Semiconductor Nanostructures. Gerhard Abstreiter

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1 Semiconductor Nanostructures Fabrication and Properties of Self-Assembled Quantum Dots Gerhard Abstreiter Walter Schottky Institute, TUM, Garching Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 1

2 Outline: introduction to low-dimensional semiconductor structures fabrication of nanostructures with MBE! cleaved edge overgrowth (CEO)! self-assembled quantum dots (SAQD) structural properties of SAQDs electronic level structure of SAQDs control of charge in novel SAQD devices coherent control of a single dot photodiode charge and spin storage in SAQDs Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 2

3 crystal - and electronic structure example: GaAs [001] [110] Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 3

4 density of states for parabolic bands ~1cm 3D Density of States D(E) ~ E E g E Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 4

5 low-dimensional semiconductors: heterostructures and quantum wells Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 5

6 fabrication by molecular beam epitaxy schematics of a Ga(Al,In)As system cooling shroud (77K) RHEED gun substrate effusion-cells: Ga, As, Al, In, Si va lve transfersystem shutter RHEED screen window substrate manipulator Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 6

materials: Ga, Al, In, As Valved cracker cell provides As 4 or As

7 ultra clean MBE system at Walter Schottky Institut excellent vacuum (p 5x10-12 mbar) long-term closed growth chamber source materials: Ga, Al, In, As Valved cracker cell provides As 4 or As 2 only Si as dopant Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 7

8 high mobility 2-d electron gas Si modulation doping + electric subbands conduction band GaAs substrate GaAs epi layer high mobility 2DEG AlGaAs GaAs cap Energy Density of States D(E) const. E F E 1 E 2 E Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 8

9 Important achievements with heterostructures: basic physics:! magnetotransport, Shubnikov-de Haas Effect! Quantum Hall Effect, Fractional Quantum Hall Effect! interband and intersubband spectroscopy! superlattice and miniband physics.. devices:! high electron mobility transistors! quantum well lasers! quantum cascade lasers! quantum well intersubband detectors. Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 9

10 towards one and zero-dimensional systems length scale: ~10 nm 1D 0D Density of States D(E) ~ 1/ E Density of States D(E) discrete:! artificial atoms E 11 E 12 E 13 E E 111 E 112 E 113 E Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 10

11 wires and dots by cleaved edge overgrowth (CEO) first growth cleavage second growth Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 11

12 natural cleavage plane: (110) (001) (110) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 12

13 Quantum wires: quantized conductance [110] 2nd growth cleavage plane Tantalum gate LT-GaAs cap Si δ AlGaAs -doping AlGaAs spacer GaAs cap AlGaAs Si δ-doping AlGaAs spacer one-dimensional electron system AlGaAs GaAs quantum well [001] 1st growth one-dimensional electron system Tantalum gate cleavage plane [001] 1st growth GaAs quantum well [110] 2nd growth area depleted at negative gate bias two-dimensional electron systems Amir Yacoby et al. PRL 77, 4612 (1996) Martin Rother, PhD thesis, TUM (2000) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 13

$4 V T=800 mk - miniband transport, quantum interference - fractional QHE > 2d Ising ferromagnets - gate voltage control of nuclear spin R. Deutschmann et al. PRL 86, 1857 (2001) J.H. Smet et al.$

14 superlattice field effect transitor, electrons in atomically precise potential landscapes 200 U= g 0.1 V V step 20 mv U= g 0.4 V T=800 mk - miniband transport, quantum interference - fractional QHE > 2d Ising ferromagnets - gate voltage control of nuclear spin R. Deutschmann et al. PRL 86, 1857 (2001) J.H. Smet et al. PRL 86, 2412 (2001) J.H. Smet, et al. Nature 415, 281 (2002) source drain current I sd ( µ A) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff source drain voltage U sd (V) 14

Quantum dots by double CEO in situ cleave 2nd growth step 1st growth step GaAs substrate GaAs quantum well AlGaAs barrier in situ cleave 3rd growth step coupled dots with precision

15 Quantum dots by double CEO in situ cleave 2nd growth step 1st growth step GaAs substrate GaAs quantum well AlGaAs barrier in situ cleave 3rd growth step coupled dots with precision on an atomic scale: photoluminescence: d (nm) Intensity G. Schedelbeck et al., Science 278, 1677 (1997) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 15

16 quantum dots by self-assembly lattice mismatched systems like InAs/GaAs or Si/Ge:! Stranski-Krastanov growth mode TEM micrographs Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 16

