Volume 1 photovoltaic solar energy 1 26 – down shifting of the incident light for photovoltaic applications

Volume 1 photovoltaic solar energy 1 26 – down shifting of the incident light for photovoltaic applications Volume 1 photovoltaic solar energy 1 26 – down shifting of the incident light for photovoltaic applications Volume 1 photovoltaic solar energy 1 26 – down shifting of the incident light for photovoltaic applications Volume 1 photovoltaic solar energy 1 26 – down shifting of the incident light for photovoltaic applications Volume 1 photovoltaic solar energy 1 26 – down shifting of the incident light for photovoltaic applications

Y Jestin, Advanced Photonics and Photovoltaics Group, Bruno Kessler Foundation, Trento, Italy

© 2012 Elsevier Ltd All rights reserved

1.26.2 The Down-Shifting Concept

1.26.3 Luminescent Down-Shifters Applied for Solar Cells

1.26.3.1 Silicon-Based Solar Cells

1.26.3.2 Gallium Arsenide-Based Devices

1.26.3.3 Cadmium-Based Solar Cells

1.26.3.4 Organic-Based Solar Cells

1.26.3.5 Critical Parameters

1.26.3.5.1 Incident spectra

1.26.3.5.2 Antireflective coating

1.26.3.5.3 Surface recombination

1.26.4 Simulation Approach – Modeling of the Spectral Response

1.26.4.1 Limit for the Efficiency

1.26.4.2 Modeling of the Spectral Response

1.26.5 Rare Earth-Based Down-Shifting Layers

1.26.5.1 Radiative and Nonradiative Transitions

1.26.5.2 Energy Transfer

1.26.5.3 Efficiency of Rare Earth Ions in Down-Shifting Layers

1.26.6 Quantum Dots-Based Down-Shifting Layers

1.26.6.1 Quantum Size Effects

1.26.6.2 Efficiency of Quantum Dots in Down-Shifting Layers

1.26.7 Organic Dyes-Based Down-Shifting Layers

1.26.7.1 Optical Properties

1.26.7.2 Efficiency of Organic Dyes in Down-Shifting Layers

1.26.8 Commercial Applications and Patents

1.26.8.1 Patents and Down-Shifting Technology

η = 25% has been measured in laboratories under the global AM1.5 spectrum [2] This difference between the experimental and the theoretical value can be explained by different loss mechanisms dependent on the fabrication process itself and intrinsic properties

of the raw materials used in fabrication

There are basically two major loss mechanisms limiting the efficiency of solar cells, which can be explained by a simple observation of the solar spectrum represented in Figure 1 The solar spectrum can be divided into three different zones correspond­ing, respectively, to (1) the high-energy or low-wavelength part of the spectrum, (2) the more intense part of the spectrum, and (3) the infrared part of the spectrum In the first zone, high-energy photons, that is, with energy higher than the band gap Eg, induce thermal losses: in this case, photons are lost via nonradiative relaxation of the excited electrons toward the conduction band in the form of heat In the third zone low-energy photons, also called sub-band gap photons, that is, with energy lower than the band gap

Eg of the semiconducting material, induce transparency losses: in most of these cases, the active material is not able to absorb the photon energy

Different concepts and ideas are currently being investigated to overcome these fundamental limits of solar cells [3] Research and development in this area generally aims to improve the characteristics of the solar cells and thus to provide higher efficiency and lower costs The third generation of solar cells tends to include nonsemiconductor technologies (e.g., polymer-based solar cells [4]), quantum dot technologies [5], tandem/multijunction cells [6], intermediate band gap cells [7], hot carrier cells [8], dye sensitized

Figure 1 Representation of the air mass 1.5G solar spectrum

solar cells [9] and up- and down-conversion technologies [10] Besides these concepts, there are two relatively simple-principle approaches to achieve more efficient utilization of the short-wavelength part of the solar spectrum The first is to improve the electronic properties of existing devices by using very narrow junctions or low doping levels [11], which is not so simple to implement and too expensive for use in production A second approach is the application of passive luminescence conversion layers

on solar cells This approach can be divided into two physical processes: down-conversion (including down-shifting) and up-conversion These phenomena are an intrinsic property of a certain class of materials, like quantum dots, rare earth ions, or organic complexes

