Lehrbuch Der Experimentalphysik: Festkorper (v. 6) [2nd ed.] 3110174855 [PDF]

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SVY

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TPU m5,67$//6758.785%(67,0081* 0,7 d(8*81*60(7+2'(1

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T m5,67$//6758.785(1

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TVR

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UPW h(67.?53(5',586,21

TVS

UPW h(67.?53(5',586,21 w17(5 f,586,21 ,0 h(67.?53(5 9(567(+7 0$1 (,1(1 o$7(5,(75$163257 $/6 h2/*( 9,(/(5 u35@1*( 921 c720(1 921 (,1(0 i,77(53/$7= J2'(5 |:,6&+(1*,77(53/$7=K =80 1>&+6O 7(1P f,( f,586,21 63,(/7 %(, $//(1 x25*>1*(1 (,1( :,&+7,*( t2//(N %(, '(1(1 c720( ,0 h(67.?53(5 809(57(,/7 :(5'(1P d(,63,(/( 6,1' ',( j202*(1,6,(581* 2'(5 ',( q5'O 181*6(,167(//81* ,1 n(*,(581*(1N ',( f27,(581* 921 j$/%/(,7(51N '$6 c86+(,/(1 921 %(56&+866)(+/67(//(1 1$&+ m$/79(5)25081*N c%6&+5(&.(1 2'(5 d(675$+/(1N '$6 c8)O :$&+6(1 921 u&+87=6&+,&+7(1 $8) q%(59>&+(1 $%(5 $8&+ ',( k21(1/(,781* ,1 k21(1O .5,67$//(1 2'(5 ',( 0(&+$1,6&+( m5,(&+9(5)25081* 921 o(7$//(1 %(, +2+(1 v(0O 3(5$785(1P k0 h2/*(1'(1 %(*,11(1 :,5 0,7 '(5 d(6&+5(,%81* '(5 f,586,216*/(,&+81*(1 81' '(6 f,586,216.2(5,=,(17(1P u2'$11 :(5'(1 (;3(5,0(17(//( g5*(%1,66( )@5 ',( u(/%67O ',586,21 81' ',( h5(0'$720',586,21 ,1 9(56&+,('(1(1 o$7(5,$/./$66(1 925*(67(//7 81' $720,67,6&+ ,17(535(7,(57P

UPWPS f,586,216*/(,&+81*(1N f,586,216.2(5,=,(17(1 f,( @%/,&+( 0$.526.23,6&+( d(6&+5(,%81* '(5 f,586,21 %$6,(57 $8) '(5 v+(25,( '(5 ,55(9(56,%/(1 r52=(66(P c167(//( ',(6(5 0(+5 )250$/(1 v+(25,( 62// ,0 h2/*(1'(1 (,1 (,1)$&+(6N $720,67,6&+(6 d,/' '(5 h(67.?53(5',586,21 925*(67(//7 :(5'(1P y,5 %(6&+5>1.(1 816 '$%(, $8) .8%,6&+( m5,67$//( J6.$/$5(5 f,586,216.2(5,=,(17KN $8) (,1( (,1',0(16,21$/( f,586,216*(20(75,( (17/$1* '(5 =Oc&+6( 81' %(187=(1 $86O 6&+/,(M/,&+ $720$5( m21=(175$7,21(1N & 3 |$+/ '(5 v(,/&+(1 352 i,77(53/$7=P y,5 1(+0(1 $1N '$66 6,&+ ',( ',581',(5(1'(1 v(,/&+(1 J=P dP i,77(5$720(N n((567(//(1N |:,6&+(1*,77(5$720(N h5(0'$720(N v5$&(5Ok62723( (7&PK ,1 '(0 ,1 c%%P UPST% '$5O *(67(//7(1 r27(17,$/*(%,5*( %(:(*(1N 81' (5+$/7(1 '$11 )@5 ',( =(,7/,&+( }1'(581* '(5 /2.$/(1 m21=(175$7,21 & J=N 7K )2/*(1'( d,/$1=*/(,&+81*\ 8M(5(1 m5$)7 m 817(5O 6&+,('/,&+(1 u3581*5$7(1 ,1 %=:P (17*(*(1*(6(7=7 '(5 =Ot,&+781*P f(5 (567( v(50 ,1 i/P JUPYK %(6&+5(,%7 ',( i(6$075$7(N 0,7 '(5 v(,/&+(1 $86 '(5 r26,7,21 = +(5$86O 635,1*(1P f,( %(,'(1 )2/*(1'(1 v(50( %(6&+5(,%(1 ',( t$7(1N 0,7 '(1(1 v(,/&+(1 $86 '(1 p$&+%$5326,7,21(1 ,1 ',( r26,7,21 = +,1(,1635,1*(1 Jc%%P UPST%KP h@5 ./(,1( m21=(175$7,216*5$',(17(1 87(57( m255(/$7,216)$.725 ) +,1=8*()@*7P f,(6(5 %(5@&.6,&+O 7,*7 (9P $8)75(7(1'( NNi('>&+71,6(5(.7(DD ,1 '(1 $720$5(1 r/$7=:(&+6(/1P g6 *,/7 ) 3 SN :(11N :,( )@5 n((567(//(1N |:,6&+(1*,77(5$720( 81' ,17(567,7,(//( h5(0'$720(N '(5 t@&.63581* (,1(6 v(,/&+(16 ,1 6(,1( 925+(5,*( r26,7,21 */(,&+ :$+56&+(,1/,&+ ,67 :,( '(5 y(,7(563581* ,1 (,1( '(5 $1'(5(1 p$&+%$5326,7,21(1P u35,1*7 '$6 ',)O )81',(5(1'( v(,/&+(1 '$*(*(1 %(925=8*7 ,1 6(,1( c86*$1*6326,7,21 =85@&.N 62 :,5' 6(,1 y(,7(5.200(1 '$'85&+ %(+,1'(57 81' (6 ,67 ) " SP d(,63,(/( +,(5=8 6,1' r/$7=O :(&+6(/ 921 0$5.,(57(1 v5$&(5$720(1 2'(5 921 h5(0'$720(1 @%(5 n((567(//(1 Jc%6&+1P UPWPUKP f(5 f,586,216.2(5,=,(17 +$7 ',( f,0(16,21 0T 62S 81' ,67 (,1 o$M )@5 ',( d(O :(*/,&+.(,7 '(5 f,586,2167(,/&+(1 ,0 m5,67$//P u,1' ',( ',581',(5(1'(1 c720( 921 '(5 */(,&+(1 u257( :,( (,1( '(5 &+(0,6&+(1 m20321(17(1 '(6 +202*(1 925$86*(O 6(7=7(1 h(67.?53(56N 62 635,&+7 0$1 921 u(/%67',586,21N u&+(1(,1+(,7 J0TK 81' |(,7(,1+(,7 J6K ,1 (,1( t,&+781* 675?0(1'(1 v(,/&+(1P xR ,67 '$6 c72092/80(1P h@5 - *,/7 '$11 '$6 62*P SP h,&.I6&+( i(6(7=\ - 3 - ',5 1- '5,)7 0,7 - ',5 32JfBpRK *5$'& 81' - '5,)7 3 JfBxRK m&B.vKP

JUPSSK

f,(6(6 i(6(7= ,67 ,'(17,6&+ 0,7 '(5 921 '(5 3+>120(12/2*,6&+(1 v+(25,( *()25'(57(1N /,1($5(1 d(=,(+81* =:,6&+(1 - 81' '(0 9(5$//*(0(,1(57(1N &+(0,6&+(1 r27(17,$/O *5$',(17(1P n(7=7(5(5 />667 6,&+ $8)7(,/(1 ,1 '(1 d(,75$* '(6 J1(*$7,9(1K i5$',(17(1 ,1 '(5 v(,/&+(1.21=(175$7,21 81' '(1 d(,75$* (,1(6 r27(17,$/*5$',(17(1N '(5 ,1 h250 921 >8M(5(1 m5>)7(1 m $8) ',( ',581',(5(1'(1 v(,/&+(1 (,1:,5.7P f(5 i(6$0767520 .$11 (17635(&+(1' ,1 (,1(1 62*P f,586,21667520 - ',5 81' ,1 '(1 f5,)7675206 - '5,)7 =(5/(*7 :(5'(1P d(,63,(/( )@5 67$7,21>5( v(,/&+(1675?0( 6,1' ',( r(50($7,21 921 i$O 6(1 '85&+ (,1( o(0%5$1 J6P c%%P UPSUK 2'(5 ',( f5,)7 921 k21(1 ,1 (/(.75,6&+(1 h(/'(51 Jc%6&+1P UPWPTKP

c%%P UPSU r(50($7,21 921 u$8(56725 '85&+ |,5.21',2;,' 81' r5,1=,3 '(5 u$8(56725621'(P k0 k11(1O %=:P c8M(15$80 (,1(6 (,16(,7,* *(6&+/266(1(1 |5qTOt2+56 /,(*(1 9(56&+,('(1( u$8O (56725Or$57,$/'5@&.( 3 J,K %=:P 3 J$K 925P c% &$P YRR@e .?11(1 qT2Ok21(1 5(/$7,9 6&+1(// '85&+ ',( t2+5:$1'N =P dP 921 J,K 1$&+ J$KN ',581',(5(1P c1 '(1 v5,3(/381.7(1 '(5 325?6(1N ,11(5(1 r7Og/(.752'( J6P c866&+1,776%,/'K :(5'(1 qT2Ok21(1 1$&+*(/,()(57N ,1'(0 qTOo2/(.@/( $86 '(0 i$6 $1 '(5 r7Oq%(59>&+( ,1 qOc720( =(5/(*7 :(5'(1 81'N 1$&+ c89$'(1 0,7 -( T (2N 2%(59>&+(11$+( u$8(56725On((567(//(1 '(6 |5qTOk21(1.5,67$//6 %(6(7=(1P w0*(.(+57 :(5'(1 $1 '(5 >8M(5(1 g/(.752'( qT2Ok21(1 $86 '(0 |5qT (171200(1 81' ,1 SBT JqTKi$6 1T (2 80O *(:$1'(/7P k0 m85=6&+/866 9,(M7 620,7 =:,6&+(1 '(1 %(,'(1 r7Og/(.752'(1 (,1 g/(.7521(1O 67520N '(5 A :(*(1 '(5 9(51$&+/>66,*%$5(1 (/(.7521,6&+(1 n(,7)>+,*.(,7 '(6 |5qT A */(,&+ '(0 k21(167520 '85&+ ',( |5qTOt2+5:$1' ,67P d(, 25(1(1 g/(.752'(1 %$87 6,&+ =85 x(5O +,1'(581* (,1(6 67$7,21>5(1 k21(1675206 (,1( q%(59>&+(1/$'81* 81' '$0,7 (,1( (/(.75,6&+( r27(17,$/',5(5(1= w 3 J.vBV (K /1J3 J,KB3 J$KK =:,6&+(1 J,K 81' J$K $8)P f,(6( 62*P p(5167Ou3$1181* .$11N :(11 3 J$K %(.$117 ,67 J=P dP )@5 n8)7KN =85 o(6681* '(6 u$8(567253$57,$/'58&.6 3 J,K 9(5O :(1'(7 :(5'(1P

TVV

U h(+/25'181* ,1 m5,67$//(1 c 4 c

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〈hkl〈 〈h’k’l’ 〈

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Haltering

piezokeramischer Aktuator Probe

Probenhalter

c%%P VPSW

Tunnelspitze

Rampe

u&+(0$ '(6 t$67(57811(/0,.526.236 1$&+ d(62&.( LUSNUTbP

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(20) (10) 0

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VPT u758.785 921 q%(59>&+(1

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z

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USR

mechanische Spannung τ x,y(z)

Teilchendichte

Ladungsdichte

ρel(z )

ρ T(z )

+

Festkörper

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σx

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(c)

σv

σy

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σv

σd

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c(2x2)

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hcp-Plätze

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UUV

V q%(59>&+(1 450 400

ungeordnet ungeordnet

p(2x2)-Inseln + Gittergas

150 0.05

0.10

0.15 0.20 Bedeckung Θ

0.25

0.30

√3x√3 R30˚

250

coex.

300

200

c%%P VPUU

p(2x2)

Antiphasen

Temperatur/K

350

0.35

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2π*

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T = 30 K

934

x200 Pt Pt

1.0

Pt

Zählrate / 105s-1

0.5 0 1.5 1.0 0.5 0

0

500 x200

1000

O-2 1262

O2 1553 1500

474

(a)

T = 300 K

Pt Pt

0 500 1500 1000 Energieverlust in Wellenzahlen / cm-1

(b)

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VPV c'62537,21

UUY

&+(1 $17,%,1'(1'(1 q5%,7$/6 *(5,1*(5 $/6 ,0 1(875$/(1 u$8(5672502/(.@/P f,( u&+:,1*81*6)5(48(1= ,67 '(6+$/% ,1 t,&+781* (,1(5 g,1)$&+%,1'81* 9(56&+2%(1P u&+/,(M/,&+ 71'(1 :,5 $8) '(5 q%(59>&+( $8&+ 3+50(1 '(5 q%(59>&+( $8) URR m ',6O 62=,,(57 '$6 qTOo2/(.@/N 81' (6 %/(,%7 $720$5(5 u$8(56725 $8) '(5 q%(59>&+(P f,( g;,67(1= 02/(.8/$5(5 u$8(567253+$6(1 +>1*7 67$5. 920 u8%675$7 $%P d(, '(1 :(,7(5 /,1.6 J5(/$7,9 =8 r7K ,0 r(5,2'(16&+(11250$/(1 (,1(1 y,1.(/ " Jc%%P VPUX%KN '(5 =:,6&+(1 WW@ )@5 c/JSSSK LZWb 81' [R@ )@5 r7JSSSK /,(*7 LZXbP f,( c8675,776$5%(,7 '(5 q%(59>&+( :,5' 5('8=,(57P f,( t('8.7,21 .$11 %(6&+5,(%(1 :(5'(1N ,1'(0 0$1

α

(a)

(b)

c%%P VPUX J$K u758.78502'(// )@5 ',( f233(//$*(1 921 y$66(5 $1 q%(59>&+(1P f,( y$66(5O 02/(.@/( 6,1' '85&+ (,1 p(7=:(5. 921 y$66(56725%5@&.(1%,1'81*(1 817(5(,1$1'(5 9(5%81O '(1P f,( d,1'81* $1 ',( q%(59>&+( (5)2/*7 '85&+ '$6 %(6(7=7(N ,0 y$66(502/(.@/ 1,&+7O %,1'(1'( T3Oq5%,7$/ '(6 u$8(56725$7206 2'(5 $8&+ '85&+ y$66(56725%5@&.(1 =80 o(7$//P J%K d,1'81* (,1(6 (,1=(/1(1 y$66(502/(.@/6 $1 (,1 c720 ,1 '(5 q%(59>&+(P f(5 y,1.(/ " .$11 =:,6&+(1 WW@ Jc/JSSSK LZWbK 81' [R@ Jr7JSSSK LZXbK %(75$*(1P

UUZ

V q%(59>&+(1

'(0 y$66(502/(.@/ (,1 f,32/020(17 '(5 i5?M( 3 3 3j q &26"13R =825'1(7N :2%(, J 3j q '$6 f,32/020(17 '(6 )5(,(1 y$66(502/(.@/6 81' 3R (,1 f,32/020(17 ,67N :(/O J &+(6 '85&+ '(1 n$'81*675$16)(5 920 y$66(502/(.@/ $8) '$6 u8%675$7 (1767(+7 LZXbP

VPVPTPV m2+/(1:$66(56725( d(, '(5 c'62537,21 921 m2+/(1:$66(56725(1 $1 q%(59>&+(1 ,67 =:,6&+(1 *(6>77,*7(1 81' 81*(6>77,*7(1 m2+/(1:$66(56725(1 =8 817(56&+(,'(1P i(6>77,*7( m2+/(1:$66(5O 6725( :,( =P dP o(7+$1 JejVKN g7+$1 JeTjXK 2'(5 |77,*7( m2+/(1:$66(56725( .?11(1 0,7 o(7$//2%(59>&+(1 (,1( y$66(56725%5@&.(1%,1'81* (,1*(+(1P u3(.7526.23,6&+ 6,(+7 0$1 '$6 '$5$1N '$66 (6 (,1( 6(+5 67$5. 5279(56&+2%(1( ejOu75(&.6&+:,1*81* 1$&+ c'62537,21 $1 (,1(5 q%(59>&+( *,%7N ',( .(,1( g17635(&+81* ,0 u3(.7580 '(6 )5(,(1 o2/(.@/6 +$7 LZYb Jc%%P VPUYKP f,( d,1'81*6(1(5*,( $1 ',( q%(59>&+( ,67 1$785*(0>M 80 62 +?+(5N -( 0(+5 jOc720( ,0 o2/(.@/ (,1( )@5 ',( c86%,/'81* '(5 jOd5@&.(1%,1'81* *((,*1(7( q5,(17,(581* $8):(,6(1P n$1*.(77,*( *(6>77,*7( m2+/(1:$66(56725( %,1'(1 $/62 67>5.(5P c8&+ %(,0 |*7 ',( d,1O '81*6(1(5*,( :(1,*67(16 (,1,*( |(+17(/ (xP f257 67(+(1 '5(, jOc720( )@5 (,1( jO d5@&.(1%,1'81* =85 x(5)@*81*P p$&+ g5:>50(1 '(5 q%(59>&+( 2'(5 1$&+ c'62537,21 %(, +?+(5(1 v(03(5$785(1 '(+77,*7(1 m2+/(1:$66(56725( 81' (6 %,/'(1 6,&+ o(7$//Oe$5%21O Vibrationsfrequenzen des Moleküls in der Gasphase

0

8

66

7

0

0

500

1000 1500 2000 Energieverlust in Wellenzahlen / cm-1

2500

2851

2544

1455 1440

H-Brückenbindung

1249 1351

1

862 904 1018 1040

2

512 533

x300

3

433

4

2902 2927

W(110) / 8L C6H12 E0 = 3.0 eV T = 110 K

5

128 238 250

Zählrate / 105s-1

6

3000

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VPV c'62537,21

UU[

c%%P VPUZ u758.785 921 g7+5081* 62/&+(5 81' $1'(5(5 BO*(%81'(1(5 q%(59>&+(1.203/(;( $8) v(0O 3(5$785(1 2%(5+$/% 921 URR m 9(5856$&+7 (,1( :(,7(5( f(+&+(P f,( %(O 6&+5,(%(1( u(48(1= '(5 g5(,*1,66( %(=,(+7 6,&+ $8) (,1( g5:>5081* ,0 wjxN 2+1( c1:(6(1+(,7 921 y$66(56725 ,1 '(5 i$63+$6(P y(5'(1 ',( q%(59>&+(1 (,1(0 y$6O 6(56725'58&. $86*(6(7=7N 62 (5)2/*7 80*(.(+57 (,1( j&+(1 %(*$11 ,1 '(1 TR,*(5 l$+5(1 '(6 925,*(1 l$+5+81'(576P f$6 k17(5(66( '$5$1 :85'( 925 $//(0 '85&+ ',( 1$&+ c/.$/,Oc'62537,21 %(2%$&+7(7( g51,('5,*81* '(5 c8675,776$5%(,7 81' ',( '$'85&+ (5(.7,9(5( i/@+(0,66,21 921 g/(.7521(1 *(:(&.7P y(*(1 ,+5(5 1,('O 5,*(1 k21,6,(581*6(1(5*,(N ',( ./(,1(5 $/6 ',( c8675,776$5%(,7 )$67 $//(5 h(67.?53(5 ,67N *(%(1 c/.$/,$720( ,+5 6Og/(.7521 %(, '(5 c'62537,21 :(,7*(+(1' $1 '$6 u8%675$7

UVR

V q%(59>&+(1

$%P f$6 '$'85&+ (1767(+(1'( +2+( f,32/020(17 3= (,1(6 $'625%,(57(1 c/.$/,$7206 5('8=,(57 ',( c8675,776$5%(,7 IR '(6 u8%675$76 (17635(&+(1' '(5 i/(,&+81* I 3 IR 2

( 3= 1 N &R 6

JVPVTK

0,7 &R '(5 $%62/87(1 ',(/(.75,6&+(1 r(50($%,/,7>7 81' 16 '(5 h/>&+(1.21=(175$7,21 '(5 f,32/(P f$6 f,32/020(17 (,1(6 $'625%,(57(1 c/.$/,$7206 1,007 0,7 =81(+O 0(1'(5 d('(&.81* 5$6&+ $%P j(85,67,6&+ .$11 0$1 ',(6( 5$6&+( c%1$+0( $/6 f(O 32/$5,6$7,216(5(.7 9(567(+(1\ f$6 921 '(1 p$&+%$5',32/(1 $8) '(1 f,32/ 5@&.:,5O .(1'( (/(.75,6&+( h(/' )@+57 =8 (,1(5 f(32/$5,6$7,21N ',( :(*(1 '(5 +2+(1 (/(.752O 1,6&+(1 r2/$5,6,(5%$5.(,7 '(6 c/.$/,Oc'625%$7Bq%(59>&+(1.203/(;(6 %(621'(56 67$5. ,67P g,1 %(66(5(6 x(567>1'1,6 9(50,77(/7 -('2&+ ',( s8$17(10(&+$1,.P f$6 6O g/(.7521 '(6 c/.$/,$7206 ,67 5>80/,&+ 6(+5 $86*('(+17 Jc%%P VPU[KP g6 .$11 '(6O :(*(1 1,&+7 $1 /2.$/,6,(57( 'O|867>1'( $%*(*(%(1 :(5'(1N $8&+ '$11 1,&+7 :(11 ',(6(N :,( %(, '(1 %(5*$1*60(7$//(1 (,1( +2+( f,&+7( 81%(6(7=7(5 |867>1'( $0 h(50,Op,9($8 +$%(1P f(5 g/(.7521(175$16)(5 (5)2/*7 185 $1 ',( 63O|867>1'(P y(*(1 '(5 *(5,1*(1 |867$1'6',&+7( '(5 63Og/(.7521(1 :(5'(1 6&+21 %(, *(5,1*(1 d('(O &.81*6*5$'(1 $//( 81%(6(7=7(1 63O|867>1'( =:,6&+(1 '(0 h(50,Op,9($8 81' '(0 6O|867$1' '(6 c/.$/,Oc7206 %(6(7=7P |86>7=/,&+ $'625%,(57( c/.$/,Oc720( .?11(1 '$11 .(,1(1 :(,7(5(1 g/(.7521(175$16)(5 %(:,5.(1P f,( c8675,776$5%(,7 :,5' 1,&+7 :(,7(5 (51,('5,*7N '$6 f,32/0(17 352 $'625%,(57(0 c720 1,007 $%P f$6 *52M( x2O /80(1 '(6 6Og/(.75216 0$&+7 $8&+ 9(567>1'/,&+N :$580 6&+21 %(, ./(,1(1 d('(&.81O *(1 (,1( /$7(5$/( y(&+6(/:,5.81* =:,6&+(1 '(1 c'625%$7(1 (,16(7=7N ',( 6&+/,(M/,&+ %(, *5?M(5(1 d('(&.81*(1 =8 (,1(0 k62/$725Bo(7$//@%(5*$1* ,1 '(5 c/.$/,6&+,&+7 )@+57P f,( ',&+7 *(3$&.7( q%(59>&+(1/$*( 9(5+>/7 6,&+ :(,7*(+(1' :,( '$6 (17635(O

