2012 12th IEEE International Conference on Nanotechnology (IEEE-NANO)
The International Conference Centre Birmingham
20-23 August 20112, Birmingham, United Kingdom
Molecule Interaction for QCA Computation
Azzurra Pulimenol, Mariagrazia Grazianol and Gianluca Piccinini 1 1 Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italia.
Email: {azzurra.pulimeno.mariagrazia.graziano.gianluca.piccinini} @polito.it
Abstract- Molecular Quantum-dot Cellular Automata (QCA) represent a new paradigm for nanoelectronics that
seems to be very promising for digital computing. The elementary nano-device is a molecular system in which the binary encoding is provided by the charge localization within the molecule, without current flow. Basing on a previous analysis of a molecule synthesized ad-hoc for QCA technology, we discussed here the efl'ect of the clock signal i) on a single molecule, ii) on the interaction between a driver and a molecule, and iii) on the interaction between two molecules. The results obtained by means of ab-initio calculations allowed to model a real QCA cell functional to a further study on the interaction between different cells ..
I. INTRODUCTION
Among all the new emergent devices alternative to CMOS
transistor, Quantum-dot Cellular Automata (QCA) is the one
that, theoretically, allows to encode binary information with
out current flow, reaching high operating frequency and low
ering the power consumption [1]. The basic computational
unit is an arrangement of six quantum dots in a rectangular
geometry like the one sketched in figure Fig. I(A). In the
theoretical implementation two free charges are present in
the structure, that occupy one of the two diagonals, because
that is the configuration which mainly favors Coulombic
repulsion. The two configurations correspondent to the two
diagonals can be associated to logic values '0' and '1'. A
third configuration might be possible (discussed in section II)
associated to a 'neutral' state. The simplest logic structure
that could be implemented according to this paradigm is
a wire (Fig. I(B» where the digital value is propagated
in a 'domino' effect according to Coulombic repulsion. A
more complex gate is the majority voter (Fig. 1 (C» where the
output assumes the digital value associated to the majority
of the three inputs. Both are the building blocks for more
complex digital systems [2].
The more promising implementations proposed in the
literature are based on nano-magnets and on molecules.
In the magnetic case single-domain nanometer pills-shaped
magnets exhibit two stable magnetic states, 'up' and 'down'.
They carry a binary information thanks to their reciprocal
influence based on a 'domino' effect [3], [4]. The main
advantage of a magnetic implementation, that has been
physically demonstrated, is the small power consumption,
that, however, comes at the cost of a working frequency that
is not improved with respect to CMOS technology.
As proposed by Lent [5], a QCA cell can also be physically
implemented by a molecular system with two or more redox
centers. The charge configuration within the molecule en-
" Ig"�1 • 0
'0' [[]]o o 0 0 • 'NULL' [[]]o
o 0 00
IN OUT [8]• [8]. [8]. [8]. [8]. 8) 0 0 0 0 0 0 0 0 0 0
.0 .0 .0 .0 .0
INI [[]]O o 0 0. [[]]o [[]]O [[]]O
0 0 0 0 0 0 0. 0. 0. IN2 [[]]O
o 0 IN3 ° • OUT
C)
Fig. 1. QCA theory: (A) binary information encoding in six quantum dots arrangement, (8) wire of QCA cells and (C) a Majority Voter, the basic logic cells where the output assumes the value of the majority among three inputs.
codes the logical state and the electrostatic repulsion provides
the device-device interaction, The molecular implementation
is expected to reach very high frequencies (tens of THz) and
exceptional compactness, still maintaining a reduced power
dissipation thanks to the absence of charge transfer between
neighbor molecules.
Concerning the physical implementation, almost all the
molecules proposed in literature [5] - [7] are ideal systems.
