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
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
crystal - and electronic structure example: GaAs [001] [110] Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 3
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
low-dimensional semiconductors: heterostructures and quantum wells Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 5
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
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
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
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
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
wires and dots by cleaved edge overgrowth (CEO) first growth cleavage second growth Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 11
natural cleavage plane: (110) (001) (110) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 12
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
superlattice field effect transitor, electrons in atomically precise potential landscapes 200 U= g 0.1 V.. 0.9 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) 150 100 50 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 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 on an atomic scale: photoluminescence: d (nm) 60 30 15 800 Intensity G. Schedelbeck 0 0.5 1 et al., Science 278, 1677 (1997) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 15
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
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: 10 11 cm -2 T g = 530 C density: 1.2x10 10 cm -2 Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 17
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
typical shapes: lenses, pyramids, trunkated pyramids AFM STM [100] TEM 15nm P.M.Koenraad, Eindhoven Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 19
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) 12 8 4 0-4 -20 Indium-content -10 0 10 20 Radius (nm) 0,6 0,4 0,2 0,0 Electron (000) hole (0±11) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 20
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 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
Photoluminescence studies PL-Intensity (a. u.) T=4.2 K 100 mw 40 mw 10 mw 1 mw 10-2 Density: 1.2 10 cm GaAs WL 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6! 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
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
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 1250 1300 1350 1400 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 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) 1280 1290 1300 1310 K. Hinzer, et al., PRB 63, 075314 (2001) Energy in mev Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 26
Charged excitons, trions s-shell In Ga As/GaAs 0.4 0.6 p-shell P(µW) L 1000 900 1X Charged excitons + X - X + PL i n te nsity ( a rb. Units ) 2X PL counts 800 700 600 500 x - x + n=2 n=2 n=1 n=1 n=1 n=1 n=2 n=2 1.280 1.285 1.290 1.295 1.300 Energy in ev 1X?? 1280 1290 1300 1310 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., 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
Single dot photodiode: control of charges E F + n -GaAs InGaAs QD s i-gaas 40 nm i- Al Ga As Ba rrie r 0. 3 0.7 Laser focus i-gaas-buffer n-gaas-substrat 40 270 nm " Single electron charging from the n + -GaAs back-contact Coulomb-charging energy: C QD ~ 5 x 10-18 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] 0.0-0.2-0.4 X 2- X - X 0 20 25 30 35 Ele ctric Fie ld [V] "Single electron charging: neutral, single and double charged single exciton states X 2-1.295 1.300 1.305 1.310 1.315 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
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
PL versus photocurrent hω hω Oulton et al., PRB 66, 45313 (2002) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 32
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
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) 0.5 0.4 0.3 0.2 0.1 0.0 F=66.7 kv/cm experiment model 0 20 40 60 80 Excitation power (arb. units) E. Beham et al, Appl. Phys. Lett. 79, 2808 (2001) Ω R ~ 3 THz 0 0 1 2 3 P. Borri et al., PRB 66,081306 (2002) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 34 Photocurrent (pa) 14 12 10 8 6 4 2 V = -1.078 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, 133603 (2001). H. Kamada et al., Phys. Rev. Lett. 87, 247401 (2001). H. Htoon et al., Phys. Rev. Lett. 88, 087401 (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 = 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
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
(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 1.20 1.25 1.30 Energy (ev) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 37
(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
Normalized peak intensity 1 τ store (10K)»1ms τ store (90K)=(60±5)µs τ store (100K)=(30±5)µs 0 1 2 3 4 5 200 400 600 800 1000 Storage time t (µs) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 39
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
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
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
Lum. Intensity [arb. Units] B=0T T=10K Excitation: σ - Detection: σ + σ - t = 1µs 1.26 1.28 1.30 1.32 1.34 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 - 1.26 1.28 1.30 1.32 1.34 Energy [ev] 1.26 1.28 1.30 1.32 1.34 Energy [ev] Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 43
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 > 100-200 µev 1/ 2(I+1>-I-1>) M=±2 1 ev dark ICGS> Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 44
Zeemann splitting σ + ~1meV @10T 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
t=1µs, B=8T Detection σ+ Detection σ- EL Intensity (arb. units) π pump σ - pump 1280 1300 1320 Energy (mev) 1280 1300 1320 1340 Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 46
P=(I + -I - )/(I + +I - ) 1.0 0.5 0.0-0.5 (a) σ + Excitation σ - Excitation -1.0 0.0 0.5 1.0 t (ms) 0.0 0.5 1.0 1.5 1 t (ms) (b) 5T 8T 10T 12T 100 10 σ+ Intensity (arb. units) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 47
Spin Lifetime T 1 (s) 10 0 10-1 10-2 10-3 10-4 Theory m= -4.0±0.6 m= -5.3±0.3 10-5 2 4 6 8 10 12 14 16 Magnetic Field (T) Gerhard Abstreiter, ICPS-27, July 25, 2004, Flagstaff 48
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
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
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 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