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Engineered nanomaterials for solar energy conversion
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2013 Nanotechnology 24 042001
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IOP PUBLISHING
NANOTECHNOLOGY
Nanotechnology 24 (2013) 042001 (11pp)
doi:10.1088/0957-4484/24/4/042001
TOPICAL REVIEW
Engineered nanomaterials for solar
energy conversion
Vladan Mlinar
School of Engineering, Brown University, Providence, RI 02912, USA
E-mail: vladan [email protected]
Received 7 November 2012, in final form 7 December 2012
Published 8 January 2013
Online at stacks.iop.org/Nano/24/042001
Abstract
Understanding how to engineer nanomaterials for targeted solar-cell applications is the key to
improving their efficiency and could lead to breakthroughs in their design. Proposed
mechanisms for the conversion of solar energy to electricity are those exploiting the particle
nature of light in conventional photovoltaic cells, and those using the collective
electromagnetic nature, where light is captured by antennas and rectified. In both cases,
engineered nanomaterials form the crucial components. Examples include arrays of
semiconductor nanostructures as an intermediate band (so called intermediate band solar
cells), semiconductor nanocrystals for multiple exciton generation, or, in antenna–rectifier
cells, nanomaterials for effective optical frequency rectification. Here, we discuss the state of
the art in p–n junction, intermediate band, multiple exciton generation, and antenna–rectifier
solar cells. We provide a summary of how engineered nanomaterials have been used in these
systems and a discussion of the open questions.
(Some figures may appear in colour only in the online journal)
1. Introduction
thin-film technologies. Examples include amorphous Si, thinfilm Si, CuInSe2 , CdTe, and dye-sensitized photochemical
cells. Current, third generation, PV should lead to an
increase in efficiency. Proposed improved solar cells include
e.g., high efficiency multi-gap tandem cells, multiple exciton
generation solar cells, intermediate band solar cells (IBSCs),
hot carrier converters, thermophotovoltaics/thermophotonics,
etc. Furthermore, it has been proposed that sunlight could be
captured by (nano)antennas and rectified using a diode by
exploiting the wave nature of the light [3–5, 2].
Engineered nanomaterials are the key building blocks
of the current generation solar cells. For example, the idea
behind the IBSCs is to introduce one or more energy levels
within the bandgap so that they absorb photons in parallel with
the normal operation of a single-bandgap cell [6]. The search
for optimal sub-bandgap absorbers has been focused on highly
mismatched semiconductor alloys that naturally exhibit an
intermediate band (IB) [7, 8, 6], and on nanostructures, in
particular arrays of quantum dots that form an IB [9–11, 8,
6].
The proposed mechanisms for the conversion of solar energy
to electricity include those exploiting the particle nature
of light in conventional photovoltaic cells, where absorbed
photons generate electron–hole pairs, and those using the
collective electromagnetic nature of the light, where sunlight
is captured by antennas and rectified. In recent years, there
has been immense progress in solar-cell technologies and a
dramatic decrease in their cost. For example, the efficiency
of solid-state photovoltaic (PV) cells started with values
of ∼5% [1], but now there are routinely achievable values
of >20% in Si-based systems and >30% in GaAs-based
systems [2].
Perhaps the best way to track the technological progress
is by examining the three generations of PV, defined by the
increase of efficiency versus the reduction in cost [2]. First
generation PV includes solar cells made of semiconducting
p–n junctions, such as single crystal Si and poly-grain
Si. Second generation PV reduced cost by introducing the
0957-4484/13/042001+11$33.00
1
c 2013 IOP Publishing Ltd Printed in the UK & the USA
Nanotechnology 24 (2013) 042001
Topical Review
2. p–n junction solar cells
Other examples include the potential usage of semiconducting nanocrystals in multiple exciton generation solar
cells, where excitation of a semiconductor nanocrystal by a
single, high-energy photon may result in a few electron–hole
pairs [2, 12–19], or nanomaterials for the design of optical
antennas with a typical dimension of ∼100–1000 nm,
supporting modes which exhibit extremely short wavelengths
and strong confinement of the electromagnetic field on the
nanometer scale [5, 2, 20].
A new playground has opened for engineered nanomaterials, and at this point it is simply not sufficient to focus
only on technological improvements. Further technological
breakthroughs depend strongly on an improved fundamental
understanding of electronic, optical, and transport properties
of nanomaterials and finding an efficient way to transfer
technology from research laboratories to industry. Recent
advances in computational nanoscience, combined with
state-of-the-art experiments, could potentially enable such
breakthroughs.
Quantum mechanical models have become sophisticated
enough to handle nanosystems of a few tens or a few
thousands up to hundreds of thousands of atoms, including
excitations and many-body effects. They are able to handle
realistic structural information obtained from the structural
characterization measurements and take into account all the
relevant effects, including the strain and piezoelectric effects,
and external magnetic and electric fields [21]. Using these
models we can, at least in principle, connect structure and
physical properties of a nanomaterial.
Furthermore, combining the quantum methods with
machine learning algorithms has opened new pathways for
the design and engineering of nanomaterials with targeted
properties [21]. Once a targeted physical property has been
defined, the quantum mechanical models and search/machine
learning algorithms are employed to deduce one or a few
best candidate nanomaterials. It was suggested that, for
technological applications, the same method could be used
to optimize the nanomaterials with respect to the targeted
physical property, avoiding a long and costly process that
includes nanomaterials’ fabrication and characterization [21].
However, before even considering the application of the
predictive-theory-guided design to solar cells, we need to
understand the current fundamental and practical problems
with the solar cells. Only then can we discuss how realistic
and potentially useful the predictive-theory-guided design
could be.
Here, we discuss the state of the art in p–n junction,
IB, multiple exciton generation, and antenna–rectifier
solar cells. We provide a summary of how engineered
nanomaterials have been used in these systems and a
discussion of the open questions. For example, we address
recent findings on how to exceed the thermodynamical limit
on light trapping [22], or very recently reported multiple
exciton generation enhancement of photocurrent in PbSe
nanocrystal-based solar cells [19]. Understanding how to
engineer nanomaterials for targeted solar-cell applications
is the key to improving their efficiency and could lead to
breakthroughs in the design.
The solar spectrum contains photons with energies ranging
from about 0.5 eV to 3.5 eV. Conventional solar-cell
technology is based on a single p–n junction, benefiting from
one electron–hole pair for each absorbed photon, as shown
in figure 1(a). When light quanta are absorbed, electron–hole
pairs are generated, and if their recombination is prevented
they can reach the junction, where they are separated by an
electric field.
Current photovoltaic technologies utilize semiconductors, such as large crystals of silicon, or thin films of
amorphous silicon, cadmium telluride (CdTe), or copper
indium gallium selenide (CIS). The semiconductor material
has to be able to absorb a large part of the solar spectrum,
which is determined by its bandgap, as illustrated by examples
in figure 1(b). For example, amorphous silicon has a higher
bandgap (1.7 eV) than crystalline silicon (1.1 eV), which
means that it absorbs the visible part of the solar spectrum
more strongly than the infrared portion of the spectrum.
The p–n junction solar cells based on crystalline
silicon now routinely achieve an efficiency of ∼22% [23,
2]. The maximum thermodynamic efficiency for singlebandgap devices, assuming detailed balance, is 31%, the
Shockley–Queisser limit [24]. It is obvious from figure 1(b)
that by layering materials with different bandgaps one can
improve the efficiency. This is the underlying idea of the
multi-layer (‘tandem’) cells, which are highly efficient, but
also expensive [2].
The energy conversion efficiency of solar cells based
on thin-film silicon is typically lower than that of bulk
silicon [23]. These limitations have been overcome by
employing light-trapping schemes. The incoming light is
obliquely coupled into the silicon and the light traverses the
film several times, enhancing the absorption in the films [23].
The minimum thickness of the material is defined by the
thermodynamical limit on light trapping [25]. However, recent
findings demonstrate that, in principle, any semiconductor
material can exceed the light-trapping limit when the local
density of optical states (LDOS) of its absorbing layer exceeds
the LDOS of the bulk semiconductor material [22]. This could
potentially allow for the design of novel solar cells that can
absorb light from the entire solar spectrum, but are ∼10 nm
thick [22].
Another way of creating the p–n junctions in semiconductors is by utilizing the electric field effect, where the
concentration of charge carriers in a semiconductor is altered
by the application of an electric field. Very recently, it has
been proposed to exploit this effect to induce a p–n junction,
enabling, at least in principle, a high quality p–n junction to be
made of basically any arbitrary semiconductor [26]. The idea
is to carefully design the top electrode so the gate electric field
can sufficiently penetrate the electrode and more uniformly
modulate the semiconductor carrier concentration and type.
The method is illustrated on the example of silicon and copper
oxide, where in the case of silicon, the top contact is made of
a single layer of graphene across the surface [26].
The major factors limiting the conversion efficiency are
the inability to absorb photons with energy less than the
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Nanotechnology 24 (2013) 042001
Topical Review
Figure 1. (a) Schematic diagram of a conventional single-junction semiconductor solar cell (CSC). Absorbed light with photon energies
greater than the bandgap produces carriers, electrons and holes. Loss processes are nonabsorption of below-bandgap photons, heat losses,
and radiative recombination. (b) Different materials absorb different parts of the solar spectrum depending on their bandgaps.
Figure 2. (a) Band diagram of an intermediate band solar cell (IBSC). Simultaneous with normal operation of the cell, below-bandgap
photons get absorbed by the two transitions to and from the intermediate level contributing to the photocurrent. (b) Limiting efficiency for
IBSC and conventional SC (CSC) as a function of E1 (intermediate band–valence bandgap). We used data from Laque and Marti [27].
bandgap, thermalization of photon energies exceeding the
bandgap, and radiative recombination losses [23, 2]; see
figure 1(a). When a photon is absorbed with energy greater
than the bandgap of a semiconductor, the resultant carrier
undergoes fast cooling via phonon scattering and emission.
Three approaches have been put forward to address
this loss of efficiency [2]: (i) increasing the number of
energy levels, typically by using a stack of multiple p–n
junctions in different semiconductor materials (figure 1(b));
in this way higher-energy photons are absorbed in the
higher-bandgap semiconductors and lower-energy photons
in the lower-bandgap semiconductor; (ii) capturing carriers
before thermalization, yielding a higher photovoltage; and
(iii) multiple-carrier-pair generation per high-energy photon
or single-carrier-pair generation with multiple low-energy
photons, leading to the enhancement of the photocurrent.
band (CB), enabling, at least in principle, IBSCs to achieve
both high current and high voltage.
The IB has to be partially occupied to enable absorption
from the VB into the empty states of the IB, and from
occupied states of the IB to the CB. Splitting the Fermi
level into three separate quasi-Fermi levels preserves the high
output voltage of the cell [6]. Of course, VB to IB and IB
to CB transitions must be optically allowed and strong, and
the IB needs to be electronically isolated from both the CB
and the VB, so VB to IB and IB to CB absorption spectra
do not have spectral overlaps with each other [8, 11, 27]. The
theoretical limiting efficiency of IBSC is 63% [27], derived
at isotropic sunlight illumination and assuming the Sun and
Earth temperatures to be 6000 K and 300 K, respectively.
Under the same conditions, the maximum efficiency of a
single-gap solar cell was 41%. Variation of the efficiency with
the IB–VB gap E1 is shown in figure 2(b), where we used data
from Laque and Marti [27].
The quest for finding optimal sub-bandgap absorbers has
been focused on (i) alloys that naturally exhibit an IB [7, 8, 6]
and (ii) nanostructures, in particular arrays of quantum dots
(QDs) that form an IB [9–11, 8, 6].
Bulk IBSCs. The electronic band structure of highly
mismatched semiconductor alloys can be tuned both
experimentally and theoretically to exhibit three electronically
isolated energy bands [8]. In highly mismatched alloys this
3. Intermediate band solar cells
The main idea behind IBSCs is to introduce one or
more energy levels within the bandgap such that they
absorb photons in parallel with the normal operation of a
single-bandgap cell [6, 8, 2, 27, 28]. A band diagram of an
IBSC is shown in figure 2(a). Sub-bandgap energy photons are
absorbed through transitions from the valence band (VB) to
the intermediate band (IB) and from the IB to the conduction
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Nanotechnology 24 (2013) 042001
Topical Review
deposited material [35, 36]. The shape and average size
of these QD islands depend mainly on factors such as the
strain intensity in the layer as related to the misfit of the
lattice constants, the temperature at which the growth occurs,
and the growth rate. The islands evolve to the state of
quasi-equilibrium in which they assume the shape of pyramids
or lenses formed on a thin wetting layer, that are then capped
by the barrier material. The main advantages of the SK
growth mode are fabrication of defect-free QDs of small sizes,
homogeneity in sizes and shapes of QDs, formation of ordered
arrays of 3D coherent islands, and fairly convenient growth
processes [35, 36]. Indeed, their structural perfectness (no
impurities, dislocations, and defects), the excellent isolation
from the environment, and the ability to charge the system
with a few electrons or holes (multiexcitons), have made
them essential in studying many-particle physics in confined
spaces [37, 38]. Unlike colloidal QDs, where nonradiative
decay channels rapidly destroy multiexcitons and, e.g., cause
blinking in photoluminescence (commonly interpreted as
being caused by the presence of extra charges that enhance
nonradiative decay rate) [39, 40], in self-assembled QDs
the multiexcitons ‘survive’ (and decay radiatively). Also,
the photocorrosion and photostability [41] of colloidal QDs,
where QDs stability depends on the solution (e.g., it was
found that CdS QDs in nonpolar solvent were remarkably
stable even under UV light irradiation) [41], do not influence
self-assembled QDs.
In order to create a mini-band, some measure of
homogeneity must exist between the successive quantum dot
layers. However, the strain may accumulate so that layers of
coherent quantum dots may no longer be formed, thus limiting
the number of QD layers [42–44]. The strain-induced limit of
the number of QD layers can be lifted by employing systems
with the strain symmetrization within the structure, such as the
(In, Ga)As/Ga(As, P) system [11]. It was found that, whereas
the number of QD layers was indeed increased, the intensity
of absorption between QD-confined electron states and the
host CB was weak (because of their localized-to-delocalized
character) and the position of the IB within the matrix
bandgap did not satisfy suitable energetic locations for the
IB [11].
Furthermore, one of the challenges in the QD IBSC
design has been the loss of output voltage at room temperature
compared to reference solar cells without an IB [6]. The loss
of voltage at room temperature is caused by the thermal escape
of electrons from the IB to the CB (in addition to tunneling of
electrons from the IB to the CB) [6, 8].
Thus, from a fundamental viewpoint, there is a need
for better understanding of the nature of the IB (localized
versus extended), and carrier relaxation processes. From
a purely technological viewpoint, the quest for improved
fabrication techniques and more suitable materials (strain
symmetrization and strong absorption between the IB and
CB) has only just begun. As an illustration of the sensitivity
of the problem, careful fabrication of InAs/GaAs IBSCs led
to a significant elimination of output-voltage reduction [45],
potentially opening pathways for room temperature IBSCs.
can be achieved by the substitution of a relatively small
fraction of host atoms with an element of very different
electronegativity. Examples include III–V and II–VI alloys, in
which group V and VI anions are replaced with the isovalent
N and O, respectively, see e.g., [29, 30]. The electronic
structure of such alloys is determined by the interaction
between localized states associated with N or O atoms and
the extended states of the host semiconductor matrix. As
a result the conduction band splits into two subbands with
distinctly nonparabolic dispersion relations [29], affecting the
optical and electrical properties of these alloys. A narrow
lower band can be formed only if the localized states
lie well below the conduction band edge. Consequently,
the absorption spectrum is modified by adding two new
absorption edges, which can be tuned, at least in principle,
to fall within the solar energy spectrum [30]. Experimental
examples include the formation of an IB within the
bandgap of highly mismatched semiconductor alloys such
as Zn1−y Mny Ox Te1−x and GaNx As1−x−y Py [29, 30]. The IB
was detected by spectral photoreflectance measurements, and
its formation was attributed to band anticrossing. In order
to obstruct electron tunneling between the IB and CB, and
consequently maintain a high open-circuit voltage, blocking
layers were introduced. This was successfully demonstrated
on an example of GaN0.024 As0.976 [28, 8].
From theoretical and computational viewpoints, numerous ab initio calculations have been performed in the quest for
optimal IB materials. The most promising of these has been
V0.25 In1.75 S3 , which has strong sub-bandgap absorption and
an inherent partially filled IB [7]. This is important because it
means that the IB is already partially filled without having to
rely on impurity doping, which reduces densities and therefore
lowers absorption levels.
Bulk IBSCs have so far exhibited efficiencies far below
their potential, and the issue of finding the best candidate
materials for this technology is essential if IBSC research is
to succeed.
Quantum dot IBSCs. An IB can also be formed from
the confined states of QDs situated within the bandgap
of a host semiconductor. QDs should be closely spaced
and with high quality interfaces, which would enable the
strong wavefunction overlap and the formation of minibands.
To achieve strong absorption to and from the IB, a high
concentration of QDs is required. By engineering the
parameters such as QD geometry (size and shape), inter-dot
separation, and dot arrangement, one can optimize IB position
and width to achieve the maximum efficiency [31, 32].
Typically, self-assembled (In, Ga)As QDs embedded in a
GaAs matrix have been used as an IB (see, e.g., [6]).
Other examples include InAs QDs in a GaAs/(Al, Ga)As
matrix [33], or GaSb QDs in GaAs [34]. Interestingly, some of
these devices have demonstrated features of IBSC operation,
and achieved efficiencies over 18% [10, 6].
Self-assembled QDs consist of 104 –106 atoms of a
semiconductor such as (In, Ga)As embedded in another
semiconductor matrix, e.g., GaAs. They are fabricated by
the Stranski–Krastanov (SK) growth mode, which uses the
natural lattice mismatch between the substrate and the
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Nanotechnology 24 (2013) 042001
Topical Review
Figure 3. The single photon generation of multiple excitons (electron–hole pairs). (a) Bulk and (b) nanocrystal.
Figure 4. (a) The ideal profiles for carrier multiplication efficiency η, the number of excitons generated by absorption of a photon, for bulk
PbSe (green), nanocrystals NC1 (blue) and NC2 (red). The shaded region represents the AM1.5G solar spectrum [49]. (b) Quantum yield
versus photon energy for PbSe [13, 50, 15, 47] and PbS [13, 17, 47] nanocrystals (NCs) and bulk; data from various groups illustrate wide
variations of reported MEG QYs. The quantum yield represents the averaged number of excitons per absorbed photon. QY = 200% means
all dots have two excitons.
4. Multiple exciton generation solar cells
photogenerated carriers may be affected by quantization
effects, and lead to more efficient solar cells (figure 3(b)). For
example, hot carrier cooling rates of impact ionization could
become competitive with the rate of carrier cooling [2, 13].
Numerous experiments have confirmed the existence
of MEG in nanocrystals (although not without controversy,
as discussed below) by showing that excitation of a
semiconductor nanocrystal by a single, high-energy photon
may result in a few electron–hole pairs (figure 3(b)) [2,
12–19]. The single photon generation of multiple excitons
occurs on a very short time scale following photon absorption,
where the efficiency increases with the energy of the photon.
Figure 4(a) shows the ideal profiles for multiple exciton
generation efficiency η [48, 46] in bulk PbSe Eg = 0.27 eV
(green), nanocrystal NC1 with Eg = 0.72 eV (1722.2 nm)
(blue) and nanocrystal NC2 with Eg = 1.3 eV (954 nm)
(red). The efficiency η is defined as the number of excitons
generated by absorption of a photon. It was calculated using
the detailed balance model under the assumptions that all
photons with energies above the bandgap were absorbed and
those with energies less than the bandgap were not, that
the only loss is the radiative recombination, and that all
photogenerated carriers are collected [48]. The calculations
also give the maximum efficiency depending on the bandgap,
Multiple exciton generation (MEG), or carrier multiplication,
is the generation of more than one electron–hole pair
(exciton) by absorption of one photon [46–48]. High-energy
photons, at least twice the bandgap energy, absorbed in a
bulk semiconductor can generate one or more additional
electron–hole pairs close to the bandgap energy through a
scattering process, known as impact ionization (the inverse
of Auger recombination) (figure 3(a)) [2, 47, 48, 46]. The
impact ionization was previously observed in bulk Si, PbS,
PbSe, Ge, InSb, etc. This effect is inefficient in bulk because
the rate of impact ionization is much slower than the rate of
radiative recombination at low electron energies (in visible
and near IR spectrum) and the need to conserve momentum. In
addition, the impact ionization in bulk is not useful for energy
conversion purposes because the required photon energies lie
outside the solar spectrum (3.5 eV); e.g., it requires ∼7 eV
photons to produce one extra carrier in silicon [19, 46, 2].
Thus, it was proposed that MEG can be more efficient
in semiconducting nanocrystals [12, 15]. Given the unique
electronic structure properties of nanocrystals–atomic-like
electronic structure and size-dependent bandgap energies [15,
38], it was suggested that the relaxation dynamics of
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Nanotechnology 24 (2013) 042001
Topical Review
defined as ηmax (Eg ) = 4/Eg [48]. In our case this gives, e.g.,
ηmax (Eg = 0.72) = 5 and ηmax (Eg = 1.3) = 3.
Figure 4(b) shows quantum yield (QY) versus photon
energy for PbSe [13, 50, 15, 47] and PbS [13, 17, 47]
nanocrystals and bulk. The quantum yield represents the
averaged number of excitons per absorbed photon. Data from
various groups illustrate wide variations of reported MEG
QYs [13–19, 50]. This caused controversies, especially at the
beginning, because the reported experimental probes of MEG
have relied only on indirect evidence of the existence and
efficiency of MEG (signature of Auger recombination within
the exciton population decay traces) [16, 46, 18, 2].
In a typical MEG experiment, ultrafast transient
absorption spectroscopy is used to infer the number of
electron–hole pairs produced per absorbed photon. Samples
are illuminated with a low-intensity beam of high-energy
photons, and the ensuing dynamics of multiexciton decay
versus single exciton decay are measured. If a fast component
with a lifetime similar to multiexciton lifetimes is observed
in addition to exciton decay, it is attributed to multiexcitons.
However, MEG artifacts exist and can give ‘false positive’
signatures of MEG. For example, the single exciton decay
can acquire a fast component due to opening of nonradiative
channels, e.g., electron or hole traps in a nanocrystal
surface [46]. Detailed discussion of the measurement of
MEG versus its artifacts, and the proposed ways to minimize
chances of overestimating MEG QY, is given in [46].
Furthermore, disagreements have arisen over the role
of quantum confinement for MEG. Interpretations range
from those showing that the MEG efficiency of the PbSe
nanocrystal is about twice the efficiency observed in
bulk PbSe [19, 48] to those stating that the advantage
of nanocrystal MEG is merely due to a possibly larger
photovoltage owing to quantum confinement [46]. Finally,
there is the issue of the impact the MEG can have on solar
energy conversion, demonstrating that MEG can occur in a
working solar cell.
Very recently, MEG-induced enhancement of photocurrent in PbSe nanocrystal-based solar cells was demonstrated [19]. For the best device measured, the external
quantum efficiency, defined as the spectrally resolved ratio of
collected charge carriers to incident photons, peaked at 114 ±
1%. The associated internal quantum efficiency, corrected
for reflection and absorption losses, was 130% [19]. The
solar-cell architecture incorporated arrays of QD layers in
p–n planar heterojunctions. Special attention was paid to
the chemistry of PbSe QD surfaces, including removing
long-chain organic ligands (such as oleic acid) while controlling electrical properties, and using four distinct chemical
treatments (1,2-ethanedithiol, which showed reduced MEG,
and hydrazine, methylamine, and ethanol, which preserved
MEG). Furthermore, the beneficial aging effect on the solar
cell performance was observed under oxygen and water-free
nitrogen storage conditions [19].
Theoretical studies regarding the basic mechanisms of
MEG give confusing results. Models offering explanations of
MEG range from those that consider a coherent superposition
of single and multiple exciton states; to excitations of a
virtual multiexciton state that is strongly coupled to a real
multiexciton state; to incoherent impact ionization, analogous
to bulk impact ionization with appropriate modifications of
the electronic states [16, 51, 2]. In order to distinguish
between different interpretations, one would need additional
constraints on the set of initial parameters. The set of initial
parameters includes the coupling strength between excitons
and multiexcitons, decay rates, and/or density of states. This
is still an open issue.
Theoretical/computational models should link structure
(typically extracted from structural characterization measurements) and predict or explain experiment. They should also
predict any size dependence, explain how MEG is influenced
by the coupling of the nanocrystal to its environment,
and provide understanding of how MEG is influenced by
coupling of nanocrystals. However, structural information
about nanocrystal systems is not complete. For example,
it is difficult to extract information about the surface of
a nanocrystal, so it is not clear whether a charge carrier
can reside at the nanocrystal surface in deep-trap energy
states or not. One could, e.g., analyze different nonradiative
decay channels for an assumed nanocrystal structure and then
discuss the plausibility of the constructed scenarios.
From a more pragmatic (but not necessarily recommended) viewpoint, whereas understanding of the underlying
physics is unquestionably important, the primary interest
should lie in demonstrating that MEG can occur in a working
solar cell. MEG-induced enhancement of photocurrent in
PbSe nanocrystal-based solar cells has been very recently
achieved [19], so the practical challenge is how to improve the
MEG-enhanced quantum efficiency and search for different or
new candidate nanomaterials for MEG, e.g., PbSe nanorods,
carbon-based nanostructures, etc [19, 21]. Usage of simple
empirical models that heavily rely on experiment can be more
useful than employment of detailed many-body atomistic
methods. Also, although not the most elegant approach, it is
not uncommon in materials science to use linear regression
or neural networks to interpret experimental data when
physical models do not exist or are difficult to implement;
see, e.g., [52]. The underlying equations do not have to be
physically justified and the parameter set is determined by
fitting the equations to a large set of experimental data [21,
52].
5. Antenna–rectifier system for solar energy
conversion
Solar energy can be converted to electricity by exploiting the
wave nature of light instead of its particle nature: sunlight
is captured by (nano)antennas and then rectified [3–5, 2].
The fact that this approach had been previously successfully
applied at longer wavelengths in radio and microwave
frequency bands [53] opened the possibility, at least initially,
for high efficiency conversion of solar energy. The uses of
rectennas in the microwave region have been investigated over
the past half century for power transmission and detection.
Applications have included long-distance power beaming,
signal detection, and wireless control systems [53, 4].
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Nanotechnology 24 (2013) 042001
Topical Review
Figure 5. (a) Block diagram of antenna and rectifier system and load; (b) proposed realization of rectenna system using nanowires.
Nanowires behave as antennas and the tip of the nanowires and surface create rectifying tunneling junctions. It was suggested that the
nanowire’s asymmetrical, nonplanar geometry in conjunction with the flat anode is an essential requirement for increasing the cut-off
frequency of the diode (for more details see [5]).
Conventional rectennas consist of two distinct elements [53,
4, 5], a dipole antenna plus a separate rectifying diode such as
an MIM or Schottky diode, as illustrated in figure 5(a).
In the case of solar energy conversion to electricity, a
rectenna device should collect and rectify electromagnetic
radiation distributed over a wide range of submicron
wavelengths (from the infrared (IR) through the visible
portion of the spectrum, extending the range to 1014 Hz
and higher), which, in contrast to monochromatic microwave
radiation, is also incoherent and unpolarized. Schottky diodes
are generally limited to frequencies less than 5 THz [54] and
conventional MIM diodes have been used up to frequencies
of about 100 THz [54–56, 5]. So, it is not obvious if an
antenna–rectifier system, as used for monochromatic radio
and microwave radiation, can be simply applied for solar
energy conversion, for example, how to design an antenna to
collect sunlight, or how to obtain efficient optical frequency
rectification.
The conversion efficiency for the rectenna system in the
case of monochromatic radio and microwave radiation is
more than 80% [53]. Estimates for the theoretical limiting
conversion efficiency of the antenna–rectifier solar cells range
from 48% [2, 57, 58] to 95% [58], depending on how the
antenna–rectifier solar cells were modeled.
In one model [2, 4, 57, 58], electrical noise power
received through an antenna is replaced by a resistor at a
temperature TR , whose resistance is equal to the radiation
resistance of the antenna. If the antenna can be replaced by
the resistor at a given temperature, the rectification occurs
only if the diode is at a lower temperature TD (TD < TR ).
There is no rectification for TR = TD , otherwise the second
law of thermodynamics is violated, the so called Brillouin
paradox [59]. Note that the equivalent arguments can be
found in Feynman analysis of the ratchet as an engine [60],
where it was shown that the engine cannot work if the
vanes and the ratchet are at the same temperature. In both
cases the efficiency is less than the Carnot efficiency because
of the unavoidable heat exchange between the two thermal
reservoirs [61]. It was shown that, if the antenna was replaced
by a resistor at the temperature TR = 6000 K, the maximum
efficiency was ∼48% [57, 58, 2, 4]. Obviously, this is a
disappointingly low value and casts doubt on the usefulness
of the approach.
Other reported values of the theoretical limiting
conversion efficiency of the rectenna system are higher than
85%, and are based on rather elementary considerations. For
example, the model Sun–space–absorber–solar cell gives the
efficiency of ∼85% [4], whereas the model Sun–space–solar
cell, which included entropy losses, led to the value of
∼93% [62, 4].
Unfortunately, it is not clear which one of these methods
applies to the rectenna system. Whereas the simple models,
which give overly optimistic values of efficiency, do not
include specific features of the antenna–rectifier solar cells,
the model based on replacing the antenna by a resistor is as
good as the initial assumption that the antenna can be replaced
by a resistor at the temperature TR . This assumption is valid
for lower frequencies (up to the near IR) [4, 53], but it is not
clear to what degree the resistor replacement can be used in
the optical frequency range. Thus, the question of determining
the theoretical limiting conversion efficiency of the rectenna
solar cell (that includes all the characteristics of the system) is
still open.
From a (more important) practical viewpoint, the design
of antennas and rectifiers operating at optical frequencies
represents a significant challenge due to the required size and
frequency of operation (see, e.g., [5, 20]). We are in a situation
in which we need to, on one hand, improve our understanding
of the behavior of materials used for antennas, e.g. metals,
in the optical regime, which differs from that at frequencies
below the IR, and on the other hand improve the ability to
fabricate optical antennas with nanometer dimensions. For
example, the common requirement for an antenna structure
is that its size is comparable to the wavelength of the
collected light. For optical antennas this gives a typical
dimension of ∼100–1000 nm. Such (nano)antennas support
localized plasmon polaritons, which exhibit extremely short
wavelengths and strong confinement of the electromagnetic
field on the nanometer scale [20]. In addition to the size
requirements, to produce an effective output signal, the
antenna must be coupled to a device that can respond in a time
t ∼ 1/f , which for optical frequencies corresponds to times of
10−15 –10−13 s [5].
So far, optical antennas have been produced in a variety
of sizes and shapes [63, 5], including, e.g., thin wire or
whisker, dipole, bow-tie, etc. For example, figure 5(b) shows
a thin wire antenna consisting of arrays of vertically aligned
nanowires, where the tips of the nanowires and surface create
rectifying tunneling junctions [5, 64, 55]. For a review and
7
Nanotechnology 24 (2013) 042001
Topical Review
be found to be Mott insulators. Also, such oxides can show
interesting behavior when driven by high frequency fields.
To summarize, whereas the entire rectenna concept for
solar energy conversion may be very difficult to realize in
practice, the problems such as understanding the materials
behavior at optical frequencies, design and fabrication of
antennas with a typical dimension of ∼100–1000 nm, or the
issue of efficient optical frequency rectification and how to
engineer nanomaterials to rectify on such high frequencies,
represent challenges that need to be addressed. As to the
solar energy conversion using rectennas, at this point only
a proof-of-concept device will provide convincing evidence
regarding this approach.
recent developments on antenna issues in rectenna solar cells
see, e.g., [5, 20, 65, 66].
In order to get an efficient rectification at optical
frequencies, the diode will have to respond fast enough
to operate at optical frequencies, and have a relatively
low turn-on voltage. It will also require sufficiently small
capacitance to minimize its time constant [5].
Quantum point-contact (QPC) devices, e.g. whisker
diodes, have been used in measurements of absolute
frequencies up to the green portion of the visible
spectrum, demonstrating a response time of the order of
femtoseconds [5].
One way to realize QPCs is in a break junction by
pulling apart a piece of conductor until broken, or, in a more
controlled way, in a two-dimensional electron gas (2DEG),
e.g. in GaAs/AlGaAs heterostructures [67]. Rectification of
the terahertz field has been discussed both experimentally
and theoretically, in terms of its coupling to the source–drain
bias, or in terms of modulating the QPC gate voltage [68].
Theoretically, one can model, e.g., current fluctuations in a
ballistic QPC biased by applied voltage and irradiated by
external field, where the external field could be considered
to be either coherent (e.g. microwave radiation) or incoherent
(e.g. representing the environment at high enough temperature
or a heat phonon pulse) [69].
QPCs can also be created by positioning the tip of a
scanning tunneling microscope close to the surface of a
conductor [70, 71]. The tunneling phenomenon in these QPC
devices is such that the current passes predominantly through
the sharp protrusion closest to the planar sample surface. The
rectification properties of tunneling junctions at fixed gap
width originate from material, geometrical, and/or thermal
asymmetry, and photo-stimulated changes in the electron flux
distribution [5, 72, 64, 55].
Material asymmetry is expected when the electrodes
have different work functions: the barrier shape will be
asymmetric at zero bias. Thermal asymmetry will occur
when there is a temperature difference between the two
electrodes causing different electron occupations of the states
involved in tunneling. Geometrical asymmetry represents
asymmetry of the electrodes comprising the tunnel junctions.
Examples include the geometrical asymmetry effect in
STM [70], or optical rectification caused by the nonlinear
tunneling conduction between gold electrodes separated by
a subnanometer gap [71]. The asymmetrical, nonplanar
geometry of the pointed whisker in conjunction with the flat
anode is an essential requirement for increasing the cut-off
frequency of the diode, but inconsistent with the planar
geometry [5].
There have been many innovative proposals on how to
achieve efficient optical frequency rectification. For example,
very recently, Sabou et al [73] theoretically investigated
idealized junctions between oppositely doped Mott insulators,
modeling them as one-dimensional chains of interacting
spin-polarized fermions. They predicted efficient rectification
at very high frequencies. For practical realizations, Sabou
et al [73] recommended transition metal oxides, which,
although often predicted to be conductors by band theory, can
6. Discussion and summary
Engineered nanomaterials are the key building blocks of
solar cells, irrespective of the mechanisms for the conversion
of solar energy to electricity—those exploiting the particle
nature of light and those using the collective electromagnetic
nature, where light is captured by antennas and rectified.
Understanding how to engineer nanomaterials for targeted
solar-cell applications is the key to improving their efficiency
and could lead to breakthroughs in the design.
The design of nanomaterial-based solar cells is far
from being straightforward. Traditional approaches for the
improvement of the design of solar cells, or the design of solar
cells based on new mechanisms, have relied on the intuition of
researchers, focusing on trial-and-error search and accidental
discovery.
Alternatively, predictive-theory-guided design combines
quantum mechanical methods and search/machine learning
algorithms, such as genetic algorithms, data mining, or
neural networks, to design optimized nanomaterials with
targeted physical properties [21]: we define a targeted physical
property and then employ the quantum mechanical and
search/machine learning algorithms to deduce the structure.
Of course, this sounds very appealing, especially because the
computer-generated nanomaterials could be counterintuitive
and difficult to discover otherwise, and the actual fabrication
of a large number of structures and their processing could be
avoided. The main premise behind this approach is that theory
is able to correctly link the structure and the property.
The real test for all those predictive methods would
be to fabricate nanomaterials using information from the
theoretically predicted structure, and then check how their
measured physical properties correspond to the targeted
ones. Let us analyze and discuss the solar-cell design from
the viewpoints of traditional versus predictive-theory-guided
design.
In the ‘simplest case’ where the underlying physical
processes are well understood, solar-cell design includes a
search for optimal constituent nanomaterials and geometries.
For example, a thermodynamical limit on the light
trapping within a semiconductor can be overcome by using
subwavelength nanomaterial-based solar absorbers, such
as nanowires that have elevated local density of optical
states [22]. Thus, the design reduces to the search for optimal
8
Nanotechnology 24 (2013) 042001
Topical Review
materials, ideally those that could absorb light from the entire
solar spectrum.
The design is more complicated for IBSCs. The quest
for finding optimal sub-bandgap absorbers has been focused
on (i) alloys that naturally exhibit an IB [7, 8, 6] and (ii)
nanostructures, in particular arrays of quantum dots (QDs),
that form an IB [9–11, 8, 6]. The problem is twofold
here—from a fundamental viewpoint, there is a need for
better understanding of the nature of the IB (localized versus
extended), and carrier relaxation processes; however, from
a more practical viewpoint, bulk- and QD-based IBSCs
have been fabricated already, but they have so far exhibited
efficiencies far below their potential. For example, to lift the
strain-induced limit of the number of QD layers in the IB, it
was intuitively clear that it could be achieved by employing
systems with the strain symmetrization within the structure,
such as the (In, Ga)As/Ga(As, P) system [11]. However,
whereas it was found that the number of QD layers was
increased, the intensity of absorption between QD-confined
electron states and the host CB was weak and the position
of the IB within the matrix bandgap did not satisfy suitable
energetic locations for the IB [11]. A careful implementation
of the predictive-theory design could have led to different
results, especially given that electronic and optical properties
of QDs are very well understood and the design rules for a QD
IBSC known [32]. Thus, the issue of finding the best candidate
materials for the current technology is still open.
Although intuitively clear, it is important to stress that
the problem is not only to design solar-cell devices based on
well understood physical principles, but also to control subtle
details such as tricks in fabrication which can play a relevant
role. Perhaps this statement is best illustrated by the example
of fabrication of InAs/GaAs IBSCs. One of the challenges
in QD IBSC design has been a loss of the output voltage at
room temperature compared to reference solar cells without
an IB [6]. The loss of voltage at room temperature is caused
by thermal escape of electrons from the IB to the CB (in
addition to tunneling of electrons from the IB to the CB).
However, ‘careful fabrication’ led to a significant elimination
of output-voltage reduction [45].
The issues with the design of MEG solar cells are
rather complex. From an experimental viewpoint, the issues
include indirect evidence of the existence and efficiency of
MEG [46], and the role of quantum confinement for MEG,
where interpretations range from those showing that the
MEG efficiency of the PbSe nanocrystal is about twice the
efficiency observed in bulk PbSe [19, 48] to those stating that
the advantage of nanocrystal MEG is merely in a possibly
larger photovoltage owing to quantum confinement [46].
Furthermore, theoretical studies disagree on the basic
mechanisms of MEG [16, 51, 2]. Theoretical/computational
models should link structure (typically extracted from
structural characterization measurements) and predict or
explain experiment. They should also predict any size
dependence, explain how MEG is influenced by the
coupling of the nanocrystal to its environment, and impart
understanding of how MEG is influenced by coupling
of nanocrystals. However, structural information about
nanocrystal systems is not complete. For example, it is
difficult to extract information about the surface of a
nanocrystal, so it is not clear whether a charge carrier
can reside at the nanocrystal surface in deep-trap energy
states or not. One could, e.g., analyze different nonradiative
decay channels for an assumed nanocrystal structure and
then discuss the plausibility of the constructed scenarios.
From a more pragmatic viewpoint, whereas understanding
of the underlying physics is unquestionably important, the
primary interest lies in demonstrating that MEG can occur
in a working solar cell. This has been very recently
achieved [19], so the practical challenge is how to improve the
MEG-enhanced quantum efficiency and search for different
or new candidate materials for MEG, e.g., PbSe nanorods,
carbon-based nanostructures, etc. The recent advances in
computational design could enable such a search for optimal
materials and geometries, as discussed in [21].
Application of the rectenna system for energy conversion
has been present in the literature for quite some time [3–5, 2],
discussing theoretical efficiency [4, 2] and proposing various
antenna–rectifier realizations [3–5, 65, 66, 71, 2]. At this
point only a proof-of-concept device will provide convincing
evidence regarding this approach. However, regardless of
how difficult it may be to realize the whole rectenna
concept for solar energy in practice, the problems such as
understanding the materials behavior at optical frequencies,
design and fabrication of antennas with a typical dimension
of ∼100–1000 nm, or the issue of efficient optical frequency
rectification and how to engineer nanomaterials to rectify at
such high frequencies represent challenges that need to be
addressed.
Acknowledgment
This work was supported by NASA EPSCoR.
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