Nano Res

1

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.

Martínez-Pastor1 (), Alfredo Segura1,2, Andrés Cantarero1, Rafael Mata1, Josep Canet-Ferrer1, Gerard

Tobias3, Enric Canadell3, Jose Marqués-Hueso4, and Brian D. Gerardot4

Nano Res., Just Accepted Manuscript • DOI 10.1007/s12274-014-0516-x

http://www.thenanoresearch.com on June 15, 2014

© Tsinghua University Press 2014

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Nano Research

DOI 10.1007/s12274-014-0516-x

1

Electronic structure, optical properties, and

lattice dynamics in atomically thin Indium

Selenide flakes

J. F. Sánchez-Royo1,*, G. Muñoz-Matutano1, M.

Brotons-Gisbert1, J.P. Martínez-Pastor1,*, A. Segura1,

A. Cantarero1, R. Mata1, J.Canet-Ferrer1, G. Tobias2,

E. Canadell2, J. Marqués-Hueso3, and B.D. Gerardot3

1Universidad de Valencia, Spain.

2Institut de Ciència de Materials de Barcelona

(ICMAB-CSIC), Spain.

4Heriot-Watt University, UK.

Summary of the work:

We show that quantum size confinement tunes the

dimensionality of the lattice dynamics, optical and

electronic properties of atomically thin InSe flakes

prepared by micromechanical cleavage. Reported results

are promising from the point of view of the versatility of

this material for optoelectronic applications

Authors’ website:.

J.F.S.R.,www.uv.es/lowdim

J.P.M.P., http://www.uv.es/umdo

2

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. Martínez-Pastor1 (), 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. 2 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.

Received: day month year / Revised: day month year / Accepted: day month year (automatically inserted by the publisher)

© Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2011

ABSTRACT The progressive stacking of chalcogenide single layers gives rise to two-dimensional semiconducting

materials with tunable properties that can be exploited for new field-effect transistors and photonic devices.

Yet the properties of some members of the chalcogenide family remain unexplored. Indium selenide (InSe) is

attractive for applications due to its direct bandgap in the near infrared, controllable p- and n-type doping

and high chemical stability. Here, we reveal the lattice dynamics, optical and electronic properties of

atomically thin InSe flakes prepared by micro-mechanical cleavage. Raman active modes stiffen or soften in

the flakes depending on which electronic bonds are excited. A progressive blue-shift of the

photoluminescence peaks is observed for decreasing flake thickness (as large as 0.2 eV for three single-layers).

First principles calculations predict an even stronger increase of the bandgap, 0.40 eV, for three single layers,

and as much as 1.1 eV for a single layer. These results are promising from the point of view of the versatility

of this material for optoelectronic applications at the nanometer scale and compatible with Si and III-V

technologies.

KEYWORDS

Indium selenide, two-dimensional flakes, micro-Raman spectroscopy, Micro-Photoluminescence, Electronic

structure.

Nano Res DOI (automatically inserted by the publisher)

Research Article

————————————

Address correspondence to Juan F. Sánchez-Royo, Juan.F.Sanchez@uv.es; Juan P. Martínez-Pastor, Juan.Mtnez.Pastor@uv.es

3

1 Introduction

The difficulties found to create semiconducting

graphene [1,2], while still maintaining the

extraordinary properties of semimetallic graphene

[3,4], constitute a major obstacle for the realization of

field effect transistors and functional junctions for

optoelectronics based on truly two-dimensional (2D)

materials. This has partly promoted increasing

research on layered dichalcogenide semiconductors

[5,6] that takes advantage of the weak interlayer

interactions to isolate, by graphene-like exfoliation

[7-10] or other techniques [11-13], either single or few

semiconducting layers. Particular optical properties

of these layers, different from the bulk, have already

been exploited in the first optoelectronic devices

already prepared, given their promising applications

in valleytronics and spintronics [14-16]. Bulk Mo and

W dichalcogenides (MoS2, MoSe2, WS2, and WSe2)

are indirect semiconductors, but single layers have a

direct character and become strongly

photoluminescent [17-19]. They have enabled the

realization of high-performance electric field effect

transistors [8-11] and photodetectors [20,21].

Bearing in mind these perspectives, it is not

surprising that research on 2D semiconductors

started to spread over other chalcogenides. In this

sense, much less is known about properties and

potential applications that layered III-VI

chalcogenides, such as GaSe and InSe, may have

when these semiconductors are reduced to the

nanoscale. Bulk GaSe is a relatively wide bandgap

semiconductor (~2.05 eV at room temperature [22])

that previously attracted some interest due to its

non-linear optical properties [23-25]. Bulk InSe is a

direct bandgap semiconductor (~1.25 eV at room

temperature [26]) that is appealing due to its optical

properties [23,24], the changes of its electronic

structure under pressure [27,28], the possibility of

preparing high-quality thin films [29], the

application of InSe for Li-batteries [30], and

photovoltaic devices that reached an efficiency of

11% [31]. Among these III-VI semiconductors, thin

GaSe platelets have been the first to show a

size-related blue-shift of the absorption edge that,

starting at ~2.0 eV in the bulk, enters into the UV for

a single layer [32]. The first potential applications of

few layer GaSe flakes seem to follow the path set out

by other layered chalcogenides. Mechanically

exfoliated GaSe [33] and InSe [34] flakes have been

successfully used as photodetectors with

outstanding responsivity and quantum efficiency.

