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博碩士論文 etd-0801111-142618 詳細資訊
Title page for etd-0801111-142618
論文名稱
Title
纖鋅結構之塊材與量子井中的自旋分裂
Spin Splitting in Bulk Wurtzite Materials and Their Quantum Wells
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
75
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2011-07-15
繳交日期
Date of Submission
2011-08-01
關鍵字
Keywords
自旋分裂、Rashba效應、纖鋅礦、Dresselhaus 效應、量子井、原子軌道線性組合
spin slitting, LCAO, Wurtzite, Rashba effect, Dresselhaus effect, quantum well
統計
Statistics
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中文摘要
利用原子軌道線性組合之方法研究應變下氮化鋁之自旋分裂。在雙能帶k.p 模型Hso=(αwz-γ’k2//+λ’k2z)(σxky-σykx)+H0so, 發現應變與晶格場不僅會引起一次線性k(αwz )還有三次方k 項( γ’and λ’ )。在這裡H0so=(-γ0k2//+λ0k2z)(σxky-σykx) 是對應於理想的纖鋅結構且會產生圓錐形的最小自旋分裂面。當雙軸應變增加時, 最小自旋分裂面的形狀會從雙葉雙曲面變成圓錐形,最後成了單葉雙曲面。
此外,也利用原子軌道線性組合之方法研究A面與M面纖鋅結構量子井中自旋分裂。在量子井中, 自旋分裂主要是來自於線性一次方項的貢獻, 但是在大k// 時三次方項的貢獻就不可以被忽略了。用雙能帶k.p 模型擬合LCAO的數據可以得到線性一次方項與三次方項的數值。當量子井的厚度增加時, 線性一次方項與三次方項的數值是在減少的。
Abstract
The spin-splitting energies in strained bulk wurtzite aluminum nitride (AlN) are studied using the linear combination of atomic orbital method. It is found that strain and crystal field induce not only a linear-k (αwz ) but also two cubic-k terms (γ’and λ’ ) in the two-band k.p Hamiltonian Hso=(αwz-γ’k2//+λ’k2z)(σxky-σykx)+H0so, where H0so=(-γ0k2//+λ0k2z)(σxky-σykx) is for ideal wurtzite and generates a cone-shaped minimum-spin-splitting (MSS) surface. As biaxial strain increases, the shape of the MSS surface changes from a hexagonal hyperboloid of two sheets in unstrained AlN to a hexagonal cone, and eventually becomes a hyperboloid of one sheet.
The spin-splitting energies of first conduction band for A-plane and M-plane wurtzite are calculated by the sp3 linear combination of atomic orbital (LCAO). The results show the spin-splitting energies are dominated by linear-k term but contribution of cubic-k terms can not be neglected for larger k//. The parameter of linear-k and cubic-k terms are evaluated from the LCAO calculated spin-splitting energies fitting to two band k•p model as increasing well width. The coefficients of linear-k and cubic-k terms decrease.
目次 Table of Contents
中文摘要…………………………………………………………………………………i
Abstact……………………………………….…………………………………………..ii
Chapter 1 Introduction...........……………………………………………………………………….01
1-1 Bulk inversion asymmetry in bulk zinc-blende……………………………………..…….....01
1-2 Bulk inversion asymmetry in bulk wurtzite………………………………………..………...06
1-3 Minimum-spin-splitting (MSS) surface in bulk wurtzite…..……………………….………..10
1-4 Spin splitting in quantum wells ……….…………………………………………………......11
Chapter 2 Methods…………………………………………………………………………..…….…..12
2-1 Atomic structure of bulk wurtzite………………………………………………………..….12
2-2 The Hamiltonian without spin-orbital interaction for ideal wurtzite………………………..12
2-3 The Hamiltonian with spin-orbital interaction for ideal bulk wurtzite……………………...16
2-4 The Hamiltonian with spin-orbital interaction for real or strained wurtzite………………..20
2-5 The Hamiltonian for wurtzite quantum wells …………………………………………….23
2-6 Two-Band k.p model in wurtzite structure…………………………………………...…….28
Chapter 3 Results……………………………………………………………………………………...30
3-1 The shape of the spin-degenerate surface in the two-band k•p model…………….………..30
3-2 Ideal bulk wurtzite…………………………………………………………………………..34
3-3 Real and strained bulk wurtzite………………………………………………………..…….40
3-4 The spin splitting of quantum wells…………………………………………………………53
Chapter 4 Conclusions........................................................................................................................65
References……………………………………………………………………………………...…..…...66
Figures
Fig. 1-1 Resonant spin lifetime transistor………………………………………………………….….…..03
Fig. 1-2 Crystal structure of zinc-blende ………………………….……………………………….….….04
Fig. 1-3 Structure inversion asymmetry…….…………………………………………………….….……05
Fig. 1-4 Crystal structure of wurtzite....................…………………………………………….….……….07
Fig. 1-5 Schematic of atomic arrangement for ideal wurtzite ……..…………………….….…………….08
Fig. 1-6 Schematic of atomic arrangement for real or stained wurtzite …………………………………..09
