Fabrication and measurement of quantum nanostructures 9/6/2016 Fabrication 9/8/2016 2D electron systems. Ihn, chapter 2, chapter 6 1. Ihn chapter 9 2. A new method for highaccuracy determination of the fine-structure constant baed on quantized Hall resistance 1. JMN 2D electron systems, 9/13/2016 cont'd. Ihn, chapter 16 9/15/2016 1.Two-Dimensional Magnetotransport in the Extreme Quantum Limit 2. Coherent branched flow in a two-dimensional electron gas 1. Last timeβ¦ β’ Effective mass in GaAs: ππ = 0.07 ππππ β’ Fermi wavevector in GaAs: πππΉπΉ = 1.58 × 106 ππππβ2 β’ πππΉπΉ β 40 ππππ β’ ΞπΈπΈ πππ΅π΅ ππ β 120 πΎπΎ β’ Quantum nanostructures must be ο± clean ο± small ο± cold β’ 2D is special. Today β’ Making 2D electron systems: β semiconductor band engineering β’ Making 0D and 1D systems out of 2D systems. β Gating β Nanofab β’ Measuring quantum nanostructures: β Low temperature measurements β Transport measurements Band engineering E Large gap Small gap Large gap Conduction band (empty states) z Valence band (filled with electrons) z Layered semiconductor structures can be used to confined electrons and holes Band engineering http://people.seas.harvard.edu/~jones/ap216/images/ bandgap_engineering/bandgap_engineering.html Band engineering β’ Band gap in GaAs: 1.424 eV β’ Band Gap in AlxGa1-xAs www.ioffe.ru www.ioffe.ru Band gap of AlxGa1-xAs increases with Al content AlGaAs-GaAs-AlGaAs quantum well Vacuum levels (electron affinity) aligned Conduction band (empty states) E Valence band (filled with electrons) AlGaAs GaAs AlGaAs Quantum well for electrons and holes z AlGaAs-GaAs heterostructure E z AlGaAs-GaAs heterostructure E EF z AlGaAs-GaAs heterostructure E EF z AlGaAs-GaAs heterostructure E EF z AlGaAs-GaAs heterostructure E EF z Negative gate voltage E EF z Si-MOS Metal SiO2 Si z Si MOS structure E gate SiO2 Si EF z Si MOS structure E gate SiO2 Si EF z What happens if we apply a positive gate voltage? E gate SiO2 Si EF z Si MOS structure E EF gate SiO2 Si bias z Si MOS transistor Where do the electrons come from? Gate: 0V channel source gate SiO2 drain Si Where do the electrons come from? Gate: +1V channel source gate SiO2 bias drain Si Making 1D or 0D systems Beenaker and van Houten Hendrik Bluhm Molecular beam epitaxy wikipedia Molecular beam epitaxy Chris Palmstrom, UCSB Other deposition/growth techniques Oxidation Integral-storage.com Hivactec.com wikipedia Carbon systems Graphene-supermarket www.graphene.ac.rs Quantum nanostructures must be ο± clean ο± small ο± cold Photolithography Deposit metal metal metal metal wikipedia Photolithography Dissolve PR metal wikipedia wikipedia Electron beam lithography Raith Purdue Quantum nanostructures must be ο± clean ο± small ο± cold Low-temperature physics Gas Boiling point (K) Methane 111.7 Oxygen 90.2 Argon 87.2 Flourine 85.2 Air 78.8 Nitrogen 77.4 Neon 27 Hydrogen 20.2 He-4 4.2 He-3 3.2 wikipedia Low-temperature physics Dangerous Expensive Gas Boiling point (K) Methane 111.7 Oxygen 90.2 Argon 87.2 Flourine 85.2 Air 78.8 Nitrogen 77.4 Neon 27 Hydrogen 20.2 He-4 4.2 He-3 3.2 wikipedia Pumping on cryogenic fluids Pumped He-4 fridge: 1.2 K Pumped He-3 fridge: 600 mK wikipedia Dilution refrigerator Janis Dilution refrigerator: 10 mK wikipedia High magnetic fields wikipedia Transport measurements ` 4 terminal measurements wikipedia NIST Next time β’ Electrical transport β’ Quantum Hall effect β’ Journal club presentation by JMN
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