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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