N OVEL S OLAR C ELL C ONCEPTS
Dissertation
zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat.)
an der Universität Konstanz Fachbereich Physik
vorgelegt von
Jan Christoph Goldschmidt
Fraunhofer Institut für Solare Energiesysteme (ISE)
Freiburg
September 2009
Tag der mündlichen Prüfung: 16.11.2009
Referent/in: Prof. Gerhard Willeke Referent/in: Prof. Thomas Dekorsy
1 Table of contents
1 Table of contents... i
2 Motivation and Introduction ... 1
2.1 Motivation ... 1
2.1.1 Why it is essential to transform the global energy system?... 1
2.1.2 Why photovoltaics?... 1
2.1.3 Why new concepts for higher efficiencies?... 2
2.1.4 Photon management for full spectrum utilization ... 3
2.2 Main objectives of this work ... 4
2.3 Structure of this Work ... 5
3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts... 7
3.1 A short theory of solar cells... 7
3.1.1 Thermodynamic efficiency limits ... 7
3.1.2 Generating chemical energy... 8
3.1.3 Extracting useful energy... 10
3.1.4 The pn-structure ... 13
3.2 Novel solar cell concepts ... 17
3.2.1 Thermophotovoltaic Systems ... 17
3.2.2 Hot carrier solar cells ... 17
3.2.3 Tandem solar cells... 18
3.2.4 Intermediate band-gap solar cells... 18
3.2.5 Photon management ... 19
4 Fluorescent Concentrators... 21
4.1 Introduction to fluorescent concentrators ... 21
4.1.1 The working principle of fluorescent concentrators ... 21 4.1.2 The factors that determine the efficiency of fluorescent
