Shockwaves in RRAM (memristive) systems Marcelo  J.  Rozenberg  

LPS  CNRS/Universite  Paris-­‐Sud  (Orsay,  France)    

collaborators:  Vlad  Dobrosavljevic  (Magnet  Lab  –  FSU)  Shao  Tang    Pablo  Levy  (CNEA-­‐Buenos  Aires)  Fernando  Marlasca    Federico  Tesler  (UBA-­‐Buenos  Aires)  Carlos  Acha    Pablo  Stoliar    (Nanogune  San  SebasMan–  AIST  Tsukuba)  

Neuromorphic  circuits  and  computaMon  is  a  very  hot  topic  

•  DARPA’s  Synapse  Program  •  EU  Human  Brain  Project  •  Facebook    •  Google  (DeepMind,  AlphaGo)  

Bio-­‐chips  (CMOS  hardware)   Deep  neural  networks  (soWware)  

Park  et  al  Nanotechnology  ‘13  

Novel  electronic  devices  for  neuromorphic  systems  

Neurons:  volaMle    ResisMve  Switching  

n°PCT/EP2015/058873    

A  Leaky-­‐Integrate-­‐and-­‐Fire    Neuron  Analogue  realized  with    a  Mob  insulator    (submibed)  

(2013)  

Synapses:  Non-­‐volaMle    ResisMve  Switching  

A  Sawa,  Mat  Today  (2008)  

non-­‐polar   bi-­‐polar  

HP’s  memristor  

TiO2,  NiO,  TaOx,  HfO2,  CuO,  FeO,  VO,  STO,  LSCO,  YBCO,  LCMO,  etc,  etc,  etc  

 Introductory  review:        MR    Scholarpedia  6(4):11414  (2011)  

Universal  funcMonality  of  TMOs    

Park  et  al  Nanotechnology  ‘13  

Neurons  and  Synapses:    Great  oportunity  for  oxyde  electronics  !  

Novel  electronic  devices  for  neuromorphic  systems  

Voltage-enhanced Oxygen difussion model (bi-polar)

Top  electrode  

Bobom  electrode  

Key ingredients Inhomogeneitites Oxygen vacancy Interfaces

Voltage-enhanced Oxygen diffusion (VEOD) model

b a

Ra Rb

Higly resistive interfaces (Schottky) Oxygen difussion (enhanced by V)

Inhomogeneity 1-d channels

(see also Jeong,Schroeder and Waser et al PRB’09 and R. Meyer et al NVMTS2008)

MR, Sanchez, Weht, Levy, Acha PRB ’10

V  

I  

V

R Rhi

Rlow

PLCMO YBCO

experiments  

Non-trivial test: “Table with legs” MR, Sanchez, Weht, Levy, Acha PRB ’10

V

R Rhi

Rlow

model  simulaMons  

Chen Ignatiev, APL’05

R  vs  V  data  on  LCMO  

Sum of two symmetric interface contributions

R

V 0

RL RR RT

Panasonic  MN101LR05D  8-­‐bit  MCU  with  Embedded  ReRAM  

Crossbar’s  integrated  device  RRAM  product  

Some  new  theoreMcal  insight  

Shock  Waves  and  Commuta=on  Speed  of  Memristors  Phys.  Rev.  X  6,  011028  (2016)                                                        Synopsis:  Waves  That  Shock  Resistance  

Recalling  shock  waves.    Key  noMon  is  the  speed  of  the  propagaMon  vs  speed  of  source  

standard  wave  equaMon,  velocity  is  c,  solve  for  u(x,t)

right  and  leW  propagaMng  

Wave  propagaMon  

iniMal  condiMon  

so,  the  propagaMon  speed  depends  on  the  perturbaMon  

one  we  may  add  a  difussive  term  

conservaMon  law  in  acousMcs  and    fluid  mechanics,  gas  dynamics,  etc  

These  last  two  are  Burger’s  equaMons  

right  propagaMng  perturbaMon  

 Burger’s  eq  can  develop  shockwaves    Key  feature  is:                The  propagaMon  velocity  increases  with  the  magnitude  of  the  perturbaMon  

Method  of  characterisMcs  

Ionic  (oxygen  vacancies)  moMon  under  an  electric  field  E

conservaMon  law:  

ion  concentraMon  

is  a  generalized  Burger’s  equaMon  

resisMvity  

Burger’s  

Then,  need  jdrift  faster  than  linear  in  u

is  a  generalized  Burger’s  equaMon  

resisMvity  

Burger’s  

Then,  need  jdrift  faster  than  linear  in  u

What  is  this  relaMon  in  the  VEOD  model?  predicts  shockwaves:  

So  it  predicts  shockwaves  

experiments  PLCMO   VEOD  model  simulaMons  

I

Rankine  –  Hugoniot  condiMon  

xint  

Scaling  law    is  realized!  

experiments  PLCMO   VEOD  model  simulaMons  

xint          width  of  Schobky  barrier    RHI        resistance  of  HI-­‐R  state

xint  

Summary  

•  We  now  have  arMficial  synapses  (and  neurons)  made  of  simple  2  terminal  oxides  

           whose  physics  is  based  on  the  physical  phenomenon  of  resisMve  switching  

•  The  way  is  open  for  neuromorphic  aplicaMons  

•  TheoreMcal  modeling  may  provide  useful  guidance  for  experiments