: Quo - UCSBonline.itp.ucsb.edu/online/excitcm_c09/lueth/pdf/Lueth... · 2009. 11. 4. · : Quo ?...
Transcript of : Quo - UCSBonline.itp.ucsb.edu/online/excitcm_c09/lueth/pdf/Lueth... · 2009. 11. 4. · : Quo ?...
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: Quo ?
Hans LüthInstitute of Bio- and Nanosystems ( IBN 1 )
Research Centre Jülich andJülich-Aachen-Research Allience (JARA)
JARA-FIT (Fundamentals of Future Information Technology)
KITP Conference, Santa Barbara, Nov.2-6, 2009
Electronic Electronic Structure Structure and Transport in and Transport in SemiconductorSemiconductorNanostructuresNanostructures: :
Experiments and Experiments and Theoretical ChallengesTheoretical Challenges
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Promising Semiconductor Nanostructures:Nano-Devices
Semicond. Nanocolumns
Carbon Nanotubes
Graphene Ribbons
Quantum Dots Q-dot
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OUTLINESemiconductor Nanowires
• Growth and Doping, Band Gap• Electronic Transport
-Effect of Space Charge Layers-Quantum Transport in Narrow Gap SC Wires
Theoretical Challenges
Graphene Ribbons• General Properties, Doping• Multilayer Stacks with Dirac Cone• Dead Edge Region: Gap and Transport
Coupled Quantum Dots as Q-bit
Theoretical Challenges
Theoretical Challenges
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metallic seedseutecticsolution
Successivegrowth of
heterostructure
III-V Semiconductor Whisker Growth (bottom-up)( Vapour-Liquid-Solid Growth )
M. T. Björk, B. J. Ohlsson, T. Sass, A. I. Persson, C. Thelander, M. H. Magnusson,K. Deppert, L. R. Wallenberg, and L. Samuelson, Appl.Phys.Lett.,80, (2002) 1058
5 µm
Marker
Preparation forTransport Measurements
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Ordered Selective Growth by means of MasksMask Preparation
HSQ Maskon GaAs (111)
GaAs pillarson GaAs (111)
Vera Klinger, J. Wensorra et al. (2008)
MOVPE Growth
Precursors: AsH3, TMGa
Growth Temp.: 7500C
Selected area Growth
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NW1 // <110> NW2 // <110> NW3 // <100> NW4 // <100> NW5 // <112>
A.K. Singh, V. Kumar, R. Note,Y.Kawazoe :Nano Lett. 6, 920 (2006)
Si Nanowires in the Quantum Confinement Regime:Electronic Band Structure Calculations (DFT)
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CdSe Nanowires in the Quantum Confinement Regime
Zhen Li, A. Kornowski, A. Myalitsin, A. Mews: Small 4, 1698 (2008)
Preparation by Solution-Liquid-Solid Synthesis (SLS)1.Step: Bi nanoparticles as catalysts:
BiCl3 and tri-n-octylphosphine (TOP) as reducing agent
2.Step: CdSe wires by addition of:CdO or Cd(Me)2 and TOPSe, Reaction Temperature 3300C
Bi
Precursor: CdO,Cd/Se=7/1
Precursor: Cd(Me)2
3.Step: Termination by Toluene
Precursors:Cd(Me)2 CdO
1.82 eV 1.72 eV
Fluorescence
Bulk gap: 1.7 eV
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Doping Deactivation in Si Nanowires: Dielectric MismatchPreparation: Vapour-Liquid-Solid Growth (CVD)
ND determined from thickwires (resistivity)
M.T. Björk, H. Schmid, J. Knoch, H. Riel, W. Riess: Nature Nanotechnology 4, 103 (2009)
22
2
0
2 2
( )(1 )2
phys f phys it oelec phys
physD A it
s
r Q r e Dr r
r ee N N D
ψ
ε ε
−= +
− +
20
0
2 s air sI I
s elec s air air
