MSc Chemistry
Science for Energy and Sustainability
Literature Thesis
Quantum Cutting in Ytterbium-Doped Cesium Lead
Halide Perovskites
by
Merlinde Wobben
UvA: 12477885, VU: 2644946
October 2019
12 ECTS
Period: September 2
nd2019 to October 31
st2019
Supervisor/Examiner:
Examiner:
Abstract
Recent advances in the synthesis of ytterbium-doped lead halide perovskite (Yb3+:CsPbX3
with x=Cl or Cl/Br) nanocrystals and thin films have shown surprisingly efficient down-conversion by quantum cutting, which has lead to an increasing interest in synthesising and understanding this material. Here, an overview of the current state of the art in both per-formance and understanding of Yb3+:CsPbX
3 is presented. Yb3+:CsPbX3 shows very high
PLQYs up to 193%, which is a result of a quantum cutting process where, after excitation of the perovskite host with high-energy photons, the excited states of two ytterbium ions are rapidly populated. Subsequently the ytterbium ions emit lower-energy photons. This pro-cess takes place in a right-angle vacancy-defect complex involving two ytterbium ions and a lead vacancy which leads to rapid population of ytterbium. Applications of Yb3+:CsPbX
3
in both downconversion and luminescent solar concentrators have shown promise. With fur-ther research to overcome challenges regarding power saturation and stability this material has great potential for commercial applications.
Yb 3+ Yb 3+ 2 F5/2 2 F7/2 CsPbX3 Excitation Photoluminescence Defect Energy Charge Transfer
Quantum cutting
Table of Contents
Abstract 1
List of Abbreviations and Chemicals 3
1 Introduction 3
1.1 Quantum Cutting in photovoltaics . . . 3
1.2 The Element Ytterbium . . . 4
1.3 Perovskites . . . 5
2 Quantum Cutting in Yb3+:CsPbX 3 5 2.1 Yb in the structure . . . 6
3 Synthesis Methods 8 4 Composition and Architecture 9 4.1 Cl anb Br concentrations . . . 9
4.2 Yb concentration . . . 9
4.3 Codoping with a second lanthanide . . . 10
4.4 Lead-free double perovskite . . . 11
4.5 Nanocrystals or Thin Films? . . . 12
5 Power Saturation 12 6 Applications 15 6.1 Downconverter Layer . . . 15
6.2 Luminescence Solar Concentrator . . . 16
7 Further Research 17 7.1 Optimisation . . . 17
7.2 Stability and lead toxicity . . . 17
7.3 Saturation of Yb3+ . . . . 18
7.4 Scarcity of Yb . . . 19
8 Conclusion 19
List of Abbreviations and Chemicals
CIGS CuIn1−xGaxSe2
DFT Density Functional Theory
DP Double Perovskite
EQE External Quantum Efficiency
LHP Lead Halide Perovskite
LSC Luminescence Solar Concentrator
MC Microcrystal
NC Nanocrystal
PL Photoluminescence
PLQY Photoluminescence Quantum Yield
PV Photovoltaic
QC Quantum Cutting
RA Right-Angle
RE Rare Earth
SSC Silicon Solar Cell
SSVD Single-Source Vapor Deposition
Cs2CO3 Cesium Carbonate
CsC18H3O2 Cesium Oleate
CsOAc Cesium Acetate
DMF N-N Dimethylformamide
DMSO Dimethyl Sulfoxide
OA Oleic Acid
OAm Oleyamine
ODE 1-Octadecene
TMS-Cl Chloro-Trimethylsilane
1
Introduction
In recent reports there has been a growing interest in ytterbium-doped perovskite materials; 19 papers on the topic have been published so far, of which 12 are from this year, 2019, alone. Surprisingly high photo luminescence quantum yields (PLQY) have been achieved by these materials and it was concluded that this is due to a quantum cutting (QC) pro-cess. In the current paper we review the progress made in recent years in synthesising and understanding this material. In section 1 we introduce the concept of quantum cutting and the potential applications. Furthermore, we show the characteristics of both perovskites and ytterbium. In section 2 we discuss the theoretical background of the quantum cutting process in this particular material and section 3 shows the various synthesis methods for making the material. A detailed discussion of the structure, composition, architecture and variations is featured in section 4. We discuss challenges regarding power saturation in section 5 and the potential applications of ytterbium-doped perovskites in section 6. We finalise the review with an outlook and conclusion in sections 7 and 8.
1.1
Quantum Cutting in photovoltaics
In photovoltaic (PV) devices, all absorbed photons can give rise to one electron-hole-pair that has the energy of the bandgap of the PV material, regardless of the energy of the photon. Photons with a lower energy than the bandgap are not absorbed. Secondly, the excess energy above the bandgap for higher-energy photons is wasted in the form of heat, a loss called the quantum defect. Thus, there is a limit in efficiency for PV, based on one bandgap, which is called the Shockley-Queisser limit1. For silicon with a bandgap of 1.1
way to reduce the loss from the quantum defect. One process to do this is quantum cutting, the transformation of one high-energy photon into two lower-energy photons2. A simplified
visualisation of quantum cutting and how its implementation in PV works is shown infigure
1. A quantum cutting material, also referred to as a downconverter, absorbs high energy photons and emits photons with roughly half of its bandgap energy with a theoretical quantum yield of 200%. The lower-energy photons not absorbed by the downconverter are absorbed by the PV layer below, together with the emitted photons from the downconverter. The energy of high-energy photons that is lost by the quantum defect in a conventional
Figure 1: (A) Schematic of a QC/PV architecture and the general QC/PV mechanism (B) Ideal regions of the solar spectrum for QC and PV absorption in a QC/PV device. Figure from Crane et al3.
silicon solar cell (SSC) can also be harvested by a so-called tandem solar cell architecture. A high bandgap PV material sits on top of a low bandgap PV material such as silicon. High energy photons are absorbed by the top cell and lower energy photons are transmitted through the top cell and absorbed by the bottom cell. In practice it is difficult to make such a device in terms of finding the right materials. The total current density of the device is equal to that of the cell with the lowest current density, so for optimal efficiency the two cells should have equal current densities. The need for passivation layers between the cells also complicates the fabrication. In contrast, a downconverter layer can be added on top of a solar cell and no additional electronics are needed, since the product of a downconverter layer is photons instead of electrons4.
1.2
The Element Ytterbium
Ytterbium-doped perovskites were shown to have PLQYs higher than 100% and even reach-ing as high as 193% which suggests a process of quantum cuttreach-ing is in play5. To understand
this process, first the two components of this material, the element ytterbium and the com-pound class of perovskites are discussed.
