Laser SemiConDutOr
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Transcript of Laser SemiConDutOr
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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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