Li Mo

Mo

Mo Mo

Mo

Mo Mo [110]

c%%P VPU[ f,5(5(1=/$'81*6',&+7( )@5 n, $8) (,1(5 o2JSSRKOq%(59>&+(P i(=(,*7 :,5' '(5 w1O 7(56&+,(' '(5 n$'81*6',&+7( 921 '(0 |867$1' 0,7 $'625%,(57(0 n, 81' '(1 $'',(57(1 n$O '81*6',&+7(1 921 n, 81' '(5 o2JSSRKOq%(59>&+( 2+1( c'62537,21P i(675,&+(/7( n,1,(1 =(,*(1 1(*$7,9( f,5(5(1= $1N 'P +P ',( n$'81*6',&+7( ,67 '257 *(5,1*(5 *(:25'(1P f(87/,&+ (5.(11%$5 ,67 ',( *52M( /$7(5$/( c86'(+181* '(6 n, T6Og/(.75216 J',( c%%,/'81* :85'( )5(81'/,&+(5:(,6( 921 lP o@//(5 =85 x(5)@*81* *(67(//7KP

Änderung der Austrittsarbeit /eV

VPV c'62537,21

c%%P VPVR

0

UVS

Mo(110)/Li

-0.5 -1.0 -1.5 -2.0 -2.5 -3.0

0

0.5 1.5 1.0 Bedeckung in Monolagen

2.0

c8675,776$5%(,7 921 o2JSSRK $/6 h81.7,21 '(5 d('(&.81* 0,7 n,7+,80P

&+(1'( c/.$/,Oo(7$// 81' '$6 u8%675$7Bc'625%$7 u&+67 6&+1(// $%N '85&+/>8)7 (,1 o,1,080N 80 6,&+ '$11 (7:$ %(, '(5 c8675,776$5%(,7 '(6 c/.$/,Oo(7$//6 =8 6>77,*(1 Jc%%P VPVRK L[TbP g,1( :(,7(5( h2/*( '(5 *52M(1 c86'(+181* '(6 6Og/(.75216 ,67N '$66 ',( d,1'81*6O (1(5*,( 185 :(1,* 920 (,1*(1200(1(1 q%(59>&+(13/$7= $%+>1*7P f$'85&+ ,67 ',( f,586,21 (,1(6 c/.$/,$7206 $8) '(5 q%(59>&+( 6(+5 6&+1(// 81' 6,( .$11 ,1 :(1,*(1 o,187(1 =8 (,1(5 /$7(5$/(1 x(5%5(,781* ,0 ]0 81' 00Od(5(,&+ )@+5(1 L[UN [VbP f,( *(5,1*( c%+>1*,*.(,7 '(5 d,1'81*6(1(5*,( 920 c'62537,2163/$7= %(, *52M(5 /$7(O 5$/(5 y(&+6(/:,5.81* )@+57 $%+>1*,* 920 d('(&.81*6*5$' =8 =$+/5(,&+(1 %(5O 6758.785(1N 0,7+,1 =8 6(+5 .203/(;(1 r+$6(1',$*5$00(1P c8&+ t(.216758.7,21(1 921 q%(59>&+(1 81' '(5 g,1%$8 921 c/.$/,Oc720(1 ,1 7,()(5( n$*(1 :(5'(1 %(O 2%$&+7(7P f,(6 0$* ,0 j,1%/,&. $8) ',( '(/2.$/,6,(57( d,1'81* =81>&+67 @%(55$6&+(1P v7 /,(*7 ,0 d(5(,&+ 7&+( ,67 '(6+$/% .29$/(17 81' /2.$/P c8) %(5*$1*60(7$//(1 ',662=,,(57 $1*(%27(1(5 02O /(.8/$5(5 y$66(56725 63217$1 81' 2+1( 0(66%$5( c.7,9,(581*6%$55,(5(P g6 :(5'(1 62:2+/ =:(,)$&+ $/6 $8&+ '5(,)$&+ .225',1,(57( d5@&.(13/>7=( (,1*(1200(1P c'O 625%,(57(5 y$66(56725 :(,67 (,1( d(621'(5+(,7 $8)N ',( ,1 '(5 *(5,1*(1 o$66( %(*5@1O

UVT

V q%(59>&+(1

'(7 ,67P f,( ./(,1( o$66( )@+57 '$=8N '$66 ',( u&+:,1*81*6$03/,78'(1 6(+5 *52M :(5'(1N 62 *52MN '$66 ',( d(:(*81*(1 '(5 y$66(56725Oc720( 48$17(10(&+$1,6&+ $/6 y(//(13$.(7 %(6&+5,(%(1 :(5'(1 0@66(1P f,( x,%5$7,216=867>1'( 6,1' '$11 5>80/,&+ '(/2.$/,6,(57( d$1'=867>1'( L[XbP f,( f,586,21 .$11 '(6+$/% $8&+ '85&+ (,1(1 v811(/352=(66 (5)2/*(1 L[YbN '(5 %(, 7,()(1 v(03(5$785(1 '$6 f,586,2169(5+$/O 7(1 %(67,007P h@5 f(87(5,80 ,67 ',( 48$17(10(&+$1,6&+( f(/2.$/,6$7,21 ,1)2/*( '(5 *5?M(5(1 o$66( *(5,1*(5P g,1( :(,7(5( d(621'(5+(,7 921 y$66(56725N 1>0/,&+ ',( h>+,*.(,7 y$66(56725%5@&.(1%,1'81*(1 $86=8%,/'(1N :,5' :(,7(5 817(1 %(6352&+(1P j$/%/(,7(52%(59>&+(1N :,( =P dP ',( 921 u,N 5($*,(5(1 1,&+7 0,7 02/(.8/$5(0 y$6O 6(56725P c720$5(5 y$66(56725N +(5*(67(//7 =P dP '85&+ f,662=,$7,21 $1 (,1(5 +(,M(1 h/>&+(N 5($*,(57 '$*(*(1 62)257 0,7 u, 81' 6>77,*7 ',( )5(,(1 x$/(1=(1 '(5 u,Oc720( $1 '(5 q%(59>&+( $%P g,1( c%6>77,*81* '(5 )5(,(1 x$/(1=(1 81' ',( j(567(//81* %(O 621'(56 *87 *(25'1(7(5N 815(.216758,(57(5 u,Oq%(59>&+(1 J=P dP (,1( JS4SKu,JSSSKO q%(59>&+(K />667 6,&+ '85&+ (,1( 1$66O&+(0,6&+( r5>3$5$7,21 (55(,&+(1 L[ZbP g,10$/ ,16 wjx *(%5$&+7N 6,1' ',(6( q%(59>&+(1 :(,7*(+(1' ,1(57 81' +$/7(1 6,&+ '257 =(,7/,&+ )$67 81%(*5(1=7P

VPVPTPY c720( '(5 i5833(1 kxAxkkk c'62537,2163+$6(1 921 u$8(56725N u&+:()(/N u7,&.6725 81' m2+/(16725 :(5'(1 ,1 '(5 t(*(/ '85&+ ',662=,$7,9( c'62537,21 921 o2/(.@/(1 $86 '(5 i$63+$6( +(5*(O 67(//7\ u$8(56725 '85&+ f,662=,$7,21 921 qT 2'(5 $8&+ jTqN u&+:()(/ '85&+ f,6O 62=,$7,21 921 jTuN u7,&.6725 '85&+ f,662=,$7,21 921 pjU 81' m2+/(16725 7&+(1 -('(1)$//6 %(, (5+?+7(5 v(03(5$785 ',662=,,(5(1 81' '$66 ',( g/(0(17( qN uN p 81' e 0,7 '(1 0(,67(1 u8%675$7(1 (,1( 67$5.( /2.$/( x$/(1=%,1'81* (,1*(+(1N '(5 y$66(56725 $%(5 185 6&+:$&+ *(%81'(1 :,5' 81' '(6+$/% '(625%,(57 :(5'(1 .$11P d(925=8*7( c'62537,2163/>7=( 921 qN uN p 81' e 6,1' ',( 0,7 +2+(5 m225',1$7,21N $/62 ',( 9,(5)$&+ .225',1,(57(1 $8) )&&JSRRKOq%(59>&+(1 2'(5 ',( '5(,)$&+ .225',1,(57(1 $8) )&&JSSSKOq%(59>&+(1 Jc%%P VPUR$N VPUR%N VPUTKP f,( 67$5.( d,1'81* =:,6&+(1 u8%675$7 81' c'625%$7 )@+57 =8 (,1(5 '(87/,&+(1 x(5>1'(581* '(5 d,1'81*6$%67>1'( =:,6&+(1 '(1 u8%675$7$72O 0(1N +>87* $8&+ =8 (,1(5 t(.216758.7,21 '(5 q%(59>&+(1P d(621'(56 %(, u7,&.6725 81' m2+/(16725 ,67 ',( v(1'(1= =85 t(.216758.7,21 $86*(35>*7P d(.$117 81' +>87* 817(568&+7 :25'(1 6,1' ,1 ',(6(0 |86$00(1+$1* 925 $//(1 ',( 3V*Ot(.216758.O 7,21(1 921 p,JSRRK Jc%%P VPUS%KP f,( t(.216758.7,21 (1767(+7 $8)*581' '(6 '85&+ ',( c'62537,21 921 p 81' e %(:,5.7(1 67$5.(1 .2035(66,9(1 q%(59>&+(1675(66(6 J6P c%6&+1P VPUPSPSK =:,6&+(1 '(1 p,Oc720(1P f,( 3V*Ot(.216758.7,21 *,%7 '(1 p,O c720(1 0(+5 r/$7= ,1 '(5 q%(59>&+(N 81' '$'85&+ :,5' ',( u3$1181*6(1(5*,( 5('8=,(57 L[[bP o(7$//( %,/'(1 0,7 '(1 g/(0(17(1 qN uN p 81' e +>87* 67$%,/( x(5%,1'81*(1P d(, +?+(5(0 c1*(%27 921 c'625%$7$720(1 .?11(1 '(6+$/%N ,1 '(5 t(*(/ 0,7 ./(,1(1 m(,0(1 %(*,11(1'N x2/80(19(5%,1'81*(1N $/62 q;,'(N p,75,'(N u8/7'( 81' e$5%,'( (1767(+(1P c8) '(0 j$/%/(,7(5 u, %,/'(7 6,&+ 62*$5 2+1( (,1( c'62537,2163+$6( ',5(.7 (,1 q%(59>&+(12;,'\ f,( u$8(56725$720( *(+(1 ',5(.7 =:,6&+(1 =:(, u,Oc720(N $//(5',1*6 ,67 '(5 u,OqOu, d,1'81*6:,1.(/ *(*(1@%(5 '(1 *(:?+1/,&+(1 q;,'3+$6(1

VPV c'62537,21

UVU

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VPW s8$17(1=867>1'( $1 q%(59>&+(1

UWW

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UWX

V q%(59>&+(1 Skimmer

θi ....................................................................................................................................

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VPW s8$17(1=867>1'( $1 q%(59>&+(1 Nachanalysator

Streukammer

Kristall

UWY

Hauptmonochromator

Linse (A1, A2, A3)

Channeltron

Hauptanalysator

Linse (B4, B3, B2, B1)

Vormonochromator

Kathode

drehbar um 90˚

c%%P VPV[ 9>&+(1P

g/(.7521(163(.7520(7(5 )@5 ',( ,1(/$67,6&+( u75(881* 921 g/(.7521(1 $1 q%(5O

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UWZ

V q%(59>&+(1 e-

O C

O C

O C

Dipolmoment senkrecht

O C

Dipolmoment parallel

c%%P VPWR f$6 921 (,1(0 g/(.7521 $86*(+(1'( (/(.75,6&+( h(/' ,67 $1 '(5 q%(59>&+( '(6 h(67.?53(56 1$+(=8 6(1.5(&+7 25,(17,(57 J& # # SKP f$5$86 )2/*7N '$66 (,1( y(&+6(/:,5.81* 185 0,7 '(1 u&+:,1*81*(1 (5)2/*7N ',( (,1 6(1.5(&+7(6 f,32/020(17 $8):(,6(1P f,( c15(*81* %(1$&+%$57(5 o2/(.@/( ,67 $11>+(51' */(,&+3+$6,* J^$ 7 RKP f,( c86:$+/5(*(/1 6,1' $/62 :,( %(, '(5 k1)5$527$%62537,21 $1 q%(59>&+(1 Jv$%P VPSKP

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0

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Bindungsenergie /eV

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Intensität

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44

33 24.8 16.5

2.5

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1.5 1.0 0.5 0 Bindungsenergie / eV

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EES

Eanlag Ediff

Ebind

Koordinate des Adatoms parallel zur Oberfläche

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(a)

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30 25 20

t = 720 s Island Radius /√Ω

t=0

(a)

t = 1440 s

t = 1800 s

15 10 5 0

(b)

Cu(111): T = 303 K

β = 0.50 eV/a II + ν 0 = 9.8x1011− 0.5 s-1

0

0.5 1.0 Zeit (103 s)

1.5

2.0

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v$%P WPX d(5(&+1(7( /2.$/( 0$*1(7,6&+( u3,1020(17( ,uJSRRK N ,uJSSRK N $1' ,uJSSSK ,0 x(5*/(,&+ =8 '(1 (17635(&+(1'(1 x2/80(1:(57(1 ,x ,1 ,d Bc720 )@5 .8%,6&+O5$80=(175,(57(6 e5 81' h(N .8%,6&+O9>&+(1=(175,(57(6 e2 81' p,N 62:,( +(;$*21$/(6 e2JRRRSKP e5 ,uJSRRK ,uJSSRK ,uJSSSK ,uJRRRSK ,x

h(

e2

p,

TPWW A A

TPZZ TPVU TPVZ

RPXZ RPYV RPXU

uRPXR

TPSU

SPZW A A SPYR SPXT

RPXS

VXX

W o$*1(7,6086

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JWPSYRK

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VXZ

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TC(d ) / TC(∞)

0.8

Re(0001)/Ni(111) Cu(111)/NiFe(111)/Cu(111) W(110)/Ni(111) Cu(111)/Ni(111) W(110)/Fe(110)/Ag

0.6 0.4 0.2 0

0

20 30 d (ML)

10

40

50

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1.0

N × (d nm Co + 1.1 nm Pd)

K.dCo(mJ/m2)

0.5 0 -0.5

KV

d⊥

-1.0 -1.5

0

0.5

1.0 dCo (nm)

1.5

2.0

2.5

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Widerstand R in Ω

0.100 Hg

0.075 0.050 0.025 0

M kJ7K 3 kR (;3LJ2tBnK 6 7b 0,7 '(5 |(,7 7 $%./,1*7P f$%(, %(=(,&+1(7 n ',( k1'8.7,9,7>7 '(6 t,1*6P y(11 675(1* t 3 R *,/7N 62//7( (,1 1,&+7 $%./,1*(1'(5 f$8(567520 9,(M(1P v$76>&+/,&+ +$7 0$1 f$8(5675?0( @%(5 l$+5( +,1:(* 2+1( 0(5.%$5( c%1$+0( %(2O %$&+7(7P f(5 p$&+:(,6 '(6 f$8(5675206 *(/,1*7 '$%(, @%(5 '$6 0,7 '(0 u7520 9(5O .1@3)7( 0$*1(7,6&+( o20(17 o 3 k 6 cN :2%(, c ',( 920 t,1* 806&+/266(1( h/>O &+( ,67P f,( 62 (5+$/7(1( 2%(5( i5(1=( 921 tBt1 " SR2SV 5(&+7)(57,*7 ',( c11$+0(N '$66 )@5 u835$/(,7(5 7$76>&+/,&+ t 3 R *,/7P

XPSPT o(,M1(5Oq&+6(1)(/'Og5(.7 f(5 u835$/(,7(5 ,67 1,&+7 185 (,1 ,'($/(5 n(,7(5N (5 ,67 $8&+ (,1 ,'($/(5 f,$0$*1(7N 'P +P (5 9(5'5>1*7 '(1 0$*1(7,6&+(1 h/866N 62 '$66 ,0 k11(51 81$%+>1*,* 921 '(5 x25*(6&+,&+7( ',( 0$*1(7,6&+( k1'8.7,21 d 3 R +(556&+7 J:,5 :(5'(1 */(,&+ g,1O 6&+5>1.81*(1 ',(6(5 d(+$83781* +,11(+0(1 0@66(1KP f,(6 :85'( =8(567 921 o(,MO 1(5 81' q&+6(1)(/' LXb *(=(,*7P k0 i(*(16$7= '$=8 :>5( '(5 |867$1' (,1(6 ,'($/(1 n(,7(56 J2+1( ,'($/(1 f,$0$*1(7,6086K $%+>1*,* 921 '(5 x25*(6&+,&+7(N :,( )2/O *(1'( %(5/(*81* =(,*7P f$=8 0@66(1 :,5 :,66(1N '$66 (,1 >8M(5(6 o$*1(7)(/' ',( u835$/(,781* 817(5'5@&.7N :,( 48$/,7$7,9 ,1 c%%P XPT '$5*(67(//7P h@5 v " v& +(556&+7 )@5 $8M(1 $1*(/(*7( o$*1(7)(/'(5 d$ 3 ,R jN :2%(, ,R ',( 0$*1(7,6&+( h(/'.216O 7$17( 81' j ',( 0$*1(7,6&+( h(/'67>5.( ,67N 817(5+$/% (,1(6 .5,7,6&+(1 h(/'6 d& JvK u835$/(,781*N )@5 +?+(5( h(/'(5 p250$//(,781*P y,( c%%P XPT =(,*7N *,%7 (6 =:(, o?*/,&+.(,7(1N 920 1250$//(,7(1'(1 |867$1' 0,7 v # v& 81' d 3 R Jr81.7 SK ,1 '(1 6835$/(,7(1'(1 |867$1' 0,7 v " v& 81' R " d$ " d& Jr81.7 TK =8 *(/$1*(1P d(,0 y(* $% :,5' '(5 u835$/(,7(5 ,0 h(/' d$ 3 R 817(5 v& $%*(.@+/7 J$KN %(,0 '$5$8) )2/*(1'(1 g,16&+$/7(1 '(6 h(/'(6 J%K :,5' :(*(1 t 3 R (,1 f$8(567520 ,1O '8=,(57N '(5 1$&+ '(5 n(1=I6&+(1 t(*(/ 9(5+,1'(57N '$66 0$*1(7,6&+(5 h/866 ,1 '$6 k11(5( '(5 r52%( (,1'5,1*7N 'P +P ,0 k11(5(1 '(6 ,'($/(1 n(,7(56 ,67 ,1 ',(6(0 h$// Ba

Bc(T ) Normalleiter 2

b

d Supraleiter

c 1 a

Tc

c%%P XPT u&+(0$7,6&+(6 r+$6(1',$*5$00 0,7 '(0 u7$%,/,7>76%(5(,&+ '(6 6835$/(,7(1'(1 |8O 67$1'6 ,0 >8M(5(1 o$*1(7)(/' d$ P g,1*(=(,&+1(7 6,1' =:(, y(*( $% 81' &'N 80 920 125O 0$//(,7(1'(1 |867$1' 0,7 v # v& 81' d$ 3 R Jr81.7 SK =80 6835$/(,7(1'(1 |867$1' v " v& N R " d$ " d& Jr81.7 TK =8 *(/$1*(1P

VZZ

X u835$/(,781*

d 3 RP y,5' $1'(5(56(,76 '(5 y(* &' %(6&+5,77(1N 62 9,(M7 %(,0 g,16&+$/7(1 '(6 h(/'(6 )@5 v # v& J&K :(*(1 '(6 (1'/,&+(1 y,'(567$1'6 ,0 p250$/=867$1' 185 .85=O =(,7,* (,1 k1'8.7,21667520P y(11 ',(6(5 $%*(./81*(1 ,67N ,67 '(5 h/866 92//67>1',* ,1 ',( r52%( (,1*('581*(1P d(,0 c%.@+/(1 ,0 (1'/,&+(1 .2167$17(1 h(/' '85&+ v& +,1'85&+ J'K 3$66,(57 1,&+76P u20,7 ,67 '(5 |867$1' '(6 ,'($/(1 n(,7(56 $%+>1*,* 921 '(5 x25*(6&+,&+7(P f(5 x(568&+ 921 o(,M1(5 81' q&+6(1)(/' =(,*7N :,( (5:>+17N '$66 ,0 k11(5(1 (,1(6 +202*(1(1 u835$/(,7(56 67(76 d 3 R ,67N 81$%+>1*,* 921 '(5 x25*(6&+,&+7(C f$0,7 ,67 '(5 6835$/(,7(1'( |867$1' (,1 i/(,&+*(:,&+76=867$1' ,0 u,11( '(5 v+(502'&+(16&+,&+7P k1 ',(6(5 9,(M7 '(5 6835$/(,7(1'( f$8(567520N '(5 127:(1',* ,67 =85 c%6&+,5081* '(6 h(/'(6 Jc%6&+1P XPTPSKP d(, 1,&+7 67$%)?50,*(1 r52%(1 6,1' g170$*1(7,6,(581*6(5(.7( =8 %(5@&.6,&+7,*(1 Jc%6&+1P XPSPUKP

XPSPU u835$/(,7(5 SP 81' TP c57 y,( 6&+21 (5:>+17N :,5' ',( u835$/(,781* '85&+ o$*1(7)(/'(5 817(5'5@&.7P u835$O /(,7(5 SP c57 81' TP c57 817(56&+(,'(1 6,&+ '85&+ ,+5 x(5+$/7(1 ,0 o$*1(7)(/'P

XPSPUPS u835$/(,7(5 SP c57 y,5 :2//(1 =81>&+67 '$6 x(5+$/7(1 (,1(5 .203$.7(1N 67$%)?50,*(1 r52%( 0,7 /$1*(5 c&+6( 3$5$//(/ =80 $1*(/(*7(1 o$*1(7)(/' d$ 3 ,R j %(75$&+7(1N 80 ',( (5:>+17(1 g170$*1(7,6,(581*6(5(.7( =81>&+67 9(51$&+/>66,*(1 =8 .?11(1P f(5 o(,M1(5Oq&+O 6(1)(/'Og5(.7 %(6$*7N '$66 ,0 k11(5(1 '(6 u835$/(,7(56 d 3 R +(556&+7P f,(6 *,/7 %,6 =80 .5,7,6&+(1 h(/' d& N %(, '(0 ',( u835$/(,781* =86$00(1%5,&+7P f$1$&+ '5,1*7 h/866 ,1 ',( r52%( (,1N 81' )@5 (,1( ,0 1250$//(,7(1'(1 |867$1' 810$*1(7,6&+( r52%( 0,7 0$*1(7,6&+(5 r(50($%,/,7>7 , 3 S ,67 d 3 d$ Jc%%P XPU$KP f$6 x(5+$/7(1 ,0 6835$/(,7(1'(1 |867$1' .?11(1 :,5 %(6&+5(,%(1 0,7 d 3 ,R Jj1oK 3 d$ 1,R o 3 R P

