Carbon nanotube-based nonvolatile random access memory for molecular computing

TL;DR: A concept for molecular electronics exploiting carbon nanotubes as both molecular device elements and molecular wires for reading and writing information was developed and the viability of this concept is demonstrated by detailed calculations and by the experimental realization of a reversible, bistable nanotube-based bit.

Abstract: A concept for molecular electronics exploiting carbon nanotubes as both molecular device elements and molecular wires for reading and writing information was developed. Each device element is based on a suspended, crossed nanotube geometry that leads to bistable, electrostatically switchable ON/OFF states. The device elements are naturally addressable in large arrays by the carbon nanotube molecular wires making up the devices. These reversible, bistable device elements could be used to construct nonvolatile random access memory and logic function tables at an integration level approaching 10 12 elements per square centimeter and an element operation frequency in excess of 100 gigahertz. The viability of this concept is demonstrated by detailed calculations and by the experimental realization of a reversible, bistable nanotube-based bit.

Summary

Summary

• A concept for molecular electronics exploiting carbon nanotubes as both molecular device elements and molecular wires for reading and writing information was developed.
• Each device element is based on a suspended, crossed nanotube geometry that leads to bistable, electrostatically switchable ON/OFF states.
• The device elements are naturally addressable in large arrays by the carbon nanotube molecular wires making up the devices.
• These reversible, bistable device elements could be used to construct nonvolatile random access memory and logic function tables at an integration level approaching 10 12 elements per square centimeter and an element operation frequency in excess of 100 gigahertz.
• The viability of this concept is demonstrated by detailed calculations and by the experimental realization of a reversible, bistable nanotube-based bit.

Figures

Figure 4. Carbon nanotube devices. (A) I–V curves for the lower (electrodes 1 and 2, solid circles) and upper nanotubes (electrodes 3 and 4, open circles). The two-terminal resistances are 11 and 58 kilohms, respectively. The inset shows a dark-field optical micrograph of the nanotube crossing (scale bar, 4 µm). The 150-nm-high chromium-gold electrodes were fabricated using electron beam lithography on an oxidized (600-nm-thick SiO2) highly doped silicon substrate. The gap between electrodes 1 and 2 is 5 µm, and that between electrodes 3 and 4 is 3.4 µm. Fiftynanometer-thick nanotube ropes were attached to the electrodes from nanotube-platinum tips using a micromanipulator under an optical microscope. (B) I–V curves of the nanotube junction in OFF (open triangles) and ON (solid circles) states measured between electrodes 2 and 3; the junction was switched from OFF to ON at 2.5 V. The ON resistance, 112 kilohms, is ~105 times lower than the OFF resistance. The inset shows the OFF state I– V on an expanded current scale. (C) Reversible switching of a suspended nanotube junction similar to the one shown in the inset of (A). The bias voltage for switching the junction ON was ±5 V and for switching OFF was 40 V. The resistance ratio between OFF and ON states is Roff/Ron ~ 10, with average OFF and ON resistances of Roff = 1.36 gigohms and Ron = 140 megohms, respectively. The junction was reversibly switchable for several days. All of the I-V data were recorded under ambient conditions at room temperature.

Figure 3. Electrostatic switching of the nanotube device. Plots of the energy, ET = EvdW + Eelas + Eelectro, as a function of separation at the cross point for (A) switching ON and (B) switching OFF. In (A), plots (i), (ii), and (iii) correspond to ET for V1 = V2 = 0 V and V1 = +3 V, V2 = –3 V and V1 = +4.5, and V2 = –4.5 V, respectively, where V1 and V2 are the potentials applied to the two crossing nanotubes. In (B), (i), (ii), and (iii) correspond to V1 = V2 = 0 V, V1 = V2 = +15 V, and V1 = V2 = +20 V, respectively. These potentials are applied with respect to the conducting ground plane (e.g., Figure 1A). The minimum magnitudes of the voltages required for switching ON and OFF are 4.5 and 20 V, respectively. The electrostatic energy was calculated by numerically solving the Laplace equation using the boundary element method with 3600 elements for a 20-nm device supported on silicon with a 1.4-nm initial separation. The calculated electrostatic potential was checked carefully to see that it satisfied the boundary conditions and asymptotic behavior.

