AC Performance of Nanoelectronics

Seminar Report 2007-08 AC Performance of Nanoelectronics

ACKNOWLEDGEMENT

I would like to express my profound thanks to The Almighty, without whose grace

I could not have completed this work. I would like to thank Head of the department of

Electronics & communication Engg, for the support during the course of seminar study. I

extend my special thanks to Mr. DINESH BABU M, Mr. RISHIDAS,

Mr. B.S SHAJEE MOHAN Asst. professors, Department of Electronics &

communication Engg., and all other tutors for their all around support.

Last but not least, I express my special thanks to family members especially

parents and friends, who stood with me during tough times and encouraged me.

SREEJISHA. P.P

Dept. of ECE GCE Kannur


ABSTRACT

The study of the ac properties of nano-electronic system is still in its infancy. In

this paper I present an overview of recent work aimed at advancing the understanding of

this new field. Specifically, First discuss the passive RF circuit model of one dimensional

nanostructure as interconnects. Next, discuss circuit models of the ac performance of

active 1d transistor structures, leading to the prediction that THz cutoff frequencies

should be possible. Third, I discuss the radiation properties of 1d wires, which could form

antennas linking the nanoworld to the macroworld.This could completely remove the

requirements for lithographically defined contacts to nanotube and nanowires devices,

one of the greatest unsolved problems in nanotechnology.



CONTENTS1 Introduction 1

2 Nanotube interconnects: Quantum Impedances 2

2.1 Electrostatic capacitance 3

2.2 Quantum capacitance 3

2.3 Kinetic inductance 4

2.4 Band structure, spin degeneracy 5

3 Active Devices: Nanotube Transistors 6

4 Relevant frequency scales 6

4.1 RC time 6

4.2 Transconductance 7

5 Small- signal equivalent circuit 8

5.1 Gate-source capacitance 8

5.2 Transconductance 8

5.3 Drain resistance 8

5.4 Series resistance 8-9

5.5 Parasitic capacitance 9

6 Cutoff frequency 11

6.1 Parasitic capacitance 11

6.2 Scaling with gate length 11-12

7 Nanoantennas 14

7.1 Applications of Nanotube Antennas 14

8 Noise Performance 17

9 Challenges 18

10 Conclusion 19

References 20



Chapter 1

INTRODUCTION

Nano-electronic devices fall into two classes: tunnel devices, and ballistic

transport devices. In tunnel devices, single electron effects occur if the tunnel resistance is

larger than h=e2 _ 25 kX. In ballistic devices with cross-sectional dimensions of order the

quantum mechanical wavelength of electrons, the resistance is of order h=e2 _ 25 kX.

At .rst glance, these high resistance values may seem to restrict the operational speed of

nanoelectronics in general. However, the capacitance for these devices is also generally

small, as is the typical source–drain spacing. This gives rise to very small RC times, and

very short transit times, of order ps or less. Thus, the speed limit may be very large, up to

the THz range.

In this paper we take a more careful look at the general arguments for the speed

limits of nanoelectronic devices. We find that the coupling to the outside world will

usually be slow or narrowband, but that the coupling to other nano-electronic devices can

be extremely fast. A more concrete goal of this paper is to present models and

performance predictions about the e.ects that set the speed limit in carbon nanotube

transistors, which form an ideal test-bed for understanding the highfrequency properties

of nano-electronics because they may behave as ideal ballistic 1d transistors.

Dept. of ECE GCE Kannur1


Chapter 2

NANOTUBE INTERCONNECTS: QUANTUM

IMPEDANCES

The first step towards understanding the high frequency electronic properties of

carbon nanotubes is to understand the passive, ac impedance of a 1d quantum system. So

proposed an effective circuit model for the ac impedance of a carbon nanotube This

model was formulated for metallic nanotubes, it should be approximately correct for

semiconducting nanotube as well.

Figure 2.1 Nanotube over ground plane, used for electromagnetic calculations

In the presence of a ground plane below the nanotube or top gate above the

nanotube, there is electrostatic capacitancebetween the nanotube and the metal. Due to the

quantum properties of the system, however, there are additional components to the ac

impedance: the quantum capacitance and the kinetic inductance. Thus, the equivalent

circuit of a nanotube consists of three distributed circuit elements.