Down-conversion and down-shifting of the layers located on the front side of solar cells can be used to make a better utilization

of the short-wavelength part of the solar spectrum The down-conversion results in the generation of more than one lower-energy photon with energy higher than Eg being generated by high-energy photons with energy higher than 2Eg The down-shifting process

is quite similar to down-conversion except that the external quantum efficiency of the down-shifting process is less than unity Up-conversion layers located on the rear of a bifacial cell can be used to absorb the low-energy photons transmitted by the cell and re-emit photons above the band gap of the cell In both cases, the solar cell and the converter are electronically isolated from each other This chapter will concentrate on the down-shifting process

The application of luminescent materials to overcome the poor blue response of solar cells was first described by Hovel et al [11]

in the late 1970s in the area of luminescent solar concentrators technology In the paper, they demonstrated experimentally the potential of the method in different photovoltaic devices Even though the efficiencies of the solar cells used in the late 1970s were worse than that of solar cells used today, the method can still be effective to enhance the performance of solar cells Later, simulations by Richards and McIntosh [12] predicted that when applied to CdS/CdTe solar cells, organic luminescent down-shifter layers could result in an increase in conversion efficiency from η = 9.6% to η = 11.2%, which corresponds to an enhancement in efficiency of nearly 17%

The influence of the luminescent down-shifting layer on photovoltaic devices can be described by the measurement of the quantum efficiency (QE) with and without the layer Two types of quantum efficiency are often considered: (1) the external quantum efficiency (EQE), defined as the ratio of the number of electron–hole pairs generated to the number of photons hitting the device surface The EQE also gives information on the current that a given cell will produce when illuminated by a particular wavelength If integrated over the whole solar spectrum, one can evaluate the current obtained outside the device when exposed to the solar spectrum; (2) the internal quantum efficiency (IQE), defined as the ratio of the number of electron–hole pairs generated to the number of photons hitting the device surface and absorbed by the cell (i.e., after the reflected and transmitted light has been lost) By measuring the reflection and transmission of a device, the EQE curve can be corrected to obtain the IQE of the device Typical curves of EQE and IQE are presented in Figure 2 for a basic c-Si solar cell In this case, it is fairly clear that such devices are not fully efficient in the short-wavelength region of the solar spectrum (i.e., the Ultra Violet and blue region) Furthermore, the IQE is always larger than the EQE A low IQE indicates that the active layer of the solar cell is unable to make good use of the photons A low EQE with respect to the IQE indicates that additional loss mechanisms exist, for example, reflection, absorption, and/or emitter recombination

An advantage of the luminescent down-shifting concept is that the luminescence down-shifter is only optically coupled to the solar cell This down-shifter mainly shifts the photons from the blue- to the red region The mechanisms of down-shifting will be discussed in the following section, followed by a description of simulation tools to model and predict the spectral response of solar cells Then, a review of different solar cells will be presented in order to identify the best candidate for application of a down-shifting layer Thereafter, the physical properties and efficiency of a large number of down-shifting species will be reviewed and compared as applied to different photovoltaic materials Finally, commercial applications and the filed patents will be highlighted

1.26.2 The Down-Shifting Concept

The concept of luminescent down-shifting has emerged in the late 1970s in the area of luminescent solar concentrators [13, 14] and was first reported by Hovel et al [11] The idea was to apply a transparent glass or plastic plate doped with fluorescent dyes on top of

a solar cell in order to absorb a fraction of the solar spectrum and re-emit it at a more favorable wavelength for the solar cell The first attempts made on silicon-based devices have shown a significant increase in the amount of generated electrical energy The interest

in this kind of approach has grown, as it has a number of advantages over the third-generation concepts [3] that could combine high-efficiency performance with low-cost production [15]

The mechanism of luminescent down-shifting can be seen as a photon-conversion process similar to up-conversion [16–18] and down-conversion [10, 19] Indeed, the down-shifting process does not differ significantly from down-conversion; down-conversion that occurs with an EQE below 100% can be referred to as a luminescent down-shifting process

