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On my honor as student of
the
U
niversity of
V
irginia
, I pledge that I have neither given nor
received
unauthorized aid on this final exam research paper
.









Memristors

Computing at the Nanoscale








Kyle Powers

ENGR 2500

Professor Bean

December 15
th
,
20
11

2

I.
Abstract

The purpose of this research paper
is

to provide an introduction to memristors (a
relatively old theory recently brought to fruition), a background of the current technology
used to produce modern
-
day microprocessors (transistors and
m
icrofabrication
), and a
connection between the two fields of study. Three different research publications are
explicitly referenced to demonstrate the success memristors have found in the
semiconductor industry

(such as in crossbar latches as a replacement

for transistors).
Conclusions are made to determine
the
memristor

s
importance

in the field of
microprocessor design, likelihood of industrial adoption, and future applications of its
existence.

II.
Author’s Aside


Intel, IBM, Infineon, and Varian Semiconductor


to the common reader,
they are
just a slew of high profile semiconductor co
mpanies; to me,
just
a rush of childhood
memories. Starting in ’95, my father began a series of employments by the aforementioned
co
mpanies with positions ranging from photolithography manufacturing technician at Intel
in New Mexico to hands
-
on microfabrication research at IBM in New York.
My mother,
having been employed by Intel since ’96, shares with me the weekly in’s and out’s of I
ntel’s
inside operations. Needless to say, I have been subliminally
, let alone explicitly,

influenced
to pursue a future in

the semiconductor industry,
which
I am currently on track to do

so
.

My focus is in VLSI (Very Large Scale Design), micro
processor d
esign of sorts. The
direction of
the
microprocessor/
central processing unit (CPU)

is obvious


smaller, faster,
and more energy efficient, but limitations become increasingly abundant in the near future

as corporations move to below the
16
-
nanometer

(nm)
t
hreshold
, as discussed in Section V
.
Intel, for example, plans to be at the

10nm mark by 2016.

So what is next
? What can we as
3

engineers do to hurdle the technological potholes that litter the streets of innovation? Are
memristors the answer? Could their v
ery existence be the technological breakthrough that
the
semiconductor
industry needs to
bypass the
future

disadvantages that plague
photolithograp
hy and the
current day
transistor? It is through this research paper that I
hope to
investigate my inquiries
and
arrive
at a concrete conclusion.

III.
History

In
his
1971

paper
,

Memristor

The Missing Circuit Element
,
UC Berkeley p
rofessor
,

Leon Chua
,

hypothesized the
two
-
terminal circuit element

he dubbed
the
memristor (a
contraction of both memory and resistor).
How he came to its formulation is

rooted in
basic circuit theory:

“The three basic two
-
terminal circuit elements are defined in terms of
a relationship between two of the four
fundamental circuit varia
bles, namely, the
current
i
, the voltage
ν
, the charge
q
, and the flux
-
linkage
φ
.”
[
1
]


From these four variables, six possible
combinations can be derived. Five of them
are

widely accepted:


(

)



(

)

(

)




and

(

)



(

)

(

)



,
the resistor (relationship
between
ν

and
i
), the inductor (relationship between
φ
and

i
), and the capacitor
(relationship between
q

and
ν
)
. Ch
ua argued that for completeness

there must exist a sixth
and final relationship
(the
relationship between
φ

and
q
), giving way to what would
eventually
become the fourth basic two
-
terminal element


the memristor.


http://www.nature.com/nature/journal/v45
3/n7191/pdf/nature06932.pdf

4

IV.
Memristor
[2]


For years
,

the memristor
went

physically

unrealized due to lack of interest among
st

engineers and scientists. This day and age, however, material experimentation has vastly
increased as the industry find
s and theorizes
numerous
uses of the memristor.

Because of
this drive to find a material with

suitable properties, numerous memristor prototypes have
been developed. The
se

prototypes can be
divided
into three main categories:
1)
Molecular
and Ionic Thin Film Memristive Systems
, 2)
Spin Based and Magnetic Memristive Systems
,
and 3)
3
-
terminal Memri
stors
.


Within the category of Molecular and Ionic Thin Film Memristive Systems exist four
types of memristors/memristive

systems:
Titanium d
iox
ide m
emristors
, polymeric
(ionic) memristors, manganite memristive
systems, and resonant
-
tunneling diode
memristors. Within the second category Spin
Based and Magnetic Memristive Systems exist
just two types of memristor/memristive
systems: Spintronic
Memristors and Spi
n
Torque Transfer (STT) MRAM. The 3
-
terminal memristor became re
alized as a basic
component of the

neural network architecture called ADALINE, developed by Bernard
Widrow and Ted Hoff.



The most prevalent of the aforementioned memristor prototypes is the
titanium
dioxide memristor
, first developed by H
ewlett
-
P
ackard

Lab
oratorie
s
.

The memristor is
comprised of a “two
-
layer thin ‘sandwich’ of titanium dioxide films, composed of

An array of 17 purpose
-
built oxygen
-
depleted
titanium dioxi
de memristors built at HP Labs”

5

symmetrical lattices of titanium and oxygen atoms.” Because the movement of elect
rons in
the material cause
s

a
motion of atoms in the films, a state change in the atomic structure of
the memristor occurs. The bottom layer acts as an insulator and due to the oxygen
vacancies in the titanium dioxide, the top

film layer acts as a conducto
r:

“The oxygen
vacancies in the top layer are moved to the bottom layer, changing the resistance, and
maintaining the state.” By applying
“crossbars” of nanowires above and below the
top and
bottom layers, a charge can
pass

through.





V.
Microprocessor


In the heart of the 21
st

century microprocessor lays a multitude of transistors


from
hundred
s to billions. Transistors serve as a switch of sorts, an ingenious manipulation of
analog circuitry into discrete
on and off modes,
1’s and 0’s.
The most common transistor
used in current day technology is the
complementary metal
-
oxide semiconductor field
-
effect
transistor, or CMOS for short. The term
c
omp
lementary is rooted in both its
opposite

and
symmetrical use of
both
n
-
type and p
-
type
transistors.
N
-
type transistors are fabricated in
such a way that there exists an excess of negative
electron charge
carriers, which can be done, for example, by doping silicon with
phosphorus. P
-
type tra
nsistors are just the opposite;
fabricated in such a way that there
The standardized symbol
for memristors for use in
circuit topologies

http://en.wikipedia.org/wiki/File:N
-
channel_mosfet.svg

6

exists an excess of positive holes, which can be done, for example, by doping silicon with
boron.



M
oore’s Law however, which states

that the number of transistors
doubles

on a
given chip every two years, meets its match when
transistors fall

below the 16nm mark


a
close approaching point in the industry.
[
3
]

The culprit lays in a fundamental concept
roo
ted
in quantum physics known as

quantum tunneling.

At the 16nm size and below, a
transistors gate’s size would be in the realm

of 5nm

or smaller



a point at which electrons
no longer need a gate voltage applied to jump the
channel and can instead burrow


or
tunnel


their way to the other side.
This occurrence is
an undesirable trait for a switch
-
like
component, as it would be “on” at times when it should not.

A shift from
silicon gates to
metallic ones
,

and advancements such as Intel’s more recent tri
-
ga
te technology
(nonplanar architecture)
have managed to push the limits of microfabrication at the
nanoscale, but there exist
s

a point in the near future in which new materials and new
components become a necessity for further technological advancement.

One

potential candidate in

replacing the transistor is a

Hewle
tt
-
Packard technology
known as the

crossbar latch. The crossbar latch is advantageous in that it assumes much
the same functionality of a transistor, but on a molecular scale.
This is possible due
to the
fact that the memristor devices that comprise
it can be s
caled down much smaller than a

transistor. A crossbar latch consists of a signal line crossed by two control lines
,

and by
varying th
e voltages sent through the control lines, a crossbar latch

can perform the major
digital logic functions AND, OR, and NOT. Follows is an analysis of Hewlett
-
Packard’s
original publishing:


7

VI.
The Crossbar Latch:

Logic Value Storage, Restoration, and Inversion in Crossbar Circuits
[
4]


Philip J. Kuekes and his tea
m at Hewlett
-
Packard Laboratories developed the
crossbar latch in solution to both signal restoration and inversion issues seen in
programmable crossbar circuits at the integrated nano
scale electronics level:

“[Signal]
restoration is essential before the d
egraded output of one logic gate can drive the input of a
subsequent logic gate. Inversion is required to generate a complete logic family.” By storing
a logic value on a signal wire, inversion and logic value restoration
is
enabled; furthermore,
when comb
ined with resistor/diode logic gates, “these operations in principle enable
universal computing for crossbar circuits, and potentially, integrated nanoscale
electronics.”


While standard semiconductor latch circuits use three
-
terminal transistors for
swi
tching, HP Labs proposes an alternative latching concept suited for application in two
-
terminal crossbar circuits. “Two control lines
C
A

and C
B

are connected to a signal line L with
bi
-
stable two
-
terminal switches S
A

and S
B
.
Each switch
h
as a polarity and
a voltage
threshold for toggling to a closed or an open
state.”

As indicated by the direction of the
arrows,
the two switches are oriented
antiparallel t
o each other in their polarity. The
signal line has at least two different voltage
8

states, ranging
from

a logical 0 to a logical 1:

“If the input to the signal line represents the
output value of a diode/resistor logic function, the magnitude of the potential will in
general be degraded from the true 0 or 1 voltage states.” To restore this signal value to t
he
appropriate full potential


a critical function


“a sequence of voltage pulses is applied to
each control line, which unconditionally opens both switches, conditionally closes on
e

of
them, then restores (and optionally inverts) the signal level.”



Ut
ilizing

varying voltage pulses and switches of opposite polarities, the necessar
y
basic logic functions
are

realized: AND, OR, and NOT. At each intersection of wire, a bit of
memory can be stored or a logic function can be performed. Conclusively, this lea
ds to
potential uses in microprocessors as a replacement for transistors
; “T
his could very well
replace transistors in computers someday, just as transistors replaced vacuum tubes and
vacuum tubes replaced ele
ctromagnetic relays before them,
"

says Kuekes.
Williams, co
-
author, adds,
"The crossbar latch provides a key element needed for building a computer
using nanometer
-
sized devices that are relativel
y inexpensive and easy to build
.”


V
I
I
.
Memristor

CMOS Hybrid Integrated Circuits for Reconfigurable Logic
[
6
]


Hewlett
-
Packard Laboratories takes an
additional

route by “creating hybrid
reconfigurable logic circuits fabricated by integrating memristor
-
based crossbars onto a
foundry
-
built CMOS platform using nanoimprint lithography…” The titanium dioxide thin
-
film memristors serve as the configuration bits and sw
itches in a data routing network and
are connected to gate
-
level CMOS components that act as logic elements, “in a manner
similar to a field programmable gate array.”


In an attempt to extend Moore’s Law beyond the
limits of transistor scaling, Qiangfei
Xi
a and team decided to obtain the equivalent circuit functionality using fewer devices or
9

components, “i.e., get more computing per transistor on a chip.” By modifying the hybrid
CMOS/molecule (CMOL) architecture, HP Labs was able to improve the manufactura
bility
and separate the routing and computing functions. This modification, called Field
-
Programmable Nanowire Interconnect (FPNI), “separates the logic elements from the data
routing network by lifting the configuration bits, routing switches, and associa
ted
components out of the CMOS layer and making them a part of the interconnect.”


Memristor crossbars can be fabricated
directly above the CMOS circuits and serve as the
reconfigura
ble data routing network:

“A 2D array of
vias provides electrical connectivity between the
CMOS and the memristor layer. Memristors are ide
al
for this FPGA
-
like application because a single device
is capable of realizing functions that need several
transistors in a CMOS circuit, namely, a
configuration
-
bit flip
-
flop and associated data
-
routing multiplexer.” Another advantage is their
memory f
unction, which is nonvolatile (they do not
require power to refresh their states, even if the
power to the chip is turned off completely).
“Moreover, with appropriate defect
-
finding and
control circuit
r
y, the redundant data paths for the crossbar structure

enable alternate
routes through the interconnects, resulting in a highly defect
-
tolerant circuit.” Through
numerical simulations, the aforementioned architecture can dramatically increase logic
“(a) Conceptual illustration of the
memristor

CMOS hybrid architecture.
(b) Schematic top view of the nanowires
forming the crossbar. (c) Schematic of a
signal path in a
logic circuit.”

10

density of an FPGA
-
like chip

without degrading “power dissipa
tion or speed even in the
presence of large numbers (up to 20%) of defective components.”


With several selected memristors turned on, gates on the CMOS layer can be “
wired
up” into digital circuits on the hybrid chip. Basic logic gates such as NOT, OR, AND, NAND,
NOR, and even a positive
-
edge
triggered D flip
-
flop can be configured
in this hybrid circuit.

Because it is
possible that neighboring memristors
that share th
e same nanowire
electrode might be configured at the
same time, the HP Labs team
designed it so that “all other
memristors are biased at half o
f

the
write voltage, which does not change the states of any memristors.”

Most importantly
are

the memristor’s st
ates (ON or OFF), which can be changed
by applying the proper voltages
making

the hybrid circuits reconfigurable.


As aptly demonstrated, the successful integration of memristors with CMOS opens
up opportunities in other areas:

“One application is for nonv
olatile random access memory
(NV
-
RAM) integrated with logic using standard CMOS processing technology, which is
compatible with the simple structures and the materials used for memristors.” Another
application of hybrid technology is for non
-
Boolean neurom
orphic computing:

“With
memristors as electronic synapses and silicon transistors as ‘neurons’, hybrid circuits may
be able to implement self
-
organization and learning.”

CMOS layer fabric on a die and possible wiring for digital
circuits using memristors

11

VII
I
.
Flexible Memristive Memory Array on Plastic Substrates
[
7
]

The team of Professor
Keon Jae Lee (Department of Materials Scie
nce and
Engineering, KAIST)
developed fully functional flexible non
-
volatile resistive random
access memory (RRAM) where a memory cell can be randomly accessed, written, and
erased on a plastic substrate. Memory is

an essential part in electronic systems, as it is used
for data processing, information storage and communication with external devices. The
development of flexible memory has been a challenge to the realization of flexible
electronics.


This is a schema
tic of a fully functional flexible memory array on flexible substrates

Several flexible memory materials have been reported. These devices
cannot

overcome
cell
-
to
-
cell interference due to their structural and material limitations. To solve this
problem, sw
itching elements such as transistors must be integrated with the memory
elements. Unfortunately, most transistors built on plastic substrates (e.g., organic/oxide
transistors) are not capable of achieving the sufficient performance level with which to
12

driv
e conventional memory. For this reason, random access memory operation on a
flexible substrate has not been realized
.

Professor Lee’s research team developed
a fully functional flexible memory t
hat is not
affected by cell
-
to
-
cell interference. They
solved
this

issue by integrating a memristor
with a high
-
performance single
-
crystal
silicon transistor on flexible substrates
.

Utilizing the two aforementioned
advanced technologies, they successfully
demonstrated that all memory functions in

a
matrix memory array (writing, reading,
erasing) worked perfectly:

“This result represents
an exciting technology with the strong potential to realize all flexible electronic systems for
the development of a freely bendable and attachable computer in the near future.”

