1. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Note that 1µm = 10 -6 m = 10 -4 cm; 1nm = 10 -9 m = 10Å A few relevant length scales

2. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Electronic properties of the 2DEG in GaAs-AlGaAs and Si inversion layers.

3. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Electron trajectories for the diffuse ( l W,L) transport regimes.

4. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Quantum Mechanical Interference P 1 = 1 P 2 = 2 P 12 = 1 + 2 2 Double Slit Interference

5. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Quantum Mechanical Interference: Experimental Results Au-Ring: Ø = 0.82 μm 50 nm thick T = 32 mK R av = 29 Ω g 0 fluctuations within ring width g 1 h/q g 2 2h/q

6. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm voltage current g 0 fluctuations g 1 fluctuations

7. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Increasing current density Effect of current density & temperature on l Effect of current density & temperature on l

8. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Weal Localization The magneto-resistance of a thin Cu-film (d=80Å, resistance per square R=98Ω) at different temperatures. The mean free path is of the order of 10 Å so that classical magneto-resistance effects can be excluded.

9. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Weal Localization Cu

10. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Weal Localization Cu-particles

11. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Weak Localization 2-d 2-d GaAs-AlGaAs System: Length: 10 μm, Width: w w = 1.5 μm w = 0.5 μm

12. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Density of States

13. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Single Electron Transistor (SET) Single Electron Transistor (SET) An example for a new nanodevice

14. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm SET Characteristics Stability conditions: Source junction: n=0 -e/2C d -[C g /C d ]V g < V d <e/2C d -[C g /C d ]V g Source junction Drain junction Drain junction: n=0 e/2[C s +C g ]+[C g /[C s +C g ] ]V g > V d > -e/2[C s +C g ]+[C g /[C s +C g ] ]V g

15. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm The Coulomb Blockade Charge transport through a metallic nanoisland Equivalent circuit: SOURCE GATE DRAIN Single Electron Transistor (SET)

16. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Realization of Coulomb Blockades

17. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm

18. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Possible Applications: Low-power three-terminal devices (Very) Very Large Scale Integration Single electron logic New standards for current and capacity

19. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm

20. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Preparation and Characterization of Al 2 O 3 /Nb(110)/Al 2 O 3 (0001) The Sapphire Substrate Sapphire(0001): miscut < 0.1° Annealed 1.5 h at 1100°C in O 2 AFM: 2 µm x 2 µm, z-scale: 1nm terrace width ~400nm miscut step height: 1/3 c 0.43nm

21. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm I-V characteristics on oxide The Tunneling Barrier (Al 2 O 3 ): preparation by evaporation of 0.9nm Al at room temperature and subsequent oxidation in oxygen atmosphere. verification of the oxidation by XPS. characterization by STM: STS: Semiconductor Gap of up to 3eV STM: Al 2 O 3 /Nb(110) 400nm x 400nm scale: 2.3nm

22. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm TEM: Au Nanoparticles/Al 2 O 3 /Nb(111) 10nm 1nm STM: 397nm x 397nm z scale: 6.58 nm Inset: autocorrelation TEM: Au Nanoparticle on Al 2 O 3 /Nb(110) Nb(110) Al 2 O 3 Au

23. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Measurement setup: Prerequisite: C < e 2 /(2k B T) C << 3aF at room temperature r << 30nm for a free sphere Fit: C 1 = 1.14×10 -19 F C 2 = 2.0×10 -20 F R 1 = 8.8×10 +09 Ω R 2 = 2.3×10 +09 Ω Q 0 = 3.4×10 -02 e T = 300 K STM: (100nm) 2 z scale 10nm 2V/30pA C1 R1 C2R2 Equivalent circuit diagram: C2C2 C1C1 R1R1 R2R2 tip particle Nb(110)

24. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm C 1 = 1.14×10 -19 F C 2 = 2.0×10 -20 F R 1 = 8.8×10 +09 Ω R 2 = 2.3×10 +09 Ω Q 0 = 3.4×10 -02 e T = 300 K increasing set current Measured Coulomb Staircase on a Gold nanoparticle

25. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Coulomb Staircases: Effect of Temperature

26. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Quantized Conductance Schematic cross-sectional view of a quantum point contact, defined in a high-mobility 2D electron gas at the interface of a GaAs-AlGaAs heterojunction. The point contact is formed when a negative voltage is applied to the gate electrodes on top of the AlGaAs layer. Transport measurements are made by employing contacts to the 2D electron gas at either side of the constriction.

27. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Quantized Conductance Conductance quantization of a quantum point contact in units of 2e 2 /h. As the gate voltage defining the constriction is made less negative, the width of the point contact increases continuously, but the number of propagating modes at the Fermi level increases stepwise. The resulting conductance steps are smeared out when the thermal energy becomes comparable to the energy separation of the modes.

28. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Quantized Conductance: Au-wire- vs – Au-Film Quantized Conductance: Au-wire- vs – Au-Film By Laetitia G. Soukiassian Purdue University STM Break Junction

29. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Naively expected behavior Experimental result

30. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm The k > 0 Problem Single Sub-BandFour Sub-Bands contributing

31. Abteilung Festkörperphysik Solid State Physics University of Ulm Abteilung Festkörperphysik Solid State Physics University of Ulm Statistics on a Breakjunction