1 1
1 1-1 1 1-9 1-3 1-1 13-17 -3 6-4 6 3 3-1 35 3-37 3-3 38 4 4-1 39 4- Fe C TEM 41 4-3 C TEM 44 4-4 Fe TEM 46 4-5 5 4-6 5 5 51 6 5
1 1-1 1991 1,1 multiwall nanotube 1993 singlewall nanotube ( 1,) sp 7.4eV atom 1 1,3 c ( ) O A C h (chiral vector) O B T A B OBB A OB AB.4nm 1nm 1µm ( ) a1 a ( n m) C h na + ma, = (1.1) 1 = n m d θ n m t d t = 3a c c n + nm + m π (1.) θ = tan 1 3m n + m θ 6 π (1.3) 3
a (.14nm) c c n=m( = /6) (n,n) m=( =) (n,) ( 1, ) (armchair) (zigzag) n m (chiral) 1,5 T T (1.1) {( m + n) a ( n + m) a } 1 T d R = (1.4) dr (m+n) (n+m) T ( )l T 3l = (1.5) d R l = Ch = 3 ac c n + m + nm (1.6) (n,m) sp 3 1 1,6 (1.1) q C h k = πq (1.7) k (1.4) T 4
E k, k x y 5 ( ) k 1,7 K ( b ) 3 1 b (1.7) k K (1.7) (1.1) k= ( b ) 3 n m = 3q 1 b (1.8) n 3 ( 1,8) ( ) ( ) 1/3 /3 5 1 6 ( 1,9) 1 F + V = E + (1.9) 5 6 7 7 6 5 F = p + h + s (1.1)
V ( 7s + 6h + 5 p) = (1.11) 3 E ( 7s + 6h + 5 p) = (1.1) (1.1),(1.11),(1.1) (1.9) s p + = h s + + p 1 + ( 7s + 6h + 5p) ( 7s + 6h + 5 p) 3 = 6 + (1.13) 5 7 1 6 = 5 1 5 7 ( 1,1) 5 7-1.36 / cm 3 (1kV) 5V
1.1 1. 1.3 7
1.4 1.5 8
1.6 1.7 1.8 (, ) 9
1.9 1.1 1
1-1,11 mm 1991 ( ) (Fe Co) ( / ) / Fe Ni Co Ni 1.11 Co (Ru Rh Pd Os Ir Pt ) (a ) (15A ) 4 1.1 / 1 1.3nm 11
11 (SiC) 17 Si Si(A AB B) 1
13
1-3 1 1 14
- - (.1).1 z z= z= x E x iwt = A e sin kz (.1) x z= z= E = sin k = nπ ncπ k =, ω = (.) n n k= / (.) / n 15 x (.) sinkz n ( z ) z= z= ( ) f z (.) (.1) z= z= E ( ) <z< f z f ( ) z = n= A n πnz sin + B n π nz cos (.3) z= z ( z) f ( z ) f + = (.4) sinkz coskz z= (.3) k=n / (.)
