compact modeling of hysteresis effects in reram devices · 2018. 9. 3. · compact modeling of...

Compact modeling of hysteresis effects

in ReRAM devices

Enrique Miranda

Universitat Autònoma de Barcelona, Spain

Distinguished Lecturer EDS

SBMICRO, Bento Gonçalves, Brazil

August 2018

Evolution of the memory market

Important increase of memory market in the last years

18%

33%

5X

1

Motivation

• Increasing need of information storage systems

G.J

urc

zak,

imec

Reaching the limits of conventional memory devices?

2

4

Classification of ReRAM or RRAM

Physical mechanism: thermo- and electro-chemical phenomena

Optane SSD: 3D-XPoint Technology

Memory application

• Selectors and memory cells are

located at the intersection of

perpendicular wires

• Each cell is individually accessed

through the top and bottom wires

touching each cell

• Cells stacked in 3D improve

storage density

• Optane SSD 905P SSD (960GB)

Bit storage is based on a change of resistance

7

• Memristor devices are capable of emulating the biological

synapses with properly designed CMOS neuron components

S. Jo et al, Nano Lett 2010

Neuromorphic application

Synaptic weight is based on a change of resistance

8

Recent announcement

July 2018

• … to develop a switch that functions like the neuron and

synapses of the human brain, based on Correlated-Electron

RAM (CeRAM) technology.

• … to speed up neural network processing while improving

power efficiency through the use of analog signal processing as

compared to current digital approaches.

9

This talk: filamentary-type ReRAM

• Capacitor-like structure with a conducting pathway

• CBRAM: metal ions (usually Ag or Cu)

• OxRAM: oxygen vacancies (usually TMO)

• Nonvolatile effect: interplay of ions and electrons

• Complex physics: relies on natural parameters

10

• Introduction to filamentary-type ReRAM

• Physical models and quantum limit

• The circuital approach

• Model implementation

• The problem of variability

• Final comments

Outline

A. Sawa, Mat Today (2008)

This phenomenon is the working

principle of RRAMs: two stable states

Ch. Walczyk et al, JAP (2009)

HfO2 (27 nm)

Formation and rupture of

a filamentary path

By applying pulsed or ramped voltages, the resistance of some oxides can

reversibly change between a high (HRS) and a low (LRS) state

Phenomenology of filamentary-type RS

LRS

HRS

11

C. Schindler et al, IEEE TED (2007)

J. Choi et al APL (2009)

C. Yoshida et al, APL (2007)

TiO2(80 nm)

Cu-doped SiO2 (12 nm)

NiO(40 nm) /SiO2(50-300 nm)

The switching

property is observed

in a wide variety of

dielectric stacks

cycles

Cycling experiments in MIM structures

12

… exhibiting a wide variety of hysteretic I-V curves

13

Some electrode materials favour the switching process

RS phenomenon observed in many material systems

14

Newcomers: 2D materials

• h-boron nitride • MoS2 • Graphene

LANZALAB, Soochow University

16

Variability and reliability:

big problems for industry!

EGG: the material of the future?

Eggs used to make memristors:

biocompatible and dissolvable

electronic devices

Researchers at two Chinese

universities, the Cavendish

Laboratory at Cambridge University

and the University of Bolton, UK,

have produced a memristor made

from egg proteins, magnesium and

tungsten

EETimes, April 2016

16

A. Sawa, Mat Today (2008)

S. Kang et al, APL (2009)

RESET and SET events: rupture and regeneration of the

filamentary path (antifuse behavior)

Cu2O

Initial electroforming step required to

activate the switching property

HRS

LRS

Forming, set and reset: unipolar mode

17

Forming, set and reset: bipolar mode

Y. Li et al, NRL (2015)

18

Memory effect: how information is stored

Logic state “0”

READ OPERATION: low current logic state “0”

19

Memory effect: how information is stored

Logic state “1”

READ OPERATION: high current logic state “1”

20

Corresponds to a breakdown

event in dielectrics (defects &

percolation path generation)

Weibits independent of device area:

BD events follow a Poisson process

Forming process

B.Govoreanu, SSDM 2011

For very thin oxides no forming

seems to be required:

Forming should be avoided

21

“… neither the set nor the reset

current shows any area

dependence due to the filamentary

nature of conduction.”

