UNDERSTANDING OF NIO-BASED UNIPOLAR RESISTIVE SWITCHING

FROM FIRST PRINCIPLE SIMULATIONS TO MACROSCOPIC MODELS

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

Hyung Dong Lee

March 2011

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/tz020gc7490

© 2011 by Hyung Dong Lee. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii

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

Philip Wong, Co-Adviser

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

Paul McIntyre

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost 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 inUniversity Archives.

iii

iv

ABSTRACT

As NAND Flash memory technology is facing challenging issues such as

electronic coupling between adjacent cells and high coupling of the control gate with

floating gate in scaling down to and beyond 16nm technology node, new functional

devices or materials has been explored to continue consecutive development of

memory technology beyond 16nm technology node. One of the new emerging non-

volatile memories is resistance change random access memory(ReRAM) possibly

meeting the requirements to replace NAND Flash; i.e., low cost, simple structure,

promising 8nm technology node, low power dissipation, high endurance, possible

integration in crossbar arrays in 3D on top of silicon base CMOS ICs.

In ReRAM, understanding the switching mechanism was very complicated

because there have been many different phenomena co-existing under circumstances

when ultimate electrical stress is applied. One of them, oxidation/reduction of

transition metals is generally accepted to results in the unipolar switching. In this

switching mode, both thermal and chemical processes are associated with the effect of

electric field. For clearer understanding of mechanism of the unipolar switching,

defect states in NiO are investigated, which is closely related to electrical conductivity

of the transition metal-based resistive switching materials. Study on feasible "ON" and

"OFF" states in atomic scale gave an insight into atomic structure of conductive

filament, role of oxygen (or oxygen vacancies) and its migration. With these first

v

principle modeling results, a quantitative model for reset/retention and filament

formation was proposed. Experimental results for reduction of reset current and long

retention time of RON by inserting interfacial layer between a metal electrode and

resistive switching material can be explained based on the quantitative model.

vi

ACKNOWLEDGMENTS

I am very happy and relieved that I am having people during my PhD program,

looking back on the past five years. They are all my sincere friends, valuable

colleagues, and highly distinctive advisers that I am respectful. Professor Yoshio Nishi

is, first and foremost, my adviser that I am extremely grateful to for his help and

excellent advice on my life at Stanford as well as memory research. His advice and

encouragement showed me solvable paths to many problems I confronted at the aspect

of both research and life. I would like to thank Professor Philip Wong and Professor

Paul McIntyre for their valuable advice on my thesis, arising form their insight, and

for giving me more opportunities to consider my works to the end. I would also like to

thank Professor Mark Brongersma for serving on a chair of my oral examination

committee.

I deeply thank Dr. Blanka Magyari-Köpe and Seong-Geon Park for their constructive

collaboration and discussions from the beginning of my simulation works. I also thank

Dr. James McVittie, Dr. Peter Griffin, and Mihir Tendulkar for their advice and effort

to assist other researchers' experiments. I would like thank all Nishi group members

and my fellows at KCF for discussions about research and life and making my

Stanford life durable.

Special thanks to my wife, Jeong-Hye Choi, and my son, Hanjoo, for showing me

consistent support and amazing experiences with happiness. She has been really wise,

strong and pure than I expected. I would like to thank my parents and parents-in-law

for having been my advisers and supporters ever.

vii

TABLE OF CONTENTS

List of Tables ....................................................................................................................... x

List of Figures .................................................................................................................... xi

Chapter 1: Introduction ....................................................................................................... 1

1.1 ReRAM as Next Generation Nonvolatile Memory ................................................. 1

1.2 Fundamental Switching Mechanism for Unipolar ReRAM .................................... 3

1.2.1 NiO-based Unipolar Resistive Switching ...................................................... 3

1.2.2 Microstructure of Conductive Filament in NiO ............................................. 8

References ................................................................................................................... 11

Chapter 2: First Principle Simulations for NiO-based Resistive Switching Memory....... 14

2.1 Computational Method .......................................................................................... 14

2.1.1 Feasibility of SGGA+U method for NiO ..................................................... 16

2.2 Vacancy Defects in NiO ........................................................................................ 18

2.2.1 Single Cation and Anion Charged Vacancy ................................................. 18

2.2.2 Stability of Charged Vacancies through Formation Energy ........................ 21

2.2.3 More Feasible formation of Anion Vacancies in NiO ................................. 23

2.3 Proposed Mechanism for Filament Formation/Rupture ........................................ 26

2.3.1 Filament Formation Driven by Electric Field .............................................. 27

2.3.2 Filament Rupture Driven by Migration of Oxygen ...................................... 28

2.3.3 Experimental Evidences for Filament Formation/Rupture Model ............... 29

2.4 Metallic Conduction through Oxygen Vacancies ................................................. 31

2.4.1 Strong Interaction and Ordering of Vacancies in NiO ................................. 32

2.4.2 Redistribution of Electrons around Ni Atom ............................................... 33

2.4.3 Contribution of Metal Atom Chain to Conductivity at Room

Temperature .................................................................................................... 35

2.5 Feasible Atomic Structure for "ON" and "OFF" States ........................................ 37

2.5.1 Suggested Atomic Structure of "ON" State ................................................. 37

viii

2.5.2 Suggested Atomic Structure of "OFF" State ................................................ 38

2.6 Conclusion ............................................................................................................. 42

References ................................................................................................................... 43

Chapter 3: Macroscopic Model for Reset/Retention and Filament Formation ................. 46

3.1 Reset/Retention Model .......................................................................................... 46

3.1.1 Physical Process of "Reset" .......................................................................... 47

3.1.2 Evaluation of Radius of "ON" and "OFF" States ......................................... 50

3.1.3 Retention Time ............................................................................................. 53

3.1.4 "Reset" Transition Time ............................................................................... 55

3.2 Filament Formation Model .................................................................................... 57

3.2.1 Physical Process of Filament Formation ...................................................... 58

3.2.2 Effect of Field Confinement on Filament Formation ................................... 62

3.2.3 Effect of Diffusivity of Interfacial Layer on Filament Formation ............... 64

3.3 Conclusion ............................................................................................................. 67

References ................................................................................................................... 67

Chapter 4: Experimental Switching Behaviors of NiO-based Unipolar ReRAM ............. 70

4.1 Formation of Small Size of Filament through Bonding of Ni and O at

Interfactial Layer ................................................................................................... 70

4.1.1 Switching Characteristics of Pt/NiO/Pt and Pt/Ni/NiO/Pt Structures .......... 72

4.1.2 Role of Interfacial Layer .............................................................................. 75

4.2 Qualitative Filament Formation Model ................................................................. 78

4.2.1 For Pt/NiO/Pt Structure ................................................................................ 78

4.2.2 For Pt/Ni/NiO/Pt Structure ........................................................................... 79

4.3 Conclusion ............................................................................................................. 81

References ................................................................................................................... 82

Chapter 5: Experimental Retention Behaviors of NiO-based Unipolar ReRAM ............. 84

5.1 Procedure of Retention Experiment ...................................................................... 84

5.2 Retention Time ...................................................................................................... 86

5.2.1 Retention Proferty of RON ............................................................................ 87

5.2.2 Activation Energy for Retention of Ni/NiO structure .................................. 88

ix

5.2.3 Retention Time according to "ON" Resistance ............................................ 89

5.3 Conclusion ............................................................................................................. 91

Chapter 6: Conclusions and Future Works ....................................................................... 92

6.1 Conclusions ........................................................................................................... 92

6.2 Future Works ......................................................................................................... 93

6.2.1 Role of Oxygen or Metal Impurity at the Interface between Metal and

Resistive Material ............................................................................................ 94

6.2.2 Addition of Thermal Effect to Filament Formation Model .......................... 94

6.2.3 Consideration of Variable Charge State of Oxygen Vacancies in

Filament Formation Model .............................................................................. 95

x

LIST OF TABLES

Number Page

Table 2-1: Physical parameters from experiments and calculations ................................. 16

Table 2-2: Feasibility of migration of oxygen vacancies in NiO ...................................... 24

Table 2-3: Direction from oxygen vacancy to oxygen and number of 1NN oxygen

vacancies in three “off” states ........................................................................ 39

xi

LIST OF FIGURES

Number Page

Figure 1-1: Schematic of (a) flash unit cell and (b) NAND flash array ......................... 1

Figure 1-2: P-BiCS (Pipe-shaped Bit Cost Scalable) for 3 dimensional stacked

NAND flash memory array ....................................................................... 2

Figure 1-3: Schematic of (a) unipolar switching and (b) bipolar switching .................... 4

Figure 1-4: Illustration of filamentary unipolar resistive switching at anode side ........... 5

Figure 1-5: Illustration of filamentary unipolar resistive switching at anode side ........... 5

Figure 1-6: Ratio of ROFF to RON as cell size decreases ................................................... 6

Figure 1-7: XRD for NiO film deposited by reactive sputtering at PO2 of 4% ................ 7

Figure 1-8: CAFM image (a) at high resistance state and (b) low resistance state .......... 7

Figure 1-9: Schematic for (a) oxygen migration and (b) formation of oxygen

vacancy-rich or nickel-rich region (metallic filament)...................................... 9

Figure 1-10: Schematic for microstructure of conductive filament, composed of

(a) interstitial nickel precipitation and (b) chain of metallic nickel

defects .............................................................................................................. 10

Figure 1-11: Effect of thermal energy on “on” resistances ............................................... 10

Figure 2-1: (a) Unit cell of NiO in simple-cubic NaCl structure and (b) Supercell

of Ni64O64 used in the calculation for both mono- and multi- oxygen

vacancy studies ................................................................................................ 15

Figure 2-2: Partial density of states (PDOS) of NiO unit cell, composed of Ni 3d

orbital and O 2p orbital ................................................................................... 17

Figure 2-3: Illustration of t2g and eg orbital in NiO 3d orbitals ...................................... 17

Figure 2-4: Partial DOS of nickel vacancies according to charge state ......................... 19

Figure 2-5: Partial DOS of oxygen vacancies according to charge state ....................... 19

Figure 2-6: Energy band diagram of nickel vacancies according to charge state .......... 20

Figure 2-7: Energy band diagram of oxygen vacancies according to charge state ........ 21

xii

Figure 2-8: Formation energy of nickel vacancies according to charge state ................ 22

Figure 2-9: Formation energy of oxygen vacancies according to charge state .............. 23

Figure 2-10: Formation mechanism in a microscopic view ........................................... 27

Figure 2-11: State of formation of metallic filament in NiO ......................................... 27

Figure 2-12: Rupture mechanism in a microscopic view ............................................... 28

Figure 2-13: State of rupture of metallic filament in NiO .............................................. 29

Figure 2-14: X-ray photoelectron spectroscopy showing neutral nickel defect

peak ................................................................................................................. 29

Figure 2-15: Secondary Ion Mass Spectroscopy showing migration of oxygen ............ 30

Figure 2-16: Supercell showing oxygen vacancies and metallic nickel chain ............... 31

Figure 2-17: Interaction energy between oxygen vacancies in NiO .............................. 32

Figure 2-18: (001) plane in simple cubic coordinate having metallic chain in

<110> .............................................................................................................. 33

Figure 2-19: Schematic illustrating Bader Charge Analysis .......................................... 33

Figure 2-20: Electronic charge of each nickel atom in a filament. Dotted circle

refers to oxygen vacancy site .......................................................................... 34

Figure 2-21: Total density of states for the supercell with a filament ............................ 35

Figure 2-22: (a) Partial charge density within EF ~ EF + 0.3 eV in (001) plane

including oxygen vacancies and Ni metal chain and (b)-(d) partial

density of states of d orbitals at each Ni atom. Dotted square in (a)

refers to Ni site ................................................................................................ 36

Figure 2-23: Atomic structure representing one of possible “on” states ........................ 37

Figure 2-24: Partial charge density for “on” structure with energy from EF – 0.45

eV to EF + 0.3 eV ............................................................................................. 38

Figure 2-25: Three different atomic structures for “off” state ....................................... 39

Figure 2-26: Total density of states for “off” structure with the exchanged

oxygen at “d” ................................................................................................... 40

Figure 2-27: Total density of states for “off” structure with the exchanged

oxygen at (a) “a” and (b) “b” .......................................................................... 41

xiii

Figure 2-28: Partial charge density for “off” structure with the exchanged

oxygen at “a”. Energy ranges from EF – 0.46 eV to EF + 0.44 eV .................. 41

Figure 3-1: Schematic picture for reset process ............................................................. 48

Figure 3-2: Reset process through the diffusion of oxygen ........................................... 48

Figure 3-3: Calculated radius of initial “on” resistances ................................................ 52

Figure 3-4: Calculated radius of increased resistances .................................................. 52

Figure 3-5: Evaluated activation energy for retention from “reset” model .................... 54

Figure 3-6: Extracted retention time at 85oC from “reset” model .................................. 55

Figure 3-7: Influence of activation energy for retention on retention time .................... 55

Figure 3-8: Calculation procedure of “off” transition time ............................................ 56

Figure 3-9: Calculated “off” transition time from “reset” model ................................... 56

Figure 3-10: Mesh structure used in filament formation model ..................................... 59

Figure 3-11: Calculation procedure of filament formation ............................................ 60

Figure 3-12: Illustration of one dominant filament formation at “on” state .................. 61

Figure 3-13: Illustration of one dominant filament formation at “on” state .................. 62

Figure 3-14: Effect of electric field confinement on filament growth ........................... 63

Figure 3-15: Effect of diffusivity of interfacial layer on filament growth ..................... 64

Figure 3-16: Concentration of oxygen vacancy at X = 120 in figure 3-15 .................... 65

Figure 3-17: Concentration of oxygen vacancy at Y = 30 in figure 3-15 ...................... 66

Figure 4-1: Schematic picture of (a) Pt/NiO/Pt and (b) Pt/Ni/NiO/Pt structures ........... 72

Figure 4-2: Switching characteristics for Pt/NiO/Pt structure ....................................... 73

Figure 4-3: Switching characteristics for Pt/Ni/NiO/Pt structure .................................. 73

Figure 4-4: Cyclic endurance for Pt/NiO/Pt structure .................................................... 74

Figure 4-5: Cyclic endurance for Pt/Ni/NiO/Pt structure ............................................... 75

Figure 4-6: Reset transition (I-V) curves for (a) Pt/NiO/Pt and (b) Pt/Ni/NiO/Pt ......... 75

Figure 4-7: Current vs Voltage for pristine Pt/NiO/Pt and Pt/Ni/NiO/Pt

structures ......................................................................................................... 76

Figure 4-8: Forming voltage for Pt/Ni/NiO/Pt structure ................................................ 77

Figure 4-9: The model for formation of metallic filament for Pt/NiO/Pt structure ....... 79

xiv

Figure 4-10: The model for formation of metallic filament for Pt/Ni/NiO/Pt

structure ........................................................................................................... 80

Figure 4-11: The model for formation of metallic filament for Pt/Ni/NiO/Pt

structure. Positive bias is applied to bottom electrode. ................................... 81

Figure 5-1: Procedure of retention experiment .............................................................. 85

Figure 5-2: Cumulative percentage of RON with annealing temperature at (a)

220oC, (b) 250

oC, (c) 270

oC, and (d) 300

oC for f = 90% ................................ 86

Figure 5-3: Cumulative percentage of RON with annealing at 270oC ............................. 87

Figure 5-4: Variation of “on” resistances with annealing time at temperature

range from 85oC to 300

oC for extraction of retention time ............................. 88

Figure 5-5: Activation energy for retention for Ni/NiO structure .................................. 89

Figure 5-6: Retention time vs RON (relation of retention time with radius of RON) ....... 90

1

CHAPTER 1

Introduction

1.1 ReRAM as Next-Generation Nonvolatile Memory

Since the realization of memory devices, increasing memory capacity in every 2

years has been significantly contributing to our lives with a variety of information

availability as well as storing more data for a longer time at decreasing cost per bit.