Also, high-performance field effect transistors based

on single layers of GaSe have been fabricated [35].

Very recently, a 0.2 eV blue-shift in the absorption

edge due to confinement effects was observed in

mechanically exfoliated InSe flakes [36]. This

blue-shift with decreasing flake thickness was

accompanied with a sharply decreasing

photoluminescence (PL), which was attributed to a

direct-to-indirect bandgap crossover [36].

While initial results on InSe flakes are quite

promising, a further extension of experimental

results to even thinner films and theoretical support

are required to understand in detail how

confinement effects alter the electronic, vibrational,

and optical properties of the flakes. In the present

paper we corroborate the findings reported in Ref.

[36] regarding the significant blue-shift of the

absorption band edge by using confocal micro-PL

(-PL) measurements at 4 K on atomically thin InSe

flakes. We also observe a strong decrease of the PL

signal. These results are supported by our

first-principles calculations of the electronic structure

on strictly 2D InSe and on InSe flakes until ten single

layers thick. The 2D material, as the bulk, shows a

direct character of the bandgap, however, thin flakes

with thickness ranging between two and ten layers

thick show an indirect character with a valence band

maximum located only 15 meV above valence band

states at the -point, where the minimum of the

conduction band appears. The rather flat

valence-band dispersion around the -point in these

indirect flakes makes that electrons can easily be

transferred between energetically near states with a

small amount of thermal energy. These results

indicate that the observed strong decrease of the PL

signal is mainly related to the enhancement of

non-radiative recombination processes in the thin

flakes rather than to the evoked direct-to-indirect

4

bandgap crossover [36]. Our first-principles

calculations also demonstrate that states defining the

bandgap in the flakes and bulk have the same orbital

origin, predicting a bandgap increase of 1.14 eV and

0.4 eV for single and triple layer (TL) flakes,

respectively. Furthermore, we have carried out

Raman micro-spectroscopy at room temperature on

InSe flakes as thin as one TL. In contrast to previous

results reported [36], we achieve to observe a shift of

the InSe Raman modes in ultrathin flakes, whose

sign depends of the excited vibration mode. These

results evidence an electronic charge rearrangement

occurring in these flakes that, according to

first-principles calculations, strengthen Se-In bonds

in the detriment of In-In bonds.

2 Results and discussion

2.1 Structure and morphology of the InSe flakes

Figure 1 shows the atomic structure of the

semiconductor and an example of flakes obtained

by mechanical exfoliation. A single layer of InSe

(Fig. 1(a)) consists of four monoatomic sheets of

hexagonally arranged atoms tetrahedrally linked in

the sequence Se-In-In-Se via covalent bonds. In bulk,

these individual InSe layers are held together by

van der Waals forces, following a stacking sequence

in which the projection of the Se atoms of one layer

lies at the center of the triangle defined by the Se

atoms of the next layer. Among the different

polytypes permitted by this stacking sequence, InSe

crystallizes, at ambient conditions, in a

rhombohedral layered phase (InSe-I) -known as

-polytype- which belongs to the space group R3m.

The hexagonal non-primitive cell of the -polytype

is formed by a TL stack whose lattice parameters

are c=24.946 Å and a=b=4.002 Å [37]. The layered

structure of InSe favors the preparation of

atomically thin flakes by mechanical exfoliation as

shown in Fig. 1(b). As in graphene flakes prepared

on SiO2/Si substrates [3], the variation of the optical

contrast in a microscope image under visible

illumination can be related to nanometric changes

in the thickness of the InSe flake (see Figs. S1-S3 in

the Electronic Supplementary Material (ESM)),

which indicates that the flake of Fig. 1(b) is

exhibiting a multi-terrace thickness with the

thinnest parts of the flake being the most

translucent ones. Atomic force microscopy (AFM)

results (Figure 1(c)) show that the flake is formed by

wide terraces of uniform thickness ranging between

2.5 and 12 nm (1 and 5 TL, respectively), which can

be univocally identified with the color-contrast

areas observed in the optical image.

2.2 Vibrational properties

As -InSe belongs to the R3m space group with four

atoms per primitive unit cell, there are twelve normal

modes of vibration. Group-theoretical considerations

[38] lead to decomposition at the point as 4A1+4E.

