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9
Molecular-scale Electronics
“Computers in the future may weigh no more
than 1.5 tons.” – Popular Mechanics, 1949
9.1
Miniaturization
At least since the Club of Rome published The Limits of Growth’ in 1973 [1], we
have been aware that many products of our civilization grow exponentially. It is less
well known that some decrease exponentially. An example of the latter is electronic
devices. In Figure 9-1 the minimum feature size of electronic components is plotted
versus the year of use. A straight line results, provided the size is plotted on logarithmic scale. Such diagrams are known as Moore plots [2]. Originally they were used to
demonstrate the continuous decrease of the price per bit in integrated memories.
Figure 9-1 Development of the structural size of electronic
devices in the course of time and extrapolation to sizes as small
as typical interatomic distances in solids by the year 2020.
One-Dimensional Metals, Second Edition. Siegmar Roth, David Carroll
Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISBN: 3-527-30749-4
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9 Molecular-scale Electronics
Because the price of a silicon chip remains more-or-less constant (some p Dollars’),
and because the number of bits per chip increases continuously (from 124 kbits in
the seventies to 16 Mbits in the mid 19902), a bit becomes cheaper and cheaper.
Extrapolating the Moore plot in the reverse direction, vacuum tubes and probably
also the Chinese abacus might be included. If extended to the future the plot would
lead to a feature size of 10 in the year 2020. This increasing density of electronics
through miniaturization has become a relatively large part of the economies of western nations. For example, increasing computational power creates machines for applications that were previously not approached with computers.
The molecular dimensions of such ultrasmall circuitry certainly justify the name
molecular electronics’. From a contemporary point of view, however, the term molecular electronics is not very well defined. It is used in connection with both electronics on a molecular level, which we discuss in this chapter, and molecular materials for electronics, which we discuss in Chapter 10 [3]. In the context of the first
meaning, molecular electronics first found expression when, in the 1970s, chemists
Mark Ratner and Ari Aviram speculated about using single molecules as rectifiers,
allowing electrical currents to pass only in one direction (discussed in more detail
below). Throughout the 1970s and 1980s, the fundamental concepts of this field
Figure 9-2
Three-terminal devices make gain possible.
9.1 Miniaturization
were laid down in a variety of topical conferences. Some of the proceedings of these
workshops on molecular electronics are listed in the Refs. [4–10]. It was not until
the 1990s, however, when a key development came, and Tour and coworkers measured the current flowing between two gold electrodes connected by a single molecule [11]. The basic premise of these early approaches is quite easy to visualize. As
shown in Figure 9-2, the conceptualization is of a single molecule between interconnecting leads that performs a signal-processing electrical function, such as rectification, resistance, etc.
One can already see that many of the issues of dimensionality discussed previously should apply to such situations. In this conformation, the electrodes are
linked to the atoms of the molecule through a chemical bond. In the example cited
above, a benzene molecule was linked to Au electrodes via sulfur atoms at each end.
The sulfur atoms, which happen to form strong bonds with gold, held the molecule
in place between the two gold wires separated by a distance of several nanometers.
By using such configurations and doping the molecule in the leads, effects such as
molecular conduction, coulomb blockade, and negative-differential resistance’
(when the current decreases as the voltage increases) have been observed.
Although these phenomena have provided interesting tests of molecular orbital
theory, they fall short of the essential element necessary for information processing
electronics: gain. The basis of computer circuits is the transistor. The transistor is
essentially nothing more than a variable-state switch. Very simply, it works like this:
two contacts are placed on a thin, doped, semiconducting film (like Si), so that
charge injection can be accomplished easily. A back electrode is placed on the back
of the semiconductor layer. When a voltage is applied to the gate, a space charge or
depletion’ region builds up in the active layer. This impedes charge flow through
the source and drain electrodes. When the bias reaches some specified large value,
the current flow between source and drain is turned off altogether. This is actually a
field-effect transistor, of which several types exist. However, they all have a singular
property: if the configuration is balanced just right, it is clear that small fluctuations
in the gate can result in rather large changes in the source–drain current. Importantly, we could take the point of view of supplying an input current at the gate (Ig)
and measuring its output at the drain (Id). If we did this, it would appear as though
small inputs of Ig lead to large outputs of Id. In fact, the gain of such a system is
generally defined in terms of this concept: b = Id/Ig. It is not a real gain of course;
the currents must all sum throughout the circuit. However, the nonlinearity in the
circuit response is quite powerful and can be useful in signal amplification, information processing, and memory applications. Essentially, it relies on a three-terminal flow-control’ system. In contrast, early experiments on molecules used two-terminal devices without the capability of exhibiting gain. Trying to achieve gain within
a single-molecule device is a significant stumbling block to the overall usefulness of
such concepts. In 2000, however, Di Ventra and colleagues showed, through rather
complex calculations, that this hurdle is surmountable under some conditions. The
predicted the behavior of a three-terminal device, based on the 1997 benzene device,
can exhibit gain by resonant tunneling [12]. Quite different from the macroscopic
charge-flow device described above, the resonant-tunneling device must express ele-
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ments of quantum mechanical confinement (i.e., be zero- or one-dimensional) to
work.
