臺灣博碩士論文加值系統

在這本論文中，我們分析在二維系統中，bulk inversion asymmetry (BIA)和structure inversion asymmetry (SIA)對自旋與軌道交互作用(spin-orbit interaction)的貢獻。因此，我們先分析材料系統中的Dresselhaus parameterγ 和Rashba parameterα，再分別地利用理論方式計算出 bulk inversion asymmetry (BIA)和 structure inversion asymmetry (SIA)造成的自旋分裂能量(Δso ，spin splitting energy)。其中Dresselhaus parameter決定於材料成長的同時，而Rashba parameter會隨著能帶結構改變，因此Rashba parameter理論上分成field和boundary兩部份貢獻加以討論。
在第一個材料系統中，分別有四個試片，其中wafer1和wafer 3 參雜層在二維量子井之上，wafer 2和wafer 4 參雜層在二維量子井之下，並且在wafer1 和wafer2中，加入25 奈米厚的InP 在量子井成長方向的上方，然後分析這樣的材料系統。經過理論計算之後，發現參雜層的位置決定了 αfield 的符號，並且InP的加入會造成αboundary 貢獻增加而對總的Rashba parameter造成影響，這樣的影響反應在自旋能量的分裂上，可以看出wafer 1和wafer 3 ，SIA 的自旋分裂能量比BIA 的自旋分裂能量來的大；wafer 2因為InP對總的Rashba parameter 有很大的減低作用，所以在sin(2φ)= 0的方向上，SIA 的自旋分裂能量比BIA 的自旋分裂能量來的大，在sin(2φ)= 1的方向上，SIA 的自旋分裂能量比BIA 的自旋分裂能量來的小；而； wafer 4，除了SIA 的自旋分裂能量隨載子密度升高而降低外，BIA的自旋分裂能量貢獻在載子密度大於9.3×1011cm-2超越SIA 的自旋分裂能量。
在第二個材料系統中，我們選擇晶格常數與基板不匹配的材料In0.2Ga0.8As作為二維的通道，參雜層皆在通道上方，並嵌入GaAs取代InP，這樣的用意是使價電帶產生階梯狀的結構，和嵌入InP形成的山谷型結構作區隔，也因為我們使用晶格常數不匹配的材料，因此應力所造成的自旋能量分裂也被考慮進去，結果即使嵌入GaAs，發現SIA 的自旋分裂能量貢獻比BIA 的自旋分裂能量來的小，而應力造成的自旋分裂能量也佔很小的比例。

In this thesis, the contributions of bulk and structure inversion asymmetry
to spin-orbit interaction in two-dimensional system were studied. In the be-
ginning, we calculated Dresselhaus parameter ° and Rashba parameter ®
of material systems, then theoretically estimated the spin splitting energy
¢0 resulting from bulk inversion asymmetry (BIA) and structure inversion
asymmetry (SIA). For Dresselhaus parameter once the structure was grown,
it was decided its value. However Rashba parameter changes with the di®er-
ence of band structure and carrier density, it can be separated into ¯eld and
boundary parts to calculate.
In material system 1, wafer 1 and wafer 3 has a doping layer above the 2D
channel, but wafer 2 and wafer 4 do below the channel. The 25 nm inserted
InP layer inset above the channel for wafer 1 and wafer 2. After calculating,
the doping layer position decided the sign of the ¯eld contribution and the
inserted InP layer enhanced or reduced the total Rashba parameter depend-
ing the doping layer position. It can be observed that for wafer 1 and wafer
3 the contribution to spin splitting energy of SIA is larger than BIA, for
wafer 2 due to InP layer the reduction to total Rashba parameter resulted
in the SIA spin splitting energy is among two of BIA spin splitting energy
of di®erent direction, for wafer4 the SIA splitting energy decreased with a
increasing carrier density, especially over ns = 9:3 £ 1011cm¡2, BIA contri-
bution is larger than SIA.
In material system 2, the lattice mismatch with GaAs material In0:2Ga0:8As
was used for 2D quantum well. The front doping and inserted GaAs was pre-
sented in order to product a step-like valence band ¡8. The strain e®ect was
also considered. The results of our analysis was that the SIA contribution is
smaller than BIA even though GaAs inset into the 2D quantum well.