Ytterbium is a rare earth (RE) element of the lanthanide series with atomic number 70. Its most common oxidation state is 3+ with valence electron configuration 4f135s25p6. It
among other REs6. No large scale applications of ytterbium are currently in use. When
added to stainless steel it improves some mechanical properties, it can be used as a laser source, and ytterbium atomic clocks hold the record for stability. However, all these and more applications are not implemented at commercial scale7.
1.3
Perovskites
Perovskites are materials of the general structure and chemical formula ABX3 as shown in
figure2. In metal halide perovskites, A corresponds to an inorganic cation, B corresponds to a different inorganic cation (usually lead), and X corresponds to a halide anion. Over the last decade, scientific attention to perovskites for use in optoelectronics and photovoltaics has grown exponentially because of the unique physical properties such as low exciton bind-ing energy, long-range charge transport, high-absorption coefficient, high dielectric constant etc. Lead-halide perovskites (LHP) such as cesium lead halide (CsPbX3) and
methylam-monium lead halide (CH3NH3PbX3) are among the most popular perovskites. Perovskite
nanocrystals (NCs) and thin films have been used for photovoltaic applications, LEDs, photodetectors, nanolasers and waveguides. However, there are problems with perovskites materials regarding the stability. Defect states and grain boundaries cause deterioration under ambient conditions, so much research has focused on increasing the stability8.
Figure 2: Crystal structure of a perovskite with the chemical formula ABX3. Position A (green) is
occupied by organic or inorganic cations, metal cations occupy position B (gray) and X (purple) is
occupied by halides. Figure from Mohan et al9.
2
Quantum Cutting in Yb
3+:CsPbX
3The absorption- and emission spectra of Yb3+:CsPbCl
3 are shown infigure 3 and tell us
why Yb3+:CsPbX
3 is so suitable for downconversion. The absorption by the perovskite is
in the higher-energy part of the spectrum, which overlaps with decreasing EQE of a sili-con solar cell. The free Yb3+ ion has two energy levels, 2F
7/2 and 2F5/2, with an energy
difference of 1.26 eV or 980 nm11. This causes emission close to the bandgap of silicon at
1.1 eV where the EQE is high and the thermalisation losses are small. According to the Laporte rule, transitions between like atomic orbitals ( s–s, p–p, d–d, f–f) are forbidden in a centrosymmetric environment, meaning atoms or molecules with an inversion center12. The2F7/2–2F5/2transition is a Laporte forbidden f–f transition and thus not very strong.
However, an excitonic transition from a host to Yb3+ may lead to a strong population of the2F
Figure 3: Absorption and photoluminescence spectra of Yb3+:CsPbCl3 (purple), AM 1.5 solar
spectrum (grey), and the external quantum efficiency of a Si solar cell. Figure from Cohen et al10.
the mechanism of population of the 2F
5/2 state in Yb3+:CsPbCl3, as two different
mech-anisms were proposed by Pan et al.13 and Milstein et al.14. Milstein et al. proposed a
shallow lattice defect, a defect that is close to the bandgap edge of the host, induced by the dopant ytterbium (figure 4A). Because the defect is so close to the conduction band, the depopulation of the host lattice is rapid. Electrons can relax to the defect state and then recombine with the valence band while transferring energy to two Yb3+ ions, which
generates two 2F
5/2–2F7/2 transitions. To test this hypothesis, both Yb3+:CsPbCl3 NCs
and La3+:CsPbCl3 NCs were made. La3+ is very similar to Yb3+, but has no emission.
Photoluminescence (PL) spectroscopy of La3+:CsPbCl3at 4.7 K shows emission at 40 meV
below the excitonic PL of undoped CsPbCl3NCs. This emission is not observed for undoped
NCs, which suggest there is indeed a shallow defect state introduced upon doping with a lanthanide.
Pan et al. proposed a mechanism that involves a deeper lying defect that is close to the middle of the bandgap (figure 4B). After excitation, electrons in the conduction band of the host lattice can transmit to the defect while transferring energy to one Yb3+ ion and
populate the 2F
5/2 excited state. The electron in the defect state can recombine with the
valence band of the host lattice and transfer energy to the second Yb3+ ion to populate
another 2F
5/2 excited state. Emission spectra for Yb3+:CsPbCl3 were collected at 300K
and 10K to test this hypothesis. At 10K there is an extra broad component centred at 596 nm that is not there at room-temperature. According to Pan et al. this is consistent with emission from a defect state between the conduction and valence band, and thus proves the deep defect mechanism13.
Since there was evidence for both of the proposed mechanisms there was a need for more understanding and scrutiny of the workings of the material to get closer to an appli-cation. Density functional theory (DFT) calculations were carried out on the cubic phase of Yb3+:CsPbCl3 NCs to investigate the properties of the system. These calculations
sup-ported the mechanism involving a shallow defect as proposed by Milstein et al. and ruled out a mechanism with a deep defect state as proposed by Pan et al.15.
2.1
Yb in the structure
To be incorporated in the lattice, the Yb3+ion must take the position of another ion. To
de-termine the position of the Yb3+ions in the perovskite structure, density functional theory calculations were carried out. Pan et al. looked at the formation energy of three different defects in the perovskite to get a first impression of which position the ions would take.
Yb 3+ Yb 3+ 2 F 5/2 2 F 7/2 Ener gy CsPbX3 Quantum cutting Excitation Charge Transfer Photoluminescence Yb 3+ Yb 3+ 2 F5/2 2 F 7/2 Ener gy CsPbX3 Defect in the middel of the bandgap Excitation Charge Transfer Photoluminescence Shallow defect Defect A B Defect
Figure 4: (A) Schematic energy diagram of the quantum cutting process in Yb3+-doped CsPbX
3
with a shallow defect. Based on Milstein et al.14 (B) Schematic energy diagram of the stepwise
quantum cutting process in Yb3+-doped CsPbX
3with a defect in the middle of the bandgap. Based
on Pan et al.13.
From the three defects, at the interstice, at the location of Cs and at the location of Pb, the formation energy of the Pb defect was always the lowest. This is a first indication that Yb3+ ions will tend to occupy the Pb2+site13.
As discussed above, a theory about the quantum cutting of Yb in perovskites is that it occurs via a shallow defect state in the lattice. Because of the extremely fast Yb sensitiza-tion it is proposed that the Yb3+ introduces defects in the lattice itself14. Since the valence
of Yb and Pb is different (3+ and 2+ respectively), charge compensation is necessary upon incorporation of Yb3+ in the lattice. Therefore, it is proposed that the introduced defects
are associated with this valence difference14. Charge compensation can be realised by the
introduction of two different cation vacancies, VCs or VP b, into the lattice. Upon higher
nominal Cs concentrations during synthesis the PLQY increases, so this should disfavour VCs formation. Thus, Milstein et al. suggest a charge-neutral Yb3+−VP b−Yb3+ defect
complex that takes the place of three lead ions, where quantum cutting is aided because there is always a shallow VP b defect in close proximity. The proximity of the vacancy to the
Yb3+ions in this configuration provides electronic coupling of the defect to both Yb3+ ions
because the Bohr radius of the VP b-localized photogenerated charge carriers is so large that
is spans the vacancy-defect complex. This proposed system is shown for general rare-earth incorporation in figure5.
