χ 2

1 N =0

1

1 2 3

npn 1 2 1 9 N =0 1 1

1 1 2

6 6 4 9 B V 70 100 10

1

2 2 2 2

a 1 a 2 δ 1, δ 2 δ 3. b 1 b 2 Γ, K, K M K K

A B a 1 = ( ) ( ) 3a 2, a 3a, a 2 2 = 2, a, 2 a = a 1 = a 2 2.46 ( ) ( a δ 1 =, 0, δ 2 = 3 ) ( a 2 3, a, δ 2 3 = ) a 2 3, a, 2 a = δ 1 = δ 2 = δ 3 1.42

( ) ( ) 2π b 1 =, 2π 2π, b 3a a 2 =, 2π. 3a a Γ M K K Γ ( ) ( ) 2π ΓK =, 2π, ΓK 2π =, 2π. 3a 3a 3a 3a H = t c n,a c m,b + n,m c n,α(c n,α ) p z n α = A, B t 2.7 3.1 n, m H(k) = 3 n=1 t 0 e ik δ n, e ik δ n 0 {c A (k), c B (k)} c n,α K q = k K

K H(q) = v F σ q. σ v F c/300 ( / ) K K H(q )=H (q) q = k K K Ψ(q) = 1 2 e iθ q/2 ±e iθ q/2, p z A B ε(q) =± v F q, q = 0 0.6

ε k K K 2 Γ K K M K K Γ, K, K M

2 α = 1 4πϵ 0 e 2 c 1 137, e 2 /4πϵ 0 r pc = c/r ϵ 0

e 2 α = 1 1. 4πϵ v F ϵ = ϵ 0 ϵ r ϵ r ϵ r 2 c/300 H(q) = v F σ q + V (r),

V (r) v l E = F V (r). V (r) a l E a. 2 V (r) a λ F l E λ F λ F =2π/q F 10 100 ε F 0.01 0.4 l E λ F l E >λ F

N =0 ε =0 ε =0 l B = eb = 26. B l B l m l m

q Π q + ea a = a = l B 2 (Π x iπ y ), l B 2 (Π x + iπ y ). K H(q) = 2 v F l B 0 a. a 0 ε = (N) v F l B 2N.

τ ee τ p, τ ee τ p

1 1

(0, 0)

2

q ϵ r φ(r) = 1 4πϵ 0 ϵ r q r.

n φ(r) = 1 4πϵ 0 ϵ r q r e k r. k k 3 = 4πe 2 ϵ n µ, k 2 = 2πe2 n ϵ µ, 3 2 ϵ = ϵ 0 ϵ r k 1 n/ µ = g(µ)

µ ε F T =0 eφ ε(k F )/ n = µ ε(n) ε(n 1) N N 1 µ ε(k F )=µ

µ E µ eφ Q = CV, Q C V C E C Q

C Q = dq dv = ed( en) = e 2 dn d(ev ) dµ. N e e V µ = ev V 1 V 2 = µ 1 µ 2, e V 2 µ 2 V 1 µ 1

C Q = e 2 dn dµ = e 2 d dµ e 2 d dµ µ dεg(ε)f(ε) dεg(ε)+ [O((T/µ) 2m )] m=1 e 2 g(µ), T 0, n T g(ε) f(ε) dn/dµ C = ( 1 + 1 ) 1 = C QC E. C Q C E C Q + C E C Q C E C C E

Q ε = ϵ 2 dr 3 E 2 } {{ } ε E µ + µ dε εg (ε)+ dε εg (ε) 0 } {{ 0 } ε Q Q + dqv 0 } {{ } ε S ε E ε Q

2 V C 2 C V =0 V > 0 eφ C µ C e V = eφ + µ g ( ) ε S

C E, = ϵ 0 ϵ r A d = ϵa d, A d ϵ r E = Q ϵa = N e, ϵ N e ε E = (N e) 2 2C E,. ε Q ε S ε S = Q V = e N V.

ε =0= N e 2 + N C E, N ( µ 0 µ ) dε εg (ε)+ dε εg (ε) e V. 0 > 10 19 3 10 12 2 N g (ε) = [ ] N, ε N + N =0, 3 3

e V = n e 2 C E, + µ, n = N /A C E, F/ 2 ev eφ µ eφ = n e 2 C E,. ev eφ V = 10 d = 300 ε r =4 2 µ = v F πn n =7.2950... 10 11 2 n µ V = n e/c E, n =7.3685... 10 11 2 µ

µ ( e V = n e 2 1 + 1 ) C E, C Q,

[ ( C Q, = 2e2 k B T π( v F ) 2 ln 2 1+ µ )], k B T F/m 2 e k B v F µ µ k B T C Q, 2e2 v F π n, n

C Q, = 2e2 v F π ng + n, n G n V = 10 90 300 2 ε F =0.1 0.3 C Q, 20 70 µ 2 C E = 2πlϵ 0ϵ r 1 (d/r) d r 2πlϵ 0ϵ r (2d/r), F l ϵ 0 ϵ r d r

300 300 100 20 10 9 1 10 9 2 ϵ r =4 r =1 d =5 C E 100 µ 1 C M Q, = 8e2 hv F 310 µ 1,

C SC,n Q, = C SC,p Q, = 2 q=1 2 q=1 e 2 [ n e (q) 1 (2N 0e x n n(q))(α +2βx n +3γx 2 ] n) k B T 2N 0 e x, n e 2 [ n h (q) 1 (2N 0e x p n(q))(α +2βx p +3γx 2 ] p) k B T 2N 0 e x, p x = 2ε ε (q), 2k B T x = 2ε ε (q). 2k B T C SC,n Q, CSC,p Q, n e(h) (q) q N 0 ε g (q) q α, β, γ q

17, 20, 23, 26, 29, 32 35 1 1 ε C k B T ε k B T ε C 500 1.6

ε = v F 2L 600 µ, k B T 200 µ, ε C = e2 C 00 5. C 00 = CM Q,C E C M Q, + C E 50, C E 100 µ 1 20 eφ C E, µ C ev = eφ + µ

2 V C 2 C V =0 V > 0

4 100 V e(v V )= µ eφ. V (V V ) φ

2 V V C C 2 C C V > 0 V > 0 C C V C V V V C 2

N + N + N =0 e(v V )=e 2 (n + n ) C E, + µ (n ), V ev = µ µ eφ. ev = µ (n )+µ (n ) e 2 n C E,. V V

V V di/dv V V V V 1.6

0.1 1 V V n V V n ev = µ +,

V V n V = en C E, + V +, V

dv dv = e2 C E, dn dµ +1. g (V,V )= dn = C ( ) E, dv dµ e 2 1 C E, dv e 2 ( dv dv ), g (V,V ) V dv /dv 1 µ = ev, ( ) dv C Q, = C E,, dv n V V C ε F = µ

n =1.2 10 10 2 v F =1.1 10 6 / χ 2 V V =0 n x

n m s x x x χ 2 s x =1 V / V V /2 V V V y x x x s x y y y s y x V y V

n m {i, j} dv dv = s y V ij s x V. ij s x s y x y {i, j} χ 2 n m {i, j} z χ 2 ij = n {z ( V [i + n + s x ], V [j + s y ] ) z ( V [i + n], V [j] )} 2 n z( V [i + n], V [j] ), z ( V [i], V [j] ) V V {i, j} n x χ 2 s x s x χ 2

