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)