Drain Voltage (mv) 4 2 0-2 -4 0.0 0.2 0.4 0.6 0.8 1.0 Gate Voltage (V)
Vds [V] 0.2 0.1 0.0-0.1-0.2-10 -8-6 -4-2 0 Vgs [V]
10 1000 1000 1000 1000 (LSI)
Fe Catalyst Fe Catalyst Carbon nanotube 1~2 nm
~10nm 0.34nm
Scanning Tunneling Microscope (STM) A IBM
A E I II III U U = 0 x 1 x 2 x h2 2m d 2 ϕ +U(x) = Eϕ T 2 dx exp 2 h x 2 x 1 2m(E U)dx
I II III U ϕ = Aexp ±i h x x 0 2m(E U) dx T = ϕ(iii) ϕ(i) 2 E U = 0 x 1 x 2 x T exp 2 h x 2 x 1 2m(E U)dx L 1 >L 2 T 1 << T 2 STM L 1A T 10 L 1 L 2
Chirality of Carbon Nanotube (n, 0) (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0) (7,0) (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (7,1) (n,n) (2,2) (3,2) (4,2) (5,2) (6,2) armchair zigzag chiral Metal Metal Semi Con. Metal Semi Con. (3,3) (4,3) (5,3) (6,3) (4,4) (5,4)
Chemical Vapor Deposition (CVD) C Fe C 2 H 5 OH Fe
Fe Fe Particle TEM Image of SWCNT Fe CH 4 Gas C C Fe Fe Fe 900C/30min. (Fe)
Carbon Nanotube Growth from Fe Particles RT Heating CVD Fe Fe 3 O 4 Fe 2 O 3 Fe 3 O 4 Fe-C CNT FeO Fe 3 C Fe-C
Position Controlled Growth of Carbon Nanotube using Patterned Catalyst 1) Photo Resist Patterning P.R. Si Sub. 2) Fe Deposition Fe Si Sub. 3) Lift Off Fe Fe Catalyst Si Sub. 4) Carbon Nanotube Growth Carbon Nanotube CH 4 Gas Si Sub. 900C/30min. Fe Catalyst ~10%
Effect of Electric Field on Direction Control of Carbon Nanotube V A CH 4 Gas Catalyst Catalyst Fe Catalyst Fe Catalyst SiO 2 Si Sub. Carbon Nanotube Carbon nanotube Catalyst Catalyst ~20% SiO 2 Si Sub. Effect of Van der Waals Force between Carbon Nanotube & SiO 2 Sub.
Effect of Applied Field 0V +20V 0V Growth without Electric field 0V Electric field effect Growth Source 10V Drain -10V Gate -40V
+ - DC Bias Current Current Time C 2 H 5 OH H 2 CNT 900 Electrode Catalyst Time 900 Current Time
1nm
Peapod
Gd@C 82 peapod Gd +3 EELS Gd Gd 3+ @C 82 3- K.Hirahara et al., Phys.Rev.Lett. 85, 5384 (2000). K. Suenaga et al., Science 290, 2280 (2000). K.Hirahara et al., Phys.Rev.Lett. 85, 5384 (2000). Gd@C 82 +3 Dy@C 82 +3 Ti 2 @C 80 +4 Ce 2 @C 80 +6 Gd 2 @C 92 +6
STS - Gd@C 82 Peapod J. Lee et al. Nature 415 1005 (2002) Gd@C 82
Peapod FET FET C 60, C 78, C 90 Gd@C 82, Ti 2 @C 80, etc. Source Peapod Drain Ti/Au SiO 2 (100 nm) + p -Si sub. Hight / nm 2 1.5 1 0.5 0 0 100 200 Length / nm Gate Ti/Au
Various Type Peapod FET and its I D -V GS Characteristics I D (A) 10-8 10-9 10-10 10-11 10-12 Ce 2 C 80 -P GdC 82 -P Ti 2 C 80 -P C 60 -P 23 K V DS = 1 mv -40-30 -20-10 0 10 20 30 40 V GS (V) Ce 2 @C 80 +6 Ti 2 @C 80 +4 Gd@C 82 +3 C 60 +0 SWNT FET p Ti 2 @C 80 FET p / n
Various Organic Molecular Doping into Carbon Nanotube CNT CNT Structure was determined by Spring-8.
