Document:

UNITED STATES

 

 

The Architecture of Colloidal Quantum Dot Solar Cells:
Materials to Devices

Chem. Rev., 2014, 114 (1), pp 863-882

 

 

Article referenced as support for the following sections:

 

Page 45 & 46: Paragraph on Tandem Solar Cells

The Architecture of Colloidal Quantum
Dot Solar Cells: Materials to Devices

Illan
J. Kramer and Edward H. Sargent*

Edward S. Rogers Department of
Electrical & Computer Engineering, University of Toronto, 10 King’s College
Road, Toronto, Ontario M5S 3G4, Canada

	
  

 	
  

 
	
 1. Introduction

 	
 A

 
	
 2. Measuring and Modeling CQD Solar Cells

 	
 A

 
	
 2.1. Solar Cell
 Characterization Considerations

 	
 B

 
	
 2.2. Drift
 Transport and the Depletion Region

 	
 C

 
	
 2.3. Di3usion
 and Recombination

 	
 C

 
	
 2.4. Interfaces
 between CQDs and Electrodes

 	
 D

 
	
 3. CQD-Sensitized Solar Cells

 	
 E

 
	
 4. Schottky CQD Solar Cells

 	
 E

 
	
 5. Depleted Heterojunction CQD Solar Cells

 	
 G

 
	
 6. CQD Solar Cells Using Quantum Funnels

 	
 I

 
	
 7. Depleted Bulk Heterojunction CQD Solar Cells

 	
 K

 
	
 8. Bulk-Nano Heterojunction CQD Solar Cells

 	
 L

 
	
 9. Quantum Junction Solar Cells

 	
 L

 
	
 10. Multiple-Junction CQD Solar Cells

 	
 M

 
	
 11. Hot-Carrier E3ects in CQD Materials: Device
 Implications

 	
 N

 
	
 11.1.
 Hot-Electron Transfer

 	
 N

 
	
 11.2. Multiple
 Exciton Generation

 	
 O

 
	
 12. Conclusions

 	
 O

 
	
 Author Information

 	
 P

 
	
 Corresponding
 Author

 	
 P

 
	
 Author Contributions

 	
 P

 
	
 Notes

 	
 P

 
	
 Biographies

 	
 P

 
	
 Acknowledgments

 	
 P

 
	
 Abbreviations

 	
 P

 
	
 References

 	
 Q

 

1. INTRODUCTION

Colloidal
quantum dots (CQDs) are nanometer-sized particles of semiconductor dispersed in a solvent with the
aid of a stabilizing ligand. CQDs’
physical dimensions and shape dictate their
optical and electrical properties.1 This size-effect tenability differentiates them from other,
non-quantum-confined nano-crystals, providing a versatile framework on which to
build a multitude of optoelectronic devices. Control over CQD size, ligand
chemistry, and annealing conditions have enabled many recent advances in the
properties and performance of solution-processed solar cells, photodetectors,2-4
and light-emitting devices (LEDs).5,6

          This
review focuses in particular on energy harvesting applications of CQDs.
Photovoltaics leverage materials’ low-cost solution processing while exploiting
their broad spectral tunability matched to the Sun’s wide spectrum. A growing
community of engineering, chemistry, physics, and materials science researchers
are pursuing the development of CQD solar cells with the goal of achieving high
efficiency at low cost.

          We
focus in particular on the device architectures, and the enabling materials
chemistry advances, that have enabled solar cells employing CQDs as the primary
active layer to see rapid advances in solar power conversion efficiency. Each
architecture presented herein builds upon the improvements of each previous
generation, thus representing a “family tree” of solar cell devices (Figure 1),
not a set of distinct, stand-alone advances. This review therefore complements
excellent recent reviews that survey the CQD field from the point of view of
chemical synthesis and CQD film processing7 as well as photophysics.8

Figure 1. Family tree of colloidal
quantum dot photovoltaic device architectures.

	
  

 
	 

 
	
  

 
	
 Received: May 31, 2013

 

 

	
  

 	
  

 
	
 

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2. MEASURING AND MODELING CQD SOLAR CELLS

          The
photocurrent in solar cells can be produced from the drift of charge carriers in an electric field, and also
from the diffusion of photocarriers. Typical silicon p-n junction solar cells
include both a comparatively thin
depletion region in which a built-in field drives drift transport; as
well as a much thicker quasineutral region
that exploits the long minority carrier diffusion length, L (L = (tD)1/2, where t is the carrier
lifetime and D is the diffusivity) in this
indirect-bandgap, long electron-hole pair lifetime, medium (Figure 2a).9
High free carrier mobilities and low defect
densities enable extraction of photogenerated carriers from these
quasineutral regions through a highly efficient diffusion processes. p-i-n
solar cells, in contrast, rely heavily on a
distributed electric field through a
thick intrinsic layer within the absorbing medium, be it amorphous silicon9-12 or
microcrystalline silicon.13 p-i-n solar devices are dominated by drift
current and provide a particularly
relevant exemplar in the analysis of CQD solar cells. 

Figure 2. (a)p-njunctionsolarcellwithbothadepletionregionand quasineutralregions.(b)TypicalJ-V(bluecurve,leftaxis)andP-V (violet curve, right axis) characteristics of a
solar cell.

2.1. Solar Cell Characterization Considerations

          In
order to consider the implications of using CQD films as the active layer in a solar cell, it is important to
understand how solar cells are
characterized. Figure 2b shows a typical J-V and P-V characteristic curve of a photovoltaic
device. Device efficiency, η,
is defined by eq 1

(1)

where
Pmax_elec is the maximum
electrical power density generated, J
is the current density, V is the
applied voltage, and PIN_OPTis the incident optical power density. At AM 1.5 G conditions, PIN_OPTis 100 mW/cm2.14 The fill factor, FF, is an
additional figure of merit and is defined as Pmax_elec/ (JSC.VOC), where JSCand VOC are the current density at
short-circuit conditions and voltage at open-circuit conditions, respectively.
The fill factor can be understood to quantify the cell’s ability to continue to
extract current even as the band bending is reduced; this condition is realized
as the device approaches the maximum power point in the direction of VOC under
a forward-like applied bias. Graphically, it is a measure of the “squareness”
of the J—V curve.

          Also
affecting the fill factor of the device are the parasitic series, RS,
and shunt, RSH, resistances.
From the J—V curve, RSis the inverse of the J—V slope at VOC, while RSHis the inverse of the J—V slope at J SC(this is strictly only true for values of RSH >> RS).9For high performing solar cells, RSshould
approach 0, while RSHshould approach Y.

          For
active materials such as CQD films where 1/a,
where alpha is the absorption coefficient, is of the same order as
the free carrier extraction length, external quantum efficiency (EQE)
measurements have proved useful in profiling the effectiveness of each
nanometer of device thickness at extracting photogenerated carriers. PbS and
PbSe CQD films fall into this category, with both free carrier dependent
depletion widths and diffusion lengths between 30 and 400 nm,15-17
and complete above-bandgap absorption at <1 mm
film thickness.18,19

          EQE,
also known as the incident photon conversion efficiency (IPCE), is defined by
eq 2

(2)

(3)

where ΦINis the incident photon flux, PINis the incident monochromatic optical power density, h is Planck’s constant, c is the speed of light, λ is the monochromatic wavelength,
and e is the elementary charge.
While the EQE provides insight into how individual wavelengths are
converted into electrical current, it does
not distinguish between the cocontributing factors of absorption and extraction. The internal quantum efficiency, IQE (also known as absorbed photon
conversion efficiency, APCE), more
closely approximates extraction efficiency by dividing the EQE by the
fraction of photon current absorbed at each
wavelength (eq 3). The absorbed light considered
in the IQE calculation takes into account both reflective and transmissive losses outside of the active layer. As these
parasitic optical losses become nontrivial, the IQE deviates from reporting the pure extraction efficiency.

          Integrating
the product of the measured EQE spectrum with the AM 1.5 G spectrum in a manner
similar to Henry’s analysis on the
total AM 1.5 G spectrum20 allows determination of an expected JSCfor reconciliation with the measured
value under AM 1.5 G conditions.

          When
characterizing solar cells, several important factors need to be taken into consideration. First, the
lamp spectrum and its relationship to
the true AM 1.5 G spectrum needs to be quantified
in the form of a spectral mismatch factor by which measured current should be scaled.21
This includes understanding the spectral response of both the calibrated solar
cell used for confirming AM 1.5 G intensity and of the solar cell under test. Second, the aperturing of the device
is crucial since, unlike in crystalline semiconductors, lateral carrier
collection is negligible.22
The device area should therefore be defined as the illuminated area, and it should be less than or
equal to the physical top contact
size. Only when the physical contacts are patterned, isolating them from the underlying substrate, can the device
be illuminated without an aperture. Unmasked exposure areas can lead to edge effects that effectively
increase the active area of the
device, yielding falsely high currents. This effect is exacerbated for very small device areas where the
relative impact of the edge is more pronounced. For this reason, efficiency results for very small devices should
be taken with caution.

	
  

 	
  

 	
  

 
	
  

 	
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2.2. Drift Transport and the Depletion Region

          In
organic photovoltaics, dye-sensitized solar cells, and CQD photovoltaics, a
carrier extraction length is often defined as WDEP+ LDIFF, where WDEPis the width of the depletion region and
LDIFFis the
minority carrier diffusion length in the active material.

