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Recent studies on a single-walled carbon nanotube transistor

Reference ：(1) Mixing at 50GHz using a single-walled carbon nanotube transistor,

S.Rosenblatt, et al, Appl. Phys. Lett. 87, 153111 (2005).

(2) First-principles calculation of charged surfaces/interfaces : a planewave non-repeated slab approach,

M. Otani and O. Sugino, preprint.

Suzuki-Kusakabe Lab.

Yoshihisa MINAMIGAWA

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Contents

• Introduction– background knowledge of CNT-FET

• Experimental results – Reference 1

• Novel calculation technique - Reference 2

• Results of calculation

• Summary

CNT-FET : Carbon nanotube Field effect transistor

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Introduction : CNT-FET

• Reason that SWNT is used in FET– High charge mobility

– Nano size structure · diameter : 1~few nano meters · length : ~1µm

Charge mobility (cm^2/V·s)

SWNT 79,000

InSb 77,000

Intrinsic Si 1,500

1) Nano letter. Vol.4 No.1 35-29 (2004)

1)

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Introduction : CNT-FET

• Air gap structure

• Field effect dope

Gate

CNT

Air gap

Electric field

ee ee e

It is our goal to elucidate physics of a CNT of such a condition theoretically.

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Introduction : Difficulty of first principle calculation of CNT-FET

- - -

+++

- - -

+++ + =

Nanotube in a condenser

+ =Electrostatic

Potential

++++

Nanotube in a FET

=

?

++++

+

Electrostatic Potential =+?

Unit cell

Unit cell

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Experiment : CNT-FET

Nanotube Contact layer : 50nm thick Pd

Gate : 2 μm width Al

Source and Drain : Au , Au-Pd alloy

Source-Drain contact gap : 3 μm

Mixer circuit

HR-Si : High resistively Si

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Experimental results – Reference 1

mixI+ : :Experimental data

elImod∘ : :Model data from Eq.(1)

(1)

The peak in correlates with the position of the peak in .

mixI

gdc VG /

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Experimental results – Reference 1

(1)

acsmix VI log2log

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Relation of experiment and calculation

When Source-drain bias is enough small, conductance can be provided by Greenwood-Kubo formula from wave function or charge density.

SVdcG

If under various is calculated, we expect that will enable theoretic analyses of CNT-FET.

dcG gV

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Novel calculation technique - Reference 2

• Main techniques of First principle calculation– APW (Augmented plane wave) method– KKR (Korringa-Kohn-Rostoker) method– Pseudo potential method– Real space method

APW, KKR and Pseudo potential method has credibility and much know-how. But, these are only used under a periodic boundary condition.

Real space method don’t need a periodic boundary condition. But, Know-how of this method is not enough.

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Novel calculation technique - Reference 2

• This novel technique’s character is…– Using Pseudo Potential method– Periodic boundary condition is not necessary

in one direction.– To place “a virtual electrode” is possible.

We can do high precision simulating “CNT-FET”.

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Novel calculation technique - Reference 2

: Electrostatic potential

: Green function

: Total electron charge density

(2)

: relative permittivity

(3)

Eq(2) and Eq(3) are solution of Poisson equation under a condition that x and y direction is uniformity.

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Condition of calculation

xy

zThe same structure repeat to direction of x and y axis.

The same structure repeat to direction of x, y and z axis.

Unit cell

Until now

GateCNTGate

Unit cell

Novel technique

16.3Å

16.3ÅGateCNT

d: 6.34Å

10.1Å

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Semi-conducting tube

Electrode

Results of calculation

Electric field near nanotubes

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Summary

• We can calculate the state of CNT which charge doped by the field effect.

• To calculate conductance G in a state of nearly zero bias( ).

Next work

0sV