Li et al. carried out DFT calculations to further investigate this model. The energies of 5 random configurations of a vacancy with two Yb3+ ions were compared with a linear
configuration as proposed by Milstein et al. Supporting this model, it was found that the linear configuration had lower energies than the random configurations.
One question that remains is whether the Yb3+−V
P b−Yb3+defect complex is linear or
in a right-angle (RA) configuration. The energies of a linear and RA configuration were also compared by Li et al. which showed that the RA configuration is the more stable than the linear configuration15. However, the energy difference is marginal, so both configurations
may coexist at finite temperatures. To answer the question, a more atomic insight into the structure was required. Pure CsPbCl3 perovskites consist of ideal PbCl6 octahedrons
which stabilize the structure. In a linear Yb3+−V
P b−Yb3+defect complex, both Yb3+ions
are bound to 5 PbCl6 octahedrals that will be distorted. The total number of distorted
octahedrals for the linear configuration is then 10. In an RA configuration one of the PbCl6
nine. Therefore, the RA configuration is more stable than a linear configuration15.
More proof for a vacancy-defect structure was provided by Erickson et al. They modeled two different scenarios; one where quantum cutting involves a Yb3+−VP b−Yb3+ complex
and one where it involves any two Yb3+ions in a NC. In the first scenario, the effective quan-tum cutting rate (k0QC), and therefore the PLQY, is linearly correlated with the number of ground state Yb3+ions: k0
QC= y0
2kQC where kQC is the fundamental quantum-cutting rate
and y0 is the number of Yb3+ ions in the ground state. In the second scenario the quantum
cutting is not linearly correlated with Yb3+ concentration because there are many more
possible pairwise combinations of Yb3+ ions at higher concentrations: k0 QC =
y0!
2(y0−2)!kQC. Previous experiments have shown that the PLQY is actually linearly correlated with Yb3+ concentration, so the second scenario can be ruled out16.
Figure 5: Charge-Neutral Vacancy-Defect structure as proposed by Milstein et al. Figure from Milstein et al14.
3
Synthesis Methods
There are many different ways in which doped Yb3+:CsPbX
3 perovskites are synthesised
in literature. Most methods are based on a hot injection nanocrystal synthesis which was also the method for the first reported Yb3+:CsPbX
3 NCs17. The hot injection method
starts with Cs-Oleate (CsC18H33O2) synthesis: Oleic acid (OA) and either cesium
carbon-ate (Cs2CO3) or cesium acetate (CsOAc) are dissolved in 1-octadecene (ODE) to react in
vacuum at 120◦C for 1 hour to form Cs-Oleate.
YbCl3 · 3H2O and lead acetate trihydrate (Pb(OAc)2 · 3H2O) are dissolved in ODE,
OA and oleyamine (OAm). The mixture is degassed, heated to 260◦C and flushed with N2.
The as-prepared Cs-Oleate is heated to 100◦C and swifly injected into the mixture. The reaction is quenched in an ice bath after 5 seconds18. Partly replacing Pb(OAc)2 · 3H2O
with PbBr2 yields Yb3+:CsPb(Cl1−xBrx)313,17,19. Yb3+:CsPbCl3 perovskites can also be
achieved by using PbCl2 instead of Pb(OAc)2 · 3H2O20. Milstein et al. reported
difficul-ties with the method above regarding solubility of the cation and halide precursers so they used metal-acetate salts and chlorotrimethylsilane (TMS-Cl) instead, where the TMS-Cl is injected into the metal-acetate salts10,14,16,21.
In the method described above, the Yb3+ ions are integrated in the perovskite
immedi-ately during synthesis of the perovskite. However, it is reported that it is also possible to add Yb3+ postsynthesis22. Yb(NO
3)3 · 5 H2O is dissolved in methyl acetate and toluene.
This solution is added to a CsPbX3 dispersion under continuous stirring for one minute to
incorporate Yb3+ ions into the nanocrystal.
A one-pot method was developed using ultrasonication. CsBr, PbBr2and a Yb3+source
which was not further defined were dissolved in N,N -Dimethylformamide (DMF), and the solution was subjected to ultrasonication at a power of 300 W for 30 minutes while be-ing cooled in a waterbath. The reported yield was 4.32% and the size distribution of the nanocrystals was broad compared to the hot injection method23.
It has been reported that it is possible to exchange the halide anion after synthesis of the nanocrystals made via hot-injection. Cl can be exchanged for Br by titration with TMS-Br or benzoyl-bromide and Br was exchanged for Cl by titration with Cl-OAm24. This research by Milstein et al. also showed that the anion exchange should be carried out under dry con-ditions since the presence of water extrudes Yb3+ from the NCs during the exchange.
Yb3+:CsPbX
3 thin-films can also be fabricated. PbCl2 was dissolved in dimethyl suloxide
(DMSO), spincoated on a glass substrate and annealed for 5 minutes at 100◦C. CsCl and YbCl3· H2O were dissolved in methanol. This solution and the PbCl2substrate were heated
to 70◦C and the solution was spincoated and annealed at 250◦C. The authors report that this also works for mixed-halide solutions5.
In an effort to reduce solvent use, a single-source vapor deposition (SSVD) method was developed25. CsX, PbX2 and YbX3 ·H2O were ground mechanochemically for 9 hours to
form powder perovskites. These were used as source materials for SSVD to make Yb3+
-doped perovskite thin films on glass. The powders are heated at low pressure to sublime and are deposited on the substrates.
Because of toxicity concerns regarding the use of lead, methods have been developed to synthesise ytterbium-doped perovskites without lead. These synthesis paths all use a hot-injection method. Cs2CO3 was dissolved in a mixture of ODE, OA and OAm with silver
acetate, indium acetate and Yb(C2H3O2)3· 4 H2O and degassed at 100◦C, put under
nitro-gen at 200◦C and TMS-Cl was injected. The reaction was quenched in an icebath and the reaction yielded Cs2AgInCl626. Instead of indium acetate, bismuth acetate can also be used
which yields Cs2AgBiCl6. TMS-Cl can be exchanged for TMS-Br27 to make Cs2AgMBr6.
Replacing Yb(C2H3O2)3· 4 H2O and TMS-Cl with Yb(NO3)3 · H2O and benzoyl chloride
also yields Cs2AgInCl628.