D. Ielmini, NiO RRAMs

“Experimental data do not display

any obvious dependence on area,

indicating that resistive switching

is a filamentary process”

F. Nardi et al, IEEE TED (2012)

Area scaling of RS

22

S. Seo et al, Samsumg Electronics (2011)

SET and RESET voltages:

“No appreciable dependence of

memory switching on thickness”

NiO

Cu/ZnO:Mn/Pt

“…little or weak dependence on film

thickness is observed, which means that

the bias voltage mainly drops on a local

effective region, and the thickness of this

region does not significantly vary with

bulk thickness.”

Y. Yang et al, NJP (2010)

Thickness scaling of RS

23

S. Seo et al, Samsumg Electronics

NiO

“…resistive switches and

memories that use SiOx

as the sole active

material and can be

implemented in entirely

metal-free embodiments.”

J. Yao et al, NL (2010) Switching site in a CNT-SiOx nanogap system

The role played by the electrodes

24

Localized switching region

B. Govoreanu et al, IEDM (2011)

“The absence of cell area and oxide

thickness effect is indicative of a

local filament switching”

25

9V

Top view of Pt/HfO2(20nm)/Pt capacitor

112 μm

Generation of filaments during constant voltage stress

AFM Infrared thermography Spatial Statistics

26

In collaboration with Tyndall National Institute, Ireland

MIS and MIM capacitors

with high-K dielectric

Multifilamentary patterns (not reversible)

27

Techniques used to assess BD spot/filament distribution

POINT-TO-EVENT DISTANCES PAIR CORRELATION FUNCTION

DISTANCE METHOD QUADRAT COUNTS

METHOD

NEIGHBOUR METHOD

INTENSITY PLOTS

Distances

De

nsity

0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.0

0.5

1.0

1.5

28

Spatial statistics using angular wavelet analysis

Muñoz Gorriz et al, Mic Eng 2017

29

Multifilamentary conduction

X. Saura et al, Mic Rel 2013

Filaments are neither spatial nor

temporal correlated

30

Constant Voltage Stress






• Final comments

Outline

• SET: generation of a filamentary conduction structure (LRS)

• Chain of oxygen vacancies exhibits ohmic behavior (linear I-V characteristic)

• RESET: The constriction vanishes or locally reduces leading to an increment of the structure resistance (HRS)

K. Szot et al, Nat Mat (2006)

Conventional model for the Set/Reset transition

REDOX model: the movement of oxygen ions by

electromigration annihilates the vacancies

31

J-K. Lee et al, APL (2012)

S. Yu et al, APL (2011)

“The value of the extracted dielectric

constant r=79 is much higher than the known value 20 for HfO2. …fitting to a

P-F model is unreasonable.”

TiN/HfOx/Pt

In most of the cases fitting

parameters are not reported!!!

Poole-Frenkel and thermionic conduction

32

“Our observed I –V curves

with current compliance

higher than 20 mA, are

probably in agreement with

the prediction of SCLC”

Space-charge limited conduction

SCLC has a precise dependence with

oxide thickness !!!

33

Sekar, IEDM (2014)

Conductive Metal Oxide (CMO) believed to be a current limiter

“Explored fit of 1kb

data with Schottky,

Frenkel Poole,

hopping models.

Hopping gave the best

fit.”

Hopping conduction

34

Tunneling + diode

“…which was chosen more for its

simplicity and ability to reproduce the

I-V behaviour than as a detailed

physics model.”

J. Joshua Yang et al, Nat Nano (2008)

tunneling through a thin residual barrier; w is the

state variable of the memristor

I-V approximation for the diode-like rectifier

Both LRS and HRS

states are treated as

separate entities

35

Borghetti et al, JAP (2009)

1exp

0

0v

iRvii S

Diode-like conduction

with series resistance

Tunneling + diode

“… transition between a nearly ohmic LRS and a HRS characterized by

conduction through a barrier of width W.”

Electroformed TiO2 memristive switch

36

J. Hur et al, PR (2010)

Schottky barrier modulation

thin oxide-layer doping-level variation

HRS LRS

“The system can be

described by electric

conduction through a

Schottky barrier

connected in series

with a variable

resistance R”

37

Resistance modulation + trap assisted tunneling

Temperature dependence of the

current in the barrier (TAT)

F. Puglisi et al, EDL (2013)

38

C. Walczyk et al, TED (2011)

Modeling of the temperature dependence:

Quantum point-contact (QPC) model

39

Conductance steps measured in the RESET process of a

unipolar Pt/HfO2/Pt RRAM device

Quantum conductance unit

h

eG

2

0

2

K9.12100 GR

V

IG

Formation of a quantum wire

Resistance of a

monomode

ballistic conductor

40

Formation of a quantum wire

J. Suñé et al, JAP (2012)

“The peaks at roughly integer multiples of G0 can either be due to the CF

behaving as a QW or to a nanoscale CF cross section corresponding to

few atomic‐size conducting defects.”