JXPSK

u20,7 ,67 ',( o$*1(7,6,(581* o 32d$ B,R P h@5 '(1 +,(5 %(75$&+7(7(1 h$// (,1(6 g//,362,'6 ,67 o 3$5$//(/ =8 d$ P y,5 .?11(1 '$+(5 '(1 v(1625&+$5$.7(5 '(5 0$*1(O 7,6&+(1 u86=(37,%,/,7>7 4N 4,- 3 ,R JXo, BXd-Kd S R 0,7 ,N - 3 ;N 66,*(1 | 81' 6&+5(,%(1 (,1)$&+ 4 3 ,R J'oB'd$Kd S R P f$0,7 )2/*7 4 32SN $/62 '(5 ,'($/( | f,$0$*1(7,6086P f,( o$*1(7,6,(581*6.859( (,1(6 u835$/(,7(56 SP c57 =(,*7 c%%P XPU%P v87* *,/7 1>+(581*6:(,6( d& JvK 3 d& JRK JS2JvBv& KTK P

JXPXK

g%(162 />667 6,&+ ',( 63(=,76&+( y>50( *(0>M e3 3 vJXuBXvK3N d $86 i/P JXPWK %(O " v& (5:$57(1P v$76>&+/,&+ 1,007 5(&+1(1P o,7 i/P JXPXK :@5'( 0$1 e3 6 v U )@5 v " '(5 (/(.7521,6&+( d(,75$* =85 63(=,76&+(1 y>50( ,0 u835$/(,7(5 (;321(17,(// $% Jc%6&+1P XPUPVKP d5,1*7 0$1 (,1(1 5>80/,&+ $86*('(+17(1 u835$/(,7(5 J=P dP (,1( 6835$/(,7(1'( m8O *(/K ,1 (,1 =81>&+67 5>80/,&+ .2167$17(6 o$*1(7)(/' d$ N 62 ,67 '$6 >8M(5( o$*1(7)(/' $0 }48$725 $8)*581' '(5 h(/'9(5'5>1*81* *5?M(5 $/6 $1 '(1 r2/(1N :,( 6&+(0$7,6&+ ,1 c%%P XPV$ $1*('(87(7P h@5 (,1 g//,362,' 0,7 (,1(5 j$837$&+6( 3$5$//(/ =80 $1O *(/(*7(1 h(/' +(556&+7 $0 }48$725 '$6 (5(.7,9( h(/' d()) 3 d$ 2p ,R o N

JXPYK

Ba Beff = 1.5 Ba

magnet. Fluss Φ durch Äquatorialfläche

:2%(, p '(5 g170$*1(7,6,(581*6)$.725 ,67N '(5 185 921 '(5 i(20(75,( $%+>1*7N =P dP p 3 SBU )@5 (,1( m8*(/P h@5 '@11( |5( @%(5$// d 3 d$ " d& P f$+(5 %,/'(7 6,&+ (,1 |:,6&+(1O =867$1' 0,7 1250$//(,7(1'(1 81' 6835$/(,7(1'(1 f20>1(1 $86P f$6 f20>1(1086O 7(5 ,67 ,0 c//*(0(,1(1N :,( c%%P XPW $0 d(,63,(/ (,1(5 6835$/(,7(1'(1 k1Ou&+,&+7 6(1.5(&+7 =80 o$*1(7)(/' Jp W SK =(,*7N 5(&+7 .203/,=,(57P h$//6 6,&+ ',( f20>O

Bc (a)

(b)

Magnetfeld Ba

c%%P XPV J$K c86*('(+17(5 u835$/(,7(5 SP c57 ,0 >8M(5(1 o$*1(7)(/' d$ P c0 }48$725 ,67 '$6 (5(.7,9( h(/' d()) # d$ P h@5 '$6 +,(5 *(=(,*7( d(,63,(/ (,1(5 m8*(/ ,67 d()) 3 SPW d$ P J%K h@5 d$ " d& " d()) %,/'(7 6,&+ (,1 |:,6&+(1=867$1' 0,7 1250$//(,7(1'(1 81' 6835$/(,7(1'(1 d(5(,&+(1 $86P f$+(5 %(71'(7 6,&+ h/866 ,1 '(5 r52%(P d(, c167,(* 921 d$ :$&+6(1 ',( 125O 0$//(,7(1'(1 f20>1(1 $1N %,6 %(, d$ 3 d& ',( r52%( 92//67>1',* 1250$//(,7(1' ,67P

XPS i581'/(*(1'( c63(.7( '(5 u835$/(,781*

V[S

c%%P XPW k1',803/$77( 6(1.5(&+7 =80 $1*(/(*7(1 h(/' ,0 |:,6&+(1=867$1' 0,7 6835$/(,7(1O '(1 J'81.(/K 81' 1250$//(,7(1'(1 d(5(,&+(1 J+(//KP f(5 d,/'$866&+1,77 %(75>*7 (7:$ TPR4SPV &0TN 1$&+ LYbP

1(16758.785 5(9(56,%(/ %(, }1'(581* 921 d$ >1'(57N ,67 ',( 0$*1(7,6&+( k1'8.7,21 ,1 '(5 }48$725,$/(%(1( '85&+ '(1 ,1 c%%P XPV% '$5*(67(//7(1 x(5/$8) *(*(%(1P

XPSPUPT u835$/(,7(5 TP c57 y>+5(1' u835$/(,7(5 $86 5(,1(1 g/(0(17(1 )$67 ,00(5 u835$/(,7(5 SP c57 6,1' Jp% %,/'(7 (,1( c861$+0(KN 6,1' n(*,(581*(1 2'(5 ,17(50(7$//,6&+( x(5%,1'81*(1 ,1 '(5 t(*(/ u835$/(,7(5 TP c57P d(, ',(6(1 A :,5 1(+0(1 =81>&+67 :,('(5 (,1( /$1*( 67$%O )?50,*( r52%( 3$5$//(/ =80 c8M(1)(/' d$ $1 A :,5' '(5 o(,M1(5Oq&+6(1)(/'Og5(.7 d 3 R 185 %,6 =8 (,1(0 817(5(1 .5,7,6&+(1 h(/' d&S %(2%$&+7(7N '$11 '5,1*7 0$*O 1(7,6&+(5 h/866 7(,/:(,6( ,1 ',( r52%( (,1N '(5 6835$/(,7(1'( |867$1' %/(,%7 -('2&+ %,6 =8 (,1(0 2%(5(1 .5,7,6&+(1 h(/' d&T (5+$/7(1 Jc%%P XPXKP k0 h(/'%(5(,&+ d&S " d$ " d&T +(556&+7 (,1 o,6&+=867$1'P w0 ',(6(1 1,&+7 0,7 '(0 2%(1 %(6352O &+(1(1 |:,6&+(1=867$1' =8 9(5:(&+6(/1N %(=(,&+1(7 0$1 ',(6( r+$6( $8&+ $/6 u+8%O

- µ 0M

B

(a)

Bc1

Bc2 Ba

(b)

Bc1 Bcth

Bc2 Ba

c%%P XPX u835$/(,7(5 TP c57 ,0 >8M(5(1 o$*1(7)(/' d$ 3 ,R jP J$K f,( 0$*1(7,6&+( k1'8.7,21 ,0 k11(5(1 ,67 d 3 R )@5 d$ " d&S 81' (55(,&+7 '(1 y(57 d 3 d$ )@5 d$ 3 d&T P f257 9(56&+:,1'(7 ',( u835$/(,781*P J%K o$*1(7,6,(581*6.859(P f$6 7+(502'M,* $1*(25'1(7P f,( f85&+672M381.7( ',(6(5 h/866/,1,(1 '85&+ (,1( g%(1( 6(1.5(&+7 =8 d$ %,/'(1 ,1 9,(/(1 h>//(1 (,1 5(*(/0>M,*(6 +(;$*21$/(6 i,77(5P f,( r,21,(5$5%(,7(1 =85 u,&+7%$50$&+81* '(6 h/866/,1,(1*,77(56 %(187=7(1 (,1( f(.25$O 7,2160(7+2'( 0,7 g,6(13$57,.(/1N ',( 6,&+ 1$&+ '(0 x(5'$03)(1 $8) ',( f85&+O 672M381.7( '(5 h/866/,1,(1 '(6 J1$7@5/,&+ *(.@+/7(1K u835$/(,7(56 1,('(56&+/8*(1P j(87( .$11 0$1 h/866/,1,(1*,77(5 $8&+ '85&+ p(87521(1%(8*81* 2'(5 t$67(5O 7811(/0,.526.23,( %(2%$&+7(1P c%%P XPY =(,*7 (,1 d(,63,(/ )@5 (,1( c%%,/'81* '(6 h/866/,1,(1*,77(56 0,7 '(0 t$67(57811(/0,.526.23P f,( w56$&+( )@5 '$6 h/866/,1,(1O *,77(5 ,67 ',( s8$17,6,(581* '(6 0$*1(7,6&+(1 h/866(6 Jc%6&+1P XPTPSKP o$1 %($&+7(

Magnetisierung µ 0M (T)

0.06 A 0.04 B 0.02

C D

0

0

0.04

0.08

0.20 0.12 0.16 magnetisches Feld Ba (T)

0.24

0.28

0.32

0.36

c%%P XPZ o$*1(7,6,(581*6.859(1 921 5(,1(0 d/(, JcK 81' d/(,Ok1',80On(*,(581*(1 0,7 (,O 1(0 k1',80Oi(+$/7 921 T $7@ JdKN Z $7@ JeK 81' TR $7@ JfK -(:(,/6 %(, VPT mN 1$&+ L[bP

XPS i581'/(*(1'( c63(.7( '(5 u835$/(,781*

V[U

'(1 ./(,1(1 c%67$1' '(5 h/866/,1,(1 921(,1$1'(5 ,0 x(5*/(,&+ =85 i5?M( '(5 125O 0$//(,7(1'(1 d(5(,&+( ,0 |:,6&+(1=867$1' (,1(6 u835$/(,7(56 SP c57P Jc%6&+1P XPTPSK y,( %(,0 u835$/(,7(5 SP c57 ,67 ',( m21'(16$7,216(1(5*,( *(*(%(1 '85&+ ',( f,)O )(5(1= '(5 )5(,(1 g17+$/3,( ,0 1250$//(,7(1'(1 81' ,0 6835$/(,7(1'(1 |867$1'\ d JvK ~J

i1 JvK2i6 JvK 32 g 0 'd 3 R

x T d JvK N T ,R &7+

JXPZK

:2%(, 0,7 '(5 5(&+7(1 i/(,&+81* '$6 7+(502'&+(1*/(,&++(,7 d ~0$

d

d ~I

d ~0$

~J

g J2JdB,RK20K 'd 3 g 0 'd N

:,( $86 i/P JXPZK +(5925*(+7N %(67,007 :(5'(1 .$11 J6P c%%P XPXKP o$1 .$11 -('(1 u835$/(,7(5 SP c57 '85&+ |8/(*,(5(1 (,1(6 *((,*1(7(1 :(,7(5(1 &+(0,6&+(1 g/(0(176 =8 (,1(0 u835$/(,7(5 TP c57 0$&+(1P c%%,/'81* XPZ =(,*7 ',(6 $0 d(,63,(/ 921 r%N '$6 '85&+ |8/(*,(5(1 921 (,1,*(1 c720352=(17 k1 =8 (,1(0 u835$/(,7(5 TP c57 :,5'N :2%(, d&T 0,7 67(,*(1'(5 k1Om21=(175$7,21 $167(,*7P f,(6 />667 6,&+ $8) ',( $%1(+0(1'( 0,77/(5( )5(,( y(*/>1*( '(5 g/(.7521(1 =85@&.)@+5(1P d(, j2&+)(/'6835$/(,7(51 6,1' d&TOy(57( 921 9,(/(1 v(6/$ (55(,&+%$5P c%%,/'81* XP[ =(,*7 '(1 x(5/$8) 921 d& JvK )@5 (,1,*( u835$/(,7(5 SP c57 62:,( d&S JvKN d&T JvK 81' d&7+ JvK )@5 (,1,*( u835$/(,7(5 TP c57P y,5 +$%(1 +,(5 185 5(9(56,%/( u835$/(,7(5 TP c57 %(75$&+7(7P d(, ',(6(1 '5,1*7 h/866 %(,0 %(56&+5(,7(1 921 d&S 5(9(56,%(/ ,1 ',( r52%( (,1 81' :,5' %(, c%1$+0( 921 d$ :,('(5 $86 '(5 r52%( 9(5'5>1*7P v(&+1,6&+ :,&+7,* 6,1' ,55(9(56,%/( u835$/(,7(5 TP c57 J62*P +$57( u835$/(,7(5KN %(, '(1(1 '85&+ j$)7=(175(1N =P dP m5,67$//'()(.7( 2'(5 1250$//(,7(1'( g,16&+/@66(N 0$*1(7,6&+(5 h/866 %(, h(/'>1'(581* +$)7(1 %/(,%7P f,(6( j$)7=(175(1 9(5+,1'(51N '$66 %(,0 h/,(M(1 (,1(6 u75206 ',( n25(17=Om5$)7 =8 (,1(5 d(:(*81* '(5 h/866/,1,(1 81' '$0,7 =8 f,66,3$7,21 )@+57P f,(6( f,66,3$7,21 (1767(+7 '85&+ ',( d(:(*81* '(5 ,0 m(51 '(5 h/866/,1,(1 925+$1'(1(1 1250$//(,O 7(1'(1 g/(.7521(1 Jc%6&+1P XPTPTPKP f,( 2%(1 )@5 u835$/(,7(5 SP c57 ',6.87,(57(1 g170$*1(7,6,(581*6(5(.7( )@+5(1 ,1 (,1(0 u835$/(,7(5 TP c57 =8 (,1(5 m2(;,67(1= 0$.526.23,6&+(5 d(5(,&+( 921 )(/')5(,(5 o(,M1(5Or+$6( 0,7 '(5 u+8%1,.29Or+$6(N :(11 d$ " d&S " d()) ,67P f(5 x2//67>1O ',*.(,7 +$/%(5 6(, (5:>+17N '$66 ,1 (,1(0 u835$/(,7(5 TP c57 817(5 %(67,007(1 d(O ',1*81*(1 u835$/(,781* ,1 (,1(5 '@11(1 q%(59>&+(16&+,&+7 3$5$//(/ =80 >8M(5(1 h(/' %,6 =8 (,1(0 h(/' d&U W SPY d&T %(67(+(1 .$11P

XPSPV c8)75(7(1 921 u835$/(,781* f$6 r(5,2'(16&+/,&+ c/.$/,ON g5'$/.$/,O 81' g'(/0(7$//(KP w17(5 (,1(0 f58&. 921 VZ ir$ =(,*7 n, c1=(,&+(1 921 u835$/(,781* %(, TR mP h(51(5 75,77 u83O 5$/(,781* ,1 0$1&+(1 0(7$//,6&+(1 j2&+'58&.3+$6(1 921 p,&+70(7$//(1 :,( u,N i(N r 2'(5 c6 81' 62*$5 ,1 )(67(0 u$8(56725 $8)P

XPS i581'/(*(1'( c63(.7( '(5 u835$/(,781* Supraleitende und magnetische Elemente

H Li

Be

B

20

0.03

11

Na

Mg

K

Ca 15

Rb

Sc Ti 0.35 0.39

Sr

Y

4.0

2.7

Zr 0.55

V

Cr

Mn

5.3 Nb 9.2

Fe

Co

Ni

Cu

2.0 Mo Tc 0.923 7.8

Ru 0.5

Rh 0.32 mK

Pd

Ag

Ir

Pt

Au

Cs

Ba

La

Hf

Ta

W

Re

Os

1.5

5.1

5.9

0.13

4.4

0.01

1.7

0.65 0.14

Fr

Ra

Ac Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

V[W He

C

N

F

Ne

S 17

Cl

Ar

O 0.6

Al

Si

1.19

8.5

P 18

Zn

Ga

Ge

As

Se

1.09

5.4

2.7

5.6

Br 1.4

Kr

0.9

Cd In 0.55 3.4

Sn 3.7

Sb 5.6

Te 7.4

I 1.2

Xe

Po

At

Pn

Yb

Lu

Hg

Ti

Pb

Bi

4.15

2.4

7.2

8.7

Dy

Ho

Er

Tm

0.1

1.7 Th

Pa

U

1.37

1.3

0.2

Np

Pu

Am

Cm

Bk

Cf

Es

Fm

Md

No

Lw

0.8

c%%P XPSR u835$/(,7(5 ,0 r(5,2'(1666,*81* '(6 x(56&+,(O %81*6675206K )2/*7 d/ 32J-B,RK 527 527d/ 81' :(,7(5 :(*(1 527 527 3 *5$' ',920T 81' ',9d 3 R 0T d/ 3

,R d/ P -

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WTX

X u835$/(,781*

f,( o&o,//$1Oh250(/ Ji/P JXP[RKK 0$&+7 $8&+ ',( 6&+21 (5:>+17(1 c%:(,&+81O *(1 '(6 k62723(1(;321(17(1 # 920 y(57 RPW 9(567>1'/,&+N '(11 hJ6K *(+7 ',5(.7 ,1 + (,1N 81' 1,&+7 185 ,1 '(1 x25)$.725 af '(5 deuOh250(/P h@5 )5(,( g/(.7521(1 J," 3 RK 81' 6&+:$&+( m233/81* + "" S *(+7 i/P JXP[RK ,1 ',( deuOh250(/ i/P JXPXSK @%(5\ v& 6 mafn (;3J2SB+K 0,7 + 3 pJghKxR P g6 0866 %(7217 :(5'(1N '$66 pJghK 81' hJ6K 1,&+7 81$%+>1*,* 921(,1$1'(5 6,1'P g,1( +2+( (/(.7521,6&+( |867$1'6',&+7( %(, gh )@+57 =8 (,1(5 1,('5,*(1 f(%&+/,&+ 71'(7 0$1 (;3(5,0(17(// )@5 ',( u835$/(,7(5 ,1 '(1 9(56&+,('(1(1 'Od>1'(51 JU'N V'N W'K + 6 pJghK 0,7 -(:(,/6 817(56&+,('/,&+(1 x25O )$.725(1P f$6 y(,&+:(5'(1 '(6 i,77(56 '85&+ +2+( (/(.7521,6&+( |867$1'6',&+7(1 %(',1*7N '$66 ',( (17635(&+(1'(1 ,17(50(7$//,6&+(1 x(5%,1'81*(1 =8 i,77(5,167$%,O /,7>7(1 1(,*(1P |8 1(11(1 6,1' +,(5 ,16%(621'(5( ',( 62 *(1$117(1 .8%,6&+(1 cSWO r+$6(1 :,( p%Uu1 Jv& 3 SZPT mK 81' '$6 (5:>+17( p%Ui(P j,(5 %(67(+7 (,1( 67$5.( v(1'(1= =8 (,1(5 7(75$*21$/(1 x(5=(5581* 0,7 67$%,/(5 i,77(56758.785 81' '(87/,&+ 5('8=,(57(0 v& P f(112&+ *(/,1*7 (6N =P dP f5>+7( $86 p%Uu1 +(5=867(//(1 J,0 x(5%81' 0,7 (,1(5 e8Oo$75,;KN ',( ,1 6835$/(,7(1'(1 u38/(1 =85 g5=(8*81* +2+(5 67$7,21>5(5 o$*1(7)(/'(5 (,1*(6(7=7 :(5'(1P o,7 p%Uu1Ou38/(1 .$11 0$1 62 h(/'(5 %,6 @%(5 TR v %(, T m (55(,&+(1P

XPWPT u835$/(,7(5 0,7 0$*1(7,6&+(1 c720(1 n2.$/,6,(57( 0$*1(7,6&+( o20(17( .?11(1 ',( k038/6O 2'(5 u3,1.255(/$7,21 '(5 e223(5Or$$5( =(567?5(1N >+1/,&+ :,( (,1 >8M(5(6 o$*1(7)(/'P y(/&+(5 o(&+$1,6086 @%(5:,(*7N +>1*7 (176&+(,'(1' 921 '(5 u7>5.( '(5 y(&+6(/:,5.81* 81' '(5 5>80O /,&+(1 c125'181* '(5 c720( ,0 o(7$// $%P %(5/$33(1 ',( y(//(1)81.7,21(1 /2.$/,6,(57(5 0$*1(7,6&+(5 o20(17( 0,7 '(1(1 '(5 n(,781*6(/(.7521(1N 62 )@+57 ',(6 =85 c867$86&+:(&+6(/:,5.81*N ',( 0$1 '85&+ (,1(1 u3,1Oj$0,/721Oq3(5$725 $86'5@&.(1 .$11\

U 32T lu6 P

JXP[TK

j,(5 ,67 l '$6 c867$86&+,17(*5$/N u 81' 6 %(=(,&+1(1 ',( u3,123(5$725(1 '(5 /2.$O /,6,(57(1 o20(17( 81' '(5 n(,781*6(/(.7521(1P f,( c867$86&+:(&+6(/:,5.81* )@+57 =85 u3,19,3Ou75(881* 81' '$0,7 =85 e223(5Or$$5%5(&+81*N '$ '(5 u,1*8/(77O|8O 67$1' '(6 e223(5Or$$5(6 '85&+ ',( u75(881* =(567?57 :,5'P f,(6 :,5' +>87* )@5 6835$/(,7(1'( n(*,(581*(1 0,7 *(5,1*(5 m21=(175$7,21 0$*1(7,6&+(5 c720( %(O 2%$&+7(7P c%%,/'81* XPTW =(,*7 ',( %(5*$1*67(03(5$785 921 n$N '(0 -(:(,/6 S $7@ 921 u(/7(1(5'$720(1 %(,*(0,6&+7 :85'(P o$1 %(2%$&+7(7 (,1( 67$5.( v&Oc%6(1.81* (v&P f$6 c867$86&+,17(*5$/ ,67 ,1 ',(6(5 u(5,( l 6 RPS (x W &2167PN 620,7 =(,*7 c%%P XPTWN '$66 8(v& 8 1>+(581*6:(,6( 3523257,21$/ =80 i(6$0763,1 J81' 1,&+7 =80 *(6$07(1 0$*1(7,6&+(1 o20(17K '(5 %(,*(0,6&+7(1 u(/7(1(5'$720( ,67P g,1,*( c720352=(17 d(,0,6&+81* 921 k21(1 0,7 0$*1(7,6&+(1 o20(17(1 =(567?5(1 $/62 ',( u835$/(,781* 9?//,*N >+1/,&+(6 *,/7 )@5 %(5*$1*60(7$//,21(1N :(11 6,( %(,0 g,1O %$8 ,1 '$6 y,5760(7$// ,+5 0$*1(7,6&+(6 o20(17 %(+$/7(1N :,( h( 2'(5 o1 =P dP ,1 r%P