V V 2 5 8 ν =1 4

9 3 0 V x 3 9 9 C q 0 9 1 2 5 7 ν =1 4

V V

3

0.3

3 3.2 50 55 µ 30 µ 150 µ 60 80 µ

1 100 µ 3

910 5 2 910 5 800 900 5

1

0.01%

10 µ 10 µ 50 µ

1 3 10 1590 1

1590 1 10 1 99.99999% 0.00001% σ(ω) = π2 64 3 ωd ϵ(ω) 1 2 d c c d ϵ(ω) ω 500 ϵ =6 ϵ ϵ > 100 σ = 1.2 10 7 µ

100 µ 1 µ 100 µ 1.2 10 7 /(hc/500 ) 3 10 7 1 10 2 10 5

(33, 33), (16, 7), (6, 5), (22, 14)

H = (p qa)2 2m. A =0 H = H 0 + V (t) = p2 2m q m A p, A(r,t)=A 0 ne i(k r ωt) + n E = A/ t V (t) = q m (n p)e 0 ω ωt = V 0 ωt. V 0 Γ i f = 2π f V 0 i 2 δ(ε f ε i + ω), f V 0 i = qe 0 f n p i mω

: k =0, E : J =0( k = 0), E : J = ±1( k = ±2/d), E ( ) j J = j s =0 E =0 J =0 j σ(ω) ϵ(ω) χ e (ω) =ϵ(ω) 1 σ(ω) ϵ(ω)

(8, 0) (8, 8) 11 22 33 ϵ(ω)

ϵ(ω) ϵ(ω) E 22 = M11 E 11 = M 11 +

E ii M ii E 11 E 22 E 11 E 22 E 11 E 22 10 50 E 33 E 44 80 90 E 33 E 44 E 11 E 22

t =2.9 a =0.144 1 2 ϵ(ω)

E ii 1/d d 12 4 400 2400 500 10 50 µ 300 400 400 1100 3240 400 1100 5 µ 150

532 2 750 450 1050 1.2 2.6 50% 25% 3240 50

532

140 5 90

140 5

3/7/20 3000 40 µ

40 µ 1 µ 10 µ 2 25 µ

4 10

4

3 E = ρ ϵ 0 B =0 E = B t B = µ 0 J + µ 0 ϵ 0 E t c

4 4 4 4 4

r α =(ct, r), ( ) α 1 = c t,, ( ) p α ε = c, p, J α =(ρc, J), ( ) k α ω = c, k, ( ) A α φ = c, A, {t, x, y, z} = {0, 1, 2, 3} 0 1, 2, 3 3 4 4 4

E = A t φ, B = A, 0 E x c E y c E z c E x F αβ = α A β β A α c 0 B z B y =. E y c B z 0 B x E z c B y B x 0 4 4 0 B x B y B z G αβ = 1 E 2 ε αβγδf γδ B x 0 z c E y c =, B y E z E c 0 x c E B y z c E x c 0

ε αβγδ +1 {αβγδ} {1, 2, 3, 4} ε αβγδ = 1 {αβγδ} {1, 2, 3, 4}, 0 4 4 4 4 1 S αβ... = L α κl β λ... Sκλ..., S αβ... =(L 1 ) κ α(l 1 ) λ β... S κλ..., S S x γ v c γ 0 0 L α v c β = γ γ 0 0, (L 1 ) α β = 0 0 1 0 0 0 0 1 v γ c γ 0 0 v c γ γ 0 0, 0 0 1 0 0 0 0 1

v γ = 1 ( 1 v2 c 2 ), γ i γ i β = v/c S αβ... = g αγ g βδ... S γδ..., g αβ = g αβ = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1. 4

S S v E = E, B = B, E = γ(e + v B), B = γ (B 1c ) 2 v E. α F αβ = µ 0 J β, α G αβ =0, ) F αβ F αβ = =2 (B 2 E2, c 2 F αβ G αβ = = 4 c E B.

B < E/c B < E/c B = E/c E B E B =0 E =0 B =0 B 2 E 2 /c 2 < > 0 h

λ = h p, λ p h i [ ] t Ψ(r,t)= 2 2m 2 + V (r,t) Ψ(r,t), = h/2π m V (r,t) Ψ(r,t)

ε 2 = p 2 c 2 + m 2 c 4, ε m c p ε = i, p = i, t

2 2 Ψ(r,t) t 2 = ( 2 c 2 2 + m 2 c 4) Ψ(r,t). 4 4 i Ψ(r,t) t = ( i c α + βmc 2) Ψ(r,t).

I 2 0 β = 0 I 2 0 σ y α 2 = σ y 0, α 1 =, α 3 = 0 σ x σ x 0 0 σ z σ z 0,, I 2 2 2 σ 0 1 σ x = 1 0, σ y = 0 i 1 0, σ z =. i 0 0 1 (ic γ µ µ mc 2 )Ψ(r,t)=0. µ 0, 1, 2, 3 t, x, y, z µ =(c 1 / t, ) γ µ 4 4

γ 0 0 = I 2 I 2 0 γ 2 0 = σ y σ y 0, γ 1 =, γ 3 = 0 σ x σ x 0 0 σ z σ z 0,. {γ µ,γ ν } = γ µ γ ν + γ ν γ µ =2g µν I 4 g µν I 4 4 4 Ψ +, (r,t) Ψ +, (r,t) Ψ(r,t)=, Ψ, (r,t) Ψ, (r,t)

3+1 2+1 (ic σ µ µ )ψ(r) =0, σ µ = σ µ µ = {0, 1, 2} {t, x, y} σ 0 = iσ z {σ µ,σ ν } = σ µ σ ν + σ ν σ µ =2I 2. 3 2 2 2 cσ pψ(r) =εψ(r),

v F c p = q = (q x,q y )= i ( x, y ) c/300 H = v F (σ q)+v (x), σ =(σ x,σ y ) q =(q x,q y ) x, y V (x) V (x)

v l E F V (r) a. l E V (r) a 1 4 l E 4 a cc 1.42

ε =0 ( ε, q, e, m, + v ) ε h = ε e, k h = k e, h e k q = k K q (+ ε, + q, + e, + m, + v )

1 K v dr dt = i [H, r] = i [ v F σ q, r] = v F σ, σ r q K σ q v = Ψ(q) v F σ Ψ(q) = ±v F q q,

v =(1/ ) ε/ k 1 V (x) x dv x dt = i [H,v x] = i [ v F σ q + V (x),v F σ x ] =2v 2 F σ z q y. q y y dq y dt = i [H,q y]=0, q y q y (t) =q y (0) q y =0

l E λ F T (θ) 2 = θθ t 2( ), θ+θ t 2 θ ( ) θ t = 1 ε V 0 ε θ + π. l E λ F T (θ) 2 = e π v F q 2 y/ee = e πq F w 2θ, ε = eew w

npn pnp T (θ) 2 = 2 θ 1 2 (q xd) 2 θ, q xd = 2πl 1 2(ε/V 0 )+(ε/v 0 ) 2 2 θ l = V 0 d/ 2π v F = V 0 d/2π npn x x

w =0 T 2 w V 0 =1 1 10 12 2 T 2 100

npn npn n =8 10 12 12 d = 100 V 0 =1

q xd = πn, N q d pn

[ (cα p + βmc 2 ) Ze ] ψ(r) =ε r H ψ(r). Z ] ε H = mc [1+ 2 (Zα) 2 1 2 ( ( ) ). 2 n j 1 2 + j + 1 2 2 (Zα) 2 1s 2 n =1 j =1/2 1/α 137 α Z = 172

r 0 Z 1/r 2 1/r ε = 2 2mr 2 Ze 2 4πϵ 0 r. r 0 = 4πϵ 0 2 me 2.