sine cosine (.4) z= z= E E E = z z ( z = ) = E( z = ), ( z = ) = ( z ) (.5) x,y,z 3 τ τ a x,y,z 3 xˆ, yˆ, zˆ k ϖ ϖ k = k x xˆ + k yˆ + k y z zˆ A ϖ ρ ( i ω t ik r ) 16 c a (.6) exp (.7) r ρ A r ϖ = xxˆ + yyˆ + zzˆ x,y,z + k ϖ - k ϖ k ϖ n, n, n x= y= z= (.) k x π π π = nx, k y = ny, k z nz (.8) x y z
k = k + k + k x y z ( n + n n ) k = π x y + z (.9) n, n, n kc ω = ( n + n + n ) c ω = π x y z (.1) x, n, n, n x,y,z x y z R = n x + n y + n z ω = πc y z (.11) n, n, n 1/8 x y z 8 3 3 4π ω ω 3 = (.1) 3 πc 3π c +d ω π c 3 dω (.13) 3 +d ( ω ) dω dω π ω m = (.14) c = / +d 8πν c ( ν ) dν dν m 3 = (.15) 17
.1. n, n, n R x y z 18
- WU W WU W WU W ω = (.16) η (spontaneous emission) 1 A W( ) p ( U ) = A B W ( ω) (.17) U + U (induced emission stimulated emission) p ( U ) = B W ( ω ) (.18) U 1 B U = B U (.19) gu g (.19) g B = g B (.) U U U 1 (.16) (.17) A U B A B U 19
A B N P abs ( ω ) N = ηωbw (.1) N P emi { A BW( ω )} N U = η ω + (.) N U ηω = N kbt exp (.3) ( ) ( ) W ω W ( ) = ( ω ) ω W W ( ) th A th P abs = P emi (.) (.1) N U th ω = (.4) B N N U (.3) W th ( ) A 1 = ω kbt B e ω η (.5) 1 1 n ( U ) = ( n + )A P 1 (.6) ( U ) na P = (.7) m( ) +d dω
( ω) m( ω) nηω W = (.8) (.6) (.7) A P ( U ) = + m ω ηω P ( U ) ( ) ( ω ) W ( ω ) A (.9) A = W ( ω ) (.3) m ηω (.17) (.18) A B = (.31) m ω η ( ) ω (.14) A B 3 ηω = m( ω) η ω = 3 (.3) π c (.5) W th ( ω ) ηω π c 1 3 = 3 ηω k T e B 1 (.33).3 1 d m( ) dω A = m ( ω) Bηω ηω (.17) (.18) W( ) ηω ( k B T ) exp ηω A= (.4) (.5) = A B 3 3 16π ν π A µ, 3 U Bν = µ 3ε hc 3ε h = U (.34) W th 1
B W( ) W th (.1) (.) B ( ω) = Bg( ω) (.35) B ( ω ) dω B B = (.36) g( ) B( ) NU N P ( N N ) ηωb( ω) c P = (.37) U z d P dz ( z) ( N N ) B( ω ) P( z) U ηω = (.38) c (amplitude absorption constant) ( ) d dz P ( z) α ( w) P( z) = (.39)
(.38) (.39) α ηω = U (.4) c ( ω ) ( N N ) B( ω ) (.35) (.34) A h = πη ν = ω π (.3) B = π ε η µ α ( ω) ( N N ) µ g( ω) 3 3 U πω = U U (.41) 6ε ηc (orentzian) Gaussian g ( ω) 1 = π ω g ( ω ω ) ( ) (.4) + ω ω ω = ± ω g ω g ω =1 π ω ( ) ( ) ω (half width at half maximum HWHM) ω ln 1 ω ω g G ( ω ) = exp ln (.43) ω ω ω ω ω = ln 1.47 g G ( ω ) = = (.44) π ω ω g ( ω ) π ln = 1. 476 g ( ω) g ( ω ).4 ω G (.19) ( ) NU N ( ω) = ( N N ) σ ( ω) α (.45) U (.45) (.41) (.4)