Figure 2.2 Equivalent RF circuit model for a nanotube



2.1 Electrostatic capacitance

The electrostatic capacitance between a wire and a ground plane is given by

CE=2επ/cosh-1(2h/d)

Where the approximation is good to within 1% for h>2d. If the distance to ground

plane becomes larger than the tube length another formula for the capacitance has to be

used, which involves replacing h with the length of the wire. For a typical value of h/d,

this can be approximated numerically as

CE ≈ 50aF/μm

2.2 Quantum capacitance

Because of the finite quantum energy level spacing of electrons in 1d, it costs

energy to add an electron to the system. By equating this energy cost with an effective

quantum capacitance e2/CQ , one arrives at the following expression for the capacitance

per unit length:

CQ=e2/ħπvF

Where his planks constant and vF is the Fermi energy. The Fermi velocity for graphene

and also carbon nanotube is usually taken as 8*105 m/s.so that numerically,

CQ ≈ 100aF/ μm

2.3 Kinetic inductance

Due to the inertia of electrons, the instantaneous velocity lags the instantaneous

electric field in time. This means the current lags the phase, which can be described as a

kinetic inductance. For 1d system we have the following expression for the kinetic energy

per unit length:

LK=ħπ/e2vF



Numerically,

LK=16nH/ μm

This shows that in 1d system, the kinetic inductance will always dominate

magnetic inductance. This is an important point for engineering nanoelectronics: In

engineering macroscopic circuits, long thin wires are usually considered to have relatively

large magnetic inductance. This is not the case in nanowires, where the kinetic inductance

dominates. This inductance can in principle be used as a part of a tank circuit for on-chip,

GHz passive signal processing components, currently under development.

2.4 Band structure, spin degeneracy

A carbon nanotube, because of its band structure, has two propagating

channels .In addition the electrons can be spin up or spin down. Hence there are four

channels. The above circuit model is still valid as an effective circuit model for the

charged mode if LK is replaced by LK/4 and CQ is replaced by 4CQ. Thus the ac impedance

of a nanotube consists of significant capacitive and inductive elements in addition to the

real resistance which must be considered in any future nano-electronics system

architecture.



Chapter 3

ACTIVE DEVICES: NANOTUBE TRANSISTORS

Typical nanotube transistor geometry is shown below

Figure 3.1 Typical nanotube transistor geometry

In contrast to silicon transistors, the fundamental physical mechanism responsible

for transistor action in nanotube transistor is still not completely understood. One action

of the gate may be to modulate the (schottky barrier) contact resistance. Experiments also

indicate that the source drain voltage drops at least in part along the length of the

nanotube, indicating that the contact s only one important element of the total source-

drain resistance.



Chapter 4

RELEVANT FREQUENCY SCALES

We begin by estimating the frequency scales for the most important processes: the

RC time and the transconductance.

4.1 RC time

The first important effect for high frequency performance is the RC time. For

typical nanotube geometry of 0.1µm length is of order 4Af. R can be as small as

6.25kᾩ.Therfore; the RC frequency is given by

1/2πRC ≈ 6.3THz

This shows that the speed limit due to RC times intrinsic to a nanotube transistor

is very large indeed.

4.2 Transconductance

The conductance gm over the gate-source capacitance Cgs sets another important

frequency. Using an experimentally measured value of 10µS, this gives

gm/2πCgs ≈ 400GHz

The above estimate indicates that a carbon nanotube transistor could be very fast,

in spite of its high impedance. For more realistic estimate of device performance a small

signal equivalent circuit model would be very useful, especially for input and output

impedance calculations and in order to investigate the effects of parasitic impedance on

device performance.



Chapter 5

SMALL- SIGNAL EQUIVALENT CIRCUIT

In this section, propose a small signal equivalent circuit model based on known

physics in the small signal limit a generally common behavior for all field effect type

devices. Our proposed active circuit model is not rigorously justified or derived. But we

can capture essential physics of device operation and at the same time provide simple

estimates of device performance.

Figure 5.1 Proposed small signal equivalent circuit model for transistor geometry.

Here shows the predicted small signal circuit model or a nanotube transistor. In

the following section discuss each of the important components.



5.1 Gate-source capacitance

The capacitance of a passive nanotube in the presence of a gate was discussed

extensively in the first section; this can be used as an estimate of the gate-source

capacitance Cgs in active mode; shown above. This capacitance includes the geometrical

capacitance (50Af/µm) in series with the quantum capacitance; the quantum capacitance

is multiplied by 4 because of the band structure degeneracy. Thus:

1/Cgs ≈ 1/ CE+1/4 CQ=1/44 aF/ μm

5.2 Transconductance

While the transconductance is the most critical parameter, the underlying

mechanism is the least understood. In order to predict device high frequency

performance, we use experimental data from dc measurements as our guide. We show in

table1 data from various research groups measured to date.Transconductance up to 20µs

have been measured [12], using an aqueous gate geometry. A transconductance of 60µs

was recently predicted [13, 14] by simulation.

