Imaging spectroscopic ellipsometry of

MoS2

Ursula Wurstbauer

Walter Schottky Institute and Physics Department, TU Munich

Nanosystems Initiative Munich (NIM)

Semiconducting 2D Materials

Photoluminescence efficiency

drastically enhanced for

monolayer

more than 3315 citations

top view

side view

< 1nm

See also: A. Splendiani et al. Nano Lett., 10, 1271 (2010)

Transition from indirect to direct gap

direct band gap (~1.9eV)indirect band gap (>1.2eV)

modified from: A. Splendiani et al. Nano Lett., 10, 1271 (2010)

bulk bilayer monolayer

• Close to Γ-point:

Band structure given by hybridized state of S pZ-orbitals and Mo d-orbitals

• K-point:

Band structure dominated by Mo d orbitals See also

A. Kuc, et al. Phys. Rev. B 83, 245213 (2011)

bulk

4L

3L

2L

1L

S. Funke, UW et al. J. Phys.: Condens. Matter 28, 385301 (2016).

S. Funke, UW et al.

Micromechanical exfoliated MoS2 on Si/SiO2

Ellipsometric enhanced

contrast micrographs

Optical Micrograph

Parameters:

angle of incidence (AOI): 50°

analyzer angle: −7.0°

polarizer angle: 34.6°

compensator angle: of 45°

Light energy: 2.82 eV.

Raman spectroscopy

Contrast and lateral resolution of

IEC sufficient for fast, automated

search of individual flakes and

determination of layer number.

370 380 390 400 410 420

bulk

1L

3L

2L

4L

A

1g

Inte

nsity (

arb

. u

nits)

Energy (cm-1)

E 1

2g

Counting the number of layers by Raman

0 1 2 3 4 5 6 7 10

18

21

24

27

Number of Layer

|A1g -

E2g|

(cm

-1)

bulk

370 380 390 400 410 420

bulk

A

1g

Inte

nsity (

arb

. u

nits)

Energy (cm-1)

E 1

2g

C. Lee, et al., ACS Nano 4(5) 2695–2700 (2010)

B. Chakraborty et al. Phys. Rev. B 85, 161403(R) (2012)

C. Rice et al. Phys. Rev. B 87, 081307(R) (2013)

R. Yan et al. ACS Nano 8, 986-993 (2014)

S. Mignuzzi et al. Phys. Rev. B 91, 195411 (2015)

U. Wurstbauer et al. J. Phys. D: Appl. Phys. 50 173001 (2017)

i

s

pe

r

r tan

-map

Imaging Ellipsometry

(Paul Drude, Lehrbuch der Optik, Leipzig, 1906 )

Change in polarization state of reflected light:

p: ‚parallel‘ – parallel

s: ‚senkrecht‘ - perpendicular

Ellipsometric angles

Imaging ellipsometry with a lateral resolution of ~1 µm

S. Funke , UW et al. J. Phys.: Condens. Matter 28, 385301 (2016)

U. Wurstbauer et al. Appl. Phys. Lett. 97, 231901 (2010)

• Large area illumination with

collimated beam (NA ~0.018).

• Reflected light guided through a

lens system and displayed on

the chip of a CCD detector.

• Full control over angle of

incidence and reflection

maintaining high lateral

resolution.

Imaging ellipsometry on transparent substrates

Suppression of backside reflection on

transparent substrate using a knife

edge maintain large field of view

Micromechanical exfoliated MoS2 on sapphire

Ellipsometric enhanced contrast Raman map

High lateral resolution allows for

spectroscopic imaging ellipsometry

(SIE) on any substrate:

• on individual terraces sites

• investigate lateral inhomogeneities

in the dielectric functions e.g. on

folded regions

S. Funke, UW et al. J. Phys.: Condens. Matter 28, 385301 (2016)

S. Funke, UW et al. Appl. Surf. Sci., in press (2017)

Layer dependent ellipsometric angles

𝝆 = 𝒓𝒑𝒓𝒔 = tan𝝍𝒆

𝒊𝚫

Spectroscopic Imaging ellipsometry

S. Funke, UW et al. J. Phys.: Condens. Matter 28, 385301 (2016)

Nulling ellipsometry:

polarizer and analyzer are adjusted such

that reflected light is linearly polarized

and intensity minimized. Angle between

polarizer and analyzer determines the

ellipsometric angle Δ and .

