Download Soft X-ray spectroscopy of single sized CdS nanocrystals: size

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Solid State Communications 112 (1999) 5–9
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Soft X-ray spectroscopy of single sized CdS nanocrystals: size
confinement and electronic structure
J. Lüning a,*, J. Rockenberger b,†, S. Eisebitt a, J.-E. Rubensson a,‡, A. Karl a,
A. Kornowski b, H. Weller b, W. Eberhardt a
a
Institut für Festkörperforschung, Forschungszentrum, Jülich, D-52425 Jülich, Germany
Institut für Physikalische Chemie, Universität Hamburg, D-20146 Hamburg, Germany
b
Received 11 June 1999; accepted 23 June 1999 by P. Dederichs
Abstract
Soft X-ray spectroscopy of CdS nanocrystals within their crystalline superlattice allows to relate unambiguously changes of
the electronic structure with the particle size and shape which is known from single crystal X-ray diffraction. We find that the
valence and conduction band edge shift contribute to the same extent to the total band gap opening of about 2 eV with respect to
CdS bulk as the particle size decreases to 10 Å. Taking a finite height of the potential walls into account, we can reproduce these
results within an effective mass approximation model. 䉷 1999 Elsevier Science Ltd. All rights reserved.
Keywords: A. Nanostructures; A. Semiconductors; B. Chemical synthesis; C. EXAFS, NEXAFS, SEXAFS; D. Electronic band structure
The development of the electronic band structure of
solids from discrete localized atomic states is one of the
key points of interest in cluster physics. To investigate
size-dependent changes most techniques require macroscopic amounts of samples with a narrow size and shape
distribution. These requirements can now be fulfilled by
colloidal chemistry for several II–VI and III–V semiconductors [1–3]. In certain cases, even crystalline superlattices of single-sized nanoparticles can be synthesized,
guaranteeing even a uniform structure of the particles [4–6].
We present here the first detailed spectroscopic investigation of single sized CdS nanocrystals (NC) within their
crystalline super-lattices. These particles resemble small
units of the bulk lattice, which are covered by thiols (SR,
R organic rest). The studied particles are a NC of 40 Å
diameter [7], and the more molecule-like NCs
Cd32S14(SR)36 (17.5 Å) [5] and Cd17S4(SR)26 (13.5 Å) [6]
whose structures are known from single crystal X-ray
* Corresponding author. Present address: IBM Almaden
Research Center, 650 Harry Road, San Jose, CA 95120, USA.
†
Present address: University of California, Berkeley, Department
of Chemistry, Berkeley, CA 94720, USA.
‡
Present address: Department of Physics, Uppsala University,
Box 530, 75121 Uppsala, Sweden.
diffraction. To extend the size range into a truly molecular
regime, we also studied a pure Cadmium thiolate whose
single crystal structure consists of Cd8(SR)16 units [8].
So far, only optical absorption measurements of these
samples have been possible in solution and on thin films
after dissolution of the super-lattice. These data reveal the
changes in the total optical gap, but the optical properties of
the NCs within their super-lattice are still unknown. The
optical excitation energies for the dissolved particles
(DEopt in Table 1) increase from 2.5 eV for CdS bulk to
around 4.7 eV for Cd thiolate [5–8].
The unique combination of properties of photon based
soft X-ray spectroscopy techniques (SXS) [9], i.e. bulk
sensitivity, element selectivity, and insensitivity to electrostatic sample charging, enables us to study the valence and
conduction band electronic structure of the NCs surrounded
by their stabilizing ligand shell in the super-lattice crystal.
Probing separately the occupied and unoccupied part of the
electronic structure, SXS can especially resolve their individual contributions to the total band gap opening [10].
In soft X-ray absorption (SXA) spectroscopy a core electron is excited into the conduction band (CB) (using as
convention the terminology of solid state physics even for
the more molecular-like particles). The transition probability is to a good approximation proportional to the local
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J. Lüning et al. / Solid State Communications 112 (1999) 5–9
Table 1
Optical excitation energies for the dissolved particles. The sizes are
taken from Refs. [5–8]. DEopt (eV) values denote the increase of the
optical excitation energies relative to the bulk value of 2.5 eV as
measured on dissolved nanoparticles. Note, that it is known from
111
Cd-NMR [24] spectroscopy that the Cd8(SR)16 unit of the Cd
thiolate single crystal structure is destroyed on dissolution. DESXE
and DESXA are the shifts (as found in Fig. 1, uncertainty is
^0.15 eV) relative to CdS bulk of the high-energy cut-off in the
SXE and the LPDOS absorption onset in the SXA spectra, respectively. The DEgap summarizes the total gap opening as found by
SXS. The shifts of the binding energy for the S 2p spin–orbit
split doublet with the lowest binding energy are given by DEL3 .