Only few experimental attempts have been carried out on a
mixed-valence complex [8], [9], even though this molecule
is not suitable for real application. In our previous works
[12], [14], we discussed the functionalities of a bis-ferrocene
molecule (Fig, 2(a» [10], [11] as an half QCA. In most of
the previous works the analysis has been performed on a
single molecule, and only in a few cases considering the
presence of the clock [15], [16]. Here we present some
preliminary results on the impact of the clock signal i) on
this real molecule, ii) on the interaction between a molecule
and a ideal driver, and iii) on the interaction between two
molecules. Our aim is to fully characterize a complete
QCA cell in order to understand whether the synthesized
molecule has the characteristics to fulfill the QCA theory.
We performed also an analysis of the effects of the clock
signal on the behavior of the entire cell.
All the results discussed in the following are obtained
by means of ab-initio simulations. We show results in term
of HOMO levels and of charge distribution: we use here
the aggregated charge [13] as a new metric to qualify the
cell functional behavior; we computed also the energy of
the HOMO in order to understand how the energy of the
system varies in presence of different stimulus. In section II
we propose our methodology and in section III we present
our results.
Fig. 2. Bis-ferrocene molecule: (A) structure of the single molecule with evidence of the three dots; (B) two nearby molecules form a complete QCA cell; (C) a simple representation of the six dots QCA cell associated to the molecule subparts; (D) a schematic representation of the molecule interaction aualysis: a driver based on two dots carrying a positive point charge +qe (+ 1) and a negative point charge -qe (-1).
II. MET HODOLOGY
In this work we performed a set of simulations in order to
evaluate the sensitivity of the bis-ferrocene molecule firstly to
a clock signal and then to the simultaneous effect of a clock
field and a driver. Following the methodology of our previous
works [12], [13], [14], we used the HOMO localization and
its energy, as well as the analysis of charge on dots as
figures of merit for the logic state encoding. In particular
the charge of each dot is an aggregate charge, computed
a sum of the charges of the atoms that form the dot. The
analysis performed on the molecule at equilibrium was the
reference point for all our analysis. The results discussed
here are computed using Gaussian09, using the DFT B3LYP
theory and the LANL2DZ as basis set.
A. The single molecule The bis-ferrocene molecule has been synthesized ad hoc
for the QCA technology [10], [11]. The structure is reported
in Fig. 2(A): the two ferrocenes represent the dots (dot1 and
dot2 hereinafter), a carbazole bridge provides the isolation
between them and the thiol group allows to bind the molecule
on a substrate. This molecule is very promising as candidate
molecule for QCA computing for many reasons: our early
results showed that its bistability properties allow to encode
the digital information and that the molecule is sensitive
to a particular electric field, as write-in system [12], [14];
moreover this molecule is a real system that exists and has
already been bonded to a gold substrate [11].
B. The complete QCA cell In order to implement a QCA cell, it is possible to align
two molecules side by side, as shown in Fig.2(B). In this
configuration the charge distribution inside each molecule
should be influenced by the electrostatic repulsion between
the two molecules. In this work we want to analyze the in
teraction between two nearby molecules and their properties
as QCA cell by means of ab-initio simulations. This is a
crucial step for a further modeling of both the QCA cell and
the information propagation, especially in the perspective of
a demonstration experiment. A simple representation of the
two molecules and of the correspondence between the dots
and the molecule elements is in figure 2(C).
The simulations for molecular interaction were performed
using as a second molecule (mol2) a driver made of point
charges, as shown in figure 2(D). The aggregated charge
method can be usefully applied when the distance between
driver molecule and the molecule under test is larger than the
distances of atom charges inside the dots: i.e. the electrostatic
interaction is equivalent. In our analysis the driver is built
with two dots: a positive point charge (+qe) and a negative
(-qe) one, placed at the same distance of the two dots of the
molecule under test (moll). The distance between moll and
mol2 (the driver) is such that the four dots form a square,
as sketched in Fig. 2(C-D).
