Enhancing solar cell efficiency: the search for luminescent materials as spectral converters

Abstract

Photovoltaic (PV) technologies for solar energy conversion represent promising routes to green and renewable energy generation. Despite relevant PV technologies being available for more than half a century, the production of solar energy remains costly, largely owing to low power conversion efficiencies of solar cells. The main difficulty in improving the efficiency of PV energy conversion lies in the spectral mismatch between the energy distribution of photons in the incident solar spectrum and the bandgap of a semiconductor material. In recent years, luminescent materials, which are capable of converting a broad spectrum of light into photons of a particular wavelength, have been synthesized and used to minimize the losses in the solar-cell-based energy conversion process. In this review, we will survey recent progress in the development of spectral converters, with a particular emphasis on lanthanide-based upconversion, quantum-cutting and down-shifting materials, for PV applications. In addition, we will also present technical challenges that arise in developing cost-effective high-performance solar cells based on these luminescent materials.

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Xiaoyong Huang

Xiaoyong Huang was born in Jiangxi, China. He obtained his BE degree from China University of Geosciences (Beijing) in 2004 and his MS degree from Institute of Geochemistry, Chinese Academy of Sciences in 2007. Subsequently, he completed his PhD (2011) in the field of lanthanide-ion-doped quantum cutting and upconversion phosphors for photovoltaic applications under the supervision of Prof. Qinyuan Zhang at South China University of Technology. He is currently working as a postdoctoral research fellow in the group of Prof. Xiaogang Liu at the National University of Singapore. His present research focuses on optical spectroscopy and application of luminescent nanomaterials.

Sanyang Han

Sanyang Han was born in Hubei, China. He received his BS (2007) and MS (2010) degrees in chemistry from Soochow University. He is currently pursuing a PhD degree under the supervision of Prof. Xiaogang Liu in the Department of Chemistry at the National University of Singapore. His research interest focuses on development of novel lanthanide-doped luminescent nanomaterials.

Wei Huang

Wei Huang received his BSc, MSc, and PhD degrees in chemistry from Peking University in 1983, 1988, and 1992, respectively. In 1993, he began his postdoctoral research with the Chemistry Department at National University of Singapore, where he participated in the founding of the Institute of Materials Research and Engineering. In 2001, he became a chair professor at Fudan University, where he founded and chaired the Institute of Advanced Materials. In June 2006, he was appointed as the Deputy President of Nanjing University of Posts and Telecommunications, where he initiated the Institute of Advanced Materials and the Key Laboratory for Organic Electronics and Information Displays. In July 2012, he was appointed as the President of Nanjing University of Technology. He is an academician of the Chinese Academy of Sciences. His research interests include organic opto-electronics, nanomaterials, polymer chemistry, plastic electronics, and bioelectronics.

Xiaogang Liu

Xiaogang Liu was born in Jiangxi, China. He earned his BE degree (1996) in Chemical Engineering from Beijing Technology and Business University. He received his MS degree (1999) in chemistry from East Carolina University under the direction of Prof. John Sibert and completed his PhD (2004) at Northwestern University under the supervision of Prof. Chad Mirkin. He then became a postdoctoral fellow in the group of Prof. Francesco Stellacci at MIT. He joined the faculty of the National University of Singapore in 2006. He holds a joint appointment with the Institute of Materials Research and Engineering, Agency for Science, Technology and Research. His interests include lanthanide-doped optical nanomaterials, supramolecular chemistry, and surface science for catalysis, sensors and biomedical applications.

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1. Introduction

Sunlight is a free and, in many parts of the world, abundant source of energy that can be captured by new technologies and transformed into electricity.^1,2 It has been reported that sunlight that reaches the Earth's surface delivers 10 000 times more energy than what we consume.³ As a result, the use of solar energy is expected to have the potential to meet a large portion of future energy consumption requirements. Despite significant development of the photovoltaic (PV) industry over the past decades, the efficient and cost-effective conversion of solar energy into electricity through PV cells remains a daunting task.^4–6 Current annual solar energy usage is well below 1% of total energy consumption, while fossil fuels account for over 90% of the energy consumption. Before the large-scale use of solar energy, more efficient PV systems at reduced costs must be developed.^7–20

A major problem limiting the conversion efficiency of PV cells is their insensitivity to a full solar spectrum. The spectral distribution of sunlight at Air Mass 1.5 global (AM 1.5G) consists of photons with wide wavelengths ranging from ultraviolet to infrared (280–2500 nm, 0.5–4.4 eV), but current PV cells only utilize a relatively small fraction of the solar photons (Fig. 1).²¹ This is attributed to the fact that each PV material responds to a narrow range of solar photons with energy matching the characteristic bandgap of the material. In principle, only photons with energy higher than the bandgap are absorbed, but the excess energy is not effectively used and released as heat. The thermalization of photon energies exceeding the bandgap and non-absorption of photons with energy less than the bandgap amount to the loss of approximately 50% of the incident solar energy in silicon-based solar cell conversion to electricity. Notably, the theoretical maximum level of efficiency for crystalline silicon (c-Si) with a bandgap energy (E_g) of 1.1 eV is approximately 31% or 41%, depending on the concentration ratio, as defined by the Shockley–Queisser limit.²²

Fig. 1 AM 1.5G spectrum showing the fraction (highlighted in green) absorbed by a typical silicon-based PV cell and the spectral regions that can be utilized through quantum-cutting and upconversion processes (highlighted in purple and red, respectively). (Adapted with permission from ref. 21. Copyright 2007, Elsevier B.V.)

The inherent thermalization and non-absorption losses can be minimized using luminescent materials as spectral converters. The approach, termed the third-generation solar photon conversion, involves the incorporation of a passive luminescent layer into PV cells.^23–28 An important aspect of using this technology is that spectral converters are readily applicable to existing solar cells with few changes as the spectral converters and solar cells can be optimized independently.

To increase the efficiency of single-junction solar cells, three luminescence processes including upconversion, quantum-cutting, and down-shifting are currently explored for developing efficient PV devices. Trivalent lanthanide ions are the prime candidates to achieve efficient spectral conversion because of their rich energy-level structure (known as the Dieke diagram) that allows for facile photon management.^29–31

Upconversion of sub-bandgap light is exploited to reduce non-absorption energy losses. The limiting efficiency of a solar cell, equipped with an upconverter, has recently been discussed by Trupke et al.³² using a detailed balance model. The system under investigation consists of a bifacial single-junction solar cell with an upconverting layer located at the rear of the solar panel (Fig. 2). The upconverter transforms two (or more) transmitted sub-bandgap photons into one usable above-bandgap photon, which is subsequently absorbed by the solar cell to generate electron–hole pairs. The maximum efficiency was calculated to be 47.6% for non-concentrated light.

Fig. 2 Spectral conversion design for PV applications involving down-shifting (DS), quantum-cutting (QC), and upconversion (UC) luminescent materials. In a typical down-shifting process, upon excitation with a high-energy photon, nonradiative relaxation takes place followed by radiative relaxation, thereby resulting in the emission of a lower-energy photon. In contrast, two-step radiative relaxation occurs in the quantum-cutting process upon excitation with a high-energy photon, leading to the emission of two (or more) lower-energy photons. The upconversion process can convert two (or more) incident low-energy photons into a single higher-energy photon. Both down-shifting and quantum-cutting processes are able to make effective use of the high-energy portion of the solar spectrum, but with dramatically different quantum efficiency. The theoretical quantum efficiency for down-shifting is always less than 100%, whereas it exceeds 100% for quantum-cutting. Note that the down-shifting and quantum-cutting materials are generally placed on the front surface of a monofacial solar cell, allowing the downconverted photons to be absorbed by the solar cell. The upconversion material is typically placed in between a bifacial solar cell and a light-reflection layer to harvest the sub-bandgap spectrum of sunlight.

Quantum-cutting through downconversion is able to split one incident high-energy photon into two (or more) lower-energy photons with a conversion efficiency higher than 100%.³³ This process could minimize the energy loss caused by thermalization of hot charge carriers after the absorption of high-energy photons, if the downconverted photons can be absorbed by solar cells. As a result, the photocurrent of the device can be doubled. A recent quantum-cutting model proposed by Trupke et al.³⁴ showed that a solar cell (E_g = 1.1 eV), modified with a downconverting layer on the front surface, can achieve a conversion efficiency of up to 38.6% (Fig. 2).

Down-shifting is a single photon process that involves transformation of one absorbed high-energy photon into one lower-energy photon. This process obeys the Stokes Law with wavelength change known as the Stokes shift. Down-shifting is similar to quantum-cutting, but its conversion efficiency does not exceed 100%. Despite this disadvantage, down-shifting can still be useful for improving PV efficiency by shifting short-wavelength sunlight (usually ultraviolet and blue) to the longer-wavelength region where the spectral response of the solar cell is more sensitive (Fig. 2). Until now, two main classes of down-shifting-based PV devices have been investigated: a luminescent solar concentrator and a planar down-shifting layer. Lanthanide-doped phosphors and glasses, semiconductor quantum dots (QDs) and organolanthanide complexes have been thoroughly explored as potential wavelength-shifting materials.

This review focuses on the importance, development, and implementation of lanthanide-doped luminescent materials for modern PV applications. We begin by describing fundamental aspects central to rational design of solar cells followed by discussing the operating principles of lanthanide-doped upconversion materials as spectral converters to reduce the transmission loss of sub-bandgap light. Furthermore, an overview of the state-of-art near-infrared (NIR) quantum-cutting using a single Ho³⁺ ion and Ln³⁺–Yb³⁺ (Ln = Tb, Tm, Pr, Er, Nd, Ho, and Dy) pairs for c-Si solar cells is presented. The underlying energy transfer (ET) mechanisms are then discussed. The attempts to sensitize Ln³⁺–Yb³⁺ couples using ion species (Ce³⁺, Eu²⁺, Yb²⁺, and Bi³⁺) in different host lattices are subsequently described. We also highlight the topic of multiple exciton generation (MEG) in QDs to reflect an important parallel development promising for solar energy conversion. Finally, we discuss the advances toward realizing spectral conversion by utilizing planar down-shifting layers composed of phosphors, QDs and organolanthanide complexes as fluorophores. Selected examples of recent experimental results will be presented.

2. Fundamental aspects of solar cell design

2.1 Solar cells

Solar cells are typically composed of special light-absorbing semiconducting materials.³⁵ When sunlight falls on a solar cell, the photons activate the electrons in the cell and promote them into a higher energy conduction band. Those electrons can then be harnessed to create electric current. To produce a solar cell, the semiconductor is doped with either positive charge carriers (p-type) or negative charge carriers (n-type). If two differently doped semiconductor layers are combined, then a so-called p–n junction results on the boundary of the layers. The conversion efficiency of solar energy is perhaps the most significant parameter that determines the performance of a PV device. For any traditional single p–n junction solar cell, the bandgap energy of the semiconductor from which the solar cell is fabricated places a fundamental upper limit on its conversion efficiency. Currently, solar cells based on crystalline, polycrystalline and amorphous silicon represent more than 90% of the world production.³⁶ The use of c-Si enables PV devices to achieve a maximum conversion efficiency of 25%.³⁷

The c-Si solar cells work most efficiently in the 950–1100 nm spectral region, but they show very low spectral response to the short-wavelength sunlight (Fig. 3). Therefore, ideal quantum-cutting and down-shifting luminescent materials for c-Si solar cells should convert the high-energy (usually ultraviolet–blue) light into the NIR emission around 1000 nm, while the most desirable upconverters for c-Si solar cells are able to absorb light above 1100 nm and convert it into emission around 1000 nm. In principle, an upconverter for c-Si solar cells should satisfy the following requirements: (i) the excitation range longer than 1100 nm (E < 1.12 eV); (ii) the emission range shorter than 1100 nm; (iii) good response under low-intensity excitation (in the range of 10–100 W m⁻²); and (iv) high conversion efficiency and high transparency toward the upconverted light. Compared to conventional c-Si solar cells, wide bandgap solar cells would benefit much more from incorporation of an upconverting layer due to the dominant transmission losses. The wide bandgap solar cells, including GaAs, amorphous Si, dye-sensitized and organic solar cells, can work well in the visible region, but their absorption is generally limited to a maximum wavelength of ∼900 nm (Fig. 4).³⁸ For example, in an ideal single-junction solar cell with a bandgap of 1.7 eV, approximately 49% of the incoming solar energy is lost because it cannot be absorbed by the solar cell. An ideal upconverter for PV applications would convert incident sub-bandgap sunlight into monochromatic above-bandgap light where solar cells have their optimum spectral response.

Fig. 3 Normalized spectral response of a typical c-Si solar cell pyranometer (courtesy of Apogee Instruments, Inc., 2008). The c-Si is an indirect bandgap semiconductor so there is not a sharp cut off at the wavelength corresponding to the bandgap (E_g = 1.12 eV).

Fig. 4 Normalized external quantum efficiency (EQE) spectra for several wide bandgap PV cells. (Reprinted with permission from ref. 38. Copyright 2010, John Wiley & Sons, Ltd.)

2.2 Luminescence

Luminescence generally refers to the emission of light by a material after it has absorbed energy.³⁹ The term ‘luminescence’ was introduced in 1888 by Wiedemann.⁴⁰ Luminescence can be generated from different types of energetic sources, including electromagnetic radiations, electric fields, X-rays, and charged particles from radioactive decay. Depending upon the nature of the excitation source, luminescence can be subdivided into several categories that are generally indicated by a prefix. In the case of photo-excitation, this luminescence is called photoluminescence. In this review, we will focus on photoluminescence-based spectral conversion approaches for PV applications. Fluorescence and phosphorescence are two major forms of photoluminescence extensively investigated in modern research. They are distinguishable from the decay time (τ). Fluorescence has a short time lapse (τ < 10 ms) after the excitation source is removed, while phosphorescence has a much longer decay time (τ > 0.1 s).⁴⁰ Inorganic solids that give rise to luminescence are called phosphors or, lately, luminescent materials.^41,42 Luminescent materials generally require a host crystalline structure that constitutes the bulk of the phosphors. The characteristic luminescence properties are obtained by doping the host material with relatively small amounts of foreign ions. The luminescence of inorganic solids can be roughly classified into two mechanisms: luminescence of localized centers or activators (Fig. 5a and b) and luminescence of semiconductors through band-to-band excitation (Fig. 5c). To induce luminescence from an activator without efficient absorption for the available excitation energy, a sensitizer ion is often incorporated into the host material to transfer its excitation energy to the activator. The emission color can be readily adjusted by varying the dopant concentration or composition without changing the host lattice. Notably, a number of lanthanide activators show emission spectra with spectral positions that are hardly influenced by their chemical environment.

Fig. 5 Luminescence in inorganic solids. (a) Emission from a luminescence activator upon excitation. (b) Sensitized emission from an activator through energy transfer from a sensitizer to the activator upon excitation of the sensitizer. (c) Emission from a semiconductor after band-to-band excitation. A and A* represent the ground and excited states of the activator, respectively. S and S* represent the ground and excited states of the sensitizer, respectively. VB and CB represent the valence and conduction bands of the semiconductor, while D and A represent the donor and acceptor energy levels, respectively.