4.1.4 Materials for fluorescent collectors ... 30
4.1.5 Fluorescence... 31
4.2 Theoretical description of fluorescent concentrators ... 36
4.2.1 Maximum concentration and Stokes shift ... 36
4.2.2 Thermodynamic model of the fluorescent concentrator ... 39
4.2.3 Photonic structures ... 43
4.3 Optical characterization of fluorescent concentrator materials ... 48
4.3.1 Photoluminescence measurements ... 48
4.3.2 Characterizing the light guiding of fluorescent concentrators ... 56
4.3.3 Measuring the angular distribution of the guided light... 74
4.3.4 Short summary of the optical characterization ... 77
4.4 Simulating fluorescent concentrators ... 79
4.4.1 Monte Carlo simulation... 80
4.4.2 The used model ... 81
4.4.3 Results of simple model ... 87
4.4.4 Improvements of model... 90
4.4.5 Conclusions from simulation... 100
4.5 Fluorescent concentrator systems ... 101
4.5.1 Solar cells for fluorescent concentrator systems... 101
4.5.2 Systems with different materials ... 103
4.5.3 Systems with silicon bottom cells ... 110
4.5.4 The effect of photonic structures ... 115
4.5.5 The influence of system size on collection efficiency ... 120
4.6 The future of fluorescent concentrators ... 128
4.6.1 The “Nano-Fluko” concept... 129
1 Table of contents
5 Upconversion... 133
5.1 Introduction to upconversion ... 133
5.2 The potential of upconversion and ways to increase upconversion efficiency ... 135
5.2.1 The potential of upconversion... 135
5.2.2 Definition of upconversion efficiency... 136
5.2.3 Upconversion efficiencies achieved so far ... 137
5.2.4 Spectral concentration... 137
5.2.5 An advanced system design for spectral concentration ... 138
5.2.6 Enhancing upconversion efficiency by plasmon resonances ... 140
5.3 Upconversion mechanisms and their theoretical description ... 142
5.3.1 Absorption and emission... 144
5.3.2 Migration of excitation energy ... 148
5.3.3 Multi-phonon relaxation... 151
5.3.4 Intensity dependence of upconversion ... 152
5.4 Suitable materials for upconversion... 156
5.4.1 Theoretical aspects of the energy spectrum of trivalent erbium ... 157
5.5 Optical material characterization ... 161
5.5.1 Absorption measurements ... 161
5.5.2 The Kubelka-Munk theory ... 163
5.5.3 Absorption coefficient and Einstein coefficients... 164
5.5.4 Time-resolved photoluminescence... 167
5.5.5 Intensity dependent upconversion photoluminescence... 176
5.5.6 Calibrated photoluminescence measurements... 179
5.5.7 Optical properties of luminescent nanocrystalline quantum dots (NQD)... 185
5.6 Simulating upconversion ... 188
5.6.1 The rate equation model... 189
5.6.3 Simulation results... 197
5.7 Upconversion systems ... 204
5.7.1 Used solar cells and experimental setup ... 204
5.7.2 Applying the upconverter to the solar cell... 206
5.7.3 External quantum efficiency with different upconverter samples... 207
5.7.4 Upconversion solar cell system under concentrated sunlight... 211
5.8 Conclusions and outlook on the application of upconverting materials to silicon solar cells ... 220
6 Summary ... 225
6.1 Fluorescent concentrators ... 225
6.2 Upconversion... 228
7 Deutsche Zusammenfassung ... 231
7.1 Fluoreszenzkonzentratoren ... 231
7.2 Hochkonversion... 234
8 References... 237
9 Appendix... 249
9.1 Abbreviations... 249
9.2 Glossary ... 250
9.3 Physical Constants ... 261
10 Author’s Publications... 263
10.1 Refereed journal papers ... 263
10.2 Conference papers... 264
10.3 Oral presentations ... 267
10.4 Patents... 268
10.5 Other publications... 269
11 Curriculum vitae ... 271
12 Acknowledgements ... 273
2 Motivation and Introduction
2.1 Motivation
2.1.1 Why it is essential to transform the global energy system?
The global energy system is based on the primary energy sources oil, coal and gas predominantly. Burning these fossil fuels releases carbon dioxide and other emissions, ultimately resulting in climate change. Global climate protection is the supreme challenge that makes it necessary to transform energy systems worldwide. Also, at the local and regional levels, mining, transport, storage, and usage of fossil and nuclear fuels destroy or put at risk complete ecosystems and human health. Therefore the persisting patterns of energy usage jeopardize the natural basis of life. The global energy resources are limited and distributed unevenly. This causes geostrategic conflict and makes a forced end to our current energy usage inevitable. About two billion people have no access to modern energy sources. They are therefore cut off from any chance to overcome their poverty. All this leaves humanity with the challenge to drastically change the global energy system and to orient it towards sustainable ecolo- gical and social criteria [1]. Such criteria are the mitigation of climate change, conser- vation of nature and ecosystems such as oceans, rivers and soil, and the reduction of air pollution. A sufficient food supply for everybody must always be more important than energy production. Everybody should have affordable access to modern energy sources. Everybody should be able to use energy without endangering one’s health and should live without fear of risks associated with the energy system. As control over energy sources has always meant political power, reshaping our energy systems also presents a chance for more democracy and a more just distribution of power [2]. While searching for solutions, all of these criteria should be considered. There is no benefit in solving one problem while worsening another one at the same time.
2.1.2 Why photovoltaics?
An increase in energy productivity and a switch to new renewable energy sources are the two main pillars of the necessary transformation in global energy systems. Among the new renewable energy sources, solar energy has the most important role to play.
The sustainably usable potential of solar energy appears to be virtually unlimited in comparison to the world energy demand. Other renewable energy sources like wind
likely to succeed in bringing solar energy to the people in developed as well as in developing countries is photovoltaics, the direct conversion of solar radiation into electric power. The modular character of the technology allows for the construction of power plants in any size. Photovoltaic devices, also known as solar cells, can serve as a power source in consumer products or be interconnected in modules as power plants of varying size: small island-systems to power houses or villages, mainly in developing countries are just as possible as grid-connected systems on residential housing in industrial countries or huge power plants in the megawatt range. The absence of moving parts makes the systems reliable and enables system lifetimes exceeding 25 years. Additionally, solar cells convert diffuse radiation into electricity as well, so they can harvest solar energy efficiently in middle and even northern Europe. Of all energy technologies, photovoltaics have the steepest learning curve. That is, no energy technology is getting cheaper faster. On average, a doubling in the cumulated installed power capacity of photovoltaic systems results in a 20% reduction in production costs.
Together with the enormous market growth [3], this leads to a fast reduction in costs.
Already now, levelized electricity costs from photovoltaics can compete with peak load prices in southern Europe [4]. Around 2015 or earlier, grid-parity will be reached in middle Europe [4]. Then the electricity from a roof-mounted photovoltaic system will cost about the same as the end consumer pays for electricity. However, prices are still high at the moment. To reach grid parity and to continue the expected development beyond 2015, continuous innovation is necessary.