Out of both volatile and non-volatile memory ICs, NAND flash memory has become a

technology driver which leads both transistor technology and memory technology by

scaling down critical dimension continuously.[1]

However, NAND flash is now facing challenging issues in further scaling down

to and beyond 16nm technology node. Some of the issues are shown in Fig. 1-1; high

capacitive coupling of the control gate with floating gate in Fig. 1-1(a) and coupling

of adjacent cells as shown in Fig. 1-1(b). Requirement for the minimum number of 16

electrons for a single level cell, i.e., 1bit/cell also limits the pursuit of simple 2

dimensional scaling down.[1]

Figure 1-1 Schematic of (a) flash unit cell and (b) NAND flash array

(a) (b)

2

Much effort to resolve the problems in the development of NAND flash memory

has been made by replacing floating gate with charge trapping layer and recently

suggested new structure called P-BiCS (Pipe-shaped Bit Cost Scalable) as one of the

major candidates for 3 dimensionally stacked NAND flash memories.[2] The P-BiCS

with U-shaped string can improve memory cell properties by reshaping NAND string

in the BiCS with I-shaped string; (i) quality of tunnel insulating film on the side wall

of the through-hole by removing a fabrication process necessary to etch tunnel oxide

at the bottom of the through-hole and (ii) improved selection transistor and the source

line used at read/write operation because they can be placed at the top of the string

avoiding high temperature process for fabrication of the string. But, P-BiCS

technology would create difficult problems due to a number of layers (more than 16

layers) for charge trapping in very small area of 20nm [2].

Figure 1-2 P-BiCS (Pipe-shaped Bit Cost Scalable) for 3 dimensional stacked

NAND flash memory

3

To continue the development of nonvolatile memory beyond 16nm technology

node, research for new functional device and material should be conducted. New

emerging nonvolatile memories must satisfy following requirements to replace NAND

flash memory; simple structure, low cost, scalability down to 8nm technology node,

low power consumption, high write/erase endurance, and possible integration in

crossbar arrays in 3D. One of the emerging nonvolatile memories, resistance change

random access memory (ReRAM) is expected to meet the above requirements.

1.2 Fundamental Switching Mechanism for Unipolar ReRAM

Resistance change random access memory (ReRAM) based on transition metal

oxides (TMO) such as NiO, TiO2 had been extensively investigated as a candidate for

the next generation of nonvolatile memory devices, due to their simplicity in

composition and scaling capability in the future [3,4]. Even though the switching

phenomena have been experimentally observed in various materials, the fundamental

understanding of the switching mechanism and its physical origin is still lacking. It is

widely accepted, that the so called “filament model” gives a qualitative explanation

for the unipolar switching in NiO ReRAM, i.e. a conductive path, called filament, is

formed and ruptured by the applied electrical stress and this process performs

repeatedly.[5]

1.2.1 NiO-based Unipolar Resistive Switching

NiO material has shown mostly unipolar resistive switching property rather than

4

bipolar switching. In some cases where nickel is used as an electrode and NiO layer is

grown by thermal oxidation, bipolar resistive switching [6] could be observed.

Scheme of unipolar switching means “on” and “off” states can be set by using only

one polarity of programming voltage, while transition between “on” and “off” states

in bipolar switching needs the reversal of applied voltage as shown in Fig. 1-3 [7].

Even though the NiO-based ReRAM devices have issues such as high power

consumption due to high “reset” current than “set” current [8], wide distribution of

operational voltage, and the likely needs of forming process, the unipolar switching

characteristics has still attracted strong interest from design community due to the

ease of circuit design with 3-dimensional integration and availability of well-

established circuitries for various applications.

Figure 1-3 Schematic of (a) unipolar switching and (b) bipolar switching

Out of many proposed models to date to explain the unipolar switching

phenomena, one of the phenomenological models, the “filament model” in Fig. 1-4

gives qualitative explanation well for the unipolar switching characteristics of NiO-

based ReRAM [9].

(a) (b)

5

Figure 1-4 Illustration of filamentary unipolar resistive switching at anode side

Even though contradictory experimental results about the cathode/anode

localized switching [10,11] have been reported in NiO, all the considerations below

are based on the results of reference [12] favoring anode interface localized switching

because many clues from both experiments and simulations could be merged with the

anode interface localized switching. Measurement result through conductive atomic

force microscopy (C-AFM) in Fig. 1-5 has supported a localized switching model in

the unipolar resistive switching with tens of nanometers in diameter of conductive

filament at “on” state ( for a few hundred ) [13].

Figure 1-5 Illustration of filamentary unipolar resistive switching at anode side

6

As cell or electrode size decreases, resistance ratio of high resistance state (HRS)

to low resistance state (LRS) has been increased as shown in Fig. 1-6 [14]. HRS

increases in inverse proportion to cell area implying that conduction at HRS does not

occur along the localized path, while LRS does not increase with the same ratio

indicating that conductive path/filament is formed within the bulk, and the area of the

conductive path/filament is almost independent of the cell size.

Cell Size (mm)

Off/O

n R

ation

108

107

106

105

104

103

102

101

100M

10M

1M

100K

10K

1K

100

10

Res

ista

nce

(

)

Figure 1-6 ROFF to RON as cell size decreases for (a) CuS and (b) NiO.

Grain boundary in polycrystalline phase may affect resistive switching. NiO

(a)

(b)

7

layers as reported in literatures [3,16] are deposited in polycrystalline state by reactive

sputtering at PO2 of ~4% (Fig. 1-7). Even though Fig. 1-8 shows a little different result

compared to that in Fig. 1-5 because mercury (Hg) was used as a top electrode for

electrical switching test and removed before C-AFM measurement, the conductive

paths at “off” state are in the grain boundary region. Conductive paths at “on” state are

observed in both grain and grain boundary regions [15].

20 30 40 50 60 70-1000

0

1000

2000

3000

4000

5000

6000

7000

8000

NiO : 43.287o (012)

NiO : 62.854o (110)

62.914o (104)

NiO : 43.287o (012)

Pt : 46.243o (200)

Ni : 51.844o (200)

Inte

nsity [

arb

.]

2 theta [o]

NiO10nm/BE

NiO20nm/BE

NiO40nm/BE

BE(Pt80nm/Ti20nm)

Ni : 44.505o (111)

Pt : 39.763o (111) / Ti : 40.170

o (111)

Figure 1-7 XRD for NiO film deposited by reactive sputtering at PO2 of 4%

Figure 1-8 CAFM image (a) at high resistance state and (b) low resistance state

8

It has been generally accepted that conductive filament or path may be formed in

oxygen vacancy-rich region in transition metal-based ReRAM. Thus, the bright spots

in Fig. 1-8 can represent oxygen vacancy-rich region at the surface. At the transition

from “on” state to “off” state, oxygen vacancy could migrate from grain to grain

boundary at the surface by thermal energy due to the Joule heating taking place by the

“on” state current until it decreases as the filament decreases.

1.2.2 Microstructure of Conductive Filament in NiO

“Filament model” could explain unipolar switching in that a conductive path

called filament is formed and ruptured by the applied electrical stress repeatedly [5].

Nevertheless, the microscopic understanding of the filament is still in question.

In the past years different models were proposed for the filament formation

[16,17,18]. It has been suggested that the metallic Ni defects in NiO film may be

responsible for the filament channel [19], and that the metallic defects are due to

injected metal ions from anode to the insulator [16]. “On” and “off” states were

interpreted as charging and discharging electronic states due to metallic defects [3,16].

However, there are additional experimentally observed facts associated with the

switching, i.e. oxygen migration [20], oxygen atoms in Pt anodic electrode after

forming process [13], metallic nickel defects in NiO [ 21 ], thermal energy

considerations [17,22], crystal disorder, electrode interface effects [23,24,25,26], etc.

Also, it has been shown that defects in TMO may change conductivity drastically [27].

Concentration or distribution of vacancy defects may vary during the “on” and “off”

transitions due to atomic migration.

9

Figure 1-9 Schematic for (a) oxygen migration and (b) formation of oxygen

vacancy-rich or nickel-rich region (metallic filament)

Furthermore, atomistic mechanism for the filament has been recently proposed

by Lee et al [12] in which, a model for formation/rupture of metallic filament and role

of oxygen vacancies for switching were investigated. As shown in Fig. I-9, negatively

charged oxygen atoms will be attracted to anode side during forming process, and

local heat generated by high current density may make it possible the migration of

oxygen into metal electrode, forming oxygen vacancy-rich region or nickel-rich

region. In case of TiO2, it is widely accepted that the oxygen reaching the anode

electrode often lift the electrode due to formation of oxygen molecule by neutralized

oxygen at the anode.

Shape or growth direction of conductive filament can be modeled in different

ways depending on assumptions to the microstructure. If metallic filament is formed

O2-

VO2+

Oxygen migration

during forming process

Vo-rich = Ni-rich,

more probability

in formation of metallic filament

(a)

(b)

10

by the precipitation of nickel atoms in oxygen vacancy-rich region, it starts to grow

from anode side to cathode side. However, if filament can be formed in a chain of

metallic nickel atoms as demonstrated in theoretical calculation, filament grows from

cathode side to anode side having anode interface localized switching, consistent with

filament shape of the unipolar TiO2 TEM results [28].

Figure 1-10 Schematic for microstructure of conductive filament, composed of (a)

interstitial nickel precipitation and (b) chain of metallic nickel defects

@270oC

101

102

103

104

105

106

50

100

Cu

mu

lati

ve

Pe

rce

nta

ge

[%

]

Resistance []

0 sec

2 min

10 min

30 min

60 min

Figure 1-11 Effect of thermal energy on “on” resistances

Ni

Vo

(a)

(b)

11

Figure 1-11 shows the effect of thermal energy on low resistance state. When

more thermal energy is applied to “on” state, more number of cells changes toward

high resistance state, that is, oxidation of conductive filament through the diffusion of

oxygen atoms under the above discussions.

References

[1] Future Memory Devices, Emerging Research Devices (ERD), ITRS 2010

[2] R. Katsumata, M. Kito, Y. Fukuzumi, M. Kido, H. Tanaka, Y. Komori, M. Ishiduki,

J. Matsunami, T. Fujiwara, Y. Nagata, L. Zhang, Y. Iwata, R. Kirisawa, H. Aochi, A.

Nitayama, VLSI 7-1 136 (2009)

[3] S. Seo, M. J. Lee, D. H. Seo, E. J. Jeoung, D.-S. Suh, Y. S. Joung, I. K. Yoo, I. R.

Hwang, S. H. Kim, I. S. Byun, J.-S. Kim, J. S. Choi, and B. H. Park, Appl. Phys. Lett.

85, 5655 (2004)

[4] C. Rohde, B. J. Choi, D. S. Jeong, S. Choi, J.-S. Zhao, and C. S. Hwang, Appl.

Phys. Lett. 86, 262907 (2005)

[5] B. J. Choi, D. S. Jeong, S. K. Kim, C. Rohde, S. Choi, J. H. Oh, J. J. Kim, C. S.

Hwang, K. Szot, R. Waser, and B. Reichenberg J. Appl. Phys. 98, 033715 (2005)

[6] L. Goux, J. G. Lisoni, D. J. Wouters, L. Courtade, and Ch. Muller J. Appl. Phys.

107, 024512 (2010)

[7] R. Waser, and M. Aono Nature Mat. 6 833 (2007)

[8] K. Kinoshita, K. Tsunoda, Y. Sato, H. Noshiro, S. Yagaki, M. Aoki, and Y.

Sugiyama Appl. Phys. Lett. 93, 033506 (2008)

12

[9] B. J. Choi, D. S. Jeong, S. K. Kim, C. Rohde, S. Choi, J. H. Oh, J. J. Kim, C. S.

Hwang, K. Szot, R. Waser, and B. Reichenberg J. Appl. Phys. 98, 033715 (2005)

[10] K. Kinoshita, T. Tamura, M. Aoki, Y. Sugiyama, and H. Tanaka. Appl. Phys. Lett.

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Kim, C. J. Kim, D. H. Seo, J-B. Park, J-H. Lee, X-S. Li, and Y. Park Nano Lett. 9(4),

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K. Yoo, J. H. Lee, S. J. Chung, Y. H. Kim, C. S. Lee, K. N. Choi, and K. S. Chung J.

Appl. Phys. 103, 013706 (2008)

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13

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(2007)

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14

CHAPTER 2

First Principle Simulations for NiO-Based Resistive Switching

Memory

A model for the filament formation and rupture based on the first principle

calculations using the density functional theory (DFT) is discussed in this chapter. We

consider several charged cation and anion vacancy defects, and determine their

stability as a function of Fermi energy. Then, we assess the structural and electronic

implications of a filament composed of oxygen vacancy chains. Feasible atomic

structure for “OFF” state as well as for “ON” state is proposed giving an insight into

atomic structure of conductive filament and the role of oxygen vacancies in resistive

switching.