          This
extraction length can often be much less than the absorption length (1/α) of the most weakly absorbed above-bandgap
optical wavelength of interest. The result is a compromise between the absorption of light and the extraction of
photocharges.

          This
compromise can be overcome using bulk hetero-junctions23 and Gratzel cell24 high-surface-area
electrodes.16 This has been particularly true of solar cells in
which CQDs are used as sensitizers,
adsorbed as a monolayer onto a high-surface-area electrode.25-30

          Nevertheless,
many advances in CQD photovoltaics have relied on CQD films, in which
photocharges must travel significant distances (many quantum dots) within the
CQD film itself.

          This
has required the development of models to describe phenomena such as drift and diffusion, electric
fields and carrier concentration
gradients, generation and recombination, and transport and trapping in CQD solids.31-33 In this picture,
the CQD film is treated as a bulk
semiconductor whose bandgap is determined
by the quantum-tuned nanoparticles, and electron affinities, ionization potentials, Fermi and quasi-Fermi levels,
average electron and hole mobilities, an average dielectric constant
(and, in the optical regime, average n and k parameters),
and average generation and recombination rates are all measured and modeled. The successful treatment of these films as classical semiconductors suggests
the Shockley-Queisser power
conversion efficiency limit34 for conventional p-n solar cells can be translated to CQD solar
cells.35,36

          In
such a picture, semiconductor theory holds that a depletion region is formed
when two noninsulating, non-metallic,
differently doped solids are placed in electrical contact with each
other. The widths of these depletion regions on either side of this junction, W1 and W2, are derived according to eqs 4 and 5, respectively.37

(4)

(5)

          In
these equations, it is assumed that side 1 of the junction is n-type, and
therefore has a free electron density of n
= ND1and permittivity of ε1, while side 2 is p-type and therefore
has a free hole density of p
= NA2and
permittivity of ε2.
Ψbirepresents
the built-in potential of the junction, while V
represents any applied bias. These expressions apply equally well to
heterojunctions and homojunctions.

          While
excitonic transport (i.e., a model in which tightly bound electron-hole pairs
diffuse together, hopping from CQD to CQD
until reaching some charge separating interface) has been postulated as a relevant transport mechanism in CQD solids,38
it has also been shown that excitons readily dissociate in CQD solids when an
electric field is present39 (and even in the absence of an electric field40).
The successful harvesting of photocharges
from a CQD layer of >200 nm, a thickness much greater than the (downhill) excitonic diffusion mechanism is predicted
to support,15 is consistent with this picture of rapid dissociation
of excitons and subsequent collection of the resultant
free electrons and holes in the presence of an electric field, and thus
supports the effective medium picture. Needless to say, the model employs quantitative parameters, especially
mobilities, that are very different (in the case of mobilities, 10-4-101 cm2/V s
for CQDs16,41,42) than those of their bulk counterparts (102-105
cm2/V s43).

          This
picture offers specific guidance in solar cell optimization. As one example, increasing the doping in an n-type electrode that forms a depletion region in
an adjacent p-type light-absorbing
CQD solid enables a deeper depletion region
to be formed in the CQD material. In a similar vein, high doping of the CQD solid shrinks the depletion
region within this heavily doped
film, harming EQE and the resultant current density. This picture explains the recent success of asymmetrical doping of CQD solar cells.44,45
Naturally, the picture also
reinforces the crucial importance of continued progress in increasing the minority carrier diffusion length,
under 1 Sun conditions, to enable efficient extraction of charge carriers generated in a quasineutral portion of the CQD
active region.

          Because
CQD films have the added complications of being made of variable-sized
constituent material building blocks as well as being deposited from solution, the nature of charge transport through the films can also be
size-dependent46,47 and matrix
(or ligand)-dependent.48-52 Even nanoparticle shape influences electronic behavior.53-56
Efforts are underway toward
achieving the type of three-dimensional periodicity ubiquitous in crystalline semiconductor lattices.57-67
The ultimate hope is that these
superlattices, made up of one or several
building block nanocrystals, have more reproducible and uniform optical and electrical properties than
their irregular counterparts,68,69
an analogue to single-crystal semiconductor lattices made from colloidal quantum dots, the latter sometimes referred
to as artificial atoms.

          A
further consideration when working with these quantum-confined nanoparticles is
the evolution of their size and shape, particularly
under illumination. Photooxidation can convert some of the semiconductor
material into an insulating oxide. The
resulting quantum dot has effectively smaller dimensions, increasing its bandgap.70,71 Notably,
this instability72 is also size-dependent.73
Large CQDs, those over 4 nm in diameter, are more prone to photooxidation than their smaller counterparts. This may explain the higher open-circuit
voltage stability of a variety of
CQD solar cells employing larger bandgap CQDs.74-78 Beyond changing the optical characteristics of the
dots, the evolution of these
insulating shells reduces the overlapping
wave functions of adjacent dots, thereby reducing dot-to-dot coupling.

2.3. Diffusion and Recombination

          Electronic
traps play a critical role in semiconductors, be they classical or excitonic. Deep traps act as
recombination centers, capturing an electron and a hole and ultimately leading
to their recombination. Shallow traps
associated with a given band retard
the egress of that charge carrier, capturing it into a low-mobility
state as it travels along its path.32 It is thus not surprising that increases in CQD film mobilities
have been achieved through improved
passivation techniques,7,41,49,67,79 as observed using field-effect transistors (FETs).
These observations are consistent
with the fact that hopping42,46-48,80-83 transport, where the relative energies of and
distances between

	
  

 	
  

 	
  

 
	
  

 	
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Figure 3. (a) Transport mechanisms
in CQD films in the dark (top) and under illumination (bottom) illustrate how
traps mediate transport and define the extent of quasi-Fermi level splitting in CQD
films with high defect densities, and specifically in optoelectronic devices.
This framework is particularly relevant to CQD solar cells, where this concept,
in tandem with an appropriate device architecture, can provide an upper bound
on VOC that is substantially
less than the optical bandgap of the material with that cell architecture would
imply. Reprinted by permission from Macmillan Publishers Ltd.: Nature
Communications (ref 91),
copyright 2011. (b) Modeled diagonal equivalency of traps and mobility on solar
cell figures of merit. Reprinted
with permission from ref 32. Copyright 2011 American Chemical Society.

localized
states determine the ability of charges to progress through the film, has been reported in the
preponderance of CQD films
successfully deployed in photovoltaic devices.

          While
the transport mechanism is clearly important for understanding current
extraction in a solar cell, simply increasing a parameter such as mobility is
insufficient. In a high defect density
paradigm, increasing mobility merely speeds up the ability for a free carrier to find a defect. Recombination rate at defects is therefore directly proportional
to mobility.42 Instead, reducing the number of recombination
cen-ters32,67,75,84-90 and
improving the monodispersity42,48,85 of the CQD populations provide a path toward improved
current collection.

          Traps
have received much attention in CQD films recently, including characterizations of their density85
and depth91 within the
bandgap. Figure 3a illustrates how a midgap band of traps (MGB) influences the transport while pinning the
Fermi level of the film.

          The
CQD films employed in the various architectures discussed in this review are deposited from solution and postprocessed with nonsolvents (such as methanol)
and/or highly reactive ligands (such
as EDT and MPA). These solid-state
treatments leave the individual quantum dots vulnerable to oxidation75 or subject to physical
reorganization.87 Crystal or surface defects manifest as electronic trap states where recombination is likely to occur, reducing both
extractable current and attainable voltage.

          The
impact of traps on CQD solar cells has been modeled32,92 and observed experimentally.44,92,93
Figure 3b shows how, within the low-to-moderate defect density paradigm,
decreasing trap density exhibits a diagonal equivalency
to increasing mobility for solar cell performance.32 These both result in an increased diffusion
length: the reduced electrontrapdensityincreasescarrierlifetime,t,whilethe highermobilityincreasesthediffusivity,D,throughtheEinstein relation.37

          Characterization
of these traps (their depth within the bandgap,
their density, the shape of their distribution, etc.) in CQD films has
been a field of great advance in recent years.44,88,89,94

          In
addition to the delicacy of the surface properties of each individual CQD, these CQD solutions have a finite
population size distribution. Despite
colloidal quantum dots having a much higher
degree of monodispersity than their epitaxial growth or chemical bath deposited
counterparts,25 they do nevertheless exhibit sufficient polydispersity that the ensemble bandgap of a disordered CQD film does not have sharp edges.95
If these Urbach tails96
extend well into the bandgap, carriers will eventually funnel to the smallest bandgap CQDs within the film where they will recombine.97-100 While
this clearly has an impact on current collection, there is also an implication
for voltage. The presence of a high
degree of polydispersity would pin the quasi-Fermi level within the film
to the smallest bandgap,renderingthenominal“bulk”
bandgapwasteful.85For current deep trap densities in the 1016
to 1017 cm-3 range, polydispersity plays only a small role in
limiting performance, but as trap
densities are reduced, CQD films may enter a polydispersity-limiting
regime.

