Photoexcited Carrier Transfer in CuInS2
Nanocrystal Assembly by Suppressing
Resonant‐Energy Transfer
メタデータ

言語: English
出版者: Wiley
公開日: 2024-08-04
キーワード (Ja):
キーワード (En):作成者: Hamanaka, Yasushi, Okuyama, Satoshi, Yokoi,
Rin, 葛谷, 俊博, 武田, 圭生, 関根, ちひろ
メールアドレス:
所属: 室蘭工業大学, 室蘭工業大学, 室蘭工業大学

URL

http://hdl.handle.net/10258/0002000172

RESEARCH ARTICLE
Photoexcited Carrier Transfer in CuInS2 Nanocrystal Assembly by
Suppressing Resonant-Energy Transfer
Yasushi Hamanaka*[a], Satoshi Okuyama[a], Rin Yokoi[a], Toshihiro Kuzuya[b], Keiki Takeda[b], andChihiro Sekine[b]

[a]

[b]

Prof. Dr. Y. Hamanaka, S. Okuyama, R. Yokoi
Department of Physical Science and Engineering
Nagoya Institute of Technology
Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
E-mail: hamanaka@nitech.ac.jp
Dr. T. Kuzuya, Dr. K. Takeda, Prof. Dr. C. Sekine
College of Design and Manufacturing Technology
Muroran Institute of Technology
Mizumoto-cho, Muroran 050-8585, Japan
Supporting information for this article is given via a link at the end of the document.

of nanocrystal applications to next-generation devices such as
solar cells, LEDs and photo sensors with high performance andhigh speed.[5,6] In particular, QD solar cells in which thesemiconductor nanocrystals are assembled and used forgeneration, transportation and separation of photoexcited charge
carriers have been considered as potential candidates beyond theShockely–Queisser limit in terms of conversion efficiency using
intermediate-band formation or multiple exciton generation.[7,8]Their photovoltaic performance is significantly influenced by the
carrier dynamics in nanocrystal solids. Therefore, obtaining a
deeper insight of the generation, transfer and recombination
processes of photoexcited carriers in semiconductor-nanocrystal
solids with densely assembled structures is important.
In semiconductor-nanocrystal solids, interaction among thenanocrystals increases as the interval between neighboring
nanocrystals decreases. When the nanocrystals are sufficiently
close to one another, the electronic wavefunctions of thenanocrystals overlap, and their discrete energy states due to thequantum-size effect change into spatially-continuous energy
states, which are analogous to the energy bands in atomic
solids.[9,10] These coupled electronic states, so-called minibands,
are a prominent characteristic of superlattice structures ofnanocrystals with a long-range order, which results in highmobilities for carrier transport.[11] The recent experiments on the
superlattices of CdTe nanocrystals with highly controlled
structural dimensionalities successfully confirmed the formation of
the minibands and related spectroscopic characteristics.[12]Without strong coupling, the carriers are transferred among thenanocrystals by a hopping mechanism with lower mobility. An
additional cooperative phenomenon often observed in
nanocrystal solids is the excitation-energy transfer among
nanocrystals that results from dipole–dipole interactions, known
as the resonant-energy transfer, which is effective over a long
distance of up to ~10 nm.[13–15] Such photoexcited dynamics has
usually been investigated by a time-resolved spectroscopy.[16]However, the carrier and energy transfers demonstrate similareffects to temporal behavior in spectroscopic measurements, andthus, distinguishing both phenomena is difficult.[16,17]

Abstract: High-density assemblies or superlattice structures
composed of colloidal semiconductor nanocrystals have attracted
attention as key materials for next-generation photoelectric
conversion devices such as quantum-dot solar cells. In thesenanocrystal solids, unique transport and optical phenomena occur
due to quantum coupling of localized energy states, charge-carrier
hopping, and electromagnetic interactions among closely arranged
nanocrystals. In particular, the photoexcited carrier dynamics in
nanocrystal solids is important because it significantly affects various
device parameters. In this study, we report the photoexcited carrier
dynamics in a solid film of CuInS2 nanocrystals, which is one of thepotential nontoxic substitutes with Cd- and Pb-free compositions.
Meanwhile, these subjects have been extensively studied in
nanocrystal solids formed by CdSe and PbS systems. A carrierhopping mechanism was confirmed using temperature-dependent
photoluminescence spectroscopy, which yielded a typical value of thephotoexcited carrier-transfer rate of (2.2 ± 0.6) × 107 s−1 bysuppressing the influence of the excitation-energy transfer.

