Metallic: 2n 1. +n 2. =3q Armchair structure always metallic = 2

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2 Properties of CNT

3 d = 2.46 n n1n2 + n2 2π Metallic: 2n 1 +n 2 =3q Armchair structure always metallic

4 a) Graphite Valence(π) and Conduction(π*) states touch at six points(fermi points) Carbon Nanotube: Quantization from the confinement of electrons in the circumferential direction b) (3,3) CNT ; allowed energy states of CNT cuts pass through Fermi point metallic c) (4,2) CNT ; no cut passes through a K point semiconducting Semiconduction CNT band gap Egap = 4hv 3d F CNT

5 Landauer s Equation G = 2e h 2 N i Ti 2e 2 /h : Quantum of conductance Ti : Transmission of a conducting conduction channel(subband) The resistance of metallic CNT N = 2, Ti =1 R 1 h = = 6. KΩ G 4e 5 2 Contact resistance due to the mismatch of the number of conduction channels in the CNT and the macroscopic metal leads

6 Single wall CNT Diameter ~ 1.6nm P-type FET I(on)/I(off) 10 5 High parastic resistance 1MΩ Low drive current few nano ampere Low transconductance ~ 1nS High inverse subthreshold slope S ~ 1-2V/dec BAD CONTACT : weak van der walls force(swcnt-au) How to reduce contact resistance? CNT first then electrode deposition, annealing TiC : stronger coupling

7 Vg = 0V: linear; 2.9MΩ Vg < 0V: linear Vg >>0V : non linear Current decreases with increasing gate voltage 1. shows field effect transistor 2. majority carrier : holes R = R + 2R T NT C V G < 0V: current saturation contact resistance dominating(~ 1.1MΩ)

8 Co electrode and annealed P-type High on-off ratio ~ 10 6 Low contact resistance ~ 30k Ω Higher current range ~ µa Transconductance ~ 0.34 µs higher than previous CNTFET To improve performance gate cap. should be increased High k or thin oxide even individual gating

9 Ti electrode: TiC formation Stronger coupling Tox ~ 15-20nm Vth ~ -0.5V(back gated -12V) Transconductance = 3.3 µs

10 Interchanging of source and drain : non symmetric I-V Saturation current should be same if operation is dictated by bulk of CNT Dominated by barrier (Schottky barrier)

11 φ M E vac χ E vac E F E F φ M φ s χ E vac E F φ M < χ+e c -E F = φ S For n-type semiconductor. Work Function(CNT) MWCNT ~4.9eV SWCNT ~3.7eV Work Function(Metal) Ni 5.2eV, Ti 4.3eV, Ag 4.3eV, Au 5.2eV φ M > χ+e c -E F = φ S For n-type semiconductor Very high density of surface states pinning the Fermi level at the surface w.r.t. the conduction band (Example: GaAs)

12 Thermionic emission Electrons emit over the barrier Low probability of direct tunneling Valid for low doping (N D < ~ cm -3 ) Thermionic-field emission Electrons use thermal energy to tunnel trough the thin barrier in the upper end of the conduction band Valid for intermediate doping (~ cm -3 < N D < ~ cm -3 ) Field emission Direct tunneling, as depletion region is very narrow Valid for heavy doping (N D > ~ cm -3 ); almost ohmic

13 Standard FET, conductance is controlled by the electrostatic potential in the channel increase capacitance SB-FET, performance is controlled by electric field at the contact

14 Oxygen doping Ambipolar property Potassium doping Non Ambipolar property But two cases show contrast of dopants Transport and switching is controlled by the Schottky barrier at the contacts

15 a) Work function change of metal electrode b) The charge on tube plays main role The principle effect of oxygen exposure is not to dope CNT body but change the work function of exposed portion of the metal electrode

16 dvg kbt S = ln10 ln 10(1 + d(ln I ) q D C C D G ) Fully depleted device, Cd = 0 CNT has no depletion capacitance because of no charge variation across tube circumference Inverse subthreshold slope only depends on temp ~60mV/dec at 300k Below 200k S is almost constant not temp. dependent

17 CNTs grown from arc discharge or Hipco form rope or bundle : How do we select semiconducting or metallic? Separation CONSTRUCTIVE DESTRUCTION

18 Vds increase: increase the avg. energy of carrier coupling between shells Higher electron energy energy dissipation breakdown Less breakdown voltage in air than vacuum oxidation Band gap of CNT can be controlled by electrical breakdown Egap ~ 1/d cnt

19 Initially both CNTFETs were p-type FET Annealing in vacuum make n-type Expose O2 O2 exposure makes p-type FET From single CNT PMMA coating and e-beam litho. Potassium doping n-type FET

20 Heavily doped Si layer and Si3N4 Electrolytical etching Si to form porous Si on sidewall PR protecting and catalyst deposition CNT growth

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