MOSFET Metal Oxide Silicon Field Effect Transistor I D : L : Ci : μ ν : Z V G1 Z I Dsat = μ n C i (V G -V T ) 2 2L g m = di Dsat dv G = Z μ n C i (V G -V T ) L V G2 V G3 V G4 L μ n C i Z V D I D I D p L Z p μ p C i p V T V G V T V G
Delft University
CNT (25,0): 1.99 nm Si GaAs InAs (19,0): 1.51 nm (13,0): 1.03 nm Eg (ev) 0.45 0.60 0.87 1.12 1.42 0.36 (cm 2 /Vs) 65,000 35,500 15,000 e: 1,500 h: 450 e: 8,500 h: 400 e: 33,000 h: 460 V. Perebeinos et al. (IBM) PRL 94, 086802 (2005) S. M. Sze, Physics of Semiconductor Devices 2nd Ed. Electron Drift Velocity (x10 7 cm/s) Carrier Velocity (10 7 cm/s) 4 CNT 3 2 GaAs Si 1 0 0 10 20 30 40 50 60 70 80 F (kv/cm) (G. Pennington et al. SISPAD 02, 279 (2002))
p type Al or Ti Ti SWNT SiO 2 (15nm) g m Si-MOSFET 2 CNT-FET Si-pMOS Lg nm 260 15 t ox nm 15 1.4 V th (V) -0.5-0.1 I on ma/mm) 2100 265 g m ( S/ m) 2321 975
High-k CNT-FET Stanford Univ. A. Javey et al. Nature Mat. 1, 241, 2002. ZrO 2 (k ~ 25) : 8 nm SiO 2 (k ~ 3): 0.9 nm p type C G I ON /I OFF ~ 10 4, g m = 6000 μs/μm, s-factor = 70 mv
n type Carbon Nanotube FET Logic n FET
I D I D p V T V G V T V G
FET IBM 52MHz Delft p 5 Hz Stanford 220Hz IBM 52MHz
IBM p type n type CNT φ=1.4nm
D IBM e h Drain Bias 0 10V(3 sec.) Repeat 190 sec. Integration S
D(E) D(E) D(E) E E 1 E 2 E 3 D(E) E E 1 E 2 E 3 D(E) E E 1 E 2 E 3 E
1 L x Ly D(E) = 2 dn x dn y dn z de 1 L x L y L z E = h 2 8π 2 m k 2 = h 2 8π 2 m (k 2 x + k 2 y + k 2 z ) L z D(E) = 2 dn x de 1 L x (1) E = h 2 2 k x 8π 2 m = h 2 n x π 8π 2 m L x 2 = n 2 xh 2 2 8mL x L x k x = n xπ L x n x = 2L x 2mE h dn x de = L x h 2m dn x de = L x E h (2) 2m E (1)(2) D(E) = 4 m h 2E 1 2
D(E) L x D(E) = 4 m h 2E 1 2 E 1, E 2 E 1 E D(E) D(E) = g s h m 2 E E n ( ) 1 2 E 1 E 2 E 3 E
Scanning Tunneling Spectroscopy (STS) J t J t A C B A V V dj t /dv D(E) C B A V
Scanning Tunneling Spectroscopy(STS) J t V C B A V Jt Tip E f C B A dj t /dv V J t E f 0 D(E) T(E,V )de D(E) : T(E,V): D(E) C B A V dj t dv D(E) T(E,V ) D(E)
STS J t A V
(0,0 ) (6,0 ) (5,0 ) (4,0 ) (3,0 ) (2,0 ) (1,0 ) (1,1 ) (7,0 ) (2,1 ) (3,1 ) (4,1 ) (6,1 ) (5,1 ) (7,1 ) (5,2 ) (6,2 ) (4,3 ) (4,4 ) (5,4 ) (5,3 ) (6,3 ) (5,5 ) (2,2 ) (3,2 ) (4,2 ) (3,3 ) Zigzag Type (n,0) Armchair Type (n,n) 1/3 Metalic 2/3 Semiconductor
I G 2e 2 h V V
E F D(E F ) = g s h m 2 E F E n ( ) 1 2 D(E) E = 1 2 mv 2 v(e F ) = v F = ( ) 2E m = 2 E E F n m 1 2 E 1 E 2 E E F 3 E n I = e D(E F ) v F ev = e g s h m 2 E F E n ( ) 1 2 2 E E F n m ( ) 1 2 g ev = s e 2 h V G = I V = g s e2 h = 2e2 h
n D(E) I = i= n i=1 2e 2 h V = n 2e2 h V 2e 2 G = I V = 2e2 h h G 3 2 E F E 1 E 2 E 3 E 1 E 1 E 2 E 3 V
1 R. M. Westervelt Science 2000 289 2323 Nature 410 183 2001
h2 2m d 2 ϕ +U(x)ϕ = Eϕ 2 dx U= = E 3 ϕ = Csin(kx) = Csin( nπ L x) E 2 k = nπ L = 0 L E 1 x E 3 = 9 8m h 2 L x 2 E n = h2 k 2 2m = h 2 nπ 8π 2 m L 2 = n 2 h 2 8mL 2 E 2 = 4 8m E 1 = 1 8m h 2 L x 2 h 2 L x 2
5nm E 3 e GaAs 0 L GaAs E 2 e E 1 GaAlAs GaAlAs x GaAs E 3 e E 2 GaAs A GaAs E 1 GaAs
Discrete Energy Level m ΔE Q m m Drain SiO 2 4μm Source
Discrete Energy Level 15 14 13 8.6K V G =0.98V ΔE Q Drain Source 12 11 V D =0.4mV SiO 2 4μm 10 9 3 3.5 4 4.5 5 Drain Voltage (mv) Drain 4.2 m Source
