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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