2.1 Computational Method

The electronic structure calculations were performed using the Vienna Ab Initio

Simulation Package (VASP) code [ 1 ]. The projector-augmented-wave (PAW)

pseudopotentials [2,3] are used for nickel and oxygen with valence configurations of

3d84s

2 and 2s

22p

4, respectively. Spin-polarized generalized gradient approximations

(SGGA) in conjunction with the Hubbard-type on-site Coulomb corrections has been

found to describe accurately NiO by taking into account the strong electronic

correlations between 3d electrons [4]. U=6.3 and J=1 were used to describe the on-site

interactions within the rotationally invariant SGGA+U method [5]. The obtained bulk

15

properties for NiO are in very good agreement with experiments, i.e. lattice constant

4.21 Å (4.19) [6,7], bulk modulus 188.55 GPa (205) [7], energy gap 3.256 eV (4)

[7,8], and magnetic moment 1.671 μB (1.64) [8,9], the values in parenthesis are

experimental.

A supercell containing 128 atoms, Ni64O64 was used for both single vacancy and

multi vacancy studies as shown in Fig. 2-1(b) rather than rock salt structure as in Fig.

2-1(a) to use the reduced number of atoms in calculations. Electronic wave functions

were expanded with a plane wave energy cutoff of 500eV. K-points in Brillouin zone

is sampled with a 2x2x2 k-points by the Monkhorst-Pack scheme. All atoms were

relaxed using conjugated gradient method until Hellmann-Feynmann forces on each

atom are reduced to 0.05eV/Å .

Figure 2-1 (a) Unit cell of NiO in simple-cubic NaCl structure and (b) Supercell

of Ni64O64 used in the calculation for both mono- and multi- oxygen vacancy

studies

16

2.1.1 Feasibility of SGGA+U method for NiO

In the development of theoretical calculations based on density functional theory,

LDA had underestimated the energy band gap for strongly correlated materials

affected by the on-site Coulomb interactions between 3d electrons. Good

approximation for exchange and correlation effect between 3d electrons in transition

metals like Ni has been successfully performed employing on-site Coulomb

corrections with Spin Polarization Generalized Gradient Approximation (SGGA+U)

method. Although empirical parameters are necessary for valid description of physical

properties of NiO, the obtained values from SGGA+U method best describes physical

properties of NiO such as lattice constant, bulk modulus, magnetic moment, and

energy band gap.(Table 2-1)

Paper

Property

Exch-correlation Supercell Methodao

(A)

Bo

(GPa)

M

(μB)

Minimum

Eg

(eV)

Optical

Eg

(eV)

PRB 77, 134103

(2008)4.19 189 1.67 2.96 3.53

SGGA+U

U=6.3, J=12x2x2 Ni32O32 VASP

PRB 57, 1505

(1998)4.19 182 3.0

LSDA+U

U=6.3, J=0.95VASP

PRB 69, 075413

(2004)

4.07 236 1.64 3.1LSDA+U

U=6.3, J=1VASP

4.2 202.5 1.72 3.2SGGA+U

U=6.3, J=1VASP

My work 4.212 188.55 1.671 3.256(?)SGGA+U

U=6.3, J=1Cell Ni2O2 VASP

My work 4.0581 182.52 1.637 2.995LSDA+U

U=6.3, J=1Cell Ni2O2 VASP

PRB 27, 6964

(1983)

Experiment

4.17

PRB 57

205

PRB 571.9

(3.7 -- 4.3)

4.2

PRB 57

Table 2-1 physical parameters from experiments and calculations

17

The calculated partial density of states (PDOS), composed of Ni 3d orbital and O

2p orbital, is shown in Fig. 2-2. Conduction band minimum (CBM) is composed of Ni

3d orbital (eg orbital) and valence band maximum (VBM) of the mixture of Ni 3d

orbital (t2g orbital) and O 2p orbital as illustrated in Fig. 2-2 and 2-3. This result

indicates that NiO has both Mott insulator property and charge transfer insulator

property.

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

-6

-4

-2

0

2

4

6

PD

OS

[#

of

sta

tes

/eV

ce

ll]

Energy [eV]

Ni(d) +

Ni(d) -

O(p) +

O(p) -

Partial DOS- Ni(d), O(p) (SGGA+U)

U(Ni) = 6.3eV

U(O) = No

Lichtenstein :Rotationally Invariant

MAGMOM = 1 -1 0 0

Ni(t2g)+O(p) Ni(eg)

Figure 2-2 Partial density of states (PDOS) of NiO unit cell, composed of Ni 3d

orbital and O 2p orbital

Figure 2-3 Illustration of t2g and eg orbital in NiO 3d orbitals

18

2.2 Vacancy Defects in NiO

The conductivity of transition metal oxides can vary enormously according to

vacancy defects‟ concentration and their distribution inside of bulk. The resistivity of

stoichiometric NiO showed ~1013

cm• [10,11] and it could be lowered even to ~1

cm• in non-stoichiometric NiO or NiO with addition of Li atoms [12,13]. Defects

generated from the formation of vacancies or addition of Li atoms may play a role like

acceptors in p-type NiO giving rise to smaller bulk resistivity [12,13]. However, the

vacancy defects may form donor-like or acceptor-like states depending on the type of

vacancies and their levels in energy band gap; cation vacancies or anion vacancies. In

other words, bulk conduction property can change towards more insulating or more

conducting property even through the same reaction process like oxidation depending

on p-type or n-type bulk properties.

2.2.1 Single Cation and Anion Charged Vacancy

Partial density of states (PDOS) of nickel 3d and oxygen 2p orbital of relaxed

NiO supercell with single cation or anion vacancy is shown as a function of the charge

state of the vacancy in Fig. 2-4 and 2-5. The states at the valence band maximum

(VBM) are composed of the mixture of nickel 3d and oxygen 2p orbital and states at

the conduction band minimum (CBM) are of only nickel 3d orbital in the same

electronic structure as for bulk NiO.

The band gap of those supercells containing cation or anion vacancy changes due

19

to the strong Coulomb potential between 3d electrons in Ni although VBM and CBM

have more O 2p orbital property and Ni 3d orbital property, respectively. The

interaction energy also changes the energy levels of VBM and CBM according to

charge state of vacancies.

-30

0

30

q = -1

PD

OS

[#

of

sta

tes

/eV

ce

ll]

q = -2

-30

0

30

-4 -2 0 2 4

-30

0

30

Ni(3d)

- - - - O(2p)

Energy [eV]

q = 0

Figure 2-4 Partial DOS of nickel vacancies according to charge state

-30

0

30

q = +2

q = +1

Ni(3d)

- - - - O(2p)

q = 0

-30

0

30

PD

OS

[#

of

sta

tes

/eV

ce

ll]

-4 -2 0 2 4

-30

0

30

Energy [eV]

Figure 2-5 Partial DOS of oxygen vacancies according to charge state

20

Energy-band diagram can be made by aligning VBMs of cells for all different

charge states of vacancies as shown in Fig. 2-6 and 2-7. The energy-band diagram

shows the position of several defect states in the band gap. Defect states in solid

symbols refer to the occupied states and states in open symbols to the empty states.

Energy level of zero represents VBM and the horizontal mark refers to the CBM. The

energy-band gap depends on the charge state of anion/cation vacancies suggesting that

electrons in the conduction band or holes in the valence band may experience more

scattering in nonstoichiometric transition metal oxide. For cation vacancy, the band

gap varies from 3.14eV to 3.41eV according to charge state of -2 to 0 within a range

of -3.5%, 0.1%, and 4.7% from bulk respectively. For anion vacancy, the band gap has

a range of 12.4%, 9%, and 4.7% from bulk with charge state of 0 to 2.

-2 -1 00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5(3.38)

Eg (3.41)Eg (3.26)

Eg (3.14)

(0.35)(0.4)

En

erg

y l

ev

el

[eV

]

q, Charge state of VNi

(0.37)

Figure 2-6 Energy band diagram of nickel vacancies according to charge state

21

NiO has been found to be mostly a Ni-deficient oxide. If oxygen vacancies are

also present, they can provide electrons to surrounding Ni atoms, as indicated by the

fact that the lowest localized band gap states are occupied by electrons in Fig. 2-7.

The lowest defect levels come from the first nearest neighbor (1NN) Ni 3d orbital,

from hybridization of 1NN Ni 3d and O 2p orbital, or from 1NN O 2p orbital with

charge state of 0 to 2. However, electrons which are expected to mostly distribute over

six 1NN Ni or O atoms may redistribute onto only one surrounding Ni atom as

discussed in section 2.4.2.

0 1 2

Eg (3.41)Eg (3.55)Eg (3.66)(3.32)(3.22) (2.97)

(3.36)

(1.63)

(1.02)

(0.15)

(1.15)

q, Charge state of VO

(1.32)

Figure 2-7 Energy band diagram of oxygen vacancies according to charge state

2.2.2 Stability of Charged Vacancies through Formation Energy

In order to assess electron transition states we have calculated the stability of the

vacancy charge states. The formation energies are shown in Fig. 2-8 and 2-9. They

were determined for each charge state of cation and anion vacancies using the

22

following equation:

(1)

where E(VNq) and E(perfect) are total energies of a supercell with and without defects

for charge state q, respectively. nNi and nO represent the number of the removed Ni and

O atoms. μNi and μO refer to the atomic chemical potentials of Ni and O. EF is the

Fermi level with respect to the VBM.

With the Fermi level in the vicinity of the VBM due to p-type semiconducting

property, the stable oxygen vacancy state is positively charged (+2), then a transition

to neutral charge state is observed at 0.95eV and finally the singly negatively charged

vacancy state is stabilized above 2.83eV. In contrast, in the case of Ni vacancies,

several charge states (-2, -1, 0) may co-exist since formation energies for those

vacancies are comparable when Fermi level is close to the VBM.

0 1 2 3 4

0

2

4

6

8

10

12

14

16

18

CBMVBM

V +2Ni

V +1Ni

V +0Ni

V -1Ni

Fo

rma

tio

n E

ne

rgy

[e

V]

EF - EV [eV]

V -2Ni

Figure 2-8 Formation energy of nickel vacancies according to charge state

Eform

q= E(V

N

q) – E(perfect) + n

Niμ

Ni+ n

Oμ

O+ q(E

F+ VBM

+q)

23

In vacancy-rich TMOs, the generated local electric field may act as a scattering

source, which makes electrons or holes localized/trapped in vacancy sites. The as-

deposited NiO films show p-type conductivity because they are mainly grown with

Ni-deficiency. In Fig. 2-6, most of the defect levels are near the VBM in the range of

0.37 eV for all negatively charged and neutral Ni vacancies. Ionization energies are

determined from Fig. 2-8, i.e. the transition states at which the charged Ni vacancies

become stable, -0.04 eV for q = -1 and 0.16 eV for q = -2. These low energies for

acceptor-like states support the possibility of p-type conductivity in Ni deficient NiO

films observed in experiments [14].

0 1 2 3 4

0

2

4

6

8

10

12

14

16

18

V +2O

V +1O

V -1O

V +0OV +2

O

CBMVBM

Fo

rma

tio

n E

ne

rgy

[e

V]

EF - EV [eV]

Figure 2-9 Formation energy of oxygen vacancies according to charge state

2.2.3 More Feasible Formation of Anion Vacancies in NiO

Even though the stability of anion and cation charged vacancies is decided, to

suggest filament formation and rupture mechanism using those stable vacancy states,

24

several factors determining feasibility of vacancy migration should be compared

between nickel and oxygen vacancies in table 2-2.

Experimentally reported migration enthalpy for the self diffusion of nickel and

oxygen atom in NiO is close to each other, i.e., 2.4eV [15] for nickel and 2.47eV [16]

for oxygen. The diffusion mechanism of nickel and oxygen are described via vacancy

mechanism and vacancy or complexes (VNi VO VNi) mechanism, respectively [17].

VO VNi

Formation energy (EF ~0.5eV+VBM) [eV] ~3.4eV ~4.7

Enthalpy for self diffusion in NiO 2.47eV 2.4eV

Diffusion mechanismVacancy or

complexes(VNi VO VNi)Vacancy

Table 2-2 Feasibility of migration of oxygen vacancies in NiO

From theoretical evaluation of the formation energies for nickel and oxygen

vacancies [18], however, formation of oxygen vacancies in the proximity of the VBM

is more favorable than that of the nickel vacancies with the energy difference of

~1.3eV. This result is in good agreement with Ref. [19]. Nevertheless, the -2 charge Ni

vacancy becomes increasingly more stable as the Fermi level approaches the CBM.

Even though self diffusion of nickel and oxygen in NiO has the similar or

comparable characteristics, i.e., diffusion mechanism and activation energy for

migration, more favorable formation of oxygen vacancy in NiO indicates that more

feasible vacancy migration is the migration of oxygen vacancy in NiO.

Furthermore, the amount of excess oxygen in NiO depends on oxygen partial

25

pressure and temperature during deposition by sputtering [24,28]. As-deposited

nonstoichiometric Ni1-xO may have a wide range of resistivity and lead to different

switching property. For example, when NiO is deposited with oxygen partial pressure

of 20% (x > 0.05 [24]), it shows threshold switching characteristics where “on” state

formed through forming process returns to initial state even when applied voltage

sweeps back to zero value. However, NiO deposited at oxygen partial pressure of 3 or

5% has shown resistive switching characteristics (-0.05 < x < 0.05 [24]). That is,

formed conductive filament can be ruptured or maintained according to concentration

of oxygen around the filament. Even though initial NiO film deposited at 5% oxygen

partial pressure can have excess oxygen [24,28], migration of oxygen during forming

process could occur resulting in resistive switching even in NiO with excess oxygen

[24,28,20].

Hall coefficient in NiO with the Li content of 0.02 atomic % changes its sign

from positive to negative in the vicinity of the Neel temperature of 523K [21]. Change

of dominant current carrier from hole to electron may be derived from both magnetic

property of NiO from antiferromagnetic to paramagnetic and reduced hole mobility

with the increase in temperature [21]. The latter case indicates that acceptors like

nickel vacancies are compensated with donors arising from oxygen vacancies. It

reveals that highly p-type NiO contains oxygen vacancies acting as donors [21] and,

migration of oxygen during forming process is feasible in lightly p-type NiO

[20,23,27] as if formation of oxygen vacancies was more favorable under extreme

electrical stress in above cases.