          As
seen in Figure 4, surface traps and these so-called “quantumtraps” (i.e.,small-bandgapCQDsoraggregatesof large-bandgap CQDS within a matrix of
larger-bandgap CQDs) have recently
been considered on an even footing; trap depth (Et),trapdensity(Nt),andCQDsizestandarddeviation(σ) can be explored and impact relative to surface
trap density distributions quantitatively compared.

2.4. Interfaces between CQDs and
Electrodes

          As
in all semiconductor devices, interfaces play an important role in CQD solar
cells. These have been addressed in another recent review,101 but will briefly be discussed here as
well. Whereas the preceding two
sections delved into transport of carriers through a CQD film, injection of
electrons and holes from the CQD
film into adjacent phases can have just as big an impact on photovoltaic
efficiency.

          In
the same spirit as section 2.3, interfacial defects such as lattice strain and dangling bonds can result in
recombination centers that pin the quasi-Fermi levels and scavenge current-carrying
charge carriers.102

          Beyond
recombination centers, interfaces can also mediate the efficiency with which charges inject from one
material into another. By tuning the conduction or valence band offsets

	
  

 	
  

 	
  

 
	
  

 	
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Figure 4. (a) Modeled η as functions of Nt (trap density,
rows 1-4, in units of cm-3), Et
(trap depth, vertical axes), and σ, the standard deviation of CQD sizes, in units relating to
bandgap (horizontal axes). (b) Modeled and experimental VOC as a function of trap density (curves) and polydispersity
(horizontal axis). Reprinted with permission
from ref 85. Copyright 2012 American Chemical Society.

Figure 5. (a) Schematic diagram
and (b) photovoltaic performance of ZnO nanowire CQD-sensitized solar cells.
Reprinted with permission from ref 108. Copyright 2007 American Chemical Society.

between the layers
adjacent to deposited CQDs, forward injection
of charges from the CQDs can be much more than, much less than, or
comparable to back injection into the CQDs.103

          These
considerations become particularly important when CQDs are deposited on a highly structured scaffold
as in sensitized architectures.25,104
Often present in monolayers or even
submonolayers, each CQD sees multiple interfaces, often sandwiched
between two materials, one responsible for collecting electrons, the other for
collecting holes. The energetics of these
interfaces must be finely adjusted to ensure that electrons injected into the electron acceptor are extracted prior to encountering a hole in the hole-transport
layer. Any back injection of
carriers, typically in regions without complete monolayer coverage of CQDs, reduces device shunt resistance and
thus degrades fill factor.

3. CQD-SENSITIZED SOLAR CELLS

          The
earliest reports of solar cells employing CQDs only used the CQDs to compliment absorption by other,
non-quantum-confined materials.77,105,106
The first report of a solar cell using CQDs
as the primary absorber in a solar cell appeared in 1998 and used InP CQDs as sensitizers in a dye-sensitized
solar cell (DSSC) configuration.107
This architecture offered high voltage and
featured absorption of light on the rectifying side of the device.

          In
these devices, known as CQD-SSCs, a monolayer of CQDs coat a transparent, nanoporous electron acceptor such as TiO2 or ZnO. This highly structured
interface is then infiltrated by an
electrolyte for hole extraction. Through the highly structured electron
acceptor coated with CQDs, high absorption can be combined with excellent
extraction to achieve high efficiency. A 2007 report showed vertically oriented ZnO nanowires sensitized with CdSe CQDs
and infiltrated with an iodine-based
liquid electrolyte (Figure 5).108

          The
shunt resistance was notable in particular and appears to be symptomatic in other instances of CQD-SSC
devices.109-111 Due to the large CQD diameter (relative to
the nanoporous titania pore diameter), forming a continuous monolayer overcoating the entire nanoporous electron
acceptor very difficult; in fact as little as 14% of the TiO2
surface may be covered by CQDs.112 The uncoated surfaces of the TiO2
or ZnO electron acceptors become free
to form soft shorts with the hole-transporting electrolyte (i.e., the
shunt resistance drops dramatically, but not
to a true short, due to direct but spatially
infrequent contact between the electron and hole-transporting phases), resulting in low shunt resistance in the absence of other titania passivation techniques. A
high degree of dye loading in DSSCs using molecular dyes ensures large shunt
resistances and obviates the need for additional titania surface passivation. Exchanging the bulky ligands
required to maintain colloidal stability in solution with shorter bifunctional
ligands designed to tether the CQDs to the titania electrode has improved CQD loading.113,114 This route
offers the most direct route to improved performance within the CQD-SSC architecture as was recently shown by improving
the loading factor to 34% through prefunctionalizing the CQDs with the
appropriate final ligand without the need for additional ligand chemistry at the interface between the TiO2
and CQD.27

          An
alternatively interesting strategy involves presensitizing colloidally stable titania nanoparticles and then
depositing the rectifying assembly at once.115

          Ultimately,
with weaker absorption per unit length than dye molecules, thicker nanoporous electrodes must be employed for sensitization with CQDs in order to absorb all
the incident light. Thicker
electrodes directly add to the series resistance as electrons have further to travel in the electron
acceptor and holes have further to
travel in the electrolyte. These thicker electrodes also become more difficult to fully infiltrate since deposition
of CQDs is typically done through a soaking procedure and therefore from the
top down.

          While
some promising results have been achieved through the CQD-SSC architecture (η = 1.8%116 to 2.9%110
and more recently η > 5%27), the
deposition of high-quality presynthe-sized
CQDs into a nanoporous matrix remains a challenge for the materials chemistry community. Research into
sensitizing nanoporous TiO2 with quantum dots has largely shifted
toward chemical bath deposition (CBD)117-121
or successive ionic layer adsorption
and reaction (SILAR) of quantum dots,114,122 wherein the quantum dot nucleation and synthesis
occurs at the same time as deposition rather than beforehand (as with storage in a colloidally stable solution). Great
strides have been made using the SILAR method to achieve greater than 5% efficiency.123,124 A remaining
challenge in this approach is to improve
optical properties, and monodispersity, in these in situ synthesized
quantum dots.25

4. SCHOTTKY CQD SOLAR CELLS

          The
first report of a solar cell using a thin film assembly of CQDs as the
primary absorber appeared in 2005.125 These

	
  

 	
  

 	
  

 
	
  

 	
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Figure 6. (a) Band diagram of
polymer/CQD solar cell. Reprinted by permission from Macmillan Publishers Ltd.:
Nature Materials (ref 125), copyright 2005. (b) External quantum efficiency of
P3OT/PbS CQD bilayers (A, B, and C) and pure PbS CQD (D) devices with optical
density of PbS
CQDs employed (inset). Reprinted with permission from ref 126. Copyright 2005
AIP Publishing LLC.

Figure 7. VOCas a function of (a) CQD
size (and thus bandgap energy and first excitonic wavelength) and (b) Schottky
contact work function. (c) Mott-Schottky analysis of PbSe CQD films of 65 and
400 nm thicknesses. Reprinted with permission from ref 131. Copyright 2008
American Chemical
Society. (d) J-V curves of champion Schottky CQD solar
cell exhibiting VOCof 0.47 V and η of 4.57%. Reprinted with permission
from ref 134. Copyright 2011
American Chemical Society.

solar
cells relied on electron affinity differences between the transparent conductive oxide (TCO), in this case
indium tin oxide (ITO) and the
reflective back contact (Mg), to produce a built-in field driving extraction of
electrons (through the dot phase) and holes (through the polymer phase)
in their respective directions (Figure 6a).

          These
cells primarily utilized PbS CQDs and blended them with the organic polymer,
poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV), to
absorb light and separate the photogenerated electron-hole pair through conduction band offsets. The electronic impact of
the polymer was subsequently further explored126 and, compared to improved hole transport in CQD solids, was in
fact found to impede hole extraction.
Figure 6b illustrates the EQE of a set of devices, wherein devices A, B, and C employ the organic polymer poly(3-octylthiophene-2,5-diyl) (P3OT)
coated with varying thicknesses of
PbS CQDs and device D employs only PbS
CQDs of the same thickness as device A with no additional polymer.

          The
advent of polymer-free CQD devices confirmed that the separation, and ensuing separate transport of
electrons and holes, can proceed efficiently in pure CQD films, in the presence of an electric field. This insight
opened the possibility of devices
based on suitably engineered CQD films alone, and

	
  

 	
  

 	
  

 
	
  

 	
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turned
the field in a direction more akin to polycrystalline inorganic semiconductors, except with the added
benefit of quantum-tuned bandgaps.

          This
picture enabled the development of Schottky CQD solar cells.127 In the first Schottky CQD solar cells, light
entered through a transparent ohmic
contact, and was absorbed by the active
CQD film. The back electrical contact was a reflective metal whose work function was selected such that
it formed a rectifying junction with
the CQD film. Employing active materials such as PbS and PbSe CQDs,
typically p-type, required a shallow work
function metal such as Mg or Al to create a Schottky barrier.

          Following
the initial 2007 report of a device employing a PbS CQD/Mg interface as the charge separating junction
of a CQD solar cell,128
many other reports of CQD Schottky-barrier-based devices were reported.74,129-134

          The
Schottky architecture, in addition to its functional simplicity and ease
of fabrication, proved an excellent architecture
for isolating characteristics of the CQD film itself. One 2008 report used the Schottky structure to
correlate the size-tuned band positions of the CQD film with the known work functions of various metals (Figure 7a,b) and
further quantified the equilibrium
free carrier density within the CQD film
through Mott-Schottky analysis (Figure 7c).131

          Remarkably,
the simple Schottky structure has been optimized
to give η > 4.5% through
appropriate selection of CQD size.134
Unfortunately, Schottky barriers impose a low upper bound on the built-in voltage and thus the VOC.9 For this reason,
Schottky devices show much lower open-circuit voltages
than their bandgap alone would predict from theory.20 Figure
7d shows the J-V characteristic for the highest performing Schottky CQD solar cell with a VOC of 0.47 V for an active CQD layer with a 1.6 eV bandgap.

5. DEPLETED HETEROJUNCTION CQD SOLAR CELLS

          Two
key limitations in the Schottky CQD solar cell remained to be fully addressed. The first, Fermi level
pinning at the Schottky junction, imposes an upper bound on the built-in voltage, and hence VOC, as a result of excessive electronic trap states that arise due to the imperfectly
passivated interface between the
semiconductor and metal.37 The second limitation was illumination from the nonrectifying side of
the device, which ensures that the
maximum in the optical generation rate occurs in a region of subunity internal
quantum efficiency. Meanwhile, active materials loading challenges in CQD-SSCs
limit light absorption, requiring ever thicker porous electrodes while ignoring
the possibility of transport through the quantum dots themselves.

          The
depleted heterojunction (DH)15 colloidal quantum dot solar
cell was developed in an effort to bring together the benefits of the Schottky and QD-SSC architectures. Figure 8 illustrates
the physical and energy band structure of the DH device. It employs as its front transparent electrode fluorine-doped
tin oxide (FTO) or ITO on glass. Onto the TCO is deposited a layer of (typically) TiO2 or ZnO, although other
wide bandgap semiconductors could be
used. While this has typically been nanoporous as in the case of DSSCs, the DH architecture does not demand it, and indeed
dense, planar films were used without
compromising performance.103 On top of this layer is processed a CQD active layer having
a thickness of 50-300 nm. A back
reflector is finally applied using a deep work function metal such as gold, or a heavily doped oxide such as MoO3 paired with a reflective metal
such as silver.

Figure 8. (Top) Structural
illustration and (bottom) schematic energy band diagram at short-circuit of depleted
heterojunction CQD solar cells.
Reprinted with permission from ref 15. Copyright 2010 American Chemical
Society.

          The
DH architecture has rapidly shown promise as an effective architecture for extracting photogenerated current from
a CQD film. Through solid-state ligand exchanges to short ligands such as 1-mercaptopropionic acid (MPA),15,44,103 1,2-ethanedithiol (EDT),38,135,136
1,3- and 1,4-benzenedithiol (BDT),137,138
formic acid (FA),139 as well as to atomic ligands,93 currents have exceeded 21
mA/cm2.44 The impact of ligand selection, specifically ligand length, has been explored in
the context of exciton dissociation40 and film conductivity48 as
illustrated in Figure 9.

          The
band structure of CQD films as a function of the constituent CQD diameters has been determined through electrochemical140
and optoelectronic methods.141 These reports suggest that some sizes of CQDs, namely larger ones, would have trouble injecting into TiO2
due to a reduction of the conduction
band offsets as CQD bandgaps become smaller. Figure 10a illustrates how the energy bands of several different PbS
CQD sizes line up relative to TiO2.

          Using
the modeling tool SCAPS 3.0.00,142 a self-consistent one-dimensional electro-optical model was employed
to determine the band diagrams (at
equilibrium) of three depleted heterojunction
devices employing 1.3, 1.1, and 0.9 eV PbS CQDs (Figure 10b). As would be
expected from Anderson’s rule,143 these band diagrams
illustrate that at least to a minimum CQD
bandgap of 0.9 eV there exists no barrier to electron injection from PbS
CQDs to TiO2.

          The
importance of band offsets between the CQD film and TiO2 film was further explored by
adding impurities to a sol-gel-derived
TiO2 electron acceptor.103 By simultaneously varying the electron affinity of TiO2
along with the bandgap of PbS CQDs, the impact of band offsets became
evident (Figure 11). Specifically, as the
device was biased toward the maximum power point, the electric field within the
device was

	
  

 	
  

 	
  

 
	
  

 	
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Figure 9. (a) Photoluminescence
decay of PbS films passivated with oleic acid (OA), EDT, BDT,
4,4′-dibenzenedithol (DBDT), and 4,4′′-tribenzenedithol (TBDT)
confirming exciton dissociation is faster in short-ligand-passivated CQD films.
Reprinted with permission from ref 40. Copyright 2010 American Chemical
Society. (b) Electron and hole mobility as a function of ligand length for PbSe
CQD films passivated with double-ended
thiols including EDT, propanedithiol (PDT), butanedithiol (BuDT),
pentanedithiol (PenDT), and hexanedithiol (HDT) demonstrating a linear relationship as measured by field-effect
transistors (FETs). Reprinted with permission from ref 48. Copyright 2010
American Chemical Society.

Figure 10. (a) Size-dependent
electron affinities (upper three curves) of PbS CQDs (red), PbSe CQDs (blue),
and bulk TiO2 (green). Also shown are the valence band positions of the same three
materials (lower three curves). Reprinted with permission from ref 140.
Copyright 2008 American Chemical Society. (b) Equilibrium electron band diagrams
of TiO2/PbS/Au depleted heterojunction structures for three
different sizes of CQDs as determined from part a. Adapted with permission from ref
15. Copyright 2010 American Chemical Society.

reduced,
thereby lowering the drift current collected. In other words, band offsets can facilitate efficient charge
extraction in the absence of a strong electric field.

          Not
surprisingly, a small (or even negative) conduction band offset (red and
green bars in Figure 11) maximizes VOC,
whereas a negative conduction band offset (red bar) reduces JSC.
The optimal conduction band interfacial condition led to a maximized product of VOC, JSC,
and FF. It should be noted that this
required the use of electron acceptors of different electron affinity to pair optimally with differently
size-tuned CQD films (i.e., zirconium-doped
TiO2 for 1.3 eV PbS CQDs and antimony-doped TiO2 for 1.0 eV PbS CQDs).103

          Equations
4 and 5 make clear that the depletion width on the CQD side of a semiconductor/CQD junction depends
on the relative free carrier
densities of each material. More specifically, a junction made up of PbS CQDs (p
= 2 x 1016 cm3, εCQD= 43 ± 4)15 and a wide-bandgap electron acceptor such as TiO2
(n = 1 x 1016 cm3, εTiO2= 55 ± 10)144-147 would have depletion
dimensions of WTiO2 = 470 nm and WCQD
= 240 nm under short-circuit conditions. The implication is that
a thinner TiO2 layer would be incapable of fully depleting a PbS CQD
layer even at zero bias, let alone at
the maximum power point.

          Engineering
the deposition conditions for the back contact of the device was also
found to be critically important. Dead zones,
regions of near-zero IQE, were seen to exist even in devices that were fully depleted under
short-circuit con-ditions.148 These were remedied by improved
thermal evaporation of the metal that was suspected to damage the film. Strategies to improve the back contact have
resulted in increased stability and
improved performance. MoO3 has been used as a degenerately doped deep work function contact that both aids in hole extraction through a back
surface field149 and protects the CQD film from subsequent
metal deposition (Figure 12).135,150
LiF has also been used to protect the CQD film from metals, such as Ni, capable of forming compounds with
the constituent CQD elements.151

          Short
thiols have proved effective at reducing recombination in some CQD films (PbS, CdTe) through improved
surface passivation, as evidenced
through photoluminescence quantum efficiency
measurements,84,152 while the same method has

	
  

 	
  

 	
  

 
	
  

 	
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Figure 11. Top row: Depleted
heterojunction energy band diagrams using undoped TiO2,
antimony-doped TiO2, and zirconium-doped TiO2. Reprinted
with permission from ref 103. Copyright 2011 WILEY-VCH Verlag GmbH & Co.
KGaA, Weinheim. Bottom row, first and second columns: Bandgap and electron affinity of undoped,
Sb-doped and Zr-doped sol-gel TiO2. Bottom row, third to sixth
columns: Performance metrics of 1.3 eV PbS CQD DH solar cells using the undoped,
Sb-doped, and Zr-doped sol-gel TiO2 including VOC, JSC, FF, and η.
Bottom row, seventh to tenth
columns: Performance metrics of 1.0 eV PbS CQD DH solar cells of same.