The conversion efficiency of a phosphor, usually expressed as either a quantum efficiency or an energy efficiency, is an important consideration in practical applications. The quantum efficiency (or quantum yield) is defined as the fraction of the input photons contributing to the desired optical process.^43,44 In contrast, the energy efficiency is the ratio of the output power to the input power. In a luminescence process, the excited state decays by a combination of radiative and nonradiative processes, and the relative rate of these processes determines the quantum efficiency. Radiative decay describes molecular deexcitation processes accompanied by photon emission. Molecules in the excited states can also relax by nonradiative processes where excitation energy is not converted into photons but is dissipated by thermal processes such as vibrational relaxation and collisional quenching. Let k_r and k_nr be the radiative and nonradiative decay rates, respectively, and N be the population density of luminescence activators in the excited state. The temporal evolution of the excited state can be described by:

The luminescence therefore decays exponentially with a time constant τ whereNote that the observed luminescence lifetime, τ, measures the combined rate of the radiative and nonradiative pathways. The fraction of the excitation contributing to radiative decay processes is k_r/(k_r + k_nr). Thus the quantum efficiency (η_PL) can be calculated using the following formula,⁴⁵Here, τ_R = 1/k_r is the radiative lifetime, namely, the lifetime of the excited state in the absence of nonradiative decay processes. The observed lifetime, τ, can be calculated from intensity decay curves. However, the radiative lifetime, τ_R, is usually estimated by the use of Judd–Ofelt theory as it is not easily experimentally determined.⁴⁶

2.3 Lanthanide ions

The lanthanide elements, characterized by the progressive filling of the 4f orbitals, are a family of 15 chemically similar elements from lanthanum (La) to lutetium (Lu). The term ‘rare earth’ is applied to lanthanide elements and also to yttrium (Y), which is found in nature always along with the lanthanides. The lanthanides, essentially existing in their most stable oxidation state as trivalent ions (Ln³⁺), are extensively investigated for their optical properties.^47–55 The lanthanide ions feature an electron configuration of 4fⁿ (0 < n < 14) and the arrangements of electrons within this configuration are substantially diverse. This results in a fairly large number of energy levels.⁵⁶ Most of the fascinating optical properties, such as photon upconversion emission, of lanthanide ions can be ascribed to the electron transitions within the 4fⁿ configuration (Table 1). Most lanthanide ions generally show sharp line spectra, much narrower and more distinct than those for transition metal ions. The spectra are associated with weak f–f electronic transitions. The narrow spectral bands indicate that the f-orbitals have a smaller radial extension than the outer 5s and 5p orbitals, thus leading to smaller electron–phonon coupling strengths and a lower susceptibility to crystal-field and exchange perturbations.

Table 1 Principle transitions in the emission spectra of common lanthanide ions utilized in upconversion (UC), quantum-cutting (QC), and down-shifting (DS) luminescence processes for PV applications

Ln	Ground state	Excited state	Final state	Emission wavelength (nm)	Energy (cm^−1)	Intensity	Remarks
Pr	^3H4	^3P2 →	^3H4	440	22 727	Weak	QC
		^3P1 →	^3H4	470	21 277	Weak	QC
			^1G4	872	11 468	Medium	QC
		^3P0 →	^3H4	480	20 833	Strong	UC and QC
			^3H5	545	18 349	Weak	UC and QC
			^3H6	606	16 502	Medium	UC and QC
			^3F2	640	15 625	Weak	UC and QC
		^1D2 →	^3F4	1037	9643	Medium	QC
Nd	^4I9/2	^4D3/2 →	^4I9/2	355	28 169	Weak	UC and QC
		^2P3/2 →	^4I9/2	380	26 316	Weak	UC and QC
			^4I11/2	410	24 390	Strong	UC and QC
			^4I13/2	452	22 124	Strong	UC and QC
		^4G7/2 →	^4I9/2	545	18 349	Weak to strong	UC and QC
			^4I11/2	587	17 036	Weak to strong	UC and QC
			^4I13/2	655	15 267	Weak to strong	UC and QC
		^4F3/2 →	^4I9/2	886	11 287	Weak to strong	QC and DS
			^4I11/2	1064	9399	Strong	QC and DS
			^4I13/2	1340	7463	Weak	QC and DS
Sm	^6H5/2	^4G5/2 →	^6H5/2	564	17 730	Medium	DS
			^6H7/2	601	16 639	Strong	DS
			^6H9/2	644	15 528	Medium	DS
Eu	^7F0	^5D0 →	^7F0,1,2,3,4	570–720	13 889–17 544	Strong	UC and DS
Tb	^7F6	^5D4 →	^7F6,5,4,3	480–650	15 385–20 833	Strong	UC, QC and DS
Dy	^6H15/2	^4F9/2 →	^6H15/2	486	20 576	Medium	QC and DS
			^6H13/2	575	17 391	Strong	QC and DS
			^6H11/2	664	15 060	Weak	QC and DS
Ho	^5I8	^5S2, ^5F4 →	^5I8	540	18 519	Strong	UC and QC
			^5I7	749	13 351	Weak	UC and QC
			^5I6	1012	9881	Weak	QC
		^5F5 →	^5I8	644	15 528	Medium	UC and QC
			^5I7	966	10 352	Weak	QC
		^5I6 →	^5I8	1180	8475	Strong	QC
Er	^4I15/2	^4G11/2 →	^4I15/2	380	26 316	Weak	UC and QC
		^2P3/2 →	^4I13/2	408	24 510	Weak	UC
			^4I11/2	480	20 833	Weak	UC
		^2H11/2 →	^4I15/2	525	19 048	Weak	UC and QC
		^4S3/2 →	^4I15/2	545	18 349	Strong	UC and QC
			^4I13/2	850	11 765	Weak	UC and QC
		^4F9/2 →	^4I15/2	665	15 038	Strong	UC and QC
		^4I9/2 →	^4I15/2	800	12 500	Strong	UC and QC
		^4I11/2 →	^4I15/2	980	10 204	Strong	UC and QC
		^4I13/2 →	^4I15/2	1540	6494	Strong	QC
Tm	^3H6	^1D2 →	^3H6	360	27 778	Medium	UC and QC
			^3F4	450	22 222	Medium	UC and QC
		^1G4 →	^3H6	475	21 053	Strong	UC and QC
			^3F4	650	15 385	Strong	UC and QC
			^3H5	786	12 723	Weak	UC and QC
		^3H4 →	^3H6	800	12 500	Strong	UC and QC
		^3F4 →	^3H6	1800	5556	Weak	QC
Yb	^2F7/2	^2F5/2 →	^2F7/2	980	10 204	Strong	UC, QC and DS

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When a 4f electron is excited into a 5d orbital that extends beyond the 5s and 5p orbitals, the spectroscopic properties of lanthanide ions in the 4fⁿ5d electronic configuration are influenced more strongly by the host lattice. Therefore, the electronic transitions between the 4fⁿ and 4fⁿ5d states, through absorption or emission of photons, are expected to be significantly different from those transitions within the 4fⁿ configuration. As the inter-configuration 4fⁿ–4fⁿ5d transitions of the lanthanide ions are parity-allowed, they have intensities up to 10 000 times stronger than the strongest 4fⁿ–4fⁿ transitions.⁵⁷

The choice of host materials is of great importance in designing lanthanide-based luminescent materials for efficient PV applications. As a general rule, the host materials require close lattice matches to the dopant ions and have low phonon energies. Despite the fact that the energy level structure of most lanthanide ions is independent of the host materials, the phonon energy plays an important role in nonradiative transitions due to multiphonon relaxation between closely spaced energy levels. The nonradiative relaxation rate can be estimated with the exponential energy gap law developed by van Dijk and Schuurmans:^58,59

k_nr = β_elexp(−α(ΔE − 2ℏω_max)) (4)

where β_el and α are constants for a given host lattice, ΔE is the energy difference between the energy levels considered, and ℏω_max is the maximum phonon energy. Hosts with low phonon energy may decrease the probability of nonradiative transitions, subsequently leading to high luminescence efficiency. The maximum phonon energies of different inorganic host materials are summarized in the following: iodide (160 cm⁻¹) < bromide (175–190 cm⁻¹) < chalcogenide (200–300 cm⁻¹) < fluoride (500–600 cm⁻¹) < tellurite (600–850 cm⁻¹) < germanate (800–975 cm⁻¹) < silicate (1000–1100 cm⁻¹) < phosphate (1100 cm⁻¹) < borate (1400 cm⁻¹).²⁴

The most promising phosphors for upconversion and quantum-cutting luminescence are found in fluoride hosts owing to their low phonon energy, high refractive index, and good thermal stability.^33,60,61 For example, LiGdF₄:Eu³⁺ shows a quantum efficiency of 1.90,^62,63 and the quantum efficiency of YF₃:Pr³⁺ approaches 1.4.^64–66 In contrast, the quantum efficiencies of Pr³⁺-activated oxides are far lower than unity.⁶⁷ However, the fluoride phosphors are believed to be unstable under sub-bandgap excitation.

2.4 Energy transfer

ET is an important optical process that dominates the luminescence of a material. Spectral conversion by luminescent materials for PV applications mostly relies on the ET between lanthanide ions. Four basic ET mechanisms have been proposed and observed in lanthanide-doped materials: (i) resonant radiative transfer through emission of a sensitizer and re-absorption by an activator; (ii) non-radiative transfer associated with resonance between an absorber (sensitizer) and an emitter (activator); (iii) multiphonon-assisted ET; and (iv) cross-relaxation between two identical ions (Fig. 6).⁶⁸ The efficiency of radiative transfer depends on how efficiently the activator fluorescence is excited by the sensitizer emission (Fig. 6a). An efficient ET process requires a significant spectral overlap between the sensitized emission and the absorption of an activator. If a radiative ET takes place predominantly, the decay time of the sensitized luminescence does not vary with the activator concentration. In contrast to the radiative ET, the nonradiative ET (Fig. 6b) is often accompanied by a significant decrease in the decay time of sensitized luminescence versus activator concentration. Two other lines of evidence for the occurrence of nonradiative ET are: (i) the presence of an excitation band of the sensitizer in the excitation spectrum of the activator, and (ii) the presence of activator emission found in the emission spectrum when the sensitizer is selectively excited. ET can occur if the energy differences between the ground and excited states of the donor (sensitizer) and the acceptor (activator) are equal and if there exists a suitable interaction, either an exchange interaction or a multipolar interaction, between both systems. Exchange interaction (Dexter ET) depends on the wave function overlap and thus only operates over very short distances (<0.5 nm). While multipolar interaction (Förster ET) primarily depends on the strength of the optical transitions involved and can occur for separations as large as 2 nm. Non-resonant ET can also occur with the assistance of phonons unless the differences between the ground and excited states of the donor and acceptor are large.

Fig. 6 A schematic diagram to illuminate the different ET processes between two ions: (a) resonant radiative transfer through emission of a sensitizer and re-absorption by an activator; (b) nonradiative transfer associated with resonance between a sensitizer and an activator; (c) multiphonon assisted ET; and (d) cross-relaxation between two identical ions. S and A denote the sensitizer and activator, respectively.

The Dexter ET probability from a sensitizer (S) to an activator (A) is generally approximated as in eqn (5):⁶⁹

where H_SA is the interaction Hamiltonian and ℏ is the Planck constant; 〈S,A* and 〈S*,A represent the initial state and the final state, respectively; the ∫g_S(E)g_A(E)dE integral stands for the spectral overlap; the factors, g_S(E) and g_A(E), denote the normalized spectral feature for the sensitizer emission and activator absorption, respectively; E is the energy involved in the transfer. Eqn (5) shows that the ET probability P_SA vanishes for vanishing spectral overlap. The square of the matrix element in eqn (5) is expressed in terms of the distance-dependent ET probability between the donor and acceptor. The distance dependence of the transfer rate varies with the type of interaction. For exchange interaction the distance dependence is exponential, while for electric multipolar interaction the distance dependence is given by R⁻ⁿ (n = 6, 8,… for electric–dipole electric–dipole interaction, electric–dipole electric–quadrupole interaction,… respectively).

Phonon-assisted ET occurs when the resonance condition is not well met between the sensitizer and the activator, resulting in a small spectral overlap (Fig. 6c). In this case, the mismatch between the transition energies of the sensitizer and the activator is compensated by phonon emission or absorption. According to Miyakawa–Dexter theory,⁷⁰ the probability of phonon-assisted transfer is expressed by,

P_PAT(ΔE) = P_PAT(0)e^−βΔE (6)

where ΔE is the energy gap between the electronic levels of sensitizer and activator ions; β is a parameter that depends on the energy and occupation number of participating phonons; and P_PAT(0) is equal to the resonant transfer probability given by eqn (5). Non-resonant phonon-assisted ET between various trivalent lanthanide ions in Y₂O₃ crystals was thoroughly studied by Yamada et al.⁷¹ In their experiments, the energy gap between the sensitizer and activator system varied in a wide range of energies up to 4000 cm⁻¹. The probability of phonon-assisted ET was measured to have an exponential dependence on the energy gap, in excellent agreement with the Miyakawa–Dexter theory. It was revealed that the phonons of about 400 cm⁻¹ in the Y₂O₃ host contribute dominantly to the phonon-assisted process.

Cross-relaxation terminology usually refers to all types of resonant ET between identical ions, acting as both sensitizers and activators. As shown in Fig. 6d, cross-relaxation may give rise to the diffusion process between sensitizers when the levels involved are identical (known as energy migration) or to self-quenching when their levels are different. In the first case there is no loss of energy, whereas in the second there is a loss or change in the energy of the emitted photons.⁶⁸ Concentration quenching of luminescence often takes place as a result of cross-relaxation among the activators when the concentration of the activator is above a critical value.

3. Upconversion materials for PV applications

3.1 Concepts of upconversion

The term upconversion describes nonlinear anti-Stokes optical processes that convert two (or more) low-energy pump photons to a higher-energy output photon.^72,73 This phenomenon was first discovered by Auzel in the 1960s.⁷⁴ Since then, there has been a surge of research interest in upconversion due to its applications in a number of diverse fields, such as infrared quantum counter detectors, compact solid-state lasers, temperature sensors, lightings and displays, as well as biomedical imaging.^75–137

As was already discussed above, only the absorption of photons with energy higher than the bandgap can generate electron–hole pairs contributing to electric current. Indeed, the transmission of sub-bandgap photons is one of the major energy loss mechanisms in conventional solar cells. In the case of c-Si solar cells, the transmission loss amounts to about 20% of the incident solar energy, which is not substantially reducible by conventional approaches. To this end, the use of upconversion materials may provide a solution to the transmission loss by converting two sub-bandgap photons into one above-bandgap photon. Indeed, Trupke et al.³² in 2002 showed that the theoretical efficiency limit of a solar cell, modified with an up-converter, can reach 63.2% for concentrated sunlight and 47.6% for non-concentrated sunlight, respectively.