26

2.3 Proposed Mechanism for Filament Formation/Rupture

A microscopic model of filament formation and rupture is presented by

employing the stable vacancy states determined in earlier calculations. The schematic

of filament formation and rupture in a microscopic view is shown in Fig. 2-10 through

2-13. Figure 2-10 and 2-12 are about the formation and the rupture mechanisms,

respectively. The resultant states after formation/rupture of filament are shown in Fig.

2-10 and 2-12. High electric fields during the so called “forming process” or at the

“on” transition may cause the migration of oxygen through the device [22,23]. In

general the removal of an oxygen atom will leave behind an oxygen vacancy of +2

charge and 2 electrons which become localized on the nearby Ni atoms [19].

Considering a Ni atom in the proximity of these oxygen vacancies, the charge state of

this Ni atom may turn Ni2+

(approx. the charge state of Ni in bulk NiO) into Ni1+

or

Ni0. Hickmott et al. had pointed out that the states formed by neutral nickel defects are

placed at the midgap and play an important role in switching by charging or

discharging the states.[24,25] However, the formation of metallic defects certainly

requires strong impulse such as relatively large local structural deformation, the

presence of several oxygen vacancies and/or migration of metal atoms. Our model is

based on the assumption that the migration of oxygen has taken place as observed in

recent experiments [23,26]. We consider that the oxygen vacancies are formed during

the deposition under specific growth conditions [24,27,28] and much more during the

forming process by strong electrical impulse since they have lower formation energy

than Ni vacancies as discussed in section 2.2.3.

27

2.3.1 Filament Formation Driven by Electric Field

During forming process or “set” process, that is, transition from “off” state to

“on” state, a high electric field is applied to oxide and oxygen atoms may migrate

leaving behind +2 oxygen vacancy, stable charge state as determined earlier, and 2

electrons to be used in the reduction of nickel atom (Fig. 2-10). They tend to cluster in

certain configurations with lower Vo-Vo interactions [5,29,30]. As a result, metallic

nickel atoms are connected in a chain as shown in Fig. 2-11. Thus, the so-formed

atomic chain can be regarded as a metallic filament representing the “on” state if the

chain of metallic nickel atoms contributes to conduction.

O2- - Ni2+ - O2-

l l l

Ni2+ - Vo2+ - Ni0

l l l

O2- - Ni2+ - O2-

Ni2+ - O2- - Ni2+ - O2-

l l l l

O2- - Ni2+ - O2- - Ni2+

l l l l

Ni2+ - O2- - Ni2+ - O2-

l l l l

O2- - Ni2+ - O2- - Ni2+

O2- = VO2+ + 2e +O(gas)

1. Migration of oxygen

2. Reduction of Ni atom

Figure 2-10 Formation mechanism in a microscopic view

Ni2+ - O2- - Ni0 - VO+2

l l l l

O2- - Ni0 - VO+2 - Ni2+

l l l l

Ni0 - VO+2 - Ni2+ - O2-

l l l l

VO+2 - Ni2+ - O2- - Ni2+

Figure 2-11 State of formation of metallic filament in NiO

28

2.3.2 Filament Rupture Driven by Migration of Oxygen

Unipolar resistive switching property strongly suggests the thermal energy as a

dominant factor for a “reset” process, transition from “on” state to “off” state. Because

symmetric switching characteristic indicates that the electric field dependence is

negligible at the “reset” process. The current density through a metallic filament has

been shown to reach high values and should be responsible for generating the thermal

energy that will activate the migration of oxygen at the highest resistive point or at

electrode-filament interface [31]. Then, the rupture process of the metallic filament as

shown in Fig. 2-12 is due to oxygen migration [32] from the region near filament to

oxygen vacancy sites near chain-like metallic nickel atoms and oxidation of those

nickel atoms to recover their bulk-like oxygen coordination. The recovery of oxygen

coordination of nickel atoms connected in a chain can be regarded as rupture of

filament representing the “off” state as shown in Fig. 2-13.

Ni0 + O = Ni2+ + O2-

Ni2+ - O2- - Ni0 - VO+2

l l l l

O2- - Ni0 - VO+2 - Ni2+

l l l l

Ni0 - VO+2 - Ni2+ - O2-

l l l l

VO+2 - Ni2+ - O2- - Ni2+

1. Migration of oxygen

(thermal effect)

2. Oxidation of Ni atom

Electrode(Pt)

Ni2+ - O2- - Ni2+ - O2-

l l l l

O2- - Ni0 - VO+2 - Ni2+

l l l l

Ni0 - VO+2 - Ni0 - VO

+2

l l l l

VO+2 - Ni2+ - O2- - Ni2+

Figure 2-12 Rupture mechanism in a microscopic view

29

Ni2+ - O2- - Ni2+ - VO+2

l l l l

O2- - Ni0 - VO+2 - Ni2+

l l l l

Ni0 - VO+2 - Ni2+ - O2-

l l l l

VO+2 - Ni2+ - O2- - Ni2+

Figure 2-13 State of rupture of metallic filament in NiO

2.3.3 Experimental Evidences for Filament Formation/Rupture Model

Proposed model of the filament structure is supported by observations of a

neutral metallic peak with X-ray photoelectron spectroscopy (Fig. 2-14) in all NiO

films that show the switching behavior [23].

Figure 2-14 X-ray photoelectron spectroscopy showing neutral nickel defect peak

With a certain oxygen partial pressure of 5% during the deposition of NiO layer,

neutral metallic nickel peak as well as nickel state (Ni2+

) bonding to oxygen was

30

observed together. When the NiO film does not show any switching behavior as in

case of 30% oxygen partial pressure, then the neutral metallic nickel peak did not

show up. This means that neutral metallic nickel may play a key role in resistive

switching.

Experimental evidence has also been presented for the oxygen vacancy migration

after the forming process in Fig. 2-15 [23]. It was observed that much more migration

of oxygen atoms from NiO to anodic side, Pt electrode was occurred after the forming

process. The result indicates that migration of oxygen atoms to metal/NiO interface

dominantly happens by high electric field. Additionally, diffusion of oxygen atoms

into Pt electrode suggests the need for consideration of thermal energy generated at

very small size, comparable to filament size, as there is no electric field in the metal

electrode.

Figure 2-15 Secondary Ion Mass Spectroscopy showing migration of oxygen

31

2.4 Metallic Conduction through Oxygen Vacancies

A “On” state atomic structure is suggested as one of the candidates for the “on”

states. From the previous model and experimental evidences, metallic nickel defects

and oxygen vacancies may be responsible for the resistive switching, especially to the

“on” state conduction. Therefore, formation of metallic nickel defects out of removal

of oxygen atoms requires redistribution of electrons around nickel atom in the vicinity

of oxygen vacancies.

Structural deformation or generation of multi vacancies may result in the

extraction of metallic nickel atoms through the redistribution of electrons. More

reasonable and suitable option to the First principle simulation is double or more

oxygen vacancies in Fig. 2-16 on the basis of several considerations based on

experimental observations.

Figure 2-16 Supercell showing oxygen vacancies and metallic nickel chain

32

2.4.1 Strong Interaction and Ordering of Vacancies in NiO

When oxygen atoms are removed, strong interaction among oxygen vacancies

must be considered (Fig. 2-17) [19]. Configuration with a certain distance or direction

between oxygen vacancies will have more energetically stable state than others. In

other words, clustering of oxygen vacancies may have a certain configuration due to

the strong interaction energy between them.

Figure 2-17 Interaction energy between oxygen vacancies in NiO

When oxygen atoms are removed intentionally from a perfect supercell to

construct metallic chain by considering interaction energies between oxygen

vacancies, metallic filament is formed in <110> direction in a simple cubic coordinate

as shown in Fig. 2-18. Figure 2-16 shows the supercell in use for “on” state atomic

structure with oxygen vacancies.

33

2.964Å4.192Å 6.628Å

Figure 2-18 (001) plane in simple cubic coordinate having metallic chain in <110>

The filament structure considered here contains four Ni atoms in each unit cell;

of which two equivalent Ni atoms are surrounded by four oxygen vacancies, while the

other two Ni atoms have only two nearest neighboring oxygen vacancies.

2.4.2 Redistribution of Electrons around Ni Atom

Electronic charge of each nickel atom in metallic chain is evaluated using Bader

Charge Analysis [33], which is the way of dividing molecules into atoms based on

electronic charge density. Finding zero flux surfaces between two atoms makes it

possible to calculate the charge of each atom as shown in Fig. 2-19.

Core Core

Surface of minimum charge density

Figure 2-19 Schematic illustrating Bader Charge Analysis

34

The filament has an alternating higher/lower electronic charge density

distribution along the <110> direction, depending on the oxygen vacancy

concentration. The electronic charge distribution around nickel atoms was calculated

for the supercell with the oxygen vacancies around the metallic filament. The (001)

plane with six oxygen vacancies, shown in Fig. 2-20 is one of the configurations with

the lowest formation energy, in agreement with reference [2]. The filament is in the

<110> direction. Bader charge analysis [33] has been performed to investigate the

amount of charge belonging to each nickel atom in a filament. We find that the

charges for the four nickel atoms along the filament are increased compared to the

charge of 8.68e for nickel in perfect NiO. The figure at each Ni atom of the filament

in Fig. 2-20 refers to the charge from Bader charge analysis. The nickel atoms in the

filament show almost neutral atomic character implying that the removal of several

oxygen atoms can generate almost neutral metallic defects, Ni0.

VO9.1

9.79

9.77

9.1

Figure 2-20 Electronic charge of each nickel atom in a filament. Dotted circle

refers to oxygen vacancy site.

35

The Bader volume (radius) of the four nickel atoms along the filament path is

also larger by 80.5% (1.23 times) compared with that of nickel atom in bulk NiO. The

electrons are spread around the Ni atoms resulting in charge redistributed around the

Ni atoms when the filament is formed.

2.4.3 Contribution of Metal Atom Chain to Conductivity at Room Temperature

To investigate the effect of the filament formation on the electronic structure, the

density of states of the supercell has been calculated (Fig. 2-21).

[T = 0 K]

-4 -2 0 2 4

-100

0

100

Spin-down

TD

OS

[#

of

sta

tes

/eV

ce

ll]

E - EF [eV]

Spin-up

Figure 2-21 Total density of states for the supercell with a filament

Defect levels are distributed over the whole range of the forbidden gap and NiO

becomes metallic. We calculate the partial density of states (PDOS) of each nickel

atom to understand its contributions to the electronic transport.

All the states near or below Fermi level are from nickel atoms further away from

the filament. The transport would be similar to polaron hopping, which could be

dominant in “off” state or in as-deposited film. This effect is in good agreement with

experimental results of Jung et al [34]; where a coexistence of weak metallic

36

conduction and polaron hopping in high resistance state is proposed. The states just

above Fermi level and below CBM correspond to nickel atoms in the filament (Fig. 2-

22). The calculation has been done at T=0K and electrons at room temperature can

populate the states above Fermi level and the filament will contribute to the observed

higher conductivity.

Figure 2-22 (a) Partial charge density within EF ~ EF + 0.3 eV in (001) plane

including oxygen vacancies and Ni metal chain and (b)-(d) partial density of

states of d orbitals at each Ni atom. Dotted square in (a) refers to Ni site.

Figure 2-22(a) shows band decomposed (partial) charge density within EF ~ EF +

0.3 eV suggesting transport path is in a direction of filament. A more thorough

examination on the electronic transport in this system may help us understand the

-10

-5

0

5

10

-10

-5

0

5

10P

DO

S [

# o

f st

ates

/eV

cel

l]

-4 -2 0 2 4

0

5

E-EF [eV]

Ni

(a) (b)

(c)

(d)

37

effect of temperature on both the transport of electrons in the filament and migration

of oxygen atoms.

2.5 Feasible Atomic Structure for “ON” and “OFF” States

Atomic structure suggested in the previous sections can be considered as one of

the possible “on” states. To investigate on atomic structure of “off” state, one of

oxygen vacancy sites are exchanged with one of oxygen atom around the vacancy site.

Oxygen atoms to occupy one site of oxygen vacancies are designated with oxygen site

of “a”, “b”, and “d” as shown in Fig. 2-23.

O

Ni

Oxygen vacancy site

Oxygen atoms to be removed

a

bd

Figure 2-23 Atomic structure representing one of possible “on” states

2.5.1 Suggested Atomic Structure of “ON” State

“On” state atomic structure showed metallic property in Fig. 2-21. Energy

decomposed partial charge density (EF ~ EF +0.3 eV) in this structure is shown in Fig.

2-22(a). Partial charge density below EF in Fig. 2-24 shows certainly that conduction

occurs through metallic chain and higher energy of electrons has stronger covalence

between metallic atoms.

38

EF~EF+0.3

No Eg

EF-0.25~EF

EF-0.45~EF -0.28

Figure 2-24 Partial charge density for “on” structure with energy from EF – 0.45

eV to EF + 0.3 eV

2.5.2 Suggested Atomic Structure of “OFF” state

As described in section 2.5, three different “off” states are prepared to investigate

“off” state atomic structure and its electronic structure. Figure 2-25 shows each

configuration corresponding to the exchanged oxygen sites (“a”, “b”, or “d”) shown in

Fig. 2-23.

39

A B D

Figure 2-25 Three different atomic structures for “off” state

Each structure for “off” state has different directions from oxygen vacancy site to

the oxygen site to be exchanged (table 2-3). Each oxygen atom also faces different

number of 1NN oxygen vacancies so that migration barrier and electronic structure

are expected to become variable accordingly.

Type Direction 1NN Vo‟s

Metallic chain <110>

VO – O at a <110> 1

VO – O at b <011> 2

VO – O at d <101> 4

Table 2-3 Direction from oxygen vacancy to oxygen and number of 1NN oxygen

vacancies in three “off” states

The electronic structure of “off” states shows reduced conductivity properties.

Total density of states for one “off” state with the exchanged oxygen at “d” shows

weak metallic property; states at EF starts splitting toward insulating property. The

40

oxygen had four 1NN oxygen vacancy sites, which compose metallic filament. Even

though one of them becomes occupied by the oxygen, the metallic property of

filament still remains.