Apart from the acoustic ones (A1+E) all modes are

Raman and infrared active, but with very different

Figure 1 (a) Crystal structure of -InSe, in which the axes of

the hexagonal unit cell are plotted. The corresponding

hexagonal Brillouin zone has also been included. (b) Optical

image of a multi-terraced InSe flake exfoliated onto a SiO2/Si

substrate. Each color areas of the image can be associated to a

single terrace. (c) AFM image of the InSe flake. The thickness

profile measured along the marked ABCD path is shown at the

bottom of the image. For the sake of clarity we have indicated,

in this plot, the height expected for the stacking of single -and

triple- layers of InSe by horizontal dashed lines.

5

relative intensities. Two of them (A1+E) are strongly

polar and, consequently, more active in infrared,

developing a TO-LO splitting. Reported bulk-InSe

Raman spectra exhibit modes whose frequency,

symmetry, and vibration schemes are shown in Fig.

2(a) [39]. All these vibrational modes can be

recognized in the measured Raman of Fig. 2(b),

which were registered in a thick flake and in

different points of the multi-terrace flake (labeled

spots in the image inset of Fig. 2(b)). Raman

scattering intensity can be enhanced by using the

excitation laser photon energy resonant with the E’1

direct allowed transition at 2.4 eV in bulk InSe

[25,39,40]. Consequently, Raman peaks appear over a

PL tail associated to this optical transition, whose

intensity progressively decreases as the thickness of

the probed terrace becomes thinner. This is an

important observation since it is a clear indication of

the blue-shift of direct band-to-band optical

transitions. Furthermore, variations in the

asymmetry degree of the 175 cm-1 E mode (panel I in

Fig. 2(b)) and the strong decrease in intensity of the

second order Raman peaks (panel II in Fig. 2(b)),

from bulk-like to thin flakes, are also indicative of

the loss of resonance in the thinnest parts of the flake

[39].

In addition to the electronic blue-shift inferred from

E’1-resonant Raman spectra, the thickness reduction

of a flake also affects its lattice dynamics, as revealed

by the shift of the different phonon frequencies

observed with respect to the bulk (Fig. 2(c)). As the

flake thickness reduces, the frequency of non-polar

A1 modes slightly decreases while that of non-polar

E and polar A1(LO) modes increases significantly.

This shift of the phonon modes as flakes thickness

decreases becomes more evident in very thin flakes

(<10 nm), which would explain why this effect has

not been detected in a previous work reporting

Raman spectroscopy results on InSe thin flakes [34].

In order to understand the results showed in Fig. 2(c),

we have assessed the evolution of the different bond

strengths with the number of layers by calculating

the so-called Mulliken [41,42] bond overlap

populations for bulk -InSe and its single layer.

Intralayer In-Se and In-In bonds are strong covalent

bonds, while interlayer bonding is due to weaker van

der Waals interactions. For both InSe bulk and single

layer, we have estimated the bonding strength in two

spatial regions in which the interlayer electronic

density reaches its maximum: the line between

closest Se atoms from adjacent layers and the line

from an In atom in one layer and the nearest Se atom

in the adjacent layer (Table I). The In-Se bonds are

stronger in the single layer than in bulk InSe,

whereas the opposite is found for In-In bonds. Of

course, the interlayer interactions weaken and finally

disappear when going from the bulk to the single

layer. The relative variations of the In-Se and In-In

bond overlap populations due to the presence of

other layers is around 3% of the strength of a full

covalent bond. Although apparently small, these

overlap population changes would give rise to a

relative variation around 2% for the natural

frequency of a single oscillator, which would already

account for the magnitude of the observed relative

shift of the Raman peaks. In any case, it must be

outlined that our calculations have been performed

using exactly the same atomic geometries in all cases,

so the estimated changes of the bond overlap

population only contain purely electronic effects that

would be subsequently magnified upon structural

optimization, similar to what happens for other

layered materials [43].

From these estimates we can expect that those

phonon modes in which the In-Se bonds play an

important role (due to bond stretching in the

vibration scheme of Fig. 2(a)) should exhibit a

frequency increase in an isolated single layer: this is

Table 1 DFT bond overlap populations calculated for bulk and

one single layer of InSe.

Bond Intralayer Interlayer

In-Se In-In In-Se Se-Se

Bulk 0.313 0.315 0.019 0.004

Single layer 0.324 0.303 0 0

6

indeed the case of the non-polar E (175 cm-1) and

polar A1(LO) phonons. In low frequency phonons E

(40 cm-1) and A1 (114 cm-1), the In-Se bond does not

play a significant role (covalently bonded In and Se

vibrate in phase) so that restoring forces are mainly

guaranteed by interlayer interactions and by either

In-In bond bending (E) or stretching (A1). Then, the

disappearance of interlayer interactions and the

weakening of the In-In bond are consistent with the

frequency decrease of the low frequency phonons

observed when going from bulk to single layer. In

the case of the non-polar A1 mode at 225 cm-1 all

bonds provide restorative stretching force and its

frequency decrease can be explained by the fact that

the disappearance of interlayer forces and the (larger)

weakening of In-In bonds overcompensate the

strengthening of In-Se bonds.

