A General Design Rule to Manipulate Photocarrier Transport Path in Solar Cells and Its Realization by the Plasmonic-Electrical Effect

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Abstract It is well known that transport paths of photocarriers (electrons and holes) before collected by electrodes strongly affect bulk recombination and thus electrical properties of solar cells, including open-circuit voltage and fill factor. For boosting device performance, a general design rule, tailored to arbitrary electron to hole mobility ratio, is proposed to decide the transport paths of photocarriers. Due to a unique ability to localize and concentrate light, plasmonics is explored to manipulate photocarrier transport through spatially redistributing light absorption at the active layer of devices. Without changing the active materials, we conceive a plasmonic-electrical concept, which tunes electrical properties of solar cells via the plasmon-modified optical field distribution, to realize the design rule. Incorporating spectrally and spatially configurable metallic nanostructures, thin-film solar cells are theoretically modelled and experimentally fabricated to validate the design rule and verify the plasmonic-tunable electrical properties. The general design rule, together with the plasmonic-electrical effect, contributes to the evolution of emerging photovoltaics.

본문

### OPEN

SUBJECT AREAS:

SOLAR ENERGY AND

PHOTOVOLTAIC

TECHNOLOGY

NANOPHOTONICS AND

PLASMONICS

Received
2 October 2014

Accepted
22 January 2015

Published
17 February 2015

Correspondence and

requests for materials
should be addressed to

[W.C.C. (w-chew@](mailto:w&hyphen;chew@uiuc.edu)

[uiuc.edu) or W.C.H.C.](mailto:w&hyphen;chew@uiuc.edu)

[(chchoy@eee.hku.hk)](mailto:chchoy@eee.hku.hk)

- These authors

contributed equally to

this work.

## A General Design Rule to Manipulate Photocarrier Transport Path in Solar Cells and Its Realization by the Plasmonic-Electrical Effect

Wei E. I. Sha 1 *, Hugh L. Zhu 1 *, Luzhou Chen 1, Weng Cho Chew 2 & Wallace C. H. Choy 1

1Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 2Department of
Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Illinois 61801, USA.

It is well known that transport paths of photocarriers (electrons and holes) before collected by electrodes
strongly affect bulk recombination and thus electrical properties of solar cells, including open-circuit
voltage and fill factor. For boosting device performance, a general design rule, tailored to arbitrary electron
to hole mobility ratio, is proposed to decide the transport paths of photocarriers. Due to a unique ability to
localize and concentrate light, plasmonics is explored to manipulate photocarrier transport through
spatially redistributing light absorption at the active layer of devices. Without changing the active materials,
we conceive a plasmonic-electrical concept, which tunes electrical properties of solar cells via the
plasmon-modified optical field distribution, to realize the design rule. Incorporating spectrally and spatially
configurable metallic nanostructures, thin-film solar cells are theoretically modelled and experimentally
fabricated to validate the design rule and verify the plasmonic-tunable electrical properties. The general
design rule, together with the plasmonic-electrical effect, contributes to the evolution of emerging
photovoltaics.

ue to a unique ability to localize, guide, and concentrate light at the nanoscale, plasmonics 1 finds a special
functionality to improve optical properties of thin-film photovoltaic devices 2–6 . By introducing metallic
nanostructures, light absorption at the active layer of devices will be enhanced, which undoubtedly boosts
# D
short-circuit current (Jsc) and thus power conversion efficiency (PCE) 6–14 . Currently, a wideband and angleinsensitive light absorption has been achieved by periodic, quasi-periodic and random metallic nanostructures to
approach or break the Yablonovitch 15–17, Lambertian 18,19, and Shockley-Queisser limits 20,21 . However, according
to semiconductor physics, bulk recombination of photocarriers (electrons and holes), which is different from light
absorption only governed by Maxwell’s equations, has a strong influence on electrical properties of solar cells
including open-circuit voltage (Voc) and fill factor (FF) and even predominantly determines the PCE. Going
beyond the well-known optical enhancement, in this work, plasmonics is explored to control bulk recombination
by modifying photocarrier transport path based on a general design rule. Plasmonics, which localizes intense light
very close to metallic nanostructures, can spatially redistribute light absorption at the active layer of photovoltaic
devices. As a result, the spatial distribution for excitons (or electron-hole pairs) generation can be plasmonically
tunable to optimize photocarrier transport path (or bulk recombination) and thus electrical properties of solar
cells. The design rule and its realization by the plasmonic-electrical effect can serve as a guideline for designing
photovoltaic devices.

