Transport Time and Quantum Scattering Time GaAs/AlGaAs ... · 1)) 2 cos( (sinh(2 / ) 2 / 2 exp( ) g...

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


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


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



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




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



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


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.


Measuring τt and τq


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


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


U. Bockelmann et al Phys. Rev. B 41 (1990) 7864


From fit to the amplitude δρ of ρxx to

With ωc=eB/m* and ξ=2π2kT/ħωc

Quantum-mechanical deviation to linear order,




Different competting scattering mechanismsCharged impurities

Interface roughness scattering

Alloy disorder scattering

Screening of the scattering potentials






τt and τq with constant well width of 5.9 nm τt and τq with constant electron density n=6.5x1011 cm-2



Chen et al Physica E 22 (2004) 312 – 315



(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




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


Measuring τt and τq – our results


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


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



))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


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



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)



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


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


Transport Time and Quantum Scattering Time GaAs/AlGaAs ... · 1)) 2 cos( (sinh(2 / ) 2 / 2 exp( ) g...

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