Molecular Circuit Design

Leone Pereira Masiero, Marco Aurélio C. Pacheco, Carlos R. Hall Barbosa

{masiero, marco, hall}@ele.puc-rio.br

Cristina Costa Santini

ccs500@ohm.york.ac.uk

ICA: Laboratory of Applied Computational Intelligence,

Electrical Engineering Departament, PUC-Rio

R. Marques de S. Vicente 225, Gávea, Rio de Janeiro, CEP 22453-900, RJ, Brasil

Abstract

In the last years, with a more realistic vision of a possible limit for miniaturization of components with conventional CMOS technology, a new technology has surfaced - the Molecular Electronics which, from the bottom-up approach, aims at the construction of electrical devices to implement computation using individual or small collection of molecules, offering an alternative way to build nanoscale circuits. These circuits have the potential to reduce device size and fabrication costs by several orders of magnitude relative to conventional CMOS. Recently, some mechanisms have been considered as a basis to molecular electronic systems design. Two terminal molecular devices that work as diodes have been synthesized, with similar behavior to rectifying and tunnel diodes. In this article, a study on the synthesis of molecular circuits is presented, integrating simulated molecular devices as the Molecular Tour-Reed Diode based on the Evolvable Hardware (EHW)

paradigm.

1 Introduction

The Law of Moore [1] states that the number of

transistors used in integrated circuit doubles each two

years. Due to this exponential growth, the limit of

miniaturization of components based on conventional

CMOS technology is about to be reached, determining

the end of the increasing of the processing power of

electronic equipment. However, due to the sprouting

of a new technology - the Molecular Electronics [2] -

it is now possible to build equipment with reduced

size and low cost of manufacture in relation to

conventional CMOS technology, by using molecules

or group of molecules [3]. In this way, the growth of

processing power of electronic equipment can be kept.

Molecular electronic devices offer many

advantages in relation to CMOS devices, including

integration in very smaller areas and fast response

time. The Molecular Electronics (figure 1) is a field

that combines the efforts of biologists, biomedical

chemistries, physicists, mathematicians, scientists,

engineers, etc. The molecules that are used to build

molecular systems are capable to lead and to transfer

energy between them. If the process can be

manipulated and controlled, it is possible to make

structures that execute tasks for information

processing. This includes basic circuit tasks, such as

codifying, to manipulating and storing information.

With all the knowledge of chemistries and

biochemists, there is a great number of possibilities to

search molecular structures for signal processing.

This means that enough possibilities of structures and

mechanisms exist, at least in the theory, where they

can be used to carry through the necessary functions at

the molecular level.

Figure 1 – Molecular Electronics – a vast field.

Proceedings of the 2005 NASA/DoD Conference of Evolution Hardware (EH’05) 0-7695-2399-4/05 $ 20.00 IEEE

Figure 2 – I(V) characteristic of three different Tour-Reed molecular NDR devices and two load lines. The x axis’ unit is Volts and the y axis’ unit is Ampere.

This concept seems to be easy in principle, but the

main problem is to synthesize safe and efficient

molecular systems. In this work, the molecular

structure studied and used to synthesize the circuits is

the Molecular Tour-Reed Diode.

This paper proposes an architecture to the design

and synthesis of molecular circuits based on the

Evolvable Hardware (EHW) [13-15] technique. The

design and implementation challenges for molecular

circuits are presented and the EHW technique is

discussed as a promising approach to overcome those

challenges. In this paper, another study was made to

allow the design and synthesis of molecular circuits

using the same molecular diodes, taking into

consideration the variation of the behavior of the I(V)

curve of these diodes. The schematic circuit presented

in this paper is very simple, but the aim of this study

was to demonstrate that it is possible to synthesize

molecular circuits using the EHW. In the following

sections, the process of synthesis of the circuits and

results are presented, followed by a conclusion on the

work [1-7].

2 The Tunnel Diode and the Molecular Tour-Reed Diode

The advantages that make the tunnel diode an

important switching device have arisen because of the

quantum-mechanics tunnelling principle involved in

producing the negative-resistance characteristic [8].

