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Gr owth and Electr onic Pr operties of AlAs/GaAs Lateral Superlattices : fr om 2D to 1D. submitted by Petra Denk from Düsseldorf Chair of Experimental Semiconductor Physics Ludwig – Maximilians – University Munich Dissertation Prof. Dr . J. P . Kotthaus Physics Department Munich, June 9 th , 2000

Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 1: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

Growth and Electronic Properties of AlAs/GaAsLateral Superlattices : from 2D to 1D.

submitted byPetra Denk

from Düsseldorf

Chair of Experimental Semiconductor Physics

Ludwig – Maximilians – University Munich

Dissertation

Prof. Dr. J. P. Kotthaus

Physics Department

Munich, June 9th, 2000

Page 2: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 3: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 4: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 6: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 22: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

L

[100]

AlGaAs

AlGaAs

N monolayers

AlAsGaAs

a)

b)

c)

r

LSL

V

z

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Page 23: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

0.035

0.05

0.08

30 60 90 120r (nm)

Alu

min

ium

con

cent

ratio

n

c)

Alu

min

ium

con

cent

ratio

n

b b bcccccb b bb b bb b bb b b

c cc cc cc cb b bb b bb b bb b b

Ideal case :

GaAs AlAs

Al Ga AsxB 1–xBAl Ga As

x W 1–x W

Segregation effect:

Step disorder effect:

b b bcccccb b bb b bb b bb b b

ccccb b bb b bb b bb b b

0

L*x

b)

a)

0

0.5

1

0

0.5

1

Resulting potential modulation:

L*(1– )x

Structure:

d d

L*xL*(1– )x d d

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Page 24: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

Al Ala)

(Ga)

b)

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Page 25: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

0 500 nm

Fourier Transform (power spectrum)

1st peak

3rd peak Mod<0.1

2nd peak

Step array

Mod=0.2

Mod=0.4

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Page 26: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

wafer:

ε > 0

ε < 0

Al0.33Ga0.67As

Al0.08Ga0.92Aslateralsuperlattice

L (1+ε)

[001]

L

r

0.283 nm

AlAs

r[110]

GaAs

a) b)

ε = 0

εL

gra.

gra.

gra.

éz

é

é

é

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Page 30: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 31: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 32: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 33: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 34: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 35: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

� �  ¢¡ £L¤¦¥ §¨ � ¤ © ª¬«~£L­¯®  ±° ° ¨ ¥j ²° ³L¡ ª´¥x£µ ¶¸·  ¹£\º�ª»°*�C 7 ;#kzy 4 e$=DC�k A =DC 7:A k A k A = 4 o 5B9-7 q A =@; 5B9 =bC 7 =¨q@; 5FA � 4 qD=���q 4 � 7 qb=¨k 7:A�4 e¼y 4X9 o > ;+= 7:9/ 584�½`¾ A 1 * 4xA o8�8� 4 qb=�; 5B9 o 5B9-7 q A =J; 5B9 =bC 7�7�� � 7 qskGy 7�5 =J; >r9 ;+=@; l ;w=bC 7�4 q 7 =sk K ; >; 5 ; > H A k Ag4 e`=DC 7 =¨q@; 5FA � 4 qD={�_q 4 � 7 qD=sk 7:A » hXkG=DC 4 o8=�yZ;#m 587 =sk K - 7�>�9 2`hXk >G> � 7w> ;+= 7 q��q 7:AI7�5 = 7:9 1 *�C 7 q 7�A o > = A�4 e�=DC�k A ; 5 ; > H A k A ;#q 7�4 �?=@;#k 587:9 �-H AI4!> ¿]k 5 mv=bC 7�> k 587 ;#q¨k)/ 7�9�lAf7 y+k |¿Kd> ; AbA k K ; > 3 46> =@/�yZ; 5?5 =sqJ; 5BA � 4 qb= 7 <IoB;+=¨k 465 A{¥�; >z7:K +&k$Àpê,EPk 5 ;Îq 7�> ; � ;:=sk 465=skGy 7 ;+�?��q 4:� kGyZ;:=sk 465 1 *�C 7�AI4!> o8=sk 4!5j4 �8=J;#k 587:9 �XHw=bC�k A y 7 =bC 4X9 k Av7�� ; K =fkÁe�=DC 7A H A = 7 y k A k Af4 =¨q 4 �Z; 5B9 kÁe 4!58> H 7�> ; A =sk K�Kd46>G> k A k 4!5BA =J;,+ 7 � > ; Kd7 AàA C K q 4 eO=�t:À�E 1�Ä 5 =DC 7; 5 k Af4 =¨q 4 ��k KK ; Af7 » 7 1 m 1 e 4 q�=bC 7 y 4X9 o > ;+= 7�9 / 584�½v2rh 7 e 4!>G>z4 h ¾ kGyZ; 5 A ¾ kGyZ; 5 Àq(�E; 5B9x9-7 - 5?7 ; #Ô& #Ô & |�9X7 � 7�5B9-7�5 =fq 7�> ; � ;+=¨k 4!5 =skzy 7 1  A kzy+k > ;#q�;+�8�_q 4 ; K C�CB; A � 7S7�5K C 4mAf7�5 �-Hw½ 7 qDCB;#q 9 = A ; 5F9wÅn7�58587 A Ån7�585?7 ê � E�= 4pK ; ><K o > ;+= 7 =DC 7 yZ;!m 587 =¨k K - 7�>�99-7 � 7�5B9-7S5 = Kd4!5B9 o K =ski¿]kz=IH 1ÂieO= 7 qgCB;�¿&k 5 mìk 5 =sq 4X9 o Kd7�9 =DC 7 3 46> =@/�yZ; 5?5\7 <IoB;+=¨k 4!5~liA � 7:K k�; >�7 y��8CF; A kß/ 7 k Am�kn¿ 7S5 = 4 =bC 7�AbK q 7�7�5 k 5 mÆy 7:K CF; 5 k A y A 1 y 587i4 e�=DC 7 q 7:A o > = A�4 e¼=bC�k A h 4 q@+}hXk >z> � 7 =DC 79-7 y 465BA =¨q@;+=¨k 465�4 e�=DC 7587:Ko7:AbA kG=IH 4 e@k 5BKd> o 9 k 5 mvC�kim!C 7 q A o?�8�B; 5F98A k 5 =DC 7v9 k 7�>G7�K =sq¨k Ke1o 5BK =¨k 4!5xK ; ><K o > ;:=sk 465BA ;+=`C�knm6C 7 q K CF;#qsm 7�9X7�5BA kz=IH 4 qvC�kim!C 7 q�= 7 y�� 7 qJ;+=so_q 7 1 *�C_k Ak A�7 <�oB; > = 4xA ;�H�=bCB;:= 4!587p9-4k7:Ag584x>G465 m 7 q Ko4!5BA k 9-7 q`=bC 7p9 k 7�>G7�K =sq¨k K e1o 5BK =sk 465 ; A; AbK ; > ;!q 1 ¥ 4!5FAf7 <Io 7�5 = > H l ; A hXk >G> � 7xA C 4 h 5 k 5 =DC 7n7�5F9�4 e`=bC�k A�K CB;+�8= 7 q l =DC 7=sq@; 5BA kz=sk 4!5 ��q 4 �B;+�_k > kz=sk 7:A CB;�¿ 7 = 4 � 7¿K ; >�K o > ;:= 7:9�9 k Á 7 q 7�5 = > H 1¸m=@;#qD=sk 5 mi� 4 k 5 =�e 4 q$=DC 7r5 o?y 7 qsk K ; >�K ; >�K o > ;:=sk 4!5BA k A =bC 7�> k 587 ;#q¨k)/ 7�9ÆAI7 y+k |�Kd> ; AbA k K ; >3 4!> =@/�yZ; 585�7 <�oB;:=sk 4!5$l mpkn¿ 7�5 �XH

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Page 36: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

¯ É n Ë YÌ GZY[ l =d2 k A =DC 7 58465 7 <Io�k > kG�_qskno?y e1o 5FK =sk 4!5 9-7 - 587:9 Af4 =DCB;+=É n Ë YÌ GZY[ G =d2 l YÌ l Y[ ó ® O�Ͷk A =DC 7n5 o8yE� 7 q 4 e 7�>z7:K =¨q 4!5FA k 5 =DC 7 W | =DC��B; 5B9 ;+==¨kGy 7 Ê k 5 =bC 7vAf7 y¶k |ÎKd> ; AbA k K ; > �8CB; Af7`A �B; Kd7vÏk4!> o8y 7 l YÌ l Y[ ;+� 4 o?=Æ=DC 7 � 4 k 5 =YÌ GZY[ 1rÄ 5Z7 <Io�k > kG��q¨kno8y É n Ë YÌ GZY[ l Ê 2@q 7:9 o Kd7�A = 4 =bC 7 V 7 qDy+k`5µknqJ; K V�o 5BK =¨k 465É n Ë YÌ G Y[ G Ê 2 � É kn Ë YÌ G Y[ G Ê 2sÊÑÐ Ë 9 n Ë Y[ 2D2hXkz=bCÐ Ë 9@n ËKY[ 2b2 � (7S� � ËSÒGÓ Å #Ô Ç µ %�ÔÔfÕXÖ 2H7d( G

