三五族半導體材料的載子與自旋動力學

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Carrier and Spin Dynamics in III-V Semiconductor Materials

Student

Shin-Chin Lin

Advisor

Dr. Kien-Wen Sun

A Thesis

Submitted to M. S. Program, Department of Applied Chemistry College of Science

National Chiao Tung University In partial Fulfillment of the Requirements

For the Degree of Master of Science

In

Applied Chemistry July 2011

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GaAs -InAs/GaAs

:

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n p GaAs GaAs : Elliott-Yafet ( EY ), D'yakonov-Perel ( DP ) 和 Bir-Aronov-Pikus ( BAP ) ( picosecond, ps ) DP ( femtosecond ) / 1ps barrier ( - ) : /

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Carrier and Spin Dynamics in III-V Semiconductor Materials

Student Shin-Chin Lin Adviser Dr. Kien-Wen Sun

M. S. Program, Department of Applied Chemistry National Chiao Tung University

Abstract

Semiconductor spintronics has open a research field devoted to the manipulation of the spin degree of freedom and the developing of electronic devices with energy conservation, low heat disspiation, and high operation speed. The studies of spin-based devices including spin injection, phase coherence and spin detection, are closely related to spin dynamics. Therefore, the research of spin dynamics in semiconductors is essential to the development of pratical spin-based electronic devices.

This thesis begins with the investigations on spin dynamics in bulk GaAs and gradually moves toward the dynamics in InAs/GaAs quantum rings in order to understand the difference of spin properties between macroscopic and mesoscopic materials. However, before the exploration on spin dynamics, we must fully understand the carrier dynamics in the same materials. Therefore, this thesis is divided into two parts: the first part deals with the carrier dynamics in semiconductor nanostructures, and the second part investigated the spin dynamics of bulk and semiconductor quantum rings.

In the first part, we investigate the carrier capture and relaxation processes in undoped and modulation-doped self-assembled InAs/GaAs QRs using time- resolved photoluminescence up-conversion spectroscopy with a time resolution of 200 fs. We find that carrier capture in the ground state and the excited states

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of the charged QRs are faster in compared to the undoped rings even at a low excitation level. This is attributed to the presence of the build-in cold carriers in the charged rings, which lead to the accelerated carrier-carrier scattering and capturing of holes or electrons into the excited and ground states.

In the second part, we use a time-resolved photoluminescence polarization spectroscopy system to investigate the spin dynamics of electrons and holes in p-, n-, and undoped bulk GaAs. From the time-resolved polarization decay rate, we analyze the relative importance of spin relaxation mechanisms, including Elliott-Yafet (EY) model, D'yakonov-Perel (DP) model and Bir-Aronov-Pikus (BAP) model at room temperature for GaAs. We find that the spin relaxation time of the electrons is only on the order of a few tens of ps and the DP mechanism plays an important role for spin relaxation in bulk GaAs. In addition, the hole spin relaxation time is also determined with a rate of less than 300 fs. Finally, we study the spin dynamics in InAs/GaAs QRs in which a longer spin coherence time than the GaAs is predicted due to the three-dimensional quantum confinement. However, the spin relaxation time in excited and ground was found to be less than 1 ps. This is because that the carriers are excited above the barriers and they have to go through many cooling stages (such as, carrier- carrier, carrier-phonon, and inter-subband scatterings) before they can arrive at the excited or ground states in the ring, which leads to the observed ultrafast spin relaxation. The spin dynamics in quantum rings should be carefully re-examined by direct excitation of the carriers inside the rings.

Keywords : carrier dynamics , spin dynamics, InAs/GaAs quantum rings, bulk GaAs, spin relaxation mechanisms, carrier cooling stages

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KB KB ! ; ; ; ;

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pass ! : ; : Meta Alex ; ; -斌 2鎵11 7

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...I ... III ... V ...VII ... X ... XI ... 1 ... 1 1-1 ... 1 1-2 ( ) ... 3 1-3 ... 7 1-4 ... 8 ... 9 2-1 ... 9 2-2 ... 11 2-2-1 Barrier ... 12 2-2-2 ... 13 2-2-3 ... 14 2-2-4 ... 17 2-3 ... 20 ... 21

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3-1 ... 21 3-1-1 ... 21 3-1-2 ... 22 3-1-3 ... 24 3-2 ... 28 3-2-1 ... 28 3-2-2 Up-conversion ... 29 3-3 ... 37 ... 38 4-1 ... 38 4-2 Modulation-doped InAs/GaAs QRs ... 42 4-3 ... 49 ... 50 ... 51 ... 51 1-1 ... 51 1-2 ... 53 1-3 ... 56 1-4 ... 57 ... 58 2-1 — ... 58 2-2 ... 64

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2-3 ... 65 2-3-1 Bloch ... 65 2-3-2 ... 67 2- 4 ... 74 ... 75 3-1 ... 75 3-2 ... 76 3-2-1 ... 76 3-2-2 ... 79 3-3 ... 80 ... 81 4-1 GaAs ... 81 4-1-1 GaAs ... 81 4-1-2 P GaAs ... 85 4-1-3 N GaAs ... 90 4-2 Modulation-doped InAs/GaAs QRs ... 100 4-3 ... 106 ... 107

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3.1 ... 27 3.2 ... 34 4.1 ... 40 2.1 ... 60 3.1 ... 78 4.1 GaAs ... 84

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1.1 ... 1 1.2 ... 2 1.3 ... 4 1.4 n p ... 4 1.5 barrier WL PL ... 5 1.6 ... 5 1.7 ... 6 2.1 ... 10 2.2 ... 11 2.3 ... 13 2.4 ... 14 2.5 ... 15 2.6 ... 16 2.7 Cross-transition ... 16 2.8 ... 17 2.9 ... 19 3.1 InAs ... 21 3.2 InAs ... 22 3.3 InAs / GaAs ... 23 3.4 p n InAs / GaAs QRs ... 24 3.5 AFM ... 25 3.6 AFM ... 26 3.7 n AFM ... 26 3.8 p AFM ... 27

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3.9 ... 28 3.10 ... 29 3.11 ( a ) SFG ( b ) DFG ( c ) SHG... 31 3.12 ... 33 3.13 ( a ) ( b ) ... 33 3.14 θ (a) (b) ... 34 3.15 ( a ) Type I ( b ) Type II ... 34 3.16 Up-conversion ... 35 3.17 Up-conversion ... 36 3.18 ( a ) SFG ( b ) ... 36 4.1 ... 39 4.2 n ... 39 4.3 p ... 40 4.4 ... 41 4.5 n ... 41 4.6 p ... 42 4.7 ... 43 4.8 n ... 43 4.9 p ... 44 4.10 ... 44 4.11 n ... 45 4.12 p ... 45 4.13 ... 46 4.14 n ... 46 4.15 p ... 47

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4.16 ( a ) ( b ) ... 48 1.1 ... 52 1.2 Datta –Das ... 54 1.3 n ... 54 1.4 p ... 54 1.5 ... 55 1.6 ... 55 2.1 GaAs ... 59 2.2 ... 62 2.3 ... 62 2.4 ... 63 2.6 ... 66 2.7 ... 66 2.8 ... 67 2.9 EY ... 69 2.10 ... 69 2.11 DP ... 71 3.1 ... 77 3.2 ... 78 3.3 ... 79 3.4 ... 80

4.1 (a) GaAs (b) (a) ... 82

4.2 GaAs ... 82

4.3 ... 83

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4.5 p-GaAs ( a ) (150 ps) ( b ) (5 ps) ... 86 4.6 p-GaAs ... 87 4.7 p-GaAs σ+ ... 87 4.8 p-GaAs ... 88 4.9 p-GaAs ... 89 4.10 n_e =4.2×1017cm−3 n-GaAs ... 90 4.11 n_e =1.0×1018cm−3 n-GaAs ... 91 4.12 1ps n-GaAs ... 91 4.13 n-GaAs σ+ ... 93 4.14 n-GaAs ... 93 4.15 n_e =4.2×1017cm−3 GaAs ... 95 4.16 n_e =4.2×1017cm−3 GaAs ... 96 4.17 ... 97 4.18 (a) n-GaAs (b) ... 99 4.19 n-GaAs ... 99 4.20 barrier (a) (150 ps) (b) (5 ps) ... 102 4.21 WL ... 103 4.22 ... 103 4.23 ... 104 4.24 ... 104 4.25 ... 105

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1-1

“ ” ” ” 1.1 [1.1] IC 1.1 I [1.2-1.3] [1.4] ( Bulk ) ( 1-100 )

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( Quantum well, QW ) ( Quantum

wire ) ( Quantum dot,

QD ) δ

( 10 nm )

1.2 II

Ex-situ In-situ Ex-situ

In-situ In-situ ( self-assembled growth )

( strain )

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[1.5-1.7]