Alternatively, we have already seen several much more simple materials in which
quantum phenomena are expressed; specifically, quantum dots and quantum wires.
Such inorganic systems could also generate gain by similar principles to those
described above. We mentioned in Section 1.2 that, in these systems with a small
electron concentration (silicon, gallium arsenide), effects of low dimensionality (socalled quantum-size effects) are seen at much larger sizes than in systems with high
electron concentration (carbonic systems). In fact, the preparation of inorganic
quantum wires and quantum dots is state-of-the-art today, and these systems are
subjects of intensive research and development [13]. Quantum dots can be made so
small that they contain only a few or even single’ electrons. The possibility of single-electron electronics has been pointed out [14,15], and single-electron transistors [16,17] and single-electron memories [18–20] have been demonstrated. Thus,
this can be seen as a second approach to molecular-scale electronics and, incidentally, an approach more easily accomplished by using the lithography tools of topdown assembly.
In both approaches, the operational parameters must be taken into account. For
single-electron devices, the level spacing of electrons-in-a-box (Section 1.2, Eq. (1)),
and also the coulombic energy of the occupants of that box, or coulombic blockade,
determine the energy to place another electron into the system. For large’ particles
the coulombic blockade can be calculated from the charging energy of a capacitor:
Echarging =
e2
2C
(1)
For a platelet of several micrometers in diameter, the capacitance is on the order
of 10–15 F and the charging energy is several tenths of a millielectronvolt. Only at
temperatures below 1 K can single-electron effects be observed; otherwise, the thermal energy kT exceeds the charging energy. The capacitance is proportional to the
cross section of a particle and, in macromolecules several nanometers in diameter,
the charging energy is comparable to the thermal energy at room temperature [21].
For individual atomic sites in a crystal lattice, the charging energy will finally correspond to the Hubbard model discussed in Section 8.2 (Figure 8-1). These considerations immediately link electronic device miniaturization and single-electron effects
to molecular electronics, and indeed, articles on multiple tunnel junctions’ in GaAs
do not fail to point out that their ideas are also applicable to macromolecules [21].
9.2
Information in Molecular Electronics
As described above, the information within a molecular circuit is carried and acted
upon by the existence and magnitude of charge. The flow of charge is literally the
flow of information within the system. We note here, that within this paradigm
there should be some inherent advantages of organic materials. Specifically, in low-
9.3 Early and Radical Concepts
dimensional organic materials, electronic excitations are usually strongly coupled to
the underlying crystal structure. The complicated structure of a macromolecule
offers additional degrees of freedom, e.g., conformational degrees of freedom,
which localize the excitations. Figure 4-2 shows an example of a molecule twisting
and puckering when its excitation state is changed. Better localization should allow
for closer packing of information than is possible in inorganic semiconductors. A
particular case of localization in one-dimensional systems is solitons/polarons in
conjugated polymeric chains (Section 5.4). They move as compact form-preserving
pulses and not as dispersing wave packages (Figure 5-14). Information transfer in
these systems is simply the group velocity of the wave function of the localized
charge.
The periodic structure of Si or GaAs, however, implies a certain degree of delocalization of electrons (Bloch waves). Under the conditions of low defect density, the
charge is well represented by plane waves across the entire molecular structure. In
this situation, not only is the modulus of the wave function preserved from one contact to the next, the phase of the wave function also is. In a phase-preserving system,
it is conceivable that gain can also be achieved in a three-terminal configuration.