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z6À

Page 37: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

ÜZÝ�Þ ßnà�á�â�â�ãä�å+æpç è×äÎégêwá`êLå:ë+åoâ~ìÅ ;,+&k 5 mg=DC 7 ; AbA o8y��8=¨k 465BA =bCB;:=¯ =bC 7 q 7 k A ; K ; ><K o > ;+� >G7 ��q 4 �B;+�_k > kz=IH�� 7 qPo 5 kz=i=skGy 7 Ë 9-7 = 7 qby+k 587:9 �-H A o�kG=J;+� >z7y+k K q 4kADKd4 �_k K�K ; >�K o > ;:=sk 4!5BA 2r=bCB;:=; 5w7�>G7:K =sq 465 k 5 �B; 5F9 W\hXkG=DCnhi; Ïk7Ïk7�K = 4 qY[ � Ë [ à G [-í 2�hXk >z>îl ; A ;­q 7:A o > = 4 e�; Kd4!>z> k A k 465$l � 7�ADK ;+=D= 7 q 7:9 k 5 = 4 �B; 5B9 WH^hXkG=DC{h�; Ïk7Ïk7:K = 4 q Y[ ^ Ë ; ADA o8y+k 5 m A �_k 5pKd4!5XÏk7 q A ;+=¨k 465 2 1¯ ¥ 4!>z> k A k 465BAgK ; 5 � 7 h 7�>G>�>G4XK ; > kß/ 7:9 k 5QA �F; Kd7 ; 5F9 =skzy 7kl�Af4 =bCB;:=�=DC 7wKd46>G> k |A k 4!5w4XK�K o_qsqsk 5 mZ;:= YÌkl =v;#q 7E9-7 = 7 qby+k 587:9 �XHn�_q 4 � 7 qD=sk 7:AÆ4 e�=DC 7gAI4!> k 9 k 5 =DC 7kGy�y 7:9 k�;+= 7iÏ k K k 5 kz=IH 4 e YÌ ; 5B9 �-HE=bC 7 =¨kGy 7 k 5 = 7 q Ï ; > Ë = |Îï =d2 14!587ÑK ; 5±9X7 - 587 ; AbK ;:=b= 7 qsk 5 m¦�_q 4 �F;+��k > kG=IHðhiC�k K C¾k A mpk Ïk7�5 �XH¹=DC 7 <�oB; 5 =¨kG=IHu n p n ËPY[ ^ Y[ 2 1 *�C 7 <�oB; 5 =¨kG=IH ñ n p n ËPY[ ^ Y[ 2 l Ê l Y[ ^Ë / O�2 � G7�� �_q 7:ADAf7:A =bC 7 ��q 4 �B;+�_k > kz=IH�=bCB;:=v; 5w7S>G7:K =¨q 465 hXkG=DCnh�; Ïk7`Ïk7:K = 4 q Y[ 4 e A o8�8�B; 5B9 WhXk >G> � 7pAbK ;:=b= 7 q 7:9 k 5 = 4 ; 5 H 46587Z4 ev=DC 7 m�q 4 o8� 4 e >G7�Ïk7S><A Ë hXkz=bCj=bC 7pA ;+y 7ZA ��k 5 2Kd4!5 =@;!k 587:9 k 5 =DC 7 k 5 - 5 kz= 7:A kGyZ; > + |�A �B; Kd7nÏk46> o8y 7�7�>z7 y 7�5 = l Y[ ^ ;:� 4 o8= Y[ ^ k 5 =DC 7A o8�8�F; 5B9 W_^ Ë ; AbA o8y+k 5 m}=bCF;+=�=bC 7:AI7v>G7�Ïk7�>�A ;#q 7 ; >G> o 584XK�K o8�_k 7:9 ; 5F9 =bC 7 q 7 e 4 q 75?4 =e 4 qb�_k 989-7S5 �XHE=bC 7v7��?Kd> o A k 465 ��qsk 5BK kG� >G7 2Àk 5 ; 5 k 5 - 5 kG= 7:A kzyZ; > =¨kGy 7 k 5 = 7 q Ï ; > l Ê 1*�C 7 �B;!qb=¨k K o > ;#qÆe 4 qby»=J;,+ 7�5 �-H usn,p n ËPY[ ^ Y[ 2 9-7 � 7�5B9?Aò465 =bC 7 �B;#qD=sk K o > ;!q ADK ;+= |= 7 q¨k 5 m`y 7:K CB; 5 k A y¢; 5B9 hXk >G> � 7¿9 k ADK o AbAI7:9 k 5 y 4 q 7v9-7 =@;#k > k 5nAI7:K =¨k 4!5 z 1 t 1>�; Ï k 5 m 9-7 - 5?7:9 =DC�k A =¨q@; 5FA kG=¨k 465 ��q 4 �B;:��k > kG=IH l =DC 7�Kd4!>z> k A k 465 = 7 qby K ; 5 � 7E7��3|��q 7:ADAf7:9 �XH

­ ¬8É kn¬BÊ VX� � ¢ ¢ � ­ Ú Y� YÏ Ë;Y[ 2 Ë ¬FÉ kn¬ � 2 � iIn p h ñ n p n ËPY[ ^ Y[ 2KA É n Ë;Y[ 2 ­ É n p ËPY[ ^ 2�EOó Ë z 1ô/ 2*�C_k A k A q 7 yZ;!q|+6;+� >G7 k 5 =bCF;+= Af7�5BAI7 =DCB;+=�kz=Xk Ai4!58> HZ=bC 7¿9-7�Ï k<;+=¨k 465 mX n ËKY[ 2re1q 4 y=bC 7v7 <Io�k > kG��q¨kno8yðe1o 5BK =¨k 465 hiC 4�9-7 = 7 qDy+k 587�A =DC 7`Kd4!>z> k A k 465 = 7 qby 1

ÜZÝ@õ ßZé�ë:öZâråSé�æ ég÷øârùpã ú¢é�ëoâ�ûòü ágæwæ ý¹þZöpá�ârå�é�æy 5FKd7 ;#mm;#k 5$l =DC 7`9 kÁÿ K o > =IH°k 5 - 5B9 k 5 mE; Af4!> o8=sk 4!5 ;#q¨k AI7:A e1q 4 y±=bC 7`Kd4 y�� >z7�� kz=IH 4 e=bC 7�Kd4!>z> k A k 465 = 7 qDy 1 y 58> Hne 4 q Ïk7 qbH A � 7:K k�; >�K ; Af7:A =bC�k Aò7 <�oB;:=sk 4!5 k A ; 5 ; > HX=sk K ; >z> HAf4!>zÏ ;+� >z7 1ZÄ 5 =bC 7 e 4!>z>G4 hXk 5 mn; AI4!> o8=sk 4!5\4 e�=bC 7 3 4!> =|/�yZ; 585 *Mq@; 5FA � 4 qD= 7 <IoB;:=sk 465hXk >G> � 7}9X7 qsk Ïk7:9�l CB; Ï k 5 mEyZ; 9-7 =bC 7 e 4!>z>G4 hXk 5 mE; AbA o8y��8=¨k 465BA Wz£t

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¯ =DC 7v7 Á 7:K =¨k Ïk7 yZ; AbA y � k Ai9 kiq 7:K =sk 465 k 5F9-7 � 7�5B9-7S5 = 1¯ =DC 7 =sq@; 5BA kz=sk 4!5 ��q 4 �B;:��k > kG=IH 9X4k7:AÎ584 = 9-7 � 7S5B9�4!5 =bC 7�9 k A =sq¨kG��o8=¨k 465 e1o 5FK =sk 4!5mÓn Ë;Y[ 2 1¯ ; >G>�ADK ;+=D= 7 q¨k 5 m 7�Ïk7S5 = A ;#q 7v7�> ; A =sk K4 q�<IoB; A k |r7S> ; A =sk K!l k 1 7 1 4 n Ë Y[ 2 � 4 n p Ë Y[ ^ 2 1� 5B9-7 q�=bC 7�Af7 ; ADA o8y��?=sk 465BA�4!5?7 q 7 ; 9 k > H0- 5B98A A��Ikim�m�k�; t=T,ErW

É n ËKY[ 2 � ­ Ú�� n Ë � n Ë;Y[ 2D2KA ÌÍ� � Y[�� Y�xE ¬8É kn Ë Y[ 2¬ � Ë z 1 z32hiC 7 q 7 � n k A =bC 7 q 7�> ; � ;:=sk 465 =skGy 79 k AbK o AbAf7�9 k 5 =bC 7v587�� = Af7�K =sk 4!5 1ÜZÝbÜ �»ã�ëSá�pá�âråSé�æ å:ü ã����~o��~� � �����������P������§��� �����;�s���6���b� � ��!"������P�#! }%$D�'&Ä 5 ; 5 o 5 y 4X9 o > ;+= 7:9 / 584�½¯=bC 7 q 7�> ; � ;:=sk 465 =skGy 7 � k A ;}e1o 5BK =¨k 4!5Z4 e 7�587 q¨m!H l ��o8=9-4k7�A 584 = 9X7 � 7�5B9�7�� � > k K kG= > H 465 Y[ 9 o 7 = 4 kG= A k Af4 =sq 4 ��k K V 7 qDy+k 7�587 q¨m!H A o�qfe0; Kd7 1rÄ =k Ai9-7 - 587�9 �XHBA Ån4 qsk � T,E

