THE JOURNAL OF CHEMICAL PHYSICS 141, 154701 (2014)
Charge separation at nanoscale interfaces: Energy-level alignment
including two-quasiparticle interactions
Huashan Li, Zhibin Lin, Mark T. Lusk,a) and Zhigang Wub)
Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
(Received 7 July 2014; accepted 3 October 2014; published online 17 October 2014)
The universal and fundamental criteria for charge separation at interfaces involving nanoscale materials are investigated. In addition to the single-quasiparticle excitation, all the two-quasiparticle effects
including exciton binding, Coulomb stabilization, and exciton transfer are considered, which play
critical roles on nanoscale interfaces for optoelectronic applications. We propose a scheme allowing
adding these two-quasiparticle interactions on top of the single-quasiparticle energy level alignment
for determining and illuminating charge separation at nanoscale interfaces. Employing the manybody perturbation theory based on Green’s functions, we quantitatively demonstrate that neglecting
or simplifying these crucial two-quasiparticle interactions using less accurate methods is likely to
predict qualitatively incorrect charge separation behaviors at nanoscale interfaces where quantum
confinement dominates. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4898155]
I. INTRODUCTION
Nanomaterials, in particular, those within the quantum
confinement regime, are promising for the next-generation
photovoltaic (PV) cells1, 2 because their electronic and optical
properties can be tuned by controlling their sizes, shapes, and
surface chemistry, as well as the potential benefit from collecting hot charge carriers3 and multiple exciton generation4, 5 by
a single photon. In PV cells based on nanomaterials, the exciton binding energy (Eb ) can be 1–2 orders higher than that
in the corresponding bulk materials, leading to much more
tightly bound excitons, so the fast dissociation of bound excitons into relatively free electrons and holes, i.e., the charge
separation process, is critical to efficient energy conversion.
Charge separation in these excitonic PV cells occurs at interfaces between nanomaterials and/or molecules, and understanding the underlying mechanisms and the ability of quantitatively assessing charge separation at nanoscale interfaces
are central to rational design of excellent nanoPV.
During the past decade, considerable progress has been
made experimentally to construct nanoscale interfaces that
facilitate efficient charge separation.6–14 However, due to the
ensemble nature of the measurements on nanostructures, experiment alone is extremely challenging in interpreting data
and accurately characterizing interfacial properties.14–17 On
the other hand, extensive theoretical efforts18–34 have been
spent on investigating a variety of nanoscale interfaces for PV
applications. The simplest model for interfacial charge carrier
dynamics is the quasiparticle (QP) energy level alignment, in
which a staggered type-II junction enables charge transfer.
Many theoretical analyses18–26 adopted this straightforward
approach; however, the excitonic effects in quantum-confined
nanomaterials and molecules play a major role in determining the electronic excitation dynamics, which might be coma) Electronic mail: mlusk@mines.edu
b) Electronic mail: zhiwu@mines.edu
0021-9606/2014/141(15)/154701/7/$30.00
pletely different from the behavior predicted by the simple QP
energy level alignment.
Only a handful previous theoretical works27–34 have considered such effects, e.g., Bittner et al.27 computed exciton binding energies and band offsets to explain the different charge separation characters using the configuration
interaction method. Similarly, the semiempirical intermediate
neglect of differential overlap Hamiltonian coupled to a single configuration interaction scheme28, 29 and the HartreeFock Austin model30, 31 gave reasonable results for charge
transfer in organic-organic interfaces. Besides, the timedependent density functional theory (TDDFT) and the unrestricted DFT calculations have been applied to obtain accurate excitonic energies in nanoscale interfacial systems,28, 32, 33
and excellent agreement between theoretical excitation energies for donor/acceptor complexes and experimental data
was achieved by employing the perturbative many-body GW
method and the Bethe-Salpeter-Equation (BSE) approach.34
However, no systematic theoretical work has ever been
published to fully address the role of all excitonic effects including exciton binding, Coulomb stabilization and exciton
transfer on charge separation at nanoscale interfaces. Furthermore, it is not clear how to include the two-QP interactions in
the manifesting single-QP energy level alignment, which has
been widely adopted to describe interface characteristics for
bulk materials.
In this work, we analyze the conditions for charge separation when the excitonic effects are important, by expanding and generalizing the QP energy level alignment model.