7

14

6

12

5

10

4

8

3

6 Spin

2

4

1 0

2 La

Ce

Pr

Pm Eu Tb Ho Tm Lu Dy Nd Sm Er Gd Yb Zusatz

WTY

magnetisches Moment in µ Bohr

Übergangstemperatur in K

XPW u3(=,(//( 6835$/(,7(1'( o$7(5,$/,(1

0

c%%P XPTW %(5*$1*67(03(5$785 v& =85 u835$/(,781* 921 n$N '(0 -(:(,/6 S $7@ 921 u(/7(1O (5'0(7$//(1 %(,*(0,6&+7 :85'( J25(1( u+5(1' (,1( 0$.O 526.23,6&+( r+$6(1.255(/$7,21N ',( )@5 '(1 6835$/(,7(1'(1 |867$1' &+$5$.7(5,67,6&+ ,67N (567 %(, v& (1767(+7P f$0,7 +$%(1 :,5 6&+21 ,03/,=,7 ',( }+1/,&+.(,7(1 =:,6&+(1 jvun 81' NN./$66,6&+(1DD u835$/(,7(51 (5:>+17\ g6 *,%7 $8&+ ,1 jvun e223(5Or$$5( 0,7 0$.526.23,6&+(5 y(//(1)81.7,21N $8&+ +,(5 1$&+*(:,(6(1 '85&+ ',( h/86648$1O 7,6,(581* 0,7 {R 3 +BT(P f$*(*(1 67(,*7 ',( n(%(16'$8(5 '(5 s8$6,7(,/&+(1 817(5+$/% v& 67$5. $1P y,5 :2//(1 ,0 h2/*(1'(1 (,1,*( :(,7(5( g,*(16&+$)7(1 '(5 jvun %(O 635(&+(1N ,1 '(1(1 ',(6( 6,&+ 921 ./$66,6&+(1 u835$/(,7(51 817(56&+(,'(1\ c1,62752O 3,(N m2+>5(1=/>1*(N h/866/,1,(1*,77(5 81' q5'181*63$5$0(7(5P

XPWPUPS c1,627523,( '(5 m835$76835$/(,7(5 d(',1*7 '85&+ ',( +2+( (/(.75,6&+( n(,7)>+,*.(,7 ,1 '(1 e8qTOg%(1(1 81' ',( *(5,1*( n(,7)>+,*.(,7 =:,6&+(1 '(1 u&+,&+7(1N 6,1' $8&+ ',( 6835$/(,7(1'(1 g,*(16&+$)7(1 6(+5 $1,627523P f,(6( c1,627523,( />667 6,&+ %(6&+5(,%(1 '85&+ (,1(1 9(5$//*(0(,O 1(57(1 i,1=%85*On$1'$8Oc16$7= *(.233(/7(5 6835$/(,7(1'(5 g%(1(1P f$1$&+ 6&+5(,%7 0$1 )@5 ',( )5(,( g17+$/3,(',5(5(1= (i6 =:,6&+(1 6835$/(,7(1'(0 81' 125O 0$//(,7(1'(0 |867$1'

6 0

# @T (i 3 s ' T 5 $ 851 8T 1 851 8V 1 T 0$% T 1 1

09

1

9 9 91 1

X51 X51 T 1 X; X
66,*7KP k1 i/P JXP[UK +$%(1 :,5 ',( c%/(,781* X5BX= '85&+ 851 2512S 8B6 ,0 ',6.5(7(1 c%67$1' 6 '(5 $%Og%(1(1 (56(7=7P o,7 51 3 851 8 ( ,3*N :2%(, $//( 851 8 $/6 */(,&+ $1*(1200(1 :(5'(1N :,5' '(5 /(7=7( u800$1' @T 85 8T JS2&26J31 2312SKKP T 0& 6 T 1

JXP[VK

f,(6 (17635,&+7 (,1(5 l26(3+621Om233/81* =:,6&+(1 '(1 e8qTOg%(1(1N ',( $8&+ (;3(5,0(17(// 1$&+*(:,(6(1 :85'(P f,( i,1=%85*On$1'$8Om2+>5(1=/>1*( ,67 :,('(5 '85&+ J. , JvKKT 3 @TBT 0, 8"JvK8 *(*(%(1 J, 3 $%N &KN 0,7 0$% "" 0& P y(*(1 T (5:$57(7 0$1 (,1( 67$5.( c1,627523,( '(6 2%(5(1 .5,7,6&+(1 h(/'(6 d&T 3 {R BT @ .in d&T P f,(6( :,5' $8&+ %(2%$&+7(7 Jc%%P XPUVKP f,( 2%(5(1 .5,7,6&+(1 h(/'(5 )@5 v S R 6,1' 62 +2&+N '$66 6,( (;3(5,0(17(// 1,&+7 ',5(.7 =8*>1*/,&+ 6,1'P f$+(5 1,007 0$1 d&T Jv 3 RK 3

0 1

{R v S2 T T /.inN v R &

JXP[WK

$% 3 $1 81' (5+>/7 '85&+ g;75$32/$7,21 Jv S RK $86 '(1 o(6681*(1 1$+( v& \ .inNR & JSPVuRPTK 10 81' .inNR 3 JRPTuRPSK 10P f,( ./(,1(1 y(57( 921 .in 6,1' 48$/,7$7,9 9(567>1'/,&+N :(11 0$1 ',( deuOm2+>5(1=/>1*( .e2 3 @9h B@DR %(75$&+7(7\ 9h W SRW 0B6 ,67 :(*(1 '(5 *(5,1*(1 n$'81*675>*(5.21=(175$7,21 J,1 {deq %(, 23O 7,0$/(5 f27,(581* (7:$ RPTW n?&+(5 352 e8qTOg/(0(17$5=(//( ,1 '(5 g%(1(K 1,('5,*(5 81' DR :(*(1 '(6 +2+(1 v&Oy(576 1$7@5/,&+ 9,(/ *5?M(5 $/6 ,1 ./$66,6&+(1 u835$/(,7(51P |86$00(1 0,7 '(1 (;3(5,0(17(// (50,77(/7(1 g,1'5,1*7,()(1 +$% W SVR 10 81' +& W YRR 10 (5*,%7 6,&+N '$66 jvun (;75(0( u835$/(,7(5 TP c57 6,1'P c8)*581' '(5 ./(,1(1 m2+>5(1=/>1*(1 . , '(5 jvun ,67 1$7@5/,&+ ',( c1=$+/ '(5 e223(5Or$$5( ,0 m2+>5(1=92/80(1 J. $%KT . & 9,(/ ./(,1(5 $/6 ,1 ./$66,6&+(1 u835$O /(,7(51N 81' '$0,7 6,1' h/8.78$7,21(1 9,(/ 67>5.(5 $86*(35>*7P f$+(5 %(2%$&+7(7

WUX

X u835$/(,781*

0.06

x = 6.94

x = 7.0

∆C/T in J/mol K2

0.04

0.02

0

Tc

Tc 70

80

90 100 70 Temperatur T in K

80

90

100

c%%P XPUW u3(=,76&+( y>50( e 921 {d$Te8UqX1; 0,7 ; W S 1$+( $0 6835$/(,7(1'(1 %(5O *$1*P eJvK =(,*7 .(,1(1 u3581* J*(675,&+(/7 ,67 '(5 +,(5)@5 (5:$57(7( x(5/$8) (,1*(=(,&+1(7KN 621'(51 (,1( +O)?50,*( c120$/,(N 1$&+ LWSbP

0$1 =P dP ,1 '(5 63(=,76&+(1 y>50( .(,1(1 u3581* %(, v& N 621'(51 (,1( +O)?50,*( u,1*8/$5,7>7N :,( 6,( 921 6835$98,'(0 Vj( 81' 921 0$*1(7,6&+(1 r+$6(1@%(5*>1*(1 %(.$117 ,67 Jc%%P XPUWKP

XPWPUPT h/866/,1,(1*,77(5 y,( ',( ./$66,6&+(1 u835$/(,7(5 TP c57 %,/'(7 6,&+ $8&+ ,1 jvun (,1 h/866/,1,(1*,77(5 2%(5+$/% '(6 817(5(1 .5,7,6&+(1 h(/'(6 d&S P k0 c//*(0(,1(1 %(:(*(1 6,&+ ',( h/866O /,1,(1 ,1 (,1(0 67520'85&+9266(1(1 u835$/(,7(5 TP c57 $8)*581' '(5 n25(17=Om5$)7 6(1.5(&+7 =85 u75205,&+781* 81' =80 o$*1(7)(/'P f,(6( d(:(*81* :,5' ,0 g1*O /,6&+(1 $/6 NN98; 92:DD %(=(,&+1(7P u,( :,5' '85&+ g,1%$8 921 j$)7=(175(1 5('8=,(57N ',( '85&+ (,1( /2.$/( x$5,$7,21 921 .N + 2'(5 d&7+ (,1( h/866/,1,( Jf85&+0(66(5 .K )(67+$/7(1 JNN3,11,1*DDKP f$ . ,1 jvun 6(+5 ./(,1 ,67N )@+5(1 +,(5 6&+21 f()(.7( 0,7 $720$5(1 c%0(6681*(1 =80 j$)7(1 921 h/866/,1,(1P v+(50,6&+ $.7,9,(57(6 j@3)(1 921 h/866/,1,(1 %(=(,&+1(7 0$1 $/6 NN98; &5((3DDP d(,'( g5(.7( )@+5(1 =80 c8)75(7(1 (,1(6 (1'/,&+(1 (/(.75,6&+(1 y,'(567$1'6 ,0 u835$/(,7(5P h@5 '(1 NN98; &5((3DD *,/7 1>+(581*6:(,6(

0

t W tR (;3 2

w .d v

0,7 '(5 c.7,9,(581*6(1(5*,( w33

0 1

T d&7+ .U P .d v

1

JXP[XK

JXP[YK

XPW u3(=,(//( 6835$/(,7(1'( o$7(5,$/,(1

WUY

Temperatur T in K 10

83

-4 91

77

ρ (µΩ cm)

-6

0 75

10-7 10

62.5

20 10

10

67

30

10-5

Widerstand ρ in Ω cm

71 40

2T

0.5T

-8

1.1

4T

1T

0.5

8T 4 2 1 80

85 T(K)

0T 90

95 100

8T

1.4 1.3 1.5 1.2 reziproke Temperatur in 10-2K-1

1.6

c%%P XPUX g/(.75,6&+(5 y,'(567$1' 0JvK 921 {d$Te8UqYOu&+,&+7(1 ,0 o$*1(7)(/' 3$5$//(/ =85 &Oc&+6(N $8)*(75$*(1 $/6 NNc55+(1,86Of$567(//81*DD /2* 0 *(*(1 SBvP g,1( i(5$'( ,1 ',(6(5 c8)75$*81* (17635,&+7 '(0 x(5+$/7(1 1$&+ i/P JXP[XKP f$6 k16(7 =(,*7 0JvK ,1 @%/,&+(5 f$5O 67(//81*N 1$&+ LWTbP

linearer thermischer Ausdehnungskoeffizient α in 10-6/K

6

a-Achse

b-Achse 11.4T

5

10.3T 9.1T

x = 7.0

8T 6.8T

4 3

0T

TC= 86.4 K

2 1

5.7T 4.6T 3.4T 0.5T 1.1T 0T 2.6T

11.4T 50

60

70

80

90 50 60 Temperatur T in K

70

80

90

100

c%%P XPUY v+(50,6&+(5 c86'(+181*6.2(5,=,(17 921 {d$Te8UqY />1*6 '(5 $O 81' '(5 %Ot,&+O 781* ,11(5+$/% '(5 e8qTOg%(1(1 ,1 9(56&+,('(1(1 $1*(/(*7(1 o$*1(7)(/'(51 d$ =:,6&+(1 R 81' SSPV vP f,( 6&+$5)( c120$/,( )@5 d$ 3 RN ',( '(5 c120$/,( '(5 63(=,76&+(1 y>50( (17O 635,&+7 J9*/P c%%P XPUWKN :,5' ,0 o$*1(7)(/' 9(5581'(7P |8 +?+(5(1 h(/'(51 75,77 (,1( 6&+$5)( u3,7=( $8)N ',( '$6 u&+0(/=(1 '(6 h/866/,1,(1*,77(56 J%(,0 c8):>50(1K 6,*1$/,6,(57P f,( 7+(5O 0,6&+( c86'(+181* (50?*/,&+7 :(*(1 '(5 t,&+781*6$%+>1*,*.(,7 $8&+ ',( g50,77/81* 921 c1,627523,(1P u2 %('(87(7 (,1( 1(*$7,9( J/,1.6K %=:P 326,7,9( J5(&+76K c120$/,(N '$66 v& 817(5 81,$;,$/(0 f58&. />1*6 '(5 (17635(&+(1'(1 m5,67$//5,&+781* $%1,007 %=:P =81,007N 1$&+ LWUbP

WUZ

X u835$/(,781*

j,(5 %(=(,&+1(7 3 '(1 d58&+7(,/N 80 '(1 6,&+ ',( m21'(16$7,216(1(5*,( '85&+ '$6 j$)7=(17580 >1'(57P k1 '(1 jvun ,67 . ./(,1N $%(5 $1'(5(56(,76 d&7+ *52MP f(5 :(O 6(17/,&+( w17(56&+,(' /,(*7 ,1 '(5 +?+(5(1 v(03(5$785P f,5(.7 817(5+$/% v& .$11 0$*1(7,6&+(5 h/866 5(9(56,%(/ ,1 ',( r52%( (,1O 81' $8&+ :,('(5 $86 ,+5 $8675(7(1P d(, 7,()(5 v(03(5$785N 817(5+$/% '(5 62 *(1$117(1 k55(9(56,%,/,7>76/,1,(N ,67 ',(6 1,&+7 0(+5 0?*/,&+P c%%P XPUX =(,*7N '$66 ,1 67$5.(1 o$*1(7)(/'(51 ,1 (,1(0 :(,7(1 d(O 5(,&+ (,1 (1'/,&+(5 y,'(567$1' 81' .(,1(6)$//6 NNu835$DD/(,781* 925/,(*7P j,(5 .$11 ',( v(03(5$785$%+>1*,*.(,7 '(6 y,'(567$1'6 '85&+ i/P JXP[XK %(6&+5,(%(1 :(5'(1P f(5 6&+$5)( g,16$7= 921 k55(9(56,%,/,7>7 %(, (,1(5 v(03(5$785 vhn .$11 $/6 r+$6(1O @%(5*$1* '(6 h/866/,1,(1*,77(56 ,17(535(7,(57 :(5'(1P q%(5+$/% 921 vhn /,(*7 ',( h/866/,1,(16&+0(/=( 925N 817(5+$/% 921 vhn '(5 h/866/,1,(1.5,67$// J0$1 635,&+7 $8&+ 921 x257(;Oh/@66,*.(,7 81' x257(;.5,67$//KP f,(6(5 r+$6(1@%(5*$1* />667 6,&+ =P dP 0,7 r5>=,6,2160(6681*(1 '(5 63(=,76&+(1 y>50( 2'(5 7+(50,6&+(1 c86'(+181* 1$&+:(,6(1P c%%,/'81* XPUY =(,*7 o(6681*(1 '(6 7+(50,6&+(1 c86'(+181*6.2()O 7=,(17(1 921 {deq )@5 =:(, 9(56&+,('(1( m5,67$//5,&+781*(1P

XPWPUPU q5'181*63$5$0(7(5 f(5 6835$/(,7(1'( q5'181*63$5$0(7(5 ,67 ,0 $//*(0(,1(1 h$// (;3(5,0(17(// 185 6&+:(5 =8*>1*/,&+N '$ (5 '85&+ (,1( c03/,78'( 81' (,1( r+$6( &+$5$.7(5,6,(57 :,5'P j>87* :,5' A :,( %(, '(1 ./$66,6&+(1 u835$/(,7(51 A ',( g1(5*,(/@&.( %(67,007N ',( 3523257,21$/ =85 c03/,78'( '(6 q5'181*63$5$0(7(56 ,67P g6 *,%7 (,1( x,(/=$+/ 921 g;3(5,0(17(1N ,16%(621'(5( v811(/0(6681*(1N ',( (,1( g1(5*,(/@&.( 921 (7:$ TD W JXuTK .d v& /,()(51N ',(6 ,67 (,1 j,1:(,6 $8) 67$5.( m233/81*P f$66 '(5 q5'181*63$5$0(7(5 $1,627523 ,67N @%(55$6&+7 $1*(6,&+76 '(5 67$5.(1 c1O ,627523,( =:,6&+(1 $%Og%(1(1 Je8qTOg%(1(1K 81' &Ot,&+781* 1,&+7P f(5 q5'181*6O 3$5$0(7(5 ,67 $%(5 $8&+ ,11(5+$/% '(5 g%(1(1 $1,627523 81' +$7 ,16%(621'(5( (,1( 1,('5,*(5( u667 6,&+ ,0 t$+0(1 '(5 deuOv+(25,( %(6&+5(,%(1P h@5 '(1 q5'181*63$5$0(7(5 JXP[ZK D. 32s x..A 8.A 9.A .A

+$77(1 :,5 )5@+(5 ,1 Ji/P JXPUPUKK D. $/6 ,627523 $1*(1200(1N 'P +P 0,7 92//(5 m8O *(/68M(5(1 0$*1(7,6&+(1 h/866 { )@5 (,1(1 l26(3+621Og&..217$.7 =:,6&+(1 (,1(0 6Oy(//(1O 81' (,1(0 'Oy(//(1Ou835$/(,7(5 J$86*(=2*(1K 81' =:,6&+(1 =:(, 6Oy(//(1Ou835$/(,7(51 J*(O 675,&+(/7KP c8&+ (,1 m$17(1.217$.7 =:,6&+(1 6Oy(//(1O 81' 'Oy(//(1Ou835$/(,7(5 /,()(57 '(1 *(675,&+(/7(1 x(5/$8)P J&K m5,7,6&+(5 u7520 ,1 c%+>1*,*.(,7 920 $1*(/(*7(1 o$*1(7)(/' )@5 (,1(1 r%B{d$Te8UqYOm$17(1.217$.7 J2%(1K 81' Og&..217$.7 J817(1KP f,( k16(76 =(,*(1 ',( *(:>+/7( i(20(75,( 0,7 {deqOm5,67$// 81' r%Ou&+,&+7N ',( '85&+ (,1( ,62/,(5(1'( d$55,(5( *(75(117 6,1' J1$&+ LWVbKP

n,7(5$785

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0

1

Metall Isolator Halbleiter

c%%P YPS[ i581'35,1=,3 '(6 oquOm21'(16$7256P c1 ',( c125'181* o(7$//.217$.7Ok62/$O 725Oj$/%/(,7(5OJq+0I6&+(5Ko(7$//.217$.7 :,5' (,1( u3$1181* $1*(/(*7P f,( '$'85&+ ,0 j$/%O /(,7(5 ,198(1=,(57( t$80/$'81* >1'(57 ,+5( y(,7( 0,7 '(5 u3$1181*P

YP[ j$/%/(,7(5%$8(/(0(17(

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JYPZVK

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Y j$/%/(,7(5 ρ (x ) q .ND

+

(a) (x )

x=0

l

x

l

x

l

x

q .N (x = 0) = - ε ε D . l +

0 HL

(b)

ψ (x ) 0 1 q .N ψ (x ) =-∫ (x )dx =- . ε ε D . (x-l )2 2 0 HL +

1 q .N 2 ψ (0) =- ε ε D .l 2 0 HL +

(c)

c%%P YPTR f,( t$80/$'81*69(57(,/81* 0J;K J$KN '$6 =8*(+?5,*( (/(.75,6&+( h(/' R J;K J%K 81' '(5 u3$1181*69(5/$8) J J;K @%(5 '(5 t$80/$'81*6=21(P Jd(5(&+1(7 ,0 t$+0(1 '(5 u&+277.+(581* '(5 r2,6621*/(,&+81*PK

1 Cdiff2

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c%%P YPTS e BwOm859( %(, 257681$%+>1*,*(5 t$80/$'81* 4p1 f ,0 t$+0(1 '(5 u&+277.+(581*P f(5 c167,(* /,()(57 p1 f P d(, *(.5@007(5 m859( ,67 pf 2576$%+>1*,*P f,( f,5(O 5(17,$7,21 '(5 m859( /,()(57 '$11 p1 J;KP f 2T ',))

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YP[PT d>1'(56&+(0$ '(6 oquOm21'(16$7256 i(+7 0$1 =81>&+67N 67$5. 9(5(,1)$&+(1'N 921 '(0 62*P r27(17,$/723)02'(// )@5 h(67O .?53(5 $86N (5+>/7 0$1 '$6 d,/' $86 c%%P YPTTP f$%(, :(5'(1 '$6 o(7$// 81' '(5 j$/%/(,7(5 '85&+ (,1(1 r27(17,$/723) '$5*(67(//7P 0 eV

Vakuum-Niveau

0 eV

q .Φ M

q .Φ HL

Vakuum-Niveau

EFHL

EFM (a)

(b)

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0 eV

q .Φ M EFM

q .ψ (x )

q .∆Φ MHL

EL EF EV

(a)

Metall

Isolator Halbleiter

(b)

Metall

Isolator Halbleiter

c%%P YPTU d5,1*7 0$1 =8 (,1(0 |(,7381.7 7 3 72 j$/%/(,7(5 81' o(7$// =86$00(1N 62 '$66 6,( '$6 */(,&+( x$.880Op,9($8 %(6,7=(1N (5*,%7 6,&+ (,1 u3581* '(5 h(50,Op,9($86 80 ',( f,5(5(1= '(5 c8675,776$5%(,7(1 4(Iojn P f$6 u/7 0$1 '$+(5 (,1( t$80/$'81* %=:P d$1'9(5%,(*81* 4J J;K ,0 j$/%/(,7(5 J%KP

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YP[ j$/%/(,7(5%$8(/(0(17(

W[Y

EL EF EV (a)

Metall

Isolator Halbleiter

E FM

(b)

EL E FHL

Metall

Isolator Halbleiter

EL E FHL

E FM (c)

EV

Metall

Isolator Halbleiter

EV

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ε ε A Cgeometrisch = 0 ox d ox

Cdiff =

dQ HL dU

c%%P YPTW g56$7=6&+$/7%,/' '(6 ,'($/(1 oquOm21'(16$7256P e*(20(75,6&+ 5(35>6(17,(57 ',( m$O 3$=,7>7N ',( '85&+ ',( q;,'6&+,&+7 %(67,007 ,67P k1 u(5,( '$=8 /,(*7 ',( 63$1181*6$%+>1*,*( j$/%/(,7(5.$3$=,7>7 e',)) N ',( '85&+ ',( 63$1181*6$%+>1*,*( }1'(581* '(5 t$80/$'81* 'sjn B'w *(*(%(1 ,67P

W[Z

Y j$/%/(,7(5 + +

EF

-

EL EF ET EV

(a)

E FM

Metall

Isolator Halbleiter

-

+ +

EL E FHL ET EV

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(a)

(b)

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(a)

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Metall Isolator Halbleiter Drain

(b)