Introduction
The most prominent characteristic of colloidal semiconductor
nanocrystals with dimensions of <10 nm is their unique sizedependent electronic and optical properties, which originate in thequantum confinement of the conduction carriers. Hence, they are
known as quantum dots (QDs) and have attracted attention overthe past three decades. [1,2] The development of semiconductor
nanocrystals as novel photonic materials have now attained thepractical use levels such as fluorophores in biolabelling reagentsand light-emitting diode (LED) backlighting in liquid crystal display
with high color rendering properties.[3,4] Furthermore, enormous
technological efforts are continuously exerted to fabricate future
optoelectronic devices composed of colloidal semiconductor
nanocrystals as building blocks. In these trends, a deeper
understanding of the charge-carrier transport in semiconductornanocrystal assemblies has become an important task in the field

1

RESEARCH ARTICLE
Most studies that report on photoexcited carrier dynamics insemiconductor-nanocrystal solids have been performed on CdSeand PbS nanocrystals owing to their excellent optical properties
resulting from the improvement in the nanocrystal quality in a longterm (e.g. high tunability in emission and absorption wavelengths,
narrow emission spectra and highly efficient luminescence).[13, 15–
18]
The rate constant for the Förster-type resonant-energy transfer(FRET) is directly proportional to the spectral overlap between theemission of the donor and the absorption of the acceptor.
Therefore, the energy transfer via the FRET process was often
observed in CdSe and PbS nanocrystals because of a small
Stokes shift between the emission and absorption bands due tothe band-edge emission characteristic of these nanocrystals,
which is typically ~50 meV, respectively, even in nanocrystal
ensemble samples. However, the use of toxic Cd and Pb in civil
applications has been restricted. Therefore, nanocrystals made ofbinary-compound semiconductors (e.g. InP and ZnS), elemental
semiconductors (e.g. Si) and some ternary chalcogenide
semiconductors have been proposed as alternative nontoxic
substitutes.[19] Among them, the nanocrystals of I–III–VI2-typechalcopyrite, such as CuInS2 (CIS) and AgInS2 (AIS), are strong
candidates. CIS and AIS have high absorption coefficients in thevisible to near-infrared region owing to their direct bandgap
structures and bandgap energy, which are suitable for highefficiency
solar-energy
conversion.[20]Therefore,bulk
Cu(In,Ga)Se2 (CIGS) cells are already practically applied, andsolar cells that employ I–III–VI2 nanocrystals have been actively
studied.[21–23] The I–III–VI2 nanocrystals have also attracted
attention as a potential candidate for non-toxic nanofluorophores
due to their moderate fluorescence properties. However, theirfluorescence mechanism is a defect emission originated inrecombination of excited carriers trapped at intragap levels, notthe band-edge emission. Thus, the I–III–VI2 nanocrystals typicallyexhibit a large Stokes shift over ~500 meV, which suggests thatthe spectral overlap between the emission of the donor and theabsorption of the acceptor in the nanocrystal ensemble issignificantly reduced compared with Cd and Pb chalcogenide
nanocrystals.[24] Such a situation can effectively suppresses the
FRET in the nanocrystal solid and enables accurate investigationof the excited carrier transfer between nanocrystals.
In the present study, we investigated the carrier dynamics inthe assembly of CIS nanocrystals in which the surface-to-surface
distance of the neighboring nanocrystals was kept at less than ~2
nm using time-resolved photoluminescence (PL) spectroscopy.
The temperature-dependent behavior characteristics of theclosely packed nanocrystals were discussed, along with thephotoexcited carrier-transfer process among nanocrystals. The
measurements at the selected energies of the PL spectra, which
suppressed the contribution of the resonant-energy transfer tocarrier relaxation processes, enabled quantitative analysis of the
hopping transfer of the excited carriers in a solid form ofchalcopyrite semiconductor nanocrystals.

However, the lack of higher order peaks indicates that asuperlattice structure with long-range ordering is not formed. The
spatial periods in the in-plane and out-of-plane directions are
estimated to be 3.8 and 3.3 nm, respectively, according to thepeak angles. These values indicate that the surface-to-surface
distance among the nanocrystals in the solid film is approximately
2.0 or 1.5 nm, on average, when the nanocrystal diameter is 1.8
nm, which is close to that of an alkyl chain length of a 1dodecanethiol (DDT) molecule, i.e. ~1.6 nm, used as surface
ligands on the nanocrystals. This result indicates that the DDT
ligands on the neighboring CIS nanocrystals are interdigitated in
the inter-nanocrystal spaces. Such conditions have been
observed in nanocrystal solids built from nanocrystals that are
passivated by monothiol ligands using various lengths of alkyl
chains.[25] Therefore, we can conclude that the CIS nanocrystals
are packed with a constant surface-to-surface distance of lessthan ~2 nm using a ligand spacer in the solid film. Figure 1 showsthat the width of the in-plane GIXRD peak is approximately twiceas large as that of the out-of-plane peak. This difference reveals
that the structural order in the out-of-plane direction is higher thanthat in the in-plane direction because the peak broadening reflects
the dispersion in the inter-nanocrystal distance.