However, we may ask if information transfer within this system now occurs at the
phase velocity. The answer to this is not so straightforward. Generally, information
is transferred when the phase between two states is compared. When these compared states are entangled, then information transfer may not be restricted to the
group velocity of the states. These concepts lead naturally to the concepts of quantum bits [22]. Of course, we do not mean to imply that organics cannot be used in
such applications. As Teich and colleagues have shown, it is quite possible to build
an addressable entangled state with heteropolymers [23]. However, the delocalizedcarrier concept seems to have a natural extension to such applications.
9.3
Early and Radical Concepts
Clearly, from the above discussion, the computational paradigm will ultimately
decide the best approach to molecular-scale electronics. Most early work revolved
around conjugated organic (synthetic metal) systems used as devices, as discussed
above. In fact, this is still the mainstay effort in molecular-scale electronics. Thus, it
is helpful to examine detailed proposals for molecular circuit elements in terms of
their excitations and their dimensionality.
9.3.1
Soliton Switching
Soon after solitons were discussed for polyacetylene [24–26], F. L. Carter introduced
the concept of soliton switching’ [27]. In Chapter 5 a soliton in polyacetylene was
described as a domain wall separating chain segments with different arrangements
of bond alternation. These arrangements can be interpreted as logical states, and a
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Figure 9-3 Polyacetylene chain with two differently-conjugated
segments separated by a domain wall (soliton). The domains
can be interpreted as different states, to which different logical
values can be assigned.
passing soliton switches’ the chain from one state to the other (Figure 9-3). To
read’ the state of a chain segment, two adjacent carbon atoms have to be marked
and the bond between them has to be inspected. Carter proposed to incorporate a
push–pull olefin (Figure 9-4) into the chain. In the ground state there is a double
bond between the two central carbon atoms. The molecule can be excited by absorption of light. The excited molecule has a single bond in the central position and
carries a dipole moment.
The substituted polyacetylene chain is depicted in Figure 9-5. The push–pull olefin is used either as a soliton valve’ – in the ground state the conjugation along the
chain is unaffected and the soliton can pass; in the excited state the conjugation is
interrupted and the soliton movement is blocked – or as a soliton detector’ – if the
unit is imbedded in a state-B segment, light can be absorbed (double bond between
central carbon atoms = ground state), but if in a state-A segment, it already has a
central single bond and cannot absorb light. There are also soliton bifurcations’
(Figure 9-6) and soliton reversals’ (Figure 9-7). Carter’s proposals have often been
ridiculed as too naive and unfeasible. But their value is not to give instructions on
how to synthesize a computer but rather to initiate the development of simple concepts for theoretical investigations.
Figure 9-4 A push–pull olefin, which changes the nature of the
bond between the central carbon atoms. It can be incorporated
into a polyacetylene chain to serve as a soliton valve’ or as a
soliton detector’.
9.3 Early and Radical Concepts
Figure 9-5 A push–pull olefin imbedded in trans-polyacetylene
can be switched off by the propagation of a soliton or can be
used as a soliton detector.
Figure 9-6 Soliton bifurcations. If the link is more complicated,
the switch could be set from the outside, and bifurcations could
be used to fan’ information from the macroscopic world into
the molecular-electronic device.
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Figure 9-7
Molecular soliton reversals’.
9.3.2
Molecular Rectifiers
Almost ten years before Carter, Aviram and Ratner designed a molecular rectifier’ [28]. An organic donor, for example TTF, is linked via an inert spacer to an
organic acceptor, e.g., TCNQ (Figure 9-8) [29]. The spacer is called the r bridge,
because it contains only saturated bonds (in Section 9.3.4 we will also meet
p bridges). Figure 9-9 depicts the level scheme of a D–r–A molecule. Evidently, it is
very asymmetric with respect to electron transfer from donor to acceptor or vice versa.
The Aviram–Ratner device is shown in Figure 9-10. The rectifying molecules have to
be organized in an ordered way between metal electrodes, so that all donor sites point in
the same direction. To extend these ideas from a single molecule, as discussed in the
introduction, to a computer in a beaker’, an ordered deposition of organic molecules is
necessary. Many researchers have suggested that molecules like the one described
may lend themselves well to Langmuir–Blodgett techniques [30,31].
