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TRANSCRIPT
Transport Time and Quantum Scattering Timein
GaAs/AlGaAs Heterostructure
MMM Charulata Barge 12-042010
Outline
GaAs/AlGaAs HeterostructureScattering Transport and scattering eventsBackscattering and quantum scatteringMeasurements of τt and τq
Conclusion and outlook
MMM Charulata Barge 12-04-2010
GaAs/AlGaAs heterostructure
MMM Charulata Barge 12-04-2010
A two-dimensional electron gas formed at the interface between gallium arsenide andaluminum gallium arsenide in a semiconductor heterostructure. The AlGaAs layer (green)contains a layer (purple) of silicon donor atoms (dark blue). Electrons from the donor layerfall into the GaAs layer (pink) to form a 2DEG (blue) at the interface. The ionized Si donors(red) create a potential landscape for the electron gas
Branislav K. Nikolić, http://www.physics.udel.edu/~bnikolic/
Scattering
Electron propagation in real materials is NOT an uninterrupted process but is instead DISRUPTED by electron SCATTERING from a number of different sourcese.g. disorder include DEFECTS and IMPURITIES in the crystal Also scattering from other ELECTRONS as well as from the quantized LATTICE VIBRATIONS (phonons) is also possible
Es IN A PERFECTLY PERIODIC POTENTIAL PROPAGATE WITHOUT BEING SCATTERED …
IN REAL CRYSTALS, DISORDER DISRUPTS ELECTRONPROPAGATION THROUGH THE CRYSTAL STRUCTURE
MMM Charulata Barge 12-04-2010
Lecture notes:-www.ocw.tudelft.nl/fileadmin/ocw/courses/MesoscopicPhysics
Elastic and inelastic scattering
scattering from a STATIC potential does NOT change the energy of the electron ---scattering from FIXED impurities in ELASTIC and that from PHONONS and other ELECTRONS will be INELASTIC
MMM Charulata Barge 12-04-2010
Lecture notes:-www.ocw.tudelft.nl/fileadmin/ocw/courses/MesoscopicPhysics
Transport and Scattering Events
Elastic scattering length, ℓ- Characteristic length between elastic collisions with static impuritiesDiffusive region (L>>ℓ)
the mean free path is much SMALLER than the sample dimensions and DISORDER scattering dominatesElectron in random walk
QUASI-BALLISTIC region the mean free path and device size are COMPARABLE
Ballistic region (L<<ℓ)NO impurities and so the dominant source of electron scattering is at the device BOUNDARIES The electron momentum is assumed to be constant
MMM Charulata Barge 12-04-2010
Lecture notes:-www.ocw.tudelft.nl/fileadmin/ocw/courses/MesoscopicPhysics
Transport and Scattering Events
Phase coherence length- Characteristic length within which the phase of electron wave is preserved
Typical values: 1 μm for Au at 1KWeak localization experiment, diffraction experimentPhase coherence destroyed by electron-electron scattering, electron phonon scattering,magnetic field
Coherent transport
Electron waves adds coherentlyMagnetoresistance : phase can be manipulated with application of magnetic fieldsImportant for quantum computing
MMM Charulata Barge 12-04-2010
Transport and Scattering Events
Fermi wavelength λFCharacteristic length, the wave length of electrons at the Fermi surface
λF=2π/kFFull quantum limit:treat electrons as quantum waves and mesoscopic conductors as waveguideQuantum conductance
Relaxation time (τ) average time over which the initial momentum of the electron is REVERSED through a series of scattering events in the crystal
MEAN FREE PATHaverage DISTANCE electrons travel before backscattering
Mobility μ=e τt /m* = e l /ħ kF
Conductivity σ= ne2 τt /m* = ne μ
MMM Charulata Barge 12-04-2010
Backscattering and quantum scattering
Transport in a two-dimensional electron gas (2DEG) is strongly affected by disorder
scattering is dominated by two types of disorderremote impurities (RI) homogeneous background (BG) impurities
The two charactersitic scattering times are the transport lifetime τt , and the quantum scattering time τq
Transport lifetime τtRelaxation time approach, related to conductivity σ=ne2 τt /m* = ne μ
Quantum lifetime τqSingle particle relaxation time Decay time of one-particle excitations and characterizing the quantum mechanical broadening of single-particle elctron state.