­ ¬FÉ n Ë;Y[ 2¬BÊ VX� � ¢ ¢ � É n Ë;Y[ 2� n Ë �}2 Ë z 1 ® 2k 1 7 1 kG=Àk A k 5XÏk7 q Af7�> HÆ��q 4 � 4 qD=sk 4!5 ; > = 4 =DC 7iKo4!>G> k A k 4!5 = 7 qby 1 *�C�k A k A k 5 =¨o�kG=¨k Ïk7�> HXo 5B9-7 q |A =@; 5F9 ;+� >z7kl k e 46587vKd465BA k 9-7 q A hiCB;:=�CB;:�8� 7�5BA hiC 7S5 =bC 7�7�� = 7 q 5 ; > e 4 q Ko7:A CB; Ïk7 � 7�7�5q 7 y 4:Ïk7:9 k 5FA =@; 5 =J; 587S4 o AI> H 1wÄ 5 =DC�k A`K ; AI7 =bC 7 � 7 qb=¨o�qb�B;:=sk 4!5 k 5 =DC 7Z9 k A =¨qskG�_o8=sk 4!5e1o 5FK =sk 4!5 hXk >z> � 7`K CB; 5 m 7:9Z9 o 7 = 4�Kd46>G> k A k 4!5BA ; 5B9p9-7:K ;�H 7S� � 4!5?7�5 =¨k<; >G> H¼WÉ n Ë;Y[ G Ê 2 � É n Ë;Y[ G Tk2 Ú µ Æ(*) ,,+ Ë z 1.- 2*�C 7 =¨kGy 7 � Ë 4�2�=bC&o A q 7 ��q 7:Af7�5 = A ; A H A = 7 y K CB;!q@; K = 7 q¨k A =sk K =¨kGy 7`Kd465BA =J; 5 =Æe 4 q=DC 7 q 7�> ; � ;+=¨k 4!5`4 eB=DC 7 � 7 qb=¨o�qb�F;+=sk 4!5$l k 1 7 1 =DC 7 =¨kGy 7 o 5 =¨k > =bC 7 o 5 � 7 qD=so�qD� 7�9gA H A = 7 yCB; A q 7 ; K C 7:9 kz= A =bC 7 qby 4X9 H 5 ;:y+k K�7 <�o�k > kz��qskio8y 1� Ë 4�2�k Ai9X7 = 7 qDy+k 5?7:9 �-H�=bC 7`Kd4 o8� >G7�9 3 46> =@/�yZ; 5?5�7 <IoB;+=¨k 4!5FA A��£knm�mpk<;ft=T�E� n Ë �}2�/ n n Ë Y[ G Y[ ^ 2 ­ In10h n p / n,n p Ë Y[ G Y[ ^ 2 � n p Ë �`2 � (!ó Ë z 1 À32hXkz=bC z �

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/�n n Ë Y[ G Y[ ^ 2 � / OÌÍ c *-, l � [ ^Ë / O�2 � Vqô W ^ Y[ ^ V�� & � !"�" � VXW Y[�\ V � Ë ( ­ J;L M32 2 ï Ë � n Ë Y[ 2 ­ ��n p Ë Y[ ^ 2b27 In p40h n / OÌÍ c l � [ ^Ë / O�2 � VZô W ^ Y[ ^ V � � Û�5,5 VXW Y[�\ V � ï Ë � n ËKY[ 2 ­ � n ËPY[ ^ 2D2

/ n n,p ËKY[ GHY[ ^ 2 � /�n p n ËPY[ ^ GZY[ 2 � / OÌÍ [ n p[ n c l � [ ^Ë / O�2 � VÓô W ^ [ ^ V�� � Û6575 VXW [�\ V � $JKL,M32 ï Ë � n Ë*8 2 ­ � n p Ë*8 ^ 2b2hXkG=bC\c Ë 4�2� 7 k 5 mn; Kd465BA =J; 5 = 7�587 q¨m!H A o_qfe0; Ko7 ; 5B9\9 �|+ � l [ È l [ � 1 *�C 7 yZ;:=sq¨k �7�>G7 y 7�5 =0V ô W ^ Y[ ^ V � � Û�5,5 VXW Y[¿\ V � 9-7:ADK qskz� 7:A =bC 7 =¨q@; 5FA kG=¨k 465 ��q 4 �B;+�_k > kz=IHn� 7 qfo 5 kz==skGy 7 e1q 4 y¹=bC 7�A =@;:= 7 V W GZY[�\ = 4 =bC 7�A =J;+= 7 VXWH^ G�Y[ ^ \ 9 o 7 = 4 ; ADK ;+=D= 7 q¨k 5 m�� 4 = 7�5 =sk�; > 1*�C�k A hXk >G> � 7`9 k AbK o ADAf7:9 k 5 y 4 q 7�9-7 =@;!k > k 5 =DC 7v587�� = Af7:K =sk 465 1Ä 5 =bC 7}K ; Af7v4 e�=DC 7v7�>G7:K =sqsk K ; > <IoB; 5 =so?y > kzy+kG= 7 <IoB;+=¨k 465 z 1 À A kzy�� > k�- 7:A = 4(� n Ë �`2 � c *-, l � [/ O ÌÍ VqôÏW ^ Y[ ^ V�� � Û�5,5 VXW Y[�\ V � Ë ( ­ JKL,M32 2 ï Ë ��n Ë Y[ 2 ­ � n,p Ë Y[ ^ 2b2 Ë z 1 t!2hXkG=bC 2 � 7 k 5 m =DC 7 ; 5 m >z7 � 7 =Ih 7�7�5 =bC 7xA =@;:= 7 V Y[ \ ; 5B9 V Y[ ^ \ 1 > 7�5FKd7kl�7�Ïk7 qbHAbK ;:=b= 7 qsk 5 m 7�Ïk7�5 =Xk A ; Ïk7 qJ;#m 7:9n4:Ïk7 qµkz= A �_q 439b7:K =sk 465w4 e�=bC 7g4 o8=¨m 4 k 5 mZhi; Ïk7}Ïk7�K = 4 q4!5 =bC 7 k 5BK k 9X7�5 = 9 kiq 7:K =sk 465 1 *�C 7 q 7�> ; � ;:=sk 4!5 =skzy 7 k A =bC&o A k 5XÏk7 q Af7�> H}��q 4 � 4 qD=sk 465 ; >= 4 =DC 7 Ë k 5 = 7 mpq@;:= 7:9 2¿��q 4 �B;+��k > kz=sk 7�A 4 eg=sqJ; 5BA kG=¨k 4!5FA k 5 = 4 ; 5F9)4 o8= 4 e 7 ; K C A =@;:= 7V Y[ \ l h 7 kim!CX= 7:9 �XHg; 5 ; 5 m >z79-7 � 7S5B9-7�5 =�e0; K = 4 qr= 4 ; >G>z4 hje 4 qr=bC 7 ��kim 7,:¼7:K = 465 =DC 7K CB; 5 m 7g4 ei=DC 7E9 k A =sq¨kG��o8=¨k 465 e1o 5BK =¨k 4!5x4 e AbK ;:=b= 7 qsk 5 m�=bC_q 4 o_m!C > ;#qsm 7 ; 5 m >G7:A 1 *�C 7; Ïk7 q@;#m 7:9 m 7�4 y 7 =sqsk K ; > e0; K = 4 qô ( ­ JKL M32 \ � ; *=< %?> � · Ô� s�tu VZô W Y[ ^ V � & � !#"�"�� VXW Y[�\ V � Ë ( ­ JKL,M32 2 ï Ë � n Ë Y[ 2 ­ � n p Ë Y[ ^ 2b2; *=< %?> � · #Ô� s�tu VqôÏW Y[ ^ V�� � Û6575 VXW Y[�\ V � ï Ë � n Ë Y[ 2 ­ � n p Ë Y[ ^ 2b2 Ë z 1ô� 2hXk >G>?A =¨q 465 m > H 9-7 � 7S5B9 465 =DC 7 =fHX� 7i4 eÀk 5 = 7 q@; K =sk 4!5 � 4 = 7�5 =¨k<; >A@ � Û6575 lk4!587 k ArKd465BA k 93|7 qsk 5 m 1�Ä e 4!5?7iKd465BA k 9-7 q A ; AbK ;:=b= 7 qsk 5 mÆ� 4 = 7�5 =sk<; >îl hiC�k K C 9-7 � 7�5B9?A 465 =bC 7�AbK ;:=b= 7 qsk 5 mÏk7:K = 4 q YB � Y[ ­ Y[ ^ ; 5B9 C 7�5BKo7�465 2 Ë YB � / Y[�ö A k 5 Ë 2 ó / 2 l�46587pK ; 5 CF; Ïk7 e0; Ïk4 q 7:9e 4 qbh�;#q 9�ADK ;+=D= 7 q¨k 5 m l37 1 m 1 ô Ë ( |rKo4kA 2 2Ðô ( l 2 ô(ê�TDC 4 qÎ�F; K +-h�;#q 9EAbK ;+=b= 7 qsk 5 m l k 1 7 12 \ ê�TDC Ë Af7�7 ; >�Af4 Vlknm 1 z 1 (+2 1 y 5 =bC 7�4 �8� 4mA kG= 7kl e 4 qi;v< | k 5B9-7 � 7S5B9-7�5 = AbK ;:=b= 7 qsk 5 m� 4 = 7�5 =sk�; > =DC 7 = 7 qbyõô Ë ( |�Kd4mA 2 2 \ hXk >G> � 7}7 <�oB; > = 4E4!587ml�7�� ��q 7:AbA k 5 mE=bC 7v7 <IoB; >��q 4 �B;+��k > kz=fH 4 e�CB; Ï k 5 mge 4 qDhi;#q 9 ; 5B9 �B; K +-h�;#q 9{ADK ;+=D= 7 q¨k 5 m 1z�ê

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The redistribution of the scattered state is isotrop.

Small angle scatteringis here prefered.