σ ηω ( ω) = µ g( ω) = B( ω) 3ε πω ηc U c (.46) NU N (.3) N U ηω kbt ( e ) N N = 1 (.47) ηω T N ηω k B N N U (.48) k T B ( ) ηω T k B N N N (.49) U ω x F dx dt dx F + γ + ω x = (.5) xt m ( ) t iω m -e E ω e (.5) d x + dt dx γ + ω dt e x = E m iωt ( ω) e (.51) x x iω t ( ω ) e = x (.5) (.51) ( ω) e E x ( ω ) = (.53) m ω iγω ω 4
x ( ω) e = mω E ω ω ( ω) iγ (.54) N N ( ) t iω P ω e P ( ) = ex( ω )( ) ω (.55) N N U χ ω = χ ω iχ ω ( ω ) ε χ ( ω ) E( ω ) P (complex susceptibility) ( ) ( ) ( ) = (.56) (.54) (.55) U χ ( ω) = ( N N ) ε U mω e ω 1 ω iγ (.57) ( ) ( ) ( ) ( ) ( ) χ ω χ ω χ ω = χ ω iχ ω χ χ ( ω ) ( ω ) = = ( N N ) U e ω ω ε mω γ ( N N ) ( ω ω ) + U e γ ε mω γ ( ω ω ) + (.58) (.59).5 ( ) χ ω ( ω) = ε { 1 χ( ω) } ε + (.6) µ = µ η η ( ω) ε η = η κ = = 1+ χ ε ( ω) i (.61) ( ) z exp iωt ikz η iκ 5
k ω ( η iκ ) c = (.6) ( iωt ikz ) = exp z exp iωt iη z κω c exp (.63) e αz ω α = κ (.64) c χ ( ω) κ χ ω c 1 (.59) α ( N N ) U e γ 4ε mc γ ( ω ω ) + (.65) e m ω 3 η (.41) g( ) (.4) 6 µ U χ χ µ U ω ω N N U (.66) 3ε η ( ω ω ) + γ ( ω) = ( ) ( ω ) = ( ) µ U γ 3ε γ N N U (.67) ( ω ω ) + f (.66) (.67) e f m ω µ 3η U = (.68) mω f µ 3e η U = (.69) f (oscillator Strength) NU N (.67) χ N N χ U
.3.4 g ω g ω ( ) G ( ).5 ( ) 7
-3 N U N N N U N N U (inverted population) N NU (pumping) -4 3 (three-level laser) 3 1,,3 W 1, W, W3 N 1, N, N3.6 W1 W W 3 N1 N N 3 1 1 1 3 (relaxation) (radiative process) (non-radiativve Process) (relaxation rate) (relaxation constant) (fluorescence lifetime) 8
W W U γ U WU W γ N U U WU W γ = = U N γ U, NU N exp (.7) kbt γ γ U U WU W = exp kbt (.71) NU N 3 (rate equation) dn dt dn dt dn dt 1 ( Γ + γ 1 + γ 13 ) N1 + γ 1N + γ 31N3 = (.7) ( γ 1 + γ 3 ) N γ 3 3 γ N 1N1 + 3 = (.73) ( Γ + γ 13) N1γ 3N ( γ 31 + γ 3 ) N3 = (.74) N 1 + N + N 3 = const = N 3 (.7) (.74) k B T (.71) γ 1 γ 1, γ 13 γ 31, γ 3 γ 3 γ, γ 13 γ 3 (.7) (.74) 1 γ 1 ( γ 31 + γ 3 ) ( γ + γ ) + ( γ + γ ) N N 1 γ 1 31 3 1 3 = (.75) N = γ 1 Γ ( γ + γ ) + ( γ + γ ) 31 γ 3 3 1 3 Γ N (.76) 9
γ Γ > + 31 1 1 γ 3 γ (.77) N1 N (.77) γ γ 3 γ 31 1 3 N = N N 1 (.75) (.76) N = γ 1 γ 3Γ γ 1( γ 31 + γ 3 ) ( γ + γ ) + ( γ + γ ) 31 3 1 3 Γ N (.78).7 lim N Γ = γ γ 1 3 N + γ 3 = N γ 1+ γ 1 3 (.79) γ γ 1 3 NU N (.65) χ ( NU N ) χ e α z z ( ) - G z e α = e Gz z (gain) G (gain constant) G/ (amplification constant) N = N N 1 1 G ηω N B ω c ( ) = (.8) 3
