![2 Historical Background
In the 1980’s advanced epitaxial growth techniques such as molecular beam epitaxy
(MBE) enabled the creation of GaAs-AlGaAs semiconductor heterostructures with
very smooth interfaces. This ability to control the composition of crystalline semi-
conductors with atomic precision made possible the formation of a highly conducting
two-dimensional electron gas (2DEG) at the interface between AlGaAs and GaAs.
Moreover, the 2DEG, which was essentially a plane of confined electrons, could be
further patterned by placing lithographically-defined metal gates on the surface of the
semiconductor. A negative potential on the gates would deplete the 2DEG under the
gate regions. In 1988 two groups measured quantized conductance through a con-
striction connecting two 2DEG regions and found that it was quantized [1, 2]. This
was convincingly explained by invoking the quantum-mechanical nature of the
electrons transiting the constriction. Using the effective mass approximation, one
could explain much of the behavior of this layer by solving the Schrödinger equation
in two dimensions.
The ability to engineer the effective wavefunction of electrons seemed very
promising for potential device applications. Throughout the 1990’s (and beyond)
many wave-based device designs were proposed which used quantum interference
effects as their operating principle, often created in analogy with microwave devices.
Truly remarkable experimental demonstrations left little doubt that these quantum
mechanical effects were real and could be potentially exploited for device behavior. In
addition, it proved possible to create quantum dots by confining the 2DEG in both
lateral dimensions (the third dimension was already confined by the heterostructure
potential. These quantum dots could be viewed as artificial atoms [3, 4], and also as
high-Q resonators for ballistic electron transport [5].
Into the optimism that these new abilities engendered, Rolf Landauer injected a
ray of pessimism and realism. In a talk at the first International Symposium on
Nanostructure Physics and Fabrication in 1991, Landauer cautioned that interference
devices were unlikely to make it in the real world [6]. A ‘‘rich’’ response with many
peaks and valleys did not, he argued, make a robust basis for devices, which would
have to be tolerant of fabrication variations and environmental perturbations. He
argued for devices whose transfer function is nonlinear and saturates at two distinct
levels, as does a CMOS inverter. This input signal should be of the same type as the
output signal, so that information can be transferred from device to devices.
Another stream of research at the time was the newly emerging and promising
phenomenon of Coulomb blockade in small structures. Electrons tunneling onto small
metal islands can raise the potential of the island by e2/C, where C is the total
capacitance of the island [7]. For very small structures this charging energy could be
significant compared to thermal energies. The ‘‘orthodox’’ theories of the Coulomb
blockade, even when treating the system quantum mechanically, characterized the
island by this macroscopic quantity—the capacitance [8]. While this is quite adequate
for metal structures containing very many free electrons, in small semiconductors one
should really use a multi-particle approach. In such a model the effective capacitance
is a result of the calculation of Coulomb effects, rather than being an input to it.
4 C.S. Lent and G.L. Snider](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-15-320.jpg)
![A study of few-electron systems under bias showed a threshold behavior for single
electron transfer that is very nonlinear [9]. The origin of this nonlinearity is funda-
mentally the quantization of charge. If a region of space is surrounded by barriers that
are appropriately high, but still possibly leaky, then the expectation value of the
enclosed charge will be very close to an integer multiple of the fundamental charge.
When the equilibrium value of the charge changes because of a tunneling event, it will
necessarily be a rather abrupt jump between two integers.
Finally, the QCA architecture was inspired by classical cellular automata (CA)
architectures [10], of the type popularized by Conway’s Game of Life. These are
mathematical models of evolution that proceed from discrete generation to generation
according to specified rules. The state of each cell is determined by the state of the
neighboring cells in a previous generation. The neighbor-to-neighbor coupling is a
natural match for nano-devices, since one expects that one very small device may
influence its neighbors, but not distant devices. CA’s represent a means of compu-
tation that departs from the current-switch paradigm of transistors. But cellular
automata are mathematical models that can operate with any set of evolution rules.
The question for device architecture was not simply what local CA rules will produce
computational behavior, but what rules does the actual physics of cellular interaction
support.
The original QCA idea was the result of the confluence of these four ideas: (1) the
ability to create configurations of quantum dots which localize charge, (2) the con-
vincing argument by Landauer that any practical device would need bistable satura-
tion in the information transfer function, (3) the nonlinearity of charge tunneling
between such dots because of charge quantization, and (4) the notion of a locally-
coupled architecture in analogy to cellular automata.
It is worth noting that the connection to cellular automata is by analogy. Classical
CA’s are almost always regular one or two-dimensional arrays of cells. The physics of
the interaction between QCA cells does not yield very interesting results for regular
arrays. QCA circuits look more like wires connecting devices; highly non-regular
layouts of cells provide the specific function. Mathematical model CA’s evolve in
discrete generations, but physical systems interact continuously.
3 Developments
The first QCA paper demonstrated the bistability of a QCA cell using a multi-electron
Hamiltonian and a direct solution of the Schrödinger equation [11]. This direct
approach avoided the problems of sorting out exchange and correlation effects; within
the site model it was exact. This bistability remains a key feature of QCA. Though it is
somewhat appealing to explore a multi-state QCA cell and multi-state logic, only a
bistable system can truly saturate in both logic states. An intermediate state is always
subject to drifting off from stage to stage.
It was soon realized that a line of QCA cells acted like a binary wire and a junction
of two or three wires could form a logic gate [12]. The first proposal was to have a
special cell at the junction which could be internally biased to the 1 or 0 state and
thereby act as an OR gate or an AND gate [13]. It was soon clear that the bias could be
The Development of Quantum-Dot Cellular Automata 5](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-16-320.jpg)
![applied by another wire, forming a three-input majority gate [14]. Inverters could be
formed from diagonal interactions between cells. With these basic elements, any
logical or arithmetic function can be formed.
With a year of the first QCA publication, other implementations were suggested.
Small metal islands could serve as dots and form QCA cells if they were coupled by
tunnel junctions [15]. One advantage of metal-dot QCA is that the electric field lines
from the dot can be guided by the conductors to influence the neighboring dots; in the
semiconductor depletion dots, the field spreads out in all directions. It was also natural
to envision molecular versions of QCA where the role of the quantum dot was played
by a part of the molecule that could localize charge [14]. A magnetic model of QCA
was constructed from three-inch magnets held in Lucite blocks which rotated on low-
friction jeweled pivots. These magnetic cells were used during talks and lectures by
both of the present authors to demonstrate QCA wires and gates. They prefigured (at
enormous scale) the nanomagnetic QCA under active research today and discussed in
other contributions to this volume.
A detailed examination of QCA dynamics and the development of several levels of
quantum description of QCA arrays [16], were prompted by another observation of
Landauer [17]. While encouraging QCA exploration, he expressed concern that a weak
link in a QCA wire would cause a switching error because the incorrect ‘‘old’’ state
downstream would have more influence than the upstream cells with the new state.
By treating the whole wire quantum mechanically it could be shown that this would
only be a temporary problem. But the exercise focused attention on the nature
of computation in QCA systems, which were designed from the beginning to map
the ground state onto the computationally correct state. This mapping can be robust,
while the details of the transient response of the system are inherently more fragile.
We wanted to avoid computing with the transient. A byproduct of these calcula-
tions was the development of several approximate treatments for both equilibrium and
dynamic calculations. The mapping between QCA and the Ising model in a transverse
field was also made precise.
Clocking of QCA arrays arose out of the detailed consideration of switching
dynamics and the desire to retain the robustness of the mapping between the ground
state and the computationally correct state for large systems. Clocking QCA entails
gradually moving cells between a neutral state and an active state with a clocking
signal. The active state can be either a binary 0 or 1; the neutral state is usually
denoted as a ‘‘null’’ state that carries no information. The first version of clocking,
proposed the year following the initial QCA papers, contemplated raising and low-
ering the inter-dot tunneling barriers [18, 19]. This would gradually (adiabatically)
transition the cell between a delocalized electron configuration (null) and the localized
configuration of the active state. Koroktov and Likharev subsequently suggested a
version of metal-dot QCA called the single electron parametron which used a com-
plicated rotating electric field as a clock [20]. This had several drawbacks (e.g.,
information could only move in one direction in an array), but the idea of using as the
null state a localized state on an intermediate dot was adopted for clocking QCA,
particularly for molecular implementations. It is much easier to change the potential
on the intermediate dot than to directly influence the tunnel barriers between dots, and
the effect is the same. Adiabatic clocking QCA [21] solved the problem of switching
6 C.S. Lent and G.L. Snider](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-17-320.jpg)
![dynamics getting caught, even temporarily, in a metastable state; this was the heart of
Landauer’s objection. It retained the advantages of (local) ground-state mapping.
During switching each cell is always very close to its instantaneous ground state (the
definition of adiabaticity). Though we did not fully appreciate it at the time, this
essentially turned QCA into a concrete implementation of the gedanken experiments
which had led Landauer to conclude that there was no fundamental lower bound to the
energy that must be dissipated to compute a bit [22]. Clocking further allowed much
larger computational structures to be envisioned, combining memory and processing.
3.1 Semiconductor QCA
The Cavendish group of Smith et al. demonstrated QCA operation in GaAs/AlGaAs
heterostructures with confining top-gate electrodes [23–25], as originally envisioned
in the earliest QCA publications. The group of Kern et al. demonstrated a QCA cell in
silicon, using an etching technique to form the dots [26–29]. The group of Mitic et al.
used a novel method to form dots from small clusters of phosphorus donors in silicon
[30]. They succeeded in demonstrating QCA operation in that system. Interestingly,
their long-term goal is coherent quantum computing and they conceive QCA devices
as providing an ultra-low-power layer of interface electronics to connect a cryogenic
quantum computer to standard CMOS electronics [31].
The challenges of all semiconductor implementations have been two-fold. Firstly,
the lithographically accessible sizes for quantum dots are large enough that kink
energies are low and cryogenic operation is required. More importantly, the perfection
of the interface and electronic environment becomes an issue. While dots with tens of
electrons effectively screen small amounts of impurity and imperfections, in the limit
of single occupancy, semiconductor dots become very sensitive to the details of the
environment. Even MBE-grown samples have enough random imperfections that the
dot is often not exactly where one expects it to be based on lithography [32].
3.2 Metal-Dot QCA
Although electronic QCA has been demonstrated in a number of material systems,
metal dot implementations have proven to be the most successful, so far, building on
the fabrication techniques developed for single-electron transistors [33, 34]. The
advantages of metal dots are that the fabrication yield is relatively high, and they are
electrically well-behaved, meaning that energy required to add each additional elec-
tron to the dot typically remains constant over the addition of many electrons. This
makes it easier to load the QCA cell with the proper number of electrons and to bias
the cell so that the two polarizations are energetically degenerate. However, in
semiconductor dots [33, 34] the fabrication yield is low and the addition energy
typically differs for each additional electron, and the electrical behavior of the dot can
change from run to run, making it difficult to prepare the cell for proper operation.
This makes the metal dot an attractive option for QCA experiments. The main dis-
advantages of metal dots are background charge fluctuations [35], and low operating
temperature. Background charge fluctuations are caused by the random arrangement
The Development of Quantum-Dot Cellular Automata 7](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-18-320.jpg)
![of stray charge in the vicinity of the QCA cell, which affects the bias point and
polarization degeneracy of the cell. The arrangement of this charge changes with time,
and the gate biases applied to each dot in the cell must be adjusted to keep the cell
operational. The low operating temperature of metal dot QCA cell is due to the size of
the lithographically defined cell.
The metal dot QCA are composed of aluminum islands separated by tunnel
junctions. Fabrication of the cell is done by electron-beam lithography using the
Dolan bridge technique [7] where the tunnel junctions are formed by evaporation of
aluminum from two angles, with an intervening oxidation step. The resulting tunnel
junctions are composed of two layers of aluminum separated by a thin layer, 1–2 nm,
of aluminum oxide. The area of the overlap between the two layers of aluminum
determines the capacitance of the junction, and since it is typically the dominant
capacitance of the dot, determines the operating temperature of the QCA cell.
Cells and Logic
The first QCA cell was demonstrated in 1997 [36]. This device had a junction overlap
area of approximately 50 9 50 nm, giving an operating temperature of 70 mK. As it
was the first demonstration, the layout was very conservative and optimized for high
yield, which resulted in a relatively large overlap and low operating temperature. In
this first demonstration the goal was to use gate electrodes to move an electron
between the top and bottom dots on the left side of a cell. The electron in the right half
of the cell would move in the opposite direction to maintain the lowest energy con-
figuration. To measure the polarization of the cell, single-electron transistors, which
are the most sensitive electrometers demonstrated to date [37], are used to measure the
potential of the dots in the right half of the cell. Measurements of the output of the two
electrometers move in opposite directions, confirming that an electron in the right half
moves in the opposite direction to the electron in the left half, confirming QCA
operation. Full details of the experimental methods are given elsewhere [38–41].
The next step in the development of metal dot QCA was the demonstration of a
logic gate [42]. The basic logic element in the QCA paradigm is the majority gate,
where three inputs vote on the polarization of a QCA cell. For this experiment we
again used metal dots defined by the Dolan bridge method. For the inputs of the
majority gate we applied voltages to the input electrodes that mimicked the potentials
of three input cells. The applied voltages were varied to step through the logic truth
table. The polarization of the cell was measured by electrometers and the output of the
cell confirmed proper operation of the gate.
These experiments showed the basic functionality of QCA cells. The next
experiment [43] showed that a QCA line could switch without getting stuck in a
metastable, partially switched, state. In this experiment three 2-dot cells were fabri-
cated in a line, and an input applied to the left side of the line. Electrometers coupled
to the output side of the line confirmed the proper switching.
Power Gain
These initial experiments used unclocked QCA cells, but clocking is an important
element in QCA systems. Clocking of QCA cells is crucial to achieve perhaps the
8 C.S. Lent and G.L. Snider](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-19-320.jpg)
![most important quantity in a logic device: power gain. Without power gain the input
signal would degrade in a line, due to the unavoidable energy dissipation at each
stage, and fan-out would be impossible. Clocking in QCA requires a variable barrier
to control the tunneling of electrons between dots. Since the tunnel barrier in metal dot
QCA is a fixed aluminum oxide layer whose barrier height cannot be modulated,
clocking dots are introduced into the QCA cell as intermediate dots. These dots are
coupled to clock electrodes that control the potential of the central dots. A positive
clock voltage pulls the electrons to the central dots to produce the null state. A
negative voltage forces the electrons to leave in a direction that is determined by the
cell’s input. In the initial experiment, a differential input voltage is applied to the left
side of the cell and electrometers measure the potential of the top and bottom dots of
the right half of the cell. Measured output waveforms confirmed proper operation of
the cell [44]. A clocked QCA cell can also be used as a latch, a short-term memory
element, as demonstrated in our experiments [45, 46].
As shown by theory, the power gain of a QCA cell is not fixed. If the input is
weak, the cell pulls power from the clock to restore the signal level. Since the signal
energy is fixed for a given cell, the amount of power pulled from the clock will depend
on the weakness of the input. An experimental demonstration of power gain involves a
measurement of the charge on the dots of the QCA cell [43] as the inputs and clock are
moved through one clock period. In this way the work done by the input on the cell
can be calculated, along with the work done by the cell on the next cell. If the work
done by the cell exceeds the work done on the cell, then the cell has demonstrated
power gain. In our experiment an input with one-half the normal potential swing was
applied to the input. The resulting experiment demonstrated a power gain of 2.07, in
agreement with theory [47].
Shift Registers
Clocking in QCA enables not only power gain, but also the control of the flow of
information in the computational system, needed for data pipelining. The basic element
in a data flow structure is the shift register. A QCA shift register consists of a row of
cells controlled by different clock phases. In our experiment we fabricated a shift
register of two cells. Although this is a very short shift register, it can be used as a long
register. For our experiment we fabricated the two clocked QCA cells with elec-
trometers coupled to each cell so that we could measure the polarization of each cell
independently. In the experiment a bit of information is latched into the first cell, and
the input removed. The bit is then copied into the second cell, and erased in the first.
Then the bit is copied back into the first cell and erased in the second. In this way the bit
is shifted between cells, just as it would be in a long shift register. The experiment
demonstrated 5 bit transfers, limited only by thermally induced errors [48–50].
Fan-Out
An important element in a general logic system is fan-out, where the output of one
element is sent to the inputs of two or more elements. Since the energy of the output is
split, power gain in the following logic elements is needed to restore the signal level.
To demonstrate fan-out in QCA we fabricated a circuit with three cells. In the
The Development of Quantum-Dot Cellular Automata 9](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-20-320.jpg)
![experiment the input is latched into the central cell, which then acts as an input to the
top and bottom cells. When a clock is applied to the top and bottom cells the bit is
copied into both cells, and full signal strength is produced in these cells [51], con-
firming the operation of the circuit.
3.3 Molecular QCA
Molecules represent the smallest artificial structures that can be engineered by humans.
To form switchable QCA molecules, at least two charge centers are required that can
be reversibly occupied or unoccupied by an electron. The field of mixed-valence
chemistry [52] concerns itself with molecules that have at least two charge centers
connected by a bridging group through which tunneling can occur. Ongoing investi-
gation concerns the questions of what makes a good dot and what makes a good bridge.
Several early theoretical investigations used model electronic p-systems as dots
[53–61]. These molecules are often radical ions containing unpaired electrons and
would be very reactive and likely unstable in real systems. Their use was to establish the
fundamentals. Electrons in molecules can exhibit bistable switching and the perturba-
tion due to a similar molecule at a reasonable distance (such that the dots form a square)
is sufficient to switch the molecule. Energy levels are such that these effects survive
room temperature operation. Kink energies are large enough that molecular QCA is
robust against variations in position and orientation of molecules. Groups surrounding
the charge centers can effectively insulate them from conducting substrates but do not
screen the field. Applied electric fields which vary at a much larger length scale can
effectively clock molecules (with three appropriately arranged charge centers).
Molecular synthesis by the Fehlner [62–66] and Lapinte [67–69] groups have
succeeded in creating molecules that show the requisite bistability. These dots use Fe
and/or Ru charge centers. Electronic measurements of the Fehlner molecules attached
to a surface showed distinctive bistable behavior as the electron was switched by an
applied electric field. This demonstrated both the bistable character of the molecules,
and the potential for clocked control of the charge configuration by an applied (and
inhomogeneous) field. The Lapinte molecules have been imaged with STM by the
Kandel group [67–70] and show the desired charge localization on one end of a
symmetric double-dot molecule. Triple-dot molecules, of the sort required for clocked
control, have also been made and imaged. More recently ferrocene-base double dot
molecules have been made by the Henderson group and imaged by the Kandel group.
There is much chemistry yet to be understood in designing QCA molecules. One
issue is what makes the ideal dot. Transition metal atoms have the advantage of using
d-orbitals that participate less in bonding and so may be more isolated. Carbon-base
p-systems, on the other hand, can be chosen such that they involve anti-bonding
orbitals and may spread the charge out more and therefore yield a lower reorgani-
zation energy. The reorganization energy is the energy associated with the relaxation
of the surrounding atoms and may in some cases trap the charge and inhibit switching.
Creating appropriate bridging groups involves choosing a system that is either long
enough or opaque enough to be an effective barrier to through-bond tunneling.
Conjugated systems may be too conducting.
10 C.S. Lent and G.L. Snider](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-21-320.jpg)
![Another approach that combines single-atom realization with lithographic control
is the STM-base lithography of the Wolkow group [71]. They have created room-
temperature QCA cells using a remarkable approach involving removing single
electrons from dangling bonds on a silicon surface. As with molecules, the single-
atom sizes easily yield room temperature operation, yet the placement and orientation
of the cells can be controlled lithographically using the STM tip.
3.4 Other Implementations
Nanomagnetic QCA was first introduced by Cowburn’s group [72] and developed
extensively by the Porod group [73] and the Bokar group [74]. The mapping from
QCA cells that represent an electric quadrupole to those that represent a magnetic
quadrupole is straightforward. Nanomagnetic implementations are discussed else-
where in this volume.
Some have proposed cell-cell coupling based on an electron exchange interaction
[75], and indeed the earliest calculations showed a small splitting between the singlet
and triplet spin states [76]. This approach has two serious drawbacks: the exchange
splitting is quite small, and it is zero if there is not tunneling from cell to cell. If there is
tunneling from cell to cell, the information is no longer localized and spin-wave
solutions predominate.
It is interesting to consider the fundamental question of what sort of systems could
implement QCA action. There are two basic features of QCA that must be satisfied:
1. A bit is to be represented completely by the local state of a cell composed of
atoms.
2. The interaction between cells is through a field, rather than by transport.
The cell’s binary information must therefore be represented by the positional or spin
degrees of freedom of the electrons and nuclei in the cell. Nuclear positions could be
used to encode the information—for molecules this would entail a conformational
change, for larger cells we would call it mechanical. Lighter mass electrons have an
advantage in that they can switch positions faster than nuclei. Spin states of either
nuclei or electrons could switch quickly.
The field connecting cells must be electromagnetic because the other candidate
fields are either too short range (the nuclear strong or weak forces) or too weak (the
gravitation force). Direct spin-spin interaction energies are very small, so for magnetic
coupling we need many nuclear or electronic spins acting collectively. Nanomagetic
QCA thus must be sufficiently large that the coupling is adequate at room tempera-
tures. The direct Coulomb interaction is quite strong and allows molecule-to-molecule
coupling between multipole moments of the charge distribution. Since by assumption
there is no transport from cell to cell, the charge of the cell cannot change and higher
moments must be used to encode the information. QCA thus far has used dipole
coupling and quadrupole coupling—the difference being what one chooses to define as
a cell. It is also possible to use contact potentials along the cell surface to coupled
mechanical (nuclear) degrees of freedom. The possibilities then can be seen to reduce
to these categories:
The Development of Quantum-Dot Cellular Automata 11](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-22-320.jpg)
![1. Mechanical cells coupled by electrostatic contact potential forces. These would
suffer from the slower response of atoms compared with electrons, but remain
largely unexplored.
2. Magnetic cells (collective nuclear or electronic spins) coupled by magnetic fields.
This is the basis of nanomagnetic QCA described elsewhere in this volume.
3. Electronic cells coupled by Coulomb multipole-multipole interactions. The
charge distribution could be the result of either mobile atoms or mobile electrons,
and could involve a few or several charges.
Few-electron QCA cells, as has been noted above, have an intrinsic bistability due to
charge quantization. If there are many charges forming the charge multipole, the
bistability must be provided by another mechanism. One example is a CMOS cell that
is an analog to QCA and switches adiabatically [77].
4 Issues in QCA Development
4.1 The Role of Quantum Mechanics in QCA
To achieve robustness against fabrication variations, the QCA paradigm uses only a
classical degree of freedom, the electric (or magnetic) quadrupole moment of the cell.
It does not use quantum phase information nor interference effects. QCA involves bits
not qubits. It is quantum mechanical precisely in that it relies on quantum tunneling
for cell switching. This is crucial because if quantum mechanics were ‘‘turned off’’
(
h = 0) there would be no tunneling and a QCA cell could not switch. If the barriers
to tunneling were removed so that classical switching were allowed, a QCA cell would
oscillate and settle into a particular configuration randomly depending on the details of
the trajectory and energy dissipation. Switching a classical double-well system is
much more prone to error because the system can get caught in a metastable state if
the timing is not perfect. Reliance on quantum tunneling stabilizes the bit information.
4.2 Power Gain
In molecular, metal dot (discussed above), or other implementations, power gain is
crucial because there is always some dissipation of energy as information moves from
stage to stage in a computation. This dissipation is the microscopic version of friction
in mechanical devices. It can be minimized, and by moving gradually can be reduced
to whatever level is desired, but cannot be completely eliminated. Therefore, unless
there is a way to restore the signal energy, it will eventually be completely attenuated.