Although the idea of using upconversion for improving the performance of solar cell devices is implicit, relatively little work has been done until recently. A considerable limitation lies in the fact that upconversion processes are only possible in trivalent lanthanide ions with metastable and long-lived intermediate levels acting as storage reservoirs for the pump energy. In this sense, Er³⁺, Tm³⁺, and Ho³⁺ ions, featuring ladder-like energy levels for facilitating photon absorption and subsequent ET steps, were generally chosen as activators to give rise to efficient visible emissions under low pump power densities. In order to enhance upconversion luminescence efficiency, the Yb³⁺ ion is usually co-doped as an excellent upconversion sensitizer due to its large absorption cross-section in the 900–1100 nm NIR region, corresponding to the ²F_5/2 → ²F_7/2 (Yb³⁺) transition. In fact, the Er³⁺–Yb³⁺ couple is by far the most studied upconversion system (Fig. 7).

Fig. 7 Proposed upconversion mechanisms for Er³⁺–Yb³⁺ and Tm³⁺–Yb³⁺ couples under 980 nm diode laser excitation. The dash-dotted, dashed, dotted, and full arrows represent photon excitation, energy transfer, multiphonon relaxation, and emission processes, respectively. Only visible and NIR emissions are shown here. (Reprinted with permission from ref. 77. Copyright 2008, American Chemical Society.)

A wide variety of upconversion mechanisms have been identified (Fig. 8). For PV applications, the majority of these mechanisms are based on some combination of excited state absorption (ESA) and energy transfer upconversion (ETU) processes. In contrast to common nonlinear processes including two photon absorption and second harmonic generation, these upconversion processes combine the benefit of high quantum efficiency without the need for intense coherent excitation sources, with the inherent advantages of large anti-Stokes shift. ESA is a single-ion process that involves sequential absorption of two (or more) photons by an excited ion using a real intermediary energy level, and results in promotion of that ion to a higher excited state. In ETU, two pump photons excite two neighboring ions to a metastable energy level through ground-state absorption (GSA). The excited ions then exchange energy nonradiatively, promoting one excited ion to an upper emitting state and demoting the other ion to the ground state. Photon avalanche (PA) is an unconventional mechanism as it could lead to strong upconverted emission without any resonant GSA when the pump power is above a certain threshold value.¹³⁸ The pump wavelength is only resonant between a metastable state and a higher energy level. The phenomenon of PA upconversion was first reported in Pr³⁺-doped LaCl₃ and LaBr₃ crystals.¹³⁹ Recently, Wang et al.⁷⁵ proposed the energy migration-mediated upconversion (EMU) involving the use of four types of lanthanide ions and a core–shell structure. Through gadolinium sublattice-mediated energy migration, efficient tunable upconversion emissions in NaGdF₄:Tm³⁺/Yb³⁺@NaGdF₄:Ln³⁺ core–shell nanoparticles were realized for various lanthanide activators (Ln³⁺ = Eu³⁺, Tb³⁺, Dy³⁺, and Sm³⁺) without long-lived intermediary energy states.

Fig. 8 Proposed typical upconversion processes. (a) Excited state absorption (ESA); (b) energy transfer upconversion (ETU); (c) photon avalanche (PA). PA is an unconventional mechanism as it could lead to strong upconverted emission without any resonant ground-state absorption when the pump power is above a certain threshold value. The pump wavelength is only resonant between a metastable state and a higher energy level; (d) energy migration-mediated upconversion (EMU) involving the use of four types of lanthanide ions and a core–shell design. Note that core and shell regions are highlighted with different background colors. The ‘nx’ denotes the occurrence of random hopping through many type-III ions.

The use of upconversion materials for improving PV system performance was first reported by Gibart's group¹⁴⁰ in 1996 using the Er³⁺–Yb³⁺ couple in bifacial GaAs solar cells. Since then, many groups have pursued the development of various upconversion-based PV devices to enhance the conversion efficiency (Table 2).^141–164 Upconversion materials singly-doped with Er³⁺ or Ho³⁺, capable of converting long-wavelength NIR light into short-wavelength NIR and visible emissions, can be combined with narrow bandgap c-Si solar cells (E_g = 1.12 eV; 1100 nm). For PV devices using wide bandgap semiconductors, such as GaAs (E_g = 1.43 eV; 867 nm)¹⁶⁵ and amorphous Si (E_g = 1.75 eV; 708 nm),¹⁶⁶ the utilization of upconversion materials co-doped with Ln³⁺–Yb³⁺ couples is very convenient due to the efficient ETU from the Yb³⁺ sensitizer to various Ln³⁺ activators.

Table 2 Selected lanthanide-doped upconversion materials used for PV applications

Dopant ion	Host lattice	Preparation method	Excitation (nm)	Emission (nm)	Solar cell type	Ref.
Er^3+	NaYF4	Solid-state reaction	1523	550, 660, 800, 980	c-Si	141
Er^3+	NaYF4	—	1523	545, 670, 800, 980	c-Si	142
Er^3+	CaF2	—	1550	660, 980	c-Si	143
Er^3+	Gd2(MoO4)3	Combustion synthesis	1530	545, 665, 800, 980	c-Si	144
Er^3+	Y2O3	Template technology	1538	562, 659, 801, 987	c-Si	145
Er^3+	Fluoride glasses	Glass melting	1532	550, 660, 820, 980	c-Si	146
Ho^3+	Glass ceramics containing PbF2 nanocrystals	Glass melting	1170	650, 910	c-Si	147
Ho^3+–Yb^3+	Fluoroindate glass	Glass melting	1155	550, 650, 750, 905, 980	c-Si	148
Er^3+–Yb^3+	Y6W2O15	Solid-state reaction	973	516–570	GaAs	149
Er^3+–Yb^3+	NaYF4	Hydrothermal method	980	525, 540, 655	Amorphous Si	150,151
Er^3+–Yb^3+	NaYF4	Solid-state reaction	980	522, 540, 653	Amorphous Si	152
Er^3+–Yb^3+	NaYF4	Hydrothermal method	980	524, 540, 660	Amorphous Si	153
Er^3+–Yb^3+	Glass ceramic containing NaYF4 nanocrystals	Glass melting	980	520, 538, 656	Amorphous Si	154
Er^3+	Y2O3	Hydrothermal method	980	525, 550, 660	Dye-sensitized	155
Er^3+–Yb^3+	LaF3	Solvothermal synthesis	980	543, 655	Dye-sensitized	156
Er^3+–Yb^3+	NaYF4	Hydrothermal method	980	510–570, 640–680	Dye-sensitized	157
Er^3+–Yb^3+	NaYF4 : Er,Yb@NaYF4	Thermal decomposition	976	510–570, 635–700	Dye-sensitized	158
Er^3+–Yb^3+	YF3	Thermal decomposition	980	525, 545, 656	Dye-sensitized	159
Er^3+–Yb^3+	YAG transparent ceramics	Solid-state reaction	980	520, 563, 677	Dye-sensitized	160
Tm^3+–Yb^3+	Lu2O3	Co-precipitation	980	476, 653	Dye-sensitized	161
Tm^3+–Yb^3+	Glass ceramics containing PbF2 nanocrystals	Glass melting	980	475, 650, 800	Dye-sensitized	162
Er^3+–Yb^3+	YF3	—	975	510–560	Organic	163
Ho^3+–Yb^3+	Y2BaZnO5	Solid-state reaction	986	545	Organic	164

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3.2 Upconversion for c-Si solar cells

Er³⁺ ion. Er³⁺-doped upconversion materials are the most promising upconverters for c-Si solar cells due to the GSA of Er³⁺ in the range of 1480–1580 nm (⁴I_15/2 → ⁴I_13/2 transition). The GSA centered at about 1540 nm results in upconversion via an ETU mechanism, giving rise to four emission bands: ⁴I_11/2 → ⁴I_15/2, 980 nm; ⁴I_9/2 → ⁴I_15/2, 810 nm; ⁴F_9/2 → ⁴I_15/2, 660 nm; and ⁴S_3/2 → ⁴I_15/2, 550 nm (Fig. 9). These emission bands match well with the absorption of c-Si. Note that the exact emission wavelength can vary by ±10 nm, depending on the host material (Table 2).

Fig. 9 Upconversion processes via the ETU mechanism between two Er³⁺ ions, resulting in c-Si above-bandgap emissions under c-Si sub-bandgap pump excitation (1520 nm). Solid, dotted, and wavy arrows represent photon absorption/emission, energy transfer, and multiphonon relaxation, respectively.

Shalav et al.¹⁴¹ in 2005 reported the application of NaYF₄:Er³⁺ (20 mol%) phosphors as the upconverters in a bifacial c-Si solar cell. These phosphors were mixed into an optically transparent acrylic adhesive medium at a concentration of 40 wt% and then placed on the rear of a bifacial c-Si solar cell. Reflective white paint was used as a reflector on the rear of the system. An external quantum efficiency of 2.5% was obtained for the solar cell under excitation at 1523 nm with a 5.1 mW laser. More recently, Fischer and co-workers¹⁴² also investigated the potential of NaYF₄:Er³⁺ to significantly reduce the sub-bandgap losses of c-Si solar cells. The optical upconversion efficiency of NaYF₄:Er³⁺ (20 mol%) was determined to be about 5.1% upon excitation at 1523 nm with a power density of 1880 W m⁻². The c-Si solar cell device combined with an upconverter showed an external quantum efficiency of 0.34% upon irradiation at 1522 nm with a power density of 1090 W m⁻².

Ho³⁺ ion. The Ho³⁺ ion has a relatively wide absorption band in the 1150–1225 nm spectral range due to ⁵I₈ → ⁵I₆ transition. The irradiation power density of sunlight in this spectral range is about 40 W m⁻², which is approximately twice more intense than that in the 1480–1580 nm range. Lahoz¹⁴⁷ in 2008 reported the use of Ho³⁺ singly-doped oxyfluoride glass ceramics as promising upconverters for efficiency enhancement in c-Si solar cells. Under sub-bandgap excitation at 1170 nm, upconversion emissions in the visible (∼650 nm, ⁵F₅ → ⁵I₈ transition) and NIR (∼910 nm, ⁵I₅ → ⁵I₈ transition) spectral ranges have been obtained via the ETU mechanism.

In a following paper, Lahoz et al.¹⁴⁸ co-doped Ho³⁺ with Yb³⁺ and found enhanced emission intensity of NIR-to-NIR upconversion as a result of ET from Ho³⁺ to Yb³⁺ ions. Importantly, owing to the high transparency to the excitation wavelength of ∼1540 nm, these Ho³⁺-based glass ceramics could be used in combination with Er³⁺-doped upconverters. The authors proposed a double-layer design with the Ho³⁺-doped upconverting layer placed directly at the rear surface of a bifacial c-Si solar cell, followed by the Er³⁺-doped upconverter and a mirror (Fig. 10). The integration of both upconverters would enlarge the absorption of the solar sub-bandgap spectral range exploited for enhancing the c-Si solar cell response.

Fig. 10 A proposed operating mechanism for a c-Si solar cell with Ho³⁺–Yb³⁺ and Er³⁺ doped upconverters. Above-bandgap light (highlighted in blue color) is directly absorbed by the solar cell, which is electronically isolated from the upconverter. The sub-bandgap light (highlighted in orange and red colors) transmitted by the solar cell is stepwise upconverted into high-energy photons, which are subsequently absorbed in the solar cell. A mirror reflector is located behind the upconverter. CB and VB are the conduction and valence bands of c-Si, respectively. The energy gap between VB and CB is around 1.12 eV for c-Si.

An alternative design proposed by Chen et al. in 2012 is to adopt a core–shell nanostructure, in which Er³⁺ and Ho³⁺ activators are separately incorporated into the core and shell layer of a nanoparticle.¹⁶⁷ The use of a core–shell layout can extend the NIR wavelength range excitable for upconversion emission, and furthermore allow facile modulation of activator concentration while minimizing luminescence quenching induced by the deleterious cross-relaxation ET between the Er³⁺ and Ho³⁺ ions. As a proof-of-concept experiment, the authors fabricated monodisperse NaGdF₄:Er³⁺@NaGdF₄:Ho³⁺@NaGdF₄ core–shell–shell nanoparticles. The middle protection shell not only enhances the upconversion luminescence of Er³⁺ in the core, but also acts as the host to realize the upconversion luminescence of Ho³⁺. As a result, intense upconversion emissions for both Er³⁺ and Ho³⁺ dopants were achieved.

3.3 Upconversion for wide bandgap solar cells

GaAs solar cells. In 1996, Gibart et al.¹⁴⁰ reported the application of a 100 μm thick vitroceramic co-doped with Er³⁺–Yb³⁺ on the rear of a substrate-free GaAs solar cell. Under 891 nm (1.391 eV) excitation, upconverted green (⁴S_3/2 → ⁴I_15/2 transition) and red (⁴F_9/2 → ⁴I_15/2 transition) emissions from Er³⁺ ions were observed. The photoresponse of the GaAs solar cell increased quadratically with the input excitation. The measured efficiency was 2.5% under 25.6 W cm⁻² illumination at 891 nm. In 2012, Lin et al.¹⁴⁹ further validated the concept by adhering a 300 μm thick layer of Y₆W₂O₁₅:Er³⁺/Yb³⁺ upconversion phosphors to the rear of a GaAs solar cell. The authors obtained a maximum output power of 0.339 μW when illuminated with a 973 nm laser at 145.65 W cm⁻². However, compared to the Er³⁺–Yb³⁺ couple, the Tm³⁺–Yb³⁺ couple with NIR-to-NIR upconversion luminescence (∼980 nm excitation, ∼800 nm emission)^168–175 is likely to be more suitable for application in GaAs solar cells (E_g = 1.43 eV; 867 nm) due to a larger emission and absorption spectral overlap.

Amorphous silicon solar cells. Amorphous Si solar cells with a bandgap of ∼1.75 eV only absorb NIR light shorter than 708 nm. To extend the absorption limit, upconversion of sub-bandgap NIR light (λ > 700 nm) to visible emission using NaYF₄:Er/Yb phosphors can be combined with the amorphous Si solar cells. These upconversion phosphors have visible emission bands at around 525, 540, and 655 nm located in the spectral region where the solar cells have high internal collection efficiency. To this end, Zhang et al.¹⁵⁰ in 2010 reported the fabrication of an amorphous Si solar cell device composed of NaYF₄:Er/Yb (2/18 mol%) nanocrystals. These authors reported that the incorporation of an upconverting layer into the solar cell could effectively increase the short circuit current density from 16 to 17 mA cm⁻².

The same upconversion phosphor was also used by de Wild et al.^151,152 to demonstrate enhanced conversion efficiency in amorphous Si solar cells. In their experiments, the upconversion powders were mixed with polymethylmethacrylate and then made into an upconverter layer with thickness of 200–300 μm. A maximum current enhancement of 6.2 mA was measured under 980 nm diode laser illumination at 28 mW. More recently, a 72-fold enhancement in photocurrent under 980 nm illumination was achieved by Li et al.¹⁵³ using NaYF₄:Yb³⁺/Er³⁺/Gd³⁺ nanorod-modified electrodes in an amorphous Si solar cell, as compared to the PV cell without an upconverter.

