Введение в физику поверхности

!"#$"%& '()*+,-.,/*,01223 ...

Author: Оура К. | Лифшиц В.Г. | Саранин А.А. | Зотов А.В. | Катаяма М.

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j

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P (r)

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2

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5 5 5 #!

# & / 0 ( ! ' ( 0 ! 6 0 & -. ! $0 ( ( ! / 0 (,. $" ,0 ' 0 ( % " $ - ' " ( " " $ % 6 00 0 & $0 $ ( $ ( !

0,. , 0 0 &- - ( ( ) # * & # . , ' , . ! ! ( ( % " " -&(-.0/(&0,'"-/!/0/"%

≤ 1000

&

-0"$ -- $ !0/( ! ( - & ! ,0-. ( , ' 0- -. ,0" " ( , ! " " -.,0 / / -. ( " " ! % " # & "( , ' ! , , & " " & -8 (-."0"!,.0- -%## ( ,'" " / - ( $ ' 0 0 ! " -. -0 $ -& ( " $ ! "$ , . - , ( ! #(& 6 # 0 . -. ( " ( $ ! -. % & / 0 0 , ! . ( ! ( - 0 ( ! ( 0-. ( % 6 & # 0 0 " $ $ ( ( - ( $ --. 0 - ' $ - - " " " - / !0-.&,-. 0 ( , ! % ( - , $ ( " 0 " 0 % 6 " '". " &,-. , $ " , 6 -. & ! -,, $ /! / - ( -"00 "( ( 0 0 ' ! " , " 6 &- 0 -. " , 0 ! ( % ! " - -0 ' $( 0 ! " ,0-. ( ! % " ( / 0 0- ( . 00 ( ) % % 6 " # & # & ( * * *

,- " $ 1 5

0 & 0 / ! ( - ( " -0 # *

--. - "( " $ , % " " " / (' $ . &--0 ( . $ % -& 0 & &0 , ( 0. " , 0 / -. $ ( % $ - , " " " 00&-, -. 0 ( $ ( -/! 0 " ! ! &0 " ,& ! ( 0 ! ( - " # & , 0 , ' ! ' " - ( , % " " $ " ( ! ' ( - , ' ! % " .-0 - , "( ! "( ' 0-.. ! ," & - $( - % % . -, 0 ( $( $ ! ( " ,0 ! " ($ --0-+

∆k⊥ ≈ 0

×

%

, -0 ! 0--.00 ! ( " ( ! . " ,0 00 - ( ! " ( ( % " + ,. 0 - , ! ( " ( " ,!

5 5 5

5 -.,0 -,, ( $ ! $0 , ( % # ! " 00 " " ,0 ! " '$

" & # / --,0-. "0 ( 0 " # &

" 0 & 0 ! ,' $

" # ! &0-"#,/-" ,0-. '

" &

! ((0 ',$0%0--, ' ,& ( "/ " " /" - 0 !0,/(("'(-. !" ( , -,0 "% -./ $ / & 1 0 " ,"-1 ( 0& " -/ ,-0 ! / & , /0 0 $ $ ( " ( ( % # -.,0 / " $ ( "0 ( 0&- , ( -00 ( $ ( % -. 0 " " ,0-. $ ! % -, - -.,0 / (0& , & ( " %00 " & # 0 0 &-0 ( 0 $ ! # " 0 -0 ,-0 / 0 ! ! 0 -0 , ! . % " ! "!$(-.,.!(-, -0 / ( " ( -. % % 7 ! . 0 ! $ , $ % + $ ! " $ & % # & &&-. $ -". ( $ "% $ &&-. " $ % ((""0&-. " $ 0&-."'"$ #- &

≥

• • • •

√ √ ◦ 2√ 3× √ 3 R30 ◦ 7× 7 R ± 19, 1 × c ×

&

+ , ( 0 ( -0 ( % 16 " " 0

"( -. ( - $*(-.,0 " -. ' ( $ ( # ' $ - 0 ( % % & 7 -0 -, , , $ 0, $ ! "$ ! + +

0 & 0 ( % # ! ! 0 & 0#0&-(" 0 ( " ",'00 -., -,& ' ( " 0& % 6- *

- -&&,-0 ! " , % " 0-.(,' % + + " ( + ( + ) $#( " )

) & ,0 &- ) # 6 + ! * #&-#6 &$6 0) 0"

*)0

• • •

◦

◦

• •

◦

%( . 4 43 /0 / 0 0 / 0 ( ( ,0 ! % -,0 & 00 ( $ "0 ! ( ! $0 % " ( 0 $ , ' ' " ! $0 ! % " & , 0 ( $ ! ( $ % # # -.,0 / - - 0& ! ' , ( ( % " & & 0 & , ! -. , ( ! ! $ " 8 0,- -.,0 -, ( $ " ( $ - , ( % " " 0 0 0-.. ( ( ( ) % # -& 0 0 & $ " " " ! " !

0&(,-. / ,(-& " - 0 -. , & ( $ ! - ( 0 & 0 0 ( 0&& " " 0 ' ! % , - " ! " ! , " , % 0 , '0&0& , . ! ( "(&0(0&& " ""-" - ! - ) 0#. ( *"-.$"*"- 0-#( 0 ( ) & 0#-( " , ( ( " % % &("$!$(.0&0- %60-"(("# %&

0 &0 / ! "( -0 ! #( % $ $ ( $ . % # % % 6 0 "0 " " " ,- ! " , 0 % % 6 (!0&!(!$0-%

∼

• •

•

!

1 3 - 0 & 0 - 0 " ! % 0 & # ( ! ( ! $0 " & -0/$( 0 & ( 0 ( 0& " $0 ( , ( - $ & ( " " # & -. ( $ ! $0 - $( (,, , 0 - ( , ,-.&0 (( ( &0 ( % 6 (!. /(", 10((0& 0 ( 0 , ! - 0- % " 0 &0 (( " " ( " #" 0--(!0-% ( " , , & ( " - ! "0 , " " "% / &-, , ' &0 "0 0 , ( -, (-,0 / --,0 " & ! % % 6 ( &0(( ,

Ep

• •

N (E)

Ep

E=0

Ep

•

Ep

Ep ∆Ep

∆Ep

E = 0

#

! "# ! &

! 00-& - , , ( ! & ( 0 ! , $ " , % "(-"/-" %

, 0 & & , ( " .,,& ( . ! ( % " /! / 0 ! $0 " " " % , , , ( ( ! ( ( % # # & 0 & /-& !- -(,$0 '"0 -" "- (- , , " ( ( " $ 6 ' ('$ -(' ( $ -.-,% -. 0 -.,& ( ! $0 % " 0 & ( - , '

(

% ! " / & ( ( 0 " 0 ( "/ ( . ( ", ( - % " $0--, -"(-0!"&(

N (E)

dN (E)/dE

2

d N (E)/dE

2

0 / 0 , "/ ( ", " $ , ( #0 '-./0-,&((0""0-((% -.,0/"0- - &0 ,- ( ! . ( $ - -,, / ,

&(-" -,-"/ &(

• •

% ! $ "# $ "#

*0'0/(0% !

$

'

( $ ! 0 & . ! "0 ! & " " , / (", ( - ,

00-0 )#0,0-. " # 0 0 -- ( ( " -"& " E0

E0 ± ∆E

E0 = eV0

Z∞ I(E) ∝ N (E)dE . E0

V0

#- &

#

! - -,, / ( ( ,

&(-" -.,0 " $ ( )0-00/!! % " # & & + $%! 0 !& 0/("0 " # + 0 (( " % % % -, 0 -, " . " ! # -.,0/" , / 0-( ! ,

$-"-,0& / 0 -- ' -0 , ! + 0&0 . -, - ,, ! ! $ ! % % " 0 ! ( 0 - 0&- $ $ ! ("&0/"-.0-% # (-$0,&0&!&#-" &&#% 0 , -.,& - ( $ ! ( " 0 0 & , -. ( - ( $ " ( % 0

--0 & "( - , % " 0 & ! ( "( ( ( - " , "0 % " 0- ! "! 0-.-,, % 0 / /0 , !

0 % " " / / -, -. & ( (

$ ( " 00 / -, ,- ! 0&- " $ % " ! -(-,-"/ &( -, / ,-1 ( ' - ! -0 -, ! ( !

*'% '-!-,# & ! $

"$ $--" 0-% # / (

."((/-.,00"% " ! , ,, '& ' - ! ! -. ' % -. 0 ' -0 ( - , ' ( ' " 0 0 ' -,, - - , 0 ' - % " 0 0 & - "/ " -. ( - " "&($"!,$((% #/0&0- ((0 0 , -. & "( ( 0 " ( ( ' % # -, -. ( " " & & -,! 0 ,, 0' $&-, -"(!" 0 ( % ( " " / 0 -, ( ' !- 0&- $ " !0-../%" ,-1 ,0 ! $ " 0 & , ( " 0- ! " , % "(-.,0/"0$(- -, (--. "

,0$ " -, / $ -, ( ' % ,-1 -.,0 / -! ( ",%( ("

• • •

◦

Va

E0

E0

Va

eVa /E0

42◦ 190

"( , (-.& 00'--. 0 ! " 0-, # & "

"! # $ & $ & ! &

$ ! & & " ◦

"

( $ %

( $ $ % & , 0 -, ) ! ( " ,", 0 -0 -0 ' ! ( ""( # -. / ' ( 0 " & ! ,. " 0-!(--"0"',-

0$- ("$ /,(0& $ % # . -0 00& ( % &-, , 0 0 - !$"0&--.,0 /"' ! (-0-!-, " % / ( " & 0 " , % % % " " 0&- " , # & & ' (

( $ , 6 " " ! ,

"$ $ "$,('( -0 &-, 0 ( ! ! # 0&- (-.,0-/""& ' ! $' - ! $ 0 0 (-""0-

*%"-,$,0 ",(0%

◦

127◦ 170 ◦

◦

!

- 0 /! & 0-.. " # (-.,0"$," "$% 60&-, &,""(! 0 & -,- " , "( "/

& " (&0 .(-.,0$,$ , ( " &, ! " " ,,(("&, ! -.,0 0 & ( " & " " &, ! " " 0 (&(0 " " , ( ", " ( - % " 0 0 -0 0 & & ! ! ( #"0&" -"" % 0- ! - , ! ( " " 0&- , % # " & & ( $&, $ , " , 8 " !" (('- #- & 0 & "( ( 0 "0 , ( " &, ! " % # ( , "( " ! ( ! ( " " 0 -0 0 , ! ( ( / ( % #

/1!, 0&! "(-.,0" 0"/ -,-"/ (",$-, # & , - - " , ( ( " % % % " -.,0$ & (, -, $ ! ( $ . % " 0 & 0 , -, % " 0 ' $ & -, ( % '0,,6.%#, %$& 1 3 3

3 6'(,%('$!(- , 0 / -) 60 ! !

0&/(% " 0 &-0 &0 - & " ( ! # " " 0- / , ( ! ( ( % # " 0 , , 0 " % % "0- - &0 0 " ($-, "-0 " , % " " , " -., 0 , " -, 0 & ( " ,0-. &,0$,,$('

• •

∆E/E ∆E

∆E/E

E0

∆E/E

∆E/E

∆E/E

I(E) ∝ EN (E) .

EN (E)

∆E

E0

∆E

∆E

L1

& & ,%0#,-/,-0!-.& ( $ " ($&" '#,-0!-.& ' & & (, $ 0 $ " " " / 0 0 00 / ' ' , "

(' -" ) % & # 0 & 0 , ! $( $ " -& % # & $0 " -0 ' ' " , ! -. , % " 0& 0 & 0 "(- ( "$( " $ 8'-. # -/ ' " % ./,%0

• •

E < 500

$ " "# ! " & # "&& ! ! &

!

$ ! $ ! KL1 L2,3

(EKL1 L2,3 = EK −EL1 −EL2,3 ) ~ω = EK − EL1

$ , ( ' $ " , 0 , , % % # -. 0 " ! " , 0 % / / 0 0 0 -. % " # 0 0 0 / ! ( ' ! , ! ! , ( $ % " " . , $0 $( ! - ' , % # 0$."!0-& -/!! -0, -.,0, " ( , ( $ ( ( . ( % % " "0/(& ( ( 0, 0 - ! % " " ! , , ' ( ( $ ( % " " " " !" ($ -,%('($ L2,3 V V

KL1 L2,3

!

0 / 0 , -0 ! - ! " 0 " # & , - , " " - " ! ( # " ,%($ -" (,

,%($$,0"% 5 2 0 & - 0 ! ( , $ -." 600% (-!,0 $ & "0 " ( 0

&0-(" (% , , 0 & ,0 , . ' " " " " -!$('" # & - & -0. ! $ ) # & / 0 , &0 0 ' % " " 0 , 0 ! " ! ( 0 ( $ " # , -.& ' " (

% " /0 0 & / $ 0 , ! - " " (0$,%0-& L2,3 V V

EKL1 L2,3

EKL1 L2,3 = EK − EL1 − EL2,3 − φ , φ = Evacuum − EF ermi

1123 4 5 % 2 0-" %-/!"#-& 0-, -0/( 0 0 0 & 0 0-0$ " - "( 0 0 ( 0 ! ( ! $0

0 -, 0 & (0-,-1 ! 0!& ! # # & -.,0 / -, / ( " ( ' - % -0 -, ! !-.- $% !"% "( ! ,!%&-- , 0 ! " #&. 0 - 0 ( ( & ( % " &-.(-"&-, (.0. , % "! / , ( ! , ( % " # & * (, ' 0 " % 0 0 & -. / "( 0 "' -,0 , 0 % ( ", ( - 00 " ! $ ! -,- 0 ' -0 % -0 -, / ,-1 ! ( ' - ! $ & &&- 0 , " $ , " #

• • •

dN (E)/dE

∆U ∝ sin ωt

! ! & $ !!

!

$ ! ! ! & & "

! ! " ω

dN (E)/dE

N (E)

dN (E)/dE

I(E0 + k sin ωt) w I0 +

2ω

dI d 2 I k2 k sin ωt − cos 2ωt , dE dE 2 4

#--&

!

!

&

# " "! & !

!! !! " N (E)

dN (E)/dE

EA

dN (E)/dE E0

N (E)

-0 , ( , . ( ! -, -0 '- ! ! ! ! $ % " !&-,! EA

dN (E)/dE

1 5

5 0 / ( 0 , % 8 / 0 /0 & / , $(-,(-0 ! "( " " % " 0 0 0 & - ( 0 ( ! 0 ( " ,/,%(, '.0 &,%% ω

2ω

# & $-"-$0 ( , " # & ' - ( -& ! # 0 ('- 0 , ( $ , " ( - " % % " $ , &0 " $ ! " $ ! % # , 0 , ," "! (0& " " , % & 0 00 , ,- " /0 - ( ( ( - ( - " , , - , " $ " , ( % # & ,'0 ""0$ - $ , ( - ! " ( % % ,0 0 0 / ! , ( ' ! % " -

! !

"" ! KLL

LM M

MNN

!

/! / 0&, , ( " ( - % % 0 ((- & ( $ &-0 . , ' " -0 ! " ( - "( ( $ " . 0'"(-,"0-& (, 0 ( & % $ 0 -., 0 ! 0 " ( $ . ( ( % ! ( ! & ( 0 ! ( 0

" ! . 0 ,-0 . , ( ""( ! ( , % " , ' 0 ' " &-0 , . % $ . - . (-"(- ! - , ' % % -& ( " 0 ' " % (-"""((-!"(&( " ( ! "/ " ! " &-0 0 / - " ( " ! .,0

% % " .0 -0 0 ! $ ! "$0 0- % % " 0 ( ' 0- " ' " - % " % &0 --. 0 & ( . , ( ! " -",%(("(,% -, --"".,, (.- ! $ ! . ( % " / $ , ( ' ' % / & ( 00

$($ , " 0 %0- , ., ( " #, & "!( ,%($ % # & & 0 & ( 0 ! ( ! $0 )0. 0- , ! ' 0&0 " ) ". ,($ &) % 0 & " " 0 ! ) " # 0 , & " "( ! $0 ' " &-0 $ -., 0 ( $ ! ( ! & ( 0 ! % ( " $ ! $0 % " 0- / ! ! -, $0 $ % " , & 0&( "( ! & (0!)&''"0-" ") 0' " &-0 0 ( " . $ , % ! &-0 , . 0 & ( . $ % ) . # &

! " )0&-$,%0-"% Ii

1 Ii = Ip σi γi (1 + ri ) T 4π

ZZZ

i KLM

ni (z) exp

−z sin θ dθ dϕ dz , λi cos θ

Ip σi (EK , Ep )

Ep

Ep

γi (KLM ) (1 + ri )

KLM

[1 + ri (EK , Ep , θ0 )]

θ0

ni (z) exp(−z/λi (EKLM ) cos θ) z

i

z

λi (EKLM )

θ

! - , ( $ -,0 $ " 0 & 0 - ( #% "

"-"'&-0$0-(-. ,00/( -0,0 -0 & & $ " ( " # &

+ 0&& " "

-,0$" - & &0 ! ! ( ( 0&& " " " # 0- / ($0 !-.0 ( 0& $ " ! ( 0. " (-!0(0&&" 0 - / 0 & 0 " " 0- ! " . ( ,0((0-,#-0& $ , & ( "( 0-. 00&-0 ( " 00& % " -0 &-0 # & (- - , & ( # /-.,%&-"! " 0-"($" -"(!$0,0-% -0 , --0/ (- # & !- ! & $ , - ( " % 8 " " &0 ., / , ""!0 0- " ! #,(

& &-0 0 ' " ( - " ( ( (

-0!," &( , . - ( - , ( 6 " , , " .. , ( ( ,-. $ ' $ % % " # /( 00 ( " . ( -0 ' " 0 & -/ , $( $ ! ( 0. ( % - 0 -.,0 - " . ( - ( ( , " ) $-0, ( . ! $ - / ! ( ! !

$" # & - ! " & 0 $ ( % - (!-, #0-0!, ##-&(

&") % "

", ($&. '0-% -"(-.,0", 0 !(0-. # . "0 % -0 , &-/ ( ! $ 1 $ , ' % - . - , ( -, % % "&0 & ! $0 ( $ , , ( . " ,%&-

T

ϕ

θ

z

•

σi γi

• •

ni (z)

z

ni (z)

ni (z)

i = A, B z

∞ IA

B

∞ IB

A

B

A

!

#-& , & ! " $ " ) " - " (( 0- ! ( - #- -&)0,,!-,0 0 & $ " , % / 0 . ' ( . 0- % " 8 # &

"60-- & " " % 6 / " " ! ! "/ " ( . , " ( % " # & ( -,& ,0 ($&(0/ "( - , ' , ,0 !0- " " - $ " " # -0!,#-&0( " #-*& 0 , . . , ! ! -0 . " % " " !00(!&0,(.,!-.%" ! - " " - $

$

$ '

- 0 #-"&"0,!"! - - - - # & " , " ( " $ 0- % 6-& $!-",(-0!. ∞ IA /IA [1 + rAB (EA )] λAB (EA ) = ∞ IB /IB [1 + rAB (EB )] λAB (EB )

[1 + rB (EB )] λB (EB ) XA × [1 + rA (EA )] λA (EA ) XB

a3A

a3B

A

3 aA , aB

A

B

B

XA

XB

XA =

1

1+

∞ ∞ (IA /IB )/(IA /IB )

XA (z) =

.

X A + XB = 1

A

dA

1, 0,

0d

XB (z) =

0, 1,

0
z

# $ "#"# $ A

B

A

dA φA

##--&& , -- - /( ( ( - " # & # & & 0 , ( ' -. ! - "/ " " " - -.,0 / , "! ( " " & 6 !-!.(-0&$$, " ∞ IA = IA

∞ IB = IB

1 + rB (EA ) {1 − exp[−dA /λA (EA ) cos θ]} , 1 + rA (EA ) exp[−dA /λA (EB ) cos θ] .

A

φA {1 − exp[−dA /λA (EA ) cos θ]}

φA

{1 − φA exp[−dA /λA (EB ) cos θ]}

! 0 0 ( 0& " ( " - " ',0 , / (--0 & $ " ( $ . & % -"#

!

# ' ('$ &((/ . , 0 & 0 &0 ( ( $ % # .,0-.,-!$('"""$ # &

0 &-0 $ 0 ) ##,,00, # , (-,0-$,,$($# &

0 ) # #,0,-($# ) 0#& $ ,0 . ! ( &0 (( ( " " "(

& " , & ( $ % %

&-0 # " / / 0-0 " " 0 " ! , 0 , " " # 0 & 0 ! ( ! & ( 0 ! -. # & &# ,0-. - 0-0!!.- " - !

! &0 (( ( % , . . ( " , 0 , ( -, , $ -"(- !& . -.,0 / 0 (&($" "0 $( ( % # &

0 0 0 ! -. $ ( # # % !# , "($( 6 & - 0 & ( ( "( " ( ! " % & , 0 & / 0# ( , % " " (

! ( ( " ,,0 . - -. ( " !$($ % -0- 10−3

104

4

• • •

−3

Ep . 20

&-0(- ! ( ( ( ( " 6 -.,0 / -, 0 $ 0 ( % 6-1- &0- -,(/'-!,% !"-,#-0!,(( 6 &, -- 0 /! " 0 " , % " /" '- -, -.,0 / ! ( % " 0 ! $ "( ! & ( 0 ! " !-,0&-"!$0-

- "(22$" ,. / , ( " .0 " ."0, &-0 !&0 &,0(,- 0-& ( $ % -- 0 " "

- 0 0 , ( " " " " " ( ) % " - , ,, -0 (0 $ ( , ( ( % - 0 , ( ! 0 , ( $ , " " # &

! " , ( %0&/( ,,(. " #

& 0(0&"(!0- 0.0&#/ &

0 0 & ! " , $ % " ! 0 - ( ! ( ( $ . , "

, ! ( ( ( &-0 $ 0 6 . . "(-& " ( ( ! 8

. , , , ( ( ( % % " " ( , ! -. ( " -, + 0 & , . ! ( ( , ( ' % " , . &0 -.,. ( $ ! ( ( . ( " " 0-&-, - -, , ! , , ( % " " ! .&- ( ( ' -. % " 0 , ' ' & " . ( $ 8 # & , - 00 (( - ! $ ( $ " " " . / 0 & ( ' ! ( - (-,(-$"

K

εc

∆E

∆E = EK + εc ,

Es = Ep − ∆E = Ep − EK − εc .

(d2 N (E)/dE 2 )

" "# ! !! K

! ! !! !

! ! ! ! E0

Ep

K

1 3 3 5 3 4

#

!

# '

( ' $

8( & , ! % % -.,0 , / " " ! " $ % " # 0 & 0 /! / $- ( " " ( ( / &, $ 0 ( ( % 6!"&"%&-0 6 -0,, , 0& ! " % . / $ ! $( --. " ,-. 0 (6" ( $0 -. $ " # #% 0 , ,, ( " 0 , ( -, 0-$,,$($#- & %-0% L1

L2,3

"-. !

-0!('"(((. " ""!-,,!

! ! ! " " ! ! !! ! ! $ ×

~ωp ~ωps

E1 E2

S1 S2 S3

,,

3

, 0 , % # -0 0 $0 $( $ ( ( $ % /! 0 ,, -& $ "( $ ( " " ,-, - - ( $( $ $ " , ( % 0 " , ( , ( ' 8&-0$0""(-.,0% -& , / (, ! ! 0 , !0 0 & .-0 &-0 $ 0 ( ! % 6 " . -. #".0 3 0 ! , , ( % 6 & / 0 , 0 , - ( - & & $,

"$ $ " - ( -, $ - % , - ! ! ( ! " &, & 0 & "! $ - / - ( ( , -., ", 0 00 % # & ",'$%% #- & , 0 / 0 , 0- & & ) " , 0-"" )(-.0- " , 8 " #- &

ωp =

4πne2 m

∆E = ~ωp

1/2

.

e

n

m

0& "0-& (0&$/#- &-"&0-% -.& &&, . $ ( - , " ,-. " " -- , . ( --."( $ % , 0 " ! 0-,0 ( " & $ " " # & ( ( ' -0 0--- , "( ( ( % " " " # & ( ( - -0 ( $ ! "$ ( -, $ ( " " # "$0!0 / 0 -0 - ( $ , " ( " -

6 - & --, ($$ "0 ( ( $ " ,0 &-0 &-0 ( -0 $ " - ! ! " 0 , & ' , 0 &,00 , ! ( $ & ( -, " ! & ( -, % # -&

, / ! ( ( ( " # 6

. 0 & 0 0 / $( ( " " "# /( , 0 , $ & & ( -, -. , , ( " ( " & 0 , " (-,

2

ωp ωsp = √ . 2

"! ! !