We propose the effective energy level combining the singleQP energy and the two-QP excitonic binding as well as the
Coulomb interaction of the separated electron and hole. For
a nanomaterial, its effective QP energy levels barely change
when interfacing with other materials whose sizes are similar. Efficient charge transfer across nanoscale interfaces can
take place only if the associated effective and original QP
energy levels form a type-II junction. In addition, exciton
141, 154701-1
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transfer is found to only suppress charge separation. Applying the present theory to four representative model inorganicorganic nanoscale interfaces between silicon quantum dots
(Si QDs) and small organic molecules by carrying out the
GW/BSE computations,20, 35–39 we show that incorrect charge
transfer behavior for such interfaces is highly likely to be
predicted unless all the many-body interactions involved in
single-QP and two-QP excitations are taken into account accurately. In addition, our theory predicts the charge separation
behavior of a practical organic interface used in PV cells, in
agreement with experiment.
qualitatively well,44 although DFT usually substantially underestimates band gap (Eg ). This is because (1) in most bulk
semiconductors exciton binding energy is negligible, compared to band gap and band offset; (2) error cancellation
on both sides of interface for similar semiconductors. However, at the hybrid nanoscale interface, both conditions above
are not satisfied, and all the many-body interactions involved
in electronic excitations and interfacial exciton/charge-carrier
dynamics must be precisely taken account. We thus propose
the effective energy levels to combine the single-QP excitation and two-QP interactions.
II. COMPUTATIONAL METHODOLOGY
A. Effective energy levels
Our DFT calculations employed a finite-difference approach in real space using the Parsec code,40 with the normconserving pseudopotentials and the local density approximation (LDA) for the exchange-correlation functional. The
grid spacings are set to be 0.2 Å for small molecules and
0.25 Å for small SiQDs, while the radials of the relevant
sphere domains are set to be 10 Å and 12 Å, respectively, so that wavefunctions vanish outside the boundary and
eigenvalues reach convergence. The Td symmetry has been
enforced on all SiQDs. The interface geometries are optimized until all atomic forces are less than 0.002 hartree/Å.
The GW/BSE calculations are carried out using the RGWBS package.39 Specifically, the self-energies are computed
within the non-self-consistent G0 Wf approximation, wherein
G is estimated by the Kohn-Sham Green’s function and W
is obtained within the time-dependent adiabatic LDA along
with the vertex correction. To ensure good convergence, 300
single-particle eigenfunctions are used to construct the twoQP exciton wavefunctions.
The Coulomb interaction energy is calculated by17
Q Q
D A
Ec =
,
(1)
RDA
The most general condition for interfacial charge separation derives from the fact that the total electronic energy before charge separation (Ei ) should be higher than that
(Ef ) after the transfer happens, i.e., the driving force G is
positive:
where QD and QA are the partial charges on donor and acceptor, respectively, RDA is the effective distance between them,
and = 3 is the dielectric constant taken to be typical value
of organic systems.32 Estimating the Coulomb interaction using a fixed dielectric constant could only be safely applied
to systems consisting of donor and acceptor with similar and
known dielectric constants. The partial charges are obtained
by Mulliken analysis implemented in Dmol package.41 The
Conductor-like Screening Model (COSMO)42 was used to account for the dielectric effect of the solvent. In Dmol calculations an all-electron approach was employed with the
generalized gradient approximation (GGA) parameterized by
Perdew, Burke, and Ernzerhof (PBE).43 A real-space, double
numeric plus polarization (DNP) basis was used along with
an octupole expansion to specify the maximum angular momentum function.41
G = Ei − Ef > 0.
(2)
This is because if Ei < Ef , the phonon-assisted charge transfer can still take place, but its rate is extremely low at room
temperature if Ef − Ei kB T ≈ 24 meV, where kB is the
Boltzmann constant and T = 300 K. In the following discussions, we thus neglect the possible charge or exciton transfer
with negative driving forces.
For an interface between materials A and B, without losing generality we assume an exciton is generated in A. The
initial total electronic energy is
A
B
+ Eg∗,A + Egs
+ Ec,i ,
Ei = Egs
(3)
A
B
where Egs
and Egs
are the ground-state energies for A and
B, respectively, Eg∗,A is the optical gap for A, and Ec, i is the
initial Coulomb interaction between A and B. The final total
electronic energy can be one of the following:
A
A
B
B
Ef = Egs
− EHOMO
+ Egs
+ ELUMO
+ Ec,f ,
(4)
A
A
B
B
Ef = Egs
+ ELUMO
+ Egs
− EHOMO
+ Ec,f ,
(5)
depending on whether the electron [Eq. (4)] or hole [Eq. (5)]
transfers from A to B. Here HOMO and LUMO denote the
highest occupied and the lowest unoccupied molecular orbitals, and Ec, f is the final interfacial Coulomb energy.
Combining Eqs. (2)–(5), one finds the charge separation
conditions for electron or hole transfer, respectively,
A
B
ELUMO
− EbA − Ec > ELUMO
,
(6)
A
B
EHOMO
+ EbA + Ec < EHOMO
,
(7)
where the Coulomb stabilization energy Ec = Ec, f − Ec, i ,
and Eb = Eg − Eg∗ = ELUMO − EHOMO − Eg∗ . It is convenient to define the effective LUMO and HOMO energy levels,
III. RESULTS AND DISCUSSION
For the bulk interface between two similar semiconductors, the energy-level alignment and band offsets predicted by
Kohn-Sham eigenvalues often agree with experiment at least
eff,A
A
ELUMO
≡ ELUMO
− EbA − Ec ,
(8)
eff,A
A
EHOMO
≡ EHOMO
+ EbA + Ec ,
(9)
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(a)
A
J. Chem. Phys. 141, 154701 (2014)
(b)
B
A
B
LUMO
LUMO
A
Effective Eb
LUMO
TABLE I. Calculated ionization potential (IP), electron affinity (EA), and
optical gap (Eg∗ ) in unit of eV for anthracene and Si35 H36 , in comparison
with available previous theoretical results and experimental data.
LUMO
∆GA→B
el
|∆Ec|
*,A
LUMO
*,A
g
Eg
Effective
|∆Ec|
HOMO EAb
E
HOMO
HOMO
∆GA→B
h
Present
theory
Previous
theory
Experiment
Anthracene
IP
EA
Eg∗
7.23
1.05
3.03
7.06a
0.91a
3.11d
7.44b
0.53c
3.11e
Si35 H36
IP
EA
Eg∗
8.20
1.46
4.23
8.0f
1.1f
4.1g
HOMO
HOMO
FIG. 1. Schematic illustrations of interfacial charge separation criteria. A
type-II junction is formed using the effective LUMO for electron transfer (a)
or using the effective HOMO for hole transfer (b). Here Eb , Eg∗ , Ec , and
G are exciton binding energy, optical gap, Coulomb stabilization energy,
and charge transfer driving force, respectively.
a
Reference 34.
Reference 45.
c
Reference 46.
d
Reference 47.
e
Reference 48.
f
Reference 39.
g
Reference 49.
b
so that the intuitive picture of interfacial level alignment can
still be used to determine if charge transfer can occur, as
schematically illustrated in Fig. 1.
If both the effective LUMO and the HOMO of A are
higher than the LUMO and HOMO of B, respectively, as
shown in Fig. 1(a), the electron will transfer from A to B;
whereas when both the LUMO and effective HOMO of A
are lower than the LUMO and HOMO of B, respectively, as
shown in Fig. 1(b), the hole will transfer from A to B. In both
cases, an effective type-II junction is formed, ensuring charge
separation at the nanoscale interface, with the driving force
eff,A
B
Gel
A→B = ELUMO − ELUMO ,
(10)
eff,A
B
GhA→B = EHOMO
− EHOMO
,
(11)
ionization potential (IP), electron affinity (EA), and optical
gap (Eg∗ ) for anthracene and Si35 H36 , and these data demonstrate that our present results agree very well with available
experimental data and previous theoretical results. Fig. 2 plots
(a)
Si35H36
(b)
C3H8N
Si35H36
anthracene
3.8
for electron or hole transfer, respectively.
In a bulk interface, both Eb and Ec are negligible, hence
eff
eff
≈ ELUMO and EHOMO
≈ EHOMO , and its junction type
ELUMO
can be safely determined by the frontier QP energy levels.
This is the reason why the bulk heterojunction type is normally defined by QP energy levels. But in a nanoscale interface, Eb and Ec are remarkably enhanced, and a full analysis is necessary. Here Eb > 0, indicating that the strength of
Coulomb interaction between electron and hole before the exciton is dissociated; while Ec < 0, whose magnitude is the
strength of Coulomb interaction between electron and hole after the exciton is dissociated. Consequently, Eb > |Ec |, and
then Eb + Ec > 0; as a result, based on Eqs. (8) and (9),
eff
eff
< ELUMO and EHOMO
> EHOMO , suggesting that for
ELUMO
an effective type-II junction facilitating either electron transfer [Fig. 1(a)] or hole transfer [Fig. 1(b)], its corresponding
QP energy level alignment is also of type-II. Therefore, a staggered type-II QP energy level alignment is only a necessary
condition for charge separation, but not sufficient. Note that
if there is partial charge transfer between the donor and the
acceptor, one has to calculate the D/A interface directly.
0.2
1.1
4.2
2.5
(c)
1.6
2.7
1.1
Si35(CH3)36
1.3
2.5
C14H4N2O4
3.7
(d)
1.1
3.0
1.1
0.5
Si35(CH3)36 anthracene
2.1
3.7
1.1
0.9
0.7
3.0
1.0
2.6
2.9
3.2
4.2
2.9
1.0
1.9
3.2
1.1
3.7
(e)
C3H8N
anthracene
C14H4N2O4
B. Applications to four nanoscale interfaces
Four model inorganic-organic nanoscale interfaces between weakly bonded Si QDs and small molecules, including Si35 H36 –C3 H8 N, Si35 H36 –anthracene, Si35 (CH3 )36 –
C14 H4 N2 O4 , and Si35 (CH3 )36 –anthracene are studied to show
that the QP energy level alignment might predict wrong
charge separation behaviors. Table I summarizes calculated
FIG. 2. Energy level alignment for interfaces (a) Si35 H36 –C3 H8 N, (b)
Si35 H36 –anthracene, (c) Si35 (CH3 )36 –C14 H4 N2 O4 , and (d) Si35 (CH3 )36 –
anthracene. The notations here follow those in Fig. 1, with energy in eV.
For each interface, on the left is plotted the effective LUMO or HOMO for
exciton being generated in the Si QD, whereas on the right is plotted the effective LUMO or HOMO if exciton has transferred to or been generated in
the organic molecule. (e) Structures of the organic molecules. Here the white,
gray, dark blue, and red spheres represent H, C, N, and O atoms, respectively.
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(a)
(a)
(c)
2.88Å
(b)
Si35H36
Complex
-2.58
-2.51
-1.43
LUMO
LUMO
LUMO
LUMO
-2.54
(d)
(e)
-2.79
HOMO
effective
HOMO
(b)
(c)
C3H8N
-6.13
-6.20
hole
transfer
HOMO
HOMO
FIG. 3. The interface between Si35 H36 and C3 H8 N. (a) The atomistic structure. The Si atoms are tan, H atoms are white, C atoms are grey, and N atoms
are blue. (b) Isosurfaces of the HOMO and LUMO wave functions of Si35 H36
on the left and C3 H8 N on the right, as well as the QP energy-level alignment.
(c) Hole transfer across the interface. Exciton is generated in Si35 H36 and
then electron and hole are separated to Si35 H36 and C3 H8 N, respectively.
The HOMO of Si35 H36 is replaced by the effective HOMO to form a type-II
junction for hole transfer.
their energy level alignment, while Fig. 3 illustrates the first
interface in details. The frontier HOMO/LUMO orbitals in
the interfacial system (not shown) well resemble those corresponding QP orbitals in the isolated QD and organic molecule
[Fig. 3(b)], because of the weak Van de Waals interaction between them. For simplicity, we assume excitons are generated
in QDs. The frontier QP energy levels for the first two interfaces [Figs. 2(a) and 2(b)] form type-II junctions with both
HOMO and LUMO in QDs lower than those in molecules,
respectively; therefore, only hole transfer might be possible. Since the effective HOMO in Si35 H36 is lower than the
HOMO in C3 H8 N, while the effective HOMO in Si35 H36 is
higher than the HOMO in anthracene, efficient hole transfer
from Si QD to molecule can occur in the former interface, as
shown in Fig. 3(c), but not in the latter case, although in both
cases the QP energy levels form a staggered alignment.
Figs. 2(c) and 2(d) show that the QP energy level alignments in these two interfaces are of type-II as well, with both
HOMO and LUMO in QDs higher than those in molecules,
respectively, so that only electron transfer is possible if excitons are located in Si QDs. Comparing the effective LUMO
of Si QDs with the LUMO of C14 H4 N2 O4 and anthracene,
we conclude that electron can transfer from Si35 (CH3 )36 to
C14 H4 N2 O4 , but not to anthracene.
Note that interface dipole will significantly affect level
alignment; however, in these semiconducting interfaces studied in our work, there is almost no interfacial dipole formed,
as verified by our DFT calculations for isolated donor and acceptor and for the D/A complex. Fig. 4 shows that energy level
alignment obtained from isolated donor and acceptor [left and
right sides of panel (a)] is very close to that obtained from the
D/A complex [center of panel (a)], and the wave functions of
corresponding frontier orbitals are also nearly identical, suggesting that there is barely any interface dipole formed.
FIG. 4. (a) DFT HOMO/LUMO energy levels (in eV) of isolated Si35 H36 ,
C3 H8 N, and the D/A complex. Isosurfaces of (b) HOMO of isolated C3 H8 N,
(c) LUMO of isolated Si35 H36 , (d) HOMO of the D/A complex, and (e)
LUMO of the D/A complex.
The absence of the surface polarization response in DFT
calculations prevent them from capturing the variation in the
electronic correlation energy. In general, the effects of surrounding environment on interfacial energy alignment are
complicated because of the induced polarization, charge redistribution, etc. However, for the interfacial systems we studied in this work, these effects are expected to be mostly negligible, since both silicon quantum dots and these organic
molecules have very small polarizabilities. At such semiconducting interfaces normally there are barely any interfacial
polarization and charge redistribution, in contrast to metalorganic interfaces where significant charge transfer across interface and surface polarization can occur.
Another assumption made in our model is that the charge
distribution of the surrounding molecules does not play a critical role. To verify this, we calculated the DFT energy levels
for various numbers of organic molecules interfacing with the
same Si QD. As shown in Fig. 5 for the Si35 H36 /C3 H8 N interface, adding three more C3 H8 N molecules barely affects
the interfacial level offsets. We also find that frontier orbital
wave functions for the interface with 4 C3 H8 N molecules are
essentially the same as those for the interface with only one
C3 H8 N molecule. For the interface with 4 C3 H8 N molecules
the nearly degenerate frontier orbitals of these molecules split
slightly. We also calculated the energy levels for the frontier
orbitals of the Si35 H36 /C3 H8 N complex with the environmental dielectric constant () varying from 1 (vacuum) to 78.5
(water) using the COSMO,42 and the data summarized in
Table II confirm that polar solvents such as water can shift
(a) Si35H36+C3H8N Si35H36+4 C3H8N
-2.51
-2.79
3.34
-6.13
(b)
-2.35
-2.51
-2.52
-2.56
-2.63
3.34
-5.97
FIG. 5. (a) Relevant DFT energy levels (in eV) for Si35 H36 with one (left)
and four (right) C3 H8 N molecules. (b) Isosurfaces of HOMO/LUMO of the
interface consisting of Si35 H36 and four C3 H8 N molecules.
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TABLE II. Calculated HOMO/LUMO energies (in eV) for the
Si35 H36 /C3 H8 N complex with two very different values of dielectric
constant ().
LUMO (C3 H8 N)
LUMO (Si35 H36 )
HOMO (C3 H8 N)
HOMO (Si35 H36 )
=1
= 78.5
− 1.43
− 2.51
− 2.79
− 6.13
− 1.64
− 2.56
− 2.85
− 6.18
these energy levels in semiconducting interfaces only by negligible amounts. We also note that due to presence of electron
and hole in the charge transfer (CT) state, the neighboring
molecules will be polarized, which in turn will further stabilize the CT state. It could make our estimation of the energy
of the CT state less accurate, though the above calculations
suggest that this effect is not expected to be significant.