Figure 12. (a) Interfacial defect
states generated at metallic back contact.
(b) Elimination of defect states in (a) through the use of MoO3 in place of the metallic back
contact. Reprinted with permission from
ref 135. Copyright 2011 American Chemical Society.

shown that, in films of
other CQD materials (CdSe), short thiols can
actually degrade surface passivation.152 A lowering of the density of deep trap states via atomic ligand
passivation was found to further improve current extraction in CQD solar
cells.93 A recent study has shown
that a combination of atomic ligand
passivation and organic thiol passivation reduces trap states even further.44 Figure 13a
illustrates how atomic ligands access
the hard-to-reach trenches on the CQD surfaces while thiols passivate
the rest of the surface. The impact of the enhanced
passivation can be seen in Figure 13b. This final hybrid approach leads
to improved CQD photovoltaic performance
with enhancements in both JSCand VOCrelative to previous records, yielding an externally
certified power conversion efficiency of 7.0%.44

          The
simplicity of the DH architecture makes it an excellent platform for testing the impact of factors
external to the oxide/ CQD junction or the quality of the CQD film itself.
Recently, plasmonic153 and
geometric154 enhancements have been shown to effectively increase photovoltaic performance
via enhanced absorption and thus current generation (Figure 14a,b, respectively). In addition, the electrical
characteristics of the TCO have been
shown to be useful as a remote dopant to the oxide, thus enhancing the built-in
field around the junction (Figure 14c).155

6. CQD SOLAR CELLS USING QUANTUM FUNNELS

          Through
bandgap engineering, crystalline semiconductors have employed back surface fields.149,156
Organic light-emitting diodes157
and organic solar cells158,159 have employed charge transport/blocking layers. A subset of bandgap
engineering, bandgap grading, was
proposed as a mechanism to further improve
PV performance in a variety of materials.160-164 Resonant energy
transfer between absorbers in organic and dye-sensitized solar cells have helped improve current collection,165-167 while compound
semiconductors have tuned stoichiometry to generate a favorable electronic band
configuration.168

          Figure
10a illustrates the relationship between PbS and PbSe band edges and diameter graphically.140,141
One of the more interesting features
of this graph is the relative variation in conduction band position versus valence band position in the 3-5
nm range. This range translates into the broad optimal efficiency bandgap peak as predicted in the Shockley-Queisser

	
  

 	
  

 	
  

 
	
  

 	
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Figure 13. (a) Schematic
representation of thiol-passivated CQD surface (left) and hybrid halogen/thiol
passivated CQD surface (right). (b) Density of states within the bandgap for organic-,
inorganic-, and hybrid-passivated CQD films as measured using the photovoltage
transient technique.
(c) J-V curves with various passivation strategies. Inset shows
EQE of hybrid passivated devices. Reprinted by permission from Macmillan Publishers Ltd.: Nature
Nanotechnology (ref 44), copyright 2012.

Figure 14. (a) Cross-section of
depleted heterojunction employing plasmonic nanoshells for improved absorption.
Scale bar, 100 nm. Reprinted with permission from ref 153. Copyright 2013 American
Chemical Society. (b) Scheme for periodic arrangement of depleted
heterojunction solar cells employing a folded-light-path configuration to allow for multiple
passes. Reprinted by permission from Macmillan Publishers Ltd.: Scientific Reports (ref 154),
copyright 2013. (c) Performance enhancement due to a shallow work function TCO
and its impact on optimal TiO2 thickness and depletion width (inset).
Reprinted with permission from ref 155. Copyright 2013 American Chemical
Society.

limit.34
Within this range, the conduction band varies by several meV, while the valence band hardly varies at all.

          Colloidal
assemblies of CQDs, suspended in solution, have demonstrated, through
liquid-phase luminescence studies that all exciton energy couples to the
smallest bandgap within the assembly.169
Exciton funneling has also been shown in CQD solids where luminescence primarily occurs at the smallest bandgap in an
array of different CQD sizes stacked on top of one another in coupled
CQD films.97-99 This funneling concept was applied to the back of a
DH PbS CQD solar cell in order to aid in current collection under operating conditions (i.e., at the maximum power point)
when the CQD film was not fully depleted (Figure 15).100

          Note
that the simulated results from Figure 15b place the optimal grading depth well
within the depletion region (at short-circuit conditions). In other
words, in order to take advantage of a
quantum funnel, it needs to be placed within the short-circuit depletion region
rather than at its edge. One might expect
that this surprising result would not, therefore, lead to an enhancement in device current (i.e., JSC),
but instead in fill factor. Further conceptual justification for this
nuance is explained in detail in Figure 16.

          Figure
16 provides a conceptual framework justifying FF improvement without an
appreciable increase in JSC.
The top left schematic shows a
typical depleted heterojunction CQD solar
cell that is fully depleted under short-circuit conditions. At the maximum
power point (bottom left schematic), the band bending
is reduced in the active material, and a quasineutral region near the
back contact begins to grow. Once the quasineutral region is longer than the
diffusion length of electrons, extracted current is reduced, and recombination
within the quasineutral region increases. By appending a quantum funnel onto the back of the standard DH
device (top middle schematic), extracted current under short-circuit
conditions is unaffected; in fact, it may even grow if the quantum funnel
absorbs a significant amount of light. Unfortunately,
when this structure moves toward the maximum

Figure 15. (a) Band diagram of a
quantum funnel device and (b) simulated monochromatic power conversion efficiency for
a device employing
an optimally placed quantum funnel. For thick devices, spectral performance is
capped by carrier extraction, while for devices with optimally placed quantum funnels, performance
increases over all wavelengths. Adapted with permission from ref 100. Copyright 2011 American Chemical Society.

	
  

 	
  

 	
  

 
	
  

 	
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Figure 16. Spatial band diagrams of a DH CQD solar cell (left column), a DH CQD solar cell with an appended quantum
funnel (middle column), and a
slightly truncated DH CQD solar cell with an appended quantum funnel
(right column) at short-circuit (top row) and maximum power point conditions
(bottom row).

Figure 17. Schematics of a (a)
planar DH device and a (b) textured DBH device. (c,d) Cross sectional SEMs of devices
of same. In each case the scale bar is 500 nm. Reprinted with permission from ref 171. Copyright 2011 WILEY-VCH
Verlag GmbH & Co. KGaA, Weinheim.

power
point (bottom middle schematic) and the bands begin to unbend, all the electrons that were successfully
funneled into the smallest bandgap
material will be faced with a large quasineutral
region they are unable to traverse. In this case, despite successful funneling, no gain in
extracted current at the maximum
power point will be observed, and overall efficiency remains unchanged relative to the standard DH
device. If, instead of using the
standard DH device, we apply the quantum funnel to a truncated DH cell,
an electric field persists throughout the device both at short-circuit (top
right schematic) and at maximum power point (bottom right schematic) conditions. This architecture would
not be expected to result in any JSCenhancements, but would be expected
to extract additional current at the
maximum power point as compared to the other two structures. Experimental
results confirmed that the fill
factor was the primary beneficiary of an optimally placed quantum
funnel.100

7. DEPLETED BULK HETEROJUNCTION CQD SOLAR CELLS

          As
described in sections 5 and 6, collecting photogenerated minority carriers (electrons) from the CQD film
is critical to improving performance.
The quantum funnel100 described a way to manipulate the energetic landscape of the CQD film to aid in carrier extraction. The organic PV
community, on the other hand, found that, by manipulating the geometric landscape of the p-n interface, it could ensure
that any photogenerated exciton was
no more than one exciton diffusion length
away from the charge separating interface. This three-dimensional interpenetrating interface is known
as the organic donor-acceptor bulk heterojunction.23

          Unlike
in organic PV, the DH CQD device is capable of collecting carriers generated within the depletion region of the device. This caps the total device thickness to
the thickness of the depletion region (plus one diffusion length of electrons
in the CQD film, 10 nm16). The implementation of a bulk
heterojunction structure extended the depletion region deeper into the device, facilitating the use of thicker,
more absorbing CQD layers.92,170,171

          Figure
17a,b171 depicts a planar DH and textured depleted bulk heterojunction (DBH) device. Here the pink
regions represent depleted portions
of the CQD film, while red regions are quasineutral. Because the DBH structure
pushes the built-in electric field
deeper within the device, thicker films can be built up, and therefore, longer, less strongly absorbed
wavelengths are more readily
converted into extracted current.

          The
DBH electron acceptor has been built using presynthesized
large TiO2 nanoparticles, through lithographically defined
nanopillars (Figure 18)172 or using bottom-up grown nanowires.170,173,174 In all
cases, PbS CQDs were infiltrated into
the large voids of the electron acceptor matrix, forming the bicontinuous bulk heterojunction.

Figure 18. (a, b) Bare TiO2
nanopillar substrates. Scale bars are 500 nm. (c) Cross sectional SEMs of PbS
CQD-infiltrated nanopillar DBH device. Reprinted with permission from ref 92. Copyright
2012 WILEY-VCH
Verlag GmbH & Co. KGaA, Weinheim.

          The
DBH architecture allowed for both enhanced absorption through increased
CQD film thickness (Figure 19a) and increased IQE through reduction of
Shockley-Reed-Hall (SRH) recombination in
the vicinity of the bulk heterojunction interface (Figure 19b). These findings are in good agreement with
previously analyzed nanopillar solar cells.175 Low hysteresis in the illuminated J-V
curves of DBH samples92 (compared
with planar DH samples) confirms that, in the bulk heterojunction
structure, carrier collection wins over carrier trapping.176,177

          DBH
devices are more susceptible to bimolecular recombination than planar DH
devices due to an increased interfacial area. Conduction band offsets therefore become more critical in such structures, wherein an electron injected
from the CQD phase into the TiO2
phase must be prevented from back-recombining over the course of its
long, narrow path to the

	
  

 	
  

 	
  

 
	
  

 	
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Figure 19. (a) DH and DBH device
absorption characteristics. Reprinted with permission from ref 171. Copyright
2011 WILEY-VCH Verlag GmbH &
Co. KGaA, Weinheim. (b) Two-dimensional device simulation illustrating enhanced
electric field and reduced Shockley-Reed-Hall recombination
in the volumetric vicinity of the TiO2 electron acceptor. All
simulations are at the maximum power point. Reprinted with permission from
ref 92. Copyright 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

cathode.
This condition imposes a slight penalty on built-in voltage for DBH
devices compared to their planar DH counterparts.