E

q independent diffusion potential, e.g. (unscreened) alloy scattering:

q – dependent diffusion potential,e.g. remote ionized impurity :

kFk GF

qF

Vlkim�o�q 7 z 1 (!WÆëX��ï[ô©í¤îuñ�òfônîpïga8 @ ï)ú£ï[ý @ ï[ý]í¨ï�ñ�ò @ õ H�ï[÷�ï[ý]ôÀø�ísó!ô©ô©ï[÷sõiý,��ú£ñ#ô©ï[ý&ô©õnó!ö~ø[ûPÿ î�õiöxïò�ñ#÷¨ÿMó!÷ @ ó!ý @ �aó!í@��ÿMó!÷ @ ø�í¨ó!ô©ô©ï�÷¨õný �>îpó é[ïÆïba[ù�ó!öIú�÷�ñ���ó��¤õiöxõnô©õiï¤ø�õnýônîpïÆí¨óUø�ïfñ)ò ó#ýpa©áõnýZ@ ï�úIï[ý @ ï[ý]ô ø�ísó!ô©ô©ï[÷sõný ��ú£ñ#ô©ï[ý&ô©õnó!ö � ø�ð�ó!önö`�4ñ!÷�ö�ó#÷ß��ï�ü�ó#ý �pöxï²ø�ísó!ô©ô©ï[÷sõný �fõ ø�ø�ô©÷�ñ!ý,�pö{�Mò�ó é�ñ!÷�ï @õiý+ônîpï±í¨ó�ø�ïPñ)ò�ó}a� @ ï�úIï[ý @ ï[ý&ô ø�ísó!ô©ô©ï[÷sõiý,�µú£ñ!ô©ï�ý&ô©õnó!ö����~o��~�} � �����������P������§��� �����;�s���JI ��!"��������K! }L$ �'&Ä 5 ;}y 4X9 o > ;:= 7:9 / 584�½ =DC 7 ; ADA o8y��8=sk 4!5Z4 e�; #Ô& #Ô & | k 5B9X7 � 7�5B9-7�5 =�q 7�> ; � ;+=¨k 4!5 =skGy 7k A�584g>G465 m 7 q Ï ; > k 9Z9 o 7 = 4 =bC 7 ; 5 k AI4 =sq 4 ��k K V 7 qby+k 7S587 qsm6H A o_qfe0; Ko7 1sr 7�Ïk7 qD=bC 7S>G7:ADAdl46587gK ; 5 =¨qbH�= 4 - 5F9 ; 5 ;+�8�_q 4:� kzyZ;+= 7:9�7�� ��q 7:AbA k 4!5 �XH 9-7 - 5 k 5 m�; Y[ |�9-7 � 7S5B9-7�5 =q 7�> ; � ;:=sk 465 =¨kGy 7 � ËKY[ 2KA ¾ kGyZ; 5 Àj(KE 1 � ËKY[ 2 K ; 5 � 7 k 5 = 7 qb��q 7 = 7�9�l k 5 ; 5 ; >z4 m6Hw= 4 =DC 7k Af4 =¨q 4 ��k KgK ; Af7kl ; A ; K CB;!q@; K = 7 q¨k A =sk K =¨kGy 7 e 4 qv=DC 7E9-7:AI7��8K kG=@;:=sk 4!5n4 e ð ñ¨î A =@;:= 7 Y[ 1Ä 5 =bC 7 e 46>G>G4 hXk 5 mg=bC 7v584 =@;:=sk 465 YM � Ë W l Y[ 2 A CB; >G> � 7 o Af7:9 1�k=@;!qb=sk 5 mE;#mm;#k 5 e1q 4 y 7 <Io 1 z 1 ® Ë ��o8=ihXkz=bCp; YM�|�9-7 � 7�5B9-7S5 =�q 7�> ; � ;+=sk 4!5 =skzy 7 2

­ ¬8É Ë YM 2¬�Ê V � � ¢ ¢ � É Ë YM 2� Ë YM 2 G Ë z 1 ê324!587v4 �?=@;#k 5BA (� n Ë YM 2 � I4N p / Ë YM G YM ^ 2UA³( ­ É Ë YM ^ 2É Ë YM 2 E0ó Ë z 1 (¼T32Ä 5FAf7 qD=sk 5 m 7 <IoB;+= 1 z 1 z>k 5{7 <�o 1 z 1 (¼T l84!5?7g9-7:9 o Kd7:A W

® T

Page 41: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

(� Ë YM 2 � ION p / Ë YM G YM ^ 2KA�( ­ � Ë YM ^ 2� Ë YM 2 Y� � Ï Ë YM ^ 2Y� � Ï Ë YM 2 E ó Ë z 1 (�(+2y 5?7�Kd>G7 ;!q > H±q 7 ; > k)/ 7�A =DCB;+= 584 h 7 ; K C°q 7�> ; � ;+=sk 4!5 =¨kGy 7 e 4 q 46587A =@;:= 7 YM�9-7 � 7S5B98A�4!5; >G> =bC 7�4 =DC 7 q YM�|�9-7 � 7�5B9-7S5 =�q 7S> ; � ;+=¨k 465 =skGy 7:A 1 4s<�oF;+=sk 4!5 z 1 (�( K ; 5 � 7�A kGy�� > k�- 7:9= 4 (� Ë YM 2 � ION p / Ë YM ^ YM 2KA³( ­ � Ë YM ^ 2� Ë YM 2 YÏ Ë YM ^ 2YÏ Ë YM 2 E Ë JKL M32 ­ Ê S1P W MRQ P 2 2 G Ë z 1 ( / 2hiC 7 q 7 W k AiK C 4mAf7�5 ; A =bC 7 ; 5 m >G7 � 7 =Ih 7�7�5 =DC 7}7�>z7:K =¨qsk K ; > - 7�>�9 Y� ; 5F9 =bC 7�Ïk7�K = 4 qY[ 1 �Ik 5BKo7�46587 k A�4658> H >G4k4 +&k 5 mne 4 q Af46> o8=¨k 465BA}> k 587 ;#qfk 5 =DC 7�7�>z7:K =¨qsk K ; > - 7S><9�l =DC 7=sq@; 5BA � 4 qb=i=skzy 7 � Ë YM 2 9-4k7�AÎ584 = 9-7 � 7�5F9�4!5 =DC 77�>z7:K =¨qsk K ; > - 7�><9 Y� 1 ¥ 465BAf7 <�o 7S5 = > H l=bC 7 W |�9-7 � 7�5F9-7�5 =�= 7 qby k A T�; 5B9 kG=Xq 7 yZ;#k 5BA W(� Ë YM 2 �:I S p / Ë YM YM ^ 2KA³( ­ � Ë YM ^ 2� Ë YM 2 YÏ Ë YM ^ 2YÏ Ë YM 2 E JKL,M32 G Ë z 1 (¼z32

*�C 7 ; 5 m >z7 2 CB; A 5?4 =g� 7�7�5 9-7 - 587:9 H 7 =�W Ä 5 ; 5 o 5 y 4X9 o > ;+= 7�9 / 584�½ l =DC 7; 5 m >G7 2 k A}K C 4kAI7�5 ; A =DC 7 ; 5 m >z7 � 7 =Ih 7�7�5 =bC 7ZA =@;:= 7 V Y[R\ ; 5B9 V Y[ ^ \ l hiC�k K C k Ak 9-7�5 =sk K ; > = 4 =bC 7 ; 5 m >G7 � 7 =Ih 7�7S5 =DC 7 mpq 4 o8� Ïk7�>z4XK kG=¨k 7:AÆ4 e A =@;+= 7 V Y[¿\ ; 5B9 V Y[ ^ \Ë 7 1 m 1 YÏ Ë Y[ ^ 2%T�V Y[�\ 2 1 ¥ 4!5 =sq@;!qsk > H l k 5 ; 5 y 4X9 o > ;+= 7:9 / 584�½ l!9 o 7 = 4 =DC 7 ; 5 k Af4 =¨q 4 ��k KV 7 qby+k A o_qfe0; Ko7kl =DC 7 ; ADA o8y��?=sk 465 =bCB;:=�=DC 7 ; 5 m >G7 � 7 =Ih 7�7�5 =DC 7pA =@;:= 7:A Ë Y[ G Y[ ^ 2Æk A7 <�oF; > = 4 =bC 7 ; 5 m >G7 � 7 =Ih 7�7S5 =DC 7 m�q 4 o8� Ïk7S>G4XK kz=sk 7�A YÏ Ë Y[ ^ 2D2Xk Ai584�>z4!5 m 7 q 9 o A =¨k³- 7:9 1Ä 5 =bC 7ZK CF;+�8= 7 q`; 5B9 --1 ® 1 z lrKd4 y��B;#q¨k AI4!5 hXk >G> � 7 yZ; 9-7 � 7 =fh 7�7�5 =bC 7�K ; ><K o > ;+= 7:9y 4 ��k > kz=sk 7�Adl =@; +]k 5 m 2 ; A =bC 7 ; 5 m >z7 � 7 =Ih 7S7�5 =DC 7 hi; Ïk7iÏk7:K = 4 q A =@;+= 7:A ; 5B9 =J;,+&k 5 m 2; A =bC 7 ; 5 m >G7 � 7 =Ih 7S7�5 =bC 7 mpq 4 o8� Ïk7�>G4XK kG=sk 7:A�4 e A =@;:= 7:A Y[ ; 5B9 Y[ ^ 1�Ä 5 =¨o�kG=¨k Ïk7�> H l64!587K ; 5 =sqDHg= 4U9 o A =¨kÁeOHg=DC�k ArK C 4 k Kd7 �-H`CB; Ï k 5 mfk 5 y+k 5F9 =bCF;+=�=DC 7 q 7�> ; � ;+=sk 4!5 =skzy 7 � Ë YM 24 e�; A H A = 7 y A C 4 o >�9�5?4 =�� 7 ; :¼7:K = 7:9 �XH}e 4 qDhi;!q 9ZAbK ;:=b= 7 qsk 5 m lX7 1 m 1 kÁe YÏ ËPY[ ^ 2�T YÏ Ë;Y[ 2 l; 5B9 � 7EA =sq 4!5 m > Hp; :¼7:K = 7:9 �XHZ�B; K +Xhi;#q 9nADK ;+=D= 7 q¨k 5 m l�7 1 m 1 YÏ Ë Y[ 2 T ­ YÏ Ë Y[ 2 1 *�C_k A k AyZ;+=DC 7 yZ;:=sk K ; >G> HE=@; + 7�5 k 5 = 4 ; K�Ko4 o 5 =�XH K C 4k4kA k 5 m 2 ; A =DC 7 ; 5 m >G7g4 ei=DC 7 m�q 4 o8�Ïk7�>G4XK kz=sk 7:A q@;:=bC 7 qi=bCB; 5 =J;,+&k 5 mg=DC 7 ; 5 m >G7 2 Ô � 7 =Ih 7�7�5 =DC 7`A =@;:= 7:A V Y[¦\ ; 5B9 V Y[ ^ \ 13�o8= l ; A y 7�5 =sk 4!587�9 ;+� 4:Ïk7kl =@; +]k 5 m 2 ; A =DC 7 ; 5 m >G7 � 7 =Ih 7S7�5 =DC 7 m�q 4 o8� Ïk7�>z4XK kG=¨k 7:AK ; 585?4 =i� 7V9 o A =sk�- 7:9 qskim 4 q 4 o AI> HBA ¾ kGyZ; 5 Àj(KE 1V 4 q�=bC 7Æ5 o8y 7 q¨k K ; >8K ; ><K o > ;:=sk 465BAdl =DC 7 ;#o?= 4}|^Kd4 C 7 q 7�5BK H 4 e 7 <�oB;:=sk 4!5 z 1 (�z}hXk >G>� 7 knm 584 q 7:9 1 *�C&o A =DC 7 =¨q@; 5FA � 4 qD=i=skGy 7�K ; 5 � 7 hXq¨kG=D= 7�5 e 4 qDyZ; >z> HÆk 9-7�5 =sk K ; > = 4 =DC 7=sq@; 5BA � 4 qb=�=skGy 7Æ4 e�; 5 o 5 y 4X9 o > ;+= 7:9�7�>z7:K =¨q 4!5 mm; Adl® (