VI
I
I.
Conclusion


T
he memristor, while theorized deca
des ago, has finally come to fruition. With its
physical realization
s

have come some of the finest technological and computational
advancements

at the nanoscale. From non
-
volatile memory applications to low
-
power and
re
mote sensing applications,
analog com
putation and circuit applications to circuits which
mimic neuromorphic and biological systems, the memristor can find itself used in a
multitude of applications.
[8
]

My initial inquiry still stands
,

however; will memristors make
the transistor go the way of

the vacuum tube?

Not just yet, it seems. Commercial production is limited and industrial adoption is
slow. With the
fine
-
tuned microfabrication techniques
of silica
developed over the past few
This is an image of flexible memory wrapped on quartz rod

13

tens of years, the transistor will undeniably serve as the go
-
to component for at least the
next five
-
to
-
ten years.

The physics do not lie
, however
. Quantum tunneling is an
undesirable attribute that will undeniably plague the future of sub
-
16nm transistors. New
components are a necessity
,

and companies that play th
e bi
-
yearly die
-
shrink game, l
ike
Intel, should indubitably research

alternative materials for their products. But are
memristors the most likely solution?

The r
esearch would suggest so. Memristors, when used in the afore
mentioned
crossbar latch setting
, h
ave the ability to not only take on the necessary attributes of
today’s transistors; but also, the more desired attributes such as low power consumption.
Digital logic functions can be realized and with that, a true computational microprocessor

at the mole
cular level
.
Granted
, the memristor and the related can fall short in some
categories

(like speed

in some cases
)
, but their development has only been in progress
for a
few years.
The

transistor to
ok decades to

achieve what it has

up to this point
,

and

the
memristor


or some future
derivation

of it


could be in that exact same position just years
from now.

The more likely result of this collective research at the nanoscale level is a type of
hybrid technology utilizing memristors on top of current mic
rofabrication techniques, as
demonstrated in the aforementioned HP Labs’ Memristor

CMOS hybrid integrated c
ircuit.
In their paper, they
ingeniously propose, “I
t may be possible and even necessary in the
future to freeze CMOS technology at a particular feat
ure size because of either physical or
economic constraints but then continue to build on top of that platform scaled crossbars
that can continue to add functionality to the hybrid system as the density of memristors
increases.


14

When Chua first proposed th
e memristor in 1971, surely he could not have foreseen
the implications of his research. For decades
,

the memristor went unrealized with
little
interest. W
hat began as a mere theory eventually
turned into

an extremely versatile
component.
Now that a need f
or nanoscale products exist, and will continue to increase as
current solutions become physically inept

and research methods improve
, memristors will
one day get
the spotlight they deserve. Predictably, transistors will be a thing of the past.

Sources

[1]

Memristor
-
The Missing Circuit Element:


http://ieeeghn.org/wiki/images/b/bd/Memristor_chua_article.pdf

[2]

Types of Memristors:


http://www.memristor.org/reference/295/types
-
of
-
memristors


[3
]

Intel scientists find wall for Moore’s Law:

http://www.zdnet.com/news/intel
-
scientists
-
find
-
wall
-
for
-
moores
-
law/133066

[4]

The crossbar latch: Logic value storage, restoration, and inversion in crossbar circuits:

http://dx.doi.org/10.1063/1.1823026


[
5
]

The m
issing memristor found:


http://www.nature.com/nature/journal/v453/n7191/pdf/nature06932.pdf


[
6
]
Memristor

CMOS Hybrid Integrated Circuits for Reconfigurable Lo
gic


http://pubs.acs.org/doi/pdf/10.1021/nl901874j


[
7
]
Flexible Memristive Memory Array on Plastic Substrates:

http://pubs.acs.org/doi/pdf/10.1021/nl203206h


[
8
]
Memristor Applications:

http://www.memristor.org/reference/294/memristive
-
memristor
-
applications