BW gives the width of the upper VBs as determined in Fig. 1.
For CdS bulk, the corresponding value is 4.8 eV
Size (Å)
DEopt(eV)
DESXE(eV)
DESXA(eV)
DEgap(eV)
DEL3 (eV)
BW(eV)
CdS40 (Å)
Cd32
Cd17
Cd8
40
0.5
⫺ 0.50
0.24
0.7
0.13
4.6
17.5
1.2
⫺ 0.76
0.40
1.2
0.31
4.3
13.5
1.7
⫺ 1.24
0.55
1.7
0.33
4.0
⬇ 10
2.2
⫺ 1.50
0.65
2.2
0.46
3.5
partial density of states (LPDOS) [11,12] 1,2 of the CB, i.e.
the DOS projected onto the site of the atom carrying the core
hole (local) and onto the angular momentum symmetry of
the core state (partial).
In soft X-ray emission (SXE) spectroscopy the radiative
decay of an excited core hole state by a transition of a
valence band (VB) electron is observed, and the occupied
LPDOS of the VB is mapped by the spectral intensity
distribution in SXE spectra [13]. 3
The experiments were carried out at the undulator beamline BW3 [14] at HASYLAB, Hamburg. S L2,3 SXA spectra
were measured with a photon energy resolution of better
than 40 meV by monitoring the fluorescence yield using a
channeltron, thereby avoiding sample charging problems.
Saturation effects were minimized due to a normal-in grazing-out geometry [15]. S L3 SXE spectra were recorded with
a resolution set to 0.7 eV for high spectrometer throughput.
The energy scales of the SXA and SXE spectra are referred
to each other better than 50 meV using reflection of the
monochromatized synchrotron radiation into the spectrometer.
All samples, prepared and characterized as described in
Refs. [5–8], were pressed as polycrystalline powders into
indium foil, including a CdS bulk sample for reference.
On the right hand side of Fig. 1 we show the S L2,3 SXA
spectra of bulk CdS (which agrees with Refs. [16,17]), of the
1
This DOS interpretation (e.g. Ref. [11]) is valid for systems like
CdS where electron correlation effects are negligible.
2
For correlation effects in SXS see, e.g. Ref. [12].
3
The applicability of the underlying ‘two-step approximation’ is
discussed in, e.g. Ref. [13].
Fig. 1. Right part: S L2,3 SXA spectra (solid) of CdS bulk, a thiolstabilized NC of 40 (CdS40), the Cd32S14(SR)36 (Cd32) and the
Cd17S4(SR)26 (Cd17) NC, and the Cd thiolate Cd8(SR)16 (Cd8). The
dotted lines show the separation into excitonic and LPDOS excitation. Left part: top part of the smoothed S L3 SXE spectra (crosses
show the non-smoothed data) mapping the local S…s ⫹ d† symmetric
DOS of the upper VB. The width of the upper VB is quantified by
the arrows indicating the full width at half maximum of the upper
VB. Gray bars indicate the linear extrapolation of the emission cutoffs and the LPDOS absorption onsets, respectively.
CdS NCs, and of Cd thiolate. As the S 2p level is spin–orbit
split, only the first 1.1 eV above the absorption onsets
belong uniquely to S L3 absorption, while for higher photon
energies the SXA spectra are a superposition of S L3 and S
L2 absorption. The pronounced structures in the CdS bulk
SXA spectrum above 163 eV result from various maxima in
the unoccupied DOS, and can be assigned to high-symmetry
points [16,18].
Comparing all SXA spectra one notices that with decreasing particle size the first shoulder of the bulk spectrum
separates increasingly from the remaining absorption spectrum and becomes a discrete peak. In addition, the energy of
the absorption onset is nearly identical for all samples (core
level binding energy shifts, which affect absorption energies
are discussed below). This indicates that the first peak does
not result from quantization of the unoccupied DOS due to
the restricted particle size. Otherwise, one would expect a
J. Lüning et al. / Solid State Communications 112 (1999) 5–9
significant shift of the absorption onset as the effective mass
approximation (EMA), using infinitely high potential walls
[19], predicts for CdS that the band gap opening (of the
order of 2 eV for the smaller particles) is mainly due to a
shift of the CB minimum (CBM).