Figure 2. Bistable nanotube device potential. (A) Plots of energy, ET = EvdW + Eelas, for a single 20-nm device as a function of separation at the cross point. The series of curves correspond to initial separations of 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, and 2.4 nm, with two well-defined minima observed for initial separations of 1.0 to 2.0 nm. These mimima correspond to the crossing nanotubes being separated and in vdW contact. (B) Calculated structures of the 20-nm (10, 10) SWNT device element in the OFF (top) and ON (bottom) states. The initial separation for this calculation was 2.0 nm; the silicon support structures (elastic modulus of 168 GPa) are not shown for clarity. (C and D) Plots of the bistability range for the crossed nanotube elements as a function of device size. The suspended nanotube is supported on silicon (C) or on an organic layer (D) with an elastic modulus of 12 GPa (29). In both plots, the range of initial separations yielding bistable devices is gray. In general, the bistable region increases with device size, and the softer organic support yields a larger range of bistability, especially in the smallest structures. The calculations were carried out for (10, 10) SWNTs with an elastic modulus of 1 TPa and Lennard-Jones parameters of C6 = 32.00 × 10 –60 erg·cm6 and C12 = 55.77 × 10 –105 erg·cm12.

Figure 1. Suspended nanotube device architecture. (A) Three-dimensional view of a suspended crossbar array showing four junctions with two elements in the ON (contact) state and two elements in the OFF (separated) state. The substrate consists of a conducting layer [e.g., highly doped silicon (dark gray)] that terminates in a thin dielectric layer [e.g., SiO2 (light gray)]. The lower nanotubes are supported directly on the dielectric film, whereas the upper nanotubes are suspended by periodic inorganic or organic supports (gray blocks). Each nanotube is contacted by a metal electrode (yellow blocks). (B) Top view of an n by m device array. The nanotubes in this view are represented by black crossing lines, and the support blocks for the suspended SWNTs are indicated by light gray squares. The electrodes used to address the nanotubes are indicated by yellow squares.

Full text

University of Nebraska - Lincoln University of Nebraska - Lincoln
DigitalCommons@University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln
Barry Chin Li Cheung Publications Published Research - Department of Chemistry
July 2000
Carbon Nanotube-Based Nonvolatile Random Access Memory for Carbon Nanotube-Based Nonvolatile Random Access Memory for
Molecular Computing Molecular Computing
Thomas Rueckes
Harvard University, Cambridge, MA
Kyoungha Kim
Harvard University, Cambridge, MA
Ernesto Joselevich
Harvard University, Cambridge, MA
Greg Y. Tseng
Harvard University, Cambridge, MA
Chin Li Cheung
University of Nebraska at Lincoln
, ccheung2@unl.edu
See next page for additional authors
Follow this and additional works at: https://digitalcommons.unl.edu/chemistrycheung
Part of the Chemistry Commons
Rueckes, Thomas; Kim, Kyoungha; Joselevich, Ernesto; Tseng, Greg Y.; Cheung, Chin Li; and Lieber,
Charles M., "Carbon Nanotube-Based Nonvolatile Random Access Memory for Molecular Computing"
(2000).
Barry Chin Li Cheung Publications
. 9.
https://digitalcommons.unl.edu/chemistrycheung/9
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Authors Authors
Thomas Rueckes, Kyoungha Kim, Ernesto Joselevich, Greg Y. Tseng, Chin Li Cheung, and Charles M.
Lieber
This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/
chemistrycheung/9