Dye-sensitized solar cells. Dye-sensitized solar cells (DSSCs) are next-generation PV cells that can be used to create low-cost, flexible solar panels.^176–179 Unlike conventional Si-based solar cells, DSSCs primarily consist of photosensitive dyes and other substances such as an electrolyte solution and metal oxide nanoparticles. Despite great efforts, the improvement in the efficiency of state-of-the-art DSSCs remains a daunting task, largely due to the limited absorption spectrum of currently available dyes.^180–182 The most commonly used dyes in current DSSCs are ruthenium-based dyes, including N3 ([Ru(dcbpyH₂)₂(NCS)₂], dcbpyH₂ = 2,2′-bipyridyl-4,4′-dicarboxylic acid), N719 ([(C₄H₉)₄N]₂[Ru(dcbpyH)₂(NCS)₂]), and N749 ([(C₄H₉)₄N]₃[Ru(tcterpy)(NCS)₃]·3H₂O, tcterpy = 4,4′,4′′-tricarboxy-2,2′:6′,2′′-terpyridine). As a result of their large optical bandgap of 1.8 eV, these dyes have an absorption threshold below ∼700 nm. To achieve higher efficiencies for DSSCs, light absorption must be extended into the NIR spectral region without sacrificing their performance in the visible region. In 2010, Shan and Demopoulos¹⁵⁶ reported, for the first time, the application of lanthanide-doped upconversion materials for enhancing the NIR sunlight harvesting in DSSCs. In their studies, the Er³⁺–Yb³⁺ co-doped LaF₃–TiO₂ nanocomposite was used as an upconversion layer to fabricate a triple-layer working electrode for DSSCs. The green emission at around 543 nm generated by the upconversion nanocomposite can be efficiently absorbed by the N719 dye, which indeed leads to photocurrent generation upon 980 nm laser excitation. However, this structure configuration was proved to be ineffective in delivering a higher photocurrent output due to apparent charge recombination at the interfaces of the triple-layer electrolyte.

In a following paper by Shan et al.,¹⁵⁷ different upconversion materials consisting of NaYF₄:Er³⁺/Yb³⁺ hexagonal nanoplatelets (particle size ∼800 nm) were tested in DSSCs. The upconverting phosphors were directly placed on the rear side of a counter electrode (Fig. 11). This design enables a dual-mode functionality that provides both light reflection and NIR light harvesting. Photocurrent was observed for the DSSC device when illuminated with a 980 nm fiber laser, clearly demonstrating the upconverting function of the NaYF₄:Er³⁺/Yb³⁺ nanomaterials. Importantly, this novel DSSC configuration greatly overcomes the drawback of charge recombination induced by the conducting upconversion layer when used internally. Moreover, the authors found that under AM 1.5G filtered spectral illumination (100 mW cm⁻²) approximately 10% enhancement in both photocurrent and overall conversion efficiency can be achieved by addition of the upconverting layer, which was predominantly attributable to its light reflecting role. Several other groups also reported the enhanced NIR response of the DSSCs by using upconverting materials doped with Er³⁺,¹⁵⁵ Er³⁺–Yb³⁺,^158–160 and Tm³⁺–Yb³⁺.¹⁶¹

Fig. 11 Schematic configuration of a DSSC device consisting of one internal TiO₂ transparent layer and an external rear layer of NaYF₄:Er³⁺/Yb³⁺ hexagonal nanoplatelets. The external upconverting layer can simultaneously reflect scattered light and harvest NIR light. (Reprinted with permission from ref. 157. Copyright 2011, American Chemical Society.)

Organic solar cells. Organic solar cells are light-weight and flexible, leading to inexpensive, large-scale production for solar energy conversion.^183–187 One of the major energy losses in organic solar cells is the sub-bandgap transmission as a result of the mismatch between the absorption properties of polymer materials and the terrestrial solar spectrum. The current organic PV cells with best performance are made of bulk heterojunctions comprising poly(3-hexylthiophene) (P3HT) and the fullerene derivative [6,6]-phenyl-C₆₁-butyric acid methyl ester (PCBM).^188–191 Owing to the large bandgap of organic molecules, the bulk heterojunction-based PV cells are only able to harvest the visible sunlight. In an attempt to utilize the NIR part of the solar spectrum, Wang et al.¹⁶³ in 2011 demonstrated the feasibility of upconversion in P3HT:PCBM organic solar cells. By using commercial LaF₃:Yb³⁺/Er³⁺ phosphors, the authors obtained an upconversion efficiency of ∼0.19% (excitation density: 250 mW cm⁻²) and an upconverted photocurrent density of ∼16.5 μA cm⁻² (excitation density: 25 mW cm⁻²) under 975 nm laser diode illumination. In their following paper published in 2012, a semiconducting nanofilm of MoO₃:Yb³⁺/Er³⁺ was incorporated into P3HT:PCBM solar cells as a buffer layer that enables both hole extraction and upconversion capabilities.¹⁹² The authors found that less than 1% of the short-circuit current was obtained from the upconversion effect under one-sun AM1.5G illumination. Wu and co-workers in 2012 observed an enhancement of 5 μA in the short-circuit current under 980 nm laser illumination of NaYF₄:Yb³⁺/Er³⁺ nanocrystals placed on the rear side of P3HT:PCBM solar cells.¹⁹³

In 2012, Adikaari et al. applied Y₂BaZnO₅:Ho³⁺/Yb³⁺ upconversion phosphors to PCDTBT:PCBM (PCDTBT: poly[N-9′-hepta-decanyl-2,7-carbazole-alt-5,5(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole]) organic solar cells in order to utilize the NIR solar spectrum.¹⁶⁴ The authors adopted two different layout designs for the PV device as shown in Fig. 12a and b. The PCDTBT:PCBM active layer showed little absorption for light with wavelengths above 700 nm, while the Y₂BaZnO₅:Er³⁺/Yb³⁺ phosphors exhibited a broad absorption band in the region of 870–1030 nm due to the ²F_7/2 → ²F_5/2 (Yb³⁺) transition (Fig. 12c). Moreover, the main upconversion emission at 545 nm that corresponds to ⁵S₂,⁵F₄ → ⁵I₈ (Ho³⁺) transition matches well with the absorption of the PCDTBT:PCBM photoactive layer (Fig. 12d). Their PV measurements showed that with the upconversion phosphors placed behind the device, a maximum photocurrent density of 16 μA cm⁻² and a power conversion efficiency of 0.45% were obtained when illuminated with a 986 nm laser (excitation density: ∼390 mW cm⁻²).

Fig. 12 Schematic design of an organic PV device with upconversion phosphors placed (a) in front of or (b) behind the device. (c) Absorption spectra of PCDTBT:PCBM and Ho³⁺–Yb³⁺ co-doped Y₂BaZnO₅ phosphors and the corresponding transmission spectrum of the PV device. (d) AM1.5G spectrum and upconversion emission spectrum of Ho³⁺–Yb³⁺ co-doped Y₂BaZnO₅ phosphors under 986 nm excitation. Note that the separation distance between the phosphor layer and the device is ∼0.5 mm. ITO and BCP refer to indium tin oxide and bathocuproine, respectively. (Reprinted with permission from ref. 164. Copyright 2012, American Institute of Physics.)

Before the conversion efficiency of PV devices can be further improved through use of upconversion materials, though, it will be necessary to put some effort into addressing a number of challenges. First, only a small fraction of the solar spectrum can be upconverted by Ln³⁺-doped materials because of their weak and narrowband absorption, so the next step will be to explore methods that enable broadband upconversion. More significantly, new materials or technologies enabling high upconversion efficiency must be developed as upconversion is a nonlinear process with low conversion efficiency (typically less than 3%).¹⁹⁴ A high-density excitation, controlled by a pulsed laser, can enhance upconversion efficiency. But for practical PV applications, the need for concentrated solar power clearly complicates the manufacture of solar cells. In this regard, photon upconversion based on sensitized triplet–triplet annihilation (TTA) involving chromophores could be utilized for wide bandgap solar cells. This emerging technology offers relatively high upconversion efficiency under low excitation power density (a few mW cm⁻²).^195–198 Sunlight is sufficient to excite the chromospheres and sensitize the upconversion process. However, a significant drawback of TTA is that the upconverted spectrum is generally limited in the range of 650–700 nm.¹⁹⁹ Although several groups have recently reported the TTA-based NIR-to-visible upconversion, thus far the attempts to obtain efficient upconverted emissions at wavelengths beyond 800 nm have not been successful.^200–202

4. Quantum-cutting materials for PV applications

4.1 Concepts of quantum-cutting

There are certain phosphor materials that can transform the energy of one absorbed photon into two (or more) emitted low-energy photons. This process is known as quantum-cutting with quantum efficiency more than 100%.³³ In general, quantum-cutting can be realized by photon cascade emission from a single lanthanide ion (e.g. Pr^3+64–66 and Gd³⁺²⁰³) or by downconversion via ET through different sets of lanthanide ions (e.g. Gd³⁺–Eu^3+62,63 and Gd³⁺–Tb³⁺–Er³⁺).²⁰⁴ The first successful demonstration of efficient visible quantum-cutting in a LiGdF₄:Eu³⁺ phosphor was reported by Wegh et al. in 1999 with a theoretical quantum efficiency of 190%.^62,63 The search for new quantum-cutting materials has gained importance in recent times in view of their promising applications in plasma display panels and mercury-free fluorescent tubes.^33,205–221

Recently, the potential of using quantum-cutting phosphors in c-Si solar cells has been explored in an effort to maximize their efficiency.²²² Trupke et al. have performed theoretical calculations that predict an enhancement up to 38.6% in conversion efficiency for a solar cell modified with a quantum-cutting layer.³⁴ The NIR quantum-cutting has been demonstrated in various Ln³⁺–Yb³⁺ (Ln = Tb, Tm, Pr, Er, Nd, Ho, and Dy) co-doped systems (Table 3)^223–237 and in phosphors with a single luminescent center (Ho³⁺, Tm³⁺, or Er³⁺).^238–243

Table 3 Selected narrowband NIR quantum-cutting materials co-doped with Ln³⁺–Yb³⁺ for PV applications

Dopant ion	Host lattice	Preparation method	Excitation (nm)	ET type	Maximum quantum efficiency (%)	Ref.
Tb^3+–Yb^3+	YPO4	Solid-state reaction	489	Second-order cooperative	188	223
Tb^3+–Yb^3+	GdBO3	Combustion synthesis	486	Second-order cooperative	182	224
Tb^3+–Yb^3+	Zn2SiO4 thin-films	Sol–gel method	485	Second-order cooperative	162	225
Tm^3+–Yb^3+	GdAl3(BO3)4	Combustion synthesis	475	Second-order cooperative	164	226
Tm^3+–Yb^3+	Glass ceramics containing LaF3 nanocrystals	Glass melting	468	Second-order cooperative	162	227
Tm^3+–Yb^3+	YPO4	Co-precipitation	468	First-order phonon-assisted	175	228
Pr^3+–Yb^3+	GdAl3(BO3)4	Combustion synthesis	489	Second-order cooperative	165	226
Pr^3+–Yb^3+	NaYF4	Hydrothermal method	443	Second-order cooperative	181	229
Pr^3+–Yb^3+	SrF2	Solid-state reaction	441	First-order resonant	140	230
Er^3+–Yb^3+	NaYF4	Solid-state reaction	380	First-order resonant	128	231
Er^3+–Yb^3+	Cs3Y2Br9	Vertical Bridgman	490	First-order resonant	195	232
Nd^3+–Yb^3+	YF3	Co-precipitation	360	First-order resonant	140	233
Ho^3+–Yb^3+	Glass ceramics containing YF3 nanocrystals	Glass melting	488	First-order resonant	159	234
Ho^3+–Yb^3+	NaYF4	Hydrothermal method	535	First-order resonant	182	235
Ho^3+–Yb^3+	NaYF4	Hydrothermal method	359	First-order resonant	155	236
Dy^3+–Yb^3+	Zeolites	Ion-exchange process	430	First-order resonant	–	237

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Several mechanisms responsible for the NIR quantum-cutting are illustrated in Fig. 13. The first mechanism is based on one luminescent center with three energy levels (Fig. 13a). It is possible to sequentially produce two NIR photons after transition of the optical center to the highest energy level by absorption of one ultraviolet or visible photon. The intermediate level is shortly populated before the optical center returns to its ground state. Representative examples have been reported for single ions like Ho³⁺, Tm³⁺, or Er³⁺.^238–243 However, one major problem presented by single ion-based quantum-cutting is the unwanted emissions in the ultraviolet–visible spectral range and nonradiative recombination that compete with the desired emission of two NIR photons.

Fig. 13 Summary of typical mechanisms of NIR quantum-cutting for PV applications. Simplified energy level diagrams for ions (types I and II) are given to illustrate the concept of NIR quantum-cutting. (a) NIR quantum-cutting on a single ion by the sequential emission of two NIR photons. (b–d) NIR quantum-cutting due to resonant ET from ion I to ion II. (e) NIR quantum-cutting due to cooperative ET from ion I to ion II. Note that two type II ions simultaneously emit two photons in the NIR spectral region. The purple solid, red solid, and dashed arrows represent excitation, emission, and ET processes (cross-relaxation for b,c and cooperative ET for e), respectively.

Alternative mechanisms involving two luminescent centers for NIR quantum-cutting are summarized in Fig. 13b–e. A plausible mechanism occurs via a two-step ET process through ion pairs of physically interacting lanthanide ions, accompanied by the emission of two NIR photons (Fig. 13b). This quantum-cutting mechanism has been reported in Pr³⁺–Yb³⁺,²³⁰ Er³⁺–Yb³⁺,²³² Nd³⁺–Yb³⁺,²³³ Ho³⁺–Yb³⁺,²³⁶ and Dy³⁺–Yb³⁺ co-doped systems.²³⁷ The emission of two NIR photons can also be achieved by quantum-cutting involving one-step ET between two optical centers (Fig. 13c and d). The quantum-cutting mechanism illustrated in Fig. 13c has been experimentally validated for phosphors doped with Tm³⁺–Yb³⁺,²²⁸ Er³⁺–Yb³⁺,²³¹ and Ho³⁺–Yb³⁺ couples.^234,235 To the authors' knowledge, there is no experimental investigation reported on the mechanism shown in Fig. 13d.

The quantum-cutting mechanisms discussed in Fig. 13b–d require resonance ET between two optical centers in close proximity. The ET can be described as a first-order rate process, governed by the degree of overlap between the donor emission and the acceptor absorption. Energy splitting is plausible by population of an intermediate energy level of the donor. In contrast, if there is no spectral overlap, a second-order cooperative sensitization may dominate the relaxation process, resulting in simultaneous excitation of two acceptors and subsequent emission of two NIR photons (Fig. 13e). For efficient cooperative sensitization to be observed, the sum of the energy of the absorption transitions of the two acceptors must equal the energy of the donor emission.²²³ This cooperative quantum-cutting has been extensively investigated in Tb³⁺–Yb³⁺,^223–225 Tm³⁺–Yb³⁺,^226,227 and Pr³⁺–Yb³⁺ co-doped systems.^226,229 While the performance enhancement achieved was encouraging, it should be noted that the possibility of the second-order cooperative ET process is about 1000 times lower than that of the first-order resonant ET process.²³⁰ Thus, a high doping content of Yb³⁺ is typically required for realizing efficient cooperative quantum-cutting.

