Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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111
R = 1/(q⋅n) , (4.35)
,dBjRU
⋅
⋅
⋅
=
(4.36)
,
.
.
nq
1
R
e
⋅
=
(4.37)
.
nq
1
8
3
R
e
⋅
π
=
(4.38)
(
)
( )
.
nn
nn
q8
3
R
2
nnpp
2
nn
2
pp
µ+µ
µ−µ
π
=
(4.39)
n
n
, n – ,
n
, –
.
:
.Ej ⋅σ=
· (4.40)
,enn
kT2
E
0
∆
−
=
(4.41)
n
0
– , ∆
–
, k – , –
.
k ,
. ,
, .
(hν > ∆E ),
.
.
(hν < ∆E ),
.
112
, " "
.
:
.
,
.
" "
,
E
hc
∆
=λ
(4.42)
– .
.
,
,
.
.
,
,
, ,
. , ,
,
n - .
. ,
( . 4.12 ).
E
. 4.12
∆
∆
d
E
)
)
113
, ,
.
n- ∆
d
. ,
n -
n
= e⋅n
n
⋅
n
, (4.43)
n
n
– ,
n
–
.
,
,
, ,
( .4.12 ). ,
,
,
- .
.
-
" ",
( ).
-
p
= e⋅n
p
⋅
p
, (4.44)
n
p
– ,
;
p
– ,
.
, -
. , n -
, - –
.
,
,
T
0
α
ρ
=
ρ
, (4.45)
,
1
ρ
⋅
ρ
=α
(4.46)
114
– ,
0
–
= 300 , – .
, (4.45)
.
=
0
exp(–∆E /2kT), (4.47)
=
0
exp(∆E /2kT), (4.48)
0
– → ∞ –
kT –
.
. 4.13 ( )
( . 4.13 ) ( . 4.13 ).
,
: 1)
, 2)
.
.
.
, .
,
. ,
, ,
,
, ,
.
< >
n
(4.34)
, ,
.
, → 0
,
.
.
ρ
a)
T
)
ρ
.4.13
115
,
.
~ 10
–5
.
n
n,p
" "
,enn
kT2
E
0p,n
∆
−
=
(4.49)
∆ – .
:
,eT
mk2
4
1
)T(n
kT2
E
2/3
2/3
2
∆
−
⋅⋅
π
=
(4.50)
m – .
, ,
-
.
, . ,
. ,
.
.
m
,
T
U
=C
m
m
(4.51)
U
m
– .
, , ,
U
1
U
2
.
116
" " –
U
3
.
U
1
, U
2
, U
3
. .
4.14
.
1
. 2
" "
.
>>
U
1
U
2
U
3
.
U
U U
1
.
,
U
m
= 3RT (4.52)
(4.52) (4.51),
m
=3R (4.53)
. ,
,
.
. ,
, ,
,
m
( 1). ,
,
.
3.
( << )
, ,
( 1 . 4.14)
. (
m
~ T
3
)
.
3R
0
m
C
m
=3R
2
1
. 4.14
117
,
0
(
), " "
( 1).
0
m
~ , .
(
m
~ T
3
) 0 .
, ,
, N
, N - .
,
, .
.
U
1
U
2
.
,
, . ν
,
v2v
ω
⋅
π
=
ν
=λ
(4.54)
v – .
. , . .
, + d
,
,
v2
d
Nd
32
2
π
ωω
=
ω
(4.55)
v
– .
. – –
. – –
.
E
=v
II
,
G
=v , G –
,
, –
118
. (4.55)
.
v
2
v
1
2
d
dN
33
II
2
2
+
π
ωω
=
⊥
ω
(4.55a)
(4.55 ) 0
m
,
:
.
v
2
v
1
6v
2
v
1
2
d
Nd
33
II
2
3
max
33
II
0
2
2N
0
max
+
π
ω
=+⋅
π
ωω
=
⊥⊥
, N = dN (
) , n, n
– (4.11),
:
( )
.
v2v
n18
3
33
II
2
max
−
⊥
−
+
π
=ω
(4.56)
: v
= v
⊥
,
32
2
v2
d3
dN
π
ωω
=
ω
,
(4.56)
,n6v
3
2
max
⋅π⋅=ω (4.56a)
v – .
.
n
2
n6
2v2
3
3
2
max
min
≅
π
π
=
ω
π
=λ
(4.57)
3
n/1
d,
min
min
≅ 2d. ,
, .
,
. .
E = hν = (4.58)
119
kp ⋅=
(4.59)
k
– , k = 2π/ ( –
).
v
p
ω
= (4.59a)
– (
), v –
.
, : ,
, , ,
, ,
.
,
- . dn
V + d
[ ]
1)kT/exp(v2
dV3
dn
32
2
−ωπ
ωω
=
ν
[ ]
.
1)kT/hexp(v
dV12
dn
3
2
−ν
ννπ
=
(4.60)
i
,
.
1)kT/hexp(
1
n
i
i
−ν
=
(4.61)
max
= k (4.62)
k – ,
max
–
(4.56 ).
,
. (
), d
3.
0 .
120
,
1e
dxxT
3RT3UU
T/
0
x
3
3
0mm
θ
−
θ
⋅+=
(4.63)
= /k ( – ), – ,
– , R –
(R = 8,31 /( · )), U
m0
–
,
.R
8
9
U
0m
θ=
(4.64)
3
-
g F u Ag u l Be Ge Si -
, [K] 406 467 165 210 339 418 76 1160
366 668 2000
d, [
A
]
– 2,86 3,52 4,078
3,61 4,05 4,95
2,55
5,66
5,43
–
( d
).
10=A1
10-
.
.
1e
)T/(3
1e
dxxT
12R3
dT
dU
C
T/
T/
0
x
3
3
m
m
−
θ
−
−
θ
==
θ
θ
(4.65)
:
1) ; 2)
<< .
1) . (4.63) (
x
– 1) ≅ x
:
.RT3Udxx
T
3RT3UU
0m
T/
0
2
3
0mm
+=
θ
⋅+=
θ
(4.66)
.R3=
dT
)RT3+U(d
=
dT
dU
=C
0m
m
m
(4.67)
, ( .
4.14). / >> 2.
,
,
θ
=ω
k
max
. >>