Fig. 2-1(a) Wurtzite structure.......………………………………………………………………….….…..13
Fig. 2-1(b) Reciprocal lattice………………………………………………………………………….......13
Fig. 2-2 The ratio of lattice constants c to a as a function of the biaxial strain ...…………………....…21
Fig. 2-3 The internal parameter u as a function of a biaxial strain ……………………………………….22
Fig. 2-4(a) The top view of the reciprocal lattice……………………………………………….…….…..25
Fig. 2-4(b) A-plane quantum wells………………………………………………………………………..26
Fig. 2-4(c) M-plane quantum wells………………………………………………………………………..27
Fig. 3-1 (a) Spin-degenerate surface in the shape of cone…………………………………………...…...31
Fig. 3-1 (b) Spin-degenerate surface in the shape of hyperboloid of one sheet……………………….….32
Fig. 3-1 (c) Spin-degenerate surface in the shape of hyperboloid of two sheets………………………....33
Fig. 3-2 (a) Spin-splitting energies as a function of k// on the plane of kz=0.0 (p/c)……………………...36
Fig. 3-2 (b) Spin-splitting energies as a function of k// on the plane of kz=0.3 (p/c)……………………...36
Fig. 3-2 (c) Spin-splitting energies as a function of k// on the plane of kz=0.5 (p/c)……………………...36
Fig. 3-3 (i) Projection of minimum spin-splitting and spin-degenerate surface onto kz=0.2 (p/c)……….37
Fig. 3-3 (ii) Projection of minimum spin-splitting and spin-degenerate surface onto kz=0.4 (p/c)……....37
Fig. 3-3 (iii) Projection of minimum spin-splitting and spin-degenerate surface onto kz=0.6 (p/c)……...37
Fig. 3-4 Three-dimensional plot of minimum spin-splitting surface for a ideal AlN wurtzite..………......39
Fig. 3-5 (a) Spin-splitting energies as a function of k// under external strain 0.00% with kz=0.0 (p/c)…...42
Fig. 3-5 (b) Spin-splitting energies as function of k// under external strain 1.57% with kz=0.0 (p/c)…….42
Fig. 3-5 (c) Spin-splitting energies as function of k// under external strain 2.00% with kz=0.0 (p/c)…….42
Fig. 3-6 (a) The value of awz in two-band k.p Hamiltonian as a function of external strain…………….43
Fig. 3-6 (b) The value of g in two-band k.p Hamiltonian as functions of external strain………...……..44
Fig. 3-6 (c) The value of l in two-band k.p Hamiltonian as functions of external strain……….............45
Fig. 3-6 (d) The value of awz.g wz in two-band k.p Hamiltonian as a function of external strain………..46
Fig. 3-7 (a) The minimum spin-splitting surface for a unstrained wurtzite…...…………………………..50
Fig. 3-7 (b) The minimum spin-splitting surface for a tensile strain 2.00 % wurtzite…………………….51
Fig. 3-7 (c) The minimum spin-splitting surface for a tensile strain 3.00 % wurtzite..…………………...52
Fig. 3-8 (a) Spin-splitting energies as function of k’ for A-plane QWs with LW=4.6 A at k’z=0.0…..........56
Fig. 3-8 (b) Spin-splitting energies as function of k’ for A-plane QWs with LW=10.8 A at k’z=0.0…........56
Fig. 3-8 (c) Spin-splitting energies as function of k’ for A-plane QWs with LW=18.5 A at k’z=0.0………56
Fig. 3-9 (a) Spin-splitting energies as function of k’ for M-plane QWs with LW=5.30 A at k’z=0.0……...57
Fig. 3-9 (b) Spin-splitting energies as function of k’ for M-plane QWs with LW=10.7 A at k’z=0.0….......57
Fig. 3-9 (c) Spin-splitting energies as function of k’ for M-plane QWs with LW=18.7 A at k’z=0.0….......57
Fig. 3-10 (a) Spin-splitting energies of A-plane QWs with LW=4.6 A and k’//=0.05 (p/c)……..................58
Fig. 3-10 (b) Spin-splitting energies of A-plane QWs with LW=4.6 A and k’//=0.10 (p/c)…..…...............59
Fig. 3-10 (c) Spin-splitting energies of A-plane QWs with LW=4.6 A and k’//=0.23 (p/c)....…..................60
Fig. 3-11 (a) Spin-splitting energy of M-plane QWs with LW=5.3 A and k’//=0.01 (p/c)……....................61
Fig. 3-11 (b) Spin-splitting energy of M-plane QWs with LW=5.3 A and k’//=0.078 (p/c)…….................62
Fig. 3-11 (c) Spin-splitting energy of M-plane QWs with LW=5.3 A and k’//=0.1 (p/c)…..…...................63
Fig. 3-12 (a) The value of a
IA in the two-band k.p Hamiltonian as functions of well width….…………64
Fig. 3-12 (b) The value of g
IA in the two-band k.p Hamiltonian as functions of well width..………..…64
Fig. 3-12 (c) The value of l
IA in the two-band k.p Hamiltonian as functions of well width…………....64
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