APS march meeting 2015
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Transcript of APS march meeting 2015
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ARPES and SPE-LEEM Study on Supported, Suspended, and Twisted Bilayer MoS2SPEAKER: PO-CHUN(FIGO) YEH
ADVISOR: PROF. R. M. OSGOOD
“SPE-LEEM” = Spectroscopic Photo-Emission and Low Energy Electron Microscopy
APS March meeting 2015 Y2: Focus Session: Beyond Graphene - New 2D Materials
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MANY THANKS!
Jurek Sadowski
DaTong Zhang
Arend van der Zande
Abdullah Al-Mahboob
Prof. James Hone
Prof. Irving Herman
Daniel A. ChenetProf. R. M. Osgood
WenCan Jin
Jerry Dadap
Nader Zaki Peter Sutter
Ghidewon Arefe
Andrea Locatelli Tevfik Onur Metnes Alessandro Salaand many!
WHY WE WANT TO STUDY THIS?
• Spin-orbit coupling
• It has a bandgap! • Photoluminescence (PL)
• Twisted Bilayer MoS2
Strong PL in monolayer MoS2 Nano. Lett. 10, 1271-1275 (2010)
High quantum efficiency 1000 times stronger PL in ML
WS2, WSe2 than in bulk
ACS Nano 7 (1), 791–797 (2013)
Direct bandgap in ML Thin, flexible devices E.g. Li-ion battery and transistors
Nano Lett., 11 (9), pp 3768–3773 (2011)
Chem. Commun. , 47, 4252-4254 (2011)
Enhanced spin lifetimes Large spin Hall angles VBM S-O splitting up to 456meV in WSe2
PRB 84, 153402 (2011)
Nano Lett. 13 (7), pp 3106–3110 (2013)
van der Zande et al, Nano. Lett. 14, 2014Liu et al, Nat. Commun. 5, 2014Huang et al, Nano Lett 14, 2014
A lot of PL and Raman studies!
OUR AIM:
With SPE-LEEM, we can:
o Measure the MoS2 band structure directly
o Study the band gap transition and the role of interlayer coupling in ML, BL, and twist bilayer MoS2
o Study the substrate effect via suspensiono Study hole effective mass directly
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WHY SPE-LEEM?Micron-size spot, Direct band structure, fast real time imaging, large area mapping, UHV, surface doping, depth profile.
NSLS I Nanospectroscopy
1. mLEED – reciprocal space mapping: surface crystalline2. LEEM – real space mapping: surface corrugation3. mARPES – band structure mapping4. PEEM and XPEEM(ELETTRA) – chemical sensitivity,
ionization, core level orbitals, surface composition
BNL, NY, USA Elettra, Trieste, Italy
2 µmLEEM, ML graphene
DIRECT TO INDIRECT BAND GAP
Photoelectron k-space mapping
Direct (1ML) to indirect(2ML+) bandgap transitionARPES – a direct probe for band structure
Jin and Yeh et al, PRL 2013
dz, pz dx2
+y2, dxy
SUSPENSION – REMOVE SUBSTRATE EFFECTS
DFT-calculated bands using the relaxed lattice parameters are overlaid onto all the band maps for comparison.
ARPES on suspended, exfoliated ML MoS2
ARPES on supported, exfoliated ML MoS2 In Elettra
In ElettraJin and Yeh et al, PRB 2015
• Band width reduced -> less electron scattering
• The UVB compression/lattice relaxation persists
• UVB less dispersive -> Smaller hole effective mass (-10.6%) -> Larger mobility (+11.6%)
SUSPENDED VS SUPPORTED
µh = h · th/ meff
Jin and Yeh et al, PRB 2015
Package/functionalS.W. Yun et al FLAPW/GGA 3.524 0.637Andor Kormányos et al VASP/HSE06 2.24 0.53H. Peelaers et al VASP/HSE06 2.8 0.44T. Cheiwchanchamnangij et al Quasiparticle GW/LDA 3.108 0.428Suspended MoS2, measured - 2.00 0.43Supported MoS2, measured - 1.85 0.48
THE MAKING OF THE TWIST BILAYER MoS2
A mixture of etching & dry transfer method(collaboration with Hone group)
SEM Bright-field LEEM Dark-field LEEM
(0°)
(60°)
THE MEASUREMENT OF TWIST BILAYER MoS2
0.556 0.416 0.405 0.355 0.376 0.516
(0°) (60°)
ANGLE–DEPENDENT BANDGAP OPENING• Since K is invariant to twist angle and CB is almost intact, bandgap opening can
be derived from energy difference between Γ and K from UVB
• When twist angle reaches ~30°, the bandgap reaches its maximum (+200meV)
• The energy difference within each angle is larger than predicted (+70meV)
• Measured data shows asymmetry between 0° and 60° data as predicted
• Agrees well with PL and DFT calculations
Interlayer Spacing vs EK - EГ
d60 = 6.23Å
van der Zande et al, Nano. Lett. 14, 2014Liu et al, Nat. Commun. 5, 2014
Align with the ~60 ° data point
Theoretical calculation Experimental data
70meV
EFFECTIVE MASS On going
Effective mass at K via DFT calculation
Huang et al, Nano Lett 14, 2014
(Work in progress) Effective mass at Γ and K
-24% in meff, hole
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CONCLUSION
Bandgap transition originates from the shifting of Γ at the top-most valence band by quantum confinement
Hole effective mass / mobility affected by the substrate Twist angle -> Interlayer coupling changes the band gap SPE-LEEM system with LEEM, µLEED, and µARPES is ideal
for studying 2D materials
SPIN-ORBIT SPLITTING• Predicted large s-o splitting at vicinity of K in ML MoS2
• Possible causes of broadening:
• a decrease in the quasi-particle lifetime
• a splitting of the spin degenerate band into two bands due to spin-orbit coupling.