2.3 Optical properties

Raman spectroscopy results revealed a blue-shift of

the direct transition E’1 connecting deep px-py valence

band states with conduction band states [25,38,39].

As these valence band states are rather localized in

the layer plane, the observed blue-shift should be a

consequence of the upshift of the conduction band as

the flake thickness decreases. A deeper analysis of

the confinement effects on the electronic properties

of InSe flakes can be performed by -PL techniques,

as reported for other layered materials

[5,13,17,18,44,45]. In bulk InSe, the low-temperature

PL signal is dominated by exciton and

impurity-related radiative recombination [46,47]. In

InSe flakes, hD0 recombination channels seem to

dominate over bound exciton recombination, as

Figure 2 (a) Vibrational structure of the detected first-order Raman active modes. (b) Left panel: Micro-Raman spectra measured under

bulk resonant conditions in the different terraces of the InSe flake labeled from a to g in the inserted image. The thickness of the probed

flake terrace is indicated on each Raman spectrum. The identified vibration modes have been labeled. Vertical dashed bars correspond

to the position that these vibration modes have in the bulk. We have included the spectrum measured in a bulk sample. We have

checked that the position of the SiO2-related Raman peak appears at 518 cm-1 in all acquired spectra. Panels I and II are zooms of the

corresponding marked-color areas in the main figure. For the sake of comparison, the photoluminescence tail has been subtracted in the

spectra shown in these two color-panels. The Raman peaks were fitted by a single Lorentzian curve (two in the case of the E mode at

175 cm-1 to account for its asymmetric line-shape). (c) Thickness-flake dependence of the relative frequency shift of the Raman modes

(with respect to bulk frequency) as obtained by Lorentzian fitting of the measured Raman peaks.

7

suggested by the comparison between the -PL

spectra measured at the thickest terrace (12 nm thick

terrace, marked as a-point in the image inset of Fig.

3(a)) and the bulk sample (Fig. S4 in the ESM). This

assignment is also supported by the analysis of the

-PL transient measured in thick InSe flakes (Figs.

S5-S6 in the ESM). Figure 3(a) shows the -PL spectra

measured at T = 4 K in the different terraces of the

flake corresponding to the points labeled from a to f

on the image at the inset. As aforementioned, hD0

transition dominates the -PL band recorded at

a-point and hence matches the low-energy tail of the

bulk PL [47]. As the collection spot moves close to

the next terrace, b-point, new components appear

towards the high-energy side of the -PL spectrum,

with the highest energy one (at 1.35 eV) clearly

separated from the main feature observed at lower

energies and located above the free-exciton

recombination line in bulk (at 1.337 eV) [47]. As the

collection spot travels to next thinner sections of the

flake (points c to f), the whole -PL spectrum shifts

undoubtedly to the blue (Figure 3(a)) with a

Figure 3 (a) Low temperature -PL spectra measured in the different terraces of the InSe flake labeled from a to f in the image at the

top. The thickness of the probed flake terrace is indicated on each PL spectrum. Solid red lines are the result of the fitting to the

experimental spectra by using several Gaussian curves of the same width. Deconvolution of the fitting curves into their single Gaussian

components is shown under each PL spectrum. A Color-code has been used to identify similar Gaussian components that result from

the deconvolution of the different PL spectra acquired. Note that the spectra measured in the 5 and 2 nm-thick terraces have been

magnified. (b) The left panel shows the maximum energy of the six different Gaussian components (labeled as from P1 to P6 as

increasing in energy) which have been found to conform to the measured PL spectra. The right panel shows the intensity of these fitted

Gaussian components. These two panels are plotted as a function of the spot position. The color and symbol codes have been

maintained in all plots included in (a) and (b). (c) Black circles: Maximum energy of Gaussian components as a function of the inverse

square of the assigned number of InSe layers. Red dashed line: Predicted bandgap of an InSe flake as a function of the number of

layers, as given by the effective mass model. White open circles: bandgap of InSe flakes as a function of the number of layers, as

predicted by first-principles band structure calculations. Blue triangles: experimental data extracted from Ref. [36].

8

lineshape that depends on the terrace scanned. At

the same time, the -PL spectra measured at these

points of the flake experience a strong decrease in

intensity, whose origin is not completely clear from

an experimental point of view and some hypothesis

will be proposed afterwards.

These results indicate the -PL signal shifts to the

blue, as the terrace thickness decreases, due to the

progressive development of higher energy

components that become dominant at the

consecutive thin parts of the flake. In order to get

insight into the analysis of these -PL spectra, a

multi-Gaussian deconvolution has been performed

by assuming all the discrete -PL components have

the same line width. Proceeding in this way, a

minimum number of six components, labeled as

P1-P6 (Figures 3(a) and 3(b)), have been found to

reproduce all -PL spectra acquired. These -PL

components are thus associated to the decreasing

thickness of the terraces from a to f points as

originated from quantum confinement effects.