In conventional devices the source of the energy is usually the constant-voltage power
supply. In QCA the restoring energy is provided by the clock; it automatically supplies
enough energy to restore the signal levels.
4.3 Metastability, Memory, and Coherence
For a physical system to act as a memory its state cannot be determined by only its
boundary conditions. A Hamiltonian system in a unique ground state, for example,
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![cannot act as a memory. A device with even short-term memory must therefore be in a
metastable state. It could be in a state representing a 1 or be in a state representing a 0.
Which state the device is in is depends not just on its boundary conditions, but also on
its past. If there is a large enough kinetic barrier between these two states they can
often be justifiably treated as distinct energetically degenerate states, but they are
actually metastable states very weakly coupled and with a very long Rabi oscillation
period.
In clocked QCA wires (i.e., shift registers), information is represented by bit
packets, a few cells in the line that are polarized in the 1 or 0 state [78]. Since they
could also be in the opposite state energetically, it is true that if the time evolution was
completely unitary, the bit could quantum mechanically oscillate from one state to the
other. There is a considerable kinetic barrier to doing that, however, just as in the case
of a CMOS bit. Moreover, in real systems entanglement with the environment sta-
bilizes the bit packet by loss of quantum phase in the system [79]. Decoherence is
precisely this sort of entanglement with the environment and, though it is detrimental
for quantum computing, it actually stabilizes QCA bits. Further exploration of the
roles of environmentally-induced decoherence and energy dissipation are part of the
broader question of the transition between the quantum and classical worlds.
4.4 Wire Crossings
QCA is naturally an in-plane technology; it does not require going out of the plane.
How can one therefore cross wires, that is move one bit independently across the path
of another? Several proposals have been made that accomplish this. (1) The original
wire-crossing proposal was to use the symmetry of cells and the second-near-neighbor
coupling (suitably strengthened by duplication) to allow one cell line to communicate
across the path of another. The limitation here is the amount of control in placement
and orientation required. (2) A permuter is a logical function which simply switches
inputs A and B to output B and A. This can be done with logic, though it does take
several cells to implement [80]. (3) With expanded clocking timing one can have one
bit packet cross a wire intersection horizontally at one time, and vertically at a later
time. The cost is in the added complexity of the clocking circuitry. (4) A bridge
crossover, similar to the CMOS via structure can be constructed that takes QCA cells
out of the plane to cross. (5) In many instances the crossing is for distribution of
signals to different parts of a logic array. Tougaw and Khatun have designed a general
matrix distribution scheme, again using augmented clocking patterns [81].
4.5 Computational Architecture
It is clear that QCA requires rethinking circuit and computer architecture on the basis
of this new device paradigm. Nevertheless because QCA still supports Boolean logic
function, it is natural that the first designs are taken over from usual logic circuitry.
Much design work is underway, supported crucially by the design tool QCADesigner
produced by the Walus group [82]. The goals of this important effort engaging many
research groups are both to capitalize on the functional density that QCA cells allow
The Development of Quantum-Dot Cellular Automata 13](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-24-320.jpg)
![(molecular cells are *1 nm square), and to exploit the clocking paradigm wherein all
communication is via shift registers. Kogge and Niemier have been early pioneers of
this [83–88], suggesting a universal clocking floorplan which supports general data-
flow. Tougaw et al. [89] and Niemier et al. [90] have explored programmable QCA
logic arrays, a promising area. Exploring QCA architectures and circuit ideas is a very
active area, as witnessed by other contributions to this volume.
4.6 Lithograph and Self-assembly
QCA circuits need to have a designed layout that reflects the circuit function; entirely
regular arrays do not have interesting behavior. As a consequence the information
contained in the circuit layout must be imposed and this is usually done, as with all
extant semiconductor circuits, through lithography. It is possible, however, to have
self-assembly take care of constructing the dots and forming the dots into cells, and
perhaps even forming the cells into lines or other functional groups. For molecular
QCA, this is particularly promising because bottom-up self-assembly of molecules
into supra-molecular structures is a common, albeit demanding, strategy. Building in
some level of self-assembly from below, where the cell size is about 1 nm, and
imposing circuit structure from above using lithographic techniques, which can reach
below 10 nm, is an appealing match of technologies.
Another approach that has received some attention is to use DNA or PNA [91]
self-assembled structures as ‘‘molecular circuit-boards.’’ DNA structures with sur-
prising amount of inhomogeneous patterning have been synthesized using Seeman
tiles [92], or the more recent DNA origami techniques [93]. The long-range concept
would be to engineering attachment sites in the DNA scaffold which would covalently
bond appropriate QCA molecules or supramolecular assemblies [94–97]. The geo-
metric information that defines the circuit layout would in this way be expressed
through the sequencing of base-pairs that self-assemble into the scaffold. Many issues
remain, of course, including the requirements of geometric matching to the DNA
repeat distance and the polyanionic nature of DNA, which could interfere with QCA
operation. PNA scaffolds are neutral and could potentially solve this problem.
4.7 Energy Dissipation
QCA has two fundamental motivators: ultra-small devices in large functional-density
arrays, and low power dissipation. Power dissipation has been a major driver in every
stage of the evolution of microelectronics. Adiabatic switching between instantaneous
ground states allows the absolute minimum dissipation of energy to the environment.
As Landauer [22] and Bennett [98] showed, there is no fundamental lower limit to the
amount of energy that needs to be dissipated as heat in order to compute a bit of
information. If information is erased, however, a minimum about of energy equal to
kBT log(2) must be dissipated. The combination of these two ideas is known as
Landauer’s Principle (LP) and is connected to the Maxwell Demon [99, 100]. Though
there is a substantial consensus on the correctness of LP, it has come under criticism
14 C.S. Lent and G.L. Snider](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-25-320.jpg)
![from both industrial researchers [101, 102] and philosophers of science [103, 104].
The low power dissipation in QCA is an example of LP in action [105]. We have
recently demonstrated experimentally that a binary switch can be operated with dis-
sipation of 0.01 kBT, in agreement with LP [106–108].
5 Future Prospects
QCA research activity continues on several fronts. Molecular QCA will require
improved understanding of the chemistry of mixed-valence molecules. This includes
exploring linker and dot moieties, the role of ligand relaxation in charge transfer,
surface attachment and molecular-scale patterning. Significant progress in nanomag-
netic implementations is reported by several other contributors in this collection.
Metal-dot QCA deserves more exploration, even though it requires cryogenic oper-
ation. New fabrication methods may raise the operating temperature considerably.
Exploration of circuits and computational architectures is crucial for fully exploiting
the potential of locally interconnected nanodevices.
References
1. Wharam, D., Thornton, T., Newbury, R., Pepper, M., Ahmed, H., Frost, J., Hasko, D.,
Peacock, D., Ritchie, D., Jones, G.: One-dimensional transport and the quantisation of the
ballistic resistance. J. Phys. C: Solid State Phys. 21, L209 (1988)
2. Van Wees, B., Van Houten, H., Beenakker, C., Williamson, J.G., Kouwenhoven, L., Van
der Marel, D., Foxon, C.: Quantized conductance of point contacts in a two-dimensional
electron gas. Phys. Rev. Lett. 60, 848 (1988)
3. Kastner, M.: The single electron transistor and artificial atoms. Ann. Phys. (Leipzig) 9,
885–894 (2000)
4. Meurer, B., Heitmann, D., Ploog, K.: Single-electron charging of quantum-dot atoms.
Phys. Rev. Lett. 68, 1371 (1992)
5. Goodnick, S.M., Bird, J.: Quantum-effect and single-electron devices. IEEE Trans.
Nanotechnology 2, 368–385 (2003)
6. Landauer, R.: Nanostructure physics: fashion or depth. In: Reed, M.A., Kirk, W.P. (eds.)
Nanostructure Physics and Fabrication, pp. 17–30. Academic Press, New York (1989)
7. Fulton, T.A., Dolan, G.H.: Observation of single-electron charging effects in small tunnel
junctions. Phys. Rev. Lett. 59, 109–112 (1987)
8. Averin, D., Likharev, K.: Coulomb blockade of single-electron tunneling, and coherent
oscillations in small tunnel junctions. J. Low Temp. Phys. 62, 345–373 (1986)
9. Lent, C.S.: A simple model of Coulomb effects in semiconductor nanostructures. In: Kirk,
W.P., Reed, M.A. (eds.) Nanostructures and Mesoscopic Systems, p. 183. Academic
Press, San Diego (1992)
10. Toffoli, T., Margolus, N.: Cellular Automata Machines: A New Environment for
Modelling. MIT Press, Cambridge (1987)
11. Lent, C.S., Tougaw, P.D., Porod, W.: A bistable quantum cell for cellular automata. In:
International Workshop Computational Electronics, pp. 163–166 (1992)
The Development of Quantum-Dot Cellular Automata 15](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-26-320.jpg)
![Nanomagnet Logic (NML)
Wolfgang Porod1()
, Gary H. Bernstein1
, György Csaba1
,
Sharon X. Hu2
, Joseph Nahas2
, Michael T. Niemier2
,
and Alexei Orlov1
1
Department of Electrical Engineering, University of Notre Dame,
Notre Dame, IN, USA
porod@nd.edu
2
Department of Computer Science and Engineering,
University of Notre Dame, Notre Dame, IN, USA
Abstract. We describe the background and evolution of our work on magnetic
implementations of Quantum-Dot Cellular Automata (QCA), first called
Magnetic QCA (MQCA), and now known as Nanomagnet Logic (NML).
Keywords: Nanomagnet logic Quantum-Dot Cellular Automata Field-
coupled computing Cellular Automata
1 Introduction
We all are familiar with the fact that magnetic phenomena are widely used for data
storage, whereas electronic phenomena are used for information processing. This is
based on the fact that ferromagnetism is nonvolatile (i.e. magnetization state can be
preserved even without power), and that electrons and the flow of charge can
be effectively controlled to perform logic. However, charge-based logic devices are
volatile, which means that a power supply is needed to maintain the logic state and to
stop information (electrons) from leaking away.
Presently, there are multiple research efforts underway to harness magnetic phe-
nomena for logic in addition to storage. Motivation for this work is two-fold. First, the
amount of static power dissipation in CMOS chips now rivals the levels of dynamic
power dissipation. In other words, even if a chip does not perform any computation,
stand-by power (i.e., needed to maintain volatile logic state, etc.) is similar to the
power dissipated when performing useful work. Anecdotally, in 2004, Bernard
Myerson – then chief technologist for IBM’s system and technology group – likened
the situation to ‘‘a car with a 10-gallon gas tank losing 5 gallons while parked with its
motor turned off’’ [2]. The nonvolatile nature of magnetic phenomena means that
there is no stand-by power dissipation. Second, the intrinsic switching energy of a
magnetic device can be orders of magnitude lower than a charge-based CMOS
transistor. While some drive circuitry overhead must be accounted for in magnetic
systems, this suggests that magnetic logic could help to minimize dynamic power
dissipation as well. Thus, while the multi-decade Moore’s Law-based size scaling
trends may continue, associated performance scaling trends are threatened by energy-
related concerns that magnetic devices could help to alleviate.
N.G. Anderson and S. Bhanja (Eds.): Field-Coupled Nanocomputing, LNCS 8280, pp. 21–32, 2014.
DOI: 10.1007/978-3-662-43722-3_2, Springer-Verlag Berlin Heidelberg 2014](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-32-320.jpg)
![One of the driving forces behind this research is the semiconductor industry itself
in the form of the Nanoelectronics Research Initiative (NRI) of the Semiconductor
Research Corporation (SRC). The NRI was formed in response to the impending ‘‘red
brick wall’’ in the industry’s road map, which is primarily the result of the inability to
manage dissipation associated with computation with field-effect transistors. In an
effort to find alternative, lower-power device technologies, the NRI is searching for
switches based on state variables other than charge. One possibility is the electron’s
spin, and associated magnetic phenomena. There now are several research efforts
underway to explore switches where the logic state is represented by the magneti-
zation of a nanomagnet. These various approaches have been summarized and
reviewed in [3], and our work on nanomagnet logic is one of these efforts.
2 Single-Domain Magnets for NML
Nanomagnet Logic (NML) is based on patterned arrays of elongated nanomagnets that
are sufficiently small to contain only a single magnetic domain. The magnetization
state of a device – i.e. whether it is magnetized along one direction or another,
commonly referred to as ‘‘up or down’’ – can be used to represent binary information
in the same way that magnetic islands are used to store information in magnetore-
sistive random access memory (MRAM). Elongated single-domain magnets are
essentially tiny bar magnets with poles on each end, that generate strong stray fields
that can be used to couple to other nearby magnets. While such magnetic interactions
between neighboring nanomagnets are undesirable for data-storage applications, we
have demonstrated that these interactions can be exploited to perform logic
operations.
It should be emphasized here that such single-domain behavior is rather special
and specific to magnets with certain sizes and shapes. For our work with patterned
ferromagnetic thin-film permalloy, these sizes are on the order of hundreds down to
tens of nanometers (nm). If the magnet is too large, its magnetization state breaks up
into multiple internal domains, and the poles at the end – along with their strong
fringing fields – disappear. If the magnet is too small, its magnetization state can be
switched by random thermal fluctuations, and it no longer has a stable magnetization
state; this is the so-called superparamagnetic limit. As a fascinating side comment,
Nature has learned to exploit the stray fields associated with single domain magnets
for navigation in the Earth’s magnetic field. Specialized, so-called magnetotactic
bacteria grow perfectly single-domain nanomagnets, that are specific to a particular
animal species [4]. By the way, much of our work on NML uses nanomagnets with
sizes and shapes between those characteristic for the pigeon and the tuna.
Figure 1 shows a magnetic force microscope (MFM) image of an array of nano-
scale magnets with varying sizes and aspect ratios. The coloring represents magnetic
contrast, and dark and light spots indicate magnetic poles. It can be seen that these
magnets display single-domain behavior if they are sufficiently small and narrow (left
side of image), and these poles generate magnetic flux lines that can interact with
external magnetic fields, or couple to neighboring magnets. Otherwise, their magne-
tization state breaks up into several internal domains (right side of image), and there is
22 W. Porod et al.](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-33-320.jpg)
![flux closure inside, without strong coupling to the exterior. Such single-domain
magnets, with typical size scales of tens to hundreds of nanometers, form the physical
basis for NML.
3 From Quantum-Dot Cellular Automata to Nanomagnet
Logic
Our current work on nanomagnet logic grew out of our previous work on Quantum-
Dot Cellular Automata (QCA), which was an attempt to base computation on phys-
ically-interacting cellular arrays of quantum dots occupied by a few electrons [6].
Instead of wires, neighboring devices interact through direct Coulomb interactions
between electrons on neighboring quantum dots. We have shown that such physical
interactions in appropriately structured arrays of quantum dots can also be used to
realize logic gates. Electronic implementations of QCA proved difficult due to tech-
nological limitations of quantum-dot fabrication (such as size variations) and elec-
tronic stray charges. For a review of electronic QCA, see Refs. [7, 8].
Nanomagnet logic can be viewed as a magnetic implementation of QCA.
(In earlier publications, we used the term magnetic QCA (MQCA), but we now prefer
to use NML in order to avoid confusion with quantum dots.) Early theoretical work on
magnetic QCA is given in the Ph.D. Dissertation of György Csaba [9]. These simu-
lations demonstrated the feasibility of using field-coupled single-domain nanomagnets
for realizing basic logic functionality [10–12]. In subsequent experimental work
stimulated by these simulations, and which constituted the Ph.D. Dissertation of
Alexandra Imre [5], we first demonstrated magnetic wires formed by chains of near-by
magnetic islands. Since the individual dots have elongated shapes, there are two basic
types of wire arrangements. In one type, the magnets are lined up side-by-side and, as
one’s intuition would tell from two bar magnets next to each other with their long
sides, the individual magnets prefer to be magnetized in the opposite direction; we call
Fig. 1. Nano-scale magnets with varying sizes and aspect ratios. Single-domain behavior is
observed if the magnets are sufficiently small and narrow. (Source: A. Imre, Ph.D. dissertation,
University of Notre Dame, 2005 [5].)
Nanomagnet Logic (NML) 23](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-34-320.jpg)
![this antiferromagnetic coupling. The other type of wire consists of the individual
magnets lined up in the same direction, and as one would expect, the individual
magnets also prefer to be magnetized in the same direction; we call this ferromagnetic
coupling.
Figure 2 shows an example of an antiferromagnetically-coupled wire consisting of
a chain of 16 dots. The top portion of the image shows an SEM (scanning electron
microscope) image of magnetic islands fabricated from a 30-nm thin film of permalloy
using electron beam lithography and standard lift-off techniques. The bottom portion
of the figure shows the structural AFM (atomic force microscope) image, and the
MFM (magnetic force microscope) image showing the magnetic contrast. The dot on
the top right (aligned in the horizontal direction) serves as an input that determines if
the wire is aligned up-down-up-down or down-up-down-up.
In these experiments, a magnetic field is required to aid the switching of the array
of nanomagnets [12]. When one dot is switched, the fringing fields are not sufficiently
strong to switch a neighboring magnet. However, the fringing fields can be used to
bias the switching event when an additional switching field is applied. Due to the
elongated shape (magnetic shape anisotropy), the dots have very stable magnetization
states along the long (magnetic easy) axis. They can be magnetized along the short
(magnetic hard) axis by the application of a sufficiently strong magnetic field in that
Fig. 2. Demonstration of a magnetically-ordered line of dots. Top panel: SEM, middle panel:
AFM, bottom panel: MFM.
24 W. Porod et al.](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-35-320.jpg)
![direction. However, when this field is removed, the dots will ‘‘snap’’ back into the
preferred ‘‘up’’ or ‘‘down’’ easy-axis direction, and the fringing fields from the
neighbors can bias which way they switch. This switching field acts as a magnetic
clock.
It turns out that the ‘‘native’’ logic element for NML is a three-input majority-logic
gate, just like for the original electronic QCA. As shown schematically below, this
gate consists of a cross-shaped arrangement of five dots, where three of the arms
(labeled ‘‘A,’’ ‘‘B,’’ and ‘‘C’’) represent the inputs, the center dot (labeled ‘‘M’’)
calculates the majority vote of these inputs, and the fourth arm (labeled ‘‘out’’) rep-
resents the output. This arrangement can also be viewed as the intersection between an
antiferromagnetic and a ferromagnetic wire segment. Note that the majority vote is
‘‘calculated’’ through magnetic interactions in this physics-driven NML computing
scheme (Fig. 3).
It is interesting to note that such a three-input majority gate can be reduced to either
a binary AND or OR gate by viewing one of the inputs as a set-input, which selects the
functionality of the gate. For example, if we view ‘‘C’’ as the set-input, and ‘‘A’’ and
‘‘B’’ as the data inputs, then a ‘‘0’’ on ‘‘C’’ means that both ‘‘A’’ and ‘‘B’’ have to be
‘‘1’’ in order to have a majority vote of ‘‘1’’ at the output. In other words, setting ‘‘C’’ to
‘‘0’’ reduces the three-input majority gate to an AND gate for the data inputs ‘‘A’’ and
‘‘B.’’ Conversely, setting ‘‘C’’ to ‘‘1’’ results in an OR gate since only either ‘‘A’’ or
‘‘B’’ have to be ‘‘1’’ in order to have a majority vote of ‘‘1.’’ This programmability
offers interesting possibilities from a computer science perspective since the func-
tionality of this gate can be determined by the current state of the computation.
We have experimentally demonstrated functioning majority-logic gates working
properly at room temperature [13]. The figure below [from the Science paper] shows
the eight possible input combinations for the three-input majority-logic gate. Note that
here the different input combinations were realized by different arrangements of the
horizontal input dots. However, the shape-dependent switching behavior of such
nanoscale magnets [14] can be exploited to individually address specific inputs, thus
providing programmability. We have since fabricated gates with input devices of
varying aspect ratios, which has allowed a single gate structure to be successfully
tested with all eight possible input combinations [15] (Fig. 4).
Fig. 3. Schematic of a magnetic three-input majority-logic gate, which consists of a cross-
shaped arrangement of five dots. Panel (a) shows the basic dot, (b) the basic logic gate, and
(c) the logic-gate symbol.
Nanomagnet Logic (NML) 25](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-36-320.jpg)
![Thus far [16–18], our work has provided a proof-of-concept demonstration of
NML – i.e. the feasibility of performing digital logic with physically-coupled nano-
magnets. However, so far we have used MFM to read the state of the dots, and
externally generated magnetic fields to switch the dots. Of course, this is not practical
for real applications. Below, we describe on-going work to develop electronic input
and output (I/O) and mechanisms for generating local magnetic fields for ‘‘on-chip’’
clocking.
Before proceeding, we want to emphasize that our experimental proof-of-concept
demonstrations satisfy five ‘‘tenets’’ that are considered essential for a digital system:
(1) NML devices have non-linear response characteristics due to the magnetic hys-
teresis loop. (2) NML can deliver a functionally complete logic set enabled by the
3-input majority gate and the NOT operation naturally achieved by the antiferro-
magnetic dot-to-dot coupling. (3) Signal amplification/gain greater than 1 has been
experimentally demonstrated by showing the feasibility of 1:3 fanout [19], where the
energy for the gain is provided by an external clocking field discussed further below.
(4) The output of one device can drive another as the fringing fields from individual
magnets can bias a neighbor. (5) Unwanted feedback is preventable through clocking.
4 Nanomagnet Logic: Towards System Integration
Recent and ongoing work addresses electronic means for both NML I/O and clocking.
Our approach leverages existing MRAM technologies for READ/WRITE operations.
After all, setting an input for NML, i.e. setting the state of an input magnet, is similar
to writing the state of an MRAM bit. Similarly, reading the state of an NML output dot
is just like reading an MRAM bit. These similarities to MRAM suggest that an NML
circuit is analogous to a patterned ensemble of the free layers in an MRAM stack.
Fig. 4. Experimental demonstration of an NML three-input majority-logic gate. (Source: Imre
et al., Ref. [13].)
26 W. Porod et al.](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-37-320.jpg)
![In this way, NML can leverage much existing technological know-how, and also
benefit from future development in MRAM technologies [20].
Under the umbrella of the DARPA Non-Volatile Logic (NVL) program, we
worked on approaches to on-chip clocking. As mentioned above, externally supplied
switching energy is needed to re-evaluate a magnet ensemble with new inputs.
To date, most NML circuits have been ‘‘clocked’’ by an external source. However, it is
essential that clock functionality be moved ‘‘on-chip.’’ Thus far, the most commonly
employed clock is a magnetic field applied along the hard axis of an NML ensemble,
which places the magnets into a metastable state such that they are sensitive to the
fringing fields from their neighbors. Such magnetic fields can be generated on-chip by
current-carrying wires for local control of NML circuits. In recent work, we have
fabricated copper wires clad with ferromagnetic material on the sides and bottom (like
field-MRAM word and bit lines), and we have demonstrated that NML magnets,
interconnect, and logic gates can be switched (i.e. re-evaluated) in this way [21, 22].
Also under the umbrella of the DARPA Non-Volatile Logic (NVL) program, we
worked on approaches for integrated electronic I/O. Electronic output can be achieved
(similar to MRAM) by a magnetoresistance measurement, where the NML output dot
is the free layer in a magnetic tunnel junction (MTJ) stack. Similarly, electronic input
can be achieved using the spin-torque transfer (STT) effect, where the NML input dot
is the free layer in an STT stack [23, 24].
As is well known from field-MRAM, there is an energy overhead associated with
generating local magnetic fields using current-carrying wires. Early on, simulations
showed that the overhead associated with such clocking is a major component of the
total energy requirement, and that the dissipation associated with the switching of the
magnets is rather small [25]. For NML, the clock energy could be amortized over
100,000s of devices as a single clock line could control many parallel ensembles [26].
Clock lines could be placed in series and in multiple planes to minimize driver
overhead. Moreover, at cryogenic temperatures, clock lines could be made from
superconducting niobium, and I2
R losses could drop to zero. In principle, this opens
the door to extremely low energy information processing hardware/memory that could
be integrated with RSFQ and SQL logic.
Also inspired by field-MRAM, another approach to lowering the energy overhead
associated with clocking is to engineer the dielectric medium between the dots, which
influences the coupling strength and thus the switching energy. Specifically, one can
enhance the permeability of a dielectric by the controlled inclusion of superpara-
magnetic particles that increase the dielectric permeability, and thus lower the current
required to achieve a certain switching field [27]. Following this approach, we have
successfully fabricated such enhanced permeability dielectrics and demonstrated the
lowering of switching fields and associated power dissipation [28–30].
Another possible approach to clocking is to exploit the strong local fields asso-
ciated with a domain wall. We have shown that the motion of domain walls can be
controlled [31, 32], and that their local fringing fields can assist in the switching of
nearby magnets [33]. This is an interesting approach to NML clocking that deserves
further investigation.
Multiferroics, magnetostriction, and spin-torque transfer have also been proposed
as potential clocking mechanisms for NML. Multiferroic materials (e.g. BFO) could
Nanomagnet Logic (NML) 27](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-38-320.jpg)
![allow for electric field control of magnetism, which would be highly attractive for
NML. Included in this volume is a contribution from the group of Sayeef Salahuddin
at UC Berkeley that addresses this interesting possibility [34].
Another important issue for NML is whether or not the magnets that form a circuit
ensemble can be switched reliably – or whether or not devices placed into a meta-
stable state by a clock are adversely affected by thermal noise (which could induce
premature switching). The group of Jeff Bokor at UC Berkeley has shown that
magnets with an extra biaxial anisotropy exhibit superior switching characteristics
[35]. Essentially, such an ‘‘engineered-in’’ magnetic anisotropy helps to stabilize the
magnets in the ‘‘vulnerable’’ metastable state against random fluctuations. We have
shown that shape engineering, i.e. exploiting the influence of geometry on magnetic
properties, can be used to not only enhance the reliability of switching, but also to
design logic gates with reduced foot print [36, 37].
At Notre Dame, all of our work to date has been based on patterned thin-film
permalloy dots, which have in-plane magnetization. An attractive alternative is to use
structures with out-of-plane magnetization, such as Co/Pt multi-layer films, where the
magnetic properties are due to the Co-Pt interfaces. In collaboration with Doris
Schmitt-Landsiedel and her group at the Technical University of Munich (TUM),
we are exploring the utility of this material system for NML. It has been shown that
such Co/Pt structures can be patterned with a focused ion beam (FIB) instrument,
where the ion beam destroys the interfaces, and thus the magnetization at these
locations. In this fashion, a film can be patterned into islands, and sufficiently small
islands also exhibit single-domain behavior. The TUM group has demonstrated
magnetic coupling between neighboring islands [38], and they have shown magnetic
ordering in arrays of coupled islands. Moreover, they have realized directional signal
propagation in lines, and basic NML logic gates [39], as well as domain-wall assisted
switching [40].
All our fabrication work so far has been based on using electron-beam lithography
(EBL) to define the NML devices and structures. EBL is a flexible and useful tool for
research, but not suitable for large-scale manufacturing. To this end, we collaborate
with Paolo Lugli and his group at the TUM to explore the use of nanoimprint
lithography and nanotransfer of permalloy structures for the fabrication of large-scale
NML arrays [41].
NML represents a technology quite different from CMOS, with its own ‘‘pros’’ and
‘‘cons.’’ Undoubtedly, this new technology will likely necessitate new circuit and
architecture approaches [42]. Along these lines, we have worked to identify specific
application spaces for NML. Our immediate focus is on low energy hardware
accelerators for general-purpose multi-core chips, and application spaces that demand
information processing hardware that can function with an extremely low energy
budget. As an example, we anticipate that NML-based hardware might be used to
implement a systolic architecture that can improve the performance of compute-bound
applications, provide very high throughput at modest memory bandwidth, and elim-
inate global signal broadcasts. (Systolic solutions exist for many problems including
filtering, polynomial evaluation, discrete Fourier transforms, matrix arithmetic and
other non-numeric applications.) Moreover, as devices are non-volatile, information
can be stored directly and indefinitely throughout a circuit (e.g. at a gate input)
28 W. Porod et al.](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-39-320.jpg)
![without the need for explicit storage hardware (and the associated area and static/
dynamic power dissipation associated with it).
Architectural-level design techniques such as these should allow us to minimize
the ‘‘cons’’ of NML (nearest neighbor dataflow and higher latency devices when
compared to CMOS FETs) and exploit the ‘‘pros’’ (inherently pipelined logic with no
overhead). As a representative example [43], our projections suggest that hardware for
finding specific patterns in incoming data streams could be *60-75X more energy
efficient (at iso-performance) than CMOS hardware equivalents. Moreover, these
projections include clock energy overheads.
5 Summary and Discussion
In this chapter, we have presented an overview of our work over the years on nano-
magnet logic, which can be viewed as a magnetic implementation of the original QCA
field-coupled computing idea. We discussed NML basics, as well as approaches and
issues related to the realization of integrated systems. This review was Notre-
Dame-centric by design, to provide a somewhat historical perspective on the work of
our group.
Finally, we would like to mention a couple of other related research efforts that
also use nanomagnets to represent logic state, but that employ different mechanisms to
couple and switch these magnets. One such effort, the Spin-Wave Bus proposed by a
group at UCLA [44], is based on spin waves propagating in a layer underneath the
magnets. Since spin waves (plasmons) decay, this scheme requires amplifying ele-
ments to restore the signals. Another scheme, the All-Spin Logic proposed by a group
at Purdue [45], is based on nanomagnet coupling by spin diffusion in a magnetic layer
underneath the magnets. This scheme requires wires to be connected to the magnetic
dots in order to inject spin-polarized electrons that then diffuse and provide the
coupling mechanism. These approaches are interesting, and further research is war-
ranted. However, in our opinion, it is hard to see how coupling between dots using
either spin waves or spin diffusion can be more efficient or lower power than coupling
by direct magnetic fringing fields.
We end with a historical note. It was recognized in the very early days of digital
computer design that magnetic phenomena are attractive for several reasons [46]:
They possess an inherent high reliability; They require in most applications no power
other than the power to switch their state; They are potentially able to perform all
required operations, i.e., logic, storage and amplification. In fact, some of the very
early computers used ferrite cores not only for memory, but also for logic. Ferrite
cores were coupled by wires strung in specific ways between them so as to achieve
logic functionality. For example, the Elliott 803 computer used germanium transistors
and ferrite core logic elements. Of course, this kind of magnetic logic technology
based on stringing wires between bulky magnetic cores was not competitive against
emerging semiconductor technology. However, with the advent of modern fabrication
technology, which allows the fabrication of arrays of nanometer-size single-domain
magnets, the old quest for magnetic logic might become a reality.
Nanomagnet Logic (NML) 29](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-40-320.jpg)
![Silicon Atomic Quantum Dots Enable
Beyond-CMOS Electronics
Robert A. Wolkow1,2,3(B)
, Lucian Livadaru3
, Jason Pitters2
, Marco Taucer3
,
Paul Piva3
, Mark Salomons2
, Martin Cloutier2
, and Bruno V.C. Martins1
1
Department of Physics, University of Alberta, 11322-89 Avenue,
Edmonton, AB T6G 2G7, Canada
rwolkow@ualberta.ca
2
National Institute for Nanotechnology, National Research Council of Canada,
11421 Saskatchewan Drive, Edmonton, AB T6G 2M9, Canada
3
Quantum Silicon Inc., 11421 Saskatchewan Drive,
Edmonton, AB T6G 2M9, Canada
Abstract. We review our recent efforts in building atom-scale quantum-
dot cellular automata circuits on a silicon surface. Our building block
consists of silicon dangling bond on a H-Si(001) surface, which has been
shown to act as a quantum dot. First the fabrication, experimental imag-
ing, and charging character of the dangling bond are discussed. We then
show how precise assemblies of such dots can be created to form artificial
molecules. Such complex structures can be used as systems with custom
optical properties, circuit elements for quantum-dot cellular automata,
and quantum computing. Considerations on macro-to-atom connections
are discussed.
Keywords: Silicon dangling bonds · Quantum-dot cellular automata
1 Preliminaries
There are two broad problems facing any prospective nano-scale electronic device
building block. It must have an attractive property such as to switch, store or
conduct information, but also, there must be an established architecture in which
the new entity can be deployed and wherein it will function in concert with other
elements. Nanoscale electronic device research has in few instances so far led to
functional blocks that are ready for insertion into existing device designs. In this
work we discuss a range of atom-based device concepts which, while requiring
further development before commercial products can emerge, have the great
advantage that an overall architecture is well established that calls for exactly
the type of building block we have developed.
The atomic silicon quantum dot (ASiQD) described here fits within ultra
low power schemes for beyond CMOS electronics based upon quantum dots that
have been refined over the past 2 decades. The well known quantum dot cellu-
lar automata (QCA) scheme due to Lent and co-workers [1,2] achieves classical
N.G. Anderson and S. Bhanja (Eds.): Field-Coupled Nanocomputing, LNCS 8280, pp. 33–58, 2014.
DOI: 10.1007/978-3-662-43722-3 3, c
Springer-Verlag Berlin Heidelberg 2014](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-44-320.jpg)
![34 R.A. Wolkow et al.
binary logic functions without the use of conventional current-based technology.
Within this scheme, the binary states “1” and “0” are encoded in the position
of electric charge. Variants exist but most commonly the basic cell consist of
a square (or rectangular) quantum dot ensemble occupied by 2 electrons. Elec-
trons freely tunnel among the quantum dots in a cell, while electron tunneling
between cells does not occur. Within a cell, two classically equivalent states
exist, each with electrons placed on the diagonal of the cell. Multiple cells cou-
ple and naturally mimic the electron configuration of nearest-neighbour cells. In
general, cell-cell interactions must be described quantum mechanically but to
a good approximation they are described simply by electrostatic interactions.
A line of coupled cells serves as a binary wire. When a terminal cell is forced by
a nearby electrode to be in one of its two polarized states, adjacent cells copy
that configuration to transfer that input state to the other terminus. This trans-
fer can happen spontaneously or can be zonally regimented by a clock signal
that controls inter-dot barriers, or some other parameter. The last key feature
of QCA is that three binary lines acting as computation inputs and one line
acting as output can converge on a node cell to create a majority gate. If two
of the three input lines are of one binary state, the fourth side of the node cell
will output the majority state. Variants of such an arrangement allow for the
realization of a full logical basis. To date, all manner of digital circuits have been
designed, from memories to multipliers to even a microprocessor.
While complex working circuits have not yet been realized, all the rudimen-
tary circuit elements have been already experimentally demonstrated [3,4]. Fur-
thermore, the input state of a QCA circuit has been externally controlled and
the output has been successfully read-out by a coupled single electron transistor
[5,6]. Until the present work, all available quantum dots, typically consisting of
thousands of atoms, had narrowly spaced energy levels requiring ultra-low tem-
perature to exhibit desired electronic properties. Moreover, approximately as
many wires as quantum dots were required to adjust electron filling, a scenario
that would greatly limit the complexity of circuitry that could be explored.
A prospect for highly complex and room temperature operational QCA cir-
cuitry suddenly emerged with the discovery of atomic silicon quantum dots.
Figure 1 shows a schematic 4-dot QCA cell on the left occupied with two elec-
trons (indicated by blackened circles). On the right is an STM image of a real
atom-scale cell made of 4 ASiQDs, the cell being less than 2 nm on a side. The
darker of the two dots are predominantly electron occupied.
The ultimate small size of the ASiQDs leads to ultimate wide spacing of
energy levels indeed sufficiently widely spaced to allow room temperature device
operation. The ASiQDs can be prepared in a native 1− charge state (charge is
expressed in elementary charge units henceforth). Close placement of dots causes
Coulombic repulsion and even removal of an electron to the silicon substrate
conduction band. By fabricating dots at an appropriate spacing, a desired level
of electron occupation can be predetermined, eliminating the need for many
wires. As all atomic dots are identical, and their placement occurs in exact
registry with the regular atomic structure of the underlying crystalline lattice,](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-45-320.jpg)
![36 R.A. Wolkow et al.
a silicon crystal, abbreviated H-Si(100). Atomically flat, ordered H-termination
is ordinarily achieved by cracking Hydrogen gas, H2, into H atoms by collision
with a hot tungsten filament and allowing those H atoms to react with a clean
silicon surface in a vacuum chamber. If the H-termination process is incomplete,
or if an H atom is removed by some chemical or physical means, a DB is created.
H atoms removed by the local action of a scanning tunneling microscopy (STM)
are the focus here. Broadly speaking, the scanning motion of the tip can be halted
to direct an intense electrical current in the vicinity of a single Si-H surface bond
[7–10]. At approximately a 2 V bias between tip and sample it is understood that
multiple vibrational excitations lead to dissociation of the Si-H bond. At near
5 V bias it is thought the Si-H bond can be excited to a dissociative state, as
in a photochemical bond breaking event. Other not well understood factors are
at play, such as a catalytic effect, intimately depending on particular tip apex
structure and composition that might ease the Si-H bond apart as a substantial
H atom-tip bond forms while the Si-H bond lengthens and weakens. The fate of
removed H atoms is unclear though there is substantial evidence, in the form of
H atom donation to the surface that some atoms reside on the STM tip [11,12].
Many details related to exact position of the tip and precise metering of the
energetic bond breaking process so as to create just the change desired and not
other surface alterations will be touched upon in the section on Quantum Silicon
Incorporated and the commercial drive to fabricate atom scale silicon devices.
Figure 2a shows a model of a H-Si(100) surface. Silicon atoms are yellow.
Hydrogen atoms are white. Note the surface silicon atoms are combined with H
atoms in a 1 to 1 ratio. Note also that the surface silicon atoms deviate from the
bulk structure not only in that they have H atom partners, but also in that each
surface silicon atom is paired-up into a dimer unit. The dimers exist in rows.
Figure 2b shows a constant current STM image of a H-Si(100) surface. The
dimer units are 3.84 Å separated along a dimer row. The rows are separated by
twice that distance, 7.68 Å. The overlaid grid of black bars marks the position
of the silicon surface dimer bonds. To reiterate, there is an H atom positioned
at both ends of each dimer unit.
Figure 3 indicates the localized creation of a dangling bond upon action
directed by a scanned probe tip. Figure 3b shows an STM image of several DBs
so created [13].
3 The Nature of Silicon Dangling Bonds
Figure 4 shows two silicon surfaces imaged under the same conditions [14]. Both
surfaces have a scattering of DBs. The left image is of a moderately n-type doped
sample. It has been shown that DBs on such a surface are on average neutral.
The DBs in that case are visible as white protrusions. The right hand image is of
a relatively highly n-type doped sample. In that case each DB has a dark “halo”
surrounding it. These DBs are negative. This results as the high concentration
of electrons in the conduction band naturally “fall into” relatively low-lying DB
surface state to make it fully, that is 2 electron, occupied. This localization of a](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-47-320.jpg)
![38 R.A. Wolkow et al.
Low doped n-type Silicon
Neutral DBs
High doped n-type Silicon
Negative DBs
(a) (b)
Fig. 4. Two silicon surfaces imaged under the same conditions. (a) A moderately
n-type doped sample where DBs are on average neutral. (b) A highly doped sample
where DBs are on average negatively charged.
negative charge at a DB causes destabilization of electron energy levels referred
to as upward band bending. To a first approximation it is the inaccessibility
of empty states for the STM tip to tunnel into that causes the highly local
darkening of the STM image, that is, the halo. A much fuller description of the
competing process involved in the imaging process have been described [15].
It is evident that the DB is effectively a dopant with a deep acceptor level.
In accord with that character, a DB acts to compensate bulk n-type doping,
causing the bands to shift up with respect to the Fermi level in the direction
of a p-doped material. Most recently it has been shown that the neutral, single
electron occupied DB can donate its charge to become positive thereby acting
as a deep n-type dopant [16]. Summarizing, single electron occupation corre-
sponds to neutral state. Two electron occupation corresponds to 1− charge. The
absence of electrons in the DB leaves it in a 1+ charge state. The combination
of dopant type, concentration, DB concentration on the surface, local electric
field, and finally current directed through a DB, all contribute to determining
its instantaneous charge state [15].
A clean silicon surface, where every site has a dangling bond, is very reactive
toward water, oxygen and unsaturated hydrocarbons like ethylene and benzene.
While H atoms immediately react with a clean silicon surface, H2 does not
[17]. It is a remarkable fact that single DBs interact only weakly with most
molecules, resulting in no attachment at room temperature. Most often, a second
immediately adjacent DB is required in order for a molecule to become firmly
bonded to the surface. Two DBs typically act together to form two strong bonds
to an incoming molecule. This has the practical consequence that a protective
layer can be formulated and applied to encapsulate and stabilizes DBs against
environmental degradation.
A special class of molecules, typified by styrene, C8H8 attach to silicon via a
self-directed, chain reaction growth mechanism [18]. As shown in Fig. 5a, a ter-
minal C reacts with a DB, thereby creating an unpaired electron at the adjacent
C on the molecule. That species follows one of two paths. It either desorbs, or the](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-49-320.jpg)
![Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics 39
(a) (b)
Fig. 5. (a) Various processes in a chain reaction resulting in the growth of lines a
special class of molecules (e.g. styrene) on a H-Si(100) surface. R here denotes various
possible radicals. (b) A line of about 20 styrene molecules grown in this fashion and
imaged at different STM setpoints. The charge on the terminal DB at the top of the
line depends on the STM setpoint and therefore causes (or not) a Stark shift in the
molecular line.
radical C abstracts an H atom from an adjacent surface site to create a stably
attached molecule, and a regenerated DB positioned one lattice step removed
from the original DB position. The process repeats and repeats to create a multi-
molecular line that gains a degree of order from the crystalline substrate.
Figure 5b shows an approximately 20 molecule long line of styrene grown in
this way. The bright feature at the end of the line is a DB. It has been shown that
under conditions where the terminal DB is negatively charged that charge acts
to gate (Stark shift) the molecular energy levels causing conduction through the
molecule where ordinarily it would not occur [19]. In other words the ensemble
forms single-electron gated, one-molecule field effect transistor. The point of
this discussion is to show there is precedent for microscopic observation of DBs
at different charge-states, and to point out that a structure like the molecule
transistor arrangement could be a useful detector of DB charge state [20].
4 Dangling Bonds Are Atomic Silicon Quantum Dots
The atoms in a silicon crystal enter into bonding and anti-bonding relationships
with neighbouring and distant silicon atoms to form bands that span the crys-
tal. In doing so the atoms give up their zero dimensional electronic character. Si](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-50-320.jpg)
![40 R.A. Wolkow et al.
Fig. 6. (a) STM micrograph (10 × 10 nm, 2 V, 0.2 nA) of a H-Si(100) surface with two
DBs. The distinct dark halo indicates each DB is negatively charged. (b) An additional
DB is created at a site near DB2 causing both the new DB3 and DB2 to appear very
differently.
atoms sharing in three ordinary Si-Si bonds and containing one dangling bond
have a special mixed character. Like 4-coordinate silicon atoms, such atoms are
very strongly bonded to the lattice and have an intimate role in the disper-
sive bands that delocalize electrons. At the same time, 3-coordinate atoms have
one localized state, approximately of sp3
character. This state is localized because
it is in the middle of the band gap and mixes poorly with the valence and con-
duction band continua. The DB-containing atom is odder still in that the DB
is partly directed toward the vacuum where it has a relatively limited spatial
extent but is also partially contained within the silicon crystal where, because
of dielectric immersion, is somewhat larger in spatial reach.
It was stated above that a DB state is like a deep dopant. Whereas a typical
dopant has an ionization or affinity energy of several tens of meV, the DB has
corresponding energies an order of magnitude larger. Consistent with that dif-
ference, the spatial extend of the DB state within the solid reaches several bond
lengths, much less than the size of a common dopant atom [21].
The zero dimensional character of the DB, combined with the capacity to
exhibit several (specifically 3) charge states leads us to think of the DB as
a quantum dot. This may at first seem a bit odd as a quantum dot is often
described as an artificial atom whereas we have a genuine atom, actually one
part of an atom, forming our dot. But if a quantum dot is most fundamentally a
vessel for containing and configuring electrons then, as subsequent examples will
show, the ASiQD naturally and ably fits the definition, especially as the ease
and precision of fabrication allows complex interactive ensembles of identical
quantum dots to be made.](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-51-320.jpg)
![Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics 41
5 Fabricating and Controlling a Quantum Dot Cellular
Automata Cell
Figure 6a shows two DBs. The distinct dark halo indicates the DBs are nega-
tively charged. Figure 4b shows that when an additional DB is created by a tip
directed H removal at a nearby site, both the new DB and the nearby pre-existing
DB appear very differently, while the somewhat removed DB is unaltered. After
extensive study it became clear that such a closely placed pair of DBs experi-
ences a great Coulombic repulsive interaction, destabilizing the bound electrons
and enabling one electron to leave the ensemble [12,14]. The reduced net charge
simultaneously stabilizes the remaining bound electron and creates an unoccu-
pied energy level on one of the atoms. Because the barrier separating the DBs
is low, of order several 100 meV, and is also very narrow, of order 2 nm, tunnel-
ing to the vacant state is very facile. Such a pair of DBs may be referred to as
tunnel coupled. Our WKB and ab initio calculations agree that the tunneling
rate for the 3.84 Å separated DBs corresponds to an extremely short tunneling
period of order 10 fs [22,23]. Conventional relatively large and necessarily widely
spaced dots would have a tunnel rate many orders of magnitude lower. Figure 7
shows the energy landscape schematically [14]. Each DB is represented by a
potential well. The well is within the silicon bandgap. In Fig. 7a the separation
between DBs is sufficiently large for the Coulombic interaction to be diminished
by distance and by screening by conduction band electrons. In Fig. 7b the high
energy repulsive relationship existing between two negatively charged DBs is
represented. Figure 7b also shows the relaxed situation resulting after removal of
one electron to the conduction band. In that final scenario one vacant electron
state is shown. That state and the low and narrow barrier enables tunneling
between the DBs.
The pairing result demonstrates a “self-biasing” effect. That is, by using
fabrication geometry and repulsion to adjust electron filling, the need for capac-
itively coupled filling electrodes is removed [14]. Figure 8a shows several pairs of
DBs of different separations and therefore different average net occupations. It
can be readily seen that closer spaced DBs more fully reject one electron, leading
to less local charge induced band bending and therefore to a lighter appearance
in the STM image. The increasingly widely spaced pairs look increasingly dark
as the net charge approaches 2 electrons. A statistical mechanical model of the
paired DBs reproduces the effect as shown in Fig. 8b. The graph stresses that
occupation is a time averaged quantity and that pairs in the cross-over region
will at any instant be either 1− or 2− charged [14].
Figure 9 shows a 4 dot ensemble or artificial molecule. The 4 dot cell was fabri-
cated to result in an average net filling of 2 extra electrons. The graphs in Fig. 9b
show the result of a statistical mechanical description of average occupation versus
distance of separation in such a square cell at different temperatures [12].
One way to localize and thereby visualize the occupying electrons is to make
an irregular shaped cell as is shown in Fig. 10 [14]. Figure 10a shows three dots,
two of which look darker indicating greater negative charge localization Upon](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-52-320.jpg)
![Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics 43
Fig. 9. (a) A fabricated ensemble (cell) of 4 tunnel-coupled DBs, or artificial molecule,
calibrated to result in an average net filling of 2 extra electrons. A corresponding dimer
lattice diagram is shown below. (b) The result of a statistical mechanical description
of average occupation versus distance of separation in such a square cell at different
temperatures (300 K top graph, 100 K bottom graph). The occupation probabilities
with 1, 2, 3, 4 extra electrons are plotted for each case.
adding a fourth dot the previously darker sites become relatively light in appear-
ance. This is due to the electrons attaining a lower energy configuration along
a newly available longer diagonal. In a symmetric square or rectangular cell the
freely tunneling electrons equally occupy the degenerate diagonal configurations.
On the slow time scale of the STM measurement no instantaneous asymmetry
can be seen.
In order to embody the QCA architecture it must be possible to break that
symmetry electrostatically and thereby to polarize electrons within a cell. This
capacity is illustrated first by referral to a 2 dot cell. Figure 11 shows the sequen-
tial building of a 2 dot cell occupied by one extra electron and the polarization
of that cell by one perturbing charge [14]. Figure 11a shows a small area, 3 nm
across, of H-terminated silicon at room temperature. Figure 11b shows the cre-
ation of one ASiQD, while Fig. 11c shows the creation of a second ASiQD and
the concomitant reduction in charge and darkness as seen by the STM. Upon
charge removal, rapid tunnel exchange ensues. The coupled entity resulting may
be described as an artificial homonuclear diatomic molecule. Like in an ordi-
nary molecule, the Born-Oppenheimer approximation is valid. In other words,
the electron resides so very briefly on one atom that nuclear relaxation does not
have time to occur. On the electronic time scale, the nuclei are frozen. Finally in
Fig. 11d another charged DB is created. Using the knowledge displayed in Fig. 6,
the last DB is placed near enough to the molecule to affect it electrostatically,](https://image.slidesharecdn.com/2348908-250526144020-9c44cc71/85/Fieldcoupled-Nanocomputing-Paradigms-Progress-And-Perspectives-1st-Edition-Neal-G-Anderson-54-320.jpg)
Fieldcoupled Nanocomputing Paradigms Progress And Perspectives 1st Edition Neal G Anderson
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- 5. Neal G. Anderson Sanjukta Bhanja (Eds.) Field-Coupled Nanocomputing State-of-the-Art Survey LNCS 8280 123 Paradigms, Progress, and Perspectives
- 6. Lecture Notes in Computer Science 8280 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, Lancaster, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Zürich, Switzerland John C. Mitchell Stanford University, Stanford, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Dortmund, Germany Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbruecken, Germany For further volumes: http://www.springer.com/series/7407
- 7. Neal G. Anderson • Sanjukta Bhanja (Eds.) Field-Coupled Nanocomputing Paradigms, Progress, and Perspectives 123
- 8. Editors Neal G. Anderson University of Massachusetts Amherst Amherst, MA USA Sanjukta Bhanja University of South Florida Tampa, FL USA ISSN 0302-9743 ISSN 1611-3349 (electronic) ISBN 978-3-662-43721-6 ISBN 978-3-662-43722-3 (eBook) DOI 10.1007/978-3-662-43722-3 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2014940849 LNCS Sublibrary: SL1 – Theoretical Computer Science and General Issues Springer-Verlag Berlin Heidelberg 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
- 9. Preface Field-coupled nanocomputing (FCN) paradigms offer fundamentally new approaches to digital information processing that do not utilize transistors or require charge transport. Information transfer and computation are achieved in FCN via local field interactions between nanoscale building blocks that are organized in patterned arrays. Several FCN paradigms are currently under active investigation, including quantum- dot cellular automata (QDCA), molecular quantum cellular automata (MQCA), nanomagnetic logic (NML), and atomic quantum cellular automata (AQCA). Each of these paradigms has unique features that make it attractive as a candidate for post- CMOS nanocomputing, and each faces critical challenges to realization. With the hope of bringing the community together to gauge the current status of FCN research and to consider its future directions, we requested support from the National Science Foundation for a dedicated workshop. The result was The 2013 Workshop on Field-Coupled Nanocomputing, which was held at the University of South Florida in February 2013. The international group of participants, which included experienced FCN researchers, postdoctoral scholars, and graduate students, embraced the objectives of this workshop and contributed generously to their achievement. The first objective was to take stock of major milestones that have been achieved in emerging FCN nanocomputing paradigms—at the device, circuit, archi- tecture levels—to provide a snapshot of the current state of research in the field. The second objective was to identify and highlight promising opportunities for FCN and critical challenges facing realization of FCN-based nanocomputers. A panel discus- sion was dedicated specifically to these concerns, providing all participants—most importantly the graduate student participants—with a variety of perspectives on emerging research priorities and critical next steps. Our third and final objective was to make the workshop proceedings available to a wide readership, and to do so in a way that allowed inclusion of more background, tutorial, and review material than is typically found in conference papers. To this end we invited participants to submit comprehensive, chapter-length expositions of research related to their workshop contributions, and we solicited a few such con- tributions from researchers who are working on intriguing aspects of FCN-related topics but were not in attendance at the workshop. This invitation was answered with a collection of quality contributions reflecting a remarkably diverse portfolio of current FCN research. These chapters were peer reviewed by referees from pool that included workshop participants and additional FCN experts. We approached Springer about publishing this collection of contributions—together with an edited transcript of the panel discussion—in their well-known Lecture Notes in Computer Science (LNCS) series. Alfred Hofmann of Springer was immediately receptive, and suggested pub- lication in the LNCS State-of-the-Art Survey series. The result—this volume—is divided into five topical sections. In the first section (Field-Coupled Nanocomputing Paradigms), pioneering FCN researchers provide
- 10. valuable background and perspective on the QDCA, MQCA, NML, and AQCA paradigms and their evolution. The second section (Circuits and Architectures) addresses a wide variety of current research on FCN clocking strategies, logic syn- thesis, circuit design and test, logic-in-memory, hardware security, and architecture. The third section (Modeling and Simulation) considers the theoretical modeling and computer simulation of large FCN circuits, as well as the use of simulations for gleaning physical insight into elementary FCN building blocks. The fourth section (Irreversibility and Dissipation) considers the dissipative consequences of irreversible information loss in FCN circuits, their quantification, and their connection to circuit structure. The fifth and final section (The Road Ahead: Opportunities and Challenges) includes an edited transcript of the panel discussion that concluded the FCN workshop. We thank all of the contributors that made this volume possible, the reviewers who enhanced its quality, and the team at Springer—especially Alfred Hofmann, Anna Kramer, and Christine Reiss—who enabled and facilitated its publication. We gratefully acknowledge Dr. Sankar Basu of National Science Foundation for engaging us in the discussions that led to the sponsorship of the FCN workshop—and thus to this volume—and Dr. Robert Trew for attending the workshop as NSF EECS Division Director. Our sincere gratitude to Dinuka Karunaratne, Srinath Rajaram, _ Ilke Ercan, Ravi Panchumarthy, Jayita Das, Drew Burgett, and Kevin Scott and all of the other student volunteers for workshop logistics, technical assistance, and recording of the panel discussion, and to the University of South Florida—especially the USF Student Chapter of IEEE—for local support and arrangements. Finally, we thank Katherine Anderson for assistance in transcribing the panel discussion. We hope that the col- lective efforts of all involved has yielded an accessible and useful resource for stu- dents and researchers who are intrigued by the possibility of future FCN-based nanocomputers and are working toward their realization. March 2014 Sanjukta Bhanja Neal G. Anderson VI Preface
- 11. Contents Field-Coupled Nanocomputing Paradigms The Development of Quantum-Dot Cellular Automata . . . . . . . . . . . . . . . . 3 Craig S. Lent and Gregory L. Snider Nanomagnet Logic (NML). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Wolfgang Porod, Gary H. Bernstein, György Csaba, Sharon X. Hu, Joseph Nahas, Michael T. Niemier, and Alexei Orlov Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics . . . . . . . . 33 Robert A. Wolkow, Lucian Livadaru, Jason Pitters, Marco Taucer, Paul Piva, Mark Salomons, Martin Cloutier, and Bruno V.C. Martins Circuits and Architectures A Clocking Strategy for Scalable and Fault-Tolerant QDCA Signal Distribution in Combinational and Sequential Devices . . . . . . . . . . . 61 Douglas Tougaw Electric Clock for NanoMagnet Logic Circuits. . . . . . . . . . . . . . . . . . . . . . 73 Marco Vacca, Mariagrazia Graziano, Alessandro Chiolerio, Andrea Lamberti, Marco Laurenti, Davide Balma, Emanuele Enrico, Federica Celegato, Paola Tiberto, Luca Boarino, and Maurizio Zamboni Majority Logic Synthesis Based on Nauty Algorithm . . . . . . . . . . . . . . . . . 111 Peng Wang, Mohammed Niamat, and Srinivasa Vemuru Reversible Logic Based Design and Test of Field Coupled Nanocomputing Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Himanshu Thapliyal, Nagarajan Ranganathan, and Saurabh Kotiyal STT-Based Non-Volatile Logic-in-Memory Framework. . . . . . . . . . . . . . . . 173 Jayita Das, Syed M. Alam, and Sanjukta Bhanja Security Issues in QCA Circuit Design - Power Analysis Attacks. . . . . . . . . 194 Weiqiang Liu, Saket Srivastava, Máire O’Neill, and Earl E. Swartzlander Jr. NanoMagnet Logic: An Architectural Level Overview . . . . . . . . . . . . . . . . 223 Marco Vacca, Mariagrazia Graziano, Juanchi Wang, Fabrizio Cairo, Giovanni Causapruno, Gianvito Urgese, Andrea Biroli, and Maurizio Zamboni
- 12. Modeling and Simulation Modelling Techniques for Simulating Large QCA Circuits . . . . . . . . . . . . . 259 Faizal Karim and Konrad Walus ToPoliNano: NanoMagnet Logic Circuits Design and Simulation . . . . . . . . . 274 Marco Vacca, Stefano Frache, Mariagrazia Graziano, Fabrizio Riente, Giovanna Turvani, Massimo Ruo Roch, and Maurizio Zamboni Understanding a Bisferrocene Molecular QCA Wire . . . . . . . . . . . . . . . . . . 307 Azzurra Pulimeno, Mariagrazia Graziano, Aleandro Antidormi, Ruiyu Wang, Ali Zahir, and Gianluca Piccinini Irreversibility and Dissipation Reversible and Adiabatic Computing: Energy-Efficiency Maximized . . . . . . 341 Ismo Hänninen, Hao Lu, Enrique P. Blair, Craig S. Lent, and Gregory L. Snider Modular Dissipation Analysis for QCA . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 _ Ilke Ercan and Neal G. Anderson The Road Ahead: Opportunities and Challenges Opportunities, Challenges and the Road Ahead for Field-Coupled Nanocomputing: A Panel Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 Neal G. Anderson and _ Ilke Ercan Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 VIII Contents
- 14. The Development of Quantum-Dot Cellular Automata Craig S. Lent() and Gregory L. Snider Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 56556, USA [email protected] Abstract. Quantum-dot cellular automata (QCA) is a paradigm for connecting nanoscale bistable devices to accomplish general-purpose computation. The idea has its origins in the technology of quantum dots, Coulomb blockade, and Landauer’s observations on digital devices and energy dissipation. We examine the early development of this paradigm and its various implementations. Keywords: Quantum-dot cellular automata (QCA) Molecular electronics 1 Introduction Quantum-dot cellular automata (QCA) is a means of representing binary information in cells, through which no current flows, and achieving device performance by the coupling of those cells through the electromagnetic field. Information is stored in the arrangement of charge (or magnetic dipoles) with in the cell. Importantly, cells have no monopole moment and are designed to be bistable, having two low energy states with different dipole or quadrupole orientation which can encode a binary 1 or 0. For large scale structures it is necessary to guide the switching of the cells with a clocking field that controllably switches the cells between a null state and an active state (either 0 or 1). Clocking provides power gain necessary to restore signal energies which would otherwise decay due to inelastic losses. The interaction energy between two cell, that is the energy difference between neighboring cells holding the same or opposite bits, is termed the kink energy, and determines thermal stability. Raising the kink energy entails moving to smaller geometries, with molecular QCA providing the limit of device density and requiring the ultra-low power dissipation made possible by adiabatic switching of QCA. Here we sketch the origins of the QCA idea, its early development, and subsequent evolution into several implementations and many research fronts. This is in no way a comprehensive review, but is particularly focused on the perspective of the Notre Dame group which originated the idea, and the basic trajectories that have arisen from the early work. We mean no slight by mentioning only a few of the major subsequent investigators. The elaboration of all the other contributors to this volume is necessary to give a fuller picture. N.G. Anderson and S. Bhanja (Eds.): Field-Coupled Nanocomputing, LNCS 8280, pp. 3–20, 2014. DOI: 10.1007/978-3-662-43722-3_1, Springer-Verlag Berlin Heidelberg 2014
- 15. 2 Historical Background In the 1980’s advanced epitaxial growth techniques such as molecular beam epitaxy (MBE) enabled the creation of GaAs-AlGaAs semiconductor heterostructures with very smooth interfaces. This ability to control the composition of crystalline semi- conductors with atomic precision made possible the formation of a highly conducting two-dimensional electron gas (2DEG) at the interface between AlGaAs and GaAs. Moreover, the 2DEG, which was essentially a plane of confined electrons, could be further patterned by placing lithographically-defined metal gates on the surface of the semiconductor. A negative potential on the gates would deplete the 2DEG under the gate regions. In 1988 two groups measured quantized conductance through a con- striction connecting two 2DEG regions and found that it was quantized [1, 2]. This was convincingly explained by invoking the quantum-mechanical nature of the electrons transiting the constriction. Using the effective mass approximation, one could explain much of the behavior of this layer by solving the Schrödinger equation in two dimensions. The ability to engineer the effective wavefunction of electrons seemed very promising for potential device applications. Throughout the 1990’s (and beyond) many wave-based device designs were proposed which used quantum interference effects as their operating principle, often created in analogy with microwave devices. Truly remarkable experimental demonstrations left little doubt that these quantum mechanical effects were real and could be potentially exploited for device behavior. In addition, it proved possible to create quantum dots by confining the 2DEG in both lateral dimensions (the third dimension was already confined by the heterostructure potential. These quantum dots could be viewed as artificial atoms [3, 4], and also as high-Q resonators for ballistic electron transport [5]. Into the optimism that these new abilities engendered, Rolf Landauer injected a ray of pessimism and realism. In a talk at the first International Symposium on Nanostructure Physics and Fabrication in 1991, Landauer cautioned that interference devices were unlikely to make it in the real world [6]. A ‘‘rich’’ response with many peaks and valleys did not, he argued, make a robust basis for devices, which would have to be tolerant of fabrication variations and environmental perturbations. He argued for devices whose transfer function is nonlinear and saturates at two distinct levels, as does a CMOS inverter. This input signal should be of the same type as the output signal, so that information can be transferred from device to devices. Another stream of research at the time was the newly emerging and promising phenomenon of Coulomb blockade in small structures. Electrons tunneling onto small metal islands can raise the potential of the island by e2/C, where C is the total capacitance of the island [7]. For very small structures this charging energy could be significant compared to thermal energies. The ‘‘orthodox’’ theories of the Coulomb blockade, even when treating the system quantum mechanically, characterized the island by this macroscopic quantity—the capacitance [8]. While this is quite adequate for metal structures containing very many free electrons, in small semiconductors one should really use a multi-particle approach. In such a model the effective capacitance is a result of the calculation of Coulomb effects, rather than being an input to it. 4 C.S. Lent and G.L. Snider
- 16. A study of few-electron systems under bias showed a threshold behavior for single electron transfer that is very nonlinear [9]. The origin of this nonlinearity is funda- mentally the quantization of charge. If a region of space is surrounded by barriers that are appropriately high, but still possibly leaky, then the expectation value of the enclosed charge will be very close to an integer multiple of the fundamental charge. When the equilibrium value of the charge changes because of a tunneling event, it will necessarily be a rather abrupt jump between two integers. Finally, the QCA architecture was inspired by classical cellular automata (CA) architectures [10], of the type popularized by Conway’s Game of Life. These are mathematical models of evolution that proceed from discrete generation to generation according to specified rules. The state of each cell is determined by the state of the neighboring cells in a previous generation. The neighbor-to-neighbor coupling is a natural match for nano-devices, since one expects that one very small device may influence its neighbors, but not distant devices. CA’s represent a means of compu- tation that departs from the current-switch paradigm of transistors. But cellular automata are mathematical models that can operate with any set of evolution rules. The question for device architecture was not simply what local CA rules will produce computational behavior, but what rules does the actual physics of cellular interaction support. The original QCA idea was the result of the confluence of these four ideas: (1) the ability to create configurations of quantum dots which localize charge, (2) the con- vincing argument by Landauer that any practical device would need bistable satura- tion in the information transfer function, (3) the nonlinearity of charge tunneling between such dots because of charge quantization, and (4) the notion of a locally- coupled architecture in analogy to cellular automata. It is worth noting that the connection to cellular automata is by analogy. Classical CA’s are almost always regular one or two-dimensional arrays of cells. The physics of the interaction between QCA cells does not yield very interesting results for regular arrays. QCA circuits look more like wires connecting devices; highly non-regular layouts of cells provide the specific function. Mathematical model CA’s evolve in discrete generations, but physical systems interact continuously. 3 Developments The first QCA paper demonstrated the bistability of a QCA cell using a multi-electron Hamiltonian and a direct solution of the Schrödinger equation [11]. This direct approach avoided the problems of sorting out exchange and correlation effects; within the site model it was exact. This bistability remains a key feature of QCA. Though it is somewhat appealing to explore a multi-state QCA cell and multi-state logic, only a bistable system can truly saturate in both logic states. An intermediate state is always subject to drifting off from stage to stage. It was soon realized that a line of QCA cells acted like a binary wire and a junction of two or three wires could form a logic gate [12]. The first proposal was to have a special cell at the junction which could be internally biased to the 1 or 0 state and thereby act as an OR gate or an AND gate [13]. It was soon clear that the bias could be The Development of Quantum-Dot Cellular Automata 5
- 17. applied by another wire, forming a three-input majority gate [14]. Inverters could be formed from diagonal interactions between cells. With these basic elements, any logical or arithmetic function can be formed. With a year of the first QCA publication, other implementations were suggested. Small metal islands could serve as dots and form QCA cells if they were coupled by tunnel junctions [15]. One advantage of metal-dot QCA is that the electric field lines from the dot can be guided by the conductors to influence the neighboring dots; in the semiconductor depletion dots, the field spreads out in all directions. It was also natural to envision molecular versions of QCA where the role of the quantum dot was played by a part of the molecule that could localize charge [14]. A magnetic model of QCA was constructed from three-inch magnets held in Lucite blocks which rotated on low- friction jeweled pivots. These magnetic cells were used during talks and lectures by both of the present authors to demonstrate QCA wires and gates. They prefigured (at enormous scale) the nanomagnetic QCA under active research today and discussed in other contributions to this volume. A detailed examination of QCA dynamics and the development of several levels of quantum description of QCA arrays [16], were prompted by another observation of Landauer [17]. While encouraging QCA exploration, he expressed concern that a weak link in a QCA wire would cause a switching error because the incorrect ‘‘old’’ state downstream would have more influence than the upstream cells with the new state. By treating the whole wire quantum mechanically it could be shown that this would only be a temporary problem. But the exercise focused attention on the nature of computation in QCA systems, which were designed from the beginning to map the ground state onto the computationally correct state. This mapping can be robust, while the details of the transient response of the system are inherently more fragile. We wanted to avoid computing with the transient. A byproduct of these calcula- tions was the development of several approximate treatments for both equilibrium and dynamic calculations. The mapping between QCA and the Ising model in a transverse field was also made precise. Clocking of QCA arrays arose out of the detailed consideration of switching dynamics and the desire to retain the robustness of the mapping between the ground state and the computationally correct state for large systems. Clocking QCA entails gradually moving cells between a neutral state and an active state with a clocking signal. The active state can be either a binary 0 or 1; the neutral state is usually denoted as a ‘‘null’’ state that carries no information. The first version of clocking, proposed the year following the initial QCA papers, contemplated raising and low- ering the inter-dot tunneling barriers [18, 19]. This would gradually (adiabatically) transition the cell between a delocalized electron configuration (null) and the localized configuration of the active state. Koroktov and Likharev subsequently suggested a version of metal-dot QCA called the single electron parametron which used a com- plicated rotating electric field as a clock [20]. This had several drawbacks (e.g., information could only move in one direction in an array), but the idea of using as the null state a localized state on an intermediate dot was adopted for clocking QCA, particularly for molecular implementations. It is much easier to change the potential on the intermediate dot than to directly influence the tunnel barriers between dots, and the effect is the same. Adiabatic clocking QCA [21] solved the problem of switching 6 C.S. Lent and G.L. Snider