Theory vs Suspended: 148 meV vs 78±19 meV
On going
Jin and Yeh et al, PRB 2015
ML MoSe2, splitting~180eVARPES with MBE growth in UHV
Zhang et al, Nat Nanotech 9, 2014
(a)
(b) (c)
(d)
(e)
van der Zande et al, Nano. Lett. 14, 2014
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SPE-LEEM - PERSPECTIVES
ELMITEC SPLEEM
Energy Analyzer
Manipulator.Grounded.(High voltage @ 2kV)
Preparation chambers
Photon energy: 15-150eV Good energy resolution: 100meV Good spatial resolution: 8nm Large mapping area: FOV = 100µm
Thermal coupler
Sample holder
d ~ 10mm
NOTES
• Work function in ML: 1.85eV; bilayer 1+ eV; highly doped, lower bound of the bandgap.
• Other ways of change lattice constant – strain: up to 2.2% (Nano Lett., 2013, 13 (8)
• LEED on suspended MoS2? Should be better. But we did not have the chance to do the measurement.
• Error bars: average of the all six high sym directions + resolution limit of the apparatus +
• Fitting the entire bands using tight binding theory instead of locally? To get a better fit for peak, etc.
Mo dx2+dy2, dxy Mo dxy, dyz Mo d3z2-r2 S pxy S pz
Cappelluti et al, PRB 88, 2013
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EFFECTIVE MASS AT K POINT
a: experimental lattices, ref Phys. Rev. B 85 (2012). b: optimized lattices from calculation
Hole effective mass agrees well with the calculations, for both 1ML and 2ML
Thickness Electron Mass Hole Mass Method Reference Lattice Constant
ML N/A 0.52 ABINIT/ GGA Our results. 3.28
ML N/A 0.48 Experiment Our results. 3.28
ML 0.53 0.52 DFT-GW-BSE A. Ramasubramanim, PRB 2012 3.32
ML 0.29a/0.26b 0.34a/0.33b DFT-GW-BSE Hongliang Shi, PRB 2013 3.286
ML 0.19 0.4 FLAPW-GGA W. S. Yun. PRB 2012 3.286
2ML N/A 0.432 Experiment Our results. 3.28
2ML 0.3 0.49 LDA A. Kumar, EPJB 2012 3.282
2ML 0.3 0.3 FLAPW-GGA W. S. Yun. PRB 2012 3.286
Foldable FETs and solar cells.
Goal toward printable solar cell on a sheet of paper (gr as an example)Flash memory
EXAMPLES OF APPLICATIONS
Constant energy plane near EF
The band near EF originates from
Mo 4dz2 orbital and S 3Pz orbital,
where Mo 4d character is dominant by a factor of ~3. Consider only the d orbital:Two cuts along high symmetric direction in BZ
Selection rules in ARPES• Fermi’s golden rule:
• Hamiltonian
• Matrix elements
The final state can be approximated by a plane wave; the initial state represents the wave function of the electrons in solid.
Our calculation and analysis
April 18, 2023
Slide 22
Many-body Physics from ARPES
Response of crystal to “hole”ARPES measures Spectral Function A(k,w) Band renormalization Re[S(k,w)] Scattering Rate Im[S(k,w)] Re[S(k,w)] and Im[S(k,w)] related by Kramers-Kronig transformation
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diffractioncontrast
sample
contrastaperture
objective
[0,0]
[h,j]
SURFACE STRUCTURE
Au+O/Rh(110)
quantum sizecontrast
d
FILM THICKNESS
Co/W(110)
geometricphase contrast
MORPHOLOGY
Mo(110)
WHAT CAN BE MEASURED WITH LEEM?
“We must be clear that when it comes to atoms, language can be used only as in poetry.” -
Niels Bohr
Updated version for the comparison
Gaussian peak fitting of LEED (00) spot.
Nature 499, 419 (2013) (DOI:10.1038/nature12385)
LATTICE RELAXATION
• Up-most valence band (UVB) compression:(UVBmax-UVBmin)experiment/ (UVBmax-UVBmin)theory
• The compression rate of ML MoS2 is 80% in exfoliated and 50% in CVD;
• Relaxation: ~3.6% lateral lattice expansion in ML MoS2 compared to bulk; lattice constant a = 3.28±0.10 Å vs 3.16 Å (-2% in c /z axis)
• Larger hole effective mass -> lower hole mobility µh = h · th/ meff
ML MoS2 UVB and calculations: Si supported and free standing