4.2 Narrowband quantum-cutting for c-Si solar cells

Tb³⁺–Yb³⁺ couple. NIR quantum-cutting for Tb³⁺–Yb³⁺ co-doped systems was first reported by Vergeer et al. in 2005 on Yb_xY_1–xPO₄:Tb³⁺ powder phosphors.²²³ In their study, a cooperative quantum-cutting mechanism was proposed by analyzing the luminescence decay curve of Tb³⁺ as a function of Yb³⁺ concentration using Monte Carlo simulations (Fig. 14a). For the Tb³⁺–Yb³⁺ couple, the ⁵D₄ → ⁷F₆ transition of Tb³⁺ (∼20 000 cm⁻¹) is approximately twice the energy of the ²F_7/2 → ²F_5/2 transition of Yb³⁺ (∼10 000 cm⁻¹).

Fig. 14 (a) Schematic partial energy-level diagram of the Tb³⁺–Yb³⁺ couple, showing the ET mechanism of NIR quantum-cutting under the excitation of the ⁷F₆ → ⁵D₄ (Tb³⁺) transition. Black solid lines show the second-order nonlinear quantum-cutting process, whereas the red dotted lines show the linear downconversion process where a virtual energy level located at the middle position (around 10 000 cm⁻¹) between the ground state and the ⁵D₄ energy level of Tb³⁺ participates in the quantum-cutting process. (b) Emission spectra of NaYF₄:Tb³⁺/Yb³⁺ (1/x mol%, x = 0, 5, and 10) phosphors under 473 nm laser excitation. (c) Double logarithmic plot of Tb³⁺ and Yb³⁺ emission intensity versus pump power of the 473 nm laser for NaYF₄:Tb³⁺/Yb³⁺ (1/x mol%, x = 0, 5, and 10) phosphors. (d) Experimental and simulated power dependence curves of Yb³⁺ luminescence for NaYF₄:Tb³⁺/Yb³⁺ (1/x mol%, x = 0, 5, and 10) phosphors. (Reprinted with permission from ref. 249. Copyright 2012, Optical Society of America.)

The ET process from Tb³⁺ to Yb³⁺ was investigated by the steady-state and time-resolved luminescence spectroscopy. The ET and quantum efficiencies were calculated from the luminescence decay curves using the following equations,

η_QE = η_Tb(1 − η_ET) + 2η_ET (8)

where I denotes intensity, x%Yb stands for Yb³⁺ concentration, and η_Tb represents quantum efficiency for Tb³⁺ and is set to 1.

Although various Tb³⁺–Yb³⁺ co-doped materials have been well studied, the issue of the underlying ET mechanism from Tb³⁺ to Yb³⁺ ions is still debatable.^244–249 Some researchers believed that a nonlinear second-order downconversion process should be responsible for the cooperative quantum-cutting (Fig. 14a).^244,245 The slope of Yb³⁺ luminescence intensity versus the excitation power was found to be nearly 0.5, indicating the emission of two lower-energy photons upon the absorption of one photon. On the other hand, two different groups found the slope of luminescence intensity curves to be near 1 instead of 0.5, indicating a one-photon process for the Yb³⁺ NIR emission.^246,247 A similar result was also obtained by Duan and co-workers in Tb³⁺–Yb³⁺ co-doped oxyfluoride glass,²⁴⁸ but they attributed it to a linear cooperative quantum-cutting mechanism. In this case, a virtual energy level of Tb³⁺ located around 10 000 cm⁻¹ could participate in the quantum-cutting process (Fig. 14a), and the downconversion emission intensity would increase linearly with the excitation intensity (Fig. 14b). Interestingly, it was experimentally found that in NaYF₄ host materials the slopes of Yb³⁺ luminescence power dependence curves were fitted to be between 0.5 and 1 (Fig. 14c and d).²⁴⁹ This sublinear power dependence phenomenon was attributed to the combination of a linear downconversion process and a dominant second-order nonlinear process.

Tm³⁺–Yb³⁺ couple. The NIR quantum-cutting for the Tm³⁺–Yb³⁺ couple was reported in a variety of host materials, including GdAl₃(BO₃)₄,²²⁶ YPO₄,²⁵⁰ glasses,^251–254 glass ceramics,^227,255 and Y₂O₃–based transparent ceramics.²⁵⁶ The mechanism responsible for quantum-cutting in these host materials is generally believed to be a cooperative ET process. In the Tm³⁺–Yb³⁺ couple, NIR quantum-cutting occurs upon excitation at the ¹G₄ (Tm³⁺) level (∼21 000 cm⁻¹ or 475 nm). The energy of the ¹G₄ → ³H₆ transition of Tm³⁺ is about twice as large as the ²F_5/2 → ²F_7/2 transition of Yb³⁺. Thus, the excited ¹G₄ (Tm) state can simultaneously transfer its energy to two neighboring Yb³⁺ ions, subsequently resulting in NIR emission in the range of 950–1100 nm (Fig. 15a). Notably, no convincing evidence thus far for the cooperative ET mechanism has been reported. As a result, it is still controversial whether the second-order cooperative or first-order ET dominates the visible-to-NIR quantum-cutting process.

Fig. 15 Schematic partial energy-level diagrams of Tm³⁺ and Yb³⁺ ions, showing the quantum-cutting mechanisms for the Tm³⁺–Yb³⁺ couple upon blue excitation of Tm³⁺ to the ¹G₄ state. (a) Quantum-cutting via second-order cooperative ET. The excited energy is simultaneously transferred to two Yb³⁺ ions, resulting in two NIR photons of Yb³⁺ ions around 1000 nm. (b) Quantum-cutting via first-order phonon-assisted ET. Part of the excited energy is transferred to one Yb³⁺ ion through the phonon-assisted ET process [Tm³⁺ (¹G₄ → ³H₅); Yb³⁺ (²F_7/2 → ²F_5/2)], which populates the ³H₅ (Tm³⁺) state and leads to another mid-IR emission from the ³F₄ (Tm³⁺) state at around 1800 nm through fast nonradiative relaxation from ³H₅. Note that the energy gap between ³H₅ and ³F₄ states is about 2250 cm⁻¹. Dotted and solid arrows represent nonradiative ET pathways and optical transitions, respectively. (Reprinted with permission from ref. 228. Copyright 2012, Owner Societies.)

Most recently, Zheng et al.²²⁸ in 2012 showed that in YPO₄:Yb³⁺/Tm³⁺ phosphors the visible-to-NIR quantum-cutting can be induced by the first-order phonon-assisted ET. In their study, one incident blue photon is cut into one NIR photon of Yb³⁺ (²F_5/2 → ²F_7/2, ∼1000 nm) and one mid-IR photon of Tm³⁺ (³F₄ → ³H₆, ∼1800 nm), rather than two NIR photons from Yb³⁺ (Fig. 15b). Pump power dependence studies on Yb³⁺ emission intensity revealed that only one emitting photon of Yb³⁺ can be achieved per absorbed blue photon. Importantly, such phonon-assisted quantum-cutting luminescence for the Tm³⁺–Yb³⁺ couple can only be realized in those host materials with high phonon energies (such as phosphates, borates, and silicates) because of the large energy mismatch (∼2500 cm⁻¹) between ¹G₄ → ³H₅ (Tm³⁺) and ²F_7/2 → ²F_5/2 (Yb³⁺) transitions. Although YPO₄ host material with the maximum phonon energy of about 1070 cm⁻¹ meets this requirement, the material is not suitable for c-Si PV application as the mid-IR photon is beyond the absorption edge of the c-Si.

Jaffres et al.²⁵⁷ in 2012 investigated the optical property of Tm³⁺–Yb³⁺ co-doped La₂BaZnO₅ phosphors with a maximum phonon energy of ∼600 cm⁻¹. Upon excitation of Tm³⁺ to the ¹G₄ level, they found no noticeable ET from Tm³⁺ to Yb³⁺, only cascade emission of three mid-IR photons due to ³F₄ → ³H₆ transition of Tm³⁺. This result is attributed to two successive cross-relaxation steps between Tm³⁺ ions.

Pr³⁺–Yb³⁺ couple. Two ET mechanisms have been proposed for quantum-cutting in the Pr³⁺–Yb³⁺ couple: (i) second-order cooperative ET from one Pr³⁺ ion to two different Yb³⁺ ions because the ³P₀ → ³H₄ transition of Pr³⁺ (∼20 700 cm⁻¹) is about twice the energy of the ²F_5/2 → ²F_7/2 transition of Yb³⁺;^{226,229,258–261} or (ii) first-order resonant ET via two sequential steps involving cross-relaxation [Pr³⁺ (³P₀ → ¹G₄); Yb³⁺ (²F_7/2 → ²F_5/2)] followed by a second ET process [Pr³⁺ (¹G₄ → ³H₄); Yb³⁺ (²F_7/2 → ²F_5/2)] (Fig. 16a).^{230,262–273}

Fig. 16 (a) NIR quantum-cutting via the first-order ET mechanism for the Pr³⁺–Yb³⁺ couple. A two-step ET occurs upon excitation onto the ³P_J (J = 0, 1, 2) and ¹I₆ levels of Pr³⁺, using the ¹G₄ level as an intermediate state. A single blue photon absorbed by these levels is converted into two NIR photons of ∼1000 nm. (b) Emission spectra for SrF₂:Pr³⁺/Yb³⁺ (0.1/x mol%; x = 0, 5, and 17) under excitation at 441 nm. (c) Diffuse reflectance (dashed line) and excitation spectra (solid line) of the SrF₂:Pr/Yb (0.1/5 mol%) sample. (d) Luminescence decay curves of the ³P₀ → ³H₄ emission at 486 nm in SrF₂:Pr/Yb (0.1/x mol%; x = 0, 0.2, 1, 5, and 17) under excitation at 441 nm. (Reprinted with permission from ref. 230. Copyright 2009, Wiley-VCH Verlag GmbH & Co. KGaA.)

Meijerink and co-workers²⁶³ argued that the dominant quantum-cutting mechanism in the Pr³⁺–Yb³⁺ couple appears to be first-order ET by cross relaxation, because the reduced cross-relaxation rate can be compensated by the much higher (∼1000 times) probability of first-order ET relative to the second-order cooperative ET process. This first-order ET scheme leads to efficient quantum-cutting of one 441 nm blue photon into two 980 nm NIR photons in SrF₂:Pr³⁺,Yb³⁺ phosphors.²³⁰ Comparison of emission spectra for SrF₂:Pr³⁺ (0.1 mol%) and SrF₂:Pr³⁺,Yb³⁺ (0.1/5%) samples (Fig. 16b) revealed an actual conversion efficiency of 140%. Furthermore, the 980 nm photon flux upon excitation of Pr³⁺ to the ³P_J,¹I₆ (J = 0, 1, and 2) levels is approximately twice that of the absorption strength of the ³P_J,¹I₆ levels (Fig. 16c), confirming that for every photon absorbed to the ³P_J,¹I₆ levels, two photons in the NIR were generated. Introduction of Yb³⁺ into SrF₂:Pr³⁺ induced faster and nonexponential decay of ³P₀ → ³H₄ emission (Fig. 16d), thus providing additional evidence for the ET from Pr³⁺ to nearby Yb³⁺ ions.

Er³⁺–Yb³⁺ couple. The combination of Er³⁺ and Yb³⁺, well-known for upconversion research, can also give rise to efficient visible-to-NIR quantum-cutting.²³² The Er³⁺ ion has excited states at ∼20 000 cm⁻¹ (⁴F_7/2) and 10 000 cm⁻¹ (⁴I_11/2) that allow for a two-step ET process, raising two neighboring Yb³⁺ ions to the ²F_5/2 excited state around 10 000 cm⁻¹. Upon 490 nm excitation at the ⁴F_7/2 level, the cross-relaxation process of [Er³⁺ (⁴F_7/2 → ⁴I_11/2); Yb³⁺ (²F_7/2 → ²F_5/2)] can occur, followed by a second ET step of [Er³⁺ (⁴I_11/2 → ⁴I_15/2); Yb³⁺ (²F_7/2 → ²F_5/2)]. Both Yb³⁺ ions then emit a NIR photon of ∼1000 nm that can be absorbed by a c-Si solar cell (Fig. 17a).

Fig. 17 (a) Schematic partial energy-level diagrams for the Er³⁺–Yb³⁺ couple showing the quantum-cutting mechanism starting from the ⁴F_7/2 level. A single blue photon absorbed by Er³⁺ is converted into two ∼1000 nm NIR photons of Yb³⁺via two sequential ET steps: (1) cross-relaxation ET of [Er³⁺ (⁴F_7/2 → ⁴I_11/2); Yb³⁺ (²F_7/2 → ²F_5/2)]; (2) cross-relaxation ET of [Er³⁺ (⁴I_11/2 → ⁴I_15/2); Yb³⁺ (²F_7/2 → ²F_5/2)]. (b) Schematic partial energy-level diagrams for the Nd³⁺–Yb³⁺ couple showing the quantum-cutting mechanism starting from the ²G_9/2 level. A single blue photon absorbed by Nd³⁺ is downconverted into two ∼1000 nm NIR photons of Yb³⁺ ions via two-step ET mechanisms: (1) cross-relaxation ET of [Nd³⁺ (²G_9/2 → ⁴F_3/2); Yb³⁺ (²F_7/2 → ²F_5/2)]; (2) cross-relaxation ET of [Nd³⁺ (⁴F_3/2 → ⁴I_9/2); Yb³⁺ (²F_7/2 → ²F_5/2)]. (c) Schematic partial energy-level diagrams for the Er³⁺–Yb³⁺ couple showing the quantum-cutting mechanism starting from the ⁴F_9/2 level. One blue photon absorbed by Dy³⁺ is downconverted into two NIR photons from Yb³⁺ through two sequential ET steps: (1) cross-relaxation ET of [Dy³⁺ (⁴F_9/2 → ⁶H_5/2); Yb³⁺ (²F_7/2 → ²F_5/2)]; (2) cross-relaxation ET of [Dy³⁺ (⁶H_5/2 → ⁶H_15/2); Yb³⁺ (²F_7/2 → ²F_5/2)]. (d) Schematic partial energy-level diagrams for the Ho³⁺–Yb³⁺ couple showing the quantum-cutting mechanism starting from the ⁵S₂,⁵F₄ level. Note that the ⁵F₃ level of Ho³⁺ is located at ∼20 600 cm⁻¹, while the ⁵S₂,⁵F₄ level is located at ∼18 600 cm⁻¹.