In these four model systems, tiny Si QDs have strong exciton binding (Eb > 2 eV) and large Coulomb stabilization
energy (Ec ≈ 1.1 eV), and our calculations have demonstrated that the excitonic effects play a substantial role on
charge separation at nanoscale interfaces. Our proposed effective HOMO/LUMO levels provide a simple and illuminating
physics picture to reveal the complex excitonic dynamics of
charge separation at these interfaces.
does not favor charge separation, then after exciton transfer it
still can not separate charges with appreciable rate.
The four interfaces shown previously in Fig. 2 are reinvestigated to explicitly elucidate the effect of exciton transfer on charge separation, and we still assume that the exciton is initially generated in Si QDs. Exciton can transfer
from Si35 H36 to C3 H8 N because the optical gap in the former (4.2 eV) is larger than the latter (2.7 eV); however, charge
separation is forbidden from the molecule to the QD since the
effective LUMO of the molecule is lower than the LUMO of
the QD, as illustrated in Fig. 2(a). This exemplifies that exciton transfer could completely suppress charge separation.
Another example is the Si35 (CH3 )36 –C14 H4 N2 O4 interface
[Fig. 2(c)], on which exciton can transfer as well. After exciton transfer, charge separation condition is still satisfied; however, the driving force is reduced to 0.7 eV from 0.9 eV. The
interface plotted in Fig. 2(b) does not favor charge transfer
from the QD to the molecule; although exciton transfer can
occur, the reverse charge transfer from the molecule to QD
is still forbidden, with an even more negative driving force
(−1.1 eV) than before (−0.5 eV). Finally, exciton transfer is
forbidden in the last nanoscale interface [Fig. 2(d)]; and if
exciton is generated in anthracene, charge separation cannot
occur as well.
D. Application to practical interfaces
C. Influence of exciton transfer on charge separation
An additional complexity originates from exciton transfer across interface, which has been observed in organic and
inorganic systems,50 but whose impact on charge transfer remains unclear, i.e., can exciton transfer induce an originally
forbidden interfacial charge separation?
Starting from the same initial conditions as expressed in
Eq. (3), the final electronic total energy after exciton transfer
is
A
B
+ Eg∗,B + Egs
+ Ec,f .
Ef = Egs
(12)
Apparently, here Ec, i ≈ Ec, f , and Ei > Ef leads to the condition for meaningful exciton transfer from A to B:
Eg∗,A > Eg∗,B .
(13)
The conditions for charge transfer from B to A can be described in Eqs. (6) and (7), if A and B are swapped, with
eff,B
A
h
driving force Gel
B→A = ELUMO − ELUMO or GB→A
eff,B
A
= EHOMO − EHOMO , for electron or hole transfer, respectively. An interface facilitating electron transfer from A to B
could only enable hole transfer from B to A, and it is easy to
∗,A
> Eg∗,B . Simverify that GhB→A < Gel
A→B because Eg
ilarly, an interface for hole transfer from A to B could only
induce electron transfer from B to A, with the driving force
h
Gel
B→A < GA→B .
Therefore, we draw an important conclusion that exciton
transfer only reduces or completely suppresses charge transfer: (1) if the interface before exciton transfer favors charge
transfer, then it can either still separate charges with a reduced
driving force or can not induce charge transfer any more after exciton transfer; (2) if the interface before exciton transfer
While the effective HOMO/LUMO levels are proposed
mainly to better illustrate the interfacial charge transfer dynamics by adopting the corresponding concepts used in bulk
materials, they can also be regarded as inherent properties for
a specific nanomaterial if its interfacing materials are similar in size so that the variation in Coulomb stabilization energy Ec is small. In these four interfaces Ec are within the
range of 1.03–1.13 eV, and the effective HOMO/LUMO for
one material barely change in various interfaces. But when
interfacing materials are distinctively different, the effective
HOMO/LUMO of a nanomaterial will depend on specific interface. However, this is also the case in bulk heterojunctions,
where the band offsets could sensitively depend on surface
orientation and termination, resulting in a variation in electron affinity 1 eV.51–54
To further illustrate the application of the effective energy
level alignment we proposed, we have performed calculations
of the poly(3-hexylthiophene) (P3HT) and fullerene derivative phenyl-C61-butyric acid methyl ester (PCBM) interface,
which is one of the most promising organic PV materials.59
Here the P3HT polymer is represented by the small molecule
P3C2 H5 T, and the experimental value (1.9 eV) of optical gap
in P3HT is adopted as suggested by previous literature.32 In
Table III our calculated IP, EA, and optical gap Eg∗ are compared with available experimental data and previous theoretical results. We note that (1) the rather large discrepancy between theory and experiment on IP and EA of P3C2 H5 T is
probably due to the overly simplified molecular structure used
in our calculations and (2) since the side chain of PCBM has
negligible impact on its energy levels,32 the C60 molecule
is used instead in our GW-BSE calculation. As shown in
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J. Chem. Phys. 141, 154701 (2014)
TABLE III. Calculated ionization potential (IP), electron affinity (EA), and
optical gap (Eg∗ ) in unit of eV for anthracene and P3C2 H5 T and C60 , in comparison with available previous theoretical results and experimental data.