Notably, multi-component -PL spectra are detected

across the flake, even when the collection spot

probes a unique flake terrace, as shown and

indicated in Figs. 3(a) and 3(b) (left panel),

respectively. In the -PL measurements the excitation

area is much larger than the collection spot (see

Experimental methods subsection), suggesting that

the multi-component -PL spectra are due to carriers

photo-excited in a particular point of the flake

drifting and recombining at the edges of the terrace.

We also observe an extremely sharp decrease of the

integrated intensity of P1-P6 components (right

panel in Figure 3(b)), which contrasts to the expected

linear trend for such thin layers. This would suggest

an enhancement of the influence of non-radiative

surface carrier recombination processes as the

thickness decreases. However, a larger density of

traps or surface defects in the thinner terraces is

rather unexpected on the basis that the surfaces of

the different terraces of the flake have suffered the

same history. -PL intensity maps measured at room

temperature (Fig. 1 in Ref. [36]) reflect an

inhomogeneous intensity distribution, accumulated

towards the edges of the terraces, which would be

expected to become more pronounced at low

temperatures (due to the higher mobility of carriers)

and in thinner terraces (due to the unavoidable

existence of recombination traps at the surface of the

SiO2 substrate underneath). Therefore, the behavior

of the -PL intensity observed in Fig. 3(b) points out,

again, that radiative recombination tends to occur at

the edge of the terraces (see also Fig. S7 in the ESM)).

All these remarks can be understood taking into

account that, really, multi-terrace InSe flakes are

expected to behave as a planar array of

heterojunctions formed by semiconductors with

different bandgap values and diffusion length of

carriers as large as that of the bulk [48]. In such

devices, photo-excited carriers in thinner terraces

(with larger band gap values due to strong

confinement effects) diffuse and recombine at the

terrace edge, whereas carriers excited in the thicker

terraces would eventually recombine further inside

neighboring terraces of lesser thickness, provided

that confinement effects are soft enough in these

thick terraces to allow lateral coupling of electronic

states at their edges. This picture would also explain

the lack of -PL signal observed in isolated very thin

flakes (2-4 nm thick) of uniform thickness (Fig. S7 in

the ESM): In these very thin flakes, mechanisms

evoked above to promote diffusion of photo-excited

carriers towards the flake edge are no longer acting

(no planar array of heterojunctions there exists).

Under these assumptions isotropic diffusion would

favor surface recombination, which is dominated by

non-radiative processes (as recombination at surface

defects and/or traps at the SiO2 substrate).

2.4 Electronic properties

The present results offer a remarkable opportunity to

study how the progressive enhancement of quantum

size confinement can strongly tune the electronic

properties of these atomically thick semiconductor

flakes. The hypothesis made above to assign each

-PL component to a flake thickness value would not

be straightforward, but the limited number of

thickness steps in the flake (Figure 1(c)) allows for a

reliable assignment. On the assumption that the

9

highest energy component corresponds to the

thinnest part of the flake (1 TL), the assignment

sequence of the P1-P6 components will be 12 (4 TL),

10, 8, 6 (2 TL), 4 and 3 (1 TL) single layers,

respectively. This assignment would tell us that the

recombination energy of impurity-related states

increases by 0.2 eV when the flake becomes as thin as

1 TL (Figure 3(c)).

An effective mass model assuming the flake as a

quantum well with infinite potential barriers of

electronic confinement (Figure 3(c)) approximately

reproduces the already reported PL results at room

temperature in flakes thicker than few TL [36] and

-PL peak energies obtained at the thicker flakes

studied in this work. However, the 1/N2 dependence

(N is the number of single layers) expected from this

simple model fails to explain results in the thinnest

flakes. On the one hand, a more refined study of the

confinement effect on the electronic properties of the

flakes is necessary in order to quantitatively

understand experimental results beyond the effective

mass model. On the other hand, the band structure

calculation based on first-principles as a function of

the number of InSe single layers is the basis to

understand future works on optical properties of

flakes prepared with this material.

First-principles band structures calculated for bulk

-InSe and flakes containing eight, four, and one InSe

single layers are shown in Fig. 4 (calculations were

carried out for one to ten single layers). For ease of

comparison, the band structure of bulk -InSe has

been represented in the Brillouin zone of the

hexagonal unit cell (Figure 1(a)) instead of the

rhombohedral one. Note that in the band structures

of Figure 4(b)-(d) the A direction has no meaning,

and that band diagrams in the -M-K and A-L-H

Figure 4 DFT band structure calculated for (a) bulk -InSe and for (b)-(d) 8, 4, and 1 single InSe layers, respectively, through high

symmetry directions of the hexagonal Brillouin zone (Figure 1(a)). In all cases, the energy zero has been placed at the top of the highest

occupied band. The bandgap has been identified in the plots by a green shaded area.

10

planes are identical since the strongly dispersing

three-dimensional bands of the bulk become a series

of N 2D bands (N=8,4,1 in Figure 4(b)-(d),

respectively). The anisotropic character of bulk

-InSe band structure is mainly reflected in the

strong difference between bands with Se px-py orbital

character, with no dispersion along the A direction,

and those with mainly Se pz, In pz and In s character,

that exhibit strong dispersion along the A direction.

The latter bands form the uppermost valence band,

with nonbonding Se pz character, and the lowermost

conduction band, with mainly antibonding In s

character. The main orbital character of these bulk

bands does not change in the flakes. In fact, note that

the upper filled and lower empty bands of the bulk,

i.e. those in the A-L-H plane of the Brillouin zone,

have the same shape as the upper valence and lower

conduction bands of the flakes with the only

difference of the progressive reduction of the flat

region around in the upper filled band. This is in

contrast to observations in flakes based on layered

transition-metal dichalcogenides, in which the

orbital origin of states defining the bandgap differs

from the bulk [17,18,44,45,49]. It is also relevant to

notice that single layer InSe is a direct semiconductor

(Figure 4(d)). However, in few layer InSe (Figure

4(a)-(c)), the valence band maximum occurs slightly

away from the point, at 1/10 of the K and M

directions, and around 15 meV above the point

energy. This change is related to the ring-shaped

valence band maximum emerging in bulk InSe under

pressure, which has been shown to contribute to the

quenching of the exciton absorption peak [27] but

has little effect on the intrinsic photoluminescence

[50]. It seems unlikely that this change in the valence

band maximum is responsible for the PL quenching

observed in Ref. [36], because the energy difference

with respect to is one half of the thermal energy at

room temperature.

Since the most visible effect of confinement on the

bulk electronic band structure occurs for the valence

and conduction bands, density functional theory

(DFT) calculations predict a bandgap increase in the

flakes which can be as high as 0.40 eV for one TL and

1.14 eV for a single layer, with respect to the bulk.

Figure 3(c) includes the results of these calculations,

using as a reference the value of the bulk bandgap at

1.35 eV at low temperatures [26] (note that DFT

calculations usually underestimate absolute bandgap

values). The hD0 recombination and the calculated

bandgap energies seem to follow a quite similar

trend with the thickness (fast increase for 1/N2<0.04

and smooth increase above this value), although a

lower blue-shift of the hD0 recombination energy

seems to occur (0.2 eV for one TL) attributable to the

shorter spatial extension of the deep donor states

involved in these optical transitions. For relatively

thick flakes (12-8 nm thick), confinement effects

mostly act on extended states defining the InSe

bandgap. In these relatively thick flakes,

impurity-related states can still be considered as bulk

ones and seem to evolve with the flake thickness as

electronic states determining the bandgap evolution.

However, for thinner flakes, confinement effects

already acting on donor-related states progressively

increase the donor activation energy similarly to

what occurs with bulk hydrogenic (shallow) excitons

[51]: When bulk excitons become localized, they go

deeper into the bandgap due to the fact that,

although they turn into 2D, Coulomb interactions

always remain three-dimensional [49,52,53].

3 Conclusions

In summary, we have demonstrated that the gradual

enhancement of quantum size confinement has

enabled tuning the dimensionality of the lattice

dynamics and electronic properties of atomically thin

InSe flakes. In this way, electronic charge rearranges

and Raman modes involving quasi-in-plane bonds

stiffen whereas those involving bonds perpendicular

to the layer soften. Of course, the most evident effect

of lateral confinement appears on the electronic

properties of extended states. DFT calculations

predict a huge increase of the electronic bandgap by

more than 1 eV for a single InSe layer (2D case). The

relative increase of the bandgap calculated by DFT in

relatively thick flakes nicely reproduces the increase

in energy of the -PL band that was assigned to hD0

transitions associated to donors in interlayer sites.

Quantum size confinement effects do not alter the

11

orbital nature of states determining the bandgap,

thus InSe arises as a relative simple model system to

study the dynamics of confined carriers and

impurity-related states. These results also suggest

that InSe has potential applications in future planar

electronic and optoelectronic nanodevices

compatible with Si and III-V technologies, in

combination with other planar materials to create

top-down heterostructures, and eventually using

graphene as a transparent electrode [54,55]. For these

devices, it is worth noting that InSe can be

intentionally n-type (introducing Si and Sn

impurities) [46,56] and p-type doped (introducing

transition metals, as Zn and Pt) [57,58]. Also, the

doping versatility of this material suggests that 2D

systems with properties difficult to combine in the

bulk can be achieved, as the recently reported InSe

nanocrystals exhibiting room-temperature

ferromagnetism when doped with Fe and Co [59].