n n+1 ΔE ΔE L E n = hν n = hv F λ n E n +1 λ n +1 E n +1 = hν n +1 = hv F λ n +1 E n λ n ΔE ΔE = E n +1 E n = hv F λ n +1 hv F λ n L = hv F (n +1) 2L hv Fn 2L = hv F 2L
Resonant Tunneling of of Hole through Quantum Level in in Carbon Nanotube Negative Conductance Drain Current-Drain Voltage 15 14 13 12 11 10 8.6K V G =0.98V V D =0.4mV ΔE Q Discrete Energy Level Drain SiO 2 L 4μm Source ν 9 3 3.5 4 4.5 5 Drain Voltage (mv) h :Plank s Constant F :Fermi Velocity L :Length of CNT between Tunneling Barriers e :Elementary Charge ΔV D ΔE L = 4.2( μm) ΔE = hν F 2L 1.4μm L : 4.5μm 1 ΔΕ 3
35 30 Resonant Tunneling of 1.4μm CNT through Quantum Well 8.6K V G =-3.2V ΔE Q Discrete Energy Level L 25 Drain SiO 2 ΔV Δ 1.4μm D E Q Source 20 V D : V D =1.2mV 8 10 12 14 16 18 Drain Voltage (mv) 1.2mV 0.4mV = 3 L =1.4 μm ( ) ΔE ΔV D =1.2mV
W. Liang Harvard Univ. CNT 2LeV c /h ν F = 2 ΔE Q Discrete Energy Level L = 530nm Vg(V) Vg(V) T = 4K L = 200nm Drain SiO 2 4μm Source L = 220nm Vg(V)
Single Electron Transistor V G e - e - V D C t C G V G C t V D C Ec = e 2 / 2C E F e - X e/c E F ΔE = (Q-e) 2 /2C - Q 2 /2C = Ec ΔE > 0 Ec > ev e/2c > V Small V D e/2c > V > - e/2c
I D E F e - X e/c E F -e/2c e/2c V D Small V D e/2c > V > - e/2c e - I D E F e/c E F -e/2c e/2c V D e/2c < V Large V D V < - e/2c
V G e - I D E F e - X e/c E F -e/2c e/2c V D V D I D e/c G Small V D e - I D n = 0 n = 1 E F e/c E F -e/2c V G Gate V G e/2c V D Small V D
10K I D -e/2c e/2c V D 0 1 e/2c > V > - e/2c I D e/c G n = 0 n = 1 V G Tunnel Capacitance C 1 = C 2 = 4 x 10-19 F Gate Capacitance C G = 1 x 10-19 F
1) kt << Ec = e 2 /2C C 2) R T >> h / e 2 = R Q = 26k kt = 26meV at 300K Ec = e 2 /2C = 80meV at C = 10-18 F r = 10nm 800meV at C = 10-19 F r = 1nm r E F kt e - X e/c E F -e/2c I D e/2c V D
Simulated Charactersitics of Single Electron Tranasistor at 10K & 300K 10K 300K Tunnel Capacitance C 1 = C 2 = 4 x 10-19 F Gate Capacitance C G = 1 x 10-19 F C Σ = C 1 + C 2 + C G = 1.8 x 10-19 F Tunnel Capacitance C 1 = C 2 = 5 x 10-20 F Gate Capacitance C G = 8 x 10-20 F
4 8.6K Coulomb Diamond Characteristics of of Hole in in Entire Carbon Nanotube Island of of 4.5μm Drain Voltage (mv) 2 0-2 -4 n n-1 n-2 n-3 n-4 n-5 n-6 n-7 Drain Current (A) Drain h + Island Source 0.0 0.2 0.4 0.6 0.8 1.0 Gate Voltage (V)
3. Vds [V] SET AFM FIB Voltage pulse 0.2 0.1 0.0-0.1 Drain SiO 2 Si Sub. -0.2-10 -8-6 -4-2 0 Vgs [V] + Back Gate AFM CNT Metal coated AFM tip Source ΔV G [V] Ids1[A] 4.0n 3.0n 2.0n 1.0n l =22 nm 0.0-5.0n -10.0n -10-5 0 Vgs[V] 2.6 2.4 2.2 2.0 1.8 1.6 1.4 12 14 16 18 20 22 24 Dot length [nm] L = 15 nm CNT 20.0n 15.0n 10.0n 5.0n 0.0 22 nm/15nm nicks Ids2[A]
CNT Single Electron Transistor by AFM Nicking 20K Source e - Gate Drain I D e/c G Island V e 2C 1 n = 0 n = 1 n n -e 2 n 0 n n e 2 Q 0 =C g U g V G -e 2C1
CNT Single Electron Transistor by AFM Twisting Source e - Gate Drain 300K Island V e 2C 1 n n -e 2 n 0 n n e 2 Q 0 =C g U g -e 2C1
1.4 10-9 (A) 1.2 10-9 1 10-9 8 10-10 6 10-10 4 10-10 2 10-10 0 ~4V -2 10-10 0 1 2 3 4 5 6 7 8
Carbon Nanotube Rope
Lightbulbs with Carbon Nanotube Filaments
Vds [V] 0.2 0.1 0.0-0.1-0.2-10 -8-6 -4-2 0 Vgs [V]