Aharonov-Bohm [1.8-1.9] ( persistent current) ( magnetization )

1-2

(

)

1.3 [1.10-1.11] D. Morris Up-conversion InAs / GaAs

( Auger process )[1.12] S. Marcinkevicius Streak

Camera ( multi-phonon process )

[1.13] 1.4 K. Gundogdu1

-[1.14] 1.5 J. Siegert

( barrier ) ( wetting layer, WL ) [1.15] K. W. Sun

[1.16]

C. H. Lin K. W. Sun InAs / GaAs

1.6 1.7 ( dark state )

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1.3 III

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1.5 barrier WL PL V

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1-3

Aharonov-Bohm [1.8-1.9] ( persistent current)

( magnetization )

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1-4

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[1.5]

625-630 2008 12

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[1.10] uWee Photonics Lab

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2-1

2.1 E=E₀ exp

(

ik⋅rr-iωt

)

r

i ( transition probability )

( Fermi golden rule )

W

2 f

H

i

(

E

f

-

E

i

-

)

2 int f i

δ

ω

π

=

→

h

, (2.1) i f H_int ( Hamitonian operator )

(

p eA

)

V(r) 2m 1 H 2 o int r r r + + = , (2.2)

(

p A A p

)

H H 2m e 2m A e ) r V( 2m p H _o o o 2 2 o 2 int = + ′      ⋅ + ⋅ + +       + = ⇒ r r r r r r r , (2.3) Hamitonian

(

p A A p

)

2m e 2m A e H o o 2 2r _r _r _r _r ⋅ + ⋅ + = ′ , (2.4) 2 A r 0 A p⋅ = r r ( Coulomb gauge : ∇⋅A=0 r r ) 2.4 A p 2m e H o r r ⋅ = ′ , (2.5) t A -E ∂ ∂ = r r ₍ ₎ t -r k i oe A A= ⋅ ω r r r (2.6)

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r

( )

L r + + + = ⋅ 2 ikr 1/2 ikr 1 ) r k i ( exp , (2.7) ( Dipole approximation ) : r ~10-9 m,k ~ 2π/λ~ 6×106 0 e-i t 2 a A A 1 ~ ) r k i ( exp ⋅ ω εω = = ⇒ ⋅r r r h r , (2.8) ( ) f a p i (E -E - ) m e 2 2 W ₂ 2 _f _i o 2 abs f i  ⋅ δ ω      εω π = → h r r h h , (2.9)

(

)

e

E

=

₀ i k⋅r-ωt r r

i

f

Interaction of electromagnetic wave and semiconductor

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2-2

2.2 GaAs barrier

: ( i ) barrier

; ( ii ) barrier WL ( ambipolar

diffusion ) ; ( iii ) barrier WL WL QRs ; ( iv )

QRs ; ( v )

( radiative recombination ) ( non-radiative recombination ) [ 2.2 ]

QRs

QRs QRs

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2-2-1 Barrier

( cooling mechanism ) ( k_BT_L 2 3 B k : Boltzmann ) [2.3] ”nonthermal” 2.3 GaAs barrier [2.4] : ( 1 ) ( coherent process ) : ( dephase time ) 100 ( 2 ) ( non-thermal process ) : - ( carrier- carrier scattering ) T_c 2

( 3 ) ( hot carrier process ) :

T_c TL ( LO LA ) 1-100 ( 4 ) ( isothermal process ) T_c TL 1

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2.3 [ 2.5 ]10

2-2-2

barrier ( recombination ) barrier WL WL barrier ( ambipolar diffusion ) [2.2][2.6] h e h e a D D D D 2 D + = , (2.10) e D D_h ( diffusivity ) ( Einstein relation ) B _e e q T k D _µ      = and _h B _h q T k D _µ      = , (2.11),(2.12) e µ µ_h ( mobility ) 2.11 2.10

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_      µ + µ µ µ = q T k 2 D B h e h e a , (2.13)

pump-probe bulk GaAs

2.4 2.4 [ 2.7 ]11

2-2-3

barrier ( LO LA ) ( 1 ) ; ( 2 ) ( ) LO LA ( phonon bottleneck ) [2.8-2.10]

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( picosecond ) 2.5 [2.11-2.12] ( quasi-continum ) cross-transition [2.13] 2.6 : (1) WL ( WLh ) ( 1Se ) WLh-1Se ; (2) ( 1Sh ) WL ( WLe ) 1Sh-WLe 2.7 2.8 (a) LA LO ( multi-LO phonon ) 2.8 (b) 2.9 (a) LA LO [2.14] 2.5 12

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2.6 13 QRs WL Barrier

-＋

-1 2 2 -＋ 1Sh 1Se ＋ -WLh WLe 2.7 Cross-transition 14

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2.8 15

2-2-4

( radiative recombination ) ( non-radiative recombination ) PL 2.9 ( state filling effect ) [ 2.15 ] c w e n n -n -dt dn τ + τ τ = , (2.14) cw g e ew w c w w w w _- n _-n _- n n n dt dn τ + τ + τ τ τ = , (2.15) -n - n n g dt dn ew w cw g g g g + τ + τ τ = , (2.16)

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n n_w n_w WL barrier c τ WL e τ WL cw τ barrier WL ew τ WL barrier w τ τ_g WL barrier 2.14-2.16 -1 w g g c w w c g cw ₁ _R _R _R _R 1 g n I         τ τ + τ τ +       τ τ + τ τ +         τ τ + = τ = , (2.17) e c R τ τ = ew cw w R τ τ = , (2.18),(2.19) 1 g cw << τ τ 1 w c << τ τ 2.17 -1 w g g c w R R R R 1 g n I         τ τ + τ τ + τ τ + = τ = , (2.20) 0 R R ≈ w ≈ PL Io ≈g 2.30 -1 w g g c w o 1 R R R R I n I         τ τ + τ τ + τ τ + = τ = , (2.21)

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QR

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2-3

[2.1] Dr. Dominique Bougeard,Optical transition of 2D and1D systems.

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277-283 1994 4

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[2.7] Brian A. Ruzicka, Lalani K. Werake, Hassana Samassekou, and Hui Zhaoa, Appl. Phys. Lett. 97, 262119 (2010).

[2.8]

93

[2.9] U. Bockelmann and G. Bastard, Phys. Rev. B. 44, 8947 (1990).

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3-1

( Molecular Beam Epitaxy, MBE )

( undoped QRs ) n ( n-doped QRs ) p

( p-doped QRs ) n p 20

3-1-1

Stranski-Krastanow ( S-K )

( ) 3.1 GaAs

InAs ( Wetting Layer, WL ) ( lattice mismatch ) 7.2 % ( strain ) [3.1-3.3] GaAs Substrate InAs WL 3.1 InAs 17 GaAs 3.2 InAs GaAs InAs GaAs

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3.2 InAs [3.4]18

3-1-2

1. InAs/GaAs :

MBE ”Varian GEN II Solid-source MBE System “

GaAs ( 001 ) :

( 1 ) 600 GaAs 200nm GaAs ( buffer layer )

( 2 ) 30nm Al 0.3 GaAs ( carrier confine

layer )

( 3 ) 150 nm GaAs ( barrier layer )

600 520

( 4 ) 0.056µm / hr 2.6 ( Molecular layers, MLs ) ( 0.8 nm ) InAs GaAs InAs

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( 5 ) 600 2nm GaAs

( capping layer ) GaAs

InAs ( 6 ) 30 nm GaAs ( 7 ) 4 5 6 ( 8 ) 4 5 ( 9 ) 150 nm GaAs ( 10 ) 30nm Al 0.3 GaAs ( 11 ) 50 nm GaAs ( 12 ) 4 5

150nm GaAs

50nm GaAs

S.I. GaAs Substrate

200nm GaAs

30nm Al

_0.3

GaAs

30nm GaAs

150nm GaAs

30nm Al

_0.3

GaAs

InAs / GaAs QRs

3.3 InAs / GaAs 19

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2. n p ( modulation doped QRs ) : n p 3 6 7 Si Be GaAs 20 150nm GaAs 50nm GaAs

S.I. GaAs Substrate

200nm GaAs 30nm Al_0.3GaAs 30nm GaAs 30nm GaAs 150nm GaAs 30nm Al_0.3GaAs InAs / GaAs QRs 3.4 p n InAs / GaAs QRs 20

3-1-3

( Atomic Force Microscopy , AFM )

Tapping Mode Digital-Instrument-D3100

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AFM 3.5 AFM [3.5]21 3.6-3.8 n p AFM -2 10 cm 10 2.1× 47 nm 0.3 nm 0.6 nm ; n 50 nm 0.4 nm 0.5 nm ; p 58 nm 0.5 nm 0.7 nm 3.1