17 density, size, shape and composition depend on growth conditions AFM images 5.04 nm 0 nm 500 nm 9.16 nm 0 nm 1000 nm 500 nm 250 nm 1000 nm 500 nm 250 nm 500 nm 0 nm 0 nm 0 nm 0 nm T g = 480 C density: cm -2 T g = 530 C density: 1.2x10 10 cm -2 Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 17

18 Growth parameters:! substrate temperature! growth rate! III to V ratio (beam equivalent pressure)! growth interuption! amount of deposited material! nominal composition (InAs or InGaAs)! capping material Structural characterisation:! STM and AFM! electron microscopy! X-ray analysis Important: shape, size and composition are changed during overgrowth due to interdiffusion and segregation Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 18

19 typical shapes: lenses, pyramids, trunkated pyramids AFM STM [100] TEM 15nm P.M.Koenraad, Eindhoven Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 19

calculations resulting in a realistic electronic level structure Growth direction (nm) 12 8 4 0-4 -20

20 A detailed analysis of the different characterisation methods leads to a consistent of size shape and composition Example for: T S = 530 C, 2,8 ML InAs as determined from X-ray and TEM This information is basis for kp calculations resulting in a realistic electronic level structure Growth direction (nm) Indium-content Radius (nm) 0,6 0,4 0,2 0,0 Electron (000) hole (0±11) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 20

21 Simpler picture of the electronic level structure based on the fact that the diameter of the dots is typically much larger than the thickness: Narrow rectangular potential well in z-direction and parabolic well in x,y direction z x,y QW like potential ~ HO like potential Level structure analogue to shell structure of atoms > artificial atoms 2 electrons in the s-shell, 4 in the p-shell,. E p-shell n=1. l=±1 s-shell n=0, l=0 Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 21

z x,y Exciton GaAs InGaAs GaAs Single particle picture: ocupation with few carriers: particle-particle interactions determine optical interband

22 z x,y Exciton GaAs InGaAs GaAs Single particle picture: ocupation with few carriers: particle-particle interactions determine optical interband transition energies Energy E n=2 n=1 E n=2 n=1 HH x,y n=1 HH n=2 n=1 n=2 allowed transitions Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 22

23 Photoluminescence studies PL-Intensity (a. u.) T=4.2 K 100 mw 40 mw 10 mw 1 mw 10-2 Density: cm GaAs WL ! Discrete recombination energies (shell structure of electronic energy levels) Energy (ev)! Inhomogeneous broadening (fluctuations in size, shape and composition) Chu et al., J. Appl. Phys. 75, 2355 (1999) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 23

24 Towards single dot spectroscopy Typical areal density 100µm -2 spatially resolved spectroscopy 1x1µm Require low QD density material and spatially resovled spectroscopic techniques Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 24

25 spectroscopy with high spatial reolution Sub Micron Mesas 200nm <λ Nano Apertures hν 500nm Structures defined by e-beam lithography PL Intensity (arb. units) 200nm 500nm 200µm Single Dot T = 10 K Spatially Resolved PL >1 QD Far Field PL ~10 7 QDs Energy (mev) Increasing spatial resolution Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 25

Photoluminescence in in the few exciton limit Multi-Exciton States: s-shell p-shell s-shell: 4X p P L (µw) Theory: 1X 2X 3X s Energy E HH x,y p-shell: 3X p n=2 n=1 n=1 n=2 n=2 n=1 n=1 n=2 E HH 4X p

26 Photoluminescence in in the few exciton limit Multi-Exciton States: s-shell p-shell s-shell: 4X p P L (µw) Theory: 1X 2X 3X s Energy E HH x,y p-shell: 3X p n=2 n=1 n=1 n=2 n=2 n=1 n=1 n=2 E HH 4X p n=2 n=1 n=1 n=2 n=2 n=1 n=1 n=2 n=2 n=1 n=1 n=2 P L in t e nsity ( arb. U n its ) 3X s 3X p 2X Findeis et al., SSC 114, 227 (2000) 1X U. Hohenesterand E. Molinari See also: E. Dekel et al., PRL 80, 4991 (1998) K. Hinzer, et al., PRB 63, (2001) Energy in mev Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 26

27 Charged excitons, trions s-shell In Ga As/GaAs p-shell P(µW) L X Charged excitons + X - X + PL i n te nsity ( a rb. Units ) 2X PL counts x - x + n=2 n=2 n=1 n=1 n=1 n=1 n=2 n= Energy in ev 1X?? Energy in mev Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 27

Pioneering work in single dot spectroscopy " localized excitons in narrow quantum wells: K.Brunner et al., PRL 69, 3216 (1992), PRL 73, 1138 (1994), APL 64, 3320 (1994) A. Zrenner et al.

