Scanning Gate Microscopy SGM

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Scanning Gate Microscopy (SGM)
Scanning Force Microscopy (SFM)
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Max Planck Institute for Solid State Research,
Stuttgart
Potential probing of the adiabatic transport in
the integer quantum Hall regime
Franck DAHLEM, Jürgen WEIS and Klaus von KLITZING
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Outline

• Adiabatic transport features
• in high mobility four-terminal Hall bar

• Local Hall potential profiles probed by
• Scanning Force Microscopy

• Microscopic model based on
• compressible and incompressible strips

• Potential measurements in front of
• voltage probing contacts

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Transport Measurements
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Six- versus Four-terminal Hall bar
T1.4 K
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Transport Measurements
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Interface of current carrying contacts oriented
in 011 or in 01-1
Disappearance of Shubnikov-de Haas Oscillations
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Non local and unconventional Hall resistance
Hall resistance asymmetrical
Non local resistance
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Adiabatic transport features
Sample with gate electrodes
Sample without gate electrode
(intrinsic phenomena)
(extrinsic phenomena)
3) Shifting of Hall plateaus
1) Disappearence of Shubnikov-de Haas peaks 2)
Voltage Reminiscent (new resistivity)
I
1)
2)
I
Komiyama and Nii, Physica B 184, 7 (1993)
Alphenaar et al., PRL 64, 677 (1990 )
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Single particle edge state picture
Equilibration by elastic or inelastic interedge-s
tate scattering
Landau level bending No backscattering Equipartiti
on of current
Adiabatic transport ??ch maintained along one
edge of the Hall bar
T. Martin et al., PRL 64, 1971 (1990)
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Compressible and Incompressible strips
A. Siddiki, PRB 70, 195335
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Screening effect, Compressible and Incompressible
strips
Incompressible strips (insulator-like)
ns (y) constant and V(y) varies
Compressible strips (metal-like)
ns (y) varies and V(y) constant
Single particle picture
Correlated electron picture
D.B. Chklovskii et al., PRB 46, 4026 (1993)
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Self-consistent screening theory
Thomas-Fermi-Poisson approximation
A. Siddiki and R.R. Gerhardts, PRB 70, 195335
(2004)
K. Lier and R.R. Gerhardts, PRB 56, 13519 (1994)
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Hall potential in 50 m² / Vs mobility
T1.4 K
Drops of the Hall potential at the inner
incompressible strip positions
Cryogenic scanning force microscope
E. Ahlswelde et al., Physica B 298, 562 (2001)
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Scan line
Hall Potential Measurements
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Current carrying contacts oriented to 011
Transport measurement
Hall potential measurement
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Current carrying contacts oriented to 0-11
Transport measurement
Hall potential measurement
Large variation of Hall potential
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Non local Resistance
Transport measurement
Hall potential measurement
Different Hall potential with respect to the
magnetic field orientation
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Hall Resistance
Transport measurement
Hall potential measurement
Different Hall potential with respect to the
magnetic field orientation
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Qualitative Model
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Qualitative model with Regular inhomogeneities

• Interface line 2DES destroyed by
• low resistive NiGeAu alloyed contacts
• Adiabatic incompressible strips insulate
• compressible areas with different
• electrochemical potentials
• Anistropy of the incompressible strips
• with respect to the crystal wafer orientation

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Isotropic case
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Anisotropic case
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Current carrying contacts oriented to 0-11

• Measurement

• Model

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Non local resistance

• Measurement

• Model

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Hall resistance

• Measurement

• Model

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Voltage probing contact oriented in 01-1
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Conclusion

• Transport measurements non equilibrium
  assumption ( Adiabatic effect )

• Local measurements of the Hall voltage direct
  proof of the adiabatic decoupling

• Local Hall potential measurements in the case of
  - Non local resistance
• - Asymmetrical Hall Resistance

Importance of the regular inhomogeneities in
front of contacts
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Acknowledgement

• Yvonne Boose, Oktay Göktas and Erik Ahlswede

• Frank Schartner and Benjamin Stuhlhofer

• Thomas Reindl and Monika Riek

• Afif Siddiki and Rolf Gerhardts

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Potential probing via cryogenic scanning force
microscope
T1.4 K
Shift of the resonance frequency
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Cryogenic Scanning Force Microscope
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Locally probing the electrostatic force
Forces Gradient
Shift of the resonance frequency
Variation of resistance (piezoresistive
cantilever)
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Model of the electrostatic force
Capacitance-like
C
Total image charge on the tip, QTotal
Surface charges
Charged donors
2DES potential
Electrostatic potential difference
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Calibration method
From E. Ahlswelde et al., Physica B 298, 562
(2001)
Local probing of the Hall potential via the shift
of the resonance frequency
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Effect of magnetic field variation
Incompressible
Compressible
?2
?1.5
B
D.B. Chklovskii et al., PRB 47, 12605 (1993)
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Anisotropic and Inhomogeneous Contacts
TLM structure
Bulk n-GaAs
- Ni/Ge/Au contact
T.S. Kuan et al., J. Appl. Phys. 54, 6952 (1983)
- Ni/Ge/Au/Ni contact

• Anisotropy of germanium diffusion rate
• Stresses induce piezoelectric effect in GaAs
• - Rectangular-shaped NiGeAs grains

Kamada et al., Appl. Phys. Lett. 49, 1263
Shih et al., J. Appl. Phys. 62, 582 (1987)
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Contact, structure and composition
NiAuGe contact on n-GaAs
High doped interface layer (model)

