Roadmap on optical energy conversion

Abstract

For decades, progress in the field of optical (including solar) energy conversion was dominated by advances in the conventional concentrating optics and materials design. In recent years, however, conceptual and technological breakthroughs in the fields of nanophotonics and plasmonics combined with a better understanding of the thermodynamics of the photon energy-conversion processes reshaped the landscape of energy-conversion schemes and devices. Nanostructured devices and materials that make use of size quantization effects to manipulate photon density of states offer a way to overcome the conventional light absorption limits. Novel optical spectrum splitting and photon-recycling schemes reduce the entropy production in the optical energy-conversion platforms and boost their efficiencies. Optical design concepts are rapidly expanding into the infrared energy band, offering new approaches to harvest waste heat, to reduce the thermal emission losses, and to achieve noncontact radiative cooling of solar cells as well as of optical and electronic circuitries. Light–matter interaction enabled by nanophotonics and plasmonics underlie the performance of the third- and fourth-generation energy-conversion devices, including up- and down-conversion of photon energy, near-field radiative energy transfer, and hot electron generation and harvesting. Finally, the increased market penetration of alternative solar energy-conversion technologies amplifies the role of cost-driven and environmental considerations. This roadmap on optical energy conversion provides a snapshot of the state of the art in optical energy conversion, remaining challenges, and most promising approaches to address these challenges. Leading experts authored 19 focused short sections of the roadmap where they share their vision on a specific aspect of this burgeoning research field. The roadmap opens up with a tutorial section, which introduces major concepts and terminology. It is our hope that the roadmap will serve as an important resource for the scientific community, new generations of researchers, funding agencies, industry experts, and investors.

Full text

Roadmap
Roadmap on optical energy conversion
Svetlana V Boriskina
1,25
, Martin A Green
2
, Kylie Catchpole
3
,
Eli Yablonovitch
4,5
, Matthew C Beard
6
, Yoshitaka Okada
7
, Stephan Lany
6
,
Talia Gershon
8
, Andriy Zakutayev
6
, Mohammad H Tahersima
9
,
Volker J Sorger
9
, Michael J Naughton
10
, Krzysztof Kempa
10
,
Mario Dagenais
11
, Yuan Yao
12
,LuXu
12
, Xing Sheng
13
, Noah D Bronstein
14
,
John A Rogers
12,13
, A Paul Alivisatos
14,4,24
, Ralph G Nuzzo
12,13
,
Jeffrey M Gordon
15
,DiMWu
16
, Michael D Wisser
17
, Alberto Salleo
17
,
Jennifer Dionne
17
, Peter Bermel
18
, Jean-Jacques Greffet
19
,
Ivan Celanovic
20
, Marin Soljacic
20
, Assaf Manor
21
, Carmel Rotschild
21
,
Aaswath Raman
23
, Linxiao Zhu
23
, Shanhui Fan
23
and Gang Chen
1
1
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA,
02139, USA
2
Australian Centre for Advanced Photovoltaics (ACAP), School of Photovoltaic and Renewable Energy
Engineering, University of New South Wales, Sydney, Australia
3
Centre for Sustainable Energy Systems, Research School of Engineering, Australian National University,
Canberra, A.C.T. 2601, Australia
4
Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
5
Electrical Engineering and Computer Sciences Department, University of California, Berkeley, CA
94720, USA
6
National Renewable Energy Laboratory, 15013 Denver West Pkwy, Golden, CO 80401, USA
7
Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku,
Tokyo, Japan
8
IBM T J Watson Research Center, 1101 Kitchawan Rd, Yorktown Heights, NY 10598, USA
9
Department of Electrical and Computer Engineering, George Washington University, 801 22nd Street
NW, Washington, DC 20052, USA
10
Department of Physics, Boston College, Chestnut Hill, MA 02467, USA
11
University of Maryland at College Park, Department of Electrical Engineering, MD 20742, USA
12
Department of Chemistry, Frederick Seitz Materials Research Laboratory, University of Illinois at
Urbana-Champaign, Urbana, IL 61801, USA
13
Department of Materials Science and Engineering, University of Illinois at Urbana Champaign, Urbana,
IL 61801, USA
14
Department of Chemistry, University of California, Berkeley, CA 94720, USA
15
Department of Solar Energy & Environmental Physics, Blaustein Institutes for Desert Research, Ben-
Gurion University of the Negev, Sede Boqer Campus 84990, Israel
16
Department of Chemistry, Stanford University, 333 Campus Drive, Stanford, CA, USA
17
Department of Materials Science and Engineering, Stanford University, 496 Lomita Mall, Stanford,
CA, USA
18
Purdue University, Electrical and Computer Engineering, Birck Nanotechnology Center, 1205 West State
Street, West Lafayette, IN 47907, USA
19
Laboratoire Charles Fabry, Institut d’Optique, CNRS, Université Paris-Saclay, 2 av Fresnel, 91127
Palaiseau, France
20
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
21
Russel Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel
22
Department of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
23
Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
Journal of Optics
J. Opt. 00 (2016)000000 (48pp)
APP Template V1.70 Article id: joptaa0bbf Typesetter: MPS Date received by MPS: 22/04/2016 PE: MAC003439 CE: LE:
UNCORRECTED PROOF
2040-8978/16/000000+48$33.00 © 2016 IOP Publishing Ltd Printed in the UK1

24
Department of Materials Science and Engineering, Kavli Energy NanoScience Institute, University of
California, Berkeley, California 94720, USA
25
Guest editor of the Roadmap
E-mail: sborisk@mit.edu
Received 17 August 2015, revised 18 November 2015
Accepted for publication 18 November 2015
Published DD MM 2016
Abstract
For decades, progress in the field of optical (including solar)energy conversion was dominated
by advances in the conventional concentrating optics and materials design. In recent years,
however, conceptual and technological breakthroughs in the fields of nanophotonics and
plasmonics combined with a better understanding of the thermodynamics of the photon energy-
conversion processes reshaped the landscape of energy-conversion schemes and devices.
Nanostructured devices and materials that make use of size quantization effects to manipulate
photon density of states offer a way to overcome the conventional light absorption limits. Novel
optical spectrum splitting and photon-recycling schemes reduce the entropy production in the
optical energy-conversion platforms and boost their efficiencies. Optical design concepts are
rapidly expanding into the infrared energy band, offering new approaches to harvest waste heat,
to reduce the thermal emission losses, and to achieve noncontact radiative cooling of solar cells
as well as of optical and electronic circuitries. Light–matter interaction enabled by
nanophotonics and plasmonics underlie the performance of the third- and fourth-generation
energy-conversion devices, including up- and down-conversion of photon energy, near-field
radiative energy transfer, and hot electron generation and harvesting. Finally, the increased
market penetration of alternative solar energy-conversion technologies amplifies the role of cost-
driven and environmental considerations. This roadmap on optical energy conversion provides a
snapshot of the state of the art in optical energy conversion, remaining challenges, and most
promising approaches to address these challenges. Leading experts authored 19 focused short
sections of the roadmap where they share their vision on a specific aspect of this burgeoning
research field. The roadmap opens up with a tutorial section, which introduces major concepts
and terminology. It is our hope that the roadmap will serve as an important resource for the
scientific community, new generations of researchers, funding agencies, industry experts, and
investors.
Keywords: optical energy conversion, light harvesting, solar technology, photovoltaics, solar cell
(
SQ1 Some figures may appear in colour only in the online journal)
Contents
1. Tutorial: thermodynamics of light and conventional limits of photon energy conversion 4
Photovoltaic technology: material and optical advances
2. The commercial push of silicon PVs to high efficiency 6
3. Optics and nanophotonics for Si cells and Si-based tandem cells 8
4. Photon recycling versus luminescence extraction for record PV efficiency 10
5. Quantum-confined semiconductor nanostructures for enhanced solar energy photoconversion 12
6. Challenges and advances in the fabrication of QD intermediate band SCs 14
7. Advanced materials for solar energy conversion 16
8. Going thin: atomic-layered 2D materials for photon conversion 18
2
J. Opt. 00 (2016)000000 Roadmap

PV and alternative technologies for the full spectrum harvesting
9. Plasmonics for optical energy conversion 20
10. Light rectification using an optical antenna and a tunneling diode 22
11. Full solar spectrum conversion via MJ architectures and optical concentration 24
12. Advanced solar concentrators 26
13. Spectral splitting and nonisothermal solar energy conversion 28
14. A path upward: new upconversion schemes for improving PVs 30
Thermal emission harvesting and radiative cooling for energy efficiency
15. TPVs: an alternative strategy for converting heat to electricity 32
16. Near-field radiative transfer in the energy-conversion schemes 34
17. High-temperature nanophotonics: from theory to real devices and systems 36
18. Endothermic-PL: optical heat pump for next generation PVs 38
19. Harnessing the coldness of the Universe by radiative cooling to improve energy efficiency and generation 40
20. Entropy flux and upper limits of energy conversion of photons 42
3
J. Opt. 00 (2016)000000 Roadmap

1. Tutorial: thermodynamics of light and
conventional limits of photon energy conversion
Svetlana V Boriskina
Massachusetts Institute of Technology
Thermodynamic properties of photon systems and their
interaction with matter define efficiency limits of light energy-
conversion schemes [1,2]. Photons can be uniquely char-
acterized by their energy wl=hc
,
momentum k,and
angular momentum, which, e.g., in the case of plane waves in
free space, defines light polarization (

p=h2is Planck’s
constant,
l
,
w
are the photon wavelength and angular fre-
quency, and
k
is the wave vector)[3,4]. In the interactions of
photons with matter—such as light emission or absorption—
the concept of temperature Tis introduced to account for
energy conservation. Some types of interactions, such as
fluorescent emission or Bose–Einstein condensation [5],
require adding a concept of photon chemical potential
m
to
account for the particle number conservation [6].
The photon density of states (DOS)defines the number
of states in the momentum space between
k
and +
k
kdper
unit volume and solid angle Wthat are available for a
photon to occupy in 3D space as: p=W
D
kk k kdd2
23
() ( )
(figure 1(a)). DOS as a function of photon energy is
expressed via the photon dispersion relation: w=
D
()
pw
w
W⋅⋅kk2dd
32
() () [3,4]. For plane waves of both
polarizations in an isotropic bulk dielectric with refractive
index
n
and pW=4, wp=
D
nc,
23 23low bulk photon DOS
is often a limiting factor in manipulating and enhancing
absorption and emission processes. However, as the DOS is
inversely proportional to the photon group velocity
u
w=-
kdd ,
g1
()
trapped modes with flat dispersion can have
DOS significantly exceeding that of bulk materials, especially
in the near field (see section 16)[7–12].
As gauge bosons for EM, photons obey Bose–Einstein sta-
tistics with the mean occupation numbers in thermal equilibrium
defined as wm wm=--
-
N
TkT,, exp 1 ,
B1
˜()((()))
where
kB
is the Boltzmann constant and
m
=0for blackbody
radiation (figures 1(a),(b)) [2–4]. The electromagnetic
energy density of radiation in a material per unit time and angle
is defined via the well-known Planck formula as
wwm ww=⋅ ⋅
U
NT D,, d()()
[1,2]. It can be tailored not
only just by the temperature as typical for the blackbody radia-
tion, but also by the photon DOS and
m
(see sections 13,15–19).
In turn, light intensity (power per unit area)is u=⋅
I
U
g[13]
(figure 1(b)). Integration of
I
over the whole frequency and
angular range yields optical energy flux through a unit surface
area per unit time, which, for the blackbody source at temperature
Tin free space, equals
s
T4(
s
is the Stefan–Boltzmann constant).
The ratio of light intensities in an absorbing medium and free
space defines the absorption limit, which, in the case of a bulk
dielectric with a backreflector and isotropic light escape, has a
well-known value of
n
4
2
[13,14]. However, high-DOS (sub-)
wavelength-scale absorbers can exceed this limit [10,11].They
can have absorption cross sections larger than geometrical ones
[9,15](see section 13)and, thus, feature higher than blackbody
emittance [16].
Light can also be characterized by the entropy of
photon gas with the entropy flux defined generally as S(T,μ)=
k
B
uw w⋅⋅+ +- WDNNNN1ln1 lndd
g
∬() [( ) ( ) ] [2,
17]. At the thermal equilibrium, the entropy reaches its max-
imum, and the photon occupation numbers obey the familiar
Bose–Einstein distribution, =
N
N
˜. The entropy flux of a
blackbody source equals s⋅T
4
3
,
3and this value decreases if
frequency and/or angular ranges shrink, tending to zero for a
monochromatic directional radiation (e.g., laser beam).The
introduction of the concept of photon entropy [17]helped to
resolve the controversy about the thermodynamic second law
violation in optical refrigeration (i.e., anti-Stokes fluorescent
cooling)[18,19]. It is also at the core of the efficiency limits of
thephotonenergyconversion[20].
Fundamental efficiency limits for conversion of
the photon energy into useful work stem from the laws of
thermodynamics and quantum mechanics. The conversion
efficiency of any photon energy-conversion platform
(figure 2(a)) can be calculated in a general form by
balancing the energy and entropy flows:
h
==-1
W
Is
+-+IT TST ST S .
Ira css ra g
1
s[( ) [ () ( ) ]]When both the source
and the absorber emit as blackbodies with
m
=0and no
entropy is generated in the engine, the above formula reduces
to the Landsberg efficiency [21], which represents an upper
Figure 1. (a)Photon DOS (red lines)in isotropic bulk dielectrics
(left)and dielectric thin films that act as thermal analogs of quantum
wells [10](right). Shaded gray areas: thermal distribution of photons
shaped by the electromagnetic (EM)potential. Insets: isoenergy
surfaces (contours)in the photon momentum space. Subwavelength-
scale particles, thin metal films, photonic crystals (PhCs), and
metamaterials also strongly modify the DOS [9], especially in the
near field [12].(b)Power flux spectra of solar photons as well as
photons emitted by the 1000 K blackbody probed in the far field
(black)and by a thin-film thermal well probed in the near field [10]
(blue). Although the Sun emits as a blackbody at T
s
∼6000 K, solar
power flux is reduced due to the small angular range of terrestrial
illumination and atmospheric attenuation.
4
J. Opt. 00 (2016)000000 Roadmap

limit of the solar energy-conversion efficiency. Landsberg
efficiency reaches maximum value at ==TTT
aec
(93.3% if
=T300
aand =T6000 K .
s)A more conventional Carnot
efficiency [22]
h
=-TT1ca
is obtained if there is no
radiative energy exchange between the source and the
absorber (95% if =TT
a
s
and =T300 K .
c)Both Landsberg
and Carnot limits assume complete reversibility, while
operation of realistic photon-conversion platforms involves
irreversible thermodynamic processes, such as photon
absorption and charge carrier thermalization, and is accom-
panied by entropy creation (see section 20). Absorption and
emission properties of realistic converters may also differ
significantly from those of a blackbody. Finally, operation at
the efficiency limit typically means that the power is extracted
infinitely slowly, while the maximum-power-out efficiency
can be found by solving hh=Wdd0() .
For example, maximum-power-generation efficiency of a
PV cell can be obtained from the general formula by
assuming entropy production in the cell due to charge carrier
thermalization with the crystal lattice as well as particle
number conservation and fluorescent emission with the che-
mical potential equal to the applied voltage (
m
=eV .)The
resulting limiting efficiency is known as the SQ limit [23,24],
which is shown in figure 2(b)for the case of a single-junction
power-conversion (PC)cell with a threshold absorption
energy corresponding to the width of the e band gap of the
cell material. It is also known as the detailed balance limit.
Higher efficiency has been theoretically predicted [25]for the
regime of operation when the photoexcited charge carriers are
extracted after they thermalize between themselves yet prior
to their thermalization with the lattice, which reduces entropy
creation (figure 2(b)). While hot-carrier photon energy con-
verters with high efficiencies have not yet been realized, there
is promising ongoing work in this direction that focuses on
quantum confinement effects and plasmonics (see sections 5,
6,9,13).
Concluding remarks
All practical realizations of photon energy converters operate
at lower efficiencies than their theoretical limits [26]due to
design and material imperfections (figure 2(b)). However, a
deep understanding of the origin and constraints of funda-
mental limits guides future research and development in the
area of light–energy conversion [27]. In particular, advanced
material developments and optimized optical designs have
recently propelled some technologies (e.g., GaAs PV cells
[28])to the brink of reaching their theoretical limits of
operation (sections 2–5), and there is still plenty of space at
the top of the efficiency scale (figure 2(b)). Many opportu-
nities still exist not only for material designers (see sections 3,
5–10,14), but also for optical scientists and engineers to
reach and to overcome the efficiency limits (see sections 2–4,
9–19). Novel optical concepts and schemes for light con-
centration, photon trapping, optical spectrum splitting, and
material emittance modification offer new insights and yield
new technological solutions for solar and thermal energy
harvestings. These insights will also benefit other fields, such
as solid state and advanced incandescent lighting, optical
refrigeration, waste heat harvesting, and radiative cooling just
to name a few.
Acknowledgments
The author thanks G Chen, W-C Hsu, and J K Tong for
helpful discussions.
Figure 2. (a)A general schematic of a solar energy converter. Blue
arrows—energy fluxes in the form of radiation (I)or heat (Q), red
arrows—corresponding entropy fluxes through the converter.
Irreversible entropy (S
g
)can be generated in the engine. (b)
Fundamental limits for photon energy-conversion efficiency. A
Shockley–Queisser (SQ)limit is plotted for an ideal single-junction
photovoltaic (PV)cell at T=300 K under one-sun illumination. For
the infinite number of PV junctions and full solar concentration, it
reaches 86.6% (dashed line)[24](see sections 11–13). The hot-
carrier efficiency limit [25]is shown for an ideal cell with an electron
(e)temperature of T=3000 K and a lattice temperature of
T=300 K under one-sun illumination.
5
J. Opt. 00 (2016)000000 Roadmap

