Published: July 14, 2011
Published 2011 by the American Chemical Society 15927 dx.doi.org/10.1021/jp205784g | J. Phys. Chem. C 2011, 115, 15927–15932
ARTICLE
pubs.acs.org/JPCC
Mobile Surface Traps in CdSe Nanocrystals with Carboxylic
Acid Ligands
Oleksandr Voznyy*
Institute for Microstructural Sciences, National Research Council of Canada, Ottawa K1A 0R6, Canada
b
S Supporting Information
’ INTRODUCTION
Since the discovery of colloidal semiconductor nanocrystals
(NCs) they have found tremendous amount of applications in
bioimaging,1 lasing,2 diodes,3 single-photon sources,4 photovoltaics,5
etc. owing to a wide range of techniques6 available to tune their
optical and electronic properties.
Many of those applications rely on emission properties of NCs
(quantum yield, emission wavelength broadening and diffusion,
Stokes shift, blinking) which are strongly affected by different
types of defects, supposedly residing at the surface.7 Surface traps
may also affect the multiexciton generation yields8 and charge
carriers extraction, relevant, e.g., for photovoltaics. Understand-
ing better the source of the trap states can help to develop the
synthesis procedures to reduce or ultimately eliminate the traps.
In contrast to absorption properties, which are determined
mainly by the bulk crystalline structure and the macroscopic
properties of the NCs (size, shape),9,10 surface and thus emission
properties require a more detailed knowledge on atomic scale.
The exact atomistic nature of surface defects remains
unknown11
13 and the interpretation of experimental data is
thus often based on available theoretical models. Several semi-
empirical studies of ligated surfaces are available14
18 but this
methodology does not reliably capture surface reconstructions
and charge redistributions. Few ab initio studies of the NC sur-
faces available to date addressed only the bare surfaces19
25 or
weakly bound (L-type) ligands.26
30 However, more and more
experimental data suggest that the main type of ligands present on
the surface are the covalently bound (X-type) ligands, e.g., depro-
tonated carboxylic or phosphonic acids.31
33 Theoretical studies of
such ligands on CdSe and PbSe only start to emerge.30,33
35
In this work we investigate from first principles the atomistic
nature of the surface states in NCs. To do this, we choose CdSe
NCs without structural defects, small enough to be treated within
the density functional theory (DFT) but large enough to
distinguish delocalized (core) and localized (trap) states, with
carboxylic acid ligands bound covalently. We find that even such
an idealized and small model is rich enough to create structures
with or without surface trap states, depending on the amount of
ligands. Contrary to expectations, apparently more passivated
structures (with more ligands and less dangling bonds) exhibit
more surface traps. Ourmost important finding is the presence of
mobile surface ligands whose energy levels fluctuate respectively,
a feature required by several phenomenological models of
blinking.36
38 We will discuss whether the observed diffusion
on its own is capable of explaining the fluorescence intermit-
tency, and whether it is capable of producing switchable long-
lived trap states.
’COMPUTATIONAL METHODS
Calculations were performed within DFT using the SIESTA
code.39 Generalized gradient approximation in a Perdew
Burke

Ernzerhoff formulation, Troullier-Martins norm-conserving pseudo-
potentials with nonlinear core corrections, semicore d-states
included in valence shell for Cd, optimized double-ζ plus
polarization basis sets, and 300 Ry mesh cutoff for charge density
were used throughout. Geometries were optimized until forces
on atoms below 40 meV/Å were achieved. Full simulation input
files are provided in the Supporting Information. The conver-
gence of the simulation parameters and the general validity of our
approach were tested by reproducing previous DFT results for
bare19 and ligated28 CdSe nanoclusters.
Received: June 20, 2011
Revised: July 11, 2011
ABSTRACT: We have performed ab initio calculations of
electronic properties of the realistic Cd-rich CdSe nanocrystals
with covalently bound carboxylic acid (X-type) ligands. Con-
figurations both with and without surface traps can be prepared
depending on the amount and geometry of the adsorbed
ligands. We find that Cd and Se dangling bonds do not nec-
essarily create surface traps, whereas traps originating from
ligands can form near the top of the valence band. Some of the
ligands are found to bemobile on the surface and this mobility is
accompanied by a spectral diffusion of the associated trap energy levels. This provides the first atomistic example of the processes
required to explain the emission wavelength and lifetime variations, and blinking of the nanocrystals.