A typical schematic representation of a photovoltaic down-shifting-based device is presented in Figure 3 It is made up of four separate layers The active material is located on the front surface of the device and is electronically isolated from the solar cell by an insulator layer, that is, the coupling between the active medium and the solar cell is purely radiative A perfect mirror is located on the rear surface of the device to provide high internal surface reflectance for all angles of incidence of light A large number of materials can be used as down-shifter for all types of existing solar cells, but they have to respect the following: (1) the EQE cannot exceed unity; (2) the absorption band has to be wide enough to cover the region where the EQE of the cell is low (UV–blue region in silicon-based solar cells as can be seen in Figure 2); (3) the absorption coefficient has to be high; (4) the emission band has to cover

a spectral band where the EQE of the cell is the best (red region in silicon-based solar cells as can be seen in Figure 2); (5) the energy difference between the absorption band and the emission band (Stokes’ shift) has to be large enough to avoid the reabsorption phenomenon of the emitted photons

The down-shifter consists of a material with a certain band gap Eg in which an intermediate level is located between the lowest and the highest energy level (in the case of a down-converter, the intermediate level will be located in the center of the band gap) In the case of a semiconducting down-shifter, the band gap energy corresponds to the difference between the conduction and the valence band; in the case of an organic complex down-shifter, the band gap energy corresponds to the difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) Figure 4 represents the schematic energy diagram of a solar cell in combination with a down-shifter The process of down-shifting, or absorption of incident high-energy photons and re-emission at lower energies that are more favorable for the solar cell, can be achieved with every three-level systems The absorption of a high-energy photon leads to an electronic transition from the lowest level to the highest

Incident light

Rear reflector

Insulator

Solar cell LDS

Figure 3 Schematic reprentation of a photovoltaic down-shifting-based device

Solar cell High-energy

photon

Down-shifter

Radiative transfer

Nonradiative

High energy level

Low energy level

Conduction band

Valence band Intermediate level

Figure 4 Schematic energy diagram of a solar cell in combination with a down-shifter

excited level A first and fast nonradiative recombination generally takes place between the highest excited level and the intermediate level; the emission of one lower-energy photon is accompanied by the radiative recombination of the electron from the inter­mediate level to the lowest level As a result of the luminescent process, a part of the incident photons is shifted to a longer wavelength before reaching the active photovoltaic material of the device The result is an increase in electron–hole pairs generation leading to an improvement in the EQE and the short-circuit current of the device The two other electrical characteristic parameters

of the device, namely, the open-circuit voltage and the fill factor, will not change significantly, as the electronic properties of the semiconducting material or the resistance of the device remains unchanged

A number of down-shifting species for different kinds of solar cells have been reported in the literature and are presented in

categories of down-shifting species can be listed: (1) semiconducting quantum dots; (2) rare earth complexes; and (3) organic dyes The rich and unique energy level structure of rare earth complexes arising from the 4f inner shell configuration gives a variety of options for efficient down-shifting They generally exhibit a high luminescent quantum efficiency but have narrow absorption peaks with low absorption coefficients; therefore, high concentrations are required, leading to increased cost of the device [28] Rare earth down-shifting species will be reviewed in Section 1.26.5 Absorption and emission bands of semiconducting quantum dots can easily be tuned by their size; as a result of quantum confinement [29], they exhibit large absorption and high emission intensity at a good stability [30] On the other hand, the overlap of the absorption and the emission band can lead to significant reabsorption losses [31] Semiconducting quantum dots will be discussed in detail in Section 1.26.6 Organic luminescent dyes exhibit near-unity luminescence quantum efficiency, and have been demonstrated to be stable for many years in a polymethylmethacrylate (PMMA) host incorporating a UV absorber [32] On the other hand, they exhibit narrow absorption bands, and significant reabsorption losses occur in solid host matrices [33] Organic dyes for down-shifting will be detailed in Section 1.26.7

Loss mechanisms have been described in detail for down-conversion systems by Trupke et al [19] From a geometrical point of view, and considering that the down-shifting layer is located on the front surface of the cell, we can assume that similar behavior is exhibited by a down-conversion and a down-shifting layer In this case, one might expect that only half of the luminescence emitted by the down-shifter contributes to the photocurrent of the solar cell, because only this contribution is emitted into the direction of the solar cell This assumption is valid if the refractive index of the material, which is emitting hemispherically, is n = 1 For large refractive indexes like n = 3.6 for silicon or GaAs solar cells, this statement is not correct Further details will be given in Section 1.26.4 The physical and chemical properties of the host matrix containing the down-shifting species can also play an important role in the performance of the device As can be seen in Table 1, the suitable host material can include different types of polymers or glasses According to the design of the cell, the down-shifting emitter can be located in the encapsulation system [23, 27, 34], but also in dielectric thin films used to enhance the performances of photovoltaic devices [20, 35, 36] If the down-shifting emitter is incorporated in the encapsulating system, the material host has to satisfy some specific requirements: (1) achieve and maintain