Results
Proposed general design rule to reduce bulk recombination. According to semiconductor physics, electrical
properties of photovoltaic devices (such as FF and Voc) strongly depend on bulk recombination of photocarriers.
Transport path for a photocarrier is the path from the initial site generated to the electrode collected. A short
transport path will reduce the recombination and enhance electrical performances of devices. However, the short
transport path cannot be achieved for electrons and holes simultaneously because both photocarriers have the
same initial sites; and the total length of the electron and hole transport paths is approximately equal to the
thickness of active layer, i.e.

LezLh<L ð1Þ

where L is the thickness of the active layer. Le and Lh are the lengths
respectively for the electron and hole transport paths.

Besides the transport path, mobility of photocarriers also affect
bulk recombination strongly. Driven by the same internal electrostatic field, photocarriers with low mobility will move slowly. Thus
low-mobility photocarriers require a long transport time before collected by electrodes. An effective way for reducing recombination
loss is to let low-mobility photocarriers travel a short path. In other
words, we should force the transport time of electrons and holes
almost to be the same. Mathematically, we have

Le
me

< Lh

ð2Þ

solar cells (OSCs) by using the multiphysics model 27–35 developed in
literatures (also see Theoretical Method Section). Particularly,
OSCs with polymer and small-molecule materials always have
unbalanced photocarrier mobility, which depend on material
morphology, temperature, and experimental procedures (thermal
annealing, etc) 26,36 . Mobility-dependent current density-voltage (JV) responses are investigated with different light absorption (exciton
generation) distributions, which can be realized by versatile
plasmonic solar cell configurations (see Figure 1). The J-V curves
and corresponding characteristic parameters are presented in
Figure 2 and Table 1, respectively. The active layer thickness is L
5 90 nm. me 5 mh 5 3 3 10 23 cm 2 /(V?s) are set for the case of
balanced mobility. Regarding unbalanced cases, hole (electron)
mobility is reduced to 1/50 of electron (hole) mobility. The
injection barriers are set to be zero for both electrodes. To model
the localized plasmonic effect and understand the plasmonicelectrical effect, spatial distributions of exciton generation inside
the active layer are approximately set as follows

where me and mh represent mobility of electrons and holes, respectively. The above also suggests electron to hole transport length ratio
should be balanced with electron to hole mobility ratio, i.e. Le/Lh 5
me/mh. The governing equation (1–2) is a general design rule to decide
photocarrier transport path tailored to arbitrary photocarrier
mobility.

Manipulation of photocarrier transport path by plasmonicelectrical effect. Using Eqs. (1) and (2), one could design transport
paths or equivalently optimize initial generation sites of excitons. If
mobility between electrons and holes are well balanced, the initial
sites should be around the middle of active layer. If hole mobility is
smaller than electron mobility, excitons should be initially generated
near the anode, which guarantees a short transport path of holes.
Figure 1 shows a conceptual diagram to manipulate photocarrier
generation by embedding configurable metallic nanoparticles
(NPs) into the active layer 22–24 . Spatial locations of NPs and
spectral locations of plasmonic resonances should be carefully
controlled to shorten transport paths of low-mobility photocarriers
and maximize light absorption of active materials. A strong and
concentrated optical field around NPs will generate dense and
inhomogeneous excitons. These non-uniformly distributed excitons
not only increase Jsc but also boost Voc and FF through manipulating transport paths of photocarriers to equalize the transport
time of electrons and holes. Additionally, light absorption redistribution can be achieved by metallic grating electrodes as
well 6,19,25,26, where the coupling between plasmonic modes and
waveguide modes will be manipulated.