Page 42: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

(� n Ë Y[ 2 � c * , l � [/ O ÌÍ VjôdW Y[ ^ V�� � Û6575 V W Y[�\ V � Ë ( ­ J;L M32 2 ï Ë ��n Ë Y[ 2 ­ ��n p Ë Y[ ^ 2D2 Ë z 1 ( ® 2��o?=Æ=DC�k A =¨kGy 7 hXkG=DCn; Y[ |�9-7 � 7�5B9-7S5 =�q 7�> ; � ;+=sk 4!5 =skzy 7 1

ÜZÝ�W X ágë:àÆöwëSá�âråSé�æ ég÷ âÎùpã Y á à�äÎé[Z�àié]\Lå:à ^ öpágæEâÎå7_âÎåSãZy 5BKd7 CB; Ï k 5 m K ; >�K o > ;:= 7:9 =bC 7 q 7�> ; � ;+=¨k 4!5 =skzy 7 � n Ë YM 2 l =bC 7¿9 k<;!m 465 ; >rKo4 y�� 4!5?7�5 = A4 er=bC 7`Kd465B9 o K =sk Ï kG=IHg= 7�5BAf4 q;!q 7v4 �?=@;#k 587:9 k 5 =bC 7 o A oB; > y�; 58587 q�W`ba�a Ëdc � T32 � I n c * , Ô l � [ É Ë YM 2 Ëfe � Ì à G Ì í 2

� Ú �/ O � I n c * , Ô l � [ Ë ­ ¬8É k Ë YM 2¬ � 2 � Ë YM 2 YÏ �a Ë YM 2Jó Ë z 1 ( - 2*�C 7 k 5 = 7 m�q@; >�4:Ïk7 q 9 � Y[ A knm 5 k³- 7:A =bCB;:= 46587 k 5 = 7 m�q@;:= 7:A�4+Ïk7 qÆ=DC 7EKd4!5FA =@; 5 = 7�5?7 qsm6HA o�qfe0; Kd7:A c % Ô W 9 � [ � 9 [ à 9 [-í hiC 7 q 7E9 [ à�k A =bC 7g7�>z7 y 7�5 = 4 ei=DC 7EA o�qIe0; Kd7g4 e�c %; 5B9n9 [ í � 9 46Ý ÌÍ Ï #N 1*�C 7 = 7 y�� 7 qJ;+=¨o�q 7r9X7 � 7�5B9-7�5FKd7r4 e?=bC 7�Kd465B9 o K =¨k Ï kG=IHPk A m�k Ïk7�5 �-H�=bC 7�A =J;+=¨k A =¨k K ; >h 7 knm6C-= ¬ m k Ë Y8 2|Ý ¬ 4iW

`Aaga Ëdc 2 � c l � Ë ­¬8É k Ë YM 2¬ � 2 `Aaga Ë �`2 hXkG=DC Ë z 1 (SÀ32

`ba�a Ë �}2 � Ú �/ O ÌÍ I n ( * , l [YÏ1h � Ë YM 2 YÏ �a Ë YM 2 G Ë z 1 ( t!2hiC 7 q 7 c % Kd4 q¨q 7:A � 465B98A = 4 ; >z>Ko4!5BA =@; 5 = 7�587 q¨m!H A o�qIe0; Kd7�A�> H&k 5 mºk 5 =DC 7n7�5?7 qsm6HqJ; 5 m 7ji 4 � 4 ö ë À,+1k¨* 1  K�Kd4 q 9 k 5 m > H l ;+=�* � T6� 4!5?> H A =@;:= 7:Av4 e�=bC 7 V 7 qDy+kA o�qfe0; Kd7EKd4!5 =sq¨kG��o?= 7 = 4 =bC 7EKd465B9 o K =sk Ï kG=IH l hiC 7 q 7 ; A ;+=8- 5 kz= 7 = 7 y�� 7 qJ;+=so_q 7gA =@;:= 7:Ak 5 � 7 =Ih 7�7�5 4 ö ë À,+1kF* Kd465 =¨qskz��o8= 7 = 4 =bC 7`Kd465B9 o K =¨k Ï kG=IH 1Ä 5 =DC 7gK ; Af7`4 e�; 5 o 5 y 4X9 o > ;+= 7:9 / 584�½ l =DC 7 k 5 = 7 m�qJ; >�4 er=DC 7}7�5?7 qsm6H A o�qIe0; Kd7k A�7 <�oF; > = 4 / OH46ó ÌÍ ; 5F9{4!5?7�4 �8=@;!k 5BA Ë W Kd4 qsq 7:A � 4!5F98A = 4 =DC 7 W | =bC A o?�8�B; 5F9 2@WM�ØjlnmporqVsut3v,qfw�Øyxft3z{v7|3},t3v7|RxVxft3wvå~tRv7�rw8å?v,zf����â�xVorq�sut3v,qfw�Ø�qf|3sutjx{t���x��,�3���7��v��%xft3w� v � |3�6��x{orv[Øjorq�oxØ3s��r|3�3w��=�¨å~t3waØ�oxØgxfw�},zd��xfoxØ3}�v��,w�z�xft3wgRRw�zf��o~� �Korzd��s�3orqfxfz{o{ã3|3xforv�Øj�4|#Ø3s�xforv�Øã�w*x�å?w�waØ��A�=�fm��g��ø���Ø3���A� �¡m��g��ø%�

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Page 43: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

` n n Ë �}2 � Ú �O ÌÍ c * % l � ­ ¬8É kn Ë �`2¬ � � � n Ë �}2 Ë z 1 ( � 2Ä 5 =sq 4X9 o K k 5 m 7�� � > k K kG= > H`=bC 7`K CB;#q¨m 7`9-7�5BA kG=IH 4 er=DC 7 W | =bC A o8�?�B; 5B9 W¢vn]£ � �O ÌÍ � c l � É kn Ë �}2%£ � �O ÌÍ � c l � ­ ¬8É kn Ë �}2¬ � �

46587�¤B5B98A =DC 7 CB;:��kG=¨oB; > e 4 qby Ëd¥ qso 9-7 e 4 qDyn2 4 e�=DC 7vKd465B9 o K =sk Ï kG=IH 4 e�=DC 7§¦~| =bCA o8�8�F; 5B9 W` n n Ë �`2�£ ¢vn Ú � � n� � Ë z 1O¨�© 2hXkz=bC

�Aª £ ;�« � µ ÁbÛ�¬ÓÁ@% � �,ª Ë �}2; « � µ ÁJÛ ¬ÓÁ�% � ó�7ª Ë �`2rCB; A = 4 � 7¿9-7 = 7 qby+k 587:9 �-HE=bC 7`Kd4 o8� >z7:9�73­ oF;+=sk 4!5BAi4 e 73­ oB;+= 1%®-1 À 1