In the past several decades, there has been
a nearly constant exponential growth in the
capabilities of silicon-based microelectron-
ics
(1). However, it is unlikely that these ad-
vances will
continue much into the new mil-
lennium, because fundamental physical
limitations, which prevent current designs
from functioning reliably
at the nanometer
scale, will be reached while at the same time
exponentially rising fabrication costs will
make it prohibitive
to raise integration levels.
Molecular electronics (2,
3) can in principle
overcome these limitations of silicon
technol-
ogy, because it is possible to have single-mol-
ecule devices
that are organized cheaply in
parallel by self-assembly. Much
effort in this
area has been focused on organic molecules
as device
elements, with very recent demon-
strations of irreversible switches
(4) and large
negative differential resistances (5)
for en-
sembles of molecules sandwiched between
metal electrodes.
The connection of molecu-
lar switching elements to the molecular
wires
that will be required for high-density integra-
tion and the
function of such structures re-
mains a substantial challenge.
Nanometer-diameter single-walled car-
bon nanotubes (SWNTs) exhibit unique elec-
tronic, mechanical, and chemical properties
that
make them attractive building blocks for
molecular electronics
(6, 7). Depending on
diameter and helicity,
SWNTs behave as one-
dimensional metals or as semiconductors (8),
which, by virtue of their great mechanical
toughness and chemical
inertness, represent
ideal materials for creating reliable, high-
density
input/output (I/O) wire arrays. How-
ever, viable strategies for
introducing molec-
ular-scale device functionality into such I/O
lines have not been established. SWNTs have
been used to make
low-temperature single-
electron (9) and room temperature
eld effect
(10) transistors. Smaller devices based
on in-
tratube junctions have been proposed (11)
and
observed recently in experiments (12), al-
though no
approaches yet exist for either the
controlled synthesis of nanotube
junctions or
the integration of many addressable junctions
as
needed for molecular-scale computing.
Our concept for integrated molecular
electronics differs substantially from previ-
ous efforts (2-5),
because it exploits a sus-
pended SWNT crossbar array for both I/
O
and switchable, bistable device elements
with well-dened OFF
and ON states (Figure
1). This crossbar consists of a set
of parallel
SWNTs or nanowires on a substrate and a set
of perpendicular
SWNTs that are suspended
on a periodic array of supports (Figure 1A).
Each cross point in this structure corresponds
to a device element
with a SWNT suspended
above a perpendicular nanoscale wire. Quali-
tatively,
bistability can be envisioned as aris-
ing from the interplay of
the elastic energy,
which produces a potential energy minimum
at nite separation (when the upper nanotube
is freely suspended),
and the attractive van der
Waals (vdW) energy, which creates a
second
energy minimum when the suspended SWNT
is deected into
contact with the lower nano-
tube. These two minima correspond to
well-
dened OFF and ON states, respectively;
that is, the separated
upper-to-lower nanotube
junction resistance will be very high,
whereas
the contact junction resistance will be orders
of magnitude
lower. A device element could
be switched between these well-dened
OFF and ON states by transiently charging
the nanotubes to produce
attractive or repul-
sive electrostatic forces. On the basis of
this
switching mode, we can characterize the ele-
ments as nano-
or molecular-scale electrome-
chanical devices.
In the integrated system, electrical con-
tacts are made only at one end of each of the
lower and upper sets of nanoscale wires
in
the crossbar array, and thus, many device el-
ements can be addressed
from a limited num-
ber of contacts (Figure 1B). At each
cross
point (n, m) in the array, the suspended (up-
per) SWNT can
exist in either the separated
OFF state or the ON state in contact
with
the perpendicular nanotube on the substrate
(lower SWNT).
The ON/OFF information at
an (n, m) element thus can be read easily
by
measuring the resistance of the junction and,
moreover, can
be switched between OFF and
ON states by applying voltage pulses
at elec-
trodes n and m. This approach suggests a
highly integrated,
fast, and macroscopically
addressable nonvolatile random access
mem-
ory (RAM) structure that could overcome the
fundamental limitations
of semiconductor
RAM in size, speed, and cost.
To quantify the bistability and switching
behavior of the proposed device element, we
calculated the total energy E
T
E
T
= E
vdw
+ E
elas
+ E
elec
(1)
where E
vdw
is the vdW energy, E
elas
is the
elastic energy, and E
elec
is the electrostatic
energy for the device. The rst
two terms in
Equation 1, which dene the static potential,
were evaluated to assess the range of param-
eters that yield bistable
devices. The vdW in-
teraction between nanotubes was calculated
by pairwise summation of a Lennard-Jones
potential that has been
previously shown to
provide good agreement with experiments for
nanotube systems (13, 14). The elastic con-
tribution
to the total energy was determined
with a beam mechanics model
(2)
where B is the product of the nanotube elastic
Published in Science Vol. 289, no. 5476 (July 7, 2000), pp. 94–97; doi 10.1126/science.289.5476.94
Copyright © 2000 by the American Association for the Advancement of Science. Used by permission.
http://www.sciencemag.org/cgi/content/full/289/5476/94
Submitted March 15, 2000; accepted May 26, 2000.
Carbon Nanotube-Based Nonvolatile Random Access Memory
for Molecular Computing
Thomas Rueckes,
1
Kyoungha Kim,
2
Ernesto Joselevich,
1
Greg Y. Tseng,
1
Chin-Li Cheung,
1
and Charles M. Lieber
1,2,
*
1
Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA.
2
Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
* Corresponding author; email: cml@cmliris.harvard.edu
A concept for molecular electronics exploiting carbon nanotubes as both molecular device elements and molecular wires for
reading and
writing information was developed. Each device element
is based on a suspended, crossed nanotube geometry that leads
to bistable, elec-
trostatically switchable ON/OFF states. The device
elements are naturally addressable in large arrays by the carbon
nanotube molecular
wires making up the devices. These reversible,
bistable device elements could be used to construct nonvolatile
random access memory and
logic function tables at an integration
level approaching 10
12
elements per square centimeter and an element operation frequency
in excess
of 100 gigahertz. The viability of this concept is demonstrated
by detailed calculations and by the experimental realization of
a reversible, bi-
stable nanotube-based bit.
94