Table 1 Down-shifting elements with their absorption and emission range

Absorption range Emission range

maximum optical coupling between the solar cell and the incident solar radiation in a given spectral region, that is, an optical transmission of 90% as well as low scattering with losses less than 5% after 30 years of use [37]; (2) achieve and maintain reliable electrical isolation of the solar cell circuit elements from both the operational and the safety points of view during the useful life

of the module Potentials above ground may exceed 1000 V; (3) provide and maintain physical isolation of the solar cell and circuit components from exposure to hazardous or degrading environmental factors; (4) provide an optimum environment for the dissolution of luminescent species If located in a dielectric thin film, some additional requirements are to be fulfilled, too: (1) the refractive index of the host matrix should be close to n = 1.5 as commercially available photovoltaic modules are optimized

to perform under glass or PMMA encapsulation; this is in fact to minimize front surface reflection [38]; (2) the film will have to be compatible with the surface passivation of the solar cell [36]

1.26.3 Luminescent Down-Shifters Applied for Solar Cells

Solar cells are composed of various semiconducting materials [2, 39–43] of which silicon actually represents 95% of the worldwide production [44] Semiconductors are materials that become electrically conductive when supplied with light or heat This phenom­enon is described by the photoelectric effect, which consists in the release of positive and negative charge carriers in a solid state when light strikes the surface of the material Three physical and fundamental steps are common to each type of solar cell independently

of the semiconducting material: (1) Photons coming from the sun hit the solar cell and are absorbed by the semiconducting material; (2) Electrons are knocked loose from the atoms in the semiconductor material, allowing them to flow through the material to produce electricity; and (3) An array of solar cells converts solar energy into a usable amount of direct current

A number of solar cells electrically connected to each other and mounted in a support structure or frame is called a photovoltaic module, and a distinction between the module and the solar cell has to be made, as the performances may differ from one to the other [2] The current produced is directly dependent on how much light strikes the module So, herein is the interest of down-shifting solar cells, trying to increase the quantity of light that can be used by the semiconducting material and thus increase the quantity of electricity produced

In the remaining part of this section, a review of the principal characteristics of different and most common types of solar cells that can be used with down-shifting species is presented: namely, silicon-, gallium arsenide-, cadmium-, and organic-based solar cells 1.26.3.1 Silicon-Based Solar Cells

One can distinguish three silicon-based solar cell types according to the crystalline phase of the silicon: monocrystalline, polycrystal­line, and amorphous To produce a monocrystalline silicon cell (c-Si), pure semiconducting material is necessary This production process guarantees a relatively high level of efficiency [45] The production of polycrystalline cells (mc-Si) is more cost-efficient, but the defects present in the crystal as a result of the production process lead to less efficient solar cells [46] Fabrication of amorphous

or thin-layer cells involves the deposition of a silicon thin film on a glass or another substrate material With a low production cost, its efficiency is much lower than that of the other two cell types [47]

The EQEs of the three silicon-based cell types are shown in Figure 5 The most important difference is located in the short-wavelength region (i.e., λ ≤ 500 nm) where the luminescent down-shifter will have to absorb efficiently In the visible region, the cells exhibit high EQE, where the luminescent down-shifter will re-emit the light Depending on the different types of silicon material used for the fabrication of the cell, the effect of the down-shifter will give different results on the performance of the device Indeed, with maximum efficiencies of, respectively, 20.4% (mc-Si), 10.5% (a-Si), and 25% (c-Si), the down-shifter should be more efficient on mc-Si and a-Si solar cells than on c-Si

1.26.3.2 Gallium Arsenide-Based Devices

Gallium arsenide-based multijunction solar cells are the most efficient solar cells to date, reaching the record efficiency of 42.3% with a triple-junction metamorphic cell [48] They were originally developed for special applications such as satellites and space investigation Their high efficiency comes from the possibility to grow three or more junctions for the same cell Furthermore, the high quality of the direct III–V semiconductors obtained by the metalorganic chemical vapor deposition technique contributes to their high efficiency A triple-junction cell may consist of the deposition of three layers of GaInP, GaInAs, and Ge, respectively As can be seen in Figure 6, each type of semiconductor has a characteristic band gap energy leading to efficient light absorption in a specific wavelength range Here the three contributions observed are the contributions of the three layers GaInP/GaInAs/Ge of the cell Materials are carefully chosen to absorb nearly the entire solar spectrum The first experiments with incorporation of down-shifting species in GaAs-based solar cells were conducted by Hovel et al [11] in the late 1970s, but the rare documentation present on this topic shows that more recent work has not focused on this technology Indeed, as presented in Figure 6, for a triple junction using the inverted metamorphic multijunction solar cell architecture there is very little room for any improvement, given the very good response of this cell at short wavelength [49]