28 Pioneering work in single dot spectroscopy " localized excitons in narrow quantum wells: K.Brunner et al., PRL 69, 3216 (1992), PRL 73, 1138 (1994), APL 64, 3320 (1994) A. Zrenner et al., PRL 72, 3382 (1994) H. G. Hess et al., Science 264, 1740 (1994) D. Gammon et al., Science 273, 87 (1996) and PRL 76, 3005 (1996) " cleaved edge overgrowth, coupled dots W. Wegscheider et al., PRL 79, 1917 (1997) G. Schedelbeck et al., Science 279, 1792 (1997) quantum dot " self-assembled quantum dots J.-Y. Marzin et al., PRL 73, 716 (1994) M. Grundmann et al., PRL 74, 4043 (1995) quantum wire quantum well more than 400 publications over the past 6 years: for an overview see: Proceedings of Int. Conf. On Semiconductor Quantum Dots 2000 and 2002, published in Pysica Status Solidi Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 28

29 Single dot photodiode: control of charges E F + n -GaAs InGaAs QD s i-gaas 40 nm i- Al Ga As Ba rrie r Laser focus i-gaas-buffer n-gaas-substrat nm " Single electron charging from the n + -GaAs back-contact Coulomb-charging energy: C QD ~ 5 x F E c ~ 20 mev see e.g. Drechsler et al. PRL 94 Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 29

0.4 0.2 15 WL filled with electrons External Voltage [V] 0.0-0.2-0.

30 WL filled with electrons External Voltage [V] X 2- X - X Ele ctric Fie ld [V] "Single electron charging: neutral, single and double charged single exciton states X Energy [ev] X - X 0 "Tunnel escape of the carriers before recombination => Photocurrent regime Findeis et al, PRB 63, R121309, (2001) Similar work: Warburton et al., Nature 2000, Finley et al. PRB 2001, Hartmann et al. PRL 2000,... Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 30

31 Resonant excitation Single QD photodiode = Electrically contacted two-level system Laser focus hω X exciton i-gaas-buffer n-gaas-substrat InGaAs QD 0 - Optical excitation of a single QD exciton - Carrier-tunneling and photocurrent detection Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 31

32 PL versus photocurrent hω hω Oulton et al., PRB 66, (2002) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 32

33 driving a two-level system Incoherent regime Coherent regime cw excitation hω X excitation with ps-pulses hω X 0 0 experimental timescales > dephasing time Pulse length < dephasing time 50% maximum inversion of the two-level system 100 occupancy (%) 50 occupancy (%) 50 time 0 π 2π 4π pulse area Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 33

34 Incoherent regime: Two-level system driven into saturation Tunable escape time of the carriers Coherent regime: Rabi-oscillations of the QD PC deterministic current source Photocurrent (na) F=66.7 kv/cm experiment model Excitation power (arb. units) E. Beham et al, Appl. Phys. Lett. 79, 2808 (2001) Ω R ~ 3 THz P. Borri et al., PRB 66, (2002) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 34 Photocurrent (pa) V = V B experiment fit hω Excitation amplitude (arb. units) A. Zrenner et al., Nature 418, 612 (2002) "all optical" work in QDs: T. H. Stievater et al., Phys. Rev. Lett. 87, (2001). H. Kamada et al., Phys. Rev. Lett. 87, (2001). H. Htoon et al., Phys. Rev. Lett. 88, (2002). X 0

Single dot photodiode: a two-level system with contacts Photocurrent I = L(A ) e f exc # Theoretical limitation for maximum photocurrent: excitation with π-pulse: L(A exc)=1 Inversion of the = e f =

35 Single dot photodiode: a two-level system with contacts Photocurrent I = L(A ) e f exc # Theoretical limitation for maximum photocurrent: excitation with π-pulse: L(A exc)=1 Inversion of the = e f = 13.1 pa two-level system # Experimentally: (12.3 ± 0.5) pa one e-h-pair per pulse I max f=82 MHz (laser repetition rate) # Quantitative proof for Rabi-flopping # QD acts as deterministic current source # Optically triggered single electron turnstile effect Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 35

36 Charge storage in in self-assembled dots Write/store n-i-hetero-schottkydiode for hole storage CB hν E F i-gaas i-algaas VB i-gaas n-gaas V reset hν Reset/readout p-i-hetero-schottkydiode for electron storage Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 36