-4 -2 0 2 4

-100

0

100T

DO

S [

# o

f s

tate

s/e

V c

ell

]

E - EF [eV]

Figure 2-26 Total density of states for “off” structure with the exchanged oxygen

at “d”

The other two “off” states show semiconducting property with the energy band

gap of 0.25 eV and 0.6 eV for oxygen site at “a” and “b”, respectively (Fig. 2-27). The

role of oxygen in the resistive switching can be verified from above results. Transition

between “on” and “off” state takes place through oxygen or oxygen vacancy migration.

Very small amount of oxygen migration can change conductivity drastically. One

oxygen migration was enough to achieve it. “Reset” process may be dependent on the

exchanged oxygen site giving rise to randomness of “reset” process, which is verified

again in chapter 3.

41

Figure 2-27 Total density of states for “off” structure with the exchanged oxygen

at (a) “a” and (b) “b”

EF+0.24~EF+0.4439

Eg : 0.2481eV

EF-0.007~EF+0.2411

EF-0.2411~EF

EF-0.4631~EF

Figure 2-28 Partial charge density for “off” structure with the exchanged oxygen

at “a”. Energy ranges from EF – 0.46 eV to EF + 0.44 eV

-4 -2 0 2 4

-100

0

100 Spin-up

TD

OS

[#

of

sta

tes

/eV

ce

ll]

E - EF [eV]

Spin-down

-4 -2 0 2 4

-100

0

100

TD

OS

[#

of

sta

tes

/eV

ce

ll]

E - EF [eV]

(a) (b)

42

Energy decomposed partial charge density (EF - 0.46 eV ~ EF + 0.44 eV) for the

“off” state atomic structure with the exchanged oxygen site at “a” is shown in Fig. 2-

28. Partial charge density below and above EF in Fig. 2-28 indicates that electronic

charge is more localized and electrons have weaker covalence between metallic atoms

resulting in the energy band gap of 0.25 eV.

2.6 Conclusion

A model for the formation and rupture of filamentary conduction path in NiO has

been presented from microscopic view of the unipolar switching in NiO, which agrees

with existing experimental observations. The formation process of a metallic filament

is regarded as a two-step process: (1) migration of oxygen vacancies under the applied

high electric field during the “forming process” or at the “on” transition and (2)

reduction in nickel atoms in proximity of the oxygen vacancies [18]. The rupture

process can be explained by migration of oxygen vacancies away from the filament

and oxidation of nickel atom to recover their bulklike coordination.

It has been shown that very small amount of oxygen (vacancy) can change

electronic structure of NiO from metallic property to insulating property and vice

versa. Several possible “off” states suggest the randomness of “reset” process or of

device characteristics related to the “reset” process depending on microstructure of the

conductive filament.

43

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p178-181

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Phys. Rev. B 77 134103 (2008)

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Kim, C. J. Kim, D. H. Seo, J-B. Park, J-H. Lee, X-S. Li, and Y. Park Nano Lett. 9(4),

1476 (2009)

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85, 5655 (2004)

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46

CHAPTER 3

Macroscopic Model for Reset/Retention and Filament Formation

In this chapter, macroscopic models about reset/retention and filament formation

are suggested based on the first principle simulation and modeling discussed in

chapter 2. Most of parameters used in setting up models come from the results of the

previous simulations where oxygen atoms (or vacancies) play a critical role in

resistive switching through oxidizing or reducing transition metals, and possible “on”

and “off” atomic structures provide useful basis for building the macroscopic models.

3.1 Reset/Retention Model

Ambipolar diffusion in a binary oxide is usually considered during sintering or

creep. This process occurs preserving electroneutrality and mass balance under

assumptions; i) oxide is a pure intrinsic oxide, where the dominant defects are Shottky

defects, ii) vacancy concentration are everywhere at equilibrium, and iii) local

electroneutrality holds everywhere [1]. In addition, the diffusion-controlled processes

are determined by ambipolar diffusion coefficient, which is a function of the

individual component diffusivities.

However, “on” state used in this model is assumed to have different vacancy

concentration in filament region and negligible concentration gradient of nickel atoms

throughout the oxide. In other words, flux of oxygen atoms is larger than that of nickel

atoms from the region outside of filament into filament region as shown in Fig. 3-1.

47

The reset process proceeds through the diffusion of oxygen atoms, that is, the

transition of oxygen atoms from the outside of filament region, i.e., oxygen-rich

region to filament region where more oxygen vacancies are in existence, thereby,

formation of metallic nickel filament. When the parameter in this model, found from

the first principle simulation, is compared to corresponding diffusion parameter, it has

been demonstrated that the reset process is in agreement with the diffusion process.

The estimated activation energies for retention are also in reasonable agreement with

experimental values. The “reset” transition time as well as the retention time could be

also evaluated from this model with a little modification.

3.1.1 Physical Process of “Reset”

The metallic filament is more likely formed in an oxygen vacancy-rich region.

The chainlike network of nickel defects, Ni0 in that region may result in the filament

with metallic conduction [2]. Even though NiO deposited at 4 or 5% oxygen partial

pressure shows nickel deficient or excess oxygen property [3,4], applied high electric

field creates oxygen vacancies forming the filament as described in section 2.2.3. The

possibility for formation of one or several filaments [5] could be bundled into

effective one filament. The shape of filament is assumed to be cylindrical for

simplicity as shown in Fig. 3-1.

48

ø

ρo(ø)

L~20nm

Vo-rich Ni1-xO

Figure 3-1 Schematic picture for reset process

Reset process in this model proceeds through the diffusion of oxygen atoms from

the region outside of conductive filament to the filament region, that is, from oxygen-

rich region to oxygen vacancy-rich region as shown in Fig. 3-2. The flux for diffusion

process is affected by both the diffusion coefficient and the concentration gradient of

diffusing species. The flux of oxygen atoms for diffusion in this model is dependent

only on the diffusion coefficient by assuming that outside of conductive filament as a

reservoir of oxygen atoms, which keeps supplying oxygen enough for reset process.

<110>ρo(ø 1) ρo(ø 2)

Metallic filament = Vo’ rich region Region occupied by oxygen

Ni1-xO

NiO1-y

VoCDW

Figure 3-2 Reset process through the diffusion of oxygen

49

The diffusion process can be described by the transition of oxygen atom to oxygen

vacancy site in atomic scale in a similar form of Arrhenius equation in (2).

(2)

where K, A and EAC represents the reaction or the transition rate, a prefactor in

Arrhenius equation, and the activation energy for oxygen migration. KB and T are

Boltzmann constant and absolute temperature, respectively. Physical meaning of

prefactor, A, is the total number of collisions in a certain direction. This term is

composed of correction factor, alpha (α) and optical phonon frequency. Optical

phonon frequency of 12THz [6] is adopted in perpendicular direction to the filament

along <110> direction which was used in the first principle simulations [2]. The

exponential term means reaction probability at any given collision. The retention time

can be evaluated by multiplying the inverse reaction rate with the number of oxygen

vacancy sites to be filled in the region between the initial radius and the reduced

radius at constant temperature as given in (3).

(3)

The number of oxygen vacancies in that region could be found in association

with planar distance between oxygen vacancies (~2.969A) in simulation [2]. The

relation between the reaction rate and the diffusion coefficient is shown in (4).

)(#1

atomsoxygenbyoccupiedbetositesOVofK

R

TK

E

TK

E

B

AC

B

AC

efrequencyphononoptical

eAK

)]([

50

(4)

Diffusion coefficient can be simply expressed by diffusion length and diffusion time.

In other words, diffusion length and reaction rate for transition become components of

diffusion coefficient as shown in (4). When a prefactor in (4) for bulk NiO with face

centered cubic (FCC) structure is compared with the corresponding term in (5) [7]

determined experimentally for bulk NiO with FCC structure, the correction factor, α is

~1/8 as follows,

(5)

where diffusion length is the distance between oxygen atom and oxygen vacancy in a

plane perpendicular to filament direction, and α represents possible number of sites

for oxygen migrating.

3.1.2 Evaluation of Radius of “ON” and “OFF” States

To obtain retention time from the “reset” process, it is necessary to calculate the

radius of initial “on” resistance and the final radius, corresponding to the increased

resistance due to thermal disturbance. In estimating radius of conductive filament,

careful considerations about conduction property and resistivity of a filament should

be carried out.

TK

E

B

AC

efrequencyphononopticalxKxt

xD

)(222

8/1~1189.0],[103472.4

)(sec]/[8102.6

2202

2

mx

FCCNiObulkformeDTK

E

B

AC

51

The conduction of “on” state has been described having both metallic and

semiconductor-like properties depending on the magnitude of “on” resistances;

resistances larger than 500 have an exponential dependence on temperature. In that

case, the activation energy for conduction ranges from 0 up to 0.3 eV suggesting

semiconductor-like conduction [8]. In this model, the resistances used for calculation

are less than 400 to be consistent with the case of simulations [2] confirming

metallic “on” state. It has been reported that resistivity of nickel nanowires increases

as the diameter decreases due to enhanced surface scattering [9]. For example, the

resistivity of filament with diameter ranging from 12 nm to 16nm is larger than 250

m·cm [9], and 31 m·cm [10] for the range from 50 nm to 100 nm. Even though the

usage of one value as the resistivity could be less accurate, Fig. 3-3 shows that 250

m·cm would be more reasonable in calculating the size of metallic filament with

constant film thickness of 20nm [11], when calculation is compared to experimental

observation in Fig. 1-5 showing filament size by conductive atomic force microscopy

(C-AFM) [11]. Initial diameter of “on” resistances is calculated using (6) for metallic

resistance.

(6)

A

LR o

52

100 150 200 250 300 350 400

4

6

8

10

12

14

Ra

idu

s [

nm

]

Initial "on" resistance []

~ 100 mcm

~ 250 mcm

Figure 3-3 Calculated radius of initial “on” resistances

The diameter of filament after the reset or the retention process was obtained by

considering semiconductor-like property of (7) with the activation energy for

conduction reported by Ielmini et al [8].

(7)

I.

II.

100 150 200 250 300 350 4000

2

4

6

8

10

12

14

mcm

Raid

us [nm

]

Initial "on" resistance []

RON

RON

x 10

RON

x 100

RON

x 1k

RON

x 100k

Figure 3-4 Calculated radius of increased resistances

kT

E

NiOo

AC

eA

tR

53

Figure 3-4 shows diameter changes with increasing “on” resistances toward “off”

states and initial “on” resistances. It shows that the ratio, 100, of ROFF/RON

corresponds to the ratio of about 3, of radiusON/radiusOFF. As the diffusion process

proceeds or oxygen atoms migrate to the filament region, resistances increase or

radius of a filament decreases with time as shown in Fig. 3-2. The transition (I) in Fig.

3-4 represents the determination of the retention time when the resistances increase by

10 times under constant temperature. The transition (II) can be used for calculation of

“off” transition time according to ROFF/RON ratio under constant “reset” current.

Constant “reset” current is assumed in the latter case, because the transition time is

very short (below around 1 ns) as found in Fig. 3-9.

3.1.3 Retention Time

Retention times are estimated for “on” resistance state using the previous

calculation procedure as in Fig. 3-4, (2), and (3). When activation energies for

retention are evaluated with the maximum α of 1 in the “reset” model, the retention

time vs initial “on” resistance plot shown in Fig. 3-5 resulted in 1.615 eV and 1.556

eV for 100 and 400 , respectively. When the value for 400 is compared with the

experimentally observed activation energy (1.21 eV), the estimated margin of error is

within 26% from 1.21 eV [8]. It has been verified that this relatively simple model

based on the diffusion process can be considered reasonable enough for the reset or

the retention model for NiO-based resistive switching.

54

100 150 200 250 300 350 40010

2

103

104

105

106

107

108

109

1010

1011

1012

Re

ten

tio

n t

ime

[s

ec

]

Initial "on" resistance []

85oC

250oC

Exp

10year

EAC,R ~ 1.615eV @ 100Ω

EAC,R ~ 1.556eV @ 400Ω

Figure 3-5 Evaluated activation energy for retention from “reset” model

The correction factor, α is adjusted for better fitting of the evaluated values to

experimental retention time at 250oC of Ielmini et al [8]. The extracted retention time

of initial resistances less than 400 at 85oC meets the requirement for 10 years in Fig.

3-6. But, more importantly, the activation energy for retention, determined from

experimental observations [8] would dramatically reduce the retention time even at

85oC (Fig. 3-7). This uncertainty in the retention characteristics makes it difficult to

incorporate the influences of thermal energy, which would further show wide variation

of retention from cell to cell or from resistance to resistance. The various activation

energies for retention and its uncertain occurrences depending on microstructures of

filaments should be pursued in more systematic way. Furthermore, more statistical

considerations must be imposed in accurately extracting retention properties of

resistive switching memory devices, which will be discussed in chapter 5. The

randomness of “reset” process or several possible paths to “off” state could be

anticipated in the first principle simulations in chapter 2.

55

100 150 200 250 300 350 40010

2

103

104

105

106

107

108

109

Re

ten

tio

n t

ime

[s

ec

]

Initial "on" resistance []

85oC

250oC

Exp

10year

EAC,R ~ 1.0eV

Figure 3-6 Extracted retention time at 85oC from “reset” model

100 150 200 250 300 350 40010

2

103

104

105

106

107

108

109

1010

1011

1.0eV

Re

ten

tio

n t

ime

[s

ec

]

Initial "on" resistance []

0.64eV

0.92eV

1.21eV

1.286eV

m cm

250oC

85oC

Figure 3-7 Influence of activation energy for retention on retention time

3.1.4 “Reset” Transition Time

Transition time as well as retention time in the reset process can be defined as the

time when the radius of initial resistance reaches certain radius of increased resistance.

Diffusion occurs from outside of the filament region to the vacancy sites at the most

outer shell assuming that the reaction rate is held constant during this process under

56

constant temperature or constant reset current for retention and “reset” process. Reset

transition times are estimated under the reset current of ~5 mA for resistances of

interest, the activation energy of 1 eV for oxygen migration, and a time step of 1 ps.

Figure 3-8 shows the calculation procedure of “reset” transition time. The high

current density through filament at “reset” process will generate joule heating

resulting in increased reaction rate and reduced radius of filament at each time step of

1 ps. The accumulated time when initial radius for “on” resistance reaches final radius

for “off” resistance becomes the “reset” transition time.

time step

(1or10ps)

Joule heating

Reaction rate, K

Resistance after (reset) diffusion

for each time step

Figure 3-8 Calculation procedure of “off” transition time

100 150 200 250 300 350 400

0.1

1

10

t OF

F t

ran

sit

ion

[n

s]

"ON" Resistance []

RON

x105

RON

x103

RON

x102

Figure 3-9 Calculated “off” transition time from “reset” model

57

The evaluated “off” transition times range around 1 ns or below as shown in Fig.