1.26.3.3 Cadmium-Based Solar Cells

Owing to its low cost and high efficiency, the heterojunction of cadmium telluride with cadmium selenide (CdS/CdTe) has attracted considerable attention [50–52] With an energy band gap of 1.5 eV, CdTe has been identified as having a band gap perfectly matching with the distribution of photons of the solar spectrum Its high absorption coefficient is larger than 103 cm−1 in the visible region [53] The typical structure of the CdS/CdTe device is presented in Figure 7, and is composed of five different layers: (1) the glass substrate; (2) a transparent and conducting oxide (TCO) which acts as a front contact; (3) a CdS film which is the so-called window layer; (4) a CdTe film which is the absorber layer made on top of CdS; (5) the metal back contact on top of the CdTe layer Nevertheless, the high band gap energy (2.41 eV) of the CdS window layer results in the fact that lights at wavelength below 514 nm

Triple-junction GalnP/GalnAs/Ge1.0

Figure 7 Typical structure of the CdS/CdTe device

will be absorbed in the CdS layer On this basis, Cadmium-based solar cells appear to be the most promising candidate for the implementation of a luminescent down-shifter Indeed, assuming a quantum efficiency equal to 1 for the down-shifter, an increase

of efficiency of 40% has been predicted [54]

1.26.3.4 Organic-Based Solar Cells

Research on the photovoltaic effect in organic solar cells began in the late 1950s when several groups measured the photo-electromotive forces of various organic semiconductors on inorganic substrates [55, 56] One can distinguish two types of organic solar cells: the organic bulk heterojunction solar cell [4, 57] and the dye sensitized solar cell [42, 58] Organic solar cells differ a lot from silicon-based solar cells Normally, silicon acts as the source of photoelectrons, as well as providing the electric field

to separate the charges and create a current In the case of organic solar cells, the semiconducting element (polymers or titanium oxide nanoparticles) is only used for charge transport, and the photoelectrons are provided by an organic dye material or fullerene-based material

According to the shape of the EQE spectrum [4, 59], organic-based solar cells could be a good candidate for the utilization of down-shifting species However, only few papers exist on the topic This could be explained by the fact that the technology of organic solar cells has not reached its maturity Indeed, significant progress is made each year always pushing the limits of efficiency

[2, 60] However, light-converter species have been introduced as a protection layer in dye sensitized solar cells, as the major loss is caused by the degradation of dye and electrolyte owing to high-energy photons [61, 62]

1.26.3.5 Critical Parameters

When considering the critical parameters that influence the performance of down-shifting solar cells, we may pin down three essential factors: (1) the energy distribution of the incident spectra; (2) the presence or not of an antireflecting coating on the front face of the solar cell; and (3) the surface recombination In the following part, the performance variations of the cells are explained

on the basis of the three essential factors cited above

1.26.3.5.1 Incident spectra

The solar spectrum changes throughout the day and with location, making the down-shifter efficiency dependent of the spectral energy distribution [63, 64] Using two different solar spectra, differences in efficiency measurements as large as 10% have been demonstrated in a Si-based cell using a fluorescent dye as down-shifter [64] Indeed, without using standard reference spectra, the author has estimated the efficiency of the down-shifter considering two different solar spectra under two different atmospheric conditions: (1) the first one under excellent atmospheric conditions with a power density of 950 W m−2, (2) the second one under diffuse atmospheric conditions with a power density of 250 W m−2 Under excellent atmospheric conditions, around 13.5% of the incident energy fits in a wavelength range going from 300 to 475 nm corresponding to the active absorption wavelength range of the down-shifter This proportion is much higher, that is, 22.5%, under diffuse atmospheric conditions, thus making in this case the down-shifter much more efficient for the solar cell