Ca rbo n nan otu be-bas ed no nvo latile raM f or Mo leC ula r CoMput ing 95
modulus and geometric moment of inertia, k
is the elastic modulus of the support,
L is the
length of the suspended nanotube, β = 1/√
¯
2
(k/B)
1/4
, and δz is the displacement of the
suspended tube from its unstrained
position
(15). Our calculations show that the proposed
SWNT device structure will exhibit bista-
bility for a broad range
of parameters (Fig-
ure 2). The 20-nm device in Figure 2A
exhib-
its ON and OFF states that are stable at room
temperature
(i.e., barrier  10k
B
T; k
B
is the
Boltzmann constant and T is
temperature) for
initial separations ranging from 1.0 to 2.2 nm.
The calculated structures of the SWNT de-
vice element in the OFF
and ON states for an
initial separation of 2 nm (Figure 2B)
high-
light the relatively minor distortion of the
upper SWNT in
the ON state (this nanotube
does not buckle or kink when deformed),
even when the initial separation is near the
upper limit for bistability
and deformation is
at a maximum. These calculations also show
that the potential is bistable for a wide range
of device sizes
when the upper nanotube is
supported on either hard (Figure 2C)
or soft
organic (Figure 2D) materials. The mini-
mum bistable
device size for a hard support
such as silicon is <10 nm, and
softer organic
supports enable bistability for devices that
are
<5 nm. Both types of materials could be
envisioned for device
fabrication.
There are several important points that
can be drawn from these calculations. First,
there is a wide range of parameters that
yield
a bistable potential for the proposed device
conguration.
The robustness of the ON/OFF
states strongly suggests that this
architecture
will be tolerant of variations in structure that
inevitably arise during fabrication by, for ex-
ample, self-assembly.
Second, the differ-
ences in separation between nanotubes in the
ON and OFF states will produce large differ-
ences in resistance
[i.e., I ~ exp(–kd), where
I is the current, k is a decay constant
on the
order of 2 Å
–1
, and d is the tube-tube sepa-
ration in angstroms] and thus should
enable
reliable reading of the ON and OFF states
independent of
variations in cross-contact
resistance. Third, the range of mechanical
strains required to achieve bistability in Fig-
ure 2A, 0.22
to 1.7%, is well below the elas-
tic limit of at least 6% [determined
compu-
tationally (16) and experimentally (17)
for
SWNTs], and the average bending angle in
the ON state is about
half the angle required
to buckle nanotubes. Hence, these device
el-
ements should be robust as required for a re-
liable molecular-scale
computer (18), and the
nanotube electronic properties
should not be
substantially affected by deformation to the
ON
state. The range of strains does exceed,
however, the failure
limit of most other ma-
terials and thus suggests that SWNTs are
cru-
cial for the suspended molecular wire. Lastly,
these results
can be used to address the pos-
sible issue of mechanical cross
talk in device
arrays. Comparison of the calculated strain
energies
to values of the nanotube-surface in-
teraction (14)
and friction suggests that (i) the
lower nanotube will remain
xed on the sub-
strate and (ii) the suspended nanotubes will
not
lift off or slip on supports on the order of
10 nm when the suspended
tube is deected
to the ON state. The interaction with the sup-
port
could also be enhanced through chemical
modication. These results
indicate that me-
chanical cross talk will not be a problem for
our architecture in densely integrated crossed
nanotube arrays.
Electromechanical switching of the sus-
pended nanotube devices between ON and
Figure 1. Suspended nanotube device archi-
tecture. (A) Three-dimensional view of a sus-
pended crossbar array showing four junc-
tions with two elements in the ON (contact)
state and two elements in the OFF (sepa-
rated) state. The substrate consists of a con-
ducting layer [e.g., highly doped silicon (dark
gray)] that terminates in a thin dielectric layer
[e.g., SiO
2
(light gray)]. The lower nanotubes
are supported directly on the dielectric lm,
whereas the upper nanotubes are suspended
by periodic inorganic or organic supports (gray
blocks). Each nanotube is contacted by a metal
electrode (yellow blocks). (B) Top view of an n
by m device array. The nanotubes in this view
are represented by black crossing lines, and
the support blocks for the suspended SWNTs
are indicated by light gray squares. The elec-
trodes used to address the nanotubes are indi-
cated by yellow squares.
Figure 2. Bistable nanotube device potential. (A) Plots of energy, E
T
= E
vdW
+ E
elas
, for a single
20-nm device as a function of separation at the cross point. The series of curves correspond to
initial separations of 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, and 2.4 nm, with two well-dened minima
observed for initial separations of 1.0 to 2.0 nm. These mimima correspond to the crossing nano-
tubes being separated and in vdW contact. (B) Calculated structures of the 20-nm (10, 10) SWNT
device element in the OFF (top) and ON (bottom) states. The initial separation for this calculation
was 2.0 nm; the silicon support structures (elastic modulus of 168 GPa) are not shown for clarity.
(C and D) Plots of the bistability range for the crossed nanotube elements as a function of device
size. The suspended nanotube is supported on silicon (C) or on an organic layer (D) with an elas-
tic modulus of 12 GPa (29). In both plots, the range of initial separations yielding bistable devices
is gray. In general, the bistable region increases with device size, and the softer organic support
yields a larger range of bistability, especially in the smallest structures. The calculations were car-
ried out for (10, 10) SWNTs with an elastic modulus of 1 TPa and Lennard-Jones parameters of
C
6
= 32.00 × 10
–60
erg·cm
6
and C
12
= 55.77 × 10
–105
erg·cm
12
.