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106 104

p-dotiertes Polyacetylen

102

Poly[p-Phenylen] Polypyrrol, Polythiohen

100

Polyphenylensulfid

10

-2

10-4 10-6 10-8 10-10

Isolatoren

Kupfer, Graphit

10

Germanium Silizium Galliumarsenid Silberbromid Glas

-12

10-14

Diamant, Nylon

10-16 10-18

c%%P ZPY 785P

Quarz, Teflon

g/(.75,6&+( n(,7)>+,*.(,7(1 9(56&+,('(1(5 h(67.?53(50$7(5,$/,(1 %(, t$807(03(5$O

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r P &R g

JZPSSK

h@5 '(1 t($/7(,/ '(5 ',(/(.75,6&+(1 h81.7,21 />667 6,&+ '(01$&+ (,1 d,/' (567(//(1N

YUT

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1 Polarisation

Orientierung +Atome + Elektronen

OrientierungsSchwingungen Oszillation der Atome Vibrationen elektronische Resonanz

Atome + Elektronen Elektronen

Frequenz Radio- und Mikrowellen

c%%P ZPZ

IR

UV

x$5,$7,21 '(5 (/(.75,6&+(1 r2/$5,6$7,21 $/6 h81.7,21 '(5 n,&+7)5(48(1=P

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JZPSTK

81' )@5 ',( .203/(;( ',(/(.75,6&+( h81.7,21 &5 3 &A5 2,&AA5 P

JZPSUK

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JZPSVK

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ZPT i581'/$*(1 237,6&+(5 g,*(16&+$)7(1 '(5 h(67.?53(5

YUU

u&+$/7(1 81' ',( g5=(8*81* 921 u800(1O 81' f,5(5(1=)5(48(1=(1P c//( ',(6( r52O =(66( 6,1' 0,7 '(1 (/(.7520$*1(7,6&+(1 o$7(5,$/*/(,&+81*(1 9(5.1@3)7N :(/&+( ',( %(=@*/,&+ '(5 (/(.75,6&+(1 h(/'67>5.( g 1,&+7/,1($5(1 c17(,/( '(5 r2/$5,6$7,21 r (17+$/7(1P g176&+(,'(1' 6,1' +,(5%(, ',( 1,&+7/,1($5(1 237,6&+(1 o$7(5,$/(,*(16&+$)O 7(1 2'(5 *(1$8(5 u86=(37,%,/,7>767(1625(1N :(/&+( ',( r2/$5,6$7,21 0,7 48$'5$7,6&+(1N .8%,6&+(1 81' +?+(5(1 r27(1=(1 '(5 (/(.75,6&+(1 h(/'67>5.(1 9(5.1@3)(1\ JTK r, J ) K 3 r,2 14,-JSK J2) K g- J ) K14,-. J2)] )S N )TK g- J )SK g. J )TK JUK J2)] )S N )T N )UK g- J )SK g. J )TK g/ J )UK1P P P P 14,-./

JZPSWK

k1 i/P JZPSWK %(6&+5(,%7 4,-JSK (,1(1 r52=(66 (567(5 q5'181* 81' '(&.7 620,7 '(1 *(O JTK %(6&+5(,%7 6$07(1 d(5(,&+ '(5 /,1($5(1 q37,. $% Jd5(&+81* 81' c%62537,21KP 4,-. JUK )2/*/,&+ (,1(1 r52=(66 =:(,7(5 81' 4,-./ (,1(1 r52=(66 '5,77(5 q5'181*P j,(5%(, ,67 (,1( u800$7,21 @%(5 ,'(17,6&+( k1',=(6 $1*(1200(1P f,( v(1625(1 :(,6(1 :,&+7,*( u+5(1' )@5 ',( v(1625(1 *(5$'=$+/,*(5 u78)( 4,-JSK JUK 81' 4,-./ J',( u78)( ,67 '85&+ ',( |$+/ '(5 k1',=(6 %(67,007K ',( 1,&+7/,1($5(1 v(1O 625.20321(17(1 $8&+ ,1 =(17526+17N =:(, d(',1O *81*(1 (5)@//7 6(,1\ (567(16 '$5) '$6 o$7(5,$/ .(,1 u7 =:(,7(5 q5'181* 4 JTKP f(5 r2&.(/6Og5(.7 %(:,5.7 (,1( f()250$7,21 '(6 d5(&+=$+/Og//,362,'6 817(5 g,1:,5.81* (,1(6 (;7(51(1 (/(.7O 5,6&+(1 h(/'(6 *(0>M U

( JSB1& TK, 3 s 5,- g-3S

81' 5,- 6 4 JTK N

JZPSXK

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YUV

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

1,&+7/,1($5,7>7 *52M *(18*N /$66(1 6,&+ 6(/%67 0,7 ./(,1(1 h(/'(51 JW xB=0K ,1 o,.O 52,17(5)(520(7(51 62 *52M( d5(&+=$+/817(56&+,('( 81' '$0,7 237,6&+( i$1*',5(O 5(1=(1 (5=(8*(1N '$66 ',( n,&+7,17(16,7>7 :,5.81*692// 02'8/,(57 81' 62*$5 ',( i5(1O =(1 R@ 81' SRR@ )$67 92//67>1',* (55(,&+7 :(5'(1P f$%(, :,5' '(87/,&+N '$66 1(%(1 '(1 1,&+7/,1($5(1 g,*(16&+$)7(1 $8&+ ,16%(621'(5( ',( u758.785,(5%$5.(,7 (,1(6 o$O 7(5,$/6 921 (176&+(,'(1'(5 d('(8781* ,67P f(5 0,7 4 JUK %(+$)7(7( v(50 )@+57 =80 x,(5:(//(10,6&+(1 Jg5(.7( '5,77(5 q5'O 181*K 81' %(6&+5(,%7 $/6 u3(=,$/)>//( ',( h5(48(1=9(5'5(,)$&+81* 81' '(1 (/(.75223O 7,6&+(1 m(55Og5(.7P h@5 ',( c1:(1'81* %(621'(56 ,17(5(66$17 ,67 ',( ,17(16,7>76$%O +>1*,*( d5(&+=$+/ (,1(6 4 JUKOo$7(5,$/6P j,(50,7 /$66(1 6,&+ =P dP t(621$7256758.785(1 5($/,6,(5(1N ',( -( 1$&+ c1:(6(1+(,7 (,1(5 237,6&+(1 u&+$/7:(//( ',( d/2&.,(581* 2'(5 ',( v5$160,66,21 (,1(5 237,6&+(1 u,*1$/:(//( 5($/,6,(5(1 JNN$//O237,&$/ 6:,7O &+,1*DDKP f,( u86=(37,%,/,7>7 4 JUK 0866 $//(5',1*6 *52M *(18* 6(,1N 80 (,1( $865(,O &+(1'( }1'(581* ,1 '(1 c86%5(,781*6(,*(16&+$)7(1 (,1(6 237,6&+(1 u75$+/6 @%(5 ',( d$8(/(0(17(/>1*( n =8 9(5856$&+(1P i/(,&+=(,7,* 0@66(1 $%(5 $8&+ ',( c%6253O 7,2169(5/867( 6(+5 *(5,1* 6(,1N :$6 =8 (,1(5 d(6&+5>1.81* $8) 1,&+75(621$17( g5(.7( =:,1*7P m21-8*,(57( r2/7(1 (55(,&+7 :85'(1P x?//,* 1(8( r(563(.7,9(1 (5?51(1 +,(5 1(8(67( g17:,&./81O *(1 :,( NNq37,&$/ e$6&$',1*DDP j,(50,7 /$66(1 6,&+ 80 i5?M(125'181*(1 67>5.(5( g5(.7( (5=(8*(1 81' ,1 d$8(/(0(17(1 187=(1N ',( 92//.200(1 237,6&+ $5%(,7(1P

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ZPU f,(/(.75,6&+( o$7(5,$/,(1

YUW

3+*7 81' 9(5+$/) 8P $P '(5 237,6&+(1 m20081,.$7,2167(&+1,. =80 f85&+%58&+P k0 h2/*(1'(1 :(5'(1 $/6 d(,63,(/ '5(, i/$6$57(1 $1*()@+57N :(/&+( 6,&+ %(=@*/,&+ v5$160,66,216(,*(16&+$)7(1N j(567(/O /81*6.267(1N j$1'+$%%$5.(,7 81' g,16$7=)(/'(51 :(6(17/,&+ 921(,1$1'(5 817(5O 6&+(,'(1P k1 '(5 t(,+( J$K p$TqOdTqUOu,qTN J%K u,qTOi(qT 81' J&K |5hTOd$hTOn8hUO v+hVOi'hVOc/hU 9(56&+,(%7 6,&+ ',( 63(.75$/( n$*( '(6 f>03)81*60,1,0806 921 J$K 1$&+ J&K ,00(5 0(+5 ,16 k1)5$527(N :2%(, */(,&+=(,7,* ',( 0$;,0$/( 237,6&+( v5$16O 0,66,21 (5+(%/,&+ =81,007N $%(5 ',( j$1'+$%%$5.(,7 %(75>&+7/,&+ 9(56&+/(&+7(57 :,5'P

ZPUPSPS i581'/$*(1 81' u758.785 c/6 h(67.?53(5 %(=(,&+1(7 0$1 (,1 67(,)(6 o$7(5,$/N '$6 1,&+7 =8 9,(M(1 %(*,117N :(11 0$1 (6 02'(5$7(1 m5>)7(1N u3$1181*(1 2'(5 f5(+020(17(1 $866(7=7P w0 ',(6( e+$5$.7(5,6,(581* =8 48$17,7=,(5(1\ h(67.?53(5 :(,6(1 x,6.26,7>7(1 2%(5+$/% 921 SRSUPX .*B6 6 &0 $8)P g,1 h(67.?53(5 :,5' $/6 $0253+ %(=(,&+1(7N :(11 (5 .(,1(

sta kri

g

rti

sa

gla

llin

Schmelze

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ZPU f,(/(.75,6&+( o$7(5,$/,(1 Brechzahl

YUY

Resonanzen der Oszillationen der Atome

(Realteil der komplexen Brechzahl)

elektronische Resonanzen

1

1011

1012

1013

1014

Absorption Extinktionskoeffizient

IR

(Imaginärteil der komplexen Brechzahl) 0 1010

c%%P ZPSR 48(1=P

1011

1012

1015

1016

sichtbarer Bereich

0 1010

1013

1014

1015

1017 Frequenz/Hz

UV

1016

1017 Frequenz/Hz

x$5,$7,21 '(5 d5(&+=$+/ 81' '(5 c%62537,21 921 s8$5=*/$6 $/6 h81.7,21 '(5 h5(O

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YUZ

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

UV-

Str

OH--Absorption

eu

un

g

orpt

800

n

igh

Abs

0.1 600

c%%P ZPSS /(1/>1*(P

yle

bsor ptio

Ra 1

ion

1000 1200 1400 Wellenlänge/nm

IR-A

log Dämpfung/(dB/km)

10

1600

1800

c%62537,21 J+,(5 u&+:>&+81*6.2(5,=,(17K 921 s8$5=*/$6 $/6 h81.7,21 '(5 y(/O

:(1'81*6=:(&. Jn(,6781*6)>+,*.(,7N y(//(1/>1*(1)(167(5N m267(1K .$11 '(01$&+ (,1( h$6(5 0,7 (17635(&+(1'(5 i/$6$57 *(:>+/7 :(5'(1P f$ ',( 63(.75$/( e+$5$.O 7(5,67,. '(5 t$7=/,&+ '$921N '$66 (,1( u7$1'$5'Oo21202'(Oi/$6)$6(5 62 .216758,(57 :(5'(1 .$11N '$66 6,&+ ',( c17(,/( '(5 o$7(5,$/',63(56,21 81' '(5 y(//(1/(,7(5',63(56,21 ,0 f,63(56,216.2(5,=,(17(1 *(5$'( .203(16,(5(1N :,( ,0 )2/*(1'(1 c%6&+1,77 *(O =(,*7 :,5'P

ZPUPSPU y(//(1/(,7(1'( g,*(16&+$)7(1 '(5 s8$5=*/$6)$6(5 81' f,63(56,216$57(1 g,1( d(*5(1=81* '(5 0$;,0$/ @%(575$*%$5(1 d,75$7( :,5' (,1(56(,76 '85&+ f>03O )81* 81' $1'(5(56(,76 '85&+ n$8)=(,7817(56&+,('(N *(1$8(5 *(6$*7 '85&+ f,63(5O 6,216(5(.7( J6P 8PK 9(5856$&+7 81' +>1*7 6(+5 921 c8)%$8 81' o$7(5,$/.20326,O 7,21(1 '(5 h$6(51 $%P o,7 j,/)( '(6 u75$+/(102'(//6 .$11 $8) '(5 d$6,6 9,(/)$&+(5 ,17(51(5 v27$/5(9(;,21(1 ',( y(//(1/(,781* 9(5$16&+$8/,&+7 :(5'(1 Jc%%P ZPSTKP k0 u75$+/(102'(// %(:,5.7 %(, '(5 u78)(13527/Oh$6(5 ',( v27$/5(9(;,21 $0 d5(&+=$+/O 63581* Jh$6(5.(51 1& S N h$6(50$17(/ 1& TK ',( n,&+7)@+581*P f,(6(6 o2'(// ,67 -('2&+ $86 0(+5(5(1 i5@1'(1 81=85(,&+(1'P g567(16 '5,1*7 '$6 n,&+7N :,( '$6 y(//(102'(// Jj(/0+2/7=*/(,&+81*K =(,*7N -( 1$&+ d5(&+=$+/3527/ 0(+5 2'(5 :(1,*(5 ,1 '(1 o$17(/ (,1 J6P c%%P ZPSUKP |:(,7(16 /,()(57 (,1 NN.@5=(5(5DD y(* 1,&+7 =:$1*6/>87* (,1( .@5=(5( n$8)=(,7 (,1(6 n,&+738/6(6 J6P 8PKP f5,77(16 ,67 1,&+7 ',( r+$6(1*(6&+:,1',*.(,7N 621O

ZPU f,(/(.75,6&+( o$7(5,$/,(1 Brechzahlprofil

LWL-Typ

Wellenausbreitung

r -a

Multimode mit Stufenprofil

0

d

a n2 n 1 r Multimode mit -a Gradienten0 profil d

n

n (r )

KernDämpfung Gesamtdurchmesser durchmesser in dB/km in µm in µm

YU[

numerische Apertur

Glas-Glas 50...500, Standard für LWL 50, (Polymere 600...3000)

Glas-Glas 100...1000, Standard für LWL 125

bei 0.85 µm 2...10, bei 1.3 µm 0.4...10

0.2...0.4

40...100, Standard für LWL 50

100...200, Standard für LWL 125

bei 0.85 µm ≈2, bei 1.3 µm ≈0.4

0.2...0.4 für Eintritt in Achsennähe

bei 0.85 µm ≈ 4, bei 1.55 µm ≈8

100...200

bei 0.85 µm ≈ 2.5, bei 1.55 µm ≈ 0.18

0.1...0.2

a n2 n 1 n

Monomode

r -a d 0 a n2 n 1

n

c%%P ZPST s8$5=*/$6On,&+7:(//(1/(,7(5 JnynK\ 6&+(0$7,6&+( f$567(//81* 921 i581'7581* '(5 c86%,/'81* (,1=(/1(5 o2O '(1P |8 '(1 ,1',9,'8(//(1 o2'(1 .255(6321',(5(1 *$1= %(67,007( y,1.(/N '(11 185 ',(6( (5/$8%(1 .216758.7,9( k17(5)(5(1= 1$&+ =:(, $8)(,1$1'(5)2/*(1'(1 t(9(O ;,21(1 LSYbP k1 08/7,02',*(1 u78)(13527/)$6(51 )@+5(1 ',( n$8)=(,7817(56&+,('( '(5 o2'(1 $0 h$6(5$86*$1* =8 %(75>&+7/,&+(1 NNx(56&+0,(581*(1DD 921 d,70867(51 81' 620,7 =8 (,1(5 67$5.(1 d(*5(1=81* '(6 d,75$7(1On>1*(1Or52'8.7(6P d(, i5$',(17(1O 3527/Oh$6(51 :,5' ',(6 '85&+ '$6 0$M*(6&+1(,'(57( d5(&+=$+/3527/ :(,7*(+(1' .203(16,(57N '(11 J67$5. 9(5(,1)$&+7K 35277,(5(1 ',( >8M(5(1 u75$+/(1 921 '(1 >8O n2 n1 m=1 Eigenfunktion (Modenprofil)

n2 n1 m=0

c%%P ZPSU

f$567(//81* =:(,(5 $86%5(,781*6)>+,*(5 o2'(1 ,0 y(//(1O 81' u75$+/(102'(//P

YVR

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

Man tel,

Steig u

ω

ng = c n1

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ω cut - off

m=2 m=1

m=0 rn

Ke

u

eig

t ,S

c = n2 g n

βm

c%%P ZPSV u&+(0$7,6&+( f$567(//81* '(5 f,63(56,2165(/$7,21 (,1(5 s8$5=*/$6)$6(5N )81'$O 0(17$/(5 o2'( 0 3 RN o2'( (567(5 q5'181* 0 3 SN o2'( =:(,7(5 q5'181* 0 3 TP

ZPU f,(/(.75,6&+( o$7(5,$/,(1

YVS

%(1$&+%$57( y(//(1/>1*(1 817(56&+,('/,&+N :$6 (,1( /(,&+7 9(56&+,('(1( (5(.7,9( d5(&+=$+/ 9(5856$&+7P f$0,7 ,67 ',( (5(.7,9( d5(&+=$+/ $8&+ @%(5 ',( y(//(1/(,7(5O 6758.785 12&+0$/6 921 '(5 y(//(1/>1*( $%+>1*,*P g6 62// 12&+0$/6 %(7217 :(5'(1N '$66 67(76 $8&+ (,1( ',5(.7( c%+>1*,*.(,7 '(5 d5(&+=$+/ 921 '(5 y(//(1/>1*( 925/,(*7 Jo$7(5,$/',63(56,21KP p$&+ c%%P ZPSV ,67 '(5 n,&+7:(//(1/(,7(5 )@5 6 " 6&87O2)) (,1O 02',*N (6 (;,67,(57 185 12&+ (,1 g,*(1:(57 81' (6 '20,1,(57 ',( e+520$7,6&+( f,6O 3(56,21 Jy(//(1/(,7(5',63(56,21 3/86 o$7(5,$/',63(56,21KP i(1$8 *(1200(1 ,67 )@5 ',( e+520$7,6&+( f,63(56,21 1,&+7 ',( y(//(1/>1*(1$%O +>1*,*.(,7 '(5 d5(&+=$+/ $866&+/$**(%(1'N 621'(51 ',( y(//(1/>1*(1$%+>1*,*.(,7 '(6 o$7(5,$/',63(56,216.2(5,=,(17(1 o0 N '(5 0,7 '(5 =:(,7(1 c%/(,781* '(5 d5(&+O =$+/ 921 '(5 y(//(1/>1*( .255(/,(57 ,67 LSWbP o,7 j,/)( .203/,=,(57(5 d5(&+=$+/3527/( *(/,1*7 (6N '$66 '(5 &+520$7,6&+( f,63(56,216.2(5,=,(17 o&+ (,1(5 i/$6)$6(5 62 0$MO *(6&+1(,'(57 :(5'(1 .$11N '$66 6,&+ (567(16 ',( c17(,/( '(5 o$7(5,$/',63(56,21 Jc%%P ZPSR 2%(1 81' c%%P ZPSWK 81' '(5 y(//(1/(,7(5',63(56,21 Jc%%P ZPSWK %(, (,1(5 %(67,007(1 y(//(1/>1*( *(5$'( $8)+(%(1 LSZbP |:(,7(16 />667 6,&+ ',(6( y(//(1/>1*( 9(56&+,(%(1 81' )(51(5 (,1 5(/$7,9 $86*('(+17(5 d(5(,&+ 0,7 6(+5 *(5,1*(0 &+520$O 7,6&+(1 f,63(56,216.2(5,=,(17(1 5($/,6,(5(1 Jc%%P ZPSWK LSYN S[bP Mm

M Einfachmantelprofil

Mch

0 Mw 1.27 1.30

Zweifachmantelprofil

0

Mch Mw

-5 Dreifachmantelprofil

λ

Mm

M

1.46

M

λ

1.76 Mch

0

Vierfachmantelprofil

-5 M

1.36

1.62

λ

0

λ

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YVT

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

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YVU

E4 E3

E3

E2 (b)

E1 E3

E2

E2 Relaxation

(a) E1

(c)

E1

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YVV

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

Intensität

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I

(a)

800

Er 3+

1000

1200

II

1400

1600

Intensität

Absorption (Pumpbänder) Emission (Verstärkungsbänder) Nd 3+

800

1000

Intensität

(b)

1.2 1260 1360 1460 1565 1675 1530 1625 O E S C L U Pr 3+

III III

(c)

800

1000

1200

1400

1600 Wellenlänge/nm

c%%P ZPSY J$K 81' J%K v5.81*6%>1'(5 $1P

ZPU f,(/(.75,6&+( o$7(5,$/,(1

YVW

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Transmissionsverlust/(dB/km)

102

(a)

10 1 10-1

(b)

10-2 10-3 10-4

1

2 3 Wellenlänge/µm

4

5

c%%P ZPSZ c%*(6&+>7=7( 63(.75$/( c%+>1*,*.(,7 '(6 237,6&+(1 x(5/867(6 Jf>03)81*K 921 h/825,'*/$6)$6(51N J$K 1$&+ LUTbN J%K 1$&+ LUSbP

YVX

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

Kleinsignalverstärkung/dB

'5(, s8(//(1 '(5 ,175,16,6&+(1 x(5/867( 6,1' $8&+ +,(5%(, ',( wxOc%62537,21N ',( t$6(51P g,1 :(,7(5(6 r52%/(0 '(5 h/825,')$6(51 ,67 ,+5( d5@&+,*.(,7 81' ,+5( g0371'/,&+.(,7 *(*(1@%(5 (;7(51(1 g,19@66(1 :,( h(8&+7,*O .(,7P f$ h/825,')$6(51 81*@167,*(5:(,6( :$66(5/?6/,&+ 6,1'N .$11 $8) (,1( +(50(7,6&+ $%',&+7(1'(N 6&+@7=(1'( x(5*@781* J(1*/P &2$7,1*KN =P dP $86 o*q 2'(5 o*hT N 1,&+7 9(5=,&+7(7 :(5'(1P v527= '(5 *52M(1 7(&+12/2*,6&+(1 u&+:,(5,*.(,7(1 ,67 (6 *(/81*(1N $8) (,1(0 .85=(1 h/825,')$6(567@&. (,1( f>03)81* 921 185 RPRTW 'dB.0 =8 (55(,O &+(1 LUUbP g,1( u$00/81* 921 ,17(5(66$17(1 %(56,&+76$57,.(/1 ,67 ,1 LUVb (17+$/7(1P k0 i(*(16$7= =8 s8$5=*/$6)$6(51 .?11(1 h/825,')$6(51 :(6(17/,&+ +?+(5 0,7 $1O '(5(1 u725(1 '27,(57 :(5'(1 81' 9(5635(&+(1 '$'85&+ ,1 h$6(59(567>5.(51 (,1( +?O +(5( g5,=,(1=P c%%P ZPS[ =(,*7 ',( 63(.75$/( m/(,16,*1$/Ox(567>5.81* (,1(6 h/825,'O )$6(59(567>5.(56 1$&+ LTTbP f85&+ ',( f27,(581* 921 h/825,')$6(51 0,7 v0N j2N g5N r5 81' p' .?11(1 1(%(1 '(5 c1:(1'81* ,1 h$6(59(567>5.(51 $8&+ h$6(5/$6(5 +(5*(67(//7 :(5'(1N :(/&+( ,1 '(1 y(//(1/>1*(1%(5(,&+(1 =:,6&+(1 RPW =0 81' U =0 (0,77,(5(1P 30 25 20 48 nm