5.3 Drain resistance

In the equivalent circuit model gd represents the output impedance of the device, if

it does not appear as an ideal current source. In table 1 (from Refs [9, 11-13, 15-18]), we

present some representative values from the literature which we have determined from the

published source-drain I-V curves.

5.4 Series resistance

In most conventional transistors the series resistance of the metallization layer and

the ohmic contact resistance. We argue that, in nanotube transistors, the intrinsic contact

resistance will be of order the resistance quantum because of the 1d nature of the system.

At dc, the lowest value of resistance possible for a carbon nanotube is h/4e2 . This

is because there are four channels for conductance in the Landauer-Buttiker formalism,

each contributing h/e2 to the conductance. To date very little experiment work has been



one to measure the ac impedance of ballistic system. From a theoretical point of view

scientists have carefully analyzed the case of capacitive contact to a ballistic conductor in

contact with one dc electrical lead through a quantum point contact. They find that the ac

impedance from gate to lead includes a real part, equal to half the resistance quantum

h/2e2 . Based on this work argue that a reasonable value for the contact resistance in our

small-signal model would be h/2e2 per channel. Since there are four channels in parallel,

this gives a contact resistance of h/8e2 . There will be an additional imaginary contribution

to the contact impedance due to the kinetic inductance on the order of a few nano henry.

5.5 Parasitic capacitance

The parasitic capacitance is due to the fringing electric fields between the

electrodes for the source, drain and gate. While these parasitic capacitance are generally

small, they may be comparable to the intrinsic device capacitance and hence must be

considered. There are no closed –form analytical predictions because the geometry of the

electrodes will vary among different electrodes designs. In order to estimate the order of

magnitude of the parasitic capacitance, we can use known calculation for the capacitance

between two thin metal films, spaced by a distance w, as shown in below figure.

For this geometry, if w is 1µm the capacitance is 10-16 F/µm of electrode

length .For a length of 1µm, this gives rise to 10 -16 F. Thus, typical parasitic capacitances

are of the same order of magnitude as typical intrinsic capacitance.


Figure 5.2 Typical geometry giving rise to parasitic capacitors




Chapter 6

CUT-OFF FREQUENCY

This section provides estimates of the cutoff frequency fT , a standard yardstick for

transistor high speed performance, defined as the frequency at which the current gain falls

to unity. Based on the circuit model in figure 4 it can be shown that fT is given by:

1/2πfT=(RS+RD)Cgd,p+1/gm(Cgs+ Cgd,p+ Cgd,p)+gd/ gm(RS+RD)( Cgs+ Cgd,p+ Cgd,p)

Here the p subscript denotes “parasitic” .Using the experimentally measured

transconductance of 10µs, a parasitic capacitance value of 10-16 F, and a Cgs of 4*10-17 F

predict a cutoff frequency of 8GHz. For this value, the parasitic capacitance is the most

important contribution. Thus, minimizing the parasitic capacitance is of prime importance

in increasing fT for nanotube transistors.

6.1 Parasitic capacitance

While the above calculation show that the parasitic capacitance is important, in

principle it should be possible to significantly reduce the parasitic capacitance by detailed

electrode geometry design. Another way to reduce the parasitic capacitance would be to

use the nanotube itself as an interconnect electrode from one nanotube transistor to

another. Then, the parasitic capacitance would be dramatically smaller than that with

lithographically fabricated electrodes.

6.2 Scaling with gate length

If we assume the parasitic capacitance can be reduced to negligible values the

above equation simplifies to

1/2πfT=Cgs/ gm

Cgs scales linearly with gate length, and was calculated above. In the ballistic limit,

gm should be independent of gate length. Using the largest measured transconductance to

date of 20µs; this gives rise to the following prediction for fT:

fT=80GHz/Lgate(μm)



We plot in FIG 6. Our predictions for fT vs. gate length for a nanotube transistor,

and compare to other technologies. The predictions are very promising, suggesting that a

nanotube transistor with THz cutoff frequencies should be possible.