15928 dx.doi.org/10.1021/jp205784g |J. Phys. Chem. C 2011, 115, 15927–15932
The Journal of Physical Chemistry C ARTICLE
Different synthesis procedures of CdSe nanocrystals have
been reported, with trioctylphosphine (TOP), trioctylphosphine
oxide (TOPO), amines, and carboxylic and phosphonic acid
ligands available in solution. The resulting stoichiometry of li-
gands on surface, however, is usually not well quantified. For
phosphine-based synthesis, species not even considered to exist
in solution were found recently to be the main ligands on NC
surfaces and were shown to come from impurities in solvents or
in source materials.32,40 Modeling of such ligands is also compli-
cated by their higher structural complexity and increased amount of
possible binding geometries. We thus choose carboxylic acids
(known to be the sole ligands in phosphine-free synthesis31,41
45)
as prototypical ligands for current study. Zincblende structure is
used throughout, since it is known to be preferred with carboxylic
acid based synthesis,31,41,44,45 in contrast to wurtzite structure
usually reported for synthesis with TOP/TOPO.
We prepare our models by carving a sphere out of zincblende
CdSe bulk and removing all singly bonded atoms. On the facets
where the formation of two dangling bonds per atom is unavoid-
able we give preference to Cd-termination, leading to Cd-
enriched clusters, as suggested by experiments.11,31,32,43 Acetate
(CH3COO

) is used as a representative model of the longer
fatty acid ligands. The diameter of the NC is adjusted to obtain a
structure that matches as close as possible the charge neutrality
condition intended to reduce the amount of surface states:14,15
NCd  ðþ 2Þ þ NSe  ð-2Þ þ NAc  ð-1Þ ¼ 0 ð1Þ
This condition has its roots in the second Pauling rule and is
also similar to the electron counting rule used to determine stable
semiconductor surface reconstructions.46,47 Both approaches
aim to ensure that the total amount of electrons in the system
will match the amount of bonds (in the idealized bulk-like
structure this means 4 bonds per Cd or Se and 1 bond per
acetate); that is, in general, they are not related to the balance of
electronic and ionic charges. In the absence of surface Se dimers,
eq 1, counting all NC atoms, remains valid and provides identical
results to the more general electron counting rule, which con-
siders only the surface atoms. One can see from eq 1 that the
amount of ligands should be equal twice the excess of Cd atoms.
The structure of the cluster thus can be widely varied by adjusting
either the amount of ligands, adding/removing Cd or Se atoms,
or artificially charging the cluster as a whole.
Prepared in such a way [Cd56Se50(OAc)13]
1- cluster is shown
in Figure 1. Our model is Cd-rich and has a tetrahedral shape,
similar to that of the thiolated ultrastable clusters48,49 and also
typically observed for larger CdSe NCs with carboxylic ligands.31
It maintains the bulk-like local geometries for all atoms after
optimization, representing well the bigger NCs with surface
faceting. The three facets available are beneficial for modeling
of ligand absorption all within one model. We believe that our
structure is a better representative of the solution-prepared NCs
than the highly reconstructed nonligated stoichiometric
Cd33Se33 cluster often observed in laser ablation experiments
50
and used in previous theoretical works.19,24,28,33
For clarity of the presentation we choose to describe the re-
sults for the cluster with∼1.6 nm diameter and minimal amount
of ligands. To comply with the electroneutrality condition (eq 1),
the model in Figure 1 has several Cd atoms removed from the
(001) facets (green arrow in Figure 1). One “extra” ligand is
added (red arrow), compensated by a net charge
1 of the
cluster as a whole. These artifacts do not affect the overall
conclusions of the paper: a similar Cd68Se50(OAc)36 charge-
neutral model with more Cd and ligands can be built (see Figure
S1 in the Supporting Information) and was in fact the starting
point in our simulations. Test calculations were also performed
on smaller zincblende clusters, as well as a wurtzite NC of∼3 nm
diameter.