• Cross-sectional microscopy STEM (structure)
• Selected area diffraction (phase)
• X ray dispersive (EDX)

Better contact resistance (10-6 O cm2) if large
area of Ni2GeAs on contact with GaAs
Kuan et al., J. Appl. Phys. 54, 6952 (1983)
Better if NiAs(Ge) grain at this interface, 0.1 O
mm Shih et al., J. Appl. Phys. 62 582 (1987)
Braslau, J. Vac. Sci. Technol. 19, 803 (1981)
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Contact, anisotropy of resistance
Transmission line structure (TLM)
Contact resistance eight time higher in 01-1
than 011 crystal orientation
Possible origin of the contact anisotropy

• Anisotropy of germanium diffusion rate
• Stresses induce piezoelectric effect in GaAs
  or/and AlGaAs
• - Solid phase epitaxy, rectangular-shaped NiGeAs
  grains

Kamada et al., Appl. Phys. Lett. 49, 1263
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NiGeAu contact on AlGaAs/GaAs heterostructure
heating
After Ni/Ge/Au layers evaporation
After annealing (400-450 C during 50 s)
2DES removed below the alloyed contacts line
interface
U. Graumann, unpublished
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Transmission Line Measurement (TLM)
TLM, sample width 10 µm
RTotal2 RCRSC L/W
2 RC 83 20 O
- in 01-1 orientation
- in 011 orientation
2 RC 51 2 O
Anisotropic, reproducible, low and ohmic
contacts resistance
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Regular Depletion at the Contact Interface
Incompressible strip doesnt enter the contacts
From E. Ahlswelde et al., Physica B 298, 562
(2001)
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Two-terminal measurements with Hall Bars
oriented in different directions
Same behaviour if current carrying contact are
oriented in the same direction (011 or 01-1)
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Hall Four-terminals measurement with Hall Bars
oriented in different directions
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Hall Four-terminals measurement with Hall Bars
oriented in different directions
B positive
B negative
c)
d)
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Four-terminals Hall Bars versus Six-terminal Hall
bar
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Finger-like shape contact
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Current carrying contact, Hot spot
Non equilibrium electrons observed by local
probing of cyclotron emission (CE)
Ikushima et al., PRL 93, 146804 (2004)
? 2
Contact
Contact
10 µm
3 µm
3 µm
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Intrinsic versus Extrinsic
Intrinsic at the transition (? i ½)
Extrinsic, via gate electrodes (? i)
McEuen et al., PRL 64, 2062 (1990)
Komiyama and Nii, Physica B 184, 7 (1993)
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Internal electronic structure of the QD
Formation of compressible and incompressible
strips
The TFA was applied to the edge regions of a
2DES, under the main hypothesis that the
confining potential at the edges V(r) varies
smoothly in the plane of the 2DES, so that its
characteristic depletion length is much larger
than the magnetic length lB.
D.B.Chklovskii et al., PRB 464026 (1992), K.Lier
et al., PRB 507757 (1994)
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Internal electronic structure of the QD
Formation of compressible and incompressible
strips
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Internal electronic structure of the QD
Formation of compressible and incompressible
strips
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(No Transcript)
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Voltage probe contact ( I 0 )
(T n ? 1)
(T n 1)
Non ideal probe
Ideal probe
Equilibrium
If all Tn 1 ( ideal probe ) or f n 1 /
? (equilibrium)
Out of equilibrium
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A model
Edge state picture
Disorder

• Shifting of the plateaux
• Assume total reflection of the innermost odd
  channel

non Equilibrium

• Rxx 0 in dissipative regime ( between ? 4
  - 5 ? 2 - 3 )
• Assume decoupling of the innermost channel
  (adiabatic)

Incompressible and compressible picture
In front of contacts different electron density
profiles induce incompressible strips with
different width
Colored strips compressible
Hot spot
White strips incompressible
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Hall potential profiles
( mobility 0.5 106 cm2/Vs )
E. Ahlswelde et al., Physica E 6, 247 (2000)
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Mesoscopic Transport

• Diffusive ( L, W gt l )
• Several elastic scattering (disordered metal)

• Ballistic (L , W lt l ) / quasi-ballistic (W lt l
  lt L)
• Geometrical effect ( wave guide)

• Adiabatic (high mobility and high B)

Decoupling of interedge channels Channels are
out of equilibrium ( up to 90 µm ! )
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Compressible and incompressible strips
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Imposed current
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• Local Ohms Law

Translation invariance equation of continuity
7 K. Güven and R. R. Gerhardts, Phys. Rev. B
67, 115327 (2003)
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Imposed current cont.

• Fixed Total current I (linear response)

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Conductivity Model
7,8

• What do we need ?

• A model that relates the local electron density
  (or filling factor) to local conductivities.

• A model that gives simple results for the
  conductivity components for even-integer filling
  factors at T0

8 T. Ando, A. B. Fowler, and F. Stern, Rev.
Mod. Phys. B 54, 437 (1982)
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The essence
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Simulating Non-locality

• Simulating QHA and relaxing Locality

• Spatial averaging over Fermi wave length
• (mean electron distance)

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Suppression of Shubnikov-de Haas oscillations due
to selective population or detection of Landau
levels absence of inter-Landau-level scattering
on macroscopic lenght scales Van Wees et al. ,
PRB 39, 8066 (1989)
1
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Influence of probe contacts
R XX 0 ( QHE )
Non-Ideal Contacts (probe the 2 outer channels)
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