41

“Statistics count of the

conductance changes from

two hundred curves

confirms the quantum

conductance behaviors,

which demonstrates

the formation of discrete

quantum channels in the

device”

X. Zhu et al, Adv. Mater. (2012)

Conductance quantization in RS devices

• Bipolar RS in Nb/ZnO/Pt

42

Data extracted from

pulsed measurements

on Ti/Ta2O5/Pt cells

“Fluctuations are likely due to the

fluctuation of filament geometry and

then the fluctuation of the number of

atoms in the contention.”

S. Blonkowski et al, J. Phys. D (2015)

TiN/Ti/HfO2/TiN

Conductance quantization in RS devices

C. Chen et al, APL (2015)

43

Large peak in the noise amplitude at the conductance quantum GQ=2e

2/h

44

T=1

V

As occurs in a potential well, a narrow

constriction induces the lateral quantization of

the electron wave function

The Landauer approach

R. Landauer, 1927-1999

T

45

T: transmission probability

V: applied voltage

000 GGTGdV

dIGTVGI

T

T: transmission probability

V: applied voltage

dEeVEfeVEfETh

eI

)1()(2

β: fraction of the potential that drops at the source side 0

Constriction

(parabolic-shaped)

Potential barrier

(not material)

0

00

1exp1

exp1ln

12)(

VVe

VVeVVe

h

eVI

Miranda & Suñé, IEDM’00, IRPS’01

Quantum point contact model for dielectric breakdown

Y. Li, NRL 2015

47

Application to Au/HfO2/TiN RS structures

0 1 2 3 410

-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

HRS

Set

LRS

Cu

rre

nt A

Voltage V

Reset

HfO2 (27 nm)

E. Miranda et al, EDL (2010), in collaboration with IHP, Germany

MODEL EXPERIMENTAL RESULTS

0 1 2 3 4

0

1x10-9

2x10-9

3x10-9

4x10-9

5x10-9

6x10-9

7x10-9

8x10-9

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

6x10-5

7x10-5

8x10-5

Experimental

Model

Cu

rre

nt A

Voltage V

2RB

HRS

LRS

T=1

T

“ …this conductance

quantization behavior is a

universal feature in

filamentary-based RRAM

devices.”

X. Zhu et al, Adv. Mater. (2012)

Nonlinear conductance quantization effects

ITO/ZnO/ITO

Peaks are also observed at half-integer multiples of G0

49

Histogram of conductance changes collected from the SET

characteristic of SiOx-based ReRAM devices

A. Mehonic et al, Sci Rep (2012)


50

“These observations confirm the picture of filament

conduction being controlled by electron transmission

through discrete energy levels.”

R. Degraeve et al, IEEE (2012)

The conductance

plateaus correspond

to integer and half

integer multiples of

2e2/h

TiN/HfO2/Hf/TiN


IMEC:

51

Cu/SiO2/W memristor with half-integer quantum conductance states

“This is attributed to the nanoscale filamentary nature of

Cu conductance pathways formed inside SiO2.”

S. R. Nandakumar et al, Nano Lett (2016)


52

Subbands in tube-like constrictions

narrow constriction wide constriction

Blue: longitudinal bands Red: transversal bands

E. Miranda et al, APL (2012)

53

Subbands in tube-like constrictions

narrow constriction wide constriction

11&1 NNN 2/31&2 NNN

2

NNN

56

-3 -2 -1 0 1 2 310

-7

10-6

10-5

10-4

10-3

-4 -2 0 2 4

0.0

0.2

0.4

0.6

0.8

a)

c)

b)=2 eV-1

N=1, =3/4

500

20

10

5

1

I=G0V

I [A

]

V [V]

Max

=2 eV

Min

=-2 eV

0=0 eV

r

-4 -2 0 2 4-3

-2

-1

0

1

2

3

R [M

Ohm

]

V [V]

[

eV

]

V [V]