C. The effects of a clock signal on QCA According to the QCA theory [15], the clock is necessary
to manage the information propagation along the logical path
in a circuit. The reason behind this is double. First it was
observed that long QCA chains incur in errors during the
'domino' information propagation, for example from left to
right, when for some reasons the subsequent cells on the
right have already a fixed logic value. When introducing the
clock, QCA cells can be organized in groups, each related to
a specific external electric field. When the clock is activated
(or deactivated, depending on the physical implementation)
in one of these groups, the interested cells reach an inactive
or neutral (NULL) state. In this situation the cells cannot
influence other cells and cannot be influenced. When the
clock is deactivated (or activated, depending on the physical
implementation) the interested cells could encode the logic
o or 1 depending on the input cells, for example on the left
clock zone, provided that molecules in the right clock zone
are in the neutral state. The second important advantage of
the introduction of the clock is that it it provides the energy
that is lost during the information propagation. It should bebl
noted, indeed, that the QCA are by nature not connected to
any power supply.
In the case of a molecular QCA, three dots are present
as discussed before. A detailed analysis is reported in [16].
In the case of a molecule organized as the one presented
in this paper, when the clock is deactivated, the molecule
has not a charge that can be localized in one of the dots.
As a consequence the molecule cannot be influenced by any
o � o
I EHOMO -0. 192
A C
EHOMO -0.177
E
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0.018
i
0.012 -0.373
i
-0.6 11 0.513 0.633
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CK=O CK=-10V/nm CK=+10V/nm ............................................................. B D F
Fig. 3. Simulation results on the single molecule. A,C,E show the HOMO distribution, while B,D,F show the aggregated charge on the three dots. Cases A and B refer to the absence of the clock signal. Cases C and D are related to a clock signal perpendicular to the dotl-dot2 axis and directed toward the thiol. Cased E and F refer to a clock in the opposite direction.
input. When the clock signal is activated a charge becomes
free to move, so that the presence of an input can force the
molecule to a logic ' l' or '0' thanks to Coulombic repulsion.
By dynamically considering the clock switching from the
first to the second condition, the molecule moves from a
NULL state to a stable logic state ' l' or '0' depending
on the configuration of a stable input that influences the
electron motion during the timing window in which the
charge becomes free to move. When the clock changes again
from activated to deactivated, the molecule moves again in
the NULL state, and the previous digital value is erased.
III. RES ULTS
The results obtained from the single molecule simulations
are shown in Fig. 3: cases (A) and (B) are related to the
absence of any external electric field. In Fig. 3(A) the HOMO
distribution is shown for the single molecule at equilibrium:
in this case the HOMO is mainly localized on the carbazole
making the molecule itself inactive (NULL state). The energy
of HOMO level is -0.192 e V and this value will be used
as the reference level when analyzing the molecule in the
following conditions out of equilibrium. The result on the
HOMO is confirmed by the charge distribution inside the
molecule, as shown in Fig. 3(B). In this case the charges on
the three dots are almost zero.
The application of a clock signal, modeled as an external
electric field in the vertical direction, leads to a change in
the internal charge distribution. In particular for a negative
clock signal (backward field) the HOMO is localized mainly
on the thiol (the third dot of the molecule) and partially on
one of the two ferrocenes (dot2) (see Fig. 3(C)). The energy
for the HOMO rose to -0.131 eV showing that the clock field
provides energy to the system. This configuration influences
the aggregated charge as reported in Fig. 3(D): the third
dot becomes positive while the dotl and dot2 are negatively
charged, with a little displacement in favor of dot2. On the
contrary when a positive clock signal is applied (Fig. 3(E)
and (F)) the HOMO moves partially from carbazole toward
the thiol and partially toward the two ferrocenes. The HOMO
level (-0177 e V) is higher than the equilibrium. Also in this
case the charge configuration inside the molecule follows the
HOMO distribution: the main dots (dot1 and dot2) have a
positive charge and are almost balanced, while the third dot
becomes negative. This condition could be envisioned like a
cationic form of the bis-ferrocene molecule since an electron
is stolen from the main dots and forced to stay in the thiol
group.