Figure 9-8
Molecular rectifier as proposed by Aviram and Ratner [28], a so-called D–r–A molecule.
9.3 Early and Radical Concepts
Figure 9-9 Level scheme of a D–r–A molecule. Because of the
energy difference between D––r–A+ and D+–r–A– it is easier for
electrons to move in one direction, and so the molecule acts as
a rectifier [29].
Molecular rectifier using D–r–A molecules as
proposed by Aviram and Ratner [28]. M1 and M2 are neutral
electrodes. Schematic view according to Metzger [29].
Figure 9-10
9.3.3
Molecular Shift Register
In 1989 Hopfield and coworkers [32] proposed a molecular shift register. A shift register is an array of cells (Figure 9-11). At each clock purse, the information of one
cell is shifted to the next cell. Hopfield’s proposal is to make a microelectronic memory based on silicon. The information would be stored in capacitors of about 1 lm2
in cross section, and to extend the storage capacity, the third dimension would be
used. That is, a molecular shift register would be set on top of each capacitor. The
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Figure 9-11 Schematic view of a molecular shift register.
The cells are polymerized and a polymer chain is suspended
between two electrodes, which are part of a microelectronic
capacitor [32].
shift register would then be loaded by injecting electrons from the metallic capacitor
plate into the first cell of the register, and it would be read by depositing the electrons into the channel of a field-effect transistor at the opposite side of the register.
A cell of the shift register would have to consist of a donor and an acceptor part, as
indicated in Figure 9-12.
Electron transfer from cell to cell is shown in the schematic energy diagram in
Figure 9-13. An organic molecule that could act as a cell in a molecular shift register
is depicted in Figure 9-14. It has not only a donor and an acceptor group, but also a
Schematic representation of the cells in a shift
register memory. The cells contain at least one donor and one
acceptor functional group [32].
Figure 9-12
Figure 9-13
The donor and acceptor levels in a typical shift register polymer [32].
Organic molecule that could act as a cell in a
molecular shift register: upon proper illumination an electron
is transferred from the left side to the right side [32].
Figure 9-14
9.3 Early and Radical Concepts
sensitizer in the bridge. The sensitizer acts as a valve. Absorption of light opens the
valve, and an electron is transferred from the donor to the acceptor. The process is
very fast, e.g., it occurs within 1 ps. When the light source is shut off, the valve
closes and the electron cannot go back. However, it can – and will – tunnel to the
next cell, e.g., within 1 ns. So if there is a clock pulse every 10 ns, each clock pulse
shifts the electrons by one step to the right, because the shift involves fast intramolecular and slow intermolecular charge transfer. The filled and empty cells carry information as 1’ and 0’ (chemically speaking, the molecules are neutral or ionized).
The molecule shown in Figure 9-14 is polymerized to a chain length of about 600
repeat units and many identical chains would be placed between the electrodes. The
device would be immersed in a solution to shield the coulombic repulsion (see the
discussion on single-electron devices in Section 9.1). If the transfer efficiency is
99.9%, at each step about half of the electrons arrive at the receiving electrode after
600 hops, and 5000 chains would provide a signal large enough for detection with
the sensitivity of present-day microcircuits. The realization of Hopfield’s proposal
does not seem to be impossible, although probably not with 600 repeat-unit polymers.
9.3.4
Molecular Cellular Automata
Figure 9-15 shows a donor and an acceptor linked by a p bridge (in contrast to the
r bridge used in Section 9.3.2). Excitation of a D–p–A molecule can be interpreted
as soliton switching: in the excited state, single and double bonds are inverted relative to the ground state. In addition, the excited state carries an electronic dipole
moment. At the risk of oversimplifying, we could say that in a D–p–A molecule the
donor and acceptor communicate by the exchange of solitons. A third functional
group in the chain, called the modulable barrier (Figure 9-16), leads to a three-terminal device and allows logical operations.
A linear array of D–p–A molecules (Figure 9-17) has been proposed as a molecular cellular automaton [33]. The scheme of a cellular automaton is presented in Figure 9-18. Here, only a one-dimensional array of cells is shown, but there could be
two- or three-dimensional arrays, or arrays with even higher connectivities. The cells
Polyene chain with donor and acceptor groups
attached at the ends. Upon optical excitation, single and double
bonds in this D–p–A molecule are inverted and the excited
molecule carries a dipole moment.