ÜZÝ�¯ ßnà�á�â�â�ãä�å+æpç è×äÎéZàiãZ°Z�ãZ K�Kd4 q 9 k 5 m\= 4 =DC 7²±�>z4XK CQ=DC 7�4 q 7 y ³Ã A C K q 4 eO=�´�ÀDµ l ; 5ø7S>G7:K =¨q 465 k 5 ; � 7 qIe 7:K = > H� 7 qsk 4X9 k K ;#qsqJ;�H 4 ev;:= 4 y Aò7S� � 7 q¨k 7�5BKo7:A584wKd46>G> k A k 4!5BA ;:=E; >G> 1 � 48l hXkz=bC�k 5 =bC 7 k 5-|9-7 � 7�5B9-7S5 = 7�>G7�K =sq 4!5 ;:�8��q 4+� kGy�;+=sk 4!5$lBKo4!>G> k A k 4!5FAÆK ; 5w4!58> Hw;!qsk AI7 e1q 4 y 9X7�Ï k�;+=¨k 4!5FAe1q 4 y²� 7 qfe 7:K =�� 7 qsk 4X9 k K kz=IH 1¶�C 7:Af7`9-7�Ï k<;:=sk 4!5BA e0; >G> k 5 = 4 =Ih 4 ��q 4 ; 9nK ;+= 7 m 4 q¨k 7:A W¨!1 · � =¨qsk 5FA k K�9-7�Ï k<;+=¨k 465BA e1q 4 y±� 7 qsk 4X9 k K kz=IHÃk 5 ;}� 7 qIe 7:K = K qDH A =@; > 1Ä y���o�q¨kG=sk 7:AÎ4 ei� 4 k 5 = 9-7 e 7:K = A Ë 7 1 m 1 k 4!5BA k 5 =bC 7�¸ hXq 4!5 m ¸ � > ; Ko7 2i��q 4+Ï k 9X7 ;>G4XK ; > k4¹ 7:9�ADK ;+=D= 7 q¨k 5 m Kd7�5 = 7 q 1iÄ 5 =DC�k A h 4 q�º l =bC 7¿AbK ;:=b= 7 qsk 5 m 9 o 7 = 4 k 465 kO¹ 7:9kGy��_o�qskz=sk 7�A k 5 =bC 7 �B;#q¨qsk 7 q l kGy���o�qskz=sk 7:A k 5 =DC 7gK CB; 58587�> ; 5B9wAbK ;:=b= 7 qsk 5 m 9 o 7= 4 =bC 7 ; >z>G4 Hºm�k Ïk7�5 k 5\4 o�q A =sq¨o K =so_q 7:A Ë 584 qbyZ; >G> H -'»  > o8y+k 5 o8yRk 5 =DC 7K CF; 58587S> 2�hXk >G> � 7`9 k AbK o AbAf7�9 1/-1�Ä 5 =¨qsk 5FA k K�9-7�Ï k<;:=sk 4!5BA e1q 4 y±� 7 q¨k 4X9 k K kG=IHuk 5 ; � 7 qIe 7:K = K qbH A =J; > 1Ä 5 =¨qsk 5FA k Kg9X7�Ï k�;+=¨k 4!5FA ;!q 7Z9 o 7 = 4 =bC 7 qbyZ; >�Ï kz��q@;:=sk 4!5BAv4 e�=bC 7 ;:= 4 y A 1 ¶�C 7k 465BA9-4p584 =fq 7 yZ;#k 5 qskim�k 9-> H ¤B�X7:9 ;+=v=bC 7 � 4 k 5 = A4 e ; 5 k 9-7 ; > � 7 qsk 4X9 k K ;#q |q@;�H lXA k 5BKd7 =DC 7 Hg� 4kADAf7:ADAiAf4 y 7 º&k 587 =sk K�7S587 qsm6HghiC�k K C°k 5FK q 7 ; Af7:A hXkz=bC�C�kim!C 7 q

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= 7 y�� 7 qJ;+=so_q 7 1  = >G4 h¹= 7 y�� 7 q@;:=so�q 7 =DC 7 º]k 587 =¨k K�7S587 qsm6H 7�5 ;+� >z7:A =bC 7 k 4!5BA4658> Hp= 4 o 5B9-7 qsm 4pA yZ; >z>�Ï kG��qJ;+=sk 4!5BA ; 5B9 =DC 7gADK ;+=D= 7 q¨k 5 mEy 7:K CB; 5 k A y k Ai584 =kzy�� 4 qD=@; 5 = 1�Ä 5BK q 7 ; A k 5 m�=DC 7 = 7 y�� 7 q@;:=so�q 7kl =bC 7EAbK ;:=b= 7 qsk 5 m�y 7�K CB; 5 k A y±� 7d|Ko4 y 7:A y 4 q 7 ; 5B9 y 4 q 7 kzy�� 4 qD=@; 5 = 1 � 7 =J;Rº 7 ; Kd4 o A =¨k K �8C 46584!5xADK ;+=D= 7 q¨k 5 mk 5w4 o�q K ; ><K o > ;+=¨k 465BA k 5 = 4 ; K�Kd4 o 5 = l ��o?= 587 m >G7:K = 4 �8=¨k K ; > �8C 46584!5BA 1 ¶�C�k A k A9 o A =sk ¤B7:9 � 7�K ;#o AI7 h 7 ;!q 7`4!58> H Kd4!5FKd7 q 5?7:9 hXkG=bCp= 7 y�� 7 q@;+=¨o�q 7�A o8�p= 4 ´3½!� lhiC 7 q 7`AbK ;+=b= 7 qsk 5 m 9 o 7 = 4g4 �8=sk K ; > �8C 4!58465BA � > ;�H A ;}y+k 584 q�q 4!>z7 1 >z> =DC 7wADK ;+=D= 7 q¨k 5 mx��q 4XKd7:AbAI7:A ;!q 7xKd465BA k 9-7 q 7�9 ; AE7�> ; A =sk KnADK ;+=D= 7 q¨k 5 mx��q 4XKo7:AbAI7:A 1¶�C�k AnA knm 5 k ¤B7:A =bCB;:=n=DC 7jA =J;+= 7j9-4k7:AZ584 =x; > = 7 q­kz= AZ7�587 q¨m!H l7 1 m 1�·%¾�¿ 5,À{Á ¿ª Ë ºB2j£·% 5�à ¿ Áª3Ä Ë ºB2 1 Ë Â A ; Kd465BAf73­ o 7�5FKd7klrK CB; 5 mpk 5 mx=bC 7nA o8�8�B; 5B9 y 7 ; 5BAol�K CB; 5 m�k 5 mL=DC 7º&k 587 =sk K�7�587 q¨m!H 4 e�=DC 7`K CB;!qsm 7kl ��o8= 584 =µkz= A = 4 =@; >�7S587 qsm6H ·i1 2Ä 5 ; >G>XK ; ><K o > ;:=sk 465BA =bC 7ÎÏ ; > k 9 kG=IH 4 e8=DC 7U±�4 q 5 ;:�8��q 4+� kGy�;+=sk 4!5 k A ; ADA o8y 7�9 1 ¶�C�k Ak A}73­ oF; > = 4xA ;�H\=DCB;+= 46587pKd4!5BA k 9-7 q A =bC 7 Ë ; > q 7 ; 9 H ADK q 7S7�587:9�l�Af7�7Z587S� = Af7:K =¨k 465 2ADK ;+=D= 7 q¨k 5 mx� 4 = 7S5 =¨k<; >�A o-ÿ K k 7�5 = > H A yZ; >G> = 4 ;+�?� > H\� 7 qD=so�qD�B;+=¨k 465 =bC 7�4 qDHj; 5B9 = 4Kd465BA k 9-7 q 4!58> H\=bC 7Ť q A =E= 7 qby Ë ¸ V 7 qby¶kî¾ A ½ 4!>�9-7�5 qso >z73¸ 2 1 ¶�C&o A =bC 7 =sqJ; 5BA kG=¨k 4!5��q 4 �B;:��k > kG=IH Ë 7 1 m 1 =bC 7 ��q 4 �B;+�_k > kz=IH�=DCB;+=�; 5{7S>G7:K =¨q 465�4 e�=bC 7Ʀ | =bC A o8�8�B; 5B9 hXkG=bCh�; Ïk7gÏk7�K = 4 qjÇÈ hXk >G> � 7�AbK ;:=b= 7 q 7:9 k 5 =DC 7ɦËÊ$| =bC A o8�?�B; 5B9 k 5 = 4 =bC 7�A =J;+= 7 ÇÈ Ê 2µk Ampk Ïk7�5 �XH/ ª3ª Ä Ë ÇÈ Ì ÇÈ Ê 2%£ /�ÍÎÏÑÐ1Ò ¦ Ê ÇÈ Ê ÐÔÓ�ÕfÖ Â Ã6Ã�× Ð ¦ ÇÈjØ Ð Ù ï Ë*Ú ª Ä Ë ÇÈ Ê 2#Û Ú ª Ë ÇÈ 2b2Jó Ë ®-1�/ ½32