-, -. 0 & ( "/ ! % #% 6 - . 0 ( , "( ( 0 ( ! , ( % 6 6 --0 / - ( ! $ " % # " ( -, !& , " , " ( 0&!" (-,$"",!-" N (E)

d2 N (E)/dE 2

-., , -0 / !, ( " $ % 6 ! ! $

$ '$ $(-.,0" 0-00&/% #(-, - & 0 0 / ( -. ( -. 0 ! $ " , " # $ - "$ ( ( -.- $0 % " & (-0( "-0 ( . ! 0 % " #-- - &-.& 0 0 & " & 0 0 -, " (-. -. ( &-0 , " 00% " "$ $8,& (-.0- ) & , "0 " " -0 - (8-, , , ." ' , '

, ( ( - ( ! , ""/( & (-, " 0& " *0#" ( ,- ! . ( ( &(-,( 0#

•

•

2

# ! 2

2

•

!

$

$

! '$

($%& -0,% & " ( " "0 ( ! $0 % % 6 & /( , .0 "0 ! $0 8 " " ,(-0 / 0 &-0 ! . ' ( - ( %

, ! ( ( ( # " * # & ( (

,(% (-!$0-& "$(!$0(-- , "(, 6$(,- 2

! 0 0 & ! ( 0- ! ( % # " (

- - $0 ( ( , , (

0."#('(" - ( - &-, 0 - ! $ $ , ( -. - 0(-

2

5 %( (22 &, - " " ( " 6 - , 0 , - ( $ 6 0 (- -0" ( "/ ! % 8 . $( " ! -,0 ( 0&& ( # " - / 0 . , ! . ( $ ! % " 0&- , "( ./((0" (, ( !

" ! " !& !

,& - $ ( % " " -, , 0 $ , ' -, " - 0 ,0,'-, ' " " *

--. ( $ $' - ! % % $$ - 0& ((0" ◦

◦

$ , -- & (-.,0/(- "!" $ & % # & "! $0 ( 0 $ " (-$0,&0"% 0 (&-0!& "#0#(& "

0 0 - ! - ) % # # & -.,0 / 0 (!$&(0!$0- -, ( " " 0 , ' " " $0 $

--, 6% 0-, -.,0 / $# - ( "' - ! ! , ( " - ! 0 & .0 . "( ( 0 "( , "( " % " & " 0 "/

(",,0,'-, % 0 0 " " " -. 0 , -. &, ( ( " "( " - " 6 "' - %( 0- - % " " , $ $ ( " ' . (, ' & $$ ! $ " % -. ! " - $ ( $ (

./% 6",- -. ", ,( ./$(% -0 , &, " -& ( - ( ( ' 6 " 0 &- (&, "(!"( ( " % 6'$ / , " - $! - "",'0# #- & 0# &, / " ( ( " " 6 6 -0 / "

$,! !

"!!&8, -0- " $ % -. ,0 " ( - $ - $ " ( &, " " , , % 6 ' !

, " ( ( ( !. " '/- " 0 " , , .,- -0- $-" ,(-. ($ $-('''"-0--(% !,

0. -0 0 "! !-&/"#"- $ ! "$ -. $ % " 0 /

$(- ",,0(-,% ! -0- ( -0 ! ' & ! ( % " ("-- -.$" 0/ $ $ "-","/"%" ($ 0, ! " ' ∼

∆E

−1

100

−1

= 12, 41

.

•

2

•

& !

&

!!

"

&

&" ! & &

&

" ! ! ! !

! ! ! 2

2

2

2

◦

•

! $ "

"!&

$

%$ (-.(-(%

&, ,-. ( " & 6 # #($-

*" & - 0-. ( ( ( " " , / - , ( ( % " " ---. &0 ( ( $ .,&-. % " # & & *

,-. & , , " 8 " ---.- , (-.- ( - $ ! " ( % ((0-"($

$% $ ! !! "

! !

"

! !

! α=θ α 6= θ

~ω

|k| = |k0 | ∆k

S||

S⊥

∆k

S||

S⊥

# &

(-.,0 0 - '$

!

! ) % 00, - " ,0 ! "0 ( $

" ( $ ( ( $ - , ! -0 0 , '$ "' " " (!-.$" ""0&", %"

(&-0&0& (-!% #

& # &

- &-"& !,&. $ ) 0 , . " " (--0/0-" 0 & & " , . ! ! ( % " 0.- . " 0 . , . ( -0 %( $ ,(".0&/-"$0& -0-(0($

Ei

~ω

Ekin = ~ω − Ei − φ ,

φ = Evacuum − EF ermi

• • •

~ω ≥ Ei + φ

!

" "#& ! !

" !

! !! ! D(Ei )

I(Ek )

# & "(-.,0$ , 0 & -- # 0-"(("!% "(,,0, "0 " "( " # &

(

! ' $

!

! - & ! #$'$ (

!

! $ ! ( $ % " -.,0 0 & " &,-0 ! #

, 0 0 0 / (

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! !&"

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, 0 0 / (

-- ) #

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% &

,- / ! " "

% % / , 0 & (-"- $%

!" ( . ( 0 " 0 " " %)0&0" ! , $ &,-0 ! " % 0 & 0 - ! ! % 0 0 $ ( $ $ " ) % " # &

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. / -" ( . ( " & -.,0 / ( & ! ( " '$

Kα1,2

Kα1,2

∼

K

α1,2

p1/2 → s

p3/2 →1s

Kα3,4

Kα1,2

Kα1,2

∼

%

# " ""#

& ! "# & ! "

" & " ! "

- -.,0 / ! $ ! " ( " & % # % ,, - & 0 &- - 0 " ( ( ! !

( $ " -"&,,"& # % ! $ , " 0# ,0 0 & 0 " $ $ - #- '&-"0## ''& -&("$#-"% # ' *0#-" ''&,". 0 " # & -- ,-.,.&- &,, ( "/ ( " ! % , $ -.- 0 " ! ) % % $ 0 (-0-.,, , $ ! 0 ,-0 , ! ! &0 ( 0 ! 0 " $ ", ) % " $! ' ( $ &,-0 ! "( " (0

0% 00-. $0 -. $ # $ 0 "( $ "

$",-. % # (-.,0 0 & --. $ ( ( 0

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/ (-0/( / . -.. 0 " , ' % " 0 / .-- / " ( ' ( 0 ! - " " $ ,-0 !

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%

◦

4 2 5 3 53 3 5 , . " # / 0 / 0 $ ! & -( ' " # &

0 -0 ! , . ! ( % % " " 0 &- - ( ( -, ( $ " ) & - 0 -0 ! -. -., , ! ( -. $ ( "

0& 0(0& 0 / $ ( ( 00 % 0 ( ( 0& $ % " # . , !0& $0!- , ( ( ( -, $( % % " & 0 ! , & & ( " -& .0 , ! ! 0 , " " " -",$0-$0,-!"!-.,%

I(Ek )

0"--.&-0 / (!( &, 0 , " $ $ 0 ,- " 0-,-

, ( $ ( % # & 0-!% , .- , & ! , ! ! % " &, - . -, 0 , " $ 0 ! " ( ! $ %

!00 &" (-.,0 $

-0!". % # -. 0 & &0 ( -, ( " 0 . 0 & , , ' " & " ! % " "

0 & / , 0 0 0 -. ( $ " 0 % 6 " % -"-"&-0$$0

& ! ! " !

0 ( " "/ " ( $ $ % - & , 0 (! ( , $ ( " "0 " " " / . 0 ! " " "$ & 0 % & & - ( 0 ( ( $0 "$" " " % " 0 -. ( 0 " ( $ -& "

, /

! ( , '

" " % ! 0 . 0 ! , " ( % 00 / & 0 -. "0 ( ( ( ,"0&"",0-$#- &

! - 0,, ! $ ( -0 (

/0 ($ , ( -. ' ' , % % " -&- ( $ . ! , % 6 # # & -, , , ( .

,-"% 0-&0"0- #- *& & . ( ! &&& ( 0 ! ))0&- , 0 ( - ( ! &&& ( 0 ! 0 ()- $ 0&-",.0 i

Ii = J0 σi (hν)T

Zπ Z2π

γ=0 ϕ=0

J0 γ

Li (γ)

Li (γ)

Z∞

z=0

ni (z) exp

−z dz dγ dϕ , λi cos θ

,'&0" 0% ! ) &

# & -. , - ! " , ! " ! # " # # & *

00 ,%-, & " " , % " " -.0&- , 0 " ( " " 0 $( $ "% # -0 & - ! & 0 $ ( & 0-&0 - "( - ( , ( .,(-0/ (

"! %

" $ #- & σi (hν)

K

hν

$" $ "

!$'

∞ λAB (EA ) λB (EB ) XA IA /IA = ∞ IB /IB λAB (EB ) λA (EA ) XB

3 aA . aB

##-- && / -& ! , " ( " , % 6!-, " # & # & # &

/! / , " " " " " % , - " " ! -- ! " "

-, - -0 - -. ! ! ! ! % % " & , -, % $

-.,0 , 0 & ( " ( , ,0 % % " / 000 !$.0 $ 0 ! ( $ # " # & ( -. ( -0 ! % % 8 , & & - &0 "0 ! ( , " " " % 0 , / - 0 & ( ! ( , " " " , % " # & &0 , $ ! , " " # & !

$ / ( $(!,% , 0 & !,"-, ( 0 $ ! $ # 6 .-0/, " , 0 0 - & " " ( " " % 0 0- 0 $ ( ", " 0 0 0 & 0 ( ", " 0& " ,/! , , $ ! " "( " &, ,0-. ! " " " " " ""0&"",0- A

dA

∞ IA = IA {1 − exp[−dA /λA (EA ) cos θ]} ,

∞ IB = IB exp[−dA /λA (EB ) cos θ] .

• •

! ! # "" ! #

$

p

p1/2

p1/2

p3/2

p3/2

! p3/2 p1/2

•

2

0 &, 0- 0 - ! " % 0 --. / ( - - " % " " # , 0$-0 #-.0 0/ ( - " 0 % &

! . " ( ( 0 % " 0-&, 0 0- " - % # & , 0 ! "0 " " (

" & 0 -&-0$0

'/$!

( . . % % , -0 ( $ ! $ " ( , -&, " #

! ' $

!

! $ !

( $ ) &#

# &, # + ( &" -- . ,/, !

-0 -0 /( /( &0 ( ! , / 0 -,

( ( 1 "

"% 0,(-.,0% , 0 " , & , " 0& $ ( ( ( % " / , , ! $-!"0,% 0 , ( "! ,-0!" -($.% "" , ,- ! , " ! % "

$0 #($ % 0 0/"

! &-0 ( (,%,% &&,-0 ! " ! & & 0 - ( " 0- ! "( $ %

-.,0 / & ! 0-. ! ( ( % % # &,-0 -., ! "( "

0&- (--&! & 0-,( &-0 0 ( " ( " -., "

0&-#!0.00/-0 % & 0 & (",& ( - ( ( " ( $ ( % " # ""( " 0&- , , " .- " &- , -,. &-0 , % " " & &-0 (- ( ( 53 3 5 $,%,% 4

5 -.,$0&

-.,0 / &#"!! ( " % & 0('($ 0 # " 0 , 0 , -.- $ 0 ! " 0 /

$,(-""($"0 0/" , - -0 , ( - $ " 6 -. 0 ! - $ " (

0!&00"$, -.,0 0, " ( $ "" ( % " % " ! "

0,0!"0% ',0-. - 0- ( ( $ ,- ! $( ' ( $ $ ' " % " " $(- $ ! ' - "

, , -.,0 ! ! ( " , # % 0$,

0&- (

%%& 0&-, " ∼

• •

(

%( $ -.-0 ! % # / 0 -0 0 " ( 0 ( ( " $ / -.,-,, ( $ . , ' ( , % / (-.,0 &(-/""((!- -0 $" ( - , ! 6 ( - "( - " , -

0-" / %( $

0 " # -. (0 ( - ( - " % *

, -0 "0 ! ( $ " ( ! % 0"-. 00&-, 0 , ( # & &- , "0 , ! ( " " " ( " ., ( ( $ $ " , .,% 0-##- & & ! "0 " ( # & 0-% -& ( & ) ---. 0 00 ( ( ( " ( $ % " " # #& 0,"!-% $ # 0 000 " 0 " . 0-- - 0 , ( ,00& -./($",,(. # & .- 0 0& -0 0 , - ( . ! ( ( $ , ! " " & ' 0,- , 0 -00 $ " " -. % (---."((0-." # & 0 0 & ()0 ( $ " " ( ( $ " " " " 6 ", % 0 -0 0 / , ( $ " & ! ( ! . ( % # " . ( $ $ " -. ( -& % / 0 (- " ( $ ( "" 0,0-.0&- /( 0 ' " &0&- (

0 & / " , & ( " &0&- , ( ( "/ % ",0- (---.0/(0-&

◦

2

E kin =

2

ex + kkex ) ~2 (k⊥

2m

,

ex kkex k⊥ kex

ex

k

ex

kex

kkex = k ex sin θ =

r

2mEkin sin θ . ~2

kin

in kex k = k k + Ghk ,

Ghk

k⊥ k⊥in

Ei (kkin )

θ

Ei

θ

# & # & # &

-.,0 ( " " ) " " # / 0 -. ! ( ( - ( % " , ( - ( "( $ $ % # &

"! -.&,!""!-0. #

0 ! $ " " " "( $ ! 0-. % % " % " ! 0--. ( $ 0 " " / 0- , ! ! 0 " ( - "! ,-. " 0-($%0 0/ ( ,-.- -. ( "/ ( . " (0/($""

kkin

! ! #"

$ ! ! ! ! $

&

"

sp

( " "( $ $ " " "( # 0 & -.,0 , ( $ " , 0 , " " " & & " -& (($ " " " ! " "" 0 -.(---. " "% $ -& - (&, &0

% " 0 ! " ! ! ( -" % " $6 ,$ ""$""0,( , - /( $ " " ! 0-. " % 6,0 ! - $$ ( ( ( ! ( $ " / - ( ' &, " ! % " " 0/($"" ,-!.,%(((.(!$ 0-7 1 -/,"($.(-,( # &(,% 0(0/0/(-0 0 ( , ,- .,0 ( " & ' ' $ # & (

0 - ,%&- ( ( - "( - % # # & +

- ! .-0,0 $ " " " " % % * 0 -0& 0- &"-0/#/ % * " 0(0-(,% # & -0 -& " ! " ( # & * . 0 & - ( ! ! ( % " & - ,, ( ( ( ( % (( 6(-.0-0&/#- &-"% "0 ! - $0 % "

*0#((,0,&(-,

•

• •

LV V

λAl (52 ) = 4, 09 dAl (1 MC) = 1, 13

−d2 N/dE 2 N (E)

N (E)

−d2 N/dE 2

• •

•

• • •

%!)++ $" ) -#(-,"$% "(%& $% 0 -, ( $ , & % % + + + *() ( && $ ) 6 " 6 % " #

/! ( ! $ ( $ " ! $!-,-"$%& %" - ,0&-6&-

$ # # 0 #6$6 0)+!0" * #

( -, $ - "$ - )* ,&- " & -"0 & & ( $ $( -, + ( + ) " ( ( " *

&, #!.-. 0 ( ) % & " )) " ( "6 ( )+ - ' & + - (# 0- ! " " 0 ( 0 % && " "0 ++ )) " (+

( " + + ) ( %-

, -, 0 0 , $ ( $ % % " $ , -.,0 / , $ " "( $ ( "( 0 ! $ -(#(-0!--0/ / !

(

!

! -,0 " 0 ( 0& " & / , 0 & 0 " ( $ . # ( , ( "( " " # &

" 0

%

'

( ) # # !

%

' ("" ) 0#&

%

' #( - +

& ! & 0 0

$ "%%( ( (

!

! ) # " # ! " -,0/"# - , ,0-.0 , ' ( 0&&- " & ! & ( 0 ! !#-,0/"% ((

!

! "(-"$($(!(0!& 0 , 0 ( $ " ( - % & -, 00 ( $ 00 % # " "! ' -. ( " % & - , ( " - , & ( " ( % "$($ (( - , " ( $ , . #((0 # / / 0&--

!' (

& & # & ( , ! ' ( $ & " !/"-.!,0""

•

∼ ∼

• •

∼

%

0 . & " " ! ! "0 " % " / -

!'& -.0&",#,0-.% / 0 " -

"!'"!.! 0,&- & -.& " " ( - " ( ! % 0 " 0&- " " , "! ' ( % # 0 /0 & / -. - ! ( ! ( ,

, 0&- , ( - ! ( " " 0 & / -- / 0

"! ' " 0 -0 / ( $ ( " -

" " . 0 & / 0 & / !' 0 " 0 & -.,0 , , ( " $ " " 0&(0-. ## && #& ϑ1

ϑ2 m1

E2 =

1 2

m2 E1 =

m2 v22

1 2

E0 =

1 2

m1 v02

m1 v12

m1 v02 m1 v12 m2 v22 = + , 2 2 2 m1 v0 = m1 v1 cos ϑ1 + m2 v2 cos ϑ2 , 0 = m1 v1 sin ϑ1 − m2 v2 sin ϑ2 .

! ! "# !

" # ! " ! " !

m1 E0

ϑ1

E1

m2

0 & -0 " ( " , ., ( 8 " #-& # - - / & . &"" # & / 0 -0 0&- , ( " "( ! % #

., " , ( ! " . % " ""((-&"", "--/ ϑ2

E2

E1

q 2 m1 cos ϑ1 ± m22 − m21 sin2 ϑ1  . E1 = E0  m1 + m2 

m2

ϑ1

◦

m1 <

◦

# & # & - -0 ", % " 0&- . .,"", , -. ( # & ! , ( -& # 0 & -0 & ( " " (, 0 ' " 0&- " " " ,- ! $ & m 1 > m2

ϑ1,max = arcsin(m2 /m1 )

E1 /E0

ϑ1

A = m2 /m1

! & !

E1 /E0

ϑ1 A = m2 /m1

! & ! !

E2 /E0

ϑ1 A = m2 /m1 A

0 & -0 ! , " ( " #0&-& & "! (", #& ! ,-. & ( "0 " ! # & 0 ' " 0&- ! " ,- ! $ - ! "! ! " - ! " " $ - ! ." " # & # & & , " "/ 0"0 % # -. -, -. & -, ( ! "0 " " & , " " " ( " $ - % " " / / 0 $! ' ( " 0 ' % # & # & $ 0 ($ (-.,0"" ",0% E2 /E0 ϑ2 A−1

E2

E2 = E0

4 m1 m2 cos2 ϑ2 . (m1 + m2 )2 ϑ2

≤ 90

m1 /m2

E2 /E0

◦

E2 /E0

m2 /m1

%

& - / / & ! ( , "( , ( -.0 0 0 / 0 . 0 & 0 ( & ( $ ( , % +"0-" ##& - & (,0& 0#-.$

! #" & $ $ ! " ! ! # " !! +

+

2

3

∼

+ -. 0 &0 $ ! $ ( " " &0 "( , "! " '" (.!($%

& ! "#

& ! !! p

rmin

'"""#& ,- !0-- ( 0 " , " , " " ! 0 % " , . ( ! 0-&- " # & + & 0 -0 -, "0-.-0 ! $0 ! $ # # # & & 0 -00 0 / ! . " 0 , % # ( 0- , ! ( " 0- " # /0 ' - 0 , 0 ' " " & '$%% # & 0 - , 0 0 ' , $ 0 ' " % " 6(, 0 / 0 0 ' " ( " % 0 & / .1 ( ( ) % - ! ! " " ! ( " " -.,0 ( "( $ " ( '- 1

5 5 6-. " & ! " 0&- ( " ! " - !

"$# (

! #-0!% , , " ! " ( ' -, " " -0 0-& 0 , , ! ( ' - " 0- # & -"!""" '$%% #*& # & , , -. ( $ ' & ) -0/0! #

& # & $ * , , " ! ! ( ( ' -. % " --. -. . " " " " " - - ," ", $ ! #

/ -' - ' ( ! " " " ,- ! $ $ 0&- " " % . . , -., ( ! ! " " % " # 0&- " " . " " ( 8 " & # 0&- -. - & " " , % & 0&- ,-(0&!( &

Z1 e

Z2 e

Z1 Z2 e2 Φ(r) . V (r) = r

Φ(r)

dσ/dΩ

dσ = dΩ

Z1 Z2 e2 4E0

g(ϑ1 , m1 , m2 )

2

1 g(ϑ1 , m1 , m2 ) , sin4 (ϑ1 /2)

g(ϑ1 , m1 , m2 ) = 1 − 2 Z1

m1 m2

2

sin4 (ϑ1 /2),

m1 m2 .

Z2

sin4 (ϑ1 /2)

4

+

%

# & -. 0 ( " 0&- 6 (!0-.. , 00- ($".!-0!,%

4

∗

10−24

+

E1

dσ/dΩ

∗

◦

2

( & (---. - 0 ! % " - / - "/ " ( ' - " , ,0 " -. , " %

" -. / /!

#!",& " $ ( & -. /! $ ,0, % " # / , "%" '0 " && ' $ ' -0 0-& ! ( ' -0, " # 0(-"0 &" #& # & -0 0 , , $ ( - , " % # # & + 0 & ! $ -& $ & " " # # & & 0 -.,0 / -- 0 , $0 & ( " , % # " # & , ( ' - 0, " , ! !"0&-/& . 0- 0 " #*&"(-,00,"",% / / - - $ -&- " $ ."-'(!""

Rs

Rs = 2

s

L

Z1 Z2 e2 L . E0

&

!

# "!

. ,00&( - ( ! & ( 0 ! , " ! 0

0 "%($ " !" " - & " , ! . ( % # & * -.,-. ! & '0&- ( ! - ! ! " " " , 0 , " 00&-&!0&"".! α

αc

αc

!

! " +

αc

& /

$ " - ( , ) % " & " $ - ! ( % " # & # & / -0& -0

& -% / 0

0!'-" -.&!- & , " " - ! ,0 " % $ ( -0 % / (& / - &00 , ! " # - ! $ " ! , 0 " ---. , !-. ( ( ( $ "

"" " 0 -., ! 0&- , 0&) " ! &( " "! ' , ! . " % # & / 0 & "- -- (', "('"- " ) " αb

%

!

" # ! " " ! # "

" ! [

]

∼ 5◦

- / . ! &

! ' " # & # -, ( - - % " & # & # - , ( ( , -0 ! - - % # & - , ( . ( -., $ ( % " # & , "/

& - -0/ & (,"0- " % 0 -0 / , 0- 0 ! " ! # (- - ( 0 ! & ' $! ! &0, " - & m 1 < m2

m 1 > m2

&

"(% , " - ) / -0"/ , ( $ " $! ' ! ' ! " ,. -.,0 ((-"(-0!" " ( " ',(-,-,($ %

& (0

! ( --. $ ( - % -- , - &- , ( " % " " ( &0 - "&-0#0 $ ( 0.&-0 " * # & . - "! & " ( , " " " & 600"00 ,/ $

" & &

"!

" !

- 0, &, " " / ( , " " .-0 ! % " # 0(& 0 & ! $ -& $ ( " & + , 0 - ' ( 0" " 0&- $ # ,0 0& -.& ( - " $ " ! % -- " ! 0&-, $! "0&,% / & (& "" -." # & , ,- ( ! ! " - , ( &0 8 # -.$&0 (" -" 0& +0#" +

ψc

Z1

Z2

d

ψc ∝

r

Z1 Z2 . E0 d

ψc

+

%

0-. (!/$(0&-" ( ( - " % & (

" " ! ! " !0&-, "" " " ! 0&-- && / & ( " - ! . -0,/! , " , " ( " # " !" , ( -,. " " ( . % + -. -0&- 0&- " "( " ' % * ! / -0 " - - ( " (0&% 0 & / , 0 (&, 0- ( " ! 0 " &- ( ' ! % ,0 / $ - !

'

( # & ! 0 & ( " '+0 # . (0"& " ,&0(('-. , " . ' $ " # & + !

0#("(-.& (-" 0 & 0 # . ( " & # 0! & 0 , ! , " # 0 ,- " ( ( $ , ! , # " # (

-0 0 -. ( 0 ! ( - " * 0-/- & #( 3

-0 0 $ ,- $ ( 0&- " "% (( $ , " &- ! - 0 & & / & - , ' 0 ! ( " $..", 0. (0.&-0 , 0& " , ( % " " / 0 /0 & / , ' ( " . ! " - . 0 ( 0& $ " #% 0 &- ,0-. ( ! 0 & / / . ( 0 ! 0 " & ! " " " ! -. - ,. , $( ! $( , ! % , 0 / $ , ! " ( $ ,"/ $ 0. ( ( ( $ .- - " # &

- -. ( , -. $ - ' $ ' 6 - 0- " ( $ ,0-. % , $

""-!(-$% ( !/ $

! ( / -0 0 - ( ! , " 0 ' " # 0 &0&- ! ( " , $ ! % " " &--& 0 & ! ' ,'! (,$(-",(---%

◦

ψc

1015

i

+

dE/dx

Z2 /E 1015

h

◦

(1/N )dE/dx

2

+

N = 5 × 1022 1015

2

∼

3

2

h

i

&

"# &"# & & ! " " & "

'" ! ! 0'!-0(&" ,- ! $ " -& & ( ( " % " " &-0"& , , , " $ ( - " " $(-"-.0."" ""-

! &! !

