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Cite this: Energy Environ. Sci., 2014, 7,
1023
Double superexchange in quantum dot
mesomaterials†
Huashan Li,a Zhigang Wu,b Tianlei Zhou,c Alan Sellinger*c and Mark T. Luskd
Received 5th September 2013
Accepted 20th January 2014
DOI: 10.1039/c3ee42991a
www.rsc.org/ees
A new optoelectronic mesomaterial is proposed in which a network of
quantum dots is covalently connected via organic molecules. Optically
generated excitons are rapidly dissociated with electrons subsequently hopping from dot to dot while holes transit via the connecting
moieties. The molecules serve as efficient mediators for electron
superexchange between the dots, while the dots themselves play the
complementary role for hole transport between molecules. The
network thus exhibits a double superexchange. In addition to
enhancing carrier hopping rates, double superexchange plays a
central role in mediating efficient polaron dissociation. Photoluminescence, dissociation, and transport dynamics are quantified
from first-principles for a model system composed of small silicon
quantum dots connected by organic moieties. The results demonstrate that double superexchange can be practically employed to
significantly improve charge generation and transport. These are
currently viewed as the critical obstacles to dramatic enhancements in
the energy conversion efficiency of photovoltaic cells based on
quantum dots.
Very small silicon quantum dots (SiQDs) have properties that
make them particularly attractive for photovoltaic and optoelectronic applications.1–4 Compared with dots of greater size,
these should absorb photons more readily, transport excitons
more efficiently,1 can be made essentially free of defects,2 and
resist oxidation better.3 In addition, these small dots use their
slice of the solar spectrum more efficiently,4 show greater
promise in multiple-exciton generation and hot carrier
a
Department of Physics, Colorado School of Mines, Golden, CO 80401, USA
b
Department of Physics, Colorado School of Mines, Golden, CO 80401, USA. Fax: +1
(303) 273-3919; Tel: +1 (303) 273-3068
c
Department of Chemistry and Geochemistry, Colorado School of Mines, Golden, CO
80401, USA
d
Department of Physics, Colorado School of Mines, Golden, CO 80401, USA. E-mail:
mlusk@mines.edu; Tel: +1 (303)-273-3675
† Electronic supplementary information (ESI) available: Computational method,
conjugated bonding, anharmonic effect of phonon modes, absorption spectra,
superexchange with different bridges, inuence of bridge density and hole
diffusion paths on hopping rate enhancement. See DOI: 10.1039/c3ee42991a
This journal is © The Royal Society of Chemistry 2014
collection paradigms,5,6 and have a higher electronic coupling
for the same surface-to-surface distance.1
To achieve their promise, though, these dots must be
assembled in a way that allows energy to be efficiently harvested. An idea that has been explored for larger dots is to
encapsulate them within an inorganic amorphous matrix.7–10 A
low binding energy allows excitons to thermally dissociate and
charge carriers hop from dot to dot by overcoming an energy
barrier imposed by the matrix—i.e. a Type-I bulk heterojunction. The inorganic matrix offers high stability and a simple
interface structure, but technologically relevant carrier mobilities would require precise control of both dot size and spacing.8
Although such precision has recently been achieved with PbS
QDs in a ZnS matrix,11 analogous delity with silicon systems
has yet to be achieved.
