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Nanoscale
PAPER
Cite this: Nanoscale, 2019, 11, 3958
Received 22nd November 2018,
Accepted 28th January 2019
DOI: 10.1039/c8nr09458f
rsc.li/nanoscale
A comparative study demonstrates strong size
tunability of carrier–phonon coupling in
CdSe-based 2D and 0D nanocrystals†
Riccardo Scott,‡
a
Anatol V. Prudnikau, §
b
Artsiom Antanovich,
b
Sotirios Christodoulou,
c
Thomas Riedl,
d
Guillaume H. V. Bertrand,
e,f
Nina Owschimikow,
a
Jörg K. N. Lindner,
d
Zeger Hens,
g
Iwan Moreels,
g,f
Mikhail Artemyev,
b
Ulrike Woggon
a
and Alexander W. Achtstein *‡
a
In a comparative study we investigate the carrier–phonon coupling in CdSe based core-only and hetero
2D as well as 0D nanoparticles. We demonstrate that the coupling can be strongly tuned by the lateral
size of nanoplatelets, while, due to the weak lateral confinement, the transition energies are only altered
by tens of meV. Our analysis shows that an increase in the lateral platelet area results in a strong decrease
in the phonon coupling to acoustic modes due to deformation potential interaction, yielding an exciton
deformation potential of 3.0 eV in line with theory. In contrast, coupling to optical modes tends to
increase with the platelet area. This cannot be explained by Fröhlich interaction, which is generally domi-
nant in II–VI materials. We compare CdSe/CdS nanoplatelets with their equivalent, spherical CdSe/CdS
nanoparticles. Universally, in both systems the introduction of a CdS shell is shown to result in an increase
of the average phonon coupling, mainly related to an increase of the coupling to acoustic modes, while
the coupling to optical modes is reduced with increasing CdS layer thickness. The demonstrated size and
CdS overgrowth tunability has strong implications for applications like tuning carrier cooling and carrier
multiplication –relevant for solar energy harvesting applications. Other implications range from transport
in nanosystems e.g. for field effect transistors or dephasing control. Our results open up a new toolbox
for the design of photonic materials.
Introduction
Optoelectronic properties of semiconductor nanoparticles
attract increasing interest because of their promising appli-
cation potential. Particularly 2D semiconductors in the form
of nanoplatelets and sheets
1–6
receive growing attention due to
fast radiative lifetimes
7,8
related to strong exciton correlation
and the giant oscillator strength effect
4,9,10
allowing high
quantum yields,
11,12
promising lasing properties
13–15
and high
two-photon absorption.
15–17
Furthermore, their directed emis-
sion
18
and polarization
19
and well-width dependent high
dark–bright splitting
20,21
of 3–6 meV are of direct interest.
High exciton binding energies (of >100 meV) have been pre-
dicted and measured,
4,14,22,23
confirming the presence of
robust excitons even at room temperature. First predictions
have suggested strong tunability of the emission spectra and
decay times for platelets and their heterostructures.
24–27
Applications of these nanoparticles for efficient field effect
devices
28
or strong electro-absorption response
22,29,30
have
been demonstrated.
In recent years, nanoplatelet heterostructures have attracted
growing attention due to various properties, which can be
engineered in these heterostructures.
11,31–35
On the other
hand the opto-electronic properties of core/shell quantum
dots are still an active research field.
36–43
First indications have
been found that nanoplatelets can exhibit unusually small
exciton–phonon coupling.
4
The authors have investigated the
†Electronic supplementary information (ESI) available. See DOI: 10.1039/
C8NR09458F
‡These authors contributed equally to this work.
§Current address: Physical Chemistry, TU Dresden, Bergstraße 66b, 01062
Dresden, Germany.
a
Institute of Optics and Atomic Physics, Technical University of Berlin,
Strasse des 17. Juni 135, 10623 Berlin, Germany. E-mail: achtstein@tu-berlin.de
b
Research Institute for Physical Chemical Problems of Belarusian State University,
220006 Minsk, Belarus
c
ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels, Barcelona, Spain
d
Department of Physics, Paderborn University, Warburger Strasse 100,
33098 Paderborn, Germany
e
CEA Saclay, 91191 Gif-sur-Yvette, France
f
Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy
g
Department of Chemistry, Ghent University, Krijgslaan 281 –S3, 9000 Gent,
Belgium
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temperature-dependent recombination dynamics, bandgap
and quantum yield in 2D CdSe–CdS core–shell platelets,
12
which exhibit a strong thickness dependence. A detailed, com-
parative study of the (lateral) size and shape dependence of
exciton–phonon coupling in different structures like 0D dots
and 2D platelets with and without a shell is still missing.