4
Composition and Architecture
4.1
Cl anb Br concentrations
One of the advantages of perovskites is that the bandgap of the material is tunable. For example by mixing the halide anions Cl and Br, the bandgap can be tuned between two extremes, from 2.99 eV for CsPbCl3to 2.32 eV for CsPbBr3. The photoluminescence energy
of ytterbium cannot be changed, and is set at 1.26 eV. This means that an efficient quantum cutter involving Yb3+ must have a bandgap of at least 2 × 1.26 eV = 2.52 eV3. In the case
of CsPb(Cl1−xBrx)3 the value of x determines the bandgap of the material. Crane et al.
calculated the bandgap to be 2.52 eV at x=0.843.
Many of the studies so far have not optimised the Cl vs. Br ratio and use CsPbCl3
perovskites as proof of concept14,16,18,21 and a few studies have made doped perovskites
with a half and half ratio with x=0.517,25. In the thin film architecture one study has been
conducted to optimise the halide ratio for PLQY. It involved five different samples with compositions of x ≈ 0.0, 0.41, 0.65, 0.87, and 1.0 and found that the x≈ 0.0, 0.41, and 0.65 had high PLQY, but at 0.87 this dropped below 100%5. These results correspond well with the calculations of Crane et al. that suggest x=0.84 as an energy threshold. More extensive research with more samples of x between 0.65 and 0.87 should be conducted to find an optimum.
Milstein et al. have studied the energy threshold for Yb3+:CsPb(Cl
1−xBrx)3
nanocrys-tals by slowly exchanging the Cl anion for Br. They conclude that PLQY over 100% can be achieved for all compositions with x between 0 and 0.7524. However, they do not show
which composition gives the highest PLQY, so more research should be conducted to find a maximum PLQY.
4.2
Yb concentration
The PLQY of the Yb3+ ion2F
5/2→2F7/2 transition seems to increase in proportion with
the doping concentration of Yb3+14. In the study by Milstein et al., the limit to this trend
is not found; from 0 to 7.4% dopant the PLQY rises in a near linear trend, but higher percentages have not been measured. In this study Yb3+ concentrations are defined as
[Yb3+]/([Yb3+]+[Pb2+]). It is suggested that this trend breaks at a certain point. At a
PL drops5. However, in this thin film research the absolute concentrations of Yb3+ in the
product have not been measured. This shows that more research should be conducted to optimise ytterbium-doped perovskites by finding the best ytterbium concentration.
It seems that the lattice structure of the material may be a limiting factor in doping con-centrations. The crystallinity of nanocrystals doped with rare-earths becomes worse in com-parison to undoped NCs and at higher concentrations the framework of CsPb(Cl0.5Br0.5)3is
partially destroyed17. Milstein et al. identified that there are physical limits to the incorpo-ration of Yb in the crystal lattice as well. At increasing nominal [Yb3+]:[Pb2+] concentration
the analytical Yb3+concentration first increases, but around a nominal concentration of 0.8
the analytical concentration starts to decrease. A similar trend is seen for the nominal [Yb3+]:[Cs+] concentration. This appears to be optimal at 1.4 and at concentrations higher
than 1.8 the purity of the crystal structure decreases14. The method of synthesis also seems
to influence the amount of Yb3+ incorporated in the lattice. The hot injection method
as proposed by Milstein et al. gives varying results, but does not seem to rise above 7% analytical Yb3+ even at 1:1 nominal [Yb3+]:[Pb2+] concentrations14,17,18. However, Pan
et al. showed that in the case of doping with Eu3+ increasing the injection temperature
of Cs-oleate drastically increases the incorporation of Eu3+. From 180◦C to 260◦C the Eu
in the lattice increased from 1.2 mol% to 11.1 mol%. It has not been tested yet whether this trend is also true for Yb3+ instead of Eu3+13. Ma et al. separated their hot injection nanocrystals based on size, and found that the concentration of Yb3+ was higher in the biggest NCs20. This shows that the hot injection can be modified and optimised to yield NCs with higher percentages of dopants. However, there are alternative methods to dope Yb3+ into perovskite NCs. The ultrasonication method by Hu et al. seems promising in
terms of lanthanide incorporation; at a precursor ratio of 10% Eu3+, the analytical
concen-tration ([Eu3+]/([Eu3+]+[Pb2+])) was 4.60%, but the overall yield of their synthesis was
only 4.32%23. This method has not been tried yet with Yb3+ . Mir et al. introduced a
postsynthesis method where Yb3+ incorporated in the lattice after synthesis of the NCs,
but in the case of CsPbCl3 and CsPbBr3 this gave low analytical concentrations of 0.6%
and 0.7% respectively22. Finally, Single-Source Vapour Deposition as proposed by Crane
et al. seems to transform precursors into thin films with almost the same compositions; a 5.0% Yb precursor lead to a film with 4.7% Yb in the crystal structure. However, this method is only suitable for thin film synthesis and not for NCs25. Overall, it is clear that
more research should be conducted to find out how the most Yb3+ can be incorporated in the NCs while keeping a stable perovskite structure to give the highest PLQYs.
4.3
Codoping with a second lanthanide
Most research discussed so far has focused on doping with only ytterbium, but one of the first papers published on the subject of Yb3+doping in perovskites already showed that codoping
with a second lantanide might be beneficial to the efficiency of quantum cutting of ytter-bium17. Codoping of CsPbCl
1.5Br1.5with 7.1% Yb and 2% Cerium (Ce) raised the PLQY to
146% whereas CsPbCl1.5Br1.5 with 7.2% Yb yielded a PLQY of 115.5%. In a second paper
by the same team they synthesised codoped perovskite NCs with Tb3+, Nd3+, Dy3+, Pr3+, and Ce3+ combined with Yb3+. Both codoping with Ce3+ and Pr3+ gave high PLQYs in comparison with doping with Yb3+, thus tridoped NCs were made with 6% Yb3+, 4% Pr3+ and 3% Ce3+. These tridoped NCs indeed gave an even higher PLQY of 173%. A mech-anism of tridoped quantum cutting was proposed and is shown in figure6. The Ce3+ ions
serve as an intermediate energy level which promotes the energy transfer from the perovskite to the Pr3+ion. Electrons on the3P
2level of Pr3+transit non-radiatively to3P0and1D2of
Pr3+. They can then emit through3P
0–3F2/3H4 and1D2–3H4transitions. The quantum
cutting via Yb3+ is achieved by a cross-relaxation [P r3+(3P
0–1G4); Y b3+(2F7/2–2F5/2)]
and a second energy-transfer process [P r3+(1G
4–3H4); Y b3+(2F7/2–2F5/2)]19. A second
quantum cutting process is the energy transfer from one Ce3+ ion to two Yb3+ ions which
is possible because the 5d –2F
transition of Yb3+. The research by Zhou et al. shows that tridoping of perovskites give
high PLQYs and that it is feasible to synthesise them with the same method as singly doped perovskites19.