G Nσ ( ω) = (.81) g 1, g g N g 1 N1 N g N = 1 ηω exp g k T 1 B (.8) g g 1 N N 1 N - N1 1 N 1, N N = N N 1 g N 1 N = (.83) g N g 1 g g 1 B B g = = (.84) B1 g1b1 1 (.8) B (.84) (.83) (.84) B (.8) (.83) (.35) (.34) B ν 3ε η U B = π µ 31
G g πω = N N1 µ 1 g( ω ) g (.85) 1 3 ε c η G g1 πω = N N1 µ 1 g( ω) g (.86) 3ε cη,1 1 P Q ( ) Q c ωw P = (.87) 1 dw κ = = W dt ω (.88) Q c (l= ) U P ωu = Q c (.89) N 3
P (.37) G P G Nηω B( ω)u = (.9) P P N G th 1 Q c = N th ( ) ηb ω (.91) R1 R /c ( 1 R )U R 1 c P ( 1 R1 R ) U = (.9) (.89) Q Q c = c ω ( 1 R R ) 1 (.93) (.9) (.93) ( R R ) c 1 1 ηωb( ω ) N th = (.94) z= +z E t( ωt kz) ( z t) = E e, (.95) k K G k k ε = ε { 1+ χ( ω )} G ω = k + i = 1 + χ c ( ω) ( ω ) k (.96) χ 33
k G ω 1 = 1 + χ ω c ( ) k (.97) ω = χ c ( ω ) G (.98) χ G (.95) (.96) z ( 1 ) ( t k ) ( t) E e G e i, E = (.99) Z, r 1, r (.99) z r -z z= r1 +z ( t k ) ( t) r r E e G e i ω, = E 1 (.1) (.95) z i t E e ω ik r r e G e 1 (.11) 1 = r1r r r R R e iθ 1 = 1 (.11) G R R e 1 (.1) 1 = n k = nπ +θ (.13) (.1) (.98) ω c 1 ( ) = ln R1 R χ ω (.14) ( ) R 1 R 1 ln R1R = R1R 1 Q (.93) (.14) 34
1 χ ( ω ) = (.15) Q c (.13) (.97) ω c { + χ ( ω )} = nπ + θ (.16) (.66) (.67) ( ω) = χ ( ω) ω ω (.17) χ γ (.15) χ ( ω) ω ω = γq c (.18) (.16) (.18) ω c ω ω + = π γ n Qc + θ (.19) ω (.16) χ = c ω = nπ π + c (.11) (.19) (.11) ω (.88) Q c c ω ω κ c ω + ω = γ (.111) ω κω + γω c = κ + γ (.11) ( 35
) Q Q ω γ (.11) Qω + Qcω c ω = (.113) Q + Q c Q Q Q Q c > 1 (frequency pulling) 1 (.11) c / = Q.6.7 36
3-1 3,1 (Nd) 53 m 1Hz Q Q Q 1 ( ) 53nm 357 337mJ 5. 5 Torr 5 1 6 1 37
3.1 38
3- ( ) 7751 3. 1mm ( ) 113381. 3 1mm ( ) 113518 1. 6 3mm 5. mm 1 1.mm 3. Fe 3 1 Fe Fe 7 Fe Fe A A B TEM 39
3-3 SEM( ) TEM( ) SEM TEM TEM TEM ( ) SEM TEM 4
4 4-1 SEM 4,1 4,( ) 4,3( ) Cu.3 m 5nm 4,1 41
4, 4,3 4
4- Fe C TEM TEM 4.4 a B 5 c 1 4,4c 3 A 3.391 B.71 C 1.179 ( ) ( ) ( ) 43
44
45
4-3 C TEM TEM 4,5 1 A H A B C ( ) 46
47
4-4 Fe TEM TEM 4,6 1 (a) 5 (b) 4,6a ( ) 48
49
4,6c 3nm.g cm 3 3 1.5g cm 4.7 6% 3 ( ) 4.7 5
51
4-5 C % 3 4-6 5
5 ( 1983) ( 1998.11.13) Carbon Nanotubes and Related Structures edited by Peter J.F.Harris (Cambridge University Press 1999 The Science and Technology of Carbon Nanotubes edited by K.Tanaka, T.Yamabe and K.Fukui Elsevier (Elsevier Science 1999) 53
6 TEM SEM TEM 54