Figure 1. GIXRD patterns of the CIS nanocrystal solid films on a quartz
substrate measured in the out-of-plane and in-plane configurations.

The absorption and PL spectra of the dilute dispersion of CIS
nanocrystals in CCl4 are shown in Figure. 2(a). The shoulder
absorption peak around 2.4 eV is due to the transition between
the lowest quantized levels of the valence and conduction bands.
The PL spectrum is broad where the full width at half maximum(FWHM) is ~370 meV. The PL peak energy is approximately 1.85
eV, which is 0.55 eV away from the absorption peak. Suchspectral characteristics, namely, shoulder absorption peak with along tail, large Stokes shift and broad spectral shape, are typicalin various types of I–III–VI2 nanocrystals and indicate that PL of
the CIS nanocrystals essentially originates in a defectemission.[19,23–26] In the CIS nanocrystals, the defect emission is
attributed to the recombination of the conduction-band electrons
and holes trapped in the Cu-related deep levels.[27] This
explanation has been most widely accepted, although the selftrapped exciton mechanism was recently proposed.[28] The peakwidth of the defect-emission band from the I–III–VI2 nanocrystals
is ascribed to both dispersions in the size or composition and the
intrinsically broad spectral feature of the individual nanocrystals
due to a strong electron–phonon interaction.[24] Figure 2(b) shows

Results and Discussion
Figure 1 shows the grazing incident X-ray diffraction (GIXRD)
patterns of the CIS nanocrystal solid film in a small-angle region
measured using a Cu–Ka line. Diffraction peaks appear at 2q =2° to 3° under both in-plane and out-of-plane conditions, whichsuggest that an ordered structure is formed in the nanocrystal film.

2

RESEARCH ARTICLE
the PL excitation (PLE) spectra of the CIS nanocrystals where PL
signals are detected at various energy ranges throughout theentire PL band (the detection energy values are marked on the
PL spectrum in Figure 2(a)). The PLE spectra exhibit shoulder
peaks on the positions indicated by the arrows in Figure 2(b). The
spectral shapes of the PLE and absorption spectra closely
resemble with one another although the positions of the shoulder
peaks of the PLE spectra exhibit a monotonous high-energy shift
over ~250 meV when the detection energy increases over ~1.8
eV. This result reveals that the broad PL spectrum is due to thenanocrystal-to-nanocrystal differences in the emission energy,
and the wide-bandgap nanocrystals demonstrate high-energyemission components that are included in the entire PL spectrum.
This result also indicates that both the PL and absorption spectraof these CIS nanocrystals are affected by apparent
inhomogeneous broadening, which is verified from theobservations of typical PL spectral width of ~200 meV from asingle CIS nanocrystal.[29,30] The size polydispersity of thenanocrystals may have caused the broadening and is a dominantfactor that determines the inhomogeneous width because thePL

AbsorbancePL Iintensity

(a)
Abs.
0
PLE peak (eV)0

PLE Intensity (arb. units)

