The spectroscopy of InSe nanoparticles

Article abstract of DOI:10.1021/jp0506686

The synthesis of several different sizes of InSe nanoparticles from organometallic precursors is reported. These particles are characterized by transmission electron microscopy, electron diffraction, and optical spectroscopy. The electron diffraction results and optical properties indicate that these particles are two-dimensional disks, consisting of single Se-In-In-Se tetralayer sheets. The absorption spectra indicate strong quantum confinement along the z axis and, for the smaller particles, in the x,y plane. The z-axis quantum confinement may be quantitatively understood in terms of the band structure of bulk InSe. The results indicate that the z-axis quantum confinement reverses the order of the direct and indirect transitions in the case of the largest particles. The smaller particles exhibit strong, polarized fluorescence, and the fluorescence polarization may also be understood in terms of the band structure of bulk InSe. ? 2005 American Chemical Society.

Full text of DOI:10.1021/jp0506686

J. Phys. Chem. B 2005, 109, 12701-12709
12701
The Spectroscopy of InSe Nanoparticles
Shuming Yang and David F. Kelley*
DiVision of Natural Sciences, UniVersity of California, Merced, P.O. Box 2039, Merced, California 95344
ReceiVed: February 7, 2005; In Final Form: April 3, 2005
The synthesis of several different sizes of InSe nanoparticles from organometallic precursors is reported.
These particles are characterized by transmission electron microscopy, electron diffraction, and optical
spectroscopy. The electron diffraction results and optical properties indicate that these particles are two-
dimensional disks, consisting of single Se-In-In-Se tetralayer sheets. The absorption spectra indicate strong
quantum confinement along the z axis and, for the smaller particles, in the x,y plane. The z-axis quantum
confinement may be quantitatively understood in terms of the band structure of bulk InSe. The results indicate
that the z-axis quantum confinement reverses the order of the direct and indirect transitions in the case of the
largest particles. The smaller particles exhibit strong, polarized fluorescence, and the fluorescence polarization
may also be understood in terms of the band structure of bulk InSe.
Introduction
molecular precursor (containing indium and selenium) in a
coordinating solvent.13 This procedure results in somewhat
Layered semiconductors are of great interest largely because
they have optical and electronic properties that are highly
anisotropic. The III-VI compounds, such as InSe and GaSe,
are layered semiconductors in which a primitive layer consists
of four atomic planes, Se-M-M-Se (M ) In, Ga). The
selenium atoms form two-dimensional hexagonally close-packed
sheets, giving these crystals their hexagonal structure. The metal
atoms are aligned along the c axis in every other trigonal
prismatic site.1 The band gap of InSe is about Eg ) 1.24 eV at
room temperature,2,3 which makes it an attractive material for
solar energy conversion. Due to the absence of dangling bonds
on the (001) surface, it has the potential to be used for
heterojunction device applications with a low density of interface
states.4,5
polydisperse InSe nanoparticles. In this study, we present more
conventional synthetic methods in an attempt to better control
the nanoparticle size distributions. InSe nanoparticles are
synthesized in a coordinating organic solvent with conventional
organometallic precursors, using procedures that are very
analogous to those used to produce GaSe nanoparticles. We find
that these procedures permit the control of the nanoparticle sizes
and size distributions. We also present some basic aspects of
the size-dependent electronic structure of the particles, based
on absorption spectra and static and time-resolved fluorescence
spectroscopy. These results permit the relative energetics of the
different particle excited states to be established.
Experimental Section
There has been a growing interest in the spectroscopic and
photophysical properties of semiconductor nanoparticles, also
referred to as quantum dots. Despite this interest, relatively few
types of semiconductor nanoparticles have electronic, optical,
and photophysical properties that are well understood. This is
particularly true for the above-mentioned III-VI layered
semiconductors. We have recently reported much of the
photophysics of GaSe nanoparticles6-10 and strongly interacting
aggregates of these particles.11,12 Electron diffraction and optical
spectroscopy show that GaSe nanoparticles consist of single
tetralayer structures (i.e., Se-Ga-Ga-Se sheets). Thus, they
have a disklike, two-dimensional morphology and are exactly
four atoms thick. This was an expected result, based on
elementary chemical bonding considerations. There are strong
covalent bonds within the Se-Ga-Ga-Se sheets, while only
weak van der Waals forces hold adjacent sheets together.
Detailed spectroscopic studies revealed that GaSe nanoparticles
have highly anisotropic optical and quantum confinement
properties. We also found that, like the bulk materials, these
nanoparticles are quite photostable.
Materials. Trimethylindium was purchased from Strem
Chemicals and used without further purification. Methyllithium,
trioctylphosphine (TOP) and trioctylphosphine oxide (TOPO)
were purchased from Sigma-Aldrich. Anhydrous ether, tetrahy-
drofuran, selenium powder, and indium chloride were purchased
from VWR. Trioctylphosphine and trioctylphosphine oxide were
distilled under vacuum before use.
Trimethylindium/TOP solutions were used in the synthesis
of all the different sizes of nanoparticles, and were prepared in
the following way. InCl3 (3.0 g, 13.56 mmol) was added in a
flask and heated at 80 °C under vacuum for 1 h. The flask was
cooled in an ice bath and purged with argon several times.
Absolute ether (20 mL) was then injected and 25.4 mL of
methyllithium ether solution (1.6 mol/L) was slowly added.
Upon completion of this addition the solution was stirred for 2
h. The trimethylindium was pumped off and collected in a liquid
nitrogen cooled trap containing 13.5 mL of TOP. The trap was
warmed and the ether was then pumped off. The resulting 1
mol/L trimethylindium in TOP solution was stored in a drybox
for further use. We find that the characteristics of this solution
are identical with those of solutions made with commercial
trimethylindium.
InSe has the same crystal structure and similar lattice
constants as GaSe, and would be expected to form similar
disklike nanoparticles. Previous studies have shown that InSe
nanoparticles can be synthesized by pyrolysis of a single
Measurements. The size distributions of the different InSe
nanoparticle samples were determined with transmission electron
* Address correspondence to this author. E-mail: dfkelley@ucmerced.edu.
