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Nano Res.
Electronic Supplementary Material
Electronic structure, optical properties, and lattice
dynamics in atomically thin indium selenide flakes
Juan F. Sánchez-Royo1 (), Guillermo Muñoz-Matutano1,†, Mauro Brotons-Gisbert1, Juan P. MartínezPastor1 (), Alfredo Segura1,2, Andrés Cantarero1, Rafael Mata1, Josep Canet-Ferrer1, Gerard Tobias3,
Enric Canadell3, Jose Marqués-Hueso4, and Brian D. Gerardot4
1
ICMUV, Instituto de Ciencia de Materiales, Universidad de Valencia, P.O. Box 22085, 46071 Valencia, Spain
MALTA-Consolider Team, Institut de Ciència dels Materials-Dpto. de Física Aplicada, Universitat de València, E-46100 Burjassot
(València), Spain
3
Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus de la UAB, 08193 Bellaterra, Barcelona, Spain
4
Institute of Photonics and Quantum Science, SUPA, Heriot-Watt University, Edinburgh EH14 4AS, UK
†
Present address: Optics and Quantum Communications group, ITEAM, UPV, Valencia, Spain
2
Supporting information to DOI 10.1007/s12274-014-0516-x
1
Identification of thin InSe films by optical microscopy
Optical microscopy has been reported to be a simple, quantitative and universal way to locate and identify the
thickness of 2D materials such as graphene [3, S1–S3] and semiconducting transition metal dichalcogenides
such as MoS2, WSe2 or NbSe2 deposited on SiO2/Si wafers [S4, S5]. For a certain thickness of SiO2, it has been
found that even a single layer of these materials can give sufficient, albeit feeble, contrast to allow a successful
identification of a few micron-sized crystallites among thicker flakes scattered around them.
We have calculated the contrast of few InSe single layers exfoliated onto SiO2/Si substrates as a function of
the illumination wavelength and the SiO2 thickness, in order to determine the optimal imaging conditions for
their optical detection. By analogy with graphene and dichalcogenides [S2–S5], the contrast between the InSe
flakes and the underlying SiO2 substrate is due to a phase shift of the interference color and material opacity. In
order to calculate this contrast, we consider the stacking of two thin films (the InSe nanolayer and the SiO2 layer
underneath) on top of a third semi-infinite Si film (Fig. S1). The InSe nanolayer is modeled by a thin homogeneous
film of thickness d1 = N × d, with N the number of InSe monolayers and d = 0.8 nm the thickness of a single InSe
single layer. For these calculations, flakes containing one-to-five InSe monolayers were assumed to have the
same optical properties, characterized by a real refractive index ñ1=2.5 [24, S6]. The SiO2 layer of thickness d2 is
optically characterized by a wavelength-dependent real refractive index ñ2(λ) [S7], ranging from 1.47 at 400 nm
to 1.455 at 700 nm. We have considered a semi-infinite silicon substrate underneath, with a wavelengthdependent complex refractive index ñ3 [S7]. Under normal light incidence, the intensity of reflected light from
the stacking of two thin films on top of a semi-infinite layer can be calculated by the Fresnel Eq. [S2, S8]
Address correspondence to Juan F. Sánchez-Royo, [email protected]; Juan P. Martínez-Pastor, [email protected]
Nano Res.
R  n 1  
Where rij 
n i  n j
n i  n j
r01e i (1 2 )  r12 e  i(1 2 )  r23 e  i(1 2 )  r01r12 r23 e i(1 2 )
2
(S1)
e i(1 2 )  r01r12 e  i(1 2 )  r01r23 e  i(1 2 )  r12 r23 e i(1 2 )
are the relative indices of refraction of the different interfaces, i 
2 di n i

are the phase shift
induced by changes in the optical path and ñ0, ñ1, ñ2 and ñ3 are the refractive indices of air, InSe, SiO2, and Si,
respectively. On the other hand, the reflected light intensity in the absence of an InSe flake can be found by
substituting ñ1 = 1 in Eq. (S1)
Figure S1 Scheme of the geometry considered in the theoretical contrast calculations. It is composed of an InSe nanolayer with
thickness d1 and complex index of refraction ñ1. The nanolayer is deposited on a SiO2 layer characterized by thickness d2 and index of
refraction ñ2 that is grown on top of a degenerately doped Si substrate characterized by an index of refraction ñ3.