Thus, standard reference spectra have been defined to allow the performance comparison of photovoltaic devices from different manufacturers and research laboratories The use of different kinds of reference spectra for efficiency measurement can be found in the literature: (1) the air mass zero spectrum referred to as AM0 is the standard spectrum for space application; (2) the air mass 1.5 global spectrum referred to as AM1.5G was designed for flat plate modules; (3) the air mass 1.5 direct spectrum referred to as AM1.5D is usually used for solar concentrator work; (4) the air mass 1.5 diffused spectrum referred to as AM1.5Diff, blue-shifted with respect to the global and direct ones, makes reference to a cloudy weather It is defined as AM1.5Diff = AM1.5G − AM1.5D (5) the xenon lamps, which produce a bright white light that closely mimics natural daylight

region As can be seen, a down-shifter can be estimated to be efficient under the AM1.5Diff spectrum with 34.7% of ‘blue light’ included in his spectrum [54], and inefficient under the AM1.5D spectrum with 12.5% of ‘blue light’ included in his spectrum [44]

Table 2 Power density of each standard spectrum with the proportion of blue light in the 300–475 nm-wavelength region

Spectral proportion useful Solar conditions

Power density (W m−2)

for down-shifters

AM0 AM1.5G AM1.5D AM1.5Diff

[11]

[12]

[54]

[63]

The thickness of the antireflective coating is chosen such that the wavelength in the dielectric material is one-quarter the wavelength of the incoming wave Although the reflection for a given thickness, index of refraction, and wavelength can be reduced

to zero, the refractive index is dependent on the wavelength, so zero reflection occurs only at a single wavelength Usually for photovoltaic applications, the refractive index and thickness are chosen so as to minimize reflection for a wavelength of 600 nm This wavelength is chosen because it is close to the peak power of the solar spectrum However, by adding more than one antireflection layer on the cell, the reflectivity can be reduced over a wide range of wavelengths, although this may be too expensive for most commercial solar cells

Antireflection coatings on solar cells thus play an important role in the efficiency of the luminescent down-shifter Indeed, the presence of an antireflective coating can have negative effects on the down-shifter efficiency, making the cell less efficient However, it can have a major influence on the performance of the cell with respect to the down-shifter itself For typical glass panels, depending on the time of the day, 4–15% of the incoming light is lost through reflection and thus is not available to generate electricity Applying an antireflective coating to the glass cover of the module will reduce these reflections and increase the module’s output power Current commercial photovoltaic technologies convert 10–20% of the incoming light to electricity The same module with a suitable antireflective coating can deliver an additional 0.3–0.6% power conversion

1.26.3.5.3 Surface recombination

Any defect or impurities within or at the surface of a semiconductor promote recombination As the surface of a solar cell represents

a severe disruption of the crystal lattice, it is a site of particularly high recombination In this case, a localized region of low carrier concentration causes carriers from the surrounding regions (i.e., high-concentration regions) to flow into that, thereby increasing the surface recombination Thus, the surface recombination rate is limited by the rate at which minority carriers move toward the surface A parameter called the ‘surface recombination velocity’, in units of cm s−1, is used to specify the recombination at a surface

In a surface with no recombination, the movement of carriers toward the surface is zero In a surface with infinitely fast recombination, the movement of carriers toward the surface is limited by the maximum velocity they can attain, and for most semiconductors this value is on the order of 107 cm s−1

Surface recombination can have a major impact both on the short-circuit current and on the open-circuit voltage of a solar cell Indeed, high recombination rates at the top surface have a particularly detrimental impact on the short-circuit current in the solar cell, as well as on the IQE In Figure 8, the IQE of a silicon-based solar cell is shown with a surface recombination velocity varying from 104 to 106 cm s−1, thus highlighting that the IQE for wavelengths lower than 450 nm, that is, the spectral region where the down-shifter has to be active, depends strongly on the surface recombination velocity [20]

Lowering the high top-surface recombination can be typically accomplished by reducing the number of dangling bonds at the top surface by growing a passivating layer on the top surface [65, 66]

Figure 8 Internal quantum efficiency of a silicon-based solar cell with a surface recombination velocity varying from 104 to 106 cm s−1 [20]