An Approximate Theoretical Model with a Mechanistic Insight.
To understand the concept that electrical properties of solar cells will
be boosted by spatially redistributing light absorption at the active
layer, we theoretically study electrical responses of thin-film organic

0, 0ƒzvL=3

3G � p, L=3ƒzv2L=3
0, 2L=3ƒzvL

0, 0ƒzvL=3

0, L=3ƒzv2L=3
3G � p, 2L=3ƒzvL

3G � p, 0ƒzvL=3
0, L=3ƒzv2L=3

0, 2L=3ƒzvL

G m pl (z)~

G m pl

G a pl (z)~

G a pl

G c

8
><

c pl (z)~

ð3Þ

ð4Þ

ð5Þ

where G m pl

m pl , Ga pl

a pl , and Gc

where G m pl , Ga pl , and Gc pl are the exciton generation rates with respect

to the three plasmonic solar cells (middle, near-anode, and nearcathode cases) as depicted in Figures 1(a), (b), and (c), respectively.
The cathode and anode are located at z 5 0 and z 5 L, respectively.
Here all the devices have the same averaged exciton generation rate
ðL

G m pl ,a,c
0

m pl ,a,c (z)dz

L~G � p. Physically, light absorption at the active

layer is spatially redistributed by the localized plasmonic effect.

From the theoretical results (Tables 1–2 and Figure 2), we find
that:

(i) The spatial distribution of exciton generation has a pronounced influence on electrical responses of OSCs. The mismatch between exciton distribution (controlled by the spatial
location of metallic NPs) and photocarrier mobility will lead to

Figure 1 | The conceptual diagram of plasmonic-electrical effect. Light absorption is spatially redistributed at the active layer for manipulating transport
paths of photocarriers (minus and plus notations denote electrons and holes, respectively). A desired light absorption distribution is realized by
spatially tuning the position of metallic NPs with strongly localized plasmonic effects. Light absorption of active materials is optimized by spectrally
tuning the shape-dependent plasmonic resonance. The arrows e and h are the transport paths of electrons and holes. Generated electron-hole pairs
(excitons) are concentrated (a) at the middle of the active layer (b) near the anode and (c) near the cathode respectively

Figure 2 | Photocarrier mobility dependence of J-V characteristics for plasmonic solar cells corresponding to Figures 1(a–c). An approximate
theoretical model is adopted for simulating the non-uniform spatial distribution of excitons. Generated electron-hole pairs (excitons) are concentrated
(a) at the middle of the active layer, (b) near the anode, and (c) near the cathode, respectively.

poor photovoltaic devices, such as the near-anode case with
low-mobility electrons and the near-cathode case with lowmobility holes.
(ii) The best electrical performance (e.g. PCE) can be achieved
when electron and hole mobility are well balanced and meanwhile light absorption is concentrated at the middle region of
active layer (as listed in the first line of Table 1). For instance, a
(standard) planar solar cell cannot achieve best efficiency even
if mobility between electron and hole are well balanced. It is
because, typically, light intensity is exponentially decayed from
the transparent electrode rather than achieving its peak value
at the middle region of active layer. On the other hand,
although the intensity peak could be around the center of active
layer via some smart optical designs, the solar cell does not
gain the best efficiency due to unbalanced electron and hole
mobility.
(iii) Shortening the transport path of low-mobility photocarriers
improves electrical properties of OSCs (Voc and FF), such as
the near-anode case with low-mobility holes and the nearcathode case with low-mobility electrons. Taking the planar
solar cell as an example again, the cell will be particularly
helpful for hole collections if its transparent electrode, where
light first penetrates, is the anode. This is also the reason why a
normal structure of planar OSCs [as shown in Figure 1(b)] has
a better performance than an inverted structure when holes
have low mobility 33,37 .

Comparatively studying Table 2 and Table 1, bulk recombination
dominates device performance. Under Voc condition (where the total
current is equal to zero), recombination rate is very large and is
almost equal to generation rate. Therefore, the recombination rates
at ‘‘different’’ Voc do not have any significance to device performances. Differently, under Jsc condition or particularly at the max

imum power point, larger recombination leads to lower Jsc and FF,
which strongly affect PCE of devices. The plasmonic-electrical effect,
which shortens the transport path of low-mobility photocarriers,
indeed reduces bulk recombination and boosts the device efficiency.
It should be noted that we adopted a simplified mathematical model
for exciton generation rates which are zeros at some regions of active
layer. From the intuitive model, one can understand the importance
of light absorption redistribution (without any light absorption
enhancements) to the solar cell performance.