1 Introduction 1
2 Theory 4
2.1 Basic Electronic Transport Concepts . . . . . . . . . . . . . . 4
2.1.1 Two-Dimensional Electron Systems . . . . . . . . . . . 4
2.1.2 Hall E®ect . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Cyclotron Oscillation and Landau Levels . . . . . . . . 8
2.2 Spin-orbit interaction . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Bulk inversion asymmetry . . . . . . . . . . . . . . . . 10
2.2.2 Structure inversion asymmetry . . . . . . . . . . . . . . 12
2.3 Shubnikov-de Haas Oscillation . . . . . . . . . . . . . . . . . . 13
2.4 Quantum Interference . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 Weak localization(WL) . . . . . . . . . . . . . . . . . . 15
2.4.2 Weak anti-localization (WAL) . . . . . . . . . . . . . . 16
3 Sample Fabrication and Processing 19
3.1 Structure Layer Design . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Sample Processing . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Material Systems 1 23
4.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 BIA spin-orbit interaction . . . . . . . . . . . . . . . . . . . . 24
4.3 SIA spin-orbit interaction . . . . . . . . . . . . . . . . . . . . 27
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Material Systems 2 33
5.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2 BIA spin-orbit interaction . . . . . . . . . . . . . . . . . . . . 36
5.3 SIA spin-orbit interaction . . . . . . . . . . . . . . . . . . . . 36
5.4 Stain E®ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.5 Sumarry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6 Conclusion 44

Bibliography
[1] Igor ·zuti¶c, Jaroslav Fabian and S. Das Sarma. Spintronics: Fundamen-
tals and applications.Review of modern physics 76,323(2004)
[2] M.N.Baibich,J.M.Broto,A.Fert,F.Petro®,P.Etienne,G.Creuzet,A.Friederich
and J. Chazelas Giant Magnetoresistance of(001Fe/(001)Cr Magnetic
Suoerlattices Phys.Rev.Lett.61,2472(1988)
[3] G. Binasch, P. GrÄunberg, F. Saurenbach and W. Zinn. Enhanced mag-
netoresistance in layered magnetic structures with antiferro- magnetic
interlayer exchange.Phys. Rev. B 39,4828(1989).
[4] T.Miyazzaki and N. Tezuda. Giant magnetic tunneling e®ect in
Fe/Al2O3/Fe junction. JMMM 139,L231(1995)
[5] Gordon Moore. The experts look ahead:cramming more components onto
integrated circuits. Electrons 38,Issue 8(1965)
[6] B. Das,S. Datta and R.Reifenberger. Zero-¯eld spin splitting in a two-
dimensional electron gas Phys. Rev B41,8278(1990)
[7] D.D. Awschalom,D. Loss and N. Samarth. Semiconductor Spintronics
and Quantum Computation
[8] E.I.Rashba,Fiz. Fiz. Tverd. Tela(Leningrad)2,1224(1960)[Sov.
Phys.Solid States 2,1109(1960)]
[9] G.Engels,J.Lange,Th. SchÄapers,and H.LÄuth Experimental and theoreti-
cal approach to spin splitting in modulation-doped InxGa1¡x/InP quan-
tum wells for B!0. Phys.Rev.B55,R1958(1997)
[10] Th. SchÄaper,G.Engels,J.Lange,Th. Klocke,M. Hollfelder,and H. LÄuth.
E®ect of the hetrointerface on the spin splitting in the modulation doped
InxGa1¡x/InP quantum wells for B!0. J. Appl. phys. 83,4324(1998)
[11] J. Nitta,T. Akazaki,H. Takayanaki,and T. Enoki Gate Controll Spin-
Orbit Interaction in an inverted In0:53Ga0:47As=In0:52Al0:48As het-
rostructure. Phys. Rev. Lett. 78 ,1335(1997)
[12] C.-M. Hu,J. Nitta,T. Akazaki,H. Takayanaki,J. Osaka,P. Pfef-
fer, and W. Zawadzki Zero-¯eld spin splitting in an inverted
In0:53Ga0:47As=In0:52Al0:48As hetrostructure: Band nonparabolicity in-
°uence and the subband dependence. Phys.Rev.B60 7736(1999)
[13] T. Matsuyama,R. KÄursten,C. Mei¼ner,and U. Merkt. Rashba spin split-
ting in inversion layers on p-type bulk InAs.Phys.Rev.B61,15588(2000)
[14] T. Koga,J. Nitta, T. Akazaki,and H. Takayanagi Rashba Spin-
Orbit Coupling Probed by the Weak Antilocalization Analysis in In-
AlAs/InGaAs/InAlAs Quantum Wells as a Function of QuantumWell
AsymmetryPhys.Rev.Lett 89,0468011(2002)
[15] Ch. Schierholz,T. Matsuyama,U Merkt,and G.Meier. Weak Localisa-
tion and Spin Splitting in inversion Layers on p-Type InAs Phys.Rev.B
70(2004)
[16] G. Dresselhaus. Spin-orbit coupling e®ect in zinkblend structurePhys.
