Memory Transistors

8/2/2019 Memory Transistors

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Memristive Systems Analysis of

3-Terminal Devices

Blaise Mouttet

ICECS 2010December 12-15Athens, Greece


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Overview Review of Memristive, Mem-capacitive, and Mem-

inductive Systems

Introduction to Mem-Transistor Systems Small signal analysis of Mem-Transistor Systems

Examples

Widrow-Hoff memistor

Synaptic floating gate transistor Nano-ionic MOSFET


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Memristive Systems Resistive dynamic system

defined by a state vector x

v= R(x,i,t)i

dx/dt = f(x,i,t)

Degenerates to linearresistor at high frequency(property 6)

Examples of memristive

behavior was originallynoted from thermistor,neural models anddischarge tubes.

L.O. Chua, S.M. Kang. Memristive Devices and Systems, Proceedings of the IEEE,

Vol. 64, iss.2 (1976)


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In 1967 Argall demonstrated

zero-crossing resistancehysteresis and frequencydependence for thin film TiO2.

F.Argall Switching Phenomena in Titanium Oxide Thin Films, Solid-State Electronics,

Vol. 11, pp.535-541 (1968).


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Mem-capacitive Systems Capacitive dynamic

system defined by astate vector xq= C(x,v,t)v

dx/dt = f(x,v,t) Degenerates to linear

capacitor at highfrequency

Examples of mem-capacitive behavior arefound in nanocrystaland perovskite thinfilms

M. DiVentra, Y. V. Pershin, L.O. Chua, Putting Memory into Circuit Elements:

Memristors, Memcapacitors, and Meminductors, Proceedings of the IEEE,vol 97, iss.8,(2009)


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Mem-inductive Systems Inductive dynamic

system defined by astate vector x

f= L(x,i,t)i

dx/dt = f(x,i,t)

Degenerates to linearinductor at highfrequency

Examples of mem-inductive behavior arefound in MEMSinductors

Y. V. Pershin, M. DiVentra, Memory effects in complex materials and nanoscalesystems, arXiv:submit/0144853 (2010)


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Transistor = Transfer Resistor

(can amplify signals but is memory-less)

Memristor = Memory Resistor(has memory but dissipates signal energy)

Is it possible to build a singular non-linearcircuit element having features of both a

memristor and a transistor?


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2-Port Model of Voltage-Controlled

Transistor

I1 = g(V1,V2)I2= h(V1,V2)

I1 = Y11V1+Y12V2I2= Y21V1+Y22V2

Small signallinearization


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2-Port Model of Voltage-Controlled

Mem-Transistor

I1 = g(V1,V2,x)I2= h(V1,V2,x)dx/dt =f(V1,V2,x)


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TransconductanceIn the LaPlace domain the transconductance is determinedfrom the small signal linearization. System stability is determined

by the sign of

g

0g0

0g0

g

0g00g0

g

dm

v)x,h(V

x

)x,f(Vs

v

)x,f(V

x

)x,h(V

(s)V(s)Ig

x

)x,f(V 0g0


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Transconductance

g

0g0

0g0

g

0g00g0

g

d

m v

)x,h(V

x

)x,f(Vj

v

)x,f(V

x

)x,h(V

(s)V

(s)I

g

For periodic excitation frequencies (s=jw) the transconductanceof a mem-transistor is generally a frequency dependent complexnumber and represents both gain and a phase shift between

the input and output signals.


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Transconductance

g

0g0

0g0

g

0g00g0

g

d

m v

)x,h(V

x

)x,f(Vj

v

)x,f(V

x

)x,h(V

(s)V

(s)I

g

At high excitation frequencies (w) the first term reducesto zero and the transconductance reduces to that of an ordinarytransistor.


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Examples


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Example #1:Widrow-Hoff Memistor

B. Widrow, An Adaptive ADALINE Neuron Using Chemical Memistors, Stanford

Electronics Laboratories Technical Report 1553-2, October 1960.

In 1960 a 3-terminalelectrochemicalmemistor was

developed by BernardWidrow and MarcianHoff.

The memistor formeda central componentto an early ANN andthe development ofthe LMS algorithm.


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Example #1:Widrow-Hoff Memistor

B. Widrow, An Adaptive ADALINE Neuron Using Chemical Memistors, Stanford

Electronics Laboratories Technical Report 1553-2, October 1960.

The memistor was experimentally shown to demonstrate acharge- dependent conductance in a similar fashion to thelater predicted memristor of Chua.


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Example #2: Synaptic Transistor

C.Diorio,P.Hasler,B.A.Minch,C.A.Mead, A single-transistor silicon synapse, IEEE

Transactions on Electron Devices, Vol. 43, No. 11, Nov. 1996.

Since the 1990sanalog floating gateMOSFET transistors

have been designed toact as synapses forneuromorphichardware.


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Example #2: Synaptic Transistor

C.Diorio,P.Hasler,B.A.Minch,C.A.Mead, A single-transistor silicon synapse, IEEE

Transactions on Electron Devices, Vol. 43, No. 11, Nov. 1996.

VVdc

Vm

d

VVdc

V

Vgc

V

VbiVdg

V

bidgg

VVdc

V

Vgc

V

Tcorner

ewi

weeVVi

ew

Qww

ww

dt

dw

1

)(

2

2

0

2

2

1

1

max

The sub-thresholdmodeling equationsdeveloped by Diorio et

al. represent a 1st

order, voltage-controlled mem-transistor with thestate variable equal tothe source current and

Vgc as the controlvoltage.


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Example #3: Nano-ionic FET

D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams The missing memristor found,

Nature, Vol. 453, May 2008.

Nano-ionic motion of oxygenvacancies in TiO2/TiO2-x hasbeen used by Strukov et al. to

explain memristive effects. If TiO2 thickness > tunneling

gap then memcapacitiveeffects would be expected as a

result of ionic drift.


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Example #3: Nano-ionic FET

2kT

w)a,qE(Vsinhfae

dt

dw

(w)V

V1(w)VV

2L

WC(w)I

0.5VV(w)VVLWC(w)I

n(w)kT

qV(w)expII

GCU/kT

A

DS2

TGSnd

2DSDSTGSnd

GS0d sub-threshold region

saturationregion

triode region

Ionic drift equation:

Long channel MOSFET equations:


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N-port Memory Resistive Systems

I1 = g1(V1,V2,..,Vn,x)I2= g2(V1,V2,..,Vn,x)

.

.In= gn(V1,V2,..,Vn,x)

dx/dt =f(V1,V2,..,Vn,x)

B.Mouttet Memristive Transfer Matrices, arXiv:1004:0041 (2010)

B.Mouttet Programmable Crossbar Signal Processor, U.S. Patent 7 302 513, (2007)


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Summary Mem-transistor systems analysis has been proposed based

on non-linear, dynamic 2-port systems. A generalized transconductance of mem-transistors

includes both gain and phase shift and may be useful todetermining mem-transistor stability.

Some 3-terminal electronic devices have been shown toexhibit memory effects over the past 50 years but thetransistor models have rarely included non-linear dynamicsystems analysis.

In addition to memristors, memcapacitors, andmeminductors, mem-transistors will likely play anincreasingly important role in 21st century electronics toachieve neuromorphic and bio-inspired computing.

Memory Transistors

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