Figure 6: Kinetic scheme for the mechanism of excitation and quantum-cutting in
Yb3+,Pr3+,Ce3+:CsPbClBr
2 NCs. Figure from Zhou et al19.
4.4
Lead-free double perovskite
Lead halide perovskites have so far shown promising results, but there are concerns regard-ing the structural stability and the toxicity of water soluble lead ions. Therefore, efforts have been made to develop lead-free perovskites that have a more stable structure. In a double perovskite (DP), with a structure of A2M+M3+X6, the architecture is the same as
in a perovskite, but the unit cell is twice the size; two cations are alternating on the B site, see figure7. Previous reports have shown that the stability of this structure is higher than in lead halide perovskites29.
Because earlier reports of Cs2AgInCl6 DPs showed structural robustness and direct
bandgap characteristics, Lee et al. synthesised Cs2AgInCl6 NCs doped with Yb3+ and
Er3+. Although the synthesis was successful, at a Yb3+ precursor concentration of 20% the dopant concentration in the NCs was only 0.9% and the PLQY was at 3.4%, much lower than for reported LHP NCs26. Yb3+-doped Cs2AgInCl6 nanocrystals and microcrystals
(MC) were also synthesised by Mahor et al. and while the Yb uptake in the nanocrystals was more successful, 52% Yb precursor lead to 6.2% Yb in the NCs, the PLQY did still not come near that of LHP. Exact numbers are not reported but the PLQYs of both NCs and MCs were more than an order of magnitude smaller than the PLQY of Yb3+ -doped
CsPbCl3NCs they had also synthesised28.
Cs2AgBiCl6also shows high structural stability, but has an indirect bandgap which may
be limiting in application26. Nonetheless, Chen et al. synthesised Yb3+-doped Cs
2AgBiCl6
and Cs2AgBiBr6 NCs. Incorporation of Yb3+ in the structure was more successful than for
the previously discussed Cs2AgInCl6; a Yb precursor concentration of 7.7% gave an
analyti-cal concentration of 5.5% Yb in Cs2AgBiCl6and 5.0% Yb in Cs2AgBiBr627. Unfortunately,
the PLQY of these NCs are not reported, so no clear comparison between Cs2AgInCl6and
Cs2AgBiX6 can be made.
As discussed in section 2.1, in a LHP two Yb3+ ions form a vacancy-defect complex, which facilitates quantum-cutting in the place of three Pb2+ ions. However, in double per-ovskites there are no ions with a valency of 2+, so a similar complex cannot be formed. In the studies discussed above it is not researched how incorporation of Yb3+ ions in the
DP works, but since indium and bismuth have a valency of 3+ we suspect Yb3+ ions can
there is also no vacancy to assist the population of the Yb3+ excited state. Therefore, we
suspect that if there is a quantum-cutting process in Yb3+-doped double perovskites, it has
a different mechanism than in Yb3+-doped LHPs.
Figure 7: Structure of a Yb3+-doped CsAgInCl6 double perovskite. Figure from Mahor et al28.
4.5
Nanocrystals or Thin Films?
Most of the research discussed so far has focused on nanocrystal structures, but the highest reported PLQY (190%) is achieved by a thin film architecture. Little is known about the possible advantages or disadvantages of the two different architectures because there are only two reports of thin films and none of the authors have made a comparison5,25. Thin
films of mixed halide perovskites are known to undergo phase segregation which creates bromide-rich and chloride-rich phases, which alters the local bandgap of the material30.
This could turn out to be problematic for quantum cutting as a bromide-rich phase may have a bandgap that is lower than twice the energy of the 2F
7/2–2F5/2transition of Yb3+.
Kroupa et al. indeed observed phase segregation in their CsPb(Cl1−xBrx)3 thin film, but
for the Yb3+-doped CsPb(Cl
1−xBrx)3 thin film this segregation was strongly suppressed
due to rapid energy capture by Yb3+so that there is no driving force for halide segregation.
One conclusion that can be made from the successful quantum cutting in thin films is that the mechanism does not rely on nanocrystal characteristics, but is a bulk process. This conclusion means easier fabrication, as preparing NCs may not be necessary, and it can also give rise to a wider range of morphologies besides cubic NCs and thin films5.
5
Power Saturation
With PLQYs reaching as high as 190%, relatively easy fabrication and reasonable stability, ytterbium-doped perovskite seems an almost ’perfect’ material. However, there is one lim-iting problem; even at relatively low excitation intensities, both NCs and thin films show power saturation effects. The PLQY drops well below 100% at higher intensities, diminish-ing the current gain from quantum cuttdiminish-ing. Figure8 plots the PLQY for 5.2% Yb3+-doped CsPbCl3 NCs from Milstein et al.14 and for a Yb3+-doped CsPb(Cl0.35Br0.65)3 thin film
from Kroupa et al.5 at varying excitation intensities, all well below the excitation flux of
AM1.5 solar irradiation in the range between 280-490 nm, which is indicated with an orange line at 3.4×1016cm−2s−1. The thin film is synthesised at a nominal [Yb3+]:[Cs+]
concentra-tion of 0.8, but the analytical Yb3+concentration in the film is not known. Figure8 shows
that both the NC and thin film architecture show saturation at higher excitation rates, and the thin film seems to perform slightly better than the NCs. Since the Yb concentration and Cl/Br concentrations are not the same in the two samples, it cannot be concluded that the architecture is the cause of this difference in saturation. However, it was shown that the
power saturation is almost independent from halide composition by Erickson et al.16. Even
for CsPbBr3, which has a low PL because its bandgap is too low for quantum cutting, they
observed the same power saturation trend.
Milstein et al. attributed the saturation to a combination of the large absorption cross
Figure 8: NIR PLQY of Yb3+-doped CsPbCl
3 NCs and CsPbCl0.35Br0.65 thin film as a function
of excitation rate. The orange line represents the excitation rate of AM1.5 solar irradiation
(280-490nm). Data from Milstein et al. and Kroupa et al5,14.
section of CsPb(Cl1−xBrx)3 and the very long average Yb3+ PL decay time of τ > 2ms.
The saturation shows that there is a nonradiative relaxation mechanism that occurs when an already excited Yb3+ ion is excited again14. The halide composition of the perovskite
does not significantly alter this long decay time16. Erickson et al. developed a kinetic model
to examine the processes that occur when an Yb3+ ion is already in an excited state and
the NC is excited a second time quantitatively. Two new Auger-type processes emerge with which the relaxation to the ground state via luminescence will have to compete. These processes are shown infigure10. In the first process, A1, the energy from the excited Yb3+
ion is transferred to the NC which creates a hot exciton and a ground-state Yb3+ ion. The
hot exciton will thermally cool to the band edge and then again transfer to an Yb3+ ion.
