike-timing dependent plasticity in RRAM synaptic devices. By applying a pulse-train RESET scheme to a potential 3-bit HfO2 RRAM, the relative standard deviations of resistance levels are improved up to 80% compared to the single-pulse scheme. This improvement significantly boosts the storage capacity of an RRAM device. Moreover, the pulse-train characterization technique is used as a monitor of filament evolution. The observed exponential relation between the saturated resistance and the pulse amplitude provides evidence for the gap-formation model of the filament-rupture process.

Thirdly, this thesis demonstrates the feasibility of ultra-thin HfO2 RRAM, which can achieve the desirable properties of forming-free and low-power operations. An estimation method based on density functional theory and non-equilibrium Green’s function formalism is proposed for the thickness scaling limit of RRAM switching layer.

Using this method, the feasibility of 2-nm HfOx RRAM is predicted for large-area devices, and verified by fabricating both planar and 3D vertical RRAM devices. The 3D ultra-thin devices demonstrate promising characteristics including ON/OFF ratio (~100), switching speed (~20 ns), endurance (108 cycles) and data retention (> 10 years at room temperature).

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Overall, this thesis addresses the key challenges of RRAM technology from materials, device, characterization and architecture perspectives. It develops deeper physical understanding towards the doping effects, filament evolution and thickness scaling of the resistive switching process. It provides some useful techniques, such as pulse-train characterization and scaling-limit estimation methods, for the future development of RRAM technology. It also demonstrates RRAM’s ability to satisfiy some critical performance parameters, highlighting its potential towards high-density mass-storage applications.

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5.2 Future Plan

The techniques and physical understanding developed in this thesis act as the foundation for exciting future work from several aspects.

With respect to the doping technology for RRAM, further understanding of the dopants’ effects on SET and RESET operations is highly desired in addition to the forming process. On the modeling side, such explorations can be achieved within the framework proposed in this thesis, with further requirements for energy-barrier calculations for ion migration. By doing so, we can evaluate the trend of switching voltages and data retention with the addition of dopants. On the experimental side, it is suggested that fabrication processes should be developed to continuously control the stoichiometry of HfOx thin film. This way, the electronic bandgap and forming voltages of each stoichiometry can be characterized using optical and electrical measurements, which will provide the most solid evidence to support the theoretical results.

With respect to the pulse-train characterization techniques, its applications in neuromorphic computing systems can be further explored. For RRAM synaptic devices, a desirable property is the spike-timing-dependent plasticity (STDP). An STDP process adjusts the connection strength of synapse based on the relative timing of a pre- and post-synaptic neuron's spike. To mimic this process using an RRAM synapse, the relative timing can be converted to the number of identical pulses, and the resistance change induced by the pulse train corresponds to change of connection strengths. Thus, adjusting the pulse-train characteristics will result in varying STDP functions, which provide space for design optimization. There are many approaches to adjust the pulse-

107 train characteristics of RRAM. For example, doping techniques can be utilized which will change the migration barrier of oxygen vacancies, and consequently changes the pulse-train characteristics.

With respect to RRAM with ultra-thin switching layers, it is highly desired to have selector devices integrated with each cell in a large RRAM array. Otherwise, the sneak- path currents during array operations will cause severe power consumption and degradation of the memory window, limiting the maximum array size. The selector devices should have non-linear I-V characteristics to eliminate the sneak-path currents.

Although it has been shown in this thesis that stacking HfO2 with TiO2 can increase the non-linearity, it is still not enough for array applications of RRAM. The development of a promising selector technology is thus a very important research topic in the future.

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