2. The commercial push of silicon PVs to high
efficiency
Martin A Green
University of New South Wales
Status
Solar cells (SCs)seem destined to play a large role in the
future energy supply due to cell prices decreasing by a factor
of 8 since 2008 and the installed PV system capacity
increasing by a factor of 50 over the last decade. Overall
manufacturing costs are continuing to decrease by ~10%/
year due to a combination of decreasing prices of purified
polysilicon (Si)source material and Si wafers, increased
manufacturing volumes, and increasing energy-conversion
efficiency [29]. Increasing the latter efficiency not only
reduces costs per unit power rating by increasing power
output for a given investment in material and processing
costs, but also it similarly leverages transportation and
installation costs when the solar modules are subsequently put
into use.
The cell structure that has been produced in the highest
volume, to date, is the aluminum backsurface field (Al-BSF)
cell shown uppermost in figure 3[29,30]. A boron-doped, p-
type wafer presently about 180 μm thick is the starting point
in the manufacture of these cells. After cleaning and surface
texturing, these wafers are diffused with phosphorus to form
the n
+
region of a p–njunction. The metal contacts are then
screen printed with most of the rear covered by a screened Al-
based paste. During firing, this layer alloys with the silicon to
form an Al-doped p
+
region at the rear, known as the Al-BSF.
This fabrication sequence became the standard produc-
tion approach in the 1980s with over 200 GW of cells based
on this approach now deployed. Ongoing improvements in
the pastes and processing sequences used in cell fabrication
have seen steady increases in cell performance to the stage
where manufacturers can routinely manufacture cells in the
17%–18% efficiency range on multicrystalline substrates in
2015, increasing to 18%–19% on better quality mono-
crystalline substrates [29].
Current and future challenges
The performance-limiting feature of the cell has now become
the Al-BSF region. To progress past the 20% efficiency mark
in production, manufacturers are looking to high-efficiency
cell structures that overcome this limitation.
Advances in science and technology to meet
challenges
The challenge of increasing cell efficiency considerably
above 20% has been met by three vastly different cell struc-
tures also shown in figure 3that have all now demonstrated
efficiencies of 25% or higher in the laboratory [31]and are
being fabricated commercially in increasing volume.
The first to reach 25% efficiency [32]was the PERC
shown lowermost in figure 3,first reported in 1989 [33].
Although the most recent to be introduced into large-scale
commercial production, PERC cells have already established
the strongest commercial position (figure 4). In the structure,
the Al-BSF is replaced by a more sophisticated rear con-
tacting approach that not only reduces detrimental carrier
recombination at the cell rear, but also improves reflection of
weakly absorbed light reaching this surface. Industry con-
sensus is that, by 2020, the PERC cell will displace the Al-
BSF approach as the dominant commercial technology [29]as
indicated in figure 4. The strength of the technology is its
robustness, being suitable for improving performance of both
Figure 3. Commercial Si SCs. From top to bottom are shown the
standard Al-BSF cell, the heterojunction (HJT)cell, the rear-junction
(rear-J)cell and the passivated emitter and rear cell (PERC).
Figure 4. Industry consensus on the present and future market share
of the different Si cell technologies of figure 3(data extracted
from [29]).
6
J. Opt. 00 (2016)000000 Roadmap

low- and high-quality Si wafers, giving it an advantage over
the other two technologies to be described.
The second cell structure, reaching 25% efficiency in
2014 [31], is the rear-J SC, shown second lowermost in
figure 3. This structure was first suggested in 1977 [34]with
the first efficient devices reported in 1984 [35]. Close to
1 GW of these cells were sold in 2014 representing about
2.3% of the total market. The industry consensus is that this
market share is poised to increase, although this likely
depends upon the availability of high-quality monocrystalline
n-type wafers at lower cost than presently available [29]. The
cells have an unusual geometry where both polarity contacts
are located on the rear unilluminated cell surface. This has the
advantage of avoiding metal contact shading the front surface,
eliminating one of the obvious losses of traditional cells.
Since most light is absorbed close to entry at the top surface,
photogenerated carriers have to diffuse across the wafer to be
collected at the rear, making the structure suitable only for
good quality wafers.
The final cell structure to have given efficiency close to
25% is the HJT cell approach pioneered by Sanyo (now
Panasonic)[36], taking advantage of the company’s con-
siderable prior experience with hydrogenated amorphous Si
(a-Si:H)thin-film cells. The high atomic percentage of H in
the a-Si:H imparts properties completely different from
crystalline Si (c-Si)including a wider band gap (1.7 versus
1.1 eV)and electron affinity about 0.1–0.2 eV lower. An
important feature is the inclusion of a very thin layer of
undoped intrinsic a-Si:H between the c-Si wafer and the
oppositely doped a-Si:H layers deposited on either side of the
wafer. Given the higher band gap of the a-Si:H regions,
essentially all recombination occurs in the pristine c-Si wafer
or at its interfaces with the intrinsic a-Si:H layer. The latter
turns out to be very low, resulting in the highest open-circuit
(OC)voltage of any c-Si cell technology. Combining with the
rear-J approach recently increased record Si-cell efficiency to
25.6% [31,37].
Concluding remarks
These high-efficiency cell technologies will enable the
ongoing incremental improvement in commercial Si-cell
efficiency to the best laboratory values of ~25%, with 29% a
fundamental limit. The most likely route to allow significant
progress beyond this point is by going to a tandem cell
approach where a higher-band-gap cell is monolthically
integrated on top of the c-Si cell. Some recent success in this
direction has been obtained by combining with perovskite
SCs [38](see section 3), although the present lack of per-
ovskite cell stability prevents serious consideration for com-
mercial use. Some industry participants, however, rather
optimistically believe that such tandem technology may be
ready for commercial application by 2019 (figure 4).
Acknowledgments
The author acknowledges support by the Australian Gov-
ernment through the Australian Renewable Energy Agency
(ARENA), although the Australian Government does not
accept responsibility for the views, information, or advice
expressed herein.
7
J. Opt. 00 (2016)000000 Roadmap

3. Optics and nanophotonics for Si cells and Si-
based tandem cells
Kylie Catchpole
Australian National University
Status
Currently, about 90% of thePV market is based on c-Si SCs.
Si is the third most abundant element on Earth and has a near
ideal band-gap energy for maximizing the efficiency of a
single-junction SC. c-Si SCs have now exceeded efficiencies
of 25% in the laboratory, and Si modules have reached an
efficiency of over 22% (see section 2). In order to take
advantage of the decades of development of Si and massive
economies of scale that have been achieved, it makes sense to
push the technology to the highest efficiencies possible. To do
this, it is essential that optical losses are minimized. Even
when this has been achieved, however, Si SCs are limited to
an efficiency of about 27% by Auger recombination. Because
of this, there has been increasing interest in combining
emerging materials, such as perovskites with Si to form high-
efficiency tandems (see also sections 11,13). For such tan-
dems, sophisticated designs that minimize optical loss are
crucial in order to go beyond the break-even point and to
realize the potential of the high-band-gap material.
Optical loss mechanisms in SCs are due to reflection
from the front surface, incomplete absorption, escape from the
SC, and parasitic absorption. All of these need to be
addressed in order to reach the maximum efficiencies.
Incomplete absorption is important when the SC is thin
compared to the absorption length of light. This is relevant as
Si wafers become thinner in order to reduce costs and for
perovskite materials, which can have relatively low diffusion
lengths. Reflection control is necessary for all types of SCs
but is particularly important for multi-c cells where aniso-
tropic wet etching cannot be used to create pyramids.
Nanophotonics, which involves structures on the scale of
the wavelength of light, is an important approach in the
optical engineering of SCs because it allows a level of control
that cannot be achieved with conventional geometrical optics.
Nanophotonic techniques can be large area and potentially
cheap. To date, many different approaches have been used for
reducing reflection and increasing light trapping in SCs,
including etched surfaces, plasmonic nanoparticles and
reflectors, diffuse reflectors, and PhCs. For a more detailed
overview of this work, see [39].
Current and future challenges
The emergence of the perovskites has led to the possibility of
cheap tandem SCs with efficiencies higher than the limit for
single crystal Si.
In order to reach the potential of perovskite/Si tandems,
it is important to consider optical losses very carefully
(figure 5). A perovskite/Si tandem consists of a perovskite
SC with a top transparent conducting oxide (TCO)layer and
either a rear transparent conducting layer (for a four-terminal
tandem)or a tunnel junction (for a two-terminal tandem).
Currently, parasitic absorption in the TCO layer is about 10%
per layer. Together with reflectance losses, this means that we
can expect a loss of about 20% of sub-band-gap light with the
present technology. This leads to required top-cell
efficiencies of 18% at a band gap of 1.5 eV just to break even
and 23% to reach tandem efficiencies of 30% [40]. Reduction
of these losses would increase the efficiencies that are
achievable, making the technology more attractive for
commercialization.
Current challenges for the optical engineering of single-
junction Si cells are reflection control and incomplete light
absorption due to nonideal light trapping. Theoretically, iso-
tropic Lambertian light trapping can increase the current
density for a 100 μm thick Si SC from about 38 to
43 mA cm
−2
. Light trapping can also increase V
oc
by
increasing the internal intensity of light. However, improve-
ments in the randomization of light and surface passivation
are necessary before these improvements can be fully rea-
lized. One promising approach for extremely low reflectance
is ‘black Si,’produced by reactive ion etching or femtosecond
laser texturing. Achieving low reflectance together with low
recombination is generally a challenge, although, recently,
effective surface recombination velocities of less than
10 cm s
−1
and 1% solar weighted reflectance have been
reported [41].
A further challenge is integration of novel structures into
high-efficiency cells as cell fabrication has many inter-
dependent processes, and it is necessary that they be opti-
mized simultaneously.
Figure 5. Schematicof a four-terminal tandem cell on Si. (Inset)
Optical distribution of absorbed sunlight (AM1.5G)through the
complete tandem structure. From [43], reproduced with permission
from IEEE.
8
J. Opt. 00 (2016)000000 Roadmap

Advances in science and technology to meet
challenges
There are several major areas where advances in optics are
important in order to improve Si cells and Si/perovskite
tandems.
The first is the development of low-loss transparent
conductors. Candidate materials for reducing the loss are
graphene and nanophotonic structures (see section 8). There
has been some work done here with silver (Ag)nanowires
[42], but there is a great deal of scope for improvement using
controlled designs and different materials. Also note that
often the optimum combination of transparency and low
resistance loss can be achieved with a grid combined with a
transparent conductor, rather than a transparent conductor
alone [43].
For perovskite tandems, wavelength-selective light trap-
ping may provide a route to high efficiency as tandem effi-
ciencies greater than 30% are potentially possible with
diffusion lengths less than 100 nm. At an optimal top-cell
band gap of 1.7 eV, with diffusion lengths of current
CH
3
NH
3
PbI
x
Cl
1−x
perovskites, tandem efficiencies beyond
35% are potentially achievable, but this will require low-loss
TCOs and highly effective wavelength-selective light trap-
ping [44].
A third major area for improvement is light trapping for
Si cells. It is incomplete light trapping and reflection, rather
than parasitic loss, that are limiting current in Si SCs. Figure 6
shows some of the structures that have been used to provide
light trapping and reflection control in Si SCs. Metal nano-
particles in combination with a diffuse reflector can give
comparable light trapping to pyramids [45]. Both pyramids
and plasmonic particles give light trapping that is compatible
with currents of over 42 mA cm
−2
, but there is still scope for
an extra 1 mA cm
−2
. Even with plasmonic particles,
improving light trapping is more important than reducing loss
(see sections 9,13).
It is also worth pointing out what we do not need for
these particular applications. For example, there has been
quite a bit of work on exceeding the Lambertian limit for light
trapping. However, this is only of interest for very thin
structures (see section 8). For a 100 μm or thicker Si SC and
for perovskite SCs, there is no significant benefit in above
Lambertian light trapping.
Concluding remarks
The global PV market is worth about $100 billionand is
completely dominated by Si. The challenge here for optics is
to use our greatly improved ability to understand and to
engineer optical structures on the nanoscale to improve the
efficiencies of Si-based SCs to levels never before seen. There
are important near-term and longer trajectory opportunities
for both standard Si cells and the rapidly emerging Si-based
tandems as SCs continue to play an ever-increasing role in
our energy future.
Acknowledgments
I would like to thank my colleagues at ANU and, in part-
icular, T White, N Lal, and C Barugkin for their contributions
to the work described in this paper.
Figure 6. SEM images of various types of texture structures on Si:
(1)metal-assisted etched texture (side view);(2)reactive ion etched
texture (angle view);(3)random pyramid texture (side view), and (4)
plasmonic Ag nanoparticles on Si wafers (top view). Adapted from
[45], with permission from the Optical Society of America.
9
J. Opt. 00 (2016)000000 Roadmap

4. Photon recycling versus luminescence extraction
for record PV efficiency
Eli Yablonovitch
University of California, Berkeley
Status
There has been great progress in SC efficiency by the
recognition of the need for luminescent extraction from SCs,
which now reach 28.8% efficiency [26]in the flat-plate single
junctions. (This is to be compared [46]with the SQ [23]limit,
33.5% efficiency (see section 1).)The improvement is often
mistakenly attributed to photon recycling, but that is only a
special case of the real mechanism, luminescence extraction,
which can be present with or without photon recycling.
Challenges and advances in science and technology
The idea that increasing light emission improves OC voltage
seems paradoxical as it is tempting to equate light emission
with loss. Basic thermodynamics dictates that materials that
absorb sunlight must emit in proportion to their absorptivity.
At an OC, an ideal SC would, in fact, radiate out from the SC,
a photon for every photon that was absorbed. Thus, the
external luminescence efficiency is a gauge of whether
additional loss mechanisms are present. At the power-opti-
mized operating bias point, the voltage is slightly reduced,
and 98% of the OC photons are drawn out of the cell as real
current. Good external extraction at the OC comes at no
penalty in current at the operating bias point.
On thermodynamic grounds, Ross derived [47]that the
OC voltage is penalized by poor external luminescence effi-
ciency η
ext
as
h=-qV qV kT ln , 1
OC OC ideal ext
|| ()
-
where η
ext
is the probability of an internally radiated photon
eventually escaping from the front surface of the cell.
Equation (1)can be derived through the detailed balance
method [46]of SQ.Green already inferred [48]the external
luminescence yield η
ext
of all the different historical SC
materials from their respective record {V
OC-ideal
—V
OC
},
employing equation (1).
As solar efficiency begins to approach the SQ limit, the
internal physics of a SC transforms. SQ showed that high
solar efficiency is accompanied by a high concentration of
carriers and by strong fluorescent emission of photons. Pho-
tons that are emitted internally are likely to be trapped,
reabsorbed, and re-emitted, i.e., photon recycling, which can
assist the external luminescent emission at the OC. Alter-
nately, surface texture on the SC, often added for absorption
enhancement, equally will lead to external luminescence
extraction by random scattering, not requiring photon recy-
cling at all. These two distinct mechanisms were first identi-
fied by Lundstrom [49].
The requirement for efficient luminescence extraction is
accompanied by many suns of trapped internal luminescence
in high index, high-efficiency SCs, and >26% efficiency as
illustrated in figure 7:
To resolve the paradox of why external luminescence is
good for SC efficiency, there are a number of different
explanations:
1. Good external luminescence is a gauge of few internal
loss mechanisms. At an OC, an ideal SC radiates a
photon for every absorbed photon. When e–hole (e–h)
pairs recombine nonradiatively or when photons are
absorbed without generating photocarriers within the
active part of the device, both the external luminescence
efficiency and the cell efficiency decrease.
2. In a rate equation analysis, external emission of photons
into free space is unavoidable. All other losses can, in
principle, be eliminated. Thus, the total losses are at
their very least when external emission is the only loss
mechanism. Maximum external emission is minimum
total losses, which leads to the highest efficiency.
3. In untextured cells, good external luminescence
requires recycled photons and reabsorption. Internal
reabsorption recreates the e–h pair, effectively extend-
ing the minority carrier lifetime. The longer lifetime
leads to a higher carrier density. Free energy, or voltage,
increases with the logarithm of density.
4. The SC and the light-emitting diode are equivalent
but reciprocal devices. Just as external emission leads to
the most efficient light-emitting diode, the reciprocal
device also benefits when there are no other loss
mechanisms.
Figure 7. The physical picture of high-efficiency SCs, compared to
conventional cells. In high-efficiency SCs, good luminescent
extraction is a requirement for the highest OC voltages. One-sun
illumination is accompanied by up to 40 suns of trapped infrared
(IR)luminescence, leading to the maximum external fluorescence
efficiency. Reproduced from [46]with permission of IEEE.
10
J. Opt. 00 (2016)000000 Roadmap

5. External luminescence is sometimes used as a type of
contactless voltmeter, indicating the separation of quasi-
Fermi levels in the solar material. This is sometimes
employed as a contactless, quality-control metric in SC
manufacturing plants. In this viewpoint, it is tautologi-
cal: Good external luminescence actually IS good
voltage and, therefore, good efficiency.
This is the preferred explanation for the paradox: Good
external luminescence IS good voltage.
Concluding remarks
Counterintuitively, efficient external luminescence is a neces-
sity for achieving the highest possible SC efficiency. Why
would a SC, intended to absorb light, benefit from emitting
light? Although it is tempting to equate light emission with
loss, paradoxically, light emission actually improves the OC
voltage and the efficiency. The voltage boost generally arises
from luminescence extraction for which photon recycling is
only one possible mechanism, or extraction by surface textur-
ing is the other possible mechanism, [49].
11
J. Opt. 00 (2016)000000 Roadmap

5. Quantum-confined semiconductor
nanostructures for enhanced solar energy
photoconversion
Matthew C Beard
National Renewable Energy Laboratory
Status
New PV technologies should have the potential to achieve PC
efficiencies (PCEs)beyond ∼33% as well as to reduce
module costs. In 1982, Ross and Nozik determined that the
PCE of unconcentrated solar irradiance into electrical or
chemical free energy could be as high as ∼66% for a single-
junction solar converter when the excess kinetic energy of
photogenerated e–h pairs is harnessed without allowing it to
dissipate as heat [25]. Excess energy arises from carriers
that are generated with photon energies greater than that of
the semiconductor band gap. Semiconductor nanostructures
where, at least, one dimension is small enough to produce
quantum confinement effects, provide new pathways for
energy management and have the potential to increase the
efficiency of the primary photoconversion step so as to
approach the Ross–Nozik limit (see sections 6,8,9,13).
Multiple exciton generation (MEG), also called carrier
multiplication, is a process where charge carriers with suffi-
cient excess kinetic energy expend that energy via excitation
of additional e–h pairs instead of dissipating the excess
energy as heat. In bulk semiconductors, the latter process is
limited by both momentum and energy conservation. In
quantum-confined nanocrystals, or quantum dots (QDs),itis
only limited by energy conservation. Thus, a MEG-active SC
with nanocrystals could achieve a PCE of ∼44% at one sun
and ∼85% under full concentration [50].
In 2004, Schaller and Klimov developed a method of
measuring the number of e–h pairs produced per absorbed
photon in colloidal QD samples using ultrafast transient
absorption spectroscopy [51]. The QD system of PbSe and
PbS has received the most attention and is used to benchmark
the prospects for quantum-confined nanostructures. The MEG
process is enhanced by a factor of ∼3 going from bulk PbSe
to quasispherical PbSe nanocrystals (figure 8). Further
enhancements have been observed with more complex
nanostructures, such as quantum rods (QRs)[52], quantum
platelets (QPs)[53], and nanoheterostructures [54].
Incorporating QDs into solar energy-conversion archi-
tectures is an active area of research [55]with current efforts
now approaching a PCE of 10%. These approaches employ
electronically coupled QDs in films, allowing for transport of
electrons and holes within QD layers to their respective
electrodes. In 2011, Semonin et al fabricated a PbSe QD SC
that achieved an external quantum efficiency (QE)exceeding
100% for high-energy photons [56]. This result demonstrated
that QD-based SCs have the potential to bypass the SQ limit
and to approach the Ross–Nozik limit.
Current and future challenges
When MEG is in competition with other exciton cooling
mechanisms, the number of e–h pairs generated per absorbed
photon (QY)can be expressed as [57]
=+
+
+
++
+
QY k
kk
kk
kkkk
1
,
MEG
1
MEG
1cool
MEG
1
MEG
2
MEG
1cool MEG
2cool
()
()()
()
()
() ()
() ()
where
k
i
MEG
() is the rate of producing (i+1)excitons from (i)
hot excitons and
k
cool is the exciton cooling rate via heat
generation. The ratio of
k
MEG and
k
cool can be characterized
by a parameter P(figure 8).Pincreases from ∼0.5 for bulk
PbSe to 1.6 for PbSe QDs and further increases to ∼2.3 for
nanoheterostructures [54]and QRs [52].
In the case where only energy conservation limits MEG
and Pis large, two e–h pairs could be produced with photons,
whose energy is twice the semiconductor band gap (2E
g
),
three at 3E
g
, four at 4E
g
, etc (black staircase line in figure 8).
In bulk PbSe, the onset for producing multiple carriers per
absorbed photon is ∼6.3E
g
and to produce two e–h pairs
requires ∼11.5E
g
(figure 8, gray squares). The onset energy
and the QY are related and can be combined to calculate an
MEG efficiency. For bulk PbSe, the MEG efficiency is ∼0.19.
For PbSe QDs, the MEG efficiency increases to ∼0.5,
showing a decrease in the onset energy to ∼3E
g
and pro-
duction of two e–h pairs when the photon energy reaches
∼6E
g
(figure 8, blue squares). Future research should
Figure 8. Case study for PbSe (bulk versus nanostructured
components). The number of e–h pairs produced from absorption of
a single photon at a scaled energy. The gray squares are for bulk
PbSe, the blue squares are for PbSe QDs, and the orange circles are
for PbSe/CdSe hetereostructures.
12
J. Opt. 00 (2016)000000 Roadmap