If that ion is in the ground state, quantum cutting can take place. In this process, the energy of one 2F5/2–2F7/2 transition of Yb3+ is lost. In the second competing process,
A2, the energy of the NC is transferred to the excited Yb3+ ion, which generates a highly excited Yb3+ion and a NC ground-state. The highly excited Yb3+ion can relax thermally to the 2F5/2 state, and emit a photon from that state. In this process twice the energy of
a 2F
5/2–2F7/2 transition is lost. These processes are discussed with an assumption that
one of the two Yb3+ ions in the vacancy defect structure is already excited. However, they
also assume that the second excitation will solely involve the excited Yb3+ion and not the
ground state Yb3+ ion. A third process might also be competing where the energy from
the excited NC is all transferred to the ground state Yb3+ to create a highly excited Yb3+
ion which can relax to the 2F
5/2 state. To the best of our knowledge this potential process
has not been discussed in literature. After identifying these processes, Erickson et al. simulated the power dependence of the NCs with a kinetic model based on these competing processes. The results of this model in figure 9 show that process A2 closely matches the experimental saturation curves. The authors did not show a modelled saturation curve of process A1, but they imply that this will have a different shape. They cannot rule out
Figure 9: Simulated experimental power dependence with kA2=1010s−1
and kA1=0. Figure form Erickson et al16.
the pathway of process A1 completely, but can conclude that the dominant pathway of PL saturation is that of process A2. A second conclusion from this simulation is that at satura-tion, the competing Auger-type process is more rapid than quantum cutting, which makes the probability of generating additional Yb∗at further photoexcitation very small. Finally, their simulations also show that quantum cutting is the competitive process until 20% of Yb3+ ions are in the2F5/2 state16.
One important question that remains to understand the mechanism of saturation is
Yb 3+ Yb 3+ 2 F5/2 2 F7/2 Excitation Relaxation Charge Transfer Energy Yb 3+ Yb 3+ 2 F5/2 2 F7/2 Excitation Relaxation Charge Transfer Energy Photoluminescence Process A1 Process A2 CsPbX3 CsPbX3
Figure 10: Kinetic schemes for two processes of photoexcitation where an Yb3+ion is already in
an excited state. Based on Erickson et al16.
why this NC∗–Yb∗Auger-type relaxation is so fast, and this question can also be answered
by the kinetic model described by Erickson et al. For all CsPb(Cl1−xBrx)3 compositions,
the transfer of NC∗ energy to Yb∗ will lead to absorption in ligand energy states of the nanocrystal, which means there is a high density of trap states that can facilitate process A2. In addition, both transitions in this Auger-type mechanism are spin allowed processes. Because of these two reasons, cross-relaxation is a fast process, which combined with long lifetimes of Yb3+ cause power saturation.
6
Applications
6.1
Downconverter Layer
The main application of Yb3+-doped perovskites is a downconverter layer for PV, which has
already been mentioned before. The general idea behind downconversion is shown infigure
1 and the calculated gains in a silicon solar cell have been discussed in the saturation chap-ter. Actual devices using Yb3+:CsPb(Cl
1−xBrx)3 as a downconversion layer have already
been realized by Zhou et al., as has been reported in two papers17,19. They were the first
to report on the synthesis of Yb3+-doped perovskites, and immediately developed a way to
use them to improve the solar conversion efficiency of a silicon solar cell. The NCs were self-assembled by liquid-phase deposition on top of a 125 × 125 mm single crystal SSC while the thickness was controlled ranging from 60-770 nm. They found that the transmittance of light decreased with increasing thickness; with thicknesses below 230 nm the transmittance is as high as 80-90%. The uncoated SSC had a power conversion efficiency of 18.1% and coated with 230 nm of doped perovskite NCs it increased to 21.5%. Ten SSCs were coated with the same NCs and the efficiency ranged from 20.5 to 21.5% and the relative enhance-ment ranged from 17.9 to 18.8%, which indicates good reproducibility17.
In a second publication Zhou et al. optimised the PLQY of the NCs as already described in section 4.3. They coated a commercial CIGS (CuIn1−xGaxSe2) cell and a commercial
silicon cell with their optimised Yb3+,Pr3+,Ce3+:CsPbClBr
2 NCs. The efficiency of the
CIGS cell increased with 20.1% relatively, increasing from 15.9 to 19.1%. They used this cell of 36 cm × 21 cm to charge a mobile phone, first once without the NC coating and the following day at the same time (noon) under very similar conditions with the NC coating. The charging time from 0 to 100% of the phone was reduced by 30 minutes with the NC coating. The efficiency of the SSC coated with the same NCs increased from 18.1 to 21.9%, a relative increase of 20.1%19.
In both of the papers by Zhou et al. commercial silicon solar cells are used. This might not give the best impression of the improvement in efficiency, since a commercial SSC is not as good as current lab records. The EQE, especially at higher energies, can be rather poor for a commercial SSC. Since the absorption of LHP at these energies is very good this might lead to artificial high improvements.
The devices made in both papers show strong 988 nm emission of the Yb3+ ions, and
considerable improvement in photoelectric response in the range of 350 to 450 nm, the ab-sorption of the perovskite. This suggests that the enhancement is due to quantum cutting, but no further proof is provided17,19.
To investigate the efficiencies and effects of saturation in a QC/PV device with a Yb3+:CsPb(Cl
1−xBrx)3 quantum cutting layer in real-world conditions, Crane et al.
per-formed detailed modeling and analysis. They considered the effects of band gap energy and PLQY of CsPb(Cl1−xBrx)3, the external quantum efficiency (EQE) of the PV, the PL
capture efficiency of the PV after quantum cutting (optical coupling), seasonal and daily variations in solar irradiance and saturation effects of the quantum cutter. With this model they calculated the hourly PLQY, energy yield and efficiency of a QC/PV in a typical me-teorological situation in Seattle, WA (USA) and Golden, CO (USA). The results of this analysis are shown infigure11.