Therefore, we investigate in this manuscript at first the size
dependent exciton–phonon coupling in core-only CdSe nano-
platelets. Furthermore, we compare the results with CdSe/CdS
core/shell nanoplatelets, as well as topologically similar CdSe/
CdS heterostructures in the form of CdSe/CdS core/shell
quantum dots based on an analysis of the temperature depen-
dent emission line width and bandgap renormalization. We
show that the exciton–phonon coupling of these structures can
be tuned over about an order of magnitude by varying the
lateral size of core only platelets or introducing a CdS shell
atop of CdSe quantum dots or platelets, where we compare 0D
and 2D systems.
Experimental
4.5 monolayer (ML) zinc blende (ZB) CdSe nanoplatelet samples
with different average lateral sizes of 17 × 6 nm
2
to 41 × 13 nm
2
and 4.5 monolayer (ML) thickness were synthesized according
to ref. 3 and 44 (see Methods) and characterized by trans-
mission electron microscopy (TEM). To produce CdSe/CdS core/
shell nanoplatelets CdSe core-only nanoplatelets with 17 ×
11 nm
2
size were coated with 1 to 3 ML CdS by a layer by layer
growth technique,
45
see Methods. The final lateral size of CdSe-
3 ML CdS core/shell platelets was 22 × 18 nm
2
. The samples
were embedded in a poly(laurylmethacrylate-co-methyl-
methacrylate) co-polymer on fused silica substrates. Zinc-blende
CdSe 4 nm (diam.) core and 2–5 ML CdS shell quantum dots
were synthesized according to ref. 40 and 46 and deposited in
the PBMA polymer on quartz substrates. The samples were
mounted in a CryoVac Micro cryostat. A 150 fs, 75.4 MHz rep-
etition rate Ti:Sa laser at 420 nm was used for confocal exci-
Fig. 1 PL emission of (a) 4.5 ML core-only platelets with varying lateral sizes, (b) CdSe 1 to 3 ML (CdS) CdSe/CdS core/shell nanoplatelets, and (c)
CdSe/CdS core/shell quantum dots at 4 K and 180 or 200 K as well as representative TEM images. Clearly a splitting can be observed for the core-
only nanoplatelets (a) at low temperatures in line with ref. 7. PL from core-only platelets is fitted with two Voigt profiles, and core/shell particles with
a modified Gaussian (black lines atop experimental curves).
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tation with a 0.4 NA objective (≈0.2 W cm
−2
CW equivalent exci-
tation density) for the nanoplatelets and a 442 nm He:Cd laser
for the core/shell dot samples with comparable excitation
density. Time integrated detection was realized by using a
Horiba IHR550 spectrometer with an attached LN
2
cooled CCD.
Results and discussion
Fig. 1 shows temperature dependent PL spectra for two exemp-
lary temperatures of (a) 4.5 ML ZB CdSe core-only platelets with
varying lateral sizes, (b) CdSe-nML CdS (n=0,1,2,3)ZBnano-
platelets (17 × 11 nm
2
core size) and (c) of 4 nm (diameter) ZB
CdSe core and 2, 3, and 5 ML CdS shell CdSe–CdS dots.
The increasing redshift with shell thickness (at fixed tem-
perature) in (b) and (c) can be attributed to a lowering of the
confinement related to lower conduction and valence band
offsets resulting in increasing delocalization of the CdSe core
exciton into the CdS shell of the heterostructures. In CdSe–
CdS core–shell nanoplatelets it has been shown that still type I
band alignment is maintained,
12
so that our observed redshift
here is not an effect of strongly different spatial electron and
hole localizations, but the band alignment.
CdSe core-only nanoplatelets
We first concentrate on the CdSe core-only nanoplatelets. In
line with recent results
7
we observe for the core-only platelets a
double emission with 20–40 meV energy spacing. Fig. 2(a)
shows the temperature dependence of the centers of the
double emission, obtained from Voigt fits (shown in Fig. 1) in
the range of 4 to 300 K. We refer to the lower energy peak as
the ground state (GS) and the higher one as the excited state
(ES), without any presumptive attribution to the nature of the
states. We would like to point out here that their origin –
excited and ground state excitons, an exciton plus trion or an
exciton plus an LO phonon replica –is still under debate.
7,21,47
However, this does not affect our bandgap analysis, since both
states show the same temperature dependence of the bandgap
(Fig. 2a). Hence, we concentrate on the results for the energeti-
cally higher emission for the core-only sample. Furthermore,
studying the emission dynamics of CdSe nanoplatelets,
Biadala et al.
20
recently demonstrated a dark–bright state fine
structure with energy splittings of about 5 meV. Even for the
presence of a higher bright and a lower dark state, Shornikova
et al.
34
have shown that the quasi dark exciton state does not
contribute relevantly to the PL emission above 10 K resulting
in no relevant impact on our measurements.
