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CHAPTER 5

SIMULATION OF DIODES FOR MOLECULAR

ELECTRONIC LOGIC CIRCUITS

5.1 INTRODUCTION

Recently, there have been significant advances in the fabrication and

demonstration of molecular electronic wires and or molecular electrons

diodes, two-terminal electrical switches made from single molecules. There

also have been advances in techniques for making reliable electrical contact

with such electrically conducting molecules. These promising developments in

the field of nano electronics suggest that it must be possible to build and to

demonstrate somewhat more complex molecular electronic structures that

would include two or three molecular electronic diodes that would perform as

digital logic circuits.

In this chapter we modeled the electron transport characteristic of

rectifying diodes based on Aviram and Ratner model [47].

A detailed analysis on the effect of the electron transfer path between

the donor and acceptor, has been carried out through frontier molecular orbital

analysis.

5.2 AVIRAM AND RATNER MODEL

The seminal work of Aviram and Ratner in 1974 led to several

experimental attempts to build molecular diodes. Aviram and Ratner have

suggested [37] that electron donating constituents make conjugated molecular

groups having a large electron density (N-type) and electron withdrawing

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constituents make conjugated molecular groups poor in electron density

(P-type). According to them, a noncentrosymmetric molecule having

appropriate donor and acceptor moieties linked with a s-bridge and connected

with suitable electrodes will conduct current only in one direction - acting as a

rectifier. They showed that in this molecule, the lowest unoccupied molecular

orbital (LUMO) and highest occupied molecular orbital (HOMO) can be

aligned in such a way that electronic conduction is possible only in one

direction making it function like a molecular diode exhibiting the transport

characteristic as in Figure 5.1. Asymmetric current-voltage characteristics for

a s- bridged system were first reported in 1990 [98,99]

The band diagram of the mono-molecular diode under zero-bios

conditions is shown in Figure 5.2. We notice that there are three potential

barriers - one corresponding to the insulating group (middle barrier) and two

corresponding to the contact between the molecule and the electrode (left and

right barriers). These potential barriers provide the required isolation between

various parts of the structure. The occupied energy levels in the metal contacts

and the Fermi energy level EF are also shown. On the left of the central barrier

all the pi-type energy levels (HOMO as well as LUMO) are elevated due to

the presence of the electron donating group X and similarly on the right of the

central barrier the energy levels are lowered due to the presence of the electron

withdrawing group Y. This causes a built-in potential to develop across the

barrier represented by the energy difference ΔELUMO.

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Figure 5.1(a) Schematic representation of molecular rectifier

Figure 5.1(b) Ideal I-V characteristic of a molecular diode

I

V

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Figure 5.2 Molecular diode orbital energy diagram under zero bias condition

Figure 5.3. Molecular diode orbital energy diagram under forward and reverse bias conditions

Donor (D)

Acceptor (A) Au

Au

ΔELUMO

Energy

Distance

Zero applied bias Femi Energy

Energy

Energy

Distance

Tra

nsm

itted

E

lect

rons

Cur

rent

(Hol

es)

Forward Bias

Reverse Bias

Distance

No Current

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In a proper applied bias voltage, electron tunneling occurs from the

acceptor part of the molecule to the donor part, through the unoccupied

manifold of the molecular orbitals. When such a molecule is connected

through two electrodes (acceptor part connected to the cathode and donor part

connected to the anode) and a proper forward bias (at least it should be

sufficient enough to raise the Fermi energy of the electron in the occupied

level of gold contact on the acceptor side to that of the energy of the LUMO

localized on the acceptor part of the molecule) is applied, then the electron can

flow from the gold contact to the LUMO, localized on the acceptor part. The

injected electron from the gold contact to the acceptor part of the molecule can

now tunnel through the central insulating bridge to the higher unoccupied

molecular orbital localized in the donor half of the molecule and finally

escapes into the gold contact lying in the donor part. In analogy to the forward

bias condition, in a reverse applied bias, for electron transfer to occur from the

donor part of the molecule to the acceptor part through the central insulating

bridge, the reverse bias must be sufficient to raise the Fermi energy of the gold

contact on the donor side of the molecule so that it is at least as high as the

energy of the empty orbital localized on the donor part of the molecule.

According to Ellenbogen and Love [100], during the process of applied bias in

the forward and reverse bias conditions, energy level alignment occurs in the

molecule which is responsible for a feasible electron transfer process in the

forward bias condition compared to reverse biased condition (reverse bias

process requires more energy than for the forward bias), and thus rectification

occurs.