eE E Fr
ε ε εε ε ε ε ε
− ⎛ ⎞− ≈ ⎜ ⎟+ ⎝ ⎠
corrected for space charge
Dopantelectricallyactive volume
From analysis of exp. data:Dit=6x1012cm-2eV-1
Effect of space chargelayer
Qf=0 fixed oxide charge
sρ0ρ bulk value
Doping: PH3, P built in as in Bulk Material
1 mμChange of Dopant Ionisation Energy:
1/ elecr∝
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OUTLINESemiconductor Nanowires
• Growth and Doping, Band Gap• Electronic Transport
-Effect of Space Charge Layers-Quantum Transport in Narrow Gap SC Wires
Theoretical Challenges
Graphene Ribbons• General Properties, Doping• Multilayer Stacks with Dirac Cone• Dead Edge Region: Gap and TransportTheoretical Challenges
Coupled Quantum Dots as Q-bitTheoretical Challenges
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d<80nm:d<80nm: photocurrents photocurrents exponentiallyexponentiallydecayingdecaying with decreaswith decreas. . thicknessthickness;;fast fast responseresponse
d>80nm: d>80nm: persistentpersistent photocurrentsphotocurrentsafterafter UV UV illuminationillumination, ,
PersistentPhotocurrent
GaN WhiskersGaN Whiskers: : Thickness dependent PhotocurrentThickness dependent Photocurrent
R. Calarco, M. Marso, R. Meijers, T. Richter, A.I. Aykanat, N. Thillosen, T. Stoica, H.L.: NanoLetters 5, 981 (2005)
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)/exp(Photo kTI Φ∝
crit
D
critcrit
D
ddfordqN
ddforconstdqNwith
<=Φ
>==Φ
2
2
16
.16
ε
ε
rateionrecombinatIntPhotocurre Photo
1∝
)/exp( kTrateionrecombinat Φ−∝Fit Fit paramparam.: .: NNDD=6.25x10=6.25x101717cmcm--33
BΦ =0.555eV=0.555eV
Model Model for Thickness dependent Surface Recombinationfor Thickness dependent Surface Recombination
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OUTLINESemiconductor Nanowires
• Growth and Doping, Band Gap•Electronic Transport
-Effect of Space Charge Layers-Quantum Transport in Narrow Gap SC Wires
Graphene Ribbons• General Properties, Doping• Multilayer Stacks with Dirac Cone• Dead Edge Region: Gap and Transport
Coupled Quantum Dots as Q-bit
Theoretical Challenges
Theoretical Challenges
Theoretical Challenges
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Resistance of InN Wires
normalized conductance:g G L d β= × ∝
2β =1β =
bulksurface
1.15β =
surface2DEG
Metallic Surface 2DEG
Th. Richter, Ch. Blömers , H. Lüth, R. Calarco, M. Indlekofer, M. Marso, Th. Schäpers: NanoLetters (2008)
grown as Whiskers on Si(111)
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Phase Coherence from Univ. Cond. Fluct.: InN WiresDimensions: L=410nm , d=67nm
lΦlΦlΦlΦ
lΦ
( a )
( b )
L
Φ1
Φ2
Φ3
B ≠ 0
B = 0
Phase Coherence Length:
Bc= Critical Correlation Field
Appl. Phys. Lett. 92, 132101 (2008)Ch. Blömers, Th. Schäpers, T. Richter, R. Calarco, H. Lüth, and M. Marso:
Correlation function
Closed Loops: Aharonov Bohm Interferencies
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InN Whisker (Nanowire): Magnetotransport
0Φ
wire dimensions: length 420nmdiameter 37nm
flux quantum:
Th. Richter, Ch. Blömers , H. Lüth, R. Calarco, M. Indlekofer, M. Marso, Th. Schäpers: NanoLetters (2008)
-1
0
1
0.0 0.5 1.0 1.5 2.00.0
0.1
0.2
0 2 4 6 8
0
1
0.0
0.1
0.2
0 2 4 6 8 10-2
0
2(e)
(d)
(b)
wire A(a)
Frequency (1/T)
wire B
FFT
Am
plitu
de (a
.u.)