Finally, it should be remarked that, given the

intrinsic exhaustion of covalent bonds in the atomic

single layers of chalcogenide families and their

natural stacking by Van der Waals forces, one can

infer that heterostructures formed by different

2D/quasi-2D materials are possible and it will

constitute a predictable field of research in next

future from both basic and applications points of

view.

4 Methods

4.1 Experimental methods

InSe monocrystals here used to prepare the flakes

were cleaved perpendicular to the (001) direction

from an ingot grown by the Bridgman method from

a nonstoichiometric In1.05Se0.95 melt in which Tin, in a

content 0.01%, was introduced previously to growth

to act as n-dopant [60]. From these ingots, thin

n-doped InSe samples were cleaved and used to

prepare atomically thin InSe flakes on SiO2/Si

substrates by means of a mechanical exfoliation

technique similar to that employed for graphene [3].

The thickness of the SiO2 layer was 300 nm, which

potentially makes few-layer InSe flakes optically

detectable (see Figs. S1-S3 in the ESM). The thickness

of the InSe flakes was measured by AFM. AFM

imaging was performed by using a Nanotec

multimode microscope operating in non-contact

mode.

For -PL measurements a CW 405 nm laser was used

as excitation source (Power ~23 W). The laser beam

is coupled to a monomode optical fiber and carried

to the excitation arm of a diffraction limited confocal

microscope, working at liquid helium temperature.

The collection spot size on the sample was less than 1

m. The -PL signal is coupled to the collection

optical fiber, and was attached to a double 0.3 m

monochromator. An ANDOR technology charge

coupled device (CCD) was attached to the

monochromator front output to record the -PL

spectra.

Vibrational properties of the InSe flakes were studied

by Raman spectroscopy. Raman spectra were

collected at room temperature with a JY-Horiba

T64000 Raman microprobe spectrometer in

backscattering configuration (laser spot diameter ~1

m, objective numerical aperture = 0.90). As

excitation source, the 514.53 nm line of an Ar+ laser

was used and its plasma peaks served as fixed

frequency references. The detector is a liquid

N2-cooled CCD. The power at the sample was

limited to 100 W, in order to limit heating effects

and to avoid any sample damage.

4.2 Electronic structure calculations

Band structure calculations were carried out using a

numerical atomic orbitals DFT approach [61,62],

which has been developed and designed for efficient

calculations in large systems and implemented in the

SIESTA code [63-65]. We have used the local density

approximation to DFT and, in particular, the

functional of Perdew and Zunger [66]. Only the

valence electrons are considered in the calculation,

with the core being replaced by norm-conserving

scalar relativistic pseudopotentials [67] factorized in

the Kleinman-Bylander form [68]. Nonlinear partial

core corrections to describe the exchange and

correlations in the core region were included [69].

12

We have used a split-valence double- basis set

including polarization orbitals for all atoms as

obtained with an energy shift of 250 meV [70]. The

energy cutoff of the real space integration mesh was

300 Ry and the Brillouin zone was sampled using

grids of (10x10x1) and (10x10x10) k-points [71] for

the different slabs and the bulk, respectively. The

calculations for the different slabs (from 1 to 10

layers) were carried out using the same geometrical

details as for the bulk [37] since Rybkovskiy et al. [32]

have recently shown that the geometrical variations

between the bulk and different slabs of GaSe are not

substantial.

Acknowledgements

This work was supported by the Spanish

Government (Grants FIS2012-37549-C05-05,

MAT2011-24757, CSD2007-00041,

MAT2012-38664-C02-02, CSD2007-00045, and

TEC2011-29120-C05-01/-05), the Comunidad

Valenciana Government (Grant

PROMETEO/2009/074) and the Royal Society, the

European Research Council, and the Engineering

and Physical Sciences Research Council (UK).

G.M.M. acknowledges his national fellowship no.

JCI-2011-10686 under Juan de la Cierva program.

Electronic Supplementary Material:

Supplementary material information on InSe thin

flakes identification processes and on low

temperature photoluminescence spectra acquired in

bulk InSe samples and single-terraces flakes is

available in the online version of this article at

http://dx.doi.org/10.1007/s12274-***-****-*.

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16

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. Martínez-Pastor1 (), 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. 2 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.

Supporting information to DOI 10.1007/s12274-****-****-* (automatically inserted by the publisher)

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 [3,72-74] and semiconducting transition metal dichalcogenides such

as MoS2, WSe2 or NbSe2 deposited on SiO2/Si wafers [75,76]. 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. In analogy with graphene and dichalcogenides [73-76], 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 (Supplementary Fig. S1). The InSe nanolayer is modeled by a

thin homogeneous film of thickness d1 = N x 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 [24,77]. The

SiO2 layer of thickness d2 is optically characterized by a wavelength-dependent real refractive index ñ2(λ) [78],

ranging from 1.47 at 400 nm to 1.455 at 700 nm. We have considered a semi-infinite silicon substrate

underneath, with a wavelength-dependent complex refractive index ñ3 [78]. 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 equations [73,79]:

17

1 2 1 2 1 2 1 2

1 2 1 2 1 2 1 2

2( ) ( ) ( ) ( )

01 12 23 01 12 231 ( ) ( ) ( ) ( )

01 12 01 23 12 23

i i i i

i i i i

r e r e r e r r r eR n

e r r e r r e r r e

, S1

where  

牋

 

i j

ij

i j

n nr

n n

are the relative indices of refraction of the different interfaces,

2 i ii

d n

are the phase

shift induced by changes in the optical path and ñ0, ñ1, ñ2 and

Supplementary Figure S1 Scheme of the geometry considered in the theoretical contrast calculations. It is composed by 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.