Figure 9-15
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9 Molecular-scale Electronics
Donor–acceptor-substituted polyene with a third
functional group incorporated, the barrier’. This three-dimensional device allows for logical operations.
Figure 9-16
Figure 9-17
Donor–acceptor-substituted polyenes as cells of a linear cellular automaton [33].
Figure 9-18
Scheme of a cellular automaton.
must exhibit at least two states to be capable of storing information. When the array
is exposed to clock pulses, e.g., to pulses from a laser, the cells switch (change their
state), and the probability of switching a particular cell has to depend on the states
of the neighboring cells (conditional switching). A cellular automaton is the extreme
of a parallel computer. It can be shown that a cellular automaton can carry out all
computations of a conventional (sequential) computer, however, often much faster.
It is easy to see that the array of D–p–A molecules is a cellular automaton: by the
absorption of light the cells switch from state A to state B. The switching probability
depends on the state of the neighboring cells, according to the dipolar moment associated with the state of the cells. The field of the dipoles detunes the resonance frequency for absorption. The relevant question is, of course, How good a cellular automaton is a D–p–A chain? Like all the proposals in this section, the D–p–A cellular
automaton also is not intended to work as a practical device; it is a model to allow
the asking and study of particular questions.
9.4
Carbon Nanotubes
With the advent of novel molecules like the carbon nanotube, another approach to
organic molecular-scale circuitry has appeared. Nanotubes are possible to manipulate spatially and, as demonstrated earlier, contacts can be added by several lithographic routes. Because of the unique one-dimensional band structure of the carbon
nanotube and the fact that it represents a single crystal (generally visualized without
defect), one might expect that charge would be transported ballistically’, that is,
9.4 Carbon Nanotubes
Schematically, the total number of available
conduction channels in a mesoscopic wire that lie between the
Fermi levels of the contacts all contribute to the current.
Figure 9-19
without scattering from one end to the other [34]. Of course, there are still the leads
that touch the tube. There is a simple way to imagine what will happen in such a
material and to understand why it would be useful as a device.
Imagine a nanowire arranged between two electrodes as in Figure 9-19. Electrodes 1 and 2 have chemical potentials l1 and l2. The wire has length L. We take
the electrodes as an unlimited reservoir of charge. If we assume no scattering at the
interfaces between electrode and nanowire, and l1 > l2, then only electrons with
energies l1 > E > l2 and having a wave vector going from left to right contribute to
current in the wire.
The pseudo Fermi level (defined by the highest occupied energy level for k > 0
and k < 0, treated as though these are independent because there is no scattering
between them) for k > 0 is l1 and for k < 0 is l2. As we saw earlier, the dimensionality of the wire causes the allowed states to spread apart into sub-bands, as shown by
the dashed lines. We can denote these energy states as Ei(k), for the ith state or band.
So, whatever the current in the system is, we must add up the currents in the individual states between the pseudo Fermi levels to get it. Typically, the sub-bands with
k states that have energies l1 > E > l2 are referred to as channels.’ The number of
channels is a function of E, generally denoted M(E). Classically, an electron with a
velocity given by v = h–1 (¶E/¶k) goes toward contact 2 in the above example, and
one with an energy l1 > E > l2 contributes to the net current as I = ev/L. L/v is simply the transit time for the carrier. We can then add up a total current as:
I = 2e/p
P Ð
i
k>0
(h–1 (¶E/¶k) [ f(Ei – l1) – f(Ei – l2)] dk = 2 {e2/h} M (l1 – l2)/e
Spin degeneracy has of course been added to the sum. The inverse of the level
spacing (demonstrated in previous chapters) has been used as the current density
per sub-band, and the f’s are the Fermi levels. Now notice that if the width of the
wire is small, as in a carbon nanotube, » 1.4 nm, the number of states between l1
and l2, M, is about 2 (spin-up and spin-down), even for large differences in the
chemical potentials (i.e., > 1 eV). However, for large wires, say > 1 lm, the number
of channels is huge (l1 – l2 = 1 eV, M » 106) [35].