Rev. 100,580 (1955)
[17] D. F. Holcomb Quantum electrical transport in samples of limited di-
mensionsAm. J. Phys. 67(4),April 1999
[18] J. J. Sakurai Advanced Quantum Mechanics (Addison-
Wesley,Reading,MA,1967)
[19] C. Kittel Quantum Theory of Solids(Wiley,New York,1963)
[20] E. I. Rashba and V. I.Sheka,Sov. Phys. Solid States 3,1257(1961)
[21] M. I. D'yakonov and V. I. Perel'.Sov. Phys. JETP 33 1053(1971)
[22] W. Knap,C. Skierbiszewski,A. Zduniak,E. Litwin-Staszewska,D. Bertho,
F. Kobbi,and J. L. Robert Weak antilocalization and spin precession in
quantum wells Phys. Rev. B 53 3912(1996)
[23] E. I. Rashba and Yu A. Bychkov Oscillatory e®ect and the magnetic
susceptibility of carriers in inversion layersJ. Phys. C17,6039(1984)
[24] S. Datta and B. Das Electronic analog of the electro-optic modulator.
Appl. Phys. Lett.56,665(1990)
[25] E. A. de Andrada e Silva,G. C. La Rocca,and F. Bassani Spin-split
subbands and magneto-oscillations in III-V asymmetric heterostructures
Phys. Rev. B 50 8523(1994)
[26] T. Ando,A. B. Fowler, and F. Stern Electronic properties of two-
dimensional systems. Rev. Mod. Phys. 54, 437 (1982).
[27] T. Heinzel Mesoscopic Electronics in Solid State Nanostructures
[28] L. W. Wong,S. J. Cai,R. Li,and Kang Wang, Magnetotransport study on
the two-dimensional electron gas in AlGaN/GaN heterostructures Appl.
Phys. Lett. 73,1391 (1998).
[29] J. Luo,H. Munekata and F. F. Fang,and P. J. Stiles Observation of the
zero-¯eld spin splitting of the ground electron subband in gasb-inas-gasb
quantum wells Phys. Rev. B 38, 10142(1988)
[30] S. Datta. Electron transport in mesoscopic systems. Cambridge Univer-
sity Press (1995).
[31] G. E. Pikus,and A. Titkov in Optical Orientation, edited by F. Mayer
and B. Zakharchenya North-Holland, Amsterdam, 1984!.
[32] F. G. Pikus and G. E. Pikus. Conduction band splitting and negative
magnetoresistance in A3B5 heterostructure Phys. Rev. B 51,16928(1995)
[33] S. V. Iordanskii,Yu. B. Lyanda-Geller,and G. E. Pikus weak localiztion
in quantum wells with spin-orbit interaction. JETP. Lett. 60,206(1994)
[34] F. Ali ,and A. Gupta HEMTs and HBTs; Device fabrication circuits
[35] M. Hueschen,N. Moll,E. Grwen ,and J. Miller. Plus Doped MOD-
FETsIEEE,IDEM Technical Digest 1984
[36] R. Winkler Spin-Orbit Coupling E®ects in Two-Dimensional Electron
and Hole Systms
[37] I. Vurgaftman, J. R. Meyer and L. R. Ram-Mohan Band parameters for
III-V compound semiconductors and their alloys. JAP. 89 5815(2001)
[38] G. E. Pikus and A. N. Titkov,In Optical Orientation, edited by F. Meier
and B. P. Zakharchenya (North- Holland, Amsterdam, 1984).
[39] Y. K. Kato et al., cond-mat/0502627.
[40] S. L. Chuang E®ctient band structure calculations of strained quantum
wells. Phys. Rev. B 43,9646(1991)