E. Miranda et al, EDL (2012)

Modulation of the barrier height/width

caused by the movement of

atoms/vacancies

Generation of the

hysteretic loop in

the I-V characteristic

of RS devices

The quantum point-contact memristor

57

Filamentary conduction in Graphene/h-BN/Graphene

𝐼 = 𝐺0𝑛 𝑉 − 𝐼𝑅𝑆 +2𝑒 𝑁−𝑛

𝛼ℎexp −𝛼𝜑 𝑒𝑥𝑝 𝛼𝑒 𝑉 − 𝐼𝑅𝑆 − 1

N: number of filaments n: number of completely formed filaments

-1 0 1 2 3 4 5 6 7 810

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

MedMax

Min

-0.50 -0.38 -0.25 -0.13 0.00

10

20

30

40Max

Median

b)

Curr

ent [m

A]

Voltage [V]

Min

LRS

HRS

Cu

rre

nt [A

]

Voltage [V]

Forming I-V

a)

C. Pan et al, 2D Materials (2017)

58

Equivalent electrical circuit model

𝐼 = 𝐺0𝑛 𝑉 − 𝐼𝑅𝑆 +2𝑒 𝑁−𝑛

𝛼ℎexp −𝛼𝜑 𝑒𝑥𝑝 𝛼𝑒 𝑉 − 𝐼𝑅𝑆 − 1

𝐼 = 𝐺P 𝑉 − 𝐼𝑅𝑆 + 𝐼0 𝑒𝑥𝑝 𝛼 𝑉 − 𝐼𝑅𝑆 − 1

This is the starting point of our own memristive approach

58






• Final comments

Outline

2008 HP’s breakthrough

A practical implementation

of a memristor?

59

As time goes by…

(2015)

• “The devices were not new and the hypothesized device

needs magnetism”

• “The originally hypothesized memristor device is missing

and likely impossible”

• “The originator of the prediction accepted the discovery”

Many researchers have

raised serious doubts!

60

and more recently …

• “The ideal memristor is an unphysical active device and

any physically realizable memristor is a nonlinear

composition of resistors with active hysteresis.”

• “We also show that there exists only three fundamental

passive circuit elements.”

(July 2018)

Many researchers have

raised serious doubts!

61

• Four fundamental

quantities: i, v, q,

• 5 out of 6 pairwise relations

known very well

• Using symmetry arguments

Prof. Chua (1971) proposed the

missing link: MEMRISTOR

• Memristor = Memory + Resistor

• M: Memristance

Memristors

M depends on the hystory of the device and

retains its value even if the power is turned off )()()( tIwMtV

Picture taken from Parcly Taxel

Memristor is a contraction of

“memory resistor,” because that

is exactly its

function: to remember its

history. A memristor is a two-

terminal device whose

resistance depends on the

magnitude and polarity of the

voltage applied to it and

the length of time that voltage

has been applied. When you

turn off the voltage, the

memristor remembers its most

recent resistance until the next

time you turn it on,

whether that happens a day later or a year later

63

MEMRISTORS cannot be constructed by combining the other

devices and are characterized by “pinched” Lissajous curves

Response to a sinusoidal excitation

Unlike capacitors and inductors, MEMRISTORS do not store energy

65

Memristive devices

• Memristive devices are defined in terms of two coupled equations:

)(),,()( tutuxgty

),,( tuxfdt

dx

u(t) is the input signal (current or voltage)

y(t) is the output signal (voltage or current)

x is the variable which describes the state of the device

g and f are continuous functions

• If both g and f are linear functions linear memristive system

Chua and Kang, Proc IEEE 64, 209 (1976)

66

HP memristor model (2008)

• V(t) across the device moves the

boundary w between the two regions

by causing the charged dopants to drift

• TiO2 film (D) has a region with a high

concentration of dopants (RON) and a

region with a low concentration (ROFF)

Transport

Equation

State

Equation

Strukov et al, Nature 453, 80 (2008)

)()()( tIRtV

1)(/ OFFON RRRDw

)(tIdt

d

67

)(1 tIdt

d

)()()( tIRtV

1)( OFFON RRR

window function (ad hoc)

Introduction of the window function

010 ff

Simulation results using HP model

• Introduced to control the state

variable at the turning points

• Introduction of window functions

can lead to serious mathematical

problems

68

Joglekar

(2009) p

Jf2

121)(

Biolek

(2009) p

B IHf2

)(1)(

Strukov/Benderli

(2008) 1)(Bf

Prodromakis (2011)

pP ff 75.05.01max)( 2

Some window functions

• Required for imposing boundary conditions on λ

Pictures from McDonald et al

69

Memdiode equations

)(/ RVI

1)( OFFON RRR

Idt

d

1

)()(exp)()sgn( 0001 IRIVRIWRVI 1)( min0max00 III

Transport

Equation

State

Equation ANALOG

BEHAVIORAL

MODEL

(ABM)

ori

gin

al

ori

gin

al

new

new

E. Miranda, TNANO 14, 787 (2015)

𝑑𝜆

𝑑𝑡=𝜂𝜆 1 − 𝜆 𝑉

70

The memdiode concept

71

Transport

Equation

(electrons)