8. BULK-NANO HETEROJUNCTION CQD SOLAR CELLS

          All
device architectures to this point have relied on transparent in-coupling
of light into the active layer. Several reports, however, use CQDs as the primary absorber, but additionally use other active materials to achieve high
performance.

          One
of the first reported devices utilizing colloidal quantum dots in a solar cell employed nanocrystals of CdTe
and CdSe.77 Here the CdTe
nanocrystals exhibited bulk-like optoelectronic characteristics (i.e., they were not quantum confined), while quantum-confined
CdSe CQDs were used to augment absorption.
The resultant planar stack was a bulk-nano heterojunction (BNH).

          Recently,
a planar BNH device employing a colloidal Bi2S3 nanocrystal178 film as the n-type layer
and PbS CQDs as the p-type layer179
was made interpenetrating through a solution-phase mixture of the two moieties.180 The resultant device exhibited current collection from both the Bi2S3
and size-tuned PbS phases. This was
achieved by allowing photogenerated carriers
in both materials to be in the vicinity of a charge separating junction, similar to organic PV bulk
heterojunc-tions.23
Figure 20 illustrates the interpenetrating p- and n-type materials.

Figure 20. (Left) Illustration of a
BNH device wherein the red spheres represent the p-type quantum dots and the blue spheres
represent the n-type nanoparticles. Substrate, TCO, and metal electrode are
also shown
for reference. (right) Schematic band diagram of BNH with interpenetrating p-type
and n-type layers. The p-type and n-type bands are drawn overlapping to accentuate the geometric relationship between the interpenetrating phases. Reprinted by
permission from Macmillan Publishers
Ltd.: Nature Photonics (ref 180), copyright 2012.

          Other
reports use infrared-absorbing CQDs to augment already functional solar cells using more conventional materials incapable of absorbing much beyond the visible or
near-IR.181-183

9. QUANTUM JUNCTION SOLAR CELLS

          While
the DH and BNH address many of the limitations of earlier architectures, they continue to surrender
available open-circuit voltage, even
if both the CQDs and electron acceptors were degenerately doped, a condition
that could have other deleterious
impacts, such as the unintended creation of a tunnel junction or the reduction
of depletion width, thus limiting drift current collection.37 At a minimum they require
re-engineering of the electron
acceptor when the CQD absorber is size-tuned to a different bandgap.103

          This
challenge was recently overcome by employing size-tuned CQDs on each
side of the rectifying junction. This required the development of both n-type
and p-type films within a CQD stoichiometry.

          CQD
doping has been demonstrated primarily through incorporation of dopant
impurities onto the CQD surfa-ces184,185
or into the CQD crystal lattice.185-189 Doping has also been demonstrated by exposing CQD films to
various atmospheres, solvents, or
redox couples.67,75,190,191

          Ligands
are one further critical factor in the net doping of a CQD film.133,191,192 In 2012, it was
reported that PbS CQD films could be manipulated to be both n-type and
p-type through selection of surface ligands
and exposure (or lack thereof) to
air.193 Figure 21a illustrates how the doping of PbS CQD
films can vary with ligand.

          Developing
n-type CQD films195 opened the door to p-n junction-like
structures wherein both sides of the junction could
be size-tuned to achieve the same or different bandgaps as desired. This
device, known as the quantum junction (QJ), removed the band offset
challenge of DH and BNH structures.194 Figure 21b shows the turn-on
behavior of quantum junctions as a function
of differently size-tuned PbS CQDs for the n-type and p-type layers.

          Figure
22a illustrates how the current for small-bandgap DH devices is blocked while it can be collected for
QJ devices. The linear relationship between CQD bandgap and VOC can be seen in
Figure 22b.

          Further
optimizations of the device electrode,45 PbS doping,45 and PbS passivation196 recently led to
solar power conversion efficiencies η of 6.6%.

	
  

 	
  

 	
  

 
	
  

 	
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Figure 21. (a) Doping density as a
function of atmosphere and ligand for PbS CQD films. Reprinted with permission
from ref 193. Copyright 2012 American Chemical Society. (b) Turn-on
characteristic of quantum junctions with different size-tuned n-type and p-type
PbS CQDs. Reprinted with permission
from ref 194. Copyright 2012 American Chemical Society.

Figure 22. (a) J-V
characteristics of DH and QJ devices for 0.6 eV PbS CQDs. (b) VOC as a function of CQD bandgap exhibiting linear
trend for a QJ structure. Reprinted with permission from ref 194.
Copyright 2012 American Chemical Society.

          A
new variant on the quantum junction, an analogue to p-i-n structures used in amorphous silicon solar
cells,10 employing a p+-n-n+ graded doping
structure further enhanced device performance to 7.4%.197

          The
potential of the quantum junction architecture can most clearly be seen in the context of multiple
junction solar cells. Whereas
heterojunction devices would require careful engineering of electron acceptor materials for the
smallest bandgap junctions, the
quantum junction avoids this problem entirely by employing both n-type and p-type phases of the same size CQDs.

10. MULTIPLE-JUNCTION CQD SOLAR CELLS

          All
the architectures discussed to this point focus on approaching as closely as
possible the single-junction Shockley-Queisser limit of η = 31%.34 Colloidal
quantum dots, however, allow for facile
tuning of the bandgap, thereby making them ideal candidates for multiple
junction solar cells. By optimally selecting the constituent bandgaps, multiple
junctions can be stacked and connected through ideal recombination layers in order to exceed the
single-junction Shockley-Queisser
limit.20 Figure 23a shows the graphical calculation of the ideal single junction solar
cell efficiency and further applies
the same concepts to multiple junction solar cells (Figure 23b).

          The
optimal tandem (also known as double junction) active material bandgaps are 1.6 and 1.0 eV for the
first and second junctions,
respectively. The first cell absorbs all photons with energy greater than 1.6 eV. The second cell
absorbs all photons with energy between 1.0 and 1.6 eV. Figure 24 illustrates
how the photogenerated electrons from
the first cell, J1, recombine with
the photogenerated holes from the second cell, J2 (or vice versa depending on the configuration of the
cells), in a recombination layer, RL.
The ideal recombination layer is transparent to all wavelengths absorbed by J2
and allows all electrons from J1 to recombine with all of the holes from J2
without any losses. As these two cells are in series, a current matching condition is imposed. For optimal
efficiency, the current generated in J1 and J2 should be equal and can be controlled by adjusting absorption or extraction
characteristics in each. The output current, therefore, in a tandem cell is
equal to the current of each constituent cell, while the output voltage is the sum of the voltages of each constituent
cell.

          Two
reports of CQD tandem cells appeared in mid-2011,198,199
both demonstrating the principle of voltage addition in tandem devices.

	
  

 	
  

 	
  

 
	
  

 	
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Figure 23. Limiting efficiencies of
solar cells for (a) single junction solar cells and their application to (b) multiple
junction solar cells. In all cases, the black curves represent the total number
of photons an opaque
active material of energy E could absorb (i.e., all photons with energy greater
than E), and gray curves represent the maximum work that can be extracted for
each of those materials of energy E. The ratio of the area in green in (a) to the area under the black curve is the device efficiency. Note that, for multiple
junction solar cells, the maximum
efficiency can exceed any solar cells composed of fewer junctions. Reprinted with permission from ref 20.
Copyright 1980 American Institute of Physics.

Figure 24. Tandem configuration
illustrating recombination between hole current from the first junction (J1) with electron
current from the second junction
(J2).

Figure 25. (a) J-V of the large-bandgap (blue),
small-bandgap (black), and tandem (green)
cells under AM 1.5 G illumination. Also shown is the small-bandgap cell when filtered by a large-bandgap cell. (Inset) Structural cross-section of the tandem
cell showing the 1.6 eV CQD first cell, recombination layer, and 1.0 eV CQD
second cell. (b) EQE performance of each junction and the overall tandem
device. Reprinted by permission from Macmillan Publishers Ltd.: Nature Photonics
(ref 199), copyright 2011.

          The
first report employed inverted depleted heterojunctions with gold islands serving as the recombination
layer,198 whereas the
second report employed depleted heterojunction cells with a graded recombination layer.199
Figure 25a demonstrates the principle
of current matching and voltage addition in optimally designed tandem cells. Highlighted in Figure 25b
is the contribution of each junction
to the overall current generated.

