711070_15353_morozov_a_i_lekcii_po_fizike_tverd…


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.



200400
























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k

cikri
exp()
-
-
-





L
m
x
2
L
n
y
2
L
p
z
2
1/2 (
z:

Vdk





Vdp
(1.4)
Vmd
312
212
312

-


222

νεε

312
3
2
n
e

223
310
(1.10)





vpm
310
21310
vpm
/10



313


exp()

-
(,)
dnFd
()()
nFd
()()
ενεε
(1.13)
0

0













E
T
F

F









-
(1.16)
IgFd
()()
εεε
-

Ggxdx
()()
IFdGGFGdF
()()()()()()
εεεεεε
(1.20)


d
0






(,)
(,)
−∞∞
GGGG
()()'()()''()()...
εµµεµµεµ
=+−+−+
IGFFGz
=−∞+−
()()()'()
''()...
z



/


IGGT
()''()
(/)
(/)
(1.24)


()()()()

IGggT
FFFF
=+−+
()()()'()
εεµε
(1.13).

Gdn
()()
ενεε
(1.27)
(1.26)
−=−
'()
(1.26)
(1.28),
EFd
ενεεε
()()
()()
EdT
=+−
ενεεενε
()()
'()
++=+
νεενε
()'()()
FFFF
TET
(1.30),


hhhh





(
)
=

=








==⋅
92710
z
-
-
-




dnB
2








-

IdnBH
===
µµνεµµνε
()()
-
-
χµµνε
0
T
T


T
0

0





=

−+=
VrE
ψψψ

VrTVr
()()




()()
rTr
()()
rTer

()()
rTTerT
++=+=
122
iTT
[()()]
TTT
()()
rTer
χχχ
()()()
TTTT
1212
+=+
T
TkT

gTn
-


ikT

ikr
rure
()()
urTur
()()



k

(2.1)









ikr
-
k
m



rrr
kVrkVrdrVr
()()()

kVrkdrVre
ikkr
'()()
(')

kkg
-
()()
kkg
kkg
()()
()()
()()

Vkkg
−+
()()
(2.16)
()()
()()
kkg
000
()()
kkg
(2.12),
kgg
k


(2.16),


ψαψαψ
kkg
rkrkgr
()()()()()
()()
=++
=−+

0

[()()]()(),
()[()()]();
εεαα
αεεα
000
kkkVkg
Vkkgkkg
−++=
++−+=
()()()
Hrkr
ψεψ

()()
()()
kkV
Vkgk
εεε
12000
(){()()
kkkg
=++±
±−++
(()())}
000
kkgV
1
2
-
+
()()
kkg
++=

000
000
()()
[()()]
kkg
kkgV
−++
120
000
000
()()
[()()]
kkg
kkgV
+=±
−++
120







kgg
(
-
d
n
-
d
n
-
-
V

II
III.
-
2
-
-
d
2
d

d
3

-






N








srrdr

ψψδ
()()
-



1










ikl
erl
()()




(2.29)
()()()
Hrkr
ψεψ
Vrl
=−+−
Vrl


l
(2.30)


erlHrldr
ikll

(')
εψψ
()()()
(')
erlrldr
ikll

rlr


hll

erHrhdr


εψψ
()()()
errhdr
ikh


N




εψψ

rHrdr
trHrdr

ψψδ




H

tekse
ikik
()[]
εεε
()()
ktse
=+−
tts
rrr

kte



(,,)
(,,)
(,,)
-
eeeeka
ikikikaika
+=+=
cos
(coscoscos)
ktkakaka
=+++
kkka
±=±
(

t
t


=±±±
(2.39),
coscoscos
222
min
-
a
,


max
t
216
ztt
12
=±±
=±±
912
=±±
(coscoscoscos
=+++
2222
coscos)
min
max
(2.42)
-3.
max
s
p
d-
(2.29),

.

(muffin tin)











&#xr000; r


-

213
πεπε
πεπ
==∝

223213
1
210



1
1
























-
-
-
-
-
-
ξεε













ξεε




(2.45)
ξεε



vpp



-
















qvB
-
-




kconst




qvBevB

evB




evB
m
0
(3.5)

2








=++
e



==+
(3.9).

