Extended Abstracts of the 2003 International Conference on Solid State Devices and Materials, Tokyo, 2003, pp. 800-801

D-7-1

Characteristics of a FET Analyzed as a Ballistic FET

Youji Kimura1, Tomo Shimizu1 and Kenji Natori 1,2

1Institute of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan Phone: +81-298-53-5311, Fax: +81-298-53-5205 E-mail: [email protected] 2CREST, JST

1. Introduction is the quantum conductance (77μS), and E0, E1, etc. are the

Recently, carbon nanotube (CN) FETs attract wide subband bottom energies. The bias VG is represented by the attention as a promising candidate of component device for level of μ in the figure. Note that the slope of the curve

the next generation electronics. Both the n- and p-channel varies according as integer-times of G0. device are already fabricated and a high performance per unit width is reported. A metallic CN is believed to enjoy a 2. Ballistic Carbon Nanotube FET Characteristics ballistic conduction[1], and a CN FET may also show a The single-walled carbon nanotube (SWNT) is a ballistic conduction if carefully made so that the channel one-dimensional tube-like nanowire that consists of carbon length is less than the carrier mean free path. The fabricated atoms, and the band structure is easily derived from that of samples are reported to show a high current level of several the two-dimensional sheet[8]. Fig. 3 shows the μA [2][3][4] in spite of a large voltage drop at the contact band structure of (19,0) SWNT which is semiconductive, for to electrodes. The conduction mechanism is not clear at example. With use of the general theory of a ballistic present. One case is analyzed as the Schottky barrier FET nanowire FET as well as the band structure of SWNT, the while the other asserts the bulk nanotube conduction current voltage characteristics of the CN FET are derived. dominates. Since the performance is improved year by year Fig. 4 shows a schematic cross section of the device. A

in pursuit of ballistic conduction, it is pertinent to the high-k gate dielectrics with ε=40ε0 is assumed in view of occasion to discuss the ballistic CN FET characteristics. TiO2 or others with thickness of 2nm. Fig. 5 and 6 are the This paper presents the I-V characteristics of a ballistic CN derived |I|-|VD| and |I|-|VG| characteristics of a (19,0) SWNT FET derived from the band structure for the first time, and FET (p-type, diameter 1.5nm) at T=0, respectively. Note that reports a surprisingly high performance per unit width both curves show a linear-like behavior with a gentle slope,

compared with the ballistic MOSFET[5][6]. First, a although the |I|-|VD| curve shows current saturation. The kink general theory of a nanowire FET is derived, and then the structure is due to abrupt change of the number of

result is applied to a CN FET. contributing subbands. The linear-like behavior of |I|-|VD| shows a sharp contrast to that of silicon MOSFET which is

2. I-V Characteristics of a Ballistic Nanowire FET rectangular. The current level of 200μA at VG~VD~1V The electronic state of a nanowire is known to consist of corresponds to 130mA/μm per unit width. This value is ~50 one-dimensional subbands, each piece of which has the times the value of a silicon ballistic nMOSFET, and shows a

maximum and the minimum energy denoted by Emax and Emin, surprisingly high potentiality of a CN FET performance. Fig.

respectively, in the Brillouin zone. By use of the Landauer’s 7 is the carrier density n per unit length as a function of |VG|, formula, the electric current I is derived as in the 1st equation and Fig. 8 the drift velocity at the beginning of the channel 7 in Fig. 1, where VD is the drain bias, μ the Fermi energy of (Vinj) as a function of n. The value n~1.1×10 /cm in Fig. 7 the source. The 2nd equation of Fig. 1 prescribes relation gives 7×1013/cm2 per unit area, and ~7 times the silicon 13 2 between the applied gate bias VG and the carrier charge. nMOSFET value (10 /cm ) with SiO2 gate dielectrics. The f(μ,E) and D(E) are respectively the Fermi function and the reason that the high-k dielectrics induces the carrier number

density of state of the subband. The threshold voltage Vt and of only 7 times as much as that of silicon MOS is that the μ0 are the value of VG and μ in flat band condition. The quantum capacitance dominates the result. The carrier 8 term (μ-μ0)/q on the left hand side gives the contribution velocity 1.1×10 cm/s in Fig. 8 is ~7 times that of silicon from the quantum capacitance[7] due to the density of state, nMOSFET(1.6×107cm/s). The extremely high current level unlike the case of silicon MOSFET. Eliminating μ from per unit width in a ballistic SWNT FET is shown to be due these two equations, I is expressed in terms of applied to both the large drift velocity and also the large carrier

voltages. Fig. 2 illustrates general features of the I-VD density. 2 characteristics at T=0 of a ballistic nanowire FET. G0=2q /h