ε = 2 c +(mc 2 ) 2 Ze2 r 4πϵ 0 r. Z 1/α α Z 1/α 137 Z = 172 Z 1s 2 Z 1.6 1s 2 Γ 2e

Z Z Z Z Z 1.6 Z Z Z

2e 2e 2e Z Z cr = 172 Zα > j ε H = ε 0 + iγ. ε 0 Γ

10 19 δε 0 (Z Z ). Γ (Z Z ) 2, Z = 118 α 1/137 α 1 Zα > 1 137

Z = 1e 1 1 2 2 1 ( v F σ p + V ) ψ(x) =εψ(x).

1 2 1.5 5 1.75 7 2 10 2 2 V = Ne2 L 2πLϵ 0 ϵ r x, 2 + d 2 L N d ε r x = L V (x = L) =0

L 500 1 1 2 4 10 L 1

1 1 y 1 x ψ(x) =Ce iq yy u A (x), u B (x) q y y u A(B) A(B) C x u A = x u B = ( ε ) + V v u B + q y u A, F ) u A q y u A. ( ε v F V x d/10 u A (x = 200 d) = u B (x = 200 d) = 1 ψ(x) 2

ψ(x) 2 2 ε q y v F π/l π/l N 1 1 1

1

5 2 2

E = v F B B > E/v F B < E/v F 2 2 100 2

2 1 1 4 10

v = E/B E B c v F B c = E/v F

H = v F σ Π, Π q + ea A =(A x,a y,a z ) B = A z ε (N) =(N) v F l B 2N, l B = /eb N H = v F σ Π + eex, E x v F iv F σ ( µ µ + i e ) A µ ψ(x µ )=0,

µ = {0, 1, 2} {t, x, y} σ µ σ 0 = iσ z A µ =(φ/v F,A 1,A 2 ) φ E B =0 B> E/v F E =0 S y E S v = E/B E =0 B = B 1 β 2 β = v/v F iv F σ ( µ µ + i e ) A µ ψ(x µ )=0. A 1 = Bx 2 x 2 = y ( ) iv F σ µ µ + iσ 1 e B x 2 ψ(x µ )=0. ε (N) =(N) v F l B 2N(1 β 2 ) 1 4, B = B 1 β 2 l B 2+1 3 v F c 3 p µ =(ε/v F,p 1,p 2 ) 3

B β = 0, 0.6, 0.8 0, 0.2, 0.4...1 3, 6, 9

v F c 3 ε (N) =(N) v F l B 2N(1 β 2 ) 3 4 v F βq y, (p 1,p 2 )= (q 1,q 2 )= (q x,q y ) q ε =(N +1/2) ω c k y E B m 2 ( ) E 2. B (1 β 2 ) (3/4) 2

V V V φ 4 20 4 V V

1 0 10 4 4 B V di/dv V V =0

E E B c

V B V V

q =4α q F =4α πn, α q F n d = d + 1 2 q 1, B c = E v F = n e C dv F = n e 1 (d /r) 2πlϵdv F, l 500 d 6 r 1 α 0.5 ϵ = ϵ 0 ϵ r ϵ r 4 n n =2

C = C (d ) d d d E = n e/c d C (d B c B c V =0 B c =0 B c V V B c

V =0 V B E =0 E = 1.25 10 6 E =3 10 6

V 10 V =0 V =3 V =6 V V V Gr =2 V V =0 V =2 B c V B c B B B c

B V G = i 4e 2 h Γ i LΓ i R (Γ i L +Γ i R) 2 +(µ ε i ) 2, i ε i Γ i L(R) i µ µ µ Γ i ε i g (ε) g (ε) = N g γ N π γn 2 +(ε ε (N)) 2

g = 4eB 2π, ε = v F 2e BN, γ N N n = µ 0 dεg (ε). V B V B B = α(b B c ) α = 1 (B c /B) 2 B c = E/v F V n

n ε C V V n /ε C ε C ε C 0 1 3 B c V B V B c V V C Q 9 C Q V V

V V 0 1 3 9 V C Q 3 1 1 C Q V V

9 V V N =0 V 150 µ 2

7 5 3 V 150 µ 2

V =1.5, 1, 0.5, 0... 1.5 9 7 5 3

V E = V = ε/e V (x) V V N =0

pp p nn n pp p nn n npn pnp V V 1 5

N =0 N =0 V V 0.2 V N =0 N =0 N =0 V B =3, 5, 7, 9 f(x) = a 1+e b (x+c) + a d. b (x c) 1+e C q 0.5 µ 2

N = 0 N = 0 B =3, 5, 7, 9 V c 1 5 < 1 14 B c = E/v F 1 µ 2

3 B c = E/v F 9 V 1.1 1 r h d V (x) = eφ 0 2 [ x 2 +(h d) 2 x 2 +(h + d) 2 ], φ 0 = φ 0 [ ], (2h r)/r φ 0 1 r 1 h d ϵ =2 1 5

B c = E/v F E c B c N =0 1 1 B c = E c /v F

6

1 2

pnp npn pnp npn pnp 1 y x q θ = q t θ t,

q θ θ t q ( ) θ c = 1 qt. q

πn = = qx 2 + qy 2 n = θ t θ. q θ c pn pnp

n n θ c n n θ c pnp M pnp pnp M =1 U 0

γ ak 2 a k =2π/λ 100 0.01

4 6 1 H(q) = v F σ q + V (x). V (x) 1 U 0 d 4 6

M

2 2 M + 1 2 d λ U0 d v F, M =0, 1, 2... v F

δµ =5 30 5 x =0 50 10 30 20 10 70 δµ =5 U 0 U 0

5 50 10

1 U 0, 45, 90, 180

1 V

V V V =0.5 V =5 V 5 V V =1.2 1.5 C q C q C q C q V =0 1.5 V =0.5 C q

0.5V 1V V

V =0, 0.5, 1 0, 50, 100 µ 2

C q 100 4 6 1 1 1 V

V 0.6 V 0.2 V 0.05 1 1 3 3 1

30 10 40 U =0.45 C V =7.25 V 17 C C V C V

40 30 U V V =7.25 V 17 C C V =4.25, 6.25, 7.25 C V C

V C 4 1

1 1 1 4 6 10

7

k B T

2 2 1

1 D ν

I V R D = V I.