2.1.3 Why new concepts for higher efficiencies?
Crystalline silicon is the dominant material in the production of solar cells. It is non- toxic and abundant. At the moment the material costs for silicon in the required purity dominate the costs for solar cell production. Therefore, alternative production techno- logies, such as thin-film solar cells or innovative silicon-wafer based concepts appear attractive. But also for new technologies, maturing production technologies will lead to a situation in which the material costs dominate. In the end, it will be the wafer, the glazing, or the substrate for thin-film technologies which sets the limit for further cost reduction. The only way to overcome this limit is to increase the efficiency of the solar cells. A higher efficiency increases the amount of electricity produced from one unit of material. This reduces the electricity costs and the amount of resources needed to meet our energy needs. Current innovations are mainly focused on production technologies.
The underlying working principle of the solar cells remains unchanged. However, to achieve substantially higher efficiencies, novel solar cell concepts are needed that also address the working principle and which overcome fundamental limits.
2.1 Motivation
2.1.4 Photon management for full spectrum utilization
Most solar cells today are made from silicon, and therefore from one semiconductor material with one band-gap. These solar cells do not use the full solar spectrum (see Fig. 2.1). Photons which have energies below the band-gap of the semiconductor are not absorbed. The energy of photons which exceeds the band-gap is converted into heat, and is therefore lost as well [5]. As more than 55% of the energy is lost by these mechanisms, it is obvious that new concepts for higher efficiencies have to make better use of the energy contained in the solar spectrum.
Fig. 2.1: Illustration of the principal losses incurred by a silicon solar cell. Photons with energies below the band-gap are transmitted straight through the device. Around 20% of the incident energy is lost this way. The energy of photons exceeding the band-gap is converted into heat. These thermalization losses account for around 35% of the incident energy. To achieve high efficiencies, novel concepts are needed to reduce these losses.
Several concepts are being discussed to overcome these fundamental efficiency- limiting problems. Most of these novel concepts require complex new solar cell structures and many are rather theoretical concepts than working devices. An alternative approach is photon management. Photon management means splitting or modifying of the solar spectrum before the photons are absorbed in the solar cells in such a way that the energy of the solar spectrum is used more efficiently. The solar cells themselves remain fairly unchanged, and well-established solar cell technologies
2.2 Main objectives of this work
The role of this work is to find and explore promising fields in the wide landscape of novel solar cell concepts. The main objectives are to increase the understanding of the concepts, investigate the materials on which the concepts are based, to realize complete systems, and to further develop the concepts to a point where their perspective and potential becomes clear.
In this work, I concentrated on two concepts from the fields of photon management that appeared to be especially promising: fluorescent concentrators and upconversion.
Both rely on luminescent materials. Luminescent materials absorb light independently from the direction of incidence. Therefore, in principle these concepts are able to use diffuse light as well. This is a big advantage to many other concepts for photon management, which rely on selective mirrors, filters, diffraction gratings, or similar, and which usually only work under direct sunlight. Both concepts share important aspects in theory as well as in technological issues, e.g. the need for a matrix material for the luminescent material, and they can be combined in one system as we will see later on.
Fluorescent concentrators are a concept well known since the late 1970s [6, 7] to concentrate both direct and diffuse radiation without tracking systems. In a fluorescent collector, a luminescent material embedded in a transparent matrix absorbs sunlight and emits radiation with a different wavelength. Total internal reflection traps most of the emitted light and guides it to the edges of the fluorescent collector. Solar cells, optically coupled to the edges, convert this light into electricity. Fluorescent concentrators were investigated intensively in the early 1980s [8, 9]. Research at that time aimed at cutting costs by using the concentrator to reduce the need for expensive solar cells. After 20 years, there has been considerable progress in the development of solar cells and luminescent materials, and new concepts have been developed.
In this work, several new ideas will be combined into one advanced concept for a fluorescent concentrator system design. The key features are a stack of different fluorescent concentrators to use the full solar spectrum, spectrally matched solar cells, and photonic structures that increase the fraction of light guided to the edges of the concentrator. To understand and to develop the different components, and finally to realize systems with all of these features is the main objective of my work on fluorescent concentrators within the frame of this PhD thesis.
Upconversion of photons with energies below the band-gap is a promising approach to overcome the losses caused by the transmission of these photons [10]. An upconverter
2.3 Structure of this Work generates one high-energy photon out of at least two low-energy photons. This high- energy photon can then create a free charge carrier in the solar cell.
In combination with a second luminescent material, the spectral range of upconverted photons can be increased. In this work, an advanced system design for such a combination is developed. The main objectives are to characterize the materials involved, to develop a theoretical model of the upconverter and to realize systems with the relevant components.
2.3 Structure of this Work
In this chapter 2, the motivation and topic of this work is introduced.
In chapter 3, I will outline fundamental theoretical concepts regarding the conversion of solar radiation into electric energy. I will restrict my presentation to very fundamental aspects that are necessary to understand how novel solar cell concepts help to increase the efficiency of solar cells and photovoltaic systems.
Chapter 4 deals with fluorescent concentrators. At the beginning, I will introduce the general working principle of fluorescent concentrators and review the results achieved so far. Following this, I will present the results from optical characterization of fluorescent concentrator materials and a method to characterize the light guiding behavior of fluorescent concentrators that I developed in the context of this work. To test different hypotheses that could explain the results of the optical characterization, a Monte-Carlo simulation of the concentrator’s light guiding is developed. Finally, investigations on complete systems of fluorescent concentrators and solar cells are presented. This includes systems with different collector materials and spectrally matched solar cells, as well as systems with photonic structures that increase light guiding efficiency.
Chapter 5 deals with upconversion. At the beginning, I will highlight by which mechanisms upconversion can occur and will introduce the theoretical concepts describing upconversion. I will discuss which materials are suitable as upconverter and show results of extensive optical characterization of the investigated erbium doped NaYF4. This includes absorption measurements, time and intensity resolved photoluminescence measurements, and calibrated photoluminescence measurements to directly measure upconversion efficiency. Based on the experimental results and the theory, a simulation tool that models the upconversion dynamics is developed. Finally,
Chapter 6 will summarize and conclude the results of this work, the summary can be found in German in chapter 7. The referenced publications, abbreviations, a glossary, the used physical constants, the list of the author’s publications, a CV, and the acknowledgements are located at the end of the work.
3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts
In this chapter, I will outline fundamental theoretical concepts about the conversion of solar radiation into electric energy, in short: the theory of solar cells. In this work, solar cells are used in systems that apply photon management. The processing and optimization of the solar cells is of minor importance. Consequently, I will restrict my presentation to very fundamental aspects that are necessary to understand how novel solar cell concepts help to increase the efficiency of solar cells or photovoltaic systems. I will start from general thermodynamic considerations and will describe which conditions result in which efficiency limits. In the following, I will show how some of these limits can be overcome by novel solar cell concepts. This presentation is based on the discussions in [5, 11, 12] where detailed information can be found.
3.1 A short theory of solar cells
3.1.1 Thermodynamic efficiency limits
A photovoltaic device converts solar radiation into electric energy. Solar radiation is nothing more than heat radiation emitted by the sun. With heat, entropy is always associated, while electricity is entropy-free. Therefore, in the conversion process, the entropy must be released to the surroundings in the form of heat. This should happen at a lower temperature, so that not all the received energy is lost in this process. An idealized way of this process of receiving energy that contains entropy, dissipation of entropy, and generating entropy-free work is the Carnot cycle. With TS being the temperature of the sun and T0 the ambient temperature, the Carnot efficiency K is
T
ST
01
K
. (3.1)WithTS = 6000 K and T0 = 300 K this efficiency is very high and exceeds 95%. The Carnot efficiency is the fundamental limit for all thermodynamic processes, and since the limit is a direct result of the second law of thermodynamics, it cannot be overcome.
However, the Carnot efficiency is a very theoretical limit. It relies on isentropic
The Carnot efficiency does not consider that energy is re-radiated from the converter to the sun. Considering the radiation emitted from the converter leads to a maximum possible efficiency of 93.3% [13]. This is the so-called Landsberg limit.
A model of a solar cell system that is a little bit more realistic is an absorber that receives solar radiation and powers a heat engine that works with the Carnot efficiency. When the temperature of the absorber TA equals TS the efficiency is zero, because the absorber would emit as much energy as it receives. When TA = T0 the efficiency would be zero as well, for there would be no temperature difference to drive the heat engine. Between these extremes, for an ideal temperature an efficiency of 85.4% can be achieved [12]. This efficiency can be increased to 86.8% if an absorber for each wavelength is used, which is operated at its individual ideal temperature. Even such an ideal system suffers losses from the emission of radiation. If this emission is re-directed to another ideal system, of which the emission is again re-directed to yet another system and so on, the Landsberg limit can be reached [14]. However, this requires breaking time symmetry. For this purpose circulators are needed that accept radiation from one direction while emitting it in a different direction [12]. There are different proposals for how such a system could be realized; probably the easiest to imagine is a rotating mirror.
3.1.2 Generating chemical energy
Up to now, I have not considered the internal structure of the photovoltaic device. In a heat engine, one usually has some kind of gas that absorbs energy and performs work during expansion. Most solar cells are realized from semiconductor materials. In a semiconductor, the electrons and holes play the role of the working gas. Directly after absorption, the electrons in the conduction band and the holes in the valence band have the same energy distribution as the absorbed photons and the electron ensemble has the same temperature as the sun. In consequence, the higher energy states are relatively frequently populated. The electron ensemble cools down fast (in around 10-12s) to the ambient room temperature by phonon interaction with the ion lattice, so that lower energy levels are now populated more frequently. The changes in the energy distribution are sketched in Fig. 3.1.