Figure 6.1 Predicted scaling of fT with gate length



Chapter 7

NANOANTENNAS

Since the wavelength of microwaves of order cm, and since we have recently been

able to synthesize electrically continuous and electrically contacted single- walled

nanotubes of order cm in length, it I appropriate to consider their possible use as nano-

antennas.In this spirit we recently developed a quantitative theory of nanowires and

nanotubes as antennas. Below, we elaborate on potential applications of these

nanoantennas

7.1 Applications of Nanotube Antennas

7.1.1 A solution to the nanointerconnect problem

Progress to date on nanoelectronics has been significant. Essentially all devices

needed to make the equivalent of a modern digital or analog circuit out of nanotubes

and/or nanowires have been demonstrated in prototype experiments and elementary logic

circuits have been demonstrated .However, one of the most important unsolved problem

in nanotechnology is how to make electrical contact from nanoelectronic devices to the

macroscopic world, without giving up on the potential circuit density achievable with

nanoelectronics. All of the nanotube and nanowire devices developed to date have been

contacted by lithographically fabricated electrodes. A canonical research theme is to

fabricate a nanodevice, contact it with electrodes fabricated with electron beam

lithography, then publish a paper reporting the electrical properties. This is not a scalable

technique for massively parallel processing, integrated nanosystems. The potential high

density circuitry possible with nanowires and nanotubes will not be realized if each

nanowire and nanotube is connected lithographically.

One potential solution to this problem is to use wireless interconnects, which can

be densely packed. If each interconnect is connected to a nanotube of a different length

(hence different resonant frequency), then the problem of multiplexing input/output

signals can be translated from the spatial domain to the frequency domain, hence relaxing

the need for high resolution (high host) lithography for interconnects. This is in contrast



to previous approaches which ultimately rely on lithography and its inherent limitations

to make electrical contact to nanosystem.This idea is indicated schematically in Fig 7

Figure 7.1 Possible architecture for a non-lithographic, wireless connection from the

nanoworld to the macroworld.

7.1.2 Wireless interconnect to nano-sensors

Another application is in the area of sensing. For example, nano-devices could be

use as chemical and biological sensors, sensitive to their local chemical environment. A

nanotube could be used as an antenna to couple to these nano-sensors, without the need

for lithographically fabricated electronics.



7.1.3 Unsolved problems in nano-antennas:

Transition from nano-antenna to thin- wire antenna. Our recent theory applies

only to quantum mechanically 1-d nanowires and nanotubes. A future problem, which has

not been solved yet, is to determine the transition from nano-antenna behavior to thin –

wire behaviour.This problem is germane to, for example multi walled nanotubes and also

nanowires not in the strict 1d limit. Additionally it may shed light on loss mechanism in

thin metallic antennas whose size approaches the nano-domain.



Chapter 8

NOISE PERFORMANCE: TOWARDS THE QUANTUM

LIMIT?

One promising potential application is in low noise analog microwave

amplification circuits. Recent work on noise in mesoscopic system has been extensive

and has shown suppressed noise due to the Pauli exclusions principle, since electrons can

travel without scattering from source to drain, and the Pauli exclusions principle

suppresses the current noise, it may be possible to engineer extremely low noise

microwave amplifiers using carbon nanotubes, possibly even approaching the quantum

limit of sensitivity.



Chapter 9

CHALLENGES: IMPEDANCE MATCHING

Nano-devices generally have high resistance values, of order the resistance

quantum RQ =h/e2. At high frequencies, for driving circuits more the one electromagnetic

wavelength away from the device, the load impedance is typically of order the

characteristic impedance of free space, ZC = (µέ)1/2 =377ᾩ.The ratio of ZC /RQ =1/377 has

a special significance in physics and is called the fine structure constant; it is set by only

three fundamental constants of nature: e, h,c. For electrical engineering, this means that

nanodevices fall always need impedance matching circuits when driving loads mi\ore

than a few cm away at RF and microwave frequencies.

Integration can provide a solution to this problem. For nanoelectronic devices

closely spaced down to the nanoscale, the capacitive loading from one device to the next

can be minimized. For full effect, the interconnects should be nanoscale as well;

lithographically fabricated interconnects may be too large to realize the full potential of

nano-electronics.Our work on the high frequency electrical properties of active and

passive nanodevices provides a very small step towards achieving this ultimate goal of

integrated nanosystems.



Chapter 10

CONCLUSION

Modeling and predictions for nanoelectronics as interconnects, transistors, and

antennas. It is clear that nano-electronic devices can fulfill all three roles, with

outstanding predicted performance. Then we can predict carbon nanotube transistor may

be faster than conventional semiconductor technologies. There are many challenges that

must be overcome to meet this goal, which can be best be achieved by integration of

nanosystems.Future work remains to be done on understanding non-linear- nano-

electronic devices for applications such as mixers and detectors.



REFERENCES

Burke PJ. An RF circuit model for carbon nanotubes. IEEE Trans Nanotechnol

P.J. Burke – Carbon nanoelectronics technology

1. www.wikipedia.com

2. www.cientifica.com


http://www.cientifica.com/

http://www.wikipedia.com/

Documents

AC Performance of Nanoelectronics