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undoped QRs InAs WL 0.3 nm 47nm 0.6 nm 100 nm 3.6 AFM 22 n-doped QRs InAs WL 0.4 nm 50 nm 0.5 nm 100 nm 3.7 n AFM 23

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p-doped QRs InAs WL 100 nm 0.4 nm 0.7 nm 58 nm 3.8 p AFM 24

Diameter ( nm ) Height ( nm ) Depth ( nm )

undoped QRs 47 0.3 0.6

n-doped QRs 50 0.4 0.5

p-doped QRs 58 0.5 0.7

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3-2

3-2-1

Ar 488 nm

( continue wave, CW ) ; ( Charge Coupled Device, CCD ) InGaAs ( Indium Gallium Arsenide ) 200-1000 nm

& 800-1600 nm ; 1200 / mm

3.9 25

3.9 ( objective )

( lens ) ( confocal focusing ) [3.7]

( focal plane ) ( beam splitter )

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; [3.6]

3-2-2 Up-conversion

3-2-2-1 Up-conversion

( ) Up-conversion ( Sum frequency generation, SFG ) 3.10 E Maxwell [3.8] 2 2 0 2 2 2 2 t P t E c 1 E ∂ ∂ µ = ∂ ∂ − ∇ , (3.1) 3.10 26

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( polarization vector, P ) PL NL P P= PL +PNL, (3.2) PL =P(1)(t)=χ(1)E1, (3.3) _PNL =_P(2)₍_t₎+_P(3)₍_t₎+L=χ(2)_E2 +χ(3)_E3 +L _(3.4) ) n ( χ n ( susceptibility ) ( n = 1,2,3… ) Up-conversion P₂(t)=χ(2)E2, (3.5) ( : ω₁ : ω₂ ) E(t)= E₁e−iω1t +E₂e−iω2t +c.c., (3.6) c.c. ( complex conjugate ) 3.5 3.5

(

)

(

)

(

∗ ∗

)

ω + ω − ∗ ω + ω − ω − ω − ω − ω − + χ + + + + + χ = + + χ = 2 2 1 1 ) 2 ( t ) ( i 2 1 t ) ( i 2 1 t i 2 2 2 t i 2 2 1 ) 2 ( 2 t i 2 t i 1 ) 2 ( ) 2 ( E E E E 2 . c . c e E E 2 e E E 2 e E e E c . c e E e E ) t ( P 2 1 2 1 2 1 2 1 , (3.7) 3 ω

( i ) Second harmonic generation ( SHG ) : P(2ω₁) =χ(2) E₁2, (3.8) ( ii ) Second harmonic generation ( SHG ) :P(2ω₂) =χ(2) E2₂, (3.9) ( iii ) Sum frequency generation ( SFG ) : P(ω₁ +ω₂)=2χ(2) 2E₁ E₂, (3.10) ( iv ) Difference frequency generation ( DFG ) :P(ω₁ −ω₂)=2χ(2)2E₁E∗₂, (3.11)

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( v ) Opticl Rectification ( OR ) :P(0) =2χ(2) (E₁E₁∗ +E₂E∗₂), (3.12) ( vi ) P(−2ω₁)=χ(2) E₁∗2, (3.13) ( vii ) P(−2ω₂)=χ(2) E∗₂2, (3.14) ( viii ) P(−ω₁ −ω₂)=2χ(2) 2E₁∗ E∗₂, (3.15) ( ix ) P(ω₂ −ω₁)= 2χ(2) 2E₁E∗₂, (3.16) 3.13-3.16 3.8-3.12 3.11 (ω₁ ω₂ ω1>ω2) 2 1 3 =ω +ω ω ( SFG ) ω₃ = ω₁ −ω₂ ( DFG )

( ω₁ ω₂ ) ( first harmonic overtones ) : 2ω1

2 2ω SHG SFG ω₁ =ω₂ [3.9] ( a ) ( b ) ( c ) 3.11 ( a ) SFG ( b ) DFG ( c ) SHG 27 SFG ( phase matching ) ∆k = k₃ −k₂ −k₁ =0, (3.17)

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₁ ₁ ₂ ₂ ₃ ₃ 3 3 2 2 1 1 n n _or _n _n _n n ω = ω + ω λ = λ + λ ⇒ , (3.18) ( isotropic crystal ) ( λ₁ λ₂ λ₃ ) ( n₁ω₁+ n₂ω₂ ≠ n₃ω₃) ( anisotropic crystal ) ( Z )

( optic axis OA ) Maxwell

₂ _x _y _z z 2 2 y 2 2 x 2 n n n , 1 n z n y n x ≠ = = + + , (3.19) 3.12 ( ordinary wave ) 0 n n₀ =n_x =n_y ( extraordinary wave ) e n n_e =n_z [3.10] 0 e n n n = − ∆ ∆n>0 3.13 ( a ) ; 0 n< ∆ 3.13 ( b ) [3.11] 3.14 θ 0 e( 0) n n∗ θ= = n∗_e(θ=π/2)=n_e n∗_e θ [3.12] θ + θ = θ ∗ 2 2 e 2 2 o e o e cos n sin n n n ) ( n , (3.20) θ n∗_e(θ) ( ∆k =k₃ −k₂ −k₁ =0 ) SFG 3.15 I SFG ; II SFG [3.13]

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( ) 3.2 SFG Incident Wave Incident Wave Ordinary Wave Ordinary Wave Extraordinary Wave Extraordinary Wave Optical Axis Optical Axis 3.12 28

( a )

( b )

3.13 ( a ) ( b ) 29

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(a) (b) 3.14 θ (a) (b) 30

(a)

(b)

3.15 ( a ) Type I ( b ) Type II 31 NLO Type Uniaxial Positive ( ∆n = n_e −n_o > 0 ) Uniaxial Negtive ( ∆n = n_e −n_o <0 ) I no₃ω₃ =n₁eω₁ +n₂eω₂ no₃ω₃ =n₁oω₁ +ne₂ω₂ II no₃ω₃ =n₁eω₁ +n₂oω₂ 2 e 2 1 o 1 3 e 3 n n n ω = ω + ω 3.2 表格 2

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3-2-2-2 Up-conversion

3.16 FOG 100

Up-conversion CDP2022 ( monochromater ) ( photon multiplier tube, PMT ) Ti:Sapphire :

780 nm 200 fs ( repetition rate ) 76 MHz 800 mW [3.4] ~ 200 fs 3.16 Up-conversion 32 3.17 [3.4] IN1 IN2 ( IN1 ) ( pre-mirror )

( beam splitter, BS ) ( pump pulse )

( gate pulse ) ( break )

(L1) PL AC ;

M2 M3 ( optical delay line )

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PL ( : ω_PL, : E_PL )

( : ω_G, : E ) _G ( L2 )

( Type II BBO ) 3.18 ( a )

PL 3.2 ( n₃eω₃ =n₁oω₁ +n₂eω₂ )

θ BBO 3.18 ( b )

( Optical delay line ) [3.14]

3.17 Up-conversion 33

(53)

3-3

[3.1] D. Leonard, K. Pond, and P. M. Petroff, Phys. Rev. B. 50, 11687 (1994). [3.2] J. M. Moison, et al. Appl. Phys. Lett. 64, 196 (1994).

[3.3] L. Chu, M. Arzberger, G. Bohm and G. Abstreiter, J. Appl. Phys. 85, 2355 (1999).

[3.4] /

2008

[3.5] The Nanoscale Informal Science Education Network [3.6]

2001

[3.7] Rudbeck Laboratoriet at Uppsala universitet. [3.8] Nicolaas Bloembergen, “Nonlinear-Opticsat”.

[3.9] Zacharias Generation of tunable ps laser pulses in the mid infrared. [3.10] Microscopy Resource Center,“ Birefringence Variations with Crystal Orientation” .

[3.11] Imp Imperial College Rock Library ,”Imperial College Rock Library Learn Tutorial - Measuring Optic Sign: Uniaxial Minerals Definition”. [3.12] Nonlinear Optical Crystals. AOTK, Inc.

[3.13] “ Phase-matching”, Crystech (2006).