MMM Charulata Barge 12-04-2010
Measuring τt and τq
MMM Charulata Barge 12-04-2010
τt and τq as a function of n and QW width (Lz)25-50 individual GaAs QWs separated by Al0.35Ga0.65As barriers d=50nmSi-dopedDensity n - 3.2x1011 cm-2 to 1.4x1011 cm-2 at constant Lz=5.9nm Seven different Lz values 3.7 to 9.5 nm at constant n=6.5X1011 cm-2 T=0.3K to 6.8 K
Measuring τt and τq
For T=0, B=0, Transport scattering time , τt
With k´=k+q, q=2kFsin(v/2), kF=√(2πn)
<k Hdef k´> - probability for scattering and angle v from k to k’ on Fermi circle due to the scattering Hamiltonian Hdef
But all scattering angles contribute equally to the braodening of single particle energy level with
MMM Charulata Barge 12-04-2010
U. Bockelmann et al Phys. Rev. B 41 (1990) 7864
Measuring τt and τq
From fit to the amplitude δρ of ρxx to
With ωc=eB/m* and ξ=2π2kT/ħωc
Quantum-mechanical deviation to linear order,
MMM Charulata Barge 12-04-2010
U. Bockelmann et al Phys. Rev. B 41 (1990) 7864
Measuring τt and τq
Different competting scattering mechanismsCharged impurities
Interface roughness scattering
Alloy disorder scattering
Screening of the scattering potentials
MMM Charulata Barge 12-04-2010
U. Bockelmann et al Phys. Rev. B 41 (1990) 7864
Measuring τt and τq
MMM Charulata Barge 12-04-2010
U. Bockelmann et al Phys. Rev. B 41 (1990) 7864
τt and τq with constant well width of 5.9 nm τt and τq with constant electron density n=6.5x1011 cm-2
Measuring τt and τq
MMM Charulata Barge 12-04-2010
Chen et al Physica E 22 (2004) 312 – 315
Measuring τt and τq
MMM Charulata Barge 12-04-2010
(a) Sample A: GaAs/AlGaAs heterostructures in whichInAs self-assembled quantum dots have been inserted(b) Sample B: conventional GaAs/AlGaAsheterostructures but with thicker spacer layer.
Dingle plot of sample A at Vg = 0
Chen et al Physica E 22 (2004) 312 – 315
Measuring τt and τq
MMM Charulata Barge 12-04-2010
τt and τq (sample A) from Dingle plots against carrier density.
For Sample B.τt as a function of carrier density
For Sample Bτq as a function of carrier density
Chen et al Physica E 22 (2004) 312 – 315
Measuring τt and τq – our results
MMM Charulata Barge 12-04-2010
0 100 200 300 400 500 600 700 800 900 1000
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
Distance from surface (nm)C
ondu
ctio
n B
and
Ene
rgy
(eV
)
At T= 23 mKn=0.68 x1011 cm-2
μ=1060 m2/VsΤt=330.5 ps
2DEG provided by L.N. Pfeiffer,Princeton University
Measuring τt and τq – our results
Hall Bar mesa etched to separate the devices ~85 nmOhmic contacts(Ni,Au,Ge) ~440 nm, annealed at 480 °c ~440 nmTop gate (Ti,Au)=50 nmAll the measurements carried in dilution refridgerator (base temp. 22 mK)Standard AC lock-in technique
MMM Charulata Barge 12-04-2010
Measuring τt and τq – our results
))12(cos()/2sinh(
/2)exp(2gg(T)
2
2
0
−−
=Δ ∑
ccB
cB
s qc
EfsTsk
Tsksω
πωπ
ωπτωπ
hh
h
0)(21(0 g
Tgxx
Δ+= ρρ
)]12(cos[0
−=∑ eBnsA
ss
xx ππρδρ h
MMM Charulata Barge 12-04-2010
For low magnetic fields, ωcτ~1 and Δg<<g0normilized oscillatory component of the magnetoresistivity is (Isihara et al.)
g0 is constant and Δg(T) is the oscillatoy part part of DOS/unit cell
With ωc=eB/m* an Ef=nħ2π/m*, τq =ħ/TD2πkB
)/2sinh(/2)2exp(4 2
22
cB
cB
c
DBs Tsk
TskTksAωπ
ωπω
πh
h
h−=
As depends on Tand perp B, and Dingle temp TD
Measuring τt and τq – our results
MMM Charulata Barge 12-04-2010
Dingle plot
q
B
emslope
BvseBTmkBAs
τπ
π
*
1))/*2sinh(.ln( 2
=
h
τq=10.5±0.13 ps,
Ratio, τt / τq ~30
B(Tm)
Rxx
(Ω)
Measuring τt and τq – our results
MMM Charulata Barge 12-04-2010
B)*e*2cos(*2 ))/(eBm*mAexp(-f22
qe eBn
eBmmTk eeB h
h
ππτπ=
τq=18.2±0.7 psRatio τt/τq=19
Isihara fit
Conclusion and outlook
MMM Charulata Barge 12-04-2010
τt and τq play significant role in transportImpurity scattering (for τt) and remote impurity scattering (for τq) are dominnat scattering mechanismsAlloy disorder and interface roughning are weakRatio of transport time to quantum scattering for our samples around 20
..........to do1) Dependency of τt and τq on gate voltage
2) τt and τq in presence of Sio2 oxide layer
Thanks for your attention
MMM Charulata Barge 12-04-2010