The presence of a driver is described by means of two
point charges placed 10 Afar from the molecule under test
(moll) reproducing the behavior of a second molecule (moI2)
in order to analyze a complete QCA cell. Fig. 4 shows the
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1 • .•• - : •. . . '. . ...... +1 -1 :. ..... ..... + 1 -1 : • •.••• ... ..
o w � w <9<9 we::: e:::« <9I <90
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o r-::... 1 -0.028 t 10A "� I
CK=OV
. . .. �
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r-:: o "'.
10A "�
? -0.84d
+0.916 r CK=-10V
0.675 0.468�
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A B C
Fig. 4. Behavior of a molecule under the influence of a driver (in this case a model of a driver based on two point charges) without (B, negative electric field) and with (C, positive electric field) the impact of a clock signal.
results for the molecule influenced by the driver, respectively
without clock signal (Fig. 4(A», with a negative clock field
(Fig. 4(B)) and with a positive clock field (Fig. 4(C)). The
charge distribution of the molecule without clock is not
affected by the presence of a driver: even though there is a
little displacement between the two main dots, the molecule
can be still considered inactive. When a negative clock signal
is applied the initial charge configuration of moll (Fig. 3(D))
varies because of the electrostatic repulsion with the driver.
As reported in Fig. 4(B), the dot I becomes almost neutral
and dot2 has a strong negative charge, while the charge on
the third dot becomes strongly positive. So the neutrality of
the molecule is preserved, that means no charge transfer (no
current flow) occurs between the two molecules. In case of
positive clock signal (Fig. 4(C)), the presence of the driver
leads to a displacement between the charges of the two main
dots so that dotl becomes more positively charged than dot2,
while dot3 balances the neutrality of the molecule with a
negative charge. These results (both for negative and positive
clock signal) are important because show that the clock
signal could activate the molecule, allowing it to encode a
logic state in presence of a nearby driver molecule. This
means that the two molecules could interact and could act
as a complete QCA cell.
We performed a preliminary analysis on a real QCA cell,
made of two bis-ferrocene molecules as shown in Fig. 5. We
simply computed the HOMO distribution and the aggregated
charges of the dots at the equilibrium. In the ground state,
the two molecules have the HOMO mainly localized on
the carbazole (Fig. 5(A)), as for the single molecule. The
charge distribution reflects the results obtained for the single
molecule, in fact all the dots of the cell are almost neutral.
This confirms that the real QCA cell for this molecule lies
in an inactive state and needs an external stimulus to be
activated and so to encode a logic state. The effects of a
clock signal to the real cell will be evaluated in our future
works, as well as the presence of a driver cell that should
influence the cell under test.
IV. CONCLUSIONS
In this work, we analyzed the interaction between two
molecules, in order to evaluate the characteristics of a
....................................................................... . , .......................................................... ,
I ! I 0.029
I 0.027
• -0.057 • -0.052
0.028 0.026
: ............... ���� .................... ��!� ..................... 1 , ....... m .. .. o .. .. 1.1 ......... .............. m .... o ... 1.2 ............. , A B
Fig. 5. Complete QCA ceU: HOMO distribution (A) and aggregated charge (B) in the ground state.
complete molecular QCA cell based on a real molecule. The
electronic structure of the cell, as well as its charge distribu
tion, were explored by ab-initio simulations. Moreover, we
evaluated the effects of the clock field firstly on the single
molecule and then on the cell with the aim to assess the
working point for this technology. The results obtained allow
us to understand whether an interaction between molecules
is feasible: our results reveal that the ground state of the
bis-ferrocene molecule is a NULL state and the molecule
is not affected by the presence of a driver (modeled here
as two point charges). The molecule is able to localize its
internal charge, encoding thus a logic state, only when a
clock signal is applied. The specific logic state encoded
by the molecule depends on the state of the driver, that
represents here the second molecule of the entire cell. These
results are important for the information propagation and
the realization of a molecular QCA cell. Moreover, our
results are the starting point for a more detailed analysis
and modeling of the QCA cell.
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