An initial observation for the nanoplatelets (Fig. 2a) is the
steeper redshift (high temperature slope) for increasing lateral
platelet size (area). At first we concentrate on the lateral size
dependence of the temperature-dependent bandgap shift and
exciton phonon coupling. Fits to a semi-empirical model for
the bandgap shift are given by
48,49
Emax ¼E0aep 1þ2
eθ=T1
;ð1Þ
where a
ep
an exciton–phonon coupling strength and θ=〈ℏω〉/
k
B
an average phonon temperature are indicated as solid lines
in Fig. 2(a). The results for the zero temperature bandgap E
0
,
a
ep
and θare displayed in Fig. 2(b)–(d).
Using eqn (1) allows the analysis of the impact of lateral
confinement on the zero temperature excitonic bandgap E
0
of
CdSe nanoplatelets at low temperature as shown in Fig. 2(b).
Starting from the approximate expression for the confinement
energy related bandgap shift ΔEof an infinitely deep semi-
conductor quantum box in x,yand transversal zdirection the
observed bandgap is
Eg¼Eg;bulk EBþnz2π2ℏ2
2μzLz2þπ2ℏ2
2Mx;y
nx
Lx
2
þny
Ly
2
ð2Þ
where E
g,bulk
is the bulk bandgap, E
B
is the exciton binding
energy, and μis the reduced exciton mass. M
x,y
is the exciton
mass and n
x,y,z
is the quantum number in the x,y,zdirection.
We note that NPLs are strongly confined in the z-direction
Fig. 2 (a) Temperature dependent excitonic bandgap of 4.5 ML core-
only nanoplatelets with different lateral sizes obtained from the Voigt
fits in Fig. 1. Solid lines are fits according to eqn (1) in order to obtain: (b)
lateral confinement part of the zero temperature excitonic bandgap
versus (1/L
x
)
2
+ (1/L
y
)
2
with L
x,y
the lateral platelet dimensions. The inset
shows the same data plotted against (n/L
x
)
2
+ (1/L
y
)
2
, with n= 1 for the
GS and n= 2 for the ES. (c) The exciton–phonon coupling a
ep
and (d)
the average phonon temperature θ.
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(quantization of relative motion), while weakly confined in in-
plane directions
7
(quantization of center of mass motion).
Under the assumption of a lowest electron and hole state tran-
sition n
x,y,z
= 1 in all directions and taking the x-direction as
the long side of the rectangular platelet, the first excited state
would be (n
x
,n
y
,n
z
) = (2,1,1) and the ground state (1,1,1) (see
also ESI†for a detailed discussion). The exciton binding
energy depends only weakly on the lateral size
7
and can be
assumed to be constant. The z-quantization energy is also con-
stant for fixed thickness as well as the bulk bandgap E
g,bulk
.
A plot of dE=E
g
−E
g,bulk
+E
B
versus (1/L
x
)
2
+ (1/L
y
)
2
assum-
ing (1,1,1) for the upper and lower emission states from Fig. 1
is shown in Fig. 2. A linear dependence is fitted in this plot
(R
2
= 0.98). The slope π
2
ℏ
2
/2M
x,y
corresponds to the quasi-par-
ticle (e.g. exciton) mass. The different slopes for the upper and
lower emission indicate different masses of the emitting
species, inferring different species or ground and excited
states. A plot under the assumption of ground state (GS) (1,1,1)
and excited state (ES) (2,1,1) excitons leads to less good corre-
lation (R
2
= 0.94) for a fit to the shifts vs. (n/L
x
)
2
+ (1/L
y
)
2
and is
shown in the inset of Fig. 2(b). However, a definite answer to
which of the two models applies cannot be given based on the
lateral confinement. As shown in the ESI,†comparing M
x,y
to
the literature values of the effective carrier masses in ZB CdSe
for excitons, positive and negative trions and biexcitons and
the ES and GS hypothesis also do not result in a final attribu-
tion. One possible scenario for the double emission discussed
based on the displayed results here is an exciton and biexciton
state.
Fig. 2(b) also allows us to extrapolate the energy difference
of the two states for laterally infinite platelets or sheets as the
difference of the intersection points of the fit curves with the
ordinate. The extrapolation to laterally infinite platelets with
vanishing lateral confinement results in an energy spacing of
17 meV. From the two fit curves in Fig. 2(b) the area dependent
energy spacing can be given as
ΔE½eV¼1:600 102þ0:652 ð1=Lx2þ1=Ly2Þ;ð3Þ
if the corresponding lengths are given in nm.
Fig. 2(c) shows the electron–phonon coupling parameter a
ep
obtained from the temperature-dependence of the bandgap
according to eqn (1). For both, the ES and GS, a
ep
tends to
increase linearly with the platelet area -with some scattering of
the data, perhaps due to not identical sample quality. A linear
fit to all data (with non-zero offset) yields a slope of 77 ±
15 μeV nm
−2
.
