(Suppression of) Dephasing in a Field-Effect Black Phosphorus Transistor. Guillaume Gervais (Physics) and Thomas Szkopek (Electrical Eng.
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1 (Suppression of) Dephasing in a Field-Effect Black Phosphorus Transistor Guillaume Gervais (Physics) and Thomas Szkopek (Electrical Eng.) July 28, 2016
2 This talk contains no quantum Hall effect at all
3 Due Credit for Black Phosphorus FETs The Device-maker boss: Engineering Prof. Thomas Szkopek, McGill Electr. CNR-Florence, Italy: M. Caporali, A. Ienco, M. Serrano-Ruiz, M. Perruzin (material synthesis) Scuola Normale Pisa: Dr. Heun, + F. Telesio, S.Xiang, S. Roddaro (weak localization) a little army of McGill Vahid Tayari Nick Hemsworth Ibrahim Fakih
4 Introduction
5 Layered Materials I C (graphite) BN (white graphite) P (black-p) MoS 2 (transition metal dichalcogenide) Bi 2 Se 3 (sesquichalcogenide) MgB 2 GaSe (group III monochalcogenide) (mica) YBa 2 Cu 3 O 7-x (high-t c cuprate) HgI 2 (transition metal halide)
6 Layered Materials II C (graphite) BN (white graphite) P (black-p) MoS 2 (transition metal dichalcogenide) Bi 2 Se 3 (sesquichalcogenid e) MgB 2 GaSe (group III monochalcogenide) (mica) YBa 2 Cu 3 O 7-x (high-t c cuprate) HgI 2 (transition metal
7 Black Phosphorus Only the second elemental allotrope that can be mechanically exfoliated down to the single atomic layer limit.
8 Black Phosphorus (bp) 1914: Bridgman produces first bp 1953: Keyes studies bp as a semiconductor 1968: Berman & Brandt; Witting & Mattias observe superconductivity at high pressure 1970 s s: burst of activity in Japan on electronic properties, Raman, cyclotron resonance 2014: ultra-thin bp FETs reported by Peide Ye (Purdue), Yuanbo Zhang (Fudan) and Jeanie Lau (UC Riverside) Puckered honeycomb layers Bulk band gap = 0.3 ev Monolayer band gap ~ 1.2 A. Morita, Semiconducting ev Black Phosphorus, Appl. Phys. A39, 227 (1986).
9 Black Phosphorus (bp) A. Morita, Semiconducting Black Phosphorus, Appl. Phys. A39, 227 (1986).
10 Black Phosphorus (bp) McGill University E E E p p p Schrödinger strain, electric field Dirac Xiang et al., Phys. Rev. Lett. 115, (2015)
11 bp Photo-oxidation: 20s of Ambient Air and Light Before After Rapid bp photo-oxidation with combination of O 2, H 2 O and light. A. Favron R. Martel, Photo-oxidation and quantum confinement effects in exfoliated black phosphorus, Nature Materials (2015).
12 Device Fabrication and Measurements
13 bp FET Fabrication : Top Approach Prof. Yuanbo Zhang, Fudan
14 bp FET Fabrication : a Poor Man s Approach bulk bp source: 99.98% purity (Smart Elements) exfoliation & processing in glove box O 2, H 2 O < 1ppm 10μm 10μm e-beam lithography & Ti/Au contacts encapsulation with MMA/PMMA avoid simultaneous O 2, H 2 O, and Our best mobility: light ~1000 cm 2 /V.s
15 R xx (k ) R (M ) R 2P (k ) (e) 90±2 layers (b) (c) Shubnikov de Haas Oscillations Source (d) (f) Drain (a) (c) PMMA 5 MMA 4 SiO 2 Si V g =-37.5 V T(K) B (T) V g =-27 V V g (V) V g (V) ±4 layers V. Tayari, G. Gervais, R. Martel, T. Szkopek Nature Communications ( B (T)
16 R xx ( ) R xx ( ) ) 50 0 Temperature -50 Dependence of SdH /B (T -1 ) T (K) (e) 60 B (T) Lifshitz- Kosevich: Damping: /B (T -1 ) T (K) m*=0.36 +/ m 0 V. Tayari, G. Gervais, R. Martel, T. Szkopek Nature Communications (2015
17 Independent Findings
18 Independent work regarding SdH Jeanie UC Riverside: N. Gillgren et al., Gate tuneable quantum oscillations in air-stable and high-mobility few-layer phosphorene heterostructures, 2D Materials Yuanbo Fudan: L. Li et al., Quantum oscillations in black phosphorus two-dimensional electron gas, Nature Nanotechnology Ning HKUST: X. Chen et al., High quality sandwiched black phosphorus heterostructure and its quantum oscillations, Nature Communications McGill + UdeM team: V. Tayari et al., Two dimensional magnetotransport in a naked black phosphorus quantum well, Nature Communications 2015.