State

Equation

(ions or vacancies: channels)

72

Origin of the nonlinear transport equation

1exp0 VII

• Schottky emission

• Electrochemical filamentation

• Tunneling through a gap barrier

• Quantum point-contact conduction

Instead of resistor-like behavior, diode-like conduction is assumed:

1exp0 IRVII

IRV 1exp0 VII

IRV VRI

II

0

0

1

:0V

:0V VII 0

73

Exponential HRS

Linear HRS

Linear LRS

• The series resistance R acts as a feedback

that controls the shape of the I-V through I0

• Consistent with the experimental I-V

curves of many RS devices


0.1 1

10-6

10-5

10-4

10-3

10-2

I0

LRS

2

1C

urr

en

t [A

]

Voltage [V]

1

3

HRS

Series resistance

1)( min0max00 III


• Analytic model (good approximations for W)

• Continuous and differentiable

• Linear (large I0) or nonlinear (small I0)

• Pinched I-V: I(V=0)=0

)()(exp)()sgn( 0001 IRIVRIWRVI

1exp0 IRVII

xWeW W is the Lambert function

Two anti-parallel diodes

73

2

2

2exp

2

1)(

VVVf

Origin of the state equation

• Let’s assume Gaussian-distributed SET voltages for the individual channels

dfVHV

)()()(• Normalized number of activated

channels at voltage V

Heaviside function

CONVOLUTION

75

1exp12

12

1)(

VV

VVerfV

0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

(V

)

V

Error function

Logistic curve


• Number of conducting channels grows up as a logistic curve

76

1dV

d

dt

dV

dt

dV

dV

d

dt

d

1

1exp1)( VVV


First-order

State Equation

𝑑𝜆

𝑑𝑡=𝜂𝜆 1 − 𝜆 𝑉

77

1exp1)( VVV

Major hysteretic loop

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

V- V

+

V

SET voltage RESET voltage

Ridge functions

Admissible inputs: V

Bounded output: 10

Logistic hysteron

Describe the creation and rupture

of conducting channels

78

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

V-

1=V

-

2

V+

1

Control of TRANSITION RATES

79

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

I(A

)@0

.1V

Voltage (V)

Current [email protected] 10nm

TiN-Ti/HfO2/W devices Results from Universidad de Valladolid

TiN/HfO2/Ti devices Results from LETI, Grenoble

Experimental hysterons (current@low voltage)

81

Experimental and model results

82

1exp1)( VVV

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

V

),(

State space: domain of feasible states

Minor hysteretic loops (neuromorphic applications)

),(0

VifdV

dChannels can neither be created

nor destructed inside

ions >> signal

State of the system ),( V

)(tV )(t

Ridge functions

Simplest case:

83

Krasnosel’skii-Pokrovskii (KP) hysteresis operator

)(],[)( 00 tVtLt

)(,max,)(min)(],[ 000 tVtVtVtL

00 )( t

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

+

V

-

Increasing

input

Decreasing

input

M. Krasnosel’skiĩ and A. Pokrovskiĩ, Systems with hysteresis, Springer, 1989

84

tttt VV ,max,min 1

• State of the system described by a recursive relationship

• Deterministic and rate-independent process

• Short memory transducer with wiping-out property

• No need to control the simulation timestep (algorithmic modeling)

• Applicable to arbitrary inputs (continuous or discontinuous)

)(,max,)(min)(],[ 000 tVtVtVtL The previous output is

the next initial state

Krasnosel’skii-Pokrovskii (KP) hysteresis operator

85

86

Systems with hysteresis (1989)

Alexei V. Pokrovskii 1948-2010

Mark Krasnosel'skii (1920-1997)