The band diagram under reverse bias conditions (left hand contact at

lower potential than the right hand contact) is shown in Figure 5.3. As a result,

electrons from the left contact would try to flow towards the right contact

which is at a higher potential. However, conduction is not possible because the

there is still an energy difference between the Fermi energy EF of the left

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contact and the LUMO energy of the electron donor doped section. It is

assumed that both the applied forward and reverse bias potentials are identical.

For a higher reverse bias, however, it is possible for the Fermi energy EF of the

left contact to come in resonance with the LUMO energy of the electron donor

doped section causing a large current to flow in reverse direction and this is

akin to the breakdown condition in a diode.

5.3 RECTIFYING DIODE

Based on the model discussed in the previous section, we propose the

diode structure as shown in Figure 5.4 consisting of two identical sections

(S1, S2) separated by an insulating group R. Section S1 is doped by NH2

donating group (X ) and section S2 is doped by NO2 electron withdrawing

group (Y ). The insulating group CH2CH2 (R) is incorporated into the

molecular wire.. The single molecule ends are connected to the contact

electrodes e.g. gold. For current to flow electrons must overcome the potential

barrier from electron acceptor doped section (S2) to electron donor doped

section (S1) and this forms the basis for the formation of the mono-molecular

rectifying diode.

Figure 5.4 Optimized Geometry of diode molecule-I (Level: B3 PW91/6-31G)

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Figure 5.5 Current-voltage characteristics of diode molecule-I

Figure 5.6 Conductance-voltage characteristics of diode molecule-I

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The rectifying ratio is the parameter that shows the amount of

rectification. As seen in Figure 5.5, the rectifying ratio of this molecule is 1.75

By choice of (X) and (Y) groups this value can be improved.

As discussed earlier in the principle of electrical rectification, the most

important thing for a D-S-A molecule to show rectification is that it should

have the localized orbitals in different parts of the molecule, which will be

helpful in tunneling of electron at a proper applied bias. For visualization of

the orbital population density, population analysis of molecule 1 has been

carried out at its B3PW91/6-31G* optimized geometry and the corresponding

few frontier molecular orbitals (FMO)s are shown in Figure 5.7-5.11.

It is observed that the molecule when connected in the circuit, LUMO

& LUMO+2 will be channel for the electron transport i.e., in a proper applied

bias voltage, the tunneling of electron will occur from LUMO to LUMO+2. At

this applied bias, resonance (energy level alignment) between the LUMO &

LUMO+2 and also coupling between the two levels occurs. Visualizing the

two orbitals, it can be expected that a constructive electronic coupling between

LUMO & LUMO+2 can occur at the backbone and ring junctions to make the

process of electron tunneling feasible. During the reverse bias condition,

electron will be injected to LUMO+2 of the donor side and the process of

tunneling will occur at higher applied voltage compared to forward bias

condition because of the energy level alignments.

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Figure 5.7 Frontier molecular orbital HOMO diagram of diode molecule

Figure 5.8 Frontier molecular orbital HOMO-1 diagram of diode molecule

HOMO

HOMO-1

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Figure 5.9 Frontier molecular orbital LUMO diagram of diode molecule

Figure 5.10 Frontier molecular orbital LUMO+1 diagram of diode molecule

Figure 5.11 Frontier molecular orbital LUMO+2 diagram of diode molecule-I

LUMO

LUMO+1

LUMO+2

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5.4 DEVICE CHARACTERISTICS OF DIODE MOLECULE-II

Figure 5.12 Optimized geometrical structure of diode molecule II obtained

from the B3PW91/6-31G*

In the following work we design a new intramolecular complex with

donor and acceptor molecular subunits and to explore the possibility of its

working as a diode.

Figure 5.12 shows the optimized geometry of the diode molecule-II.

In particular, we have substituted OCH3 and CN group in the benzene

ring, among the different combinations of donor (OCH3, CH3, NH2) and

acceptor (CN, CF3, NO2). On the basis of the above results, it is of interest to

investigate the electronic structure for a combined molecular complex of these

subunits. An aliphatic group like methylene CH2 or dimethylene CH2 CH2 is

required to be attached between the n-type and p-type molecules to act like a

spacer and form a potential barrier to electron transport across the molecule.

Accordingly, we have decided to use spacers such as CH2 or CH2CH2 between

the donor and acceptor subunits to form an intramolecular donor spacer

acceptor (D-S-A) rectifier. The molecule is attached to two gold leads.

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Figure 5.13 Current - voltage characteristics of diode molecule-II

Figure 5.14 Conductance - voltage characteristics of diode molecule-II

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Figure 5.13 shows the calculated I-V curves, which show that the

device acts as an effective molecular diode. Thus, the current is mostly small,

until the bias voltage approaches 1V, at which point the current begins to rise

steeply.