A Rigorous Theoretical Model and Validation. The approximate
exciton generation model presented in Eqs. (3–5) offers a
mechanistic insight for plasmonically induced light redistribution
at the active layer. But a rigorous model for calculating exciton
generation of a practical solar cell is needed to accurately describe
photocarrier transport and validate the proposed design rule. A
small-molecule bulk heterojunction solar cell with an active
material of copper phthalocyanine (CuPc): Buckminsterfullerene
(C60) is theoretically investigated. In contrast to other solar cells, a
standard optimized small-molecule solar cell has an ultrathin active
layer due to large absorption coefficients of small molecules and a
short exciton diffusion length 38,39 . Hence, by incorporating metallic
NPs into active layer, the small-molecule device favors a very strong
near-field plasmonic effect. In this work, silver NPs with a size of
10 nm and a spacing distance of 10 nm are embedded into the active
layer. Using such small-sized NPs, which have large metal absorption
loss, is an unusual design. These small NPs do not significantly
enhance the total absorption of active materials; albeit extraordinarily redistribute light absorption at the active layer 40 . Exciton
generation is calculated by the finite-difference frequency-domain
method 41 . Regarding optical simulation details, please see Supplementary Note 1. It should be noted that metal absorption by

Table 1 | Electrical parameters for plasmonic solar cells with different photocarrier mobility of active materials and spatial distributions of
exciton generation. The Jsc, Voc, FF, and PCE are the short notations of short-circuit current, open-circuit voltage, fill factor, and power
conversion efficiency. N-Anode and N-Cathode are the short notations of near-anode and near-cathode

NPs position Mobility Jsc (mA/cm 2 ) FF Voc (V) PCE (%)

me 5 mh 9.198 0.669 0.522 3.21
Middle mh 5 0.02me 8.494 0.480 0.523 2.13
Fig. 1(a) me 5 0.02mh 8.490 0.480 0.523 2.13
me 5 mh 8.099 0.535 0.509 2.21
N-Anode mh 5 0.02me 7.953 0.535 0.549 2.33
Fig. 1(b) me 5 0.02mh 4.581 0.278 0.464 0.59
me 5 mh 8.022 0.533 0.509 2.18
N-Cathode mh 5 0.02me 4.578 0.278 0.464 0.59
Fig. 1(c) me 5 0.02mh 7.868 0.533 0.548 2.30

Table 2 | Averaged bulk recombination rates under short-circuit Jsc, maximum power Pmax, and open-circuit Voc conditions for plasmonic
solar cells with different photocarrier mobility of active materials and spatial distributions of exciton generation. N-Anode and NCathode are the short notations of near-anode and near-cathode

NPs position Mobility Recombination Jsc (10 27 m 23 s 21 ) Recombination Pmax (10 27 m 23 s 21 ) Recombination Voc (10 27 m 23 s 21 )

me 5 mh 0.014 0.849 13.507
Middle mh 5 0.02me 0.317 2.792 10.916
Fig. 1(a) me 5 0.02mh 0.317 2.789 10.884
me 5 mh 2.762 6.574 15.796
N-Anode mh 5 0.02me 1.678 4.332 12.639
Fig. 1(b) me 5 0.02mh 9.306 11.984 14.759
me 5 mh 2.972 6.574 15.700
N-Cathode mh 5 0.02me 8.434 11.036 13.74
Fig. 1(c) me 5 0.02mh 1.574 4.109 12.118

silver NPs, which does not contribute to exciton generation, has been
subtracted from the total absorption of active layer in the
calculation 23 .