          The
graded recombination layer facilitates efficient electron-hole
recombination between the two junctions thereby satisfying the current matching condition.200 Meanwhile, optimization of each constituent cell201,202
is also crucial to achieving the overall single junction to double
junction efficiency enhancement predicted
by theory.20

11. HOT-CARRIER EFFECTS IN CQD MATERIALS: DEVICE
IMPLICATIONS

          When
photons with energy greater than the bandgap are absorbed, they generate excitons whose energy is also greater than
the bandgap. These hot excitons typically relax very quickly to the band edge through phonon emission, losing their energy in excess of the fundamental excitonic
level. While this relaxation time is typically very fast, it is much slower in
CQDs than in bulk solids due to the
relative scarcity of available states.8,203-205
CQDs also offer the promise of entering the hot-photon bottleneck regime206,207 at solar intensities without
the use of a concentrator.8,208,209
Taking advantage of these hot excitons to exceed the Shockley-Quiesser
limit34 within the constraints of
a single-junction solar cell can take two forms: hot electron transfer and
multiple exciton generation. 

11.1. Hot-Electron Transfer

          Theory
dictates that solar cells capable of extracting hot carriers can in principle exceed the single-junction
Shockley-Queisser limit.210,211
Extracting hot carriers directly presents a significant challenge due to fast relaxation from the excited
state to the band edge.212
The ideal hot-electron structure involves all hot electrons converging
to one excited state energy level that aligns
with the work function of a selective contact. In this configuration, hot
electrons warm up band edge electrons, and, in principle, no energy is lost due to phonons.212,213
Figure 26 shows a possible n-i-p
implementation of a hot-carrier solar cell
where tunnel junctions are used as selective contacts.214

          The
ultimate architecture notwithstanding, the most important obstacle to overcome
in realizing hot-carrier extraction is
increasing the hot-carrier lifetime. It has been demonstrated in PbSe CQDs that one carrier can sacrifice its excited state energy to promote a longer excited
state lifetime in the complementary
carrier.215 This slow cooling of excited states was further
demonstrated to 20 ps through core-shell CQD structures.216 Indeed this same structure showed that
the hot electron tunneled to the shell and could be extracted before relaxing
to the band edge. A 2010 report demonstrated that hot electrons could be
extracted into a titania electron acceptor,217

	
  

 	
  

 	
  

 
	
  

 	
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Figure 26. Conceptual n-i-p implementation of a hot carrier solar cell. Reprinted with permission from ref 214.
Copyright 2010 Institute of Electrical and Electronics Engineers.

a
remarkable achievement since cold, band edge electrons could also be
injected into the titania within this system.218 This report hints at the possibility of a viable path
to such structures employing PbSe CQDs.

11.2. Multiple Exciton Generation

          Multiple
exciton generation (MEG) and extraction has been studied in bulk materials219,220 and has recently been of
much interest in the CQD community.8,203-205,221-223
In ideal MEG solar cells, excitons
whose energy is well above twice the bandgap
will decay to the bandgap energy and produce extra electron-holepairs.Iftheseextraexcitonscanbecollected prior to rapid recombination mechanisms such as
Auger recombination,224-233againthesingle-junctionShockley-Quiesser limit34
can be overcome. Along these lines, developing methods to observe hot
exciton cooling has become of paramount
importance. Many of these techniques have been developed, either for CQD films in particular, or previously for other materials systems, but some of the results
have led to conflicting conclusions surrounding whether or not MEG is enhanced in CQD films versus their bulk
counterparts.55,234-250 A past problem now resolved was the
overestimation of quantum yield due to
photocharging of quantum dots.251

          Figure
27 illustrates the MEG quantum yield for different MEG efficiencies with the expected efficiency
enhancement.252

          A
2010 report222 demonstrating IQE over 100% was followed by a 2011
report223 demonstrating EQE of over 100%, both within photovoltaic devices, emphatically demonstrating useful MEG (Figure 28). Prior reports had
limited the observation of MEG to structures specifically designed for MEG observation/characterization253-256
or other, nonphoto-voltaic applications.257

Figure 28. Measured EQE (red
curves), modeled absorptance (black curves), IQE (blue curves), reflectance (brown
curves), modeled reflectance (dashed black curves), and EQE/(1 - R) (purple curves) illustrating an increase
in IQE at 3Eg. From
ref 223. Reprinted with permission
from AAAS.

12. CONCLUSIONS

          The
materials chemistry of CQDs suspended in solution and processed into films has
provided a foundation onto which

Figure 27. Quantum yield (left) and η
limit (right) for different MEG efficiencies. Reprinted with permission from
ref 252. Copyright 2012 American Chemical Society.

	
  

 	
  

 	
  

 
	
  

 	
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useful
photovoltaic devices can be built. These active materials offer the
benefits of solution processing paired with the flexibility of adjustable bandgaps, tailored to suit a particular need.

          In
parallel with these advances, pursuing device geometries that better leverage
the available electronic properties of CQD films has borne fruit in further advancing CQD solar cell performance.
Through the architectures discussed here, CQD-based solar cells have achieved over η
of over 8.5%. They have also been
employed in multijunction architectures and have been deployed to
exploit multiple exciton generation. A summary of performance versus device
architecture is presented in Table 1.

Table
1. Best Power Conversion Efficiency Achieved by Each Device Architecture
Class

	
  

 	
  

 	
  

 
	
                architecture

 	
 η (%)

 	
 ref

 
	 

 	 

 	 

 
	
 CQD-SSC

 	
 5.4

 	
 27

 
	
 QD-SSC
 (SILAR or CBD)

 	
 5.6

 	
 124

 
	
 Schottky

 	
 4.6

 	
 134

 
	
 depleted heterojunction

 	
 8.5

 	
 155

 
	
 quantum funnel

 	
 2.7

 	
 100

 
	
 depleted
 bulk heterojunction

 	
 7.3

 	
 173

 
	
 bulk-nano heterojunction

 	
 4.9

 	
 180

 
	
 quantum junction

 	
 7.4

 	
 197

 
	
 multijunction (tandem)

 	
 4.2

 	
 199

 

          Further
advances in performance will continue to benefit from parallel improvements in CQD materials chemistry, especially the
realization of CQD solids that combine high mobility for electrons and holes, and that simultaneously minimize the density of midgap recombination
centers. Much remains to be achieved
in the materials processing of CQD solids
as well to enable dense, and potentially ordered, CQD films that offer a smooth
and consistent energy landscape for the flow of charge carriers.

          At
the same time, the field of CQD PV architecture offers much room for further progress. The bulk
heterojunction architecture has yet to be fully mastered: indeed, models
suggest that further performance progress
will result when structured electrodes are taller, thinner, and more
heavily doped, and when an interpenetrating
top electrode is deployed to
overcome transport limitations of the majority carrier in the CQD film. While tandem CQD solar cells have been
built, their further optimization is
set to produce further advances in performance
over single-junction devices, which will in turn set the stage for quantum-tuned triple-junction and
multijunction CQD photovoltaics.
Finally, absorption enhancements via photonic
in-coupling, plasmonic near-field enhancements, and geometric optics remain fertile ground for
improving the absorption of light in
thin CQD films by increasing the effective path length of weakly absorbed light within the absorber.

          Broadly,
the rapid pace of CQD solar cell performance shows no signs of abating, and indeed has much more
room, and also an urgent need, to improve further, in view of the ever-growing global hunger for renewable energy solutions that
harvest the clean, free, and
abundant solar resource reaching the earth’s surface.

AUTHOR INFORMATION

Corresponding Author

*E-mail:
ted.sargent@utoronto.ca.

Author Contributions

          I.J.K.
and E.H.S. generated a detailed outline of the manuscript, I.J.K. drafted the full manuscript, and I.J.K.
and E.H.S. reviewed and edited to produce the final submission.

Notes

          The
authors declare no competing financial interest.

Biographies

          Illan
Kramer received a B.A.Sc. (Electrical Engineering) from the University of
Waterloo in 2004 and a M.Eng. from McGill University (Electronics) in 2006.
He recently completed a Ph.D. in Professor EdwardH.Sargent’sgroupattheUniversityofToronto.Hisresearch focused on developing and optimizing architectures for
colloidal quantum
dot photovoltaic devices with emphasis on energetic considerations for efficient charge
extraction.

          Ted
Sargent received the B.Sc.Eng. (Engineering Physics) from Queen’sUniversityin1995andthePh.D.inElectricalandComputer Engineering (Photonics) from the University of Toronto
in 1998. He holds
the rank of Professor in the Edward S. Rogers Sr. Department of Electrical and Computer
Engineering at the University of Toronto, where he holds the Canada Research Chair in
Nanotechnology. He is a Fellow of
the AAAS and Fellow of the IEEE.

ACKNOWLEDGMENTS

          The
authors would like to thank Oleksandr Voznyy for illuminating discussions on
transport mechanisms in CQD films. This
publication is based in part on work supported by Award KUS-11-009-21, made by King Abdullah
University of Science and Technology (KAUST).

ABBREVIATIONS

JSC
          short-circuit current density

	
  

 	
  

 	
  

 
	
  

 	
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 VOC

 	
 open-circuit voltage

 
	
 FF

 	
 fill factor

 
	
 η

 	
 power conversion efficiency

 
	
 EQE

 	
 external quantum efficiency

 
	
 IQE

 	
 internal quantum efficiency

 
	
 DH

 	
 depleted heterojunction

 
	
 DBH

 	
 depleted bulk heterojunction

 
	
 BNH

 	
 bulk nano heterojunction

 
	
 QJ

 	
 quantum junction

 
	
 RL

 	
 recombination layer

 
	
 MEG

 	
 multiple exciton generation

 

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 S

 	
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 XXX-XXX

 

	
  

 	
  

 
	
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 T

 	
 dx.doi.org/10.1021/cr400299t | Chem. Rev. XXXX, XXX,
 XXX-XXXExhibit 10.30

 

JetPay
Corporation

 

Non-Qualified
Stock Option Agreement

(“Award Agreement”)

______________________________________

 

JetPay Corporation,
a Delaware corporation (the “Company”) hereby grants to _____________________(the “Optionee”) a stock option
(the “Option”) to purchase a total of _________shares of the Company’s Common Stock, par value $.001 per share
(the “Shares”) at the price of ______per share, pursuant to the Company’s 2013 Stock Incentive Plan, as amended,
(the “Plan”). The Option is subject to the applicable terms and conditions of the Plan, which are incorporated herein
by reference, and in the event of any contradiction, distinction or difference between this Award Agreement and the terms of the
Plan, the terms of the Plan will control, unless it is otherwise specified in the Plan that such contradiction, distinction or
difference is allowed. All capitalized terms used herein have the meanings set forth herein or in the Plan. As used herein, the
term “Company” includes any Affiliates of the Company.

 

1.          Vesting.

 

For as long as the
Optionee remains employed by the Company, the Option shall vest according to the following schedule:

 

(a)          _______of
the Option shall vest on each anniversary of the option grant date (provided that fractional shares shall be rounded down to the
nearest whole share).

(b)          Notwithstanding
the above vesting schedule, any then-remaining unvested portion of the Option shall vest immediately upon a Change in Control.

 

2.          Duration.

 

(a)          As
to any portion of the Shares, the Option granted hereby shall first become exercisable on the date of vesting set forth above,
provided that the Option has not terminated as set forth in Section 6 of this Award Agreement prior to the time of vesting or exercise.

 

(b)          The
Option shall expire on the earlier of the dates set forth in Section 6 of this Award Agreement and ten years from the date of this
Agreement (“the Termination Date”).

 

    	1

    	 

    

  

3.          Exercise.

 

All or part of the
exercisable portion of the Option may be exercised by the Optionee upon duly executed written notice of such exercise, in a form
acceptable to the Secretary or Treasurer of the Company, at its principal office. The notice shall specify the number of Shares
for which the Option is being exercised (which number, if less than all of the Shares then subject to exercise, shall be 100 or
a multiple thereof) and shall be accompanied by payment in full of the purchase price of such Shares. If a registration statement
under the Securities Act of 1933 is not then in effect with respect to the Shares issuable upon such exercise, it shall be a condition
precedent that the person exercising the Option give to the Company a written representation and undertaking, satisfactory in form
and substance to the Board that he or she is acquiring the shares for his or her own account for investment and not with a view
to the distribution thereof. Upon full compliance by the Optionee, a certificate for the Shares purchased shall be delivered or
mailed to the Optionee. The method of payment of the purchase price for the applicable Shares shall be payment (a) in United States
dollars in cash or by check, bank draft or money order payable to the order of the corporation, or (b) by delivering a properly
executed notice of exercise of the Option to the Company and a broker, with irrevocable instructions to the broker promptly to
deliver to the Company the amount of sale or loan proceeds necessary to pay the exercise price of the Option. If the Optionee is
subject to Section 16 of the Exchange Act, the Optionee may direct the Company to withhold Shares otherwise to be delivered to
him or her upon the exercise of all or part of the exercisable portion of the Option in order to pay the exercise price and/or
withholding taxes due on such Option.

 

4.          Withholding.

 

The Company’s
obligation to deliver Shares upon the exercise of the Option shall be subject to applicable federal, state, and local tax withholding
requirements, which may be satisfied by withholding shares that otherwise would be delivered upon the exercise of the Option, subject
to the approval of the Committee (except as set forth above).

 

5.          Certain
Rights Not Conferred by Option.

 

The Optionee shall
not, by virtue of holding this Option, be entitled to any rights of a stockholder in the Company. Any person exercising an Option
shall not be considered a record holder of the Shares so purchased for any purpose until the date on which he or she is actually
recorded as the holder of such Shares in the records of the Company.

 

6.          Termination
of Employment.

 

(a)          Nothing
in this letter shall confer on the Optionee the right to continue in the service of the Company or interfere in any way with the
right of the Company to terminate the Optionee’s service at any time. If the Optionee’s employment with the Company
terminates for any reason, this Option shall be canceled and shall terminate for no further consideration to the extent of the
number of Shares covered by this Award Agreement which were not vested on the date of such termination of employment.

 

    	2

    	 

    

  

(b)          If
the Optionee’s employment with the Company terminates by reason of Cause, as hereinafter defined, this Option shall remain
exercisable to the extent of the number of Shares covered by this Agreement which were vested on the date of such termination of
employment until the first to occur of (i) three months after the date of such termination of employment or (ii) ten years from
the date of this Award Agreement. If any portion of the Option is not exercised within such time period, such portion shall not
thereafter be exercisable and the Option shall be canceled and shall terminate for no further consideration. For purposes of this
Award Agreement, “Cause” shall mean that the Optionee has (i) engaged in any type of disloyalty to the Company or a
subsidiary or affiliate of the Company, including without limitation fraud, embezzlement, theft, or dishonesty in the course of
his employment or service to the Company or a subsidiary or affiliate of the Company; (ii) been convicted of a felony; (iii) disclosed
any proprietary information of the Company or a subsidiary or affiliate of the Company, without the consent of the Company or a
subsidiary or affiliate of the Company; or (iv) breached the terms of any written confidentiality agreement or any non-competition
agreement with the Company or a subsidiary or affiliate of the Company in any material respect.

 

(d)          If
the Optionee’s employment with the Company terminates for any reason other than Cause, this Option shall remain exercisable
by the Optionee or the Optionee’s personal representative or representatives to the extent of the number of Shares covered
by this Agreement which were vested on the date of such termination of employment until ten years from the date of this Award Agreement.
If any portion of the Option is not exercised within such time period, such portion shall not thereafter be exercisable and the
Option shall be canceled and shall terminate for no further consideration.

 

7.          Acceptance
of Terms; Compliance with Law.

 

The acceptance by the
Optionee of this option shall constitute the acceptance of and agreement to all of the terms and conditions contained herein and
in the Plan. The Company may impose any additional conditions or restrictions on the Award or the exercise of the Option as it
deems necessary or advisable to ensure that all rights granted under the Plan satisfy the requirements of applicable securities
laws. The Company shall not be obligated to issue or deliver any Shares if such action violates any provision of any law or regulation
of any governmental authority or national securities exchange.

 

8.          Lost
Award Agreement.

 

Upon receipt of evidence
satisfactory to the Company of the loss, theft, destruction or mutilation of this Award Agreement and upon delivery of a bond of
indemnity satisfactory to the Company (or, in the case of mutilation, upon surrender of this Award Agreement), the Company will
issue to the holder a replacement Award Agreement (containing the same terms as this Award Agreement).

 

9.          Choice
of Law.

 

This Award Agreement
shall be governed by and construed in accordance with the internal laws (and not the principles relating to conflicts of laws)
of the State of Delaware, except as superseded by applicable federal law. This Award Agreement shall inure to the benefit of and
be binding upon the Company and its successors and assigns and the Optionee and his or her heirs and legal representatives, subject
to the restrictions on assignability and transferability set forth in the Plan.

 

    	3

    	 

    

  

10.         Amendment.

 

The Committee may amend
the terms of this Award Agreement to the extent permitted by the Plan. The construction and interpretation of any provision of
this Award Agreement or the Plan shall be final and conclusive when made by the Committee.

 

11.         Notices.

 

All notices hereunder
shall be in writing and shall be deemed given when sent by certified or registered mail, postage prepaid, return receipt requested,
to the Optionee’s last known address as noted on his or her Company personnel file or to the Company at JetPay Corporation,
1175 Lancaster Avenue, Suite 200, Berwyn, PA 19312 or such other addresses (including any electronic mail addresses) as the recipient
party has specified by prior written notice to the sending party, as applicable. The address for such notices may be changed from
time to time by written notice given in the manner provided for herein.

 

12.         Entire
Agreement.

 

This agreement constitutes
the entire agreement between the Optionee and the Company with respect to the subject matter hereof and controls and supersedes
any prior understandings, agreements or representations by or between the parties, written or oral with respect to its subject
matter, including but not limited to the provisions of any and all employment agreements and offer letters, and may not be modified
except by written instrument executed by the Optionee and the Company, except as otherwise permitted by the Plan.

 

13.         Nonqualified
Stock Option.

 

The Option granted
hereby is not intended to be an incentive stock option pursuant to Section 422 of the Code and will not be treated as an incentive
stock option.

 

    	4

    	 

    

  

This acknowledgement
must be signed by the Optionee and returned to the attention of the undersigned within fifteen (15) days; otherwise, the Option
will lapse and become null and void. The Optionee’s signature will also acknowledge that the Optionee has received and reviewed
the Plan and that the Optionee agrees to be bound by the terms of the Plan.

 

	 	JetPay Corporation
	 	 	 
	 	By:	 
	 	 	Peter B. Davidson, Corporate Secretary

 

	Accepted as of __________, 201_:	 
	 	 
	 	 
	Signature of Optionee	 

 

    	5

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