A possible explanation for this linear increase is the coher-
ent delocalization of the 2D excitons over the whole nanoplate-
lets. The number of unit cell dipole moments contributing to
the exciton transition dipole moment increases with the plate-
let area via the giant oscillator strength effect (GOST).
50
These
elementary dipole moments coherently add up to the tran-
sition dipole moment of the exciton, which then couples to
the phonon modes, leading to a linear increase of the coupling
strength with the platelet area. Clear indications for this coher-
ent delocalization over the whole nanoplatelet and the result-
ing increase of the transition rates in our size range of nano-
platelets have been found in ref. 8 and 10. In particular the
scaling of the transition rates with the platelet area leads to a
quadratic area (volume) scaling of the two photon absorption
cross section with the lateral platelet size as well as a constant
intrinsic absorption in the continuum. We remark that these
effects of coherent delocalization are observed, as the nanopla-
telets are atomically flat systems
51
due to their anisotropic col-
loidal synthesis. In contrast epitaxial quantum wells suffer e.g.
from interface roughness effects, which limit the spatial coher-
ence of excitons more strongly.
We remark that the trend of increased exciton–phonon
coupling is also observed, if a
ep
is converted in the dimension-
less Huang–Rhys parameter S, often used to quantify the
strength of phonon coupling, and that the resulting values are
comparable to laterally quasi infinite 2D transition dichalco-
genide materials
52,53
(see the ESI†).
The linear increase of a
ep
shown in Fig. 2(c) allows for a
control of electron–phonon interaction and the accompanied
temperature-dependent bandgap red shift with the platelet
area. Additionally, it directly implies control over dephasing in
the system, as discussed later. Furthermore, this degree of
freedom is practically independent of the emission energy of
the system –the bandgap shifts are less than 30 meV and
small compared to the ∼2.5 eV band gap that is controlled by
the platelets’thickness.
Fig. 2(d) shows the average phonon temperature θ.It
corresponds to a weighted average phonon energy of acoustic
and optical modes. The observed increase of θwith lateral
size may be related to alterations in the average coupling to
acoustic and optical phonons. It can be shown (later) that the
coupling to acoustic phonons in 2D systems scales with 1/A
(Abeing the platelet area), so that the contribution of acous-
tic modes is reduced with increasing platelet size. At the
same time the contribution of optical modes increases. Since
these exhibit energies higher than acoustic modes, the
average phonon energy (temperature) increases with lateral
size.
CdSe/CdS core/shell nanoplatelets and dots
In the following section we concentrate on the CdSe/CdS
core/shell nanoplatelet and quantum dot samples. Fig. 3(a)
and (b) compare the temperature dependent excitonic band
gaps E
max
deduced from fits to the PL (Fig. 1) and fitted with
eqn (1). The CdSe/CdS platelet values presented here for
comparison are in agreement with those recently obtained
on CdSe/CdS NPLS.
12
Fig. 3(c) and (d) show the resulting
exciton–phonon coupling a
ep
, and (e) and ( f ) the average
phonon temperatures θ.
As seen in the case of core-only platelets in Fig. 2(c), the
exciton–phonon interaction a
ep
is linear in the platelet area A.
On the other hand, the density of states in a 2D system is pro-
portional to 1/d(inverse thickness) and alters the interaction
strength. For this reason, we plot in Fig. 3(c) the interaction
strength per CdSe nanoplatelet area versus 1/d
CdS
, the CdS
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layer thickness. The slope is equivalent to plotting a
ep
per
surface area (2A)versus the inverse total CdS thickness of
2d
CdS
. For quantum dots shown in Fig. 3(d) we use the inter-
face area given by 4π(d/2)
2
, with the core diameter d.We
observe a linear dependence with a slope of 4.1 ± 0.1 μeV nm
−1
for the core/shell platelets and 40 ± 6 μeV nm
−1
for the core/
shell dots.
Thus –in addition to the lateral size –a CdS shell also
allows for controlling the exciton–phonon interaction in CdSe
nanoplatelets and dots, in line with the first indications in
ref. 12 and 42 in PL and Raman spectroscopy. Interestingly,
the same concept applies to topologically similar core/shell
quantum dots, which can be considered as spherical 2D CdSe/
CdS interface structures, where the interaction is proportional
to the interaction (interface) area. A decreasing coupling with
CdS shell thickness is consistent with the results of Lin
et al.,
42
who observed in Raman measurements that the
Huang–Rhys factor for LO-phonon coupling tended to decrease
upon introduction of a shell. There, a model assuming a
Fröhlich-only mechanism was not able to reproduce this
trend. They offer surface charging and related S- and P-type
wavefunction mixing as a possible mechanism for increasing
the e–h separation and counteracting the Fröhlich coupling
trend. Finally, considering the slopes in Fig. 3(c) and (d), the
exciton–phonon interaction per unit area in CdSe/CdS nano-
platelets is lower than that in CdSe/CdS dots. We remark that
as the platelets exhibit type I band alignment,
12
there are no
effects of spatially indirect exciton formation, which alters the
coupling to phonons. For CdSe–CdS dots type I band align-
ment is also suggested,
54
but is still under discussion.