96 ru eCk es, kiM, Jo sel eviCh , ts eng , Che ung , & li eb er et al. in Scie nce 289 (2000)
OFF states has been assessed by evaluat-
ing the
voltage-dependent contribution of
the electrostatic energy to
the total energy.
In this calculation, we used the boundary el-
ement
method to numerically solve the La-
place equation for the complex
three-dimen-
sional (3D) geometry of the crossed nanotube
device
(19). Calculations of E
T
for switch-
ing a 20-nm device
ON and OFF (Figure 3)
demonstrate that it is possible to
change re-
versibly between the ON/OFF states by us-
ing moderate
voltages, which do not exceed
the threshold eld for nanotube
failure (20).
The switching voltages vary, depending
on
the specic device geometry (i.e., shape of
the static potential),
and thus could be fur-
ther optimized. For example, by using a thin-
ner
dielectric layer (that is, 4- versus 20-nm
SiO
2
) the ON and OFF
switching thresholds
would be reduced from 4.5 and 20 V to 3 and
5 V, respectively. The calculations also show
that the electrostatic
forces between adjacent
nanotubes are insufcient to distort
an array
of elements, even at a 10-nm device scale,
because most
of the electrostatic interaction
is localized in the small crossing
region of the
individual elements.
Our proposed electromechanical device
elements differ in important ways from pre-
vious fullerene (21) and nanotube
(18) elec-
tromechanical systems. In the fullerene case,
scanning tunneling microscopy (STM) mea-
surements showed that the
conductance of in-
dividual C
60
clusters varied as a function of
deformation by the STM tip. The variation in
conductance can be
associated with ON and
OFF states, although the “device” can nei-
ther
store information, because the change
is reversible, nor can any
scheme integrate
many elements as required for computing.
The
nanotube nanotweezers (18), which con-
sist of two nanotubes
with freely suspended
ends, do exhibit electrostatically switchable
OFF (open) and ON (closed) states but can-
not be readily integrated
into a parallel sys-
tem required for computing.
The bistable and reversible nanotube de-
vice elements can be used both as nonvola-
tile RAM and as congurable logic tables
and
thus could serve as the key building blocks
for a molecular-scale
computer. The potential
of a system based on these nanotube device
elements is substantial. First, it will be pos-
sible to achieve
integration levels as high as
1 × 10
12
elements per square centimeter us-
ing 5-nm device elements and
5-nm supports
while maintaining the addressability of many
devices
through the long (~10-µm) SWNT
wires. In our architecture, interconnects
to the
outside are needed only at the ends of these
long nanotubes,
and thus, one interconnect
can be used to address many individual
junc-
tion elements. We also stress that each ele-
ment can store
a nonvolatile bit, whereas in
current silicon-based devices a
transistor and
capacitor are required to store a bit in dy-
namic
RAM or four to six transistors are re-
quired to store a bit in
static RAM. Second,
the switching time for a 20-nm device, 10
–
11
s, suggests that ON/OFF switching opera-
tions can be carried out
at 100 GHz (22). This
switching time will decrease
to ~5 × 10
–12
s
(200-GHz operation frequency) for a 5-nm
element owing to the
smaller effective mass,
because the switching time is determined
by
the time to move the upper nanotube between
its ON or OFF positions.
The electrostatic
charging time could also be important in de-
vice
arrays made from SWNTs longer than
10 to 100 µm (22).
Finally, we note that the
nonvolatile nature of our devices is
preferable
from the standpoint of power consumption
and corresponding
heat dissipation as com-
pared to dynamic RAM, which must be con-
tinually
refreshed.
To determine whether this nanotube de-
vice concept can be realized, we have studied
the properties of suspended, crossed nanotube