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4. Conclusion [1] T.Ando et al., J. Phys. Soc. Jpn, 67, 2857 (1998). A general expression of a ballistic nanowire FET is [2] S. J. Wind et al., Appl. Phys. Lett., 80, 3817 (2002). derived, and the I-V characteristics of a ballistic CN FET are [3] A. Javey et al., Nature Materials, discussed. A ballistic CN FET shows a high current level per [4] F. Nihey, Private communication. unit width as large as ~50 times that of a ballistic silicon [5] K. Natori, J. Appl. Phys. 76, 4879 (1994). nMOSFET. The high performance is afforded by a large [6] K. Natori, Jpn. J. Appl. Phys., drift velocity and also the large carrier density. [7] J. Guo et al., IEDM Tech. Digest, (2002) [8] R. Saito et al., Physical Properties of Carbon Nanotubes, RRefefeferenceserences Imperial College Press, 1998.

N −1 I 2q µ − D ∑ ( Ei ) h =  + µ −  G i 0 = 2qkT ( 1 exp[( Emin ) / kT] 0 ≤ µ ≤ I ln  E N −1 E N h ∑subband ∑dE(k )/ dk≥0 part 1+ exp[(µ − E ) / kT]  max  + µ −  1 exp[( -qVD Emin ) / kT]  − ln  ) (N − 1)G ∑dE(k )/ dk≤0 part + µ − − 0 1 exp[( qVD Emax ) / kT] 1 2q µ − ∑ ( Ei ) h i =0 ≤ µ ≤ E1 E 2 2q NG 0 µ − ( E 0 ) ≤ µ ≤ Emax h E0 E1 C[(V −V ) − (µ − µ ) / q] = 2q  D(E) f (µ, E)dE G t 0 ∑subband ∑dE (k )/ dk≥0 part  ∫Emin V µ − E − µ − E µ − µ − D Emax O N 1 N − 2 E E 0 + D(E) f (µ − qV , E)dE ) 1 ∑dE (k )/ dk≤0 part ∫E D q q min q q

Fig. 2. I-VD characteristics of a ballistic nanowire Fig. 1. Summary of the I-V characteristics of a FET at T=0. ballistic nanowire FET.

4.0 10 |Vg-Vt| = 1.4[V]

8 3.0 1.2

6 A] 1.0 -4 2.0

E [eV] 0.8 4 [10 |I| 0.6 1.0 2 0.4 0.2 0 0 π /a 3 0.0 √ 0.0 0.5 1.0 1.5 k Vd [V] Fig. 3. The band structure of a Fig. 4. Schematic cross section of Fig. 5. I-VD characteristics of a (19,0) SWNT. a CN FET. (19,0) SWNT FET, derived from the band structure.

1.4 4.0 2.5 1.2 Vd = 0.2[V] Vd = 0.4[V] 2.0 3.0 Vd = 0.6[V] d = 1.5 [nm] 1.0 Vd = 0.8[V] Vd = 1.0[V] 1.5 Vd = 1.0 [V] 0.8 A] Vd = 1.2[V] cm/s]

-4 8 /cm] 2.0 Vd = 1.4[V] 7 0.6 1.0 v [10 n [10 |I| [10 |I| 0.4 d = 1.5 [nm] 1.0 Vd = 1.0 [V] 0.5 0.2

0.0 0.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 7 n [10 /cm] |Vg-Vt| [V] |Vg-Vt| [V] Fig. 8. Drift velocity of carrier Fig. 6. I-VG characteristics of a Fig. 7. Carrier density at the (19,0) SWNT FET. beginning of the channel in the at the beginning the channel in ballistic SWNT FET. a ballistic SWNT FET.

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