55
The performed renormalization by the surface area is also
substantiated by the results of Takagahara et al.
56
for spherical
CdSe core-only quantum dots. They found a 1/r
2
∝1/Adepen-
dence for coupling in dots, where ris the crystallite radius. In
Fig. 3(e) and (f ), we further observe a reduction of the average
phonon temperature with increasing CdS thickness. While the
starting point for core-only samples is comparable for platelets
and dots, the decrease is faster for platelets. This difference
can be attributed to the different phonon densities of states
for the 2D system and the spherical CdSe/CdS hetero system,
so that a different scaling of the coupling to acoustic and
optical modes may be the reason for these findings. As for the
core-only platelets we recalculated from Fig. 3(c)–(f) the
Huang–Rhys parameter S(see Fig. S1 in the ESI†) and found
that Sdecreases with the CdS thickness in line with Fig. 3(c)
and (d).
Based on an analysis of the emission line width, we will
now investigate the acoustic and optical phonon coupling in
more detail.
Linewidth
Fig. 4(a) shows the temperature dependent linewidth (FWHM)
obtained from the log-normal function fits to the PL spectra in
Fig. 1. We fit the temperature dependence with the well known
expression
ΔðTÞ¼Δ0þΔACTþΔLO 1
eELO=kBT1;ð4Þ
where Δ
0
is the sum of the (temperature independent) inhomo-
geneous and zero-temperature linewidth. Δ
AC
is the coupling
to acoustic and Δ
LO
the coupling to LO phonons, with the LO
phonon energy E
LO
= 25.4 meV.
57
(See also the ESI†for the dis-
cussion of line width related effects.)
The results for core-only nanoplatelets are shown in
Fig. 4(b) and (c). While there is a clear trend of a reduction of
Δ
AC
with the platelet area, only a by trend increase is observed
for Δ
LO
. Both trends are in line with the results in Fig. 2(d),
where with increasing lateral size LO phonons provide increas-
ingly major contribution to the average phonon temperature. θ
approaches the LO phonon temperature of ∼300 K (equal
to 25.4 meV) for large platelets. The demonstrated strong area
scaling of the acoustic phonon interaction can be understood
from the underlying theory of deformation potential inter-
action
58,59
of acoustic phonons. According to Fermi’s golden
rule the transition rate Γis proportional to the absolute value
squared of transition matrix element. The effective defor-
mation potential coupling u
DP
=(D
e
−D
h
)(ℏq/2Ωρν
s
)
1/2
relates
Fig. 3 Temperature dependent excitonic bandgaps deduced from fits
to PL in Fig. 1 for 4.5 ML core/shell nanoplatelets (a) and 4 nm diameter
CdSe core/shell dots (b) with 0–3 ML and 0–5 ML CdS shell, respect-
ively. Exciton–phonon coupling a
ep
per interface area for the platelets
(c) and dots (d) versus the inverse CdS thickness. For the platelets the
system has two interfaces as well as their average phonon temperature θ
(e) + (f ) determined from fits in (a) and (b).
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the phonon wave number q(absolute value of the wave vector),
the volume Ωof the structure under consideration, the density
ρ, the sound velocity v
s
and the deformation potential differ-
ence of D
e
−D
h
of electrons and holes. The corresponding
matrix element is M
k,k′
=(D
e
−D
h
)(ℏq/2Ωρν
s
)
1/2
f(q)δ
k,k′+q
.
f(q) is the form factor that can be shown
59
to be (1 + (qa
B
/4))
−3/2
for a hydrogen (S-)like lowest envelope function and small
acoustic phonon wave vectors, as estimated from ref. 7 and 60.
Due to Fermi’s golden rule the transition rate Γscales with
the square of u
DP
. In our platelets with dimensions L
x,y,z
and
volume Ω=L
x
L
y
L
z
, the quantized phonon wave vector is q=
π(1/L
x2
+1/L
y2
+1/L
z2
)
1/2
. Following ref. 61 and 59, and assum-
ing small acoustic phonon wave vectors (as e.g. also shown in
ref. 62), the third contribution is the dominant one and is
given by the z-breathing mode frequency (taken from ref. 60)
since L
x
,L
y
≫L
z
. The contribution of acoustic phonon scatter-
ing to the homogeneous line width is Δ
acoust
=2ℏΓ.