bandgap increases due to the quantum-size effect, and thespectral peak energy gradually changes after a precise size
selection.[31] However, the composition variation among thenanocrystals can also be a possible cause because the PL energy
depends on the composition ratio between Group I and III
elements in the I–III–VI2 nanocrystals.[32] As shown in the inset in
Figure 2(b), the peak energies of the PLE spectra are constant,~2.15 eV, for the detection energy of 1.6–1.8 eV unlike for higher
detection energy. This characteristic feature means that 2.15 eVis the minimum bandgap of the nanocrystals included in theensemble sample and their PL bands are extended to at least~1.6 eV indicating the significantly broad homogeneous width of~200 meV as pointed out by the single nanocrystal
spectroscopy.[29,30]
The absorption and PL spectra of the CIS nanocrystal solid
and the CIS nanocrystals dispersed in poly(methyl methacrylate)(PMMA) measured at 295 K are shown in Figure 3(a). The carrier
and energy transfer in PMMA can be avoided because theconcentration of the nanocrystals in PMMA was enough low.[26]The spectra show that the overlapping between the absorption
and emission spectra is very small because of the large Stokes
shift, in contrast to a prominent sharp band-edge emission in the
II–VI nanocrystals. A negligible spectral overlap indicates that theemission–reabsorption phenomenon and the resonant-energy
transfer can be suppressed even in a CIS nanocrystal solid where
the nanocrystals are closely packed. However, as shown in the
PLE spectra in Figure 2, the emission energies of the relativelywider bandgap nanocrystals are actually located on theabsorption tails of the narrower bandgap nanocrystals. Therefore,
the FRET between these nanocrystals cannot be completelydenied. Figure 3 shows that the absorption spectrum of thenanocrystal solid agrees well with that of the nanocrystal
dispersion in PMMA. On the other hand, a minute difference intheir PL spectra is observed. We can see that the high-energy
component of the PL band of the nanocrystal solid is slightly
weaker than that of the nanocrystals dispersed in PMMA. The PL
spectral width is extended by the size dispersion, and thus, thesmaller nanocrystals included in the size distribution tend to emit
higher energy photons, as previously mentioned with regards to
the PLE spectra. Therefore, the reduction in the PL intensity
detected on the high-energy region in the PL band suggests that
the PLs from relatively small nanocrystals are effectively
quenched under the assembled condition in the nanocrystal solid.
Such an emission behavior indicates that de-excitation of carriers
created in smaller nanocrystals via a nonradiative route is more
frequent in close-packed nanocrystals than in the isolated
condition in the nanocrystal dispersion. We can observe that thistendency, i.e. reduction in the PL intensity of the high-energy
component, is remarkable at low temperature. Figure 3(b) shows
the PL spectra of the same nanocrystal samples measured at 5
K. The PL bands of both the solid film and dispersion exhibit peakshifts of 30–40 meV in the direction opposite each other from thepeak positions at 295 K. The small blue shift observed in the
nanocrystal dispersion may have been affected by the increase in
the temperature-dependent bandgap. The FWHM of the PL
spectrum of the nanocrystals in PMMA remains almost
unchanged from that at 295 K, which is consistent with the findingthat the spectral width of the CIS nanocrystals is dominated by
the size or composition dispersity. In contrast, the PL band of thenanocrystal solid exhibits a small red shift and becomes slightly
narrower at FWHM of 320 meV compared with that at 295 K. Such

2.4
2.3
2.2
2.1

(b)

1.8 2.0 2.2
PLE detect. (eV)detect.

1.58 eV

1.64 eV
1.71 eV
1.74 eV
1.78 eV
1.82 eV
1.86 eV
1.90 eV
1.95 eV
2.00 eV
2.05 eV
2.10 eV 2.15 eV

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Photon Energy (eV)Figure 2. (a) Absorption and PL spectra of CIS nanocrystals dispersed in
CCl4. (b) PLE spectra of CIS nanocrystals dispersed in CCl4. Detection energy
values of 1.58–2.15 eV are marked in (a) and indicated in (b). The arrows in(b) indicate the shoulder peak positions. The inset in (b) shows the relation
between the PL detection energy and peak energy of the corresponding PLE
spectra. The arrow indicates the peak position of the ensemble PL spectrum.

3

RESEARCH ARTICLE
spectral characteristics demonstrate that the PL-quenching
phenomena in the nanocrystal solid appear to be stronger undera low-temperature condition especially for high energy
component of the PL spectrum. We hypothetically consider thatthe energy transfer from the wider bandgap nanocrystals
exhibiting higher energy emission can result in such PL quenching,because the FRET rate is proportional to the PL quantum yield(PL-QY) of the donor species which increases at cryogenic
temperature in CIS nanocrystals due to suppression of thenonradiative recombination in the individual nanocrystals.[26]However, the excited carrier transfer to adjacent nanocrystals in
the nanocrystal solid can also contribute PL quenching because
the carrier-transfer probability exponentially increases as the
distance between the nanocrystals decreases.[33]in the microsecond order in both cases. Such longer decay times
are due to the remarkable suppression of the nonradiative
recombination of carriers in the individual nanocrystals at
cryogenic temperature.[26]The structural analyses reveal that the neighboring
nanocrystals are located at small intervals of 1–2 nm in the solid
film of the CIS nanocrystals. This close-packed structure supports
the explanation that the above-mentioned PL characteristics inthe nanocrystal solid, namely, quenching and fast decay, can becaused by the transfer of excited carriers and/or energy between
adjacent nanocrystals. When the nanocrystals are isolated, thephotoexcited carriers generated in each nanocrystal decay via
two competing routes, namely, radiative and nonradiative routes,
within an individual nanocrystal. In this case, total decay rate of
the carriers kNC is expressed by the following equation:[34]𝑘!" = 𝑘# + 𝑘$# .
(1)
Here, kr and knr denote the radiative and nonradiative decay
rates, respectively. If the excited carrier were lost via carrier
and/or energy transfer to neighbouring nanocrystals (as in the
nanocrystal solid), the carrier-decay rate of the relevant
nanocrystal in the solid film is rewritten as Eq. (2) in which transfer
rate ktrans with a nonradiative characteristic is added.
𝑘!"# = 𝑘$ + 𝑘%$ + 𝑘&$'%((2)
In such a situation, the transfer rate ktrans can be expressed asa sum of the carrier transfer rate kCT and the energy transfer ratekET as follows:
𝑘%#&$' = 𝑘"( + 𝑘)( . (3)The PL-decay time, i.e. the lifetime of the excited carriers, isexpressed as an inverse of the total decay rate. Hence, the PLdecay of the CIS nanocrystals in the solid form is faster, as shownin Figure 3. The PL intensity is also affected by the carrier-decay
processes because intensity is proportional to PL-QY in isolated
nanocrystals[34], as expressed by*