A second approach is to encapsulate the dots within an
organic polymer blend.12–19 The energy level alignment between
dots and the polymer is such that holes prefer one material
while electrons prefer the other so as to create a Type-II heterojunction. A large interface area is arranged for which the
donor–acceptor separation is within an exciton diffusion length
of the absorption site.16,19 The approach takes advantage of
solution processing and the strong absorption of conjugated
polymers but suffers from its instability in ambient environments.16 In addition, the efficiency of current SiQD/P3HT solar
cells are only 1.1%.12,13,18 This is most likely due to the difficulty
in controlling the interface morphology2,13,19,21,22 which results
in high carrier recombination rates and low carrier mobility.23
These considerations have motivated the current proposal of
a new Type-II paradigm in which covalent bonding between
donors and acceptors allows for a much more controlled
interfacial architecture. Specically, an assembly of closepacked SiQDs are cross-linked by short ligands as illustrated in
Fig. 1(a) so that a Type-II interface is established between the
dots and their bridging units. This is crucial because it provides
a means of overcoming the relatively high exciton binding
energies of small SiQDs, allowing charges to separate. Excitons
can be generated via photon absorption by the SiQD and/or
Energy Environ. Sci., 2014, 7, 1023–1028 | 1023
Energy & Environmental Science
(a) A mesomaterial composed of SiQDs (blue) covalently
bonded by short molecules (purple). The structures of the Si147 QD and
the bridging molecule 2,5-divinylthiophene-3,4-diamine (C8H8N2S)
used in our prototype system are shown with the following atom
coloring: Si (tan), H (white), C (grey), N (blue) and S (yellow). (b) Double
superexchange mechanism: HOMO (red), LUMO (green), vibrational
energy levels (black).
Fig. 1
molecules. Such chemical connections between donor and
acceptor are thought to result in much faster charge separation
for QDs within organic blends such as P3HT/CdSe24 and PbS/
MEH-PPV.25 Since no exciton diffusion is required as in standard bulk heterojunction materials, charge separation will also
benet from state superposition resulting from Heisenberg
uncertainty with respect to photon absorption.26 Because of the
precise chemical bonding in such collections of dots and
molecules, it seems appropriate to view them as quantum dot
mesomaterials with emergent optoelectronic properties.27 We
focus on mesomaterials that do not exhibit translational
symmetry which would otherwise introduce the possibility of
band-like carrier transport behavior.28
In the proposed system of interpenetrating networks, electron hopping is from dot to dot while the linking molecules
transport holes. Such networks can be designed so that the rate
of electron hopping is enhanced by the linking molecules even
though no intermediate hop is made. The connecting moiety
has energy levels that are not resonant with either the donor or
acceptor, but it can still improve the electronic coupling of their
respective orbitals. The electronic overlap between the dots is
increased by establishing conjugated covalent bonds between
the dots and the bridge (Fig. 1(b) and ESI†). Such a modication
to the orbital overlaps is particularly important in covalent,
bidentate bonding.29 The process is known as superexchange
because of the congurational similarity to Kramers–Anderson
1024 | Energy Environ. Sci., 2014, 7, 1023–1028
Communication
superexchange,30 wherein strong magnetic coupling can exist
between two cations that are separated by a nonmagnetic but
mediating anion. Within the new paradigm, a further design
step is taken though. Quantum dots adjacent to neighboring
bridges are designed to improve the electronic overlap of states
localized on the bridge molecules. The result is that hole
hopping from bridge to bridge is also enhanced. We refer to the
combined electron and hole dynamics as double superexchange
(DS), and this is illustrated in Fig. 1.
This new Type-II heterostructure is fundamentally distinct
from recently considered networks of PbSe and CdSe dots. Such
dots are initially terminated with long organic groups but can be
made to undergo a ligand exchange reaction with small inorganic molecules. This allows them to be more closely packed.31–34
Although initially a matter of conjecture, new experimental
analysis has conrmed that the resulting network is composed
of dots that are covalently bonded to each other through
bidentate ligands.35 This results in dramatically improved
charge mobilities attributable to improved electronic overlap as
explored in a recent computational investigation of CdSe QDs
with bidentate Sn2S6 linkers.36 However, these are Type-I heterostructures and the ligands constitute a barrier to both electron
and hole hopping between the dots. Our proposed architecture
is also similar to that of small molecule solar cells37,38 but is
distinguished by its double superexchange property.
In order to demonstrate the DS paradigm, we consider the
charge dynamics of a model system based on 1.7 nm diameter
SiQDs (Si147H100) bridged by 2,5-divinylthiophene-3,4-diamine
(C8H8N2S) molecule (Fig. 1(a)). The photovoltaic efficiencies
associated with this simple architecture are expected to be
relatively low due to large energy gaps and interfacial energy
losses, but the intent is only to establish that the new paradigm
is viable. This is carried out via an ab initio analysis within the
setting of phonon-assisted, nonadiabatic charge dynamics
(see, ESI†). The approach is used to estimate several key carrier
rates: (1) charge transfer (CT) from localized excitonic states to a
coulombically bound exciton at the interface between dot and
molecule; (2) charge recombination (CR) wherein the bound
exciton nonradiatively recombines to return the system to the
ground state; (3) carrier hopping; and (4) photoluminescence
(PL). Ground state properties and all vibrational data were
calculated using Density Functional Theory (DFT) while quasiparticle and excitonic corrections were made for better optical
property estimates (ESI†).
The methodology is consistent with our earlier investigation
of charge dynamics associated with a SiQD/P3HT interface.23
Specically, the calculated CT rate (4.0 1012 s 1) and PL rate of
P3HT (7.9 108 s 1) reasonably reproduce the experimental
values of 7 1012 s 1 and 1.5 109 s 1 respectively.12,39 With the
dangling bonds (DBs) accounted for, the calculated CR rate
(2.7 1012 s 1) and electron hopping (EH) rate (1.3 107 s 1)
are in good agreement with the values of 1 1012 s 1 and 2 107 s 1 observed experimentally.12,23,40 Furthermore, our
computed PL rate of 1.8 104 s 1 for the alkyl terminated
1.7 nm SiQD is consistent with the values obtained in two recent
measurements (1.7–5.0 104 s 1 for 1–5 nm SiQDs41 and 1.3 104 s 1 for 2.6 nm SiQD42).
This journal is © The Royal Society of Chemistry 2014
Communication
The computational analysis of our prototype SiQD mesomaterial indicates that the requisite Type-II energy level alignment is formed at the dot/bridge interface with HOMO and
LUMO localized on the molecule and dot, respectively
(Fig. 2(a)). A majority of absorbed photons would generate
singlet excitons localized on the dot (3.2 eV) or on the molecule
(3.6 eV) (Fig. 2(b)). Despite a large exciton binding energy (1.7 eV
for the dot and 3.1 eV for the molecule), the exciton dissociation
from either the dot or the molecule is still energetically favorable with an energy loss of 0.6 and 1.0 eV, respectively. In
addition to the generation of an exciton on either the dot or
molecule, a computed absorption spectrum (Fig. S4, ESI†)
indicates that direct photo-excitation of the charge transfer (CT)
state is also possible.
The dot/bridge interface also supports rapid charge separation and transport dynamics for the efficient extraction of free
carriers. As summarized in Fig. 3, charge separation rates for an
exciton initially absorbed on either the dot or the bridge are
much higher than the respective PL rates. This implies that the
exciton should efficiently dissociate to a coulombically bound
electron–hole pair—i.e. a polaron.
To be of practical use, of course, interfacial polarons must
dissociate into free carriers. The associated Coulomb well—i.e.
the energy difference between CT and SC states—can be as large
as 0.31 eV (Fig. 2(b)), and an electric eld is required to promote
efficient dissociation. However, an analysis based on the Onsager–Braun model43–45 indicates that the voltage drop across the
cell during normal operation should provide the electric eld
required. The analysis is based on the assumption that polarons
either dissociate to free carriers or decay to the ground state and
requires that the internal voltage across the cell be specied.
Provided that the internal voltage is larger than 0.2 V, a condition easily satised in the normal operation of photovoltaic cells
with a reasonable ll factor,44 essentially all of the polarons will
dissociate into free carriers (Fig. 4).
As indicated in the gure, relatively large uctuations in
donor–acceptor spacing would not change the separation
Fig. 2 (a) HOMO (blue) and LUMO (red) of an Si147H100–C8H8N2S
interface. The isosurface densities are 0.01 Å 3/2. (b) Energy levels of
ground state (GS), local exciton state on the dot (LEdot), local exciton
state on the C8H8N2S (LEbridge), charge transfer state (CT) for a coulombically bound electron–hole pair, and separated charge (SC) state
for free carriers. Values indicating the span of black arrows are the
energy difference between many-body states (eV), and red arrows
denote the direction of exciton dissociation.
This journal is © The Royal Society of Chemistry 2014
Energy & Environmental Science
Charge transfer, photoluminescence, charge recombination
and carrier hopping rates at the dot/bridge interface. Blue and green
arrows draw attention to competing rates.
Fig. 3
Fig. 4 Polaron dissociation probability at the Si147H100/C8H8N2S
interface for a range of internal cell voltages (Vin). The red vertical line
identifies the actual donor–acceptor distance in this model system.
The lowest value of internal voltage (0.2 V) is deemed to be least value
for which the Onsager–Braun model can be applied (ESI†).
efficacy. The Onsager–Braun analysis shows that polaron
dissociation is this efficient as a result of both slow charge
recombination from interfacial PL (1.4 105 s 1) and high
electron and hole mobilities (0.15 and 1.5 cm2 V 1 s 1
respectively). While slow charge recombination is attributable
to the large energy drop of 2.6 eV from CT to GS (Fig. 2(b)), the
high carrier mobilities are a direct result of DS.
Photon absorption on either dots or bridges will rapidly
produce interfacial polarons which themselves dissociate into
free charge carriers. As indicated in Fig. 3, the subsequent
carrier hopping rates are much higher than both radiative and
non-radiative interfacial charge recombination, a prerequisite
for efficient carrier collection.
The DS mechanism can be elucidated by calculating carrier
hopping rates without the mediating material between donor
and acceptor. As summarized in Table 1, the presence of a
single C8H8N2S between two dots increases the electron
hopping rate between the dots by three orders of magnitude.
This is expected to cause a similar enhancement in the electron
mobility since the diffusion is nearly homogeneous.
In contrast, the hole hopping rates between C8H8N2S
molecules strongly depend on the interface congurations.
When the bridges form a parallel arrangement, the coupling
Energy Environ. Sci., 2014, 7, 1023–1028 | 1025
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Communication
Table 1 Electron hopping rate between neighboring Si147H100 and
hole hopping rate between adjacent C8H8N2S molecules with and
without bridge material (molecule and dot, respectively). The associated configurations, shown in Fig. 5, highlight hole hopping when
linker molecules are not aligned. An analysis of five different donor–
acceptor molecule orientations is provide in the ESI†
Hopping rate (s 1)
Bridge
No bridge
Electron
Hole
4.7 1011
9.6 1011
1.8 108
1.6 107
between stacked p-orbitals is so strong that additional
enhancement due to superexchange is negligible (ESI†).
However, superexchange is still crucial to the effective hole
mobility because it facilitates rapid hole hopping at the corner
and ridge positions of the dots (Fig. 5). This superexchange
enhancement of the hole hopping rate can be as large as four
orders of magnitude (Table 1) even though is derived from only
a modest spreading of donor and acceptor HOMOs to the
mediating dot (Fig. 5). In fact, it is this large change in electronic coupling, in association with a comparatively small
change in orbital overlap, that is the hallmark of superexchange. For hole hopping between bridge molecules that do
not exhibit p-bonding, superexchange can enhance the rate by
orders of magnitude even when the molecules are closely
spaced and parallel—e.g. benzenedithiol.
Control experiments involving three additional connector
molecules provides a deeper understanding of bridge assisted
carrier hopping. As detailed in the ESI,† we compared the
transport dynamics associated with C10H10O2S, C8H6S, and
C6H4S2 bridges. The electronic coupling induced by C8H6S and
C10H10O2S is 1.5 and 1.9 times that of C8H8N2S. These factors
correlate with reductions in the LUMO offsets, consistent with
the notion that bridge molecules with LUMO energy levels
closer to those of the dots result in higher electron hopping
rates. In contrast, C6H4S2 has a larger LUMO offset than C8H6S
and has an electronic coupling that is reduced by a factor of
Effectively degenerate LUMO (pink) localized on neighboring
Si147H100 dots with (panel a) and without (panel b) a C8H8N2S molecule. Effectively degenerate HOMO (blue) localized on the C8H8N2S
with (panel c) and without (panel d) an Si147H100 dot. The isosurface
densities are 0.007 Å 3/2 for LUMO surfaces (a and b) and 0.01 Å 3/2 for
HOMO surfaces (c and d).
0.35. Interestingly, this is the case even though the dot separation has been reduced from 21.9 to 21.1 Å. This is reasonable
since superexchange is dominated by the state coherence
between donor, acceptor and bridge, and closer energy levels
would lead to strengthened electronic coupling.
The DS rate enhancement is even more dramatic when the
dots are connected by multiple C8H8N2S molecules, an architecture that would most likely be realized in reality. Two
C8H8N2S bidentate molecules gives an enhancement of electron
mobility compared to no bridge that is approximately twice that
with one C8H8N2S (8.4 104) (ESI†). The hole superexchange is
small in this parallel conguration of bridges, but it is much
larger when the bridging molecules are not parallel as occurs on
dot edges and corners (ESI†).
While the concept of double superexchange is new and
necessarily involves interpenetrating electron and hole transport networks, we have identied a number of systems in which
single superexchange may already play a role in quantum dot
assemblies. For instance, the high carrier mobilities associated
with cross-linked QD assemblies may be a signature of superexchange.31–33,46–52 Along these same lines, the enhanced
mobility of 5.1 10 3 cm2 V 1 s 1 has been reported for PbS QD
lms treated with 3-mercaptopropionic acid (MPA)50 which may
be due to superexchange. In support of the feasibility of creating
interpenetrating networks of charge carriers, there are a
number of recent works in which this has been shown to be
possible.53–58
In summary, we propose a new Type-II assembly of quantum
dots connected via covalently bonded, short-bridge molecules.
The functionalization scheme envisioned amounts to the
construction of a quantum dot mesomaterial. While challenging to generate, the architecture amounts to an extension of
recent developments in solution processing techniques.59–62 A
proper choice of dot and molecular connector results in rapid
exciton separations relative to competing recombination rates.
Our rst-principles calculations of a model system indicate that
both polaron dissociation and subsequent carrier hopping are
signicantly enhanced by a double superexchange mechanism
due to enhanced electronic coupling of both carrier types. In
addition, no exciton diffusion is required and excitonic superpositions required by Heisenberg uncertainty offer an initially
well-distributed exciton distribution.
Although only SiQD mesomaterials have been considered in
this work, it should be possible to design double superexchange
dynamics into other material systems as well because the
underlying superexchange mechanism is ubiquitous in both
articial31–33,46–52,63–66 and natural67,68 systems. Related studies on
PbSe,31,46–49,52 PbS,31,49,50,62 CdSe,32,33 CdTe,31 Au,32,33 and Pd32 QDs,
CdS32 and Bi2S3 (ref. 32) nanorods, CdSe nanowires,32 and
organic molecules bridged by small molecules64–68 may provide
valuable hints to synthesize realistic materials with our
proposed architecture.
Fig. 5
1026 | Energy Environ. Sci., 2014, 7, 1023–1028
Acknowledgements
This research is supported by the Renewable Energy Materials
Research Science and Engineering Center (NSF Award
This journal is © The Royal Society of Chemistry 2014
Communication
DMR-0820518), by startup funds from Colorado School of Mines
(CSM) and the U.S. DOE early career research award (no.
DE-SC0006433). We also acknowledge the Golden Energy
Computing Organization at the Colorado School of Mines for
the use of resources acquired with nancial assistance from the
National Science Foundation and the National Renewable
Energy Laboratories.
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