221
eBn
eBn
(,)
kkdk
zzz

eBneBnVeB
2122
z
(3.7).
dkd

πεε
eBm
()()
-



()()
n




-






1
-










10
,


2
1
(
2
2
n
m
eB
m
k
2
1
(
)
(
2
)
2
1
(
2
1
n
S
e
n
k
e
B
e
F
n
-
(3.17)
1

S
S
e
B
e
F
e
(
10
55
,
9
)
(
2
1







-
(4,2
B
1
-










GaSb,














-
-

(1.13),
-

F
e







),

n
e
e



e
n
2
0
ϕκϕ
d
2



-d/2

ϕκϕ

shx

(/)
xEr
shx
chd
ExE
chx
chd
(/)



1.2,
(1.11).
310
283

εεε
een
202
=≈≈
101




0
r
r
r

()()
rrr
(4.11)
(4.7)


exp()
q


exp(
4
)
(
r
q
r




nnWT
exp(/)
-
-
nnnneT
=−=
()()
e







,



()





cos()
-
nrtAe
ikrikt
(,)

FeE
/
-
enx



(4.19)
2
2
0
2
0


310
283
010
161
T




kak
()()()
/()









(,)
(,)
(4.12).
0
2
q
k


ϕϕε
()()/(,)
kkk
(,)/
(4.12)
(,)
0



(,)

eEeEe
=−=−



Penx
=−=−
-

(,)
011
=−=−
e
(4.29)






(,)
→−∞


(
-
(4.25),
-
(4.29).





-






-

-
-


-



rotE
rotHj
=−=+







0

y


EEikxit
exp()
HHikxit
exp()
-
t
H
=−−=
(4.31), (4.32).
ikEiH
ikHE
µσω
µσω
EEei
exp()
µσω



-
).
210
711

nkc
2222
(4.35).
σεω
122
εωσ
0






z






-




-





(3.4),
(3.6)









FkFkfk
()()()


FkFkfk
()()()
FkkT
()exp(()/)

fkFk
()()



:
jqfkvk
eheheheh
()()()()
()()
rrr
Qkfkvk
eheheh
()()()
()()()
-

(5.3)
(5.4)

Frpt
Frpt
Frpt
(,,)(,,)(,,)
++ℑ=
rvp
jjj
-
-




(5.5)
000
()()()



vkE
(),



()()

fkqkvkE
eheheh
()()()
()()(),


jekvkvkE
eheheh
()()()
()()(),
T




ehF




z


-

-

vkvkEvE
ehehF
()()
()(),cos
jevE
ehF
cos
222
1/3.
νεξ
kdk
-
F
d
F
()
0
(5.2),
(5.12)
1/2.
τνε
τνε
(5.5)
000
()()()
==−∇


−∇=−
(,)
(5.16)
(5.4)
τνε





=−∇−
τνε
2
T

=−∇
πτνε
(5.19)
=−∇
-
πτνε
(5.14)
(5.20)
2
T
e








-
-
-
imp
rVrR
impi
()()
kWk
imp

-
(2.9)


kWkikkRdrurVrR
impi
'exp(')()()
⋅−−
urikkrR
()exp(')()
(5.23)

kWkVikkR
imp
'exp(')

n

(
n

c



cnnn


cnnn
=−+
$$$$
$$$$
cccccccc
1221
1221
++++
+=+=
$$$$
cccc
$$$$
cccc


c


eimp
()()
Hkckckkdkdk
kkkk
σσσσ
rrrrrr
-
exp(')
(')
HVikkRckck
eimp
kkk
rrrrr
VikkRdkdk
kkk
rrrrr
exp(')
(')







Vkk
=−⋅
δξξ
(()('))
⋅−−+−⋅
FkFkFkFk
()(('))(')(())

⋅−−
exp(')()
kkRR

imp

Vkkfkfk
imp
=−−
δξξ
rrrr
(()('))(')()


δξξ
eimp
imp
Vkk
(()('))
(())

eimp
imp
(')


'
(5.35)
eimp
(')
(cos)
eimp
imp
-

kVrdr
eimp
xnV
imp
-
-


-
-


RRu
-
-
WrRWrR

jls
(5.38)
(5.38),
rRWrR
,()

kHk
eph
kHkeur
WrR
eph
ikkr
lsj
(')
uurdr
(2.26)

p
(,)exp()
NMq
epqiql
⋅+−
aqaq
-
-
s,
-
p-
rrl

rrr
kHk
NMq
iqkkl
eph
exp(('))
+−⋅
eur
WrRl
ikkr
(')
(())

⋅+−
epqurdraqaq
(,)()
3
lsls
s



()()
Wr
r
ls
j
s
,

kHk
NMq
eph
eurWrepqurdr
ikkr
(')
()(
(),(,))()