(54)

4-1

PL ( Confocal System ) Ar 488nm ND filter 4.1 4.2 4.3 n p 3000 W/cm2 300K Gaussian ( 4.1) ( barrier )

( wetting layer, WL) ( excited state, ES ) ( ground state, GS ) 4.1

∑

= _          λ λ × ⋅       π × + = n 1 k 2 c 0 w -2 -exp /2 w A I I , ( 4.1 ) I PL I₀ A n w

( Full width at half maximum, FWHM ) λ_c

4.2 p n

5meV ( blue-shift ) ( red-shift ) p

( interdiffusion )

; n

[4.1-4.3]

4.4- 4.6 n p 300

W/cm2

(55)

800 900 1000 1100 1200 0.0 0.1 0.2 0.3 Barrier WL 1stES GS In te n si ty ( a .u . ) Wavelength ( nm ) undoped QRs Gaussian fitting N_ex = 300 W /cm2 T = 300K 4.1 35 800 900 1000 1100 1200 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Barrier WL 1st ES GS In te n si ty ( a .u . ) Wavelength ( nm ) n-doped QRs Gaussian fitting N_ex = 300 W /cm-2 T = 300K 4.2 n 36

(56)

800 900 1000 1100 1200 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Barrier WL 1st ES GS In te n si ty ( a .u . ) Wavelength ( nm ) p-doped QRs Gaussian fitting N ex = 300 W /cm 2 T = 300K 4.3 p 37

Sample State Barrier WL 1st ES GS

undoped QRs 1066 nm ( 1.163 eV ) 1106 nm ( 1.121 eV ) n-doped QRs 1060 nm ( 1.170 eV ) 1111 nm ( 1.116 eV ) p-doped QRs 873 nm ( 1.420 eV ) 932 nm ( 1.330 eV ) 1065 nm ( 1.164 eV ) 1101 nm ( 1.126 eV ) 4.1 3

(57)

800 900 1000 1100 1200 0.0 0.5 1.0 1.5 2.0 2.5 In te n si ty ( a .u . ) Wavelength ( nm ) undoped QRs T =300 K 3000 W / cm-2 1000 W / cm-2 300 W / cm-2 4.4 38 800 900 1000 1100 1200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 In te n si ty ( a .u . ) Wavelength ( nm ) n-doped QRs T =300 K 3000 W / cm-2 1000 W / cm-2 300 W / cm-2 4.5 n 39

(58)

800 900 1000 1100 1200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 In te n si ty ( a .u . ) Wavelength ( nm ) p-doped QRs T =300 K 300 W / cm-2 1000 W / cm-2 3000 W / cm-2 4.6 p 40

4-2 Modulation-doped InAs/GaAs QRs

4.1 PL 4.7 - 4.9 n p Ti sapphire Laser eV 59 . 1 = ω h _N_ex =_300W/cm2 30 ps GaAs ( 50 ps ) WL p n ( random filled )

(59)

4.10 - 4.12 n p ; 4.13 - 4.15 0 100 200 300 400 500 600 700 800 0.0 0.2 0.4 0.6 0.8 1.0 N o rm al iz ed I n te n si ty Delay time (ps) undoped QRs 300 W/cm2 barrier wetting layer 1st excited state ground state 4.7 41 0 100 200 300 400 500 600 700 800 0.0 0.2 0.4 0.6 0.8 1.0 N o rm al iz ed I n te n si ty Delay time (ps) n-doped QRs 300 W/cm2 barrier wetting layer 1st excited state ground state 4.8 n 42

(60)

0 100 200 300 400 500 600 700 800 0.0 0.2 0.4 0.6 0.8 1.0 N o rm al iz ed I n te n si ty Delay time (ps) p-doped QRs 300 W/cm2 barrier wetting layer 1st excited state ground state 4.9 p 43 0 5 10 15 0.0 0.2 0.4 0.6 0.8 1.0 undoped QRs 1st excited state N o rm a li ze d I n te n si ty Delay time ( ps ) 3000 Wcm-2 2000 Wcm-2 1200 Wcm-2 800 Wcm-2 500 Wcm-2 300 Wcm-2 4.10 44

(61)

0 5 10 15 0.0 0.2 0.4 0.6 0.8 1.0 n-doped QRs 1st excited state N o rm a li ze d I n te n si ty Delay time ( ps ) 3000 Wcm-2 2000 Wcm-2 1200 Wcm-2 800 Wcm-2 500 Wcm-2 300 Wcm-2 4.11 n 45 0 5 10 15 0.0 0.2 0.4 0.6 0.8 1.0 p-doped QRs 1st excited state N o rm a li ze d I n te n si ty Delay time ( ps ) 3000 Wcm-2 2000 Wcm-2 1200 Wcm-2 800 Wcm-2 500 Wcm-2 300 Wcm-2 4.12 p 46

(62)

0 5 10 15 0.0 0.2 0.4 0.6 0.8 1.0 undoped QRs ground state N o rm a li ze d I n te n si ty Delay time ( ps ) 3000 Wcm-2 2000 Wcm-2 1200 Wcm-2 800 Wcm-2 500 Wcm-2 300 Wcm-2 4.13 47 0 5 10 15 0.0 0.2 0.4 0.6 0.8 1.0 n-doped QRs ground state N o rm a li ze d I n te n si ty Delay time ( ps ) 3000 Wcm-2 2000 Wcm-2 1200 Wcm-2 800 Wcm-2 500 Wcm-2 300 Wcm-2 4.14 n 48

(63)

0 5 10 15 0.0 0.2 0.4 0.6 0.8 1.0 p-doped QRs ground state N o rm a li ze d I n te n si ty Delay time ( ps ) 3000 Wcm-2 2000 Wcm-2 1200 Wcm-2 800 Wcm-2 500 Wcm-2 300 Wcm-2 4.15 p 49 4.10 4.15             τ = r o t -exp -1 I I(t) I(t) t I o τr 4.16 - ( carrier- carrier scatter )

(64)

-0 500 1000 1500 2000 2500 3000 0 1 2 3 4 5 ((((a )))) R is in g T im e ( p s ) Photoexcitation Density ( W / cm2) 1st excited state undoped QRs n-doped QRs p-doped QRs 0 500 1000 1500 2000 2500 3000 0 1 2 3 4 5 ((((b )))) R is in g T im e ( p s ) Photoexcitation Density ( W / cm2) ground state undoped QRs n-doped QRs p-doped QRs 4.16 ( a ) ( b ) 50

(65)

4-3

[4.1] D. G. Deppe, N. Holonyak, Jr., W. E. Plano, V. M. Robbins, J. M.

Dallesasse, K. C. Hsieh, and J. E. Baker, J. Appl. Phys. 64, 1838 (1988).

[4.2] D. G. Deppe and N. Holonyak, Jr., J. Appl. Phys. 64, R93 (1988).

[4.3] O. B. Shchekin, D. G. Deppe, and D. Lu, Appl. Phys. Lett. 78, 3115 (2001). [4.4] K. Gundogdu, et al. Appl. Phys. Lett. 85, 4570 (2004)

(66)

200 ( fs )

- ( carrier- carrier scatter )

;

-WL p

(67)

1-1

( charge ) —

( spin ) ( spin-up state ) ( spin-down state )[1.1]

;

( i )

Non-Volatile MRA M ( Magnetic

Random Access Memory ) DRAM

( Dynamic Random Access Memory ) ; ( ii )

1.1 Spin-FET ( source )

( drain )

( ON ) 1.1(b);

( OFF ) 1.1(a) [1.2] (iii) ( )

( ) ( )

( exciton )

(68)

: ( 1 ) ( 2 )

Elliott-Yafet (EY), D'yakonov-Perel (DP), Bir-Aronov-Pikus (BAP) ( hyperfine interaction )

( 3 )

( 4 )

(69)

1-2

1936 Mott [1.4] Elliott Yafet 1954 1963 [1.5-1.6] - ( Spin-flip ) 1971 D'yakonov Perel' ( inversion asymmetry ) [1.7] 1975 Bir-Aronov-Pikus ( exchange interaction ) [1.8] 1990 Datta Das

( spin-field effect transtor ) [1.9-1.10]

1.2 (source)

( structure inversion asymmetry, SIA )

( precession ) ( drain )

2002

1.3 1.4 EY

[1.11] D. J. Hilton pump probe

GaAs 110 [1.12] K.Gündogdu InAs 1.5 77K 40% 120ps 29ps [1.13] 1.6 S. Marcinkevičiusa InAs 80K p n [1.14]

(70)

1.2 Datta –Das 52

1.3 n 53

(71)

1.5 55

(72)

1-3

InAs/GaAs [1.15-1.16] (exciton) [1-3] — [1.17-1.18] ; barrier GaAs -InAs/GaAs

(73)

1-4

[1.1]

577-580 2004 8

[1.2] K.C. Hall and M.E. Flatte, Appl. Phys. Lett. 88 (16) (2006), [1.3]

497-501 2003 8

[1.4] N. F. Mott, Proc. R. Soc. London, Ser. A 153, 699 (1936). [1.5] R. J. Elliott, Phys. Rev. 96, 266 (1954).

[1.6] Y. Yafet, Solid State Phys. 14, 1 (1963).

[1.7] M. D'yakonov and V. Perel', Sov. Phys. JETP Lett. 13, 144 (1971).

[1.8] G. L.Bir, A.G. Aronov and G. E. Pikus, Zh. Eksp. Teor. Fiz. 69, 1382(1975). [1.9] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).