3.1 A short theory of solar cells
Fig. 3.1: Directly after absorption, the electrons in the conduction band and the holes in the valence band have the same energy distribution as the absorbed photons. In 10-12 s the electrons and holes cool down to the ambient temperature. For the population of the energy levels dne/dEe and dnh/dEh this means that the population is shifted to lower energies. After the cooling, the concentration of electrons and holes is still higher than in equilibrium. To describe this non-equilibrium situation, two Fermi distributions are necessary. The idea for this picture was taken from [5].
The cooling does not change the electron or hole concentration. Therefore, the concentration of both is higher than in equilibrium with the ambient temperature. To describe this non-equilibrium situation, two (quasi-)Fermi distributions are necessary:
one for the electrons in the conduction band, and one for the holes in the valence band.
The Fermi energy of the electrons in the conduction band EFC can be identified as the electrochemical potential Ke of the electrons [5], and the Fermi energy of the holes in the valence band EFV can be identified as minus one times the electrochemical potential Kh of the holes. Consequently, the difference of the Fermi energies equals the sum of the electrochemical potentials:
EFC - EFV = Ke + Kh = Pe + Ph=:Peh (3.2) Because of the opposite charges of electron and hole, the sum of their electrochemical potentials equals the sum of their chemical potentials [5]. The final consequence is that the splitting of the Fermi energies equals the chemical potential of electrons and holes.
The splitting of the Fermi energies, and therefore the chemical potential, has been a result of the generation of extra carriers by photon absorption and subsequent cooling.
Because of the band-gap, no complete equilibrium is reached and an electronically
It is illustrative to consider the case without a band-gap like in a metal. The absorbed photons do not generate extra free carriers, as they only excite electrons within the band to higher energies. Directly after absorption, the electron temperature is also increased, but after the cooling equilibrium is reached, because concentration had not changed. Therefore, no chemical energy is generated.
3.1.3 Extracting useful energy
As we have seen in the previous section, in a semiconductor solar energy is converted into chemical energy. This happens without any special structure, such as a pn- junction. Nevertheless, to use this energy we have to extract the electrons and holes, together with their energy from the semiconductor. In this section, I will show which aspects are important for the extraction of useful energy independent from any special structure.
The chemical potential Peh is the amount of energy that can be extracted with one electron-hole pair. Therefore, multiplying this amount with the particle flux per illuminated area of extracted electron-hole pairs jeh gives the extracted power density pext:
pext = jeh .Peh (3.3)
The particle flux jeh that can be extracted from an illuminated semiconductor is given by the difference of the rates of generation geh and recombination reh (in this case the rates are defined per area):
jeh = geh - reh. (3.4)
In an idealized case, only radiative recombination occurs, so the recombination rate equals the emission of photons from the semiconductor.
The number of emitted photons per time, per area, per unit solid angle, and per frequency interval is given by the generalized Planck’s law [5]
1 exp
1 )
( , 2
, 2
2 2 ,
¸¸
¹
¨¨ ·
©
§
T k c h
T n B
B
pQ
Q P Q Q D Q Q P
,(3.5)
where Qis the frequency of the photons, T the temperature of the emitter, µ the chemical potential within the emitter (which has to be identified with Peh in this case), n(Q) is the refractive index into which the emission takes place, DQis the absorption coefficient, c the speed of light in vacuum, h the Planck constant and kBthe Boltzmann
3.1 A short theory of solar cells constant. With this definition, Bp,Q cos(T)dA dQ d: is the number of photons emitted from the surface element dA in the frequency range of QtoQ +dQ into the solid angle d: into the direction given by the polar angle T and an azimuth angle I.
For the efficiency of a solar cell, especially two features of the generalized Planck’s law are important: the dependence on the chemical potential and the influence of the solid angle in which radiation is emitted.
To increase the extracted power jeh*Peh a high chemical potential in the semiconductor seems beneficial. On the other hand, following equation (3.5) a high chemical potential means high emission of photons. Therefore, a high chemical potential decreases the extracted current. For a maximum chemical potential POC, all photons are emitted, so the extractable current is zero. As a result, although the chemical potential is at its maximum, no power is extracted. The contrary situation is achieved when all the electron-hole pairs are extracted. Since there are no excess carriers left in the semiconductor, the chemical potential is zero in this case. Again, the extracted power is zero. In between, there is a point where the extracted power is at its maximum (see Fig. 3.2).