The observed spectral changes are, however, consistent
with an assignment of the peak to a S L3 core exciton. Since
no distinct structure is observable in the bulk SXA spectrum,
the S L3 core exciton is weakly bound, i.e. the bulk exciton
radius is of the order of several 10 Å [20]. In particles with a
size comparable to the exciton radius, the core exciton binding energy thus increases with decreasing particle size due
to confinement [19], increasing the separation between the
exciton and the remaining absorption features in line with
the observation in Fig. 1. So, the apparent absorption onset
appears to be size independent while the unoccupied states
shift to higher binding energies.
This assignment of the first structure in the NC SXA
spectra implies that the shoulder in the SXA spectrum of
CdS bulk is due to S L3 core exciton excitation, in contrast to
previous interpretations [16,17].
For a quantitative analysis of the first 2 eV of the SXA
spectra we make a two-Gaussian fit representing excitation
into excitonic and unoccupied states. The description of the
latter part by a single Gaussian assumes that the vibrational
broadening of around 700 meV, as found for the core exciton excitation, masks the fine structure of the CB LPDOS
close to the CBM.
All fits give the same energy position of the core exciton
of 162.7 eV within their accuracy, and a similar full width at
half maximum (FWHM) around 700 meV. Subtracting the
Gaussian representing the core exciton from the SXA spectra we obtain the parts of the SXA spectra which we relate to
the LPDOS (dotted lines in Fig. 1). Comparing the LPDOS
absorption onsets one observes the expected shift to higher
energies with decreasing particle size which we quantify by
linear extrapolation (gray bars in Fig. 1, DESXA in Table 1).
Note, that due to broadening these onsets do not necessarily
indicate the position of the CBM itself. We further note that
this interpretation of the absorption spectra ignores any core
hole influence on the unoccupied states which may lead us
to underestimate the shift for the smaller particles.
The upper part of the photon excited S L3 SXE spectra is
shown on the left hand side of Fig. 1. The spectra map the
local S…s ⫹ d† symmetric DOS of the upper VB, as only S L3
core hole states contribute to the spectra due to the selected
photon excitation energy of 162.9 eV (bandwidth 100 meV)
just below the S L2 threshold. Note that only due to hybridization the states of the upper VB, derived mainly from the
S 3p and Cd 5s states, have local s and/or d symmetric
character at the S sites.
The influence of the size restriction on the VB structure of
the nanoparticles can clearly be seen in Fig. 1. As expected
in a quantum confinement framework the high-energy cutoff shifts to lower emission energies with decreasing size.
This is accompanied by a decrease of the intensity in the top
7
part of the upper VB reflecting changes in the shape of the
local S…s ⫹ d† symmetric DOS.
By linear extrapolation we determine the shift of the highenergy cut-off in the nanoparticle SXE spectra relative to the
bulk case (DESXE in Table 1) which we take as a measure for
the shift of the VB maximum (VBM) position [21]. 4
Adding the SXS shifts of VBM and CBM one obtains the
total band gap opening (DEgap in Table 1) for the nanoparticles in their crystalline environment relative to the bulk
material. Within the experimental uncertainties we find
these values to be in agreement with the optical excitation
energies recorded after dissolution of the super-lattice (note,
that the present uncertainty exceeds the estimated optical
exciton binding energies by which the optical excitation
energies are smaller than the band gaps).
The quantum confinement effects are not restricted to the
bandgap region alone, but one notices a general decrease of
the upper VB width. We quantify this by measuring the
FWHM as indicated by the arrows in Fig. 1 (BW in Table
1). This shows that due to the size restriction the width
decrease from 4.8 eV for CdS bulk to only 3.5 eV for the
Cd thiolate. We further report that the lower VB (compare
Ref. [17]), which is derived from the more localized S 3s
and Cd 4d states, is nearly unaffected by the size restriction.
In order to determine the individual contribution of the
VBM and CBM shift to the total band gap opening by
comparing the NCs SXS spectra to the CdS bulk spectra,
the SXS energy scales have to be corrected for possible
shifts of the S 2p core level binding energy. We, therefore,
have recorded S 2p photoelectron spectra (XPS) of CdS
bulk, the NCs, and the Cd thiolate, which refer the binding
energies against each other. These XPS spectra will be thoroughly discussed in a forthcoming publication [18], while
here we only report that the nanoparticle spectra show additional intensity on the side of higher binding energies (absolute values) which increases with decreasing particle size.