&

%

, . 0 -. 0& " ! " ! ) " ./(-" &-% / - 0 -

. , ",, $ ( - "( , . "-0/ , &% - -.&0&(( - ( " ! " &-0 " . " 0 " - % " - " ' ( ( $ - # ,0-. $ ( - " , ( "(-"-/"(-.,! *)"(- $!& . , $ ( - " , ( $ " -. / ! (

$(-.," 0&-"% " " / / / / "( $ . ( , ' ( " 0 & ! &- ! " " ( $ %

. -0 ! ( ( % " --- 0 , " , ( $( ! $ , ' # -0 -- 0 ! "

0 -% , . - " 0&- " $ ( - " " -, θ

cos θ

1/ cos θ ◦

θ∼

% ! ! ! ! & ! θ

& ( - " "( $ &-, % 6 "0$$- $ ! ' ( - ( $ 0 % #'/%( " " " 0 ( $ % ' " ! $ "/ 0 # &

( " "

•

&

•

% / $ ( - ( -0 0- #( " -.,$ , . ( " & ! " " &(--.0" . $ - , " . " " # - &-, , ,

' $ ! % # &

0 ,-. (( - ( " ( % " % % / $ - , ' 0 ' &-0 !,/

( $ !

3 #$-

/ " ( $ . &-,- ! ,0-. 0 0 ,, ( $ % 0 0 $ , " " " $( ' % , $0 -, ' " , ' " % " " $ ,0' 0 / " "0 0-0 % /0 , &0 ( ( . 0,0 $ , , % $$, ! "0 " '-."0" (

5 5 , , $ " ( ! ( % 0 & 0 0- - ( ' ! -. 0 . & -. ! 80-&"!".& " "(00 0 & 0 0 , . ( -. 0 & , 0 , . & " " # ,., / 0 / &0 !, ' " ( " " - ,0 / & ' ! $ "0 " " % " & +

, 0 / 0 & 0 0 "( ( " ) % # " # & & / / ! "0 " ( "/ 0 -. % # 0"&/ !$! 01 ( " & , " " , 0 , " " " 0 , 0 , ,0-. % " 0,"%0-, -. 0 !- ( 0 && -.,0 / -, ( ' ( " " " (

$ $

%$

(

' " " "

%$

'$

' . 0 % " 6 ! 4 5 "0" 5 !, 0 "( ' -. 0 % -., & "%-$ !"$0 ( - ( % " 0 -0 , ! ( ' " #

• •

K

L

∼

%

0 / , 0 ( $ . & $0 % " - / 0 ' ( " ( ' ,""-"/" 0, - ( ' " -, ' " " , " , ' " " '" ,, " -, 0,$0- ( ' -, ' " % # ,%-'" " % + &

" /

!

$" ! ( - " * !- /! 0 (,- ," 0- % , , ( $ ( ' % 8 --, - -, ' - ! " % -. -. ""#( $ " "$ ( $ % * & "

•

•

∼

" ! "# &

! & $ !

&

&

& & ! $ $! & & ! ! $

$! $ $&

Ei

EF φ = EV ac − EF

EV ac

# & '

! " ! ( ! - ) " (-, '""! , -, ' . % " 0 ' " ., & "

, / " " -

!'0" (%" $ 0-0, ( $ . " # * "

!

$" ! ( ! - &

- ( $ &, ( 0. ( $ % " " 0 & - / - ( 0 ! 0 ( , -,, ( % & # # 0 / 0 " ( 0 % #

" " " & #

0 . - ! $ "$ / 0 . ) % # 6 * # & $.1 ,, 0 ( ( $ " ,000" ,",,$%% &

d

−24, 8 −22, 2

(,, -"$ 0 ' " , 0,, -, ' 0 , ' ( " " " / 0 '--""'/#"$ ( $( 0 " &

# & & *

'

$" ! ( ! ( $ " *

0 - ! " "$ ) " 6 0#-0-0, - &-0 ( " 0. 0 0 & 0 0 , "( "( " 0 ( % 0 $ ( 0 " , ( 0- % " " 0&"&- - , 0 !$ ,' ! ( $ " # & &

0 & -, ! % " " 0 $ ( ( 0 $ ,0-. ( ' % " " " -.,0 -, ' ( "

$"

" # &

" ,0 ! "( - " ( $ % $-' $"!#(! -" &)!(% / ' ! ( ' - "! ' " " " " , /! 0 , " ' " " 6 ,&- / & 0 (-&0 " - % 0 ,, ( 0 0 , & " " % & 0, - " 0 ! , ' " % " 0 / , &0 -.-.-0 ! 0 , % ! ! -. ( $ "$ ( $ " ,0-.0 /

"0 .('0-& " ,0 (! $ " $( " ! $ "

" # & !

#

! ! % # !0- - ", " . " $( - $ , ! 0 & " ( " " " " # 0#($-- ) ,% s

−24, 6

.

∼

Ei > 2φ

P+

4

+ PHe w

−3

−1

+

P+

%

& & &

!

!

&

"# ! &

" # & "

! & " & & "#

4

+

& & - " " " "

! $ % " # &

" 0 -- ,- ( ! " . ( ! ' - "( " . " - ! 0- ( " , -, ' ( " " % " "-"$ 0 " " " " # " -- (!,(!-"""- $ " ( " )

0-#0" " -. " , 0 & $ % ", # " "!$" -." " 0

00-.% &((-" -"'- -!&-, 7

+

+ PLi w

Ei > 2φ Ei (He) = 24, 6 φ

+

+

P+

Ei (Li)

1 5 3

#

! & -(

!

!

$

#

#

&(-.,0/"0%

(

!

! & ) 0#"$($-"-$-%

( $ , ! "( $ "! 0-. % -. -. . 0-- ! " " * & #

- ! &0 00, " ! " &0 - !-. ( 0.&-0 0 " ! -. " - -. ( $ $ $ ( % + $ / 00 " ( - " ( $ % -,(" (00/ $($% !" -0 0 $! ! " ! ( " # # & & ( , " - ! $ ! % " -, -. ( ' ! $ ' (' % , " -"/ 000&-, + $ - " - ! % " - & ( " $ - ( - ( ( " " $ ",-0/ ,--.0 # ". / ( ! , " , 0 ( $ . % #-, & -0 ' ! , ! ( - " % / !0 "" &-,0 " -. " " " " $ &, !-0 ('-, " !, " 8 ! ( ( - ! % " 0, " " , " 0 / / 0 0

-.& && " $ %-!0--,("$0 ( - " -, ' " ,/ , ! " " ( "/ 0.0-.0 % . 0 , 0 ( $ ' ' % / -0 . " && ( 0 ! ! " " /

$0/".# -, ' " & ! % " " &- . (!!., " $ $ % " 0 / ,. ,0 ( ! $ ! , ( , % " , . ( $ &- " -, ' , ! .-,0, (0, " - ( -., % ",0"(-00($% ∼

•

• •

%

&&"",!-.0-,"/% -,$

11 5

53 , 0 , ( 0 ( - "( ! - $ % , 0 , " "( - " $ " % " 0 0 / ,/! ( $ " ! " " 6 " # (0- " -, ' $ &, % & / / , , ,0 " . $ " " "/ % # , - !! $-- -- -'" $ " . $ " " ( % & -., - 0 ( " ! % 6

,/ $!" ( --/ ( $ % #

" $! ' . " " # & *

-., , ! " ( % ! $-,#0/-. 0 & # (& -,#(!/

! $

0& -, , ! $! ' , $ " & % " & ""

! $ $

!

" ! " ! " ! ! ! +

+

E0 = 2 ψ = 20◦ ϑ1 = 47◦ ϕout = 30◦

+

0 -.,0 - ( " "( - " -," (, -,"!"&%

! & & & !

! "

& !

& "

ψin

0

+

ϑ

◦

+

' ( 0-. ( ! && ( 0 ! ( - , ( " % # & 0 ,(!. "!( - " ( " & ( " %

' ' "( ! $ ( ( ) 6 0/ - / 00-( ("( "( $!,,, -0 "( - ( " # 0 & ! ' ",- ( - " #

& ,- 0 & " ,- ! "! ' ! % "--. " ( ! "( - ( " -. $ 0 " 8"-" 0& 0#"(- ! ( -"! - " "( - $ , # 0 0 ! ( -.,0,/- "" -. ( - ! % ! 0-. % " ! 0 & -. ! ' -. ! ' ./" !%

0#&-0- /0 0/",(. 0"(% " ( % # 6 & ./,&-& ( &-.&-, ' % " ( ( - , . ( , % % 0&! ( " 0

t

L

m1

r m1 t=L , 2E1 E1

L=1

4

+

F (t)

N (E)

E1

%

! ! ! &! #" ! #

! " "# ! "

# & -.. ,/& (-"" (0&(0-." (0-"/(!.- % ! - % -.- --. 0 ( " 0. ( $ " ( - % % % - &0 & ( $ ( , .- % # " 0 / & 0 -. $! '( - , ( ' - - - "/ 0 ( , ! ( 0 ( - % " # ,, , ",(,0 , $( ( % " & . , ! ( ' " $ "( % % # " 0 . 0 /0 ., - ! ( ("-.!'&0/" N (E) =

F (t)t3 . m1 L2

∆E/E

∼ %

# & ---. ( (

./&-. - , , ( ! $ ! " " ( ( % " " # & . , ., ! -.0 ! % " " -&"" !,0/

1

35 5 ('(, ("'00 ( ' " - ( " ( % #- / $ ( & " " % -0 -. ! ,0-. " ! % " , 0 0, && " " ( - % % . / 0 , & ( ' - ! % " .00 -, && " " , , , % -. - -.,.& / " ( ( " ( "

( ' ! ( ( ( " " 0&% & " " , "

!

(

!

! ! # &#

! (#$& - !# &#- ( ! -. " " " 0 -, $#

(

! # &

! ! ( $

! ( 0-. " , -. ( 0 ! ( $ ! ' % -., -.& ( -. ( - 6 ( " " - -. ( - , ' ( 0&-0

- " ! & " " " "

-". " " %$6%,-/!"-.

" $ 0&.-. $ ( % " " " # & - 1 - ( ( " / - " % # ( !-- " ' ( ! ( $ %

, &0& ( ( " " & - , 0 . ! - " , , , % % " , / ,0-. " ( ! " ( $ -0&- - $ ,0-.& % " % 6 % !

/ ,0 0 0( ' " & ( " " 0&- (& $ ( ( ! % " " , 0, " , & ( $ ! ' % # ! 0 && ( ! ( " " & 0- - , (( ! ( ( ' "

, 00, " " " , % " " (" 1011

2

◦

◦

◦

◦

◦

αin

αc

L

d

% Rs = d sin αc ,

L = d cos αc .

# &

" & & & ! & $! $

& & ◦

0&- , , "" ! ( $ "$ 8 " , , " " ( - ( $ " ,(0 ( -. ! ( -. 00, " % # , 0 -. ( ( 0, 0& 0#""$$#% " " # & # &

0 -.,-& ( ( -- "

/ / 000 ( $ ( 0 " " % -. $ " ( $ ( " ! "/ " , ( % " &-- αc

+

×

! +

×

×

0,"," ",, & -, - ! & "( $ ! # # ( $ ( ! - &

&0 ,.0&0& , . " " " " - . ("0 ( , ! , " ( ! ' % " " & / & ( " $ 0 ' 0&- ( " " # & &

" / ",%,, " .0 , ( ! % " , , 0 0 $ 0&- $ ( $ ! 0 , % % " -. - "( ! ( " ( $ % + , 0&- ( - " "$ , . ! 0& " # & ,$0 , 0&- 0 ' % " # & -. / . ! , 0 " " -. , , ""0 ( 8 " &

, " " ( ( , ( -. " " " , ( - " " , " " . ( . " " -! 00 -,($ A

B

B

α

α = α0

B

αc1

A

αc2

α0

α0

A

B

αc1

d

αc2 ∆αc d

∆αc

"# ! ! #" &

$ ! $

A

B

(

%( (% -. ( ( ( - " - - -& ' ( ( - " ! ( 0 6 # .-, $ " -0 ! 0-. 0& ( % " & &-. -" 0 ' " -.0- , - ! 0 $ % # & (

$

$($ ,0(-.&

×

×

%

! #" !

$

& "# $ !

+

Φ

α = 4◦

Φ = 0◦

◦

◦

, &0&- - ( - ! ! " ! % " # & (

---. / ""(( $ , 0 ,0

" *

" " "

5

#

& &" 0/!% #

!

! # , ! & " /

( (

!

! & -(0& )+ 0 -.,0 / ( " " # , & -.,0 ( ! ! "0 (

8 -. ! " &"-,,00# #

! " !

'

( ,!$('("-, $0$0$% # & 0 ! ( ! " , " $ $ ( % " " ,- / (# " -, ' " , , & ! "! ! " " & ! 0,0/ $$ ×

×

δ = 13 ± 1◦

±

+

∼

, ( ( ( + 0#-.$ 0#-0/ ! - --. " " 0, " 0, %( " " " # / , " " ( " " ( " (/ $($. " 00," * * & +

0 0 ( ( # # " . -, ' , " #-.0-&0"('-""-" , . ( ( 0-, -0 0 & - - , ! ! " . 6(( " " """ !-" & $" " , & & ( $0 # - (.&& " " " , % &&""" !-"(" ( $0&& 0 & - ! " " " ! $ 8 / 0 . ( -&-0 . , ' , ( ! " " -. ( $ " " ,0 ! " "!($#% 0'&-0% -, ' ",0"/!00 && , , ( - , # -. , . " " &-0 " , % " & # & . ( ( $0 ( " & , 0 &-0 " -0 ! , % " " "! 0-. ( $ & ( ! " (-0"!-. $ ( - % 0 -0 - ! ,,!0 -"

•

+

0, 2

• •

Rs ∼ = 0, 09

Rs ∼ =

•

3 10 / ---. ' & ( ( 0 ! ( ! $ " (# ( $ .---. ( - " - " & -0 -. ! ! 00 " # & - /&-0.1-. $ &- " " " 0 --. -. " 00 " " &0.- " $ & " " # -.-0 ! (0 $, " !!- $ " " -0 0- ' ! , # /1 -&-0 / ( ( - " - " & ( 0 ! ! ( - " " --&-

%

/! , $ & " " " - 8 " -&-0$- # -& &- & " .0-.& ( " " ) " 0 % / -. ( - ( -0- ( 6 / 00, - -&-0 " % " # , $ ! $ " $ " " & & "

I

I=

X

Pi ,

i

Pi

i

P1 = 1

$ " & ! $ $ !

&$ "# $

& Rs

ρ

! 0 -. ( -- ! ( ( % &/ -&1 ( & " " # &

0&#$ +0#& , ' -. ( - " " (/ $ " " ( $ ( " " " 0 & - &

( ! ( , ( % " # & 0 -. " " ! ( ( % " -. $ ( , --. $ -, , -. $ $ ! &, "0 ( % % 0 -, & ( (&-0 $0 ( $ & # (-" 0/ &" - ,. ρ/Rs

+

h100i

-&-0 - " $ ,'(0% $ , 0 & / , , 0 ( ( " - , %

0 - - " $ $ " $ " - -0 ! &0&- $( " ! " ( - " " # -0 - " / - 1/ ! 1 ( & - ∼

! "#! ! ! ! +

h100i

'/ -, ( $ & ( ! 00 ( $ $( ( ( 0 ( $ - % % " " /./#$0 ---. & " " ( $ % & -0 0 ! " ( - $ - % " # . ( $ & ( -0 0 0 & ! ,-0 " ( ! 0 ( $ % " & $

--." --." " , &- - " 0 , ( ( 0- % # -., !(/ ( $ & ( & / / -0 - -0 ! -.&-- ! % # - ( $ & $

( % " # & 0 - ( ( " ( $ . " " " ($&((-.(0-0

%

" "# $

$ & $ ! $

-/( -., 0&- ' "( " " "( ( ( "( - $ &0, "( $ $ " , / / "

( " # & " ( ("-"" "( " -& ( % %-0-..& , " ( " - - ,-.&- ( , # & - - , ( , ( , ( ( " " - . . ( $ & ( ( , -.0 " % - ! ( -00 $( ( $ , ! , "$ 0&- ( $ % &(#! ( (--'

- (0"$ . ' , & " " , 0 " # & * * +

$ - " -- ,- (--/

" ! & & $ ! " ! ! & ! ! # " !

&" ∆d12

∆α

∆α

! ( 0 ! ( - , ! % 6 " &&- &0-. " -. ( % -&-0 -, "$" $ --. -. % " $"$"-" /-. ( $ & ( &0 0. $ $ ( ( $ . " $ (,-. &- -/( ( - " " " " &- 0 - ( " $ ( - "$ ""0$& #""#,% / / & ! -/

% $ ( - " . / "( $ 0 - ( " " # & $ , &&- , ( $" "! ( % " # - ",00"$-" '"(

%$∆d12

∆α

%

& -.& - ( " " " 0 ( % $ ,-, "-"-. - ( $ -. ( % 0 -. , . ( - ( ( 0, " . 0 & 0 / $

"/% " # & & 0 -0 ! 0 - $ " " # !&(-" -0&-% -.--& & (- -"'"

-"($ " " , . ( " ! - (

./( # & & " # & - & , " ,' '% - -. " , " ( , -. " ", " '(% ! & " ( ( - "( $ - #

& #0( * , "! ( $

* 0 & 0 (-0!"( --. ( % " # 0 -- , ' - $ - , $

# , - - 0- "$ ( , $ , ( $ 0 $ " " # - - ( ! ( $ " " 0 0 " (-0 -0"-"0% α

∆α

∆d12

∆d12 tg(α + ∆α) = −1, d tan α d

∆α

∆d12

×

[1¯11]

# ! &! #

#" ! ! ×

◦

[011]

∆d12 /d = −(17, 2 ± 0, 5) %

∆d23 /d = +(8, 0 ± 2, 0) %

& ! / $00 & ( -

($&0% . -- ! 0 0 $ 0&- % " / " " , 0 ( - # +

*" ( "-. -. - - -0 ! % % , , , 0 ( ( - - ( ! % " & -. , - /( (& ! ( ! ( , % " - / & , & " " " ", , % -&"" " " ◦

±

%

3 & 0 & 0. ! , ( 0.&-0 - & &- " . " &-0 , % 0 & 0 - ! ( " ( ' ( " " " 000$- & ($"0& ( "( "0 ( , % #(, # &- , "( " , . ( , 0- % % -. - 0 & " --. - % " #, . ( , -0&-0 0 & - 0 $ ( "0 " " ! %(&- " # " 0 & ( " " /&% # -& , ( & " " , ' , 8 " / & ' $ ! 0 ' &-0 # -0 - #! ( ! ( - ( , " & ( " " " ( ( - - 6 # ( -0 0 ( 0& % 6 " 0 & "-&(-$ ( " " ( -0 " " ,- - ("- ( , & ' ( - ( , % % " - ,-0 / ( , & ' ( 0 &- - /, ( , 0(-.$($% &-0 ( & , -, ( " "0 ! " % , -.,0 / -0 & & " " ( "( ( %

/ 0 & 0 , ( ! " /(&-0 * -#! " 0, -, -.,0 ( ( ( " " " $0&" (!/,(0& 0#-0!%

±

%

•

dE/dx

•

d

∆E

E1

∼

%

! & # !

#

" m1

m2

2

1

m3

E0 3

d

0 , ., &-0 (0)& ! ( " ( % # " *

!" '00--," -0 "( ! - -0 & " "( " " , " % # & --- 0 ! ( % -. / ( - $ & " " - % & # & , -. 1 ( $ #!! &- &

)- /-0 !-&1 $ 0& ( -.-0 % # & --- & ( ( ! % - -0 0& $ ! "$ &--- ( - # ! " "-! -,&%% - , (,-0,.(,---!&!

∼

χmin

%

χmin = 100 %

χmin

! " , / $ " !"%%( ,

#

" ! " "-,0/"(0& ! ' % "/"(! 0&%

,0$!!$0(0&$0" ! -0 , , -& ( ( & " " " $ % " -.,0 0 ( " , $ , & "/(, ! ! ! !% ('!!-,!'0(0&!-0/

&

-, -.,0 " ! ' 0 ( 0& ! ( " & "( " % & " "( -., "

$0&- $( "( ! & ( 0 ! # &

0&- ! 0 " -. / -"00/ $ , (

-,. ! ! ! , " " "-/ & - / -, ! ' ! 0 ! ( " ( ( & " " ! 0- " % " " ,0-. $ " - " $

( " ! , , . " -, ! ' # " 0 0 ! ' , ) % # 0 -,,0 - $ -0 ! , - , , " & $ "( $ ,%($$,0"-!"% ,' " "0 " " & $ -0 ! " -, ( ( & " " ! ' ! 6 00 (""#-&"(- " ( $ % % &- "/ 0"0 % # &# + , -.,0 / & 0 ( "( ! $0 " & # & 0- / $ ! " ! $ , , " &(- -0 , ( $ $( ! $0 % # # & 0 -. - , "/ " ! ( # " &0 .(/

/ - -., 0 , ! ( ( % , - , ' $ -., -, ( " ! ' 0 ( 0& ! " - % 6 "-0,-($. &00&-, !- ( - (

# & (-0(,'% $ 0 , 0 ( ( ! ( $ " # & ! ", 0- "$( ( # / (&

)( -./" -(-0&-",% & , 0 " " ! ( ( ) ) % " # # & (

*

- 0& $ . % 0(# (00&- - # # & & - ! ( ( % " 6 ! " &0 ! "!(( -, " 0 &,"

& " (

..0&!("% # & !0&- , ! ( " ( % ( - - "( $ " !"!$-0(0&$0$!!$-%%

•

ϑ2 < 90◦

•

dσ/dΩ ∝

2

∝ (1 + m1 /m2 )

◦

×

β

◦

×

+

%

$ $ !#" & " "#&

$ ! #"# " $ $ ! &!

$ ! ! β

×

+

+

◦

ϑ2 = 30

α = 20◦

!

, 0 / ( ( 0 - "

0&" % ( (

,0"",", 0,) , ! $ ! ( ) "-0 " ! 0 & ( $ % !(" "-!0& / ! "( ! 0 . / 0&- ( " ! " % " 0, ,-. 0 !!8& , ! ( ' % " -. , ( $( "( " ! ( 0 , "( $ ! 0&-. " % 00&- -. ,0-. , ( $ $ ! ( ! "

-,(-$

( , 0",")( )(( & " - ! ( - " # 00& -.,- ( ( ( & ! -

($,0!00(% $ (

./-,!'0(0&!" 0 ' (' , " - ( 0 - " ! (0 " ( ( & " " ( ! " -0 -. 0&- , ! "( " $ ! % ,. / $ ! ' ! $ ! 0 0 ( ' % -," -0 ( $ , ' ( ! ( 0 ! ( % /

%( (0$!$! ' % # &

( " " 0. "

" 0% -.,0 / " ! ( "

0 0 & ( " ! ' ! ) # " - - -. - , , ' 0 ' ( % " , / 0 ,&-. - -. " - ! % $ + 00 " -, # # % / , ! -. ! ' ( 00 ! % " 0 & ( 0 ! - ( ( $ - , % " -& / ' - ( 0 " -. ($ " (-,"60(-.& " % ( ##!$+"% (, " ( ( "( " ( ' ( % % -.0 / &-, , , ." - ! . ' % " & / ' " ( ( 00

$(($ " 0- & , ' , . ! -,, " / $!$ ,-"(-,-.%% β

◦

+

+ 2

◦

+

%

! & ! & !

$ ! ×10−9

2

$ 0- ,' , .,( # & & ( ! && ( 0 ! ))-. " " #"''"0- " 0 ( - " ! - ( - $ )($ & /

" # $ & "(-$0- " )$,-. " ,0&-.0 /( / ( 00 ( . ( % % 0, " & ( 0 , & 0 ! ( ( ( " % " - , ' -& ! , " (.-" '-.$ " " ,!, - - -, ! ( ! % ! $ + 0 0 / ., ( ! ) # % 0-"-,'" (!$ "'"" 3

Ii+

i

j

Ii+ = Ip Ci Si,j α+ i,j T ,

Ip Ci Si,j

i

i

α+ i,j

i

T

i, j

!

- - " ( " " " & $0 ! $ ( % " " -, ,, -. $ "0 ( ' - -. - ' $ ' $ "0 " 0 0 --.

-#!-- % " 0 / - $ ( , -. $ ( " " # "&"&-& -. $ ' $ ( % & # ) ! & -" (0 '-"% " " " 0 , "---- , ' ! -.0- ! $ ) # --& ( , ! & ( $ " ,"!-" -& (!&,-. $ " -""-"-&( !&( 0% / -0!*( -!&&-0 (((0!

$,0 !(" 8 - -, ! - $ ( , % , -. -. $ ! ' " $ ' $ " &0&. ' ! $( " - ! % # 6 $ + 0( 0" "( -, ( - ! ! # % - 0 -.& ( ( - " $ % 0- -.,-. 0 $ , ' $ ! ( $ '% ! 0-. 0 0/$ ,#$+% $ + ! # % !#$+% (-.,0/"!.,(-% ( !& (!0 !( # &" ,0-. #

) # . ., - ( - " , ! " ( " - " &!-0,,0 -. ! "( $ #0-0 " " ,0 ! " ( $ , ' $ % " 0 !$,'- #,(%,,& $ $ "((-(-. ! & & 0 " " " &. - (-0-!"$!!0-. , -& ( " $

- " - ! ( "

! (

( - ! $ #) .(-"- #(

! -. % & -00 0 -, 0 ( ! $ (6-". " (-(&-0& , , . -0-! / - ( 00

$,'# & "

, 0-. ! - , ( 6

$+- + !, "/ &-0 ( & " # -. ( ' ( - " ( % #" % " (0 - &0 ( - - " " & # -. "0 ( " -.. +

+

+

−

−

−

• •

−10

−9

2

−8

−5

−4

2

12

16

2

%

! #!

#" !

. ( - " ( ! & ( 0 ! " " & 0 $&/-0 0/-.'0-%

/ 0 & , 0 "$ ( $ . ( # # +

0 , & -.,0 ( ! ! "0 ( $ % # " & 7 0 &-- % ( ( ' ( , " - *&6-(" #! 7 0 0 & , (- " 0, ( # + 1 $ (!0& 0 - / " # / - - -0 (". ,,& ( 0&& " 6 & # / 0 & &0 " , " 7 + 0 - ,& # 7 0,0- $ 0& + 0 -. ( ( $ . % # * & # & # (

&-0 '" " , 0 & ( ( $ . , ' " ' 0 & ( " .. ( , # &," 0#( 0& ∼

∼

∼

4

4

+

+

E0 = 2

ϑ1 = 180◦

E1 = 1, 1

4

+

ϑ1 = 180◦

4

+

1015

2

# & # &

# &- / 0 " #(!0&- # 0 & ! ! ' % % # -, 0 , ( "( - - % & 0 ! -0 ! ( $ " ' ,-0!

1

16

◦

(

4

+

' )- + ' #+(( + ) - " " $ ) " &

( + $- ' + ( (+ ' ) ) #00 % & "$(./& " " "&" $0 & ,% )* + + " )& # ,' & ()+', & " " ( (

' * + (+ + + + # *

$ ) ) " " - & " " $ " " $0 " & ! ( ( % (

+ %' ++ ' ++

( ( + "

'')) ( " + " ) - #('$, , 0 ( $ % & / . (%! $ %#-"($% + +

, ( ' $ " , 0 ) ) " & / ( $ . ( + *) + + " ' * * +&#( "+ +'

"

) " ) &-(-" '"!%((

•

•

•

•

•

• •

+ -0 ( -0 , "( ! " 0- ! $ , , % , / 0 ( $ ( $ ( $ . % " -0 -0 / &- "(#-& ! ' " ( ! " ( . % " # . " --& ( $ % " & # / -& . ( " ( $ ( $ " & -& , ! $0 ( $ % # . ( $ ( & ( - "0 & , $ ( $ . ' ( " " 6 -., /! / " " " , $ ( ( ( % # , / $ ,(0-" ! , ' ( ! "0 " & # 0 / , , ' , "0 % " - 0 " ( " ( " $0 % " " & # /"0&"0 -/"0" - -"" ((""0 ( "0 ( % " 0-. " % " # & - ( " ( " " ( " ( $ % # & 0 / ( 0 ! 0 "0 " ( " # / / -,0 &- 0 " 0-. " ( " % " & -. - " " ( " ( % " -.,0 -, / (& $-"((-$" ( ! , % " 0 / " ( " " " " - ,0-. " ( " " " ( "( "/ (-0!.(!,,", + / -$ #!'

! ! -, & &0 (!.(%% -- , ! , ' &- ( % #

& " &-(--/,'-.00 ! " &0 -. ' ( ' --. !('- ) 0#"0,"

*

--. 0 - &- ! ( -, " & % " " *

/ , / - - ! 0 ( " ( " #8 # --. ,% (--0 /0"/0 - & ∼

$ ! $ ! !

&- / - ( 0 ,- " -.-. % " " -$-"0-!(( # & "&-" )"&-0 & #) "0 & ! &0-

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1 #

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! '--" - ' ! -0 ! ( $ # " #(" . &, - . , " " 0 " * "$",!-."

d12

∆12 = (d12 − dbulk )/dbulk

−8, 6 %

+5, 0 %

−1, 6 %

"# ! " # !

"!

I−V

∆12 = −8, 6 % ∆23 = +5, 0 % −1, 6 %

∆34 =

& & & & ! #

!

11 1 $-. # & #

-, " - "( $ , ' % & * , -. . /( -- ( ! $ % 6 # &

" " " ! $ &- " ( % " - - / $( , "$ ! ( , ( % &- &- (- " ( " ! % , "( - 0 ! 0 , & 0 ! " -,$" ( 00 %

& & & &

&

i j i, j $d " ! & d & d & & ! ∆ ∆ ∆ ∆

z

d d d

x

dz = 1, 433 z

= 2, 027

z

= 0, 827

z

= 0, 641

dx = 1, 923

d d d

dz = 1, 762

12

23

34

−5 ± 2

+5 ± 2

−16, 9 ± 3

−9, 8 ± 3

−22, 0 ± 5

−11, 1 ± 5

+4, 2 ± 4

+17, 0 ± 5

−2, 2 ± 4

−4, 8 ± 5

+7, 1 ± 1, 6 +1, 4 ± 2, 6 +0, 0 ± 2, 6 +4, 0 ± 0, 6

z

= 1, 246

z

= 2, 033

z

= 1, 062 −15, 9 ± 1, 0 +4, 1 ± 1, 5 −1, 6 ± 1, 6

dx = 1, 878

45

−8, 5 ± 1, 5 +3, 5 ± 1, 5 +1, 0 ± 1, 5 +3, 0 ± 1, 5

−0, 8 ± 1, 9 −1, 4 ± 1, 9 −0, 5 ± 3, 2

"# !

$ $ & " # & "" &"

∆12 =

= −10, 4 % ∆23 = +5, 4 %

∆34 = −1, 3 %

(- 0./,&% " &.&- "--. ",0 ( , 8 "

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./ -,+-(#--0 % % &

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I−V

+2, 2 ± 1, 8 d12 10, 4 ± 2, 6 5, 4 ± 2, 6 1, 3 ± 3, 4

−14, 5 ± 1, 8

d23

d34

∼

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×

×

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[001]

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×

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√

◦

2× 2 R45

×

# & # &

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( -" " # &%0" 0 (!. ( $ % #,0-.(" " &0 .#" & (-"$ 6$,00% ∼ √ √ 2× 2 R45◦

c ×

∼

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◦

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c(4×2)

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×

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• •

• •

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×

×

#" (%00 #**,0 & &. ! " , $ "

0 /"! . -0 0 , $ ( $ " " " /" -. 0&-0 0 ! -0 ! % % " * * 0 ( ( $ ""! , -$",

×

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$ $

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0 $(00 00 "(" ( -.

((0$",$$ 0 ( "% # & , - 0 - ( $ - , ( 0 ( "!00 ×

(2n + 1)×(2n + 1)

×

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&!

%- "($. #

& 000 %",$ # & (

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( $ 0 ' " 6 , -. " - ! ( ( $ % " # & # # &

/ 000 ( & 0&0 % " # & # &

( $ . , . , 6 ( &-,0-.-. $' - ( - "( $ % 0- , & ( ( $ . 6 #000

& # & ( ($,0("!" ( # & # &

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( $ $ "/ " # & ! , / " ,

% " # , 0 -. "! " 0 0 $ & # & /"! / 0 $ ( 0 0 , 0 % % "

, . "! " , 0 % 6 (0"!,(-""--,% (2n + 1)×(2n + 1)

×

×

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×

◦

c × × c × × T

+

4

×

×

× ×

c × ◦

c ×

π

×

c ×

×

c ×

c ×

c ×

!! " ! $ $ " $ c ×

×

, - $ ( " " $ % % " " ,0-. &-0 / -0, - ! " ( ( " " ,- (( $ . -,0 " ! 0 , % & # "!$ - ($* % ( "! (-, " 00-% / -. 0 &, 0 -. " ! ( % % " # & "! - c ×

×

c ×

×

c × ×

c ×

∼

) 0& -0 ( ( " ( % 6&-- # & & " %%%" &' % " , (-,"" 0 " (-, " " (&'"! III

III

V

V

III

V

1 1 1 4 4 4

$ $$. . ##

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,,&,& , $' ( % " "# 0 / $! " &-- " . " , & , ( $ ,0 " ( $ % # & # & 0 ,. ' ( ! " % " ! ,. 0 &- " " " % " # &

0 &, ( $ ( $ ( " &, - 0 ,0-. ! ( " " ' % " /0& , - "0&($# $ ( " " " & * , " ( , " 6 $" ," (0-",%

" "# $ $ !

×

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# & & *

, "( ! " "

0 -0 !0 ($. ! $ " ( ! . $ # &

-0 ' "( $ ( ! "( ( ) 00 ' " $0 $ 000&-- , " " , # & - -'* !

&

×

III

V

α = 29◦ ± 3◦

! $ $ $! ! ! !

! +1, 9

−1, 9

a0

∆1,⊥

α

◦

!

& ! V

$ $ $ #" III

a0

∆1,⊥ α

I−V

61$. #

&)0$! ! #" !,!" !$-,,.--.%

¯1¯1¯1

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8 , ( - ' " # & # &

(-.

(0& -. " " " -& ! " & " " !-"(-0$ !.,. ((-,0/(", -."0- # & * 0 " # &

/ , " ! ( $ % " "00 0 / 0 0 ' $ 0 ' %

,-!/" III

A

V

(¯1¯1¯1) h111i

B

A

B

(1¯1¯¯1)

×

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"

h111i

A

(¯ 1¯ 1¯ 1)

B

(-0!/"(11""'-& !0/( #

& ! $ . (-",&$("

+ (' / (0 $ "! " % # &

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-0 -. ! ( ( $ , 0 ,. -.0 / " " "" " " " -0 0 & (0- $ ",(- ( ! ! & % " / ( $ ,0 " % 6

×

×

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, , , $ " " $ $ " " " " 0 &, ",$ ,0-. ( ! " # ", ,0" , $ " 00, - , -. / , -. " ( " " ( % , 0 0 ( - " " - 0 , ! ' " " # & #

$ " " " "( $ % & ''' - -0 &0 (( , $( ( 00 ' # & ( ( ' (" " " 1 16$-00 ",0-. 0' % ." &0- 0 ! "$ , % % # # -0 (",0-.,&% ! , & ,- ' 0 "( $ .0 ' % , ! ( $ . " #' - ,-, &-" ( , ! & * ",0"0&% , ,&-"8,0/&% &-. #0-"! %

×

A

(¯1¯1¯1)

(¯ 1¯ 1¯ 1) ×

×

√

(¯1¯1¯1) ×

T4

×

! !

#! ×

√ 19× 19 R23, 4◦

×

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! ¯1 ¯¯ (1 1) ×

%

(00,% -&!" ' 00 " - 0 , ( $ "$

' ( 0'(%( # * * &,(--'0*- ! ! " !

(¯1¯1¯1)

(¯ 1¯ 1¯1)

" #

# # ! ! ! × × ×

× (2n+1)× (2n+1)

102 = 2, 08 49

# &

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/ 0- " % 6 # &

/ 000 0 ( $ " ( $ , % " 0 , $" "( - " "0 " " 7 -.-0!

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• •

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&

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0 & , 0 -0 ( ! " ! ( " ) %0 , #0-. 8

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kB T ' 25

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√ 3× 3 R30◦

I V

• •

1 # ! & 0 ( $ " ' ' " - ) & # &

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% "

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%

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1−x

x

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√ 3× 3 √ √ 3× 3 √ √ 3× 3 √ √ 3× 3 √ √ 3× 3 √ √ 3× 3

√

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√ 3× 3 √ √ 3× 3 √ √ 3× 3 √ √ 3× 3 √ √ 3× 3 √ √ 3× 3

% ", $ #1-0 1 3 ! , / $ ' , $ ! -

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(0 < x < 0, 5)

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x = 0, 19

• • •

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◦

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×

×

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√

√ 3× 3

√

√ 3× 3

$ $ ! "# !

!

! $ ! $

$ " "#

$

√ √ 3× 3

√ √ √ 3×√ 3 3× 3

×

# $ / 0 % ! / " 1 " ) " & # + - 1 -. , , / " % 8 " " & , ",. " -. ( , % % # 0 0 .0 " (

% * # & & (

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* * + -, ( ( $ " % # &

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% $* *&0/ (,00 $ $ - " " ' % % ( (

-. & $,/ , ,0-. ! " % " % " +

/ / - $ 1 - " 0 ,

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(,(/")% ( # & (

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#

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& %$$"(% - ( (

#

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√

√

√ 3× 3

×

√ 3× 3

×

×

√ √ 3× 3

√

√ 3× 3

√

ΘSi3 ×

√ √ 3× 3

7×7 (ΘSi

7×7 ΘSi

Sh

√

− ΘSi3 )Sh

√

7×7 (ΘSi3 + 2 − ΘSi )Si

√

7×7 ΘSi3 = ΘSi −

2 . 1 + Sh /Si

√

×

√ √ 3× 3

S

√ 3× 3

×

× 7×7 ΘSi S

√

√ 3× 3

Si

$ ! " " # " ! !

" ! " ! "

! ! ! $ ! "# " ! √

√ 3× 3

√ √ √ √3× 3 3× 3

√u l 3 √ √ 3× 3

√ 3

" "#

$ $ ! "# ! !

×

u

√ 3

√

√ 3×√ 3 l 3

,( #

& " 0 $ 0 ( $ % 0%(& ( ( --. , 0 , $ 0 % # & # & ! , , 0. " " !/ 1 , " ( -

. , " # & 1 . $ 0. " ,/ ( -

#, "60-$"

√ √ 3× 3

√

√ 3× 3

Sl

Su

√

(ΘSi3 + 2)Su

√

ΘSi3 Sl

√ √ 3× 3

×

( % (0 !("$- ! - $ , 0 % , . , ! $ ( $ " #

&* *"!(,-",(.0 - # & !""! "(-0! # & # & # &

0 "! , " ( ! 0 / ( ( 00 $ ( $ % 8 " &0-0 , .-0 - ! "( , $ % " $" ( ( --." 0 ! % - $ ( , $ ! -0 ( - % " % . , 0 ! ,0 ! ( $ " ,(," "(-.((-, / 0 ( ! 0 / , / " ( - % # & ( +

, / 0 ( , . % " ( / !,, %! , "( % " / ,0 $ " % " " # & / / -& 0 0 " , , 6 ,,(. # -& . & " "( - " & ) % ( "0($& (" (- , ! )(-0,--., # 0 - ( ( ' ( " "% 0(( / -. 0 ( . , & . , , ( - % " -

√

√

3

7×7 ΘSi Sl + (ΘSi3 + 2)Su = ΘSi S.

Sl + Su = S

√

7×7 ΘSi3 = ΘSi − 2Su /S .

√ √ 3× 3

√

√ √ 3× 3

7×7 ΘSi3 = ΘSi − 2s/S ,

S

√ √ 3× 3

√ √ 3× 3

s

s/S

l/L

" & "

√

!

√ 3× 3

#

,

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0/-/($ , !(-0&

0 0& ( ) $ (, - $ % # " .,((,(0"(0(!%

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0

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# Θ2

Θ2 Θ3

Θ3

%

(- ,0 " $ ! ( #0, &

, , " " ,0-. % # / , ( ( ( ( $ " # &

/ , (-00 $ 0- ! ( " %

, , . , , "( $ " " 0 " " " " " " 0- 0 , ! " 0 ( ( ( ( % 6 " " , 0 , 0 , ( & ( - " " #0 -. /! . .&, 0 ( -

0% & + / & / / 0 - ' 0 ( " ,,/(-(% & " $

Θ2

Θ3 Θ2

Θ3

"# # ! "# !

#

! !

! #

√ √ √ √ 3× 3 31× 31

√ √ 31× 31

√ √ 3× 3

%

,-.(-$ , " 0 ( " ! "( $ " & & 0& , & ! ( ( ( ! ' 6 0& , , &0 ( ( $ " ( $ ( $ . -

• •

%

& ! ,# , -0 0 ! (

, ( " % # & ,0

# 00 / ( $ ( & ( & ,0 -0 / - "( (

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! ! ,!($,00% ) , / 000 "& 0(!"!6 ( $

,-!0/ " ! ! "( " ( "

! )

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,",, % , & " "/ "$ ! ( $ ( ( % ! ! , ("$0&0 ( ( ( 6 /" " " 0 0 ,,- ( ( ( $ % !! --/(0(-.$,%

$!& ( - )

, , -0( " & " " & % # & && ( , % " # & 0 / , " " '-. 0(& " " & ) # " # & 0 , , $ ( $ $ ) % - , 0 ' ( , , 0 , % # / , 00 -0- ( % -0-&, - ( , ( $ , & " 0&-. & 0&- .& ,0 ( $ % "

& , , "( (

-0 / , 0- ! ( " 0 " % % 6 , "( -0 ( " " , 0 - , * *

, " " " , " " ,-."'"(0&-0-"% &-"

• •

• •

2

'

√

√ 3× 3

2

√

√ 3× 3

2

√

√ 3× 3

$ !

$ 2

,"& #

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0 & 0 0 " ' ' % " # " , ( ""( $ ' $ % # &

, & 0 ' ( $ # 0 - 0"! " - ' "( $ " " -. / & ! ( " 0

0 - -& &0 ((# (( ""! √ √ 3× 3

'

$ ! $

"#" "# !

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& ,/ 0 & # 0/ "($% -, , 0 " , " ,)0 # &(!"+% (! / / ( , 0 ! $( "$ " ! "*%6 + - / ( ( , -. , " ,$$&' !-//",($( ,# &( 0 / (" ( " 1 ( ( " ) , " ,"&-"0-% !

, ( ' -.&,

( #

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*

0 ! $ "( $ . 0 , % " # & ( * ' 000 , ,

% 6 # & (

* *

/( - &0 , 0 0 ' " ,0 " ( % # & (

- $ . ( , "( ! ( ' / 0 " ,0 ( $ 000

% ' $ ! (

"+%60-!(% 0/"($, "-'

( --. ,(," $ 0'($(-,( #

& ((

c ×

×

c ×

×

×

×

√

√ 3× 3

√

√ 31× 31

×

!

√31×Θ √&31 1

'

, , " " " % " % " % ' 6 -.$("$' # %&-/"% + #- -& &"%8+-/" / ,&&-. (#, ! ( $ . , " % %' &,("0&-.# +% %' &, ,- ( - ( ( $ $ #,/ --1

In

√ √ 7× 3

√

×

31 12 √

√ 7× 3

√ 7× 3

3

# &

-- ' " & $ ( $ & ' / 00 ( ( %

(%, - 0 ( , " 00 #, "/ " $ & # & , , " - ( $ ( - , &( ! / / 00 $ $ " ( % #( # & # &

, $ & "

,($0 , "(/ " ((!(& 0"(("

, , /& 5(! , $ ! ( % # &

( $ & ' -- # 0$- 00 , / -

( , " - - ( , , ( ( , 8 " + , 0, ,-( ,&0 , " " % ( - $( - ( $ % # & # & # & # & * *

0"$- 0- ( ( " $(- " ( ($ #

&((0" # & * - - -- ( , ! $ " " # &

0 (%&& $. ""( ( (% , / 0 / - - , " , 0&, $( , % " ( ( " -. $ -,# - 0 & (&, ! " 0- ! % * # (" -" " -"

√ • •

√ √ √3×√3 3× 3

√

√

√ 3× 3

√ √ √ √ 3× 3 3× 3

√ 3× 3

√ 3× 3

√

√3×√3

√ √ √3× 3 3× 3

◦

√3×√3

◦

∆d

! # #!

" " # & ! #

" ! ! ! ! ! ! !

!

√ √ 3× 3

∆d

√ √ 3× 3

#

& *"-(*--",*#(#

&" 0. " ( " % * # & ( *

" # & 3 " -"( #

&# " *& , 0 & $ ( % # # &

- $ " " ( $ ( % # &

- 0 ,,$$ ""8, ( ( , $ "%% +

0 ,- 0 ! ( ! % # &

#' - $-- $( , ( $ & ' &

# & % " # ++ ((--,,/ $ 01 /0&-0-&'(1 % &" a0

a = 3, 52 √3×√3

0

= 3, 92 √ √ 3× 3

• •

!

! & " !

! ! & !! ! ! ! ! !

! √

√ 3× 3

√ √ 3× 3

# & + 1 (/-1 ,/0&-0 -& ( 0 ( % (-,# 6&- , %")0(% - , ! ( % - $ $ &- "( , % & - ( , " %( $ % $

( " %($%&$

(% ""( "% 0 (-$,&- ,0 % - , % - ( $ ( , . % &&- " " " - 0

( , )

& ! (-,,00"

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&

% ! ,-. , ( ! " (-,%%

! ,,.-/, ! - !8-'$, , $( , ( (

• •

&

" & ! √ √ 3× 3

& & & +

& & & &

& & & & & &

& +

61$"1,*#

& % / 0 "( %

-0' ( % 0 ( % 6 /,(.&0-. -0- % (%(,%##% &- -. " # & &, 8 6 0 $0- "$ 0 "( $ % # & *

, " % % " , "00 ( * +

-0- $ " " - /"$ $ $ 1 ( , % , / , " ( $ . " " % * * (- $" % #-."-0- - - (((- !

# &

- ( % - 0&-- " " " ! & ( - " " # 00 -.,-. ( & ,,- ! $ ( % + " 00 &, -""(- " % "% 6 $ , , ( ( " " " " +

-, "&" '"" %0&-," )%

× ×

P ' 10 × −6

CO

[¯110]

×

19 ± 2◦

I V

+ 0&-- " ( - " ' $ % 8 ! +

, &, ( , , " % % 8 # & *

+

, 0 / 0 , , % % -0 -.- $ $ % # /,0/,&,&,'(!

×

! !

% & "

"

!

×

×

# &

0 , ( $ . ( ( -, " --. / ( ( 0 % "

00 ( ( ( % " ! +

( , % % % % 8 # &

, , -0- ! "

,00 0--, , & & " % % + 0 ( - , 0 " % - " % $ &- " ( , " - -. ( - " ( ,

" # & + , , $ - , . ! , ' % " $,$/(-1$$ ,

- , $ " , , $ " "

, $$"" -"" , " $!0$ , % " *-% -% ,

"

, -%% -%% , " n×

n×

ΘPb = 0, 778

×

× ΘPb = 0, 75 ΘPb = 0, 80

[001]

[¯110]

n×

× × ×

×

n

× × ×

! "

# !! ! ×

×

! $ $ !

$ ! !

! !! ! !

×

n× ×

×

/ -0- ! ( ( $ % " # & # & # & )

, % #

&- %(0/%00 % ! * , (0" ""( $ " / , . ( -/ " 1 ( # & # &

, 00 " % %

# "

-& 00 / ! , " ( % # & ( *

-1"/-,1" , % ×

×

×

×

×

×

! !

$

#" & ! ! ! #

$! ! #

& !

! &

& ×

×

-1 " ' " " / ( " % # & 0 , /-,%1 , 8 " %

ΘS = 3/4

ΘNi = 1/2

!

& ! !

! ×

-.-/ , . $( % .&, , / , "( $ $ 0 $ " ( $ % " "&" % ( !$ # & (

0 00 / ( ,0 $ " ( $ "

&- -- 0 00 "# ( ' ( ! % " 0 00 ! , " ,-!$ ,"/$,( 3 - 0 ( " %

0 , "(!%(($ " (#

& -& / ( ##,0-. ( , " " $ &- " &",( , $ $ " " ! - (-& " ( " " " ( & ( % " # & (

/ 0 0 / " ( $ " ( - 0 - ' $( , " , $ " ( % " , - ,!(&- ( , ,((&- "-", " ""(-, 6 $ - ! " ( , - ( -.0- --. 0 " " ! % # / - "! , ( , " + ,0-. / , / ( " % % 8 " " / - 0 ( , & ! , ( , " % " # , (% 0 -(&- ( $ . "$($* *" -0 ! $ -.,0 , ( " ! ! " # & ( * * -,"( 0 - ( , " , (0. 00 " - , , ( $ % * * / -.-.- ( & ' 0 , 0 6&& ( " # , , / - ( ! ( , " " " " - ! ( -. % " " + - ,. - ( , "$ ( " & ! ( ! " " " % 8 0 (,-%00 "! ,- ! . , , -/"( - ( , "$ # & ''' ' ' ' &0 (( &0 (( % " " # # & ( '& ( )

(( ( $ , ( " # & (" )&0 ($

√

T

√ √ √ √ 3× 3 3× 3

H3

√ 3× 3

√

√ 3× 3

T4

4

H3

T4

√

√ 3× 3

√ √ 3× 3

T4

×

×

H3

√

√ 3× 3

T

4

T4 √ √ 3× 3 × T4

& ! $

$ !

! $ #

!

T4

H3

T1

√ √ 3× 3

+ , - , . ! ( 0& " 0-'''&0((#" ' & ,0/ T4

000 , & ( , " ! , % " --&, " &0 ' " ( % # # -. , -. 0 " % 0 00 ( # (

-., $ ( $ -. " & ) 00 , " " " ( " % % " " (

,

&-"" (-,( # (

) - - , ( , ( , ! % - !'/ ( , - , " &0 % (

0#"% 0 &, " " "( " & ,0-. ! ( $ " 0--

% " (

,./-0 - -""( " , ( " # & (

)

, 0 0-. ! "

( % % '"0-& ",-, %, $

√

√ 3× 3 √

√ 3× 3

T4

√ √ 3× 3

T4

S5

√ √ 3× 3

$ ! "#

" # # ! $ $ !

A A

×

√ √ 3× 3

H3

! ! "# √

√ 3× 3

# )") &($( #

&* *"% ( " " -(,&-.-&$ * & ) ( #

&((0) , ' 3 0 & 00 % % # & ( )

(#( *$0 "( ' &0 (( % # & (

*

0 00 & ) " # &(-,(0 0(-,"$ S5

◦

√

2

10

×

14

◦

√ 3× 3

∼

√

◦

√ 3× 3

! "# & √

√ 3× 3

/,0-. $ 01# &"-.

0'0(-, & / ! ,0 ( " % * # 0- , -- " ( -0 ! % " " & ( + , . ! , ,00 " (

$&-"",0"0&% ,. " 0 0 &0 (( ) 8 " - " - $0 0 ( % " + . / , - , - ( " , , "$ ( $ % #% 8 /0 #" 0& ($0 ,( #

& % $ " % 6 (

#

&* *( 0 "(

/ ' ( $ ,( #

& 0- ( % ! - , ( - ( ! - 0 , % , -& 00 "0 ( ( - " % (

" !, - "$ - ( % #!0&( - - ( - , % (", - ,-! $!00 $ ! ( -. - # # !

$ # "

$

&"(," ,, &- - - $ % / ,0

$0/000 ' ( - % " * * ! *

$-" " , ) " " " (

(-,- %($ T4

T1

T4

∼

√

√

√ 3× 3

◦

√ 3× 3

√ × √ 3× 3

(

#

& , # - % % % & ,

-&!% 0- ( $ " % " / 000 0 3 5 ($"$( #

& #

& 0/% ' 6"

,

, & 0 $ ( ( ( , " ! "

/ ,0 "( ( ( 0 %

"

% # &

000 ,& & ( ( , % " " ! ,0 "( ( %

"(- (

0 (" ( -0

" # & - ""! , - , / - ( , ( , "

"

, $ "/

$(-," # (-,"&,/ " #-0"!%

,"

% ($ ' $ ! #

&- , -"&" ,0-. & , 0 / 000 ! %

, ($( #

&, -,% !0-. %

!" -. - ( , " "

! "(00,( #

& % ," 1 1 ( # &% , ! , " -.-0 ! & ( " % " & 0 &""(-"!, ! -. ! % 6 ""!-0- (,-.'0/

√

√ 3× 3

ΘAg = 1, 0 √

√ ΘSi√= 1, 0 3× 3

√ 3× 3

√ √ √ √ 3× 3 α− 3× 3

√ √ β− 3× 3

√

◦

√ 3× 3

H3

T1 T4 T1

√ √ β− 3× 3

T1

√

√ √ β− 3× 3

√

√ β − 3× 3

×

×

%

√ 3× 3

%

×

2

$ ! # !

!$ ! &

√

EF

√ 3× 3

−2, 0

& ! √

√ 3× 3

($" 6&!(-0%

!! ! !

# ! ! & ! √ √ β 3× 3

√ √ 3× 3

H3

T1

T4

T1

-0 !-/",- , ( $ -. ( %

- / & ( , ( ( $ . ) #,0-., ,' " , % 0 - / ( ( , , 0 " # & # & # & ( ( (

, 0 ( " ! % % " # & (

% ! 1 5 -. ! % # 0 0 , . ' ( ( ( ( ' & !

/ . 0 - ( ( "$ % % ( ("%( , 0 00 $ " "$ ( " & , "#,0-. 0 " " " (# & $

%""(,

"$! " ◦

×

×

2

×

∼

×

×

∼

! !

! $ $ ! $ ! ! !! ×

×

×

, ! ( " . " " (%(' " " ! -0 ( ,. ! % % " " " 0 / "( ( ( # & (

0 ( $ ( $ 0- "$ % " $ & " & ! ( % " # & (

0("!0/'/&0 / ,0 -0 !-.$$(. % " 0- ( ( 0 & -. ( ( $ # / &-00 -. / & (# 0 ,0 " % #

, ,0 / " $ " ( % & (# &

5 , 0 % % # & & 0 / "( ( & ( ( % " " ( ( / , / , " $ , % % $ ("# , 00& , " -. " & % & !

(, " (0 ,!

◦

×

×

×

×

∼

◦

×

& &&

2

◦

" 0-- , , ! -.- ! (

(-," !(,% , , " # / &, .- / &- ,&- & 0 (-!$ " ( ( $ " " & , 5 6'&% 0"0(% 0 ( ( , 0 ! ( ,( # & % -0-" 0, "" ! " ,!0/""&," &

, ( , -. ( " 8 "

0!, " " % + / 0 / ( - , , " - % 8 " # & # & # & ( ( (

, ( $ $ % % % " , , / 0/'/($( #

&* * (

(% , / (-,(- ! ,

600 " # & -0 ! & ) " " ( &

-,

-0 ! & -, ) % " " (

- 0 ( % % & "!**#-. ("(- 0( ×

110 ± 20◦

×

×

×

×

×

Θa

×

ΘSi

%

! $

$ $ ! !

! ×

×

(#

&, (%

,' , %(#

0 "( % 1 & (% , $ %

0 ( - ( - ! ( % % # "

,- ,,, 0! ( $ ! $ /##-0 / - ( - & $ 0. ) " & * , 0. ) " &

##,$ 0. 0.& )) " ( ! ( " 6((#

"&, " " * *(#

"&% %(#

& % "(-(% & 0/"( ,00 % #'#(-#

-&00 & ,&% # & # ' + &-. , 0&-. , ( " " " % % % &# & ' ! +

&, , , "$ % % % 8 0 0 /"! ! " (" . 0 0-0 % % %' . ' + -0 0 ! % % "!, ( 00 0 60'("-!,--. ' -", , % ×

×

√ √ √3×√3 3× 3 × ×

×

√

√ 7× 3

√ 7× 3

√3×√3

√ √ 3× 3

×

% % % %

×

√

√7×√3

√ √ 3× 3

√7×√3

31 12

√7×√3

• •

•

•

( + ,0 ) + " -)-- #00 ( + % " & (

( $ "$ ' " -+) - (# + )* (!.00"%

,0 $ ! $( $ "$ -- ( % " & - -! " * ' #((

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( ' " " / &- ( -

( $, (- % # &

SA

SB

∼

DB ε(DB ) < ε(SA ) + ε(SB )

◦

◦

∼

×

A

B

◦

×

×

×

×

%

%

!

!

! ! & & ! × ×

0 , 0& ( ( 0 ( " & ) " (,0 "( , " ! ( -- " % "

/ ( 0 - ' " # -0%! 0 / ( - " / $( ( " 1 ( - 0 ( 0 ( ( ( -/ , ( ( " 1 ( % " - -0- ! , ( ( $ ( ( " $0$!-%% " -/00"-,0-.0(-.$-/ ×

A

×

B

( ./,/ 0-((-

!

& !

$ ! #

! !

! $!

"

!! !

$

"

! ! A

×

×

B

A

B

1

4 3 #'-.% # & (

"( $ . , " ( - " , 0 0 $ ( ( ( $ ( % " # & * *

0 '$ $ $ - , " ) % # * * ** / 0- , ( ( ! ( " (#

&, 0 ( ( $ -. ( - ( $ # & ( * *

0 -. ( , ( % 6 / 0 / 0 , " ( " ( % " 0 &-- ( ( 0- ! " & " *

&( ((0, "0(

[11¯ 2]

◦

×

×

◦

×

◦

◦

◦

×

× ×

× ×

0/"0 # &0&-% 0 - ( " "( $ . 6 # & # & # &

-., % * * 0 / & ( 0 ' ' " % " # & # &

#"-.0, / $ $ ( -& $ " & + , . ! ' -. ( $ % " # & (

* *

, --. ( $ ( ) " " " -" " ( !

(

%%

◦

◦

&

2

4 3

! (

! # ! & 0 -

( ' % " # & (

/ & ' -. ( $ - 0& % "

, - 0 / (000 - " ( $ . & $ ( ! $ 0 ( % % " # & " $0 #,0-. ' ( "", 00 " % % " % 0 & /( " " 0 ' " " $ $ 0-1 0 -&0" $ ( 0 " 000/ & # % % 1&"" 0/,$# &# / % &

-, / 0 ( 0 " 6 # & & $ + 00 / ( ! % % " " "0,/ 00 % ◦

[

DB

]

×

×

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×

[11¯ 2]

◦

◦

× ◦

×

"

%

0 ( ( ( " 0 ( " , ! ! % " # & # & (

- ( $ " $ "( $ . , % -. %"( " - 5a A

×

B

!

& &$ &

$ ◦

$ (, -.,0 -. 0 , " ! " -. , 0 $- 8 % & " ( , " "0 % " 0(0( " ($-.,0 / "( 0-. ( -0 0 1$, # " $ & & ( &0 ! -- 0 ! " 8 % " " -," ##&&-. , 0 ,0("

' ( $ 6( # &,0#/0' # & ( ( " -!"0&& %/0(000,& (000 % $ " ,- $ " " (, / 0 '(00 ' ' ( $ " % " - ( , ! - $ % 6 " " , " $ $ / / $ ( - , $ ! 0 0 " #

",-$/ (-1 &

6 ≤ n ≤ 10

×n

×n

• •

% # ) % !# !&($ ( ) /&$( ( $ - *) # ) $ $ ! % & $( $- "$ #! $ ) & ( ( "$ 8 - # 8 ) ( "$& %

* (+ + ( + + + ( (+ ,

-0 ")-&0

)

( ( + ( •

(+ (

+ + + + ( • ((

+ ) ''' )

00 " ,- -- ''' ) • ( - %$ " (+ )

( • +" - %$ •

III

V

II

VI

$ , ,, $ ( ! &--0-% % / 0 -, ( $ -.- ! " % $ (--. ' % + / 0 ' "( $ ' "( ( - % "( -, " ( ( $ - ( " - " ( ' !$0-$"" ,$($%% 00 " " - " ( " " " $ $ ($"($"(.$

,. 0 0 / 000 " & ! $ & " - $ .0 &" $0 % " -. , - ! " ! % "

0 - , ( " " " . !-&!-0 " &, , -." ! # & 0 0 / , ( " & 0 0 " % 6 " !-.0 (

/ (-,"%0& $-. / $, . ! 0 ! . , . ! $( % # &#

)

! % " $$ #)& (,-"0!($-"% - , "0 ' , " - ' ( % !

0# , - -.0 0 " ( ( $ &0 # & ,, 0'-(-%0 0% -. ( $

! " ) " " 0 0 / 000 -0- -. (," ! . % - -. $ - , " &0 -0 ! $ % " 0 ,. 0 ( $ -- ( 0 , . " " " " 0 0'-(-"" % " 8 0- $&# & ""&-% 23

3

# - & ! ( "0 " ( ---& ( % " " & -. / 0 $ ( ( " " ( - ( - % # & -&", & " (-. 0'-0& #

& 0 -/ ! 0 & % " " /( ( - - " % ! ( "/ 0 $! - # & 0 0 & !0& ! -0- " %-"'&!- #

& 0 &0 0 & - ! ! 0 / ,

&&0-&&,&% " 0- ! - ! - ! ( 0-", 0 /0 & / / ! ,

0/,%,0-&(% " 0 " , 0- " % " - "0 , 0 - " , 0 #

& # -& # & # & # & - 0 & ( ( , ) " & 0 "( % % " ( 0 ( 0 - "' ! - " ) &$- !-,, $ ! $0 % 0'($- , ! - " ( ) % " 0--. 0 ( ( % 6 & / & 0 0 0 , - , " ,0-. ! ) % " . 0 / --0 "

& % 0(&, / 0 & --. - ( $! - # / $,,00-((-,"

n(r)

E = E[n(r)],

n(r)

E[n(r)] T

U

Exc

E[n(r)] = T + U + Exc .

U = Uec + Uee + Ucc

Uec = −e

Uee

Ucc

2

X R

1 = e2 4 X = e2

Z

Z

n(r) dr, |r − R|

n(r)n(r 0 ) drdr 0 , 0 |r − r | ZZ 0 , | R − R0 |

ZZ

RR0

Z

R

Exc

&

& / (- ( ( "/ "' "0 " & / ! ! "0 " 0- ! - -, , ! " " - ! "' & ! - ) % "

0 &, 0 " ( ! " ( " " 0&"(- -."' 0 ( - ,0 % " # &

0' &- $ " -0& % " 0 $ 0 && (#,$0") 0# )(& & #

*& 0-('- 0 " (-"% # & $ 0 "0 "( -. $ "( -0'" #

&

-. ! ( "' ) % " & --. "0 " "' ( % % " " 0 / , 0 " ' -"((#&# '" 8, % " & " " $ '

$$# $ # & )

"0-.0 !($#0"(-,(! ( % ( -. 0 & 0 "' $$# ( - ) ! !

( ( - "0 (( 0 " % ! ! 0 &&, / - !0- -"

( , ( -. & , , "' "0 " ( % % " " " # & & & "' "0 " ( $ "

"" ) ) " 0 -& 0 &&, " (-"% , ! ! " ," $( - / $,,"!- ! -"( ! $ ! - 0'(-0- %

n(r)

E[n(r)]

~2 2 − ∇ ψi (r) + υeff (r)ψi (r) = εi ψi (r) 2m

υeff (r)

υeff (r) = −e

n(r) =

X

2

X R

Z + e2 |r − R|

Z

n(r 0 ) dr 0 + υxc [n(r)] . 0 |r − r |

|ψi (r)|2 .

Exc υxc [n(r)] = δExc /δn(r)

n(r)

Exc [n(r)] = εxc [n(r)]

Z

n(r)εxc [n(r)]dr 0 ,

εxc [n(r)]

(-% ! $' $ ", "/ " #,-.&, / -0 ( -. - ! ( ! ( " " , 0 ( ( 0 ( - " " ( % -.,0 / 0 " ! . ( $ * -- " -" -"$ ( $ $ " ,0( 0 "/ -. % % -. -, ( , " ! ( $ "( % - -0 ! ( $ ( - -. ( $ % - 0 ( - ( , -.&, " ( ( ". #

& ! . - ( ( " , ( -. ( , -.&, " % # ,, $ - ! & " " * & ,0/0- ( - 0 % 6 0 0 0 ,

) " " . #

& 6-.0--,0-".-0/ 0-# " & -.''0-"-"(% 6 - - -0 ! , ! - ! "

(-., 0, $ &# & ( ( ) % 8 6 6 6 " %($"( 0 , ( - ( ! ( $ . #00 *

" 0" " ( $ ) % " 6 -0 - , " ( ( , -.& % & '0--.&, " ,0-. ! ( $ 0 " " -. -. / ! ( ' ( $ 0 0 $ &-0 . ( -. ' --0 #% !"(-,".-!(- "(% # ! &" / ( " &- "$$ ! "

$ !

' -"' " , % / 0 &&,,, ( -(-,-.&,""-"/"$% s

p

z

n+ (r)

z=0

n+ (r) =

n, 0,

z60 z > 0.

n

rs a0 = ~ /me2 = 0, 529 2

rs a0

4π 1 (rs a0 )3 = . 3 n

lim n(r) =

n, 0,

z → −∞ z → +∞.

•

•

n

1/3

kF = (3πn)

π/kF

!

!!

! ! ! ! ! ! &

rs = 2

rs = 5

2π/kF

rs = 2

rs = 5

--$'-"-.($% . / -& - / " ", ( . ' -"' "

" "'--"'0- (-($% "" , 0 ( " , ", " ( ./0/ 0-.(# &

! !

!

& !! &&& ! ! ! !! & ! & ×

2

0 0 ( $ & ( "( ' " % 6 & , ! ( ' - ( ( 0 - "

-& 0 & ' ( ( ' - # " -/!",!-",)-"'% v(z)

" 0 -

veff (z) = v(z) + vxc (z)

(, (-

& & ! v(z)

veff

, 0 - ! ( ' - ( " ( -. % . -. 0 & $""0/ " $ "( % " , -- ! 0 ( 0 % " -0 ( ! " ( $ % - 0 & 0 - " ! ! % 6 "

0 /0 & / /0 & --/ ! 0 "

, . ! $ " " #

-& - -- ! $ ! "( $ # " - - 0 $ , $ " " ,0 ( % " # &

-.(-,!"

rs = 5

EF = (~2 /2m)(3π 2 n)2/3 φ

φ = veff (+∞) − veff (−∞) − EF .

! ! !

!

0 , /! $ -," 0

,,$0&" ,-$,,% & 0 (& $0 " &"( ! % ,& ( ' - " ! -- ! % " 0 ( , ' " -- "- ! /( ! ( $ ( ( ! % --. 0- , " " 0 " % " " , & " ! ( ' - , ( " .0 ( %

"(, " #0-0!/" ( # & & &

0 ( "

60! " !(- 0 ' " ( "/

" " / ' -.,0 $

00 # &

0 ( "

# " !

! - 0 ' $ --, - " ( $ ",0$"0('-."00 0 . , ( $ $ " ( " - ! % 6 - / 1 " " " ( $ % 8 $" "($$,

/ 0 !$ !-$(!, " & 0 $0 ( - , # 0-)0-,(&/"

• •

•

$ & & $!! $

0'%0 "% 0 ( - $ - $ - 0---.- ! & ' -- - 0 $ $((% % -. -- $0,, ( " $ $ -0 $( ( ((-.,--.

",! -0 /

! ( ! 0'""(% / -- " , ( $ - ( $ ( " " " % ! - ! --, $0 ! " 8 , ($ (-&, ! -. 0

"('--(% # , 0 ( , ' ( $ - ( 0 % % " # & & "

$ $ ",($( -- -0 ",( $ $ , "( ( %0- % " " ( - ( $ " " % # # &

/ &, 0, (

, " # . /( $ -0 ( $ % ,,0 $ ---/00, "( $# ( ' $ & &

- ( $ " " " ( , (

,($#$ , , & "

!

! ( " & & (-- " %"""(/%

•

d

E(k⊥ )

E(kk )

/ ('! /!#(, $,"(,

& &

, 0 - % " & " "" "/ "0 ! , % , - , 0 ' ( " #

/0-!0/(-00-($ " &

$ !

& " ! # $! ! &" &

! $ & E(k⊥ )

E(kk )

(( $ $ " $ &-. ! % 8 " " # & ,

!

! !#/&-

$$

! & '-./(!0." ! 0(( ,0 / 0 / $ " "$ $ 0 ( " ! % $ .-- " % "000 / $0--, 0& ( $ " " " "('--.($

( $ " " ( $ " " ( '-, ," # & &

!

! ",0 " 00 ( $ % " 0 ! 0 , ( ! ( $ % " " / "'""0-- - 0 " % " -. ( $ $ - 0 ' " --, -, & &

!

! % $ $

"$ # &#

'(

! ! ! "$ -" & '

! % / , 0 ""!&, ( $ " " ,

,% - % " &, "0 " , , " 0 / -- ( $ 0 ( $ . 6 / , (! ( ( - " -- , " , ( ' ( ", " ", , ( % 6"-.&0-% .0-&, - 0 , --& ( , -.&, " , , " 0 -0 --#( ! ( ' -, , " - " ( $ ( ' " & ) " ,0 $,($.,,( 0/,0-% 0 " 00 $ "

"0($" " " , ( 0. &-#,0-." 0- , , ., $ ! " " " "( % & '--,00 -(/"0 ( " " " * " -. $ - 0 " - "( $ $ "

0-.% 0/"(-.$"-,,$"-"% -"0"0&-, 0-. 0",( 0 "/

"0-."("((" #

$# $

! ' ! %( $

&)0 " " - " $

!

-., ,/! ( ' ( ( " " , % % % 0 &-& 0 ! ( 0 % " 0 $ --,0-. ( " (($ -0!( (-. $0$& ,- $ " % --

•

•

vimage = −e2 /4z

• • •

z

kk

# &#

& ! !

# & / ! ! #(' '

$ 0# *"& 0-0& ((-,(-",0,% k ' k

kk

, -,, " ( $ % " (- " "/

""(00&"0" # 0

0/-"&' % -$"" (, ( # &"%

!

! % & , .0 "0 "( ! $0 " " $ " 0&# *"&& &" 0&!"( (!$0#$-%

!# " " &

*

((0$ " eU E1 = eU E2 ~w = E1 − E2

• •

$ " &

&

! $ $

, 0&- , ( $ " ( - " " ( ( $ $ " & "( 0, % " "& (- "( 0!0-(-.,"(% ! - 0& " - " , ( $ " % ) ,-

! '

! ! 6'(0& /!",-,(-$" (0 ,% E(k)

,,. 0 , "( 0 ! -, $ (

./% " 0 !%

$# ! ! !#

% &# &

* ,0- , $

-

$

" &

" #,! !, ( " ( - , ( ", % -0 , ( ! . ( - " % 8 % + -0 / --. - & , ( ! # % 8 , , "( & ( - " ( - ( - % , " " ( - " ( ( $ % ! + $ " (

./% , "/

( $ $ 8 # &

--. '--"'- " ,& ( " $ "( % " 0 & , ( " ( ", % " # &

"(-,,0&- ,'

E(kk )

E

kk

! & & !

! !

! & # ! # " ! ! ! ! !

$ $ ! & & ! !

! E(k k )

dI/dV

E

|k k | = (2m∗ E/~)1/2

m∗

π/kk

!

0 -.& ( - ( ( ( - " , / ( ( $ $ " (

. % # & # &

+

"( $ % % % % " % % 8

(/($$" ,0& (-"% EF

- (

./ %% ",-."!(-!0/ 000- " -"/ "- & 0 , 0 0 , " #

( " ( - " (

./ %% "&- "

+ ,0-. -0 0 " ( ! (

./ % % " # & $(/ / 0& , , %( 8 -! ", 0 " 0#, m∗

me

EF

EF

EF

EF

∗

m = 0, 38me

% ! ! !!

#" & ! ! ! !

! !!

!

%

!! & EF

0 00-. .0 " $( $ % . # & (

,( " " ( $ ! ( " % # " # # & (

( -.- " 0 ' # & & # # & # & ( ( ( * * * *

(#

& % # & & ( '

0 0 / 000 ( $ % % 00 0-- ! " % " , ,0 $( $ $ ! ( " % " ,. / 0 . " , 0 ( $ % """ 00($

√3×√3

×

×

×

×

×

$ 1 (#

&

000 , ( ! - "( $ . % " " # & & *

/ -. / , 0 0 " $' ( ! % % 6 " 0 -. /" ,&,& ! "/ " , ' ( ! , , (0"$ $ " $ 0&0& " " ( % " 0 & - ( $ ! $ $ , "$,,((- / , , 0 $( $ $ , %( % " 0 , / , " " " % % " # & - , / , " " $ "/ " % % , 0 ( "0 $ ( $ $ " - ( - ( %

-. / ( . ! % % % % # &

- , ! " $' ( ! % . & # / / - (0/"-"/(-.0 ( -. ( - "' ( ! % # & /( ,- ! ( ' ( ! . ,( , " 0#

×

×

π

π

π

π

J

π

π

∗

ΓJ

JK

π

π

∗

∼

!

! ! ! ! &

%

! &

! " " # " ×

π

×

×

×

1 , - ! -. " 0 ' "( $ % " # & ( ( * $

,0 / - 000 ( % % " # & ( * *

/ "( $ ( . " - % % 0 0 , -0#! $ ( $ $ " # " #

0 , / , " " " ! " "

,0-.- ( % % % ,0/0 ,, - ( $ "

0 -0 " ( ! # " "

×

1, 7

×

0, 2

S1

0, 8 S2 S3

U1

0, 5

!

!

" !! #" ! ! !! ! ! % ! & ×

×

$ , , &, ( $ $ " - " % 6 +

/ - ( . & - ( - % % 8 % 8 % " ( ( - ( $ $ " 0 # &",-. "!,, 0-"" - *(*- ! , ( % " ! --, - (" " --,

" % # ! ! & " ( ! ! $ '

! -.&0 ( - % " , ( ( $ $ " " * *

/0 , /0 , , - ( $ - % " * * /0 . , - ( $ ., ! "( % "

$ "0&-&,"!$0 %%

×

S1

U1

S2

S3

×

×

×

×

! # " $ "#

$

" ! " ! & ! #" ! # " " # $ $ ! ×

#-!.0 & !0-.&0 ! " & ! , % " * * / 0000 -. , /0 - -.0 , ! - ! , !

, ( ( $ & % . * * , /0 , "" , " - ( "

" V = −0, 35

V = −0, 8

×

∼ 0, 3◦

×

$% "

" % !! $ " ! ×

×

(#

&

,0 -0 / ( ! , & ( $ % 60( #

$&*0 * *(""(/0 * ' 0 ' " , % "6

( "( $ . &$&-", #" -"& ×

×

× ×

4

×

×

! $ #"# $

! "" #" ! %

& ×

0-% 000 # (

, , " "0 " # & ! / , -0 / 0 / ,. ,00-/ (-. ( " (

#

& %0 $ ( $ ( $ 0 0 , (" (0&" " &

, ( $ & " "( % " 6 " 0 "(.$( ' $, " " " " , " , -, ! ! & " " $,( 0/,0('$,

×

×

(#

& ' $. ,0/% $)"( 0 ' 0 ! - ' 6(( ''' -- &0 ( % " / / / 000 -& ! 0 0 % # " -- , - , "( , " " " # &# & (

0 00 $ &- "( $ # ( / 0 , 0 0 / $ " ' 0 0 0 / "!"!00 !" % 0 , - ( "/ , ( $ $

, / 00 " ! $ ( % " " # & ( '

/ , 0 ( $ $ ( $ ( -0 % "

( / . " % % % %

0 0. " -,0 " " # & ( * *

!. ( $ ( " 0 & -0- . " " " " , % " ,' --((-,"! & ( 0 '&

(#! " 0-- & , " K

kk

√

√ 3× 3 √ √ 3× 3 √ √ 3× 3

S2

T4

√ √ 3× 3

S3

p

S3

S1

√

√ 3× 3

S1

S2

×

! ! # ! !! " ! ! ! ! ! √

√ 3× 3

! - ( $ , ,-. % 6-- # & -0 ,-0 / ,- ( ( % 00 " , ( $ $ "

, 0 /( 0 $$ ! # -. $

0 0 " 0 - 0& - ( $ % " "

/ " ( ( 0. " , - , ! ! , ( $ & " " ( ! ! " % !

" $%

0. $ " , ( , / . ! , ( $ $ " % " # 0 0 0/(/(., "!0 " -. ( % " & -. , , ( - ! % # , -0 , ( 0-,- ( ( & 0-. ,0 -#0(,-00 ( , ( " , % " ( ' ( -.&,- ! " % ".((#

& #" , . ! ( $ % " " & # & # & (

, % % " # & # & ( '

"( / -0( $ . ( % % # & # &

( $ " # & # & ( * *

-- - ((, ! % " 6 -0 . ! -( ( , " (6-00 $.-- ! $"($% 0 $( $ 0 0 / 000 ( ( , 0 ( % & - (,& -0 ( " ( % ( ( $ % " - -0 / " - , ( . % # &

- -0 " ! ( ( ( % "

- 0 , , -& -0 ( , " % % ,0, ", ( ( % !" ( 0 & - , $ ! ( , ( $ $ , - 0, ( 6 , - (/ 1 ( $ ( % 0 , / , - " ( $( $ $ & 0 " "0 ! & " ' " , . 8 0 -. $ $ 0 00 ( % " 0 $. ( $ " " $( ( % " # & &

( $ "/ " ""( #% , ,0-. ( " ( $ 0 0-0 -. , -. ' " ( $ " -. % 6 0-" --." ,",(-,-. 0%

E(kk )

m∗ = ~2 (d2 E/dk 2 )−1

m∗

×

√ √ × 3× 3

×

×

n

" & ! $ $ " " " $ &"! !" $ & $ $ n

p

EC

EF

EA

QSS

EV ED = −QSC

! ! / -., $

( ! % /0 & ((-, " ( , ! / ' - ,

"$ 0 ( % " 6

/ ((-,"!''",$ ""( /( (" 0- &, " ( ' 0- "( &, " #

& 0 -0 & ! "( " "( ( " ) ) " ( $ ,& , " & ! ( . 0-- ( % " " - ! ( ' - ( . ! ' % " " -. ,"($-0-".

eVS = ev (z = 0)

Nd d

v(z)

v(z) = vbulk −

ε

2πNd (z − d)2 , ε

z

"(

"0-,($.. 0,,&0 $ ( $ -& ! % -0 -0 , " ! "( ( ( ( ! ( $ . % " 0 - , 0-0 ( , -. " ,,&0, ( $ % # &

( "

0 / / ( -0 ! % 6 " " " & ! " &- ( &, " ( "

# " $ .- --. , ( ( $ - " " & .- - ( "( &, " "($$"(-, -,/ & , , , , (/ " ,& ,,(.,% & & (

( $ ! -

" -, -- , (0- $ $ " -, ( " - , ( $ " -,, ( % " & /(

" ( 0- ! % -0 -.&,& , $ ( ! # &0 - ( -.- ( &, " . " " " ,0 "

$ /( . ,. ( $ 0 " , 00 % % 0 (

"($,($% * ( - 0 ,

$ & $( -& % % ( -#" *

,,0-. 0 !( ( % ( -., "( % + / 00 " ( $ $ # & (

( $ , $ & , &-& , ' % " .0 . 0 "( ,0 ' -

" ("( 0 !,!,( 0( ( , *$ ($ p

×

×

◦

! &

* * 00 -0, . ! ( ' "0 $ " " / ,0-., ! , ! (

!% " " -. 0 , , ' ( " 0 $ % " ---. $ - - 0-- "( % -( , ( $ $ " - ( &, " ,' 0 - -0 / 0 " ( ( (

& 6 " " 0(,-.&,- 0 ,,(. #

& -0 /( . , )0,'- % .(.+" ( . / $ ", (( / - - "( &, " ( $ $ " % " -0!!.0,-.0- -& #-0!-&($- ("% -. $ ,.- 0"(-.,% -. ( ' -. $0 ( $ !

/ - ( -( $ , .0-(0.,!$%,&-

×

• • •

g

d

g = g0 + ∆σSC + ∆σSS . g0

[

[

]

] g0 = σB d ∆σSC

! & ! &

"

& !

! ! & $ ×

R = ρ/2πd Ω

ρ =

σB

∆σSS

! , 0 - -. ( ! ! $ ! ( ) % % " ,0 " " , "0 ! ( # "( , //( 0, ( ( ( 0 "! ( % " , ", " , " " 0 ( ( % "

, ( - , ! $ % % " # , & ! ( ( ! " , , - "

,'"",0,% " &

-. , / ( ! ( ( % #

--- " ( 0-. ( - ) % " & # & (

* *

0 , ' ( $ % " " , , ! $ 0 ' " " " % " " - , ",, 0, " " ( ( ! % & ! ! ." $ %

( (,'"(% -& " , & 0-. ( ) % " , --- , ( " . " - - ( ( , . ! ( " , 0, " " , ( ! --" -" " &-0!& , ( "

0 -. &-0 / ! ( " "

, ! -.- , $ " ) -. . , , ( $ ( $ ! "$ % " 6 " -0 !

, ' ( - , ( % " " "

& -0 ! & , ' " -." ! " & ( " ) " -. '" " $ &- ! (

0,% "" (-& !

,'",. - ( ( " . " ( -. % 6 0 -. , . , -, ( $ ( " ( " " $&- !,0-.&-0 (-(" ( " ! " ! - ( &, % " # & (

* *

, " , ( $ ( , " " ,0-. , / . ( ! ( 0 % 6 " - " " , 0, , " " " ! 0-. % (-0 -0 ( $ , ( ,0-. " / ! $( , "$ ( $ (

. , ""$( #

&* *( #

& %%% , ( $ * *", (

./ (- "( $ % # - / , ! " ( " - ! ( - " & *("& $*' (,, ( , (

./%

./" -.,",. $ " - ( $ ( (0($ 0(!!

I V

R = V /I

Ω

n

×

3

×

×

d

R = ρ/2πd ρ R ∝ 1/d

d

d

d

d

d

d

R ∝ 1/d

d < 10

×

√

×

√ 3× 3

%

× ×

√ √ 3× 3

0 / . " "0 ( $ $ %

/ ! , " ' -"' " -, " # &-,(.,% 0 ( / --.& ( ( - " 0 ( "$ ! - " % " ,, ( "$ (

./,%(-" 0 , ( ( ( & ! ( - " " " # &

, ,0(

$ ! " ! & "

$ #" $ ! & % !

# "

! " & ! " & ! ! & &

√

√ 3× 3

×

0 -- $ -.0 / 0 ! ( "/ " / , -- 0 $ 0 " 0- "0 ( - # , 0 & $ 0 $ " &% -. 0 - ! " ! -. -- # $""0& # 0- 0 0-,-- ! " - 0 0 & 0 / / -. ! 0 0 % " 0 0 ( $ -- " 0 & 0 " , 8 " $,,(. #

*& -, &, " ! " " " ,. 0 & . ( - ( , 0 ( !-0 ! ' ( ( " ( ( " 0 0 , " $ ! ( ) % 6 # &

'- 0- (0-$(0$0&" # & " --." ,-"$ #

& & / -00 --- ! &, ! % " - 0 - .-0! ( , ( " ! 0 " -- ! ! & ( " ! . ! % # " 0 -. " ( $ , . ! " # !"-, , " 0 , -, ! -. ! % &

- 0& , . " ( " / ,0 " 0& $ & -- $ % " /$-""0 ,! " $ ,/00$ 0 $ ! , - - " -- 6 ( " "0 ! ( ' -&-0 #'0-. & (0(, ,-. . & ( " $( % #

0 " " # - ! - ! 0-. ( $ ) % " " ,",./0-!$('-.$0&

N

Evac

EN

N −1 EN −1

φ = EN −1 + Evac − EN .

EN −1 −

EN F

N

T

V

(∂F/∂N )T,V

µ

EF

EN −1 − EN →

∂F ∂N

=µ

T,V

φ = Evac − EF .

Evac

∼

v(−∞)

# & 0 &, & ( - ( - " ) ) " - (-. ( , -.&, " (!$!" & / ! -, #

'$ / 0 0 $ ."( % " , -. - -!"0 ! ( ( $ -.& ( " " "$ ( $ % # && " " ( $ 0& " &&! # &- ,/-- ( -0 ( # -. -. / / ( ( $ - 1 % & - $ 0 & " , ( " . ! 0 /( ( . $ $ . % " " & ,'-.- 0/!. $ -., ", % " . / -.& " ! ( 0 ( " " ("--. -. -- $ & " " . !- "/$-"0$& (! ! $ " " #0(--0 &

'0 ∆v = v(+∞) − v(−∞) = 4πe

Z∞

−∞

n(z)

z [n(z) − n+ (z)] dz ,

n+ (z)

!

φ

& & & & & &

- -0-, -. ' " " ( " --. 0 , " $ , ' ! ( " #

,, , ( " $ % " # &

'" $$# -"'(,"(0- $ -- 8'$ 0 -. ( " ($0-!""("0$

!" '

# " 0 -( $ / $ '

$ # % " & " & " ( -, 0 / -. ( $ 0 ( % , - / 0 ( - ( ( , 0 " " # &

/ -. 0 (, ( 0 ! ( $ " # & &

. / !--(0 $ " - -- " ( ! " ' ! $ # - & !-! $( $ "$ ! ( ( % " & -.&0 . -0 & ! " $ % , -. 0- / & 0 ! - % " .-0 / - " ( , ( " , - ! , 0-. # 0$600",-, (% - ,,'.- -.& & 0- "! ! 0 ( - / ( " ( ! / ! 0.1 ( " %$(- ,0-.,(-.&,"% "! $!"!(-0($(-

∆φ

&

$& $

-"(1-0 (, 33 --. 0 ,& , ( -0 0 0 " $ ( ( ! ( " % # &

$!- #

& 0 0 0 , . ( ,& ) . " " !- ,!,.0&,00

φ = χ + eVS + (EC − EF ) . χ (EC − EF )

eVS

, ( (-"," -& -0 - "/ ( ! - ( ( " !-

$ $!!

$ $ $

$ φ

χ

eVS

EV

EC

EF

0 0-. 5 0("/-. $ " , " % %$(," &0(( -. -/ , " , " & ! / 0 $

" " - "$0 % "$ # 0 , 0 (-! "0 " "0 " % " & ( " # 0 0 , "0 " "0 " % " & 0 ( # 0 0 , " "0 " -0 ! % " & 5 5 - 0 / ( ( -

, 0 /( / ( $ ! ' -.0 % " & & 0-0 ! ( 0 "0 ! ( " -, ( $ % # $ . ,. $ (( ( ' -, % & & , " 0 "( ' - ( - , ( % / 0 -&"('-1 ( 0 ( -0 / % " 0 . 0 . 0 / %

0!0/0 0

• •

• • •

−F ez

F

∼ −e2 /4z

∼ φ/eF

& ! ! & & &!

$ ! & ! & $ ! F

φ

δφ

* #

- "0 ! $( ( " , $( ( % # * &

- , &-0, % # * -. 0 -0 0 0. " ! , ( # $!&0-"!, % --,0-. % % & . "0 ( ' ( " '

# & !

%$ 6-. " ) ( ) # & +" )$-% 0 ( - , ( ", & ) # 0 - - "/

"0' ,,% ) # " / &-. (&, " - ! ( % 6- -.,0 / ( " "

(- / - " $ ( -" 0 -& 0 "0(""( , /& " (" ,( % 6&

5 5 60-(00-% / / . ! 0 " . ( -. ( ' -. 0 & ( $(0.--. % 6 -- 0 ( $ ( ( ( % # & ! ) " '

) % ) # & z0

∼

∼

j

1, 54 × 10−6 F 2 −(6, 83 × 107 φ3/2 f (ξ)) j= exp [ φ t2 (ξ) F

F

2

φ

t(ξ)

f (ξ)

ξ

ln(j/F 2 )

(1/F )

φ

j

j = AT 2 exp(−φ/kB T ) ,

T

],

$ !!

& #

-& - 0 " ( " " ), ) " " -. ( " " ' ) 6,-, " 0 $0 ( $ $ ( " " #

, ( " #-' % " -. $ & ---. "(- -. $ 0($((-0-0 2 e 4πmkB A= ≈ 120 A h3 m e kB

−2

K−2 ,

ln(j/T 2 )

h

(1/T )

$ ! φ

∼

$

!

. -0, ! ( " , "

/ % % " 0 & & $ ( - , . , ' 00 " % / $ /( ' .(% ( - "!."(-, (,' -.& ,0- 0 $ , . ' " " -"(00&('- # & #,0-.(-0!(-,0 #

& 0'/(",0"% , $ " / &("," #

*& 5 5 ---0!"% (% 0 &0 &-. 0 & / 0. " ( " , / - ( ' ' $

' # ",- "

-(- ' -. 0 " & $ 0 , / ( 0 ' $

% -- 0 -. & " ( 0- ( "0 " 0-#(' &" $ " " , " " $ # & d dz

e2 − − F ez 4z

=0.

z0

z0 =

1 1/2 −1/2 e F 2

δφ

δφ = e3/2 F 1/2 .

hν0 = φ .

0 0 , / ! ( % 6

0 & . &0 ",". 0 " ! " ",& " --

0 / ((0 (" '

%$ # & , - & ( " 0-. " 0 ) ) % " "

0- '"-" . / ",#! &, .((% , ( ! ( -. " 0 . /! $ " , % " .

&, , &,0&- " -, ( $ ( - " ) % 0, ( ! ( ( "/ (( / ! "- ( . ( % # "

/ ( -( - " $-"-.$& ( ./ 0-!&

2

j = B(kB T ) f

B

T

hν − φ kB T

hν0

,

hν − φ > 2kB T j ∝ (hν − φ)2

f

j 1/2

hν

hν

hν0 = φ

&

! !!

! ! " & !

! " ±

/ 0 $ ( $

0 " " ! -.

$ #

, " $ % # / -- " ! , 00 " ! % " / 0 , '

! % " " # & ,0 " ! #

"$ " " # & $ - 0 , , $ $ ( $ , " "$($,',0-.$%-%%

& , $('#( &0 !(--. ,0-. ' . " 0 - , $ ( 0, % "$- 0 - ! , 0 0 "( $ " % 6 , , ! , -. " % " &0 / , $ , ' . ( ! " !-!(-.,0 $# ! - /

&"#--.&

5 & ' (0 ( %

6

/ --, ( $ . , % '0- ,0/ ( ' ( # (% , & ! ( ( ! , ! ( ", " ( ", , 0 , ' #

& & " ,. ( ' - ) ) " & (", ( ! , , , , ' 8 " " / . ,"

• •

U = ∆φ/e + Ucomp , ∆φ/e = (φ2 − φ1 )/e

Ucomp

C

& "# !

& ""# ! $ "# "& ! ! "# !

$

&! $ " & " Ucomp Ucomp = 0 Ucomp = −∆φ/e

#

& -,- - " ( " ! % " . ( ! " " ( " & ' ' ( (& " # & ( ", " ! 0- " 6 # &

/ , 0 0 , " & " " ,('- #

& / , $ " $ , ' ( 8 0 -0,0 0 -.,0 ( " " $ & # " -.,0 - 0 -0 ! ( "0 " + , -0 , ' , " % - ! , $ ! 0 " , 0 /$ 0 -. ( ( % " * !

- ( , $ , " (0(('- ,"& ( ("-!%

Q = CU = C(∆φ/e + Ucomp ) .

I=

dC dC U= (∆φ/e + Ucomp ) . dt dt

Ucomp

Ucomp

Ucomp = −∆φ/e .

∆φa

∆Ua = ∆φa

& ! ! ! # % ! # ! Ia

Ua

φ φ2 < φ3 ∆Ua = (φ3 − φ1 )/e

φ1 <

-#"*"$ -,"- ! ( ' -"' " - -- " " ! ' * 000(" "

1$& ,& , , , " $ % " # &

, , ' ' " ( $ ( " &

-. ' ( ! & " " # &

#

& ' ' " ( $ 6$+"# -0 , ( ! ,0-. # & "$ %% + # &

$((-.,0 " , ! 0 ' ) " 00 - ( , ( ! - % " "

$ +-'"(!/(-.0-& "0# " + "

" %) ""

)

1, 77 · 1015 −2 = −18

2

6

φ

j

2

T

◦

"

(

(

) + -

) + ) " # " " 8 & "$ (+

+ * # " +(+ + (+ ( + , ) % " ,- 0 00 ( ! ( ( $ & -0 ( ( -- (+ % + + +

+ %(%

+

+ (( + ) #

0 , , ( - ( ) %

& "( $ (

- ( +

++ ) + (( ( " *-*

0 - " ' ' 0 , , -.&- ( " % "

00($#!"- ,% - ( , " " " -.% 0 '"",0-. $'(""'( , - " 0 , " ' ' ( ' " " " "( "

&-" "-"% & ' ' 00 $ ! ( $ % $,-/! , '( " 0- " , 0 " 0'$(% - -0' " 0 - $ $ - ( ( ( , ( " " " 00 - 0 ( $ ( , - &) "(%% ( " - ! $( ' $&-""0.0.

$($ -,!$$(,-",% , , $ $ $ ' " # 0 &0 0 ' ! ' ' # " & 0-& .&-0 ! $ 0 ( ' -. $" ! ( % "/,0(-.$!$$

& -0 ( ! ( $ " ! " % &- ( $ &, ! % # & -0 / &, ( &, ( (

($% " ."(", #

& # -0 & ( ' -.-&, ) ) % " & -. 0 &, ( " " ' ( ) ) " " / -0- ( (

( $ . 0 " /"/-.' (% I

p I= √ , 2πmkB T

p

m

kB

T

&&&

'

/ 0 ' ( 0 ( ( " " "

# & $ ! -

! #$ ! 8 ,".' #

&

,-"0'(-("-0!% '',(" #

& ,-0/ !- ! , " ' "

" ! % "', " # # & 0 ! ( , -. # &

+ + ,(!00&$-0- 0'"" ," "("" "(% ) -0- " . ' " ( ' 8 # & . -0-- , ' ' ' % " - -0- , ( " " ( , . ( 0 '"#-"&-"/!- -.'0-- 0 0& !-", " ' ( " ' -0$,- --. 4 43 5

#!(!% ! ! & -0 ( ! ,

$ # " '

( " + -. 0 / / - & " -0

$( ( , % "$'"&!-( ' 0 - #8-. ' -0-,,". / / / ' 0 ' 0 ' # &

$-0&/ 5 5 #-0!'% / ' (

($.-0-,/% " ( #

-& '0&/", s

ra

ra = sI .

s = σf (Θ) exp(−Eact /kB T ) .

σ

f (Θ)

f (Θ)

exp(−Eact /kB T )

• • •

f (Θ)

f (Θ) = 1 − Θ,

&

& &

s = s0 (1 − Θ)n

n=1− n=2−

& (n = 1) & (n = 2)

Θ = 1 − exp(−s0 I · t) Θ=

s0 I · t 1 + s0 I · t

& &! & & " & & " (n = 1) (n = 2)

#

& & )".(-("(0-(

5

5 " ' % -0 / -0- ' 0 $ $ & ( " ' 0 " /'" ",, #

& -(0''(," #

*& - 0 ( 0 ' ' ( , . ! - - , ) % . $$#-.,-!,0,"% dΘ/dt = s0 I(1 − Θ) ,

s 0

f (Θ) = (1 − Θ)2 , f (Θ) =

z (1 − Θ)2 , z−Θ

z

&&&

- (-., #

&#

*&-.- "( , $ &% - / -0- , 0

" " ' 0 # &

,-. ( ( , " " " #(&8" ( -0- -", ''" !

0&/,(% " #

& &, !"!

0&/((' ! ( " " -0 ' $ -. $ ! "$ ! ( # "

, 0 & -0 ( " ' ! $ # &

0 -. , ( $ ! ( % # " 0 / , -.0 !

$ " 0!-- &" &/&(0 ("' ! % "!0, " , -0" " 5 5 $'"-0-($% , , ( " ! ( , 0 !

%

% " " - -0- ,& ! #"(&" ! ( ( -. ' ., " . ! $-0-! ', " 0 " , . 6 0 -0 0 , ' ' ! ! ! # " -0- " " , &. ( ( $ $ (","(,$'" -.0& Θ

n

4

4

n f (Θ) =

(1 − Θ)

f (Θ) = (1 − Θ)n , n

2

s(Θ)

&! ! " #

! $ "# ! " ! 2

&

' "( ! ( % " " $ ' , $ ! ( " '"'" #

& '"'"" #

& , / -0-&, , ! . " . , / -0- ! ( 0 " $ ) % " ,&, ! ' " . ( $ ) % " , ( 0 " " ' ) " -. ,"(0& " " ! $ ' % ' , ( 0& " ) % " - ",#, 0 " , . ( ( 6 "'#&

" %% # " #&&-, "

% ,0-.0 / " ' , & 0 & 0 ! -- " (0

5

5

- - ( ( , . ! ( 0 " 0 &!0-".',,(. #

& ""(-0 '(-(" #

& " &!

"(),& ( # &

, " ' % " # & & ,- ( ( " ! , ! " & !

(' ! & " % !& " (,-& # & # & ( " -0 ""&" % !&-& ' , ( 0& # -0 ! ' , ( 0& / 0 / " " . " & & " " '" 0 - (-. ! ,, ( % " "."(0 " - , , 0& , . sp I

ka

(A)g (A)p → (A)a kd

sp I

ka

(A2 )g (A2 )p → 2(A)a

n=

kd

(A)g

(A2 )g

(A2 )p

(A)a

sp

(A)p

ka

kd

rads =

sp Ika (1 − Θ)n kd + ka (1 − Θ)n

f (Θ) =

(1 + K)(1 − Θ)n , 1 + K(1 − Θ)n

K = ka /kd

n

n=1

K

n=4

K→0 s → 1−Θ

K

K→∞ s →1

&&&

% &

! & "# $ $

!

0 -. ( ( ( ' ( ($( # &"0(% -0- ' / , . / -. $ ( " ! % " # &

& 0 ( 0- ! ( " ) ( - ''-0- ! ( 5 5

# 0! -00! / & ( 0 ! "0 % -8," n=1

n=4

K = ka /kd

4

n=4

4

%

!

&

K = 2500 1000

n = 4 K=

&

, . & ! ' , ( 0& % # & - & - " " ( , ( 0 ( , $ ' " ", . ! ' , & ( 0& % # " (-,&,"(-,$'& -,-0 / !

,-"'% % '$0-"$ #

& & " .& ! $ ) " " , " ' ( 0 ( -,& ( % ( " . , " 0 ( " ! " 00 0 - $ - ( 0 ("%0

" (- 0 ( " 0 0-#

&"(, $ ! $( " , " &, ! " -. $ ! " &

, 0 " " ( ( % " # & *

-. " ' ( $ 0 -. - ( ( , " ! " ! " -,'&-0",0-.+%% kd kd0

f (Θ) = [1 + K 0 (1/PV V − 1)]−1 , K 0 = kd0 /(ka + kd )

PV V PV V

Θ

B

B =1

B=0

B

2

B

&

!

! & "# $ ! $ B

=

0, 99

K0

=

kd0 /(ka + kd ) K 0 = 0, 05

B

K0

&&& c ×

/ , / 0 ( 0 ( " ! % " # & # & * 0 %

&

&

"# 2

1 4 3 (0 , . 0 " ' ( - ( "( " " % 8, 0 & / , ' " -' $ % 0 , " ( ' % -0-&, / , " , " ( $ . -0 ! % # & *

0 ( ' -. " "$ ' , -. ( ' ( 0& " " " % 8 $ $ ( % " , --. 0 ! -. ' ( - ( " " " !, " 0 (#-0 ' ( ( ! ( 0 $ ' ( ' -. " & -0 /" , " 0" , ' & ( 0& 0 /" " " &-0 0" ! & $ ' & " % # & !

" " '(-0( $ " ' % /! & ( ' ' " " /''-.% / -0- -0 , ' ( ",0/(!$!",(-,%

Eads kB T

&

! & & &

!

" !! &&

. " ,- ' - ! & " (-"(00/,.0'(-("

& & & & $

& $ & & &

& ! $ $$

& & & & & $ $&&

Eact = εa − εd (2A)a

Eads

Edes

εa < εd (A2 )g → (A2 )p → εa

εd

-0-0 - ( 0 " , % / ,0 . " ,&,0 - . " " ' $0& " ' ' , ( % % "", .,( Eact = εa − εd

Ediss

&&&

#

-& #

& & ( ( 0 ) ) " " !-.0 '(-(", . % " ,( #

& 0 , . , , . ( " " -",-!$#-.$-! # - .-0 ! ' ' 0 0-!!"0- ! ( -

"&" #.-0 # , ' ' & &

" " 0."0-!(0 0 -.& - , ,- ! .,- ( ! 0 # & # 0 ' & 0 ( & " " " # & $ *

,& (!, " ' "" 0 . 0 ' ( - ( " 0 " ( 0 -& - ! 0 #

0& ( ( - & ( - % " -"' '-0- ($ kd = Θp νd exp(−εd /kB T )

ka = Θp νa exp(−εa /kB T ) , νd

νa

Θp

−1 ka νd εd − εa s0 = = 1+ exp − . ka + kd νa kB T

s0

εd

•

εa

εd < εa s0 εd > εa s0

•

(εd −εa ) 1/s0 −1

1/T

2

(εd − εa ) = 0, 19

2

2

& & 1/s0 − 1

1/T

2

&

(0 # '& & ( % " 8,. 0 ( - ( " 0- ! " ( ( % " , " ! ' " ' $ % " * '& . " 0# s0 1

s0

1/kB T

Eact = εa − εd

&

& ! 2

Tgas = 300

2

-0! 4

-0- / ' ( ( ( $ % #.!' " 0 & &0 ! ( " ( % " $ -. . ' 0 "( 0 " " " -0- / 0 ! ( ' -, " ( $ . ) " 0. "0! -. '" ( $ , , % " " -. -0- - " ( , 0 "(- , "0 0 ' ( - ( " , . 6'0" " , - ! % " " / "$#

"' (18(--/0% 0 -. , 0 ( ( ' ( % -. 0 &($- " ! " ' "'( 0 '(( -#

(&#

&0 , -(! " # 0 ' , "( " - ! % # " '& .

z

2

% = 0, 4

E⊥ = Ei cos2 ϑi

E⊥

E⊥ = 0, 1

&&&

! &

& ! & !

&

! " # 2

◦

◦

ϑi

1 #

& -0- -0 '$- - ( ! ( % 6- " 0 & ( $ ! ! 0 " 0. , ' ( ' -. " ( ( $ . , " ! & "

" " " #!!&(-,%% ' " ( " $

" " " # & - -0/ ! -0 ! ' 0 $ " % " - . '('- ' 0 # #

*& . 0 & ( , ( " ! ) " 0 ''

- ( ( , ! % # " -0-, / , - ! % 0 / . 0&0& ' , " % " # &

( ,$ ) ( ) #

& 0 & & " ' ' ( " ) ) % " '" )'

rdes

rdes = σ ∗ f ∗ (Θ) exp(−Edes /kB T ) ,

f (Θ) ∗

σ∗

rdes = −dΘ/dt = kn Θn = kn0 Θn exp(−Edes /kB T ) , Edes

n

kn

&

5 " ' " - ! % 6 # & !

- , , -0 ( " ( %

!6 (--/ # & ! . ' ,

%$

( ! % ( " . " " "( " ( ( % " / , 0 0-& ( " " -0 ! % &0 &&, &0 " , , 0 , , ( ' , &- ( - # & ! .

( ! ' ( ( % 6'-. - / -. ( 0-0 ! & 0 " / , , 0 ( " $ % ' & $ ( ( " , . ! ! , " " # & ! 0 "!- -- !"(("0- % # &

! -.,0 , "

( " " - ! "! - ! ! ! &

' '

! "

& # ! . ' ( ( ! % 6(&'"-. ! " " -0 ! "

$

%$ !

/ -0- & 0 " " ,0 " ,0 $ % " , / -.,-. - $ , ! ' % " . &0 -0 ! -.- , ( % % " .,-!("'"-/!"'-

0. " & ! ( ( $ . % 2 5 " " # & -0- "! ' - , ( -. % ! & " .'! " ' , '

(

" "

"! # &

" -0!'0 0 & "

$ ' " # " 0 & , " $ ' " 0-0 & ' ' # & " !

"

$ ' #'(0&",$ '

"&&0&""% -0 0 & ,. ! ! " ' , " " ( ! , ( . , " " % " -- -. ' , ! -. , ! ( % " ! ,6-)#& (",0&%

n

•

n=0

•

Θ

n=1

k10

−1

ν0

•

τ = 1/ν

Θ

2

n = 2

Edes •

Edes = Eads + Eact

•

Edes = Eads

∼

13

−1

&&& n = 0

Θ = Θ0 1 −

k0 · t Θ0

k0 = k00 exp

−Edes kB T

[k0 ] =

.

,

,

n = 1 Θ = Θ0 exp(−k1 · t),

−Edes kB T

k1 = k10 exp

[k1 ] =

1

,

.

n = 2 Θ=

Θ0 , 1 + k2 Θ0 · t −Edes kB T

k2 = k20 exp

[k2 ] =

1

·

,

.

! &

& " & 13

10

kn Edes = 3

Θ0 = 1

&

, - ' , , . $ ' ( $ " ( 4 $

#-0-% '-.(0/% "$ ( -& "

$"-0-", #

& , -. ( - ' ( 8 " ,00 0&- ( ! " " ( - ( " " - , " -" " #-- -. " % # " " &

&0 .0

#-0!'% 0&- - ' ( - ( ' ( -. / ( - ( ( , , % & -0- 0 ""0 " $ ! " " # &

-, , ,.," -" (0(% -0 ' " ( $ # &"(

, / & ( " ( ! 0&- % " -0,0 (-0- - ( !

" " ,(- -& ! " , . ! ( % , & ! ( ! " - "

, / ( ! ( - % " -0, ! ( - $ -0- (0& " +&--0, - 0 ! -. %

-0--" ,(0 drdes = n

m 2πkB T

3/2 mv 2 · exp − v 3 cos ϑ dv . 2kB T

2

∼ cos8 ϑ

2

cosn ϑ

n 2

! "# ! " !

! ! 2

∼ cos8 ϑ

cos ϑ

&&&

!

!

!

" 2

11 53 3 5 0 & -.,0 / " ( - "( " ' ( $0(-.$ , ! (&"(0 #

, ! , # & ! & " " " / ,

"

(% / / 00 , ' ( ( , ( , 0 ! $ ( . ( ' ' ( $ % "

0-"$#0(,"/. / ' - ( 0 ' " 6 , , $ , ( -. ( " # & $

, - ! 0 " % !0 0 -0 - , $( ,- ! $ ( $ , ( ! . " '0& ,-, " % (

(% 0! # 0(-.&- " " !' ,0-. (#

& !

(,!,% (" 0- & (( % " $ $ "( $ . ( " ( $ % # & (

/ ,0 ( % " % 0 % (-&/"$ %!-'"($

• •

Ts

n

kn

Edes

ln kn

ΘAg

1/Ts

√ √ 3× 3

&

!

&! &!

!! ! # ! " & ! !

! " & ! " # ! ◦

◦

◦

!

& !

& "# ! !

&&& √3×√3 × ×

× √3×√3 ×

√ √ × 3× 3

& / , , ! ( " , % " " . / ( " ( ( " - % # & (

, ( -. , & % % 6

'0 , % " (("($ "/, "(-,"! " $ "( % # & ( * *

/ $ . 0-& ( " 0, " ,0 &&, ! ' " ( $ " % # / / , . " " 1 # & (

, -0 - ( $ , ! # &

, , ,0 $ " % % % " ! -, ' 0 # &

0&$ / 0 -0 - ! % * *

0 0 ' " $ $ " % " # " " #

, 3 5 3 % " 0#-" , % #0(% - 0- &- 0 , ' ! " , 0- - , ( & ! " ' " " 0'"(0 &0 " "

"",.,0./'&('-.% -00 ("0! #

& #

& ( -

.($,'" )" )('% & ) -.- . ! ) " , " - ! ' % # !-"/,,$,(-0!"$ -. . - . ! ! " - " " & # (, (',-. ' " # & ! &

" / " , , (

" # & "!(-.,0"(% " &, 0 , ( '

&-! ) -. .- ! ! - ( ( ' -. % " # - -. ' ! ( % ! ,0 , , "

%

(

!

& ) ! & "!!# ! #"&#)&"

! # &## & / 0,06-0 ! ""0"-. 0 % 0 0 ,086

V dΘ = −A dt kB T A

dp S + p , dt V

V

p

S

•

•

dp/dt ∝ dΘ/dt

p ∝ dΘ/dt)

&

-. 0 ( ( " " - % # 86 (0 #

& # . 0 !" (" " ( & ) ) " &

) $, #

&#

&-0 #

&

, "(#

&" -0 / $0 ,-. ((.

,6,$(0% --. . ' -. ! - ( , ! " 0 .' 0- ' 6 ! $ ( $ -0 0 ! " " 0 ( ' % " -.& . ! - , , 0 ( " $ ' , " ' ( % " -. / " -. & ( ( " ,0-. " # "% / "( ( ( - $ , ! 0 ( , 0 & -0 0

! ( ( % # -.& - '-""-0(!" ! ( " " & - " ( ( " ( ( , ! " # &

0-(% -,-. ,"( " $ ,0 #

& "#

&-"

" " (,

* (-"

0 / 0 , , % - 0 ." ' ! , $ ( 86 ." !,0-.,((-,"-! ( $86"0'"!-.&("% '/("'#! ( , "

, -. ( $ ( " 86 + && ! $ 0-& ( ( " , " / -.-0

$!-"$("% # & ! -. "

%$

( ! " $ ! % / $(

( ,0/( (0$ (0( "0 T (t) = T0 + βt , t

β

dΘ kn0 Θn p∝− = exp(−Edes /kB T ) . dt β p(T )

p(T )

Tm

Tm

Edes

ν1

Edes

Edes = kB Tm

ν1 Tm ln − 3, 64 β

Tm

.

ν1 = 1013

Edes

ν1

•

n = 0

Tm

Tm

−1

β =

&&&

! ! & &

&! Edes

Tm

T (t) =

T0 + βt ν1 = 1013

−1

-$(0(0-!!-.&(" " (!! # & ($0/ 0(0( ", / ! 0 (0- ! (!!# &((!% " 0!( !,0$/(0 0 ((0- "0 - # &

-. ( ( " ( - % 86

-. / ! ( % 6 % #

, " ( - ( ( - - &

& ( ( %"("-"" # & (,(0-

8

( 0 , ( ( 0 (% " # &

- , - , 0 & " " ( , ( " " (0 &-"" (-, $ (&-" (-"&-"0, (-"(&-" 00-& ( " " 0 & ( ( " ( " - ! , ( ( " % " % "

-"( -,$ -$("$ Θ0

•

n = 1

Tm

Θ0

•

n = 2 Tm Θ0

∼

∼

Edes

ν1

& n=0

n = 1

n = 2

& !

& ! & &

# ! & ! &# & " Θ0

Θ

β =

Θ0

&&&

! ! & ! !

!

& ! ! "

& 0-"$, ! " , 0- #&, .'' #

-& # & # & # & # & $ *

, 0 , " ! " ,(-0!. #

& & #

& !$(0. ' ' " " # &

, - " ( ( - $( ( , "$ $ % ,. , , 0. " , 0 -&, ( ( ( " ! & 0 ( . ( -.

% " " #(-0!"&0/" 0 ,0&0& ' - " , ' " " #

*& rads = rdes .

p=

1 f ∗ (Θ) , K f (Θ)

K=

σ exp(Eads /kB T ) √ , σ∗ 2πmkB T

√ kads ∝ 1/ 2πmkB T

kads /kdes

f ∗ (Θ)

f (Θ) = 1

f ∗ (Θ) = Θ

Θ(p) = Kp ,

f (Θ)

kdes ∝ exp(−Eads /kB T )

&

,

( / (&"$( ('-.- &, ( -" . - ( , $ - "$ $( "$ 0 / & " ' & ( ( " #

&

,-0 ,0-. ( ! " %!&" ' ( -0/ & #

& / , / ,

0& " ,- ! $ ! ( -% # -. , , . ! , ! % " " - -. ,. " , ( , 0 -, 0 ( ! 6 -. , 0 -. 0 ,- ! $ ! % - -. & ' . ( ! ' $ " 6 - - . 0 "( , $ - "$ " 6 0 / ., & , . ( ( - "$ % " (, f (Θ) = 1 − Θ

Θ(p) =

f ∗ (Θ) = Θ

Kp . 1 + Kp

K K

Θ(p) K

K

Eads Θ→1 Θ → Kp

& " ! K

5

5 - 0 " 0 " & % /-0 , ( " . , 0 % $ , &&, ! ' ' " 0 % ( ", , 0 ! ' ( " " # &

) ,%

$$) % ) #

& ,0 , & $ ( , 0 - , % "$!'" )-."-.

1 p(Θ) = K a

Θ 1−Θ

exp

Θ 1−Θ

−

2aΘ kB T b b

,

&&&

, - ($ "! ' ! ( % " # " # &

/ 0 / -. & , $0 ( % , 0 /! ' -. $! - ! - ! " 6 ,0&0--.&, (- ", " -. -- 0 ! " % "

0 0 , ( # # " 0 0 $ ( $ , $( "$ , ( % 60 / 0 / , & , ! ( !"(,-"!% / 0, , , / 0 & ! -.. ( " 0 ( $ ( " &&,0 , 0 . " !.- ! , % 0"#( "

! "0 0 " " , 0 -- - " / 0 / ,0 ,,0& ./(- ""( " ( -0 0 & , ( " -.0 " &0 % " , "," " $ " 0 & %

,, / ( -. & - $( "$( 00-.0 " % 6 , 0 " ( $ ! ! 6 , , -.&,- " , 00 0&,"!"-0'

Eads = 200

2a/b = 60

Θ−p

$ "

! "#" &" " " "" ! Eads = 200

2a/b = 60

&

!&('&,#-.$-0% 5 5 -0'(-(" %

- -&, - & - " 0- ( ( ( "( " ( % " $- &- " ' " -0 ! &- ' % # & 0 -- ( 00 " 8 8 #0)/

& " #)&"-,0-% " #-. 8& #

& & $),0 - ( ," , , ( -(- -0(/ ($-& -"$" !-(&/% #/0&/'# " ,,0& 0

- 0 ," ! -. " ,- ! $ -! (--/

Θ(p) = p0

KBET p p0 , (p − p0 )[p0 + KBET (p − p0 )]

KBET

KBET

!

! & !

- 0 & $( ( , " ! " ' " ! # " & -0 "-,$- ( , . ! &- " " " (0% ! . " & , ! "

&-"".-,."$"($. , &- " ' "! ( ( % #--. 0 -/ 0 / 0 -. ,0-. , ( % " # &

" ' & 6- (% (-&"!0&"'""-"-/ KBET

&&&

-. -- ( $ , 0 , 0- ! % " (", 8

!

& !

0 0 0 ' $" - $ ( %& " ( -"/ 0/-.!-,,$-0/ 0- %' 0- " ' " " ' " 0 -"'" (2 52 8(!,% 5 -.,0 , 0 !"0!& ( $ - , ( , " % " # & -0- "0 " ( " 0- ( - % " ! 0 - 0 &- ! ( . " " 0 0 , " -& $ $0 " # " # # &

, ! 0&(0-. 0#-",. ''/ -.-0 % 600" (!""( , % ,., 0 $! ' , $ % " - 0 ! ' " "/ "( ' , 0 0 , % " $ , , 0 $ $ 0- % % - / , ' ( , $ , $ % 6 # & + , $, " $

) ) ) ) % " # &

) -. )

• • • •

∼

∼

& ) ) -

, -.-

- " $! ( ! ! ($ '! # ( / "&% ! ' " , "" " # & # & , -, 0 , " $ "" " ! -. ,- 0 & " ( $ # & , , ' 0 , " ! ' " - % # & , 0- " , ' " 0 , $! ' , // / , ! ( $ , $ 0 ( % "

- / -. $ -. 1 " ( 6 "% , & 0 & - " $ ( , - ! ' " , ( $ ( % " $ -.- " $ ! ' , " #--0% . " -, 0 , & & 0 & - ! $ "

"(,"0, "

-"

&" "#&! "# ! &! & &

$ $ " $$

/ ( 0 ( $ ! 0 % # , ". -,. " 0 , ! ' & / / ! 0 " .0. " , 0 , " , , , $ -, ' ( # #,0-."!', "0&!0/ ,- / & 0 & 0 " " , ! ! " " # , , , (& " & -, 0 , % " # & &

" " -!"0&"%

&&&

! ! ' 0 -., 0 , " &

0 & " ! 0, " " & " 0

$ # " 0 ) % % / - 0,- , $ -- ( 0

!

0 , / ' $ ( - 0(" -0!" ,0 - "0-&0 ( ',0-. !("0 " &-0 -- --- 0 --0 % # , -, $0 ( , -.,0-. % , -

'

( '

"

( " ( " " " 0$-, - 0 0 ( ( 0 " , % , 0 - ( $0 " -. % % - 0 , ( ' " % 6 0 - -- , ( , -., ", " "(0"-&0"($

2

+

" "# ! & $ "# !

!& !

!

2

3p

0&- ( - ( -. $! ' &0 " $('% ,&/",

%$ &

/ !"'"", 0 "( -,-.-. ( - % . , ,0-., 0 , " " -.,0 0 -. ( " ( , %( $ % " ! ! & " & $6

'$

%$

" #& $ -., ( " " ,0 ! " % # & (

' ( $ ( % !

/ , / 0 - "( ! ( , ( % " , / - ' ( , " ! % " $ - , " 0 , & % 6 $ " " ( " "/ "! % , 0 / 0 0-. & ( " % " ( $ , ' 0 $ $ ( $,0 0 & , , , ! -. $ " % % " /$0&- -./($

×

◦

±

◦

$ &

& $

"# & $ $

"# " 2

5 , -, 0 , , . % / 0 & 0 ( ' ' ' % 0 - ( 0- ' ! % . , ' " ! ! "0 % " 6 (-.,&(0! ,,,,.%

&&&

, ,-. / & , ' ! , ! ' " / 0 / / ! 0 ! ' 5 &!#("% 0& 0#& (-,'(/ / 0 /0 & / , ! ( $ " $ % " & / '

( ( ' ! ( ! ,

,- $

! ( $ " 5 " 5 $0-!(-"(" +&0,,.'/-0-($% # -.,0 / -0 ( ' ( " "( ! " , , 8 # & (#- ( ," $ % / 0 / &0-.& $,-(0- "'- & ( .

( '(-("-" ! -&, -. 0 !

( - ' 0 % 8 # & *

"(0 $ -. . / ( ! " % *

&'000(% 8"" *- 1 0$ &, $ 0 " ' ( $ % -- , ! , ' ( 0 " & " ' " ' , $ ' & ( %

0 0 0& " " % " # " # " . , 0 $ ' ( 0 " %

0 0 " ' ( , % " # - ' " " 8 " - ' ( , ! 6 " " !#$ -/""'( ", , (

#

&-"( (*% 0&/'' +

8

2

−7

p = 10−4

10

= 10

15

−2

◦

13

T = 400 n0 =

◦

( (

• • • • •

- # ) / ( $ ' " '"$ '"& * ) ) *- ) -) ) ) % -)* %

+ + + ' + *

" '' ,&, . " , " -0-&, " "

+ " " " + ( + ( (+

+ +

+ +(+ *

( + +

(+

( + +

+ ( (+ {

}

0 $ " 0, " , $! ' ) 60 " -0- - $/ - ( ( $ ( , 0 % " # &0 . -0 - 0 ! ' ( - , ( , & # ! -0 & 0 -0 ! " % - . ! 0 , ! (

!"(%&,#-.,%,-0 ! "! ' ! ' , -0 ! & -0 , " ( 0& ' % # # & - -0 & & ' ! $ ! ( ' - -0 -. & ! -0 , ! - ! '( $ 0 % / - 0 0, 0 , ( - ( ( , % " ! &0 ( ' 0,- "/ & " / , , 0 00 ! ' , % " ($$ ,"(0 -

1

-. ( - , -- ! % # &

( $ ( $ . ( % # - " ( ! ' $( , % " #

0 / - 0 & - ( , " 0 ( , &

, -& " ! 0 , " % " - &0,(.,& ' & ( , " 0& % ( ( $ , . ( - ( -0!, $( ' " & ! % " " #

& # . & - ( " , 0 ' ) & " )!!

t

h∆r2 i = νa2 t , a

ν

&

! "# $ &!

! $

$ $ ! & !

$ && ! & ! & z

x

z

Ediff

& ! - ! " ! ) " 0--.. -. & / ,!"0" ! - ( % / !& % ! , " ,'"

!% #

& - &!) !- $( , 0 , ( ! . " ! " 0,#(, " &" & " - , ( ! .- - ( ( % " & -,- " $0, "( -"($0,&&-. ,& - ' & ( , " 0& 6 . 0 0 ( - "( ' -.& . ' % " - - ( ' ! ( ' -. " # & 0 0. . "( " -""! ( ( ( -. " ! ( " " , .(- Edes

h∆r2 i

νt

t

h∆r2 i

D=

t

D

h∆r2 i νa2 = , zt z

z

z =2

z=4 z=6

ν0

Ediff

#

& & ("" -. '"0&"" ('0 ) ) 0, 0 & , ( ' -. ' % # & #

- - - " ( , ( $ ! ( % & # . 0 & " ) & ' ! , & ' 0 -0 "$ $! ! % # ! , $ ( "/ ! %! & 0, - . ! ( % " " //"(! ' ( "$0 &, ( , " , % 8 # & !