ΔG
/(e2 /h
)
B(T)
st12nd
2
wire A
1st ndndst
1 +2st
2
meas.
1
nd
B (T)
ΔG/(e
2 /h)
wire B
0 periodicityΦ −
0 / 2 periodicityΦ −0 / AΦ
(B // c-axis)
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Flux Quantisation: Transport through Angular Momentum States
22 2
22 2
1 12 2 2
z zH L eB rm r m z
∧ ∧
∗ ∗
⎛ ⎞ ∂⎜ ⎟= − −⎜ ⎟ ∂⎝ ⎠
h
( ) ( ) ( ) ( ), ,lH r z E r zψ ϕ χ ψ ϕ χ∧
=
22 2 2
202 2
zl
kE lm m r
ΦΦ∗ ∗
⎛ ⎞= + −⎜ ⎟⎝ ⎠
h h
2zr BΦ π= 0
eh
Φ =
( )2 / 2e m∗−p A
Period 0Φ
( )Re ,rψ ϕ
B
3l =
5F nmλ ≈26l ≈
Typical values:( ) 0.9F c surfE E eV− ≈
0Φ =@
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InAs Columns: Magnetoresistance Oscillations
Column diameter:95 - 115 nm
Offset:0.1kΩ
B c
B
J. Wensorra et al., to be published (IBN, Res. Centre Jülich 2009)
0 / 2Ω
60nm length128nm diameter
125nm length83nm diameter
T=0.9K
T=0.3K
MBE grown Columns (Bottom-up)
105nm diameter
Columns lithographically shaped fromMBE grown Layers in [111] Direction (Top-down)
0 / 2Ω
0 / 2Ω
0 / 2Ω0Ω
0Ω
1 21 2
( ) exp expie ied d⎛ ⎞ ⎛ ⎞
Ψ = Ψ ⋅ + Ψ ⋅⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠∫ ∫r s A s A
h h
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛ΦΦ+=Φ
0
22cos πDCG
Alt`shuler-Aronov-Spivak Interferences
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InAs Nanowires from MOCVD selected area Growth:Stacking Faults
K. Tomioka, J. Motohisa, S. Hara, T. Fukui:Jap. J. Appl. Phys. 46, L1102 (2007)
Spontaneous (pyroelectric) Polarisationalong [0001]
H. Hardtdegen et al.IBN, Res.Centre Jülich (2009)
Effect of Surface States masked by Polarisation Charges at Surface
No Surface Accumulation !?S.A. Dayeh, D. Susac, K.L. Kavanagh, E.T. Yu, D. Wang: Adv.Funct. Mater.,in pressand S.A. Dayeh et al.: Nano Today 4, 347 (2009)
InAs Slab InAs Wire (WZ, ZB segments)
E V, E
C( e
V )
EF
(ZB)
(WZ)
Thickness Axis
ND=5x1016cm-3
Qs/q=1012cm-2
Depletion
Accumul.
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Theoretical Challenges
Growth and Doping• Tailoring of Stacking Faults in III-V Nanowires ?
Substrate, Growth Conditions........• Built-in of Dopants, Dopant Deactivation ?
Electronic Band Structure and Band Gap
Surface States and Space Charge Layers ?• Nano Surface Science• Space Charge Layers in the Presence of Defects ?
Electronic Transport• Scattering Mechanisms ?
Surface, Stacking Faults......• Phase Coherence Length, Coherent Transport ?• Spin related Transport and Interferences(Weak Antilocalisation) ?