10.1021/jp0506686 CCC: $30.25 © 2005 American Chemical Society
Published on Web 06/10/2005

12702 J. Phys. Chem. B, Vol. 109, No. 26, 2005
Yang and Kelley
Figure 1. (a) Absorption spectra of 2.9 nm, 4.8 nm, and very large (>80 nm) InSe nanoparticles. (b) Plots of absorbance versus energy for the 2.9
nm, 4.8 nm, and very large particles. Also shown are the extrapolations to zero used to determine approximate band gaps in each case. (c) Plot of
the square root of absorbance versus energy for the red edge of the large particle spectrum. Also shown is an extrapolation to zero absorbance.
Figure 2. TEM images of (a) 2.9 nm, (b) 4.8 nm, and (c) very large (>80 nm) InSe nanoparticles. Scale bars indicating 20 nm (a and b) and 1
µm (c) are also shown.
microscopy (TEM). This was done with a Phillips CM-12 TEM,
operating at 100 kV. A small fraction of the InSe nanoparticle
solution is diluted with toluene by a factor of 3, and a drop of
the diluted solution is spread over a copper/Formvar grid (300
mesh size). Electron diffraction results were obtained on the
same instrument. The absorption spectra were measured in a
HP 8452A spectrophotometer. The static fluorescence spectra
were obtained on a Spex Fluorolog-3 with a liquid nitrogen
cooled CCD detector. Time correlated single photon counting
results were obtained with an apparatus described earlier.11
Synthesis of 2.9 nm InSe Nanoparticles. All InSe nano-
particle samples were synthesized with schlenck line methods
under an argon atmosphere. InSe nanoparticles are synthesized
with a method that is a modification of the high-temperature
synthesis of CdSe14 and GaSe8 nanoparticles. This synthesis is
based on the reaction between the organometalic In(CH3)3 and
trioctylphosphine selenium (TOPSe) in a high-temperature
solution of trioctylphosphine (TOP) and trioctylphosphine oxide
(TOPO). The nucleation and growth of the nanoparticles were
monitored by the absorption spectroscopy of small sample
aliquots.
absorption spectrum appears at about 410 nm. The reaction is
allowed to proceed about 2.5 h and a distinct peak appears at
410 nm, see Figure 1. The solution is then cooled quickly to
room temperature. TEM images of this sample are obtained and
the size distribution is determined, see Figure 2. Measurement
of many particles indicates that the particle diameter is 2.9 (
0.4 nm (standard deviation).
Synthesis of 4.8 nm InSe Nanoparticles. Se (0.35 g), TOPO
(2.5 g), hexyl phosphonic acid (0.045 g), and TOP (3.5 mL)
are added to a flask under an argon atmosphere. The mixture is
then stirred at 150 °C overnight. The solution is cooled to room
temperature and 0.4 mL of trimethylindium in TOP (1 mol/L)
is injected. The mixture is then slowly heated to 233 °C for
nucleation and subsequent particle growth. The solution becomes
yellow and a shoulder in the absorption spectrum appears at
460 nm at about 26 min. The temperature is then maintained at
233 °C for 3.5 h. During this time a more distinct shoulder grows
at 475 nm. The solution is then quickly cooled to room
temperature. The absorption spectrum of these particles is also
shown in Figure 1.
Synthesis of Very Large (>80 nm) InSe Nanoparticles.
Se (0.35 g), TOPO (2.5 g), (0.075 g) hexyl phosphonic acid
(2.5 g), and TOP (3.5 mL) are added to a flask under an argon
atmosphere. The mixture is stirred then at 150 °C overnight.
The solution is then cooled to room temperature and 0.4 mL of
trimethylindium in TOP (1 mol/L) is injected. The mixture is
then slowly heated to 237 °C. It becomes red at about 18 min
and a shoulder appears at about 460 nm in the absorption
spectrum. The temperature is kept at 237 °C for the growth of
The synthesis of 2.9 nm InSe nanoparticles is as follows.
Initially, 0.3158 g (4 mmol) of Se, 2.6 g of TOPO, and 3.5 mL
of TOP are added to a flask and stirred at 150 °C overnight
under an argon atmosphere. The solution is then heated to 250
°C and 1.5 mL of trimethylindium in TOP (1 mol/L) is injected.
Upon injection, the temperature drops to 236 °C and the solution
is reheated to 248 °C for the growth of the InSe particles. The
solution becomes yellow at about 35 min and a shoulder in the

The Spectroscopy of InSe Nanoparticles
J. Phys. Chem. B, Vol. 109, No. 26, 2005 12703
the InSe particles. The entire reaction takes about 5 h and the
absorption onset is measured at 580 nm. The solution is then
quickly cooled to room temperature. The absorption spectrum
of these particles is also shown in Figure 1.
down as the particles get smaller. As any particle becomes
smaller, the momentum vector, which defines the band structure
of the crystal, becomes less well defined. In sufficiently small
nanoparticles, the wavelength and hence momentum associated
with specific standing waves (symmetry points in the Brillouin
zone) are not well defined and the momentum selection rule is
relaxed. These two-dimensional nanoparticles are extremely thin
(four atoms) and this is particularly true of the z-axis symmetry
points; it makes little sense to refer to standing waves when
the distance over which the wave is defined is one-half of the
shortest wavelength. The situation is less severe in the x,y plane.
Particles range from about 8 to over 200 unit cells in diameter,
and this is a sufficient distance for the wavelength of a standing
wave to be reasonably well defined. Thus, we expect that in
the case of the largest particles, there will be little mixing of
momentum states in the x,y plane. The M point is in the x,y
plane and the Γ f M transition will have low intensity. More
mixing will occur in smaller particles and the distinction between
direct and indirect transitions starts to break down. This
phenomenon has been extensively studied, primarily in the
context of porous silicon.16,17 The above breakdown of mo-
mentum selection rules notwithstanding, the zeroth order
description of the electron and hole states in terms of symmetry
points in the first Brillouin zone is very useful. Furthermore,
despite some amount of mixing, the nodal properties of the
electron and hole wave functions are of central importance in
understanding the nanoparticles spectroscopy and we will
elucidate this (size dependent) behavior below.