15 10 5 0 1260

1270

1280

1290 1300 1310 Wellenlänge/nm

1320

1330

1340

c%%P ZPS[ u3(.75$/( x$5,$7,21 '(5 m/(,16,*1$/9(567>5.81* (,1(6 r5O'27,(57(1 h/825,')$6(5O x(567>5.(56 )@5 (,1( r803/(,6781* 921 V[R 0y 1$&+ LTTbP

ZPUPT c0253+( ',(/(.75,6&+( o$7(5,$/,(1 )@5 f@117/0O 81' y(//(1/(,7(5O 6758.785(1 c0253+( J*/$6$57,*(K o$7(5,$/,(1 71'(1 ,1 '(5 q372(/(.7521,. x(5:(1'81* ,1 h250 921 o8/7,6&+,&+76758.785(1 )@5 u3,(*(/ 81' 237,6&+( d(6&+,&+781*(1 J(1*/P &2$7O ,1*6KN $/6 y(//(1/(,7(50$7(5,$/,(1N $/6 237,6&+ 1,&+7/,1($5( o$7(5,$/,(1 +$8376>&+/,&+ )@5 o2'8/$725(1 81' 62*$5 $/6 (;27,6&+( n$6(50$7(5,$/,(1P k0 t$+0(1 '(5 925/,(O *(1'(1 c%+$1'/81* :,5' $0253+ 81' */$6$57,* $/6 */(,&+:(57,*( d(=(,&+181*(1 *(%5$8&+7P c8) *(5,1*( w17(56&+,('( (,1=8*(+(1N :@5'( '(1 t$+0(1 '(5 925/,(O *(1'(1 c%+$1'/81* 635(1*(1P

ZPU f,(/(.75,6&+( o$7(5,$/,(1

YVY

Reflektivität

c8) '(5 d$6,6 921 x,(/)$&+6&+,&+76758.785(1 /$66(1 6,&+ $8) '(1 h$&(77(1 2372O (/(.7521,6&+(5 d$8(/(0(17( 81' 237,6&+(5 m20321(17(1N :,( =P dP n,16(1 81' r5,6O 0(1N 6(+5 +2&+:(57,*( 237,6&+( x(5*@781*66&+,&+7(1 0,7 2;,',6&+(1N 1,75,',6&+(1 81' 9825,',6&+(1 f,(/(.75,.$ 5($/,6,(5(1 LUWbP f$%(, .?11(1 ',( 63(.75$/(1 g,*(1O 6&+$)7(1 Jt(9(;,216O 81' v5$160,66,21663(.7580K 0$M*(6&+1(,'(57 :(5'(1 81' =P dP c17,5(9(;9(5*@781*(1N +?&+675(9(.7,(5(1'( u3,(*(/9>&+(1 2'(5 237,6&+( h,/7(5 5($/,6,(57 :(5'(1P f$%(, .20%,1,(57 0$1 o$7(5,$/,(1 817(56&+,('/,&+(5 d5(&+=$+/ :,( =P dP u,UpV N u,qT N v,qT N |5qT N j)qT N p%TqW N v$TqW N v,p; N o*qN e$hT N o*hT N e$qN e$qT N v,eN xTqW N v$e 81' c/TqU P f,( j(567(//81* ',(6(5 u&+,&+7(1 (5)2/*7 0,77(/6 c8)'$03)(1N c8)63877(51 2'(5 i$63+$6(1'(326,7,21P k1 c%%P ZPTR J2%(1 5(&+76K ,67 ',( 63(.75$/( t(9(.7,9,7>7 tJ+K (,1(5 o8/7,6&+,&+7O 6758.785 0,7 -(:(,/6 SV r(5,2'(1 *(=(,*7N :2%(, (,1( r(5,2'( $86 TXZ10 u,qT BS[Z 10 u,UpV %(67(+7P |:,6&+(1 SPUY =0 81' SPXWU =0 =(,*7 ',(6(5 u3,(*(/ (,1( (;75(0 +2+( t(9(.7,9,7>7 J%(, + 3 SPV[W =0 ,67 t0$; 3 RP[[Y[K LUXbP

maximale Reflektivität

99.9999 %

1.0 0.8 0.6 0.4 0.2 0

Rmax

1000 1200 1400 1600 1800 2000 2200 Wellenlänge/nm

InP/Luft, α InP = 3.34 cm-1

99.999 % 99.99 %

α = 0.1 cm-1 α = 1 cm-1

Si3N4/SiO2

99.9 % 99 %

SiO2/Si3N4

α = 10 cm-1

AlAs/GaAs

90 % 0

5

15 10 Anzahl der Gitterperioden

20

25

30

c%%P ZPTR o8/7,6&+,&+7Ou758.785 (,1(6 fdtOu3,(*(/6 J/,1.(6 v(,/%,/'K 0,7 t(9(;,21663(.7O 580 J5(&+7(6 v(,/%,/'KP f(5 r)(,/ ,0 5(&+7(1 v(,/%,/' 0$5.,(57 ',( 0$;,0$/( t(9(.7,9,7>7N :(/&+( $/6 h81.7,21 '(5 r(5,2'(1=$+/ 3 ,0 j$837%,/' )@5 9(56&+,('(1( o$7(5,$/603)81* 9(56&+,('(1(5 r2/03)81* 921 r2/1*(5( y(&+6(/:,5.81*6675(&.(1 '(6 n,&+7(6 '(5 y(//(1/>1*( + 0,7 '(0 o$7(5,$/ (5)25'(5/,&+ 0$&+7P f$%(, =$+/7 6,&+ '(5 *52M( 237,6&+( v5$163$5(1=%(5(,&+ 921 UWR10 " + " VPW =0 $86N '(5 ',( t($O /,6,(581* $8&+ />1*(5(5 d$8(/(0(17( (50?*/,&+7P n,p%qU ,67 (,1 237,6&+ '233(/O %5(&+(1'(6 J(,1$&+6,*(6K o$7(5,$/ 0,7 (,1(5 d5(&+=$+/N ',( :(6(17/,&+ *5?M(5 $/6 ',( 921 i/$6 ,67N :$6 -('2&+ c17,5(9(;%(6&+,&+781*(1 )@5 ',( n,&+7(,1.233/81* (5)25O '(5/,&+ 0$&+7P f,( d5(&+=$+/(1 )@5 '(1 25'(17/,&+(1 u75$+/ 12 81' '(1 $8M(525O '(17/,&+(1 u75$+/ 1& ( 6,1' ,1 v$%P ZPU )@5 (,1,*( y(//(1/>1*(1 $1*(*(%(1P n,p%qU ,67 (,1 +(5$865$*(1'(6 (/(.752O237,6&+(6 o$7(5,$/P d(, + 3 XUR 10 :85'( )@5 '(1 (/(.752237,6&+(1 m2(5,=,(17(1 5UU ,0 g;3(5,0(17 US 6 SR2ST 0Bx (50,77(/7N :$6 6(+5 1$+ $1 '(0 7+(25(7,6&+ %(5(&+1(7(1 y(57 921 UX 6 SR2ST 0Bx /,(*7P f,(6 (5/$8%7 =P dP ',( t($/,6,(581* 921 o2'8/$725Od$8(/(0(17(1N ',( 0,7 5(/$7,9 *(5,1*(1 u3$1181*(1 =:,6&+(1 W x 81' SR x %(75,(%(1 :(5'(1 .?11(1P n,p%qU %(6,7=7 (,1( 75,*21$/( m5,67$//61*,*.(,7 '(5 d5(&+O =$+/>1'(581* $/6 h81.7,21 '(5 v,7$1 Jv,KOm21=(175$7,21 %=:P '(5 g,1'5,1*7,()(P f,( d5(&+=$+/(1 1(+0(1 0,7 67(,*(1'(5 m21=(175$7,21 =8N $//(5',1*6 =(,*(1 ',( 25'(17/,&+( 81' ',( $8M(525'(17/,&+( d5(&+=$+/ 817(56&+,('/,&+( )81.7,21(//( c%O +>1*,*.(,7(1 Jc%%P ZPTUKP y(//(1/(,7(5 :(5'(1 :,( )2/*7 5($/,6,(57\ c8)'$03)(1 (,1(6 o(7$//7/06 J=P dP v,7$1KN 3+272/,7+2*5$3+,6&+( u758.785,(581* 81' 7+(50,O 6&+( g,1',586,21P f,( $8)*('$03)7( v,Ou&+,&+7',&.( /,(*7 '$%(, 71'(581* .$11 $8&+ '85&+ r52721(1$867$86&+ 925*(1200(1 :(5O '(1 LVXN VYbP k0 q%(59>&+(1%(5(,&+ '(6 n,p%qU :(5'(1 '$%(, n,1Ok21(1 '85&+ r52721(1 $86*(7$86&+7 LVXN VYbP |81>&+67 :,5' (,1( o(7$//0$6.( $8) '(5 q%(5O 9>&+( '(6 n,p%qU 3+272/,7+2*5$3+,6&+ '(71,(57P f$6 u8%675$7 :,5' '$1$&+ ,1 (,1( 9@66,*( r52721(148(//( *(7$8&+7N :2%(, =P dP d(1=2(6>85( 0,7 S@ n,7+,80O %(1=2$7 %(, v(03(5$785(1 =:,6&+(1 TRR 81' VRR@e 9(5:(1'(7 :(5'(1 .$11P f85&+ '(1 r52721(1$867$86&+ (1767(+7 j;n,S2;p%qU N :2%(, ,1 819(5'@117(1 u>85(1 ; %,6 =8 RPY %(75$*(1 .$11P f,( $8M(525'(17/,&+( d5(&+=$+/ .$11 '$'85&+ 80 %,6 =8 RPST $1*(+2%(1 :(5'(1 81' ',( 25'(17/,&+( d5(&+=$+/ %,6 =8 2RPRV $%*(6(1.7 :(5'(1P f85&+ (,1( $16&+/,(M(1'( v(03(581* .$11 '$6 d5(&+=$+/352O 7/ ,1 9(57,.$/(5 t,&+781* 12&+ $86*('(+17 :(5'(1P c86 (,1(0 $11>+(51' 678O )(1)?50,*(1 r527/ (1767(+7 '$%(, (,1 */2&.(1)?50,*(6 LVZbP f,( 3+&+67 :85'( (,1( x,(/=$+/ 3$6O 6,9(5 m20321(17(1 5($/,6,(57\ i,77(57/7(5N u75$+/7(,/(5N i,77(5.233/(5N t(621$725(1N r2/$5,6$725(1 81' n,16(1P f$1(%(1 (;,67,(5(1 (,1,*( $.7,9( m20321(17(1N :(/&+( SP (/(.752237,6&+( g5(.7( $861@7=(1 :,( 237,6&+( o2'8/$725(1 81' u&+$/7(5N

YWT

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

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ZPV Jc125*$1,6&+(K j$/%/(,7(5

YWU

ZPV Jc125*$1,6&+(K j$/%/(,7(5 ZPVPS i581'/$*(1 j$/%/(,7(5 67(//(1 (,1( o$7(5,$/./$66( '$5N :(/&+( =$+/5(,&+( c63(.7( 816(5(6 02O '(51(1 n(%(16 (176&+(,'(1' *(35>*7 81' 5(92/87,21,(57 +$7N :,( =P dP ',( g/(.7521,.N ',( e20387(57(&+1,.N ',( f$7(1O 81' v(/(.20081,.$7,21N ',( t(*(/81*67(&+1,.N ',( u(1625,.N ',( c1$/5 '$'85&+ (5?51(7N '$66 (6 (567(16 '85&+ 67(7( q37,0,(581* '(5 y$&+67806352=(66( *(/81*(1 :$5N (,1( x,(/)$/7 9(56&+,('(1(5 j$/%/(,7(5.5,67$//( ,1 +(59255$*(1'(1 t(,1+(,76*5$'(1 +(5=867(//(1N '$66 =:(,7(16 '85&+ f27,(581* 81' o$7(5,$/:$+/ ',( 3+1*/,&+( t$1'%(',1*81*(1N '$66 %(, '(0 %(5(,1$1'(5:$&+6(1 921 u&+,&+7(1 817(56&+,('O /,&+(5 j$/%/(,7(50$7(5,$/,(1 $8) ,'(17,6&+( i,77(5.2167$17( Ji,77(5$13$6681*K *($&+O 7(7 :(5'(1 08667(N 6,1' ,1=:,6&+(1 :(1,*(5 %('(876$0P k0 i(*(17(,/N 02'(51( 23O 72(/(.7521,6&+( d$8(/(0(17( (17+$/7(1 6(+5 2)7 62 *(1$117( 9(563$117( j$/%/(,7(5O 6&+,&+7(1N '(5(1 i,77(5.2167$17( 921 '(5 '(6 u8%675$76 $%:(,&+7P f$%(, +$1'(/7 (6 6,&+ =P dP 80 *(=,(/7 9(563$117( '@11( j$/%/(,7(56&+,&+7(1)2/*(1 2'(5 80 (,1( ',&.(N *,77(5)(+/$1*(3$667( r85(56&+,&+7 $8) '(0 u8%675$7N :2%(, ',( m5,67$//2%(59>&+( '(5 r85(56&+,&+7 :,('(5 ',( 1$7@5/,&+( i,77(5.2167$17( '(5 r85(56&+,&+7 $8):(,67 81' 1$+(=8 '()(.7)5(, ,67P g,1( :(,7(5( o?*/,&+.(,7N o$7(5,$/(,*(16&+$)7(1 0$M=86&+1(,'(51 J(1*/P NN0$7(O 5,$/ (1*,1((5,1*DDKN ,67 '85&+ '(1 g,16$7= 1,('(5',0(16,21$/(5 j$/%/(,7(561*( =:,6&+(1 9(5O 6&+,('(1(1 o$7(5,$/,(1P g1*7 0$1 ',( @%/,&+(5:(,6( '5(,',0(16,21$/( d(:(*81*6O )>+,*.(,7 '(5 n$'81*675>*(5 $8) :(1,*( p$120(7(5 .@167/,&+ (,1N 62 75(7(1 ,17(5(6O 6$17( s8$17,6,(581*6(5(.7( ,1 =:(,ON (,1O 2'(5 18//',0(16,21$/(1 n$'81*675>*(56&+(1O =(175,(57(1 i,77(5 LSTb $8)*(%$87 92567(//(1P c/6 1>&+67(6 62// 0,7 k1r (,1 %,1>5(5 kkkBxOx(5%,1'81*6+$/%/(,7(5 %(75$&+7(7 :(5O '(1N '(5 $86 (,1(5 ,'(17,6&+(1 c1=$+/ 921 c720(1 '(5 kkkP 81' '(5 xP j$837*5833( '(6 r(5,2',6&+(1 u5( x(5%,1'81*6+$/%/(,7(5 %(621'(56 ,17(5(66$17 *(:25'(1P k1 7(51>5(1 o$7(5,$/,(1 .?11(1 =P dP =:(, g/(0(17( '(5 kkkP j$837*5833( 81' (,1 g/(0(17 '(5 xP j$837*5833( (17+$/7(1 6(,1 J=P dP c/=i$S2=c6 0,7 R o = o S 2'(5 i$S2;k1;c6 0,7 R o ; o SKN :2%(, ,0 (567(1 h$// ,0 x(5*/(,&+ =80 i$c6 *(5$'( '(5 d58&+7(,/ JS2=K '(5 i$Oc720( '85&+ '(1 d58&+7(,/ J=K $1 c/Oc720(1 (56(7=7 :85'(P g17635(&+(1' 6,1' ',( ,1 '(5 r+2721,. >8M(567 :,&+7,*(1 48$7(51>5(1 x(5O %,1'81*6+$/%/(,7(5 i$S2;k1;c61'(502'(// ,0 q576O 5$80 '85&+ '$6 d>1'(502'(// ,0 .Ot$80 J6,(+( $8&+ c%6&+1P YPVPS 81' SPVK (5*>1=7 81' *$1= :(6(17/,&+( j(7(526758.785$63(.7(N 1,('(5',0(16,21$/( u87(57K 81' :(5'(1 j$/%/(,7(5 0,7 ',5(.7(5 d$1'6758.785 *(1$117 Jv$%P ZPVKP j$/%/(,7(5N %(, '(1(1 '$6 x$/(1=O %$1'0$;,080 %(, . 3 R /,(*7 81' ',( 7,()67(1 n(,781*6%$1'0,1,0$ %(, 8.8 # R JzO 2'(5 nOr81.7K /,(*(1N 1(117 0$1 j$/%/(,7(5 0,7 ,1',5(.7(5 d$1'6758.785P d(,O 63,(/( +,(5)@5 6,1' u, 81' u,i(N :(/&+( +(87( %(, (/(.7521,6&+(1 d$8(/(0(17(1 (,1( '20,1,(5(1'( t2//( 63,(/(1P k1 '(5 q372(/(.7521,. 63,(/7 u, ,1 r+272'(7(.O 725(1 )@5 y(//(1/>1*(1 + " SPS =0 (,1( :,&+7,*( t2//(P q% u, ,1 '(5 |8.81)7 $8&+ %(, /,&+7(0,77,(5(1'(1 d$8(/(0(17(1 Jngf6 81' n$6(51K :,&+7,* :(5'(1 .?117(N :,5' ,1 c%6&+1P ZPVPW ',6.87,(57P

YWX

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

2 0

K U

-4 X

Γ

-6 -8

Energie/eV

-2 L

-10 -12

gi

der ebän

Ener

c%%P ZPTW

v$%P ZPV

aAs

von G

r(563(.7,9,6&+( UfOc16,&+7 '(5 i$c6Od$1'6758.785 1$&+ h5(16/ LYSbP

y,5.81*6*5$'( '(5 m219(56,21 (/(.75,6&+(5 ,1 237,6&+( g1(5*,( )@5 ',9(56( n$6(5P

i$6/$6(5 c51

j(p(

eqT

h(67.?53(5/$6(5 k62/$725(1 J=P dP p'\{ciK

j$/%/(,7(5

" RPS@

"S@

UR@

SATR@

# XR@

UP f$6 x$/(1=%$1' ,67 %(, . 3 R (17$57(7 81' 63$/7(7 6,&+ )@5 . # R ,1 '$6 6&+:(5( n?&+(5%$1' J++N (1*/P +($9< +2/(K 81' '$6 /(,&+7( n?&+(5%$1' J/+N (1*/P /,*+7 +2/(K $8)P f$ SB0" 3523257,21$/ =85 d$1'.5@0081* ,67N (17635,&+7 ',( 67>5.(5( m5@0081* '(6 /(,&+7(1 n?&+(5%$1'(6 (,1(5 ./(,1(5(1 J'P +P /(,&+7(5(1K (5(.7,9(1 o$66( 0"N 81' ',( 6&+:>&+(5( m5@0081* '(6 6&+:(5(1 n?&+(5%$1'(6 (,1(5 *5?M(5(1 J'P +P 6&+:(5(5(1 (5(.7,9(1 o$66(KN :2'85&+ ',( p$0(16*(%81* '(5 d>1'(5 62)257 (9,'(17 :,5'P k1 '(5 p>+( 921 . 3 R ,67 ',( m5@0081* 1$+(=8 3$5$%2/,6&+ 81' '(5 n$'81*675>*(5 9(5+>/7 6,&+ %(,1$+( :,( (,1 )5(,(6 v(,/&+(1N -('2&+ 0,7 *(>1'(57(5 (5(.7,9(5 o$66( J|$+/(1%(,63,(/ )@5 k1r ,1 t,&+781* JSNSNRK\ 0"( 3 RPRZ 02 N 0"++ 3 RPWX 02N 0" /+ 3 RPST 02KP f(01$&+ />667 6,&+ '$6 g/(.7521 $0 /(,&+7(67(1 81' '$6 6&+:(5( n2&+ $0 6&+:(567(1 %(6&+/(81,*(1P g,1 )5(,(6 v(,/&+(1 %(6,7=7 185 .,1(7,6&+( g1(5*,(N :(/&+( 6,&+ $/6 0"9TBT 3 @T . TBJT 0"KN $/62 ,1 3$5$%2/,6&+(5 h250 '$567(//(1 />667] @ ,67 +,(5%(, '$6 r/$1&.I6&+( y,5.81*6O 48$1780 + ',9,',(57 '85&+ T @P VP k1 '(1 t,&+781*(1 JSNSNSK 81' JSNRNRK (;,67,(5(1 ,0 n(,781*6%$1' %(, *5?M(5(1 .Oy(57(1 :(,7(5( /2.$/( o,1,0$P f(5 d(:(*81*6925*$1* (,1(6 g/(.75216 />667 6,&+ ,0 gJ.KOf,$*5$00 :,( )2/*7 9(5$16&+$8/,&+(1\ k67 .(,1 h(/' $1*(/(*7 81' ,67 '$6 n(,781*6%$1' 0,7 185 (,1(0 (,1=,*(1 g/(.7521 %(6(7=7N 62 71'(7 0$1 (6 %(, v 3 R ,0 |867$1' . 3 RP p$&+ g,16&+$/7(1 '(6 h(/'(6 :,5' '$6 g/(.7521

ZPV Jc125*$1,6&+(K j$/%/(,7(5

YWY

%(6&+/(81,*7N . 1,007 67(7,* =8N %,6 (6 =P dP =85 y(&+6(/:,5.81* 0,7 (,1(0 r+2121 .2007P f$%(, 75(7(1 g1(5*,(O 81' k038/6>1'(581*(1 $8)N :(/&+( '85&+ '(1 g1(5O *,(O 81' '(1 k038/6(5+$/781*66$7= %(6&+5,(%(1 :(5'(1P k1 '(1 0(,67(1 h>//(1 %(6,7=7 '$6 g/(.7521 1$&+ '(0 u72M ,1 '(5 85635@1*/,&+(1 d(:(*81*65,&+781* (,1( ./(,1(5( k038/6.20321(17(P d(, c1/(*(1 6(+5 67$5.(5 h(/'(5 *(/,1*7 (6 '(0 g/(.7521 -('2&+ 0,7817(5N (,1 p(%(10,1,080 =8 (55(,&+(1N %(925 (6 =8 (,1(0 u72M 0,7 (,1(0 r+2121 .2007P f257 %(6,7=7 (6 -('2&+ $8)*581' '(5 +,(5 925O /,(*(1'(1 *5?M(5(1 (5(.7,9(1 o$66( (,1( *(5,1*(5( d(:(*/,&+.(,7P g,1( $86)@+5O /,&+( d(6&+5(,%81* (/(.75,6&+(5 n(,7)>+,*.(,7 ,67 ,1 m$3P Y 81' ,1 LWVb %(6&+5,(%(1N :2%(, %(621'(56 $8) 9(56&+,('(1( u75(80(&+$1,60(1 (,1*(*$1*(1 :,5'N :,( =P dP y(&+6(/:,5.81* 0,7 *(/$'(1(1 u7?567(//(1N y(&+6(/:,5.81* 0,7 $.867,6&+(1 81' 237,6&+(1 r+2121(1 62:,( '(1 g,19866 921 n(*,(581*698.78$7,21(1P