C2 C1

C3

C4

1.26.4 Simulation Approach – Modeling of the Spectral Response

A common practice in science and engineering is to make an equivalent model of a device or system so as to better analyze and predict its performance It is a challenge to develop an equivalent circuit for a down-shifting solar cell and provide the cell output characterization using a computer program The fundamental electrical parameters of a solar cell are defined as: (1) the short-circuit current, Isc, (2) the open-circuit voltage, Voc, (3) the maximum power, Pm, and (4) the fill factor, FF This simple model is then generalized to take into account series and shunt resistive losses and recombination losses

To create a model of the performance of a down-shifting solar cell, a mathematical description and the effect the environment has on the transmitted spectrum must be determined Once the mathematical descriptions of the various components are combined, then the model can be used to evaluate the performance and electrical parameters of a theoretical solar cell without the necessity of fabricating it A particular emphasis on the theoretical limit of efficiency of down-shifting solar cells will be placed in the following section in order to identify the best candidate for down-shifting Then, one method consisting in the modeling of the spectral response will be detailed

1.26.4.1 Limit for the Efficiency

Considered to be one of the most significant contributions in the field of solar cells, Shockley and Queisser [67] have determined the Shockley–Queisser limit or detailed balance limit, which refers to the maximum theoretical efficiency of a solar cell using a p–n junction This fundamental limit places the maximum solar conversion efficiency around 31%, assuming

a p–n junction band gap of 1.1 eV Trupke et al [19] have determined an upper theoretical limit for the efficiency of a down-shifting solar cell as a function of its band gap by using detailed balance calculations The proposed model was not developed exclusively for down-shifting solar cells, but for a mixture of the down-shifting and down-conversion processes, the down-shifting process being a particular configuration of the down-conversion process as previously seen in Section 1.26.2 The model has later been improved by Badescu et al [68] For this model, the schematic representation of the solar cell in combination with a down-shifting layer is presented in Figure 3 In this case, the down-shifter is described as a three-level system: (1) the absorption of a high-energy photon leading to an electronic transition from the lowest level to the highest excited level representing a band-to-band transition, (2) a two-step recombination of the electron between the conduction band and an intermediate level and between the intermediate level and the valence band, accompanied by the emission of a lower-energy photon These three types of transitions may be seen as three independent two-band systems with individual electrochemical potentials As can be seen in Figure 9, the whole down-shifting system may be represented by an equivalent circuit consisting of three fictitious solar cells connected in series [68] The two solar cells C3 and C4 represent the intermediate transitions, whereas the band-to-band transitions are represented by C2 Finally, C1 represents the real solar cell

The efficiency of the solar cell/down-shifter system is calculated as the ratio of the electrical power of the solar cell C1 to the incident power The solar cell power is determined from the current–voltage (I–V) curve of the cell C1, which, according to an approach introduced by Shockley and Queisser [67], is calculated as the difference between the absorbed photon current and the emitted photon current Details on the photon current emitted by a solar cell, and described by a generalization of Kirchhoff’s law, can be found in the literature [19, 69]

The results obtained by Trupke et al and Badescu et al are presented in Table 3 and compared with the Shockley limit for a solar cell with a refractive index of 3.6 In both cases, the ideal band gap is found to be around 1.1 eV, which is the band gap of silicon, and with efficiency limits of 38.6% or 26%, respectively, thus highlighting the interest in down-shifting solar cell for the improvement of the efficiency The quite large difference observed in the results obtained by Trupke et al and Badescu et al essentially owes to the different approximations made in the calculation

Figure 9 Schematic representation of an equivalent circuit consisting of three fictitious solar cells connected in series

Photoluminescence intensity emitted into air

Ideal band gap Limit on efficiency

1.26.4.2 Modeling of the Spectral Response

Among the available solar cell-modeling programs, PC 1D, developed by the University of New South Wales in Australia, which allows the simulation of solar cells in 1 dimension, seems to be the most commonly used [20, 70, 71] This program written for personal computers is intended to solve the fully coupled nonlinear equations for the quasi-one-dimensional transport of electrons and holes in crystalline semiconductor devices, with emphasis on photovoltaic devices Its success is based on its speed, user interface, and continual updates to the latest models

One simple approach to evaluate the input parameters to include in the PC 1D program has been proposed by Van Sark [22, 70]

and consists in the modification of the incident solar spectrum and its introduction as input data for the solar cell simulation model