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OUTLINESemiconductor Nanowires
• Growth and Doping, Band Gap• Electronic Transport
-Effect of Space Charge Layers-Quantum Transport in Narrow Gap SC Wires
Graphene Ribbons• General Properties, Doping• Multilayer Stacks with Dirac Cone• Dead Edge Region: Gap and Transport
Theoretical Challenges
Theoretical Challenges
Coupled Quantum Dots as Q-bitTheoretical Challenges
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Graphene: Electronic Structure
//k
K- Doping
1.1x1013 3.7x1013
0
-1
-20 0-0.1 -0.10.1 0.1
ARPES: Photon energy 94eVT=30K
1// (0.1 )k nm−
Bin
ding
ene
rgy
(eV)
A. Bostwick, T. Ohta, Th. Seyller, K. Horn, E. Rotenberg: Nature Physics, 3, 36 (2007)
Dirac point
Young-Woo Son, M.L. Cohen, S.G Louie: Phys. Rev. Lett. 97, 216803 (2006)
Calcul. Band Gap of RibbonsNa=No. of arm chair dimers
Zhihong Chen, J. Appenzeller(IBM, Perdue Univ.)
Top Ti/Au-gate10nm Al2O3 Ribbons
DFT(LSDA)
Edgepassivatedby H Atoms
Removed by atomic H treatment:Graphane
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Graphene Ribbons: n-Doping with Ammonia
Xinran Wang et al.: Science 324, 768 (2009) (Stanford, Gainsville, Livermore)
Peel-off Graphene (Monolayer)
Doping: Joule Heating to 3000Cin NH3/Ar, 1Torr
Si
SiO2300nm
Ribbons by e-beam Lithography
0
Ox
EF
Gate GrapheneVgs
Ids Dirac Point
E
300 K
SEM AFM
Unchanged Electron Mobility after Doping:Edge Doping rather than Surface Doping
Stable Doping Conditions, in contrast to physisorbed NHx Species
Ribbon
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Multilayer Graphene on 4H-SiCa Dirac Cone like in a Single Sheet
J. Hass, F. Varchon, J.E. Millan-Otoya, M. Sprinkle, N. Sharma, W.A. de Heer, C. Berger, P.N. First, L. Magaud, E.H. Conrad:Phys. Rev. Lett. 100, 125504 (2008)
, C-face :
M.L. Sadowski, G. Martinez, M. Potemski, C. Berger, W.A. de Heer: Phys. Rev. Lett.. 97, 266405 (2006)
1sgn( ) 2 sgn( )nE n c e B n n E n∗= =h
Landau levels for a Dirac cone:
1( ) /2nE n eB m∗= + h )
Electron velocity: c*~108cm/sDirac mass: mD=E/c*~0.0012 m0
bi-layer
R30/R2fault pair
single layer
( for standard 2DEG:
Far IR
(0001)
Interleaved Growth with:300 rotated or+/- 2.20 rotated vs. SiC 1010⎡ ⎤⎣ ⎦
Stacking Faults: Layer Decoupling
3-5 Graphene Monolayers
By Annealing to 1400 0C:
STM
fault pairunit cell
(commensurate)
DFT (VASP code)
Landau Levels
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Graphene Nanoribbons:Transport and Gap
M.Y. Han, B. Özyilmaz, Y. Zhang, Ph.Kim: Phys. Rev. Lett. 98, 206805 (2007)
/( )gE W Wα ∗= −
0.2eVnmα 016W nm W∗ ≈
0( ) /G W W Lσ= −
Inactive Widths:
0W W ∗≈
tilted
T=300K
1.6K2e WG
h L from Theory
np
Gap
~16 nm
(lateral confinement)
Graphene Single Sheetson SiO2/Si (gate)
DifferentWidths
DifferentOrientations
Con
duct
ance
0
20
40
60
80
100
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Graphene Nanoribbons: Electronic Confinement andCoherence from Magnetotransport
Landau Levelsin confining Ribbon:
SdH Peaks270W nm W∗ = ≠
Fit with
Universal Conduct. Fluctuations :@ 2K:
@ 58K:
1.1l mμΦ ≈430l nmΦ ≈
Claire Berger et al. : Science 312, 1191 (2006)
3 ML graphene on SiC(000-1)Ribbon Width W=500nm
Dead Edge Region
1/ 44 2 20 0( / ) (2 )nE n v W neBvπ⎡ ⎤≈ +⎣ ⎦h h
80 1 10 /v cm s= ×
From Analysis of
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Theoretical Challenges
Multilayer Graphene with Dirac Cone (Dispersion)• Why growth of R30/R+/-2 decoupled layers on Si(000-1) ?
