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10

2 109 /cm

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eEg/2kbT

V(r)

V(r) = V(R+ r)

R

2

2m2 +V(r)

=

nk(r+R) =ei .R.nk(r)

V(x) =N10

(xja)

0< x < a

2

2m

d2

dx2 =E

d2

dx2 =k2

k=

2mE

(x) =A.sin(kx) +B.cos(kx) 0< x < a

(x) =eiKx[A.sin(k(x+a)) +B.cos(k(x+a))] a < x

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(x)

x= 0

B =eiKa[A.sin(ka) +B.cos(ka)]

kAeiKak[A.cos(ka)B.sen(ka)] =2m

2 B

sin(ka)

cos(Ka) =cos(ka) +m

2ksin(ka)

z=ka

f(z) =cos(z) +sin(z)

z

f(z)

f(z)

= 10

[1, 1]

k

K

f(E, T) = 1

e(E)/kT

+ 1

E

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(E)dE

E

E+dE

(E)dE=f(E, T)D(E)dE

D(E)

T = 0

Ef

H0

|n

H0|n= En|n

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W(t)

(t)

(t) =n

an(t)|neiEnt/

|n

E

n=

n

i

t(t) = (H0+ W(t))(t)

i

t

n

an(t)|neint = (H0+ W(t))n

an(t)|neint

in

an(t)

t |n

eint =

n

an(t)H0

|n

eint

in

eint

tan(t) =

n

an(t)W(t)|neint

m|

m|n

id

dtam(t) =

n

an(t)Wmneimnt

Wmn=m|W(t)|n H0

n

m

am

mn=EmEn

am an(t= 0) = 1

am(t) = 1

i

t=tt=0

Wmneimntdt

Em

Pn(t) =|am(t)|2 = 12

t=tt=0

Wmneimntdt

2

=|Wmn|2

2

eimnt 1

mn

2

Pn(t) =2t

|Wmn|2(EmEn)

E

E+dE

Pn(t) =2t

|Wmn|2

D(E)(EmEn)dE

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Pn(t)

dPn(t)

dt =

2

|Wmn|2D(E)

1

n=

2

|Wmn|2D(E)(EmEn)

n |n

Dopt3 (k)dk= 24k2 dk

(2)3 =

k2

2dk

nr k = nr/c

Dopt3 ()d=2n3r3c3

d

S= E

H/2

|S|= 12

c0|E0|2

U() =1

20| E0|2

U() =Dopt3 ()fBE()

f(E) = 1

ekbT 1

U() = 3n3r

2c31

ekbT

1

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k

E1 E2

|1

|2

|2

|1

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E2 = Eg+2k2

2me

me

E1=2k2

2mh

mh h

=E2E1=Eg+ 2k2

2

1

me+

1

mh

mr

1mr

= 1me

+ 1mh

= Eg+2k2

2mr

k= (Eg)1/2

2mr

1/2

dk= 12

(Eg)1/2

2mr

1/2

D(E) =D() = 1

22

2mr2

1/2(Eg)1/2

E= = ckopt dk= cnrdkopt

Dopt3 (E) = E2

23c3

nr() E = ckopt/nr

P(E) =Dopt3 (E)f(E) = E2n3r23c3

1

eEkbT 1

E21 = E2E1

B12=2

|W12|2

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Rest12 =B12P(E21)f1(1f2)

Rest21 =B21P(E21)f2(1f1)

Resp21 =A21f2(1f1)

Rest12 =Resp21 +R

est21

B21=B12

fi

Ei fi(1fj)

P(E21) = A21

B21(eE21

kbT

1)

A21B21

=Dopt3 (E21) = E221n

3r

23c3

=Rest12Rest21

S/

S= (c/nr)P(E21)

=nr

cB12(f1f2)

=Resp

12

B12(f1

f2)

A21f2(1f1) =2c22

E221n2r

Resp12 (e(E21

)/kbT1)

g

E21

f2 f1

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fh= 1f1 fe= f2

g() =() =2nrc |W21|2 1

22

2mr2

3/2(Eg)1/2(fe+fh1)

|W12|

Eopt= E0.ei opt. t

=Uek(x)ei( . )

Whe=h|W|h=e| E|

Uhk(x)Uek(x)xei( opt)dx

=

opt

opt

=

W

gopt= g0(Eg)1/2(fe+fh1)

g0

300K

Eg = 1.4eV g0 = 2.64104cm1eV1/2

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D()(fe+ fh1) = Eg

41019cm3

D()(fe+ fh1)

= Eg

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I

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