ZPVPT s8$17(1(5(.7( 81' 9(563$117( j$/%/(,7(5Oj(7(526758.785(1 k1 02'(51(1 2372(/(.7521,6&+(1 d$8(/(0(17(1 :(5'(1 =81(+0(1' j$/%/(,7(5Oj(O 7(526758.785(1 (,1*(6(7=7N ,1 '(1(1 (,1( h2/*( 921 o$7(5,$/,(1 9(56&+,('(1(5 |8O 6$00(16(7=81* @%(5(,1$1'(5 $8)*(:$&+6(1 :,5'P y,5' =:,6&+(1 =:(, o$7(5,$/,(1 +?+(5(5 d$1'/@&.( (,1( u&+,&+7 *(5,1*(5(5 d$1'/@&.( (,1*(%(77(7N '(5(1 f,&.( ,1 '(5 i5?M(125'181* '(5 g/(.7521(1:(//(1/>1*( /,(*7N 62 75,77 $1$/2* =8 '(1 g1(5*,(=8O 67>1'(1 ,0 c720 (,1( s8$17,6,(581* '(5 n$'81*675>*(5%(:(*81* $8) Jc%%P ZPTX$KP o$1 635,&+7 '$11 921 (,1(5 s8$17(17/06758.785 JsyN (1*/P 48$1780 :(//N 6,(+( $P c%%P SPSTKN '(5(1 g,*(16&+$)7(1 6,&+ 0,7+,/)( '(5 s8$17(10(&+$1,. %(6&+5(,%(1 /$66(1N :2%(, 6,&+ '$6 g/(.7521 ,1 (,1(0 n(,781*6%$1'Or27(17,$/723) 81' '$6 n2&+ ,1 (,1(0 x$/(1=%$1'Or27(17,$/723) $8)+$/7(1 LWZN W[bP c%%,/'81* ZPTX% =(,*7 '(1 r27(17,$/723) '(6 g/(.75216 ,0 n(,781*6%$1'P f,( d(:(*81* '(6 n$'81*675>*(56 ,67 6(1.5(&+7 =85 h,/0(%(1( 67$5. (,1*(6&+5>1.7 81' 48$17,6,(57N :2%(, ',( s8$1O 7(10(&+$1,. ',( c8)(17+$/76:$+56&+(,1/,&+.(,7(1 $/6 s8$'5$7 '(5 *(675,&+(/7 (,1O *(=(,&+1(7(1 y(//(1)81.7,21(1 $1*,%7P g,1( 48$6,)5(,( d(:(*81* ,0 j$/%/(,7(5.5,6O 7$// /,(*7 ,1 ',(6(0 h$// 185 12&+ ,1 '(5 h,/0(%(1( 925P f,(6( =:(,',0(16,21$/( JTfK d(:(*81* 63,(*(/7 6,&+ ,1 (,1(5 TfOd$1'6758.785 gJ.; N .=K :,'(5 Jc%%P ZPTX&KP E

Potentialtopf Ly

z (a)

LB

II

I

II 3e

E x y

II

I

II (b)

E

0

Ly

E3

2e

E2

1e

E1 y

(c)

kx, kz

(d)

D(E)

c%%P ZPTX J$K s8$17(17/06758.785 ,0 q5765$80N J%K r27(17,$/723) ,0 n(,781*6%$1' 0,7 '5(, 48$17,6,(57(1 p,9($86 81' '(1 (17635(&+(1'(1 y(//(1)81.7,21(1 J*(675,&+(/7KN J&K d$1'6758.O 785 ,0 TfOk038/6Oy(//(19(.7255$80 J.; N .=KN J'K .255(6321',(5(1'( |867$1'6',&+7( fJgKP

YWZ

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

f,( n(,781*6O 81' x$/(1=%>1'(5 63$/7(1 '85&+ ',( s8$17,6,(581* ,1 u8%%>1'(5 $8)N :2%(, /(,&+7( 81' 6&+:(5( n?&+(5 $8)*581' ,+5(5 817(56&+,('/,&+(1 o$66(1 *(75(117( u8%%$1'Ou1'(5 fJgK : g SBT *,/7 Jc%%P ZPTY$KN (5*,%7 6,&+ $86 (,1(5 TfOd$1'6758.785 gJ.; N .=K 352 u8%%$1' (,1 .2167$17(5N (1(5*,(81$%+>1O *,*(5 d(,75$* =85 |867$1'6',&+7(P f85&+ '$6 |86$00(1:,5.(1 $//(5 u8%%>1'(5 (5O *,%7 6,&+ ',( ,1 c%%P ZPTX' 81' c%%P ZPTY% '$5*(67(//7( 678)(1)?50,*( |867$1'6O ',&+7(P u&+5>1.7 0$1 ',( d(:(*81* '(5 n$'81*675>*(5 ,1 (,1(5 :(,7(5(1 t$805,&+781* (,1 J=P dP ,1 =O 81' /7 0$1 (,1 (,1',0(16,21$/(6 n$'81*675>*(56*(56*(51 ,1 s8$17(17/0( 81' ,16%(621'(5( c%62537,21 2'(5 63217$1( 81' 67,08/,(57( g0,66,21 921 n,&+7K 63,(/7 ',( |867$1'6',&+7( (,1( =(175$/( t2//(P d(,0 g17:85) 2372(/(.7521,6&+(5 d$8(/(0(17( .?11(1 0,7 '(5 y$+/ '(5 f,0(16,21$/,7>7 '(6 n$'81*675>*(565.7 81' 81(5:@16&+7( 817(5'5@&.7 :(5'(1P f,( t($/,6,(581* 921 TfOj$/%/(,7(5+(7(52O 6758.785(1 (5)2/*7 0,7 02'(51(1 g3,7$;,(9(5)$+5(1 :,( '(5 odg 81' '(5 oqexf Jc%6&+1P ZPVPUKP x21 ',(6(1 i581'6758.785(1 $86*(+(1' /$66(1 6,&+ SfO 81' RfO u758.785(1 '85&+ *((,*1(7( /$7(5$/( u758.785,(581* J=P dP }7=(1 2'(5 k03/$17$7,21K +(567(//(1N ',( ,1 0$1&+(1 h>//(1 (3,7$.7,6&+ 12&+0$/6 @%(5:$&+6(1 :(5'(1 LXRbP D(E)

D(E)

2D

3D E=

h2 2 2 2 (k +k +k ) 2m* x y z

E= E

(a)

(b)

h2 2 2 (k +k )+E 2m* x z y

E2

E1

Ey

D(E)

D(E)

0D 1D E= (c)

E11

E12

h2 k2x +E 2m* yz

E = Exyz

Eyz

(d)

E111

Exyz

c%%P ZPTY |867$1'6',&+7( fJgK 81' d$1'9(5/$8) ,1 3$5$%2/,6&+(5 p>+(581* )@5 J$K (,1(1 ,1 $//(1 '5(, t$805,&+781*(1 $86*('(+17(1 j$/%/(,7(5N UfN J%K (,1(1 s8$17(17/0N TfN J&K (,1(1 s8$17(1'5$+7N Sf 81' J'K (,1(1 s8$17(1381.7N RfP

ZPV Jc125*$1,6&+(K j$/%/(,7(5

YW[

SfOu758.785(1 .2117(1 6,&+ $8)*581' 81*@167,*(5 '87(581* 1$&+)2/*(1'K '(6 k1c6 *(*(1@%(5 '(0 i$c6 (,1( =(175$/( t2//(P c86 7+(502'&+( *(6$07O (1(5*(7,6&+ :(6(17/,&+ *@167,*(5N (,1 /2.$/(6 ,16(/)?50,*(6 y$&+6780 $1=86&+/,(M(1P g,1( 0?*/,&+67 *(20(75,6&+( h250 '(5 s8$17(1381.7( ,67 '$%(, (,1( r&+( 0,7 (,1(5 1$127(&+12/2*,6&+ +(5O *(67(//7(1 8/75$O)(,1(1 p$'(/ $%*(7$67(7N *$1= (17)(517 9(5:$1'7 0,7 '(0 c%63,(/(1 (,1(5 u&+$//3/$77(KP k0 1>&+67(1 r52=(666&+5,77 :(5'(1 ',( s8$17(1381.7( :,('(5 0,7 i$c6 @%(5:$&+6(1 81' '$'85&+ 6&+/,(M/,&+ 581'80 (,1*(%(77(7P g;3(5,0(17(// &+$5$.7(5,6,(57 0$1 ',( u&+,&+7)2/*(1N ,1'(0 0$1 ',( u758.785(1 .5,67$//2*5$3+,6&+ 63$/7(7 81' ',( u3$/79>&+(1 0,7 v5$160,66,216Og/(.7521(10,.526.23 $1$/&+( =8 (5+?+(1N :,('(5+2/7 0$1 '(1 *(6$07(1 k1c6Or52=(66 1$&+ (,1(5 '(71,(57(1 i$c6Ou&+,&+7O ',&.(P f$'85&+ (5+>/7 0$1 (%(1(1$57,*( s8$17(1381.7$16$00/81*(1P c%%P ZPTZ& 81' ' =(,*(1 '$6 (;3(5,0(17(//( g5*(%1,6 )@5 (,1(1 g%(1(1$%67$1' 921 VR 10 81' TR 10N :2%(, ,0 h$//( '(6 *(5,1*(5(1 g%(1(1$%67$1'(6 ',( r26,7,21(1 '(5 s8$1O 7(1381.7( ,1 9(57,.$/(5 t,&+781* .255(/,(57 6,1'P c%%P ZPTZ( =(,*7 ,1 (,1(5 6(+5 +2+(1 x(5*5?M(581* J0$1 %($&+7( ',( -(:(,/6 817(56&+,('/,&+( d(0$M81* '(5 d$/.(1/>1O *(1K ',( s8$17(1381.7$86%,/'81* ,1 '(0 kkBxkOj$/%/(,7(567 81' (,1( 6(+5 +2+( ',5(5(1=,(//( 237,6&+( x(567>5.81* J'$'85&+ (;75(0 +2+( %(575$*81*65$7(1K =8 (5:$57(1P q%:2+/ :(/7:(,7 $8) '(0 i(%,(7 '(5 s8$17(1381.7Og3,7$;,( 6(+5 ,17(16,9 *($5%(,7(7 :,5' 81' %(5(,76 =$+/5(,&+( s8$1O 7(1381.7/$6(5 5($/,6,(57 :85'(1N :(,6(1 ',( 35.81*63527/N :$6 :,('(5 )@5 $1'(5( c1:(1'81*(1 921 x257(,/ ,67P l('2&+ 0866 $8&+ '$5$1 (5,11(57 :(5'(1N '$66 (6 0(+5 $/6 SR l$+5( '$8(57(N %,6 ',( n$6(5 0,7 $.7,9(1 TfOu&+,&+7(1 5(352O '8=,(5%$5 ',(-(1,*(1 0,7 $.7,9(1 UfOu&+,&+7(1 @%(575$)(1P o,7 '(5 y$+/ '(6 j$/%/(,7(50$7(5,$/6 81' '(5 y$+/ '(5 n$'81*675>*(5',0(16,2O 1$/,7>7 6,1' -('2&+ 12&+ 1,&+7 $//( o?*/,&+.(,7(1 $86*(6&+?3)7N 80 )@5 d$8(/(0(17(O c1:(1'81*(1 %(67,007(N 'P +P 48$6, .@167/,&+( o$7(5,$/,(1 0,7 1(8$57,*(1 81' +(O 5$865$*(1'(1 3+5( x(5%,1'81*6+$/%/(,7(5N :(/&+( '85&+ (,1 *((,*1(7(6 NNo,O 6&+81*69(5+>/71,6DD $86 -(:(,/6 =:(, %,1>5(1 m20321(17(1 (1767(+(1N '$5*(67(//7P

ZPV Jc125*$1,6&+(K j$/%/(,7(5

YXS

T = 300 K 0.66

InSb

Gitterkonstante a/nm

0.64 0.62 InAs

GaSb

0.60

InP

0.58

AlAs

0.56 0.54

GaAs

GaP

0

0.2 0.4 0.6 0.8 Kompositionsparameter

1.0

c%%P ZPT[ i,77(5.2167$17( $ $/6 h81.7,21 9(56&+,('(1(5 7(51>5(5 81' 48$7(51>5(5 x(5%,1O '81*6+$/%/(,7(5P

f,(6( /,1($5(1 |86$00(1+>1*( :(5'(1 $/6 x(*$5'I6&+(6 i(6(7= %(=(,&+1(7P h@5 ',( o$7(5,$/:$+/ ,67 -('2&+ )(51(5 ',( */(,&+=(,7,*( x$5,$7,21 '(5 d$1'/@&.( (,1 (176&+(,O '(1'(6 m5,7(5,80 Jc%%P ZPURKP f$6 $%)$//(1' 6&+5$5,(57( i(%,(7 %(6&+5(,%7 '$6 48$O 7(51>5( c/=i$S2;2=k1;pP f$6 $167(,*(1' 6&+5$5,(57( i(%,(7 %(6&+5(,%7 '$6 48$7(5O 1>5( i$S2;k1;c6S21*( J5(&+76K $/6 h81.7,21 '(5 i,77(5.2167$17( $P

YXT

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1 (2.16 eV) AlAs 0.566 nm 1.0 1.0 0.574 nm 0.8

v

0.606 nm

0 1.0 InAs (0.36 eV)

1.0 eV 0.8 eV 0.6 e V

0.8

0.6 Gitteranpassung auf InP

1.8

eV

0.4

1.6

1.4

1.2 0.6

n

0.598 nm 0.2

0.8 2.05 eV

0.582 nm 0.6 0.590 nm 0.4

indirekter Bereich

eV 0.2

eV

eV

0.4 (1-v)

0 0.565 nm 0 GaAs (1.42 eV)

0.2

c%%P ZPUS m20326,7,21(//( c%+>1*,*.(,7 '(5 d$1'/@&.( 81' '(5 i,77(5.2167$17( ,1 Jc/8i$S28K9k1S2 9c6] m20326,7,2163$5$0(7(5 R o 9 o S 81' R o 8 o SP

GaP Ga1-xInxP 0.5576 nm 0.5653 nm 0.5869 nm InP 0.596 nm

InP 1.0

indirekt

1.8 eV 1.6 eV 1.4 eV

GaAs1-yPy GaAs

1.2 eV 1.0 eV

Ga1-xInxAs

0.8 eV

GaAs 0

0.6 eV 0.5 y InAs1-yPy InAs

Energie

1(1 35>=,6( *,77(5$1*(3$667 J,'(17,6&+( i,77(5.2167$17(K $8) '(0 -(:(,/,*(1 u8%675$7 $8)*(:$&+6(1 :(5'(1P i(0>M c%%P ZPUR 81' '(5 *(675,&+(/7(1 n,1,(1 ,1 c%%P ZPUS 81' c%%P ZPUTN %(6,7=7 c/RPVZk1RPWTc6 81' i$RPVYk1RPWUc6 ',(6(/%( i,77(5.2167$17( :,( k1rN '$6 $/6 6&+(,%(1$57,*(6 u8%675$70$7(5,$/ 0,7 %,6 =8 SWR 00 f85&+0(66(5 .20O 0(5=,(// 9(5)@*%$5 ,67P d(,63,(/6:(,6( .$11 i$RPVYk1RPWUc6 Jg* 3 RPYW (xK $8) i581' '(5 i,77(5$13$6681* ,1 %(/,(%,*(5 f,&.( $8) c/RPVZk1RPWTc6 Jg* 3 SPVU (xK 2'(5 k1r Jg* 3 SPUV (xK $8)*(:$&+6(1 2'(5 =:,6&+(1 ',(6( o$7(5,$/,(1 (,1*(%(77(7 :(5'(1P

0.5 x

c%%P ZPUT m20326,7,21(//( c%+>1*,*.(,7 '(5 d$1'/@&.( 81' '(5 i,77(5.2167$17( ,1 i$S2;k1;c6S2&+( '(5 %(,'(1 m5,67$//6758.785(1 /,(*(1 i,77(5)(+/(5 925N 62*(1$117( x(56(7=81*(1 Jm$3P UPYN LSTbKP k0 c//*(0(,1(1 5(,&+(1 ',(6( 9,(/ :(,7(5 ,1 %(,'( m5,67$//92/80,1$ +,1(,1 $/6 ,1 c%%P ZPUU& $1*('(87(7 ,67P g,1( 9(563$117( f(&.6&+,&+7 2'(5 |:,6&+(16&+,&+7 ,67 -('2&+ 185 %,6 =8 (,1(0 921 '(5 u&+,&+7',&.( n< 81' '(5 x(563$1181* $%+>1*,*(1 n,0,7 67$%,/P f,( 0$;,0$/ 0?*/,&+( u&+,&+7',&.( J.5,7,6&+( u&+,&+7',&.(KN %(, '(5 12&+ .(,1( i,77(55(/$;$7,21 $8)75,77N 1,007 0,7 :$&+6(1'(5 x(563$1181* $%P h@5 (,1( (,16(,7,* )5(,/,(*(1'(N 9(5O 63$117( f(&.6&+,&+7 Jc%%P ZPUU%K ,67 %(, ,'(17,6&+(5 i,77(5)(+/$13$6681* ',(6( .5,O 7,6&+( u&+,&+7',&.( 185 81*()>+5 +$/% 62 ',&. :,( )@5 (,1( 9(563$117( (,1*(%(77(7( u&+,&+7 Jc%%P ZPUV$N &KN %(, :(/&+(5 ',( x(563$1181* $1 %(,'(1 j(7(52*5(1=9>&+(1 =85 j>/)7( $%*()$1*(1 :(5'(1 .$11P t($/( j$/%/(,7(5.5,67$//( 6,1' ,0 i(*(16$7= =8 '(1 ,1 '(1 c%%P ZPUV$A& '$5*(67(//7(1 m5,67$//$866&+1,77(1 ,1 ;O 81' =Ot,&+781*

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

Ga0.3In0.7As

InP

InP

Ga0.47In0.53As

biaxial zugverspannt

biaxial druckverspannt

InP

unverspannt

YXV

Ga0.64In0.36As

y x k⊥

(a)

InP

(b)

E

lh

kII

k⊥,kII

k⊥

hh lh

hh

lh (e)

(c)

InP

E

E

E

kII (d)

InP

E

kII lh hh

hh

lh

k⊥

hh

(f)

c%%P ZPUV w19(563$117( 62:,( %,$;,$/ '58&.O 81' =8*9(563$117( UfOj$/%/(,7(56758.785(1N J$K A J&K i,77(56758.785(1N J'K A J)K .255(6321',(5(1'( Uf d$1'6758.785(1 gJ.KN '$%(, *,%7 .( ',( t,&+781* 6(1.5(&+7 81' .o ',( t,&+781* 3$5$//(/ =85 j(7(52*5(1=9>&+( $1] ++\ 6&+:(5(6 n2&+N /+\ /(,&+7(6 n2&+P

:(6(17/,&+ :(,7(5 $86*('(+17P h(51(5 ,67 =85 x(5(,1)$&+81* 185 ',( .8%,6&+( g,1O +(,76=(//( J6P c%%P SPSK '(5 m$17(1/>1*( $ Ji,77(5.2167$17(K 9,(/)$&+ $1(,1$1'(5*(O 6(7=7N 2+1( $8) f(7$,/6 '(5 $720$5(1 u758.785 (,1=8*(+(1P x(5*5?M(57 0$1 -('2&+ $86*(+(1' 921 ; 3 RPWU '(1 k1Oi(+$/7 '(6 i$S2;k1;c6N 62 1,007 1$&+ c%%P ZPT[ ',( i,77(5.2167$17( =8P f(0 $/6 d(,63,(/ %(75$&+7(7(1 i$RPUk1RPYc6 :,5' ,1 ;O 81' =Ot,&+781* ',( ./(,1(5( i,77(5.2167$17( '(6 k1r $8)*(O =:81*(1P o$1 635,&+7 '$%(, 921 (,1(5 '58&.9(563$117(1 u&+,&+7 J(1*/P &2035(66,9( 675$,1KP c8) i581' '(5 i(6(7=( '(5 m217,188060(&+$1,. 9(5*5?M(57 6,&+ '$)@5 ,1 87*( d$1'6758.785 gJ.K (,1(6 UfOx2/80(1+$/%/(,7(56 0,7 ',5(.7(5 d$1'/@&.(P f$6 6&+:(5( n2&+%$1' J++K 81' '$6 /(,&+7( n2&+%$1' J/+K 6,1' %(, . 3 R (1(5*(7,6&+ (17$57(7P k1 '(5 6(1.5(&+7(1 81' 3$5$//(/(1 t,&+781* /,(*7 '$6 ++Od$1' -(:(,/6 @%(5 '(0 /+Od$1'P f85&+ '$6 x(563$11(1 ',(6(5 u&+,&+7 Jc%%P ZPUV'N )K :,5' ',( x$/(1=%$1'.$17( %(, . 3 R '85&+ '(1 +7=/,&+(1 g1(5*,((17$5O 781*P c%%P ZPUV' =(,*7 (,1( c%6(1.81* '(5 x$/(1=%$1'.$17(1 817(5 %,$;,$/(5 f58&.O 9(563$1181*P k1 3$5$//(/(5 t,&+781* J/,1.(6 v(,/%,/'K .2007 (6 '85&+ ',( c8)63$/O 781* 6&+(,1%$5 =8 (,1(5 %(5.5(8=81* '(6 6&+:(5(1 81' '(6 /(,&+7(1 n?&+(5%$1'(6P s8$17(10(&+$1,6&+ ,67 ',(6 -('2&+ $86*(6&+/266(1N :(6+$/% '$6 ++Od$1' %(, ./(,1(1 .o '(5 m5@0081* '(6 85635@1*/,&+(1 /(,&+7(1 n?&+(5%$1'(6 )2/*7 81' '$11 $0 7.7,9(1 %(5.5(8=81*6381.7 '(5 6&+:>&+(5(1 m5@0081* '(6 85635@1*/,&+(1 6&+:(5(1 n?&+(5%$1'(6 )2/*7N 2+1( '$66 (,1( 5($/( %(5.5(8=81* '(6 ++O 81' '(6 /+Od$1'(6 $8)75,77P f(0=8)2/*( :(,67 '$6 /+Od$1' %(, ./(,1(1 .o (,1( 6&+:(5( o$66( 81' %(, *5?M(5(1 .o (,1( /(,&+7( o$66( $8)P f$6 5(&+7( v(,/%,/' =(,*7 '(1 x(5/$8) gJ.(KN :2%(, %(, . 3 R ',(6(/%(1 g1(5*,(:(57( :,( ,0 /,1.(1 v(,/%,/' $8)75(7(1 0@6O 6(1P f,( m5@0081* '(6 ++Od$1'(6 %(6,7=7 )@5 $//( .( '(1 e+$5$.7(5 (,1(6 6&+:(5(1 n2&+(6] ',( m5@0081* '(6 /+Od$1'(6 =(,*7 )@5 $//( .( '(1 e+$5$.7(5 (,1(6 /(,&+7(1 n2&+(6P c%%P ZPUV) '(021675,(57 (,1( c1+(%81* '(5 x$/(1=%$1'.$17(1 817(5 %,$;,$/(5 |8*9(563$1181*P k1 3$5$//(/(5 t,&+781* J/,1.(6 v(,/%,/'K ,67 '$6 /+Od$1' -('2&+ )@5 $//( .o 6&+:$&+ *(.5@007 J6&+:(5( (5(.7,9( o$66(CK 81' '$6 ++Od$1' ,67 )@5 $//( .o 6&+:$&+ *(.5@007 J/(,&+7( (5(.7,9( o$66(CKP k1 6(1.5(&+7(5 t,&+781* J5(&+7(6 v(,/%,/'K .2007 (6 %(, '(5 c8)63$/781* 6&+(,1%$5 (%(1)$//6 =8 (,1(5 %(5.5(8=81* '(6 85635@1*/,&+(1 6&+:(5(1 81' '(6 /(,&+7(1 n?&+(5%$1'(6P f$6 ++Od$1' /,(*7 -('2&+ +,(5 817(5+$/% '(6 /+Od$1'(6 81' :(,67 %(, ./(,1(1 .( (,1(1 u&+:(5/2&+Oe+$O 5$.7(5 81' %(, *5?M(5(1 .( (,1(1 n(,&+7/2&+Oe+$5$.7(5 $8)P w0*(.(+57 =(,*7 '$6 /+Od$1' %(, ./(,1(1 .( (,1( /(,&+7( o$66( %(, *5?M(5(1 .( (,1( 6&+:(5( o$66(P c%%P ZPUV) =(,*7 ,0 /,1.(1 81' 5(&+7(1 v(,/%,/' %(, . 3 R ,'(17,6&+( g1(5*,(:(57(P d(621'(56 ,17(5(66,(57( n(6(5 6(,(1 $8) :(,7(5)@+5(1'( n,7(5$785 LXZAYRb 9(5:,(O 6(1\ f,( 6(1.5(&+7( 81' 3$5$//(/( t,&+781* 6,1' ,1 '(5 n,7(5$785 /(,'(5 1,&+7 '85&+O