37 (a) writing (d) CB (c) CB hω exc. hω exc. VB hω QD hω exc. hω QD VB t hω QD E F V read E F EL Intensity (arb. units) (b) t=12µs S R ω exc. PL readout Energy (ev) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 37

38 (a) (b) (c) AlGaAs Barrier F V store i-gaas Buffer p-substrate V read CHARGING Illumination STORAGE t READOUT ON OFF Voltage V reset V store Detector Spin Doping Spin Storage Spin Readout ON OFF Time Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 38

39 Normalized peak intensity 1 τ store (10K)»1ms τ store (90K)=(60±5)µs τ store (100K)=(30±5)µs Storage time t (µs) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 39

40 Spin storage based on optical selection rules GaAs bandstructure energy levels in QDs CB -1/2 +1/2 CB + σ -3/2 HH σ + -1/2 LH σ +1/2 LH σ +3/2 HH heavy hole light hole splitting in quantum dots Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 40

41 p s cb Electrons: J e,z = ±1/2 Heavy holes: J h,z = ±3/2 M = ± 1 s σ + σ - p vb Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 41

42 Operation principle (a) (b) (c) AlGaAs Barrier σ + F σ + V store i-gaas Buffer p-substrate V read CHARGING Illumination STORAGE t READOUT ON OFF Voltage V reset V store Detector Spin Doping Spin Storage Spin Readout ON OFF Time Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 42

43 Lum. Intensity [arb. Units] B=0T T=10K Excitation: σ - Detection: σ + σ - t = 1µs Energy [ev] Lum. Intensity [arb. Units] B=8T T=10K Excitation: unpol. Detection: σ + σ - Lum. Intensity [arb. Units] B=8T T=10K Excitation: σ - Detection: σ + σ Energy [ev] Energy [ev] Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 43

44 Exchange splitting IX p > Isotropic e-h exchange Anisotropic e-h exchange 1/ 2(I+1>+I-1>) 50 mev I+1>, I-1> <150 µev IX s > µev 1/ 2(I+1>-I-1>) M=±2 1 ev dark ICGS> Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 44

45 Zeemann splitting σ + σ -, σ + 1/ 2(I+1>+I-1>) 0.1 1T σ + σ - 1/ 2(I+1>-I-1>) σ - Increasing B Increasing B Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 45

46 t=1µs, B=8T Detection σ+ Detection σ- EL Intensity (arb. units) π pump σ - pump Energy (mev) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 46

47 P=(I + -I - )/(I + +I - ) (a) σ + Excitation σ - Excitation t (ms) t (ms) (b) 5T 8T 10T 12T σ+ Intensity (arb. units) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 47

48 Spin Lifetime T 1 (s) Theory m= -4.0±0.6 m= -5.3± Magnetic Field (T) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 48

49 Towards ordering of dots Vertical stacking is achieved nearly perfectly if the thickness of intermediate layers is smaller than 50 nm 20 nm Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 49

surfaces Examples form the work of O. Schmidt et al.

50 Lateral ordering: Growth on patterned substrates (requires lithography) Growth on vicinal or high index surfaces Examples form the work of O. Schmidt et al. MPI FKF, Stuttgart Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 50

51 Combination of of CEO and and self selfassembly 1 st : grow AlAs stripes in GaAs matrix 2 nd : cleave in MBE machine [110] [001] 3 rd : grow InAs Dots on MBE patterned (110) surface Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 51

substrate first results InAs on superlattices SL1 SL2 SL3 SL4 [110] [001] InAs (+ 50 nm GaAs) surface AlAs / GaAs superlattice 500 300 165 300 200 500 400 nm 2365 nm 1000 nm [110] [110] [001] 1µm

52 substrate first results InAs on superlattices SL1 SL2 SL3 SL4 [110] [001] InAs (+ 50 nm GaAs) surface AlAs / GaAs superlattice nm 2365 nm 1000 nm [110] [110] [001] 1µm SL1: 5x 32nm AlAs / 68nm GaAs SL2: 5x 20nm AlAs / 40nm GaAs Model: nucleation and collection of InAs on AlAs due to less desorption and lower surface mobility SL3: 5x 11nm AlAs / 22nm GaAs SL4: 10x 20nm AlAs / 20nm GaAs GaAs AlAs GaAs Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 52

interband transitions in semiconductors M. Fox, Optical Properties of Solids, Oxford Master Series in Condensed Matter Physics

interband transitions in semiconductors M. Fox, Optical Properties of Solids, Oxford Master Series in Condensed Matter Physics interband transitions in quantum wells Atomic wavefunction of carriers in