If the -1 in the denominator of equation (3.5) is neglected, for monochromatic irradiation and emission equations (3.4) and (3.5) can be combined to
¸¸ ¹
¨¨ ·
©
§
const k T g
j
B eh eh
eh
exp P
. (3.6)The structure of equation (3.6) is quite similar to that of the IV-characteristic of a pn- junction solar cell, if the electrochemical potential is identified with the voltage of the solar cell. From this derivation, it becomes clear that the exponential current voltage characteristic is not a result of the pn-junction, but a fundamental consequence of the balance between generation and recombination of electrons and holes.
This is still true even when the dominant recombination mechanism is not radiative recombination. Recombination can be interpreted as a reaction with the electron and the hole being the educts. Whether such a reaction does occur is governed by the chemical potential of both in comparison to the chemical potential of the product of the reaction. In semiconductors, the chemical potential depends approximately exponentially on the concentration [15] of the electrons and holes, which is the case for most educts in chemical reactions. In a standard silicon solar cell, the current voltage
the concentration of holes and electrons, which is again equivalent to an exponential dependency on the chemical potential of the electron-hole pairs [15]. So we can state more generally, that the extraction of useful energy is described by three cases: first, maximum extraction that reduces the chemical potential to zero; second, the maximum chemical potential in the case where there is no extraction but maximum recombination; and third, the range in between. The height of the chemical potential determines the extent of the recombination in the most cases with an approximately exponential relation and therefore the remaining number of charge carriers that can be extracted.
Fig. 3.2: Illustration of how the extracted current jeh and the extracted power depend on the sum of chemical potentials of the electrons and holes in the semiconductor Peh [11]. At Peh=POC all photons are emitted, so the extractable current is zero. Therefore the extracted power jeh*Peh is zero as well. At Peh= 0 the extracted current is at its maximum jSC, because the radiative recombination is at its minimum. Nevertheless, because of Peh= 0 the extracted power is again zero. In between, a maximum power point (MPP) exists, at which the extracted power reaches its maximum jmpp*Pmpp (indicated as blue rectangle).
Without any special means, a semiconductor emits into a complete hemisphere. In contrast, the solid angle of the sun, from which radiation is received, is very small.
Concentration with lenses or mirrors increases this solid angle. The maximum concentration is reached when radiation is received from the complete hemisphere.
Equation (3.5), with T = Ts and P = 0, describes as well the absorbed photon flux
3.1 A short theory of solar cells received from the sun and therefore the generation rate [11]. It is obvious that an expanded solid angle, from which radiation is received, increases the generation rate geh. Because the concentration of electrons and holes rises, the chemical potential is also higher with concentration. In consequence, more power jeh*Peh can be extracted and the efficiency increases. An alternative approach with the same result is to narrow the solid angle in which radiation is emitted. With a narrower solid angle of emission, the losses due to radiative recombination are smaller and the extracted current, the chemical potential, and consequently the extracted power are higher.
We have seen that only from the generalized Planck’s law an exponential current/chemical potential characteristics with a maximum power point can be derived, and the effect of concentration can be explained. Now the question arises of how exactly the electrons are extracted from the semiconductor and how the chemical energy is converted into electric energy. For this purpose, electrons and holes have to be extracted at different points of the semiconductor. If these two points are connected over an electric load, the difference in the electrochemical potential of the electrons and the holes drives a current through the load and work is performed. One structure that is able to separate electrons and holes is the pn-structure of common semiconductor solar cells.
3.1.4 The pn-structure
A pn-structure consists of one p- and one n-doped region. Without illumination, in the p-doped region, the concentration of holes is higher than in intrinsic material, therefore the Fermi energy is close to the valence band edge. In the n-doped region, the electron concentration is higher and the Fermi energy is close to the conduction band edge.
Illumination creates excess carriers, so both the electron and the hole concentration increases. As mentioned before, this situation is described with two Fermi distributions and therefore also two Fermi levels. This is the so-called splitting of the Fermi levels.
The relative effect of the increase in charge carrier concentration is more pronounced for the minority charge carriers in each region, i.e. for the holes in the n-doped region and the electrons in the p-doped region. Consequently, the Fermi level of the majority charge carriers hardly moves, while the Fermi level of the minority charge carriers is at a distinctly different position than the common Fermi energy of the non-illuminated case.