Results and Discussion
Particle Synthesis and Characterization. The basic idea of
these syntheses is to obtain InSe nanoparticles with methods
similar to those used to prepare GaSe nanoparticles.8,10 However,
the reactivities of the indium and gallium precursors are
different, and the central challenge of these syntheses is the
control of the reactivity with respect to particle nucleation and
growth. The synthesis of monodisperse small particles requires
a rapid burst of nucleation, followed by relatively slow particle
growth. In general, we find that the presence of TOPO and
especially alkyl phosphonic acids inhibits both the nucleation
and growth processes. Thus, small (2.9 nm diameter) particles
are synthesized by the injection of In(CH3)3/TOP into a hot
solution of TOP/TOPO/TOPSe. Nucleation occurs very rapidly,
followed by particle growth. This results in a relatively
monodisperse distribution of particle sizes. If the solution is
allowed to further react, it will eventually undergo Ostwald
ripening, resulting in a defocused, polydisperse sample.
The synthesis of larger (4.8 nm) particles requires the
production of fewer nuclei. This is accomplished by mixing the
reactants together at room temperature in a solution containing
0.7% hexyl phosphonic acid. InSe nuclei are formed as the
solution is heated, with the extent of nucleation controlled by
the presence of the hexyl phosphonic acid. Since there are fewer
nuclei, subsequent growth results in fewer, larger particles.
Addition of larger amounts of hexyl phosphonic acid further
inhibits nucleation, permitting the synthesis of very large
particles.
Absorption spectra of small (2.9 nm), intermediate (4.8 nm),
and very large (>80 nm) InSe nanoparticles are shown in Figure
1a. The corresponding TEM images are shown in Figure 2.
Analysis of the size distribution indicates that the standard
deviation is about 15% for the case of the 2.9 and 4.8 nm
particles. Electron diffraction results on the 4.8 nm and large
particles are similar to those obtained for single tetralayer GaSe
nanoparticles. Specifically, they show the (1,0,0) and (1,1,0)
reflections, while (1,0,2), (1,0,4), (1,1,2), etc. reflections are
absent. This indicates that both types of nanoparticles have the
same two-dimensional, single tetralayer morphologies. This is
exactly what one would expect. The tetralayers are held together
by covalent bonds, but are held to each other by much weaker
van der Waals forces.
Quantum confinement effects involve energies that are much
larger than the Γ-M conduction band energy separation in bulk
InSe and there is no a priori way to know whether the lowest
point of the conduction band in these particles would be at Γ
or M, i.e., the transition could be either direct or indirect. In
principle, the functional dependence of the absorbance on energy
near the band edge could be used to determine the nature of
the lowest energy transition. However, the presence of a finite
distribution of particles sizes makes this analysis problematic
for the 2.9 and 4.8 nm particles. This determination will be made
based on relative oscillator strength results (discussed below),
and we will only estimate the band gaps from the results
presented in Figure 1b. Absorbance is plotted versus energy
and the extrapolation to zero absorbance is used to estimate
the band gap. Direct (momentum allowed) transitions are
typically much more intense than indirect (momentum forbid-
den) transitions. As a result, the direct transitions are expected
to dominate these plots, and the extrapolations give reasonable
estimates for the direct transition energies. (This is a slightly
different approach than that used in our initial study of GaSe
nanoparticles,10 but yields similar results.) The 2.9 and 4.8 nm
particles show absorption onsets at 21 050 (475 nm) and 18 830
cm-1 (531 nm), respectively.
Size-Dependent Absorption Spectra. Bulk InSe has a room
temperature absorption onset at 1.24 eV (10 000 cm-1 or 1 000
nm).2 The onsets of the spectra in Figure 1 are shifted into the
450-600 nm region, and therefore show considerable quantum
confinement. Approximate absorption onsets for each size
particle may be determined from graphs of absorbance plotted
as a function of energy, Figure 1b. One of the central questions
about the absorption spectra is regarding the nature of the lowest
energy transition in terms of the initial and final momentum
states. In the case of bulk InSe, the top of the valence band and
the bottom of the conduction band are both at Γ and the lowest
energy transition is therefore momentum allowed; it is a “direct”
transition.2,3 A slightly higher (750 cm-1) local minimum of
the conduction band is at the M point and the corresponding Γ
f M transition is a much less intense, momentum-forbidden
“indirect” transition.15 The momentum selection rule breaks
The situation is somewhat different for the largest particles.
The Bohr radius of an exciton in InSe is about 5 nm and the
largest particles are expected to exhibit very little x,y-plane
quantum confinement.2 The height of these single tetralayer
particles is much less than the Bohr radius, and there is
considerable z-axis quantum confinement. However, all of the
particles have the same height, giving a constant amount of
z-axis quantum confinement. As a result, the finite distribution
of particle sizes is not expected to broaden the absorption onset
of the largest particles. We will show (below) that based on
band structure calculations, the lowest energy transition in the
largest particles is expected to correspond to an indirect band
gap. We suggest that this transition is responsible for the weak,

12704 J. Phys. Chem. B, Vol. 109, No. 26, 2005
Yang and Kelley
Figure 3. (a) Absorption spectrum and fluorescence spectra of 2.9 nm particles following excitation at 380, 400, 430, and 450 nm (indicated by
arrows). (b) Plot of the fluorescence anisotropy as a function of the excitation wavelength for 2.9 nm particles.
low-energy tail observed in the absorption spectrum. The
magnitude of the indirect gap may be estimated from a plot of
(absorbance)1/2 versus energy,18 as shown in Figure 1c. A value
of 15 900 cm-1 for the indirect band gap is obtained. Most of
the absorbance is due to the far more intense direct (momentum
allowed) transition, and an approximate value for its onset
(consistent with the values obtained for the smaller particles)
is obtained from the extrapolation in Figure 1b. However,
absorption into the low-energy indirect transition affects this
extrapolation and we conclude that the direct transition may be
at somewhat higher energy than the 17 350 cm-1 intercept.
In addition to the lowest energy onsets, Figure 1 shows that
in each case, a more intense transition is observed further to
the blue. For example, the 2.9 nm particles show a low energy
transition having an inflection at about 440 nm and a higher
energy transition at about 360 nm. We will first discuss the
assignment of these transitions in terms of the valence and
conduction bands. This will be followed by a discussion of the
direct versus indirect nature of the transitions and the quantum
confinement effects.
Fluorescence Polarization Measurements. Assignment of
the transitions observed in the absorption spectra is facilitated
by fluorescence polarization measurements. Since the small
particles are the only ones that are strongly fluorescent we will
primarily discuss this case. The fluorescence spectra of the 2.9
nm particles following excitation at several different wave-
lengths are shown in Figure 3a. This fluorescence is polarized
and the polarization reveals much about the assignment of these
excited states. The fluorescence polarization is characterized by
the anisotropy, r, given by19
of the lowest energy transition (λ > 400 nm) results in a large
positive anisotropy, independent of excitation wavelength. This
anisotropy has a value of about 0.18. This is greater than 0.10,
the value associated with coplanar absorption and fluorescence
oscillators, and we conclude that this fluorescence can only result
from the excitation and fluorescence oscillators being collinear
or the same linear oscillator. With the disklike geometry of these
nanoparticles, this transition is assigned to excitation and
fluorescence occurring along the z axis, perpendicular to the
plane of the nanoparticle. Consistent with the polarization results
in bulk InSe,3 the low-energy absorption may be assigned to
excitation of the bandedge state. Fluorescence occurs from this
state and/or other states that derive oscillator strength from it.
At shorter wavelengths (λ < 380 nm), some of the excitation
goes into the higher energy oscillator and smaller fluorescence
anisotropies are obtained. This indicates that the higher energy
transition is polarized in the x,y plane of the nanoparticles.
Similar behavior is observed for the 4.8 nm particles. Fluores-
cence from the largest particles is sufficiently weak that useable
anisotropy results cannot be obtained. The above results can
be understood in terms of band structure and spectroscopy of
bulk InSe.15,20-22 (Although the crystal structure of a single
1
tetralayer has D3h symmetry, we will discuss the electronic
4
states in terms of D6h notation, because that is what usually
4
appears in the literature. The conclusions are the same for D6h
and D3h1 symmetries.23) In bulk InSe the lowest energy transition
is at Γ (Γ4 f Γ3+) and is z polarized. At somewhat higher
-
energy there is an x,y-polarized transition from a lower level of
the valence band to the bottom of the conduction band (Γ6- f
Γ3+). We make an analogous assignment here: the lower and
higher energy transitions are due to excitation from the Γ4- and
r ) (Ipar - Iperp)/(Ipar + 2Iperp) ) 1/5(3 cos2 θ - 1)
-
Γ6 valence band levels, respectively, to the bottom of the
conduction band. This indicates that despite quantum confine-
ment effects, the energy of the Γ6- state remains below that of
where Ipar and Iperp are the fluorescence intensities polarized
parallel and perpendicular to the polarization of the excitation
light, respectively, and θ is the angle between the fluorescence
and excitation transition oscillators. Several limiting cases are
of interest. The case of collinear excitation and fluorescence
oscillators results in the largest possible anisotropy for an
incoherent process, 0.40. Similarly, the case of coplanar
excitation and fluorescence oscillators requires integration over
the plane and gives an anisotropy of 0.10. If the excitation and
fluorescence oscillators are at 90° angles, an anisotropy of -0.20
is obtained. Figure 3b shows a plot of the fluorescence
anisotropy as a function of excitation wavelength. (The anisotro-
pies are essentially constant across the fluorescence spectrum,
i.e., they are independent of detection wavelength.) Excitation
-
the Γ4 state in these nanoparticles.
Quantum Confinement Effects. The size-dependent absorp-
tion and fluorescence spectra of these particles can be qualita-
tively understood in terms of the two-dimensional nature of these
particles. The blue shift of the absorption spectrum occurs
because of quantum confinement along the z axis and in the
x,y plane. Since all of the particles are exactly four atoms thick,
the extent of z-axis quantum confinement is constant. In contrast,
the extent of x,y-plane quantum confinement varies with the
particle size. The simplest possible way in which the extents of
z and x,y quantum confinement can be analyzed is using an
effective mass (EM), particle in a cylinder model. In this model,
the cylindrical symmetry of the particle results in the electron

The Spectroscopy of InSe Nanoparticles
J. Phys. Chem. B, Vol. 109, No. 26, 2005 12705
and hole wave functions separating into z and x,y functions.
Specifically,
Ψ
mnp(r,æ,z) ) NnmJm(Rmnr/R) exp(imæ) sin(pπz/H)
where R is the particle radius, H is the particle height, Jm is an
mth order Bessel function, Rmn is the nth root of a Bessel
function of order m, Nmn is a normalization factor, and p is an
integer. From ref 24 we know that Nnm ) (2/πH)1/2(1/R)(1/Jm+1
(Rmn)).
The electron and hole energy levels are given by
-
2
p2Rmn
p2p2π2
Em,n,p
)
+
2me(h)zH2 2me(h)xyR2
Figure 4. Plots of the measured direct band gap as a function of
1/(particle radius)2 (solid squares), the direct band gap corrected by
the Coulombic term (solid circles), and the indirect band gap of the
large particles (open circle). Also shown is a line through the points
where me(h)xy and me(h)z are the electron (hole) effective masses
in the x,y plane and along the z axis, respectively, and m, n,
and p are quantum numbers. The x,y and z designations for the
effective masses reflect the fact that these quantities are highly
anisotropic, i.e., they are different for motions in the plane and
perpendicular to the plane of the nanoparticle. The total (electron
plus hole) quantum confinement of the observed transitions is
given by the sum of the electron and hole zero point energies
plus a Coulombic term. The electron/hole Coulombic interaction
energy may be evaluated through a first-order perturbation
approach. The interaction potential is obtained by integrating
the electrostatic force. We define
having an intercept of 17 400 cm-1 and a slope of 10 100 cm-1/nm-2
.
energy of the indirect band gap for the large particles (Figure
1c) is also shown in Figure 4. As the particle size decreases,
the absorption onset shifts further to the blue because of
additional quantum confinement in the x,y plane. The roles of
z and x,y quantum confinement are dealt with separately, below.
The diameter of the large particles (>80 nm) is much larger
than the InSe Bohr radius (5 nm), the result being that these
particles exhibit large z-axis quantum confinement but very little
x,y quantum confinement. The direct and indirect band edges,
and hence the absorption spectrum of the large particles, can
be understood in terms of measurements on bulk InSe and band
structure calculations.15,20-22 Bulk InSe has significant interac-
tion between the tetralayer sheets and z-axis quantum confine-
ment can be thought of as being due to the loss of this
interaction. Interlayer interactions split the Γ4- and Γ1+ valence
V (x) ) xF(x′) dx′
∫
0
0
where
x(J (R x′))2x′ dx′
∫
0
01
0
F(x) ) (1/x2)
+
-
band states and the Γ3 and Γ2 conduction band states. The
extent of z-axis quantum confinement can be assessed by
comparing the calculated conduction and valence band energies
at the Γ (the direct band gap) and A (where the interlayer
interaction is zero) symmetry points. The energy differences
are 4875 cm-1 in the valence band and 3810 cm-1 in the
conduction band, with the total, 8685 cm-1, being the calculated
z-axis, direct band gap quantum confinement energy.20 However,
the presence of a Γ f M indirect transition complicates the
spectroscopy of InSe nanoparticles, and insight into the energet-
ics of this transition comes from optical measurements on γ-InSe
and calculations. Bulk InSe exists in â- and γ-polytypes, having
hexagonal and rhombohedral lattices, respectively. The differ-
ence is in the stacking of the tetralayer sheets, and the two forms
have very similar energetics. As a result, measurement on γ-InSe
can be used to establish the energetics of the band structure
1(J (R x))2x dx
∫
0
01
0
The resulting electron/hole interaction is obtained from the above
integrals and is
Ve(h) ) (Q2/4πꢀ0ꢀ)(1/R) J0(R01x)|V0(x)|J0(R01x) )
-1.12(Q2/4πꢀ0ꢀ)(1/R)
where Q is the electronic charge and ꢀ is the dielectric constant
of InSe, ≈9.2
The electronic transition energy is therefore given by
p2R01
2R2 me
2
p2π2
1
1
1
xy
1
E0 ) Ebulk
+
+
+
+
-
2
z
z
xy
(
)
(
)
2H me
mh
mh
4
calculated for the D6h crystal structure (â-InSe). The energy
1.12Q2
4πꢀ0ꢀR
difference between the direct and indirect transitions has been
accurately determined in the case of γ-InSe, and the indirect
transition is 750 cm-1 higher.15 This energy difference is
strongly dependent on the extent of interlayer interactions. The
(1)
where Ebulk is 1.24 eV (10 000 cm-1) for room temperature InSe
and R01 has a numerical value25 of 2.405. Equation 1 indicates
that the Coulombic term may be added onto the observed
transition energies and the resulting corrected energies may be
plotted versus 1/R2. The intercept of this plot is the bulk band
gap plus the z-axis quantum confinement energy. Such a plot
is shown in Figure 4, and a reasonable linear fit with 1/R2 is
obtained. The intercept of this plot, 17 490 cm-1, corresponds
to a z-axis quantum confinement energy of 7490 cm-1. As
discussed above, the absorption is dominated by the direct
transition and this value applies to the direct band gap. The
+
calculated20 conduction band interlayer splitting at M (M3
versus M4-) is relatively small, about 3000 cm-1. So, the indirect
band gap z-axis electron quantum confinement energy may be
taken to be about half this value, 1500 cm-1. With the above
750 cm-1 bulk Γ-M energy difference, we get that loss of the
interlayer interaction will result in an electron energy at the M
point of 2250 cm-1 above the bottom of the bulk InSe
conduction band. In the absence of interlayer interactions, this
puts it below the energy of an electron at Γ by 1560 cm-1 (3810
cm-1 - 2250 cm-1). It is important to note that these

12706 J. Phys. Chem. B, Vol. 109, No. 26, 2005
Yang and Kelley
particles exhibit very similar decay kinetics following 430 and
450 nm excitation. However, the fluorescence is sufficiently
weak following 380 and 400 nm excitation that reliable decay
curves could not be obtained. The dependence of decay times
on excitation wavelength can be made more quantitative by
comparing the areas under the decay curves, normalized to unity
at t ) 0. The decay curves are nonexponential, and with this
normalization, the area under the curve is a measure of the
“average” decay time. Average decay times are seen to increase
with further red excitation, as shown in Figure 6. A similar effect
has been observed for GaSe nanoparticles,8 and is due to
additional nonradiative relaxation pathways (probably carrier
trapping) available at higher energy. The emission decay time
correlates with the observed fluorescence quantum yields, as is
also shown in Figure 6. Longer decay times give similarly higher
quantum yields. This suggests that all of the particles of any
given size have similar oscillator strengths.
Figure 5. Fluorescence decay kinetics for 2.9 and 4.8 nm particles.
The 2.9 nm fluorescence decays (solid curves) are obtained following
excitation at 380, 400, 430, and 450 nm. The 4.8 nm fluorescence decay
(dotted curve) is obtained following excitation at 450 nm. In all cases
the detection wavelength is 500 nm.
The most important point resulting from the data in Figure 6
comes from the comparison of the fluorescence quantum yields
of the 2.9 and 4.8 nm particles (Figure 6a,b). This comparison
reveals a very strong particle size dependence. The 2.9 nm
particles exhibit high fluorescence quantum yields. The exact
values vary from sample to sample, and in some cases approach
40%. Quantum yields in the range of 12-25% (Figure 6) are
typical. In contrast, the 4.8 nm particles consistently exhibit very
small quantum yields, typically less than 0.5%, which is a factor
of about 50 lower than the 2.9 nm particles. We emphasize that
this difference is not due to differences in quenching rates.
Figure 5 shows roughly comparable fluorescence decay kinetics
for both sizes of nanoparticles. For example, following 430 nm
excitation, both 2.9 and 4.8 nm particles exhibit an approximate
decay time (e-1 times) of 2.5 ns. The excitation wavelength-
dependent results also suggest that the quantum yield difference
between the 2.9 and 4.8 nm particles is not due to larger Γ-M
mixing in the smaller particles. If this were the case, further
red excitation (which excites the largest particles in the size
distribution) would result in weaker fluorescence. Figure 6
shows that the opposite is observed. The quantum yield and
fluorescence decay results suggest the emitting states are
different for the two particle sizes. In the case of the small
particles the high fluorescence quantum yield suggests that the
emitting state is the same as the absorbing state and is allowed.
In contrast, in the case of the 4.8 nm particles, the low quantum
yield suggests that the emitting state has very little oscillator
strength. This trend with particle size continues and the largest
(>80 nm) particles are almost completely nonfluorescent. There
are two possible assignments for this trend. First, that in the
larger particles the (weakly) emitting state is localized, a trap
calculations indicate that loss of the interlayer interactions
reverses the ordering of the Γ and M energies and results in the
lowest energy transition being momentum forbidden. The direct
transition is calculated to be at about 1560 cm-1 higher energy.
This is in agreement with the difference in the extrapolated
values shown in Figures 2 and 4, supporting the assignments
to the indirect and direct transitions. Combined with the 4875
cm-1 quantum confinement of the hole, the Γ f M and Γ f Γ
transition energies in large, tetralayer particles are calculated
to be about 17 125 and 18 685 cm-1, in reasonable agreement
with the 15 900 and 17 490 cm-1 experimental values.
The energetic ordering of the Γ f Γ and Γ f M transitions
in smaller particles can be assessed from time-resolved fluo-
rescence and fluorescence quantum yield measurements. These
results (discussed below) suggest that the nature of the lowest
energy state (direct versus indirect transitions) is size dependent.
Fluorescence Kinetics and Quantum Yields. The above
fluorescence polarization results show that the lowest excited
-
+
state corresponds to the Γ4 f Γ3 transition, or a transition
that through some mechanism (such as vibronic coupling)
derives oscillator strength from it. Thus, in all cases, the lowest
-
energy absorption can be assigned to either the direct (Γ4
f
Γ3+) or the indirect (Γ4- f M3+) transition. Fluorescence decay
and quantum yield measurements give insight into these
assignments and suggest that the ordering of these transitions
is particle size dependent. Fluorescence decay times are a
function of excitation wavelength, and to a lesser extent, particle
size, as shown in Figure 5. (Laser tunability limits the excitation
wavelength to e450 nm.) Decay times increase with further
red excitation, particularly in the 2.9 nm particles. The 4.8 nm
Figure 6. (a) Fluorescence quantum yields (solid squares) and areas under the fluorescence decay curves (open squares) for 2.9 nm particles as
a function of excitation wavelength. (b) Same as part a, except for 4.8 nm particles.

The Spectroscopy of InSe Nanoparticles
J. Phys. Chem. B, Vol. 109, No. 26, 2005 12707
more fluorescent than others, and we suggest that small
variations in the size distribution and hence ordering of these
states may be the reason for this.
The above assignments are consistent with time-resolved
fluorescence spectral reconstruction results. In the case of the
4.8 nm particles, excitation is primarily to the direct transition
(it has most of the oscillator strength) and is followed by
relaxation to the weakly fluorescing indirect state. Prior to this
relaxation, the fluorescence is predicted to be more intense and
further to the blue. Consistent with this explanation, the 4.8
nm fluorescence kinetics show a small spike coincident with
zero time, particularly at wavelengths blue of the static
fluorescence maximum. However, this effect can most clearly
be seen in the reconstructed time-resolved fluorescence spectra.
These fluorescence spectra can be reconstructed from the static
spectra and wavelength dependent fluorescence kinetics. Fluo-
rescence kinetics are obtained at 5 nm intervals and normalized
such that the area under each decay curve is proportional to the
static fluorescence intensity at that wavelength. Low-resolution
(5 nm) time-resolved fluorescence spectra may then be obtained
directly from these decay curves. An example of these spectra
is shown in Figure 7. The fluorescence maximum may be
obtained by interpolating these points with a fourth order
polynomial, and finding the polynomial maximum. The results
of this procedure for the 2.9 and 4.8 nm particles are shown in
Figure 8. The fluorescence spectra of the 4.8 nm particles show
a rapid, greater than 10 nm red shift that is absent in the case
of the 2.9 nm particles. The time resolution of time correlated
single photon counting is about 40 ps, and this shift is limited
by the time resolution of the apparatus. The magnitude of the
spectral shift reflects the energy loss associated with relaxation
and the results in Figure 8 indicate the spectral shift is on the
order of 450 cm-1. We note that because this measurement is
limited by the response time of the instrument, the actual
magnitude of the spectral relaxation could be considerably
larger. However, this result suggests that the magnitude of the
Figure 7. Reconstructed time-resolved fluorescence spectra for 4.8
nm particles, following 450 nm excitation. Spectra are shown at times
of 0 ps (solid squares), 12 (open squares), 35 (solid circles), 105 (open
circles), and 295 ps (solid diamonds). The fluorescence maximum shifts
from approximately 505 to 515 nm in this time interval.
state. Second, that the large particle emitting state is a delocal-
ized electronic state corresponding to an indirect band gap. The
first possibility cannot be ruled out based on the results presented
here, but several considerations suggest that it is unlikely. This
assignment would require that the 4.8 nm and very large
particles have a much higher density of trap states than the 2.9
nm particles. This seems unlikely because these results are very
reproducible and the synthetic conditions used to obtain the
different sizes of particles are very similar. Alternatively, the
second possibility would require that the energy of the indirect
band edge be at a lower energy than the direct band edge for
all but the smallest particles, in which the opposite is true. This
latter assignment is consistent with the band structure calcula-
tions discussed above, which place the direct band edge 1560
cm-1 above the indirect edge in the large particles. This
assignment requires that the 4.8 nm and large particles have
qualitatively similar energetics; they both have a lowest indirect
band edge. In contrast, the 2.9 nm particles are strongly
fluorescent, indicating that the lowest transition is at Γ and
therefore allowed. The indirect transition must be at a higher
energy in these particles. We also suggest that the energies of
the direct and indirect transitions are quite close in the case of
the 2.9 nm particles, and the reversal of these energies occurs
at only slightly larger sizes. In this case, some of the small
particles in the distribution will have a direct lowest energy
transition and some will not, as a result of a finite distribution
of particle sizes. The fraction that do will change with small
variations in the average particle size and the sample polydis-
persity. We observe that some samples of about this size are
energy relaxation must be at least on the order of 450 cm-1
.
The magnitude of the spectra shift is consistent with the low
fluorescence intensity observed in the case of the 4.8 nm
particles. If the energy relaxation were less than or on the order
of 200 cm-1 (thermal energy at room temperature) both the high
energy, optically allowed, and lower energy, forbidden, states
would have significant populations when in thermal equilibrium.
In this case, a significant amount of fluorescence would be from
the higher energy allowed transition, and a large change in the
fluorescence intensity and spectral maximum would not be
observed.
Figure 8. Plots of fluorescence maxima as a function of time for 2.9 nm (solid circles) and 4.8 nm (open circles) particles, following excitation
at (a) 430 and (b) 450 nm. These results are obtained from reconstructed fluorescence spectra such as those shown in Figure 7, as described in the
text.

12708 J. Phys. Chem. B, Vol. 109, No. 26, 2005
Yang and Kelley
Comparison with an Effective-Mass Treatment. It is
possible to attempt to quantitatively analyze the size-dependent
energetics in Figure 4 in terms of the simple effective mass
model described above. In the simplest form, this amounts to
the use of eq 1 to fit the size-dependent direct band gaps, with
the appropriate values of the effective masses. The effective
masses are known26-29 and have values (in units of electron
1. Different sizes of InSe nanoparticles may be synthesized
with the methods presented here. The particle sizes are
controlled through the chemistry of the reaction mixture and
the temperatures at which nucleation and growth take place.
2. InSe nanoparticles are two-dimensional, consisting of single
tetralayer (Se-In-In-Se) disks. Sizes from 2.9 to >80 nm may
be obtained.
3. Most of the quantum confinement of the largest (>80 nm)
and intermediate size (4.8 nm) particles is due to z-axis quantum
confinement. Although bulk InSe is a direct band gap semi-
conductor, these particles have an indirect band gap. The reversal
of these states can be understood in terms of the InSe band
structure.
4. The smallest nanoparticles (2.9 nm) exhibit intense
fluorescence, while larger (4.8 and >80 nm) particles exhibit
at most very weak fluorescence. Time-resolved measurements
indicate that this is due to differences in oscillator strength, rather
than fluorescence lifetimes. Also, the fluorescence spectrum of
the 4.8 nm (but not 2.9 nm) particles exhibits a rapid (<40 ps)
shift to the red immediately following photoexcitation. These
results are interpreted in terms of size-dependent quantum
confinement effects causing the direct transition to be at lower
energy than the indirect transition for the 2.9 nm, but not 4.8
nm or >80 nm particles.
z
z
xy
mass) of 0.081, 2.5, 0.131 and 1.0 for me , mh , mexy, and mh
,
respectively. The effective masses for the indirect transition have
not been reported, so we will confine our discussion to the direct
transition. The observed z-axis quantum confinement energy
(≈7500 cm-1 at Γ) can be compared with the value of p2π2/
2H2(1/me + 1/mh ). Similarly, the observed slope (≈10 100
z
z
cm-1/nm-2) of the Coulomb-corrected energies may be com-
xy
pared to the value of R012p2/2(1/me + 1/mhxy). In addition to
treating the particle energies through their effective masses, this
model makes several other approximations. The nanoparticles
are taken to have cylindrical symmetry, which is probably a
pretty good approximation. A more serious approximation is
that eq 1 tacitly assumes that the potential well is infinitely deep.
Most importantly, it is an effective mass treatment and assumes
that the bands are parabolic. Because of these approximations,
we find that the agreement of the observed and effective mass
calculated z-axis quantum confinement energies is poor. This
simple model predicts a very large value for the z-axis quantum
confinement, about a factor of 8 larger than the observed value.
Part of the problem is that the model assumes that the electron
and hole are confined in a cylinder having infinite potential
walls. This is not a very good approximation, and charge density
is expected to “spill over” these walls, particularly along the z
axis. A finite, realistic well depth can be readily incorporated
into these calculations.30 This decreases the discrepancy, but
the predicted z-axis quantum confinement is still about a factor
of 2 larger than the observed value. We conclude the effective
mass approximation provides only a semiquantitative description
of the z-axis quantum confinement.
These particles are much larger in the x,y dimensions than
along the z axis. Because of this, both the parabolic band
effective mass approximation and the infinite potential ap-
proximation might be expected to give a better description of
x,y quantum confinement. Evaluation of the x,y quantum
confinement term gives a 1/R2 coefficient of 15 250 cm-1/nm2.
The slope of the plot in Figure 4 gives an experimental value
of 10 100 cm-1/nm2, about a factor of about 1.5 below the value
derived from the effective mass model. It is also possible to
calculate the extent of x,y quantum confinement by using a
realistic well depth. This calculation is analogous to the one-
dimensional calculation with a finite well depth30 and is outlined
in another publication.31 This diminishes the size of the error
and the calculated value for the 2.9 nm particles is about 24%
larger than the observed x,y quantum confinement. We conclude
that the effective mass model significantly overpredicts the
extent of z quantum confinement, but only slightly overpredicts
the extent of x,y quantum confinement. In both cases, the basic
problem is that the bands are not parabolic.32,33 There are several
reasonably close lying conduction bands that interact, reducing
the extent of quantum confinement. More accurate treatments
have been applied to other types of semiconductor nanoparticles,
but as yet, such calculations have not been performed for InSe
nanoparticles.
Acknowledgment. This work was supported by grants from
the U.S. Department of Energy, grant no. DE-FG03-00ER15037,
and from the Army Research Office, grant no. W911NF-04-1-
0331.
References and Notes
(1) Levy, F. Crystallography and Crystal Chemistry of Materials with
Layered Structures; Reidel: Dordrecht, The Netherlands, 1976.
(2) Camassel, J.; Merle, P.; Mathieu, H.; Chevy, A. Phys. ReV. B 1978,
17, 4718.
(3) Piacentini, M.; Doni, E.; Girlanda, R.; Grasso, V.; Balzarotti, A.
NuoVo Cimento 1979, 54B, 269.
(4) Martinez-Pastor, J.; Segura, A.; Julien, C.; Chevy, A. Phys. ReV. B
1992, 46, 4607.
(5) Lang, O.; Klein, A.; Pettenkofer, C.; Jaegermann, W.; Chevy, A.
J. Appl. Phys. 1996, 80, 3817.
(6) Chikan, V.; Kelley, D. F. Nano Lett. 2002, 2, 1015.
(7) Chikan, V.; Kelley, D. F. J. Chem. Phys. 2002, 117, 8944.
(8) Chikan, V.; Kelley, D. F. Nano Lett. 2002, 2, 141.
(9) Chikan, V.; Kelley, D. F. J. Phys. Chem. B 2002, 106, 3794.
(10) Tu, H.; Chikan, V.; Kelley, D. F. J. Phys. Chem. B 2003, 107,
10389.
(11) Tu, H.; Yang, S.; Chikan, V.; Kelley, D. F. J. Phys. Chem. B 2004,
108, 4701.
(12) Tu, H.; Mogyorosi, K.; Kelley, D. F. J. Chem. Phys. 2005, 122,
44709.
(13) Revaprasadu, N.; Malik, M. A.; Carstens, J.; O’Brian, P. J. Mater.
Chem. 1999, 9, 2885.
(14) Peng, X.; Wickham, J.; Alivisatos, A. P. J. Am. Chem. Soc. 1998,
120, 5343.
(15) Manjo´n, F. J.; Errandonea, D.; Segura, A.; Mun˜oz, V.; Tob´ıas, G.;
Ordejo´n; Canadell, E. Phys. ReV. B 2001, 63, 125330.
(16) Ben-Chorin, M.; Averboukh, B.; Kovalev, D.; Polisski, G.; Koch,
F. Phys. ReV. Lett. 1996, 77, 763.
(17) Takagahara, T.; Takeda, K. Phys. ReV. B 1992, 46, 15578.
(18) Yu, P. Y.; Cardona, M. Fundamentals of Semiconductors;
Springer: Berlin, Germany, 2001.
(19) Albrecht, A. J. Mol. Spectrosc. 1961, 6, 84.
(20) Camara, M. O. D.; Mauger, A.; Devos, I. Phys. ReV. B 2002, 65,
125206.
(21) Gomes-da-Costa, P.; Dandrea, R. G.; Wallis, R. F.; Balkanski, M.
Phys. ReV. B 1993, 48, 14135.
(22) Ferlat, G.; Xu, H.; Timoshevskii, V.; Blase, X. Phys. ReV. B 2002,
66, 85210.
(23) Koster, G. F.; Dimmock, J. O.; Wheeler, R. G.; Statz, H. Properties
of the Thirty-Two Point Groups; M.I.T.: Cambridge, MA, 1963.
(24) Arfken, G. Mathematical Methods for Physicists; Academic
Press: New York, 1970.
Conclusions
Several conclusions may be drawn from the results presented
here.

The Spectroscopy of InSe Nanoparticles
J. Phys. Chem. B, Vol. 109, No. 26, 2005 12709
(25) Abromowitz, M.; Stegun, I. A., Eds. Handbook of Mathematical
Functions; Dover: New York, 1965.
(30) Landau, L. D.; Lifshitz, E. M. Quantum Mechanics; Pergamon
Press: Oxford, UK, 1977.
(26) Kress-Rogers, E.; Nicholas, R. J.; Portal, J. C.; Chevy, A. Solid
State Commun. 1982, 44, 379.
(27) Segura, A.; Guesdon, J. P.; Besson, J. M.; Chevy, A. J. Appl. Phys.
1983, 54, 876.
(31) Tu, H.; Mogyorosi, K.; Kelley, D. F. Phys. ReV. B 2005, submitted
for publication.
(32) Efros, A. L.; Rosen, M. Annu. ReV. Mater. Sci. 2000, 30, 475.
(28) Williams, R. H.; McCanny, J. V.; Murray, R. B.; Ley, L.; Kemeny,
P. C. J. Phys. C 1977, 10, 1223.
(29) McCanny, J. V.; Murray, R. B. J. Phys. C 1977, 10, 1211.
(33) Banin, U.; Lee, C. J.; Guzelian, A. A.; Kadavanich, A. V.;
Alivisatos, A. P.; Jaskolski, W.; Bryant, G. W.; Efros, A. L.; Rosen, M. J.
Chem. Phys. 1989, 109, 2306.