𝐼!" ∝ * +*) .
)

(4)

*)

This equation is modified when the excited carrier can also be
lost via carrier transfer and/or energy transfer. Thus, the following
expression is assigned to the PL intensity of the nanocrystal solid:

𝐼!", ∝ * +*)*)*) +*+),*-.

(5)

Therefore, both the excited carrier transfer and energy
transfer can quench the emission from the nanocrystal thattransfers the carrier or its energy to other nanocrystals. However,the nanocrystal does not only deliver an excited carrier or energy
to the other nanocrystals but also receive them alternatively. After
having received an excited carrier or energy, the nanocrystal may
emit a photon at a certain probability. Therefore, the actual PL
process in the nanocrystal solid is more complicated, whereas thecontribution of the latter process is not considered in this study.
We consider that the effect of such an emission process after
receiving the carriers or energies can be negligible because PLQY of our nanocrystals is quite low (<1%).
ktrans can be derived by subtracting kNC from kNCS, and the kNC
and kNCS values can be obtained as the inverse of the carrier
lifetimes of the nanocrystal solid and nanocrystals dispersed in
PMMA, respectively. Thus, to estimate the total transfer rate
including both the carrier and energy transfer in the CIS
nanocrystal solid, we measured the PL-decay times andestimated kNC and kNCS. Figures 4(a)–(c) show the PL-decay
curves measured at various detection energy values that cover
the entire spectral region. The measurements are performed at 5

Figure 3. PL spectra of the CIS nanocrystals dispersed in (black lines) PMMA
and (red lines) CIS nanocrystal solid measured at (a) 295 K and (b) 5 K. The
absorption spectra are also shown in (a). The insets in (a) and (b) show the
PL-decay curves measured at PL peak energy.

Differences between the emission properties of the isolated
and close-packed nanocrystals can also be clearly observed intheir PL-decay behavior. The insets in Figures. 3(a) and (b) show
the PL-decay curves measured at 295 and 5 K detected on the
PL peak energy, respectively. In both temperatures, the decay ismuch faster in the nanocrystal solid than that in the nanocrystals
dispersed in PMMA, which indicates a much shorter excited
carrier lifetime in the nanocrystal solid. The shorter PL-decay inthe nanocrystal solid is also presumed to be due to the resonantenergy transfer and/or excited carrier transfer. Compared withthose at 295 K, the PL decays are much slower at 5 K, which are

4

RESEARCH ARTICLE
K to obtain accurate decay times with minimal effect on
nonradiative
recombination
term
knr.
Low-temperature
measurements can also minimise the influence of the inverse
carrier transfer from large to small nanocrystals via a thermallyassisted process. The results show that the decays at higher
emission energy are much faster even in isolated nanocrystals in
PMMA. Such decay-time variation has been widely known and istypical of the defect emission in I–III–VI2 nanocrystal
ensembles.[35] Furthermore, the decay is much faster in the
nanocrystal solid than that in the isolated nanocrystals at thesame detection energy, which clearly illustrates the carrier- and/or
energy-transfer-mediatednonradiative
pathwayinthenanocrystal solid. PL decay features deviated from a singleexponential decay behaviour due to some inhomogeneity ofnanocrystal ensembles. Thus, for convenience, we fit the decay
curves using the following three-component exponential function
to estimate the carrier-decay rates:.

+

𝐼(𝑡) = ∑/-01 𝐴- 𝑒 ./ .

(6)
From decay times t1, t2 and t3 and contribution factors A1, A2
and A3 of each component, average decay time <t> is calculated
as

〈𝜏〉 =

20 30 +21 31 +22 32
20 +21 +22.