10
Since
according to eqn (4) Δ
acoust
(T)=Δ
AC
T, this leads, apart from a
scaling factor C
DP
, to the following dependency
ΔAC ¼CDP2Lx2þLy2þLz2
1=2
LxLyLz
CDP21
LxLyLz2¼CDP21
ALz2;
ð5Þ
where the last line is an approximation for L
x
,L
y
≫L
z
and fixed
well width L
z
. Hence, we can understand the decrease of the
acoustic phonon coupling with increasing platelet area as
shown in Fig. 4(b). A fit to the function above is indicated.
C
p2
=2π
2
ℏk
B
(D
e
−D
h
)
2
/ρE
ph2
is a material dependent propor-
tionality constant, resulting from the considerations discussed
above. Using an effective exciton mass from ref. 7, a ZB CdSe
sound velocity of v
s
= 2.26 km s
−1
,
60,63
an acoustic phonon
energy of E
ph
= 3.42 meV calculated
60
from the sound velocity,
a platelet thickness of 4.5 ML and a mass density of ρ= 5.66
gcm
−3
,
60
we obtain from the fit to eqn (5) |D
e
−D
h
| = 3.03 ±
0.3 eV. This value is in excellent agreement with a value of
−2.87 eV calculated from elastic constants based on DFT
results
64
and results on ZB CdSe.
65
It further shows that the
deformation potential is unaltered by the strong anisotropic
size quantization in CdSe nanoplatelets. The agreement of the
deformation potentials directly justifies our approach, the val-
idity of our fits to the emission lines and the assumptions of
our model. It proves that we demonstrate for the first time an
independent control of the acoustic phonon coupling or
dephasing from the transition energy in a nanosystem. As the
homogeneous line-width is shown to be acoustic phonon scat-
tering limited, we obtain a direct control over dephasing in
our system via the lateral platelet area. A tuning range of more
than a factor of four with increasing values for small platelets
Fig. 4 Temperature dependent line width of CdSe platelets (a), CdSe/CdS nanoplatelets (17 × 11 nm
2
CdSe core) (d) and nano-dots with 4 nm core
size (g), with fits to eqn (4). Resulting acoustic Δ
AC
(b) and LO phonon Δ
LO
(c) contribution to the linewidth as a function of the nanoplatelet area. (b)
shows a 1/Afit according to eqn (5). (e, h) and (f, i) acoustic Δ
AC
and LO phonon Δ
LO
contribution for core/shell platelets and dots versus the CdS
layer thickness.
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gives great prospects that for smaller platelets even higher
Δ
AC
values can be obtained.
Slight deviations of the actual platelets from the fit curve in
Fig. 4(b) may be related to slight variation of sample quality or
size determination by TEM.
We remark that the observed trend of a decrease of acoustic
phonon coupling with nanostructure size is in-line with calcu-
lations by Kelley
66
and Takagahara et al.
56
for spherical CdSe
quantum dots. With increasing size the exciton coupling to
acoustic phonons was observed to decrease due to decreasing
deformation potential coupling. Our results for large platelets
are comparable to large dots, for which Takagahara et al.
found the coupling to be about 7 μeV K
−1
. For small quantum
dots, of diameter comparable to the thickness of our 4.5 ML
platelets (1.4 nm), they obtained ∼100 μeV K
−1
–in good agree-
ment with the values of smaller platelets as shown in Fig. 4(b).
We also note that they found a 1/r
2
dependence for dots,
where ris the crystallite radius. This corresponds to an inverse
surface area dependence of the nanocrystal analogous to our
findings for the nanoplatelets (∝1/A).
This inverse relationship between coupling to low energy
acoustic modes and platelet area Afurther substantiates our
interpretation of the increase of the average phonon temperature
θas shown in Fig. 2(d) with A. For larger lateral sizes the contri-
bution of low energy acoustic modes decreases due to the
reduced coupling while optical modes with higher phonon ener-
gies increasingly contribute to the average phonon temperature.
In Fig. 4(c) we further observe a by trend increase of the
coupling to LO-phonons with increasing nanoplatelet area.
The coupling to optical modes tends to increase with Aand
then saturate for large platelet areas towards values
reported by Chia et al. for laterally infinite MBE grown CdSe
epilayers (≈20 meV).
67
As the Fröhlich interaction is con-
sidered the dominating mechanism
42
for the LO phonon
coupling in polar semiconductor nano-structures we briefly
investigate whether this can explain the observed complicated
behavior directly. The corresponding interaction potential
59
uF¼iðe=qÞELO
2Ωε0
εr1ε1
1
1=2
results in a predicted
scaling Δ
LO
∝(1/L
x2
+1/L
y2
+1/L
z2
)
−1
L
x
L
y
L
z
∝A/2L
z
[(L
x
−L
y
)
2
+A],
where the first proportionality is an approximation due to
L
x
,L
y
≫L
z
and the last proportionality due to L
x
∼L
y
for fixed
well width L
z
. A nonlinear increase for larger platelet areas is
expected for more quadratic nanoplatelets. The observed
scatter of data points may be related to the lateral aspect ratio
sensitivity (via the (L
x
−L
y
)
2
dependence), as the used platelets
have varying aspect ratios. However, the actual trend in Fig. 4(c)
cannot be fully explained by this simple theory. Another expla-
nation for deviations from the simple scaling theory presented
could be a varying defect density which alters the LO phonon
coupling, as e.g. the number of defect sites scales with the
platelet area. A detailed analysis, however, is beyond the scope
of this article.