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9 Molecular-scale Electronics
Schematic view of a nanotube field-effect transistor
(taken from the homepage of the Molecular Biophysics Group at
Delft University of Technology, C. Dekker www.mb.tn.tudelft.nl).
Figure 9-20
The voltage between the two leads is obviously V = (l2 – l1)/e and the resistance
is given by Rc = V/I = h/2e2 (1/M), a very famous result. This is generally referred to
as the contact resistance’, and h/2e2 is the quantum of resistance, » 12.9 kX. Thus,
a wire with no scattering has a resistance proportional to M–1 or a conductance proportional to M. Because we have M = 2 for a metallic nanotube, as stated above, we
should measure 2 · 12.9 kX for its resistance.
If the scattering mechanism is time-independent, Landauer has shown that the
conductance formula above is modified by adding a probabilistic term (the transfer
matrix). This is essentially the probability of scattering between channels as the
charge travels between the leads. It looks like this:
R = h/2e2 (1/M T)
where T is the probability for transmission and is given as
P
ij
‰tij‰2
where the sum is over all M, and tij is the probability of scattering from the ith state
to the jth state. Thus, for a nanotube, we expect the resistance to be
R = 2 · 12.9 kX (1–T)/T
Note that the reflected wave function causes a drop in the wire’s potential and
that resistance is proportional to (1 – T). Of course, the actual predicted value then
depends on a specific model for the scattering phenomena. It is also important to
note that the phase relation of the carrier’s wave function can be lost in the scattering events. However, when it is preserved, scattering can lead to interference effects
9.4 Carbon Nanotubes
that result in localization of charge on the nanowire. The most important expression
of these phase-preserving interactions is universal conductance fluctuations in
which the noise observed in a transport IV curve is not noise at all, but rather interference patterns formed by the impurities and defects within the quantum
wire [36].
This formulation holds only when a high degree of delocalization exists in the
wire. This is certainly true for nanotubes, and a number of experiments have demonstrated this [34]. Shown in Figure 9-20 is a nanotube placed on two electrodes.
Notice too, that the tube has been placed in a field-effect transistor configuration
as described above. The behavior of this system as a transistor is shown in Figure 9-21. The conductance is given in the inset, and the numbers are different from
our expectations above. Clearly, the contacts here are not quite ideal. Nevertheless,
many people have now repeated these experiments and suggest that such performance is more than adequate in transistor design.
In fact, carrying the concepts of molecular circuits one step further, several
groups, including researchers at Delft and IBM [38] have constructed more complex
signal-processing circuits from these basic transistors. Figures 9-22 and 9-23 show
circuits developed by the Delft group.
The circuits demonstrate the use of molecular electronics in inverters, logic gates,
memory systems, and oscillators; all the basic building blocks of computational systems. To date, the question remains: How will this be done on the scale of modern
semiconductor chips? However, it is clear the conceptually, there are a number of
routes to achieving molecular-scale electronics.
IV characteristics as a function of gate voltage
shows that nanotubes would make rather good transistors at
room temperature [38].
Figure 9-21
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9 Molecular-scale Electronics
Figure 9-22
Height image of a single-nanotube transistor, acquired with an atomic force
microscope. Whereas in Figure 9-20 the nanotube is placed on a SiO2 layer over doped
silicon, here the nanotube is placed on Al2O3
over Al. The gate contact is Al, which allows
better coupling and higher gain.
Demonstration of one-, two-, and
three-transistor logic circuits with carbon nanotube FETs. (A) Output voltage as a function of
the input voltage of a nanotube inverter. (inset)
Schematic of the electronic circuit. The resistance is 100 MX. (B) Output voltage of a
nanotubes NOR for the four possible input
states (1,1), (1,0), (0,1), and (0,0). A voltage of
0 V represents a logical 0 and a voltage of
–1.5 V represents a logical 1. The resistance is
50 MX. (C) Output voltage of a flip-flop memory cell (SRAM) composed of two nanotube
FETs. The output logical stays at 0 or 1 after
the switch to the input has been opened. The
two resistances are 100 MX and 2 GX. (D)
Output voltage as a function of time for a
nanotube ring oscillator. The three resistances
are 100 MX, 100 MX, and 2 GX [39].