- 18. dynamics getting caught, even temporarily, in a metastable state; this was the heart of Landauer’s objection. It retained the advantages of (local) ground-state mapping. During switching each cell is always very close to its instantaneous ground state (the definition of adiabaticity). Though we did not fully appreciate it at the time, this essentially turned QCA into a concrete implementation of the gedanken experiments which had led Landauer to conclude that there was no fundamental lower bound to the energy that must be dissipated to compute a bit [22]. Clocking further allowed much larger computational structures to be envisioned, combining memory and processing. 3.1 Semiconductor QCA The Cavendish group of Smith et al. demonstrated QCA operation in GaAs/AlGaAs heterostructures with confining top-gate electrodes [23–25], as originally envisioned in the earliest QCA publications. The group of Kern et al. demonstrated a QCA cell in silicon, using an etching technique to form the dots [26–29]. The group of Mitic et al. used a novel method to form dots from small clusters of phosphorus donors in silicon [30]. They succeeded in demonstrating QCA operation in that system. Interestingly, their long-term goal is coherent quantum computing and they conceive QCA devices as providing an ultra-low-power layer of interface electronics to connect a cryogenic quantum computer to standard CMOS electronics [31]. The challenges of all semiconductor implementations have been two-fold. Firstly, the lithographically accessible sizes for quantum dots are large enough that kink energies are low and cryogenic operation is required. More importantly, the perfection of the interface and electronic environment becomes an issue. While dots with tens of electrons effectively screen small amounts of impurity and imperfections, in the limit of single occupancy, semiconductor dots become very sensitive to the details of the environment. Even MBE-grown samples have enough random imperfections that the dot is often not exactly where one expects it to be based on lithography [32]. 3.2 Metal-Dot QCA Although electronic QCA has been demonstrated in a number of material systems, metal dot implementations have proven to be the most successful, so far, building on the fabrication techniques developed for single-electron transistors [33, 34]. The advantages of metal dots are that the fabrication yield is relatively high, and they are electrically well-behaved, meaning that energy required to add each additional elec- tron to the dot typically remains constant over the addition of many electrons. This makes it easier to load the QCA cell with the proper number of electrons and to bias the cell so that the two polarizations are energetically degenerate. However, in semiconductor dots [33, 34] the fabrication yield is low and the addition energy typically differs for each additional electron, and the electrical behavior of the dot can change from run to run, making it difficult to prepare the cell for proper operation. This makes the metal dot an attractive option for QCA experiments. The main dis- advantages of metal dots are background charge fluctuations [35], and low operating temperature. Background charge fluctuations are caused by the random arrangement The Development of Quantum-Dot Cellular Automata 7
- 19. of stray charge in the vicinity of the QCA cell, which affects the bias point and polarization degeneracy of the cell. The arrangement of this charge changes with time, and the gate biases applied to each dot in the cell must be adjusted to keep the cell operational. The low operating temperature of metal dot QCA cell is due to the size of the lithographically defined cell. The metal dot QCA are composed of aluminum islands separated by tunnel junctions. Fabrication of the cell is done by electron-beam lithography using the Dolan bridge technique [7] where the tunnel junctions are formed by evaporation of aluminum from two angles, with an intervening oxidation step. The resulting tunnel junctions are composed of two layers of aluminum separated by a thin layer, 1–2 nm, of aluminum oxide. The area of the overlap between the two layers of aluminum determines the capacitance of the junction, and since it is typically the dominant capacitance of the dot, determines the operating temperature of the QCA cell. Cells and Logic The first QCA cell was demonstrated in 1997 [36]. This device had a junction overlap area of approximately 50 9 50 nm, giving an operating temperature of 70 mK. As it was the first demonstration, the layout was very conservative and optimized for high yield, which resulted in a relatively large overlap and low operating temperature. In this first demonstration the goal was to use gate electrodes to move an electron between the top and bottom dots on the left side of a cell. The electron in the right half of the cell would move in the opposite direction to maintain the lowest energy con- figuration. To measure the polarization of the cell, single-electron transistors, which are the most sensitive electrometers demonstrated to date [37], are used to measure the potential of the dots in the right half of the cell. Measurements of the output of the two electrometers move in opposite directions, confirming that an electron in the right half moves in the opposite direction to the electron in the left half, confirming QCA operation. Full details of the experimental methods are given elsewhere [38–41]. The next step in the development of metal dot QCA was the demonstration of a logic gate [42]. The basic logic element in the QCA paradigm is the majority gate, where three inputs vote on the polarization of a QCA cell. For this experiment we again used metal dots defined by the Dolan bridge method. For the inputs of the majority gate we applied voltages to the input electrodes that mimicked the potentials of three input cells. The applied voltages were varied to step through the logic truth table. The polarization of the cell was measured by electrometers and the output of the cell confirmed proper operation of the gate. These experiments showed the basic functionality of QCA cells. The next experiment [43] showed that a QCA line could switch without getting stuck in a metastable, partially switched, state. In this experiment three 2-dot cells were fabri- cated in a line, and an input applied to the left side of the line. Electrometers coupled to the output side of the line confirmed the proper switching. Power Gain These initial experiments used unclocked QCA cells, but clocking is an important element in QCA systems. Clocking of QCA cells is crucial to achieve perhaps the 8 C.S. Lent and G.L. Snider
- 20. most important quantity in a logic device: power gain. Without power gain the input signal would degrade in a line, due to the unavoidable energy dissipation at each stage, and fan-out would be impossible. Clocking in QCA requires a variable barrier to control the tunneling of electrons between dots. Since the tunnel barrier in metal dot QCA is a fixed aluminum oxide layer whose barrier height cannot be modulated, clocking dots are introduced into the QCA cell as intermediate dots. These dots are coupled to clock electrodes that control the potential of the central dots. A positive clock voltage pulls the electrons to the central dots to produce the null state. A negative voltage forces the electrons to leave in a direction that is determined by the cell’s input. In the initial experiment, a differential input voltage is applied to the left side of the cell and electrometers measure the potential of the top and bottom dots of the right half of the cell. Measured output waveforms confirmed proper operation of the cell [44]. A clocked QCA cell can also be used as a latch, a short-term memory element, as demonstrated in our experiments [45, 46]. As shown by theory, the power gain of a QCA cell is not fixed. If the input is weak, the cell pulls power from the clock to restore the signal level. Since the signal energy is fixed for a given cell, the amount of power pulled from the clock will depend on the weakness of the input. An experimental demonstration of power gain involves a measurement of the charge on the dots of the QCA cell [43] as the inputs and clock are moved through one clock period. In this way the work done by the input on the cell can be calculated, along with the work done by the cell on the next cell. If the work done by the cell exceeds the work done on the cell, then the cell has demonstrated power gain. In our experiment an input with one-half the normal potential swing was applied to the input. The resulting experiment demonstrated a power gain of 2.07, in agreement with theory [47]. Shift Registers Clocking in QCA enables not only power gain, but also the control of the flow of information in the computational system, needed for data pipelining. The basic element in a data flow structure is the shift register. A QCA shift register consists of a row of cells controlled by different clock phases. In our experiment we fabricated a shift register of two cells. Although this is a very short shift register, it can be used as a long register. For our experiment we fabricated the two clocked QCA cells with elec- trometers coupled to each cell so that we could measure the polarization of each cell independently. In the experiment a bit of information is latched into the first cell, and the input removed. The bit is then copied into the second cell, and erased in the first. Then the bit is copied back into the first cell and erased in the second. In this way the bit is shifted between cells, just as it would be in a long shift register. The experiment demonstrated 5 bit transfers, limited only by thermally induced errors [48–50]. Fan-Out An important element in a general logic system is fan-out, where the output of one element is sent to the inputs of two or more elements. Since the energy of the output is split, power gain in the following logic elements is needed to restore the signal level. To demonstrate fan-out in QCA we fabricated a circuit with three cells. In the The Development of Quantum-Dot Cellular Automata 9
- 21. experiment the input is latched into the central cell, which then acts as an input to the top and bottom cells. When a clock is applied to the top and bottom cells the bit is copied into both cells, and full signal strength is produced in these cells [51], con- firming the operation of the circuit. 3.3 Molecular QCA Molecules represent the smallest artificial structures that can be engineered by humans. To form switchable QCA molecules, at least two charge centers are required that can be reversibly occupied or unoccupied by an electron. The field of mixed-valence chemistry [52] concerns itself with molecules that have at least two charge centers connected by a bridging group through which tunneling can occur. Ongoing investi- gation concerns the questions of what makes a good dot and what makes a good bridge. Several early theoretical investigations used model electronic p-systems as dots [53–61]. These molecules are often radical ions containing unpaired electrons and would be very reactive and likely unstable in real systems. Their use was to establish the fundamentals. Electrons in molecules can exhibit bistable switching and the perturba- tion due to a similar molecule at a reasonable distance (such that the dots form a square) is sufficient to switch the molecule. Energy levels are such that these effects survive room temperature operation. Kink energies are large enough that molecular QCA is robust against variations in position and orientation of molecules. Groups surrounding the charge centers can effectively insulate them from conducting substrates but do not screen the field. Applied electric fields which vary at a much larger length scale can effectively clock molecules (with three appropriately arranged charge centers). Molecular synthesis by the Fehlner [62–66] and Lapinte [67–69] groups have succeeded in creating molecules that show the requisite bistability. These dots use Fe and/or Ru charge centers. Electronic measurements of the Fehlner molecules attached to a surface showed distinctive bistable behavior as the electron was switched by an applied electric field. This demonstrated both the bistable character of the molecules, and the potential for clocked control of the charge configuration by an applied (and inhomogeneous) field. The Lapinte molecules have been imaged with STM by the Kandel group [67–70] and show the desired charge localization on one end of a symmetric double-dot molecule. Triple-dot molecules, of the sort required for clocked control, have also been made and imaged. More recently ferrocene-base double dot molecules have been made by the Henderson group and imaged by the Kandel group. There is much chemistry yet to be understood in designing QCA molecules. One issue is what makes the ideal dot. Transition metal atoms have the advantage of using d-orbitals that participate less in bonding and so may be more isolated. Carbon-base p-systems, on the other hand, can be chosen such that they involve anti-bonding orbitals and may spread the charge out more and therefore yield a lower reorgani- zation energy. The reorganization energy is the energy associated with the relaxation of the surrounding atoms and may in some cases trap the charge and inhibit switching. Creating appropriate bridging groups involves choosing a system that is either long enough or opaque enough to be an effective barrier to through-bond tunneling. Conjugated systems may be too conducting. 10 C.S. Lent and G.L. Snider
- 22. Another approach that combines single-atom realization with lithographic control is the STM-base lithography of the Wolkow group [71]. They have created room- temperature QCA cells using a remarkable approach involving removing single electrons from dangling bonds on a silicon surface. As with molecules, the single- atom sizes easily yield room temperature operation, yet the placement and orientation of the cells can be controlled lithographically using the STM tip. 3.4 Other Implementations Nanomagnetic QCA was first introduced by Cowburn’s group [72] and developed extensively by the Porod group [73] and the Bokar group [74]. The mapping from QCA cells that represent an electric quadrupole to those that represent a magnetic quadrupole is straightforward. Nanomagnetic implementations are discussed else- where in this volume. Some have proposed cell-cell coupling based on an electron exchange interaction [75], and indeed the earliest calculations showed a small splitting between the singlet and triplet spin states [76]. This approach has two serious drawbacks: the exchange splitting is quite small, and it is zero if there is not tunneling from cell to cell. If there is tunneling from cell to cell, the information is no longer localized and spin-wave solutions predominate. It is interesting to consider the fundamental question of what sort of systems could implement QCA action. There are two basic features of QCA that must be satisfied: 1. A bit is to be represented completely by the local state of a cell composed of atoms. 2. The interaction between cells is through a field, rather than by transport. The cell’s binary information must therefore be represented by the positional or spin degrees of freedom of the electrons and nuclei in the cell. Nuclear positions could be used to encode the information—for molecules this would entail a conformational change, for larger cells we would call it mechanical. Lighter mass electrons have an advantage in that they can switch positions faster than nuclei. Spin states of either nuclei or electrons could switch quickly. The field connecting cells must be electromagnetic because the other candidate fields are either too short range (the nuclear strong or weak forces) or too weak (the gravitation force). Direct spin-spin interaction energies are very small, so for magnetic coupling we need many nuclear or electronic spins acting collectively. Nanomagetic QCA thus must be sufficiently large that the coupling is adequate at room tempera- tures. The direct Coulomb interaction is quite strong and allows molecule-to-molecule coupling between multipole moments of the charge distribution. Since by assumption there is no transport from cell to cell, the charge of the cell cannot change and higher moments must be used to encode the information. QCA thus far has used dipole coupling and quadrupole coupling—the difference being what one chooses to define as a cell. It is also possible to use contact potentials along the cell surface to coupled mechanical (nuclear) degrees of freedom. The possibilities then can be seen to reduce to these categories: The Development of Quantum-Dot Cellular Automata 11
- 23. 1. Mechanical cells coupled by electrostatic contact potential forces. These would suffer from the slower response of atoms compared with electrons, but remain largely unexplored. 2. Magnetic cells (collective nuclear or electronic spins) coupled by magnetic fields. This is the basis of nanomagnetic QCA described elsewhere in this volume. 3. Electronic cells coupled by Coulomb multipole-multipole interactions. The charge distribution could be the result of either mobile atoms or mobile electrons, and could involve a few or several charges. Few-electron QCA cells, as has been noted above, have an intrinsic bistability due to charge quantization. If there are many charges forming the charge multipole, the bistability must be provided by another mechanism. One example is a CMOS cell that is an analog to QCA and switches adiabatically [77]. 4 Issues in QCA Development 4.1 The Role of Quantum Mechanics in QCA To achieve robustness against fabrication variations, the QCA paradigm uses only a classical degree of freedom, the electric (or magnetic) quadrupole moment of the cell. It does not use quantum phase information nor interference effects. QCA involves bits not qubits. It is quantum mechanical precisely in that it relies on quantum tunneling for cell switching. This is crucial because if quantum mechanics were ‘‘turned off’’ ( h = 0) there would be no tunneling and a QCA cell could not switch. If the barriers to tunneling were removed so that classical switching were allowed, a QCA cell would oscillate and settle into a particular configuration randomly depending on the details of the trajectory and energy dissipation. Switching a classical double-well system is much more prone to error because the system can get caught in a metastable state if the timing is not perfect. Reliance on quantum tunneling stabilizes the bit information. 4.2 Power Gain In molecular, metal dot (discussed above), or other implementations, power gain is crucial because there is always some dissipation of energy as information moves from stage to stage in a computation. This dissipation is the microscopic version of friction in mechanical devices. It can be minimized, and by moving gradually can be reduced to whatever level is desired, but cannot be completely eliminated. Therefore, unless there is a way to restore the signal energy, it will eventually be completely attenuated. In conventional devices the source of the energy is usually the constant-voltage power supply. In QCA the restoring energy is provided by the clock; it automatically supplies enough energy to restore the signal levels. 4.3 Metastability, Memory, and Coherence For a physical system to act as a memory its state cannot be determined by only its boundary conditions. A Hamiltonian system in a unique ground state, for example, 12 C.S. Lent and G.L. Snider
- 24. cannot act as a memory. A device with even short-term memory must therefore be in a metastable state. It could be in a state representing a 1 or be in a state representing a 0. Which state the device is in is depends not just on its boundary conditions, but also on its past. If there is a large enough kinetic barrier between these two states they can often be justifiably treated as distinct energetically degenerate states, but they are actually metastable states very weakly coupled and with a very long Rabi oscillation period. In clocked QCA wires (i.e., shift registers), information is represented by bit packets, a few cells in the line that are polarized in the 1 or 0 state [78]. Since they could also be in the opposite state energetically, it is true that if the time evolution was completely unitary, the bit could quantum mechanically oscillate from one state to the other. There is a considerable kinetic barrier to doing that, however, just as in the case of a CMOS bit. Moreover, in real systems entanglement with the environment sta- bilizes the bit packet by loss of quantum phase in the system [79]. Decoherence is precisely this sort of entanglement with the environment and, though it is detrimental for quantum computing, it actually stabilizes QCA bits. Further exploration of the roles of environmentally-induced decoherence and energy dissipation are part of the broader question of the transition between the quantum and classical worlds. 4.4 Wire Crossings QCA is naturally an in-plane technology; it does not require going out of the plane. How can one therefore cross wires, that is move one bit independently across the path of another? Several proposals have been made that accomplish this. (1) The original wire-crossing proposal was to use the symmetry of cells and the second-near-neighbor coupling (suitably strengthened by duplication) to allow one cell line to communicate across the path of another. The limitation here is the amount of control in placement and orientation required. (2) A permuter is a logical function which simply switches inputs A and B to output B and A. This can be done with logic, though it does take several cells to implement [80]. (3) With expanded clocking timing one can have one bit packet cross a wire intersection horizontally at one time, and vertically at a later time. The cost is in the added complexity of the clocking circuitry. (4) A bridge crossover, similar to the CMOS via structure can be constructed that takes QCA cells out of the plane to cross. (5) In many instances the crossing is for distribution of signals to different parts of a logic array. Tougaw and Khatun have designed a general matrix distribution scheme, again using augmented clocking patterns [81]. 4.5 Computational Architecture It is clear that QCA requires rethinking circuit and computer architecture on the basis of this new device paradigm. Nevertheless because QCA still supports Boolean logic function, it is natural that the first designs are taken over from usual logic circuitry. Much design work is underway, supported crucially by the design tool QCADesigner produced by the Walus group [82]. The goals of this important effort engaging many research groups are both to capitalize on the functional density that QCA cells allow The Development of Quantum-Dot Cellular Automata 13
- 25. (molecular cells are *1 nm square), and to exploit the clocking paradigm wherein all communication is via shift registers. Kogge and Niemier have been early pioneers of this [83–88], suggesting a universal clocking floorplan which supports general data- flow. Tougaw et al. [89] and Niemier et al. [90] have explored programmable QCA logic arrays, a promising area. Exploring QCA architectures and circuit ideas is a very active area, as witnessed by other contributions to this volume. 4.6 Lithograph and Self-assembly QCA circuits need to have a designed layout that reflects the circuit function; entirely regular arrays do not have interesting behavior. As a consequence the information contained in the circuit layout must be imposed and this is usually done, as with all extant semiconductor circuits, through lithography. It is possible, however, to have self-assembly take care of constructing the dots and forming the dots into cells, and perhaps even forming the cells into lines or other functional groups. For molecular QCA, this is particularly promising because bottom-up self-assembly of molecules into supra-molecular structures is a common, albeit demanding, strategy. Building in some level of self-assembly from below, where the cell size is about 1 nm, and imposing circuit structure from above using lithographic techniques, which can reach below 10 nm, is an appealing match of technologies. Another approach that has received some attention is to use DNA or PNA [91] self-assembled structures as ‘‘molecular circuit-boards.’’ DNA structures with sur- prising amount of inhomogeneous patterning have been synthesized using Seeman tiles [92], or the more recent DNA origami techniques [93]. The long-range concept would be to engineering attachment sites in the DNA scaffold which would covalently bond appropriate QCA molecules or supramolecular assemblies [94–97]. The geo- metric information that defines the circuit layout would in this way be expressed through the sequencing of base-pairs that self-assemble into the scaffold. Many issues remain, of course, including the requirements of geometric matching to the DNA repeat distance and the polyanionic nature of DNA, which could interfere with QCA operation. PNA scaffolds are neutral and could potentially solve this problem. 4.7 Energy Dissipation QCA has two fundamental motivators: ultra-small devices in large functional-density arrays, and low power dissipation. Power dissipation has been a major driver in every stage of the evolution of microelectronics. Adiabatic switching between instantaneous ground states allows the absolute minimum dissipation of energy to the environment. As Landauer [22] and Bennett [98] showed, there is no fundamental lower limit to the amount of energy that needs to be dissipated as heat in order to compute a bit of information. If information is erased, however, a minimum about of energy equal to kBT log(2) must be dissipated. The combination of these two ideas is known as Landauer’s Principle (LP) and is connected to the Maxwell Demon [99, 100]. Though there is a substantial consensus on the correctness of LP, it has come under criticism 14 C.S. Lent and G.L. Snider