’RESULTS
Ligand Geometries and Energetics. Figure 2 presents the
optimized geometries of the ligands. First we populate all avai-
lable adsorption sites on a (001) facet, the remaining “extra”
ligand is then placed elsewhere on the surface. Binding energies
were computed for charge-neutral desorbed species, without
corrections for solvent effects. Obtained values should not be
used for direct comparison with experiment, nevertheless, they
are reliable for relative comparison of different adsorption sites.
Adsorption of the ligand on a (001) facet (Figure 2a,b) is the
most stable since its departure would leave one (or both) Cdwith
two dangling bonds. Calculated binding energy of the deproto-
nated acetate (Eb > 4 eV) is much larger than the values reported
previously for protonoated case (Eb < 1 eV),27,33 consistent with
similar findings for CdSe33 and PbSe34 surfaces. Simulations
starting from the ‘bridge’ (Figure 2a) or “chelate” geometries
(similar to Figure 2d) both relaxed to a ‘tilted bridge’ geometry
(which is ∼0.25 eV lower in energy), with one of the oxygens
bonding to two Cd atoms (Figure 2b). This geometry is
consistent with Cd NMR data for CdSeTe magic-size NCs43
and single-crystal XRD data for some Cd salts.51 Previous
theoretical studies on smaller Cd33Se33 clusters could not resolve
Figure 1. Optimized structure of the [Cd56Se50(OAc)13]1- nanocrystal
used in calculations. Green arrow marks the missing Cd atoms on the
(001) facet; red arrow, an “extra” ligand.
Figure 2. Optimized geometries of acetate on CdSe NC surface: (a and
b) on (001) Cd-rich surface facet of the NC and (c and d) on (111)
Cd-rich facet. The atoms legend is the same as in Figure 1.

15929 dx.doi.org/10.1021/jp205784g |J. Phys. Chem. C 2011, 115, 15927–15932
The Journal of Physical Chemistry C ARTICLE
the tilt and reported bridge structure as the most stable one.33
Due to small energy difference, at room temperature the ligand
will be continuously switching between the bridge and left-tilted-
and right-tilted-bridge configurations.
Adsorption on a Se-rich (
111) facet is unfavorable since Se
dangling bond is filled with electrons and repels the oxygen. The
ligand tries to move to a nearby Cd atom on a (001) facet (as also
reported previously27,28). If however this is not possible, e.g.,
when ligand is placed in the middle of Se (
111) facet, the ligand
pulls out the Cd atom from the underlying layer, breaking its
bond to the even deeper Se atom and leaving that Se with a
dangling bond. Such a reconstruction stabilizes the ligand on the
surface but remains ∼1 eV less favorable than adsorption on a
Cd-rich (111) facet.
On a Cd-rich (111) facet, the extra ligand adsorbs in either
bridge (Figure 2c) or chelate (Figure 2d) geometry. The “titlted
bridge” geometry is not favorable due to a larger distance
between Cd atoms, a three-bonded geometry of Cd prohibiting
its large inplane displacements, and the preference for a normal
direction of the Cd dangling bond. Binding energies Eb ∼ 2
3
eV depend on the exact cluster geometry and the amount of
ligands and are noticeably weaker than on (001) facet. We find
that adsorption of the extra ligand on the already occupied Cd
atoms of a (001) facet (sites a,b in Figure 1) is still possible and is
in fact slightly more stable than on (111) facet (sites c,d). The
energy difference between the most and the least stable geome-
tries of the extra ligand (bridge on sites a-b vs chelate on site d,
respectively) is ∼0.6 eV.
Mobility of Ligands. Bridge geometry on (111) facet is only
0.2 eV more stable than the chelate. We did not perform the
analysis of the vibrational modes in the chelate geometry to
determine whether it is the saddle point of the transition between
two bridge structures or it is a local energy minimum. In the latter
case the actual barrier for diffusion may increase slightly, other-
wise, diffusion should be possible already at temperatures as low
as 50 K. Molecular dynamics simulations at 420 K (typical exper-
imental temperature) indeed confirm that the ligand can easily switch
between the bridge and chelate geometries and can “walk” from site
to site (see Figure 2, panels c and d) on a subpicosecond time scale.