The two-terminal current-carrying molecular

Tour-Reed diode has a current-voltage response

similar to that of the Rectifying Tunnel Diode (RTD).

The primary characteristic of the RTD current-voltage

(I-V) response is the appearance of a region known as

negative differential resistance (NDR). When a device

exhibiting NDR is placed in series with a resistor and

a voltage source, a bistable latch can be created. As

shown in figure 2, the load line will intersect the I(V)

curve of the NDR device in three locations. The

intersection with the NDR regions is unstable, leaving

only two stable operating points (the two stars in

figure 2). The molecular device has a peak current of

approximately 1nA, a valley current of approximately

1pA and a peak-to-valley current ratio of 1030:1.

The magnitude and position of the current peak

differs from device to device. These differences do not

result in large variations in the required load resistor,

but have a significant impact on the assembled circuits

[6].

2.1 Determining the Load Line

There is a trade-off when determining the

appropriate value for the load resistor. If too small, the

latch could only have one stable state if the device

current peak shifts slightly to the left. In addition, a

resistor too small will result in minimal separation

between the high and low voltage states in the latch. In

order to increase the separation between these two

states, a much larger resistor is required, one that

might not be chemically synthesizable.

If these molecular devices exhibiting NDR are to

be assembled into bistable latches with consistent

voltage states across an entire chip, molecular resistive

elements on the order of several hundreds of mega

ohms will need to be synthesized and integrated into

the circuits.

In addition, variations in the current peak

magnitude and position should be kept to a minimum

in order to ensure that two stable points of operation

occur, and that those two points are consistent from

latch to latch [5].

This is a straightforward example to which the

EHW technique can be applied and evaluated, due to

its already studied and proved potential to evolve and

synthesize analogue circuits. It is yet too hard or even

impossible to correspond to these desired restrictions

in order to build a functional circuit integrating

millions of molecular devices.

Proceedings of the 2005 NASA/DoD Conference of Evolution Hardware (EH’05) 0-7695-2399-4/05 $ 20.00 IEEE

2.2 Simulation

SPICE simulations of circuits based on resonant

tunnelling diodes (RTDs) with a current-voltage

response similar to that of a Tour-Reed molecular

diode have been made. A bistable latch circuit model

has been created in [5] using a voltage-current source

that corresponds to the Tour-Reed molecular diode, as

shown in figures 3 and 4. From that circuit model, we

have created our circuit model.

Figure 3 – The bistable latch circuit model.

Figure 4 - Input V(1) and output V(2) of the molecular diode circuit which characteristic I-V curve A is represented in Figure 2.

3 Inverter circuit based on the molecular diode

In order to illustrate the effects of the variations

on the characteristic curve of the molecular diode, as

shown in figure 2, some inverters have been simulated

and its topology is shown in figure 5.

Inverter 1

The values of the resistors R1 and R2 (Rload) in

figure 5 have been defined respectively as 373M and

10M . The voltage controlled current source, the G1

element in figure 5, has a peak current of 1.03nA in a

voltage of 2.12V, corresponding to the characteristic

I(V) curve A represented in figure 2.

Figure 5 - Inverter circuit.

Figure 6 – Output and input of the inverter circuit in Figure 5. The stronger curve is the output of the circuit and the lighter is the input current, measured respectively at the points ‘out’ and ‘in’ of the circuit shown in figure 5.

Inverter 2

In order to experiment what would have happened

to the inverter circuit if the molecular diode

represented as the G1 element in figure 5 had the

characteristic I(V) curve B shown in figure 1, with

peak current 0.93nA and 2V, Spice simulations of the

same circuit represented in figure 5 have been made.

As shown in figure 7, the circuit’s output does not

represent an inverter function anymore, confirming

what have been exposed in [5], that the differences in

the magnitude and position of the current peak can

have a significant impact on the assembled circuits.