3-9. The transition time decreases as RON increases, because the difference of radius

for the initial and the final resistances is getting smaller with the increase in RON. In

other words, the number of oxygen vacancies to be filled with oxygen atoms

decreases as RON increases. Higher RON gives rise to the reduced “reset” current under

the assumption that necessary energy for migration of oxygen is same. The

experimentally observed reset transition time could be less than 20ns [11]. Therefore,

the calculated times would be meaningful as a lower bound estimates for the “reset”

transition time, because the estimation comes from the intrinsic property of resistive

component during the “reset” process not considering any latency during rapid

transition.

3.2 Filament Formation Model

Filament formation model considers only electric field as a dominant factor.

Even though local thermal distribution is not considered, the formation of conductive

filament under the assumptions and boundary conditions based on the first principle

simulations can result as a function of time.

Oxygen vacancy defects can exist in multiple charge states, i.e. +2, +1, 0, -1, and

-2. Charge state of oxygen vacancies can be decided if defect states in energy band

gap and Fermi level are found as proposed by Fahey et al [12]. However, experimental

results or theoretical evaluations about defect states in energy band gap for multi

vacancy case and concentration of oxygen vacancies for each charge state, which is

affecting the determination of Fermi level, have not been yet reported.

58

Even though we assume valency of oxygen vacancy stays unchanged (Z=2), this

simulation is useful from the aspect of growing filament in various situations such as

diffusion coefficient or field confinement. This model basically solves Poisson

equation to obtain the potential distribution in 2D, and then concentration of oxygen

vacancy can be found in 2D (preserving charge neutrality) through current continuity

equation.

3.2.1 Physical Process of Filament Formation

The “unipolar” resistive switching mechanism is also generally believed to be

strongly associated with the electric field-driven “set” or “filament formation” process,

that is, electric field makes the preferred migration of oxygen, generating oxygen

vacancy-rich region of conductive filament region. The concentration of oxygen

vacancy for the filament region in this model is set to be 5.098 x 1021

/ cm3 with

reference to 6 oxygen vacancies in Ni64O64 supercell [2]. The relative dielectric

constant of 11.9 for NiO [13], initial concentration of nickel vacancy of 6.5 x 1020

/

cm3 [3,14,15] and diffusion constant of 6.2 x 10

-4 cm

2/s [7] are used. It has been

assumed that a valency of oxygen and nickel vacancy remains unchanged from +2 and

-2, respectively. Time step of 1ps is used in solving continuity equation.

For the boundary conditions in terms of concentration of oxygen vacancy at the

top and bottom electrode, Pt is treated as a reservoir of oxygen vacancies having same

concentration in the filament region. The solubility of oxygen atoms in the noble

metal, Pt is low and the diffusion of oxygen atoms along grain boundaries in Pt

becomes enhanced up to 9.3 1.8 cm2/sec at the elevated temperature (1435

oC ~

59

1504 oC) [16]. However, the oxygen gas bubbles in Pt electrode under high electric

field have been observed in vacuum [11, 17 ] where formed and subsequently

accumulated O2 gas at anode/resistive material is assumed to produce a certain

pressure and temperature through electrochemical process. To accommodate oxygen

atoms in the Pt electrode during electroforming process in this simulation, Pt

electrodes are assumed to have same concentration of oxygen vacancies as in filament

region as an extreme boundary condition for oxygen vacancy distribution. The

potential gradient and concentration of oxygen vacancy gradient have been set to zero

at both ends in x axis used in a mesh structure as shown in (8) and Fig. 3-10.

(8)

+Vp = 5V

Y=42mesh

X=200mesh

2nm/1mesh36nm

Anode Electrode

Cathode Electrode

Figure 3-10 Mesh structure used in filament formation model

020002000

andx

Vo

andx x

C

x

V

60

The mesh structure for filament formation model has 200 x 42 meshes and 1

mesh point means physically 2nm length. The red part at the bottom side represents Pt

anode electrode and green part at the top side does Pt cathode electrode. All the

filament formation simulations in the following sections are performed by applying +5

V to bottom electrode and using same cell size as in figure 3-10 unless explicitly

designated.

The calculation procedure for the filament formation model is first to obtain the

potential distribution in 2 dimensions (2D) by solving Poisson equation (Fig. 3-11).

One of the terms in space charge concentration, background charge of Qa accounts for

nickel deficient pristine NiO [3,4,14,15]. Flux of oxygen vacancies is subsequently

calculated. The mobility of oxygen atoms in that equation can be determined by

Einstein relation between mobility and diffusion coefficient of oxygen atom in NiO.

The concentration of oxygen vacancies in 2D can be found through the continuity

equation. Filament growth can be observed as time elapses by performing iterative

calculations of above procedure as shown in Fig. 3-11.

V(x,y) : Poisson equation

W(x,y) : Flux of Vo’s

C(x,y) : Continuity equationTime step

: 1ps

aVo QCqZV

2

VCCDW VoVo m

Wt

CVo

Figure 3-11 Calculation procedure of filament formation

61

As filament starts to grow either in one filament or in several filaments, one

filament growing faster than others will finally become an actual filament as shown

conceptually in Fig. 3-12. We believe that observation of one filament growth in high

electric field would be reasonable enough to represent actual case. Therefore, the

filament shape is emphasized to become sharper and larger in the used mesh structure

of Fig. 3-10, i.e. (a) 40nm x 2nm (width and height) for plain cathode and (b, c) 24nm

x 18nm and 2nm x 22nm for sharper cathodes, respectively in Fig. 3-14. The influence

of the electrode shape on filament shape is discussed in section 3.2.2.

Figure 3-12 Illustration of one dominant filament formation at “on” state

62

3V, 1ps, 6Vo(5.09X1021/cm3)

4V, 1ps, 6Vo(5.09X1021/cm3)

400 nm

400 nm

84 nm

84 nm

Figure 3-13 Illustration of one dominant filament formation at “on” state

In this simulator, we could not observe any filament growth unless enough

electric field is applied to the structure. When 3V is applied to anode side, there was

no change in concentration of oxygen vacancies up to 300 ps. With the applied 4V,

grown filament is about to reach anode side at the elapsed time of 210 ps.

3.2.2 Effect of Field Confinement on Filament Formation

Real devices may have different local electric field distribution between two

electrodes due to the surface roughness or existence of a kind of nano-dots resulting in

different shape or size of filament. To investigate the effect of field confinement

arising form them, shape of cathode electrode (top electrode) is varied from plain

shape to sharper ones as shown in Fig. 3-14.

63

(a)

(b)

(c)

400 nm400 nm

84 nm

84 nm

84 nm

215 ps

170 ps

90 ps

Figure 3-14 Effect of electric field confinement on filament growth

The observed filament growth in all simulations occurs from cathode electrode to

anode side as shown in Fig. 3-13, which will be discussed in chapter 4. The shape or

size of the formed filament at cathode side becomes sharper or smaller as cathode

electrode shape is getting sharper because of enhancing electric field in Fig. 3-14.

64

X = 120

Do X2

Do /5

Do /10

Y=15

Y=15

Y=15

400 nm

84 nm

30 ps

100 ps

115 ps

84 nm

84 nm

(a)

(b)

(c)

Figure 3-15 Effect of diffusivity of interfacial layer on filament growth

3.2.3 Effect of Diffusivity in Interfacial Layer on Filament Formation

Modulating interfacial layer in terms of diffusivity could provide several benefits

in device characteristics like “on” resistance and its retention. Interfacial layers having

different diffusion constant, Di from the diffusion constant, DO in bulk are inserted

between top electrode and NiO layer as shown in Fig. 3-15. For interfacial layer with

larger Di than DO, the highest resistive part of the filament is formed at anode side

(Fig. 3-15(a)). It has been suggested that NiO has anode interface localized switching

property [18]. The result for the structure without interfacial layers in Fig. 3-14(a)

65

shows good agreement with same characteristics, i.e. anode side interface localized.

More interestingly, the highest resistive part of the filament can be formed at

cathode side when diffusivity of interfacial layer is smaller than bulk diffusivity

resulting in cathode interface localized switching property as shown in Fig. 3-15(c). It

is expected that the interfacial layer having lower diffusion constant can decide

filament shape, thereby switching property due to slow process for formation of

filament in the interfacial layer.

The concentration of oxygen vacancy at 120th mesh points in x axis (40nm

distance from the center of the filament) in Fig. 3-15 is shown in Fig. 3-16(a)

according to different Di. The concentration near filament maintains initial value after

formation of a filament for all interfacial layers as shown in Fig. 3-16(b).

Figure 3-16 Concentration of oxygen vacancy at X = 120 in Fig. 3-15

However, the concentration of oxygen vacancy at 15th mesh points in y axis

(6nm distance from the cathode electrode) is shown in Fig. 3-17. High vacancy

concentration region becomes narrower as diffusivity of interfacial layer is decreased

as compared to the bulk diffusivity. Both width and height of high vacancy

(a) (b)

25 30 35 40 45 50 55

0

1

2

3

4

5

CV

o x

10

21[/

cm

3]

Vertical distance [nm]

Do X2

Do /5

Do /10

CVo

at X=120

50 550.60

0.62

0.64

0.66

0.68

0.70

CV

o x

10

21[/

cm

3]

Vertical distance [nm]

Do X2

Do /5

Do /10

CVo

at X=120

Initial CVo

66

concentration region decreases with lower Di. This means that a small size of filament

is formed resulting in increased “on” resistance.

100 200 300

0

20

40

60

80

100

120

140

160

180C

Vo at Y=15

CV

o x

10

21[/

cm

3]

Horizontal distance [nm]

Do X2

Do /5

Do /10

Figure 3-17 Concentration of oxygen vacancy at Y = 30 in Fig. 3-15

In addition to increased “on” resistance, retention characteristics of “on” state

may become improved because of reduced flux of oxygen into filament region.

Retention process based on diffusion of oxygen is dependent on concentration

gradient of oxygen vacancy in or near conductive filament and the process can be

retarded enormously for lower Di as shown in Fig. 3-17.

67

3.3 Conclusion

Reset and retention model and filament formation model for unipolar NiO-based

resistive switching have been proposed. They are based on the physical understanding

on atomic structures of feasible “on” and “off” states; role of oxygen atoms/vacancies

in resistive switching. The reset/retention process, that is, atomic transition driven by

thermal energy, could allow us to calculate both the retention time and “reset”

transition time according to different “on” states. Theoretically estimated ranges for

retention and „reset” transition time are appropriately in agreement with

experimentally observed values.

A macroscopic filament formation model, the field-driven process suggests the

importance of interface engineering to achieve low diffusivity of vacancies, thereby

would enable low power and long retention of the “on” states.

References

[1] M. W. Barsoum, Fundamentals of ceramics, Taylor and Francis 2003

[2] H. D. Lee, B. Magyari-Kope and Y. Nishi, “Model of metallic filament formation

and rupture in NiO for unipolar switching”, Phys. Rev. B, vol. 81, no. 4, p. 193202,

May 2010

[3] S. Seo, M. J. Lee, D. H. Seo, E. J. Jeong, D.-S. Suh, Y. S. Joung, and I. K. Yoo, I.

R. Hwang, S. H. Kim, I. S. Byun, J.-S. Kim, J. S. Choi, and B. H. Park, “Reproducible

resistance switching in polycrystalline NiO films”, Appl. Phys. Lett. vol. 85, no. 23, p.

5655, Oct. 2004

68

[4] M. J. Lee, Y. Park, S. E. Ahn, B. S. Kang, C. B. Lee, K. H. Kim, W. X. Xianyu, I.

K. Yoo, J. H. Lee, S. J. Chung, Y. H. Kim, C. S. Lee, K. N. Choi, and K. S. Chung J.

Appl. Phys. 103, 013706 (2008)

[5] J. Y. Son and Y.-H. Shin, “Direct observation of conducting filaments on resistive

switching of NiO thin films”, Appl. Phys. Lett. vol. 92, no. 22, p. 222106, Jun. 2008

[6] R. A. Coy, C. W. Tompson, and E. Gurmen, “Phonon Dispersion in NiO”, Solid

State Communications., vol. 18, no. 7, pp. 845-847, 1976

[7] M. O‟keeffe and W. J. Moore, “Diffusion of Oxygen In Single Crystals of Nickel

Oxide”, J. Phys. Chem., vol. 65, no. 8, pp. 1438-1439, Aug. 1961

[8] D. Ielmini, F. Nardi, C. Cagli, and A. L. Lacaita, “Size-Dependent Retention Time

in NiO-Based Resistive-Switching Memories”, IEEE Electron Device Lett., vol. 31,

no. 4, pp. 353-355, Apr. 2010

[9] N. D. Davydov, J. Haruyama, D. Routkevitch, B. W. Statt, D. Ellis, M. Moskovits,

and J. M. Xu, “Nonlithographic nanowire-array tunnel device: Fabrication, zero-bias

anomalies, and Coulomb blockade”, Phys. Rev. B. Condens. Matter, vol. 57, no. 21,

pp. 13550-13553, Jun. 1998

[10] T. Ohgai, L. Gravier, X. Hoffer, M. Lindeberg, K. Hjort, R. Spohr, and J.-P.

Ansermet, “Template synthesis and magnetoresistance property of Ni and Co single

nanowires electrodeposited into nanopores with a wide range of aspect ratios“, J. Phys.

D, Appl. Phys., vol. 36, no. 24, pp. 3109- 3114, Nov. 2003

69

[11] M.-J. Lee, S. Han, S. H. Jeon, B. H. Park, B. S. Kang, S.-E. Ahn, K. H. Kim, C. B.

Lee, C. J. Kim, I.-K. Yoo, D. H. Seo, X.-S. Li, J.-B. Park, J.-H. Lee, and Y. Park, Nano

Lett., vol 9, no. 4, pp. 1476-1481, Apr. 2009

[12] P. M. Fahey, P. B. Griffin, and J. D. Plummer Rev. Mod. Phys. vol. 61, no. 2, pp.