- 26. from both industrial researchers [101, 102] and philosophers of science [103, 104]. The low power dissipation in QCA is an example of LP in action [105]. We have recently demonstrated experimentally that a binary switch can be operated with dis- sipation of 0.01 kBT, in agreement with LP [106–108]. 5 Future Prospects QCA research activity continues on several fronts. Molecular QCA will require improved understanding of the chemistry of mixed-valence molecules. This includes exploring linker and dot moieties, the role of ligand relaxation in charge transfer, surface attachment and molecular-scale patterning. Significant progress in nanomag- netic implementations is reported by several other contributors in this collection. Metal-dot QCA deserves more exploration, even though it requires cryogenic oper- ation. New fabrication methods may raise the operating temperature considerably. Exploration of circuits and computational architectures is crucial for fully exploiting the potential of locally interconnected nanodevices. References 1. Wharam, D., Thornton, T., Newbury, R., Pepper, M., Ahmed, H., Frost, J., Hasko, D., Peacock, D., Ritchie, D., Jones, G.: One-dimensional transport and the quantisation of the ballistic resistance. J. Phys. C: Solid State Phys. 21, L209 (1988) 2. Van Wees, B., Van Houten, H., Beenakker, C., Williamson, J.G., Kouwenhoven, L., Van der Marel, D., Foxon, C.: Quantized conductance of point contacts in a two-dimensional electron gas. Phys. Rev. Lett. 60, 848 (1988) 3. Kastner, M.: The single electron transistor and artificial atoms. Ann. Phys. (Leipzig) 9, 885–894 (2000) 4. Meurer, B., Heitmann, D., Ploog, K.: Single-electron charging of quantum-dot atoms. Phys. Rev. Lett. 68, 1371 (1992) 5. Goodnick, S.M., Bird, J.: Quantum-effect and single-electron devices. IEEE Trans. Nanotechnology 2, 368–385 (2003) 6. Landauer, R.: Nanostructure physics: fashion or depth. In: Reed, M.A., Kirk, W.P. (eds.) Nanostructure Physics and Fabrication, pp. 17–30. Academic Press, New York (1989) 7. Fulton, T.A., Dolan, G.H.: Observation of single-electron charging effects in small tunnel junctions. Phys. Rev. Lett. 59, 109–112 (1987) 8. Averin, D., Likharev, K.: Coulomb blockade of single-electron tunneling, and coherent oscillations in small tunnel junctions. J. Low Temp. Phys. 62, 345–373 (1986) 9. Lent, C.S.: A simple model of Coulomb effects in semiconductor nanostructures. In: Kirk, W.P., Reed, M.A. (eds.) Nanostructures and Mesoscopic Systems, p. 183. Academic Press, San Diego (1992) 10. Toffoli, T., Margolus, N.: Cellular Automata Machines: A New Environment for Modelling. MIT Press, Cambridge (1987) 11. Lent, C.S., Tougaw, P.D., Porod, W.: A bistable quantum cell for cellular automata. In: International Workshop Computational Electronics, pp. 163–166 (1992) The Development of Quantum-Dot Cellular Automata 15
- 27. 12. Lent, C.S., Tougaw, P.D.: Lines of interacting quantum-dot cells: a binary wire. J. Appl. Phys. 74, 6227–6233 (1993) 13. Lent, C.S., Tougaw, P.D., Porod, W., Bernstein, G.H.: Quantum cellular automata. Nanotechnology 4, 49 (1993) 14. Tougaw, P.D., Lent, C.S.: Logical devices implemented using quantum cellular automata. J. Appl. Phys. 75, 1818–1825 (1994) 15. Lent, C.S., Tougaw, P.D.: Bistable saturation due to single electron charging in rings of tunnel junctions. J. Appl. Phys. 75, 4077–4080 (1994) 16. Tougaw, P.D., Lent, C.S.: Dynamic behavior of quantum cellular automata. J. Appl. Phys. 80, 4722–4736 (1996) 17. Landauer, R.: Is quantum mechanics useful? Philos. Trans. R. Soc. Lond. Ser. A: Phys. Eng. Sci. 353, 367–376 (1995) 18. Lent, C.S., Tougaw, P.D., Porod, W.: In: Proceedings of the Workshop on the Physics and Computation, PhysComp’94, pp. 5–13. IEEE (1994) 19. Lent, C.S., Tougaw, P.D.: A device architecture for computing with quantum dots. Proc. IEEE 85, 541–557 (1997) 20. Korotkov, A.N., Likharev, K.K.: Single-electron-parametron-based logic devices. J. Appl. Phys. 84, 6114–6126 (1998) 21. Tóth, G., Lent, C.S.: Quasiadiabatic switching for metal-island quantum-dot cellular automata. J. Appl. Phys. 85, 2977–2984 (1999) 22. Keyes, R.W., Landauer, R.: Minimal energy dissipation in logic. IBM J. Res. Dev. 14, 152–157 (1970) 23. Gardelis, S., Smith, C., Cooper, J., Ritchie, D., Linfield, E., Jin, Y.: Evidence for transfer of polarization in a quantum dot cellular automata cell consisting of semiconductor quantum dots. Phys. Rev. B 67, 033302 (2003) 24. Perez-Martinez, F., Farrer, I., Anderson, D., Jones, G., Ritchie, D., Chorley, S., Smith, C.: Demonstration of a quantum cellular automata cell in a GaAs/AlGaAs heterostructure. Appl. Phys. Lett. 91, 032102–032103 (2007) 25. Smith, C., Gardelis, S., Rushforth, A., Crook, R., Cooper, J., Ritchie, D., Linfield, E., Jin, Y., Pepper, M.: Realization of quantum-dot cellular automata using semiconductor quantum dots. Superlattices Microstruct. 34, 195–203 (2003) 26. Macucci, M., Gattobigio, M., Bonci, L., Iannaccone, G., Prins, F., Single, C., Wetekam, G., Kern, D.: A QCA cell in silicon-on-insulator technology: theory and experiment. Superlattices Microstruct. 34, 205–211 (2003) 27. Single, C., Augke, R., Prins, F., Wharam, D., Kern, D.: Towards quantum cellular automata operation in silicon: transport properties of silicon multiple dot structures. Superlattices Microstruct. 28, 429–434 (2000) 28. Single, C., Augke, R., Prins, F., Wharam, D., Kern, D.: Single-electron charging in doped silicon double dots. Semicond. Sci. Technol. 14, 1165 (1999) 29. Single, C., Prins, F., Kern, D.: Simultaneous operation of two adjacent double dots in silicon. Appl. Phys. Lett. 78, 1421–1423 (2001) 30. Mitic, M., Cassidy, M., Petersson, K., Starrett, R., Gauja, E., Brenner, R., Clark, R., Dzurak, A., Yang, C., Jamieson, D.: Demonstration of a silicon-based quantum cellular automata cell. Appl. Phys. Lett. 89, 013503-013503-013503 (2006) 31. Dzurak, A.S., Simmons, M.Y., Hamilton, A.R., Clark, R.G., Brenner, R., Buehler, T.M., Curson, N.J., Gauja, E., McKinnon, R.P., Macks, L.D.: Construction of a silicon-based solid state quantum computer. Quantum Inf. Comput. 1, 82–95 (2001) 32. Davies, J.H., Nixon, J.A.: Fluctuations in submicrometer semiconducting devices caused by the random positions of dopants. Phys. Rev. B 39, 3423 (1989) 16 C.S. Lent and G.L. Snider
- 28. 33. Lafarge, P., Pothier, H., Williams, E.R., Esteve, D., Urbina, C., Devoret, M.H.: Direct observation of macroscopic charge quantization. Z. Phys. B 85, 327–332 (1991) 34. Pothier, H., Lafarge, P., Orfila, P.F., Urbina, C., Esteve, D., Devoret, M.H.: Single electron pump fabricated with ultrasmall normal tunnel junctions. Phys. B 169, 573 (1991) 35. Zimmerman, N.M., Huber, W.H., Simonds, B., Hourdakis, E., Fujiwara, A., Ono, Y., Takahashi, Y., Inokawa, H., Furlan, M., Keller, M.W.: Why the long-term charge offset drift in Si single-electron tunneling transistors is much smaller (better) than in metal-based ones: two-level fluctuator stability. J. Appl. Phys. 104, 033710 (2008) 36. Orlov, A.O., Amlani, I., Bernstein, G.H., Lent, C.S., Snider, G.L.: Realization of a functional cell for quantum-dot cellular automata. Science 277, 928–930 (1997) 37. Aassime, A., Gunnarsson, D., Bladh, K., Delsing, P., Schoelkopf, R.: Radio-frequency single-electron transistor: toward the shot-noise limit. Appl. Phys. Lett. 79, 4031–4033 (2001) 38. Amlani, I., Orlov, A.O., Snider, G.L., Bernstein, G.H.: Differential charge detection for quantum-dot cellular automata. J. Vac. Sci. Technol. B 15, 2832–2835 (1997) 39. Amlani, I., Orlov, A.O., Snider, G.L., Lent, C.S., Bernstein, G.H.: Demonstration of a six- dot quantum cellular automata system. Appl. Phys. Lett. 72, 2179–2181 (1998) 40. Bernstein, G.H., Bazan, G., Chen, M., Lent, C.S., Merz, J.L., Orlov, A.O., Porod, W., Snider, G.L., Tougaw, P.D.: Practical issues in the realization of quantum-dot cellular automata. Superlattices Microstruct. 20, 447–459 (1996) 41. Snider, G.L., Orlov, A.O., Amlani, I., Zuo, X., Bernstein, G.H., Lent, C.S., Merz, J.L., Porod, W.: Quantum-dot cellular automata: review and recent experiments (invited). J. Appl. Phys. 85, 4283–4285 (1999) 42. Amlani, I., Orlov, A.O., Toth, G., Bernstein, G.H., Lent, C.S., Snider, G.L.: Digital logic gate using quantum-dot cellular automata. Science 284, 289–291 (1999) 43. Toth, G., Orlov, A.O., Amlani, I., Lent, C.S., Bernstein, G.H., Snider, G.L.: ARTICLES- semiconductors II: surfaces, interfaces, microstructures, and related topics-Conductance suppression due to correlated electron transport in coupled double quantum dots. Phys. Rev.-Section B-Condens. Matter 60, 16906–16912 (1999) 44. Orlov, A.O., Amlani, I., Kummamuru, R.K., Ramasubramaniam, R., Toth, G., Lent, C.S., Bernstein, G.H., Snider, G.L.: Experimental demonstration of clocked single-electron switching in quantum-dot cellular automata. Appl. Phys. Lett. 77, 295–297 (2000) 45. Kummamuru, R.K., Liu, M., Orlov, A.O., Lent, C.S., Bernstein, G.H., Snider, G.L.: Temperature dependence of the locked mode in a single-electron latch. Microelectron. J. 36, 304–307 (2005) 46. Orlov, A.O., Kummamuru, R.K., Ramasubramaniam, R., Toth, G., Lent, C.S., Bernstein, G.H., Snider, G.L.: Experimental demonstration of a latch in clocked quantum-dot cellular automata. Appl. Phys. Lett. 78, 1625–2627 (2001) 47. Kummamuru, R.K., Timler, J., Toth, G., Lent, C.S., Ramasubramaniam, R., Orlov, A.O., Bernstein, G.H., Snider, G.L.: Power gain in a quantum-dot cellular automata latch. Appl. Phys. Lett. 81, 1332–1334 (2002) 48. Kummamuru, R.K., Orlov, A.O., Ramasubramaniam, R., Lent, C.S., Bernstein, G.H., Snider, G.L.: Operation of a quantum-dot cellular automata (QCA) shift register and analysis of errors. IEEE Trans. Electron Devices 50, 1906–1913 (2003) 49. Orlov, A.O., Kummamuru, R., Lent, C.S., Bernstein, G.H., Snider, G.L.: Clocked quantum-dot cellular automata shift register. Surf. Sci. 532–535, 1193–1198 (2003) 50. Orlov, A.O., Kummamuru, R., Ramasubramaniam, R., Lent, C.S., Bernstein, G.H., Snider, G.L.: A two-stage shift register for clocked quantum-dot cellular automata. J. Nanosci. Nanotechnol. 2, 351–355 (2002) The Development of Quantum-Dot Cellular Automata 17
- 29. 51. Yadavalli, K.K., Orlov, A.O., Timler, J.P., Lent, C.S., Snider, G.L.: Fanout gate in quantum-dot cellular automata. Nanotechnology 18, 1–4 (2007) 52. Demadis, K.D., Hartshorn, C.M., Meyer, T.J.: The localized-to-delocalized transition in mixed-valence chemistry. Chem. Rev. 101, 2655–2686 (2001) 53. Blair, E., Lent, C.S.: In: Third IEEE Conference on Nanotechnology, 2003. IEEE-NANO 2003, vol. 1, pp. 402–405. IEEE (2003) 54. Blair, E.P., Lent, C.S.: In: International Conference on Simulation of Semiconductor Processes and Devices, 2003. SISPAD 2003, pp. 14–18. IEEE (2003) 55. Hennessy, K., Lent, C.S.: Clocking of molecular quantum-dot cellular automata. J. Vacuum Sci. Technol. B: Microelectron. Nanometer Struct. 19, 1752–1755 (2001) 56. Isaksen, B., Lent, C.S.: In: Third IEEE Conference on Nanotechnology, 2003. IEEE- NANO 2003, vol. 1, pp. 5–8. IEEE (2003) 57. Lent, C.S.: In: APS Meeting Abstracts, vol. 1, pp. 14002 (2000) 58. Lent, C.S., Isaksen, B.: Clocked molecular quantum-dot cellular automata. IEEE Trans. Electron Devices 50, 1890–1896 (2003) 59. Lent, C.S., Isaksen, B., Lieberman, M.: Molecular quantum-dot cellular automata. J. Am. Chem. Soc. 125, 1056–1063 (2003) 60. Lieberman, M., Chellamma, S., Varughese, B., Wang, Y., Lent, C.S., Bernstein, G.H., Snider, G.L., Peiris, F.C.: Quantum-dot cellular automata at a molecular scale. Ann. N. Y. Acad. Sci. 960, 225–239 (2002) 61. Lieberman, M., Chellamma, S., Wang, Y., Hang, Q., Bernstein, G., Lent, C.S.: In: Abstracts of Papers of the American Chemical Society. (Amer Chemical Soc 1155 16th ST, NW, Washington, DC 20036 USA, 2002), vol. 224, p. U474 (2002) 62. Joyce, R.A., Qi, H., Fehlner, T.P., Lent, C.S., Orlov, A.O., Snider, G.L.: In: Nanotechnology Materials and Devices Conference, 2009. NMDC’09, pp. 46–49. IEEE (2009) 63. Qi, H., Gupta, A., Fehlner, T.P., Snider, G.L., Lent, C.S.: In: Abstracts of Papers of the American Chemical Society. (Amer Chemical Soc 1155 16TH ST, NW, WASHINGTON, DC 20036 USA, 2006), vol. 232 (2006) 64. Qi, H., Gupta, A., Noll, B.C., Snider, G.L., Lu, Y., Lent, C.S., Fehlner, T.P.: Dependence of field switched ordered arrays of dinuclear mixed-valence complexes on the distance between the redox centers and the size of the counterions. J. Am. Chem. Soc. 127, 15218–15227 (2005) 65. Qi, H., Li, Z., Snider, G.L., Lent, C.S., Fehlner, T.: Field driven electron switching in a silicon surface bound array of vertically oriented two-dot molecular quantum cellular automata (2003) 66. Qi, H., Sharma, S., Li, Z., Snider, G.L., Orlov, A.O., Lent, C.S., Fehlner, T.P.: Molecular quantum cellular automata cells. Electric field driven switching of a silicon surface bound array of vertically oriented two-dot molecular quantum cellular automata. J. Am. Chem. Soc. 125, 15250–15259 (2003) 67. Lu, Y., Quardokus, R., Lent, C.S., Justaud, F., Lapinte, C., Kandel, S.A.: Charge localization in isolated mixed-valence complexes: an STM and theoretical study. J. Am. Chem. Soc. 132, 13519–13524 (2010) 68. Quardokus, R.C., Lu, Y., Wasio, N.A., Lent, C.S., Justaud, F., Lapinte, C., Kandel, S.A.: Through-bond versus through-space coupling in mixed-valence molecules: observation of electron localization at the single-molecule scale. J. Am. Chem. Soc. 134, 1710–1714 (2012) 18 C.S. Lent and G.L. Snider
- 30. 69. Wasio, N.A., Quardokus, R.C., Forrest, R.P., Corcelli, S.A., Lu, Y., Lent, C.S., Justaud, F., Lapinte, C., Kandel, S.A.: STM imaging of three-metal-center molecules: comparison of experiment and theory for two mixed-valence oxidation states. J. Phys. Chem. C 116, 25486–25492 (2012) 70. Quardokus, R.C., Wasio, N.A., Forrest, R.P., Lent, C.S., Corcelli, S.A., Christie, J.A., Henderson, K.W., Kandel, S.A.: Adsorption of diferrocenylacetylene on Au (111) studied by scanning tunneling microscopy. Phys. Chem. Chem. Phys. 15, 6973–6981 (2013) 71. Haider, M.B., Pitters, J.L., DiLabio, G.A., Livadaru, L., Mutus, J.Y., Wolkow, R.A.: Controlled coupling and occupation of silicon atomic quantum dots at room temperature. Phys. Rev. Lett. 102, 046805 (2009) 72. Cowburn, R., Welland, M.: Room temperature magnetic quantum cellular automata. Science 287, 1466–1468 (2000) 73. Imre, A., Csaba, G., Ji, L., Orlov, A., Bernstein, G., Porod, W.: Majority logic gate for magnetic quantum-dot cellular automata. Science 311, 205–208 (2006) 74. Lambson, B., Carlton, D., Bokor, J.: Exploring the thermodynamic limits of computation in integrated systems: magnetic memory, nanomagnetic logic, and the Landauer limit. Phys. Rev. Lett. 107, 010604 (2011) 75. Bandyopadhyay, S., Das, B., Miller, A.: Supercomputing with spin-polarized single electrons in a quantum coupled architecture. Nanotechnology 5, 113 (1994) 76. Tougaw, P.D., Lent, C.S., Porod, W.: Bistable saturation in coupled quantum-dot cells. J. Appl. Phys. 74, 3558–3566 (1993) 77. Hänninen, I., Lu, H., Lent, C.S., Snider, G.L.: Energy recovery and logical reversibility in adiabatic CMOS multiplier. In: Dueck, G.W., Miller, D. (eds.) RC 2013. LNCS, vol. 7948, pp. 25–35. Springer, Heidelberg (2013) 78. Blair, E.P., Liu, M., Lent, C.S.: Signal energy in quantum-dot cellular automata bit packets. J. Comput. Theor. Nanosci. 8, 972–982 (2011) 79. Blair, E.P., Lent, C.S.: Environmental decoherence stabilizes quantum-dot cellular automata. J. Appl. Phys. 113, 124302-124302-124316 (2013) 80. Fijany, A., Toomarian, N., Spotnizt, M.: Implementing permutation matrices by use of quantum dots. NASA Technical Briefs 25 (2001) 81. Tougaw, D., Khatun, M.: A scalable signal distribution network for quantum-dot cellular automata. IEEE Trans. Nanotech. 12, 215–224 (2013) 82. Walus, K., Dysart, T.J., Jullien, G.A., Budiman, R.A.: QCADesigner: a rapid design and simulation tool for quantum-dot cellular automata. IEEE Trans. Nanotechnol. 3, 26–31 (2004) 83. Dysart, T.J., Kogge, P.M., Lent, C.S., Liu, M.: An analysis of missing cell defects in quantum-dot cellular automata. In: IEEE International Workshop on Design and Test of Defect-Tolerant Nanoscale Architectures (NANOARCH) (2005) 84. Frost, S.E., Rodrigues, A.F., Giefer, C.A., Kogge, P.M.: In: IEEE Computer Society Annual Symposium on VLSI 2003. Proceedings, pp. 19–25. IEEE (2003) 85. Frost, S.E., Rodrigues, A.F., Janiszewski, A.W., Rausch, R.T., Kogge, P.M.: In: First Workshop on Non-Silicon, Computing, vol. 2 (2002) 86. Niemier, M.T., Kogge, P.M.: In: The 6th IEEE International Conference on Electronics, Circuits and Systems, 1999. Proceedings of ICECS’99, vol. 3, pp. 1211–1215. IEEE (1999) 87. Niemier, M.T., Kogge, P.M.: Exploring and exploiting wire-level pipelining in emerging technologies. ACM SIGARCH Comput. Archit. News 29, 166–177 (2001) 88. Niemier, M.T., Kogge, P.M.: In: Proceedings of the Third Petaflops Workshop, with Frontiers of Massively Parallel Processing (1999) The Development of Quantum-Dot Cellular Automata 19
- 31. 89. Tougaw, D., Johnson, E.W., Egley, D.: Programmable logic implemented using quantum- dot cellular automata. IEEE Trans. Nanotechnol. 11, 739–745 (2012) 90. Niemier, M.T., Rodrigues, A.F., Kogge, P.M.: In: 1st Workshop on Non-silicon Computation, pp. 38–45 (2002) 91. Lukeman, P.S., Mittal, A.C., Seeman, N.C.: Two dimensional PNA/DNA arrays: estimating the helicity of unusual nucleic acid polymers. Chem. Commun. 2004, 1694–1695 (2004) 92. Winfree, E., Liu, F., Wenzler, L.A., Seeman, N.C.: Design and self-assembly of two- dimensional DNA crystals. Nature 394, 539–544 (1998) 93. Rothemund, P.W.: Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006) 94. Gu, H., Chao, J., Xiao, S.-J., Seeman, N.C.: Dynamic patterning programmed by DNA tiles captured on a DNA origami substrate. Nat. Nanotechnol. 4, 245–248 (2009) 95. Kim, K.N., Sarveswaran, K., Mark, L., Lieberman, M.: DNA origami as self-assembling circuit boards. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds.) Unconventional Computation. LNCS, vol. 6079, pp. 56–68. Springer, Heidelberg (2010) 96. Sarveswaran, K., Huber, P., Lieberman, M., Russo, C., Lent, C.S.: In: Third IEEE Conference on Nanotechnology, 2003. IEEE-NANO 2003, vol. 1, pp. 417–420. IEEE (2003) 97. Sarveswaran, K., Russo, C., Robinson, A., Huber, P., Lent, C.S., Lieberman, M.: In: Abstracts of Papers of the American Chemical Society. (Amer Chemical Soc 1155 16TH ST, NW, Washington, DC 20036 USA, 2002), vol. 224, p. U421 (2002) 98. Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973) 99. Leff, H., Rex, A.F.: Maxwell’s Demon 2 Entropy, Classical and Quantum Information, Computing, vol. 2. CRC Press, Boca Raton (2010) 100. Timler, J., Lent, C.S.: Maxwell’s demon and quantum-dot cellular automata. J. Appl. Phys. 94, 1050–1060 (2003) 101. Cavin, R.K., Zhirnov, V.V., Hutchby, J.A., Bourianoff, G.I.: Energy barriers, demons, and minimum energy operation of electronic devices. Fluctuation Noise Lett. 5, C29–C38 (2005) 102. Zhirnov, V.V., Cavin III, R.K., Hutchby, J.A., Bourianoff, G.I.: Limits to binary logic switch scaling - a Gedanken model. Proc. IEEE 91, 1934–1939 (2003) 103. Earman, J., Norton, J.D.: Exorcist XIV: the wrath of Maxwell’s demon. Part II. From Szilard to Landauer and beyond. Stud. History Phil. Sci. Part B: Stud. History Phil. Mod. Phys. 30, 1–40 (1999) 104. Norton, J.D.: Waiting for Landauer. Stud. History Phil. Sci. Part B: Stud. History Phil. Mod. Phys. 42, 184–198 (2011) 105. Lent, C.S., Liu, M., Lu, Y.: Bennett clocking of quantum-dot cellular automata and the limits to binary logic scaling. Nanotechnology 17, 4240 (2006) 106. Orlov, A.O., Lent, C.S., Thorpe, C.C., Boechler, G.P., Snider, G.L.: Experimental test of Landauer’s principle at the sub-kBT level. Jpn. J. Appl. Phys. 51, 06FE10 (2012) 107. Snider, G.L., Blair, E.P., Thorpe, C.C., Appleton, B.T., Boechler, G.P., Orlov, A.O., Lent, C.S.: In: 12th IEEE Conference on Nanotechnology (IEEE-NANO), 2012, pp. 1–6. IEEE (2012) 108. Boechler, G.P., Whitney, J.M., Lent, C.S., Orlov, A.O., Snider, G.L.: Fundamental limits of energy dissipation in charge-based computing. Appl. Phys. Lett. 97, 103502–103503 (2010) 20 C.S. Lent and G.L. Snider
- 32. Nanomagnet Logic (NML) Wolfgang Porod1() , Gary H. Bernstein1 , György Csaba1 , Sharon X. Hu2 , Joseph Nahas2 , Michael T. Niemier2 , and Alexei Orlov1 1 Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA [email protected] 2 Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, USA Abstract. We describe the background and evolution of our work on magnetic implementations of Quantum-Dot Cellular Automata (QCA), first called Magnetic QCA (MQCA), and now known as Nanomagnet Logic (NML). Keywords: Nanomagnet logic Quantum-Dot Cellular Automata Field- coupled computing Cellular Automata 1 Introduction We all are familiar with the fact that magnetic phenomena are widely used for data storage, whereas electronic phenomena are used for information processing. This is based on the fact that ferromagnetism is nonvolatile (i.e. magnetization state can be preserved even without power), and that electrons and the flow of charge can be effectively controlled to perform logic. However, charge-based logic devices are volatile, which means that a power supply is needed to maintain the logic state and to stop information (electrons) from leaking away. Presently, there are multiple research efforts underway to harness magnetic phe- nomena for logic in addition to storage. Motivation for this work is two-fold. First, the amount of static power dissipation in CMOS chips now rivals the levels of dynamic power dissipation. In other words, even if a chip does not perform any computation, stand-by power (i.e., needed to maintain volatile logic state, etc.) is similar to the power dissipated when performing useful work. Anecdotally, in 2004, Bernard Myerson – then chief technologist for IBM’s system and technology group – likened the situation to ‘‘a car with a 10-gallon gas tank losing 5 gallons while parked with its motor turned off’’ [2]. The nonvolatile nature of magnetic phenomena means that there is no stand-by power dissipation. Second, the intrinsic switching energy of a magnetic device can be orders of magnitude lower than a charge-based CMOS transistor. While some drive circuitry overhead must be accounted for in magnetic systems, this suggests that magnetic logic could help to minimize dynamic power dissipation as well. Thus, while the multi-decade Moore’s Law-based size scaling trends may continue, associated performance scaling trends are threatened by energy- related concerns that magnetic devices could help to alleviate. N.G. Anderson and S. Bhanja (Eds.): Field-Coupled Nanocomputing, LNCS 8280, pp. 21–32, 2014. DOI: 10.1007/978-3-662-43722-3_2, Springer-Verlag Berlin Heidelberg 2014
- 33. One of the driving forces behind this research is the semiconductor industry itself in the form of the Nanoelectronics Research Initiative (NRI) of the Semiconductor Research Corporation (SRC). The NRI was formed in response to the impending ‘‘red brick wall’’ in the industry’s road map, which is primarily the result of the inability to manage dissipation associated with computation with field-effect transistors. In an effort to find alternative, lower-power device technologies, the NRI is searching for switches based on state variables other than charge. One possibility is the electron’s spin, and associated magnetic phenomena. There now are several research efforts underway to explore switches where the logic state is represented by the magneti- zation of a nanomagnet. These various approaches have been summarized and reviewed in [3], and our work on nanomagnet logic is one of these efforts. 2 Single-Domain Magnets for NML Nanomagnet Logic (NML) is based on patterned arrays of elongated nanomagnets that are sufficiently small to contain only a single magnetic domain. The magnetization state of a device – i.e. whether it is magnetized along one direction or another, commonly referred to as ‘‘up or down’’ – can be used to represent binary information in the same way that magnetic islands are used to store information in magnetore- sistive random access memory (MRAM). Elongated single-domain magnets are essentially tiny bar magnets with poles on each end, that generate strong stray fields that can be used to couple to other nearby magnets. While such magnetic interactions between neighboring nanomagnets are undesirable for data-storage applications, we have demonstrated that these interactions can be exploited to perform logic operations. It should be emphasized here that such single-domain behavior is rather special and specific to magnets with certain sizes and shapes. For our work with patterned ferromagnetic thin-film permalloy, these sizes are on the order of hundreds down to tens of nanometers (nm). If the magnet is too large, its magnetization state breaks up into multiple internal domains, and the poles at the end – along with their strong fringing fields – disappear. If the magnet is too small, its magnetization state can be switched by random thermal fluctuations, and it no longer has a stable magnetization state; this is the so-called superparamagnetic limit. As a fascinating side comment, Nature has learned to exploit the stray fields associated with single domain magnets for navigation in the Earth’s magnetic field. Specialized, so-called magnetotactic bacteria grow perfectly single-domain nanomagnets, that are specific to a particular animal species [4]. By the way, much of our work on NML uses nanomagnets with sizes and shapes between those characteristic for the pigeon and the tuna. Figure 1 shows a magnetic force microscope (MFM) image of an array of nano- scale magnets with varying sizes and aspect ratios. The coloring represents magnetic contrast, and dark and light spots indicate magnetic poles. It can be seen that these magnets display single-domain behavior if they are sufficiently small and narrow (left side of image), and these poles generate magnetic flux lines that can interact with external magnetic fields, or couple to neighboring magnets. Otherwise, their magne- tization state breaks up into several internal domains (right side of image), and there is 22 W. Porod et al.