Surprisingly, figure 11A shows that at every hour of illumination, the saturation is not too strong to cancel out the benefits of the QC layer. The highest additional PLQY is observed in winter and at the beginnings and ends of the days, when the solar irradiance is lower, and thus the saturation is less severe. Figure11B compares the performance of the same QC/PV device in Seattle, WA and Golden, CO. In 2-axis tracking the path of the sun is followed during the day, and Crane et al. simulated the device with and without the use of 2-axis tracking. They used three different values for optical coupling. In the worst case scenario of 50% OC, halve of the photons emitted by the QC layer are absorbed by the PV layer; effectively the quantum cutting characteristic of the device is lost. This scenario is
Figure 11: (A) Hourly PLQY of QC material in Seattle, WA using experimental saturation data,
plotted over the course of a year. (B) The energy production efficiency of a Yb3+:CsPb(Cl1−xBrx)3/
SHJ QC/PV device with and without 2-axis tracking for two geographical locations, which different
optical coupling (OC) efficiencies. Figures from Crane et al3.
unrealistic since the refractive indices of air, the perovskite layer and silicon will generally guide the photons towards silicon if it is in direct contact31. However, it is interesting that
even in this case the efficiency of the device is still improved over the course of the year. The EQE for the commercial silicon solar cell used in this model decreases for blue light, which will be absorbed by the QC layer in a QC/PV device. So with only 50% OC, the function of the QC layer is merely increasing the EQE of the device, which will still improve the power conversion efficiency. Without saturation effects the efficiencies in all cases will increase with 20.6% (relative), which is a drastic improvement. However, saturation decreases this to a maximum of 12.7% increase, which is still a surprising improvement3.
Comparing these results from Crane et al. with experimental results from Kroupa et al. and Milstein et al. infigure8 raises some questions. The results from Crane et al. seem very positive with up to 10.9% increase in efficiency, butfigure8 shows that the quantum-cutting improvement is already diminished at intensities of roughly one-thousandth sun since the PLQY is then below 100%. It is not completely clear which experimental data is used in the models of Crane et al. and they do not comment on these discrepancies.
6.2
Luminescence Solar Concentrator
A second possible application of Yb3+:CsPb(Cl1−xBrx)3NCs is the use in Luminescent
So-lar Concentrators (LSC). In an LSC, incident sunlight is absorbed in a So-large-area collector which will emit PL photons. These photons are waveguided by internal reflection to the edges of the collector, where it is collected in PV cells. LSCs can reduce the costs of PV technologies (especially expensive III-V PVs) because small PV cells can be attached to much larger area LSCs. They also enable the fabrication of (semi)-transparent solar win-dows. The internal efficiency (ηint) is defined as the ratio between edge-emitted photons and
absorbed solar photons, and the external efficiency (ηext) is the ratio between edge-emitted
photons and incident solar photons, which is given by ηext = ηint× ηabs where ηabs is the
absorption efficiency of solar photons. A common problem in LSCs is the reabsorption of PL photons along the path to the edge of the device, which lowers the ηint. Quantum
cutting can improve the ηint to values over 100% by emitting two photons per absorbed
photon, especially by emitting at a wavelength far from the absorption of the material, eliminating the reabsorption loss. Luo et al. reported the synthesis of a 25 cm2 QC-LSC using Yb3+:CsPbCl3 NCs with a ηint of 118.1%. They predict that even with a window
of an area of 1 m2 they can still achieve a ηext of 6.3%, which is four times as high as the
CsPb(Cl1−xBrx)3 instead of CsPbCl321. It should be noted that in these devices the QC
NCs still suffer from the same saturation problem as described before.
The low absorption of Yb3+:CsPb(Cl1−xBrx)3 NCs limits its application in LSCs in a
single layer device. Similar problems in traditional LSCs have been solved by a tandem architecture with two different materials and two waveguides. However, Cohen et al. pro-posed a model of a bilayer LSC device where the photons from both layers are all directed by the same waveguide to the same PV, which reduces the complexity and costs of the ar-chitecture. They modeled the performance of a bilayer LSC using Yb3+:CsPb(Cl
1−xBrx)3
and CuInS2 using experimental data of the performance of the two separate layers. With
x=0.75 they predict a 28 cm2Si cell coupled with a 175 times larger bilayer LSC of 4900 cm2
to give 63 more current than when the same SSC is operating without a LSC. This is a 19% increase from state of the art CuInS2 NC LSCs10. So far, this has only been investigated
in a simulation, and the next step would be to fabricate a device following this design.
LED
Doping LHP NCs with rare earth elements has shown to be promising for the development of light-emitting devices. Pure CsPbI3 NCs emit red light, but are unstable under ambient
conditions. The perovskite structure transitions into a a phase with 1D chains of octahedra, which makes the development of white LEDs based on perovskites a challenge. However, because Eu3+ has a stable red emission, doping of CsPbCl
3 NCs with Eu3+ ions may be
an alternative to CsPbI3. Ce3+ has blue and green emission, so Eu3+ anc Ce3+ codoped
CsPbCl3 NCs were constructed and coated on a commercial ultraviolet LED emitting at
364 nm. They were shown to exhibit cool white emission at a luminous efficiency of 24 lm/W. Note that in these doped perovskites the dopants facilitate the conversion of light to lower energies, but no quantum cutting is involved. The as-prepared LEDs were very stable with almost no decay through 288h of working times at a bias of 3.0 V13. This shows that
stable white LEDs can be made from lanthanide-doped perovskites, but Yb3+doping is not interesting since it emits at IR wavelengths instead of in the visible light.
7
Further Research
7.1
Optimisation
As identified above in section 4.1 and 4.2, more research should be conducted to optimize the performance of the Yb3+-doped perovskite. By calculations it is shown that the most
optimal value for x in CsPb(Cl1−xBrx)3should be ∼0.84, but the values tried so far that are
closest to 0.84 are 0.7519 and 0.875. Therefore more research should be carried out where
a series of perovskites are synthesised with values of x close to 0.84. More optimisation can be achieved by looking into the best Yb3+ concentrations. There seems to be a trend of
increasing PLQY for increasing Yb3+ concentration. It is believed that this trend has a
limit because with every two Yb3+ ions a defect is introduced in the lattice, so at a certain
concentration the perovskite lattice will become too distorted. Therefore, it will be beneficial to analyse the theoretical limit of Yb3+ doping and afterwards optimise towards this limit
through synthesis. By the optimisation of these two values the most optimal Yb3+-doped perovskites with the highest possible PLQY can be synthesised.
7.2
Stability and lead toxicity
One issue not discussed so far is the stability of Yb3+-doped perovskites. CsPbX
3NCs show
large drops in PLQY upon exposure to ambient atmospheric conditions, which is mostly attributed to the ionic character of the material and the metastable structure32. Besides
oxygen and water, UV-light can also have a negative effect on LHPs, especially for mixed halide perovskites. Upon illumination, halide anions will segregate to form two regions with
Figure 12: Photoluminescence decrease for CsPbCl3 and Yb3+:CsPbCl3 under irradiation of 365
nm. Figure from Zhang et al18.
a different bandgap energy, this is a reversible process33. Permanent photodegradation of
all LHPs is a known issue that is difficult to overcome and the mechanism is not fully understood yet34. Zhang et al. have shown that upon doping CsPbCl3 with Yb3+ ,
pho-todegradation becomes much slower, see figure1218. However, they did not find a reason for this improvement and it has not been investigated further.