Meijerink et al.²³² have demonstrated that the use of the Er³⁺–Yb³⁺ couple in Cs₃Y₂Br₉ phosphors can lead to achieving efficient visible-to-NIR quantum-cutting with an internal quantum efficiency of 195%. Despite the relatively narrow energy gap (∼1250 cm⁻¹) between the ⁴F_7/2 level and the next lower ²H_11/2 level for Er³⁺, the low phonon energy (∼180 cm⁻¹) of the bromide host results in a long-lived ⁴F_7/2 state. This is attributed to slow-rate multiphonon relaxation when the energy gap exceeds five phonons. However, visible-to-NIR quantum-cutting from the ⁴F_7/2 level for the Er³⁺–Yb³⁺ couple was found to be very inefficient in fluoride (NaYF₄, maximum phonon energy ∼400 cm⁻¹) and chloride (KPb₂Cl₅, maximum phonon energy ∼200 cm⁻¹) host materials. A feasible explanation for this optical phenomenon is that multiphonon relaxation from the ⁴F_7/2 to ²H_11/2 and ⁴S_3/2 levels is faster than cross-relaxation with a neighboring Yb³⁺.^231,274 Efficient ultraviolet-to-NIR quantum-cutting from the ⁴G_11/2 (Er³⁺) level was observed for the Er³⁺–Yb³⁺ couple in NaYF₄ and YF₃ phosphors, resulting in one NIR photon from the Yb³⁺ ion (²F_5/2 → ²F_7/2, 980 nm) and one red photon from the Er³⁺ ion (⁴F_9/2 → ⁴I_15/2, 650 nm) after absorption of a single ultraviolet photon with a wavelength less than 380 nm.^231,275

Nd³⁺–Yb³⁺ couple. Close inspection of the energy levels of the Nd³⁺–Yb³⁺ couple shows that NIR quantum-cutting from the ²G_9/2 (Nd³⁺) level (∼21 000 cm⁻¹ or 470 nm) via the cross-relaxation process of [Nd³⁺ (²G_9/2 → ⁴F_3/2); Yb³⁺ (²F_7/2 → ²F_5/2)], followed by a second ET step from the ⁴F_3/2 (Nd³⁺) level (∼11 547 cm⁻¹ or 866 nm) to the ²F_5/2 (Yb³⁺) level (∼10 000 cm⁻¹ or 1000 nm), could lead to emission of two NIR photons from Yb³⁺ ions (Fig. 17b).^233,276 However, fast multiphonon relaxation from the ²G_9/2 to lower ⁴G_7/2 (Nd³⁺) level was observed in the YF₃ host, preventing efficient quantum-cutting from the ²G_9/2 level.²³³

The energy difference between the ²G_9/2 and ⁴G_7/2 (Nd³⁺) levels is only 1012 cm⁻¹ and thus multiphonon relaxation dominates in the YF₃ host material where the maximum phonon energy is about 500 cm⁻¹. The multiphonon relaxation from the ²G_9/2 level to lower-energy levels results in population of the ⁴F_3/2 (Nd³⁺) level, from which efficient one-step ET to Yb³⁺ occurs through dipole–dipole interaction. This may explain the reason for realizing efficient NIR quantum-cutting for the Nd³⁺–Yb³⁺ couple in a host lattice with much lower phonon energy (e.g., bromides or chlorides) ions. By comparison, ultraviolet-to-NIR quantum-cutting was observed from the higher energy ⁴D_3/2 (Nd³⁺) level (∼28 000 cm⁻¹ or 360 nm) in YF₃:Nd³⁺/Yb³⁺ phosphors with an internal quantum efficiency of 140%.²³³

Ho³⁺–Yb³⁺ couple. The ⁵F₃ → ⁵I₈ transition of Ho³⁺ is approximately twice the energy required for the ²F_5/2 → ²F_7/2 transition of Yb³⁺. However, the second-order cooperative quantum-cutting process of [Ho³⁺ (⁵F₃ → ⁵I₈); 2Yb³⁺ (²F_7/2 → ²F_5/2)] is unlikely because the ⁵F₃ (Ho³⁺) excited state can decay rapidly to the next ⁵S₂,⁵F₄ states.²⁷⁷ Lin and co-workers²³⁴ first reported the first-order quantum-cutting luminescence for the Ho³⁺–Yb³⁺ couple in glass ceramics with an internal quantum efficiency of 159%. Under 488 nm blue-light excitation, Ho³⁺ could be excited to the ⁵F₃ state followed by nonradiative relaxation to ⁵S₂,⁵F₄ states, from which the resonant cross-relaxation ET of [Ho³⁺ (⁵S₂,⁵F₄ → ⁵I₆); Yb³⁺ (²F_7/2 → ²F_5/2)] occurs. This leads to NIR quantum-cutting involving the emission of one 1180 nm photon (⁵I₆ → ⁵I₈ transition of Ho³⁺) and one 980 nm photon (²F_5/2 → ²F_7/2 transition of Yb³⁺) (Fig. 17d). In addition, some of the electrons in ⁵S₂,⁵F₄ states of Ho³⁺ could further relax nonradiatively to the lower ⁵F₅ level, which induces another resonant cross-relaxation process of [Ho³⁺ (⁵F₅ → ⁵I₇); Yb³⁺ (²F_7/2 → ²F_5/2)], and results in the intensity enhancement of Yb³⁺ emission.²³⁴

The first-order NIR quantum-cutting for the Ho³⁺–Yb³⁺ couple was later confirmed by Yu and co-workers in NaYF₄ phosphors.²³⁵ However, Deng et al.²³⁶ proposed a different ET mechanism in these phosphors under ultraviolet (359 nm) excitation. They argued that the NIR quantum-cutting occurs at the ⁵G₄ level, which involves two-step sequential cross-relaxation: [Ho³⁺ (⁵G₄ → ⁵F₅); Yb³⁺ (²F_7/2 → ²F_5/2)] followed by [Ho³⁺ (⁵F₅ → ⁵I₇); Yb³⁺ (²F_7/2 → ²F_5/2)]. Thus, one ultraviolet photon absorbed by Ho³⁺ gave rise to two NIR photons of Yb³⁺, with a maximum quantum efficiency of 155.2%.²³⁶

Dy³⁺–Yb³⁺ couple. NIR quantum-cutting through the Dy³⁺–Yb³⁺ couple has been investigated to a lesser extent. Bai et al.²³⁷ in 2011 demonstrated that under 430 nm blue-light excitation, NIR quantum-cutting could be achieved in Dy³⁺/Yb³⁺ co-doped zeolites through a two-step ET process from the ⁴F_9/2 (Dy³⁺) level to two neighboring Yb³⁺ ions: cross-relaxation ET of [Dy³⁺ (⁴F_9/2 → ⁶H_5/2); Yb³⁺ (²F_7/2 → ²F_5/2)] followed by another cross-relaxation ET of [Dy³⁺ (⁶H_5/2 → ⁶H_15/2); Yb³⁺ (²F_7/2 → ²F_5/2)] (Fig. 17c). Note that the ⁴F_9/2 (Dy³⁺) level is located at ∼21 000 cm⁻¹, while the ⁶H_5/2 (Dy³⁺) level is situated at ∼10 000 cm⁻¹. Therefore, the energy of the ⁴F_9/2 → ⁶H_15/2 transition of Dy³⁺ is about twice as much as that of the ²F_7/2 → ²F_5/2 transition of Yb³⁺. The ⁶H_5/2 (Dy³⁺) level serves as the intermediate level between ⁴F_9/2 and ⁶H_15/2. The ET efficiency from the ⁴F_9/2 level was estimated to be 42%, and the intrinsic luminescence quantum efficiency of Yb³⁺ emission reached 54%.

Ho³⁺ single ion. Yu and co-workers in 2011 reported NIR quantum-cutting in Ho³⁺-doped NaYF₄ phosphors.^238,239 It is of interest to note that the quantum-cutting through Ho³⁺ depends on the excitation wavelength. Under 300–500 nm excitation, the NaYF₄:Ho³⁺ phosphors gave rise to two NIR photons with a sequential two-step process: ⁵S₂,⁵F₄ → ⁵I₆ transition (1015 nm) followed by ⁵I₆ → ⁵I₈ transition (1180 nm).²³⁹ The ⁵I₆ acts as an intermediate level. In contrast, upon 287 nm excitation of Ho³⁺ to the ³G₃,³L₈ level, cascade emissions of three NIR photons occur: ³D₃ → ³K₈,⁵F₂, 850 nm; ⁵S₂,⁵F₄ → ⁵I₆, 1015 nm; ⁵I₆ → ⁵I₈ transition, 1180 nm.²³⁸ The electronic states of ³K₈,⁵F₂, and ⁵I₆ in Ho³⁺ act as intermediate levels. The occurrence of the NIR quantum-cutting in the NaYF₄:Ho³⁺ phosphors was confirmed by time-resolved emission spectra as well as distinct emission spectra recorded at different excitation wavelengths. The quantum efficiency calculated using the Judd–Ofelt theory was about 124%.²³⁸ This low internal quantum efficiency might result from the loss of a substantial amount of light in the ultraviolet/visible spectral region, thereby preventing their practical application in solar cells. Quantum-cutting via photon cascade emission was also reported in YVO₄:Ho³⁺ phosphors and LaF₃:Ho³⁺ nanocrystals.^243,278

4.3 Broadband quantum-cutting for c-Si solar cells

Ideal NIR quantum-cutting materials for c-Si solar cells should be able to downconvert the ultraviolet–green (300–550 nm) part of the solar spectrum to ∼1000 nm photons. Despite their usefulness, the quantum-cutting materials based on Ln³⁺–Yb³⁺ (Ln = Tb, Tm, Pr, Er, Nd, Ho, and Dy) couples are still far from practical application because of low excitation efficiency. A main limiting factor for the conversion efficiency is the low absorption cross-section (typically on the order of 10⁻²¹ cm²) of the lanthanide ions arising from the parity-forbidden 4f–4f transitions.²⁷⁹ In contrast, the dipole-allowed 4f–5d transitions have much higher absorption cross-sections of up to 10⁻¹⁸ cm².²⁷⁹ Recently, much attention has been paid to broadband NIR quantum-cutting through use of Ce³⁺, Eu²⁺ and Yb²⁺ with strong absorption intensity in the ultraviolet–blue spectral region as energy donors for Yb³⁺ (Table 4).^279–293 The Bi³⁺ ion was also shown to be an efficient sensitizer for Yb³⁺.^294–298 A significant parallel development for efficient emission of Yb³⁺ is to utilize host sensitization through direct cooperative ET from the host to Yb³⁺.^299–302

Table 4 Selected broadband NIR quantum-cutting materials for c-Si solar cells

Dopant ion	Host lattice	Preparation method	Excitation (nm)	Maximum quantum efficiency (%)	Ref.
Ce^3+–Yb^3+	Borate glasses	Glass melting	250–380	174	279
Ce^3+–Yb^3+	YBO3	Solid-state reaction	326–377	175	280
Ce^3+–Yb^3+	LuBO3	Hydrothermal method	325–375	181	281
Ce^3+–Yb^3+	Y3Al5O12	Sol–gel	400–500	153	282
Ce^3+–Yb^3+	Y3Al5O12 transparent ceramics	Solid-state reaction	400–500	175	283
Ce^3+–Yb^3+	Y2SiO5	Combustion synthesis	355	160	284
Ce^3+–Tb^3+–Yb^3+	GdBO3	Combustion synthesis	300–400	—	285
Ce^3+–Tb^3+–Yb^3+	Ca2BO3Cl	Solid-state reaction	300–380	—	286
Ce^3+–Tb^3+–Yb^3+	Borate glasses	Glass melting	250–350	—	287
Eu^2+–Yb^3+	Borate glasses	Glass melting	250–400	164	288
Eu^2+–Yb^3+	Aluminosilicate glasses	Glass melting	250–500	127	289
Eu^2+–Yb^3+	CaAl2O4	Solid-state reaction	250–450	155	290
Eu^2+–Yb^3+	Glass ceramics containing CaF2 nanocrystals	Glass melting	230–390	151	291
Eu^2+–Yb^3+	Silicate glasses	Glass melting	250–400	134	292
Yb^2+–Yb^3+	CaAl2O4	Solid-state reaction	250–400	—	293
Bi^3+–Yb^3+	Gd2O3	Combustion synthesis	300–400	173	294
Bi^3+–Yb^3+	Y2O3	Combustion synthesis	300–400	173	295
Bi^3+–Yb^3+	Y2O3 thin-films	Pulsed laser deposition	300–400	152	296
Bi^3+–Yb^3+	YVO4	Solid-state reaction	250–400	187	297
Bi^3+–Yb^3+	YNbO4	Solid-state reaction	250–350	180	298
Yb^3+	YVO4	Solid-state reaction	200–350	185	299
Yb^3+	SiO2–YVO4 thin-films	Sol–gel	200–350	—	300
Yb^3+	YVO4 thin-films	Pulsed laser deposition	200–350	128	301
Li^+–Yb^3+	ZnO	Thermal growth	300–420	—	302

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Ce³⁺–Yb³⁺ couple. The Ce³⁺ ion could serve as an ideal broadband sensitizer for Yb³⁺, because its 4f–5d transition covers a broad spectral range and, more importantly, the energy of its 4f–5d transition can be tuned by changing the crystal field strength as well as the covalency of the host. The NIR quantum-cutting for the Ce³⁺–Yb³⁺ couple has been reported for many host materials, and the cooperative ET [Ce³⁺ (5d → 4f); 2Yb³⁺ (²F_7/2 → ²F_5/2)] appears to be the dominant relaxation route to achieve the NIR emission of Yb³⁺.^{279–284,303,304} When compared to the most common Ln³⁺–Yb³⁺ (Ln = Tb, Tm, and Pr) couples, the Ce³⁺–Yb³⁺ couple could harvest a broad solar spectral range to give rise to intense NIR emissions. This result can be ascribed to the large absorption cross-section of Ce³⁺ acting as the energy donor (Fig. 18). However, some researchers believe that the ET from Ce³⁺ to Yb³⁺ is possibly due to metal-to-metal charge transfer through the facile redox reaction of Ce³⁺+Yb³⁺ → Ce⁴⁺+Yb²⁺.^305–307 This charge transfer may complicate the quantum-cutting process.

Fig. 18 (a) Representative excitation spectra for YAG:Ce³⁺,Yb³⁺ (Y_2.91–3xCe_0.09Yb_3xAl₅O₁₂, x = 0.1) monitoring the emission of Ce³⁺ at 530 nm, and the emission of Yb³⁺ at 1030 nm, respectively. For comparison, the excitation spectra of Yb³⁺ of quantum-cutting materials activated with ion pairs of Yb³⁺–Ln³⁺ (Ln = Tb, Tm, and Pr; the host is a borogermanate glass) and Yb³⁺–Ce³⁺ (the host is a borate glass) are also given. The AM 1.5G solar spectrum in this spectral region is shown in the background as a reference. (b) Concentration-dependent emission spectra of YAG:Ce³⁺,Yb³⁺ (x = 0–0.5) and YAG:Yb³⁺ (Y_2.7Yb_0.3Al₅O₁₂) under the excitation at 470 nm. (Reprinted with permission from ref. 282. Copyright 2009, Optical Society of America.)

