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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)
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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)
Preface: 2DEG and Mesoscopic Physics Mobility: ~25,000 cm2/V∙s
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
2DEG in AlGaAs/GaAs 2DEG in AlGaAs/GaAs -scattering Illumination Background Impurities Remote Ionized Impurities GaAs AlGaAs(x~0.3) T<1K Doping Spacer (d) BG RI 2DEG ΔEc E0 EF 2DEG Total Depth (D)
DX centers Gates Delta or uniformdoping 30-40% AlGaAs spacer Shallow donor 2DEG Pure GaAs DX center The “standard” 2DEG structure: 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.
Applications 5/2 Gateable 2DEG: QDs, QPC, Spin-pump, Quantum shot noise, etc… Deep structures Measurements after illumination Shallow structures Measurements in the dark
5/2 in the “standard” 2DEG Data from ~1998 “Standard” Al0.36Ga0.64As/GaAs 2DEG Mobility: ~14 ×106 cm2/V∙s Density: 2.2 ×1011 cm-3 Measurements: After illumination Ungateable 5/2
How to Achieve Ultra-High Mobility ? Background Impurity Scattering MBE system design Raw materials (i.e. Gallium (7N) → 2÷5×1015 cm-3 ) (*) Optimal growth conditions (rate, temperature, III/V ratio, etc…) Optimal 2DEG structure design Optimal growth sequence design (*) background impurity density ~ 1×1014 cm-3 limits mobility by ~1÷2 ×106 cm2/V∙sec
Double – Side Doping ns* d d EF E0 2DEG Total Depth (D) W For the same spacer width: Concern: Interface scattering in QW → Inverse interface Used first by L. Pfeiffer to produce samples with > 30 ×106 cm2/Vsec
Doping in Short Period Super-Lattice 6ML AlAs Γ X ~250 meV 9ML GaAs 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
Results on Electron Mobility e e RIBER MBE32 machine Uniform Doping in Al0.35Ga0.65As EF 2DEG SPSL d-doping ~36x106cm2/V·s 2DEG in QW EF SPSL d-doping
BG scattering vs RI scattering uniform doping EF 2DEG SPSL d-doping EF EF Spacer 80 nm BG limited mobility ~ 16 ×106 cm2/V∙s For spacer > 80 nm contribution of RI scattering < 13÷15 %
Mobility, Disorder & FQHE BG BG BG RI Disorder In high mobility 2DEG the main scattering mechanism – BG scattering BG impurities ~1013 cm-3 in 30 nm QW→ average distance ~2 mm RI disorder potential characteristic length → spacer → ~80÷100 nm FQHE is governed by RI induced disorder
How to control the RI disorder? Over-doping: Freeze-out temperature: (Efros A.L. 1988) Introduce Spatial Correlations between Ionized Donors !!! g ~ 20
Over-doping & FQHE e e SPSL d-doping EF 2DEG Uniform Doping in Al0.35Ga0.65As Concern: Over-doping leads to “Parallel” conductance Minimal Doping ~2×1011 cm-2 Average distance between donors ~200 Ǻ Bohr Radius for X-electron 20÷30 Ǻ → over-doping of ~ 2÷5 times looks feasible
Application for 5/2 EF SPSL d-doping
There’s no such thing as a free lunch Double side doped 2DEG n~(3.0÷3.3)×1011 cm-2, m~(29÷33)×106 cm2/V∙s g ≈ 2 g ≈ 2.5 g ≈ 2.3 5/2
Phase transition in Donor layer (s) B g ≈ 2 +1 +2 0 0 g ≈ 2.3 g~2.3 g~1.1
Ideal 2D system for mesoscopic device Ultra-high purity 2DEG Spatially correlated 2D electron system However, frozen at low T
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
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