1 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, (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

2 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

3 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) SWNT79,000 InSb77,000 Intrinsic Si1,500 1) Nano letter. Vol.4 No (2004) 1)

4 Introduction : CNT-FET Air gap structure Field effect dope Gate CNT Air gap Electric field It is our goal to elucidate physics of a CNT of such a condition theoretically.

5 Introduction : Difficulty of first principle calculation of CNT-FET = Nanotube in a condenser + = Electrostatic Potential Nanotube in a FET = ? Electrostatic Potential = + ? Unit cell

6 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

7 Experimental results – Reference 1 + : :Experimental data ∘ : :Model data from Eq.(1) (1) The peak in correlates with the position of the peak in.

8 Experimental results – Reference 1 (1)

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

10 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.

11 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”.

12 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.

13 Condition of calculation x y z The 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 Gate CNT Gate Unit cell Novel technique 16.3Å Gate CNT d: 6.34Å 10.1Å

14 Semi-conducting tube Electrode Results of calculation Electric field near nanotubes

15 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