Multilayer model

Reflectivity of light from an n-layer stack:

Multilayer systems Reflection of light on surface:

inout ERE

Reflection matrix depends on material

properties (d, ) of each layer.

Layer 1: d0, 0

Layer 2: dMoS2, MoS2

Layer 3: dS, S

Regression analysis:

Complex dielectric functions of MoS2 MoS2 are extracted from and as an input

of a Levenberg-Marquardt-fit based on Berreman 4 x 4 matrix method for

multilayered films together with Tauc-Lorentz and Lorentz profiles.

Assuming an isotropic dielectric tensor for MoS2 - Lorentz oscillators:

𝜀 𝐸 = 𝝐1 + 𝑖𝑛=4 𝑠𝑖∙𝑓í

𝑓𝑖2−𝐸2−𝑖∙𝑑𝑖∙𝐸

f: oscillator frequency (eV)

s: oscillator strength

d: damping

E: photon energy (eV) S. Funke, UW et al. J. Phys.: Condens. Matter 28, 385301 (2016)

Accurion EP4 modelling software

Anisotropic dielectric tensor for MoS2:

𝜀𝑥 = 𝜀𝑦 ≠ 𝜀𝑧

A) In-plane component 𝜺𝒙,𝒚 described by 5 Lorentz-oscillators:

𝜀𝑥,𝑦 𝐸 = 1 +

𝑖

𝑛=5𝑠𝑖 ∙ 𝑓í

𝑓𝑖2 − 𝐸2 − 𝑖 ∙ 𝑑𝑖 ∙ 𝐸

B) Out-of-plane component 𝜺𝒛 (imaginary part):

𝜀𝑧,𝑖𝑚𝑎𝑔 𝐸 =

0 ; 𝐸 ≤ 𝐸𝑔

𝐸−𝐸𝑔2

𝐸2∙𝐴∗𝐸0∗Γ∗𝐸

𝐸02−𝐸2 2+Γ2∙𝐸2; 𝐸 > 𝐸𝑔

Anisotropic modelling

f: oscillator frequency (eV)

s: oscillator strength

d: damping

E:photon energy (eV)

Eg: band gap enery (eV)

A: amplitude of oscillator at energy E0

: damping at E0

z

x,y

S. Funke, UW et al. J. Phys.: Condens. Matter 28, 385301 (2016)

Accurion EP4 modelling software.

out-plane component of 1, 2

for 1L, 3L and FL MoS2

Dielectric tensor from spectroscopic ellispometry

See also recent work:

Y. Li et al. Phys. Rev. B 90, 205422 (2014)

W. Li et al. Phys. Rev. B, 90, 195434 (2014)

C. Yim et al. Appl. Phys. Lett., 104, 103114 (2014)

J. W. Park et al. J. Appl. Phys., 116, 183509 (2014)

• Position of critical points

independent from fit

approach

• Magnitude of in-plane

component reduced for

anisotropic approach, but

in better agreement with

literature values.

• Only one weaker critical

point in out-of plane

component.

in-plane component of 1, 2

for 1L, 3L and FL MoS2

S. Funke , UW et al. J. Phys. Condens. Matter 28, 385301 (2016).

U. Wurstbauer et al. J. Phys. D: Appl. Phys. 50 173001 (2017) .

Lateral homogeneity of optical properties

determination of the dielectric

tensor with a lateral resolution

better than 2µm.