2

dp 1 dt dp 2 dt = q 1 (E 1 + v 1 B) p 1 τ 1 (p 1 p 2 ) τ D, = q 2 (E 2 + v 2 B) p 2 τ 2 (p 2 p 1 ) τ D, {1, 2} q i =+ n i e, n i e p i = m i v i B τ 1,2 τ D v 2 =0 ρ D = E 2 en 1 v 1 = m 1 n 1 n 2 e 2 τ D, 2 n =[ 2 ] ρ D (L/W )=R D τ D

1 2 dp 2 dt = = ( dq (2π) 2 q dq (2π) 2 q df (q) dt dk1 (2π) 2 ) { } dk2 (2π) 2 W k1,k 1 +q,k 2,k 2 q { f(k 1 ) [ 1 f(k 1 + q) ] f 0 (k 2 ) [ 1 f 0 (k 2 q) ] f(k 1 + q) [ 1 f(k 1 ) ] f 0 (k 2 q) [ 1 f 0 (k 2 ) ]}. f f 0 q 1, 2 W k1,k 1 +q,k 2,k 2 q = 2π V(q) 2 δ(ε k1 + ε k2 ε k1 +q ε k2 q). 2 V(q) = 2πe 2 q 2πe 2 q e qd 2πe 2 q e qd 2πe 2 q. e d

q 1 d. 2 2 2 2 0.5 1 0.5 1 0.3 10 1 q = mv/

dp 2 dt = v 1 2 1 k B T dq (2π) 2 ( q)2 V (q) 2 dk1 (2π) 2 { f 0 (k 2 ) [ 1 f 0 (k 2 q) ]} δ(ε k1 + ε k2 ε k1 +q ε k2 q). dk2 {f (2π) 2 0 (k 1 ) [ 1 f 0 (k 1 + q) ]} dp 2 dt = v 1 2 1 k B T dq (2π) 2 ( q)2 V (q) 2 dω [χ 1(q,ω)] [χ 2 (q,ω)] 2. ( ω/k B T ) χ i (q,ω)= dk i f 0 (k i ) f 0 (k i + q) (2π) 2 ω ε(k i )+ε(k i + q) iη. [χ i (q,ω)] = dk i (2π) 2 [ f0 (k i ) f 0 (k i + q) ] δ( ω ε(k i )+ε(k i + q)).

1 2 2 1 q 2 1 dp 2 dt = n 2 ee 2.

ρ D = 1 1 n 1 n 2 e 2 2k B T dq (2π) 2 ( q)2 V (q) 2 dω [χ 1(q,ω)] [χ 2 (q,ω)] 2. ( ω/k B T ) k B T ω ρ D = π 2 ζ(3) (k B T ) 2 1 e 2 16 ε F 1 ε F 2 q 1 q 2 k F 1 k F 2 d 4, ζ(3) 1.202 q ε Fi k Fi T 2 2 T 2 T 2 (ε F /k B T ) T 2 T 2 1 1

q 1 1 k B T V (q) q d 1/n [χ(q,ω)]

dσ ρ D ρ 1 dσ 2 2 d(en 1 ) d(en 2 ) ρ 1, σ i n i ρ i i B B 2 B 2

(κ 1 δt 1 )+a(δt 1 δt 2 )+λδt 1 = j 1,q, (κ 2 δt 2 )+a(δt 2 δt 1 )+λδt 2 =0. δt(r) =T (r) T 0 T 0 T i (r) i j 1,q 1 κ i i λ a dε dt = 2π dq 2 (ε(k + q) ε(k)) V (q) 2 (2π) dk2 {f (2π) 2 0 (k 1 ) [ 1 f 0 (k 1 + q) ]} dk1 (2π) 2 { f 0 (k 2 ) [ 1 f 0 (k 2 q) ]} δ(ε k1 + ε k2 ε k1 +q ε k2 q).

dε dt = π dω(n 2 (ω) N 1 (ω))( ω) dq (2π) 2 V (q) 2 [χ 1 (q,ω)] [χ 2 (q,ω)], N i (ω) = 1 e ω/k BT i 1, i a d 2 ε/dtdt j el 11 /T el 12 µ =, j q L 21 /T L 22 1 T

L L 11 = T e 2 σ, L 12 = eql 11, L 22 T 2 κ, L S = 1 et L 12L 1 11, Q = 1 e L 12L 1 11 = st e = ST, j q = Qj.

Q S s S Q s σ κ 2 x, y j q j L 12 (B) =L 21 (B). j =0 E = µ e = T e L 1 11 L 12 1 T = 1 T L 1 11 QL 11 T = Q T T, [Q, L] =0

(κ 1 + κ 2 ) δt = DQ 1 j 1. D D = I 2 I 2 2 2 δt 2 j 1,q ρ D = Q 2DQ 1 T (κ 1 + κ 2 ). Q j q = Qj Q Q R D,H 1 T (κ 1 + κ 2 ) Q 1,xyQ 2,xx, R D L WT(κ 1 + κ 2 ) Q 1,xyQ 2,xy, L W D = I 2

[Q 1, Q 2 ]=0 ρ D (1) (2) D I 2 ρ D [Q 1, DQ 2 ] 0 κ

0.6 150 δt(r)

δt (r) δt (r) ρ D = 1 Q 1 Q 2 δµ 2 ( q)δµ 1 (q) 2T (κ 1 + κ 2 ) µ 1 µ 2 q 1+lq 2, l q Q δµ 2 ( q)δµ 1 (q) Q = π2 3e (k BT ) 2 σ 1 σ µ. σ Q B 2

T 2 T 4

α δα i δt = j L ij γ j, δs δt = j γ j δα j δt, L ij (B) =L ji ( B). γ s γ δs/δt 0 L L ij i j γ j α j α, γ

j L 11 /T L 12 µ =, j q L 21 /T L 22 1 T L 12 (B) =L 21 ( B). V 1 R 11 R 12 = V 2 R 21 R 22 I 1 I 2, R 12 (B) =R 21 ( B) j 1 σ 11 σ 12 ( V + S T ) 1 =, j 2 σ 21 σ 22 ( V + S T ) 2

S σ 12 σ 21 α γ

V p C p V ac I p 5

10

50 1 2 > 100 1 2 230

1µ 2 2 4 80 2 3 40 2 3 180 250

V = 5

250, 230, 210 180 160

160 0.7 2.5 µ 2

200, 170, 140 110 2 5 µ 2

0.14Ω/K µ 130, 000 2 /V s V

V 0.1 1 Ω

100 150 150 V 4.2 5.3 V 10 Q D 1

8

2 2

1 1 1 1 1

1 2 1 1 1

2 1

A

a 1 a 2 δ 1, δ 2 δ 3. b 1 b 2 Γ, K, K M K K a 1 = ( ) ( ) 3a 2, a 3a, a 2 2 = 2, a, 2

a = a 1 = a 2 2.46 ( ) ( a δ 1 =, 0, δ 2 = 3 ) ( a 2 3, a, δ 2 3 = ) a 2 3, a, 2 a = δ 1 = δ 2 = δ 3 1.42 k k k