In the following we analyze the cases of CdSe/CdS platelets
and dots for varying CdS layer thicknesses. Fig. 4(e) and (f )
show the coupling to acoustic and optical modes. Δ
AC
can be
(roughly) approximated with a linear increase with the CdS
layer thickness. The 1 ML CdS sample is excluded from the
linear fit shown in Fig. 3(e). The trend –which is in line with
the reduction of the average phonon temperature in Fig. 3(c + d)
via increasing coupling to low energy acoustic phonons –may
be interpreted in terms of an increase of the interaction
volume with increasing shell thickness. In bulk the acoustic
branches of the phonon dispersion in CdSe and CdS are quite
similar and have a continuous spectrum. Here we have quan-
tized acoustic modes, but the energy spectrum is still quite
similar in both materials, which can be seen from the fact that
the acoustic sound velocities 2.3 km s
−1
and 2.6 km s
−1
for
CdSe and CdS (calculated based on ref. 60) are quite similar.
Hence there is no strong mode confinement due to the CdSe–
CdS interface and to a first approximation the acoustic modes
can be considered as to extend over the whole particle, includ-
ing the CdS shell. In contrast these arguments do not apply to
the optical modes, as the energies of LO phonons in CdSe
(∼210 cm
−1
) and CdS (∼302 cm
−1
) are well distinct. Hence, an
increased shell thickness and wavefunction delocalization may
tend to decrease the LO coupling as the core (LO) phonon
modes cannot couple to the shell modes and the wavefunction
overlap of the exciton with the core mode decreases relatively
for stronger delocalization into thicker CdS shells.
A reduction of the coupling to LO phonons is further
observed in (f ). Lin et al.
42
measured a non Fröhlich-like
reduction of the coupling (Huang–Rhys factor S) with increas-
ing shell thickness in CdSe/CdS quantum dots –in-line with
our result. This seems to be a universal trend in hetero-nano-
platelets and quantum dots. Furthermore, the decreasing
coupling to high energy LO-phonons with increasing layer
thickness is also reflected in the reduction of the average
phonon temperature θas seen in Fig. 3(e) and (f). This also
confirms the consistency of our whole analysis via the inde-
pendent experimental quantities, bandgap and line width.
The same trends of acoustic and optical phonon
coupling with CdS shell thickness discussed now for platelets
(Fig. 4(e + f )) are also observed for the topologically similar
CdSe/CdS dots. On an absolute scale, they show smaller coup-
ling than nanoplatelets. This may stem from smaller transition
dipole moments in dots as compared to platelets coupling to
phonons, or a not perfect spherical shape of the nanoparticles.
The dots are smaller than the nanoplatelets. This may result in
a smaller number of acoustic or LO-phonon modes in the
system to which the exciton can couple, leading to an overall
reduction in CdSe/CdS dots compared to platelets.
Furthermore, due to different crystallographic orientations on
the dot surface, CdS monolayers are not as ideally smooth as
on the platelets, which may result e.g. in the larger data point
scatter.
The demonstration of the tuneability of exciton–phonon
interaction in colloidal quantum-wells by lateral size and shell
growth has strong application potential, for example, for
tuning carrier cooling, which is relevant e.g. in solar energy
harvesting applications. Furthermore, carrier multiplication is
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a very active field, where carrier cooling and carrier multipli-
cation are competing processes. The former tunes the multi-
carrier pair generation efficiencies and poses a promising way
to boost solar cell efficiencies. Hence 2D materials of finite
lateral size, like the nanoplatelets in this manuscript, with a
control of the carrier cooling rates are desirable model
systems, for both basic understanding of the involved pro-
cesses as well as optimization of the performance of solar
energy converters. Also for transport in nanosystems our
results show the feasibility of tuning exciton–phonon inter-
action, for example in field-effect transistors, varying the
lateral size of the structure and e.g. tuning from ballistic to
diffusive transport. A further interesting implication of our
results is that the quantum yield of nanoplatelets with or
without a shell, which has been found to be considerably
different,
12
will depend on the phonon interaction, which
governs exciton cooling and relaxation in non-radiative chan-
nels. For large platelets or core/shell platelets with thin shells
the average phonon coupling is the highest, so that e.g.
phonon assisted nonradiative recombination is stronger.