" %

! -0 / ! - ." -. $ , ' $ " " . 0 11 -. (0& ' ' -0 ! -0 , " % #& ! - ( " $ 0 0 0, 0 % / . ,, ( - - ' ' & / 0,& ( ' ( " 0 " , "

&- ! 0, % " 0 ( ( ( ' -&0 ' ' % 0 ' ( ( ' -. ' 0 0, "" " 0, & ' ' " , " " -.

, -.& ( -& ( - " ( , ( % " " #

-& # &

-. , ' , 0, ! ( % " - / (-0 ( ( , 0 &0 ' ' " (" ('%

/ 0 / 0 ' & 0, ( ' ' " " " " -"&-0!",(" # & - --. , ' ' % " " # &

", "

ν = ν0 exp(−Ediff /kB T ) , kB

Ediff ∼

T

Edes

Edes

Ediff kB T

Ediff

kB T

Ediff

Ediff

J

x

J = −D

∂c . ∂x

∂ ∂c = ∂t ∂x D

x

∂c D ∂x

.

∇c D

&

#

&

, 0 0 0 ( ' " , " ) # # $ -&0 " ( , $ , ( ' 0, . ( ! - ! - % " " "((( / / - $ 0 -. ( $ ! " ! - " # & / & $ , ( --. " % " " " # & 0 '0 ' " -, " " 0 - ! " - ! 0 !, (-!"0"# &-" -. ! $ ! $ & ! $ 0- ( , % & "!",/"( ./ % " # *& !$ $# "% "& #

&

!

5

35

- -. ( - ' ' 00 ( " '"&'(,"(("-! %" '. # &

-" # & 0" ", # & # & !

,& ( , " "! $ ! , - , ,- ! $ ! ! ! " # " %

0,"!$ """-""$-!-"&$,! ! 0 -0-0 ( ( " ' " ! ( $ % - 0 - 0,, ( "( " % " ! /( 0 0 -0 $ ( ( ( % , - $ $ , ( ! . $ % & - ' ' ' ( ( ( % "0 ∂c ∂2c =D 2 . ∂t ∂x

2 erf(z) = √ π

Zz

2

e−ξ dξ

0

erfc(z) = 1 − erf(z) .

c0

c(0, t) = c0 , c(x, 0) = 0

c(x, t) = c0 erfc

x>0,

x √ 2 Dt

√ 2 Dt

.

√ 2 Dt

& ! & & &

(- 5 3 -!-. "-" #

& #

&

(, -0 / / ( $ 0 0, -0 ! % " , -. - & (!- , ' ! ( 0 ( - $ -0 , ! . ( ! $( ( % " ."!(",.!(- & 0,

-

5 ! 35 ( -"(-0" " -" # & " # -& # -& √ c0 2 Dt

c(x, 0) = c0 c(x, 0) = 0

x < 0, x≥2,

c0 c(x, t) = erfr 2

x √ 2 Dt

,

√

h∼ =

√

Dt

c(x, 0) = c0 c(x, 0) = 0

c0 c(x, t) = 2

| x |< h | x |≥ h

h−x h+x √ √ erp + erf 2 Dt 2 Dt

Dt

&

!

&

& " & &" √ c0 2 Dt

c = c0 /2

x=0

t>0

& ! &"

& & "

√ c0 2 Dt/h

0,/-0!"&,% -. 0 " ' " ( ,,-.(-! -.0 - ! " ! - ( "( , . ( &- ( % " ,!0 - ! ( " ( --.& " 0," . , & , ' ( - & -0 , ' , ! . ! - ( % 6!00-

√

Dt

00/ $!'% , ( " ( #-"/ !%""!!' $# (,0#, 0 &#/!&., ( % # ! , -., % % ( " $ $ ! % " & , 0!' 5 4 #-.-0!0' 0,-.&",/ !

( # + 1&( -1 ( ( $ ! ( 0.-/ / " '0,",# &-"% 0 "! ' "$ ( - , $( ( " /, 0&0& !-0!'"!. &0- ( -" # &

$( ! ( " , % " % / -. & -0

$!#' "!"-- & ! ! ' - ! & ! - ! ' $ % " # .-& , . ! " " ! & ( - " # &

0 ((!-&-. , 0.

"( " '-" # & & )!-! '

" %!' ) "

5 5 -" -$("&,% 00/ !'"0 % , 0 # &

, -0, - ( ( .

" #

& 00/ $!'" ,% & $ ! ( ' - ) # & / -., ' "

# &

, , ( ,. # #

*& !% "," (" ! +' "--. '"

" ,(,. "!-" • •

D

N

1 X D= h∆ri2 i , zN t i=1 N

J = −L

∆ri2

i

∂µ , ∂x

µ L

J = −L Θ

∂µ ∂Θ ∂Θ = −Dc (Θ) ∂Θ ∂x ∂x

Dc x

&

# & ! / ,

' - # & $ ,6"(- $("$ #0, " & ) " & $# &! ('-",#

& ",/ -0 0 , ( ! , ( ! ! - 6 " # & ,. " , ! ( % " &0- . ( " ! , -. " ., ,- !#, ! ,, " "00/!'"0 ' 0,-.% 0 & / , ( " 0 " 0 ( % " "!($ , ν(Θ)a2 Θ Dc (Θ) = 4kB T

∂µ ∂Θ

T

8 = ν(Θ)a4 4

∂(µ/kB T ) ∂(ln Θ)

.

T

∂(µ/kB T )/∂(ln Θ)

Θ1 µ = µ0 + kB T ln Θ

µ

ν(Θ)

µ

µ0

Θ Dc

0,"" ( $ & ( #, " -"/ 0,/# + &#.0,/ 0 0/!-0 00/ $!'& 0,/(# &#.0% , / "'"&0 -"&'",$00/ $!% % 5 5 #-0'&

"! ( , ( ( $ ( ' % # & ! - . 0 - ' ( % 00,0 ,!, -., 0 " ' " !-"(- , ! ' ( - $ % ( 0- ! -0 " -. " # - - & ! ! 0 0, - ! % * &

0 ( " ( - $ -0 - ! # / --. -0 00 ! - ( , $! ' " " 0 0 / 0, ( ' " " 0 & 6 " / / 0, ( "/ 0

0/0'"&!- 00/ $!'"("(,(%

0 -. 0- / 0 ( " " " 8 0, 0,-.&(!

• •

-0 / ! ! , 0 - 0

% " &,- ! " 53 -.($#,$ & "! , -- 0,(,- ( $ % ! 0 ( ,- - % " " " " - ( "/ % & ,- 0 & , $0 " " ! " " ( - " -0,"(""""(/ "0'% 0 " , 0 0, 00-".,$-&'"(,$!'0$ ! $(" 0 -0 !- && " %

! # , 0 0 . , $! ' ( 0

, , ! . ( , 0, ( % 0' -. , 0 ' 0, ( " 0, % #

& -. ! - ( , $! ' $ & ) ) % " -. -"! -0, 0($'% 0 -. ', (- , ! 0,"(% 0 - ( ( , ! 6 " 0

-"",!&'-" '',(. #

& 0, &", " &8 ) # & # & # & # &

, ( % " " " -0! #

& 0,% ., . ' " " /! .. (" " & ' " , % - "( , $! ' -0 ! 0, " " (0 ( " " , - ( % # &

-0 .0 / " , ( % "

0& " 0, ,!($0/'% -0 & ! # / - ' $! 0 , $ % !'(," "--." DM

DI

DM =

n DI , n0

n

n0

n0

n/n0 1

∆GA nA = n0 exp − kB T ∆GA

DM

,

ν0 a2 ∆GA + Ediff = exp − . z kB T

n0

n = n0

D M = DI

&

&0. " ( , ( , % / ,0 0 $-0 - ( ( $ 0 ! "-" 0,!-.-#!."

!,-"/(,(0, # , #

+

&& ' " ( " ,("((-" -& 5 3 5 6$,-!$-% !$'/,- / / 000 ! 0 0 " --. ( "/ "( $ 0,,- ! % " -. . 0 ( ' -. ' 0, . ' ( $ ( " "

"

! , / ! ( ' ( ( %

&- " (

./(- ( 0,(",-!$&"$ -- # &

- ' , . ( % " 0,- 0 ( ! ' 0," ,- ! $ & ,&.-.$("-! n/n0

DM

DI

• •

2

D0

Ediff

2 · 10−4

0, 16 ± 0, 02

−1

0, 60 ± 0, 03

−3

2 · 10 3 · 10

−2

1 · 10

−3

0, 54 ± 0, 05 0, 64 ± 0, 04

3 53 3 5 / , ( 0, % # .& 0 ( $ ' 0,, & " / (! %- " ( $ ,

$

0 / 0 ( ! ( " , ( ((-"($ "0,

1 · 10

0, 88 ± 0, 07

&

! ! "

$

$ ! & [

[

]

]

N

!",("#",,(% --& & 00 ( $ # , ,, 00 0(-& ! " ( " " ( ($& - ! $$( % # " ( $ " 0, " , ( ( ( - " $"$ (., &&-. , , % " /( 0&-. ( ( - " -0 ! ( " % - -.&, ( $ . , - & % " " -. $ ( - 0, " - -.- ! ! ( ( $ ( " % " -. 0 0&-. ' 0, -. '0, -. " -. 0 " '0,(,-.(-"(% 0 & -"-!(-"&0&- " 0 #

& 0'""("(-"$$-"-.%

, $,! " ( " # & *

-0 0, " ( $ ( % ,( 0,((-",%,--& ! l

• •

Dx

x

Dy

ϕ

D(ϕ) = Dx cos2 ϕ + Dy sin2 ϕ . Dx /Dy

y

&

! & !

"# " $ & ! Dx

Dy

0,"&, , - ( ( $ ( , & -. " ( -0 ( $ ( - ! ( % " *

!0 (,- $" ( - , . 0$0$(-"$ %" '0, 0 ' 0&- , . 0 " ( " - ! " " 0,$(",# & [1¯11]

[100]

&

& ! !

D ∼ = 110

T ∼ = ϕ [1¯ 10]

- / " ' " & 0 ( "/ , ( " 0,((-"#. $( ( $ & 0,%

%( ( - " # & *

0(!($ +

, . ! " 0," -.0( .,,% '0,(-"$,$( 0 - !0( "

! & !

!

D

T = 1170

0," -.0 / ( " ! ( $ " " ! ,(., ,- , , ! ! $ $ $ $$,(-,

1 0,

, 0 $ & " " " " ,&& ! ( % # & - / ',& ( , " 0& , ' $ % " , , "0 ( ,, , $ $ % " ""! ( -. ( 0,& % 0, & ! - $ -. $ $ ! ( #

/ -. ( -( , " 0, " % # & *

, 0 $- ( $ ( # # & +

" -. &0 ! ( $ % 8 0 , ( ( $ , ( ., ( " - % !

,/ 0 & ,+,-. 00 ( 1, " # + 0 , ! %,8,&,, % 8 / - ( , " 0&-0 - "$ , 0 ! . " # &

( $ - , " , + -. $ -. -0- ! . % 8 " " / 0 (-. ( ! " " 0 ( ( ' % ,-0## "&& 0, . . , -0 ! , " " ( , 0, % % " " " -.("" 0,(,."(&,&-"

Ediff = 0, 92 ± 0, 04

ν0 = 4, 3 × 1012

−1

&

$

$ ! ×

2

*

, / , !, ! ( ! 0, " % 8( " # &

0 " , 0 0& ,0-. ) -& 0 , ( 0 " -.& 0 % - ( , 0- ! " % " # &

0,&( Ediff = 0, 92 ± 0, 04

ν0 = 4, 3 × 1012

−1

& & !

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×

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c ×

c ×

h100i

]

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$ " & & ! " $ ! " " # # #" ! h100i

c ×

0 & / , , ( , # (-0 c ×

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D = a2 ν/4

ν

" &/% 0 ( $ 6 0 & . ! ! ( -. 0, ( - % " " , - ! "( , " 0, " " ( " % " 0 . / 0 # 0 0 , ( $ , & ' " " "( $ 0 6&0- . / , " ( ! " " (0 1+ 0, -& &'"!& ( & ( $ &- " #.-0 -. ( "/ $( ! % & 0 $, " ! ( " " , & ' % 0& - ( (

%

% " #% -0 / $ ! "$ , , . ( (

-0 "/"(""0," ,, ( !-" (%% ×

2

a = 2, 55

ν = 1012,9±0,3

−1

E

diff

= 0, 197 ± 0, 04

&

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F = F d + F w = e(Zd + Zw )E = eZE ,

Z = Zd + Zw

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( "( ( '"-.,-. 0&/' % x η=√ , t

d η dΘ(η) − = 2 dη dη

dΘ D(Θ) dη

,

Θ

0 ZΘ 1 dx D(Θ0 ) = − x dΘ , 2 dΘ Θ=Θ0

0

Θ0

x=0

ZΘ0 x dΘ = 0 , 0

D(Θ)

D0 (Θ)

Ea (Θ)

&

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0,/ √ x/ t

µ

K

µ(K) = µ(0) + γΩK , γ

Ω

K

µ

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/ ' 0 0. ( ! % " %% . " & ( ( ' -.0

0 (,-0 0. ( " % % 6 # & # &

, . " " " "&0&- ",(" # & A(t) = A(0) exp(−Bq 4 t) , γDn0 Ω 2 2π , q= , B= kB T λ A

D

λ

t

n 0

ϕ

q

I(ϕ)

2

A (q)

ϕ

I(ϕ, t) = I(ϕ, 0) exp(−2Bq 4 t) .

! ! $

$

! $ &

I(ϕ, t)

-. , ( " -. $ 0&- % & *

"("( , , $ % " (0,"

I(ϕ, t)

#& ! &)#0 (

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, "(- , ( " ( -.

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+ 0#

[

2

]

×exp

◦

B

N∼

RΘ ν

R

χ

i=1

N

,

ν

Θ χ = i/(i + 2) = 1/3

= 0, 45 ± 0, 04

D0 = 7, 2 × 10

−4

2 −1

Ediff =

&

$ "

$

&

& &

#" 2

×

= 1, 214 × 1015

2

# & (

1 (- -0!&0(($ %

, ! " + " 0 ( (0 # # &

11 %. , ! ( ( $ " %

0 ( ( ' % 0 & / ' 0, ! - ' ( " " -, 0 " ! , ' -- ( " ) " * "* 6(-," !!- 1 6. -/(- / " $ - ! " ( " ( ( $ . ' ' " -

+ + 0 ( ( ' % / & ' ( $ 0, ! " !,!& "

◦

−3

−1

0

ν0 = 4, 3 × 10

10

D

= 10 3 · 10−2

−3

2 −1

−1

√

√ 3× 3

Ediff = 0, 33

12 −1

−2

◦

12

−2

i=1

◦

(

• • • •

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(-"&% " $( 0, ! - $ $ $ ( + +" ' & (

+ + ( ( + " - ) ) ( " ) '''

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0- # & (- γ

γ

ϕ

γS = γS/F + γF cos ϕ , γS

γF

γS/F

ϕ=0

γS ≥ γS/F + γF

(

).

--. 0 / &

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& - / & - - "( & ( ! ( " " 0- % % % # &

- "( & ( , 0 ! & " - - & - " , " ! ,0-. ! ( " " " # &

0- -"(-0/ && ϕ > 0

γS < γS/F + γF

(

).

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γS/F

$

$! & $ "#!

γS

γF

γS/F

+ , 0 -. $ , ( -. ( - % " - "8,( 0 " , &- ( - ( , $ ( - % %

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1 5 5 0 ( ' ( $ " ( "

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n 0

n1

R

Eads

D = (ν/4n0 ) exp(−Ediff /kB T )

τads

= ν exp(E /k

−1

ads

BT )

" "# &!

%

"-. - ( 0- .& &0 .-!($ ( ' ' ! $ 0 "(#!(" ,(" (-&"/ ) / (, ' ' -. $ " ,!& nj

j
i

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0/0!$0 j

j

nj

•

nj

j j −1 σj−1 Dnj−1 n1 j+1 j

j +1

δj+1 nj+1 nj

•

j

j+1

σj Dnj n1

j

j −1

δj nj

n1

σ

∆Ejj+1

j

n1

D

δj+1 ∼ exp(−∆Ejj+1 /kB T ) j+1

j>i

nx

##

-&& #

& # &

( , ' ' . , 0 0 ! 0- ! ! ( % # , / -"/ ! ('. - $( % , $ $ ! , " 0 ( ! $ - ( % # / ( , , -. , ! " & 0 / , , $( ' , -0 $ " ( / ! , ( , - -. -, ! -( ., $ % 6 -. ! " # &

/ ( ' ' -. $ % / , - ( ! ( - # &

0 - , ( , ' ' -. $ , ( " % % &, ! ! ( - #("" -'%% 0 $ 0 ( ' ,&, , '- -&((" &- (( &0 $ " ( ' ( . " " " -0 / 0! $! - # & # & $

/ &0 ' ' ) % / 0 ' ! ( #

-0 #.& ! - $ ! " ! " (-,0-. & 0 , " " " -. - " 0 ! , $ ( & , ( ! . ( " / ( , . , . ! % " # & # & ( ' ' , -.!, # - , , , "( $( "$ ! 0 % &

,0 !"$(#! 0 &" , ( # & , && ' ! 0 # ,-''(-"' ! 0 & i

i

j=3

j=2

X X dn1 n1 2 = R− + 2δ2 n2 + δj nj − 2σ1 Dn1 − n1 σj Dnj − dt τads −n1 σx Dnx

dnj = n1 σj−1 Dnj−1 − δj nj + δj+1 nj+1 − n1 σj Dnj dt dnx = n1 σi Dni . dt n1

n1 n1 /τads

R

2δ2 n2

2σ1 Dn21

σj

i

i

j

nx

i=1

n1

• • • •

nx

L

I

A

C

%

& & & ! !

& && & i=1

n1 D/R = 108

nx

L

! & ! -. !

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! ' % ',", & ' ' " . " " &-. ( " . ( % 0 0 " ,

0/ 00#0,% ! 0- , " ' ' " % " " #$ , " ' ' % 0 0& " " -0. " % 6 - , ( . " 0 , " " -0 "0! 0 !

'

' % % & , ' ' " 0 % # # & !0 . . 0 " ( ' ' " " 0- . / (&, ! . " 0 , " #("! 0- ' " ! " &' " , 0 " - & ' -. , ( " /! -.0, ' ' " " " &

- ! 0

' %

! / ("- (%""- ' "( ( , 0 " $ "

" $!" % I

A

C

n1 ∝ Θ

nx ∝ Θ 3

n1 ∝ Θ−1/3

nx ∝ Θ1/3

# & - / -0 / . "/ " ' 0 ( ! 0 % " /$'"' '., ' "(-!&! " &- " # ! " -0 & ! $

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! "

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n0

nx = η(Θ, i) n0

χ = i/(i+ 2)

R Dn20

χ

exp

Ei (i + 2)kB T

,

i

Ei

η(Θ, i)

−2

η(Θ, i)

nx = η(Θ, i) n0

i=1 ±

4R ν0 n0

Θ i=1

i/(i+2)

exp

iEdiff + Ei (i + 2)kB T

η ' 0, 2

.

±

i=3

Ediff

%

"# ! # & &

% #"# & ! & !

! ! ! !

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−3

χ = i/(i + 2)

0% " , 0- ! ,& / '0'0 # 0*! "! ' 8 ' % # " # " &" ,0/0'-/"0" -((-'-,""! i

Eb

Ediff = 0, 351 ± 0, 017

ν0

Eb = 0, 46 ± 0, 19

11 , 0- &0 .,- / ! 0 # . / 0 ( $ , # ,-.$-

E3 ∼ = 2Eb

ν0 = 4 × 1011±0,3

i=1

5 × 1012±2

i=3

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0, 87 ± 0, 02

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sNs .

s≥1

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sNs

s>i

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=

Θ−

P

s≤i

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SNs

.

s>i

hsi =

i=1

Θ − N1 Θ ' , N N

N1

N

Ns = Θhsi−2 fi (s/hsi) , fi (s/hsi)

i

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Ns (s/hsi)

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◦

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×

2

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" 0 ,&-0 ( % # $"00$$

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◦

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2

( , 6 1- (-"" ( ' & ' " / , % " "

' ' " ! ( # " / 0 - -"( ' ' ' 0 $ ($ #

&"-/( ./%8+

" "# ! &&

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+

0 , ) " .- ($" $(0- "$ ! ! % " & , ! ! " " ! " " &0-.- , 0( " . $ " 0 / 0, $( ' ( "/ % " -. # 0,"((- " " . % $

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0 '$"! ,0 & - "$ ( ' , & ( # (/ '-. -. ( $ " -,0 ( &

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• •

Ediff

EES

&!

$ $

! EES

# & ) & -" ", $

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'

! # -&

# 0 ( " . ( ! " ( % - 0 -. 0, ( ( ( , ! ( ( % " , 0 ' -. , -" 0, ( ( ( &

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, , , , $ $ ( $ " , / $ -0

# 0 % & , ! , " ( (- &-

EES s = exp − kB T

,

s'0

s'1

• • •

$ $ $! " -

# & ! " /

'

! %

" (0-"$" -,$#0-0!(

&&, - 0 ( , . " " ,0-.&/0(,

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-

( $

$ % # & &

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" , " 0," (," -",-,0(-&% -(-""0- # & 0 , ($0, ! , " ( " "(-""0- # & s=1

s'0

s·λ = 1 ⇔ R =

2(i+2)/i λ0 exp

Ei /i + Ediff + EES · 2(i + 2)/i − , kB T

L 2(i+2)/i λ E /i + E 0 i diff λ∼ exp − , =L⇔R= L kB T

!

. & " , 0 ) ) " # &

& (# - " , ! , "$ ) " # &

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&-% " "00 - - !$ - ( - ( , ,- ! ! " # & 0 &,- ! "

) " ( " " -. " ,. ( " $ % -.,"%

λ = N −1/2 i

R

k

h001i

h001i k h011i

h011i

ε = (b − a)/a

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! $ $ $ &

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ab . |b − a|

Eε

ED

εc

hc

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hc

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&"(-.,0$8 " 0,"-(&

◦

ESP E V = V0 exp − kB T

,

ESP E

!

! & !

,,. , & " " ! ( " ! , ! % " 0 ( --& " ( ) ! / , $

$ # $

(

$

$ -&0

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5 53 5 $(- ( $ ! $ ' ( $ % ! ! ( "/

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$$ (

# " # & - "$% "' " 4

[

[

2

5 3

∼

]

4

]

3 3

[

2

3

5 3

]

3

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, / (! ! ( ( " # " " -- . ( - ! , # & . - "( 0 ! ( ! , $ " 0 - ! &-., " # . -0 ( 0 ( -" ( ! ,- , " &

3

% !

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3 3

]

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+ / / ( - ( . $ ! 6 0(, -- !- -0 ! -. , ! 0 % 0 - $ ( ( ! % " &00& ( $ ! ( - --. 0 ( ( 0 $ ! -0 ! ( " % ,0. -.,. - - -"( ",", ( ( & " " - , , 0, $"! ! , ! ,& % # . 0 - "( , ( ! $ ( $ ( " & ) * &- - ! , ! "( "" " " "

# & (, 0 0,-0$ ( $ ( ! "

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√ 3× 3

◦

×

×

A

B

◦

$ ! & ! " " !!

"! "

! " & $

" ◦

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∼

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0 & ( # & 00( ( #

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0 -., ' ( 6 % - - , $ $ ( ( , !($(-(#0& ( "( - % (

/ 0 , "$ ( " ! "( $ " % ( % ◦

×

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∼

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$ $

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∆EES

Ediff

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. ( , ( "

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($ A

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A

i=1

i = 1

i = 2

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) --*& )- # !% " " " "$ # ( ) - ! , , " " % & + - "

+ ( ( * & ) #% "

(+

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+ (( ( )*

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%% " -. -- ! % 800 / -. , % " # &

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L

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ψn (r) = exp(ik · r)

k

kx =

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n

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~2 k 2 ~2 = (kx2 + ky2 + kz2 ) . 2m 2m D

k

k

(2π/L)3 4πk 2 dk

dk

dN

4πk 2 dk

k 2 L3 dk dN = 2 · . 3 = π2 (2π/L) (2m∗ E)1/2 k= , ~

E

dN 1 D3D (E) = 3 = 2 L dE 2π

2m∗ ~2

3/2

E 1/2 .

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(2π/L)

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2πk dk

kL2 dk dN = 2 · . 2 = π (2π/L) 2πk dk

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dN m∗ = . L2 dE π~2

D2D (E)

En

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m∗ X H(E − En ) , π~2 n

H(E − En )

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0, 1,

E < En E ≥ En .

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k

dN = 2 ·

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k

2 dk

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