±�7 e 4 q 7Z9 k ADK o ADA k 5 m 7 ; K C AbK ;:=b= 7 qsk 5 mw��q 4XKd7�AbA k 5j9-7 =@;#k >îl =DC 7 q 7:A � 465BAf7p4 ev=DC 77�>z7:K =¨q 4!5FA = 4 h�;#q 9?A ; 5\7�� = 7 q 5 ; > � 4 = 7�5 =¨k<; > Ë 7 1 m 1 AbK ;+=b= 7 qsk 5 mn� 4 = 7�5 =sk�; > 2 A CB; >G> � 77�� � > ;#k 5?7:9 1ÜZÝ�Ü ßnàiärãã�æwå:æpç ég÷¯á æ ý¹ëSã�à�â�äré�æ Ý á�ZßÞáà åSã�ëSã�à�â�ä�å:àX é�æâZ~â�ágæ�âäã#å�æç�è± H K ; ><K o > ;+=�é 5Aê =bC 7�AbK q 7�7�5 é 5Aê�4 e~; 5g7�>z7:K =¨q 4!5�ê ; Adlk46587 CB; A ; K�Kd7�AbA = 4 =DC 7iADK q 7�7S587:9ADK ;+=D= 7 q�é 5Aê � 4 = 7�5 =�é�; >�@ ÕfÖ Â Ã6Ã�× hiCëé K Cyé A é 5 =sq 4X9 o Kd7:9 é 5 =bC 7EAbK ;:=b= 7 q�é 5ëê yZ;+=¨q�é ��7�>G7o|y 7S5 = Adl89 é AbK o AbAI7:9 é 5 =DC 7 ��q 7SÏ é 4 o AiAI7:K =�é 4!5 1Uì ;:=so�qJ; >G> H l =DC 7 é 5 = 7 q@; K =�é 4!5 � 7 =Ih 7�7�5; AbK ;:=b= 7 q�é 5ëêwKd7�5 = 7 qv; 5B9 ; 5\7�>z7:K =¨q 4!5 é AvA =sq 4!5Aê6> Hxy 4X9 é ¤B7:9 �XHw=bC 7 ��q 7�Af7�5BKo7�4 e=DC 7v4 =bC 7 q 7�>z7:K =¨q 4!5FA 1 ¶�C 7}ADK ;+=D= 7 q�é 5Aê¿Kd7�5 = 7 qUé 5B9 o Kd7:A é 5 e0; K =i;}� 7 qD=so�qD�B;+=�é 4!5 � 4+|= 7�5 =�é<; >îl hiCAé K Cj; K = A}465 ; >G>�7�>G7�K =sq 4!5BA`A o�q¨q 4 o 5B9 é 5ëê =DCAé AgKd7S5 = 7 q 1 ¶�C 7{7S>G7:K =¨q 465BA¸ q 7 ; K = ¸ �-H�q 7 ;!qsq@; 5Aê é 5Aê =DC 7 y AI7�>GÏk7�Adl8>G7 ; 9 é 5Aê = 4 ; A �B;+=�é<; >z> H 9-7 � 7�5B9-7S5 = K CB;!q ê!79-7S5BA éz=fH]é 5 =bC 77�>G7�K =sq 4!5�ê ; A 1 ¶�Cëé Aîír4 o >G4 y��E� 4 = 7�5 =�é<; >$K q 7 ;+= 7:9 �XHg=bC 77S>G7:K =¨q 465BA

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Page 45: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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L (1+ε)

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AlAs

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Barrier Ga0.67Al0.33As

Substrat GaAs

(misorientation 0.5º)

doping layer Si

vertical superlattice(GaAs)3/(Ga0.67Al0.33As)1

300 Å

1000 Å

4000 Å

r

rr "

z

//

[001]

[110]

[110]

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Page 65: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 66: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 73: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 74: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

q / 2 kF

0.0

0.2

0.4

0.6

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T = 70 K

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�T = 10 K

0

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Page 75: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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0 50 60

E n

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2010

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g (E , T = 50K)

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Page 76: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

0 0.5 1 1.5 2 2.5

T = 0 KN = 4.5*10 cms

–211

7

m /

8 h*

2(q

, T)

/

E00

E01

E02

E04

q / 2 kF

E03

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0.2

0.4

0.6

0.8

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Page 77: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

q / 2 k

T = 0 K

N = 4.5*10 cms–211

T

m /

U h*

2(q

, T)

/

E = 26 meVF

E0

= 101 meV

E1

= 127 meV

E = 2 meVF

E = 12 meVF

E = 22 meVF

E = 18 meVF

E = 8 meVF

E = 4 meVF

F

0 1 2

q / 2 k

0.0

0.2

0.4

0.6

0.8

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Page 79: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 81: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

all

(a.u

.)

N = 4.5 10 cms11 –2

T = 0 K

|<0|

V

|0>

|

10 ¶¶ · ¸ ¹ º »¼

F= 15.6 meV

q/2k0 0.2 0.4 0.6 0.8 1

|<0|

V

|0

>|

im

p2

Impurity scattering

F

(a.u

.)

0

10

N = 4.5 10 cms11 –2

T = 0 K

¼F= 15.6 meV

Alloy scattering

2

0 0.2 0.4 0.6 0.8 1q/2kF

0

0 0

éb�^�����D�Á¾��¢ÜUâE}3�0pU|�q#m�n[u%ts|�tc��n �lq#��9�m�9%tsy�tc|�tsp%u�½§'³¾�½À¿�ª�Á�ÁZ½À¾x%½ à m,u]m÷��k�n � |�tc�5nE�#��î�ï�),+ ä�%��qR|s��p�u � q4pwp�ndp6oJq#p�vx�5|�pJtc��ndt:í%pwoJtcv��lk�q6ts|��÷u � m�|�|�p�q6tsn�r.��y�p¨��|���m�ndo)�%��qR|s�0p�u � q#pwp�n=pwoJm�ysy����u � m�|�|�p�qwtcn5r��¥��|�p�n=|�tsm�yR�+qwt r5�0|���<ÄÃ?p�v���|�p�tc��ndt:í%pwo'tsv��lk0qwts|�tcp7u=�%m�z���q�u%v�m�ycy�m�n5r0y�p�u � m�|�|�p�qwtsn�r��ø3��p�q#p6mëu |s�0p�m�ysy�����u � m5|�|�p�qwtcn5rU�¥��|�p�n=|�tsm�y��%m�z���q�uÚy m5qcr�pÁm�n5r0y�p%uUu � m�|�|�p�q6tsn�r5�Ju���q4pwm�o³tsnKmy�m�qsr�p=`�-Ro�tNu�|�qwtZ9%k�|�tc��n�?�^Å¡ÆO���,Ç�È4�^Å��xÆkÉ¡Ç,�D����Ê��tÅ¡È���Ë�Ô Ç�ÅÌÊ\ËD�tÍ�Ρ���kÇ,ËD�����Úféb�����'¾��ÏB���ÐLËk���É��ZÈ�ÑÈ�Ê��ZÈ�ÆO�¡ÈDÈ4�,Ê\��ÅÍ�Ò����2Ê���˦Ç��^Ó¨�^Å ]Á �^�kÇ,��ÇfÃ�Ç�Ü0h Ú ���Òx�,��Ç�Ó^�ÌÇ�ËD��ËDÉ��ÔÊ��Ná¨������Å¡ÆO�ÕÈ�С��ËeÃ�t��Å(ËDÉ��ÔÇ�СÒ��:�/Î����,È���Å�Ë=ÈDÆ;�D����ÅR�^Å��xÍ�Ò�Ê���ÓÑÈOÖ�^Åiéb�����]¾��^1t×�ËDÉ��xÍ�Ò�ÐR�^Ó^��ËeÔuÓ��^Í���ËD�,Ê�Ð Ô��D�tÍ�Ò�Ë��/�^Ò�Å��a�t�,Ê\��Í�Î������^ËeÔ(ÈDÆtÇ�ËDË����D��Å��.fØǹËÇ�Å¡Ê2Ó^�^Í �^ËD�tÊ�ÐUÔ2Ç,Ó^Ó�ÒfÔ�ÈDÆtÇ�ËDË����D��Å��]fÙÐ<Ë¡�ÑÈ�Æ�Ç�ÓÑÆO��ÓZÇ,ËD�,Ê2Ç�ÈbÇSÚh��ÅÌÆOËD��Ò�Å/Ò,Ú¡ÆkÉ¡Ç,�D����Ê��tÅ¡È���Ë�ÔÚhÒ��=�üùÛ×��ÛÚhÒ��&Ë�É���Ç�СÒ��:��Ê��ZÈ�ÆO�¡ÈDÈ4�,Ê(ÈDÆO������Å���Å��.Í�Ò�Ê��tÓZÈO�� Å���Ê��ÑÈ�Ë��^Å������ZÈ4É��,ÈËDÉR�D���2Ê��Ná¨���D�tÅ�Ëm��Ò�Å��,È�â1���Ü�â�å Ü�â%f Ð Ñ§Ý ÿ ú5Ç,Þ¡ß;ßOà Ñ Â á âÄÒ�Å�ÓaÔ(Ò�Å���È���Ð�ÐÌÇ�Å¡Ê(�ZÈÒ�Æ�ÆO�RÎ��^�,ʨ�����Ü�â�ùâÜ�â%f Ð Ñ§Ý ÿ ú5Ç,Þ¡ß;ßOà Ñ Â á â"Ë�É��(È��ÕÆOÒ�Å¡Ê�È���Ð�ÐÌÇ�Å¡ÊoÈ�˦Ç���ËkÈ/ËDÒ�С��ΡÒ�Î���ÓÑÇ�Ë��,ÊK��É��ZÈKС�,Æ;Ò�Í��,ÈKÒ�Ðd���^Ò��¡È��^Å2ËDÉ���Í�Ò�ÐR�^Ó^��ËeÔ�ÐUÔ2Ç=Ê��,Æ;�D�,Ç�È���Ê����AËDÒ=�^Å�ËD���¦È���Ð�ÐÌÇ�Å¡ÊÈDÆ�Ç,ËDË����D��Å����ã ��Ü�â�ç Ü�â%f Ð Ñ§Ý ÿ ú5Ç,Þ¡ß;ßOà Ñ Â á âÄË�É����¡�kÈ4Ë�Ç,Å¡Ê�È4�,ÆOÒ�Å¡Ê(È���Ð�ÐÌÇ�Å¡ÊfÇ,�D�2ΡÒ�Î���ÓÑÇ�Ë��,ÊK�Ü�1

Page 82: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

105

106

1 10 100

Mob

ility

(cm

V

s

)

2

degenerate 2DEG not deg. 2DEG

n = 2.0 10 cms11 –2

n = 1.0 10 cms12 –2

n = 4.5 10 cms11 –2

Remote Impurity Scattering

–1–1

105

106

1 10 100Temperature (K)

degenerate 2DEG not deg. 2DEG

n = 2.0 10 cms11 –2

n = 1.0 10 cms12 –2

n = 4.5 10 cms11 –2

Alloy Scattering

Mob

ility

(cm

V

s

)

