Molecular Quantum Dot Cellular Automata (MQCA) are among the most promising emerging technologies for the expected theoretical operating frequencies (THz), the high device densities and the non-cryogenic working temperature. In this work we simulated a molecular QCA wire, based on a molecule synthesized ad-hoc for this technology. The results discussed are obtained by means of iterative steps of ab-initio calculation

Demarchi, Danilo

Graziano, Mariagrazia

Piccinini, Gianluca

Pulimeno, Azzurra

English

PORTO Publications Open Repository TOrino

Simulation of a molecular QCA wire
Azzurra Pulimeno∗, Mariagrazia Graziano∗, Danilo Demarchi∗ and Gianluca Piccinini∗
∗Department of Electronics and Telecommunications, Politecnico di Torino, Italy
Email: {azzurra.pulimeno, mariagrazia.graziano, gianluca.piccinini}@polito.it
Abstract—Molecular Quantum Dot Cellular Automata
(MQCA) are among the most promising emerging technologies
for the expected theoretical operating frequencies (THz), the high
device densities and the non-cryogenic working temperature.
In this work we simulated a molecular QCA wire, based on
a molecule synthesized ad-hoc for this technology. The results
discussed are obtained by means of iterative steps of ab-initio
calculations.
I. INTRODUCTION
Among all the new emergent devices alternative to bulk
MOSFET, Quantum-dot Cellular Automata (QCA) is the one
that, theoretically, allows to encode binary information without
current flow, reaching high operating frequency and lowering
the power consumption [1]. As proposed by Lent [2], a QCA
cell could be physically implemented by a molecular system
with two or more redoxcenters: the charge configuration within
the molecule encodes the logical state and the electrostatic
repulsion provides the device-device interaction. The simplest
demonstration of logic propagation that could be performed
according to this paradigm is a molecular wire (see Fig. 1 (A)).
Concerning the physical implementation, all the molecules
proposed in literature [3], [4], [6] are ideal systems. Only
few experimental attempts have been carried out on a mixed-
valence complex [7], [8], even though this molecule is not
suitable for real applications. In our previous works [11]–[13],
we discussed the functionalities of a bis-ferrocene molecule
(Fig. 1 (B)) [9], [10] as an half QCA cell. In this work
we emulated a molecular wire, evaluating simultaneously the
interaction between two molecules (a complete QCA cell)
and the information propagation at different inter-molecule
distances.
II. METHODOLOGY
A. The single molecule
The bis-ferrocene molecule has been synthesized ad hoc for
the QCA technology [9]. The structure is reported in Fig. 1
(B): the two ferrocenes represent the dots, 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
seems sensitive to a particular electric field, as write-in system
[11]–[13]; this molecule is a real system that exists and has
already been bonded to a gold substrate [9], [10]. In this
work we considered the oxidized molecule: at the equilibrium
(no external stimuli) the free positive charge is delocalized
x
z
y
Molecule 1
Molecule i-1
Molecule i
Molecule n
Dot1
Dot2
Dot3
Molecular Wire
d
Q1
Molecule i
Q3
Q2
D1 D3
D2
x
z
y
carbazole
ferrocenes
Dot2
Dot3
thiol
1.0 nm
1
.8
 n
m
Dot1
(A)
(B) (C)
Fig. 1. (A) Schematic view of a MQCA wire of bis-ferrocene molecules.
(B) Bis-ferrocene molecule: two ferrocenes linked together by means of a
carbazole central group; the ferrocenes represent the two dots responsible for
the logic state encoding, while the carbazole acts as the central third dot. (C)
Section of the wire: the aggregated charges of the (i-1)th molecule (Q1, Q2
and Q3) act as a driver for the Molecule i varying its dot charges (D1, D2
and D3).
between the two main dots (the ferrocenes) and the molecule
is in a neutral state.
B. The molecular wire
We emulated a molecular QCA wire made of bis-ferrocene
molecules by means of iterative simulation steps. In particular,
we forced a logic state on the first molecule of the wire
(Molecule 1, as shown in Fig. 1 (A)) applying an electric field
of 2 V/nm along the ferrocenes axes. Then we used the charge
configuration of this molecule as stimulus for the following
cell (Molecule 2). As explained in Fig. 1 (C), at a generic
point of the wire we evaluated the response of Molecule i
to the charge distribution of Molecule i-1, assuming that the
Molecule i is in the neutral state (charge delocalized) and ready
to switch [13]. We performed this analysis firstly on a wire in
which the distance d between two molecules is 1.0 nm (equal
to the width of the molecule, in order to form a square cell)
and then setting the distance to 0.8 nm.
In order to do this, we defined a new figure of merit for our
analysis, the aggregated charge of the dots, simply summing
up the charge of the atoms that constitute the dot [12]. In
addition, for each step of our simulation we emulated the
driver molecule (Molecule i-1) with a system of point charges
built placing the aggregated charge Q1, Q2 and Q3 in the
same position of the dot, as shown in Fig. 1 (C). In this way,