289, Apr. 1989

[13] V. Biju, and M. A. Khadar J. Mat. Sci. 38 4055 (2003)

[14] N. Tsuda, K. Nasu, A. Fujimori, and K. Shiratori, Electronic Conduction in

Oxides, p. 213, Springer, New York, 2000

[15] D. Adler and J. Feinleib Phys. Rev. B 2, 3112 (1970)

[16] L. R. Velho, and R. W. Bartlett, Metallurgical Transactions, 3, 65 (1972)

[17] J. J. Yang, F. Miao, M. D. Pickett, D. A. Ohlberg, D. R. Stewart, C. N. Lau, and R.

S. Williams, Nanotechnology 20, 215201 (2009)

[18] K. Kinoshita, T. Tamura, M. Aoki, Y. Sugiyama, and H. Tanaka. Appl. Phys. Lett.

89, 103509 (2006)

70

CHAPTER 4

Experimental Switching Behaviors of NiO-based Unipolar ReRAM

As expected from filament formation model in chapter 3, a thin nickel metal

layer may generate an interfacial layer having lower diffusivity of oxygen than bulk

diffusivity resulting in increased “on” resistance and improved retention property. To

experimentally reveal the role of interfacial layer in filament formation, this chapter is

dedicated to switching behaviors and chapter 5 to retention experiments.

The role of interface between electrode and NiO on switching characteristics has

been investigated for unipolar NiO-based resistive switching. The 10 times reduction

of reset current is achieved from a few milliamperes in many literatures, by inserting a

thin nickel interfacial layer between cathodic electrode and NiO. A model describing

the reduction of reset current mechanism was derived from the combination effect of

oxygen vacancy formation/migration and the interfacial oxide layer at cathodic

electrode. The qualitative filament formation model is proposed from the results from

quantitative filament formation model discussed in chapter 3; i.e. direction of filament

growth and size of filament.

4.1 Formation of Small Size of Filament through Bonding of Ni and O

at the Interfacial Layer

There have been various considerations and suggestions about resistive switching

in NiO-based ReRAM [1,2,3,4,5]; Resistive switching occurs at the interface between

71

electrode and resistive switching material through the migration of oxygen atoms. If

we can incorporate an interfacial layer, acting as a barrier of oxygen migration or

having different diffusivity from bulk property, a different conductive filament or

different switching characteristics can be expected for improvement. In this section,

we suggest that inserting of thin nickel metal layer may meet the above requirements.

We observed the reduction in the reset current in the Pt(Top

Electrode)/Ni/NiO/Pt(Bottom Electrode) structure as compared with the reset current

in the reference structure of Pt(TE)/NiO/Pt(BE). The reduced reset current is directly

ascribed to the increase of the “on” resistance or the decreased filament size [6]. A

smaller filament diameter size could exhibit improved switching characteristics, i.e.

more uniform distribution of “on” and “off” resistance [7].

A polycrystalline NiO layer of about 20nm thick was deposited at room

temperature on the Pt(BE)/Ti/SiO2/Si substrate by ac reactive sputtering with an

oxygen partial pressure of 4% and RF power of 150W. The thicknesses of the bottom

electrode, Pt, Ti as the adhesion metal layer, and silicon oxide were 80nm, 20nm, and

50nm, respectively. The size of top electrode of 80nm thick was 20x20 μm2.

Interfacial layer of Ni(4nm) was fabricated by photolithographic patterning of a layer

and followed by subsequent deposition of dc sputtering method of the next layer and

lift-off process as shown in Fig. 4-1. All the electrical measurement data in this report

were taken by applying the positive bias to the bottom electrode. Set/forming

operation has been performed in the current sweep to reduce the effect of excessive

current increase and reset operation has been conducted by the voltage sweep. All the

electrical (I-V) data were collected using Agilent 4156C semiconductor parameter

72

analyzer.

Figure 4-1 Schematic picture of (a) Pt/NiO/Pt and (b) Pt/Ni/NiO/Pt structures

4.1.1 Switching Characteristics of Pt/NiO/Pt and Pt/Ni/NiO/Pt

Structures

Figure 4-2 and 4-3 show basic switching characteristics of the NiO with and

without the thin nickel interfacial layer; the first forming/reset process and fifth

set/reset process. The forming process and high reset current process were

unavoidable for all devices to obtain the consistent switching property as shown in Fig.

4-2 through 4-6. After the forming and reset process, the reset current decreased to the

range of 0.5~3 mA for the one without nickel layer and to the range of 200~350 mA

for the device with nickel layer. Switching behavior for NiO device showed

reasonably symmetry irrespective of applied positive bias to the TE or the BE as

shown in Fig. 4-1(a). The symmetric switching behavior represents a unique property

of “unipolar” resistive switching. For Ni/NiO device, positive bias should be applied

only to the BE as shown in Fig. 4-1(b) to achieve better switching behaviors in Fig. 4-

5 and 4-6(b). Cyclic endurance was observed more than 2,500 cycles and 1,250 cycles

NiO 34nm, PO2 ~ 4%

10uA@0.5V

Pt 80nm

Pt 80nm

NiO 34nm, PO2 ~ 4%

Ni 2nm

Pt 80nm

Pt 80nm

(a) (b)

73

for without and with the interfacial layer of nickel, respectively.

0 1 2 3 4

1E-3

0.01

0.1

1

10

Cu

rre

nt

[mA

]

Voltage [V]

Forming(NiO)

Reset(NiO)

5th Set(NiO)

5th Reset(NiO)

IRESET 0.5~3mA

Figure 4-2 Switching characteristics for Pt/NiO/Pt structure

IRESET 0.2~0.35mA

0 1 2 3

1E-3

0.01

0.1

1

10

Curr

en

t [m

A]

Voltage [V]

Forming(Ni/NiO)

Reset(Ni/NiO)

5th Set(Ni/NiO)

5th Reset(Ni/NiO)

Figure 4-3 Switching characteristics for Pt/Ni/NiO/Pt structure

Even though endurance becomes deteriorated, improved switching characteristics

in Fig. 4-3 and 4-5 can be obtained with the addition of nickel interfacial layer. “On”

74

and “off” resistances were measured at 0.1V at the “set” and “reset” state, respectively.

“On” resistance was increased and the distribution of “off” resistance was narrowed

leading to the reduction of reset current ranges from 0.5~3 mA to 0.2~0.35 mA. The

increase of “on” resistance can most likely come from the smaller size of filament.

Additionally, the increase of “off” resistance is more favorable in terms of leakage or

stand-by power reduction. Figure 4-6 shows the reset transition for the NiO reference

device and for the Ni/NiO device. It is shown that wide distribution of “on” resistance

and relatively high reset current for the reference device, while the device with nickel

interfacial layer gives rise to narrower distribution of “on” resistance and lower reset

current. Furthermore, uniform distribution of “on” resistance is observed after a few

hundred switching cycles in the modified structure. This improved switching behavior

with repetition of set/reset cycle may suggest a creation of more reliable path for

oxygen migration.

0 500 1000 1500 2000 25000.01

0.1

1

10

R(OFF)

R(ON)

Resis

tance [

K

]

# of switching cycles

Figure 4-4 Cyclic endurance for Pt/NiO/Pt structure

75

0 250 500 750 1000 1250

0.1

1

10

100

R(OFF)

R(ON)R

esis

tan

ce

[K

]

# of switching cycles

Figure 4-5 Cyclic endurance for Pt/Ni/NiO/Pt structure

0.0 0.4 0.8 1.20

1

2

Curr

en

t [m

A]

Voltage [V]

IRESET 0.5~3mA

0.0 0.4 0.8 1.2

50

100

150

200

250

300

350

Curr

en

t [m

A]

Voltage [V]

IRESET 0.2~0.35mA

Figure 4-6 Reset transition (I-V) curves for (a) Pt/NiO/Pt and (b) Pt/Ni/NiO/Pt

4.1.2 Role of Nickel Interfacial Layer

When a nickel layer of 4nm is inserted into the cathodic interface, more defect

states are generated at Ni/NiO interface as shown in Fig. 4-7. These defect states due

to nickel layer can give an indirect evidence of bonding of nickel and oxygen at the

interface.

(a) (b)

76

-4 -3 -2 -1 0 1 2 3 4

-2

-1

0

1

2

Cu

rre

nt

[mA

]

Voltage [V]

NiO

Ni/NiO

Figure 4-7 Current vs Voltage for pristine Pt/NiO/Pt and Pt/Ni/NiO/Pt structures

where the thickness of NiO and Ni/NiO are 20nm and 24nm, respectively.

Forming voltages change depending on bias configurations as shown in Fig. 4-8.

Bias on the TE results in higher forming voltage as compared to bias on the BE.

Although the difference of mean values is about 0.25V, the electric field difference for

samples in this report is in the range of 7.35MV/m, which is large enough for making

the difference of oxygen loss at forming process. When different electrodes (Ta or Al)

were used from Pt, the interfacial reaction layer, that is, oxidation layer of Ta and Al

were observed by both C. B. Lee [4] and S. R. Lee [5], respectively. The existence of

interfacial reaction layer was predetermined by the Gibb‟s free energy change of

oxidation of electrode atoms, and it affected the switching properties. The decrease of

oxygen content in p-type semiconducting NiO and oxidation of the inserted nickel

layer will increase the resistance of the cell. Thus, it is more likely that metallic nickel

at the Ni/NiO interface is partly oxidized by the oxygen atom in NiO as described

below.

77

Vform, mean(3.1822V)

Vform, mean(3.4187V)

BE TE

3.1

3.2

3.3

3.4

3.5

3.6

Positive Bias

+ on BE

+ on TE

Fo

rmin

g V

olta

ge

[V

]

Figure 4-8 Forming voltage for Pt/Ni/NiO/Pt structure

When positive bias is applied to the top electrode near interfacial layer, the

occurrence of switching behavior was rare. Instead, the phenomena like hard

breakdown took place during the forming process. The similar breakdown

phenomenon was reported by Lee et al [4,5]. Switching behavior was observed when

positive bias is applied to the bottom electrode. Moreover, better endurance

characteristics and reset current reduction were observed for the Ni/NiO structure.

Even though nonoccurrence of switching in the structure having interfacial reaction

layer could be explained by the hard breakdown of interfacial oxide layer [4,5], it is

noteworthy that each interfacial layer of Ta [4] and Al [5] shows much higher

resistance at as-deposited state than that for the interfacial layer of Ni. It means that Ta

or Al atoms with low free energy of oxidation become oxide phase more easily and

the nonoccurrence of switching [4] can be ascribed to the hard breakdown process of

the film. However, in case of the nickel interfacial layer, less capability of oxidation of

nickel would make nickel atoms at the cathode electrode barely interact with oxygen

78

atoms in NiO, resulting in only a local or very thin oxide layer formation. This

oxidizing reaction between nickel and oxygen would be stronger for structure with

nickel interfacial layer than for structure without interfacial layer. Thus, the formation

of oxygen vacancy at the cathodic interface becomes more difficult giving rise to

small size of metallic filament during the “set” process as predicted in the following

model or in previous filament formation model in chapter 2 where interfacial reaction

layer is assumed to have lower Di than DO, bulk diffusivity.

4.2 Qualitative Filament Formation Model

Figure 4-10 and 4-11 illustrate the filament formation model explaining why

smaller filaments can be formed by the reaction layer at the cathode electrode. Even

though contradictory experimental results about the cathode/anode localized switching

[1,8] have been reported, the model suggested below is based on the results of

reference [3] favoring anode interface localized switching.

4.2.1 Pt/NiO/Pt Structure

As discussed in section 2.2.3, the qualitative explanation for the filament

formation model is based on preferred oxygen vacancy migration in NiO. Under the

assumption of perfect NiO having no vacancies inside bulk NiO, oxygen vacancy

should be produced at the anodic side due to the negatively charged oxygen atoms in

NiO with assistance of thermal energy due to current concentration in a small size of

conductive spot. As described in Fig. 4-9(a), the diffusion process proceeds from (I) to

79

(IV), forming the oxygen vacancy-rich region where more metallic filaments are

possibly generated through the reduction of nickel atoms. At the forming/set process,

cone shaped oxygen vacancies accumulate at the cathode electrode, as demonstrated

in transmission electron microscopy (TEM) results of unipolar TiO2 ReRAM [9].

Negatively charged oxygen atoms in contact with anode electrode can be neutralized

electrochemically as reported in [10] while electrons are provided from cathode

electrode to oxygen vacancy-rich region, which results in metallic nickel defects or

growth of conductive filament.

+O2-Vo

2+

Pt

Pt

NiO

I II III IV

+O2-

Vo2+

Pt

Pt

NiO

I II III IV

(a) (b)

Figure 4-9 The model for formation of metallic filament for Pt/NiO/Pt structure

When any polarity of bias is applied to the NiO reference structure, similar

switching characteristics have been observed as shown in Fig. 4-9.

4.2.2 Pt/Ni/NiO/Pt Structure

If oxygen diffusion barrier exists at the top electrode in Fig. 4-10 and 4-11,

generation of the oxygen vacancy sites at the top electrode would be impeded by the

reaction layer. As negatively charged oxygen atoms move to Ni/NiO interface when

80

positive bias is applied to the nickel interfacial layer, subsequent movement

(diffusion) of oxygen atoms through nickel layer would be impeded by oxidation of

the nickel layer, which is acting as a barrier against ionic movement. Most of devices

showed the hard breakdown-like forming process; no reset transition up to 100mA.

Even a few of them showed very poor switching characteristics with 2 or 3 switching

cycles as shown in [11]. This means that “on” resistance is so small, i.e. larger

diameter of filament, that more current than 100mA would be necessary to rupture the

filament. We call it hard breakdown-like state in this report.

+O2- Vo

2+

Pt

Pt

NiO

Ni,Ti, TiN (interfacial)

I II III IV

Figure 4-10 The model for formation of metallic filament for Pt/Ni/NiO/Pt

structure. Positive bias is applied to top electrode.

Resistive switching can be explained in a similar manner among the cases of Ta,

Al, Ni electrodes. High electrical stress would cause more loss of oxygen atoms

during the forming process or the breakdown like state of interfacial layer resulting in

a large size of conducting filament [4,5] as illustrated in Fig. 4-10; small “on” and

“off” resistance for the case of nickel interfacial layer can be generated by oxygen

81

migration rather than migration of nickel metallic atoms [11] as suggested above.