Several groups also used the Ce³⁺ ion to sensitize the Tb³⁺–Yb³⁺ quantum-cutting process.^285–287 A possible indirect ET mechanism was proposed for the Ce³⁺–Tb³⁺–Yb³⁺ quantum-cutting system. First, the Ce³⁺ ion directly absorbs an ultraviolet photon via allowed 4f–5d transitions. Subsequently, the excitation energy in the lowest 5d (Ce³⁺) excited level relaxes to the ⁵D₃ and ⁵D₄ (Tb³⁺) levels via phonon assistance. From the ⁵D₄ level, the energy of the excited Tb³⁺ ion is simultaneously transferred to two different Yb³⁺ ions. The NIR emission of Yb³⁺ in the Ce³⁺–Tb³⁺–Yb³⁺ system can be enhanced by about 10 times as compared to that obtained with the Tb³⁺–Yb³⁺ couple. Nonetheless, the quantum-cutting mechanism in this triply doped system remains elusive. Further experimentation is clearly needed. Another interesting development of quantum-cutting is the work on sensitization of the Pr³⁺–Yb³⁺ couple using Ce³⁺ ions.³⁰⁸

Eu²⁺–Yb³⁺ couple. The first example of NIR quantum-cutting using Eu²⁺ and Yb³⁺ was reported by Qiu et al. in glasses and CaAl₂O₄ phosphors.^288–290 Eu²⁺ shows a broad excitation spectrum in the 250–400 nm ultraviolet region due to 4f⁷ → 4f⁶5d transition. The energy of the 4f⁶5d → 4f⁷ (Eu²⁺) transition is approximately twice as much of the ²F_5/2 → ²F_7/2 (Yb³⁺) transition. Therefore, cooperative ET from one Eu²⁺ ion to two Yb³⁺ ions was proposed by these authors to be the dominant relaxation process, and the calculated maximum quantum efficiency approached 200%. Subsequently, several other groups also reported broadband quantum-cutting via the Eu²⁺–Yb³⁺ couple in glass ceramics and silicate glasses.^291,292

Yb²⁺–Yb³⁺ couple. Similar to Eu²⁺ and Ce³⁺, Yb²⁺ commonly exhibits 4f–5d broadband luminescence.³⁰⁹ The optical feature of Yb²⁺ originates from 4f¹⁴ ↔ 4f¹³5d transitions. Teng and co-workers recently reported the efficient broadband quantum-cutting in Yb²⁺–Yb³⁺ co-doped CaAl₂O₄ phosphors prepared under a reducing atmosphere.²⁹⁰ The CaAl₂O₄ crystal has tridymite structure, which consists of AlO₄-tetrahedra. Both Yb²⁺ and Yb³⁺ ions substitute the Ca²⁺ site in the CaAl₂O₄ crystal because of their similar ionic radius (0.099 nm for both Ca²⁺ and Yb³⁺, and 0.102 nm for Yb²⁺, while 0.051 nm for Al³⁺). After a direct ultraviolet excitation (250–400 nm) of Yb²⁺ ions, the authors observed intense Yb³⁺ NIR emission. The dependence of Yb³⁺ luminescence intensity on the excitation power exhibited a sublinear relationship with a slope of 0.43. On the basis of these results, a three-photon or phonon-assisted two-photon quantum-cutting process involving cooperative ET from Yb²⁺ to Yb³⁺ ions was proposed to be the main mechanism.

Bi³⁺–Yb³⁺ couple. Bi³⁺ with the 6s² electronic configuration has been extensively investigated as both the activator and sensitizer for luminescent materials.^310,311 The ³P₁ and ¹P₁ levels of Bi³⁺ are mixed by spin–orbit coupling, and as a consequence, ¹S₀ → ³P₁ and ¹S₀ → ¹P₁ transitions have reasonable absorption strength. Two research groups recently demonstrated efficient NIR quantum-cutting in Bi³⁺–Yb³⁺ co-doped Ln₂O₃ (Ln = Gd, Y) phosphors and thin-films.^{294–296,312} Ln₂O₃ (Ln = Gd, Y) host lattices have excellent chemical durability and thermal stability, as well as low phonon energy (maximum phonon energy, ∼600 cm⁻¹).^313–315 In these hosts, Bi³⁺ exhibits strong absorption in the ultraviolet region of 300–400 nm through the allowed ¹S₀ → ³P₁ transition. After a direct excitation of Bi³⁺, an intense NIR emission band centered at 977 nm from Yb³⁺ was recorded. It was also demonstrated that the charge-transfer between O²⁻ and Yb³⁺ did not have any influence on Bi³⁺ and Yb³⁺ emission. Decay lifetime measurements for Bi³⁺ emission further evidenced the occurrence of cooperative ET from Bi³⁺ to Yb³⁺ ions, and a maximum quantum efficiency close to 200% was calculated. The NIR quantum-cutting of the Bi³⁺–Yb³⁺ couple was also recently reported in YVO₄ and YNbO₄ phosphors.^297,298

Host–Yb³⁺ combination. Broadband quantum-cutting luminescence was also realized using the combination of host and Yb³⁺ ions.^299–301 Wei and co-workers recently reported NIR quantum-cutting in YVO₄:Yb³⁺ phosphors.²⁹⁹ Cooperative ET from the excited VO₄³⁻ group to two neighboring Yb³⁺ ions resulted in the conversion of 250–350 nm light into NIR emission around 980 nm. The calculated maximum quantum efficiency reached as high as 185.7%.²⁹⁹ However, this estimated value must be interpreted in the context of the following considerations: (i) concentration quenching effect of Yb³⁺; (ii) direct ET from the excited VO₄³⁻ group to the charge transfer state of O²⁻–Yb³⁺; and (iii) the quenching effect caused by the direct ET from VO₄³⁻ group to quenching centers. For practical applications in c-Si solar cells, these effects have to be significantly minimized to ensure enhanced emission of Yb³⁺.

In a following paper by Shestakov et al., Li⁺–Yb³⁺ co-doped ZnO nanocrystals were tested for NIR quantum-cutting.³⁰² ZnO is a direct wide gap semiconductor with large absorption cross-section in the 250–400 nm ultraviolet wavelength range and high transparency in the visible and NIR ranges. Upon ultraviolet excitation, the authors observed two broadband emissions centered at 770 and 1000 nm, which can be ascribed to Li⁺–Li⁺ and Yb³⁺–Li⁺ dimer dopants, respectively. Pump power dependence and temperature dependence of these emission bands indicated that the ET from the ZnO host to Li⁺–Li⁺ and Yb³⁺–Li⁺ dimers was responsible for the quantum-cutting mechanism.

4.4 Quantum-cutting for germanium solar cells

The energy of the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ around 1540 nm is slightly larger than the bandgap of germanium (0.67 eV; 1850 nm). To this end, the NIR quantum-cutting of Er³⁺ has potential to improve the efficiency of germanium-based solar cells. Chen et al. in 2009 reported three-photon NIR quantum-cutting of Er³⁺ in the GdVO₄ crystal.²⁴⁰ Upon 523 nm excitation of Er³⁺ to the ²H_11/2 level, they observed a characteristic NIR emission at 1532 nm due to ⁴I_13/2 → ⁴I_15/2 transition, with a quantum efficiency of about 178%. The principal drawback of this system is the low effective absorption cross-section of Er³⁺ at 300–550 nm. To solve this problem, Zhou et al.^316,317 in 2010 demonstrated that the incorporation of Ce³⁺ and Eu²⁺ in YAG:Ce³⁺/Er³⁺ and Ca₈Mg(SiO₄)₄Cl₂:Eu²⁺/Er³⁺ phosphors results in strong erbium sensitization, leading to significantly increased NIR emission intensity of Er³⁺.

Subsequently, two research groups independently reported a novel quantum-cutting mechanism based on resonant ET from Er³⁺ to Yb³⁺ in Er³⁺/Yb³⁺ co-doped glass ceramics and NaYF₄ nanocrystals, respectively.^318,319 In these systems, a photon, absorbed by Er³⁺ in the wavelength range of 350–550 nm, was converted into two photons of 650–1550 nm that can be subsequently emitted by Er³⁺ and Yb³⁺, with the maximum quantum efficiency approaching 200%.

4.5 Multiple exciton generation in quantum dots

Different from the above-mentioned quantum-cutting in lanthanide ions, another viable approach to significantly enhance solar energy conversion is to utilize multiple exciton generation (MEG, also termed carrier multiplication) in QDs, whereby the absorption of one photon bearing at least twice the bandgap energy can produce two or more electron–hole pairs (Fig. 19a).^320–322 This approach enables effective harvesting of high-energy photons in the violet and ultraviolet parts of the solar spectrum that are normally lost as waste heat.³²³ Thus, the application of MEG in third-generation PV cells has the potential to achieve maximum efficiency as high as 44%, well exceeding the Shockley–Queisser limit of 31% for single-junction solar cells.³²⁴ Since its first discovery in PbSe nanocrystals by Schaller and Klimov in 2004,³²⁵ the MEG effect has been experimentally observed in many QD systems, such as PbS, PbTe, CdSe, and Si,³²⁶ as well as recently in single-walled carbon nanotubes.^327,328 Several recent reviews have discussed the mechanisms, characterization techniques, and application prospects of the MEG effect, but problems and disagreements have arisen over the measurement of MEG quantum efficiency in colloidal QDs and its impact on solar energy conversion.^329–334 Most of the previous studies have used ultrafast transient absorption techniques, as proposed by Schaller and Klimov,³²⁵ to measure the MEG efficiency, which is defined as the number of electron–hole pairs produced per absorbed photon. The indirect nature of this method, however, has contributed to the diversity in the reported experimental data resulting from experimental artefacts, material degradation and surface effects of carrier trapping and photocharging.³³⁵

Fig. 19 (a) A schematic drawing showing multiple exciton generation, whereby excited carriers generated in a quantum dot can channel excess photon energy to promote another electron across the bandgap rather than undergo thermalization. (b) External quantum efficiency measurements for 18 independent devices made with QD bandgaps of 0.71 eV (yellow), 0.72 eV (blue), and 0.73 eV (red), as well as a device with an antireflective coating (black). A maximum external quantum efficiency of up to 114% is achieved, confirming the generation of multiple excitons in QDs. (c) Collected internal quantum efficiency curves versus the ratio of photon energy to bandgap, hν/E_g, for three QD sizes. (Reprinted with permission from (a) ref. 320, (b) ref. 336, and (c) ref. 336. Copyright 2009 and 2011, respectively, Nature Publishing Group and American Association for the Advancement of Science.)

In 2011, Semonin and colleagues demonstrated direct proof of carrier multiplication in QDs.³³⁶ They found that about 4% of total photocurrent in PbSe-based solar cells arises from the MEG effect. In such solar cells, the MEG was measured by determining the cell's external and internal quantum efficiencies at zero applied bias. In their work, a peak external quantum efficiency of 114% and a peak internal quantum efficiency of 130% were obtained (Fig. 19b and c). These findings are important because they not only provide direct evidence for MEG in QDs, but also show that MEG charge carriers can be collected with reasonable efficiency in suitably designed QD solar cells. Nevertheless, the impact of MEG on the power conversion efficiency of QD solar cells is limited, largely due to the high energy threshold of ∼3.0 E_g required for MEG in PbSe QDs (as shown in Fig. 19b, only ultraviolet photons can result in efficient MEG). To make MEG have a substantial impact on PV devices, QD-based solar cells that can generate multiple excitons per visible photon at wavelength near the solar peak need to be developed in the future.

5. Down-shifting materials for PV applications

5.1 Concepts of luminescent down-shifting

Luminescent down-shifting can be utilized in many PV devices that exhibit poor spectral response to short-wavelength light. The down-shifting materials absorb the short-wavelength light, typically in the 300–500 nm range, and re-emit it at a longer wavelength where the external quantum efficiency of the PV device is high. While luminescent down-shifting could potentially enhance the solar cell efficiency, it is important to note that the design will not be able to overcome the Shockley–Queisser efficiency limit, as the absorption of a high energy photon by the down-shifting materials can only result in the generation of one electron–hole pair in the solar cell. To date, two main classes of down-shifting-based PV devices have been investigated: luminescent solar concentrators and planar down-shifting layers.³³⁷ A luminescent solar concentrator is used to concentrate sunlight onto PV cells as a simple means to reduce the amount of expensive PV materials required.^338,339 The concentrator, typically composed of polymer sheets doped with luminescent species, converts a fraction of the incident sunlight into longer wavelength light that is subsequently guided towards a PV cell (Fig. 20a).^340,341 On the other hand, a planar down-shifting layer is generally placed directly onto the front surface of a solar cell to improve the device performance by overcoming the poor spectral response of the solar cell to short-wavelength light (Fig. 20b).³⁴²

Fig. 20 (a) Schematic design of a solar cell device equipped with a luminescent solar concentrator. The solar concentrator consists of a flat transparent slab with embedded luminescent down-shifting materials. The luminescent material absorbs incoming solar light and re-emits it at a longer wavelength isotropically. The emitted light, trapped in the slab via total internal reflection, is then guided to solar cells placed next to the edge of the slab. (b) Schematic design of a solar cell device with a luminescent down-shifting layer directly placed onto the surface of the solar cell. The down-shifting layer absorbs short wavelength photons and then re-emits them at a longer wavelength where the device exhibits a better spectral response.

The ideal materials for luminescent down-shifting should possess the following characteristics: (i) broadband absorption, particularly in the region where the spectral response of the solar cell is low; (ii) high absorption coefficient and high luminescence quantum efficiency so that all incident light results in emission; (iii) high transmittance and narrowband emission, particularly in the region where the device response is high; (iv) large Stokes shift to minimize the self-absorption energy losses due to the spectral overlap between the absorption and emission bands; and (v) long-term stability.³⁴³ Up to now, inorganic phosphors and glasses, colloidal QDs and organolanthanide complexes have been widely investigated as potential candidates, as will be discussed below.

5.2 Phosphors and glasses

Table 5 summarizes the recent development of phosphors and glasses as down-shifting layers for a variety of PV devices (e.g., c-Si, DSSCs, organic, and GaSb solar cells).^{297,344–371} In these studies, the principal strategy has been to convert the ultraviolet–blue radiation into red–NIR emission by utilizing Stokes-shifted photoluminescence.

