[paper] SPICE Model for Bipolar Resistive Switching Devices

Miranda, Enrique, and Jordi Suñé

Departament d’Enginyeria Electrònica,

UAB, 08193 Barcelona, Spain

Fundamentals and SPICE Implementation of the Dynamic Memdiode Model

for Bipolar Resistive Switching Devices

(2020 - techrxiv.org)

Abstract: This paper reports the fundamentals and SPICE  implementation of the dynamic memdiode model (DMM) for the  conduction characteristics of bipolar resistive switching (RS)  devices. Following Chua’s memristive devices theory, the  memdiode model comprises two equations, one for the electron  transport based on a heuristic extension of the quantum pointcontact model for filamentary conduction in dielectrics and a  second equation for the internal memory effect related to the  reversible displacement of atomic species within the oxide film.  The DMM represents a breakthrough with respect to the previous  quasi-static memdiode model (QMM) since it describes the  memory state of the device as a rate balance equation  incorporating both the snapback and snapforward effects,  features of utmost importance for the accurate and realistic  simulation of the RS phenomenon. The DMM allows simple setting  of the memory state initial condition as well as separate modeling  of the set and reset transitions. The model equations are  implemented in the LTSpice simulator using an equivalent  circuital approach with behavioral components and sources. The  practical details of the model implementation and its use are  thoroughly discussed.   

Fig: Hysteretic behavior of the filamentary-type I-V characteristic.

Filament stages: A) formation, high resistance state (HRS), B) completion, C) expansion,

D,F) complete expansion, low resistance state (LRS), G) dissolution, I) rupture.

Supplementary information: The memdiode model script for LTSpice XVII reported in this Appendix includes not only the DMM but also the QMM. It is important to activate one of the options at a time (DMM or QMM) by inserting asterisks (*) in the corresponding lines. The parameter list, I-V, and Auxiliary functions sections are common to both approaches. This does not mean that the obtained curves will be identical. The meaning of the parameters is discussed in the text and in previous papers.

LTSPICE script

.subckt memdiode + - H

*created by E.Miranda & J.Suñé, June 2020

.params

+ H0=0 ri=50

+ etas=50 vs=1.4

+ etar=100 vr=-0.4

+ imax=1E-2 amax=2 rsmax=10

+ imin=1E-7 amin=2 rsmin=10

+ vt=0.4 isb=200E-6 gam=1 gam0=0 ;isb=1/gam=0 no SB/SF

+ CH0=1E-3 RPP=1E10 I00=1E-10

*Dynamic model

BV A 0 V=if(V(+,-)>=0,1,0)

RH H A R=if(V(+,-)>=0,TS(V(C,-)),TR(V(C,-)))

CH H 0 1 ic={H0}

*Quasi-static model

*BH 0 H I=min(R(V(C,-)),max(S(V(C,-)),V(H))) Rpar=1

*CH H 0 {CH0} ic={H0}

*I-V

RE + C {ri}

RS C B R=RS(V(H))

BD B - I=I0(V(H))*sinh(A(V(H))*V(B,-))+I00

RB + - {RPP}

*Auxiliary functions

.func I0(x)=imin+(imax-imin)*limit(0,1,x)

.func A(x)=amin+(amax-amin)*limit(0,1,x)

.func RS(x)=rsmin+(rsmax-rsmin)*limit(0,1,x)

.func VSB(x)=if(x>isb,vt,vs)

.func ISF(x)=if(gam==0,1,pow(limit(0,1,x),gam)-gam0)

.func TS(x)=exp(-etas*(x-VSB(I(BD))))

.func TR(x)= exp(etar*ISF(V(H))*(x-vr))

.func S(x)=1/(1+exp(-etas*(x-VSB(I(BD)))))

.func R(x)=1/(1+exp(-etar*ISF(V(H))*(x-vr)))

.ends

Acknowledgements: This work was funded by the WAKeMeUP 783176 project, co‐ funded by grants from the Spanish Ministerio de Ciencia, Innovación y Universidades (PCI2018‐093107 grant) and the ECSEL EU Joint Undertaking and by project TEC2017-84321- C4-4-R funded by the Spanish Ministerio de Ciencia, Innovación y Universidades. Dr. G. Patterson and Dr. A. Rodriguez are greatly acknowledged for their contributions to the development of the ideas reported in this work