This is related to the increasing relative number of S atoms
at the particle surface which are covalently bound to the C
atoms of the thiols. As a consequence, the NC SXA spectra
in Fig. 1 are not as structured as the bulk spectrum for higher
photon energies, as for higher excitation energies all the S
atoms with different binding energies contribute to the SXA
spectra.
For the determination of the VBM and CBM shifts only
the S atoms with the lowest S 2p binding energy (absolute
values) are of importance, as these electrons are selectively
excited for excitation energies in the vicinity of the absorption threshold. Thus, the determined energies of the LPDOS
absorption onsets and the energy scales of the recorded SXE
spectra are related to these binding energies. We find that
with decreasing particle size the binding energy of this
component decreases by the amounts DEL3 listed in Table
4
We assume dynamics like energy dissipation (e.g.Ref. [12]) and
vibrational relaxation (e.g. Ref. [21]) in the intermediate state to be
comparable for the bulk and the nanoparticles.
8
J. Lüning et al. / Solid State Communications 112 (1999) 5–9
Fig. 2. Experimentally determined contributions of the occupied
and unoccupied states (black dots) to the total band gap opening
are compared to the EMA using infinitely high potential walls (solid
lines, IP-EMA) [19], the EMA taking the finite height of the potential walls into account (dashed lines, FP-EMA) [22] 5, and the tightbinding calculation of Lippens and Lannoo (gray diamonds, TB)
[24].
1. According to these values, the SXS energy scales of the
different samples have to be corrected.
In Fig. 2 the corrected VBM …DESXE ⫹ DEL3 † and CBM
…DESXA ⫹ DEL3 † shifts are compared to theoretical models.
The solid line is the EMA calculation for infinitely high
confining potentials (IP-EMA) [19] which predicts the
CBM shift to dominate the band gap opening. In contrast,
the experimental results show that both, VBM and CBM
shifts, contribute about equally to the gap opening.
Using an EMA algorithm developed to account for finite
potential heights (FP-EMA) in quantum-dot/quantum-well
heterostructures [22] 5 we obtain the predictions given by the
dashed lines. We note a surprisingly good agreement with
the experimental values, especially, the calculation also
predicts the shift of the VBM and CBM to be about equal.
This effect of the finite potential height can be understood
in a simple picture as for a smaller potential well the
confinement is not as effective, resulting in a smaller
VBM and, especially, a substantially reduced CBM shift.
The importance of the finite height of the confining potential
for the optical absorption and photoluminescence spectra of
CdSe–CdS core shell NCs has also been recently discussed
[23].
The FP-EMA results are in general agreement with the
results from a tight-binding calculation by Lippens and
Lannoo [24] shown by the gray diamonds. For the compar5
Parameters for CdS are Eg ˆ 2:5 eV; mⴱe ˆ 0:19; mⴱh ˆ 0:80;
1ⴱ ˆ 5:5; approximating the organic shell by an aqueous environment mⴱe ˆ mⴱh ˆ 1; 1ⴱ ˆ 1:78; the confining potentials are Ve ˆ
2:66 eV and Vh ˆ 2:77 eV:
ison with our experimental values one has to keep in mind
that the structures used in the calculations differ significantly from the actual structures of the NCs investigated.
Nevertheless, our results support the theoretical prediction
that VBM and CBM shift contribute about equally to the
total gap opening.
To summarize, we have investigated size-selected CdS
nanoparticles in their crystalline environment using soft
X-ray spectroscopy. We observe a strong influence of the
size confinement on the electronic structure. The determined
opening of the band gap is in agreement with optical data
observed for the nanoparticles after dissolution of the superlattice.
The contribution of the occupied and the unoccupied
states to the total band gap opening is resolved by combining the SXS data with XPS results for the S 2p binding
energy in the nanoparticles. We experimentally observe
VBM and CBM shifts of comparable size, which we can
reproduce within the EMA using finite heights of the confining potential barriers. Apparently, the EMA can be used to
estimate the effect of size confinement even in particles of
only a few tens of Ångströms, if the finite height of the
confining potentials is taken into account.
In addition, we assign the first shoulder in the S L2,3 SXA
spectrum of CdS bulk, which was previously interpreted as a
DOS maximum, to the excitation of S L3 core excitons. In
the nanoparticles the binding energy of this core exciton is
increased due to size confinement. This demonstrates how a
study of the development of the electronic structure with
particle size can lead to a better understanding of the properties of the bulk materials.
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