Voltage

Me

mo

ry s

tate

Voltage

Me

mo

ry s

tate

Voltage

Me

mo

ry s

tate

Voltage

Me

mo

ry s

tate

Voltage

Me

mo

ry s

tate

Voltage

Me

mo

ry s

tate

Time

Me

mri

sta

nce

Time

Curr

en

t

Voltage

Cu

rre

nt

Time

Vo

lta

ge

Time

Vo

lta

ge

Voltage

Cu

rre

nt

Time

Curr

en

t

Time

Me

mri

sta

nce

Time

Vo

lta

ge

Time

Me

mri

sta

nce

Voltage

Cu

rre

nt

Time

Curr

en

t

Time

Voltage

Voltage

Cu

rre

nt

Time

Curr

en

t

Time

Me

mri

sta

nce

Time

Voltage

Time

Me

mri

sta

nce

Time

Curr

ent

Time-independent model

87

Model and simulation results for LCMO

0.0 2.5 5.0 7.5 10.00

100

200

300

400

500

I

Iexp

I(A

)

V (V)

(a) Linear

2.5 5.0 7.5 10.010

-7

10-6

10-5

10-4

I

Iexp

I(A

)

V (V)

(b) Semilog

J. Blasco, UAB PhD Thesis, 2017

88

Remember: we are interested in

simulating the synaptic weight

which is a continuous variable

100 120 140 160 180 200 220 240

-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5 MODEL

EXPERIMENT

I(m

A)

t(s)

-1.0 -0.5 0.0 0.5 1.0 1.5 2.00.0

0.2

0.4

0.6

0.8

1.0

V(V)

loop 1

loop 2

loop 3

loop 4

loop 5

loop 6

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.7510

-4

10-3

10-2

I(A

)

V(V)

Superposition of hysterons: super-hysteron

3

1

)()(i

ii VVS

1 i

: sigmoidal hysterons

: weight coefficients

HfO2

J. Blasco, UAB PhD Thesis, 2017

89

EU project PANACHE 2014-2017

Pilot line for Advanced Nonvolatile memory technologies for Automotive microControllers, High security applications and general Electronics

91

Typical switching behavior

92

VDS

[V]

0.0 0.5 1.0 1.5 2.0 2.5

Dra

in C

urr

ent [m

A]

0

1

2

3

4V

G=0.75

VG=1

VG=1.25

VG=1.50

VG=2.00

VG=2.50

VG=3.00

VG=3.5

VG=4

Curr

ent [m

A]

0

100

200

300

400

500

600V

G=1.2 V

VG=1.3 V

VG=1.4 V

VG=1.5 V

VG=1.6 V

Current Compliance [mA]

102 103

Reset C

urr

ent [m

A]

102

103

(a)

(c)

Voltage [V]

-1.0 -0.5 0.0 0.5 1.0

Curr

ent [A

]

10-7

10-6

10-5

10-4

VRESET

=1.2V

VRESET

=1.0V

VRESET

=0.8V

(d)

(b)

Transistor as selector

93

F63.2%

Ln(tS) [s]

-20 -15 -10 -5 0

Ln

(-L

n(1

-F))

-6

-5

-4

-3

-2

-1

0

1

2

VCVS

[V]

0.2 0.3 0.4 0.5 0.6 0.7

t 63

% [

s]

104

102

100

10-2

10-4

10-6

10-8

E-model

E1/2

-model

Power-law

1/E-model

(b) (a)

0.65V 0.3V

Censoreddata~ 1.178

steps: 0.05V

VCVS

[V]

0.2 0.3 0.4 0.5 0.6 0.7

V [V

-1]

20

40

60

80

100E-model

E1/2

-model

Power-law

1/E-model

(c)

tS63 data

tS63 data

Set statistics: accurate determination of acceleration law

0

Ve

E-model:

Experimental results for CVS confirm this model for the switching time

94

Constant voltage stress experiments

A. Rodriguez et al, EDL (2018)

(a)

Voltage [V]

-1.0 -0.5 0.0 0.5 1.0

Cu

rre

nt

[mA

]

-100

-50

0

50

100

5.10 V/s

5.102 V/s

5.103 V/s

5.104 V/s

RR

RR @ SET

RR=50 V/s @ RESET

(b)

Voltage [V]

-1.0 -0.5 0.0 0.5 1.0

Cu

rre

nt

[mA

]

-200

-100

0

100

200

5.10 V/s

5.102 V/s

5.103 V/s

5.104 V/s

RR @ RESET

RR =50 V/s @ SET

RR

VSET

=0.021 ln(RR) + 0.39

VRESET

=0.021 ln(RR) + 0.49

Voltage [V]-1.0 -0.5 0.0 0.5 1.0

Me

mo

ry S

tate

[]

0.0

0.2

0.4

0.6

0.8

1.0

Voltage [V]

-1.0 -0.5 0.0 0.5 1.0

Me

mo

ry S

tate

[]

0.0

0.2

0.4

0.6

0.8

1.0(c) (d)