devices made from SWNT ropes (23) by me-
chanical manipulation
(Figure 4). Current-volt-
age (I–V) measurements made on
the lower
and upper nanotubes of a typical model de-
vice show ohmic
behavior with resistances of
11 and 58 kilohms, respectively (Figure 4A).
The I–V curves between the upper and lower
ropes in the OFF state
were nonlinear, which is
consistent with tunneling, with a resistance
on
the order of a gigohm. After switching ON, the
I–V curves exhibited
ohmic behavior with a re-
sistance of 112 kilohms (Figure 4B).
This large
change in resistance is consistent with our pre-
dictions
for OFF versus ON states in the sus-
pended device architecture.
Reversible switch-
ing between well-dened ON and OFF states
has
also been observed in several devices (Fig-
ure 4C). The
smaller change in ON/OFF resis-
tances for the device in Figure 4C
is thought
to arise from large contact resistances that are
sometimes
observed with nanotube ropes (24).
Nevertheless, this
change between ON and
OFF states is 10-fold and persisted over
sev-
eral days of study. We think that these experi-
ments represent
clear proof of concept for our
proposed architecture. Lastly,
we have found
that some of the devices fabricated from ropes
could
only be switched ON for reasonable ap-
plied voltages. This behavior
is expected for
potentials that have deep vdW minima (Figure
2A).
Irreversible switching could be exploited
to congure logic elements
for computing (3).
We think that our calculations and exper-
imental results clearly demonstrate the po-
tential of our nanotube-based device archi-
tecture.
There are several issues that must be
addressed in order to take
the next steps to-
ward integrated molecular electronics. First,
it is recognized that current SWNT samples
consist of a random
distribution of metallic
(M) and semiconducting (S) tubes (8),
and
this might complicate device reading. How-
ever, the differences
in resistance for M/M, S/
S, and M/S SWNT crosses are much smaller
than that between the ON and OFF states,
and thus, these states
will be robust even with
a mixture of different tubes. Second,
an inher-
ent limitation of crossbar memory architec-
tures, such
as in Figure 1, is the possibility of
multiple electrical
pathways (25). A standard
solution to this problem
is the incorporation
of diodes at each cross point. This effective
solution could be implemented in our system
without the incorporation
of additional ele-
ments by using semiconductor nanotubes or
nanowires
(7) for the lower molecular wires
and metallic nanotubes
for the upper SWNT
because this would create a rectifying M/S
junction at each cross point. Although it is not
clear that it
will be possible to exploit such
an elegant solution with nanotubes
until sep-
arated M and S SWNTs can be produced, the
use of semiconductor
nanowires for the lower
Figure 3. Electrostatic switching of the
nanotube device. Plots of the energy,
E
T
= E
vdW
+ E
elas
+ E
electro
, as a function of
separation at the cross point for (A) switch-
ing ON and (B) switching OFF. In (A), plots (i),
(ii), and (iii) correspond to E
T
for V
1
= V
2
= 0 V
and V
1
= +3 V, V
2
= –3 V and V
1
= +4.5, and
V
2
= –4.5 V, respectively, where V
1
and V
2
are the potentials applied to the two cross-
ing nanotubes. In (B), (i), (ii), and (iii) corre-
spond to V
1
= V
2
= 0 V, V
1
= V
2
= +15 V, and
V
1
= V
2
= +20 V, respectively. These poten-
tials are applied with respect to the conduct-
ing ground plane (e.g., Figure 1A). The mini-
mum magnitudes of the voltages required for
switching ON and OFF are 4.5 and 20 V, re-
spectively. The electrostatic energy was calcu-
lated by numerically solving the Laplace equa-
tion using the boundary element method with
3600 elements for a 20-nm device supported
on silicon with a 1.4-nm initial separation. The
calculated electrostatic potential was checked
carefully to see that it satised the boundary
conditions and asymptotic behavior.