( ) ( ) 2π b 1 =, 2π 2π, b 3a a 2 =, 2π, 3a a Γ M K K Γ ( ) ( ) 2π ΓK =, 2π, ΓK 2π =, 2π. 3a 3a 3a 3a

H Ψ(k, r) = ε(k) Ψ(k, r), Ψ H H = 2 2m 2 + N [U(r R n )+U(r R n δ 1 )]. n=1 R n = {n 1,n 2 } n n 1a 1 + n 2 a 2 N n {n 1,n 2 } δ 1 B A A B Ψ(k, r) = C A (k) Φ A (k, r) + C B (k) Φ B (k, r). Φ A (k, r) Φ B (k, r) A B C A C B

k r N Φ A (k, r) = 1 N Φ B (k, r) = 1 N N n=1 N n=1 e ik R A n φ(r RAn ), e ik R B n φ(r R Bn ), φ(r R An ) φ(r R Bn ) R An R Bn A B R Bn = R An + δ 1 sp 2 2s 2p x 2p y sp 2 σ σ σ 2p z 2p z ε(k) Ψ(k, r) Ψ(k, r) H Ψ(k, r) = ε(k) Ψ(k, r) Ψ(k, r),

ε(k) k {Φ A (k, r), Φ B (k, r)} C A (k) Ψ(k) =, C B (k) Φ A (k, r) H Φ A (k, r) Φ A (k, r) H Φ B (k, r) H(k) = Φ B (k, r) H Φ A (k, r) Φ B (k, r) H Φ B (k, r) H AA = H AB = H AA H AB H BA H BB HAB H AA = H (k), Φ A (k, r) Φ A (k, r) Φ A (k, r) Φ B (k, r) S(k) = Φ B (k, r) Φ A (k, r) Φ B (k, r) Φ B (k, r) = S AA S BA S AB = S AA S AB S BB SAB S AA = S (k).

A B S lm = δ lm. H(k)Ψ(k) =ε(k)s(k)ψ(k), [H(k) ε(k)s(k)] = 0,

ε(k) = ε 0(k) ± ε 0 (k) 2 4(S AA (k) 2 S AB (k) 2 )(H AA (k) 2 H AB (k) 2 ) 2(S AA (k) 2 S AB (k) 2, ) ε 0 (k) =(2H AA (k)s AA (k) S AB (k)h AB(k) H AB (k)s AB(k). S AB S AB S AA =1 S AB =0 H AA = 1 N = 1 N N N e ik (R A R l Am ) φ(r R Am ) H φ(r R Al ), l=1 m=1 N l=1 m=1 N e ik (R A R l Am ) ε 2 δ lm = ε 2, H φ(r RAl ) = ε 2 φ(r RAl ) φ(r R Al ) 2p z R Al ε 2

H AB = 1 N 1 N N N e ik (R B R l Am ) φ(r R Am ) H φ(r RBl ), l=1 m=1 N l=1 n=1 3 e ik δ n t =(e ik δ 1 + e ik δ 2 + e ik δ 3 )t. φ(r R Am ) H φ(r R Bl ) δ n 1,2,3 A B t t 2.7 3.3 t γ 0 ε(k) =±t 1+4 3a a 2 k x 2 k y +4 2 a 2 k y. ε 2 =0 K K

K π p z π p z K K K K K K 0 H(k) = H AB = H BA 0 3 n=1 t 0 e ik δ n. e ik δ n 0

ε k K K Γ K K M K K Γ, K, K M

q = k K, q = k K, K 3t a 0 e i5π/6 (q x iq y ) H(q) (1 + O(q/K) 2 ) 2 e i5π/6 (q x + iq y ) 0 3t a 0 q x iq y H(q) =. 2 q x + iq y 0 K {Φ A (k, r), Φ B (k, r)} {Φ A (q, r), Φ B (q, r)} {Φ A,K, Φ B,K } q K K {Φ A,K, Φ B,K } {Φ A,K, Φ B,K }

0 H(q) =± v F q x iq y, q x + iq y 0 H(q 0 )=± v F q x + iq y, q x iq y 0 v F = 3t a 2 c/300, c 3 10 8 K H(q) = v F σ q, σ 0 1 σ x = 1 0, σ y = 0 i, i 0 σ z q 2 xy σ z

K K H(q )=H (q) K K {Φ A,K, Φ B,K, Φ A,K, Φ B,K } σ q 0 H(q) = v F, 0 σ q ε(q) =± v F q. q 2 c v F pc mc 2 ε = ω = ck = pc

K H(q) = v F σ q + m vf 2 σ z = m vf 2 v F (q x iq y ), v F (q x + iq y ) m vf 2 m ε(q) =± ( v F q ) 2 +(m vf 2 ) 2, σ z =2m v 2 F.

k k it it x x k k H(k) =H ( k), H(k) =H( k). k q

A B 0 H(q) = v F q e iθ q, e iθ q 0 H(q )= v F q 0 e iθ q, e iθ q 0 q 2 = q 2 x + q 2 y ( ) θ q = 1 qx, q y

Ψ(q) = 1 2 Ψ(q )= 1 2 e iθ q/2 ±e iθ q/2 e iθ q /2, ±e iθ q /2, {Φ A,K, Φ B,K } {Φ A,K, Φ B,K } k q q K K Ψ(q )=Ψ (q) Ψ(r) = r Ψ = kf 0 qf 0 = 1 2 ( qf dk r k k Ψ q F dq r q q Ψ + 0 dqe iq r 0 e iθ q/2 ±e iθ q/2 dq r q q Ψ + q F 0 dq e iq r e iθ q /2 ±e iθ q /2 ). k F

K K Ψ(q, r) = 1 2 Ψ(q, r) = 1 2 e iθ q/2 ±e iθ q/2 e iθ q /2 ±e iθ q /2 e iq r, e iq r. A B A B π 2π

q i q f V (r) Γ i f = 2π Ψ(q f, r) V (r) Ψ(q i, r) 2 δ(ε f ε i ). Ψ(q f, r) V (r) Ψ(q i, r) = V (q i q f ) (θ qi,q f /2), θ qi,q f θ qi,q f = π q K K K

K K K K K K q σ Ψ(q) =±Ψ(q), q q σ q Ψ(q )= Ψ(q ),

d g(ε) = g L d N i=0 δ(ε ε(k i )) L g g(ε) g k dk d =2 g 2 (ε) = g 4π 2 0 dk 2πk δ(ε ε(k)). g =2 2=4 ε = v F q k q g (ε) = 2ε π 2 vf 2, g 2 (ε) = m/(π 2 )

m =( 2 ε/ k 2 ) 1 ω c = eb m, B m τ c = 2 A(ε) eb ε, A(ε) ε m = 2 2π A(k) k k ε, ω c =2π/τ c A(k) =πk 2 m = k v F.