Only the ligands adsorbed on (111) facets can diffuse. On the
Cd56Se50(CH3COO)12 cluster, which is similar to experimental
magic-size thiolated clusters,48,49 we do not have such ligands at
all. However, on Cd68Se50(CH3COO)36 (see the Supporting
Information), which likely represents better the real synthesis
conditions with the excess of Cd and ligands in solution, there are
many ligands capable to diffuse. We expect that even at the high-
est coverage, ligand diffusion would not be eliminated since steric
repulsion between the ligands does not allow covering every
surface atom.18
Mobility of the covalently bound (X-type) ligand on a surface
is unexpected but not surprising; numerous examples of such
behavior can be found, e.g., mobile adatoms, ligands, and ligand

adatom complexes on Au(111);52 diffusion of covalently bound
species on surface is also considered crucial for the formation of
organic self-assembled monolayers on semiconductor surfaces.53,54
Nevertheless, mobility was never fully appreciated for ligands on
NCs, although NCs partially covered by ligands were studied
theoretically previously.27,28 We speculate that the nature of the
carboxylate ligand, utilizing two oxygen atoms to bind to the
surface and thus being able to cover two surface atoms, helps it to
reduce the diffusion barrier significantly, compared to single-
bonded ligands studied previously.
Electronic and Optical Properties. Electronic properties of
the NCs are summarized in Figure 3. Valence band of the NC is
formed predominantly from Se 4p states (yellow), whereas the
conduction band consists of Cd 5s states (green), similarly to
bulk CdSe either in zincblende or wurtzite structures. The
corresponding localization of the holes on Se and electrons on
Cd atoms is visible in the charge density plots of the HOMO
(Figure 3e) and LUMO (Figure S2, Supporting Information),
respectively.
In the absence of “extra” ligands (a charge-neutral Cd56Se50-
(CH3COO)12 cluster (Figure 3b), the HOMO and LUMO are
delocalized over the whole NC, both forming S-like envelopes
(Figure 3e and Figure S2 in the Supporting Information). The
three levels above the LUMO have P-like envelopes (Supporting
Information, Figure S2). The HOMO
LUMO optical transi-
tion is allowed (bright).
This cluster has no surface traps despite numerous surface
atoms not covered by ligands (see Figure 1). Since the electro-
neutrality condition is satisfied, the resulting dangling bonds are
either completely filled (Se) or completely empty (Cd) and do not
get into the band gap. The absence of the trap states in the gap is a
well-known fact for reconstructed flat surfaces.46,47 Similar ob-
servations were also made previously for the self-healed bare19,22
and ligated28 Cd33Se33 clusters and PbSe NCs,
25 where surface
traps were observed only on surface atoms with more than one
dangling bond. Ligand-related levels in our NC remain deep in the
valence and conduction bands (red and black bands in Figure 3b)
and their significant broadening compared to a free ligand
molecule (Figure 3a) indicates strong mixing with CdSe.
Introduction of the “extra” ligand does not affect the deloca-
lized electron and hole states, except for some distortion of their
Figure 3. Projected density of states of (a) free CH3COOH molecule,
(b) Cd56Se50(CH3COO)12 cluster, (c and d) [Cd56Se50(CH3COO)13]
1-
cluster with an “extra” ligand in the bridge and chelate geometries,
respectively. A 50 meV Gaussian broadening of the peaks is used. (e
g)
charge densities of the HOMO for the cases of no extra ligand, bridge,
and chelate ligand, respectively.

15930 dx.doi.org/10.1021/jp205784g |J. Phys. Chem. C 2011, 115, 15927–15932
The Journal of Physical Chemistry C ARTICLE
envelopes (Figure S3 in the Supporting Information). This extra
ligand, however, creates a new subband in the gap near the top of
the valence band. Such positioning is expected for oxygen, being
strongly electronegative and thus a strong acceptor. Similar
behavior is expected for sulfur in thiolate ligands. A more careful
examination shows that a similar ligand-related component
shifted to higher energies appears for every ligand-related energy
level (red and black PDOS bands with arrows in Figure 3c,d).
Investigation of the wave functions in the newly formed subband
confirms their localization on the ligand (Figure 3f,g). These
(trap) states show a noticeable delocalization over the nearby
surface Se atoms (Figure 3f and a strong yellow PDOS compo-
nent of trap states in Figure 3c), despite that ligand is
adsorbed on Cd.