we computed the aggregated charges (D1, D2 and D3) of the
nearby molecule (Molecule i), that became the driver system
in the following step Molecule i+1). Iterating this method for
all the molecules of the wire, we simulated the information
propagation through the wire. All the results reported here
were obtained by means of ab-initio simulations.
III. RESULTS
In Fig. 2 the charges of the two main dots (dot1 and dot2)
are reported: for sake of brevity, we focused on the first part
of the wire, considering only five molecules. As depicted in
Fig. 2, in the ideal case (distance equals to 1.0 nm) the charge
displacement between the two dots (empty points) decreases
with increasing number of molecules. We could consider the
logic signal valid only for the first three molecules, while from
the fourth molecule on the state is not defined. On the other
hand, when the molecules are placed 0.8 nm far from each
other, the difference of charge between the two dots is still
huge enough to consider the molecule in a defined logic state
(see Fig. 2, filled points). In both the cases, the switching of
the molecule along the wire is preserved, since the polarity of
the dots is inverted at each stage.
-0.2
 0
 0.2
 0.4
 0.6
 0.8
 1
Mol-1 Mol-2 Mol-3 Mol-4 Mol-5
D
ot
s 
ag
gr
eg
at
ed
 c
ha
rg
e 
Molecule in wire
Dot1 d=1nm
Dot2 d=1nm
Dot1 d=0.8nm
Dot2 d=0.8nm
Fig. 2. Dot charges along the wire, as function of the distance d.
As additional figure of merit for our analysis, we computed
the electric field generated by a charge system by means of
mathematical calculations. In particular, each molecule along
the wire, depending on its logic state, generates an electric
field whose absolute value is maximum near the occupied
dot. Fig. 3 show a top view of the electric field (computed
basing on the aggregated charges of Fig. 2) generated by the
first five molecules of the wire for two different inter-molecule
distances (d=0.8 nm top and d=1.0 nm bottom). Both the pic-
tures show how the peak of the electric field moves following
the position of the free charge in the molecule. However, in
the bigger distance case the peak become smoother along the
wire.
These results are notable because they reveal the strength
of the logic signal in two MQCA wires. In particular, the one
with the ideal distance for the bis-ferrocene molecule (d=1.0
nm) shows a degradation already at the fourth molecule, while
in case of d=0.8 nm the signal is preserved and is expected
to be so even for a greater number of molecules.
Generated E-field [V/nm], MQCA WIREs, d=0.8nm (top) d=1nm (bot.)
WIRE-2 d=1nm
WIRE-1 d=1nm
0 1 2 3 4
Y [nm]
-2
-1
0
1
-2
-1
0
1
X 
[nm
]
-2
-1.5
-1
-0.5
 0
 0.5
 1
 1.5
 2
Fig. 3. Electric field generated by the charge distribution along the wire,
when molecules are placed at d=0.8 nm (top) and d=1.0 nm (bottom)
REFERENCES
[1] C.S. Lent, P.D. Tougaw and W. Porod, Quantum cellular automata:
the physics of computing with arrays of quantum dot molecules, IEEE
PhysComp’94, pp.5-13, 17-20, Nov 1994
[2] C.S. Lent, P.D. Tougaw,W. Porod, and G. Bernstein, Quantum cellular
automata, Nanotechnology, vol. 4, pp. 49-57, 1994
[3] C. S. Lent, B. Isaksen and M. Lieberman, Molecular Quantum-Dot
Cellular Automata, J. Am. Chem. Soc., vol. 125, pp. 1056-1063, 2003
[4] C.S. Lent and B. Isaksen, Clocked molecular quantum-dot cellular
automata, Electron Devices, IEEE Transactions on, vol.50, no.9, pp.
1890-1896, Sept. 2003
[5] Y. Lu and C.S. Lent, Self-doping of molecular quantum-dot cellular
automata: mixed valence zwitterions, Phys. Chem. Chem. Phys., vol. 13,
pp. 14928-14936, 2011
[6] Z. Li, A. M. Beatty and T. P. Fehlner, Molecular QCA Cells. 1. Structure
and Functionalization of an Unsymmetrical Dinuclear Mixed- Valence
Complex for Surface Binding, Inorg. Chem., vol. 42, pp. 5707-5714, 2003
[7] H. Qi, S. Sharma, Z. Li, G. L. Snider, A. O. Orlov, C. S. Lent and
T.P. Fehlner, 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., vol.
125, pp. 15250-15259, 2003
[8] R.A. Joyce, H. Qi, T.P. Fehlner, C.S. Lent, A.O. Orlov and G.L. Snider,
A system to demonstrate the bistability in molecules for application
in amolecular QCA cell, IEEE Nanotechnology Materials and Devices
Conference, pp. 46-49, 2-5 June 2009
[9] L. Zoli, PhD Dissertation, Universita´di Bologna, 2010.
[10] V. Arima, M. Iurlo, L. Zoli, S. Kumar, M. Piacenza, F. Della Sala,
F. Matino, G. Maruccio, R. Rinaldi, F. Paolucci, M. Marcaccio, P.G.
Cozzi and A.P. Bramanti, Toward quantum-dot cellular automata units:
thiolated-carbazole linked bisferrocenes, Nanoscale, V4, 813-823, 2012
[11] A. Pulimeno, M. Graziano, C. Abrardi, D. Demarchi, and G. Piccinini,
Molecular QCA: A write-in system based on electric fields, IEEE Nano-
electronics Conference (INEC), June 2011
[12] A. Pulimeno, M. Graziano, D. Demarchi, and G. Piccinini, Towards a
molecular QCA wire: simulation of write-in and read-out systems, Solid
State Electronics, vol.77, pp. 101-107, 2012
[13] A. Pulimeno, M. Graziano, D. Demarchi, and G. Piccinini, Molecule
interaction for QCA computation, IEEE Nanotechnology Conference
(IEEE-NANO), August 2012


A system to demonstrate the bistability in molecules for application in amolecular

Clocked molecular quantum-dot cellular automata, Electron Devices,

Molecular QCA Cells. 1. Structure and Functionalization of an Unsymmetrical Dinuclear Mixed- Valence Complex for Surface Binding,

Molecular QCA: A write-in system based on electric ﬁelds,

Molecular Quantum Cellular Automata Cells. Electric Field Driven Switching of a Silicon Surface Bound Array of Vertically Oriented Two-Dot Molecular Quantum Cellular Automata,

Molecular Quantum-Dot Cellular Automata,

Molecule interaction for QCA computation,

Quantum cellular automata,

Quantum cellular automata: the physics of computing with arrays of quantum dot molecules,

Self-doping of molecular quantum-dot cellular automata: mixed valence zwitterions,

Toward quantum-dot cellular automata units: thiolated-carbazole linked bisferrocenes,

Towards a molecular QCA wire: simulation of write-in and read-out systems,

Simulation of a molecular QCA wire

Molecular Quantum Dot Cellular Automata
(MQCA) are among the most promising emerging technologies
for the expected theoretical operating frequencies (THz), the high
device densities and the non-cryogenic working temperature.
In this work we simulated a molecular QCA wire, based on
a molecule synthesized ad-hoc for this technology. The results
discussed are obtained by means of iterative steps of ab-initio
calculations

PULIMENO, AZZURRA

GRAZIANO, MARIAGRAZIA

DEMARCHI, DANILO

PICCININI, GIANLUCA

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALESimulation of a molecular QCA wire / Pulimeno A.;Graziano M.;Demarchi D.;Piccinini G.. - ELETTRONICO. - (2013).((Intervento presentato al convegno Workshop on Field-Coupled Nanocomputing tenutosi a Tampa, Florida nel 2013.OriginalSimulation of a molecular QCA wirePublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2510678 since:Simulation of a molecular QCA wireAzzurra Pulimeno∗, Mariagrazia Graziano∗, Danilo Demarchi∗ and Gianluca Piccinini∗∗Department of Electronics and Telecommunications, Politecnico di Torino, ItalyEmail: {azzurra.pulimeno, mariagrazia.graziano, gianluca.piccinini}@polito.itAbstract—Molecular Quantum Dot Cellular Automata(MQCA) are among the most promising emerging technologiesfor the expected theoretical operating frequencies (THz), the highdevice densities and the non-cryogenic working temperature.In this work we simulated a molecular QCA wire, based ona molecule synthesized ad-hoc for this technology. The resultsdiscussed are obtained by means of iterative steps of ab-initiocalculations.I. INTRODUCTIONAmong all the new emergent devices alternative to bulkMOSFET, Quantum-dot Cellular Automata (QCA) is the onethat, theoretically, allows to encode binary information withoutcurrent flow, reaching high operating frequency and loweringthe power consumption [1]. As proposed by Lent [2], a QCAcell could be physically implemented by a molecular systemwith two or more redoxcenters: the charge configuration withinthe molecule encodes the logical state and the electrostaticrepulsion provides the device-device interaction. The simplestdemonstration of logic propagation that could be performedaccording to this paradigm is a molecular wire (see Fig. 1 (A)).Concerning the physical implementation, all the moleculesproposed in literature [3], [4], [6] are ideal systems. Onlyfew experimental attempts have been carried out on a mixed-valence complex [7], [8], even though this molecule is notsuitable for real applications. In our previous works [11]–[13],we discussed the functionalities of a bis-ferrocene molecule(Fig. 1 (B)) [9], [10] as an half QCA cell. In this workwe emulated a molecular wire, evaluating simultaneously theinteraction between two molecules (a complete QCA cell)and the information propagation at different inter-moleculedistances.II. METHODOLOGYA. The single moleculeThe bis-ferrocene molecule has been synthesized ad hoc forthe QCA technology [9]. The structure is reported in Fig. 1(B): the two ferrocenes represent the dots, a carbazole bridgeprovides the isolation between them and the thiol group allowsto bind the molecule on a substrate. This molecule is verypromising as candidate molecule for QCA computing for manyreasons: our early results showed that its bistability propertiesallow to encode the digital information and that the moleculeseems sensitive to a particular electric field, as write-in system[11]–[13]; this molecule is a real system that exists and hasalready been bonded to a gold substrate [9], [10]. In thiswork we considered the oxidized molecule: at the equilibrium(no external stimuli) the free positive charge is delocalizedxzyMolecule 1Molecule i-1Molecule iMolecule nDot1Dot2Dot3Molecular WiredQ1Molecule iQ3Q2D1 D3D2xzycarbazoleferrocenesDot2Dot3thiol1.0 nm1.8 nmDot1(A)(B) (C)Fig. 1. (A) Schematic view of a MQCA wire of bis-ferrocene molecules.(B) Bis-ferrocene molecule: two ferrocenes linked together by means of acarbazole central group; the ferrocenes represent the two dots responsible forthe logic state encoding, while the carbazole acts as the central third dot. (C)Section of the wire: the aggregated charges of the (i-1)th molecule (Q1, Q2and Q3) act as a driver for the Molecule i varying its dot charges (D1, D2and D3).between the two main dots (the ferrocenes) and the moleculeis in a neutral state.B. The molecular wireWe emulated a molecular QCA wire made of bis-ferrocenemolecules by means of iterative simulation steps. In particular,we forced a logic state on the first molecule of the wire(Molecule 1, as shown in Fig. 1 (A)) applying an electric fieldof 2 V/nm along the ferrocenes axes. Then we used the chargeconfiguration of this molecule as stimulus for the followingcell (Molecule 2). As explained in Fig. 1 (C), at a genericpoint of the wire we evaluated the response of Molecule ito the charge distribution of Molecule i-1, assuming that theMolecule i is in the neutral state (charge delocalized) and readyto switch [13]. We performed this analysis firstly on a wire inwhich the distance d between two molecules is 1.0 nm (equalto the width of the molecule, in order to form a square cell)and then setting the distance to 0.8 nm.In order to do this, we defined a new figure of merit for ouranalysis, the aggregated charge of the dots, simply summingup the charge of the atoms that constitute the dot [12]. Inaddition, for each step of our simulation we emulated thedriver molecule (Molecule i-1) with a system of point chargesbuilt placing the aggregated charge Q1, Q2 and Q3 in thesame position of the dot, as shown in Fig. 1 (C). In this way,we computed the aggregated charges (D1, D2 and D3) of thenearby molecule (Molecule i), that became the driver systemin the following step Molecule i+1). Iterating this method forall the molecules of the wire, we simulated the informationpropagation through the wire. All the results reported herewere obtained by means of ab-initio simulations.III. RESULTSIn Fig. 2 the charges of the two main dots (dot1 and dot2)are reported: for sake of brevity, we focused on the first partof the wire, considering only five molecules. As depicted inFig. 2, in the ideal case (distance equals to 1.0 nm) the chargedisplacement between the two dots (empty points) decreaseswith increasing number of molecules. We could consider thelogic signal valid only for the first three molecules, while fromthe fourth molecule on the state is not defined. On the otherhand, when the molecules are placed 0.8 nm far from eachother, the difference of charge between the two dots is stillhuge enough to consider the molecule in a defined logic state(see Fig. 2, filled points). In both the cases, the switching ofthe molecule along the wire is preserved, since the polarity ofthe dots is inverted at each stage.-0.2 0 0.2 0.4 0.6 0.8 1Mol-1 Mol-2 Mol-3 Mol-4 Mol-5Dots aggregated charge Molecule in wireDot1 d=1nmDot2 d=1nmDot1 d=0.8nmDot2 d=0.8nmFig. 2. Dot charges along the wire, as function of the distance d.As additional figure of merit for our analysis, we computedthe electric field generated by a charge system by means ofmathematical calculations. In particular, each molecule alongthe wire, depending on its logic state, generates an electricfield whose absolute value is maximum near the occupieddot. Fig. 3 show a top view of the electric field (computedbasing on the aggregated charges of Fig. 2) generated by thefirst five molecules of the wire for two different inter-moleculedistances (d=0.8 nm top and d=1.0 nm bottom). Both the pic-tures show how the peak of the electric field moves followingthe position of the free charge in the molecule. However, inthe bigger distance case the peak become smoother along thewire.These results are notable because they reveal the strengthof the logic signal in two MQCA wires. In particular, the onewith the ideal distance for the bis-ferrocene molecule (d=1.0nm) shows a degradation already at the fourth molecule, whilein case of d=0.8 nm the signal is preserved and is expectedto be so even for a greater number of molecules.Generated E-field [V/nm], MQCA WIREs, d=0.8nm (top) d=1nm (bot.)WIRE-2 d=1nmWIRE-1 d=1nm0 1 2 3 4Y [nm]-2-101-2-101X [nm]-2-1.5-1-0.5 0 0.5 1 1.5 2Fig. 3. Electric field generated by the charge distribution along the wire,when molecules are placed at d=0.8 nm (top) and d=1.0 nm (bottom)REFERENCES[1] C.S. Lent, P.D. Tougaw and W. Porod, Quantum cellular automata:the physics of computing with arrays of quantum dot molecules, IEEEPhysComp’94, pp.5-13, 17-20, Nov 1994[2] C.S. Lent, P.D. Tougaw,W. Porod, and G. Bernstein, Quantum cellularautomata, Nanotechnology, vol. 4, pp. 49-57, 1994[3] C. S. Lent, B. Isaksen and M. Lieberman, Molecular Quantum-DotCellular Automata, J. Am. Chem. Soc., vol. 125, pp. 1056-1063, 2003[4] C.S. Lent and B. Isaksen, Clocked molecular quantum-dot cellularautomata, Electron Devices, IEEE Transactions on, vol.50, no.9, pp.1890-1896, Sept. 2003[5] Y. Lu and C.S. Lent, Self-doping of molecular quantum-dot cellularautomata: mixed valence zwitterions, Phys. Chem. Chem. Phys., vol. 13,pp. 14928-14936, 2011[6] Z. Li, A. M. Beatty and T. P. Fehlner, Molecular QCA Cells. 1. Structureand Functionalization of an Unsymmetrical Dinuclear Mixed- ValenceComplex for Surface Binding, Inorg. Chem., vol. 42, pp. 5707-5714, 2003[7] H. Qi, S. Sharma, Z. Li, G. L. Snider, A. O. Orlov, C. S. Lent andT.P. Fehlner, Molecular Quantum Cellular Automata Cells. Electric FieldDriven Switching of a Silicon Surface Bound Array of Vertically OrientedTwo-Dot Molecular Quantum Cellular Automata, J. Am. Chem. Soc., vol.125, pp. 15250-15259, 2003[8] R.A. Joyce, H. Qi, T.P. Fehlner, C.S. Lent, A.O. Orlov and G.L. Snider,A system to demonstrate the bistability in molecules for applicationin amolecular QCA cell, IEEE Nanotechnology Materials and DevicesConference, pp. 46-49, 2-5 June 2009[9] L. Zoli, PhD Dissertation, Universita´di Bologna, 2010.[10] V. Arima, M. Iurlo, L. Zoli, S. Kumar, M. Piacenza, F. Della Sala,F. Matino, G. Maruccio, R. Rinaldi, F. Paolucci, M. Marcaccio, P.G.Cozzi and A.P. Bramanti, Toward quantum-dot cellular automata units:thiolated-carbazole linked bisferrocenes, Nanoscale, V4, 813-823, 2012[11] A. Pulimeno, M. Graziano, C. Abrardi, D. Demarchi, and G. Piccinini,Molecular QCA: A write-in system based on electric fields, IEEE Nano-electronics Conference (INEC), June 2011[12] A. Pulimeno, M. Graziano, D. Demarchi, and G. Piccinini, Towards amolecular QCA wire: simulation of write-in and read-out systems, SolidState Electronics, vol.77, pp. 101-107, 2012[13] A. Pulimeno, M. Graziano, D. Demarchi, and G. Piccinini, Moleculeinteraction for QCA computation, IEEE Nanotechnology Conference(IEEE-NANO), August 2012

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