[1.10]

792-795 2006 10

[1.11] P. H. Song and K. W. Kim, Phys. Rev. B 66, 035207 (2002). [1.12] D.J. Hilton and C.L. Tang, Phys. Rev. Lett. 89, 146601(2002). [1.13] K. Gundogdu, K. C. Hall, Appl. Phys. Lett. 86, 113111(2005).

[1.14] S. Marcinkevicius J. Siegert, and Q. X. Zhao, Journal of Appl. Phys. 100, 054310(2006).

[1.15] S. Cortez, O. Krebs, S. Laurent, M. Senes, X. Marie, P. Voisin, R. Ferreira, G. Bastard, J-M. Ge´rard, and T. Amand, Phys. Rev. Lett. 89, 207401(2002).

[1.16] P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang , and D. Bimberg, Phys. Rev. Lett. 87, 157401(2001).

[1.17] R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, Phys. Rev. B 65, 113303(2002). [1.18] H. Pettersson, R. J. Warburton, A. Lorke, K. Karrai, J. P. Kotthaus, J. M. Garcia, and P. M. Petroff, Physica E (Amsterdam) 6, 510 (2000).

(74)

2-1

( spin polarization )

( optical orientation ) [2.1]

( conservation law of angular

momentum ) ( selection rule )

1 ± = − ′ = ∆l l l 0 m m m = ′− = ∆ ; ∆m ±1 [2.3] (σ+ σ−) ( spin polarization, Pn ) [2.2] ↓ ↑ ↓ ↑ + − = n n n n P_n , (2.1) ↑ n n _↓ ( GaAs ) ( Si ) Lampel 0.1% GaAs 2.1 ∧ z hω _E_g _E_g +∆_SO + σ ( z ) J =3/2;m_j =−3/2

(75)

2 / 1 m ; 2 / 3 J= _j =− J=1/2;m_j =−1/2 J=1/2;m_j =1/2 p s

( Fermi golden rule )

Γ_V_→_C = 2π c H_int υ 2 δ(E_C -E_v -hω) h , (2.2) _C _v _C _C 2 int C V c H (E -E - ) (E )dE 2 dΓ = π υ δ ω ρ ⇒ _→ h h , (2.3) ⇒Γ= 2π

∫

c H_int υ 2δ(E_C -E_v -hω)ρ(E_C)dE_C h , (2.4) ∴ Γ = π υ ρ ₌ ₊_h_ω h C EC EV 2 int (E ) H c 2 , (2.5) c v int H ( Hamitonian operator ) HH , LH SO -3/2 -1/2 +1/2 +3/2 +1/2 CB ＋＋＋＋

σ

+

σ

_σ

σ

+

-Excitation

Excitation

︱︱︱︱↓↓↓↓>

-

︱︱↑︱︱↑↑↑> -1/2 2.1 GaAs 57

(76)

( Hamitonian operator , H ) ) r ( V m 2 P H c 2 0 = + Hint H = Ho+Hint

Hint ( electric dipole )

   ∝ ± =           ⋅           ± ∝ ⋅ ε = −1 , 1 1 , 1 T int Y Y iY X Z Y X 0 i 1 R H , (2.6) ε R X Y Z

( )

±ϕ ±m θ,ϕ = 3/8πsinθ⋅e i

Y_l m _{( spherical harmonic function )}

l₌₁ _{m = ±1} _{: “+”} _“-” σ+ σ−

2.1

(77)

(2.5) (2.7) ( transition probability ) ₂ 11 2 11 2 2 2 / 1 ; 2 / 3 Y 2 / 1 ; 2 / 1 2 / 3 ; 2 / 3 Y 2 / 1 ; 2 / 1 R c R c − − − = υ ⋅ ε υ′ ⋅ ε ′ , (2.7) 3 n n = ⇒ ↑ ↓ _{, (2.8)} 2 1 3 1 3 -1 n n n -n P 0) (t P_n ₀ =− + = + = = = ↑ ↑ ↑ ↑ _{, (2.9)} 2.2 pump probe 800nm ( 1.55 eV ) σ+ PL 3200 nm 3000nm 3800nm σ+ σ- 2.3 110 fs [2.4] σ+ σ- 2.4 τ

( the degree of circular polarization )

25% 4 1 2 P ) n n 3 ( ) n 3 n ( ) n n 3 ( ) n 3 n ( I I I I P_circular =− 0 = = + + + + − + = + − = ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ − + − + , (2.10)

(78)

2.2 58

2.3 59

(79)

HH , LH SO -3/2 -1/2 +1/2 +3/2 +1/2 CB ＋＋＋＋

σ

+

_σ

σ

_σ

+

-Recombination

Recombination

︱︱︱︱↓↓↓>↓

-

︱︱︱︱↑↑↑↑> -1/2

σ

-

_σ

-＋＋＋＋ 2.4 60

(80)

2-2

( spin-orbit coupling, SOC )

V(r) v Homitonian

(

)

⋅σ ∂ ∂ λ − = σ ⋅ × ∇ = r h r r r h L r V(r) r 1 v (r) V c 4m ) r ( H vac 2 o SO , (2.11) V(r) m_o vr L

σr Pauli Dirac gap : -2m c2 1MeV o ≈

SOC eV

1

E_g ≈ Dirac gap : -2m_oc2 ≈1MeV SOC

SOC ( inversion center )

k ( k = 0 ) SOC [2.5]

[2.6]

SOC Dresselhaus Rashba 掺

( 1 ) Dresselhaus ( bulk inversion asymmetry, BIA )

( inversion center )

Homitonian

H3_DD =β₃_D

(

σ⋅K

)

, (2.12) β₃_D K_x = k_x

(

k2_y −k_z2

)

K_y =k_y

(

k_z2 −k2_x

)

K_z =k_z

(

k_x2 −k2_y

)

k

( 2 ) Rashba ( structure inversion asymmetry,

SIA ) ( heterostructure )

H_SO(r)

H_R =α_R

(

σ_zk_y,−σ_yk_x

)

, (2.13)

(81)

2-3

Bloch equation

2-3-1 Bloch

sr z B₀ ( oscillating field ) B₁(t) B=B₀z+B₁(t) ∧

( spin relaxation time,T ) ₁ ( spin dephasing

time, T ) ₂ Bloch equation [2.7]

(

)

2 x x x T s B s t s r r r − × γ = ∂ ∂ , (2.14)

(

)

2 y y y T s B s t s r r r − × γ = ∂ ∂ , (2.15)

(

)

1 z 0 z z z T s s B s t s r r r r − − × γ = ∂ ∂ , (2.16) h / gµ_B = γ ( gyromagnetic ratio) g g

β ( Bohr magneton ) g Zeeman g

(T )₁ - ( spin

longitudinal or spin-lattice relaxation time ) 2.6 1/T₁

z s r 0 B ↑ ↓ ; (T )₂

( spin transverse or spin decoherence time ) B₀

larmor

1

(82)

2.6 [2.8]61 ( donor states ) T₂ ( spin-echo ) 2.7 T [2.1] [2.9]₂∗ 2.7 62

(83)

2-3-2

2.8 [2.10-2.11] : ( 1 ) Elliott-Yafet ; ( 2 ) DP ; ( 3 ) BAP (exchange interaction) p 2.8 63

(84)

2-3-2-1 EY

( Elliott-Yafet Mechanism )

2.9 2.10 [2.11-2.12] -( Spin-flip) Hamitonian [2.9]

(

)

L S r V r c 2m 1 p V c 4m H 2 2 e 2 2 e SO _∂ ⋅ ∂ = σ ⋅ × ∇ = h , (2.17) V p σ Pauli L S

( Bloch function ) σ_Z ( eigenstate )

Pauli ↑ ↓

Ψ_kn_↑(r)=

[

a_kn(r)↑ +b_kn(r)↓

]

eik⋅r, (2.18)

Ψ_kn_↓(r)=

[

a∗_-_kn(r)↑ -b∗_-_kn(r)↓

]

eik⋅r, (2.19)

k ( lattice momentum ) n ( energy index )

E_k p 2 2 g B EY 1 /3 -1 /2 -1 E T k A 1 τ       η η η         = τ , (2.20) g E (energy bandgap) η=∆_SO/

(

E_g +∆_SO

)

∆_SO p τ A ( 2~6) 2.21 EY τ_EY τ_p

(85)

2.9 EY 64

(86)

2-3-2-2 DP

( D'yakonov-Perel' Mechanism )

D'yakonov Perel' ( inversion asymmetry )

GaAs Pauli ↑ ↓ (ε_k_↑ ≠ε_k_↓) Pauli ↑ ↓ [2.1] k B(k) Hamitonian [2.2] = + ∗µ ⋅σ= + Ω(k)⋅σ 2m k B(k) g 2m k H e 2 2 B e 2 2 h h h , (2.21) α ; Ω(k) ( Larmor procession vector ) Ω(k)=αh2

(

2m3_eE_g

)