- 34. flux closure inside, without strong coupling to the exterior. Such single-domain magnets, with typical size scales of tens to hundreds of nanometers, form the physical basis for NML. 3 From Quantum-Dot Cellular Automata to Nanomagnet Logic Our current work on nanomagnet logic grew out of our previous work on Quantum- Dot Cellular Automata (QCA), which was an attempt to base computation on phys- ically-interacting cellular arrays of quantum dots occupied by a few electrons [6]. Instead of wires, neighboring devices interact through direct Coulomb interactions between electrons on neighboring quantum dots. We have shown that such physical interactions in appropriately structured arrays of quantum dots can also be used to realize logic gates. Electronic implementations of QCA proved difficult due to tech- nological limitations of quantum-dot fabrication (such as size variations) and elec- tronic stray charges. For a review of electronic QCA, see Refs. [7, 8]. Nanomagnet logic can be viewed as a magnetic implementation of QCA. (In earlier publications, we used the term magnetic QCA (MQCA), but we now prefer to use NML in order to avoid confusion with quantum dots.) Early theoretical work on magnetic QCA is given in the Ph.D. Dissertation of György Csaba [9]. These simu- lations demonstrated the feasibility of using field-coupled single-domain nanomagnets for realizing basic logic functionality [10–12]. In subsequent experimental work stimulated by these simulations, and which constituted the Ph.D. Dissertation of Alexandra Imre [5], we first demonstrated magnetic wires formed by chains of near-by magnetic islands. Since the individual dots have elongated shapes, there are two basic types of wire arrangements. In one type, the magnets are lined up side-by-side and, as one’s intuition would tell from two bar magnets next to each other with their long sides, the individual magnets prefer to be magnetized in the opposite direction; we call Fig. 1. Nano-scale magnets with varying sizes and aspect ratios. Single-domain behavior is observed if the magnets are sufficiently small and narrow. (Source: A. Imre, Ph.D. dissertation, University of Notre Dame, 2005 [5].) Nanomagnet Logic (NML) 23
- 35. this antiferromagnetic coupling. The other type of wire consists of the individual magnets lined up in the same direction, and as one would expect, the individual magnets also prefer to be magnetized in the same direction; we call this ferromagnetic coupling. Figure 2 shows an example of an antiferromagnetically-coupled wire consisting of a chain of 16 dots. The top portion of the image shows an SEM (scanning electron microscope) image of magnetic islands fabricated from a 30-nm thin film of permalloy using electron beam lithography and standard lift-off techniques. The bottom portion of the figure shows the structural AFM (atomic force microscope) image, and the MFM (magnetic force microscope) image showing the magnetic contrast. The dot on the top right (aligned in the horizontal direction) serves as an input that determines if the wire is aligned up-down-up-down or down-up-down-up. In these experiments, a magnetic field is required to aid the switching of the array of nanomagnets [12]. When one dot is switched, the fringing fields are not sufficiently strong to switch a neighboring magnet. However, the fringing fields can be used to bias the switching event when an additional switching field is applied. Due to the elongated shape (magnetic shape anisotropy), the dots have very stable magnetization states along the long (magnetic easy) axis. They can be magnetized along the short (magnetic hard) axis by the application of a sufficiently strong magnetic field in that Fig. 2. Demonstration of a magnetically-ordered line of dots. Top panel: SEM, middle panel: AFM, bottom panel: MFM. 24 W. Porod et al.
- 36. direction. However, when this field is removed, the dots will ‘‘snap’’ back into the preferred ‘‘up’’ or ‘‘down’’ easy-axis direction, and the fringing fields from the neighbors can bias which way they switch. This switching field acts as a magnetic clock. It turns out that the ‘‘native’’ logic element for NML is a three-input majority-logic gate, just like for the original electronic QCA. As shown schematically below, this gate consists of a cross-shaped arrangement of five dots, where three of the arms (labeled ‘‘A,’’ ‘‘B,’’ and ‘‘C’’) represent the inputs, the center dot (labeled ‘‘M’’) calculates the majority vote of these inputs, and the fourth arm (labeled ‘‘out’’) rep- resents the output. This arrangement can also be viewed as the intersection between an antiferromagnetic and a ferromagnetic wire segment. Note that the majority vote is ‘‘calculated’’ through magnetic interactions in this physics-driven NML computing scheme (Fig. 3). It is interesting to note that such a three-input majority gate can be reduced to either a binary AND or OR gate by viewing one of the inputs as a set-input, which selects the functionality of the gate. For example, if we view ‘‘C’’ as the set-input, and ‘‘A’’ and ‘‘B’’ as the data inputs, then a ‘‘0’’ on ‘‘C’’ means that both ‘‘A’’ and ‘‘B’’ have to be ‘‘1’’ in order to have a majority vote of ‘‘1’’ at the output. In other words, setting ‘‘C’’ to ‘‘0’’ reduces the three-input majority gate to an AND gate for the data inputs ‘‘A’’ and ‘‘B.’’ Conversely, setting ‘‘C’’ to ‘‘1’’ results in an OR gate since only either ‘‘A’’ or ‘‘B’’ have to be ‘‘1’’ in order to have a majority vote of ‘‘1.’’ This programmability offers interesting possibilities from a computer science perspective since the func- tionality of this gate can be determined by the current state of the computation. We have experimentally demonstrated functioning majority-logic gates working properly at room temperature [13]. The figure below [from the Science paper] shows the eight possible input combinations for the three-input majority-logic gate. Note that here the different input combinations were realized by different arrangements of the horizontal input dots. However, the shape-dependent switching behavior of such nanoscale magnets [14] can be exploited to individually address specific inputs, thus providing programmability. We have since fabricated gates with input devices of varying aspect ratios, which has allowed a single gate structure to be successfully tested with all eight possible input combinations [15] (Fig. 4). Fig. 3. Schematic of a magnetic three-input majority-logic gate, which consists of a cross- shaped arrangement of five dots. Panel (a) shows the basic dot, (b) the basic logic gate, and (c) the logic-gate symbol. Nanomagnet Logic (NML) 25
- 37. Thus far [16–18], our work has provided a proof-of-concept demonstration of NML – i.e. the feasibility of performing digital logic with physically-coupled nano- magnets. However, so far we have used MFM to read the state of the dots, and externally generated magnetic fields to switch the dots. Of course, this is not practical for real applications. Below, we describe on-going work to develop electronic input and output (I/O) and mechanisms for generating local magnetic fields for ‘‘on-chip’’ clocking. Before proceeding, we want to emphasize that our experimental proof-of-concept demonstrations satisfy five ‘‘tenets’’ that are considered essential for a digital system: (1) NML devices have non-linear response characteristics due to the magnetic hys- teresis loop. (2) NML can deliver a functionally complete logic set enabled by the 3-input majority gate and the NOT operation naturally achieved by the antiferro- magnetic dot-to-dot coupling. (3) Signal amplification/gain greater than 1 has been experimentally demonstrated by showing the feasibility of 1:3 fanout [19], where the energy for the gain is provided by an external clocking field discussed further below. (4) The output of one device can drive another as the fringing fields from individual magnets can bias a neighbor. (5) Unwanted feedback is preventable through clocking. 4 Nanomagnet Logic: Towards System Integration Recent and ongoing work addresses electronic means for both NML I/O and clocking. Our approach leverages existing MRAM technologies for READ/WRITE operations. After all, setting an input for NML, i.e. setting the state of an input magnet, is similar to writing the state of an MRAM bit. Similarly, reading the state of an NML output dot is just like reading an MRAM bit. These similarities to MRAM suggest that an NML circuit is analogous to a patterned ensemble of the free layers in an MRAM stack. Fig. 4. Experimental demonstration of an NML three-input majority-logic gate. (Source: Imre et al., Ref. [13].) 26 W. Porod et al.
- 38. In this way, NML can leverage much existing technological know-how, and also benefit from future development in MRAM technologies [20]. Under the umbrella of the DARPA Non-Volatile Logic (NVL) program, we worked on approaches to on-chip clocking. As mentioned above, externally supplied switching energy is needed to re-evaluate a magnet ensemble with new inputs. To date, most NML circuits have been ‘‘clocked’’ by an external source. However, it is essential that clock functionality be moved ‘‘on-chip.’’ Thus far, the most commonly employed clock is a magnetic field applied along the hard axis of an NML ensemble, which places the magnets into a metastable state such that they are sensitive to the fringing fields from their neighbors. Such magnetic fields can be generated on-chip by current-carrying wires for local control of NML circuits. In recent work, we have fabricated copper wires clad with ferromagnetic material on the sides and bottom (like field-MRAM word and bit lines), and we have demonstrated that NML magnets, interconnect, and logic gates can be switched (i.e. re-evaluated) in this way [21, 22]. Also under the umbrella of the DARPA Non-Volatile Logic (NVL) program, we worked on approaches for integrated electronic I/O. Electronic output can be achieved (similar to MRAM) by a magnetoresistance measurement, where the NML output dot is the free layer in a magnetic tunnel junction (MTJ) stack. Similarly, electronic input can be achieved using the spin-torque transfer (STT) effect, where the NML input dot is the free layer in an STT stack [23, 24]. As is well known from field-MRAM, there is an energy overhead associated with generating local magnetic fields using current-carrying wires. Early on, simulations showed that the overhead associated with such clocking is a major component of the total energy requirement, and that the dissipation associated with the switching of the magnets is rather small [25]. For NML, the clock energy could be amortized over 100,000s of devices as a single clock line could control many parallel ensembles [26]. Clock lines could be placed in series and in multiple planes to minimize driver overhead. Moreover, at cryogenic temperatures, clock lines could be made from superconducting niobium, and I2 R losses could drop to zero. In principle, this opens the door to extremely low energy information processing hardware/memory that could be integrated with RSFQ and SQL logic. Also inspired by field-MRAM, another approach to lowering the energy overhead associated with clocking is to engineer the dielectric medium between the dots, which influences the coupling strength and thus the switching energy. Specifically, one can enhance the permeability of a dielectric by the controlled inclusion of superpara- magnetic particles that increase the dielectric permeability, and thus lower the current required to achieve a certain switching field [27]. Following this approach, we have successfully fabricated such enhanced permeability dielectrics and demonstrated the lowering of switching fields and associated power dissipation [28–30]. Another possible approach to clocking is to exploit the strong local fields asso- ciated with a domain wall. We have shown that the motion of domain walls can be controlled [31, 32], and that their local fringing fields can assist in the switching of nearby magnets [33]. This is an interesting approach to NML clocking that deserves further investigation. Multiferroics, magnetostriction, and spin-torque transfer have also been proposed as potential clocking mechanisms for NML. Multiferroic materials (e.g. BFO) could Nanomagnet Logic (NML) 27
- 39. allow for electric field control of magnetism, which would be highly attractive for NML. Included in this volume is a contribution from the group of Sayeef Salahuddin at UC Berkeley that addresses this interesting possibility [34]. Another important issue for NML is whether or not the magnets that form a circuit ensemble can be switched reliably – or whether or not devices placed into a meta- stable state by a clock are adversely affected by thermal noise (which could induce premature switching). The group of Jeff Bokor at UC Berkeley has shown that magnets with an extra biaxial anisotropy exhibit superior switching characteristics [35]. Essentially, such an ‘‘engineered-in’’ magnetic anisotropy helps to stabilize the magnets in the ‘‘vulnerable’’ metastable state against random fluctuations. We have shown that shape engineering, i.e. exploiting the influence of geometry on magnetic properties, can be used to not only enhance the reliability of switching, but also to design logic gates with reduced foot print [36, 37]. At Notre Dame, all of our work to date has been based on patterned thin-film permalloy dots, which have in-plane magnetization. An attractive alternative is to use structures with out-of-plane magnetization, such as Co/Pt multi-layer films, where the magnetic properties are due to the Co-Pt interfaces. In collaboration with Doris Schmitt-Landsiedel and her group at the Technical University of Munich (TUM), we are exploring the utility of this material system for NML. It has been shown that such Co/Pt structures can be patterned with a focused ion beam (FIB) instrument, where the ion beam destroys the interfaces, and thus the magnetization at these locations. In this fashion, a film can be patterned into islands, and sufficiently small islands also exhibit single-domain behavior. The TUM group has demonstrated magnetic coupling between neighboring islands [38], and they have shown magnetic ordering in arrays of coupled islands. Moreover, they have realized directional signal propagation in lines, and basic NML logic gates [39], as well as domain-wall assisted switching [40]. All our fabrication work so far has been based on using electron-beam lithography (EBL) to define the NML devices and structures. EBL is a flexible and useful tool for research, but not suitable for large-scale manufacturing. To this end, we collaborate with Paolo Lugli and his group at the TUM to explore the use of nanoimprint lithography and nanotransfer of permalloy structures for the fabrication of large-scale NML arrays [41]. NML represents a technology quite different from CMOS, with its own ‘‘pros’’ and ‘‘cons.’’ Undoubtedly, this new technology will likely necessitate new circuit and architecture approaches [42]. Along these lines, we have worked to identify specific application spaces for NML. Our immediate focus is on low energy hardware accelerators for general-purpose multi-core chips, and application spaces that demand information processing hardware that can function with an extremely low energy budget. As an example, we anticipate that NML-based hardware might be used to implement a systolic architecture that can improve the performance of compute-bound applications, provide very high throughput at modest memory bandwidth, and elim- inate global signal broadcasts. (Systolic solutions exist for many problems including filtering, polynomial evaluation, discrete Fourier transforms, matrix arithmetic and other non-numeric applications.) Moreover, as devices are non-volatile, information can be stored directly and indefinitely throughout a circuit (e.g. at a gate input) 28 W. Porod et al.
- 40. without the need for explicit storage hardware (and the associated area and static/ dynamic power dissipation associated with it). Architectural-level design techniques such as these should allow us to minimize the ‘‘cons’’ of NML (nearest neighbor dataflow and higher latency devices when compared to CMOS FETs) and exploit the ‘‘pros’’ (inherently pipelined logic with no overhead). As a representative example [43], our projections suggest that hardware for finding specific patterns in incoming data streams could be *60-75X more energy efficient (at iso-performance) than CMOS hardware equivalents. Moreover, these projections include clock energy overheads. 5 Summary and Discussion In this chapter, we have presented an overview of our work over the years on nano- magnet logic, which can be viewed as a magnetic implementation of the original QCA field-coupled computing idea. We discussed NML basics, as well as approaches and issues related to the realization of integrated systems. This review was Notre- Dame-centric by design, to provide a somewhat historical perspective on the work of our group. Finally, we would like to mention a couple of other related research efforts that also use nanomagnets to represent logic state, but that employ different mechanisms to couple and switch these magnets. One such effort, the Spin-Wave Bus proposed by a group at UCLA [44], is based on spin waves propagating in a layer underneath the magnets. Since spin waves (plasmons) decay, this scheme requires amplifying ele- ments to restore the signals. Another scheme, the All-Spin Logic proposed by a group at Purdue [45], is based on nanomagnet coupling by spin diffusion in a magnetic layer underneath the magnets. This scheme requires wires to be connected to the magnetic dots in order to inject spin-polarized electrons that then diffuse and provide the coupling mechanism. These approaches are interesting, and further research is war- ranted. However, in our opinion, it is hard to see how coupling between dots using either spin waves or spin diffusion can be more efficient or lower power than coupling by direct magnetic fringing fields. We end with a historical note. It was recognized in the very early days of digital computer design that magnetic phenomena are attractive for several reasons [46]: They possess an inherent high reliability; They require in most applications no power other than the power to switch their state; They are potentially able to perform all required operations, i.e., logic, storage and amplification. In fact, some of the very early computers used ferrite cores not only for memory, but also for logic. Ferrite cores were coupled by wires strung in specific ways between them so as to achieve logic functionality. For example, the Elliott 803 computer used germanium transistors and ferrite core logic elements. Of course, this kind of magnetic logic technology based on stringing wires between bulky magnetic cores was not competitive against emerging semiconductor technology. However, with the advent of modern fabrication technology, which allows the fabrication of arrays of nanometer-size single-domain magnets, the old quest for magnetic logic might become a reality. Nanomagnet Logic (NML) 29
- 41. References 1. Calamia, J.: Magnetic logic attracts money. IEEE Spectrum (2011) 2. Markoff, J.: TECHNOLOGY; Intel’s Big Shift After Hitting Technical Wall, New York Times, 17 May 2004 3. Bernstein, K., Cavin III, R.K., Porod, W., Seabaugh, A., Welser, J.: Device and architecture outlook for beyond-CMOS switches. Proc. IEEE 98(12), 2169–2184 (2010) 4. Blakemore, R.: Magnetotactic bacteria. Science 190(4212), 377–379 (1975) 5. Imre, A.: Ph.D. Dissertation, University of Notre Dame (2005) 6. Lent, C.S., Douglas Tougaw, P., Porod, W., Bernstein, G.H.: Quantum cellular automata. Nanotechnology 4, 49–57 (1993) 7. Porod, W.: Quantum-dot cellular automata devices and architectures. Int. J. High Speed Electron. Syst. 9(1), 37–63 (1998) 8. Snider, G.L., Orlov, A.O., Amlani, I., Zuo, X., Bernstein, G.H., Lent, C.S., Merz, J.L., Porod, W.: Quantum-dot cellular automata: review and recent experiments (invited). J. Appl. Phys. 85(8), 4283–4285 (1999) 9. Csaba, G.: Ph.D. Dissertation, University of Notre Dame (2002) 10. Csaba, G., Porod, W.: Simulation of field-coupled computing architectures based on magnetic dot arrays. J. Comput. Electron. 1, 87–91 (2002) 11. Csaba, G., Imre, A., Bernstein, G.H., Porod, W., Metlushko, V.: Nanocompting by field- coupled nanomagnets. IEEE Trans. Nanotechnol. 1(4), 209–213 (2002) 12. Csaba, G., Porod, W., Csurgay, A.I.: A computing architecture composed of field-coupled single-domain nanomagnets clocked by magnetic fields. Int. J. Circ. Theory Appl. 31, 67–82 (2003) 13. Imre, A., Csaba, G., Ji, L., Orlov, A., Bernstein, G.H., Porod, W.: Majority logic gate for magnetic quantum-dot cellular automata. Science 311, 205–208 (2006) 14. Imre, A., Csaba, G., Orlov, A., Bernstein, G.H., Porod, W., Metlushko, V.: Investigation of shape-dependent switching of coupled nanomagnets. Superlattices Microstruct. 34, 513–518 (2003) 15. Varga, E., Niemier, M.T., Bernstein, G.H., Porod, W., Hu, X.S.: Non-volatile and reprogrammable MQCA-based majority gates. Presented at the Device Research Conference (DRC), Penn State University, June 2009 16. Bernstein, G.H., Imre, A., Metlushko, V., Orlov, A., Zhou, L., Ji, L., Csaba, G., Porod, W.: Magnetic QCA systems. Microelectron. J. 36, 619–624 (2005) 17. Imre, A., Csaba, G., Bernstein, G.H., Porod, W.: Magnetic quantum-dot cellular automata (MQCA). In: Macucci, M. (ed.) Quantum Cellular Automata: Theory, Experimentation and Prospects, pp. 269–276. Imperial College Press, London (2006) 18. Orlov, A., Imre, A., Ji, L., Csaba, G., Porod, W., Bernstein, G.H.: Magnetic quantum-dot cellular automata: recent developments and prospects. J. Nanoelec. Optoelec. 3(1), 55–68 (2008) 19. Varga, E., Orlov, A., Niemier, M.T., Hu, X.S., Bernstein, G.H., Porod, W.: Experimental demonstration of fanout for nanomagnet logic. IEEE Trans. Nanotechnol. 9(6), 668–670 (2010) 20. Bedair, S.M., Zavada, J.M., El-Masry, N.: Spintronic memories to revolutionize data storage. IEEE Spectrum (2010) 21. Alam, M.T., Siddiq, M.J., Bernstein, G.H., Niemier, M.T., Porod, W., Hu, X.S.: On-chip clocking for nanomagnet logic devices. IEEE Trans. Nanotechnol. 9(3), 348–351 (2010) 30 W. Porod et al.
- 42. 22. Alam, M.T., Kurtz, S., Siddiq, M.J., Niemier, M.T., Bernstein, G.H., Hu, X.S., Porod, W.: On-chip clocking of nanomagnet logic lines and gates. IEEE Trans. Nanotechnol. 11(2), 273–286 (2012) 23. Liu, S., Hu, X.S., Nahas, J.J., Niemier, M., Bernstein, G., Porod, W.: Magnetic-electrical interface for nanomagnet logic. IEEE Trans. Nanotechnol. 10(4), 757–763 (2011) 24. Liu, S., Hu, X.S., Niemier, M.T., Nahas, J.J., Csaba, G., Bernstein, G., Porod, W.: Exploring the Design of the Magnetic-Electrical Interface for Nanomagnet Logic. IEEE Trans. Nanotechnol. 12(2), 203–214 (2013) 25. Csaba, G., Lugli, P., Csurgay, A., Porod, W.: Simulation of power gain and dissipation in field-coupled nanomagnets. J. Comput. Electron. 4(1/2), 105–110 (2005) 26. Niemier, M.T., Alam, M.T., Hu, X.S., Bernstein, G.H., Porod, W., Putney, M., DeAngelis, J.: Clocking structures and power analysis for nanomagnet-based logic devices. In: Proceedings of International Symposium on Low Power Electronics and Design, pp. 26–31 (2007) 27. Pietambaram, S., et al.: Appl. Phys. Lett. 90, 143510 (2007) 28. Li, P., Csaba, G., Sankar, V.K., Ju, X., Hu, X.S., Niemier, M.T., Porod, W., Bernstein, G.H.: Switching behavior of lithographically fabricated nanomagnets for logic applications. J. Appl. Phys. 111(7), 07B911-1–07B911-3 (2012) 29. Li, P., Csaba, G., Sankar, V.K., Ju, X., Varga, E., Lugli, P., Hu, X.S., Niemier, M., Porod, W., Bernstein, G.H.: Direct measurement of magnetic coupling between nanomagnets for nanomagnetic logic applications. IEEE Trans. Magn. 48(11), 4402–4405 (2012) 30. Li, P., Sankar, V.K., Csaba, G., Hu, X.S., Niemier, M., Porod, W., Bernstein, G.H.: Magnetic properties of enhanced permeability dielectrics for nanomagnetic logic circuits. IEEE Trans. Mag. 48(11), 3292–3295 (2012) 31. Imre, A., Csaba, G., Metlushko, V., Bernstein, G.H., Porod, W.: Controlled domain wall motion in micron-scale permalloy square rings. Physica E 19, 240–245 (2003) 32. Varga, E., Csaba, G., Imre, A., Porod, W.: Simulation of magnetization reversal and domain-wall trapping in submicron permalloy wires with different wire geometries. IEEE Trans. Nanotechnol. 11(4), 682–686 (2012) 33. Varga, E., Csaba, G., Bernstein, G.H., Porod, W.: Domain-wall assisted switching of single-domain nanomagnets. IEEE Trans. Magn. 48(11), 3563–3566 (2012) 34. Salahuddin, S., group contribution, this volume 35. Lambson, B., Gu, Z., Monroe, M., Dhuey, S., Scholl, A., Bokor, J.: Concave nanomagnets: investigation of anisotropy properties and applications to nanomagnetic logic. Appl. Phys. A-Mater. Sci. Process. 111(2), 413–421 (2013) 36. Kurtz, S., Varga, E., Niemier, M., Porod, W., Bernstein, G.H., Hu, X.S.: Non-majority magnetic logic gates: a review of experiments and future prospects for ‘shape-based’ logic. J. Phys. Condens. Matter 23(5), 053202 (2011) 37. Niemier, M.T., Varga, E., Bernstein, G.H., Porod, W., Alam, M.T., Dingler, A., Orlov, A., Hu, X.S.: Shape-engineering for controlled switching with nanomagnet logic. IEEE Trans. Nanotechnol. 11(2), 220–230 (2012) 38. Becherer, M., Csaba, G., Porod, W., Emling, R., Lugli, P., Schmitt-Landsiedel, D.: Magnetic ordering of focused-ion-beam structured cobalt-platinum dots for field-coupled computing. IEEE Trans. Nanotechnol. 7(3), 316–320 (2008) 39. Breitkreutz, et al.: IEEE Trans. Mag. 48(11) (2012) 40. Csaba, G., Kiermaier, J., Becherer, M., Breitkreutz, S., Ju, X., Lugli, P., Schmitt- Landsiedel, D., Porod, W.: Clocking magnetic field-coupled devices by domain walls. J. Appl. Phys. 111(7), 07E337-1–07E337-3 (2012) 41. AtyabImtaar et al., to be presented at IEEE-NANO 2013 Nanomagnet Logic (NML) 31
- 43. 42. Niemier, M.T., Bernstein, G.H., Csaba, G., Dingler, A., Hu, X.S., Kurtz, S., Liu, S., Nahas, J., Porod, W., Siddiq, M., Varga, E.: Nanomagnet logic: progress toward system-level integration. J. Phys. Condens. Matter 23(49), 493202 (2011) 43. Ju, X., Niemier, M., Becherer, M., Porod, W., Lugli, P., Csaba, G.: Systolic pattern matching hardware with out-of-plane nanomagnet logic devices. IEEE Trans. Nanotechnol. 12(3), 399–407 (2013) 44. Khitun, A., Nikonov, D.E., Wang, K.L.: Magnetoelectric spin wave amplifier for spin wave logic circuits. J. Appl. Phys. 106(12), 123909 (2009) 45. Behin-Aein, B., Datta, D., Salahuddin, S., Datta, S.: Proposal for an all-spin logic device with built-in memory. Nat. Nanotechnol. 5, 266–270 (2010) 46. Gschwind, H.W.: Design of Digital Computers 1967 by Springer 32 W. Porod et al.