Figure 9-23
References and Notes
References and Notes
1 D.H. Meadows, D.L. Meadows, and J. Randers.
The Limits of Growth, Report to the Club of
Rome, 1972.
2 H. Queisser. Kristallene Krisen: Mikroelektronik; Wege der Forschung, Kampf und
Mrkte. Piper, Mnchen, 1985.
3 D. Bloor, M. Hanack, A. Le Mhaut, R. Lazzaroni, J.P. Rabe, S. Roth, and H. Sassabe.
Conjugated polymeric materials, opportunities in electronics, optoelectronics, and molecular electronics. NATO ASI Series E:
Applied Science 182, 587. J.L. Bredas and
R.R. Chance (Eds.), Kluwer, Dordrecht, 1990.
4 F.L. Carter. Molecular Electronic Devices.
Marcel Dekker, New York, 1982.
5 F.L. Carter. Molecular Electronic Devices II.
Marcel Dekker, New York, 1987.
6 F.L. Carter, R.E. Siatkowski, and H. Wohltjen.
Molecular Electronic Devices. North Holland,
Amsterdam, 1988.
7 A. Aviram. Molecular Electronics – Science
and Technology. United Engineering Trustees, New York, 1989.
8 F.T. Hong. Molecular Electronics – Biosensor
and Biocomputers. Plenum Press, New York,
1989.
9 G.J. Ashwell. Molecular Electronics. Wiley,
New York, 1992.
10 Ch. Ziegler, W. Gpel, and G. Zerbi. Molecular
Electronics. Proceedings of Symposium H of
the 1993 E-MRS Spring Conference, North
Holland, Amsterdam, 1993.
11 J. Chen, M.A. Reed, A.M Rawlett, and J.M.
Tour. Large on–off ratios and negative differential resistance in a molecular electronic
device. Science 286, 1550 (1999).
M.A. Reed, C. Zhou, C.J. Muller, T.P. Burgin,
and J.M. Tour. Conductance of a molecular
junction. Science 278, 252 (1997).
12 M. Di Ventra, S.T. Pantelides, and N.D. Lang.
The benzene molecule as a molecular resonant-tunneling transistor. Applied Physics
Letters 76, 3448 (2000).
13 C.W.J. Beenakker and H. van Houten. Quantum Transport in Semiconductor Nanostructures. Solid State Physics 44, 1. H. Ehrenreich
and D. Turnbull, Academic Press, San Diego,
1991.
S. Sarkar (Ed.), Exotic States in Quantum
Nanostructures. Kluwer, Amsterdam, 2003.
P. Harrison (Ed.), Quantum Wells, Wires and
Dots: Theoretical and Computational Physics.
John Wiley & Sons, New York, 2000.
14 K.K. Likharev. Possibility of creating analog
and digital integrated circuits using the discrete, one-electron tunneling effect. Soviet
Microelektronics 16, 109 (1987).
K.K. Likharev. Correlated discrete transfer of
single electrons in ultrasmall tunnel junctions. IBM Journal of Research and Development 32, 144 (1988).
15 D.V. Averin and K.K. Likharev. Mesoscopic
Phenomena in Solids. p. 173. B.L. Altshuler,
P.A. Lee, R.A. Webb (Eds.), Elsevier, Amsterdam, 1991.
D.V. Averin and K.K. Likharev. Single Charge
Tunneling. p. 311. H. Grabert and H.M.
Devoret (Eds.), Plenum Press, New York,
1992.
16 T.A. Fulton and G.J. Dolan. Observation of single-electron charging effects in small tunnel
junctions. Physical Review Letters, 59, 109
(1987).
17 L.S. Kuz’min and K.K. Likharev. Direct experimental observation of discrete correlated single-electron tunneling. JETP Letters 45, 495
(1987).
18 L.J. Geerlings, V.F. Anderegg, R.A.M. Holweg,
J.E. Mooij, H. Pothier, D. Esteve, C. Urbina,
and M.H. Devoret. Frequency-locked turnstile
device for single electrons. Physical Review
Letters 64, 2691 (1990).
19 P. Lafarge, H. Pothier, E.R. Williams, D. Esteve,
C. Urbina, and M.H. Devoret. Direct observation of macroscopic charge quantization.
Zeitschrift fr Physik B 85, 327 (1991).