-1/2

[

k_x

(

k_y2 -k_z2

)

xˆ +k_y

(

k_z2 -k2_z

)

yˆ+k_z

(

k_x2 -k2_y

)

zˆ

]

_{, (2.22)} 2.11 [2.13] DP : ( i )τ_pΩ_av ≥1 ( ii )τ_pΩ_av <<1 Ωav Ω(k) τp ( i ) τ_pΩ_av ≥1 τ_p τ_s 1/τ_s Ω(k) 1/τ_s ≈ ∆Ω Pauli ↑ ↓ Ω(k) [2.1]

(87)

2 3 -2 1 -2 3 - ( ) ; τ_p ( ) ( )[2.14] ( ii ) τ_pΩ_av <<1 τ_p <τ_s (i)

( nuclear magnetic resonance , NMR )

( motion narrowing ) DP [2.15]

(

)

_p g 2 3 B 2 DP E T k C~ 1 τ α = τ h , (2.23) C~ ( dimensionless factor ) α (cubic band-structure ) 0 e m m -3 4 η η ≈ α e m k=0 m₀ 2.24 τ_DP τ_p [2.2] 2.11 DP 66

(88)

2-3-2-2 BAP

( Bir-Aronov-Pikus Mechanism )

BAP (exchange interaction)

p BAP Hamitonian

[2.2]

H_exc = AS⋅Jδ(r), (2.24)

A (exchange integral) S

J δ(r) δ ( Dirac delta function ) r

( critical hole concentration N )_C

BAP (N_A <N_C) [2.16]             − + Ψ υ τ υ α = τ A b , a 4 A f , a B 0 k A 3 B BAP s N n 1 3 5 ) 0 ( N n N 2 1 , (2.25) 2 / 1 e c k m E 2       = υ

(

0 R

)

0 0 B = m /m ε a

α ( exciton Bohr radius )

b , a f , a A n n N = + f , a n 、n_a_,_b 、 0

τ (exchange splitting parameter)

2 ) 0 ( Ψ (Sommerfeld factor) ; (N_A >N_C) [2.17]

(

)

(

)

   > = υ < = υ       υ τ υ α = τ 2E /m if E E (m /m ) ) m / m ( E E if m / E 2 E E N 2 1 h e c Fh 2 / 1 h c k h e c Fh 2 / 1 e c k Fh c B 0 k A 3 B BAP s , (2.26)

(89)

BAP s τ 2 ) 0 ( Ψ na,f 1 ) 0 ( 2 = Ψ na,f =NA BAP s τ NA BAP s / 1 τ N_A 1/τ_sBAP 3 / 1 A N [2.1]

(90)

2-4

[2.1] I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004). [2.2] Nicholas J. Harmon, The Generation and Relaxation of Spin Polarization in Bulk Semiconductors (2007).

[2.3] 29

6 404-410 90 3

[2.4] D.J. Hilton and C.L. Tang, Phys. Rev. Lett. 89, 146601(2002). [2.5]

792-795 2006 10

[2.6]

14-18 2009 9

[2.7] J. Fabian, Acta Physica Slovaca Vol. 57, No. 4&5, 565–907 (2007). [2.8] Group of Prof. Michael ,Flatte Optical generation of spin-polarized Distributions.

[2.9] Glenn Facey, Gradient Spin Echoes for Selective Excitation (2010). [2.10]J. Fabian and S. Das Sarma. J. Vac. Sci. Technol. B17 (1999).

[2.11] http://physik.kfunigraz.ac.at/~jaf/research/spintronics/spin_relaxation/ relaxation.html

[2.12]Markus G. Münzenberg, Nature Materials 9, 184 (2010). [2.13] Roland Winkler, University Hannover

[2.14] Culcer,Dimitrie, Phys. Rev. B 76, 245322 (2007).

[2.15] Ohms, T., Hiebbner, K., Schneider, H. C., Aeschlimann, M,” Spin- and energy relaxation of hot electrons at GaAs surfaces.” (2005).

[2.16] P. H. Song and K. W. Kim, Phys. Rev. B. 66, 035207 (2002).

[2.17] K. Zerrouati, F. Fabre, G. Bacquet, J. Bandet, J. Frandon, G. Lampel, and D. Paget, Phys. Rev. B. 37, 1334 (1988).

(91)

3-1

GaAs InAs/GaAs

( self-assembled Quantum rings )

GaAs : ( 1 ) : undoped GaAs ( 2 ) : p-doped GaAs ( n_h =5.8×1018cm−3 ) ( 3 ) : n-doped GaAs ( n_e =4.2×1017cm−3 ) ( 4 ) : n-doped GaAs ( n_e =1.0×1018cm−3 ) InAs / GaAs : ( 1 ) : undoped QRs ( 2 ) : n-doped QRs ( 20 e- / QRs ) ( 3 ) : p-doped QRs ( 20 h+ / QRs )

(92)

3-2

+ σ _σ−

3-2-1

[ 3.1-3.2 ]

E B E B E E z x y ω θ x =asinωt, ( 3.1 ) y = bsin

(

ωt-φ

)

, ( 3.2 ) 3.1 3.1 t + φ= 2φ 2 2 2 2 sin cos ab 2xy -b y a x , ( 3.3 ) (1) a ≠ b φ≠0 y

(elliptically polarized light) (2) a =b φ=0 x = y x y

( linearly polarized light ) (3) a =b φ≠0 x2 +y2 =a2

x y

(circularly polarized light)

(93)

X Y X Y X Y X Y X Y Y X Y X Y 0 = φ 2 0<φ<π 2 π = φ π<φ<π 2 π = φ 2 3π < φ < π 2 3π = φ π<φ<2π 2 3 3.1 67 3.2 4 π = θ D C n -C n D -D t o e e o       = υ υ = ∆ , ( 3.4 )

(

n -n

)

D 2

(

n -n

)

D C 2 t 2 _o _e o e o       λ πυ =       πυ = ∆ πυ = φ ∆ , ( 3.5 ) D n_o n_e

(94)

(1) D 2 π = φ ∆ ， 1/4 2 π 4 π (2) D 2 π = φ ∆ ， 1/2 2θ。 3.2 68 3.1 表格 5

(95)

3-2-2

3.3 Up-conversion

1/4 (quarter wave plate, QWP)

BS F2 QWP1; AC L2 QWP2 3.4 QWP1 QWP2 QWP1 QWP2 3.3 69

(96)

( a )

( b )

3.4 70

3-3

[3.1]

[3.2] Polarization and Polarization Control, NEW FOCUS, Inc.

[3.3] /

(97)

GaAs -InAs/GaAs III-V

4-1

GaAs

( 1 ) Elliott-Yafet ; ( 2 ) DP ; ( 3 ) BAP

4-1-1

GaAs

4.1(a) GaAs hω=1.59eV 3 17 ex 5.0 10 cm N = × − σ+ I+(t) I−(t) ) t ( I ) t ( I ) t ( I ) t ( I P_circular ₊ ₋ − + + − = , (4.1) 4.1(b) PL σ+ − σ ( P₀ ≈50% ) ( 1 ) ( t < 1ps ) : 50% 15% ; ( 2 ) ( t > 1ps ) : 90 ps ) t ( I+ I−(t) 4.1(b) 1 t/ 2 2 / t 1e A e A (%) P = − τ + − τ 4.2 1 τ τ2 0.38 ps 50.49 ps 1 τ fs 4-1-3-3

(98)

0 25 50 75 100 125 150 0 10 20 30 40 50 60 − σ + σ undoped GaAs N_ex= 5.0x1017 cm-3 I+ I -In te n si ty ( a .u .) ( b ) ( a ) P o la ri z at io n ( % ) Delay Time (ps) Pcirc

4.1 (a) GaAs (b) (a) 71

4.2 GaAs 72 0 25 50 75 100 125 150 0 10 20 30 40 50 S p in P o la ri z a ti o n ( % ) Delay Time (ps) undoped GaAs N_ex= 5.0x1017 cm-3

(99)

4.3 GaAs 4.4 4.3 4.1 0 25 50 75 100 125 150 0 10 20 30 40 50 60 S p in P o la ri za ti o n ( % ) Delay Time ( ps ) undoped GaAs Nex = 5.0x1016 cm-3 Nex = 1.0x1017 cm-3 Nex = 5.0x1017 cm-3 Nex = 7.5x1017 cm-3 Nex = 1.0x1018 cm-3 4.3 73 1016 1017 1018 0.00 0.25 0.50 20 40 60 80 100 1 τ 2 τ S p in L if et im e ( p s) Excitation Density ( cm-3) undoped GaAs 4.4 GaAs 74

(100)