ε = pv F = kv F, p = m v F v F c m 1 1

B

(n, m) = (37, 1) 2.9995 (33, 9) 1 132, 000, 000 1

a 1 a 2 30 C T θ C = na 1 + ma 2, n m 0 m n (n, m) C T = t 1 a 1 + t 2 a 2, t 1 t 2 C T =0.

30 (0, 0) (n, m) C T θ m =0 θ =0 n = m θ = π/6 1 C a 1 (θ) = C a 1 C a 1 = 2n + m 2 n. 2 + nm + m 2 K

K K G G = 1 N H (mb 1 nb 2 ), G = 1 N H ( t 2 b 1 + t 1 b 2 ), G G N H N H = C T a 1 a 2. 2 1 e ik C =1,

(10, 0) (10, 5) (10, 10) k k = 2πj C, j =0, 1,...,N H 1, j

L = N uc T N uc e ik N uc T =1, k = 2πl N uc T, l =0, 1,...,N uc 1, l N uc 1 k = ( π ) T, π. T G G k = k G + k G G = k G + 2πj G C G, π/ T <k <π/ T j =0, 1,...,N H 1 G / G G / G k j j 2π/ T

1 (n, m) 1 k = ΓK (θ).

(n, m) =(8, 0) (12, 0)

(n, m) =(8, 8) (12, 12)

(n, m) =(8, 2) (12, 2)

n m =3l, l =0, 1, 2,... l 0 1/3 2/3 1 2 1 (n m, 3) = 1 2 (n m, 3) = 2 0

1 g 1 (ε) = g k π ε, ε g g(ε) g g (ε F )=g = 8 = 8 2 1 1, 3aπγ0 hv F g γ 0 3.1 a 2.46 v F (n, 0) (n, m)

g (ε, j) g γ 0 ε 2 ε, ε 2 ε 2 1 ε ( jπ ε 1 (j) =±γ 0 1+2 n ( jπ ε 2 (j) =±γ 0 1 2 n ),(m=0) ± γ 0 1+2 ),(m=0) ± γ 0 1 2 ( ) ja, d ( ) ja, d j a d d = C π = a n 2 + nm + m 2 π,(m=0) an π. j 0 Γ j = (2n/3) ε 1 (j) ε =0

n = dεf(ε)g (ε, j), f(ε) n M,e(h) = ±g (ε ε F ), n e n h 2 n e (q) = q=1 2 n h (q) = q=1 2 2N 0 e x j=1 1+Ae αx +βx 2 +γx 3 2 j=1 2N 0 e x 1+Ae αx +βx 2 +γx 3, x = 2ε ε 2k B T,, x = 2ε ε 2k B T. α, β, γ A α = 0.88,β = 3.57 10 3,γ = 4.23 10 5,A =0.66 q j j = (2n/3)

ε g N 0 (2ε N 0 = g γ 1 + k B T ) 2πk B T 0 4ε 2 ε 1 g πk 4 B Tε, ε 1 + k B T/2 ε /2 ε 2 2γ 0 µ <k B T n e(h) = n i e ±µ/k BT, 3 n i ε g m n i = 2g γ 0 (ε g + k B T ) πk B T e ε g/2k B T, ε g +4γ 0 ε g ( ) πj ε g =2ε (j) =2γ 0 1+2 n m = 2a ccγ 0, d 4 2 3γ 0 a 2 ε 2γ 0 + ε g. a cc a 1.42 2.46 j = (2n/3)

11 22 33 3 11 1 2 2 11 > 1 11 1 22 > 2 22 1 2 K K E ii 2ja ccγ 0, d

(8, 0) (8, 2) (8, 8)

t =2.9 a =0.144 1 2 j i γ 0 d j =1, 2, 4, 5... E 11,E 22,E 33,E 44... j =3, 6... E11 M,E22 M...

(8, 0) (8, 8) E 11,E 22,E 33 π/2 π/2

π π π π

C λ F =2π/k f

1 1 1

k = π L, L L ε = v F k = v F π L. ε v F /2L 1

1 1 1 1 200 ε 1 ε C ε 1 dk x dk y dk z k x k y k z dk x dk y dk z k x k y dk z 1 1 L λ F L

{0, 1, 2, 3} 2 hγ <ε C, h Γ ε C ε C

e V 0 Q = Nq = CV, q =, e V < 0 Q N q e = e = +1.602176634 10 19 C V U E = Q 0 = Q2 2C, dq V (q ) dq = e dn N

ε C du E dn = N e2 N=1 C = e2 N=1 C. τ = RC R C τ t t

ε t 2. ε t RC t = RC ε = 2RC. t RC RC RC

ε C = e2 C ε = 2RC. R h e 2 R Q. R Q R Q = 25.812807557(18) Ω π Γ 1/τ

k B T<ε C. ε i U E ε(n) = N ε i + U E (N). i=1 ε i ε i 1 = ε Q i = j C ij V j.

{i, j} = {0, } {0, 1, 2, 3} Q i i 3 Q 0 = C 00 V 0 + C 0j V j, j=1 V 0 V 0 = Q 0 3 j=1 C 0jV j C 00. C 00 C 00 = 3 j=1 C 0j U E = Q 0 dq 0 V 0 (Q 0 ) 3 = Q2 j=1 Q C 0jV j 2C 00 C 00 Q = Ne ε(n) = N i=1 ε i + e2 N 2 2C 00 en 3 j=1 C 0j C 00 V j

µ E (N) =ε(n) ε(n 1) ( = ε N + e2 N 1 ) + e C 00 2 ( = ε N + e2 N 1 ) e C 00 2 3 j=1 C 0j C 00 V j 3 α j V j. j=1 µ E µ µ = ε N α i = C 0i C 00, C 00 i

10 12 N =0 N = 10 N = 11 N = 11 N = 12

ev e 2 /C 00 ε C kt e 2 /C 00 ε C ev = µ E, µ E, V µ E, µ E (N) µ E,

N 1 N +1 C 00 ) C C α ε c ε V > 0 µ E, µ E (N) µ E, V < 0

V ε C V > 0 µ E, µ E (N) µ E, µ E, =0 ev = µ E, ev µ E (N) 0 V α 1 α V + V α α V g + 1 eα 1 [ε e(1 α ) N + e2 C 00 ( [ε N + e2 N + 1 2 C 00 ( N + 1 )], 2 )]. i {i} = {0, } {0, 1, 2, 3} V < 0

V V + dv dv = α g 1 α s = dv = α g = C g, dv α s C s C g C 00 C s, µ E (N) µ E (N 1) = ε N ε }{{ N 1 + e2 } C 00 ε (N) = ε (N)+ε C. V =0 V = V =0 µ E (N) =0 V N V (N) = 1 ( [ε eα N + e2 N 1 )]. C 00 2

V (N) V (N 1) = 1 eα ( ε (N)+ε C )= ε (N) eα + e C 00. V N N 0 N

g 0 (ε) =g δ(ε ε N ), N=0 g g(ε) ε N ε N = v F πn. L ε ε k B T ε C T =1 0 1 1 g (ε) = gl v F π,