10µm

-mapEllipsometric anglesMap of fit error (grid of 2x2µm)

large homogeneous areas

(blue regions) of a 1L MoS2

flake on sapphire (~20x8 µm2)

S. Funke, UW et al. J. Phys.: Condens. Matter 28, 385301 (2016).

MSE error

< 80

MSE error

80 < MSE

< 300

Optical

micrograph

and Raman

Very homogenous region of 1L MoS2

1.5 2.0 2.5 3.0 3.5 4.0 4.5-20

-10

0

10

20

30

40

"C" DA

MoS2 Monolayer

co

mp

lex d

iele

ctr

ic f

un

cti

on

Energy (eV)

1

2

B

Fine structure and line spliting in C and D excitonic transitions

critical point analysis

A, B excitons:

Direct transition at K point between

CB and spin-split VB states.

”C” exciton:

Van Hove singularities, parallel

bands close to M point.

“D” exciton:

Higher lying exciton transition.

1.5 2.0 2.5 3.0 3.5 4.0 4.5

fit

fit

d2

d

E2

Energy (eV)

Interband critical point analysis

𝒅𝟐𝝐

𝒅𝑬𝟐= 𝒏 𝒏 − 𝟏 𝑨𝚪−𝒏𝒆𝒊𝝓 𝑬 − 𝑬𝒕 + 𝒊𝚪

𝒏−𝟐, 𝒏 ≠ 𝟎

−𝑨𝚪−𝒏𝒆𝒊𝝓 𝑬 − 𝑬𝒕 + 𝒊𝚪−𝟐, 𝒏 = 𝟎

Critical point analysis:

A, B

(Exciton)

C2

(2D)

C1

(Exciton)D1, D2

(Exciton)

n = -1: exciton character

n = -1/2: 1D character

n = 0: 2D character

n = ½: 3D characterP. Lautenschlager et al. PRB 36(9), 4821 (1987).

W. Li et al. PRB 90, 195434 (2014)

A, B exciton:

Direct transition at K point between

CB and spin-split VB states.

A2D: 2D band-to band transiton

(single particle band gap

C1 exciton:

Van Hove singularities, parallel

bands close to M point.

C2: 2D higher lying band-to band

transition

D1, D2 exciton:

Higher lying exciton transition.

A2D

(2D)

1.5 2.0 2.5 3.0 3.5 4.0 4.5

fit

fit

d2

d

E2

Energy (eV)

Interband critical point analysis

𝒅𝟐𝝐

𝒅𝑬𝟐= 𝒏 𝒏 − 𝟏 𝑨𝚪−𝒏𝒆𝒊𝝓 𝑬 − 𝑬𝒕 + 𝒊𝚪

𝒏−𝟐, 𝒏 ≠ 𝟎

−𝑨𝚪−𝒏𝒆𝒊𝝓 𝑬 − 𝑬𝒕 + 𝒊𝚪−𝟐, 𝒏 = 𝟎

Critical point analysis:

A, B

(Exciton)

C2

(2D)

C1

(Exciton)D1, D2

(Exciton)

n = -1: exciton character

n = -1/2: 1D character

n = 0: 2D character

n = ½: 3D characterP. Lautenschlager et al. PRB 36(9), 4821 (1987).

W. Li et al. PRB 90, 195434 (2014)

A, B exciton:

Direct transition at K point between

CB and spin-split VB states.

A2D: 2D band-to band transiton

(single particle band gap

C1 exciton:

Van Hove singularities, parallel

bands close to M point.

C2: 2D higher lying band-to band

transition

D1, D2 exciton:

Higher lying exciton transition.

Comparison of critical point analysis with caclulation of interband transitions with and w/o

Coulomb interaction are on good agreement; Energy difference between A and A2D transition

provides an estimate of the exciton bidning energy ~400meV.

Theory by Dr. Steinhoff , Prof. Jahnke (University of Bremen)

A2D

(2D)

1.5 2.0 2.5 3.0 3.5 4.0 4.50

2

4

6

8

10

12

14

16

D

exciton

C

"exciton"

A B

exciton

ab

so

rban

ce

(%

)

Energy (eV)

• High absorbance in the visible range

• Absorbance > 15% for one layer (0.65 nm thick)

• Spin-split A and B excitons due to SOC splitting

• High energy excitonic signature

< 1nm

MoS2

Y. Li et al. Phys. Rev. B 90, 205422 (2014)

S. Funke UW et al. J. Phys.: Condens. Matter 28, 385301 (2016).

1L TMDs – strong light-matter interaction

How can the light matter interaction be enhanced?