(7)

The average decay times estimated for the CIS nanocrystal
solid and nanocrystals dispersed in PMMA are 7.0 ± 1.7 and151.3 ± 21.1 ns at 2.07 eV and 88.0 ± 14.0 and 581.5 ± 19.9 ns
at 1.62 eV, respectively.
Figure 4(d) shows the total transfer rates estimated at 5 K,
which is calculated as ktrans = kNCS ‒ kNC, where carrier-decay rates
kNC and kNCS are defined as the inverse of average PL-decay time<t> measured for the nanocrystals in PMMA and nanocrystal
solid, respectively. The horizontal axis in Figure 4(d) shows thephoton energy used to detect the PL decays. Figure 4(d) showsthat the ktrans values strongly depend on the monitored emission
energy. An important point to note is the remarkable increase in
ktrans measured at the energy positions exceeding ~1.9 eV whichcorrespond to the high-energy side of the PL peak, such as ktrans= (9.64 ± 1.04) × 106 s−1 at 1.62 eV and (1.35 ± 0.17) × 108 s−1 at
2.07 eV. The PLE measuement indicated that the emission
energy of >1.9 eV agrees with those of the nanocrystals which
can be the donors for the FRET. Thus, the significant
enhancement of the ktrans values are possibly due to efficientenergy transfer to the acceptor nanocrystals. This characteristic
increase in ktrans measured at higher energy indicates that theenergy transfer from smaller nanocrystals is more rapid comparedwith that from larger nanocrystals. The more efficient energy
transfer from the smaller nanocrystals can be attributed to thepresence of a large number of acceptor nanocrystals, which are
relatively larger in size. This characteristic property results inexcess PL quenching in the high-energy region of the PL bandand red shift of the PL peak in the CIS nanocrystal solid at 5 K,
that is shown in Figure 3(b) and Figure 4(b). In contrast, the ktransvalues are less than 2 × 107 s−1 and almost constant evaluatedusing the emission at the energies below ~1.85 eV. Such abehavior is possibly due to lack of the acceptor nanocrystals
contributed to the FRET process from these nanocrystals,
because their bandgap is almost minimum between the
nanocrystal unsemble, as was pointed out from the detectionenergy dependence of the PLE peak positions shown in the inset
of Figure 3(b). Therefore, the ktrans values obtained at the emission
energy below ~1.85 eV are not affected by the energy transfer,and hence, the kCT values can be estimated as ktrans in this energy
region.
Hopping and tunnelling mechanisms have been predicted for
carrier transfer in assemblies of semiconductor nanocrystals.[10]However, the carrier-tunnelling mechanism is effective only when
adjacent nanocrystals are located very close so that theirwavefunctions overlap. The face-to-face distance between
neighbouring CIS nanocrystals in this study is estimated to be 1–
2 nm, which is too far for tunnelling. Thus, we consider that thecarrier-hopping mechanism is dominant. Carrier-transfer rate kCT
due to the hopping mechanism depends on the temperature anddifference between the energy levels on the corresponding
nanocrystals. kCT from the donor nanocrstal designated as i to theacceptor nanocrystal designated as j at temperature T isexpressed as follows:[18]Figure 4. PL-decay curves measured at (a) 2.07 eV, (b) 1.85 eV and (c) 1.62
eV for the CIS nanocrystals dispersed in (black dots) PMMA and (red dots)
nanocrystal solid. The green lines in (a)–(c) denote the fitting curves. The
sample temperature is 5 K. (d) (Circles) Transfer rates and PL spectra of the
CIS nanocrystals dispersed in (black dots) PMMA and (red dots) nanocrystal
solid film measured at 5 K. The error bars are added based on the error in the
average decay times.

5

RESEARCH ARTICLE) .)𝑘"( = 𝑘 ′ 𝑒𝑥𝑝 1− *3 ( /3 (𝐸4 > 𝐸- )4

decay times measured at the spectral peaks by suppressing theinfluence of the energy transfer as mentioned above. Figure 5(a)shows the temperature dependence of the carrier-decay rates.
The decay rates are always larger in the nanocrystal solid, andthe decay rates of both forms of nanocrystals monotonously
increase as the temperature increases. Carrier transfer rates kCT
are calculated as the difference between these decay rates andare shown as a function of inverse temperature in Figure 5(b). The
carrier-transfer rate is approximately 6 × 106 s−1 in the lowtemperature region and rapidly increases above ~150 K as thetemperature increases. At 270 K, it reaches (2.2 ± 0.6) × 107 s−1.
We can estimate the efficiency of the photoexcited carrier transfer
in the CIS nanocrystal solid using these values, which is definedas(8)𝑘"( = 𝑘 ′ (𝐸4 < 𝐸- ). (9)Here, k' is the temperature-independent rate constant, kB is
the Boltzmann constant and Ei and Ej are the energy levels on the
ith and jth nanocrystals, respectively. According to Eq. (8), thecarrier transfer from a large to a small nanocrystal is suppressedwith the decrease in the temperature because the energy level of
excited carriers in a large nanocrystal is lower than that in a small
nanocrystal due to the quantum-size effect. In contrast, the carriertransfer from a small to a large nanocrystal is independent of thetemperature, as indicated in Eq. (9). Therefore, in a lowtemperature region, the carrier transfer is restricted to thedirection from small to large nanocrystals.