In section 3.1.2, it was shown that the Fermi level can be identified with the electro- chemical potential of the respective kind of charge carrier (considering the sign of its
jeh = - ne/q me grad(EFC), (3.7) with ne being the electron concentration, q the elementary charge and me the mobility of the electrons. The particle flux density of the holes can be calculated accordingly but the different sign of the charge must be considered.
In equation (3.7), the carrier concentration plays an important role. Usually, the concentration of the majority carriers is higher by orders of magnitude than the minority carrier concentration. Therefore, the total charge current density J
J = - q je + q jh, (3.8)
can be mainly attributed to the flow of the majority charge carriers in the respective region. Additionally, at the interface between metal contact and semiconductor, a lot of recombination occurs and in the metal itself no separate Fermi levels exist. Therefore, at the contacts the charge carriers have the same concentration as under the equilibrium without illumination. Because of these two facts, only the electro-chemical potentials of the majority carriers at the contact points determine the current through an external load. The difference of these two potentials is the voltage of the solar cell Vcell that can be measured externally between the two contacts of a solar cell.
Fig. 3.3: The pn-structure of common semiconductor solar cells under illumination.
This figure shows the solar cell under short circuit conditions. Because of the short circuit, the electrochemical potentials of the majority carriers at the contact points are on the same level. The light-induced Fermi level splitting results into a large gradient of the Fermi levels across the pn- junction. This gradient causes a large current to flow. Because of their different charges, the electrons move to the contacts of the n-doped region, while the holes move to the contact of the p-doped region. The charge carriers are effectively separated. Because the external voltage is zero, no work is performed
3.1 A short theory of solar cells If the two contacts are connected without any resistance (short circuit conditions), then the two electrochemical potentials EFC and EFV at the contact points are on the same level (see Fig. 3.3). Since the illumination has induced a splitting of the Fermi levels, a large gradient within the Fermi levels exists across the pn-junction. Following equation (3.7), this results into a large current. Further away from the junction, because of the higher charge carrier concentrations a smaller gradient of the Fermi levels is sufficient to maintain the same current. Because of their different charges, the electrons move to the contact of the n-region and the holes to the contact of the p-region. This constitutes a successful separation of electrons and holes. The resulting charge carrier density is designated short circuit current density JSC. Under short circuit conditions, no energy is extracted. As with the discussion of the chemical potential, without an external voltage, the product of current and voltage is zero.
To drive a current through a load and to perform work, a voltage difference - that is a difference between the electrochemical potentials of the majority carriers at the contact points - is necessary. As visible in Fig. 3.4, this reduces the gradient of the Fermi levels within the solar cell and therefore the extracted current. If the voltage is further increased to the open circuit voltage VOC so that the gradient is zero, no current flows (Fig. 3.5).
Fig. 3.4: Illuminated pn-structure of a solar cell under working point conditions.
The electrochemical potentials of the majority carriers at the contact points determine the current through an external load. The difference of these two potentials is the voltage of the solar cell Vcell that can be measured externally between the two contacts of a solar cell. When this potential difference drives a current through the external load, work is performed. In comparison to Fig. 3.3 the internal gradient of the Fermi levels is reduced so the resulting current is smaller.
Fig. 3.5: Illuminated pn-structure under open circuit conditions. At the open circuit voltage VOC the gradients of the electrochemical potentials across the pn- junction are zero and no current is flowing.
The maximum efficiency of a solar cell with one pn-junction has been calculated in [16] and also in [11]. Under the assumption that only radiative recombination occurs, the efficiency limit is 33% for an optimum band-gap of 1.3 eV under illumination with non-concentrated light and an AM1.5g spectral distribution. The band-gap of silicon is 1.12eV and therefore the achievable efficiency is very close to the optimum value.
Experimentally, an efficiency of 24.7% [17] has been reached so far for a silicon solar cell under non-concentrated sunlight.
These values are considerably lower than the efficiency limits presented in the beginning of this chapter. The reason for this is that energy is lost in the cooling of the electrons and that photons are transmitted that have an energy below the band-gap, as it was visualized in Fig. 2.1. For a silicon solar cell, about 20% of the incident energy is lost because low-energy photons are not absorbed. The thermalization losses are specified to be around 35% of the incident energy. This value is calculated under the assumption that all electrons thermalize to the energy of the band-gap. As we have seen in this chapter, the energy distribution of the electrons has an average above the band-gap (Fig. 3.1). However, it is not the band-gap that determines the voltage, but the splitting of the Fermi levels. Additionally, to extract current, the voltage must be reduced in order to enable a current flow. So even under idealized conditions, the unavoidable losses are even higher.
In conclusion, the band-gap that played an important role in converting heat into chemical energy is also a source of fundamental losses. Therefore, most novel concepts deal with the question of how these losses associated with the band-gap can be overcome.