Monolayer MoS2:

• Si/SiO2 substrate

• A-exciton at ~1.85 eV

• B-exciton at ~2 eV

Monolayer of Au nanoparticles:

• ~ 10nm diameter

• distance ~ 2nm also to MoS2

• SPP resonance: ~ 1.9 eV

(broad)

Coupling between MoS2 and plasmonic gold nanoparticle arrays

Overlap between SPP resonance of Au NP and A, B excitons of MoS2 -

plasmonic enhancement?

10 µm

MoS2 +

AuNP

Optical micrograph

100 nm

SEM image

S. Diefenbach, UW et al. arXiv (2017).

How can the light matter interaction be enhanced?

Photoluminescence

(non-resonant excitation)

Absorbance

(from imaging elliposmetry)Photoluminescence

(resonant excitation)

PL

(a

.u.)

Eexc 2.6 eV

PL

(a

.u.)

Eexc=1.96 eV

Absorbance:

• no enhancement for A, B excitons;

• A, B excitons redshifted by 100meV for MoS2/Au NP

PL:

• enhancement by a factor between 8 and 20 (dependent on sample) for resonant

as well as non-resonant excitation;

• PL blueshifted by < 10 meV for MoS2/AuNP

How can this discrepancy be understood?

Energy (eV) Energy (eV)

S. Diefenbach, UW et al. arXiv (2017)

Multiple interaction for MoS2 Au NP hybrid

Possible interaction mechanism:

a) Plasmonic coupling

b) Dielectric engineering – band gap renormalization Egap

c) Coulomb engineering – modified exciton binding energy EB

d) Modification of charge carrier density n (Fermi energy work function)

(a) unlikely:

• ‚gap‘ mode localized > 7nm above MoS2

• A-, B- exciton Bohr radii only few nm

S. Diefenbach, UW et al. arXiv (2017)

Multiple interaction for MoS2 Au NP hybrid

Possible interaction mechanism:

a) Plasmonic coupling

b) Dielectric engineering – band gap renormalization E

c) Coulomb engineering – modified exciton binding energy EB

d) Modification of charge carrier density n (Fermi energy work function)

d) Raman: n

ΔEA= 1.9 cm-1

Δn - 8.0*1012 cm-2

ΔEF -38 meV

d) KPFM: work function EWf

ΔEWf -130 meV

4.77 eV 4.90 eV 4.85 eV

for plasmonic structure

(E) strongly dependent

on excitation energy and

so does confinement

b) Reduction of single

particle band gap:

ΔEgap -92 meV

b) Absorbance: optical band gap

ΔEop -115 meV

c) Increase of A exciton

binding energy:

ΔEB 23 meV

Confinement:

QW with different barriers

air

s= 1

s

d < 1 nm

Au-NP

thiols

Al2O3

S. Diefenbach, UW et al. arXiv (2017)B, Miller, UW et al. Appl. Phys. Lett. 106, 122103 (2015)

Acknowledgement

Prof. Holleitner

Eric Parzinger

Bastian Miller

Sandra Diefenbach

Fabian Merbeler

Jonas Kiemle

Collaborators:

Sebastian Funke (Accurion GmbH)

PD Dr. Peter Thiesen (Accurion GmnH)Prof. Alexander Holleitner

All members of the Holleitner group

Anisotropic dielectric tensor

Exciton dominated absorbance

Summary: Light matter interaction in 2D materials

Spectroscopic Ellipsometry on terraces

Multiple interaction in MoS2/Au-NP hybrid

1.5 2.0 2.5 3.0 3.5 4.0 4.50

2

4

6

8

10

12

14

16

D

exciton

C

exciton

A B

exciton

ab

so

rba

nce

(%

)

Energy (eV)