19 New Developments in Bp: Device Engineering
20 Dual Gated Velocity Modulator (Engineering) V. Tayari, G. Gervais, T. Szkopek Phys. Rev. Applied 5, (2015)
21 See Talk by Prof. ICPS Monday 14h: 2D Materials beyond graphene (Mo-E3)
22 New Developments in Bp: Dephasing
23 Recent Work on Weak Localization in bp (Purdue)
24 Weak Localization in bp (McGill/Pisa)
25 Weak Localization in bp (McGill-Pisa)
26 Hikami-Larkin-Nagaoka (HLN) Theory WL correction to conductivity in 2D: with field parameters given by: where B 0 describes the elastic and Bf the inelastic (dephasing) scattering.
27 HLN Lengthscale and Timescales Scattering length L i associated with a field B i : and correspondingly the dephasing time t n is: where D is the elastic coefficient diffusion.
28 HLN Fits (at 0.26K)
29 HLN Fits (at 10K)
30 Temperature Dependence of Dephasing Length Lf
31 L f (nm) Dephasing in 2D Electron-electron scattering in the presence of elastic scattering in Graphene - A Graphene - B T -1/ T (K)
32 Temperature Dependence of Dephasing Length Lf
33 So, to conclude
34 Some Thoughts A Puckered Graphene experiment. Dephasing length/time more robust than what is expected in 2D. Anisotropy? 1D-like chain?
35 どうもありがとうございます Doumo arigatou gozaimasu
36 Temperature Dependence of Dephasing Length
37 Temperature Dependence of Dephasing Length
38 Temperature Dependence of Dephasing Length
39 Zero-field Transport 12.5±1 nm 24±2 layers 47±1 nm 90±2 layers
40 LL Index, N (b) Landau 1/B (TLevel -1 ) Fan Diagram Analysis b Hall bar V g = -50V V g = -100V Berry phase: F B =0 (c) /B (T -1 ) 0.06 two-terminal Hall bar holes = Schrödinger fermions V g (V) V. Tayari, G. Gervais, R. Martel, T. Szkopek Nature Communications (2015
41 bp FET Fabrication : a Much Better Approach Prof. Yuanbo Zhang Prof. Yuanbo Zhang best mobility: ~6000 cm 2 /V.s
42 More Temperature Dependence of SdH Prof. Yuanbo Zhang m*=0.34 m 0 F B =0 Nature Nanotechnology (2015)
43 Atomic Force Microscopy (a) (b) (c) 4μm 8μm 8μm 6±1 nm 12.5±1 nm 47±1 nm 11±2 layers 24±2 layers 90±2 layers AFM performed after electrical transport measurements
44 2D Character from Angle-Resolved Data Prof. Yuanbo Zhang Nature Nanotechnology (2015)
45 Fermi Surface and Carrier Density 2D (Fermi disc) model: 3D (Fermi sphere) model:
46 Schrödinger-Poisson Simulation Self-consistent Schrödinger-Poisson simulation: 2D hole accumulation layer rms width 2.7nm 5-6 layers E 1 - E 2 = 28 mev sub-band confinement energy V. Tayari, G. Gervais, R. Martel, T. Szkopek Nature Communications (2015
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