2–1

–1

äb���������.¾��µB�å�æ�ç�9kè^éµè�êZë\éÏè^ì�è�êZíDîf9kë(è^ìSïRð�ñDè^êZë(òkó�ô�êZêZí;ñDè�õ�ö÷�ÙôD�(ô,õ�î�9@ë(ô,é^éµç,ë�òkó�ô,êZêZíOñ�è^õ,ö�Ø9Ø��ô�ò=ôøkð�õ�ó;êZè^ç,õ�çFø�êZíOìAï:í;ñFô,êZð�ñFí>ø¦ç�ñ�ê^ù�ñFí�í2î�è X�íOñFí;õ�êbókù�ô�ñ�ö�í�î,í;õ¢ò¦è^êZè�í@ò@<&úKù�í�ì�ç�9@è�éµè^êZëè�õ�ó;ñFíDô�ò¦í@ò ø�è^ê^ù�è^õ�óOñFí�ô�òkè^õ,ö�ó@ù�ô,ñ^ö�íSî,í;õ¢ò¦è^êZëAô,õ�îJø�è�ê^ù=è^õ�óOñØíDô�òkè�õ�ö�êZíOìAï:í;ñFô,êZð�ñFíAè�õ"ê^ù�íAóDô�ò¦íçFø�ñFíOì�ç�êZí�è^ìSïRð�ñ�è^êZë/ò¦óDô,êZêZíOñ�è^õ,ö�û øKù�íOñFí�ô�ò=è^ê$î�í�óOñØíDô�òkíkò�è�õuê^ù�í2óDô�òkí�ç´ø=ô,é�éµç,ë_ò¦óDô,êZêZí;ñDè^õ,öV?

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Page 83: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

104

106

2.1012

N (cm )

1011

s–2

T.F.

sb: 5

sb: 1

sb: 5,no inter.sb: 2

(

(5sb

.) –

(

1sb.

))/

(1

sb.)

(%

)

ý þþþ

0

70a)

Remote Impurity Scattering

1012

ND

+= N s

N (intersubband)s

b)

1012N (cm )

1011

s–2

withoutscreening

T = 0K

T.F.

screened potentials

Alloy scattering

2.1012104

106

N (intersubband)s

Mob

ility

(cm

V

s

)

2–1

–1M

obili

ty (

cm

V

s

)2

–1–1 T = 0K

sb: 5

sb: 1

sb: 5,no inter.

sb: 2

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Page 84: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 85: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 87: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 88: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 89: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 92: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 93: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 100: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 106: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

T = 4.5K

0

40

80

150

5 10 15 20 250

T = 0 K

T = 10K

T = 20K

T = 30K

Total mobilityparallel direction

120

T = 4.5K

0

10

20

5 10 15 20 25

Fermi energy (meV)

0

T = 0 K

T = 10K

T = 20K

T = 30K

Total mobilityperpendicular direction

Mob

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T = 40K

T = 40K

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0

6

12

18

5 10 15 20 25

Fermi energy (meV)

0

Total mobility

¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾¾ ¾ ¾ perpendicular direction

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Page 113: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

0

200

400

600

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parallel direction

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B

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60

120

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Page 115: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

0

200

400

600

0 10 20 30 40 50 60 70

parallel directionImpurity scattering

only 1 subband

3 subbands

0

20

40

0 10 20 30 40 50 60 70Temperature (K)

perpendicular direction

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only 1 subband

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D

C

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Page 116: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

0

100

200

300

350

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parallel directionAlloy scattering

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N = 6.8 * 10 cm–2s

11

A:

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Page 122: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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Page 123: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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4

5

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0 20 40 60 80Temperature (K)

N

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0 20 40 60 80Temperature (K)

N

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Q�[�]�cZ`5Y�¾3e2��RcäOZefZV�V2`_VpåÀV2`Y\9W�æ�Z�]�mcbd`�eYb�`_]%m�U�^�8�V2Z�e'åve�Uµqj�W�æ�~{ZV�V%^9j�Z�eq�`�m�`_]�[FUWYX�Z�[CZ \98�]%^9tWYU�S]4SM\�WY`_acbd`�eMZ�WY8�eM`�±�Wj�`xa�`�Z�[F8�eM`+m#mU ·C`�eM`_]�^�`�U�]�Wj�`�~�Z�VV£��S�V2WYZ9q�`noOV2`�Z�m�U]�qJWYS#Zwm�U \�t\F`�eM`_]�^�`��_Z�V28�`�U]#Wj�`�~{ZV�V%^9j�Z�eq�`�m�`�]�[9U�WYX�o©T.`_WYgi`�`_]!Wj�`�WYgiSIm�U�eM`�^_WYUS�]�[zU�[z[9arZV�V2`_ecWj�Z�]<�ç�u

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Page 129: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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2.0

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

0 20 40 60 80

Res

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Temperature (K)

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

0 20 40 60 80

Mob

ility

ani

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ê

Temperature (K)

2.2

2.4

C : NH (T=4K)= 6.5*1011 cm–2

D : NH (T=4K)= 6.8*1011 cm–2

B : NH(T= 4K)= 5.9*1011 cm–2A : NH(T=4K)= 5.5*1011 cm–2O : NH(T=4K)= 5.2*1011 cm–2

C : NH (T=4K)= 6.5*1011 cm–2

D : NH (T=4K)= 6.8*1011 cm–2

B : NH(T= 4K)= 5.9*1011 cm–2A : NH(T=4K)= 5.5*1011 cm–2O : NH(T=4K)= 5.2*1011 cm–2

Q�[v]zcZ`bY�¾3e2¾�R�6�S�T9UV2U�WYX#åÀV2`Y\9W�ærZ�]�m!eM`9[9U?[9WYZ�]%^+`�åve�U�q�j�W�æ�Z�]�U�[9S�WYeMS�b�X�Z�[�Zc\F8�]�^�WYU�S�]wSM\�WY`_a'tb�`_eMZ�WY8�eM`�±��©j�`�bdZefZV�V2`_VLarS�T9UVEUWYX!U?[�8nb,WYS#Z�T.S�8�W�Z�\9Z�^_WYS�eÎ\FS8�e'[9WYefS]�q�`�e�Wj�Z�]hWj�`�bd`�e"tb�`_]%m�U�^�8�V2Z�e�S]�`9o�eM`n[F8�V2WYU�]qxU]JZ![9WYefS]�qxZ]�U�[FS�WYeMS�b�X�u

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Page 130: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

Parallel mobility

Perpendicular mobility

50

60

70

80

90

100

C : NH = 6.5*1011 cm–2

D : NH = 6.8*1011 cm–2

B : NH = 5.9*1011 cm–2A : NH = 5.5*1011 cm–2

0 20 40 60 80

Mob

ility

(*1

0 c

m

V

s

)2

–1–1

3

15

20

25

30

35

0 20 40 60 80

C : NH = 6.5*1011 cm–2

D : NH = 6.8*1011 cm–2

B : NH = 5.9*1011 cm–2A : NH = 5.5*1011 cm–2

Temperature (K)

Mob

ility

(*1

0 c

m

V

s

)2

–1–1

3

L206.1

L206.1

Q�[�]�cZ`5Yx¾ e�ñdR'äOZefZV�V2`_V åv8nb�bd`�e|k£q�8�eM`MæxZ]�m'bd`�eYb�`_]%m�U�^�8�V2Z�e�åÀV2S�gi`_e|k|q�8�eM`Mæxa�S�T9UV2U�WYX!Z�[�Z\F8�]�^�WYU�S]hSM\�WY`_acbd`�eMZ�WY8�eM`�±�Wj�`�bdZ�eMZ�VV2`_V|a�S�T9UV2U�WYX!m�`Mb�U�^�W[rZ�T.`9j�Z��_US�e.oOg|j�U^9j�U?['[FUa�U�V2Z�eWYSxWj�`�S�]%`9oiS�]�`�giS�8�V2mxS�T9WYZ�U]�oig|j�`_]w^+ZVE^�8�V2Z�WYU]�q�Wj�`�WY`_acb�`_eMZ�WY8�ef`'m�`Mb�`_]%m�`_]%W£a�S�TnU�V2UWYX\FSezZ�]�8�]�a�S_m8�V2Z�WY`�m�WYgiS'tim�U�a�`�]�[9U�S�]%Z�V�`�VE`�^_WYeMS�]yq�Z�[zgiUWjrWj�`c[FZar`c[9WYe+8�^_WY8�eM`ib�Z�eMZ�a�`9tWY`_e.[nu�ó+]!^+S]�WYeMZ�[9Wo�Wj�` bd`_elbd`�]�m�U^_8�V2Z�eza�S�TnU�V2UWYX�[+j�Sg|[Cm�U ·C`_eM`_]%WpWY`_acb�`_eMZ�WY8�ef`�T.`9j�Z��_US�e.[+om�`Mb�`_]%m�U�]q#S�]�Wj�`�^9j�Z�eq�`�m�`_]�[FUWYX�u

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Page 131: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

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3–2

Mob

ility

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m

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s

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0

T = 0KTotal mobility

N = 5.3 * 10 cm–2s

11

N = 5.7 * 10 cm–2s

11

N = 6.5 * 10 cm–2s

11

N = 6.9 * 10 cm–2s

11

(A)

(B)(C)

(D)

–1–1 band

(1)Egap(1)E

band(2)E

gap(2)E

band(3)E

0

20

40

60

80

100

120

5 10 15 20 25

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Page 136: Growth and Electronic Properties of AlAs/GaAs Lateral ... · Growth and Electronic Properties of AlAs/GaAs Lateral Superlattices : from 2D to 1D. submitted by Petra Denk from Düsseldorf

1.2

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Temperature (K)

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