These findings can be used for emitters of optimized photo-
luminescence efficiency. Our results open up a new toolbox for
the design of photonic materials.
Conclusion
In summary we have shown that CdSe nanoplatelets possess a
lateral confinement of ∼30 meV, which can be adjusted via the
lateral size of the nanoplatelets. We demonstrated that
exciton–phonon coupling in CdSe nanoplatelets can be varied
strongly via the lateral size or the thickness of a CdS shell. The
coupling to acoustic phonons decreases with the platelet area
by a factor of ∼4, in line with deformation potential theory.
The resulting −3.03 eV exciton–acoustic phonon deformation
potential is in line with theory predictions. The coupling to
LO-phonons is observed to decrease with decreasing platelet
area. We further demonstrated that a CdS shell results in an
increased coupling to acoustic modes and reduced coupling to
optical modes for both CdSe–CdS core–shell platelets and
quantum dots. The absolute coupling strengths are lower for
quantum dots than for nanoplatelets, which may be attributed
to the higher transition dipole moments to which the phonon
modes couple in nanoplatelets and more phonon modes to
couple to in the larger nanoplatelets. We further demonstrated
that the average exciton–phonon coupling strength increases
linearly with the platelet area for core-only platelets, while it is
linear in the interface area versus the inverse CdS layer thick-
ness in core/shell platelets as well as in nanodots. As the
trends for both core/shell structures are similar, there is a uni-
versal mechanism for 2D platelets and similar core–shell dots
also exhibiting a 2D interface. Our results regarding the tun-
ability of phonon interaction are of immediate interest for
carrier cooling and multiexciton generation, relevant for solar
light conversion, for transport and high quantum yield emit-
ters and open up a new toolbox for the design of photonic
materials. We remark that further in-depth studies beyond the
scope of this article are necessary to give a definite answer to
the nature of the two emissive states in CdSe nanoplatelets,
however our experimental results presented in this paper are
not influenced by this.
Methods
Synthesis and characterization
Nanoplatelets. 4.5 ML-thick CdSe NPls were prepared using a
modified procedure based on the protocols described in ref. 3
and 44. 170 mg of cadmium myristate, 12 mg of elemental sel-
enium and 15 ml of octadecene-1 were charged into a three-
necked flask. The flask was degassed for 15 minutes, purged with
argonandsettoheatupto240°C.At190°Camixtureof56mg
of cadmium acetate dihydrate and 21 mg of anhydrous cadmium
acetate was swiftly added into the reaction mixture. The ratio of
anhydrous/hydrate allows tuning the aspect ratio. When the tem-
perature reached 240 °C, the flask was kept at this temperature
for 45 s to 2 min. After that, the reaction mixture was cooled to
80 °C and nanocrystals were precipitated with isopropanol and
hexane and isolated by centrifugation. The cadmium sulfide shell
was deposited onto CdSe NPL cores by a colloidal atomic layer
deposition technique.
45
At first, 2 ml of hexane colloidal solution
of CdSe NPls were mixed with 2 ml of N-methylformamide
(NMF). Then 10 μL of 40 wt% ammonium sulfide aqueous solu-
tion was added and NPls were transferred into the NMF phase
due to the growth of a sulfide surface layer. After 10 minutes of
vigorous mixing the hexane layer was discarded and then, in
order to remove the excess of sulfur precursor, the NPLs were pre-
cipitated with isopropanol, isolated by centrifugation and redis-
persed in fresh NMF. To ensure complete removal of the
unreacted sulfide the precipitation step was repeated twice. In
order to complete the deposition of 1 ML of CdS by growing a
cadmium layer, 20 μLof0.1Msolutionofcadmiumacetatein
water were added to the solution of sulfide-covered NPLs in NMF.
After 20 minutes of mixing the NPLs were purified from the
excess of the cadmium precursor by the precipitation procedure
described above. NPLs were then transferred into hexane by
adding 10 μL of oleic acid and thorough mixing. Second and
third layers were grown by repeating the steps described above.
Zinc-blende CdSe core-only and 2–5 ML CdS shell quantum
dots. These were synthesized according to ref. 40 and 46 based
on 4 nm CdSe cores and deposited in PBMA polymers on
quartz substrates. Sizes and diameters were determined by
TEM in all samples.
TEM analysis of all samples was performed through
different instruments (Jeol ARM200F operated at 200 kV and
Zeiss Leo 906E at 120 kV). At least 50 platelets per sample were
used for size determination.
Conflicts of interest
There are no conflicts to declare.
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Acknowledgements
R. S., U. W. and A. W. A acknowledge the DFG grants WO477-1/
32 and AC290-2/1., M. A. the CHEMREAGENTS program, and
A. A. the BRFFI grant no. X17KIG-004.
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