Figure 3 shows the laterally-averaged exciton generation along the
vertical direction of active layer. Compared to the standard cell without NPs, plasmonically induced light absorption redistribution and
thus non-uniform exciton generation can be clearly observed (also
see Figure S2). Hence, the approximate exciton model given by Eq.
(4) is quite reasonable. Figure 4 illustrates the J-V response with
respect to the exciton generation of Figure 3. The electron and hole
mobility are respectively set to be 10 22 cm 2 /(V?s) and 10 25 cm 2 /
(V?s), which are typical values in small molecule devices 39 . Due to
short transport paths of holes, the near-anode case achieves the best
FF, Voc and PCE among all the cells including the standard one,
which agrees with the approximate theoretical results as listed in
the Table 1 highlighted by bold. However, in view of light blocking
effect by metal NPs, the near-anode case induces the worst light
absorption according to the exciton generation result (Figure 3). So
these unusually-small NPs efficiently redistribute (not significantly

Figure 3ð | Laterally-averaged exciton generation

Figure 3ð

G� (z)~

G(x,y,z)dxdy=Sxy at the active layer of a small-molecule bulk

enhance) light absorption at the active layer; and boost PCE by the
plasmonic-electrical effect.

From Table 1 and Figure 4, Jsc results show an interesting feature
that the middle case obtains the largest Jsc, although with a low FF.
Firstly, under Jsc condition, the drift current is dominantly larger
than the diffusion current; and photocarriers are fast swept out of
devices. Consequently, bulk recombination is weak, which can be
seen in Table 2. From the theoretical results at Table 1, the middle
and near-anode cases have comparable Jsc in contrast to the nearcathode one. The increased Jsc for the middle case in comparison
with the near-anode case is due to a nonlinear behavior for bimolecular recombination of photocarriers. However, bulk recombination
becomes larger and larger as the built-in electrostatic field is reduced.
At the maximum power point or under Voc condition, the diffusion
current competes with or even dominates over the drift current.
Under this situation, shortening the transport path of low-mobility
photocarriers will significantly reduce the bulk recombination and
boost electrical properties of devices especially for FF and Voc.
Secondly, exciton generation of a practical plasmonic solar cell is
the exciton generation of a standard device without metallic NPs
multiplied by the spatial-dependent (plasmonic) enhancement factor, which should be obtained with a rigorous simulation. Regarding

Figure 4 | Theoretical J-V characteristics for plasmonic small-molecule
solar cells corresponding to Figures 1(a–c). A rigorous exciton generation
result as depicted in Figure 3 is adopted in the simulation. The electron and
hole mobility are respectively set to be 10 22 cm 2 /(V?s) and 10 25 cm 2 /(V?s).
The PCE are 1.50%, 1.23%, 1.09%, and 1.26% respectively for the nearanode middle near cathode and standard cases

heterojunction solar cell. Silver NPs with a size of 10 nm and a spacing
distance of 10 nm are embedded into different locations of the active layer
corresponding to Figures 1(a–c). The result of a standard cell without NPs
is also given for comparisons. The volume-averaged exciton generationð

ð
G�~

G(x,y,z)dxdydz=Vxyz (10 27 m 23 s 21 ) are 8.34, 9.26, 9.27, 8.93

respectively for the near anode middle near cathode and standard cases

practical plasmonic devices, the near-anode case [Figure 1(b)] has
the shortest transport path of low-mobility holes but blocks a portion
of light due to metal absorption. From the results in Figure 3, the
volume-averaged exciton generation of the near-anode case gets the
lowest value; and is even lower than that of the standard cell without
NPs. This is the reason why the near-anode case induces a lower Jsc
compared to the middle case. On the other hand, the near-cathode
case [Figure 1(c)] has the longest hole transport path to the anode,
which causes a large recombination loss and thus the lowest Jsc. From
above discussions, Jsc of practical solar cells depends not only on the
transport path of photocarriers but also on the magnitude of volumeaveraged exciton generation rate.

Although the middle case achieves the largest Jsc, the near-anode
case still gains the highest PCE confirmed by the rigorous theoretical
results. Therefore, Voc and FF, which strongly depend on bulk
recombination and are tunable with photocarrier transport paths,
play more important roles than Jsc in determining the overall performance of plasmonic devices.