Present
theory
Previous
theory
Experiment
P3C2 H5 T
IP
EA
Eg∗
5.76
1.25
2.45
5.89a
1.09a
5.1b
3.2b
C60
IP
EA
Eg∗
7.65
3.12
2.12
7.41c
2.31c
2.24f
7.6d
2.65e
1.94f
a
The B3LYP functional, Ref. 55.
Reference 56.
c
Reference 34.
d
Reference 57.
e
Reference 58.
f
Reference 17.
b
Fig. 6(a), our results imply that the exciton dissociations from
both PCBM and P3HT are energetically favorable. In addition, the driving force of charge separation from P3HT to
PCBM is predicted to be 0.80 eV in the present model, in
good agreement with previous calculation (0.97 eV) and experiment (0.9 eV),32 suggesting that the matrix has similar
effects on the frontier energy levels of the donor and acceptor,
which lead to an error cancellation.
We emphasize that our present approach is appropriate
to be applied to the cases that neither donor nor acceptor is
metallic or strongly polarized. This condition is satisfied by
many bulk hetero-junctions for PV/PL: photoluminescence
devices containing organic molecules or inorganic nanostructures. But in other interfaces such as the Schottky junction
this condition is not well maintained so that this approach
will fail. While the GW-BSE approach could provide accurate
energy levels for charge separation states including the long
range Coulomb interaction,34 it is currently not applicable to
realistic interfacial systems. One future approach is to reduce
the computational cost of GW-BSE calculations for such systems. Our present model could work well for chemisorbed
molecules provided that the frontier orbitals of the donor and
acceptor do not change too much compared to those in isolated components. Again this condition is satisfied in most
semiconducting interfaces where interfacial polarization and
(a)
PCBM
P3C2H5T
0.5
0.8
1.0
1.9
2.1
0.9
0.5
(b)
(c)
1.0
FIG. 6. (a) Energy level alignment for the PCBM/P3C2 H5 T interface. The
notations here follow those in Fig. 1, with energy in eV. (b) Side view and (c)
top view of the interface structure. The H atoms are white, C atoms are grey,
and S atoms are yellow.
charge redistribution will not significantly modify the energy
levels against those for isolated materials.
IV. SUMMARY
In summary, to fully account of the significant twoQP excitonic effects at nanoscale interfaces, we have proposed the effective HOMO/LUMO on top of the traditional
single-QP energy level alignment to determine junction type
and the interfacial charge separation character. Our calculations clearly demonstrate that, due to strong quantum confinement, incorrect charge transfer behavior at nanoscale
interfaces could be predicted without precisely considering
exciton binding and Coulomb stabilization. Furthermore, exciton transfer is found to only suppress charge transfer. Since
the QP energy level alignment is widely accepted and applied
to determine the interfacial junction type, present results raise
a grave caution. Instead, a universal theory for charge separation at any interfaces is presented, and an accurate and illuminating description is made by adding the two-QP excitonic
effects to the single-QP energy levels, which shall be useful
for designing and characterizing nanoscale interfaces for optoelectronic devices.
ACKNOWLEDGMENTS
This work was supported by the Renewable Energy Materials Research Science and Engineering Center (REMRSEC), the DOE Early Career Award No. DE-SC0006433, and
the startup fund from Colorado School of Mines (CSM). We
also acknowledge the Golden Energy Computing Organization at the CSM for the use of resources acquired with financial assistance from the National Science Foundation (NSF)
and the National Renewable Energy Laboratories (NREL).
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