RRRR

Pulsed measurements with different ramp rates

96

0

Ve

E-model: Experimental results for RVS confirm this model for the switching time

Pulsed measurements with different ramp rates

95

Ramped voltage stress experiments

Voltage

Me

mo

ry s

tate

Time

Curr

ent

Voltage

Curr

en

t

Time

Me

mo

ry s

tate

Time

Volta

ge

Time-dependent model

97

0

Ve

E-model:

(a)

Voltage [V]

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Cu

rre

nt

[A]

10-7

10-6

10-5

10-4

RR = 50 V/s (Model)

RR = 500 V/s (Model)

RR = 5 KV/s (Model)

RR = 50 KV/s (Model)

RR = 50 V/s (Exp)

RR = 500 V/s (Exp)

RR = 500 KV/s (Exp)

RR = 50 KV/s (Exp)

(b)

Voltage [V]0.0 0.2 0.4 0.6 0.8

Curr

ent

[A

]0

50

100

150

200

Imax

= 1.3e-4 A

Imin

= 3.5e-5 A

max = 3.5 V

-1

min = 1 V

-1

del = texp

RESET = 70 V

-1

SET = 50 V

-1

RESET = 5e+19s

SET = 1e+7s

RS = 500

98

Effect of ramp rate: experimental and model results






• Final comments

Outline

Memristor simulation using SPICE

Implementation of

the variable state

equation

Two-port equation

• It is of great benefit for circuit designers to be able to model memristive

devices in SPICE-type simulators

100

.SUBCKT memristor Plus Minus PARAMS: + Ron=1K Roff=100K Rinit=80K D=10N uv=10F p=1 *********************************************** * STATE EQUATION MODELING * Gx 0 x value={ I(Emem)*uv*Ron/D^2*f(V(x),p)} Cx x 0 1 IC={(Roff-Rinit)/(Roff-Ron)} Raux x 0 1G *********************************************** * RESISTIVE PORT MODELING * Emem plus aux value={-I(Emem)*V(x)*(Roff-Ron)} Roff aux minus {Roff} *********************************************** * WINDOW FUNCTION MODELING * .func f(x,p)={1-(2*x-1)^(2*p)} .ENDS memristor

Memristor simulation using PSPICE

101

V1

FREQ = 0.1VAMPL = 1VOFF = 0

U2

MEMRISTOR

0 1PLUSMINUS

0

I

input


The figures show how this

memristor model reacts to a

simple sinusoidal input voltage

Voltage

Curr

ent

102


V1

FREQ = 0.1VAMPL = 1VOFF = 0

U2

MEMRISTOR

0 1PLUSMINUS

0

I

inputThe figure shows that the

memristor current is not only

related to the applied voltage but

also to the history of the device as

expected for a hysteretic system

103

Memristor models in LTSPICE (free software)

A complete library of memristor models in LTSPICE can be found in: “MEMRISTOR DEVICE MODELING AND CIRCUIT DESIGN FOR READ OUT INTEGRATED CIRCUITS, MEMORY ARCHITECTURES, AND NEUROMORPHIC SYSTEMS”, PhD Thesis, Chris Yakopcic, University of Dayton, May 2014

104

http://www.linear.com/designtools/software/

105

Memristor models in Verilog-A

Z. Jiang et al, SISPAD (2014)

• Industry standard modeling language for analog circuits (subset of Verilog-AMS)

Memristor models in MODELICA

Fraunhofer Institute for Integrated Circuits IIS Design Automation Division EAS

Open-source Modelica-based modeling and

simulation environment intended for industrial and

academic usage (https://www.openmodelica.org/)

(free software)

106

https://www.openmodelica.org/https://www.openmodelica.org/

Memdiode model in LTSPICE

.subckt memdiode + -

.params ion=1e-2 aon=3 ron=100 ioff=1e-4 aoff=1 roff=100 + nset=10 vset=0.5 nres=10 vres=-0.5 CH0=1e-4 H0=0 ******************************************* * STATE EQUATION MODELING * BH 0 H I=min(R(V(+,-)),max(S(V(+,-)),V(H))) Rpar=1 CH H 0 {CH0} ic={H0} ****************************************** * RESISTIVE PORT MODELING * BR + - I=sgn(V(+,-))*(1/(a(V(H))*RS(V(H)))*w(a(V(H))* + RS(V(H))*I0(V(H))*exp(a(V(H))*(abs(V(+,-))+RS(V(H))* + I0(V(H)))))-I0(V(H))) Rpar=1e10 ****************************************** * AUXILIARY FUNCTIONS * .func w(x)=log(1+x)*(1-(log(1+log(1+x)))/(2+log(1+x))) .func I0(x)=ion*x+ioff*(1-x) .func a(x)=aon*x+aoff*(1-x) .func RS(x)=ron*x+roff*(1-x) .func S(x)=1/(1+exp(-nset*(x-vset))) .func R(x)=1/(1+exp(-nres*(x-vres))) .ends memdiode