Frequently asked questions

Q1. What is the effect of the n-type nanowires on the speed of the device?

If the lower wires in their architecture are made from n-type nanowires, then rectifying behavior will be observed at each cross element, irrespective of whether the upper SWNT is metallic or semiconductor. 

Q2. What is the resistance of the upper and lower ropes in the OFF state?

The I–V curves between the upper and lower ropes in the OFF state were nonlinear, which is consistent with tunneling, with a resistance on the order of a gigohm. 

Q3. What is the capacitance of the nanotube?

The capacitance, C, is given by C = 2πεL/log(2h/r), where ε is the dielectric constant of the dielectric layer, L is the nanotube length, r is the nanotube radius, and h is the height of the dielectric layer. 

Q4. What is the main reason for the development of SWNTs?

The developments in these growth and assembly areas suggest that highly integrated SWNT device arrays, which represent the next step in their plans for molecular electronics, may be soon realized. 

Q5. How many elements can be used to construct nonvolatile random access memory and logic function tables?

These reversible, bistable device elements could be used to construct nonvolatile random access memory and logic function tables at an integration level approaching 1012 elements per square centimeter and an element operation frequency in excess of 100 gigahertz. 

Q6. What is the minimum bistable device size for a hard support?

The minimum bistable device size for a hard support such as silicon is <10 nm, and softer organic supports enable bistability for devices that are <5 nm. 

Q7. What is the simplest example of a reversible, bistable device element?

Each device element is based on a suspended, crossed nanotube geometry that leads to bistable, electrostatically switchable ON/OFF states. 

Q8. How many pF of a nanotube leads to a limited operation frequency?

The calculated nanotube capacitance of 10–4 pF for a 10-µm tube leads to an RC limited operation frequency on the order of 100 GHz. 

Q9. What is the effect of the strain energies on the nanotubes?

Comparison of the calculated strain energies to values of the nanotube-surface interaction (14) and friction suggests that (i) the lower nanotube will remain fixed on the substrate and (ii) the suspended nanotubes will not lift off or slip on supports on the order of 10 nm when the suspended tube is deflected to the ON state. 

Q10. What is the optimum voltage for switching a nanotube?

Calculations of ET for switching a 20-nm device ON and OFF (Figure 3) demonstrate that it is possible to change reversibly between the ON/OFF states by using moderate voltages, which do not exceed the threshold field for nanotube failure (20). 

Q11. What is the difference between the two nanotubes?

The calculations also show that the electrostatic forces between adjacent nanotubes are insufficient to distort an array of elements, even at a 10-nm device scale, because most of the electrostatic interaction is localized in the small crossing region of the individual elements. 

Q12. How was the electrostatic energy of the system evaluated?

The electrostatic energy of the system was evaluated by solving the Laplace equation for the suspended nanotube geometry (Figure 1), including the dielectric support layer. 

Q13. How is the range of strains required to achieve bistability in nanotubes determined?

the range of mechanical strains required to achieve bistability in Figure 2A, 0.22 to 1.7%, is well below the elastic limit of at least 6% [determined computationally (16) and experimentally (17) for SWNTs], and the average bending angle in the ON state is about half the angle required to buckle nanotubes.