determine systems that can further approach the staircase
characteristics.
The thermodynamic PCE limit of SCs is a function of P
(figure 9). For example, the PCE limit is ∼44% when Pis
large and 39% with a Pof 100. These conditions should be
achievable within suitably designed quantum-confined
nanostructures. For example, recent efforts within Si nanos-
tructures suggest that such high MEG efficiencies are
achievable [58].
Advances in science and technology to meet
challenges
Semiconductor nanocrystals offer many avenues toward
increasing the MEG yields through internal and external
modifications. To achieve the largest benefit, one should
either look for systems that can reduce
k
cool or can increase
k
.
MEG Within the Fermi-golden-rule approximation,
k
MEG
depends upon two factors: (1)the density of final biexciton
states
r
fand (2)the Coulomb matrix element
W
.
cTo achieve
improvements in these characteristics, researchers are
exploring several options: (1)multicomponent systems where
either the e or the h experience slowed cooling that allows for
a greater probability of undergoing MEG. Multicomponent
systems may also increase
W
c
by breaking the spherical
symmetry and, thereby, decreasing carrier screening effects.
Enhanced MEG in QRs and QPs can also be ascribed to such
a breaking of spherical symmetry. (2)New low-band-gap
semiconductor systems. A good place to start is those systems
with known low e–phonon coupling strengths and/or are
semimetals in bulk form (such as HgTe, graphene, and bSn-)
but whose band gap can be tuned via quantum-confinement
effects. (3)Matrix-QD coupling effects that can achieve slo-
wed cooling and/or higher
W
c
[59].
In order to identify new systems with enhanced MEG
characteristics, researchers should develop new faster and
more robust means of testing for MEG as well as a theory to
predict promising systems for exploration. Currently, the
most used approach for measuring carrier yields is based upon
ultrafast transient absorption or photoluminescence (PL)
spectroscopy [51,57]. Both techniques are laborious and are
prone to experimental errors, and, thus, great care must be
taken in order to extract the photon-to-carrier quantum yield
[57]. SC architectures where current is measured are prefer-
able [56]. Developing a QD SC from QD systems can be time
consuming, and, thus, knowing whether high MEG yields are
possible prior to undertaking such an endeavor is necessary.
Developing device current-based approaches for mea-
suring enhanced light to current yields but which are less
complex than a SC should be pursued. For SCs, the basic
strategy is to sandwich a QD layer between an n-type window
layer, which accepts electrons while blocking holes, and a
metal electrode that accepts holes. Light is absorbed in the
QDs, and excitons separate to form free electrons and holes.
Critical issues that need to be addressed are robustness of QD-
layer formation and optimization of the front and back
interfaces. Adapting such architectures for fast and reliable
MEG measurements would benefit the search for systems
with enhanced MEG characteristics.
Concluding remarks
QD SCs remain a promising technology for inexpensive,
scalable, and efficient SCs. Such semiconductor nanos-
tructures are synthesized in solution phase chemical reactions
where the reaction conditions can be modified to produce a
variety of shapes, compositions, and structures. Thanks to
their size, surface tunability, and solution processing, it
should be possible to find systems that enable inexpensive
and highly efficient devices from QD-based inks. Surpassing
the SQ limit for a single-junction solar converter system is a
scientific and technological challenge with a significant ben-
efit to society. The challenge is to increase the MEG effi-
ciency to approach the energy conservation limit.
Acknowledgments
Support from the Solar Photochemistry program within the
Division of Chemical Sciences, Geosciences, and Biosciences
in the Office of Basic Energy of the Department of Energy is
acknowledged. DOE funding was provided to NREL through
Contract No. DE-AC36-086038308.
Figure 9. (a)Detailed balance calculations for various values of P.
(b)Nanostructures allow for control of various relaxation channels.
(c)QD SC illustration. Reprinted with permission from Acc. Chem.
Res., 2013, 46, 1252–1260, Copyright 2013 American Chemical
Society.
13
J. Opt. 00 (2016)000000 Roadmap

6. Challenges and advances in the fabrication of QD
intermediate band SCs
Yoshitaka Okada
The University of Tokyo
Status
The QD intermediate band SCs (QD-IBSCs), which com-
monly suffer from small absorption and low density of QDs,
result in a drop of V
OC
. However, V
OC
and, hence, the effi-
ciency recover fast, and cell performance improves with
concentrated illumination of sunlight [60]. Current QD-IBSCs
require light concentration to ensure that the photogeneration
rate outperforms the recombination rate via IB states. The
areal density of QDs has a direct influence on the generation
and recombination processes via the IB because the DOS of
the IB (N
IB
)is linked to the areal density as
N
IB
=N
areal
×N
stacks
/W, where N
areal
is the areal density of
the QD array, Wis the intrinsic QD region width, and N
stacks
is the number of QD stacks.
Assuming an energy band gap of E
g
=1.40 eV for the
GaAs host material, the generation and recombination rates
for the widely studied InAs/GaAs QD-IBSC with different
positions of the IB can be calculated based on the detailed
balance theory as shown in figure 10 [61]. Here, the QD areal
density corresponds to the total QD density given by
N
areal
×N
stacks
. The absorption cross sections are taken as
3×10
−14
cm
2
for both optical transitions between the
valence band (VB)to the IB and the IB to the conduction
band (CB). It can be clearly seen that, if the QD areal density
is below 1×10
16
cm
−2
, the net generation rate G
net
becomes
negative with deepening the location of the IB in the QD
region.
The highest areal density of InAs QDs on GaAs
experimentally demonstrated, to date, is ∼1×10
12
cm
−2
[62], which means that the recombination rate would dom-
inate over the photogeneration rate under one sun as from
figure 10. However, the situation will significantly improve if
the cell is under light concentration. Figure 11 shows the
dependence of net generation rate G
net
on the concentration
ratio for the case of the IB being located at 0.2 eV below the
CB edge. It shows that G
net
turns positive after 10 suns. When
the concentration exceeds 1000 suns, a positive G
net
value can
be expected even for the QDs areal density of 1×10
12
cm
−2
,
and the simulation results are consistent with the experimental
results reported in literature [63,64].
Current and future challenges
In the last decade, there has been an extensive effort to
demonstrate QD-IBSCs with high efficiency. The QDs are
required to be homogeneous and small in size and to be
regularly and tightly positioned in the active region of the cell
in order to form an IB or a superlattice miniband that is well
separated in energy from the higher-energy states [65]. Fur-
thermore, dense QDs arrays are required to achieve sufficient
photoabsorption resulting in a positive G
net
. The most com-
monly used fabrication method of QD structures is to utilize
spontaneous self-assembly of coherent 3D islands in lattice-
mismatched heteroepitaxy, the Stranski–Krastanov (S–K)
growth mode in molecular beam epitaxy or metal organic
vapor phase epitaxy. The InAs/GaAs material system has a
lattice mismatch of 7.2%, and the strain induced by this lattice
Figure 10. Detailed balance calculation of the dependence of net
generation rate from the IB to the CB, G
net
on InAs QDs density, and
the IB energy position relative to the CB band edge. Reproduced
with permission from [61].
Figure 11. Detailed balance calculation of the dependence of G
net
on
concentration ratio. The IB is located at 0.2 eV below the CB edge.
Reproduced with permission from [61].
14
J. Opt. 00 (2016)000000 Roadmap

mismatch drives into 3D coherent S–K growth after formation
of a thin 2D InAs wetting layer in the initial growth stage. The
typical areal density of InAs QDs achieved by the S–K mode
is N
areal
=10
10
–10
11
cm
−2
grown on the GaAs (001)sub-
strate. However, the size is still large, and the density is much
less than what is required. The QD sizes and density are
dependent on the growth conditions, such as the V/III flux
ratio, substrate orientation, growth temperature, and material
used for the buffer layer. The areal density of the QDs is
increased by irradiating Sb to the buffer or wetting layer, and
Sakamoto et al have recently demonstrated N
areal
=1×
10
12
cm
−2
[62].
For further increasing in the total QDs density, the fab-
rication of a multistacking configuration is necessary. One has
to consider that a gradual buildup of internal lattice strain with
an increased number of stacking leads to an increase in both
the size and its fluctuation for the multistacked QDs grown by
S–K growth. In addition, the strain accumulated above the
critical thickness generally results in a generation of misfit
dislocations, which occurs typically after 15–20 layers of
stacking in the case of InAs/GaAs QD growth. Recently,
Sugaya et al have demonstrated stacking of In
0.4
Ga
0.6
As/
GaAs QDs fabricated by an intermittent deposition technique
[66]. The critical thickness of the In
0.4
Ga
0.6
As/GaAs system
is much thicker than that of the InAs/GaAs system, and no
dislocations are generated even after stacking up to 400
In
0.4
Ga
0.6
As QD layers.
Meanwhile, tensile-strained barriers have been studied in
order to compensate for the compressive strain induced by the
QD layers. This growth method is called the strain-compen-
sation or strain-balanced technique, and, to date, InAs QDs in
an AlGaInAs matrix on an InP substrate, InAs QDs in GaAsP,
in a GaP matrix on a GaAs substrate, and InAs QDs in
GaNAs on GaAs (001), and on (311)B substrate of high
material quality have been reported [67].
Advances in science and technology to meet
challenges
The IBSC concept shown in the inset of figure 10 represents
the optimal cell configuration under maximum solar con-
centration. However, practical SCs operate at lower solar
concentrations, usually below ∼1000 suns, and there is an
efficiency advantage to be gained by introducing a relaxation
stage. The principle is that the optical transitions between this
relaxed IB, or so-calledratchet band (RB)and a VB are
critically forbidden, hence, the only route for relaxation via
the IB now involves surmounting a potential barrier from the
RB to the VB. The fundamental efficiency benefit of relaxa-
tion has also been recognized in up-converting (UC)systems
that rely upon sequential absorption. To date, a molecular
system [68]and a ferromagnetic dilute magnetic system [69]
promoting this scheme have been proposed.
The carrier lifetime in the IB also directly influences the
conversion efficiency of QD-IBSCs. The detailed balance
calculations for the case of ideal IBSCs often neglect the
effect of nonradiative lifetime. However, QDs have a finite
nonradiative lifetime and could affect the photogeneration
rate because they act as recombination centers just as
absorption levels. The carrier lifetime and, hence, the effi-
ciency is influenced by the carrier recombination strength,
thermal escape, and the tunneling escape rates out of QDs. A
long carrier lifetime is obtained by controlling the recombi-
nation rate using a type-II QD heterostructure, using a high
potential barrier preventing the thermal carrier escape from
QDs, and by introducing an electric field damping layer
preventing the field-assisted tunneling out of the QDs. Fur-
thermore, introducing a RB into the SC assists with the pro-
blem of maintaining long carrier lifetime. Assuming that the
VB–IB transition is direct and allowed, a typical carrier
lifetime in an IB on the order of 10 ns can be assumed.
Assuming a Boltzmann statistics for the carrier distribution,
introducing the relaxation step of ΔE(between the IB and the
RB)could increase the lifetime by a factor of exp
(ΔE=k
B
T). This effect is responsible for intermediate-state
lifetimes on the order of 100 μs measured in some molecular
UC systems.
Concluding remarks
Significant effort and rapid progress have been made in the
device physics as well as practical demonstration of high-
efficiency IBSCs. These achievements have been possible due
to mature and highly uniform III–V QDs, nanostructure
material growth, and processing technology. For this, the
demonstration of QD-based IBSCs is presently undergoing
three main stages. The first is to develop technology to fab-
ricate high-density QD arrays or superlattices of low defect
densities and long carrier lifetimes. The strain-compensated or
strain-balanced growth technique significantly improves the
QD material quality and characteristics of SCs even afterthe
stacking of 100 QDs layers or more in S–K growth. The
second is to increase the carrier lifetime in IB states by
controlling the recombination rate using a type-II QD het-
erostructure, a high potential barrier preventing the thermal
carrier escape from QDs, and an electric field damping layer
preventing the field-assisted carrier escape. Furthermore,
introducing a RB into the SC assists with the problem of
maintaining long carrier lifetime. The last is to realize ideally
half-filled IB states to maximize photocurrent generation by
two-step photon absorption. The doping of the IB region,
photofilling by light concentration, and photon confinement
structures are all considered important.
In addition to further improvements in the material
quality, the control of absorption matching in IB materials is
expected to improve the efficiency of QD-IBSCs in the near
future (see also sections 5,14).
15
J. Opt. 00 (2016)000000 Roadmap

7. Advanced materials for solar energy conversion
Stephan Lany
1
, Talia Gershon
2
, and Andriy Zakutayev
1
1
National Renewable Energy Laboratory
2
IBM T J Watson Research Center
Status
The PV market, dominated by c-Si technologies, has seen
remarkable cost reductions in recent years. The current module
cost of 0.5–0.7 $/W should translate into 5–10 ¢ kWh
−1
electricity prices after further reductions in the balance of
system and soft costs. However, recent macroeconomic ana-
lysis [70]suggests that the scaling to and beyond the terawatt
(TW)level will depend strongly on the rate of future capital
investment in manufacturing capacities (see section 2). Poten-
tial barriers toward multi-TW-scale PV include the relatively
large capital expenditures (capex)for PV grade Si production
as well as supply limitations of Te and In for CdTe and Cu(In,
Ga)Se
2
beyond the TW scale. The scalability challenge
becomes an even bigger one if aiming for both electricity and
fuel generation by solar energy conversion.
The development of new PV technologies based on novel
advanced materials could create a new industry with inde-
pendent supply chains, foster market diversification, and
attenuate market volatility and, thereby, enhance the odds for
beyond-TW scaling of solar energy production (see also
section 8). Such disruptive PV technologies must be com-
petitive with current technologies in efficiency, cost, and
reliability, and they must use readily available elements [71],
but they also have to be compatible with low-capex produc-
tion processes to ensure rapid industry growth after initial
commercialization.
Over the past decade, considerable research effort has
addressed alternative approaches, including dye sensitized cells
and organic and inorganic PVs. Particularly noteworthy are the
Cu
2
ZnSn(S,Se)
4
kesterites [72]as well as the hybrid methyl-
ammonium lead-halide perovskites that have reached SC effi-
ciencies above 20% in just a few years of research and
development [73]. We note, however, that both systems must
still overcome significant hurdles (e.g., performance and sta-
bility)before they will become commercial. Beyond the further
development of such individual materials systems, the Mate-
rials Genome Initiative provides a framework for broader
search, design, and discovery of materials for PVs, solar fuel
generation, and a wide range of other applications [74].
Current and future challenges
In order to identify promising and under-explored PV mate-
rials worthy of future development, the band gap and the
optical absorption strength are often used as a first selection
criterion [71]. Despite being good screening metrics to
quickly winnow out unfeasible candidates, there are many
additional material criteria needed to be fulfilled beyond the
band gap and optical properties. The absorber material must
have high carrier mobilities, particularly for minority carriers,
low densities of detrimental point or extended defects (e.g.,
grain boundaries)that can accelerate recombination and can
limit minority carrier lifetimes, as well as a high level of
control of the electrical doping to enable formation of p–n
junctions with a suitable depletion width.
Besides Si and epitaxial III–V systems, there are few
known bipolar dopable semiconductors that could be suitable
for p–nhomojunction PVs. Therefore, most thin-film SCs use
a HJT with two different materials (see figure 12): typically, a
p-type absorber and an n-type contact. In this configuration,
the quality of absorber/contact heterointerface becomes cru-
cial for achieving high-efficiency cells, i.e., it should have low
interface defect densities and a small CB offset. Considering
that the interface at the backcontact can also play a role in
device performance, it is clear that the development of a new
PV technology must address the entire device structure, not
just individual absorber and contact materials.
A significant number of potential inorganic absorber
materials has been suggested and has been studied in recent
years, including Zn
3
P
2
,Cu
2
SnS
3
, WSe
2
,Cu
2
S, ZnSnN
2
,
FeS
2
, BiFeO
3
,Cu
2
O, SnS, and Sb
2
Se
3
. However, solving all
of the above-mentioned bulk transport and interface issues
under the constraints of a limited choice of elements (avail-
ability, cost, and toxicity), processing considerations, and
anticipated production cost, remains a huge challenge. In
particular, this task requires a balance between sufficient
breadth and depth; we must address all requirements on the
materials’bulk and interface properties while, at the same,
time screening a large number of materials including uncon-
ventional and unsuspected candidates that might have been
overlooked before. Furthermore, the search should not only
enumerate the possible stoichiometric binary, ternary, and
multinary compounds, but also include the possibility to
design desirable properties through deliberate variation of the
composition, such as in the case of semiconductor alloys.
Considering the vastness of the full phase space of compo-
sitions and process parameters, it is clear that the traditional
way of case-by-case studies is too time consuming. Thus, new
research approaches (outlined below), and arguably new
funding mechanisms are needed to bridge the wide gap
between basic materials science and the commercialization of
new TW-scalable PV technologies.
Figure 12. (a)Schematics of a SC structure; (b)band diagram
illustrating some of the material issues, i.e., doping, band offsets, and
defect states.
16
J. Opt. 00 (2016)000000 Roadmap

Advances in science and technology to meet
challenges
In order to be successful, the research has to span the entire
PV development cycle: from broad materials exploration, to
targeted research on individual materials, and to device inte-
gration and testing. This formidable task can be accomplished
by the complementary use of computational materials science
and synthesis/characterization/analysis. Besides accelerating
the development cycle of investigations via high-throughput
and combinatorial approaches for both computations and
experiments, the research strategy should also include in-
depth studies of the underlying materials science to distill
composition–structure–property relationships and to for-
mulate design rules. For example, the need for low-cost
synthesis routes increases the need for ‘defect tolerant’
materials, i.e., materials that maintain favorable electronic
properties, despite the presence of structural defects, disorder,
or impurities [75].
Computational advances
High-throughput computing has enabled the creation of
databases for structural, mechanical, thermodynamic, magn-
etic, and electronic properties [76]. The capability of quasi-
particle energy calculations in the GW approximation is now
implemented in several electronic structure codes. Although
limitations and challenges remain, particularly, for more
complex systems, the reliable GW prediction of band gaps
and optical properties is now in reach for a broad range of
materials. Supercell calculations, which are traditionally
employed to describe doping and defects in the dilute limit,
can now be extended to the case of aliovalent alloys, allowing
the prediction of both band gaps and doping as a function of
composition [77], as illustrated in figure 13(a)for the case of
Cu
2
O-based alloy absorbers.
Experimental advances
Combinatorial experiments have traditionally been used to
screen large elemental composition variations for their
intrinsic properties, such as crystal structure and absorption
spectra. Recent advances in the combinatorial methods allow
the deposition and analysis of ‘libraries’with a gradient in
both composition and growth temperature, thereby enabling a
high-throughput exploration of the phase space (see
figure 13(b)as an example for ZnO:Ga contact [78]). Finally,
combinatorial optimization of multilayer PV devices is now
possible [79], implicitly taking into account the interaction
effects of individual material layers at their interfaces,
including band offsets and interdiffusion.
Future needs
Further development of computational capabilities would be
desirable for the routine calculations of electron and hole
mobilities and minority carrier lifetimes, which would enable
device modeling based on computational parameters. In order
to assess the electronic properties of the interface at HJTs, it
would be of high importance to establish theoretical methods
for generating structural models of nonepitaxial interfaces.
Development of faster and more accurate experimental
methods for measuring the lifetimes of the photoexcited
charge carriers and for determining band offsets at hetero-
interfaces is equally important. Additional research needs
are the improved understanding of nonequilibrium effects
in thin-film deposition and the implications on the defect
densities.
Concluding remarks
Many promising PV materials remain undiscovered or
underexplored due to the lack of information regarding their
optoelectronic, structural, and intrinsic defect properties.
Individual experiments exploring one composition at a time
could consume years of effort before the system is fully
understood. Reducing this time is, therefore, of paramount
importance. Improvements in computational and exper-
imental techniques are accelerating the screening of the fun-
damental optoelectronic and defect tolerance characteristics at
the individual material level. This information is invaluable
for down-selecting systems worthy of a more targeted
development. Future approaches for developing new PV
technologies will consider more specifically kinetic limita-
tions during deposition and the structure and electronic
properties of interfaces, which are crucially important for
integrating individual materials into high-efficiency devices.
The feedback between computational and experimental
approaches will significantly reduce the time needed to
achieve disruptive materials discovery for TW-level PV
production in the future.
Acknowledgments
S.L. and A.Z. are supported by the U.S. Department of
Energy, Office of Energy Efficiency and Renewable Energy
(DOE-EERE)under Contract No. DE-AC36-08GO28308 to
NREL. T.G. is supported by DOE-EERE under Award No.
DE-EE0006334.
Figure 13. (a)Calculated composition dependence of band gaps and
doping in Cu
2
O-based alloy absorbers [77].(b)Measured electrical
conductivity of combinatorial libraries for a ZnO:Ga contact as a
function of temperature and O partial pressure [78].
17
J. Opt. 00 (2016)000000 Roadmap