Graphene/SiC Interaction or Growth Kinetics• General Conditions for R30/R+/-2 Stacking Fault Growth ?
Surface and Edge Doping of Ribbons,Surface Chemistry in General
• Chemistry and Doping Activity ?• 2D-doping and Dopant Deactivation ?
Edge Structure of Ribbons
• Electronic Edge States and 2D-Space Charge Zones ? • Atomistic Structure and States of Disorder ?
Coherent Transport In Ribbons• Type of Scattering ?• Effect of Substrate ?
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OUTLINESemiconductor Nanowires
• Growth and Doping, Band Gap• Electronic Transport
-Effect of Space Charge Layers-Quantum Transport in Narrow Gap SC Wires
Theoretical Challenges
Graphene Ribbons• General Properties, Doping• Multilayer Stacks with Dirac Cone• Dead Edge Region: Gap and TransportTheoretical Challenges
Coupled Quantum Dots as Q-bitTheoretical Challenges
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V xL xR
+
+
_
_
EE+
E-
R
R
L
L
g
g
e
e
μ
μ
x
x
x
ψ
ψ
( a )
( b )
( c )
( d )electr. Field
⊂
⊂
E0+
E0-
μ
μ
Realisation of a Q-bit by 2 coupled Q-Dots
Q-bit = 2-level System:
g eα β+Superposition Statefor ~0∈
With increasing electric Field>0∈
Preparation ofR Lor
2 2 20 LRE E t μ= ± + ∈m
LRt is Tunnelling Amplitude between
L RandProbability for Electron in :R
2 2( ) sin ( / )R LRc t t t= h
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µS
µD
µS µD
µS
µD
VSD=VP
VSD=0VSD=VPΔ
Preparation of L Q-bit Realisation Recording
Puls generatorAlGaAs/GaAs 2DEG-Mesa
0 0,5 1 1,5 2Puls duration tP ( ns )
Elec
tron
num
ber
n
0,5
0
T. Hayshi, T. Fujisawa, H.D. Cheong, Y.H. Yeong, Y. Hirayama: Phys. Rev. Lett. 95, 090502-1 (2005)
Q-bit Realization: 2 coupled GaAs Qantum Dots
Dephasing time:1 ns
Measurement contactscoupled electrically
(after pulses tp of variableduration time)
Q-dot within 2DEGSplit-gate Technique:
(by puls tp=80....2000ps)
Osc. Frequ. 2.3Ghz
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J. Gorman, D.G. Hasko, and D.A. Williams : Phys. Rev. Lett. 95, 090502-1 (2005)
Q-bit Realization: 2 coupled Si Qantum Dots in SOI
Dephasing time:200 ns
SET coupled onlyvia electric field!
Manipulation in time domain
For preparation of or L R
Pulse sequence:1) Preparation of R2) Q-bit Realization:
R L±3) Measurement
of L
SET
Sign
al
Puls Duration
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Theoretical ChallengesDecay of Superposition State (Q-bit)
• Coupling of 2-state System to Environment (E) ?• Dephasing time ?
General Description by Density Matrix ρQ-bit: ( )g eα β+Superposition State
Time Development ( U unitary) of Q-bit imbedded in Environment Eleads to Entangled State:
( )g eα β+ E U 0 1g E e Eα β+
2 20 0 1 1g g E E e e E Eρ α β= + 0 1 1 0g e E E e g E Eαβ βα∗ ∗+ +
Only Q-bit is interesting: 2
1 02
0 1
red E
E ETr
E E
α αβρ ρ
βα β
∗
∗
⎛ ⎞⎜ ⎟= =⎜ ⎟⎝ ⎠
Environment develops according to: 1E E = U 0 1 0E E =
Q-bit decays according to /0 1
tE E e τ−∝
τ
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CONCLUSIONS
Preparation, Doping and Electronic Bands
Nano-Surface(Edge) Science
Electronic (Qantum) Transport incl. Spin
Dephasing of Superposition States
The great theoretical Challenges: