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

". ......................................................... . o w !;i: w

(9(9 wo:: 0::« (9I

(9U «

0.018

i

0.012 -0.373

i

-0.6 11 0.513 0.633

i -1.146

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

�" " " " " " " " " " " " " " " " " " " " " " " " '': , ................................................. ':

1 • .•• - : •. . . '. . ...... +1 -1 :. ..... ..... + 1 -1 : • •.••• ... ..

o w � w <9<9 we::: e:::« <9I <90

«

0.022

VO.006

o r-::... 1 -0.028 t 10A "� I

CK=OV

. . .. �

.... ,

r-:: o "'.

10A "�

? -0.84d

+0.916 r CK=-10V

0.675 0.468�

r-:: o ... 10A "�

-1.143 r CK=+10V

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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