8. Going thin: atomic-layered 2D materials for
photon conversion
Mohammad H Tahersima and Volker J Sorger
George Washington University
Status
The field of atomically thin 2D materials has grown rapidly
over the last few years since it exhibits nonclassical phe-
nomena. The field of atomically thin 2D materials has grown
rapidly over the last few years since they exhibit non-classical
phenomena, diverse electronic properties, and can cover a
wide range of electromagnetic spectrum (see figure 14). The
well-studied carbon material, graphene, is characterized by an
absence of a band gap (for monolayers)[80]. This is relevant
for photon absorption since, unlike semiconductor materials,
this band structure is spectrally not band-edge limited, thus,
enabling broadband absorption. Transition-metal-dichalco-
genides (TMDs), however, do have a band gap and have been
found to be stress and composition band-gap tunable [81].
The band gap (0.8 eV)of black phosphorous matches that of
the telecom c-band (1550 nm)and, hence, could find appli-
cations in photoreceivers [82].
Taking a closer look at one material system (MoS
2
)
reveals some unexpected properties relating to interactions
with light; the band structure of MoS
2
transforms from being
an indirect band gap (1.2 eV)for bulk material to a direct
band gap (1.8 eV)for single layers, which is accompanied by
a10
4
-fold PL enhancement [81]. Unlike in classical physics
where the optimum thickness of an absorber is given by the
imaginary part of the permittivity, 2D materials behave quite
differently. For instance, the photodetection can be tuned for
different wavelengths where single- and double-layer MoS
2
absorbs green light, while triple-layer MoS
2
, which is less
than a nanometer thicker absorbs in the red visible spectrum
[83]. Such thickness-modulated absorption in conjunction
with their relative earth abundance open up prospects for
atom-thin 2D material-based multijunction (MJ)SCs that
capture photons from the visible to the near IR.
Heterostructures, such as MoS
2
/graphene or MoS
2
/WS
2
,
have shown that a layer as thin as 1 nm is able to absorb 5%–
10% of the incident light [84]. This is an order of magnitude
higher compared to the same thickness of GaAs or Si and
might translate into 1–3 orders of magnitude higher power
densities than the best existing ultrathin SCs. The origin for
this is found in the electronic DOS, which exhibits peaks
known as Van Hove singularities.
With intriguing prospects for 2D material-based photon-
conversion applications, a variety of fundamental challenges
need to be overcome and to be investigated as discussed next.
Current and future challenges
For instance, these atom-thin materials are rather sensitive to
surface charges, neighboring materials, and stresses. While
such sensitivity can be exploited (if properly controlled)to
achieve higher functionality, the field is still in the exploratory
phase. Improvements are needed from fundamental band
structure engineering to control of chemical synthesis and
material processing.
Although semiconducting TMDs exhibit high absorption
coefficients, TMD-based PV cells with superior PV perfor-
mance have yet to be demonstrated. This is because a
monolayer material has obvious physical thickness limitations
and is mostly transparent at visible frequencies. Furthermore,
in order to obtain a reasonable photocurrent and voltage for
PV applications, stacked multilayer devices might be needed.
This, however, demands a clear understanding and control of
the interface physics and might encompass novel structures to
increase the light–matter interaction or processing approaches
to create built-in potential in multilayers, such as via plasma
doping.
An exciting avenue for 2D materials is the controlled
introduction of strain, which offers the flexibility in con-
trollable and potentially tunable functionality for device
engineering; strain reduces the crystal symmetry, leading to
significant shifts in the energy band edges, which changes the
electronic and optical properties of the material.
Regarding e transport and field effect transistor devices,
monolayer TMDs have shown low electronic mobility. For
instance, the value for single-layer MoS
2
is about 2 orders of
magnitude lower compared to that of bulk. In this regard, a
complete understanding of the microscopic picture for the e
transport in monolayer or few-layer TMD films remains
unclear.
Regarding the synthesis of TMD sheets, low-temperature
approaches and catalyst-free synthesis are highly desirable for
practical applications. However, to date, no practical method
for the large-scale, defect-free, and scalable production of
TMD sheets with fine control over the number and the
structure of the layers over the entire substrate has been
developed. If successful, however, it would dramatically
accelerate the production and deployment of these materials
in photon-conversion industries, such as for PV. However,
even if the synthesis is mastered, techniques for transferring
large-scale TMD sheets also need to be developed since direct
growth often conflicts with temperature budgets.
Advances in science and technology to meet
challenges
Addressing the low photon absorption of 2D materials can be
met by deploying light–matter interaction enhancement
techniques. Here, three options are possible; (a)enhancing the
optical DOS via incorporating optical cavities, (b)designing
momentum-bending options that feed waveguidelike struc-
tures that allow for lateral (versus normal)absorption, and (c)
field density enhancements using metal-optics approaches,
such as found in plasmonics if loss management can be
achieved.
Furthermore, physical strain creates an opportunity to
create multiband-gap designs within one material system. For
instance, the induction of periodic changes in strain values
could lead to advanced PV cells. Regarding the electrical
18
J. Opt. 00 (2016)000000 Roadmap

transport, Lee et al [85]reported that, although Van der Waals
HJTs exhibit both rectifying electrical characteristics and PV
responses, the underlying microscopic processes differ
strongly from those found in conventional devices in which
an extended depletion region plays a crucial role. In atomic
heterostructures, the tunneling-assisted interlayer recombina-
tion of the majority carriers is responsible for the tunability of
the electronic and optoelectronic processes.
Interestingly, the combination of multiple 2D materials
has been shown to provide high photon-conversion perfor-
mance; for instance, sandwiching an atomic p–njunction
between graphene layers enhances the collection of the pho-
toexcited carriers [85]. Hexagonal boron nitride (h-BN)was
shown to be a promising substrate (improved 2D material
mobility)for high-quality 2D electronics due to its atomically
smooth surface that is relatively free of dangling bonds and
charge traps [86].
On the processing side, plasma-assisted doping can serve
as a reliable approach to form stable p–njunctions in multi-
layer MoS
2
resulting in a significant enhancement of the PV
response, such as a higher OC voltage and a lower dark
current [87]. Applying field enhancement techniques via
using plasmonic resonances in nanoparticles can improve
absorption; Britnell et al placed gold nanospheres on top of
the 2D heterostructures showing a tenfold photocurrent
increase [88]. Rolling a stacked heterolayer of semiconduct-
ing, metallic, and insulating 2D materials in a core–shell
fashion allows for broadband photoabsorption up to 90% due
to a broadband nanocavity and an opportunity for strain
engineering for multiband-gap PV cells [89].
Concluding remarks
Although still at an early stage of development, the known
properties of atomically thin material systems for photon
conversion are motivating for ongoing research. Together
with graphene and insulating materials, such as h-BN, 2D
semiconducting materials are an attractive choice for con-
structing SCs on flexible and transparent substrates with
ultrathin form factors and potentially even for mid-to-high-
efficiency SCs. While some fundamental and practical chal-
lenges are still present, the field of nanophotonics has a wide
variety of toolkits available toward handling these challenges.
In addition, 2D materials show a decent potential for highly
functional and tunable material platforms if synthesized and
controlled properly. Incidentally, the latter is the aim of the
Materials Genome Initiative and the DMREF program of the
National Science Foundation of the United States (see also
section 7). In conclusion, the rapid progress of this field might
overcome control and design challenges in the near future.
Acknowledgments
We thank the National Science Foundation and the Materials
Genome Initiative for support under Award No. NSF DMREF
14363300.
Figure 14. The 2D atomic-layered materials offer a variety of band
structures toward designing highly functional photon absorption
devices. While this emerging material class exhibits some non-
classical band structures, more research is needed to fully understand
the interplay among transport, light–matter-interaction properties,
and mechanical properties, such as stress. Abbreviations: see the
main text.
19
J. Opt. 00 (2016)000000 Roadmap

9. Plasmonics for optical energy conversion
Michael J Naughton and Krzysztof Kempa
Boston College
Status
Plasmonics is the study of plasmons, quasiparticles associated
with collective oscillations of e density in a metal. Plasmon
waves can exist and can propagate within the bulk or at the
surface of a metal and can be generated by interactions of EM
radiation or an e beam with the metal. Most of the phenomena
associated with waves, in general, apply to plasmons, perhaps
most importantly that of resonance. The energy-momentum
dispersion relation for plasmons also differs greatly from that
of EM radiation in vacuum or air, a fact that affords numerous
routes to manipulating light–matter interactions. For example,
surface-bound plasmons can be localized on size scales far
smaller than the wavelength of light in free space and can
propagate (as surface plasmon polaritons (SPPs)) along
channels of comparable small size. In addition, structured
media forming metamaterials can be fabricated that incorpo-
rate plasmonics to enable new functionalities in nanopho-
tonics and electronics.
Numerous applications have been envisioned and have
been implemented that take advantage of this light confine-
ment and light waveguiding with plasmons. These include
molecular and neurosensing, color filtering, nanoscale litho-
graphy, lasing, imaging, waveguiding, and the topic of this
contribution, energy conversion. The ability to excite plas-
mons with light means that the energy in light can be trans-
formed and can be manipulated in tailorable and potentially
useful ways [9].
Current and future challenges
It can be said that the most significant scientific challenges to
increased optical energy-conversion efficiency, especially in
PVs, are color matching and the ‘thick–thin’conundrum. The
former refers to the spectral nature of sunlight versus the
single energy (band-gap)nature of semiconductors, and the
latter refers to a thick SC being required to maximize optical
absorbance, while a thin one is advantageous for e–h
extraction. To date, the series MJ cell is the only proven
solution to the spectral issue (see sections 11,13). As also
described elsewhere in this roadmap, there are several alter-
native concepts proposed to deal with the problem, from
carrier multiplication to hot e extraction (see sections 5,13),
to a parallel MJ (as in a prism)(see sections 11,13), and to a
thermal PV (see sections 15–20). Likewise, for the optical
absorber thickness issue, various light-trapping innovations
are being conceived and are being implemented to enable
high absorption in ultrathin media. These include textured
front and/or back electrodes, radial-junction architectures that
strive to decouple the optical and electronic pathlengths by
orthogonalizing their respective directions, periodic back-
reflectors that channel, or waveguide light along the plane of a
film, thus, extending the optical path length, and others. One
of the most interesting and perhaps promising new routes to
increased light trapping involves plasmonics.
Atwater and Polman [90]gave a thorough review of
plasmonics for PV in 2010, discussing how plasmonic
metallic nanoparticles/nanostructures could be used to scatter
light at oblique angles into a PV absorber, as nanoantennas to
enhance near-field scattering within an absorber, or as
waveguides supporting SPP modes at the backreflector with
the evanescent EM wave in the semiconductor at the metal
interface that enhances carrier generation.
In 2011, a review of plasmonics by Wang et al [91]
included a chapter that described key plasmonics concepts in
solar plasmonics, including Mie resonance, nanotransmission
lines,metamaterials for light trapping, as well as plasmon-
induced charge separation for a novel class of SCs.
In 2012, Green and Pillai [92]also briefly summarized
the prospects for plasmonics in SCs but added to the dis-
cussion mentions of possible roles of plasmonic metamater-
ials and for hot es which, in concert, could potentially yield
conversion efficiencies well in excess of the SQ limit.
Each of these schemes can be advantageous for reducing
the thickness of a PV absorber while maintaining or even
increasing optical absorbance. Independently, a great deal of
research is underway that uses plasmonics for photocatalytic
(water splitting)and photoelectrochemical optical energy
conversion. It remains a challenge, however, to successfully
implement an energy-conversion scheme, aided by device
architecture, plasmonic interactions, or a yet-to-be-discovered
method that yields energy conversion greater than that of
conventional devices and of the scale needed to address the
global energy challenge.
Advances in science and technology to meet
challenges
A great deal of research is ongoing to improve light collec-
tion/trapping in materials and to use that optical energy for
the purpose of energy conversion. An increasing amount of
those efforts is devoted to exploiting plasmonics in this realm.
Much of the pioneering work of the 19th and early 20th
centuries on EM from the origins of the diffraction limit to
light scattering in the Mie and Rayleigh regimes to wave-
guiding and radio technology is being revisited on smaller
spatial dimensions and optical frequencies in nanostructures
with plasmonic interactions playing a leading role.
Ongoing developments in metamaterials are bringing
novel concepts to the field, wherein optical constants (e.g.,
refractive index)are tailorable not only by material compo-
sition, but also by architecture. The combination of plas-
monics and metamaterials affords new opportunities for
creative nanoscale manipulation of light and the conversion of
EM energy into usable thermal, electrical, or chemical forms.
The various plasmonics concepts can lead to greatly
improved photon management materials, including in SCs
where they address the thick–thin issue. However, the main
challenge of solar PVs still remains the color matching pro-
blem, i.e., the recovery of the energy of hot es. This energy is
20
J. Opt. 00 (2016)000000 Roadmap

typically lost to heat due to the rapid times scale of e–phonon
scattering. The expensive MJ scheme is the only working
scheme today and aims at eliminating hot es altogether by
capturing multiple parts of the light spectrum in successively
higher-band-gap semiconductor.
Hot es have very short mean-free paths due to phonon
emission on the order of 1 nm. Various schemes have been
proposed to recover this hot e energy. For example, narrow
band energy filters at the absorber–electrode contacts were
proposed to facilitate the needed isoentropic cooling of the
hot es, while semiconducting QDs were proposed as an active
medium of a SC to create a phonon bottleneck to slow down
phonon emission [93]. In a recent paper [94], a small voltage
increase due to the direct recovery of hot es was demonstrated
in ultrathin a-Si PV junctions, illuminated by laser light at
different frequencies in the visible range. Plasmonics could
enhance this effect [95,96].
A specific approach to accomplish this task has been
recently proposed [97], based on the fact that e–plasmon
scattering can be much faster than e–phonon scattering. Thus,
by providing conditions for the former, the hot e energy could
be protected from the latter, and it would remain in the
electronic degree of freedom for an extended amount of time.
Such hot e plasmonic protection (HELPP)could be enabled
by plasmonic resonators. In one version, these could be
embedded directly in a PV junction [98]as shown in figure 15
(top). In another, a planar array of plasmonic resonators could
be adjacent to a junction as shown in figure 15 (bottom).
Here, the planar plasmonic resonators also become a part of a
metamaterial light-trapping structure, which facilitates
broadband absorption in the ultrathin absorber. This dual
function is evident from the simulated absorption spectrum
shown in figure 15 (bottom), which consists of two sharp
plasmonic peaks in the IR range for the HELPP and a
broadband feature in the visible range for light trapping.
HELPP effectively increases the lifetime of hot es and, thus,
increases the probability of their arrival at the collector in the
hot state. Successfully implemented, this scheme would lead
to increased OC voltage with no loss of current.
Concluding remarks
While most proposed plasmonic energy-conversion concepts
focus on light trapping, leading to a significant improvement
in, e.g., solar performance, the main challenge is to solve the
color matching problem: recovery of the energy of hot es
usually lost to heat. Novel plasmonic concepts, such as the
HELPP mechanism, offer possible solutions.
Figure 15. Examples of plasmonic energy-conversion schemes. Top:
Plasmonic metal nanopattern embedded in a semiconductor
enhances near-field scattering [98]; Bottom: Plasmonic metal–
insulator–metal (MIM)structure where excess energy from hot es
resonantly couples to IR plasmon modes [97].
21
J. Opt. 00 (2016)000000 Roadmap

10. Light rectification using an optical antenna and a
tunneling diode
Mario Dagenais
University of Maryland
Status
The integration of an optical antenna with a tunneling diode
with proper impedance matching leads to what is now called a
rectenna [99]. This device allows the capture of an optical
signal falling on an optical antenna and the efficient rectifi-
cation of this signal by the tunneling diode. The demodulator
of choice for the rectenna is the MIM tunnel diode [100].
Schottky diodes are also a candidate for the rectifier, but they
typically operate at lower frequencies than MIM diodes. The
response time of the rectenna consists of several contribu-
tions: (1)the collective response of the conduction e that
establishes the AC bias, which extends to frequencies well
beyond the UV, (2)the tunneling time for es to cross the gap
region before field reversal, and (3)the electrodynamical
(parasitic)response of the junction to the changing field, in
particular, the resistance and capacitance (RC)response time.
The antenna is modeled as a voltage source V
A
in series
with a resistance R
A,
and the MIM diode is modeled as a
resistor R
D
in parallel with a capacitor C
D
.Efficient transfer of
power from the antenna to the load R
D
requires matching R
A
with R
D
and keeping the time constant τ=(R
A
|| R
D
)C
D
much below the time period of the source V
A
[101]. For a
parallel plate capacitor, the time constant τ=R
D
C
D
is inde-
pendent of the diode area and is determined by the compo-
sition of the MIM diode. Assuming a breakdown current
density of 10
7
Acm
−2
at 0.1 V and a dielectric constant ε=1
at a thickness of 10 nm, a time constant of τ=10
−15
sis
extracted, which is too large for coupling at a visible wave-
length. It is, then, concluded that a planar MIM diode,
represented by a parallel plate capacitor, would operate well
in the IR, say up to 30 THz, but would not operate in the
visible. The extension of the planar MIM diode to the visible
wavelength is a challenge. By contrast, point-contact devices
(i.e., whisker diodes)have demonstrated frequency responses
up to frequencies in the green part of the visible spectrum, but
they are very irreproducible and are hard to use. The asym-
metrical nonplanar geometry of the whisker, together with the
flat anode, are essential requirements for increasing the cutoff
frequency of the diode. The present challenges include rea-
lizing these structures in a reproducible and stable way, using
well-established nanofabrication techniques, and scaling up
these structures to large arrays.
Current and future challenges
It was recently demonstrated that the response time for a point
contact with a spherical tip is proportional to A
−1/4
, where A
is the area of the junction [102]. This implies that it is possible
to decouple RC and to appreciably improve the response time
of the diode, possibly to the visible frequencies of the solar
spectrum. Rectification requires an imbalance between the
forward and the reverse currents circulating during the posi-
tive and negative cycles of the AC potential at the junction.
An electrical asymmetry in the I–Vcharacteristics can be
obtained using various approaches including material asym-
metry, thermal asymmetry, and geometric asymmetry. By
applying a bias, efficient rectification can be realized for
detector applications. However, for energy harvesting appli-
cations, it is necessary to operate the diode at zero external
bias. The geometric asymmetry diode (see figure 16)was
demonstrated in [104], and it allowed energy harvesting at
zero external bias. A sharply pointed planar triangular tip
emitter incident on the boundary of a square receiver provides
electric field asymmetry (see figure 17)[100]. When the
square is biased positively, the electric field line density
incident on the triangular tip is enhanced by the lightning rod
effect. The inverse tunneling current is very reduced because
Figure 16. The (a)forward and (b)reverse asymmetric potential
barriers for a geometrically asymmetric point-contact diode
structure. Figure taken from [4].
Figure 17. SEM micrograph of Ni/NiO
x
/Ni geometrically asym-
metric tunneling diode/nanoantenna.
22
J. Opt. 00 (2016)000000 Roadmap

of the lower electric field at the surface of the flat electrode.
Four parameters are typically used to characterize the recti-
fication efficiency. They are: (1)the differential junction
resistance R=dV
DC
/dI
DC
,(2)the nonlinearity I″=d
2
I
DC
/
dV
2
DC,
(3)the sensitivity or responsivity =
S
,
IV
IV
1
2
dd
dd
2DC DC
2
DC DC
and
(4)the QE 
h
=wS.
qeThe equations for Rand Sare altered in
a quantum description of the photon-assisted tunneling. This
is required when the incident optical photon energy on the
antenna corresponds to V
nonlinear
on the order of 100 meV,
typical of low-barrier MIM diodes and is typical of MIM
barrier height. In this quantum description, the classical
values of resistance and the responsivity decrease as the
photon energy increases [105]. The maximum achievable
conversion efficiency (ratio of output DC power to the input
AC power)for monochromatic illumination is 100%. For
broadband illumination, the diode operating voltage plays the
role that the band gap plays in conventional SCs and effi-
ciencies approaching the SQ limit are expected [106]. Fur-
thermore, because sunlight is spatially coherent only over a
limited area, concentration of the incident light is limited (see
section 12). A coherence of 90% for a broadband solar
spectrum is reachable only for a circle of radius 19 μm[107].
Advances in science and technology to meet
challenges
The power-conversion efficiency in a rectenna depends on:
(1)the efficiency of the coupling of incident radiation to the
antenna, which depends on the antenna radiation pattern as
well as its bandwidth and the coherence of the light, (2)the
efficiency with which the collected energy propagates to the
junction and is governed by resistive losses at high fre-
quencies in the antenna, (3)the coupling efficiency between
the antenna and the diode, which depends on impedance
matching, and (4)the efficiency of rectifying the power
received in the diode, which is related to the diode respon-
sivity. It is also important to consider the use of noble metals
and plasmonic resonances on the field enhancement and
rectification properties on a tunneling junction (see section 9).
Recent results demonstrate the importance of the plasmon
frequency on both the material and the geometry of the tip,
which could be used to control the frequency at which the
junction is most efficient for the rectification of optical signals
[102]. At optical frequencies, the classical skin depth in
metals is on the order of 30 nm, and optical losses can be very
large. Characterization of nanojunctions as a function of
wavelength, polarization, and materials is required for opti-
mizing the rectenna. The difficulty of producing arrays of
nanometer gap junctions over areas of order cm
2
has to be
studied. By using constructive interference, it is possible to
coherently combine the electric fields from the different
antennas of an array. This would allow the control of the
antenna array far field. This needs to be studied in more detail.
Tips of radii of a few nanometers have to be produced in
order to get very high frequency responses. Ultimately, the
junctions will be limited by dielectric breakdown. More
research needs to focus on this issue.
Concluding remarks
Rectennas have the potential for converting solar energy to
electrical power all the way from the IR to the visible using
arrays of potentially low-cost devices with conversion effi-
ciencies similar to PV devices. As discussed, geometrically
asymmetric diodes can rectify radiation all the way to the
visible and, therefore, appear most promising. Rectennas can
also be used for beaming monochromatic IR and visible
power with detection efficiencies approaching 100%. Another
potential application of this technology is for waste heat
harvesting in the IR if the coherence area of the IR radiation is
appropriately selected. Rectennas can use nanoimprints and
roll-to-roll technologies for reducing the manufacturing cost.
So far, low-efficiency rectennas (on the order of 1%)have
been demonstrated in the IR. Much work obviously remains
to be done to demonstrate the full potential of this technology.
23
J. Opt. 00 (2016)000000 Roadmap

11. Full solar spectrum conversion via MJ
architectures and optical concentration
Yuan Yao
1
,LuXu
1
, Xing Sheng
1
, Noah D Bronstein
2
, John A
Rogers
1
, A Paul Alivisatos
2,3
, and Ralph G Nuzzo
1
1
University of Illinois at Urbana-Champaign
2
University of California, Berkeley
3
Lawrence Berkeley National Laboratory
Status
Significant advances have been made in research to
improve the performance of single-junction PV devices.
Currently, the best Si and GaAs devices have achieved
efficiencies of 25.6% and 28.8%, respectively [26](see
sections 2,4). The realization of significant further
enhancements in the efficiencies of PV energy conversion,
however, resorts to MJ architectures using semiconductor
materials with subcell band gaps tuned to target different
portions of the solar spectrum in order to minimize carrier
thermalization losses and to increase spectrum coverage to
exceed the SQ limit [24]. In theory, a MJ cell can achieve
an efficiency as high as 86.8% with an infinite number of
junctions [108](a value lower than the Landsberg limit
[21]due to entropy losses), and a number of different cell
designs have been intensively explored by the PV research
community as a means through which such forms of per-
formance enhancement can be realized. These include, most
notably, devices that embed the semiconductor elements in
the form of MJ SC stacks [109]and, to a lesser degree,
optical approaches involving various forms of spectrum
splitting [110](see also section 13). In the first design, the
subcells are either epitaxially or mechanically stacked
together in the order of decreasing band gaps to divide the
incident sunlight using the absorption of the subcells (see
also section 3). In the second approach, separate optics
(e.g., prisms, holograms, and dielectric bandpass filters)are
used to split the solar spectrum and to direct different
portions to the relevant subcell. It has been persuasively
argued that both designs would benefit from high geometric
concentration of the solar irradiance as one means to both
offset the high material costs encumbered by the III–V
semiconductor device elements and to enhance the system
power-conversion efficiency. To date, cell stacking designs
have achieved the highest benchmark performances in solar
energy conversion with world-record efficiencies of MJ
cells reaching 46.0% with a four-junction design (InGap/
GaAs/GaInAsP/GaInAs)under 508 suns [26]. Exemplary
recent progress includes a report from our group of 43.9%
efficient quadruple-junction four-terminal microscale SCs
that were fabricated by mechanical stacking of a top 3-J
device onto a bottom Ge cell via transfer-printing-based
assembly [111].
Current and future challenges
For epitaxially grown MJ devices, the difficulty of sustaining
lattice matching through multiple layers of growth limits the
material selections that are available for use in each subcell and,
thus, directly restricts achievable limits for device performance.
Mechanically stacked devices, on the other hand, can be fab-
ricated via high-temperature wafer bonding [112]to circumvent
this issue but still carries a requirement for current matching at
the electrically conducting interfaces, which is difficult to rea-
lize as the number of subcells increases to subdivide the solar
spectrum. Alternatively, insulating adhesives can be used
between mechanically stacked subcells to enable multiterminal
connections and, in this way, to avoid the need for current
matching. These interfaces need to be carefully designed to
minimize reflection losses as well as to manage heat flow and
thermal-mechanical stresses at high optical concentration [111].
Additional electro-optical challenges exist for the material used
in each subcell. For example, a top wide-band-gap subcell (i.e.,
E
g
>1.4 ev)generally cannot be doped to a sufficiently high
level to enable efficient carrier collection under high-irradiance
concentration; it requires incorporation of highly doped low-
band-gap materials that either degrade its optical transparency
for low-energy photons or complicate backcontact grid con-
figurations [109].
It has been noted that the limitations associated with
stacked MJ devices can be tackled, in principle, by employing
external optical components to split and to distribute the solar
radiationtoanarrayofspatiallyseparatedsubcells[113].By
decoupling material compatibility from band-gap optimization,
this approach also enables MJ designs with larger numbers of
subcells and, thus, higher theoretical efficiencies. As the cell
fabrication steps are reduced to provide a set of single-junction
devices, simplified process flows for the semiconductor com-
ponents are possible (see sections 2,7). The commonly pro-
posed optical designs include holographic gratings and
wavelength-selective mirrors (e.g., multilayer dielectric Bragg
stacks). Their practical use, however, is hindered by the for-
midable requirements for high-optical quality as well as the
complexity of the optical designs needed to achieve competitive
system-level efficiencies.
The high cost of III–V materials, especially in MJ cell
contexts, likely necessitates a high-optical-concentration
design to achieve commercial viability (see section 12).
Optical losses figure importantly in all forms of concentrator
PV designs. Stacked cells, for example, are subject to sig-
nificant Fresnel losses (e.g., 12% of incident photons are lost
to reflection before reaching the SCs for a system with three
glass/air interfaces)that limit their optical (and, thus, power-
conversion)efficiencies. Broadband antireflection (AR)
coatings would afford an ideal solution, but materials that can
span the refractive index range needed to mitigate these
effects have yet to be developed. The use of common light-
trapping designs on the PV cells also become more complex
as they can scatter light and, otherwise, limit the broad-
spectrum performance of high-concentration optics (see
section 3). Geometric solar concentrators (GSCs)also require
24
J. Opt. 00 (2016)000000 Roadmap

solar tracking and, even more significantly, do not utilize
diffuse light—a significant component of the solar spectrum.
(The diffuse component is 10% in AM1.5G illumination;
most locations in the United States having 24% to 50% dif-
fuse sunlight [114].)
Advances in science and technology to meet
challenges
Light management within and between subcells
It has been shown in single-junction devices that high external
radiation efficiencies (EREs), as achieved by luminescence
extraction enhanced by photon recycling, are crucial for high
PV performance (as demonstrated by the world-record GaAs
device where the radiatively emitted photons are reflected by a
metal backsurface rather than absorbed by the substrate)
[46,115](see section 4). Likewise, MJ devices with inter-
mediate reflectors that enhance ERE with photon recycling
would improve the V
OC
for each subcell (figure 18),although
these reflectors also need to transmit sub-band-gap photons for
the next cell. Different designs have been examined theoreti-
cally that provide such effects, such as stacks spaced by an air
gap coupled with AR coatings as the intermediate reflector in-
between subcells [116]. The elements of this design have been
demonstrated experimentally using microscale SCs stacked
onto prepatterned air gap spacers using a soft-transfer-printing
technique [117]. The opportunities for progress have also been
demonstrated theoretically in the design of a high-performance
spectrum-splitting PV system that uses polyhedral specular
reflectors coupled to spatially separated devices to enhance
both photon recycling within a subcell and radiative coupling
between them [118].
Improving the optical efficiencies of GSCs
There exist numerous opportunities to improve the perfor-
mance of concentrator PV systems. Providing improved
broadband AR coatings (e.g., porous films with sub-
wavelength features to avoid scattering)forms one obvious
direction in research to reduce the Fresnel losses associated
with concentrating optics. The development of strategies that
would allow the utilization of diffuse light within a con-
centrator PV design is also of significant interest. We might
envision, for example, the coupling of a GSC with a lumi-
nescent solar concentrator (LSC), wherein, diffuse radiation
striking the backplane can be absorbed by the luminophore
and can be down-converted into total internal reflection
modes that are directed to the embedded PV device elements.
A possible geometry for such a system suggested by elements
of our past work is one of embedding arrays of microscale
SCs directly in the LSC waveguide (figure 19)such that, in
addition to diffuse light conversion, the direct illumination
from the Sun can be concentrated at the top surface of the
devices using a GSC with a higher concentration ratio and
optical efficiency [119,120]. We have shown that QD
luminophores (see also sections 5,6)are particularly advan-
tageous for use in such microcell LSC arrays as compared to
traditional organic dyes as they have high quantum yields,
large (and tunable)Stokes shifts for reduced reabsorption
losses, and better long-term photostability. Their narrow
emission peaks also facilitate photonic designs to better trap/
manage the luminescent photons to improve optical efficiency
[120,121]. It is also of particular interest to note that high-
optical efficiency LSCs may engender specific capabilities for
high-performance concentrator PV designs that would be
transformational, specifically to obviate the need for solar
tracking as well as the intriguing possibility that they might
enable new approaches to spectrum splitting using discrete
subcell arrays that can achieve efficiencies approaching those
associated with monolithic MJ cell stacks.
Concluding remarks
MJ architectures are required to achieve full spectrum con-
version and to surpass the SQ limit. Concentration is advan-
tageous in a MJ system in both improving their efficiency and
reducing their cost. This perspective outlines new materials,
optical integration strategies, and approaches to spectrum
splitting that beget new opportunities through which the
grand challenge of full-spectrum conversion might be
realized.
Acknowledgments
This work is part of the ‘Light-Material Interactions in
Energy Conversion’Energy Frontier Research Center funded
by the U.S. Department of Energy, Office of Science,
Office of Basic Energy Sciences under Award No. DE-
SC0001293.
Figure 18. Illustrations demonstrating photon dynamics in a MJ
device (reproduced from [117]).(a)No photon recycling: the
radiative emission from the top cell is coupled to the bottom cell. (b)
With photon recycling: using a low index interface as an
intermediate reflector, the ERE and V
OC
of the top cell are enhanced. Figure 19. Schematic of a hybrid concentration system with an
embedded microscale SC module, both the device and the
luminescent waveguide can be configured as a MJ architecture for
full spectrum conversion.
25
J. Opt. 00 (2016)000000 Roadmap

12. Advanced solar concentrators
Jeffrey M Gordon
Ben-Gurion University of the Negev
Status
Concentrating sunlight has fascinated people since time
immemorial [122]. Heat production and electricity generation
comprise the main current applications (unorthodox uses
include nanomaterial synthesis [123]and medical surgery
[124]). Generally, solar concentration is motivated by cost
and efficiency. Cost because expensive receivers are
largely replaced by inexpensive optics. Solar-thermal
efficiency benefits from markedly reducing heat-loss area.
PV-conversion efficiency can increase linearly with the
logarithm of the concentration at low series resistance.
‘Advanced’refers to concentrators that approach the
thermodynamic limit for the relation between flux con-
centration Cand acceptance half-angle θ
a
at high collection
efficiency:Csin
d−1
(θ
a
)n
d−1
sin
d−1
(θ
e
), where nis the
refractive index in the concentrator (air but, occasionally, a
transparent dielectric for PVs),θ
e
is the maximum half-angle
irradiating the absorber, and dis the dimensionality [125–
127]. Minimally, θ
a
is the convolution of the Sun’s
angular radius (0.27°)with manufacturing, installation,
and tracking imperfections. Maximally (for static low-
concentration collectors),θ
a
is the angular range from
which beam radiation is collected over the day. The
familiar solutions of spherical-cap or Fresnel lenses and
parabolic or Fresnel mirrors that have dominated solar tech-
nologies, to date, fall far short of the thermodynamic limit
[125–127].
Advanced concentrators range from static 2D systems
(θ
a
≈25°–90°), to single-axis tracking line-focus
systems (C≈5–100), and dual-axis tracking point-focus
systems (C≈100–100 000). Nonimaging optics uniquely
provides static designs that approach the thermodynamic
limit [125–127]. Some enjoyed commercial realization
(figure 20(a)). The higher concentration domain is still
dominated by parabolic and Fresnel mirrors and Fresnel
lenses, although a variety of advanced nonimaging second-
stage concentrators have been developed [125–127]. The
simultaneous multiple surface (SMS)method [125,126]was
the first to spawn advanced concentrators that both were
ultracompact and could accommodate a sizable gap between
the absorber and the optic. The nonimaging strategy maps
incident extreme rays to the extremes of the absorber
[125,126].
Advanced aplanatic concentrators [128]opened new
vistas, recently adopted for PVs (figure 20(b)). The imaging
aplanatic strategy (viable for θ
a
∼2°)completely eliminates
spherical aberration and coma [128]while admitting ultra-
compact pragmatic optics.
Current and future challenges
For PVs, current challenges subsume (a)ultraminiaturization
that enhances the feasibility of SMS and aplanatic con-
centrators (especially, dielectric-filled units), and (b)spectrum
splitters that take better advantage of the spectral conversion
of separate SCs. Another tack is quasistationary high-con-
centration optics that would markedly simplify and downsize
solar trackers via the use of either: (1)light guides (that have
remained at the developmental level due, in part, to sub-
stantial optical losses), and (2)spherical gradient-index
(GRIN)lenses (figure 21(a)) that await accurate high-volume
fabrication methods. A recent GRIN advance demonstrated
lens refractive index profiles for off-the-shelf solar-transpar-
ent materials with efficient performance that approaches the
thermodynamic limit [129]. The prior conventional wisdom
had been that only the refractive index profiles of eponymous
Luneburg lenses (with refractive indices for solar frequencies
for which no materials have yet been identified)could achieve
the objectives [129].
Another tantalizing new direction is solar aperture recti-
fying antennas (rectennas), predicated on exploiting the par-
tial spatial coherence of sunlight with microconcentrators,
nanoantennas, and ultrafast rectifiers (AC to DC conversion)
(see section 10)[130]. The topic of light rectification is ela-
borated in section 08b of this article. Solar aperture rectennas
have been shown to possess fundamental limits (for
Figure 20. (a)Sample advanced static nonimaging concentrator with
an evacuated tubular absorber for steam production. (b)Two
generations of advanced aplanatic concentrators for PVs, first air-
filled for 1 cm
2
cells, then, transitioning to glass-filled for 1 mm
2
cells plus a photograph of an installed 15 kW
peak
array comprising
the former.
26
J. Opt. 00 (2016)000000 Roadmap

conversion efficiency)that exceed those of solar-thermal and
concentrating PVs but require microconcentrators within the
spatial coherence area of solar beam radiation, to wit, radii on
the order of tens of micrometers [130](figure 21(b)), such
that Cis on the order of 10
3
. Because phase-conserving optics
are needed, devices should approach perfect imaging and,
hence, the thermodynamic limit (figure 21(c)).
Advances in science and technology to meet
challenges
The technological advances needed to address these chal-
lenges fall mainly into two categories: microfabrication and
materials. For the latest miniaturized concentrator SCs with
linear dimensions of ∼0.5 mm, all-dielectric optics that are
unfeasible for conventional cells with linear dimensions on
the order of a centimeter (simply due to the mass per aperture
area)present promising alternatives. This will require
integrated production methods (micromodularity)with SCs,
micro-optics, wiring, bypass diodes, and heat sinks compris-
ing a single manufactured unit. Accurate micro-optical fab-
rication both for lenses and for highly reflective specular
mirrors will be essential. This also necessitates the precise and
reproducible fabrication of sheets comprising thousands of
PV miniconcentrators per m
2
of collection area.
For solar rectennas, this will correspond to the order of
10
9
aperture rectennas per m
2
of collection area. These units
will require the development of efficient broadband
nanoantennas and broadband ultrafast rectifiers (a bandwidth
on the order of 10
6
GHz).
Although viable spherical GRIN lenses have been pro-
duced by the trillions for millions of years (chieflyfish eyes),
the development of accurate, robust, and affordable fabrica-
tion procedures has proven elusive, albeit with recent
encouraging progress [131]. The newly discovered GRIN
solutions for available materials can also be tailored to fab-
rication constraints, such as an extensive constant-index core
and constant-index shell regions [129]. Lens diameters will
vary from the order of centimeters (for concentrator PVs)to
tens of micrometers for solar aperture rectennas.
Finally, specifically for the optical aspects of solar-ther-
mal power conversion, the challenge shifts to the develop-
ment of superior (and robust)selective coatings (i.e., high
solar and low IR emissivity)at progressively higher tem-
peratures that give rise to higher turbine efficiencies. This
relates both to line-focus (evacuated)receivers in the quest for
efficient operation above ∼700 K as well as to point-focus
(nonevacuated)receivers aiming to operate at temperatures
exceeding 1000 K.
Concluding remarks
Achieving ultraefficient solar conversion could basically be
solved if efficient and feasible methods could be found to
convert broadband solar to narrow band radiation, which
could then be exploited by a plethora of radiation converters
(including those from physical optics, such as diffractive and
holographic elements, rectifying antennas, etc., that are
insufficiently efficient due to the narrow spectrum they can
accommodate). Proposals of PV UC and down-conversion
notwithstanding (see sections 13–18), current proposals are
far below the required performance. Hence, in the foreseeable
future, the focus will likely be on the types of nonimaging and
aplanatic optics, GRIN optics, and micromodularity (permit-
ting optics precluded by common large-absorber collectors)
that not only can raise solar-conversion efficiency, but also
can render them more practical and amenable to large-volume
production.
Figure 21. (a)Illustration of new solutions (for refractive index as a
function of radius)for spherical GRIN lenses accommodating
refractive indices available for off-the-shelf materials that are
transparent in the solar spectrum. The substantial constant-index core
region facilitates lens fabrication [129]. This unit-radius ultrahigh-
concentration f/0.66 lens was ray traced for the full solar spectrum
and the extended solar disk. (b)E micrograph showing current state-
of-the-art fabrication for microconcentrators. (c)A candidate high-
concentration aplanat [128]that could be used in solar aperture
rectennas [130]. The aplanat can be dielectric filled and satisfies total
internal reflection.
27
J. Opt. 00 (2016)000000 Roadmap

13. Spectral splitting and nonisothermal solar
energy conversion
Svetlana V Boriskina
Massachusetts Institute of Technology
Status
The broadband nature of thermal radiation—including sun-
light and that of terrestrial thermal sources—imposes limita-
tions on the light-to-work efficiency of the whole-spectrum
energy converters [27]. Quantum-conversion platforms, such
as PV cells are unable to harvest the low-energy photons and
to convert the high-energy ones very inefficiently (see
sections 2,3). In turn, thermal energy converters with
blackbody receivers suffer from re-emission losses at high
temperatures and require high levels of solar concentration to
overcome such losses (see section 12). Achieving high optical
concentration (e.g., by using a large heliostat field)may not
only be costly, but also introduces additional loss mechanisms
that negatively impact overall system efficiency.
Sorting photons by their energies and processing them
separately helps to increase the light-to-work-conversion
efficiency. The most explored approach to spectral splitting is
based on using MJ PV cell stacks (figure 22(a)) where the
wide-band-gap top cells absorb high-energy photons, while
the lower-energy ones are transmitted through to the narrow-
band-gap cells at the bottom of the stack (see section 11). The
stacked spectral splitters/converters can also incorporate
catalytic platforms to harvest UV light and thermal receivers
to absorb low-energy IR photons. Yet, efficient stacking and
electrical wiring of several converters is challenging, espe-
cially in hybrid configurations that include converters with
different operating temperatures, which might require thermal
insulation between the PV and the thermal receivers.
To address these issues, cascade reflection and external
spectrum splitting schemes are being actively explored, which
make use of perfect and dichroic mirrors, holograms, dielectric
prisms, polychromats, etc [132,133].(figures 22(b),(c)).This
shifts the R&D focus from the PV material design and fabrication
issues to the development of efficient optical elements. Even
traditional stacked PV configurations can benefitfromadding
photon-management elements, such as embedded wavelength-
selective filters for photon trapping and recycling [134].
Current and future challenges
The solar radiation is dilute and is even further diluted by
spectral splitting, which, in turn, reduces the energy-conver-
sion efficiency, especially for the solar-thermal converters.
Although spectral splitters can be combined with external
solar concentrators, fully integrated platforms may help to
reduce optical losses and to provide cheaper and more com-
pact technological solutions. Spectral-splitting holograms can
simultaneously provide some optical concentration. Higher
concentration can be achieved with planar light guides either
passively (by light trapping and guiding)or actively—by
down-converting photon energy by embedded luminescent
material (figure 22(d)), yet the optical efficiencies of such
schemes need to be improved (see section 11).
Light-conversion platforms would greatly benefitfromthe
development of integrated elements that simultaneously provide
spectral and spatial selectivities, which translates into optical
concentration [135](see section 9). This approach is schemati-
cally illustrated in figure 22(e)and makes use of wavelength-
scale selective absorbers with large overlapping absorption cross
sections. Spectral selectivity of individual absorbers can be
governed by their localized optical resonances [9,135]and/or
via long-range interactions that form quasilocalized lattice
modes at different wavelengths [136]. Although challenging,
this scheme can be realized with resonant plasmonic and di-
electric nanoantennas. Photons not captured by localized
absorbers are harvested in the bottom layer. Such a scheme
makes possible designing inverted stacks with PV receivers as
the bottom converter, and the top layer selectively harvesting
shortest- and longest-wavelength photons, which are not effi-
ciently converted by the PV cells (figure 22(f)).
Advances in science and technology to meet
challenges
The MJ stacked PV is the most mature spectral-splitting
technology. Despite reaching impressive 46% efficiency, it
still falls below the theoretical limits (figure 23(a)) [26].
Additional external spectrum-splitting elements can further
Figure 22. Various types of spectral splitters.
28
J. Opt. 00 (2016)000000 Roadmap

improve the efficiency of PV stacks (e.g., in University of
New South Wales cells). In turn, solar-thermal converters rely
on high concentration to compensate for the radiative losses at
high temperatures. This technology can significantly benefit
from the development of selective absorbers [10,137], which
suppress emission at longer wavelengths and can operate at
high temperatures (see section 17). Absorbers with angular
selectivity (i.e., those that can only absorb/emit light within a
narrow angular range to match that of incoming sunlight
[138])can offer even higher efficiency (figure 23(b)). Spectral
and angular selectivities can be achieved via external filters or
by designing the absorber itself to be selective.
Another important issue in the solar energy conversion is
the intermittent nature of the sunlight, which calls for the
development of the energy storage solutions. The high cost of
electrical storage and a possibility of combining PV and solar-
thermal engines in hybrid platforms fueled interest in the
thermal storage [139].Efficiency of the PV cells degrades if
they operate at high temperatures matching that of the heat
receiver (figure 23(c)). This calls for the development of
transparent thermal insulators and integrated spectral splitters
to further boost the hybrid device efficiency. External spectrum
splitting also alleviates thermal issues, and—in combination
with spectral and angular selectivities of the thermal emitter—
is predicted to offer promise of achieving thermal UC of
photon energy (figure 23(d)) [140]. Another way to reduce
radiative losses can be by topping thermal absorbers with
transparent thermal insulators, creating nonisothermal (i.e.,
externally cool internally hot)converters [141,142].
Another type of nonisothermal converter—known as the
hot-carrier converter—is based on harvesting photoexcited
charge carrier before they thermalize to the temperature of the
crystal lattice (see also sections 5,9,14). Despite high pre-
dicted efficiency limit [143], development of such converters
has been stymied by the difficulties in efficient extraction of hot
carriers. Not only the carriers need to be harvested within an
ultrashort time period (below a picosecond), but also the effi-
ciency of commonly used filters, such as, e.g., Schottky bar-
riers is low (figure 23(e)). Furthermore, large enough
population of carriers hot enough to pass through the energy
filter cannot be easily created by sunlight in conventional
materials, such as noble metals [144]. Our calculations predict
that material engineering (see sections 5–8)to tailor the e DOS
in combination with spectral-splitting schemes can boost effi-
ciency of hot-carrier converters (figures 23(e),(f)) [145].Hot-
carrier converters that make use of plasmonic nanoelements
naturally benefit from high spectral and spatial selectivities and
can make use of the integrated spectral-splitting scheme shown
in figure 22(f).
Concluding remarks
Spectral selectivity can be achieved by the choice of the receiver
material, which calls for the development of high-quality PV
materials and heat absorbers stable at high temperatures (see
sections 7–9,15–17). The use of external splitters shifts the
emphasis to the design of optical elements, which ideally com-
bine selectivity, high concentration, and low losses. Non-
isothermal energy converters are promising but call for significant
advances in material design and integration. Hybrid schemes with
energy storage in the form of heat or fuels are highly desirable.
Acknowledgments
The author thanks G Chen, B L Liao, W-C Hsu, J K Tong, Y
Huang, J Loomis, L Weinstein, and J Zhou for discussions.
This work was supported by DOE-BES Award No. DE-FG02-
02ER45977 (for thermal emission tailoring)and by ARPA-E
Award No. DE-AR0000471 (for full spectrum harvesting).
Figure 23. Predicted and achieved efficiencies of solar-conversion
platforms with spectral splitting. In theoretical limit calculations, thermal
engines are assumed to be operating at Carnot efficiency and PV cells—
at SQ efficiency; solar concentration: (a),(d)one sun, (c),(f)100 suns.
29
J. Opt. 00 (2016)000000 Roadmap

14. A path upward: new upconversion schemes for
improving PVs
Di M Wu, Michael D Wisser, Alberto Salleo, and Jennifer
Dionne
Stanford University
Status
Thermodynamic considerations limit PV efficiency to a max-
imum of 30% for single-junction SCs under one-sun illumi-
nation. The Carnot limit, however, sets the maximum for
terrestrial SC efficiencies at 95% (see section 1,20).Toclose
the efficiency gap between these limits, MJ cells (see
sections 3,11),thermo-PV(TPV)cells (see sections 15–17),
and solar concentrators (see sections 10–13)are each promis-
ing approaches. UC can complement these strategies. As illu-
strated in figure 24(a), UCs convert sub-band-gap solar
photons to above band-gap photons, increasing the cell’sshort-
circuit current. Modeling predicts that UC could increase the
theoretical maximum efficiency of a single-junction SC from
30% to 44% for nonconcentrated sunlight [146].Animportant
advantage of UC is electrical isolation from the active layer of
the cell, eliminating the need for current or lattice matching.
In recent years, UC materials have been used to bolster
the performance of photoelectrochemical cells, c- and a-Si
cells, organic cells, and dye-sensitized SCs [147]. The record
improvement was demonstrated this year with lanthanide UC
applied to a bifacial c-Si cell under 94-sun concentration,
resulting in a 0.55% increase in cell efficiency [148].
Current and future challenges
While the performance of solar UC devices has been steadily
improving, a substantial gap remains between theoretical cell
improvements and experimental realizations. Three major
challenges include: (1)increasing the efficiency of UC; (2)
ensuring spectral overlap with SCs; and (3)increasing the UC
absorption bandwidth.
The limitations on UC efficiency are rooted in the UC
mechanism. Generally, UC of incoherent low-power light
requires a metastable intermediate state for the first excited e to
populate until a second photon is absorbed as highlighted in
yellow in figure 24(b). Two material systems that have the
requisite energy levels include lanthanide ion systems and
bimolecular systems. In lanthanide ions, the long-lived state is
an f-orbital with parity-forbidden decay to the ground state; in
bimolecular systems, it is a long-lived triplet state populated
through intersystem crossing. Lanthanide UC is often less
efficient than bimolecular UC, in part, because in the former,
both absorption and emission occur between weak f–ftransi-
tions, limiting both the light absorbed and the efficiency with
which it is emitted. In bimolecular UC, absorption and emis-
sion occur between bright singlet states and, with the proper
selection of sensitizer and emitter dyes, the major bottleneck to
efficiency is the energy transfer between triplet states. The UC
emission from both material systems has a quadratic
dependence on incident power in low-flux illumination con-
ditions, and efficiency typically increases with incident power
density. Consequently, all demonstrations of effective UC-
enhanced SCs, to date, have been performed under laser or
concentrated solar illumination.
The second challenge is tuning the spectral position of
UC absorption and emission to make optimal use of sub-
band-gap light. For example, the energy levels of lanthanide
ions allow absorption of low-energy light below the Si band
gap and re-emission above it, but the f-orbital energies can
only be slighted tuned with the host lattice and are effectively
fixed. Bimolecular UCs have synthetically tunable absorption
but often operate above the band gap of many SC materials.
Continued exploration of IR-absorbing triplet sensitizers will
increase the relevance of these materials for PV.
Afinal challenge is extending the absorption bandwidth.
As shown in figure 24(c), the potential cell-efficiency
improvements increase with UC bandwidth [146]. Most stu-
dies, to date, have examined the performance of an individual
UC; combining sensitizers to increase the absorption band-
width for both lanthanide and molecular UCs is a direction
that merits further exploration.
Advances in science and technology to meet
challenges
Two approaches to address these challenges include: (1)
improving existing lanthanide and bimolecular systems, and
(2)exploring radically new UC schemes. Extensive investi-
gations of the host lattice for lanthanide UC have yielded
Figure 24. (a)UC-enhanced PV device. (b)Simplified UC
mechanism highlighting the metastable intermediate state. (c)Effect
of the cell band gap and UC bandwidth on cell efficiency [146].
30
J. Opt. 00 (2016)000000 Roadmap

many key design principles, including low phonon energy,
optimized interion spacing, and minimization of defects. New
host lattices, such as Gd
2
O
2
S, that fulfill these requirements
have demonstrated lanthanide UC quantum yields exceeding
15% (with a theoretical maximum of 50%)[151]. While
bimolecular UC in solids is often limited by intermolecular
energy transfer, novel matrices have efficiencies approaching
those in solution with up to 17% reported in a polymer [152].
To address spectral considerations for solar energy con-
version, design of new IR absorbing supramolecular dyes and
hybrid UC-nanoantenna materials are promising approaches.
For example, adsorbing of IR dyes to the surface of UC
nanoparticles led to a 3300×increase in UC emission relative
to the bare nanoparticle [153]. Plasmonic nanoantennas can
increase the UC absorption bandwidth while also increasing
the radiative rate of emission (see sections 9,13)[154].
An emerging approach that could revolutionize the effi-
ciency and spectral tunability of UCs is the use of hybrid
semiconductor materials. Semiconductors generally absorb
light with greater bandwidth than molecules or ions. Fur-
thermore, their band gaps can be tuned with composition over
the energy range most relevant for PV (see sections 7,8). This
tunability can be used to craft a potential energy landscape
allowing sequential absorption of low-energy photons in one
material followed by radiative recombination in a neighboring
semiconductor.
For example, figure 25(a)illustrates hot-carrier UC in
plasmonic materials interfaced with semiconductors. Here, a
hot h and a hot e are independently created through absorp-
tion of light in a metallic nanostructure. These hot carriers are
injected into a semiconductor quantum well where they are
trapped until radiatively recombining with the corresponding
carrier. Judicious selection of plasmonic materials and semi-
conductors leads to light emitted with higher energy than that
absorbed. This scheme has a theoretical UC efficiency of 25%
using 5 nm Ag nanocubes with absorption and emission
tunable through geometry and material (see sections 9,
13)[149].
A second approach to semiconductor UC is shown in
figure 25(b)(see also sections 5,6). Here, light absorption
occurs in QDs with VB edges matched to a neighboring
semiconductor with a graded band gap. After a low-energy
photon is absorbed by an InAs QD, exciting an e into the CB,
the h is rapidly injected into the InAlBiAs layer. As in hot-
carrier UC, the energy barrier back into the InAs is high
enough to prevent the reverse process, establishing a long-
lived intermediate state. A second low-energy photon excites
the intermediate-state e above the CB edge of the neighboring
material. The e is injected into the InAlBiAs where the h and
e can radiatively recombine, emitting a photon of higher
energy than either of those absorbed [150].
Finally, research on triplet energy transfer between
organic dyes and SC nanostructures is another promising
development for UC. For example, a recent study has shown
that a semiconductor QD can serve as a triplet sensitizer for
dyes attached to its surface [155]. The QDs can absorb near-
IR light, improving spectral overlap with the needs of PVs.
Design of hybrid UCs that selectively incorporate the best
properties of each material is a strategy that merits further
attention.
Concluding remarks
UC holds significant potential as an inexpensive and gen-
eralizable way to improve the efficiency of any SC. Existing
UCs, however, lack the efficiency or optimal spectral char-
acteristics for integration into commercial SCs. The study of
canonical UC materials, including lanthanide and bimolecular
systems, has provided key insight into the UC process and the
limiting factors at play. Design of radically new materials and
new UC schemes—including those based on semiconductors
—is rapidly moving the field forward (and upward).
Acknowledgments
This work is part of the ‘Light Material Interactions in Energy
Conversion’Energy Frontier Research Center funded by the
U.S. Department of Energy, Office of Science, Office of Basic
Energy Sciences under Award No. DE-SC0001293. D.W.
acknowledges support from the Gabilan Stanford Graduate
Fellowship and the National Science Foundation Graduate
Research Fellowship.
Figure 25. New UC schemes: (a)hot-carrier UC using metals near
quantum wells [149]and (b)photon ratchet UC using graded band-
gap semiconductors [150].
31
J. Opt. 00 (2016)000000 Roadmap

15. TPVs: an alternative strategy for converting heat
to electricity
Peter Bermel
Purdue University
Status
TPVs convert heat into electricity by using thermally radiated
photons to illuminate a PV cell as shown in figure 26 [156].In
comparison with alternative strategies for converting heat into
electricity, TPVs have the potential for a quiet, compact,
reliable, and highly efficient operation, although several bar-
riers to widespread adoption remain. The original demon-
stration of TPVs at Lincoln Laboratories in 1956 used a
camping lantern to illuminate a Si-based ‘solar battery’to
generate electricity [157]. However, compared to a solar PV,
a TPV thermal emitter is much colder, emitting pre-
dominantly in the IR. Thus, within a decade, work began on
TPV systems with smaller band-gap PV cells.
Initial work focused on germanium, but more recent
work has included higher-efficiency gallium antimonide
(GaSb)[158]as well as ternary and quarternary III–V mate-
rials, such as InGaAs and InGaAsSb [159]. Nonetheless, the
broad bandwidth of thermal radiation gives rise to a great deal
of wasted midwavelength and long-wavelength IR radiation
[156]. To address this problem, optical short-pass filters have
been placed on the front or back side of PV cells to reflect
otherwise unused light back to the emitter. This approach
constitutes external photon recycling and has been demon-
strated to improve overall efficiencies [159,160](see also
sections 4,13). Combining these innovations has led to
conversion efficiencies of radiated power into electricity as
high as 23.6% [159].
Nonetheless, theoretical calculations have shown that
there is room for a great deal of further improvement in TPV
efficiencies (see also sections 16,20). In particular, several
theoretical studies have shown that ultimate efficiencies are
highly dependent on the maximum emitter temperature and
emitter designs and that, in some scenarios, the efficiency of
the overall TPV system can exceed 50% [156]as shown in
figure 27. By creating structures with emissivity concentrated
primarily at wavelengths matching the regions of high
external QE for the PV cells utilized, selective emission can
be a key driver of improved performance. Specific structures
with the potential for high efficiencies that have been pro-
posed and have been built, to date, include 1D multilayer
stacks [161], 2D metallic arrays of holes [162], and 3D
woodpile PhCs [163].
Current and future challenges
In order for the TPV to approach its theoretical limits and to
make the transition to a practical technology, there are a
number of challenges that must first be overcome.
First, it is critical to further improve the theoretical design
and experimental fabrication of selective emitters to offer
greater high-temperature stability and performance (see also
section 17). Many simpler emitter structures, such as metallic
sheets, inevitably experience significant degradation in
wavelength selectivity at high temperatures. More complex
nanostructures can avoid some of these challenges but are
more vulnerable to structural degradation even at tempera-
tures well below the bulk melting point of the underlying
elements (e.g., refractory metals, such astungsten).
Second, it is important to consider strategies for reducing
the need for precise alignment between emitters and receivers.
Figure 26. Overview of TPV operation along with a summary of the
remaining challenges and possible advances to help address them.
Figure 27. Illustration of the potential of TPVs. Using an integrated
selective emitter structure can shape thermal radiation to match the
PV cell band gap. Efficiency is plotted as a function of band gap and
temperature. Maximum efficiencies may reach up to 50% for PV cell
band gaps of 0.7–1.1 eV at 1200 °C.
32
J. Opt. 00 (2016)000000 Roadmap

High-performance external photon-recycling strategies, in
particular, generally require precise alignment, yet have zero
tolerance for direct mechanical contact because of the thermal
gradient. This combination may be experimentally unrealistic
to achieve, so more straightforward alternatives would be
highly beneficial.
Third, it is crucial to achieve improved understanding of
novel physical phenomena in thermal radiation and to
develop appropriate strategies for harnessing them. One
particular emerging topic concerns the potential to achieve
thermal radiation power levels that appear to exceed the
common understanding of Planck’s blackbody law (see
section 1)through alternative geometric surfaces with
increased surface area offering improved impedance matching
between high DOS materials and air [164]. Another promis-
ing approach uses subwavelength gaps between emitter and
receiver structures to transfer power in the near field
exceeding that of a blackbody (see section 16). However,
alignment of macroscopic plates at nanometer-scale distances
without physical contacting would seem to be an even more
prohibitive experimental challenge than discussed previously.
Finally, reducing the cost and improving the performance
of the low-band-gap PV cells is often a challenge. Even for
relatively expensive GaSb cells (E
g
=0.7 eV), this difficulty
manifests primarily in low OC voltages (typically 250 mV or
less), which has follow-on effects for the fill factor and overall
efficiency of the TPV system, even in the presence of an ideal
thermal emitter with excellent photon recycling.
Advances in science and technology to meet
challenges
To surmount the challenges discussed above, a number of
promising approaches are under active investigation at this
time. To improve the selectivity and thermal stability of
emitters, a couple of key strategies are emerging. First, quality
factor matching approaches that combine naturally selective,
albeit, weak emitters, such as rare-earth-doped crystals (e.g.,
erbium aluminum garnet), with PhCs having resonant modes
at the same key wavelengths [165]. Second, next-generation
photon-recycling approaches that sharply reduce the effective
emissivity observed from outside the photon-recycling sys-
tem. With sufficient selectivity, additional benefits can be
realized, such as dielectric waveguides for increasing
separation between emitters and receivers—particularly use-
ful for maintaining large thermal gradients outside of ultra-
high vacuum.
In parallel, advances are needed in terms of reliability
and stability of selective thermal emitters (see section 17). For
example, work has recently been performed to fill in the voids
for 2D and 3D PhC structures with optically transparent dif-
fusion barrier materials to greatly improve thermal stability.
With the appropriate choice of materials, transparent encap-
sulation can be performed to package the high-temperature
emitters against softening and oxidation, which are often
difficult to avoid. This also offers the possibility of hetero-
geneous integration with other types of structures that pro-
mote photon recycling without mechanical failures from large
thermal gradients.
In terms of realizing new physical mechanisms for TPVs,
one promising approach would be to develop and to use
angle-selective thermal emitters to more naturally concentrate
light on a distant receiver, which would reduce the need for
precise alignment between emitter and receiver. For near-field
thermal transfer, promising alternative strategies include
using an array of sharp tips (as in transmission e microscopy)
to achieve precise alignment and sufficient power transfer.
Another needed advance would be improvements in both
efficiency and manufacturability for low-band-gap PV diodes.
Here, several possibilities could be considered. First, epitaxial
liftoff of high-quality direct band-gap III–V materials on
reusable substrates could allow for record efficiencies at much
more reasonable costs. Second, in situ vapor–liquid–solid
growth from metallic precursors should be considered as
recently demonstrated for indium phosphide PVs. Third,
solution-processed low-band-gap materials could be used in
TPVs, such as perovskites for PVs.
Concluding remarks
In conclusion, TPVs is a technology that has the proven
capability of quietly converting heat into electricity without
moving parts [156]. The best designs, to date, have combined
high-temperature operation, high-performance InGaAs PV
cells, and long-pass filters to achieve up to 23.6% conversion
of thermal radiation into electricity [159]. TPVs also has the
potential for even higher performance in the future, poten-
tially exceeding 50% [156]as shown in figure 27 (see also
sections 13,16)as well as lower costs. Achievement of such
metrics could be enabled by future advances in selective
emitter or PV technology, which may include the exploration
of novel materials as well as the incorporation of novel
physical phenomena, such as enhanced out coupling for
thermal emitters in the near or far fields as summarized in
figure 26.
33
J. Opt. 00 (2016)000000 Roadmap

16. Near-field radiative transfer in the energy-
conversion schemes
Jean-Jacques Greffet
Institut d’Optique, CNRS, Université Paris-Saclay
Status
The field of radiative heat transfer on the nanoscale started
with the experimental observation [166]that the flux
exchanged between two metallic plates separated by a sub-
micrometer gap dcould be larger than the Stefan–Boltzmann
law (figure 28). We now have a simple picture that explains
the reason for this extraordinary flux [167]as depicted in
figure 29(a). The radiative flux is given by the sum of the
intensity over all angles from normal incidence to grazing
incidence. Let us, instead, adopt an electromagnetic point of
view and sum over all parallel wave vectors of the electro-
magnetic fields on the (k
x
,k
y
)plane. For parallel wave vectors
with a modulus k
p
<ω/c, where ωis the frequency and cis
the light velocity, the waves are propagating (figure 29(b)),
and there is no difference with summing over all angles.
The additional heat flux can be partly attributed to
additional modes that are propagating in the medium but not
in the air with k
p
in the range [ω/c,nω/c]producing the so-
called frustrated total internal reflection (figure 29(c)). A more
complete theoretical explanation provided by Polder and van
Hove [168]clarified the role of the evanescent modes with
arbitrary large wave vectors (figure 29(d)) (see also section 1).
The transmission factor associated with each mode decays
exponentially as exp(−k
p
d)and introduces a cutoff: only
modes with k
p
<1/dcontribute to the heat flux. Hence, the
heat flow increases as 1/d
2
because the number of modes
increases as the area of the disk is limited by
k
x
2
+k
y
2
=1/d
2
.
Experimental observation of this enhanced flux appeared
to be extremely difficult at ambient temperatures [169]so that
this effect remained a physics peculiarity until it was dis-
covered [170]that the heat flux can be much larger for
dielectrics than for metals. This is due to the fact that the
transmission factor associated with each mode is very low for
metals but close to 1 for dielectrics at a particular frequency in
the IR due to the resonant excitation of gap modes produced
by surface phonon polaritons. It follows that the flux is qua-
simonochromatic. Large heat fluxes have been observed
[171,172]confirming theoretical predictions. As shown in
figure 29(e),the flux is expected to be orders of magnitude
larger than in the far field so that there is a potential gain for
energy-conversion devices.
Current and future challenges
How can we take advantage of this extraordinary large and
quasimonochromatic heat flux for energy conversion? In what
follows, we restrict the discussion to near-field TPVs, which
has been proposed as a possible candidate [170,173,174]
(see also section 15). Single-junction PV cells have an
efficiency limited by the so-called SQ limit. The key issue is
the mismatch between the narrow absorption spectrum of a
single-junction PV cell and the broad incident spectrum of a
blackbody: either the Sun or a secondary source at lower
Figure 29. Schematic of the modes contributing to the radiative heat
transfer. Modes with wave vectors k
p
<ω/ccorrespond to propagat-
ing waves and modes with k
p
>ω/ccorrespond to evanescent waves
(reprint from 170, copyright 2010 by the American Physical Society).
(e)h
R
versus the gap width dbetween two SiC half-spaces [182].The
heat flux per unit area is given by h
R
ΔTwhere ΔTis the temperature
difference between the two surfaces.
Figure 28. Spectral density of the heat transfer coefficient h
R
between
two SiC half-spaces [182].Itisseenthattheflux is mostly exchanged
at a frequency corresponding to the SiC surface phonon polariton.
34
J. Opt. 00 (2016)000000 Roadmap

temperature. Hence, IR photons with hν<E
g
are not
absorbed, while photons with hν>E
g
lead to a loss of energy
hν−E
g
. TPVs is a concept that has been proposed to cir-
cumvent this limit. It amounts to illuminate the cell through a
filter so that only energy at the right frequency is used, the rest
being recycled in an isolated system.
Working with a near-field TPV system would have two
key advantages: (i)the flux is increased by several orders of
magnitude as compared to the far-field case so that the output
power would be dramatically increased; (ii)the near-field
thermal radiation can be quasimonochromatic so that the
efficiency could be above the SQ limit. Furthermore,
increasing the current in a junction results in a larger OC
voltage so that the output electrical power is further increased.
Alternatively, the larger flux for a given temperature differ-
ence may be a way to use energy from low-temperature
sources, the so-called waste heat issue. Hence, near-field
TPVs appears as a promising option [173–178]. What are the
key challenges to fully benefit from the physics of near-field
heat transfer? Fabrication and thermal management raise
serious difficulties as the cell needs to remain at ambient
temperature while being at a distance of around 100 nm from
a hot surface. The second key issue is the design of a qua-
simonochromatic source at a frequency matching the cell
band gap (see sections 15–17).
Advances in science and technology to meet
challenges
The heat flux has been measured in the nanometric range
[171,172]between a sphere and a plane. Fabricating a system
with two planar surfaces separated by a submicrometer dis-
tance is a challenge. The feasibility of a planar system has
been demonstrated in the micrometer size regime by the
company MTPV [175]. In this range, the gain in flux is
limited to one order of magnitude, and there is almost no
benefit regarding the efficiency. The design and modeling of
the thermal management of the system will play a critical role
in the final performance of the system [176].
An important feature of the near-field TPV cell is its
potential to generate quasimonochromatic fluxes and,
therefore, to increase the efficiency [177]. It has been shown
that an ideal surface wave resonance producing a quasimo-
nochromatic flux could generate efficiencies on the order of
35%. Yet, this would be obtained at unrealistically short
distances on the order of less than 10 nm. In addition, there is
no obvious material providing a phonon resonance at the
required frequency. Using a quasimonochromatic emitter is
not necessarily the best option. Finding the best near-field
emitter is an open question. It could be either a new material
or a metasurface with appropriate engineered resonances.
This issue is all the more challenging as the system needs to
operate reliably over a long time at temperatures above
1000 K.
Another challenge is related to the development of the
PV cell. As the flux is due to evanescent waves, the absorp-
tion takes place very close to the surface. As a rule of thumb,
if the gap has a width d, then, the absorption takes place
within a distance dof the interface. In other words, the cell is
very sensitive to surface defects and to e–h recombination
processes taking place close to the interface [178]. This calls
for the development of efficient surface passivation processes.
Optimizing the detector is also an open question. It has
recently been suggested to use graphene to tailor the detector
[179,180]or the flux [181].
Concluding remarks
Radiative heat transfer can be increased by orders of magni-
tude in the near field. It also provides the opportunity to tailor
the spectrum with a potential benefit for the energy-conver-
sion efficiency. A near-field TPV energy converter could be
extremely compact and could operate at relatively low tem-
peratures offering new avenues to harvest waste heat. Yet,
designing a practical device raises a number of challenges.
Many groups have now reported experimental measurements
of the flux with different geometries in the near field. The
challenge is now to move on to design practical devices
operating with gaps on the order of 100 nm in order to take
full advantage of the potential.
35
J. Opt. 00 (2016)000000 Roadmap

17. High-temperature nanophotonics: from theory to
real devices and systems
Ivan Celanovic and Marin Soljacic
Massachusetts Institute of Technology
Status
While tailoring optical properties of solid state materials at
room and cryogenic temperatures have been the focus of
extensive research (see sections 5–8), tailoring optical prop-
erties of materials at very high temperatures is still a nascent
field. Being able to engineer optical properties beyond what
naturally occurring materials exhibit and maintaining these
properties over high temperatures and over the device life-
cycle has the promise to profoundly influence many fields of
energy conversion, i.e., solar-thermal, TPV, radioisotope
TPV, IR sources, and incandescent light sources [183–185].
Indeed, the opportunities for game-changing applications that
would benefit immensely from high-temperature nanopho-
tonic materials are vast, yet challenges remain formidable (see
also sections 13,15,16).
In general, high-temperature nanophotonic structures
enable us to control and to tailor spontaneous emission by
virtue of controlling the photonic DOS (see section 1). These
structures enable engineering spectral and/or directional
thermal emission/absorption properties where it appears that
the current state-of-the-art materials exhibit better control
over spectral than directional properties. Indeed, the impor-
tance of tailoring both spectral and directional emission
properties can be understood through the lens of specific
applications.
TPVs energy-conversion devices require spectrally
broadband, yet omnidirectional, thermal emission (usually
1–2.5 μm)with a sharp cutoff corresponding to the band gap
of the PV diode [184]. Solar absorbers, for solar-thermal and
solar TPVs (STPVs)need high absorptivity over the solar
broadband spectrum but only within a very confined spatial
angle [185–187]. Furthermore, many IR sources require both
spectrally and angularly confined thermal emission properties
[188](see also sections 13,15).
Current and future challenges
Numerous challenges arise when trying to design nanopho-
tonic materials with precisely tailored optical properties that
can operate at high temperatures (>1100 K)over extended
periods of time including the thermal cycling, such as TPV
portable generators, shown in figure 30, and STPV shown in
figures 31,32. These challenges can broadly be categorized in
two groups: material selection and fabrication challenges and
design and optimization challenges (given the performance
and operating condition constraints). Material selection and
fabrication challenges include proper material selection and
purity requirements to prevent melting, evaporation, or che-
mical reactions; severe minimization of any material inter-
faces to prevent thermomechanical problems, such as
delamination; robust performance in the presence of surface
diffusion; and long-range geometric precision over large areas
with severe minimization of very small feature sizes to
maintain structural stability. Indeed, there is a body of work
that approached the design of high-Tnanophotonics.
Two types of materials are most often considered for
high-temperature nanophotonics, namely, refractory metals
and dielectrics. Refractory metals have extremely high melt-
ing temperatures and are, hence, stable at high temperatures.
The down side of these materials is that they tend to chemi-
cally react with O and other elements (i.e., C)at high tem-
peratures. However, they have a relatively high reflectivity in
deep IR making them amenable for 2D and 3D PhC-selective
emitters. Dielectrics, such as SiO
2
, HfO
2
are often considered
for dielectric and metalodielectric PhCs since they tend to be
Figure 30. Micro-TPV MIT generator prototype; left: image of
2×2 cm reactor during operation; right: cross-sectional drawing of
the prototype system.
Figure 31. Operating principle and components of the STPV.
Sunlight is converted into useful thermal emission and, ultimately,
electrical power via a hot absorber–emitter. Schematic (a)and
optical image (b)of our vacuum-enclosed devices composed of an
aperture/radiation shield, an array of multiwalled nanotubes as the
absorber, a 1D PhC, and a 0.55 eV band-gap PV cell (adopted
from [187]).
36
J. Opt. 00 (2016)000000 Roadmap

less reactive at high temperatures and are standard micro-
fabrication materials. Interface minimization is another aspect
of design that has to be taken into account due to thermally
induced stresses and potential reactions and interdiffusion.
Hence, the simpler the interfaces the better. Surface diffusion
is especially pronounced for metallic PhC, 2D and 3D due to
relatively high diffusion constants that tend to drive diffusion
around sharp features, hence, degrading optical performance.
Finally, nano- and microfabricating structures that maintain
long-range geometric precision and geometrical parameters at
high-Tremain a fabrication, a design constraint, and a
challenge.
Advances in science and technology to meet
challenges
Two key opportunities toward practical high-temperature
nanophotonic devices remain: new and more robust material
systems and fabrication processes; and even higher level
of control of directional and spectral properties (i.e.,
even more selective emission/absorption, both spectrally and
directionally). In terms of materials and fabrication
challenges: demonstrating high-Tphotonic devices with tens
of thousands of hours operational stability at temperatures
above 1000 K; mastering materials and fabrication processes
to fabricate metalodielectric photonic structures; developing
passivation and coatings for refractory metallic structures
that will be oxidatively and chemically stable in noninert
environments.
In terms of achieving the next level of control of direc-
tional and spectral properties, several key challenges remain:
angularly selective broadband absorbers; spectrally highly
selective broadband wide-angle emitters, spectrally highly
selective broadband narrow band emitters, and near-field
highly resonant energy transfer.
Concluding remarks
The main driver for high-performance high-temperature
nanophotonic materials are energy-conversion applications,
such as: solar-thermal, TPVs, radioisotope TPV, IR, and
incandescent light sources. These applications would benefit
greatly from robust and high-performance high-Tnanopho-
tonic materials. Indeed, more work is needed that is strongly
grounded in the experimental and application worlds. Real
life constraints need to be brought into the design process in
order to inform the theoretical and exploratory work. In the
end, fresh and innovative thinking in terms of new theoretical
approaches is always critical, and it drives the field forward.
However, it needs to be well targeted and directly coupled to
experimental and application work to provide rapid evalua-
tion of advanced concepts and ideas.
Figure 32. SEM images of fabricated (a)PhC absorber and (b)PhC
emitter. (i)Photograph of a STPV setup absorber/emitter sample
mounted on top of a PV cell. (d)Normal emittance determined from
reflectance measurements at room temperature (solid lines)and
simulated normal emittance (dashed lines)of the fabricated PhC
emitter, PhC absorber, and flat Ta absorber.
37
J. Opt. 00 (2016)000000 Roadmap

18. Endothermic-PL: optical heat pump for next
generation PVs
Assaf Manor and Carmel Rotschild
Technion, Israel Institute of Technology
Status
Single-junction PV cells are constrained by the fundamental SQ
efficiency limit of 30%–40% [23](see section 1). This limit is,
to a great extent, due to the inherent heat dissipation accom-
panying the quantum process of electrochemical potential gen-
eration. Concepts, such as STPVs [189,190]aim to harness
these thermal losses by heating a selective absorber with solar
irradiation and coupling the absorber’sthermalemissiontoa
low-band-gap PV cell (see sections 13–17). Although, in theory,
such devices can exceed 70% efficiency [191],thusfar,no
demonstration above the SQ limit was reported. This is mainly
due to the requirement to operate at very high temperatures.
In contrast to thermal emission, PL is a nonequilibrium
process characterized by a nonzero chemical potential, which
defines an enhanced and conserved emission rate [6](see
section 1). Recently, the characteristic of PL as an optical heat
pump at high temperatures was theoretically and experimentally
demonstrated [192]. In these experiments, PL was shown to be
able to extract thermal energy with minimal entropy generation
by thermally induced blueshift of a conserved PL rate.
Here, we briefly introduce and thermodynamically ana-
lyze a novel thermally enhanced PL (TEPL)device for the
conversion of solar energy beyond the SQ limit at moderate
operating temperatures. In such a device, high solar photon
current is absorbed by a low-band-gap thermally insulated PL
material placed in a photon-recycling cavity. Due to the rise
in its temperature, the blueshifted PL generates energetic
photons in rates that are orders of magnitude higher than
thermal emission at the same temperature. The PL is har-
vested by a high-band-gap PV cell, yielding enhanced voltage
and efficiency (see the detailed description below).
In addition, we present proof-of-concept experiments for
TEPL operating at a narrow spectral range where sub-band-
gap photons are harvested by a GaAs SC. Future challenges in
this new direction include: i. Material research (see sections 5–
8)for expending the overlap between the absorption line shape
and the solar spectrum while maintaining high QE. ii. Opti-
mizing the band gaps with respect to the absorbed spectrum
and operating temperature. iii. Optimizing the photon-recy-
cling efficiency (see sections 4,15). iv. Exploring the funda-
mentals of endothermic PL. The low operating temperatures
associated with the minimal entropy generation together with
overcoming future challenges may open the way for practical
realization of high-efficiency next-generation PV.
Current and future challenges
Figure 33(a)depicts the conceptual design of the TEPL-based
solar energy converter. A thermally insulated low-band-gap
PL absorber completely absorbs the solar spectrum above its
band gap and emits TEPL toward a higher-band-gap PV cell,
maintained at room temperature. Such a device benefits from
both the high photon current of the low-band-gap absorber
and the high PV voltage.
For minimizing radiation losses, a semiellipsoidal reflec-
tive dome recycles photons by reflecting emission at angles
larger than the solid angle Ω
1
[193]. In addition, the PV’s
backreflector [194]reflects sub-band-gap photons to the
absorber. Figure 33(b)shows the absorber and PV energy
levels, where μ
1
and T
1
define the absorber’s thermodynamic
state and its emission. In the detailed analysis of such a device,
the PL absorber satisfies the balance of both energy and photon
rates between the incoming and the outgoing radiation currents,
while the PV satisfies only the rate balance due to the dis-
sipated thermal energy required to maintain it at room temp-
erature. By setting the PV’s voltage, we solve the detailed
balance and find the thermodynamic properties Tand μas well
as the system’sI–Vcurve and its conversion efficiency (see
section 1). The analysis for various absorber and PV band-gap
configurations shows a maximal theoretical conversion-effi-
ciency limit of 70% for band-gap values of 0.5 and 1.4 eV
under ideal conditions of photon recycling and thermal insu-
lation (figure 33(c)). More importantly, the expected operating
temperatures at such ideal conditions are below 1000 °C, about
half of the equivalent temperature required in STPV.
When approaching the experimental proof of concept, we
need to address the challenges of realizing a TEPL-based solar
converter. First, high QE must be maintained at high tem-
peratures. This limits the use of semiconductors due to non-
radiative recombination mechanisms, which reduces QE with
temperature. In contrast, rare-earth emitters, such as neody-
mium (Nd)and ytterbium, are known to maintain their QE at
high temperatures as their es are localized and are insulated
from interactions [195]. Although they have superior QEs, the
use of rare earths as PL absorbers raises another challenge: the
poor overlap between the solar spectrum and their absorption
Figure 33. (a)The device’s scheme. (b)The absorber and PV energy
levels with the currents flow. (c)The maximal efficiency versus E
g1
and E
g2
.
38
J. Opt. 00 (2016)000000 Roadmap

line shape. Within these limits, as a proof of concept for the
ability to harvest sub-band-gap photons in a TEPL device, we
experiment with a Nd
3+
:SiO
2
absorber coupled to a GaAs PV.
Thesampleisplacedinvacuumconditions(10
−4
mbars),
pumped by a 914 nm (1.35 eV)laser. This pump is a sub-band
gap with respect to the GaAs SC (1.44 eV). At room temper-
ature, the 914 nm induces a PL spectrum between 905 and
950 nm. The temperature does not rise since each emitted
photon carries similar energy to the pump photons. An addi-
tional 532 nm pump, which matches the Nd
3+
absorption line,
is used to mimic an average solar photon in order to increase
both temperature and PL photon rate. The first experiment is
performed only with the 532 nm pump in order to measure the
pump power that is required for a significant blueshift.
Figure 34(a)shows the PL spectrum evolution with the
absorbed pump intensity, indicated in suns (one
sun=1000 W m
−2
). At the pump power of 400 suns, the PL
exhibits a significant blueshifting from 905 to 820 nm, which
can be harvested by the GaAs PV. Figure 34(b)shows the time
dependence of the PV current under dual pump lasers. At first,
an increase in current is observed when only the 914 nm pump
is switched on as a result of a room-temperature blueshift (red
line at t=5). Then, the 532 nm pump is switched on (red line
at t=10), and the current gradually rises due to the rise in
temperature. When the sample reaches 620 K, the 532 nm
pump is switched off, leaving only the 914 nm pump. The
current, then, drops to a level two times higher than its initial
value at t=5. This demonstrates how the heat generated in the
thermalization of the 532 nm pump is harvested by blueshifting
of 914 nm sub-band-gap photons. The green line shows the
PV’s current time dependence when only the 532 nm pump is
on with insignificant thermal current when both pumps are off.
Advances in science and technology to meet
challenges
A future demonstration of efficient TEPL -conversion devices
requires advances in material science, development of tailored
optics, and an understanding the fundamentals of PL. The pre-
sented proof of concept demonstrates the ability to harvest sub-
band-gap photons in TEPL, yet this demonstration can operate
only at a narrow spectral range due to the typical absorption
lines of rare earths. The challenge of expending the absorption
spectrum while maintaining high QE requires the use of laser
technology knowhow where a broad incoherent pump is cou-
pled to a narrow emitter with minimal reduction in QE. Such
sensitization may include the development of cascaded energy
transfer [196]between rare earths and transition metals. Another
challenge is replacing the Nd
3+
absorber with a lower-energy
gap material for enhancing photon rate and overall efficiency. In
addition to the material research, realization of an efficient
device requires the development of high-quality photon-recy-
cling capabilities. This includes clever optical engineering with
tailored narrow bandpass filters and cavity structures. Finally,
focusing on the fundamental science, our experiments on
endothermic PL [192]show a discontinuity in the entropy and
chemical potential at a critical temperature where the PL
abruptly becomes thermal emission. It is fascinating to explore
the thermodynamic properties of this discontinuity.
Concluding remarks
Based on our recent experimental observations showing that PL
at high temperatures is an efficient optical heat pump, we propose
and analyze a solar energy converter based on TEPL. In addition,
we experimentally demonstrate the TEPL’s ability to harvest sub-
band-gap radiation. Finally, the roadmap for achieving efficiency
in such devices is detailed. We describe the expected challenges
in material research, optical architecture, and fundamental sci-
ence. We believe that successfully overcoming these challenges
will open the way for disruptive technology in PVs.
Acknowledgments
This report was partially supported by the Russell Berrie
Nanotechnology Institute (RBNI)andtheGrandTechnion
Energy Program (GTEP)and is part of The Leona M and Harry
B Helmsley Charitable Trust reports on Alternative Energy
series of the Technion and the Weizmann Institute of Science.
We also would like to acknowledge partial support by the Focal
Technology Area on Nanophotonics for Detection. A. Manor
thanks the Adams Fellowship program for financial support.
Figure 34. (a)PL evolution with pump power. (b)PV current
versus time.
39
J. Opt. 00 (2016)000000 Roadmap

19. Harnessing the coldness of the Universe by
radiative cooling to improve energy efficiency and
generation
Aaswath Raman, Linxiao Zhu, and Shanhui Fan
Stanford University
Status
With the rise of PVs, we have made significant progress in
exploiting a powerful and renewable source of thermo-
dynamic heat, the Sun (see sections 2–14). However, our
society has, thus far, largely ignored another ubiquitous
resource that is equally important from a thermodynamic and
energy-conversion point of view: the cold darkness of the
Universe. Exploiting and harnessing this resource represents
an important frontier for both energy and photonics research
in the coming decade with the potential to dramatically
improve the efficiency of any existing energy-conversion
process on Earth.
This resource can be accessed due to a feature of Earth’s
atmosphere: between 8 and 13 μm, it can be transparent to
electromagnetic waves. Thus, a significant fraction of thermal
radiation from a sky-facing terrestrial object (at typical tem-
peratures ∼300 K)is not returned to it from the sky, effec-
tively allowing such a surface radiative access to the
Universe. Beginning in the 1960s, researchers investigated
exploiting this concept, known as radiative cooling, at night
using black thermal emitters [197]. Moreover, it was noted
early on that the spectral features of the atmosphere’s trans-
parency meant that a spectrally selective thermal emittance
profile should allow a radiative cooler to reach lower tem-
peratures [198]. Subsequent work, thus, tried to find materials
with suitable emissivity profiles or to engineer selective
emitters based on a thin-film approach [199,200]. While over
the last two decades, research interest in this topic declined,
some recent work also examined the use of photonic nano-
particle effects for radiative cooling [201]. However, all of
these efforts focused on radiative cooling at night, and until
recently, radiative cooling during the day remained an open
challenge.
Current and future challenges
If radiative cooling is to play a role in energy efficiency, it is
critical that it be accessible precisely at hours when the need
for a colder cold sink is greatest: the day. Achieving radiative
cooling during the day requires being able to maintain strong
thermal emission, ideally selective to the atmospheric trans-
parency window, while reflecting nearly all incident sunlight
(figure 35). Our theoretical proposal [202]showed that day-
time radiative cooling was, indeed, possible, and our recent
experiment demonstrated [203]a performance of 5 °C below
ambient steady-state temperatures and 40 W m
−2
cooling
power at air temperature in clear sky conditions (figure 36).It
is important to note, however, that this performance is
strongly dependent on the IR properties of the atmosphere,
which are, in turn, influenced by humidity and cloud cover.
Under dry hot conditions, better performance can be achieved
with the same radiative cooler form [203]. In less favorable
conditions, the net positive radiative flux at IR wavelengths
lessens, and an even higher solar reflectance is needed to
achieve meaningful cooling power during the day. To further
improve performance in all conditions and to enable useful
cooling powers even in humid climates, achieving near-unity
emissivity within the window is also important. While this is
challenging, a recent paper demonstrated daytime cooling in
Figure 35. Schematic of how a surface can cool itself radiatively
below air temperature. Strong selective thermal emission in the mid-
IR must be achieved while also reflecting nearly all incident sunlight.
Figure 36. Outdoor test of a daytime radiative cooling surface. A test
stand that insulates and minimizes parasitic heat gain is essential to
maximize performance. A unique feature of radiative cooling
experiments is the need to perform tests outdoors.
40
J. Opt. 00 (2016)000000 Roadmap

challenging atmospheric conditions, offering cause for opti-
mism [204].
Effectively using radiative cooling also entails minimiz-
ing parasitic heating from the environment. This is a non-
trivial challenge given the constraints of operating under the
Sun, and the lack of cheap and rigid IR-transparent materials
that could serve as a window for the large areas typically
needed. Making practical use of such surfaces for cooling also
requires engineering systems that can efficiently transfer heat
loads to the sky-facing surfaces while minimizing other heat
gains. Radiative cooling systems will be particularly sensitive
to such gains given that cooling powers available will typi-
cally be <100 W m
−2
.
In the demonstrations of daytime radiative cooling
shown, so far, the sunlight is reflected and goes unused. One
challenge is, thus, to make use of this sunlight while preser-
ving the cooling effect. In this spirit, we recently proposed the
use of radiative cooling to cool SCs [205]by engineering the
thermal emissivity of a top surface above the PV material
while transmitting the same amount of sunlight through it.
This was one example of the broader vision of enabling and
improving energy generation in addition to efficiency. Rela-
ted to this, there was also a recent proposal to make use of the
imbalance between outgoing and incoming IR-thermal
emission from sky-facing objects directly for energy con-
version [206]. In both cases, experimental demonstrations
pose challenges and are fruitful areas for further research.
Advances in Science and Technology to Meet Challenges
—A variety of photonic approaches can be leveraged to
achieve both the spectral and the angular selectivities desir-
able for radiative cooling (see sections 1,13,15–17). A recent
metamaterial-based design, for example, experimentally
achieved extremely strong and selective emissivity within the
atmospheric window [207].
Creative interdisciplinary research recently showed how
the geometric shape and arrangement of hairs on Saharan
silver ants not only increase their solar reflectance, but also
increase their thermal emissivity in the mid-IR, enabling their
survival through cooling in very hot environments [208].
Such research opens up possibilities for biologically inspired
metasurface designs that can achieve some of the same effects
sought for radiative cooling during the day.
A key challenge and opportunity with radiative cooling
will be to balance the need for low costs for what is inherently
a large-area technology with the higher performance poten-
tially achievable with more complex designs. While [203]
showed that good performance can be achieved with a non-
periodic 1D photonic structure, recent advances in imprint
lithography make more complex designs tractable given
sufficient performance gains.
Concluding remarks
Radiative cooling allows access to a thermodynamic resource
of great significance that we have, thus far, not exploited in
our energy systems: the dark Universe. By effectively har-
nessing it during the day, we are not only able to access a
universal heat sink precisely when it is most needed, but also
able to demonstrate that such systems can have a ‘capacity
factor’of 24 h a day—distinguishing this technology from
PVs. These demonstrations, however, are just the first
building block in what we believe is a worthwhile and game-
changing broader project: engineering all terrestrial energy
systems to take advantage of this dark resource to improve
their efficiency and potentially directly generate energy as
well. Improvements in spectral control of thermal emission
through metamaterial and metasurface concepts could, thus,
rapidly translate to improved performance both for direct
cooling and for indirectly improving the efficiency or gen-
eration ability of any terrestrial energy system.
41
J. Opt. 00 (2016)000000 Roadmap

20. Entropy flux and upper limits of energy
conversion of photons
Gang Chen
Massachusetts Institute of Technology
Status
The entropy of photons has been studied by many researchers in
the past [209,21,6](see also section 1)(1),buttherearestill
unsettled questions. Understanding the entropy of photons will
help set the correct upper limits in the energy conversion using
photons from SCs to light-emitting diodes to optical refrigeration.
We will use blackbody radiation as an example to lead the dis-
cussion. Considering an optical cavity of volume Vat temperature
T, the temperature and entropy (S)of photons inside the cavity
obey the relation: TS=4U/3, where U(=4VσT
4
/c)is the
internal energy of the blackbody radiation field inside the cavity,
s
is the Stefan–Bolzmann constant, and cis the speed of light.
While this relation is well established, the trouble arises when one
considers the thermal emission from a black surface with emis-
sive power J
b
=σT
4
Wm
−2
with the corresponding entropy flux
J
s
,
s==JT
J
T
4
3
4
3.2
sb
3()
This expression does not follow the familiar definition for
entropy flow across a boundary: Q/Tif the heat flow Qis set
equal to the emissive power J
b
.
Current and future challenges
The entropy flux as definedinequation(2)is valid and the
inequality between J
s
and J
b
/Tis fundamentally due to the
nonequilibrium nature of thermal radiation leaving a surface
[20,210]. Consider that an object at temperature Treceives heat
Qat one boundary by conduction and emits as a blackbody
thermal radiation via surface A, the rate of entropy generation in
the process is, according to the second law of thermodynamics,
s=-=

SAJQ
TAT
1
3.3
gs 4()
If emission generates entropy, the reverse process should
not work: an external blackbody radiation source is directed at
an object, delivering radiant power s=
Q
AT.
4This same
amount of power cannot be conducted out since, otherwise,
the process will lead to entropy reduction. The key to show
this, indeed, is the case of the Kirchoff law. We assume that
the object’s surface facing the incoming radiation is black.
According to Kirchoff’s law, the object will also radiate back
to the incoming radiation source (we will assume a view factor
of unity to simplify the discussion), so the net heat that can be
conducted out is: s=-
Q
AT T.
h
44
()
Entropy generated in
the object is, then, ss=+ -

S
AT AT.
Q
Th
4
3
44
3
4
˙
This function
is always positive, reaching a minimum when T=T
h
(and
Q=0). Hence, the heat that can be conducted out is less than
the radiant power that comes in (unless T=0K).
At first sight, the idea that thermal emission from a surface
generates entropy might be surprising. Careful examination,
however, reveals that thermal emission from a surface is a
sudden expansion of photon gas bearing a similarity to the
irreversible sudden expansion of gas molecules from a pres-
surized container to vacuum. Of course, there are also differ-
ences since photons normally do not interact with each other
while molecules do. Hence, if a perfect photon reflector is
placed in the path of the emitted photons to completely reflect
back all photons leaving the black surface, there is no heat
transfer and no entropy generation. In this case, photons at the
emission surface are at an equilibrium state, and their temper-
ature can be well defined, and, hence, no entropy is generated.
In the case of molecules expanding into a vacuum, it will be
difficult to completely reflect back all molecules as they scatter
each other, and, hence, entropy will eventually be generated.
A standard way to make a black surface is a small
opening on a large cavity. Immediately outside the opening,
photons only occupy isotropically the half-space since no
other photons come in. The local temperature of photons
cannot be defined, and correspondingly, one should not
expect, then, that J
b
/Tgives the entropy flux. If one is forced
to use the local photon energy density to define a local
equivalent photon temperature, this equivalent equilibrium
temperature will be lower than T
h
[211](see section 1). In this
sense, it is not surprising that the entropy flux as given by
equation (3)is larger than J
b
/T
h
.
Although some researchers did use equation (2)for the
entropy flux, they sometimes introduce a photon-flux temperature
T
f
equaling the ratio of J
b
/J
s
in the thermodynamic analysis of
heat engines based on photons. Landsberg and Tonge [21]
used the concept of photon-flux temperature to derive the max-
imum efficiency of a heat engine at temperature Treceiving
thermal radiation from a heat source at temperature T
h
as
h
=- +1.
L
T
T
T
T
4
3
1
3
4
hh
()
This efficiency is called the Lands-
berg efficiency and has been derived by different researchers
[210–212]. As we will see later, although the Lansberg and Tonge
result is correct with proper interpretation (i.e., Tequals the
ambient temperature), their derivation did not, in fact, consider
the ambient temperature (except in an alternative availability
argument). We will re-derive below the Landsberg limit and
show a higher limit when the radiation source is not from the Sun.
Our model considers a thermal emitter coupled to a heat
reservoir at temperature T
h
, heat engine at temperature T(our
results are valid if Tis time varying, but we will not include
time here for simplicity), and a cold reservoir at T
c
as shown in
figure 37(a). We assume the surfaces involved in the radiative
heat transfer between the heat reservoirs are blackbodies. The
key is to recognize that when a heat engine absorbs thermal
radiation, it also radiates back to the thermal emitter according
to Kirchoff’s law as illustrated in figure 37(a). Correspond-
ingly, the net rate of entropy flowing into the heat engine is
s=-
S
AT T.
h
in
4
3
33
()
The maximum power is reached when
this entropy is rejected to the cold reservoir T
c
without addi-
tional entropy generation in the heat engine and the heat
rejection process. The rate of heat rejection is, then,
s== -
Q
TS AT T T .
cc c
h
in
4
3
33
()
The power output can be
42
J. Opt. 00 (2016)000000 Roadmap

obtained from the first law of analysis for the heat engine,
⎟
⎛
⎝
⎜⎞
⎠
⎟
⎛
⎝
⎜⎞
⎠
s
s
=--= -
-
WQ Q Q AT T
T
ATTT
14
3
4
3.
hrc h
c
h
c
4
43
The above expression is maximum when T=T
c
,
⎛
⎝
⎜⎞
⎠
⎟
ss=-+WAT T
TAT14
3
1
3.4
h
c
h
c
max 44
()
We can define two efficiencies using the above analysis.
One is based on the radiant energy leaving the heat reservoir,
⎛
⎝
⎜⎞
⎠
⎟
hs
=
D
=- +
W
AtT
T
T
T
T
14
3
1
3.5
h
c
h
c
h
1
max
4
4
()
This expression is the Lansberg efficiency. This efficiency
definition is appropriate for solar radiation. However, if the
thermal emission comes from a terrestrial heat source, such as
in a TPV device (see sections 15–18), the heat supplied to the
heat reservoir should be the difference of radiated and absorbed
radiation by the reservoir s=-
Q
TTAhc
44
(
)
, and the effi-
ciency should be defined as
⎛
⎝
⎜⎞
⎠
⎟
⎡
⎣
⎢
⎢
⎛
⎝
⎜⎞
⎠
⎟
⎤
⎦
⎥
⎥
h==-+ -
-
W
Q
T
T
T
T
T
T
14
3
1
31.6
c
h
c
h
c
h
2
max
44
1
()
This efficiency is higher than the Landsberg efficiency.
Thus, although the Landsberg efficiency is appropriate for solar
radiation and is often considered as an upper limit for thermal
radiation-based energy-conversion systems, a higher limit exists
when terrestrial heat sources are used as the photon source.
Advances in science and technology to meet
challenges
Our discussion, so far, has been limited to the blackbody
radiation. We believe that the same strategy can be applied to
search for the upper limits of all other photon-mediated
energy-conversion processes involving nonblack objects,
emission from SCs, light-emitting diodes, lasers, photo-
synthesis, optical UC, optical refrigeration [19,213], near-
field radiation heat transfer, near-field to far-field extraction,
etc. For analyzing these processes, one should bear in mind
two key results obtained from past studies. First, a general
expression for the entropy of photons in a quantum state,
whether they are at equilibrium or not, is
=+ +-
S
kf fff1ln1 ln,
B1[( ) ( ) ] where fis the number
density of photons in the quantum state. From this expression,
one can obtain entropy flux leaving a surface by considering
the velocity of photons and summing up all their quantum
states [21]. The other key result is photons possess an effective
chemical potential when the radiation field is created via
recombination of excited states at different chemical potentials
(see sections 1,4,18), although purely thermally radiated
photons do not have a chemical potential (μ=0)since their
numbers are not fixed. This fact is used in analyzing photon-
based energy-conversion processes and devices, such as PV
cells [24], light-emitting diodes, photosynthesis, etc. However,
there does not seem to be studies starting from the entropy-
flux consideration to arrive at the maximum efficiency of
energy-conversion processes. The SQ limit [23]for the PV
cell, for example, is based on consideration of the balance of
photon and charge number densities.
Concluding remarks
To summarize, thermal emission from a surface is a none-
quilibrium process involving entropy generation. For black-
body radiation, the entropy flux expression, i.e., equation (2),is
valid. By considering the entropy flux of photons, one can
arrive at proper upper limits for different photon-based energy-
conversion devices. More research along this direction can
stimulate further advances in photon-based energy conversion.
Acknowledgments
The author thanks S. Boriskina, V. Chiloyan, B. L. Liao, W. C.
Hsu, J. Tong, and J. W. Zhou for helpful discussions. This work
was supported, in part, by the ‘Solid State Solar-Thermal Energy
Conversion Center (S
3
TEC),anEnergyFrontierResearch
Center funded by the U.S. Department of Energy, Office of
Science, Office of Basic Energy Sciences under Award No. DE-
SC0001299/DE-FG02-09ER46577 (for TPV applications)and
by DOE-BES Award No. DE-FG02-02ER45977 (for extracting
photons from the near field to the far field).
Figure 37. (a)A heat engine operating between a heat source at T
h
and a heat sink T
c
. Heat transfer between the engine and heat source
is coupled via thermal radiation. Kirchoff’s law dictates that some
photons, their associated energy, and entropy are sent back to the
heat source, (b)comparison of three different efficiencies, the
Carnot, the Landsberg, and efficiency η2, which is higher than the
Landsberg efficiency.
43
J. Opt. 00 (2016)000000 Roadmap

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JOURNAL: Journal of Optics
AUTHOR: S Boriskina et al
TITLE: Roadmap on optical energy conversion
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