Γ,i Γ,i i i Γ i = Γ,i + Γ,i = τ, τ G = e2 h MT. M T

Γ k B T ε C. i G i = ( ge2 1 + 1 4k B T Γ,i Γ,i ) 1 2 ( α (V V,i ) 2k B T ). k B T Γ ε C, ( G = ge2 1 + 1 ) 1 h 2 Γ h Γ Γ α (V 2,i V ) 2 +(hγ/2) 2.

i g 1 1

R<R Q hγ ε C

D 2 1

1 1 F = q(e + v B). 2 I x B z L W V H V xy = v x B z W. V = IR R xy = V H I x = v xb z W nev x W = B z ne

2 R xy = V H I x = E yw j x W = E y j x = ρ H ρ xy. R xx = ρ xx (L/W ) R H = E y j x B z = 1 ne, j x = I x /W = nev x 2 e = e n R H 2 /C R H h/e 2

C dr p(r) =h(n + γ), h N A γ 1/2 v d = 1 q F B B 2 = E B B 2,

1 K K q Π q Π q + ea 0 Π x iπ y 0 0 Π x + iπ y 0 0 0 H(q) =v F, 0 0 0 Π x + iπ y 0 0 Π x iπ y 0

{Φ A,K, Φ B,K, Φ A,K, Φ B,K } ψ A,K (q) ψ B,K (q) Ψ(q) =, ψ A,K (q) ψ B,K (q) ψ (A,B),(K,K ) (q) K v F (Π x + iπ y )ψ A,K = εψ B,K, v F (Π x iπ y )ψ B,K = εψ A,K. v 2 F (Π x iπ y )(Π x + iπ y )ψ A,K = ε 2 ψ A,K, v 2 F (Π x + iπ y )(Π x iπ y )ψ B,K = ε 2 ψ B,K. ψ B,K

A =( B z y, 0, 0) p i = q i ε 2 ψ B,K = v 2 F ( (px eb z y + ip y )(p x eb z y ip y ) ) ψ B,K = v 2 F ( (px eb z y) 2 + i[p y,p x eb z y]+p 2 y) ψb,k = vf 2 ( (px eb z y) 2 e B z + p 2 y) ψb,k ( 1 ( ε ) ) ( 2 p 2 y + e Bz ψ 2m v B,K = F 2m + (eb z) 2 ( y p ) ) 2 x ψ 2m eb B,K z [p x,p y ] = 0 [p y,y] = i y 0 ( p 2 y 2m + 1 ) ( 2 mω2 (y y 0 ) 2 ψ = ω N + 1 ) ψ, 2 N 0, 1, 2... 1 2m ( (ε,k,b v F ) 2 + e Bz ( )ψ B,K = ω c N + 1 ) ψ 2 B,K, ε ε,k,b B z 2 B

ε,k,b ω c = eb z m, y 0 = q x eb z = l 2 Bq x, ε,k,b = (N)v F 2 ebz N = (N) v F l B 2 N = (N) ω D N, l B = = 26 eb z Bz [T ], ω D = v F 2eBz. ω c 2 y 0 ε,k,b B K N ω D l B N... 1, 0, 1... 2 2 N N N =0 ε =0

ψ A,K ε,k,a = (N)v F 2 ebz ( N + 1) = (N) ω D N +1, N =... 1, 0, 1... ε =0 ψ B,K ψ A,K ε =0 K A B

K (N)( i)φ N 1 (q x ) Ψ N,K (q x )= C N e iq xx φ N (q x ). W 0 0 K 0 Ψ N,K (q x )= C N e iq xx 0, W φ N (q x ) (N)( i)φ N 1 (q x ) φ N (y, q x )= 1 N =0 0 N =0 C N =, (N) =, 1 2 N 0 N N N 0 ( ) 1 ( 1 1 4 2 N N! πlb 2 1 (y q x lb) 2 2 ) [ (y qx l 2 ] 2 lb 2 H B) N. l B H N φ N y 0 y 0 x 0 <y<l y q x 0 q x L y /lb 2 N 0 A B

N =0 N =0 K B K A L x = L L y = W y y x x q x =2π/L x 0 <y<l y q x 0 q x L y /lb 2

N = g L Ly /l 2 B x dq 2π x = g L xl y 0 2πlB 2 = g B za Φ 0. g g =4 Φ 0 l B A g N N Φ 0 = h e =2πl2 BB z, l B = 26, eb z Bz n = N A g = g 2πlB 2, ν = n e n. = g B z Φ 0, Φ 0 2πlB 2 l B Φ 0 n g g ν n e

ω C,D τ 1, ω C,D k B T, τ k B T ω C,D ω C 1 ω D 1500

a = a = l B 2 (Π x iπ y ), l B 2 (Π x + iπ y ), V (y) y x H(q) =v F σ Π + V (y)σ z = ξ 2 v F 0 a V (y) 0 +, l B a 0 0 V (y) σ =(σ x,σ y ) ξ =+1, 1 K, K K K {Φ A,K, Φ B,K } {Φ B,K, Φ A,K }

y 0 V (y) V (y 0 )+ V y +..., y0 y 0 = lbq 2 x V (y) =V (y 0 ) ( ) 2 ε,n 0 = ± V (y 0 ) 2 vf +2 N, l B ε,n=0 = ξv (y 0 ). y 0 x v x (q x )= 1 ε q x = l2 B V (y 0 ) y 0 = 1 eb z V (y 0 ) y 0,

I x = dq x λv x (q x ) = e L x L x 2π Ly /l 2 B 0 Ly dq x v x (q x ) = e 1 V (y 2πlB 2 dy 0 ) 0 0 eb z y 0 = e ( V (Ly ) V (0) ) 2π = e h µ. λ = e /L x V H = µ e, R xy = V H I x = h e 2 = R Q. R Q R Q = 25.812807557(18) Ω ( σ xy =4 N + 1 ) e 2 2 h, G Q = e2 h, ( ν =4 N + 1 ) = ±2, ±6, ±10... 2

g = g s g v =2 2=4 1/2 2π π p p + ea dr k + e C C dr A +Γ B =2π(N + γ). Γ B Γ B = π

R xx R xx R xx R xy k = e(v B), k = e(r B)+. A = B B dr r ds B = 2π C S e (N + γ γ B) 2Φ Φ=Φ 0 (N + γ γ B ) Φ=Φ 0 (N + γ γ B )

S Φ 0 = h/e γ B =Γ B /2π γ B =1/2 B πk 2 N =(N + γ γ B ) 2πeB = (N + 1 2 ) 2πeB N 2πeB, γ =1/2 γ B =1/2 γ B =0 k =0 k 0 N 1/2

ν =2

E

n = N/ = [ 3 ] ρ = mn = [ 3 ] p = mnv = ρv = [ 2 1 ] µ = η = [ 1 1 ] ν = µ/ρ = [ 2 1 ] φ = E = P = neφ = [J 3 ] J = nv = [ 1 2 ] = v L/ν = ρ v L/µ = γ p =1/τ p = [ 1 ] D ν = ντ p =