*𝜂"( = * +* 56+*
)

*)

*

56

= * 56 .
758(10)Efficiency hCT is estimated to be as high as ~70% at 5 K. The
efficiency is suppressed as the temperature increases, but ~40%
is maintained even at 270 K.
Excited carrier transfer has been actively studied in a systemcomposed of semiconductor-nanocrystal donors and metal-oxide
acceptors from the nanocrystal-sensitiser perspective [36].
Although the carrier-transfer rates among the I–III–VI2
nanocrystals have not yet been reported, the photoexcitedelectron-transfer processes from CIS nanocrystals to TiO2 films
have been investigated for nanocrystal-sensitised TiO2 electrodes
fabricated using simple immersion in a nanocrystal solution.
Electron-transfer rates of 107–108 s−1 and efficiency of 60%–80%
have been reported at an ordinary temperature, whereas thesevalues depend on the nanocrystal size and distance.[37,38] The
estimated carrier-transfer rate and its efficiency in the CIS
nanocrystal solid in this study are slightly lower than those in the
CIS/TiO2 system. Such differences can be attributed to the large
energy gap between the conduction electron levels of the CIS
nanocrystals and TiO2, which are estimated at 200–450 meV,
because this energy difference acts as a driving force for moving
the electron.[37,39] However, a much higher transfer rate of ~1011
s−1 has been reported for a similar CIS/TiO2 system fabricated byelectrophoretic deposition of CIS nanocrystals on TiO2.[40] On theother hand, a photoexcited carrier transfer in assemblies of PbS
nanocrystals modified by ligands with variable lengths has been
investigated. The transfer rates are approximately 108 s−1, which
systematically depend on the ligand length.[41] Therefore, thecarrier-transfer rate in the CIS nanocrystal solid reasonably
agrees with that in the PbS system.
The thermal-activating behavior of the carrier-transfer rate
shown in Figure 5(b) can be represented by an expression of the
combination of Eqs. (8) and (9) as follows, assuming carriertransfer to other nanocrystals:

Figure 5. (a) Carrier-decay rates of CIS nanocrystals dispersed in (blacksquares) PMMA and (red circles) nanocrystal solid film measured between 5
and 270 K. (b) (Circles) Carrier-transfer rates in the CIS nanocrystal solid film
estimated between 5 and 270 K. The red line shows the fitting curve. The error
bars are added based on the error in the average decay times.

The carrier-transfer rate is expected to increase as thetemperature increases because the carrier transfer to high-energy
states whose rate is expressed in Eq. (8) cannot be ignored athigh temperature, whereas the carrier transfer to low energy
states is dominant at low temperature. To confirm thesetendencies, the temperature dependence of kCT was investigatedin the same manner as that in the PL decays of the nanocrystal
solid and nanocrystals dispersed in PMMA measured between 5
and 270 K. The decay rates are calculated from the PL-decay
times of both the nanocrystal solid and dispersion obtained atspectral peak energy of the CIS nanocrystals dispersed in PMMA,
because accurate kCT values can be estimated using the PL𝑘"( = 𝑘1 𝑒𝑥𝑝 1−

Δ)
*4 (

3 + 𝑘5 . (11)Here, DE denotes the effective value of the difference in the
excitation-energy levels between the donor and acceptor
nanocrystals for carrier hopping, and k1 and k2 are the rate
constants. The temperature dependence of kCT can be well fitted
by Eq. (11), as shown by the red line in Figure 5(b). The fitting
yields parameters DE = 72 meV, k1 = 3.6 × 108 s−1 and k2 = 6.0 ×
106 s−1. The energy-level difference of ~70 meV is reasonablebecause this value is within the bandgap inhomogeneity of ~200
meV predicted by the PLE spectra. Such effective energy
difference between the CIS nanocrystals with donor and acceptor

6

RESEARCH ARTICLE
H20), a single-photon-counting diode (Perkin Elmer SPCM-AQR16) and a
TCSPC module (Pico Quant TimeHarp260). The excitation source was apulsed diode laser with a 70-ps duration and a wavelength of 404 nm(Hamamatsu PLP-10) and its fluence at the sample position was <0.3µJ/cm2. To measure the temperature dependence of the PL properties, thesample temperature was controlled to be between 5 and 270 K using aclosed-cycle cryostat (Nagase Techno Engineering Co., Ltd.).

characteristics is much smaller than the conduction-band
discontinuity of the above-mentioned CIS/TiO2 interfaces, namely,
300–450 meV,[37,39] which leads to the comparatively low carriertransfer rate found in the CIS nanocrystal solid.

Conclusion
We have studied the photoexcited carrier transfer among CIS
nanocrystals in dense solid films of nanocrystals in which thesurface-to-surface distance was fixed, 1.5–2.0 nm, by surface
ligands. The steady-state PL spectra of the nanocrystal solid
exhibited a peak shift towards the low-energy side, and the PLdecay time was apparently reduced compared with that in theisolated nanocrystals. These findings were explained in terms ofPL quenching due to the carrier-transfer phenomena where
photoexcited electrons and/or holes escaped from excited
nanocrystals and moved to nearby nanocrystals as well as theexcitation-energy transfer phenomena. The carrier-transfer rate
was estimated to be (2.2 ± 0.6) × 107 s−1 at 270 K and decreased
as the temperature decreased due to the thermal activation
characteristics of the carrier-hopping mechanism. These results
contribute to the understanding of the photoexcited charge-carrier
dynamics in I–III–VI2 nanocrystal solids, which are key materials
for various opto-electronic devices such as next-generation solar
cells that have been investigated in numerous studies.

Acknowledgements

Experimental Section[3]This work was supported by the JSPS KAKENHI, Grant Numbers
JP20K05256, 26400316 and 25420785. A part of this work was
conducted in Institute for Molecular Science, supported by“Advanced Research Infrastructure for Materials andNanotechnology in Japan (ARIM)” of the Ministry of Education,
Culture, Sports, Science and Technology (MEXT). Proposal
Number JPMXP1222MS1025. GIXRD measurements were
supported by the Equipment Sharing Division, Organization for
Co-Creation Research and Social Contributions, Nagoya Instituteof Technology.
Keywords: Chalcopyrite, Excited carrier transfer, Nanocrystal
assembly, Quantum dots, Time-resolved spectroscopy
[1]
[2]

[4]

The colloidal CIS nanocrystals with DDT ligands were synthesisedusing a previously described metathesis method.[35] The crystal structure
and average diameter of the nanocrystals were tetragonal chalcopyrite
and approximately 1.8 nm, respectively. The PL-QY of the CIS
nanocrystals was estimated to be ~1% or less. Solid films of CIS
nanocrystals were fabricated on a quartz substrate. The quartz substrate(20 mm × 25 mm) was repeatedly washed by deionised water, ethanol andacetone using the ultrasonic method. After drying, the substrates werevertically immersed in a glass vial filled with dispersion of the CIS
nanocrystals in hexane. Then, the vial was placed in a pressure-tightvessel, and the inside of this vessel was continuously evacuated using adiaphragm vacuum pump. Approximately 40 min later, the solvent wascompletely evaporated, and a dense solid film of CIS nanocrystals with auniform thickness was formed on the substrate. The arrangement of theindividual CIS nanocrystals inside the film was characterised using GIXRD.
Both in-plane and out-of-plane diffraction measurements were conductedusing a Rigaku Smart Lab diffractometer. As a reference for investigating
the characteristic phenomena in closely packed nanocrystals, dilutedispersions of the same CIS nanocrystals in PMMA film was prepared on
the quartz substrate using the spin-coating method.[26] The distance
between adjacent nanocrystals in the PMMA film was estimated to be as
far as ~30 nm;[26] thus, individual nanocrystals were isolated where bothcarrier and energy transfers among the nanocrystals did not occur.[9,18,42]
Such situation was also confirmed by observations that the absorption and
PL spectra and PL-decay profiles of the film agreed well with those of adilute dispersion of the same nanocrystals in hexane.[26]

[5]
[6]
[7]
[8]

[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]

The absorption spectra were obtained using a standard double-beam
UV/VIS/NIR spectrophotometer (JASCO V570). The PL spectra wereobtained after excitation by a 405-nm continuous wave diode laser (SOC
JUNO405) using a spectrophotometer (focal length of 0.47 m) equippedwith a cooled charge coupled device detector (Andor iDus420). The PLE
spectra were obtained using a spectrofluorometer (Horiba SPEX Fluorolog3-21). The PL-decay profiles were measured by the time-correlated singlephoton counting (TCSPC) method using a monochromator (Jobin Ybon

[20]
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Entry for the Table of Contents

Photoexcited carrier transfer in high-density assemblies of Cd- and Pb-free semiconductor nanocrystals of chalcopyrite CuInS2 wasinvestigated. By suppressing competing process via excitation-energy transfer between nanocrystals, thermally activated scheme of
excited carrier transfer was observed and their characteristic parameters were determined.

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