As quoted before the choice of (X) and (Y) groups can change the

rectifying ratio, the rectifying ratio of this molecule is 1.5. This seen in

Figure 5.13 and Figure5.14.

The workings of this device can be understood from a straightforward

analysis of the molecular levels of the device. For the most part, the donor and

the acceptor portions of the molecule have levels that are well separated from

each other. Hence, electrons tunneling through the CH2 barrier have nowhere

to go, and so the current is small. However, under the influence of a bias of

about 1V, the levels are shifted into alignment. Electrons can therefore tunnel

through these levels and then into the device electrodes signaled by the

subsequent current rise.

For an active device like diode one needs to control the flow of

electrons to obtain the desired electronic properties. In the case of benzene

molecule substituted by an electron donating group, the π electron density is

enhanced and the molecular energy levels typically orient in such a way that

the electrons can flow in one direction while the other direction the flow of

electrons is blocked the frontier molecular orbitals of the molecule under

investigation are plotted from orbitals population densities obtained from the

optimized structure and are presented in figure 5.15, 5.16 and 5.17

The analysis shows stabilized HOMOs and LUMOs. Due to this, this

molecule has lower value of potential barrier . To show electrical rectification,

the molecular energy levels typically orient in such a way that the electrons

can flow in one direction while the other direction the flow of electrons is

blocked.

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Figure 5.15 Frontier molecular LUMO orbital diagram of

diode molecule-II

Figure 5.16 Frontier molecular orbital LUMO+1 diagram

of diode molecule-II

Figure 5.17 Frontier molecular orbital HOMO diagram of diode molecule-II

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5.5 NEGATIVE DIFFERENTIAL RESISTANCE IN MOLECULAR

JUNCTIONS

The discovery of negative differential resistance (NDR) in

semiconductor diode has opened a new chapter in device technology. Through

the use of NDR devices circuits with complicated function can be

implemented with significantly fewer components.

The negative differential resistance is observed in ethynyl phenyl

based organic molecules at room temperatures [82]

We have used a molecule consisting of three aromatic phenyl rings in

series. The two hydrogen atoms of the middle ring are substituted by acceptor

group NO2 and donor group NH2, while the whole molecule is chemisorbed

onto the contact surfaces of gold leads. The optimized geometry is shown in

Figure 5.18

Figure 5.18 Optimized geometrical structure NDR molecule

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Table 5.1 Geometrical parameters (angle) for NDR molecule

Definition Value (degrees) Definition Value (degrees)

C2,C1,C6 118.6052 C18,C19,S39 119.4471

C2,C1,N11 120.8071 C20,C19,S39 119.9428

C6,C1,N11 120.5876 C19,C20,C21 119.6668

C1,C2,C3 120.7142 C19,C20,H25 119.7494

C1,C2,H7 119.4879 C21,C20,H25 120.5833

C3,C2,H7 119.7978 C20,C21,C22 120.0782

C2,C3,C4 119.6124 C20,C21,H26 120.6236

C2,C3,H16 121.2279 C22,C21,H26 119.2978

C4,C3,H16 119.1596 C17,C22,C21 119.9405

C3,C4,C5 120.7446 C17,C22,H27 120.988

C3,C4,N10 119.6106 C21,C22,H27 119.0707

C5,C4,N10 119.6449 H16,H27,C22 158.5336

C4,C5,C6 119.7394 C29,C28,C33 119.4579

C4,C5,H8 119.137 C29,C28,H34 120.3406

C6,C5,H8 121.1236 C33,C28,H34 120.1976

C1,C6,C5 120.5841 C28,C29,C30 120.3802

C1,C6,H9 119.4796 C28,C29,H35 119.4409

C5,C6,H9 119.9362 C30,C29,H35 120.176

C6,H9,H36 145.8164 C29,C30,C31 119.7356

C4,N10,O12 118.4752 C29,C30,H36 120.1553

C4,N10,O13 118.4228 C31,C30,H36 120.1091

O12,N10,O13 123.1021 C30,C31,C32 120.337

C1,N11,H14 120.7991 C30,C31,H37 120.2221

C1,N11,H15 121.5765 C32,C31,H37 119.4395

H14,N11,H15 117.6085 C31,C32,C33 119.4697

C3,H16,H27 112.8626 C31,C32,H38 119.9467

C18,C17,C22 120.237 C33,C32,H38 120.5834

C18,C17,H23 119.5735 C28,C33,C32 120.6123

C22,C17,H23 120.1895 C28,C33,S40 117.7412

C17,C18,C19 119.5141 C32,C33,S40 121.6219

C17,C18,H24 120.7495 H9,H36,C30 40.228

C19,C18,H24 119.7364 C19,S39,H41 97.1422

C18,C19,C20 120.5569 C33,S40,H42 97.0493

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Table 5.2 Geometrical parameters (distance) for NDR molecule

Definition Value (Angstroms) Definition Value (Angstroms)

C1,C2 1.4178 C18,C19 1.3971

C1,C6 1.418 C18,H24 1.0847

C1,N11 1.3637 C19,20 1.3978

C2,C3 1.3829 C19,39 1.8554

C2,H7 1.0856 C20,C21 1.3985

C3,C4 1.401 C20,C25 1.0849

C3,H16 1.0828 C21,C22 1.3986

C4,C5 1.4015 C21,H26 1.0853

C4,N10 1.4341 C22,H27 1.0847

C5,C6 1.3827 C28,C29 1.3979

C5,H8 1.0828 C28,C33 1.3976

C6,H9 1.0849 C28,H34 1.0846

H9,H36 4.982 C29,C30 1.3975

N10,O12 1.2665 C29,H35 1.0852

N10,O13 1.267 C30,C31 1.3977

N11,H14 1.0055 C30,H36 1.0848

N11,H15 1.0106 C31,C32 1.3982

O12,H26 3.3241 C31,H37 1.0853

H16,H27 4.8041 C32,C33 1.3981

C17,C18 1.3992 C32,H38 1.0855

C17,C22 1.3977 C33,S40 1.8475

C17,H23 1.086 S39,H41 1.3797

S40,H42 1.3737

The calculated I-V and G-V characteristics are shown in Figure 5.19

and 5.20. The current voltage characteristics show negative differential

resistance (NDR), which is drop, in the current with increase in voltage in one

direction of the applied voltage. The benzene molecule containing a electron

withdrawing nitro group (NO2), and electron rich amino (NH2) exhibits this

property.

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Figure 5.19 Current - voltage characteristics of NDR molecule

Figure 5.20 Conductance - voltage characteristics of NDR molecule

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Figure 5.21 Frontier molecular orbital HOMO diagram of NDR molecule

Figure 5.22 Frontier molecular orbital HOMO-1 diagram of NDR molecule

Figure 5.23 Frontier molecular orbital HOMO-2 diagram of NDR molecule

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Figure 5.24 Frontier molecular orbital LUMO diagram of NDR molecule

Figure 5.25 Frontier molecular orbital LUMO+1 diagram of NDR molecule

Figure 5.26 Frontier molecular orbital LUMO+2 diagram of NDR molecule

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To understand the electron transport through this molecule we have

analysed the spacial extent of the frontier orbitals (HOMO, LUMO), which

provides a strategy by which the rectifying properties of this molecular system

can be understood. The Figures 5.21, 5.22 and 5.23 show HOMO – k

(k= 0,1,2) and plots of Figure 5.24, 5.25 and 5.26 show LUMO + k (k- 0,1,2)

plots of the molecule. It is observed that while the HOMO -1 and HOMO -2

are localized at the ring 1, the LUMO+1 and LUMO +2 are localized at the

ring3. Both HOMO and LUMO at k=0 are localized on the middle ring.

Therefore in this device electrons are injected from cathode to the LUMO state

on the ring3. The incoming electron of the ring3 is then transferred to the

unoccupied orbital localized on ring1.

Diode-like behavior of the asymmetric molecular complex is not

observed in the case when charging is completely neglected. Within our

model, the mentioned phenomenon is a combined effect of the asymmetric

structure of molecule itself and the charging profile. Current rectification is

due to the presence of chemical substituent groups and their influence on

charge redistribution within the molecular system. Since the location of

substituent is spatially asymmetric with respect to the direction of the current

flow, the response upon the applied bias is also asymmetric in the case of non-

zero charging.

5.6 SUMMARY

The electron transport characteristic of rectifying diodes based on

Aviram Ratner model is investigated. The diode is formed by two sections,

one doped with NH2 and other with NO2 separated by an insulating CH2CH2

group. The current in forward bias of 4V is 8µA and at reverse bias 0f-4V is

4.The rectifying ratio is 1.75. Similar asymmetric behavior is also observed on

a molecular diode reported in [106] using MCBJ setup. The experiment is

focused on 1V measurements at a temperature of 30k, showing clearly

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asymmetric behavior. We have also substituted OCH3 and CN group in the

benzene ring with CH2 as tunneling barrier. This donor-spacer-acceptor shows

a rectifying ratio of 1.5.