N e =1.602... 10 19 ( ) m E v 2 3 ρ + (ρv) =0, t v t = (v )v 1 ρ P + ν 2 v + f, P, v ρ n r t (v )v P/ρ ν 2 v f = F/m

(v )v ν 2 v v L (106 1 ) (10 6 ) ν (0.1 2 1 = 10 10 3, ) v F 10 3 (v )v =0 P = P (r) v = v(r) ρ = f = γ p v v(r) =0, 1 ρ P (r) =ν 2 v(r) γ p v(r).

n J(r) =0, σ e φ(r)+d2 ν 2 J(r) =J(r). J(r) 1 2 1 2 σ = ne 2 τ p /m ej(r) =σe(r). 2 xy v x = ψ y, v y = ψ x, ζ = v x y v y x, ψ = ψ(x, y) ζ = ζ(x, y) 2

x, y v x x + v y y =0, ( 1 P 2 ρ x = ν v x x 2 + y 2 ( 1 P 2 ρ y = ν v y x 2 + 2 v y y 2 2 v x ) γ p v x, ) γ p v y. y x 2 ζ = γ p ν ζ, 2 P =0. ψ, ζ, P 2 ψ = ζ. γ p ν

v v b = l v b n, n v v b l b l b =0 v = v b v b =0

: v b =0,v b =0 ψ b =0, ψ x = v y b =0, ψ b y = v x b =0. b ψ x,y+1 = ψ x,y + ψ y + 2 x,y 2 0+0+ 2 2 ψ 2 y 2 x,y 2 ψ y 2 +... x,y = 2 2 ζ. 1 ν τ =1/γ p D ν = ντ

ν τ ν τ D ν = ντ D ν 30

τ ee τ p τ ee τ p τ p τ e ph τ e

2 e ph e e 150

τ e = ev F µ πn, µ ( ) 100 ε τ ee =0.1 1, F, T k B T T 1 T 2 T 4 T 0.1T BG τ e ph, T 1 T 0.1T BG T BG 1000 0.1T 100

µ = 10 µ = 50 µ = 100 τ e 0.1 0.5 1 l e 100 500 1 µ T = 10 T = 100 T = 200 τ ee 1 0.1 0.05 l ee 1 µ 100 50 τ e ph 1 10 1 l e ph 10 10 µ 1 µ 150 f(r, k,t) f t f = v r F 1 f k + f t, f = f(r, k,t) F = F(r) v = ε(k)/ ( k) f(r, k,t) t = f 0(r, k) f(r, k,t), τ(k)

f 0 f 0 (r, k) = 1 e (ε(k) µ(r))/k BT (r) +1. τ(r, k) F =0 f(r, k,t)=f(r, k,t= 0)e t/τ(r,k) + f 0 (r, k). f = ( ) m 3/2 4πv 2 e mv2 2k B T. 2πk B T k p = mv = k p

A(r, k) p = k ( d 3 ( k) A(r, k) t + v r + F 1 k ) f = d 3 ( k) A(r, k) f t, A n(r,t)= d 3 ( k) f(r, k,t), A(r,t) = 1 n(r,t) d 3 ( k) A(r, k)f(r, k,t), t na + r nva n v A n F 1 A = r k d 3 ( k) A f t, A = A(r,t) f/ t = 0 A =1

A = k = mv t (mn v )+ mn vv nf =0, r f t =0, vv v v vv δvδv = (v v )(v v ) = vv v v v v + v v = vv v v v v + v v = vv v v, t (ρ v )+ρ ( v v + δvδv ) nf =0, r f t =0.

σ = ρ δvδv σ xx τ xy τ xz = τ yx σ yy τ yz τ zx τ zy σzz P 0 0 σ xx + P τ xy τ xz = 0 P 0 + τ yx σ yy + P τ yz 0 0 P τ zx τ zy σ zz + P } {{ } } {{ } = P I 3 + τ {r} = {x, y, z} = {x 1, x 2, x 3 } σ ii τ ij P = 1 3 (σ xx + σ yy + σ zz ), σ ii = v i x i

( vi τ ij = µ + v ) j + δ x j x ij λ v i...... λ (ρv)+ρ( v)v + ρ(v )v + P τ nf =0. t λ =0 v =0 τ = µ 2 v v t = (v )v 1 ρ P + ν 2 v + f, f t =0, ν = µ/ρ F/m

F

60 60 90 110 25 45 45 60 90 110

120 140 15 100 165 154 165 0.2 µ 2 1000 6000 2 2000 10 3 3

90 60 120

120 1 184 10 184 30 160 47 3 3

3 150 20 30 10 µ 950 6 3000 180 2 470 500 µ 2 30 100 10 µ 150 10 10 µ 2 10 6 495 4 3000 180 2 420 450 µ 2 600 µ 2 950 6 2 3:1 4

120 350 400 1/3 15 5, 15, 60 0.2, 0.3, 1 2 3 2 2+1 45

30 2 2 2 3 80 2 0.015 20 1 100 10 250 2 0.015 10 2 80 0.3 0.015 2 20 0.9

2 3 2 ϵ 9 ϵ 15 0.3 0.5 500 µ 0.001 0.005 Ω 285 2 2 285 2 7% 90 2 2% 1 µ 2 3 50 80 µ3 9 9 350 380 µ 3200 µ 50 55 µ

100 1 10 Ω 500 µ 100 115 5 3000 30 115 1 1822 3000 45 60 115 1 10 160 1822 1822 3 405 20 50 µ 26 2 2 1822 115 1 8 2 2 5 3 2 2 2 70 417661 45 2 17 19 500 150 70 80 100 2 20 17 70 80 14 16 20 10

3000 30 115 1 4620 3000 45 60 115 10 10 200 4620 80 µ 150 µ (x, y) =( 4500, 4500), (4500, 4500) 400 2 1:4 10 2 8 2 2 5 3 10 30 52 µ 2 8 2 100 2 4 2 2 3 1 20 8 2 2 5 2 2 2 3 2 11 2 30 2 10 2 1 1100

8 10 10 2 2 10 3 10 13.56 30 13.56 10 20 2 10 10 2 13.56 30 13.56 10 20 30 2 35 45 2 13.56 800 13.56 50 20 3 6 2 4 50 3 13.56 600 13.56 125 20 15 150 10 1 55 300 100 2 100 4 8 1 6 1 0 2500

2 60 1 2 350 4 8 1 6 1.7 0 2500 3 30 1 2 1 4 8 300 6 1.7 210 2500 4 60 1 2 1 4 8 660 6 12 40 3000 1 4 30 127 2 +( 2 ) 2 5 2 2

86578 2443 98+ 40, 302 4 98% 232076 0.1 200 > 99.5 1.04 6.3 0.5 0.1 70 1 4.5 127 99 66 50 1 5.5 2 5.0 200 2 5.0 200 200 99.5% 100 910

5 10 2 500 1000 6 8 80 10

400 30

30 1 0 2 1000 18 910 840 7 7 400 45 2 100 30 250 80

80 1000 6

1.6

G

V V V =1 V =2 20 1 0

6 6

4

9

70 100

10 10

n p

ϵ µ