Increasing the amount of “extra” ligands increases the height
and width of the trap band and leads to its significant overlap and
mixing with valence states. The optical transitions from this trap
band into LUMO are allowed by symmetry, and the intensity of
such transitions depends mainly on their delocalization (i.e.,
overlap with LUMO). For the nanocrystal size used in this work,
the intensity of such trap-LUMO optical transitions is compar-
able to the intensity of HOMO
LUMO transitions, consistent
with the experimental observation of white emission from
ultrasmall nanocrystals.43,44,55,56 For larger nanocrystals we ex-
pect the reduction of the trap-LUMO overlap and, consequently,
reduction of the trap emission intensity relative to excitonic
emission.
The ligand in a chelate geometry couples weaker to the NC,
resulting in its energy level being shifted deeper into the gap
(purely red peak in Figure 3d) and a stronger charge localization
on the ligand (Figure 3g). As a result, the optical transition from
ligand to LUMO becomes practically invisible in absorption
spectrum even for such a small NC.
A varying pattern of ligands on the surface and their coupling
to the states inside the dot will affect the overall shape of the ele-
ctron and hole envelopes (Figure S3, Supporting Information)
and the degree of their overlap (transition dipole moment),
affecting in such a way the radiative lifetime of the exciton. In the
presence of the competing (nonradiative) relaxation pathway,
this can explain the fluctuating emission intensity observed
experimentally.57 Similarly, the rearrangement of ligands may
affect the energetic positions of the electron and hole states,
resulting in a diffusion of exciton emission wavelength.58
’DISCUSSION
Role of Electronic Balance. Our simulations show that trap-
less NC surfaces can be prepared with minimal (and even with-
out) participation of ligands. To achieve this, it is required to find
a NC geometry where each surface atom possesses only a single
dangling bond and the overall electronic balance (amount of
electrons vs amount of bonds) of the NC is fulfilled. This is not
possible for any NC stoichiometry but only for some specific
sizes and/or shapes. Stronger ligand binding to a balanced NC
also suggests a close relation of such trap-less NCs to magic size
(ultrastable) NCs.44,48,49 Their potentially lower ligand coverage,
however, would impose lower colloidal stability.
In experimental conditions, such geometries may not always
be achieved kinetically. Deviations from ideal stoichimetries and
thus from electronic balance are ineviteable. As a result, partially
filled, and thus situated in the gap, dangling bonds can form. The
surface of the NC will try to self-heal (readjust the amount of
bonds)19,22,47 by creating dimers, changing hybridization of
atoms from sp3 to sp2, etc. However, even if this readjustment
is able to eliminate the partially filled dangling bonds, the result-
ing local strains will affect the bandstructure, pushing some of the
states into the gap. Charged ligands can help in restoring the
electronic balance of the NC and at the same time preserving
more bulk-like environment for surface atoms. Naively, this
should help eliminate the amount of surface traps. However,
some ligand geometries (e.g., on (111) facet) remain weakly
bound to the surface and form the trap states themselves.
Based on binding energies calculated for our model NC, one
might expect the ligated (001) facet to be the most stable, favor-
ing the cube-shapedNCs. Nevertheless, NCs of tetrahedral shape
(i.e., (111)-terminated) are typically observed experimentally.31,59
Previously, for identical adsorption geometries on flat surfaces,
we observed a strong dependence of binding energy on the ele-
ctronic balance.53 For NCs, the balance may change with the
change of NC size or shape due to possibility of charge transfer
between different facets (independent of the chemical potentials
of Cd, Se or ligands). Two facets, apparently unfavorable in the
infinite surface calculations, may become favorable when brought
together in a NC. Similar findings were recently reported for
PbSe NCs.34 This highlights the inappropriateness of the infinite
surface models for prediction of NC shape based on Wulff’s
rule.26,59
It should be noted that cubic or platelet-like NCs (with only
(001) facets) have been reported by adjusting the kinetics of NC
synthesis59,60 and they represent an interesting system as poten-
tially trap-less NCs. Our preliminary analysis suggests, however,
that a cubic shape does not provide enough adsorption sites for
ligands to fulfill the electronic balance of the NC (since ligand in
bridge geometry covers two Cd sites). We expect, thus, that in
order to become more stable than tetrahedral shape, cubic NCs
have to adsorb additional ligands in less favorable geometries,
potentially creating surface traps.