One of the problems of degradation in ambient conditions is that water soluble lead will form and this will be able to leak into the environment. Even at low exposure levels, lead can cause significant health problems, such as nerve damage, renal failure and impaired brain development. Therefore, lead perovskites require fail-safe encapsulation before they can be commercialized33. However, so far no steps towards the development of
encapsu-lated Yb3+-doped perovskites have been taken, so an important topic for further research
is ensuring safety regarding lead toxicity in these materials.
In section 4.4 lead-free double perovskites were briefly discussed. While it has been shown that it is possible to synthesise Yb3+-doped DPs, not much research has been done
towards the functionalities of the material. Reports have shown that the PLQY can be in-creased upon doping, but it is not clear whether this is caused by quantum cutting as it is in Yb3+-doped LHPs. The incorporation of Yb3+ ions in the lattice of LHPs was discussed in section 2.1, but no similar research has been conducted for DP to date. Because the charge of the cations is not the same in DPs as in LHPs, the charge matching vacancy-defect con-figuration as proposed by Milstein et al. in figure 5 is not possible. More research should be conducted to find out how the Yb3+ ions are incorporated in the lattice, and whether quantum cutting can take place in this configuration.
7.3
Saturation of Yb
3+Saturation effects in Yb3+-doped perovskites have already extensively been discussed in section 5. Although considerable research has already been conducted towards the cause and mechanism of saturation, not much has been done to overcome or diminish the sat-uration effect. Guided by the results of their simulations, Erickson et al. devised three engineering routes to reduce saturation. The first is to shorten the Yb3+ lifetime. It does
not seem likely that the radiative lifetime itself can be shortened, but it could be possible to shorten it non-radiatively by non-radiative energy transfer to the Si PV itself in a QC/PV device. The second route is to increase the concentration of Yb3+, which will reduce the
photoexcitation rate per Yb3+ ion. The same result can be achieved by stacking various
Yb3+:CsPb(Cl
1−xBrx)3 layers with different bandgap energies so that the layers will filter
solar flux and decrease the excitation rate in each layer. The third route is to decrease the cross-relaxation rate, which could possibly be achieved by an alteration of the host-lattice
such that the transfer of NC∗energy to Yb∗will not lead to absorption in a metal-like energy band as described above16. So far these routes are only theory and have not been explored
in detail. More research should be conducted towards these and potentially additional ways to decrease effects of saturation to work towards a commercially viable material.
7.4
Scarcity of Yb
The element Ytterbium is a so-called ’rare-earth’, which raises the question of how Yb3+
-doped perovskites can be commercialised if they need an element which is so rare. However, REs are not as rare as the name suggests, they are present in low concentration in all minerals and can be economically extracted from some less common minerals35. The abundance of
ytterbium in the earth’s crust is 2.8 × 10−6 g/g, the density of the crust is 2.97 g/cm3, the
diameter of the earth is 12.7 × 103 km36 and a mining depth of 3 km is assumed. However, 71% of the earths surface is covered in water, so it will not be possible to mine there. This gives the following calculation of the available ytterbium:
Volume 3 km deep crust = 4
3πdearth− 4 3πdmining = 4 3π12.7 × 10 3−4 3π3 = 6.12 × 10 9 km3
Mass Yb on land = Volume 3 km deep crust · ρcrust· abundance Yb · 29%
= 6.12 × 109· 2.97 · 2.8 × 10−6· 29% = 1.47 × 1013g
The best results of Yb3+-doped perovskites so far have been achieved with concentrations of 7% ytterbium, and layer thickness for downconversion is optimal at 230 nm19. The density of CsPbBr3 perovskites is 4.42 g/cm337. Now the mass of ytterbium needed per 1 m2 of
PV and how much solar PV can be covered can be calculated. Mass Yb per m2= ρCsPbBr3× dlayer× [Y b]
= 4.42 · 230 × 10−7· 0.07 = 0.07 × 10−6 g/m2 Surface of Yb3+-QC/PV = Mass Yb on land
Mass Yb per m2
= 1.47 × 10
13g
0.07 × 10−6 g/m2 = 2.1 × 10 14m2
Estimates show that only half a million square km of the earth’s surface should be covered with 20% efficient solar panels38 to provide for all the electricity demand worldwide, which
means there is 414 times more Yb available on earth and only 0.24% of all ytterbium in the top three kilometres of crust should be mined. To put this into perspective, we have so far mined 190 × 106kg gold39and the abundance of gold in the earth’s crust is 3.1 × 10−9g/g36. A similar calculation as above shows that we have mined roughly 1% of all the reserves of gold in the crust. Every year, roughly 1.4 ×10−6% of all the iron is mined as it has an abundance of 0.063 g/g36 and in 2016 4.6 ×1012kg was mined40.
Although a ball-park estimation of 0.24% of all ytterbium sounds quite promising, it can still be a challenge to mine materials based on the spread of elements over the earth. Therefore, more research is needed to make more accurate estimations of the mineable ytterbium including a cost analysis before this can be a commercial product.
8
Conclusion
In this review, the fundamentals and current efforts of ytterbium-doped perovskites are pre-sented. Yb3+:CsPbX
3 NCs and thin films show surprisingly high PLQYs exceeding 100%
where high-energy photons are converted into two lower-energy photons. This gives op-portunities for application in downconversion, a technique where a quantum cutter layer is deposited on top of a solar cell to shape the solar spectrum to be more suitable for the bandgap of the solar cell. The emission energy of ytterbium is ∼1.26 eV, very suitable for silicon solar cells which have a bandgap of 1.1 eV.
The quantum cutting in Yb3+:CsPbX3 occurs via a right-angle vacancy-defect complex
of two Yb3+ ions and one vacancy, taking the place of three lead ions in the perovskite host lattice. The vacancy introduces a defect with energy close to the conduction band of the perovskite and will lead to fast population of the2F
5/2 excited state of the Yb3+ ion.
The long lifetime of the2F
5/2 state of Yb3+ of up to 2 ms cause a power saturation effect
which results in decreasing photo luminescence at increasing incident flux; the PLQY drops below 100% even at intensities below one sun. When a second excitation happens, photo-luminescence competes with a fast Auger-type process, which results in the loss of energy in the form of heat. However, even with saturation effects both models and experiments show that a downconversion layer of Yb3+:CsPbX
3on top of a solar cell can lead to relative
efficiency increases up to 21.5%. Especially in winter and at hours of the day with less solar irradiation, Yb3+:CsPbX
3 can drastically improve the efficiency.
Additional research should be conducted to limit the negative effects of saturation. There is potential for optimization regarding halide and ytterbium concentration, and also the sta-bility of the material should be investigated more thoroughly. Despite challenges regarding saturation and stability, Yb3+-doped perovskites are a promising material for both down-conversion and luminescent solar concentrators.
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