Experimental Design and Validation. Very recently, it has been
reported that device performance of OSCs is affected by the
position of a silver film within the active layer 42 . To understand the
underlying physics and experimentally demonstrate the general
design rule, we fabricated the small-molecule bulk-heterojunction
solar cell with the active material of CuPc:C60. Different-sized Ag
NPs are embedded into different positions of the active layer by using
thermal evaporation at different stages of film formation of the active
layer. Experimental details are discussed at the Experimental Section.
It is worthy of noting that the plasmonic solar cells are fabricated
within a high-vacuum chamber, and thus metal NPs are not
passivated. The device structures corresponding to Figures 1(a–c)
are given as follows:

ITO/MoO3 (10 nm)/CuPc:C60 (40 nm)/Ag NPs/CuPc:C60
(40 nm)/BCP (10 nm)/Ag

ITO/MoO3 (10 nm)/CuPc:C60 (20 nm)/Ag NPs/CuPc:C60
(60 nm)/BCP (10 nm)/Ag

ITO/MoO3 (10 nm)/CuPc:C60 (60 nm)/Ag NPs/CuPc:C60
(20 nm)/BCP (10 nm)/Ag

Figure 5 shows the cross sectional scanning electron microscopy
(SEM) images of the small molecule solar cells. Ag NPs are well
located at a specific region of the CuPc:C60 active layer.

To study the plasmonic-electrical effect, on one hand, the size of
Ag NPs is tuned to be an optimized value for favoring a strong nearfield plasmonic effect. Using the structure of ITO/CuPc:C60 (40 nm)/
Ag NPs (various sizes)/CuPc:C60 (40 nm), the optical absorptance of
CuPc:C60 films incorporating different-sized Ag NPs (see Figure S3)
suggests a strong and tunable plasmonic enhancement (see Figure 6).
On the other hand, photocarrier mobility in the bulk-heterojunction
active material (CuPc:C60) is very unbalanced, which can be confirmed by the experimental results of Figure S4. Here, the hole mobility is four orders of magnitude smaller than the electron one.

From the experimental results as illustrated in Figures 7 and 8 for
different device structures (Figure 5), we find that:

(i) The optical absorption of plasmonic small molecule solar cells,
which is almost independent on the NP positions at the active
layer, shows no significant differences (see Figure 7). This
agrees with our argument and theoretical results (presented
in Figure 3), i.e. light absorption is spatially redistributed by
the localized plasmonic effects.
(ii) Voc and FF are noticeably improved when Ag NPs are embedded close to the anode (the near-anode case). From experimental results in Figure 8, FF of the near-anode case is 0.42
compared to 0.39 and 0.32 respectively for the middle and
near-cathode cases. Moreover, Voc of the near-anode case is
0.48 V in contrast to 0.44 V and 0.36 V for the middle and
near-cathode cases, respectively. These experimental results
agree with the theoretical predictions as listed in the Table 1
(highlighted by bold) and Figure 4. According to Eq. (2) and
relevant physical explanations, shortening the transport path
of low-mobility holes will reduce bulk recombination resulting
in the improved electrical properties.
(iii) Jsc shows peculiar features after comparing experimental
results (Figure 8) to theoretical ones (Figure 4). For the theoretical results, Jsc of the near-cathode case is much smaller than
that of the near-anode case. For the experimental results, Jsc of
the near-cathode case is larger than that of the near-anode case.
One of reasons is that bimolecular recombination rate in
experimental devices is lower than that in theoretical models
based on Langevin theory 43 . Another reason is the exciton
quenching at the surface of unpassivated metallic NPs 44 .
Thus it is not fair or meaningful to make a direct comparison
between the plasmonic devices and standard one. In spite of
the peculiar feature of Jsc, the near-anode case still achieves the
best efficiency among all the plasmonic devices. Again, Voc and
FF, highly tunable by the plasmonic-electrical effect, determine
the overall plasmonic device performance.

Extension of the Design Rule to Other Thin-Film Solar Cells.
Manipulating photocarrier transport path is not only important to
OSCs with low and unbalanced mobility but also important to other
thin-film solar cells with high and balance mobility. The amorphous
silicon solar cell with a device structure of anode-p 1 silicon (10 nm)intrinsic silicon (460 nm)-n 1 silicon (30 nm)-cathode is studied.
Most photocarriers are generated at the intrinsic layer with high
and balanced photocarriers mobility, i.e. me 5 4.6 3 10 22 cm 2 /
(V?s) and mh 5 9.2 3 10 23 cm 2 /(V?s). According to our
theoretical results (see Supplementary Note 2), the near-anode
case, which redistributes light absorption (exciton generation)
tailored to electron-to-hole mobility ratio, achieves the best PCE
with the maximum Voc and FF. Due to a significantly reduced

Figure 5 | Cross sectional SEM images of small molecule solar cell devices. Ag NPs are embedded (a) at the middle of CuPc:C60 active layer, (b) near the
anode and (c) near the cathode which respectively correspond to Figures 1(a) (b) and (c)

Figure 6 | Experimental optical absorption enhancement of CuPc:C60
films after embedding Ag NPs. The absorption enhancement of CuPc:C60
films embedded with different-sized Ag NPs were measured based on the
structure of ITO/CuPc:C60 (40 nm)/Ag NPs (various sizes)/CuPc:C60
(40 nm). The enhancement is defined as the absorption of plasmonic cells
(with Ag NPs) over that of standard cells without Ag NPs. It should be
noted that the thickness of initially evaporated metal film as depicted in the
legend is not equal to the size of corresponding metal NPs as shown in
Figure S3.

built-in potential at the maximum power point, photocarriers cannot
be fast sweep out and thus bulk recombination dominates the device
efficiency of solar cells. Additionally, depending on effective mass
and average scattering time, mobility of photocarriers, cause
different bulk recombination features in different active materials.
Consequently, controlling photocarrier transport path by the
proposed general design rule is important to thin-film photovoltaics.

In conclusion, we propose a general design rule to manipulate
photocarrier transport in photovoltaic devices. Through spatially
redistributing light absorption at active layer, the design rule is successfully demonstrated in a configurable plasmonic device with the
help of the plasmonic-electrical effect. The dense exciton generation
around plasmonic nanostructures provides a flexible and integrated
way to both increase Jsc and simultaneously boost Voc and FF.
Balancing the transport time for photocarriers with different electron
to hole mobility ratio reduces bulk recombination and thus improves
the electrical performance of photovoltaic devices. The work is highly
important for high-performance photovoltaics.

Methods
Device fabrication. The Ag NPs embedded solar cells were fabricated on clean
conductive ITO coated glass substrates (sheet resistance of,20 V/sq, purchased
from TINWELL Tech. LTD.), which were previously cleaned in ultrasonic bath in
detergent, deionized water, acetone, and ethanol, subsequently. After dried by
nitrogen gas, substrates were transferred into a vacuum chamber for thermal
deposition. MoO3 (10 nm, purchased from Aladdin China) was evaporated at the
speed of 0.04 nm/sec. A blend CuPc:C60 layer (CuPc and C60 were purchased from
Kintec and Nichem Taiwan, respectively) was deposited at the evaporation rate of
0.05 nm/sec in the organic chamber. Ag NPs were thermally evaporated at different
stages of film formation of the active layer. Finally, electron-blocking layer BCP
(10 nm, purchased from Kintec) and Ag cathode (Ag pellets were purchased from
Kurt J. Lesker) were evaporated in sequence onto the organic active layer to complete
the plasmonic solar cells. The evaporation rate and the final thickness of MoO3,
organic active layer, and Ag NPs were controlled by in situ quartz monitors. All of the
materials we utilized in this work were commercially available and used without
further purification.

Characterization. The absorption spectra of Ag NPs embedded organic active films
and plasmonic small-molecule solar cells were determined by the diffused reflection
(R) and transmission (T) spectra utilizing a CCD spectrometer (Ocean Optics
QE65000) and an integrating sphere. Current-voltage (J-V) curves of plasmonic
small-molecule solar cells were measured using a Keithley 2635 SourceMeter and
ABET AM1.5G solar simulator. The morphology of Ag NPs thermally deposited on
the surface of organic active layers was characterized by LEO 1530 scanning electron