Consequences for Blinking. Dependence of the trap level
energy on ligand geometry, combined with the surface diffusion
of the ligand, results in a spectral diffusion of the trap levels. Such
a feature is a central requirement in some phenomenological
models of blinking.36
38,61 The spectral diffusion due to switch-
ing bridge-chelate configurations observed in this work is so fast
(subpicosecond) that it hardly can induce the irregularities in
tunneling from the core to the traps required for the power-law
blinking statistics.36,37 The ligand diffusion on a larger scale,
however, provides a mechanism of a random walker in a phase
space of dark and bright configurations.36 A switchable long-lived
trap state, required by the conceptually similar multiple recom-
bination centers (MRC) model of blinking,61 can be prepared
within our model. As we have discussed, adsorption of the ligand
on the Se-rich (
111) facet can be stabilized by pulling out the
Cd atom from the subsurface layer. Here we note that this pro-
cess is accompanied by the formation of a deep and strongly
localized trap level in the gap. A low frequency of activating such
defects (long fluorescence ON times) is achieved by the require-
ment for the diffusing ligand to appear in a specific area of theNC
surface (especially if this area is energetically unfavorable). A
longer fluorescence OFF state can be achieved by consecutive
activation of multiple similar defects, as suggested in the original
model.61 We believe that adsorption of ligand on Se facet can be
sufficiently long-lived for nonradiative recombination to happen
and render the NC dark. We cannot however estimate at this
moment whether our particular example of a diffusion-activated

15931 dx.doi.org/10.1021/jp205784g |J. Phys. Chem. C 2011, 115, 15927–15932
The Journal of Physical Chemistry C ARTICLE
defect (or multiple such defects activated consecutively) can last
for hundreds of seconds.
The presence of the whole band of trap states overlapping with
the valence band in our model implies the need to populate all
of those states with holes before excitonic emission becomes
possible. In the absence of a similar trap band near the conduc-
tion band this would lead to accumulation of multiple electrons
in the core. Recent findings challenging the validity of the
(single) charging model of blinking8,62 suggested that photo-
luminescence quenching due to Auger process could still be com-
patible with experimental observations if multiple charging was
possible. Significant imbalance in the amount of electrons and
holes in the core is clearly easily achievable when many traps are
available. Even in the presence of the energetic gap between the
valence band and traps, the transfer of the carriers from core to
traps would still be possible due to rare significant spectral shifts
of the trap levels accompanying ligand diffusion. Similarly, in the
presence of the shell, excitation with energies beyond the barrier
also allows for a significant part of photogenerated holes to be
lost into traps.
’CONCLUSIONS
In conclusion, we have investigated with ab initio methods the
surface states in realistic CdSe NCs with carboxylic acid ligands,
highlighting the importance of the electronic balance for the ele-
ctronic properties and growth of the NCs. Developed proto-
typical model of the NCs should come useful for future
simulations.
We show that it is possible to construct trap-less NCs even
in the presence of surface atoms with dangling bonds (i.e., un-
covered by ligands). On the contrary, excess ligands can produce
surface traps even in the idealized NCs. The ligand-related trap
states are found to reside near the top of the valence band.
NCs are found to be highly dynamic even when external envir-
onment is not considered. Some of the ligands have a negligible
energy barrier for diffusion over the surface. Spatial diffusion is
accompanied by a spectral diffusion of the trap energy levels and
a varying degree of charge localization. Ligand diffusion can
explain the emission wavelength and lifetime variations, and
offers a flexible tool to build atomistic examples of the processes
required by phenomenological blinking models.
’ASSOCIATED CONTENT
b
S Supporting Information. Simulation input files, 3D struc-
tures of the NCs, and charge densities of states from conduction
band. This material is available free of charge via the Internet at
http://pubs.acs.org.
’AUTHOR INFORMATION
Corresponding Author
*E-mail: ovoznyy@gmail.com.
’ACKNOWLEDGMENT
We thank Eleonora Piven, Kui Yu, Pavel Frantsuzov, Svetlana
Kilina, and Pawel Hawrylak for fruitful discussions and NRC-
NSERC-BDC project for funding.
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