20 K. Nakazato, R.J. Blaikie, R.J.A. Leaver, and H.
Ahmed. Single-electron memory. Electronics
Letters 29, 384 (1993).
21 K. Nakazato and H. Ahmed. The multiple tunnel junction and its application to single-electron memories. Advanced Materials 5, 668
(1993).
22 There are now a number of excellent monographs on quantum computing. An excellent
hands-on’ treatise comes from
C. Williams and S. Clearwater. Explorations in
Quantum Computing. Springer Verlag, Berlin, 1997.
23 W.G. Teich, K. Obermayer, G. Mahler. Structural basis of multistationary quantum sys-
209
210
24
25
26
27
28
29
30
31
32
9 Molecular-scale Electronics
tems. II. Effective few-particle dynamics.
Physical Review B 37, 8111 (1988).
M.J. Rice. Charged p-phase kinks in lightly
doped polyacetylene. Physics Letters A 71,
152 (1979).
W.P. Su, J.R. Schrieffer, and A.J. Heeger. Solitons in polyacetylene. Physical Review Letters
42, 1698 (1979).
S.A. Brazovskii. Electronic excitations in the
Peierls–Frhlich state. JETP Letters 28, 606
(1978).
S.A. Brazovskii. Self-localized excitations in
the Peierls–Frhlich state. Soviet Physics
JETP 51, 342 (1980).
F.L. Carter. Molecular Electronic Devices. p.
51. Marcel Dekker, New York, 1982.
A. Aviram and M.A. Ratner. Molecular rectifiers. Chemical Physics Letters 29, 277
(1974).
R.M. Metzger. Electricity and Magnetism in
Biology and Medicine. p. 175. M. Blank (Ed.),
San Francisco Press, San Francisco, 1993.
For a monograph, see for example:
G. Roberts. Langmuir–Blodgett Films. Plenum Press, New York, 1990.
R.M. Metzger. Biomolecular Electronics:
Advances in Chemistry Series 240, 81.
R.R. Birge (Ed.), American Chemical Society,
1994.
J.J. Hopfield, J.N. Onuchic, and D.N. Beratran.
A molecular shift register based on electron
transfer. Science 241, 817 (1988).
J.J. Hopfield, J.N. Onuchic, and D.N. Beratran.
Electronic shift register memory based on
molecular electron-transfer reactions. Journal
of Physical Chemistry 93, 6350 (1989).
D.N. Beratran, J.N. Onuchic, and J.J. Hopfield.
Electronics: Biosensor and Biocomputers. p.
352. Plenum Press, New York, 1989.
33 S. Roth, G. Mahler, Y.Q. Shen, and F. Coter.
Molecular electronics of conducting polymers. Synthetic Metals 28, C815 (1989).
34 S.J. Tans, M.H. Devoret, H. Dai, A. Thess, R.E.
Smalley, L.J. Geerligs, and C. Dekker. Individual
single-wall nanotubes as quantum wires. Nature 386, 474 (1997).
Z. Yao, H.W. C. Postma, L. Balents, and C.
Dekker. Carbon nanotube intramolecular
junctions. Nature 402, 273 (1999).
H.W.Ch. Postma, T.F. Teepen, Z. Yao, M. Grifoni, C. Dekker. Carbon nanotubes single-electron transistors at room temperature. Science
293, 76 (2001).
35 These numbers are from R. Saito, G. Dresselhaus and M. Dresselhaus (Eds.), Physical Properties of Carbon Nanotubes. p. 142. Imperial
College Press, London, 1998.
36 P.A. Lee, A.D. Stone, and H. Fukuyama. Universal conductance fluctuations in metals:
effects of finite temperature, interactions, and
magnetic field. Physical Review B 35, 1039
(1987).
37 V. Derycke, R. Martel, J. Appenzeller, and P.
Avouris. Carbon nanotube inter- and intramolecular logic gates. Nano Letters 1, 453 (2001)
38 S.J. Tans, A.R.M. Verschueren, and C. Dekker.
Room-temperature transistor based on a single carbon nanotube. Nature 393, 49 (1998).
39 A. Bachtold, P. Hadley, T. Nakanishi, C. Dekker.
Logic circuits with carbon nanotube transistors. Science 294, 1317 (2001).