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 Equation S1:

2 2

2 2

2( ) ( )

02 231 ( ) ( )

02 23

1i i

i i

r e r eR n

e r r e

, S2

where 0 202

0?

牋

 

n nr

n n

is the relative index of refraction at the interface between air and the dielectric thin film.

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

1 1

1

1Contrast ?

1

R n R n

R n

. S3

Supplementary 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

18

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 [74].

Supplementary 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.

Supplementary 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.

Supplementary Figure S3 Contrast spectra of InSe flakes with different thicknesses (one, two, three, four and five monolayers) on

SiO2(300 nm)/Si substrate calculated under normal incidence based on the Fresnel equation.

19

2 Photoluminescence in bulk InSe

In the PL spectrum recorded in the bulk sample (Supplementary Fig. S4) on a backscattering geometry

(standard lens, no confocal), we observe several contributions that we split in two groups:

Supplementary 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 [45,47,51,80]. On the other hand, native donors in not purposely doped InSe (always n-type) are due

to In in excess that can be 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).

20

3 Micro-Photoluminescence in thick InSe flakes.

The -PL spectra showed below were acquired in a bulk-like (12 nm) InSe flake, as a function of excitation

power (Supplementary Fig. S5(a)) and temperature (Supplementary Fig. S6(a)). The -PL spectra showed in

the Supplementary Fig. S5(a) are characterized by recombination times comprised between 5 and 9 ns

(Supplementary Fig. S5(b)) depending on 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 (Supplementary Fig. S6(a)-S6(b)). All these facts

point out to the impurity-related origin of the -PL signal measured in the flakes at low temperatures.

Supplementary 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

Supplementary 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

21

4 Micro-Photoluminescence in single-terraced InSe flakes.

The -PL spectra showed below were acquired in bulk-like InSe flakes (1-and 4-labelled flakes) and in

single-terraced, 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 showed 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 showed 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 main text).

Supplementary Figure S7 Left plots are optical images of single-terraced InSe flakes. Thickness of the selected 1-5 flakes 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 than that used in Fig. 3.

22

Taking into account these results, the following facts can be remarked:

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 fact can be understood on the basis of the

hypothesis stated in the main text on the unidirectional diffusion of photo-generated carriers from thicker to

thinner flakes. This hyphothesis conveys that -PL spectrum lineshape can be 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 it can be appreciated in the images of the Supplementary 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) showed in the Supplementary 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 single-terraced flakes gave rise to -PL signal, when probed). We believe that this observation is a

clear consequence of the unidirectional diffusion of photo-generated carriers in multi-terraced flakes: In very

thin flakes of uniform thickness, photogenerated carriers isotropically diffuse before recombination. However,

in multiterraced flakes, these carriers would tend to diffuse towards the flake edge. Comparing these two

situations, surface recombination would tend to play a more determinant role in flakes of uniform thickness.

Therefore, the -PL signal intensity coming from these uniform flakes would 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.

Supplementary References

[72] Bassani, F.; Tosatti, E. Phys. Lett. A 1968, 27, 446.

[73] Blake, P. et al. Appl. Phys. Lett. 2007, 91, 063124.

[74] Wang, Y Y. et al. Nanotechnology 2012, 23, 495713.

[75] Benameur, M. M. et al. Nanotechnology 2011, 22, 125706.

[76] Castellanos-Gomez, A.; Agraït, N.; Rubio-Bollinger, G. Appl. Phys. Lett. 2010, 96, 213116.

[77] Viswanathan, C.; Rusu, G. G.; Gopal, S.; Mangalaraj, D.; Narayandass, Sa. K. J. Optoelectron. Adv. M. 2005, 7, 705.

[78] Borghesi, A.; Guizzetti, G. Handbook of Optical Constants of Solids II, 449–460 (Academic, Boston, 1991).

[79] Anders, H. Thin Films in Optics (London: Focal) (1967).

[80] Zhirko, Y.; Skubenko, N.; Dubinko, V.; Kovalyuk, Z.; Sydor, O. J. Mat. Sci. and Eng. A 2013, 3, 162.

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Address correspondence to Juan F. Sánchez-Royo, Juan.F.Sanchez@uv.es; Juan P. Martínez-Pastor, Juan.Mtnez.Pastor@uv.es