Figure 7 | Experimental optical absorption of plasmonic small-molecule
solar cells. The optical absorption is obtained by using 1-diffused
reflectance (R)-diffused transmittance (T). Ag NPs are embedded at the
active layer with different spatial locations corresponding to Figures 1(a–
c). The device structure of the middle case is: ITO/MoO3 (10 nm)/
CuPc:C60 (40 nm)/Ag NPs/CuPc:C60 (40 nm)/BCP (10 nm)/Ag; The
device structure of the near-anode case is: ITO/MoO3 (10 nm)/CuPc:C60
(20 nm)/Ag NPs/CuPc:C60 (60 nm)/BCP (10 nm)/Ag; The device
structure of the near-cathode case is: ITO/MoO3 (10 nm)/CuPc:C60
(60 nm)/Ag NPs/CuPc:C60 (20 nm)/BCP (10 nm)/Ag.

microscope (SEM). Cross sectional SEM images of Ag NPs embedded small molecule
solar cells were measured by Hitachi S4800 FEG SEM.

Theoretical model. The electrical properties of OSCs can be modeled by solving
organic semiconductor equations involving Poisson, drift-diffusion and continuity
equations 45,46

+ : ("+w)~{q(p{n) ð6Þ

Ln

ð7Þ

1 q +:({qmnn+wzqDn+n)zQG{(1{Q)R

LLnt ~ 1 q

Lp

ð8Þ

1 q +:({qmpp+w{qDp+p)zQG{(1{Q)R

LLpt ~{ 1 q

Figure 8 | Experimental J-V characteristics of plasmonic small-molecule
solar cells. Ag NPs are embedded at the active layer with different
spatial locations corresponding to Figures 1(a–c). The hole mobility is four
orders of magnitude smaller than the electron mobility. The statistical
parameters of three different plasmonic solar cells are summarized in the
inset

where q is the electron charge, w is the potential, and n and p are electron and hole
densities, respectively. Moreover, mn and mp are the mobility of electrons and holes
respectively. Furthermore, Dn and Dp are the diffusion coefficients of electrons and
holes respectively, which are accessible by the Einstein relations and mobility. Jn 5
2qmnn=w 1 qDn=n and Jp 5 2qmpp=w 1 qDp=p are respectively electron and hole
current densities, and G is the exciton generation rate. Here, the recombination rate R
is taken as the Langevin bimolecular form 47 ; and the field-dependent exciton
dissociation probability Q is evaluated by the Onsager-Braun theory 48,49 .

The potential boundary condition at the electrodes is given by

w~V{ Wm ð9Þ

where V is the applied bias voltage and Wm is the work function of the electrode. The
electrodes are assumed to be ohmic contacts without injection barriers for understanding the influence of photocarrier transport paths on the electrical properties of
solar cells, i.e.

n~Nc, p~Nv ð10Þ

where Nc and Nv are the effective density of states for bulk heterojunction active
materials.

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Acknowledgments
The authors acknowledge the support of the General Research Fund (grants: HKU711813
and HKU711612E), the National Natural Science Foundation of China (NSFC)/Research
Grants Council (RGC) grant (N_HKU709/12) and Ministry of Education (MOE)/Research
Grants Council (RGC) (M-HKU703/12) from RGC of Hong Kong Special Administrative
Region, China. This project is also supported by Collaborated Research Fund (CUHK1/
CRF/12G) of RGC and the UGC of Hong Kong (No. AoE/P-04/08), by The National
Natural Science Foundation of China (No. 61201122), by Collaborative Research Fund
(C7045-14E), by CAS-Croucher Funding (CAS14601), and in part by a Hong Kong UGC
Special Equipment Grant (SEG HKU09).

Author contributions

W E I S and H L Z contributed equally to the work W E I S and L C conducted

theoretical modeling. H.L.Z. fabricated and measured small-molecule solar cells. W.C.H.C.
and W.C.C. planned and supervised the project.

Additional information
[Supplementary information accompanies this paper at http://www.nature.com/](http://www.nature.com/scientificreports)
[scientificreports](http://www.nature.com/scientificreports)

Competing financial interests: The authors declare no competing financial interests.

How to cite this article: Sha, W.E.I., Zhu, H.L., Chen, L., Chew, W.C. & Choy, W.C.H. A
General Design Rule to Manipulate Photocarrier Transport Path in Solar Cells and Its

Realization by the Plasmonic-Electrical Effect. Sci. Rep. 5, 8525; DOI:10.1038/srep08525
(2015).

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