R  n 1  1 
where r02 
r02 e i(2 )  r23 e  i(2 )
2
e i(2 )  r02 r23 e  i(2 )
(S2)
n 0  n 2
is the relative index of refraction at the interface between air and the dielectric thin film.
n 0  n 2
Therefore, the contrast, as defined as the relative intensity of reflected light in the presence and absence of the
InSe flake, can be written as
Contrast 
R  n 1  1  R  n 1 
R  n 1  1
(S3)
Figure S2 shows the theoretically calculated contrast of (a) a single InSe monolayer and (b) three InSe single
layers (one hexagonal-unit-cell thick) as a function of the incident light wavelength and SiO2 thickness. For both
cases, the contrast for visible light wavelengths exhibits three characteristic bands with high, positive contrast
and three bands with high, negative contrast. As can be seen from this figure, these high contrast bands are
more intense in the case of the three InSe monolayers calculations. Despite of this, if the excitation wavelength
and the SiO2 thickness are properly chosen, the contrast of the single InSe monolayer is large enough to detect
it. Under green illumination and with the widely used 300 nm SiO2 substrates, it is possible to obtain contrast
values around 0.1, which is higher than the contrast of 0.08 obtained for a single graphene monolayer using the
same criteria [S3].
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Figure S2 Color plot of calculated contrast as a function of incident light wavelength and SiO2 layer thickness for (a) an InSe
monolayer and (b) three InSe monolayers (one unit cell thick). Both plots have been drawn in the same contrast scale.
Figure S3 gives the calculated contrast spectra of InSe samples with different thicknesses (from one to five
single layers) on SiO2 (300 nm)/Si substrates under normal incident light based on the Fresnel equation (Eqs.
(S1)–(S3)). As can be seen from this figure, the absolute contrast value increased as the number of layers increased,
which made unambiguous identification of the thickness of InSe possible.
Figure S3 Contrast of InSe flakes with different thicknesses (one, two, three, four and five monolayers) on SiO2 (300 nm)/Si substrates
calculated under normal incidence based on the Fresnel equation.
2
Photoluminescence in bulk InSe
In the PL spectrum recorded in the bulk sample (Fig. S4) on a backscattering geometry (standard lens, no
confocal), we observe several contributions that we split in two groups.
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Figure S4 PL spectrum measured in a bulk InSe sample. Deconvolution of this spectrum has resulted into five Gaussian components,
which have been included.
In the first group, we consider three high energy and narrow peaks (3–9 meV) at 1.337, 1.329, and 1.319 eV.
The origin of these PL lines in either not purposely or slightly doped InSe has not been a subject of intensive
research and the authors that studied this semiconductor attributed them to free and different donor bound
excitons [45, 47, 51, S9]. On the other hand, native donors in not purposely doped InSe (always n-type) are due
to In in excess that can give rise to shallow donor levels if incorporated in interstitial sites of the bulk lattice, but
also to deep levels when they are presumably located in intralayer sites [50]; in fact most of these impurities can
be promoted to interstitial sites (shallow donors) after annealing. The ionization energy of shallow donor levels
was found to be 24 meV and hence the line at 1.319 eV (1.35 eV would be the InSe bandgap energy at low
temperatures) [26] can be reasonably assigned to the h–D0 and D+X (D0 and D+ associated to shallow donors)
transitions.
In a second group of peaks, we detect a relatively wide PL band (21 meV wide) at 1.310 meV that could be
related to h–D0 transitions, either shallow (because of its overlapping with the narrower line at 1.319 eV) and
deeper donor levels at inter-layer sites. Given the random nature of the spatial position for these inter-layer
impurities, the donor binding energy can vary over a wide range of values. Such energy distribution of donor
levels can be responsible of this PL band at 1.310 eV and its low energy tail (simulated by using a wide
Gaussian band at around 1.288 eV).
3
Micro-photoluminescence in thick InSe flakes
The -PL spectra shown below were acquired in a bulk-like (12 nm) InSe flake, as a function of excitation power
(Fig. S5(a)) and temperature (Fig. S6(a)). The -PL spectra shown in Fig. S5(a) are characterized by recombination
times between 5 and 9 ns (Fig. S5(b)) depending on the detection wavelength where the PL transient is measured.