G. Patterson et al, IEEE Trans Comp Aided Design, 2017

107

Simple circuits with memdiodes

Memdiodes driven by voltage and current sources

108

Simple circuits with memdiodes

Parallel and series memdiodes driven by voltage and current sources

109

Simulations of 1T1R structures (EU Project PANACHE)

Memdiode controlled by access transistor

In collaboration with LETI, France

MODEL

EXPERIMENT

110

In collaboration with UCL, UK

Simulation of MEMDIODE

using LTSpice

Model and simulation results for SiOx

Modeling multi-level conduction

Simulation of

MEMDIODE

using EXCEL

111






• Final comments

Outline

-3 -2 -1 0 1 2 310

-7

10-6

10-5

10-4

10-3

Experimental

Average

Median

LRS

Cu

rre

nt

[A]

Voltage [V]

RESET

SET

HRS

Variability in SiOx-based ReRAM devices

LRS: fully

formed filament

HRS: partially

formed filament

35

Origin of variability

VARIABILITY

EXTRINSIC INTRINSIC

Device-to-device:

• area

• thickness

• roughness

• composition

• contacts

• …

Discrete nature of

the problem:

• dopant

fluctuations

• morfophology

of the CF

• …

MEASUREMENT

• Cycling protocol

• Current limitation

• Ageing effects

• Signal excursion

36

Variability is also affected by the way we measure

-3 -2 -1 0 1 2 310

-7

10-6

10-5

10-4

10-3

Experimental

Average

Median

LRS

Cu

rre

nt

[A]

Voltage [V]

RESET

SET

HRS

0 10 20 30 40

5x102

103

1.5x103

6x104

9x104

1.2x105

1.5x105

1.8x105

HRS

LRS

Re

sis

tan

ce

@0

.5V

[

]

# Cycle

4x102

6x1028x10

210

52x10

5

0.0

0.2

0.4

0.6

0.8

1.0 LRS

HRS

Cu

mu

lative

pro

ba

bili

ty

[email protected] []

x 2102

• Excellent cyclability

• Good resistance window

• Trend in HRS

Effects of cycling on SiOx (C2C)

37

2.00 2.25 2.50 2.75 3.00

2x10-4

4x10-4

6x10-4

8x10-4

10-3

LRS

Curr

ent [A

]

Voltage [V]

End point of

voltage sweep

HRS

0 10 20 30 40 503x10

-5

4x10-5

5x10-5

6x10-5

7x10-5

8x10-5

9x10-5

1x10-4

V=1.5V

Trend

Experimental

Cu

rre

nt

[A]

# Cycle

• The trend in HRS is associated with the end point of the reset curve

• C2C is a stochastic process: trend + volatility

Effects of cycling on SiOx (C2C)

38






• Final comments

Outline

Source: Semiconductor Engineering (2017)

Latest news:

• Fujitsu and Panasonic are jointly ramping up a second-generation ReRAM device (OxRAM)

• Crossbar is sampling a 40nm ReRAM technology (CBRAM)

• TSMC and UMC recently put ReRAM on their roadmaps

• HP has moved towards a more traditional memory scheme for the system (“The machine”) and has backed away from the memristor

• 4DS, Adesto, Micron, Samsung, Sony and others are also developing ReRAM

• GlobalFoundries is not pushing ReRAM today

• ReRAM has proven to be far more difficult to develop than anyone initially expected

• NAND has scaled farther than previously thought, causing many to delay or scrap efforts in ReRAM

• ReRAM won’t replace NAND or other memories, but it is expected to find its place, particularly in embedded memory applications

• ReRAMs are well-positioned as a low-cost solution for IoT, wearable devices, and neuromorphic computing

• Today, 3D-XPoint and STT-MRAM have the most momentum

Will ReRAM technology succeed?

Source: Semiconductor Engineering (2017)

Muito obrigado!

Any doubt? Write me: [email protected]

compact modeling of hysteresis effects in reram devices · 2018. 9. 3. · compact modeling of...

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