1. 1 Engineering of Disorder in MBE grown Ultra- High Mobility 2D Electron System Vladimir Umansky Braun Center for Submicron Research Weizmann Institute of Science, Rehovot, Israel Collaborators: Moty Heiblum & group (Braun Center for Submicron Research) Jurgen Smet & group (Max-Planck-Institut für Festkörperforschung, Stuttgart)

2. 2 Preface: 2DEG and Mesoscopic Physics Mobility: ~25,000 cm 2 /V∙s

3. 3 Electron mobility progress

4. 4 Outlook 2D Electron Gas - basics DX centers – why we are lucky to have them? How to observe 5/2 quasiparticles ? New ideas for band gap engineering Ultra – High Mobility. Is it enough ? How to control disorder ? Conclusions

5. 5 2DEG in AlGaAs/GaAs 2DEG in AlGaAs/GaAs -scattering Background Impurities Remote Ionized Impurities Illumination 2DEG ΔEcΔEc EFEF E0E0 Spacer (d) AlGaAs(x~0.3) Doping GaAs 2DEG Total Depth (D) BG RI T<1K

6. 6 DX centers Shallow donor DX center The “standard” 2DEG structure: Pure GaAs 2DEG 30-40% AlGaAs spacer Delta or uniform doping Gates In the dark: Pros: Frozen charge (in the dark) allows gating Cons: Low doping efficiency (in the dark) → high RI scattering After Illumination in the dark: Pros: Almost double density after illumination → high mobility. Cons: Parallel conduction/gate instability.

7. 7 Applications Gateable 2DEG: QDs, QPC, Spin-pump, Quantum shot noise, etc… Deep structures Measurements after illumination 5/2 Shallow structures Measurements in the dark

8. 8 5/2 in the “standard” 2DEG “Standard” Al 0.36 Ga 0.64 As/GaAs 2DEG Mobility: ~14 ×10 6 cm 2 /V∙s Density: 2.2 ×10 11 cm -3 Measurements: After illumination Data from ~1998 5/2

9. 9 How to Achieve Ultra-High Mobility ? (*) background impurity density ~ 1×10 14 cm -3 limits mobility by ~1÷2 ×10 6 cm 2 /V∙sec MBE system design Raw materials (i.e. Gallium (7N) → 2÷5×10 15 cm -3 ) (*) Optimal growth conditions (rate, temperature, III/V ratio, etc…) Optimal 2DEG structure design Optimal growth sequence design Background Impurity Scattering

10. 10 Double – Side Doping Concern: Interface scattering in QW → Inverse interface For the same spacer width: EFEF E0E0 2DEG Total Depth (D) W d d ns*ns* Used first by L. Pfeiffer to produce samples with > 30 ×10 6 cm 2 /Vsec

11. 11 Doping in Short Period Super-Lattice Γ X 6ML AlAs 9ML GaAs ~250 meV Higher transfer efficiency Higher mobility due to better screening by X electrons No parallel conductance due to ~3 times shorter Bohr radius Short Period Super-Lattice - SPSL

12. 12 Results on Electron Mobility Uniform Doping in Al 0.35 Ga 0.65 As 2DEG EFEF e e 2DEG in QW SPSL  -doping EFEF ~ 36x10 6 cm 2 /V·s RIBER MBE32 machine

13. 13 Is Mobility a Relevant Parameter for FQHE ?

14. 14 BG scattering vs RI scattering uniform doping SPSL  -doping 2DEG EFEF EFEF EFEF BG limited mobility ~ 16 ×10 6 cm 2 /V∙s Spacer 80 nm For spacer > 80 nm contribution of RI scattering < 13÷15 %

15. 15 Mobility, Disorder & FQHE In high mobility 2DEG the main scattering mechanism – BG scattering BG impurities ~10 13 cm -3 in 30 nm QW → average distance ~2  m RI disorder potential characteristic length → spacer → ~80÷100 nm RI Disorder BG

16. 16 How to control the RI disorder? Introduce Spatial Correlations between Ionized Donors !!! Over-doping: Freeze-out temperature: (Efros A.L. 1988)

17. 17 Over-doping & FQHE Concern: Over-doping leads to “Parallel” conductance Minimal Doping ~2×10 11 cm -2 Average distance between donors ~200 Ǻ Bohr Radius for X-electron 20÷30 Ǻ → over-doping of ~ 2÷5 times looks feasible Uniform Doping in Al 0.35 Ga 0.65 As 2DEG EFEF e e SPSL  -doping

18. 18 Application for 5/2 SPSL  -doping EFEF

19. 19 Measurements of ¼ electrons charge

20. 20 There’s no such thing as a free lunch  ≈ 2  ≈ 2.3  ≈ 2.5 Double side doped 2DEG n~(3.0÷3.3)×10 11 cm -2,  ~(29÷33)×10 6 cm 2 /V∙s 5/2

21. 21 Phase transition in Donor layer (s) 0+2+1 0  ~2.3  ~1.1 B  ≈ 2  ≈ 2.3

22. 22 Phase Transition in Disordered 2DES QPC

23. 23 Ideal 2D system for mesoscopic device Ultra-high purity 2DEG Spatially correlated 2D electron system However, frozen at low T

24. 24 Engineering of Disorder: Doping Schemes Shallow donor DX center Using another AlAs-GaAs SPSL for doping Using multiple doping layers in SPSL Using “shallow” DX centers in AlGaAs

25. 25 Conclusions High mobility (low total scattering rate) is just a precondition to obtain very low disordered 2D systems. FQHE is governed by RI induced disorder Spatial Correlations of Remote Ionized Donors are necessary to obtain perfect 5/2 FQHE