⋅+−+−
exp(')
iqkklaqaq
kqkg
−−=
-
kHk
Mkkg
eph
(')
∇−−⋅
rWrepkkgrdr
()(
(),(,'))()
⋅−−++−
(')
(')
akkgakgk
eph
-
-
eph
{(,',,)
(')
Hkkpgckck
eph
kkk
⋅−−++−+⋅
(')
(')(,',,)
akkgakgkkkpg
kkk
⋅−−−−++−+
(')
(')
(')
dkdkakkgakgk
+−+−
kkpgckdkakgk
(,',,)
(')
(')
h
+−−−
kkpgckdkakgk
(,',,)
(')
(')}
kkpg
Mkkg
(,',,)
(')
∇−−
rrr
rWrepkkgrdr
()(
(),(,'))()
kkpgkkpg
(,',,)(',,,)


kkpg
(,',,)
⋅−−−−⋅
δξξω
((')()(')
kkkkg
⋅−−−−+
[()(())()
FkFknkkg
eep
+−+−−+
FkFknkkg
eep
(')(())((')]
−−−−⋅
kkpgkkkkg
(,',,)()(')(')
δξξω
⋅−−+−
[(')(())(')
FkFknkkg
eep
−−+−++
FkFknkkg
eep
()(('))(('))]

+−−−⋅
kkpgkkkkg
(,',,)()(')(')
δξξω
⋅−−++−+
[()('))((')
FkFknkgk
ehp
+−−−+−
(())(('))(')]}
FkFknkgk
ehp





-

(












eph

eph
kkpg
(,',,)

{((')()(')
⋅−−−−⋅
δξξω
kkkkg
⋅−−++
[(')(')]
nkkgFk
+−+−−⋅−+
δξξω
((')()(')[(')
kkkkgFk
+−+
nkkg
(')]}
-

nqTq
()/()
≈hh
eph



eph
eph
-
-
EmM
e
-
eph
hhh

-
τγθ
exp(/)







exp(/)
exp(/)
e
M
E

eph
(5.14)
exp(/)



phD
exp(/)




-
100%,
eph
eph
rDt
-
keph
τττ
eph
eph
eph
,,,
eph
(5.49).
0

z


qkk
eph
kkqp
(,,,)

⋅−+++
{cos()()
qvsqnqFkg
Fppe
++−++
qvsqFkgnq
Fpep
cos(()()}

z


(,,)

cos


()(,,,)
eph
dxqdqkkqp

⋅−+++
{()()
qvxsqnqFkg
Fppe
++−++
qvxsqFkgnq
Fpep
(()()}





kkqp
(,,,)
(5.47)
const
(,)
−∇==
rWrrdrF
()()
-
kkqp
(,,,)

kkqpq
(,,,)
eph
1

eph
eph
eph

T

T

/10


epheimp
(5.20),
eph

eimp
eph
()()

T








-
kkVkk
3412
rrrr
rrdrdr
021
()()()()
-
-
kkVkk
3412
urur
urur
021
()()()()
⋅−+−
exp()()
ikkrikkrdrdr
242131



rrrr
kkVkkurur
341211
,()()
=+⋅
περ
⋅+−⋅
ururikk
1124
()()exp()
⋅+−−=
exp()
ikkkkrdrd
12341
=+−−
exp()
ikkkkldrd
1234
⋅++⋅
urur
urur
()()()()
περ
⋅−+−−
exp()exp()
ikkikkkkr
2412341

-

N

kkkkg
3412
+−−=


kkkg
123
,,,

kkVkk
3412
{=+⋅
++−
VkkkgNdrdur
kkgk
(,,,)()
123
123
⋅+−−−
urukkgigr
()()()exp()exp
περ
ρρρ
qkkg
=−−
(4.23)).
(5.23)
(5.45),
4,
(,)
(,)
e (h)
e (h)
e (h)
e
e
e







dkdk
Vkkkg
rrr
()()
(,,,)
⋅+−−++−⋅
δξξξξ
()()()()
kkkkkgk
2323
⋅−−−++−+
[()()(())(())
FkFkFkFkkgk
2323
+−−++−
(())(())())()]
2323
FkFkFkFkkgk





kTv


qkkg
=++
−=−+
kqk
kkq



k

(/)


eph







D


T

jET
=+∇
QET
=+∇
,,,
-
-
(5.70)
(5.71).
QjT
=−∇
-
-

A

B
EdldTdTdT
−==−−
1
1
2
2
0

a
b
b

).



0




b


.




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