Proceedings of the 2005 NASA/DoD Conference of Evolution Hardware (EH’05) 0-7695-2399-4/05 $ 20.00 IEEE

The EHW technique presents characteristics that

make it a promising technique to be applied to

molecular electronics, in order to overcome challenges

with the implementation of circuits based on

molecular devices, such as precision. To evaluate this

proposed approach, the values of the resistances of an

inverter circuit based on the Tour-Reed molecular

diode have been automatically determined. This

experiment is described in the following section.

Figure 7 – Output and input of the inverter circuit with the shifted I(V) curve.

4 Tests

The two first tests described in this section aimed at

finding the values of the resistances of the inverter

circuit based on the tunnel diode with the molecular

Tour-Reed diode characteristic curve. To run those

experiments the following parameters of the Genetic

Algorithm (GA) were used:

Generations: 50

Population: 20

Steady State: 2

Crossover: 0.7

Mutation: 0.9

Exponential Normalization c=0.9

Inverter 1

In this test, the tunnel diode was set to correspond to

the molecular diode described by the characteristic

I(V) curve A in figure 2, with Ip=1.03nA and 2.12V.

The GA found that the inverter circuit with the best

evaluation after 50 generations had the resistances

values R1=600M and R2(Rload)=7 . The input and

output signals of this circuit are shown in figure 8.

Inverter 2

In order to finally evaluate the EHW technique when

applied to the implementation and design of circuits

based on molecular electronics, mainly when these

devices precision is concerned, the same inverter

circuit has been simulated, based on a molecular diode

described by the characteristic curve B in figure 2,

with Ip=0,93nA and 2V.

Figure 8 – Output (stronger curve) and input of the inverter circuit in figure 5, with the diode I(V) curve with Ip=1.03nA a 2.12V.

Figure 9 – Output (stronger curve) and input of the inverter circuit in Figure 5, with the diode I(V) curve with Ip=0.93nA a 2V.

Proceedings of the 2005 NASA/DoD Conference of Evolution Hardware (EH’05) 0-7695-2399-4/05 $ 20.00 IEEE

The values of the resistances found by the GA that

correspond to the inverter circuit with best evaluation

are R1=800M and R2(Rload)=800 . The input and

output signals of this circuit are shown in figure 9.

Therefore, the GA has been able to find the

different resistance values that made possible the

inverter circuit to continue working even when the

molecular diode performs differently, proving the

flexibility and applicability of the proposed approach.

The third test was made by varying the diode I(V)

curve. This variation was made using a cumulative

normal distribution with average µ and variance . A

list with 10 values of V is calculated through one same

cumulative normal distribution, or either, 10 values of

voltage that determine the position of the peak of the

curve. For each value of the list, one diode curve was

generated and used by the circuit designed through the

genes of the chromosome. The chromosome

evaluation was the average of the evaluation of the 10

circuits generated through the curves.

The values of µ and are respectively 2.14V and

0.5V. The value of µ is defined by the curve of figure

2, where the current of maximum peak is in V = 2.14.

The figures 10, 11, 12, 13 and 14 present the results of

this third test.

0.00E+00

2.00E-10

4.00E-10

6.00E-10

8.00E-10

1.00E-09

1.20E-09

0.00

E+0

0

3.00

E-0

1

6.00

E-0

1

9.00

E-0

1

1.20

E+0

0

1.50

E+0

0

1.80

E+0

0

2.10

E+0

0

2.40

E+0

0

2.70

E+0

0

3.00

E+0

0

3.30

E+0

0

3.60

E+0

0

3.90

E+0

0

4.20

E+0

0

4.50

E+0

0

4.80

E+0

0

Input

Output

Figure 10 – Curve with peak current at V = 2.14V -0.15V.

0.00E+00

2.00E-10

4.00E-10

6.00E-10

8.00E-10

1.00E-09

1.20E-09

0.00E

+00

3.00E

-01

6.00E

-01

9.00E

-01

1.20E

+00

1.50E

+00

1.80E

+00

2.10E

+00

2.40E

+00

2.70E

+00

3.00E

+00

3.30E

+00

3.60E

+00

3.90E

+00

4.20E

+00

4.50E

+00

4.80E

+00

Input

Output

Figure 11 – Curve with peak current at V = 2.14V - 0.1V.

0.00E+00

1.00E-10

2.00E-10

3.00E-10

4.00E-10

5.00E-10

6.00E-10

7.00E-10

8.00E-10

9.00E-10

0.00

E+0

0

3.00

E-0

1

6.00

E-0

1

9.00

E-0

1

1.20

E+0

0

1.50

E+0

0

1.80

E+0

0

2.10

E+0

0

2.40

E+0

0

2.70

E+0

0

3.00

E+0

0

3.30

E+0

0

3.60

E+0

0

3.90

E+0

0

4.20

E+0

0

4.50

E+0

0

4.80

E+0

0

Input

Output

Figure 12 – Curve with peak current at V = 2.14V.

0.00E+00

1.00E-10

2.00E-10

3.00E-10

4.00E-10

5.00E-10

6.00E-10

7.00E-10

8.00E-10

9.00E-10

0.00

E+0

0

3.00

E-0

1

6.00

E-0

1

9.00

E-0

1

1.20

E+0

0

1.50

E+0

0

1.80

E+0

0

2.10

E+0

0

2.40

E+0

0

2.70

E+0

0

3.00

E+0

0

3.30

E+0

0

3.60

E+0

0

3.90

E+0

0

4.20

E+0

0

4.50

E+0

0

4.80

E+0

0

Input

Output

Figure 13 – Curve with peak current at V = 2.14V + 0.1V.

0.00E+00

1.00E-10

2.00E-10

3.00E-10

4.00E-10

5.00E-10

6.00E-10

7.00E-10

8.00E-10

9.00E-10

0.00

E+0

0

3.00

E-0

1

6.00

E-0

1

9.00

E-0

1

1.20

E+0

0

1.50

E+0

0

1.80

E+0

0

2.10

E+0

0

2.40

E+0

0

2.70

E+0

0

3.00

E+0

0

3.30

E+0

0

3.60

E+0

0

3.90

E+0

0

4.20

E+0

0

4.50

E+0

0

4.80

E+0

0

Input

Output

Figure 14 – Curve with peak current at V = 2.14V + 0.15V.

The values found for R1 and RLoad were

respectively 4.09 x 108.63 and 3.13 x 10-12.74 . The

values of the parameters of the GA were the following

ones:

Generations: 20

Population: 40

Crossover: 0.65

Mutation: 0.7

Steady state: 0.20

In the following section these results will be

discussed thoroughly in relation to the desired

Proceedings of the 2005 NASA/DoD Conference of Evolution Hardware (EH’05) 0-7695-2399-4/05 $ 20.00 IEEE

characteristics of an architecture aimed at the design

and implementation of circuits based on molecular

electronics.

5 Conclusions and future works

There is a concern that is frequently pointed out

by researchers that aim at building functional devices

based on molecular electronics [5][9-12]: many

devices such as resistors, capacitors and two-terminal

non-linear devices would have to be synthesized with

a high degree of precision and then interconnected in

varying degrees of complexity.

In order to overcome those design and

implementation challenges, architectures that could

implement logical functions without the need for

precise molecular devices and complex synthesis

techniques would be desirable.

The proposed approach based on EHW presents

those desirable characteristics, which have already

been studied, discussed and presented in the solution

of different problems. Generally speaking, as it has

been experienced in [13-15], EHW has the ability to

explore the intrinsic characteristic of the elements,

presenting analogue circuits’ configurations which are

beyond the scope of conventional design

methodologies. Robust circuits can be synthesized

using the Tour-Reed molecular diode as it was showed

in third test.

In this paper, initial simple experiments have been

presented. However, they were able to show that

EHW can be a promising technique when applied to

Molecular Electronics. Beyond the inverting circuit,

we also intend to synthesize gates NAND and NOR.

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