- 44. Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics Robert A. Wolkow1,2,3(B) , Lucian Livadaru3 , Jason Pitters2 , Marco Taucer3 , Paul Piva3 , Mark Salomons2 , Martin Cloutier2 , and Bruno V.C. Martins1 1 Department of Physics, University of Alberta, 11322-89 Avenue, Edmonton, AB T6G 2G7, Canada [email protected] 2 National Institute for Nanotechnology, National Research Council of Canada, 11421 Saskatchewan Drive, Edmonton, AB T6G 2M9, Canada 3 Quantum Silicon Inc., 11421 Saskatchewan Drive, Edmonton, AB T6G 2M9, Canada Abstract. We review our recent efforts in building atom-scale quantum- dot cellular automata circuits on a silicon surface. Our building block consists of silicon dangling bond on a H-Si(001) surface, which has been shown to act as a quantum dot. First the fabrication, experimental imag- ing, and charging character of the dangling bond are discussed. We then show how precise assemblies of such dots can be created to form artificial molecules. Such complex structures can be used as systems with custom optical properties, circuit elements for quantum-dot cellular automata, and quantum computing. Considerations on macro-to-atom connections are discussed. Keywords: Silicon dangling bonds · Quantum-dot cellular automata 1 Preliminaries There are two broad problems facing any prospective nano-scale electronic device building block. It must have an attractive property such as to switch, store or conduct information, but also, there must be an established architecture in which the new entity can be deployed and wherein it will function in concert with other elements. Nanoscale electronic device research has in few instances so far led to functional blocks that are ready for insertion into existing device designs. In this work we discuss a range of atom-based device concepts which, while requiring further development before commercial products can emerge, have the great advantage that an overall architecture is well established that calls for exactly the type of building block we have developed. The atomic silicon quantum dot (ASiQD) described here fits within ultra low power schemes for beyond CMOS electronics based upon quantum dots that have been refined over the past 2 decades. The well known quantum dot cellu- lar automata (QCA) scheme due to Lent and co-workers [1,2] achieves classical N.G. Anderson and S. Bhanja (Eds.): Field-Coupled Nanocomputing, LNCS 8280, pp. 33–58, 2014. DOI: 10.1007/978-3-662-43722-3 3, c Springer-Verlag Berlin Heidelberg 2014
- 45. 34 R.A. Wolkow et al. binary logic functions without the use of conventional current-based technology. Within this scheme, the binary states “1” and “0” are encoded in the position of electric charge. Variants exist but most commonly the basic cell consist of a square (or rectangular) quantum dot ensemble occupied by 2 electrons. Elec- trons freely tunnel among the quantum dots in a cell, while electron tunneling between cells does not occur. Within a cell, two classically equivalent states exist, each with electrons placed on the diagonal of the cell. Multiple cells cou- ple and naturally mimic the electron configuration of nearest-neighbour cells. In general, cell-cell interactions must be described quantum mechanically but to a good approximation they are described simply by electrostatic interactions. A line of coupled cells serves as a binary wire. When a terminal cell is forced by a nearby electrode to be in one of its two polarized states, adjacent cells copy that configuration to transfer that input state to the other terminus. This trans- fer can happen spontaneously or can be zonally regimented by a clock signal that controls inter-dot barriers, or some other parameter. The last key feature of QCA is that three binary lines acting as computation inputs and one line acting as output can converge on a node cell to create a majority gate. If two of the three input lines are of one binary state, the fourth side of the node cell will output the majority state. Variants of such an arrangement allow for the realization of a full logical basis. To date, all manner of digital circuits have been designed, from memories to multipliers to even a microprocessor. While complex working circuits have not yet been realized, all the rudimen- tary circuit elements have been already experimentally demonstrated [3,4]. Fur- thermore, the input state of a QCA circuit has been externally controlled and the output has been successfully read-out by a coupled single electron transistor [5,6]. Until the present work, all available quantum dots, typically consisting of thousands of atoms, had narrowly spaced energy levels requiring ultra-low tem- perature to exhibit desired electronic properties. Moreover, approximately as many wires as quantum dots were required to adjust electron filling, a scenario that would greatly limit the complexity of circuitry that could be explored. A prospect for highly complex and room temperature operational QCA cir- cuitry suddenly emerged with the discovery of atomic silicon quantum dots. Figure 1 shows a schematic 4-dot QCA cell on the left occupied with two elec- trons (indicated by blackened circles). On the right is an STM image of a real atom-scale cell made of 4 ASiQDs, the cell being less than 2 nm on a side. The darker of the two dots are predominantly electron occupied. The ultimate small size of the ASiQDs leads to ultimate wide spacing of energy levels indeed sufficiently widely spaced to allow room temperature device operation. The ASiQDs can be prepared in a native 1− charge state (charge is expressed in elementary charge units henceforth). Close placement of dots causes Coulombic repulsion and even removal of an electron to the silicon substrate conduction band. By fabricating dots at an appropriate spacing, a desired level of electron occupation can be predetermined, eliminating the need for many wires. As all atomic dots are identical, and their placement occurs in exact registry with the regular atomic structure of the underlying crystalline lattice,
- 46. Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics 35 2nm Fig. 1. Left: schematic representation of a square QCA cell with 2 electrons (blackened circles) positioned on the diagonal configuration. Right: STM map of an actual ASiQD structure with 4 dots in a square pattern as an embodiment of the QCA cell on the left. Electron population is predominant on the same diagonal as indicated on the schematic on the left. structures with uniquely homogeneous and reproducible characteristics can be in principle fabricated. A further advantage lies in the fact that these dots are entirely made of and upon silicon, enabling compatibility with silicon CMOS circuitry. This allows the merging of established and new technologies, greatly easing the path to deployment. Challenges in the precise positioning of single silicon atom dots previously limited creation of more than a 4-atom ensemble. New developments have enabled patterns with hundreds of atoms to be fabricated with error rates close to those required for functioning computation circuit elements. A path to further improvements appears to be in hand. Information storage, transfer and computation without use of conventional electrical current, with several orders lower power consumption than CMOS appear within reach. Prospects for extremely small size and weight appear good, too, as are those for extreme speed. Existing true 2-dimensional circuit layouts indicate a great reduction in the need for multilayer interconnects. The all-silicon aspect of this approach leads to a natural CMOS compatibility and therefore an early entry point via a hybrid CMOS-ASiQD technology. Room temperature as opposed to cryo operation is very attractive. The materials stability of the system up to 200 ◦ C is comparable to conventional electronics. Furthermore, the possibility of deployment in an analog mode broadens the appeal and power of the approach. A natural ability to merge with Si-based sensor circuitry is desirable too. As discussed below, potential applications in quantum information are also very appealing. 2 Preparing and Visualizing Silicon Surface Dangling Bonds A silicon dangling bond, DB, exists at a silicon atom that is under-coordinated, that is where a silicon atom has only 3, rather the regular 4 bonding partners. In this discussion we will focus on the DB on the hydrogen terminated (100) face of
- 47. 36 R.A. Wolkow et al. a silicon crystal, abbreviated H-Si(100). Atomically flat, ordered H-termination is ordinarily achieved by cracking Hydrogen gas, H2, into H atoms by collision with a hot tungsten filament and allowing those H atoms to react with a clean silicon surface in a vacuum chamber. If the H-termination process is incomplete, or if an H atom is removed by some chemical or physical means, a DB is created. H atoms removed by the local action of a scanning tunneling microscopy (STM) are the focus here. Broadly speaking, the scanning motion of the tip can be halted to direct an intense electrical current in the vicinity of a single Si-H surface bond [7–10]. At approximately a 2 V bias between tip and sample it is understood that multiple vibrational excitations lead to dissociation of the Si-H bond. At near 5 V bias it is thought the Si-H bond can be excited to a dissociative state, as in a photochemical bond breaking event. Other not well understood factors are at play, such as a catalytic effect, intimately depending on particular tip apex structure and composition that might ease the Si-H bond apart as a substantial H atom-tip bond forms while the Si-H bond lengthens and weakens. The fate of removed H atoms is unclear though there is substantial evidence, in the form of H atom donation to the surface that some atoms reside on the STM tip [11,12]. Many details related to exact position of the tip and precise metering of the energetic bond breaking process so as to create just the change desired and not other surface alterations will be touched upon in the section on Quantum Silicon Incorporated and the commercial drive to fabricate atom scale silicon devices. Figure 2a shows a model of a H-Si(100) surface. Silicon atoms are yellow. Hydrogen atoms are white. Note the surface silicon atoms are combined with H atoms in a 1 to 1 ratio. Note also that the surface silicon atoms deviate from the bulk structure not only in that they have H atom partners, but also in that each surface silicon atom is paired-up into a dimer unit. The dimers exist in rows. Figure 2b shows a constant current STM image of a H-Si(100) surface. The dimer units are 3.84 Å separated along a dimer row. The rows are separated by twice that distance, 7.68 Å. The overlaid grid of black bars marks the position of the silicon surface dimer bonds. To reiterate, there is an H atom positioned at both ends of each dimer unit. Figure 3 indicates the localized creation of a dangling bond upon action directed by a scanned probe tip. Figure 3b shows an STM image of several DBs so created [13]. 3 The Nature of Silicon Dangling Bonds Figure 4 shows two silicon surfaces imaged under the same conditions [14]. Both surfaces have a scattering of DBs. The left image is of a moderately n-type doped sample. It has been shown that DBs on such a surface are on average neutral. The DBs in that case are visible as white protrusions. The right hand image is of a relatively highly n-type doped sample. In that case each DB has a dark “halo” surrounding it. These DBs are negative. This results as the high concentration of electrons in the conduction band naturally “fall into” relatively low-lying DB surface state to make it fully, that is 2 electron, occupied. This localization of a
- 48. Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics 37 3.84 Å 7.68 Å 2.25 Å (a) (b) Fig. 2. (a) Model of a H-Si(100) surface with silicon atoms in yellow and hydrogen atoms in white. (b) Constant-current STM image of a H-Si(100) surface. Dimer rows are visible in the vertical direction and the atom separation along and across dimer rows are marked. Some dimer bonds are also marked by an overlaid grid of black bars (Color figure online). H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H 10 nm (a) (b) Fig. 3. (a) Schematic of the fabrication of a dangling bond on the H-Si(100) surface by a scanned probe tip at a chosen location. (b) STM image of several DBs created in a line.
- 49. 38 R.A. Wolkow et al. Low doped n-type Silicon Neutral DBs High doped n-type Silicon Negative DBs (a) (b) Fig. 4. Two silicon surfaces imaged under the same conditions. (a) A moderately n-type doped sample where DBs are on average neutral. (b) A highly doped sample where DBs are on average negatively charged. negative charge at a DB causes destabilization of electron energy levels referred to as upward band bending. To a first approximation it is the inaccessibility of empty states for the STM tip to tunnel into that causes the highly local darkening of the STM image, that is, the halo. A much fuller description of the competing process involved in the imaging process have been described [15]. It is evident that the DB is effectively a dopant with a deep acceptor level. In accord with that character, a DB acts to compensate bulk n-type doping, causing the bands to shift up with respect to the Fermi level in the direction of a p-doped material. Most recently it has been shown that the neutral, single electron occupied DB can donate its charge to become positive thereby acting as a deep n-type dopant [16]. Summarizing, single electron occupation corre- sponds to neutral state. Two electron occupation corresponds to 1− charge. The absence of electrons in the DB leaves it in a 1+ charge state. The combination of dopant type, concentration, DB concentration on the surface, local electric field, and finally current directed through a DB, all contribute to determining its instantaneous charge state [15]. A clean silicon surface, where every site has a dangling bond, is very reactive toward water, oxygen and unsaturated hydrocarbons like ethylene and benzene. While H atoms immediately react with a clean silicon surface, H2 does not [17]. It is a remarkable fact that single DBs interact only weakly with most molecules, resulting in no attachment at room temperature. Most often, a second immediately adjacent DB is required in order for a molecule to become firmly bonded to the surface. Two DBs typically act together to form two strong bonds to an incoming molecule. This has the practical consequence that a protective layer can be formulated and applied to encapsulate and stabilizes DBs against environmental degradation. A special class of molecules, typified by styrene, C8H8 attach to silicon via a self-directed, chain reaction growth mechanism [18]. As shown in Fig. 5a, a ter- minal C reacts with a DB, thereby creating an unpaired electron at the adjacent C on the molecule. That species follows one of two paths. It either desorbs, or the
- 50. Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics 39 (a) (b) Fig. 5. (a) Various processes in a chain reaction resulting in the growth of lines a special class of molecules (e.g. styrene) on a H-Si(100) surface. R here denotes various possible radicals. (b) A line of about 20 styrene molecules grown in this fashion and imaged at different STM setpoints. The charge on the terminal DB at the top of the line depends on the STM setpoint and therefore causes (or not) a Stark shift in the molecular line. radical C abstracts an H atom from an adjacent surface site to create a stably attached molecule, and a regenerated DB positioned one lattice step removed from the original DB position. The process repeats and repeats to create a multi- molecular line that gains a degree of order from the crystalline substrate. Figure 5b shows an approximately 20 molecule long line of styrene grown in this way. The bright feature at the end of the line is a DB. It has been shown that under conditions where the terminal DB is negatively charged that charge acts to gate (Stark shift) the molecular energy levels causing conduction through the molecule where ordinarily it would not occur [19]. In other words the ensemble forms single-electron gated, one-molecule field effect transistor. The point of this discussion is to show there is precedent for microscopic observation of DBs at different charge-states, and to point out that a structure like the molecule transistor arrangement could be a useful detector of DB charge state [20]. 4 Dangling Bonds Are Atomic Silicon Quantum Dots The atoms in a silicon crystal enter into bonding and anti-bonding relationships with neighbouring and distant silicon atoms to form bands that span the crys- tal. In doing so the atoms give up their zero dimensional electronic character. Si
- 51. 40 R.A. Wolkow et al. Fig. 6. (a) STM micrograph (10 × 10 nm, 2 V, 0.2 nA) of a H-Si(100) surface with two DBs. The distinct dark halo indicates each DB is negatively charged. (b) An additional DB is created at a site near DB2 causing both the new DB3 and DB2 to appear very differently. atoms sharing in three ordinary Si-Si bonds and containing one dangling bond have a special mixed character. Like 4-coordinate silicon atoms, such atoms are very strongly bonded to the lattice and have an intimate role in the disper- sive bands that delocalize electrons. At the same time, 3-coordinate atoms have one localized state, approximately of sp3 character. This state is localized because it is in the middle of the band gap and mixes poorly with the valence and con- duction band continua. The DB-containing atom is odder still in that the DB is partly directed toward the vacuum where it has a relatively limited spatial extent but is also partially contained within the silicon crystal where, because of dielectric immersion, is somewhat larger in spatial reach. It was stated above that a DB state is like a deep dopant. Whereas a typical dopant has an ionization or affinity energy of several tens of meV, the DB has corresponding energies an order of magnitude larger. Consistent with that dif- ference, the spatial extend of the DB state within the solid reaches several bond lengths, much less than the size of a common dopant atom [21]. The zero dimensional character of the DB, combined with the capacity to exhibit several (specifically 3) charge states leads us to think of the DB as a quantum dot. This may at first seem a bit odd as a quantum dot is often described as an artificial atom whereas we have a genuine atom, actually one part of an atom, forming our dot. But if a quantum dot is most fundamentally a vessel for containing and configuring electrons then, as subsequent examples will show, the ASiQD naturally and ably fits the definition, especially as the ease and precision of fabrication allows complex interactive ensembles of identical quantum dots to be made.
- 52. Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics 41 5 Fabricating and Controlling a Quantum Dot Cellular Automata Cell Figure 6a shows two DBs. The distinct dark halo indicates the DBs are nega- tively charged. Figure 4b shows that when an additional DB is created by a tip directed H removal at a nearby site, both the new DB and the nearby pre-existing DB appear very differently, while the somewhat removed DB is unaltered. After extensive study it became clear that such a closely placed pair of DBs experi- ences a great Coulombic repulsive interaction, destabilizing the bound electrons and enabling one electron to leave the ensemble [12,14]. The reduced net charge simultaneously stabilizes the remaining bound electron and creates an unoccu- pied energy level on one of the atoms. Because the barrier separating the DBs is low, of order several 100 meV, and is also very narrow, of order 2 nm, tunnel- ing to the vacant state is very facile. Such a pair of DBs may be referred to as tunnel coupled. Our WKB and ab initio calculations agree that the tunneling rate for the 3.84 Å separated DBs corresponds to an extremely short tunneling period of order 10 fs [22,23]. Conventional relatively large and necessarily widely spaced dots would have a tunnel rate many orders of magnitude lower. Figure 7 shows the energy landscape schematically [14]. Each DB is represented by a potential well. The well is within the silicon bandgap. In Fig. 7a the separation between DBs is sufficiently large for the Coulombic interaction to be diminished by distance and by screening by conduction band electrons. In Fig. 7b the high energy repulsive relationship existing between two negatively charged DBs is represented. Figure 7b also shows the relaxed situation resulting after removal of one electron to the conduction band. In that final scenario one vacant electron state is shown. That state and the low and narrow barrier enables tunneling between the DBs. The pairing result demonstrates a “self-biasing” effect. That is, by using fabrication geometry and repulsion to adjust electron filling, the need for capac- itively coupled filling electrodes is removed [14]. Figure 8a shows several pairs of DBs of different separations and therefore different average net occupations. It can be readily seen that closer spaced DBs more fully reject one electron, leading to less local charge induced band bending and therefore to a lighter appearance in the STM image. The increasingly widely spaced pairs look increasingly dark as the net charge approaches 2 electrons. A statistical mechanical model of the paired DBs reproduces the effect as shown in Fig. 8b. The graph stresses that occupation is a time averaged quantity and that pairs in the cross-over region will at any instant be either 1− or 2− charged [14]. Figure 9 shows a 4 dot ensemble or artificial molecule. The 4 dot cell was fabri- cated to result in an average net filling of 2 extra electrons. The graphs in Fig. 9b show the result of a statistical mechanical description of average occupation versus distance of separation in such a square cell at different temperatures [12]. One way to localize and thereby visualize the occupying electrons is to make an irregular shaped cell as is shown in Fig. 10 [14]. Figure 10a shows three dots, two of which look darker indicating greater negative charge localization Upon
- 53. 42 R.A. Wolkow et al. CBM VBM Vel/2 E 0 (a) (b) Unfavourable R12 E F R12 ~4d E 0 – t – U/2 Fig. 7. The schematic energy landscape of a DB pair with each DB represented by a potential well with the ground state in the band gap. In (a), the separation between DBs is very large for the Coulombic interaction to be negligible and each DB is negatively changed (doubly occupied). In (b), DBs are much closer together (d is the dimer- dimer spacing) and a great Coulombic repulsion is associated with the doubly occupied configuration on both DBs. The diagram also shows the relaxed situation resulting after removal of one electron to the conduction band thus enabling tunneling of the remaining excess electron between the DBs. Fig. 8. (a) Several tunnel-coupled pairs of DBs fabricated at different separations (spec- ified in each case) on the H-Si(100) surface. (b) Average occupation probability of a DB pair with 1 and 2 excess electrons as a function of DB separation. The three cases labeled in (a) are marked here with blue arrows (Color figure online).
- 54. Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics 43 Fig. 9. (a) A fabricated ensemble (cell) of 4 tunnel-coupled DBs, or artificial molecule, calibrated to result in an average net filling of 2 extra electrons. A corresponding dimer lattice diagram is shown below. (b) The result of a statistical mechanical description of average occupation versus distance of separation in such a square cell at different temperatures (300 K top graph, 100 K bottom graph). The occupation probabilities with 1, 2, 3, 4 extra electrons are plotted for each case. adding a fourth dot the previously darker sites become relatively light in appear- ance. This is due to the electrons attaining a lower energy configuration along a newly available longer diagonal. In a symmetric square or rectangular cell the freely tunneling electrons equally occupy the degenerate diagonal configurations. On the slow time scale of the STM measurement no instantaneous asymmetry can be seen. In order to embody the QCA architecture it must be possible to break that symmetry electrostatically and thereby to polarize electrons within a cell. This capacity is illustrated first by referral to a 2 dot cell. Figure 11 shows the sequen- tial building of a 2 dot cell occupied by one extra electron and the polarization of that cell by one perturbing charge [14]. Figure 11a shows a small area, 3 nm across, of H-terminated silicon at room temperature. Figure 11b shows the cre- ation of one ASiQD, while Fig. 11c shows the creation of a second ASiQD and the concomitant reduction in charge and darkness as seen by the STM. Upon charge removal, rapid tunnel exchange ensues. The coupled entity resulting may be described as an artificial homonuclear diatomic molecule. Like in an ordi- nary molecule, the Born-Oppenheimer approximation is valid. In other words, the electron resides so very briefly on one atom that nuclear relaxation does not have time to occur. On the electronic time scale, the nuclei are frozen. Finally in Fig. 11d another charged DB is created. Using the knowledge displayed in Fig. 6, the last DB is placed near enough to the molecule to affect it electrostatically,
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