YXX

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1

*>1*,* ,1 '(5 */(,&+(1 y(,6( '(71,(57P h(51(5 .$11 )2/*(1'( v$76$&+( =85 m21)86,21 %(,75$*(1N '$66 ,1 9,(/(1 c57,.(/1 (,1 j$/%/(,7(5 %(75$&+7(7 :,5'N '(5 %(, .2167$17 *(+$/7(1(5 |86$00(16(7=81* ,1 (,1(5 *('$&+7(1 NNf58&..$00(5DD 9(563$117 :,5'P k1 ',(6(0 h$// 9(5856$&+(1 ',( +1'(5N (6 :(5'(1 =8'(0 ',( m5@0081*(1 J(5(.7,9( o$66(1K '(5 d>1'(5 02',7=,(57P c8&+ +,(5 @%(5/$*(57 6,&+ ',( '85&+ ',( x(563$1181* 81' ',( m20326,7,216>1'(581* $86O *(/?67( x$5,$7,21 '(5 o$66(1P h@5 ',( d$8(/(0(17($1:(1'81* .?11(1 '85&+ ',( c86187=81* *(=,(/7(5 x(563$1181*(1 ,1 j$/%/(,7(5+(7(526758.785(1 )2/*(1'( $775$.O 7,9( g,*(16&+$)7(1 0$M*(6&+1(,'(57 :(5'(1\ f,( x$/(1=%>1'(5 :(,6(1 %(, . 3 R ,1 3$5$//(/(5 81' 6(1.5(&+7(5 t,&+781* -(:(,/6 ,19(56( m5@0081*(1 $8)P k1 3$5$//(/(5 t,&+781* :(,67 '$6 +?+(5/,(*(1'( 81' '$'85&+ 7+(50,6&+ 67>5.(5 %(6(7=7( n?&+(5O %$1' %(, . 3 R ,1 (,1(5 '58&.9(563$117(1 u758.785 (,1( ./(,1( 81' ,1 (,1(5 =8*O 9(563$117(1 u758.785 (,1( *52M( (5(.7,9( o$66( $8)P f58&.9(563$117( j$/%/(,7(5O 6&+,&+7(1 :(5'(1 '$+(5 %(621'(56 $/6 $.7,9(6 u&+,&+70$7(5,$/ )@5 j$/%/(,7(5/$6(5 9(5:(1'(7 J80 ',( g/(.7521(1O 81' n?&+(50$66( *5?M(10>M,* %(66(5 $1=8*/(,&+(1K 81' =8*9(563$117( j$/%/(,7(56&+,&+7(1 :(5'(1 2)7 $/6 $.7,9(6 u&+,&+70$7(5,$/ )@5 j$/%/(,7(59(567>5.(5 9(5:(1'(7N 80 ',( r2/$5,6$7,216$%+>1*,*.(,7 =8 5('8=,(5(1P c%6&+/,(M(1' 6(, 12&+0$/6 %(7217N '$66 ,1 c%%P ZPUV 185 UfOj$/%/(,7(56&+,&+7(1 %(+$1'(/7 :(5'(1P f,(6 ,67 8P $P '$5$1 =8 (5.(11(1N '$66 '$6 x$/(1=%$1' ,0 819(5O 63$117(1 h$// %(, . 3 R (17$57(7 ,67 Jc%%P ZPUV(KP f$ -('2&+ $8) i581' '(5 /,0,7,(O 5(1'(1 .5,7,6&+(1 u&+,&+7',&.( ',( 67$5. 9(563$117(1 h,/0( 0(,67 6(+5 '@11 6(,1 0@66(1N 75(7(1 =86>7=/,&+ s8$17(1(5(.7( $8)P k1 %(,'(1 h>//(1 .2007 (6 %(, . 3 R =8 (,1(5 c8)+(%81* '(5 g17$5781* '(5 x$/(1=%$1'6758.785 gJ.KN :2'85&+ 6,&+ 0(+O 5(5( r+>120(1( 0,6&+(1P c86 ','$.7,6&+(1 i5@1'(1 :(5'(1 +,(5 ',( g,19@66( '(5 s8$17,6,(581* 81' '(5 x(563$1181* 6(3$5$7 %(+$1'(/7P f,( NN(5(.7,9( o$66(DDOp>+(581* Jc%6&+1P ZPVPS 81' m$3P YK ,67 -('2&+ ,1 UfO 81' TfOu758.785(1 185 )@5 1>+(581*6:(,6( (17.233(/7( u8%%>1'(5N =P dP ,1 r27(1O 7,$/7?3)(1 ,0 n(,781*6%$1'N (,16(7=%$5P h@5 ',( 67$5. *(.233(/7(1 u8%%>1'(5 '(6 x$/(1=%$1'(6 0866 ',( u&+5?',1*(5*/(,&+81* 180(5,6&+ *(/?67 :(5'(1P c%%,/'81* ZPUW =(,*7 '$6 g5*(%1,6 '(5 t(&+181* LYSb )@5 9,(5 9(56&+,('(1( i$c6Bc/i$c6O s8$17(17/06758.785(1 )@5 .o J3$5$//(/ =8 '(1 j(7(52*5(1=9>&+(1KP g,1 819(563$11O 7(5 Z 10 %5(,7(5 i$c6Or27(17,$/723) 0,7 c/RPSWi$RPZWc6 d$55,(5(1 ,67 ,1 c%%P ZPUW$ %(+$1'(/7P f,( m233/81* '(5 d>1'(5 )@+57 =8 67$5. 1,&+73$5$%2/,6&+(0 x(5+$/7(1 ,0 h$//( '(6 (567(1 /(,&+7(1 n2&+%$1'(6 JS/+K 81' '(6 '5,77(1 6&+:(5(1 n2&+%$1'(6 JU++K 62*$5 =8 1(*$7,9(1 o$66(1 $0 'Or81.7P k1 c%%P ZPUW% ,67 *(*(1@%(5 ZPUW$ ',( v23)%5(,7( +$/%,(57N :$6 ',( u8%%>1'(5 =8 +?+(5(1 g1(5*,(1 9(56&+,(%7P f$'85&+N

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YXY

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Filmbandkante

Filmbandkante

hh1

-0.02 1lh

-0.04

Energie/eV

3hh

-0.08

2hh Barrierenbandkante

2lh

4 nm

-0.10

Filmbandkante

1hh

-0.12

1lh AlGaAs GaAs AlGaAs

8 nm GaAs/Al0.15Ga0.85As

-0.14

Barrierenbandkante

2hh (b)

(a) 1hh

-0.02

Filmbandkante hh

8 nm GaAs/Al0.3Ga0.7As 1hh

Filmbandkante lh

1lh

-0.04

1lh

2hh

-0.06

Energie/eV

effektive * , m* 3D-Masse m hh lh

1lh

2hh

-0.06

4 nm GaAs/Al0.15Ga0.85As

2hh

-0.08

3hh 3hh

-0.10

QW Kompression = 0.36 % -0.12

2lh 8 nm In0.05Ga0.95As/Al0.15Ga0.85As

-0.14 0 (c)

0.02 0.04 0.06 Wellenvektor kII(2π /a0)

0.08

0.10 0 (d)

0.02 0.06 0.04 Wellenvektor kII(2π /a0)

0.08

0.10

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YXZ

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Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1 Aggregatzustand der Quellenmaterialien für die Epitaxie fest

gasförmig

flüssig mehrkomponentige metallische Lösung

metallalternative metallische Hydride organische ln Schmelze PH3, AsH3, SiH4, Quellen NH3 Verbindungen Gruppe V + HCl Gas Gruppe III

Verdampfen von Sublimation (As, P, Si, Be, Sb, C) (Ga, In, Al, Sb) aus Schmelzen

mittels Träger-Gas H2

(Ga, As, Al, In, Sb, P)

H2 N2

N2

Gas

Träger-Gas

Gas

Gas InCl2

MolekularStrahl

MolekularStrahl

LPE

MBE

GS MBE

VPE

MOVPE

MO MBE

CBE

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PRestgas ≈ 10-11 mbar

Quadrupol Massenspektrometer

Heizung

Elektronenbeugungskanone (RHEED)

InP Substrat T = 800 K Leuchtschirm

Pyrometer

Ultrahochvakuum

flüssiger Stickstoff

Ga T = 1150 K

As T = 570 K

In Al T = 1070 K T = 1170 K

Effusionszellen (Öfen)

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N2

H2

AsH3

PH3

NH3

H2

SiH4

Ga(CH3)3 In(CH3)3 Fe(C2H5)2 Zn(CH3)3 Al(CH3)3

Reaktorkammer Tor Gas Mischsystem Lampenheizung

Handschuhbox + Ladeschleuse Abgas

Abzug

Suszeptor (Graphit) rotierender Substratträger

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Regelung des Druckreaktors

Abgaswäsche Filter

Pumpe

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E

1e 2e

l=2

1hh

  l = 1

1lh 2hh

1e

1ehh 1elh

1ehh 1elh 2ehh

l=1

LB

LB

Absorption

1e

1e

5 2

E’g

1 4

2

3

4 5

1 E’g

k E

1hh 1lh

hh

3

VB

VB

l=2

lh

E y

(a)

(b)

(c)

(d)

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(a)

fLB - fVB

Dred, 3D

optische Verstärkung g(E)

YY[

Dred, 2D

spontane Emission

Eg

∆Ef

Abs.

E

(b)

Eg E g’

∆Ef

E

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0 1

S T T 05 @ @T T

UBT

Jg2g*KSBT P

JZPSZK

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f5('N Tf 3

05 n P @@ T
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YZR

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1 1.0

Intensität (normiert)

0.8

T = 10 K Ly = 13

8

4

2

1

0.5 nm

0.6 0.4 0.2 0 0.7

1.1 0.8 1.0 0.9 Photolumineszenz-Emissionsenergie/eV

1.2

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ZPV Jc125*$1,6&+(K j$/%/(,7(5

YZS

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YZT

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u8%675$7

y(//(1/>1*(1%(5(,&+

(;7(51( s8$17(1$86%(87(

i$k1c6r Jc/Ki$Jk1Kc6 c/i$k1r Jc/Ki$k1p c/i$Jk1Kp

k1r i$c6 i$c6 u$3+,5N u,eN JJi$pKK u$3+,5N u,eN JJi$pKK

SASPX =0 JpktK XVRASRRR JpktK W[RAXUR VRRAWVR UVR JwxK

SR@ WAWR@ SWAWR@ SRAUR@ "S@

ZPV Jc125*$1,6&+(K j$/%/(,7(5

+

YZU

Ni/Au semitransparente p - Kontaktschicht

Au p - GaN p - AlGaN i - GalnN/GaN

Ti/Al

n - GaN

y

Saphirsubstrat (a)

x

p - GaN

p - AlGaN

aktiver Bereich i - GalnN/GaN

n - GaN

QWs

EL

EV E

(b)

c%%P ZPVV

y

u&+(0$7,6&+(5 c8)%$8 (,1(5 %/$8(1 c/i$k1pOngf J$KN d$1'6758.785 J%KP

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YZX

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352 s8$'5$7=(17,0(7(5 (,1( (5+(%/,&+( g5,=,(1=5('8.7,21 %(2%$&+7(7 :,5'N 9(575$O *(1 %/$8( i5833(OkkkOp,75,'Ongf6 (567$81/,&+(5:(,6( x(56(7=81*6',&+7(1N ',( 0(+5 $/6 W i5?M(125'181*(1 *5?M(5 6,1'P g17635(&+(1' '@5)7(1 i$pOn$6(5 $8)*581' (,1'(87,*(5 1,&+7675$+/(1'(5 t(.20%,1$7,216352=(66( '85&+ ',(6( +2+(1 x(56(7O =81*6',&+7(1 A 0,7 i$c6Oo$M67>%(1 *(0(66(1 A ,0 i581'( *$5 1,&+7 67,08/,(57 (0,77,(5(1P c8)*581' '(5 67$5. 32/$5(1 p$785 '(5 d,1'81* '(5 g/(0(17( '(5 kkkP j$837*5833( 0,7 u7,&.6725 5(68/7,(57 (,1 (;75(0 67$5.(5 3,(=2(/(.75,6&+(5 g5(.7 81' '$0,7 67$5.( ,17(51( (/(.75,6&+( h(/'(5 ,1 j(7(526758.785(1 J6P c%%P ZPVVK LZTN ZUbP f,(6( h(/'(5 %(:,5.(1 ,1 '(1 s8$17(17/0(1 '(5 $.7,9(1 |21( @%(5 '(1 s8$1O 780Oe2171('Ou7$5.Og5(.7 (,1( (5,=,(17( t279(56&+,(%81* '(5 g0,66,21 ,1 ngf6P f,(6 ,67 @%(5+$837 '(5 i581'N '$66 1(%(1 '(1 (;=(//(17(1 %/$8(1 ngf6 $8&+ :,5./,&+ (5,=,(17( *5@1( ngf6 (;,67,(5(1P o$1 (5.(117 $86 c%%P ZPVXN '$66 ',( u7>5.( '(5 i5833(OkkkOp,75,'( -('2&+ (,1'(87,* ,0 d/$8(1 /,(*7P g,1( :(,7(5( '$0,7 =86$00(1O +>1*(1'( m85,26,7>7N ,67 ',( v$76$&+(N '$66 (6 7527= *5@1(5 1,75,',6&+(5 ngf6 .(,1( (5,=,(17(1 *5@1(1 1,75,',6&+(1 j$/%/(,7(5/$6(5 *,%7P k0 i(*(16$7= =8 '(1 ngf6N %(, '(1(1 ,0 d(75,(% ',( d$1'.$17(1 '(5 $.7,9(1 u&+,&+7 67$5. 9(5.,337 6,1' Jc%%P ZPVVKN ,67 ',(6 %(, j$/%/(,7(5/$6(51 J6P c%%P ZPWUK 1,&+7 '(5 h$//N 62 '$66 '(5 ,16 n>1*(5:(//,*( 9(56&+,(%(1'( s8$1780Oe2171('Ou7$5.Og5(.7 %(, j$/%/(,7(5/$6(51 1,&+7 817(567@7O =(1' :,5.6$0 :(5'(1 .$11P

ZPVPY m/$66,7.$7,21 921 j$/%/(,7(5/$6(51 c%%,/'81* ZPVY =(,*7 (,1( ./$66,7=,(5(1'( %(56,&+7 '(5 :,&+7,*67(1 j$/%/(,7(5/$6(5O d$8)250(1N :(/&+( =80 v(,/ ,1 '(1 )2/*(1'(1 '5(, c%6&+1,77(1 %(+$1'(/7 :(5'(1P f$%(, 6,1' '85&+*(+(1' ',( j$/%/(,7(5*5(1=9>&+(1 +25,=217$/ 25,(17,(57P |81>&+67 817(56&+(,'(7 0$1 =:,6&+(1 +25,=217$/(1 J/,1.6K 81' 9(57,.$/(1 J5(&+76K t(621$O 7256758.785(1N :$6 -(:(,/6 '85&+ ',( q5,(17,(581* '(6 n,&+7)(/'(6N 'P +P '(6 %5(,7(1 *5$8(1 f233(/3)(,/(6 $1*('(87(7 ,67P k0 (1*/,6&+(1 u35$&+*(%5$8&+ 635,&+7 0$1 921 NN+25,=217$/ &$9,77=O /,&+( h$&(77(1%(6&+,&+781*(1 J(1*/P &2$7,1*6K />667 6,&+ '(5 t(9(;,216*5$' =:,6&+(1 R 81' SRR@N 'P +P =:,6&+(1 (,1(5 g1763,(*(/81* 81' (,1(5 x2//9(563,(*(/81*N )5(, :>+/%$5 (,167(//(1P f,( g,*(16&+:,1*81*(1 2'(5 o2'(1 J6P d(5*0$11Bu&+$()(5N d$1' kkkK '(6 t(621$7256 (5*(%(1 6,&+ $86 0)3 J+d BT 1& ()) K 3 n P

JZPTRK

c16&+$8/,&+ *(6352&+(1 +(,M7 '$6N '$66 ',( t(621$725/>1*( n (,1 *$1==$+/,*(6 x,(/O )$&+(6 '(5 +$/%(1 n,&+7:(//(1/>1*( ,0 o(',80 %(75$*(1 0866N :2%(, 1& ()) ',( (5(.7,9( d5(&+=$+/ Jg,*(1:(57 '(5 j(/0+2/7=*/(,&+81* J6P c%6&+1P ZPUPSPUK '(6 y(//(1/(,7(56 ,67P k0 =:(,7(1 h$//N ,1 62 *(1$117(1 u758.785(1 0,7 9(57(,/7(5 t@&..233/81* Jfhd )@5 (1*/P ',675,%87(' )(('%$&.KN (5)2/*7 ',( 237,6&+( t(9(;,21 '85&+ '$6 fhdOi,77(5 $8) '(1 *(6$07(1 t(621$725 9(57(,/7P g,1( (5,=,(17( t@&..233/81* :,5' %(, '(5

ZPV Jc125*$1,6&+(K j$/%/(,7(5 (a) horizontaler Resonator

FP

hohe Facettenreflektivität erwünscht

YZY

(b) vertikaler Resonator (vc)

DFB

geringe Facettenreflektivität erwünscht

DBR 2 Kavität

Kantenemitter

Oberflächenemitter

DBR 1 VCSEL

DBR-Laser (2. Ordnung)

externer Resonator

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d5$**Oy(//(1/>1*( +d (5=,(/7N :(/&+( 0,7 '(5 fhd i,77(53(5,2'( M @%(5 ',( d5$**O d(=,(+81* .255(/,(57 ,67 0')% J+d B1& ()) K 3 TM P

JZPTSK

f$%(, ,67 0')% (,1( 1$7@5/,&+( |$+/ 81' %(6&+5(,%7 ',( q5'181* '(6 i,77(56P 1& ()) ,67 :,('(580 ',( (5(.7,9( d5(&+=$+/P h@5 (,1(1 %(, +d 3 SPWW =0 (0,77,(5(1'(1 fhdO n$6(5 ,67 )@5 (,1 i,77(5 (567(5 q5'181* J0')% 3 SK 81' (,1( (5(.7,9( d5(&+=$+/ 921 UPTY (,1( i,77(53(5,2'( 921 &$P TUY 10 (5)25'(5/,&+P c16&+$8/,&+ *(6352&+(1 0866 (,1 *$1==$+/,*(6 x,(/)$&+(6 '(5 y(//(1/>1*( ,0 o(',80 1$&+ i/P JZPTSK '(5 '23O 3(/7(1 i,77(53(5,2'( (17635(&+(1P o$1 %($&+7(N '$66 ',( 0$7+(0$7,6&+( u758.785 921 i/P JZPTRK 81' i/P JZPTSK ,'(17,6&+ ,67P k1 n$6(51 (,1(5 71*( 921 TRR =0 ,67 ,0 h$//( '(5 hrOn$6(5 0)3 )@5 o2'(1 ,11(5+$/% '(6 237,6&+(1 x(567>5O .81*63527/6 6(+5 *52M Ji5?M(125'181* SRRRK 81' ,0 h$//( '(5 fhdOn$6(5 ,67 0')% 0(,67 S Ji,77(5 (567(5 q5'181*KP

YZZ

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B si

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A

si

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Y[T

Z o$7(5,$/,(1 '(5 q372(/(.7521,. A i581'/$*(1 81' c1:(1'81*(1 (a)

FP

y

(b)

z DFB Stoppband

(c)

DFB Stoppband VCSEL

log Intensität

(d)

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(1)

(2)

(3)

(4)

(5)

E EVB

(5)

(2)

p-seitige Confinementschicht

ELB

(1)

n-seitige Confinementschicht

Elektronen im LB

(4) (3)

(2)

(1)

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(d)

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λ 2 Kavität 3

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  Selektion der Kavitätenmoden

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1.0

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2.5 λ Luft /µm



DBR 2 QW 3 QW 2 QW 1 DBR 1

1.5



 

Reflektionsspektrum eines DBR-Spiegels

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Membranen

0

Verbindungsbrücken

(a)

     

(b)

DBR 1 2.5 Perioden GalnAsP/Luft

λ /2 Luftkavität

-40

Wellenlängenabstimmung/nm

Halteblock

-20

DBR 2 2.5 Perioden GalnAsP/Luft InP-Substrat

-60 -80

1400

1600

-100 -120 -140 1400

-160 (c)

1500

0

1500

1600

-0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 Aktuationsspannung / V

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1.55 µm VCSEL

(a)

(b)

(c)

100 nm AlGalnAs/AlGalnAs MQWs Elektronenwellen-Resonator

(d)

3 µm GalnAsP/Luftspalt DBR Lichtwellen-Resonator

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EF

organischer Festkörper

Kathode

h+

h+

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EF e-

HOMO (Valenzband)

(a)

ohne Kontakt

Vext = 0

Vext = Vbi

Vext > Vbi

EC

EF

EF (b)

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