By increasing power, the high energy PL tail grows in importance. In addition to this, the recombination time
and the -PL intensity decrease as temperature increases (Figs. S6(a) and S6(b)). All these facts point to the
impurity-related origin of the -PL signal measured in the flakes at low temperatures.
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Figure S5 (a) Low-temperature -PL spectra measured in a bulk-like ~12 nm thick InSe flake, at two different excitation-power values.
(b) -PL decay curves obtained at three different energy positions in the -PL spectrum of (a) measured with P = 23.8 W. Decay curve
at the top (bottom) was measured at the low (high) energy side of the -PL spectrum. Decay times are indicated.
Figure S6 (a) -PL spectra and (b) -PL decay curves measured in a bulk-like ~12 nm thick InSe flake with P = 23.8 W, at different
temperatures. Decay times are indicated.
4
Micro-photoluminescence in single-terraced InSe flakes
The -PL spectra shown below were acquired in bulk-like InSe flakes (1- and 4-labelled flakes) and in singleterraced, 8 nm-thick, flakes (2- and 5-labelled flakes). The -PL spectra of the bulk-like flakes are very similar to
that measured in the thickest terraces of the flake shown in the Fig. 3 of the main text. The line shape of the
-PL spectra measured in the 8 nm-thick flakes seems to depend on the flake studied: The -PL spectra acquired
in the 2- and 5-flakes show a wider or narrower lineshape, respectively, than that obtained for the d-labelled
terrace (8 nm-thick) of the flake shown in Fig. 3. In all cases, deconvolution of the -PL spectrum can be performed
by taking into account some of the six P1–P6 components (see the main text).
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Figure S7 Left plots are optical images of single-terraced InSe flakes. Thickness of the selected flakes 1–5 was determined by AFM.
Right plots show the -PL spectra recorded in the 2- and 5-flakes, 8 nm-thick, and in bulk-like terraces joined to these thin flakes. The
results of the deconvolution of the -PL spectrum measured in the 8 nm-thick flakes are shown. Note that the peaks obtained from this
deconvolution have been represented using the same color-code as that used in Fig. 3.
Taking into account these results, the following facts can be noted:
(i) The presence of the P1–P6 components is a common signature of all the low-temperature -PL spectra
recorded in the thin InSe flakes, which supports the physical origin of each one of the P1–P6 components
discussed in the main text.
(ii) The -PL spectra obtained in terraces with similar thickness can be deconvoluted into P1–P6 components
whose relative intensities appear to differ from flake to flake. This can be understood on the basis of the hypothesis
stated in the main text on the unidirectional diffusion of photogenerated carriers from thicker to thinner flakes.
This hyphothesis states that the -PL spectrum lineshape is strongly determined by the characteristics (i.e.,
thicknesses variations) of the flake edge. In fact, the fact 5-flake has a sharper flake-edge than the 2-flake, as can
be appreciated in the images in Fig. S7, which would explain the differences observed between the lineshapes
of the -PL spectra recorded in these flakes.
Finally, it must be noticed that no -PL signal was recorded when very thin flakes of uniform thickness were
probed, as the 3-labeled flake (3 nm-thick) shown in Fig. S7. This behavior contrasts to that observed in terraces
of similar thicknesses which are part of multi-terraced flakes (as the f-labeled terrace of the flake of Fig. 3). At
this point, it is worth to mention that this observation applies to very thin flakes (already 5-nm thick singleterraced flakes gave rise to -PL signal, when probed). We believe that this observation is a clear consequence
of the unidirectional diffusion of photogenerated carriers in multi-terraced flakes: In very thin flakes of uniform
thickness, photogenerated carriers isotropically diffuse before recombination. However, in multiterraced flakes,
the carriers tend to diffuse towards the flake edge. Comparing these two situations, surface recombination will
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tend to play a more determinant role in flakes of uniform thickness. Therefore, the -PL signal intensity coming
from these uniform flakes will suffer from a strong attenuation due to the fact that surface recombination is
mainly determined by non-radiative processes, as surface defects or SiO2/InSe interface traps.
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