Table 5 Selected phosphors and glasses used as down-shifting layers for PV applications

Materials	Preparation method	Excitation (nm)	Emission (nm)	Solar cell type	Ref.
Y2O3:Eu^3+	—	250	570–700	c-Si	344
La2O3:Eu^3+	Sol–gel Pechini method	285	570–700	c-Si	345
YVO4:Bi^3+,Eu^3+ thin films	Aqueous precipitation	250–400	570–700	c-Si	346
YAG:Ce^3+,Cr^3+	Solid-state reaction	400–500	688	c-Si	347
MgSrAl10O17:Eu^2+,Cr^3+	Solid-state reaction	250–450	693	c-Si	348
SrB4O7:5%Sm^2+,5%Eu^2+	Solid-state reaction	300–600	685	c-Si	371
YAG:Ce^3+,Nd^3+	Co-precipitation	400–500	888, 1064	c-Si	349
YAG:Ce^3+,Nd^3+	Sol–gel	400–500	850–950, 1062	c-Si	350
Cr^3+–Yb^3+ co-doped fluorosilicate glass	Glass melting	300–700	950–1100	c-Si	351
ZnO–LiYbO2 hybrid phosphors	Solid-state reaction	200–400	950–1100	c-Si	352, 353
Yb^3+-doped glass ceramics containing ZnO nanocrystals	Glass melting	200–400	950–1100	c-Si	354
LiYbMo2O8:Pb^2+	Solid-state reaction	300–450	950–1100	c-Si	355
CaLaGa3S6O:Yb^3+	Solid-state reaction	250–500	950–1100	c-Si	356
Yb^3+ doped LaSi3N5	Solid-state reaction	300–400	950–1100	c-Si	357
Ag nanoclusters and Yb^3+ ions co-doped oxyfluoride glasses	Glass melting	300–500	950–1100	c-Si	358
Yb^3+-doped glass ceramics containing Ba2TiSi2O8 nanocrystals	Glass melting	250–350	950–1100	c-Si	359
Yb^3+-doped SrO–TiO2–SiO2 glasses	Glass melting	250–350	950–1100	c-Si	360
Dy^3+–Tb^3+ co-doped glass ceramics containing YF3 nanocrystals	Glass melting	300–500	450–650	c-Si	361
Cu^+ doped glasses	Glass melting	250–320	495	c-Si	362
Tb^3+ doped glasses	Glass melting	300–400	520–700	Thin film	363
LaVO4:Dy^3+	Hydrothermal method	250–320	450–600	DSSCs	364
Y2O3:Eu^3+	Co-precipitation	230–320	570–700	DSSCs	365
TiO2:Ln^3+ (Ln = Eu, Sm)	Sol–gel	200–400	570–700	DSSCs	366, 367
YVO4:Bi^3+,Ln^3+ (Ln = Eu, Sm)	Solid-state reaction	250–400	570–700	DSSCs	297
LaOF:Eu^3+	Hydrothermal method	325–550	570–700	Organic	368
YVO4:Bi^3+,Eu^3+ thin films	Solid-state reaction	250–400	570–700	Organic	369
Bismuth-doped oxide glasses	Glass melting	300–800	1000–1600	GaSb	370

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Crystalline silicon solar cells. The c-Si solar cells show significant differences in spectral response for short wavelength (ultraviolet–blue) and long wavelength (red–NIR) sunlight as discussed in Section 2.1, making them ideal systems for exploring down-shifting processes. Among various Ln³⁺ ions, NIR-emitting Nd³⁺ and Yb³⁺ ions have attracted significant attention.^372–375 Their typical NIR emission around 1000 nm is just above the band edge of c-Si where the solar cell exhibits the greatest spectral response.^376–378 However, the luminescence of Nd³⁺ and Yb³⁺ is relatively weak due to parity-forbidden 4f–4f transitions.³⁷⁹ To solve this problem, several research groups used other luminescent species (e.g., Ce³⁺, Bi³⁺, Pb²⁺, and Cr³⁺) with higher absorption coefficients to sensitize the Nd³⁺ or Yb³⁺ ions.^{349–351,356–360,380} In addition, host sensitization via ET from an excited host (such as ZnO and TiO₂) to Ln³⁺ (Ln = Nd and Yb) ions also offers an effective way to boost the luminescence signal.^{352–354,381–383}

Dye-sensitized solar cells. DSSCs based on the association of light-absorbing materials with wide bandgap semiconductor nanocrystals can work well in the visible range,³⁸⁴ but they suffer from degradation when exposed to ultraviolet radiation.³⁸⁵ Liu et al. in 2006 reported enhanced lifetime for DSSCs using LaVO₄:Dy³⁺ film as an ultraviolet filter.³⁶⁴ The LaVO₄:Dy³⁺ transparent film was coated onto the back surface of an indium tin oxide (ITO) glass substrate modified with TiO₂ (Fig. 21a). The film converts the ultraviolet light (250–320 nm) into visible emission (450–700 nm), which is subsequently absorbed by the N3 ([Ru(dcbpyH₂)₂(NCS)₂], dcbpyH₂: 2,2′-bipyridyl-4,4′-dicarboxylic acid) dye (Fig. 21b and c). It was found that a thin layer of LaVO₄:Dy³⁺ results in an energy conversion efficiency enhanced by 23.3% as compared to the LaVO₄ film without the Dy³⁺ dopant. A major limitation of using Dy³⁺-doped LaVO₄ nanocrystals is that only a small portion of the deep ultraviolet sunlight (250–320 nm) is harvested. An ideal ultraviolet-absorbing luminescent converter for DSSCs should effectively capture the whole ultraviolet part of the solar spectrum (λ ≤ 400 nm) and then convert these ultraviolet photons into narrowband emission exactly matching the absorption of the dye.

Fig. 21 (a) Structure of a DSSC coupled with the LaVO₄:Dy³⁺ ultraviolet-filtering thin-film. Note that ultraviolet light could be absorbed and converted to visible light via the thin-film. (b) The absorption spectrum of LaVO₄:Dy³⁺ nanocrystals compared with the absorption spectrum of N3 dye. Inset: the transmittance spectrum of the LaVO₄:Dy³⁺ thin-film. (c) The emission spectrum of LaVO₄:Dy³⁺ nanocrystals compared with the absorption spectrum of N3 dye. (Reprinted with permission from ref. 364. Copyright 2006, American Institute of Physics.)

In 2011, Hafez et al.³⁶⁶ reported the fabrication of lanthanide-doped TiO₂ photoelectrodes that are used to boost the conversion efficiency of DSSCs. Efficiency as high as 5.81% and 5.16% was reported for Sm³⁺ and Eu³⁺, respectively. In contrast, the undoped titania photoelectrodes only yielded 4.23% efficiency. The higher improvement with the Sm³⁺ dopant in the overall efficiency of the solar cells was attributed to the smaller lifetime values of Sm³⁺ than that of Eu³⁺. Due to efficient host-to-Sm³⁺ ET, the Sm³⁺-doped TiO₂ thin films exhibited a characteristic orange-red emission upon excitation in the range of 250–400 nm. The orange-red emission was then absorbed by a sensitizing ruthenium dye N719 [RuL₂(NCS)₂, L = 4,4-dicarboxylate-2,2-bipyridine]. With further device optimization and new dyes (e.g., N749), much higher efficiencies are likely.

Organic solar cells. Organic solar cells are promising low-cost alternatives to conventional solid-state solar cells, but their rather low photostability under prolonged ultraviolet irradiation has kept them from widespread commercial use. If the harmful ultraviolet photons could be converted into visible light, both the lifetime and the power conversion efficiency will be enhanced.^368,369 Xu et al. in 2011 used the YVO₄:Eu³⁺/Bi³⁺ luminescent nano-film converter as an ultraviolet-filter to improve the photostability of poly(3-hexylthiophene) (P3HT).³⁶⁹ The YVO₄:Eu³⁺/Bi³⁺ nano-film efficiently converts broadband ultraviolet light of 220–400 nm into red emission around 621 nm with a quantum efficiency of up to 69%. The authors observed that the photostability of the P3HT polymer increased by 3 times with the YVO₄:Eu³⁺/Bi³⁺ nano-film, as opposed to that measured without the nano-film.³⁶⁹

GaSb solar cells. Owing to their excellent quantum efficiency at longer infrared wavelengths, gallium antimonide solar cells have emerged as the dominant cell technology for constructing high performance thermophotovoltaic generators. Peng and Wondraczek in 2009 demonstrated the use of bismuth-doped glasses as plain-shifting layers to improve the efficiency of GaSb solar cells (E_g = 0.70 eV; 1771 nm).³⁷⁰ Such glasses exhibit strong absorption in the ultraviolet–green spectral range but high transmission at wavelengths larger than ∼800 nm, while showing broad NIR luminescence (1000–1500 nm) possibly due to Bi⁺ emission. At an optimum molar concentration of 1% Bi, the cell exhibits an increase by a factor of ∼1.5 in the overall external quantum efficiency.

5.3 Semiconductor quantum dots

Semiconductor QDs are a different class of luminescent down-shifting materials that have been recently reported for solar cell applications. In particular, CdSe, CdSe–ZnS, CdS, and CdSe–CdTe have generated great excitement because they feature broadband absorbance, high quantum yield, and tunable emission characteristics in the visible region.^386–401 However, the overall efficiencies of these solar cells need to be improved due to large overlap between the emission and absorption spectra of the QDs.^402,403 In contrast, the use of NIR-emitting QDs (e.g., Ag₂S,⁴⁰⁴ PbS,⁴⁰⁵ ZnTe–CdSe,⁴⁰⁶ CdSe–ZnTe,⁴⁰⁷ and CdTe–CdSe⁴⁰⁸) can greatly reduce re-absorption. As an added benefit, the NIR emission of QDs can be tuned to match the bandgap of c-Si solar cells, thereby opening the possibility of developing luminescent solar concentrators with much higher conversion efficiency.

In 2010, Shcherbatyuk et al. investigated the viability of using PbS NIR-emitting QDs as down-shifting materials in luminescent solar concentrators.⁴⁰² When compared with CdSe–ZnS, the PbS QDs exhibited a broad spectral response extending from the visible to the NIR region of the solar spectrum (Fig. 22). Furthermore, the PbS QDs showed a large Stokes shift of 122 nm (versus 23 nm for CdSe–ZnS QDs) due to a strong quantum confinement effect. More importantly, the authors found that the NIR emission wavelength of the QDs is slightly larger than the bandgap of c-Si (1.1 eV), achieving calculated optical and power conversion efficiency in the luminescent solar concentrator as high as 12.6% and 3.2%, respectively.

Fig. 22 Comparison of absorption and emission spectra of CdSe–ZnS and PbS QDs. The Stokes shifts for CdSe–ZnS and PbS QDs are 23 and 122 nm, respectively. (Reprinted with permission from ref. 402. Copyright 2009, American Institute of Physics.)

5.4 Rare-earth organic complexes

Rare-earth organic complexes, composed of a ligand acting as an antenna (or sensitizer) and an emitting lanthanide ion, are an important class of down-shifting materials for PV modules. Unlike conventional organic dyes and QDs, these organolanthanide complexes feature large Stokes shift and completely avoid self-absorption losses (Fig. 23a).^409–411 In principle, the luminescence process in organolanthanide complexes occurs in three steps: (i) light absorption by a properly selected ligand; (ii) highly efficient intra-energy conversion from the singlet (S₁) to the triplet (T₁) states of the ligand by inter-system crossing; and (iii) resonant ET from the T1 state of the ligand to the excited state of the Ln³⁺ ion (Fig. 23b). Europium complexes that feature a main emission at 612 nm have been investigated for c-Si and DSSCs.^412–420 In contrast, Tb³⁺-based organic complexes are more suitable for amorphous Si solar cells with a wavelength of maximum efficiency at about 500 nm.^421,422 In particular, NIR-emitting metal–organic frameworks that contain Yb³⁺ or Nd³⁺ are promising candidates for c-Si solar cells.^423–426 It is important to note that the organolanthanide complexes with high luminescence quantum efficiency and a broad absorption plateau in the visible region are preferred for PV applications.

Fig. 23 (a) Normalized absorption (solid line) and emission spectra (dashed line) of Eu(TTA)₃(TTPO)₂ where TTA and TTPO stand for thenoyl trifluoroacetone and triphenyl phosphine oxide, respectively. (b) Schematic diagram showing the ET process from the organic ligand to Eu³⁺ in organometallic compounds of europium. (Reprinted with permission from ref. 410. Copyright 2011, Elsevier Ltd.)

6. Conclusions and outlook

In this review, fundamentals for luminescent materials as spectral converters are presented in the context of enhancing solar cell efficiency. One of the major challenges in designing solar cell devices is how to minimize energy losses due to the spectral mismatch between the solar cell and incident solar spectrum. To make full use of the solar spectrum, innovative approaches through use of upconversion, quantum-cutting, and down-shifting luminescent materials, albeit still very much in its infancy stage, have shown promise for the development of these materials as spectral converters to effectively reduce the spectral mismatch losses and, as a consequence, boost the efficiency of solar cells.

Upconversion is able to harvest the sub-bandgap sunlight. Proof-of-concept experiments have been widely performed for Er³⁺-doped upconverters (for c-Si solar cells) and Ln³⁺–Yb³⁺ (Ln = Er, Tm, and Ho) co-doped upconverters (for wide bandgap solar cells). However, two major drawbacks associated with this approach currently limit the practical application of upconverters for solar cells. First, the efficiency of current Ln³⁺-doped upconverters investigated for solar cells is generally low (less than 3%).¹⁹⁴ The upconversion efficiency may be enhanced by using plasmonic resonance⁴²⁷ or photonic crystals.⁴²⁸ High excitation density, which can be easily realized using lasers, also can lead to high upconversion efficiency, but it will require concentrated sunlight. In this respect, low-power TTA-based upconversion in organic molecules is particularly promising for wide bandgap solar cells, provided that efficient NIR-to-visible upconversion can be achieved.^197,198 Second, only a small fraction of sub-bandgap sunlight can be upconverted due to the small absorption cross-sections of Ln³⁺ ions. Transition metal ions,⁴²⁹ quantum dots,⁴³⁰ and organic dyes⁴³¹ with large absorption cross-sections might be exploited as sensitizers to enable broadband absorption of Ln³⁺ ions.

Quantum-cutting allows the efficient use of the high-energy above-bandgap sunlight, which provides potential for efficiency enhancement of narrow bandgap solar cells (c-Si solar cells and germanium solar cells). Efficient narrow-band NIR quantum-cutting with internal quantum efficiency close to 200% has been extensively demonstrated in the Ln³⁺–Yb³⁺ (Ln = Tb, Tm, Pr, Er, Nd, Ho, and Dy) couples for c-Si solar cells. In these couples, Yb³⁺ ions function as ideal acceptors with a single NIR emission band around 1000 nm, just above the bandgap of c-Si. To solve the absorption problem inherent in Ln³⁺ donors, other species (e.g., Ce³⁺, Eu²⁺, Yb²⁺, and Bi³⁺ ions) or hosts have been explored for sensitization. NIR quantum-cutting with Ce³⁺–Er³⁺ and Eu²⁺–Er³⁺ couples, which can give rise to NIR emission around 1500 nm from Er³⁺ donors, has been reported for germanium solar cells. Quantum-cutting has been proven to be a linear process independent of the incident power. This allows for the use of non-concentrated sunlight. However, quantum-cutting with external quantum efficiency larger than 100% has been rarely reported.⁴³² Thus far, no proof-of-concept experiment has been reported for quantum-cutting in PV applications. Urgent tasks for the distant future in this area are: (i) developing novel characterization techniques to provide direct evidence of the existence of NIR quantum-cutting; and (ii) investigating the effect of quantum-cutting materials on the performance of solar cells.

Down-shifting offers the ability to improve the spectral response of solar cells to short-wavelength sunlight. Lanthanide-doped phosphors and glasses, QDs, and organolanthanide complexes can be used in luminescent solar concentrators and planar down-shifting layers for enhancing power-conversion efficiency in solar cells. However, the fabrication of a highly efficient luminescent solar concentrator remains difficult,⁴³³ and the optimal configuration may involve a combination or design layout of different luminescent materials.^434,435

In conclusion, the application of luminescent materials as spectral converters to PV applications could not come at a more opportune time given the significant increase in the global demand for energy in recent years. Despite the daunting challenges of realizing low-cost and highly efficient solar cells, further exploration and attempts to use these spectral converting materials for PV devices and systems will certainly be exciting.

Acknowledgements

X.L. acknowledges the National Research Foundation and the Economic Development Board (Singapore-Peking-Oxford Research Enterprise, COY-15-EWI-RCFSA/N197-1), the Singapore-MIT Alliance, the Ministry of Education (MOE2010-t2-1-083), and the Agency for Science, Technology and Research (A*STAR) for supporting this work. W.H. acknowledges financial support from National Basic Research Program of China (973 Program, 2009CB930601), National Natural Science Foundation of China (BZ2010043, 20974046, 20774043, 51173081, 50428303, 61136003) and Natural Science Foundation of Jiangsu Province (BK2008053, BK2009025, 10KJB510013).

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