XXXIV International School on the Physics of Semiconducting ...

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Outline• Introduction• Measurement technique• Imaging a quantum point contact• Interference fringes• Measuring electron density• Electron optics• Electron-electron interactions• Conclusions
Therefore want a local probe of densityMeasuring densityElectron density measured by Shubnikov-de Haas oscillationsgives the average value over the entire sample.Usually a Hall bar of~ 100 micronsns=2e1h ∆( 1 B)For nanoscale devices, important to be able to measure thedensity in the vicinity of the device
Page 1:
Imaging Coherent Electron FlowBrian
Page 5 and 6:
Two-dimensional electron gasQuantum
Page 8 and 9:
Quantum point contactsElectrons flo
Page 10 and 11:
Quantum point contacts-quantization
Page 12 and 13:
Quantum point contact-energy levels
Page 14 and 15: Outline• Introduction• Measurem
Page 16 and 17: Liquid helium temperature scanning
Page 18 and 19: Experimental techniqueAFM Cantileve
Page 20 and 21: Effect of tip height10 nm 15 nm 20
Page 22 and 23: Quantum mechanical simulationGatesT
Page 24 and 25: Imaging requirementsPerturbation fr
Page 26 and 27: Topinka, LeRoy et al., Science 289,
Page 28 and 29: Opening QPCNew Modes of current onl
Page 30 and 31: Extracting a modal patternExperimen
Page 32 and 33: Selective mode suppressionNo TipTip
Page 34 and 35: Coherent electron flow through a 2D
Page 36 and 37: Simulated imageDoes the presence of
Page 38 and 39: Unperturbed Currentand Tip Perturba
Page 40 and 41: Formation of CausticsClassical Traj
Page 42 and 43: Shifting QPCUnequal voltage on QPC
Page 44 and 45: Imaging a QPCImaged electron flow n
Page 46 and 47: Interference fringesPresence of int
Page 48 and 49: Finite temperature- thermal smearin
Page 50 and 51: Thermal smearing (continued)As the
Page 52 and 53: Fringe persistenceFringe Size (%)Di
Page 54 and 55: Fringe persistence far from the QPC
Page 56 and 57: Scattering induced fringe enhanceme
Page 58 and 59: Single BounceFringe movementDouble
Page 60 and 61: Fringe amplitudeFringes enhancedRef
Page 62 and 63: Temperature dependenceIncreased tem
Page 66 and 67: Electron densityFree electrons in t
Page 68 and 69: Effect of reducing Fermi energyBack
Page 70 and 71: Is it really local?Calculate spacin
Page 72 and 73: Electron densityInterference fringe
Page 74 and 75: Electron opticsCreate elements to e
Page 76 and 77: Electron optics element - prism1µm
Page 78 and 79: Electron optics element - channel
Page 80 and 81: Outline• Introduction• Measurem
Page 82 and 83: DC bias techniqueNo Energy LossCond
Page 84 and 85: Images of electron flow2.74 µm fro
Page 86 and 87: Measuring e-e scattering lengthElec
Page 88 and 89: Differential conductance vs. excess
Page 90 and 91: InteractionsImages are sensitive to
Page 92 and 93: Image pattern of electronflow from
Page 94 and 95: Improved fringe resolutionWiggling
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XXXIV International School on the Physics of Semiconducting ...

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