N_ex(cm-3) Spin Lifetime (ps) 16 10 5.0× 1.0×1017 5.0×1017 7.5×1017 1.0×1018 1 τ 0.45 0.46 0.45 0.38 0.35 2 τ 65.80 77.39 72.18 50.49 29.73 4.1 GaAs 表格 6 (τ₂) 4.4 N_ex 5.0×1016cm−3 3 17 cm 10 0 . 5 × − DP ( τ_pΩ_av <<1 ) [4.1 - 4.2] ex N 1.0×1017 cm−3 1.0×1018cm−3 DP ( inhomogeneous broadening ) Ω_k 2 −Ω2_z(k) ∝ N2_ex [4.3] larmor

(101)

4-1-2 P

GaAs

P DP BAP BAP (exchange interaction) p BAP [4.4]

4-1-2-1

n_h =5.8×1018cm−3 p-GaAs 4.5 p-GaAs eV 59 . 1 = ω h σ+ 4.8 P( t = 0 ) 25% 4.6 1ps 4.7 ∧ z hω=1.59eV _E ₁_.₄₂_eV g = eV 76 . 1 E_g +∆_SO = σ+ (z ) 2 / 1 m ; 2 / 1 J = _j =− J=1/2;mj =1/2 3 : 1 J =3/2;mj =−3/2 J =3/2;mj =−1/2 3 : 1 N_ex =1.0×1016 ~1.0×1018cm−3 3 18 h 5.8 10 cm n = × − 4.8 + σ σ

-( the degree of circular polarization )

(102)

25% n 4 3 n 4 1 n 4 3 n 4 1 n 4 1 n 4 3 n 4 3 n 4 1 I I I I P_circular =       + +       +       ₊ −       ₊ = + − = ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ − + − + , (4.2) 0 25 50 75 100 125 150 0 10 20 30 40 50 ( a ) S p in P o la ri za ti o n ( % ) Delay Time ( ps ) p-doped GaAs n_h = 5.8x1018 cm-3 N_ex = 1.0x1016 cm-3 N_ex = 5.0x1016 cm-3 N_ex = 1.0x1017 cm-3 N_ex = 5.0x1017 cm-3 N_ex = 1.0x1018 cm-3 0 1 2 3 4 5 0 10 20 30 40 50 60 _{( b )} S p in P o la ri za ti o n ( % ) Delay Time ( ps ) p-doped GaAs n_h=5.8x1018 cm-3 Nex = 1.0x1016 cm-3 Nex = 5.0x1016 cm-3 Nex = 1.0x1017 cm-3 Nex = 5.0x1017 cm-3 Nex = 1.0x1018 cm-3 4.5 p-GaAs ( a ) (150 ps) ( b ) (5 ps)75

(103)

1016 1017 1018 0 10 20 30 40 50 _p-GaAs n _h = 5.8x1018 cm-3 Excitation Density ( cm-3) In it ia l S p in P o la ri z at io n ( % ) 4.6 p-GaAs 76 HH , LH SO -3/2 -1/2 +1/2 +3/2 -1/2 +1/2 CB ＋＋

-＋＋

- -

-σ

σ

+

_σ

+

Excitation (

p

-

GaAs

)

＋＋＋＋︱︱︱︱↓↓↓↓> ︱︱︱︱↑↑↑>↑ ＋＋＋＋ 4.7 p-GaAs σ+ 77

(104)

HH , LH SO -3/2 -1/2 +1/2 +3/2 -1/2 +1/2 CB ＋＋

-＋＋

- -

-σ

σ

+

_σ

+

Recombination (

p

-

GaAs

)

＋＋＋＋

σ

-

σ

-︱︱︱︱↓↓↓↓> ︱︱︱︱↑↑↑>↑ ＋＋＋＋ 4.8 p-GaAs 78

4-1-2-2

BAP p-GaAs GaAs 4.9 N_ex 5.0×1016cm−3 3 17 cm 10 0 . 5 × − τ₂ DP (τ_pΩ_av <<1) 2 τ 16 3 cm 10 0 . 5 × − 3 17 cm 10 0 .

5 × − p-GaAs GaAs BAP

ex N 1.0×1017 cm−3 3 18 cm 10 0 . 1 × − τ2 DP ( inhomogeneous broadening ) Ω_k 2 −Ω2_z(k) ∝N2_ex [4.3] BAP Dresselhaus

(105)

(

γ β

)

_

(

−

)

+

(

−

)

+

(

−

)

_ = ∧ ∧ ∧ 2 y 2 x z 2 x 2 z y 2 z 2 y x SO 2 /g xk k k yk k k zk k k H [4.3]。 (<1 ps ) 1 τ 1016 1017 1018 0.0 0.5 1.0 25 50 75 100 125 150 2 τ1 τ p-GaAs n_h=5.8x1018 cm-3 Excitation Density ( cm-3) S p in L if e ti m e ( p s) 4.9 p-GaAs 79

(106)

4-1-3 N

GaAs

N BAP

4-1-3-1

n_e =4.2×1017cm−3 n_e =1.0×1018 cm−3 n-GaAs 4.10 4.11 n-GaAs hω=1.59eV σ+ 4.12 1ps n-GaAs 0 25 50 75 100 125 150 0 10 20 30 40 50 60 S p in P o la ri za ti o n ( % ) Delay Time ( ps ) n-doped GaAs n e = 4.2 x 10 17 cm-3 Nex = 1.0x1016 cm-3 Nex = 5.0x1016 cm-3 Nex = 1.0x1017 cm-3 Nex = 5.0x1017 cm-3 Nex = 1.0x1018 cm-3 4.10 n_e =4.2×1017cm−3 n-GaAs 80

(107)

0 25 50 75 100 125 150 0 10 20 30 40 50 60 S p in P o la ri za ti o n ( % ) Delay Time ( ps ) n-doped GaAs n_e = 1.0 x 10 18 cm-3 Nex = 1.0x1016 cm-3 Nex = 5.0x1016 cm-3 Nex = 1.0x1017 cm-3 Nex = 5.0x1017 cm-3 Nex = 1.0x1018 cm-3 4.11 n_e =1.0×1018cm−3 n-GaAs 81 1016 1017 1018 0 10 20 30 S p in P o la ri za ti o n ( % ) Excitation Density ( cm-3) n-GaAs t = 1 ps n_e = 4.2x1017 cm-3 n e = 1.0x10 18 cm-3 4.12 1ps n-GaAs 82

(108)

n-GaAs P ( t = 1ps ) 3 7 1 e 4,2 10 cm n = × − 3 8 1 e 1.0 10 cm n = × − 4.13 n GaAs n_e = n ∧ z eV 59 . 1 = ω h _E_g =₁_.₄₂_eV _E_g +∆_SO =₁_.₇₆_eV + σ (z ) J =3/2;m_j =−3/2 2 / 1 m ; 2 / 3 J = j =− J =1/2;mj =−1/2 J =1/2;mj =1/2

( Fermi golden rule ) (transition probability) 3 2 / 1 ; 2 / 3 Y 2 / 1 ; 2 / 1 2 / 3 ; 2 / 3 Y 2 / 1 ; 2 / 1 R c R c n n 2 11 2 11 2 2 = − − − = υ ⋅ ε υ′ ⋅ ε ′ = ↑ ↓ _{, (4.3)} N_ex =n_↑ +n_↓ =4n_↑, (4.4) 4.14 110 fs τ n-GaAs n_e =n 2 / 1 m ; 2 / 3 J = j =− J=3/2;mj =1/2 2 n

( the degree of circular polarization )

        + = + + + + + + + − + + = + − = ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ − + − + ) n 4 / n ( 1 1 4 1 ) 2 / n n 4 3 n 4 1 ( ) 2 / n n 4 3 n 4 1 ( ) 2 / n n 4 1 n 4 3 ( ) 2 / n n 4 3 n 4 1 ( I I I I P e circular ,(4.5) ↑ ↓ ↑ + = =n n 4n N_ex n_e =n 25% ) N / n ( 1 1 4 1 P ex e circular ≤      + = , (4.6)

(109)

HH , LH

SO

-3/2 -1/2 +1/2 +3/2 -1/2 +1/2

CB

＋＋

-＋＋

- -

-σ

σ

+

_σ

+

-Excitation (

Excitation (

n

-

GaAs

)

-︱︱︱︱↓↓↓↓>

-

︱︱︱︱↑↑↑↑> 4.13 n-GaAs σ+ 83

HH , LH

SO

-3/2 -1/2 +1/2 +3/2 -1/2 +1/2

CB

＋＋

-＋＋

- -

-σ

σ

+

_σ

+

-Recombination (

Recombination (

n

-

GaAs

)

-︱︱︱︱↓↓↓↓> ︱︱︱︱↑↑↑↑>

σ

-

_σ

-＋＋＋＋

-

-4.14 n-GaAs 84

(110)