In this case, the incident spectrum, converted into the amount of photons per wavelength Φs(λ), is modified by the absorption of photons in the down-shifting layer The amount of absorbed photons in the down-shifting layer Φa(λ) is determined from the absorption spectrum of the down-shifting species This absorbed amount is then subtracted from the incident spectrum:

Φsa(λ) = Φs(λ) – Φa(λ) As seen in the previous section, down-shifting species will re-emit at a red-shifted wavelength The amount of emitted photons Φe(λ) is calculated from the emission spectrum of the down-shifter, which can be determined by the help of the SCOUT program [72, 73], thus permitting to optimize the shape of the luminescent bands

To this end, the quantum efficiency of the down-shifter has to be taken into account, as well as the fact that owing to the isotropic emission of the down-shifting species, only a part of the emitted photons will be used by the solar cell In this case, one can calculate the photoluminescence emission patterns for different angles from 0 to 90° for both light emitted into the solar cell and emitted into the air Integration of the emission patterns over the solid angles gives the fraction of light emitted into the solar cell [20, 74]

Figure 10 represents the angular dependence of the integrated photoluminescence intensity emitted from the luminescent down-shifter layer into the air (blue) and into the solar cell (red) The intensity is represented in arbitrary units

The amount of emitted photons is then added to the already modified spectrum: Φsae(λ) = Φs(λ) − Φa(λ) + Φe(λ) The resulting spectrum then serves as input data for the solar cell simulation model The absorption of photons can be calculated using the Lambert–Beer equation: the photon flux density Φ(x,λ) after passing a distance x in a film with an absorption coefficient α(λ) is reduced by a factor exp [–α(λ) x] which can be written as follows:

Φðx; λÞ ¼ Φ0ðλÞ : exp½−αðλÞx

where Φ0(λ) is the incident photon flux density The absorption coefficient can be measured from the absorption spectra of the luminescent down-shifter and depends on the concentration of down-shifting species in the host material and the thickness of the host material In Figure 11 is presented the modified AM1.5G spectrum for a luminescent down-shifting layer of TiO2 nanoparticles doped with europium ions The fraction of light absorbed and re-emitted by the down-shifting layer is also depicted [74]

Figure 10 Angular dependence of the integrated photoluminescence intensity emitted from the luminescent down-shifter layer into the air (blue) and into the solar cell (red) The intensity is represented in arbitrary units

Table 4 Results of efficiency simulation obtained on different solar cells

Performance difference

In Table 4 are presented the simulated results of efficiency obtained on different solar cells The large disparity in values shows, for example, that for silicon-based devices the influence of a luminescent down-shifter is low as compared to CdS/CdTe-based devices Furthermore, it is important to note that the results are dependent on the input parameters introduced in the simulation program; they are usually chosen as close as possible to the experimental ones of the fabricated solar cells However, the optimum parameters of experimental solar cells have changed over the years, making solar cells always more and more efficient Input parameters such as cell thickness, doping rate, depth of the p–n junction, bulk recombination lifetime, surface recombination, and surface reflection owing to the presence or not of an antireflective coating can have a significant effect on the down-shifter efficiency, thus making the direct comparison of down-shifting solar cells difficult

1.26.5 Rare Earth-Based Down-Shifting Layers

Lanthanides are usually known as rare earth elements The potential applications of these elements are various; indeed, owing to an incompletely filled 4f shell, each rare earth element can be characterized by a unique and particular luminescence spectrum [76] Their use in converting photons to a different, more useful wavelength is well known from a wide range of applications like fluorescent tubes, lasers, and optical amplifiers [77–79] Rare earth ions have the electronic configuration 4fn –5s2 –5p6

where n varies from 0 to 14 For luminescent applications, the rare earth is usually in a mostly stable ionized state, and, in most of the cases, with an oxidation degree of +3 The position of the energy levels and the possible electronic transitions responsible for the luminescence depend only barely on the host material in which the rare earth element is incorporated This is because of the optically active 4f orbital being well shielded from the host environment by the outer-filled 5s and 5p orbitals

The energy levels of trivalent rare earth ions are presented in Figure 12 in the so-called Dieke diagram [76] As can be seen, the rich and unique energy level structure gives a variety of options for efficient down-shifting The two essential types of transitions, that is, radiative and nonradiative, induced by the excitation of the rare earth ion will be presented in the following section Then, the rules of energy transfer between rare earth ions will be explained, in order to fully understand the physical process permitting the use of rare earth ions as down-shifing species for solar cells