If positive bias is applied to the bottom electrode, the reaction force of nickel

atoms at the Ni/NiO interfacial layer on oxygen atoms in NiO will retard the

generation of oxygen vacancies near the interface resulting in smaller size of cone

shaped filament as shown in Fig. 4-11.

+O2-

Vo2+

Pt

Pt

NiO

Ni (interfacial)

I II III IV

Figure 4-11 The model for formation of metallic filament for Pt/Ni/NiO/Pt

structure. Positive bias is applied to bottom electrode.

4.3 Conclusion

The reduction of reset current for unipolar NiO-based ReRAM was achieved by

inserting a thin homogeneous metal layer to the interface of resistive material, NiO

and Pt electrode. Based on experimental observations and theoretical considerations,

the model for the filament formation was built, and it can explain the reduction of

reset current due to the interfacial layer playing an important role of supplying enough

vacancies. The stoichiometry of reaction layer becomes close to perfect NiO phase

82

from nickel deficient pristine state due to nickel interfacial layer. When diffusivity of

the interfacial layer, Di, is considered lower than DO, then smaller filament can be

formed with the improved retention property as predicted by the quantitative filament

formation model in chapter 3. To further investigate the prediction from quantitative

model, retention experiments are performed and reported in chapter 5. The proposed

model can also delineate the role of anodic/cathodic interfaces between NiO and

electrode; where anodic electrode for forming and cathodic electrode for “on”

resistance.

References

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89, 103509 (2006)

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(2010)

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Stefanovich, Y. Park, and I. K. Yoo, Appl. Phys. Lett. 93, 042115 (2008)

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031102 (2010)

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U-I. Chung, C.-J. Kim, D.-S. Kim, and H. Lee, IEEE Elec. Dev. Lett. 31, 725(2010)

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Lett. 91, 082104 (2007)

84

CHAPTER 5

Experimental Retention Behaviors of NiO-based Unipolar ReRAM

It has been demonstrated in chapter 4 that addition of a thin nickel layer to the

interface of cathode electrode and NiO resulted in increased “on” resistances and

small size of conductive filament. Different expectations regarding the highest

resistive part of the filament by qualitative and quantitative filament formation models

can be verified by performing retention experiments. Small size of filament in Ni/NiO

structure shows better retention property, which can be explained by considering the

diffusivity change in the interfacial layers as proposed by the filament formation

model in chapter 2. Lower diffusivity of oxygen at the interfacial layer makes smaller

size of filament at the layer and increases stability of “on” state due to the reduced

flux of oxygen atoms for oxidation of conductive filament.

5.1 Procedure of Retention Experiment

Figure 5-1 shows the procedure of retention experiment. After finding several

switchable cells (at least 5 cycles) and setting them to the “on” state, they are treated

with rapid thermal annealing (RTA) process for a certain time (t1) at one temperature

(T0) under N2 atmosphere. The degraded “on” states of cells are measured at room

temperature. Then, annealing and measurement of cells are performed repeatedly,

followed by increasing annealing time as shown in Fig. 5-1. The temperature applied

in RTA process ranges from 85oC to 300

oC.

85

time

RT

Temp

Anneal.

To

Measuring RON of cells at RT

Annealing at To for t1 (RTA, N2 atmosphere)

Switching cells set to “ON” state

t1 t2 t3

S A M A M A M

To : 85oC ~ 300oC

Figure 5-1 Procedure of retention experiment

Figure 5-2 shows the effect of thermal disturbance on “on” resistances at

temperature ranging from 220oC to 300

oC. Especially, Fig. 5-2(a) clearly indicates

that more number of “on” resistances start increasing with increasing annealing time.

These results are in consistent with the proposed rupture mechanism by the diffusion

of oxygen atoms into filament region by oxidizing it.

As annealing temperature increases, number of memory cells, deviating from the

initial value, increases. Retention property of cells is variable from cell to cell as

expected from the retention model in chapter 2. Statistical data analysis of cumulative

distribution is performed to derive information about retention of RON.

Furthermore, thermal disturbances below 220oC did not make substantial change

in “on” resistances. Most of cells remain at their initial values at the retention test. It

should be noted that specific range of “on” resistances (1 k < RON < 4.5 k are

selected for retention experiment.

86

Figure 5-2 Cumulative percentage of RON with annealing temperature at (a)

220oC, (b) 250

oC, (c) 270

oC, and (d) 300

oC for f = 90%

5.2 Retention Time

Retention times of “on” resistances are obtained through the above procedure of

retention experiment. The degree of change of “on” state under the applied thermal

energy varies from cell to cell so that cumulative distribution (probability distribution)

is used in extracting retention times for a certain structure or device. The so-obtained

retention characteristics, i.e. activation energy for retention, and relation of retention

time with radius of “on” resistance strongly supports both the reset/retention model

and the filament formation model indicating that those macroscopic models are

suitable for NiO-based unipolar resistive switching devices.

@220oC

101

102

103

104

105

106

107

0

50

100

Cu

mu

lati

ve

Pe

rce

nta

ge

[%

]

Resistance []

0 sec

2 min

10 min

30 min

60 min

RON < 4.5kΩ

101

102

103

104

105

106

107

50

100

Cu

mu

lati

ve

Pe

rce

nta

ge

[%

]

Resistance []

0 sec

2 min

10 min

30 min

60 min

@250oC

RON < 4.5kΩ

101

102

103

104

105

106

50

100

Cu

mu

lati

ve

Pe

rce

nta

ge

[%

]

Resistance []

0 sec

2 min

10 min

30 min

60 min

@270oC

RON < 4.5kΩ

101

102

103

104

105

50

100

Cu

mu

lati

ve

Pe

rce

nta

ge

[%

]Resistance []

0 sec

2 min

10 min

30 min

60 min

@300oC

RON < 4.5kΩ

(a) (b)

(c) (d)

87

5.2.1 Retention Property of RON

Figure 5-3 shows a way to extract retention time from the cumulative percentage

graph of “on” resistances. Specific times are picked up at cumulative percentage of f

equals 90%, 75%, 50%, and 25%. Those represent the time when a certain portion of

cells out of all cells vary by thermal energy, that is, at temperature of 270oC.

101

102

103

104

105

106

25

50

75

100

Cu

mu

lati

ve

Pe

rce

nta

ge

[%

]

Resistance []

0 sec

2 min

10 min

30 min

60 min

f = 90%

f = 75%

f = 50%

f = 25%

RON < 4.5kΩ

@270oC

Figure 5-3 Cumulative percentage of RON with annealing at 270oC

The degree of change of “on” resistance with respect to annealing time and

annealing temperature can be defined at a certain cumulative percentage of f as in Fig.

5-4. The structure of Ni/NiO shows good retention property of “on” resistances at

annealing temperature below 220oC for f = 90%. It means that 90% of cells maintain

their initial “on” state from thermal disturbance. However, degradation rate of RON by

thermal energy is increased as annealing temperature increases at temperature ranges

above 250oC.

88

Retention time of the Ni/NiO structure is defined as the time when initial “on”

resistance is increased by 10 times at constant temperature. The dotted line in Fig. 5-4

represents resistance value for determination of retention time. We could obtain

retention times only above 250oC. Retention properties below 220

oC show very stable

states with negligible change in resistance.

1 10 100 100010

3

104

105

106

107

f = 90% (Ni/NiO)

"o

n" R

es

ista

nc

e [

]

Time [sec]

85oC

150oC

220oC

250oC

270oC

300oC

To : 85oC ~ 300oC

Figure 5-4 Variation of “on” resistances with annealing time at temperature

range from 85oC to 300

oC for extraction of retention time

5.2.2 Activation Energy for Retention of Ni/NiO structure

From the obtained retention times at several regimes of temperature, the

activation energy is extracted for different f values in Fig. 5-5. Even though the points

for f = 75% are not enough for linear fitting due to small changes of resistances at the

cumulative percentage, extracted activation energy for retention for Ni/NiO structure

are very close to 0.314 eV for both f = 90% and 75%. The activation energy for

retention for NiO structure, reported by D. Ielmini et al, is 0.64 eV for f = 90%.

89

Even though activation energy for retention for Ni/NiO structure is smaller than

that for NiO structure, absolute retention time for Ni/NiO structure is longer than that

for NiO structure. The enhanced retention time can be thought as a contradiction with

the result of increased “on” resistance if they are considered from a filamentary

switching point of view. In other words, small size of filament has longer retention

property or more stable “on” state.

However, both results, high “on” resistance and longer retention time can be

explained if an interfacial reaction layer with lower diffusion coefficient is formed as

shown in the filament formation model in chapter 3.

20.0 20.5 21.0 21.5 22.0 22.57.0

7.5

8.0

8.5

9.0

EAC,R ~ 0.314eV

EAC,R ~ 0.315eV

R (f=90%)

R (f=75%)

ln(

R)

1/ [1/eV]

Figure 5-5 Activation energy for retention for Ni/NiO structure

5.2.3 Retention Time according to “on” Resistance

In the reset or retention model, relatively simple description of diffusion process

has been employed. From (3) for retention time calculation, it can be found that

90

retention time is proportional to the square of radius of “on” resistance as shown in (9).

(9)

3000 4000 5000 6000

3000

6000

9000

Rad

ius

2 [

nm

2]

R [

se

c]

RON

[]

R

Reciprocal Fit of R

(Radius of RON

)2

3.0

3.5

4.0

4.5

5.0

Figure 5-6 Retention time vs RON (relation of retention time with radius of RON)

It is verified in Fig. 5-6 that retention time decreases with increasing “on”

resistance and retention time is proportional to the square of radius of “on” resistance.

It indicates that the reset or retention model suggested in chapter 3 is suitable for

representing reset/retention property of NiO-based unipolar resistive switching

devices.

2)(

1

)(#1

ONR

radiusON

A

ONR

atomsoxygenbyoccupiedbetositesOVofK

R

91

5.3 Conclusion

With a thin nickel layer inserted between cathode electrode and NiO, resistive

switching characteristics shows better retention and lower “on” state current, resulting

in lower programming energy. Generated defect states and difference of forming

voltage when applied to TE or BE indicate the role of nickel layer as a barrier against

ionic movement through the formation of thin reaction layer. Loss of oxygen atoms at

the forming process can be reduced with a bias to BE resulting in high “on”

resistances. The partially or locally oxidized nickel layer modifies the composition of

the surface of NiO, from Ni1-yO to more stoichiometric NiO and lowers the diffusivity

of the reaction layer resulting in long retention of “on” resistances. Both results can be

used for verification of “filament formation model” suggested in chapter 3.

Additionally, relation of retention time with radius of “on” resistance treats

“reset/retention model” in chapter 3 suitable for NiO-based unipolar resistive

switching devices.

92

CHAPTER 6

6.1 Conclusions

A model for the formation and rupture mechanism in NiO has been proposed in a

microscopic view for the unipolar switching in NiO accounting for experimental

observations, i.e., metallic nickel defects in switchable devices and migration of

oxygen after forming process. The formation and rupture process of a metallic

filament is regarded as a two-step process: (1) migration of oxygen vacancies by the

applied high electric field and/or generated thermal energy, in the “forming/set

process” or “reset” process and (2) reduction or oxidation of nickel atoms in the

filament region. From this point of view, the conductive filament does not require

precipitation of nickel atoms after oxygen is removed, but only migration of oxygen to

generate Vo-rich region.

It has been shown that very small amount of oxygen (vacancy) can change

electronic structure of NiO from metallic property to insulating property, which is in

consistence with that small difference of filament radius (x3) in the reset model

changes “on” resistances greatly (x100). The randomness of “reset” process by

thermal effect, suggested from coexistence of several “off” states, could be matched

with the results in both the reset/retention model and the retention experiment.

Relatively simple physical model based on the understanding on atomic

structures of feasible “on” and “off” states could enable estimation of retention time

and “reset” transition time as intrinsic property of “on” states. Reset process for NiO-

93

based unipolar resistive switching has been found to be closely related to diffusion

process of oxygen atoms.

A filament formation model could suggest another parameter, diffusion

coefficient of moving ions. The field-driven forming process suggests the importance

of interface engineering in terms of low diffusivity of vacancies, thereby would

achieve improved characteristics for resistive switching.

Improved switching characteristics expected by the filament formation model has

been demonstrated by implementing a low diffusivity of interfacial layer through a

thin nickel layer between cathode electrode and NiO for low power and long retention

of “on” state. The partially or locally oxidized nickel layer could reduce both the loss

of oxygen atoms during forming process and the diffusivity of oxygen atoms in the

interfacial reaction layer from more stoichiometric NiO resulting in reduced “reset”

current and increased retention property of “on” state.

6.2 Future Works

It is important to understand fundamentals in depth as if macroscopic models

based on understandings in the first principle simulations are demonstrated in

experiments giving rise to more benefits in device characteristics. More works on first

principle simulations and further development in macroscopic models and

experiments will make or suggest further improved device characteristics for resistive

switching memory.

94

6.2.1 Role of Oxygen or Metal Impurity at the Interface between

Metal and Resistive Material

Modulation of interface property between metal electrode and resistive material

could change resistive switching characteristics. The first principle simulations in this

paper are performed in bulk NiO and at 0K. Further investigation on the role of

oxygen (vacancies) or metal impurity at the metal/resistive switching material

interface would give more in-depth understandings, regarding bonding state of metal

atoms and oxygen atoms, electronic states of the interface, migration of oxygen

along/across the interface, etc. Those understandings will provide improved models

which will guide experimental approach for optimum choices for the electrodes,

resistive switching materials.

6.2.2 Addition of Thermal Effect to Filament Formation Model

Even though it is still challenging to extract thermal distribution near filaments

within a certain device structure, it is obvious that thermal effect appears in

“forming/set” process as well as in “reset” process. Amount of oxygen migration

through/near interface into metal electrode would be as important as the amount

occurring in bulk because the effect is expected to change structure and electronic

state at the interface, which could be dominant in determining device characteristics

during switching cycles.

95

6.2.3 Consideration of Variable Charge State of Oxygen Vacancies in

Filament Formation Model

Apart from additional thermal effect in filament formation model, it would be

necessary for clearer understanding of migration of oxygen vacancies to consider

variable charge state of oxygen vacancies because their charge state, concentration of

charged vacancies, and Fermi level are related to one another. In spite of high

calculation cost due to determination of Fermi level for all cells at every time step in

2D, the result will elucidate the migration/concentration of charged oxygen vacancies

and their effect on filament shape.