P n_e /N_ex n_e N_ex P 4.12 n_e =4.2×1017cm−3 3 8 1 e 1.0 10 cm n = × − GaAs N_ex P 3 7 1 e 4.2 10 cm n = × − N_ex 1.0×1018cm−3 P 3 18 ex 1.0 10 cm N = × − ( inhomogeneous broadening ) Ω_k 2 −Ω2_z(k) ∝N2_ex Ω_k 2 larmor P [4.3]

4-1-3-2

4.15 n_e =4.2×1017cm−3 GaAs 1 τ 0.3 ps N_e =1.0×1016 cm−3 P 1 ps 5.25% P 2 τ τ2 ex N 1.0×1016cm−3 5.0×1017 cm−3 ( τ_pΩ_av <<1 ) τ_p s τ ex N 5.0×1017cm−3 3 18 cm 10 0 . 1 × − 105 ps 45 ps : Ω_k 2 −Ω2_z(k) ∝ N2_ex ex N [4.3]

(111)

1016 1017 1018 0.00 0.25 0.50 25 50 75 100 125 150 2 τ1 τ n-GaAs n_e=4.2x1017 cm-3 Excitation Density ( cm-3) S p in L if et im e (p s) 4.15 n_e =4.2×1017 cm−3 GaAs 85 GaAs τ₂ 4.16 Dresselhaus Ω_k 2 −Ω2_z(k) ∝ ε3_k [4.8] τ−₂1 ≅ Ω(k)2 −Ω_z2(k) τ_p, (4.7)

(112)

undoped 4.2E17 1E18 0 25 50 75 100 125 150 L if e ti m e (p s) Doping Concentration , n_e( cm-3 ) N_ex = 5.0 x 1017 cm-3 Momentum scattering Spin relaxation 4.16 GaAs 86 τ_p GaAs n_e =4.2x1017cm−3 e n 1.0x1018cm−3 GaAs 3 17 e 5.0x10 cm n = − 4.17 E1 ) ( f_FD ε 1 / 2 Pauli E1 E2 ( backward scattering ) ( forward scattering) [4.6] W= W₀ ×f_i ×f_f, (4.8)

(113)

0 W f_i ( >1/2 ) f f ( <1/2 ) f_i f f f_i W n_e 4.2×1017 cm−3 1.0×1018 cm−3 W 25.78 ps 76.70 ps 4.17 [4.7] 87 Dresselhaus    ≥ < ∝ ε ∝ Ω − Ω ₁₇ ₋−₃ e 2 e 3 17 e 0 e 3 k 2 z 2 k cm 10 x 0 . 5 n , n cm 10 x 0 . 5 n , n ) k ( , (4.9) ( n_e <5.0x1017cm−3 ) Ω_k 2 −Ω2_z(k) n_e GaAs n_e = 4.2x1017cm−3 GaAs ( n_e ≥5.0x1017cm−3 ) Ω_k 2 −Ω2_z(k) e n n_e =1.0x1018cm−3 GaAs

(114)

: n_e =1.0x1018cm−3 GaAs GaAs 3 17 e 4.2x10 cm n = − GaAs ; Ω_k 2 −Ω2_z(k) :n_e =1.0x1018cm−3 GaAs n_e =4.2x1017cm−3 GaAs

[

]

1 p 2 z 2 2 (k) (k) T ≅ Ω −Ω τ − : n_e =1.0x1018cm−3 GaAs GaAs n_e = 4.2x1017cm−3 GaAs

4-1-3-3

n_e N_ex 0 n n n n ) 0 t ( P_n ≈ + − = = ↓ ↑ ↓ ↑ 4.18 n_e =1.0x1018cm−3 n-GaAs eV 59 . 1 = ω h _N_ex =₃_.₀_x₁₀15_cm−3 σ+ I+ I+ 1ps 4.18 t/ 1 1e A P= − τ ( fitting ) 4.19 1 τ 0.29 ps [4.9-4.10]

(115)

0 1 2 3 4 5 0 10 20 30 40 50 n-doped GaAs n_e= 1.0x1018 cm-3 N ex= 3.0x10 15 cm-3 I+ I -In te n si ty ( a. u .) ( b ) ( a ) P o la ri za ti o n ( % ) Delay Time (ps) Pcirc 4.18 (a) n-GaAs (b) 88 0 1 2 3 4 5 0 10 20 30 40 50 n-doped GaAs n e = 1.0 x 10 18 cm-3 N ex= 3.0x10 15 cm-3 S p in P o la ri z a ti o n ( % ) Delay Time (ps) 4.19 n-GaAs 89

(116)

4-2 Modulation-doped InAs/GaAs QRs

4.20-4.23 barrier WL ES GS eV 59 . 1 = ω h _N_ex =₈₀₀_W/cm-2 σ+ 4.20 0 1 ps QRs ( n-QRs) 48% ( 42% ) 20% ( 18% ) GaAs barrier barrier p-QRs 32% 18% QRs GaAs p-GaAs (n_h =5.8×1018cm−3 ) QRs n-QRs p-QRs barrier 38.29 ps 50.50 ps 41.22 ps n-QRs p-QRs n-QRs QRs QRs barrier 4.20 4.21 barrier WL 1ps ps ES GS fs ES GS barrier WL barrier WL 1ps 30% ~ 50% 20% 銦 25% ) 1ps

(117)

QRs ES 20-30% 20% 1ps QRs 10% 1ps barrier ( - - ) 4.24 4.20-4.23 GS p-QRs ( 0.88 ps ) QRs ( 0.63 ps ) n-QRs ( 0.48 ps ) p-QRs QRs -QRs p-QRs QRs ; n-QRs n-QRs QRs QRs p-QRs barrier GS n-QRs QRs n-QRs

(118)

0 25 50 75 100 125 150 0 10 20 30 40 50 ₍_a₎ S p in P o la ri za ti o n ( % ) Delay Time ( ps ) Barrier N ex = 800 W/cm 2 undoped QRs n-doped QRs p-doped QRs 0 1 2 3 4 5 0 10 20 30 40 50 ((((b )))) S p in P o la ri za ti o n ( % ) Delay Time ( ps ) Barrier N ex = 800 W/cm 2 undoped QRs n-doped QRs p-doped QRs 4.20 barrier (a) (150 ps) (b) (5 ps)90

(119)

0 25 50 75 100 125 150 0 10 20 30 40 50 S p in P o la ri za ti o n (% ) Delay Time ( ps ) Wetting Layer N ex = 800 W/cm 2 undoped QRs n-doped QRs p-doped QRs 4.21 WL 91 0 1 2 3 4 5 0 10 20 30 40 50 D eg re e o f sp in p o la ri za ti o n ( % ) Delay Time ( ps ) Excited State undoped QRs n-doped QRs p-doped QRs 4.22 92

(120)

0 1 2 3 4 5 0 10 20 30 40 50 D eg re e o f sp in p o la ri za ti o n ( % ) Delay Time ( ps ) Ground State undoped QRs n-doped QRs p-doped QRs 4.23 93 Barrier WL ES GS 0.0 0.5 1.0 10 20 30 40 50 60 S p in L if et im e (p s) Energy State T=300 K N_ex = 800 W/cm2 undoped n-doped QRs p-doped QRs 4.24 94

(121)

Barrier WL ES GS 0 10 20 30 40 50 60 70 80 S p in P o la ri z at io n ( % ) Energy State T=300 K N_ex = 800 W/cm2 undoped n-doped QRs p-doped QRs 4.25 95

(122)

4-3

[4.1] M. D'yakonov and V. Perel', Sov. Phys. JETP Lett. 13, 144 (1971). [4.2] S. Oertel, J. Hübner and M. Oestreich, Appl. Phys. Lett. 93, 132112

(2008).

[4.3] J H Jiang and M W Wu , J. Phys. D, Appl. Phys. 42 238001(2009).

[4.4] G. L. Bir, A. G. Aronov and G. E. Pikus, Zh. Eksp. Teor. Fiz. 69, 1382 (1975).

[4.5] M.W. Wu, J.H. Jiang and M.Q. Weng, Physics Reports. 493, 61-236(2010)

[4.6] Peter Ney Saeta, Optical Studies of Ultrafast Carrier Dynamics in Semiconducting Materials.(1991).

[4.7] Sergey Smirnov, Physical Modeling of Electron Transport in Strained

Silicon and Silicon-Germanium (2003).

[4.8]J. H. Jiang and M. W. Wu, Phys. Rev. B. 79, 125206 (2009). [4.9] D. Culcer and R. Winkler, Phys. Rev. B. 76, 195204 (2007). [4.10] D.J. Hilton and C.L. Tang, Phys. Rev. Lett. 89, 146601 (2002).

[4.11] Jiang Hong-Liang, Zhang Rong-Jun, Zhou Hong-Ming , Yao

(123)

n GaAs 1 p GaAs p GaAs [4.9-4.10] GaAs DP ( inhomogeneous broadening ) [4.3][4.5][4.8] 1ps barrier ( - )