3.2 Novel solar cell concepts
3.2 Novel solar cell concepts
3.2.1 Thermophotovoltaic Systems
A system design that resembles the idealized system, with an absorber that powers a Carnot engine (section 3.1.1), is the thermophotovoltaic system [18, 19]. In a thermo- photovoltaic system, the sun heats an absorber. The heated absorber then radiates energy to a solar cell. A filter can be placed between absorber and solar cell that trans- mits only monochromatic radiation and is reflective otherwise. In this way, the solar cell is illuminated monochromatically. With the right band-gap, the solar cell converts the monochromatic radiation very efficiently. The radiation that is reflected by the filter heats the absorber and therefore is not lost. Also the photons emitted from the solar cell are either reflected back to the solar cell, or transmitted by the filter and used by the absorber. Since the photons emitted from the solar cell are not lost, it is not necessary to operate the solar cell at its maximum power point. The solar cell can be operated with a higher voltage close to open circuit conditions [11]. In consequence, the efficiency limit of 85.4% presented in section 3.1.1 can be achieved theoretically.
In practice the achieved efficiencies are very low and no system has been commercialized yet [20]. The reasons for this, among others, are that very high concentration is needed and that very high absorber temperatures are necessary for reasonable efficiencies, posing a serious challenge for material development.
3.2.2 Hot carrier solar cells
Another system design that avoids thermalization losses is the hot carrier cell. The idea is to extract the energy of the hot electron and hole ensembles before they cool down by interacting with the lattice [12, 21]. As mentioned before, the time scale in which thermalization usually takes place is 10-12s and is therefore very short. Since the carriers have a finite velocity, they hardly can travel a reasonable distance to the contacts in this time. Therefore, phonon interaction must be slowed down in a hot carrier solar cell. There are possibilities discussed to achieve this by nano-structuring the device such that the phonon spectrum is modified and a phonon bottleneck created [22].
In the metal contact, the charge carriers are thermalized at the lattice temperature.
Therefore the charge carriers in the metal must be prevented from interacting with the hot carriers in the solar cell. This could be achieved with energy-selective contacts, through which the hot carriers are extracted [21]. It becomes clear that the hot carrier
3.2.3 Tandem solar cells
In contrast to the rather theoretical aforementioned concepts, tandem solar cells are an already established concept to reduce the band-gap associated losses. The general idea is to combine solar cells with different band-gaps in one stack, such that each solar cell uses a different part of the solar spectrum efficiently. The solar cell with the highest band-gap must be placed on top of the stack. It absorbs all high-energy photons and transmits the photons with energies below its band-gap. Under the top cell, the solar cell with the second highest band-gap is placed and so on. Theoretically, a stack of an infinite number of solar cells could reach a maximum efficiency of 86.8% for direct sunlight [12].
In practice, three to four different solar cells are stacked on top of each other. With a system of three solar cells, the highest confirmed efficiency of 41.1% for a photovoltaic system was reached under 454 suns concentration [23]. Such tandem cells are usually made by growing several solar cells made from III-V compound semiconductors on top of each other. Therefore the solar cells are forced to be connected in series, with a tunnel diode between each pair of cells. Since in a series connection, the current through all cells must be the same, the cell with the lowest current limits the performance of the stack. Another disadvantage of this concept is that the needed cell structures are very complex and expensive to fabricate. Therefore, tandem solar cells are only used in conjunction with concentrating systems in terrestrial applications.
3.2.4 Intermediate band-gap solar cells
In a tandem solar cell, stacking different solar cells on top of each other creates different energy thresholds for the absorption of photons. An alternative approach realizes different energy thresholds within one solar cell by creating an intermediate band [24, 25]. The general idea is that a half-filled band located between valence and conduction bands creates the opportunity for lower energy photons to be absorbed. An electron can reach the conduction band by the absorption of two photons using the intermediate band as stepping-stone. On the other hand, the high-energy photons do not lose most of their energy due to thermalization as they only thermalize to the conduction band edge. A problem is that the intermediate band also creates more opportunities for recombination losses, so in practice no improvement of the solar cell performance has yet been achieved with this concept.
3.2 Novel solar cell concepts
3.2.5 Photon management
Most of the presented novel concepts require complex new solar cell structures. An alternative approach is photon management. Photon management means splitting or modifying the solar spectrum before the photons are absorbed in the solar cells, such that the energy of the solar spectrum is used more efficiently. The solar cells themselves remain fairly unchanged, and well-established solar cell technologies can be used giving the concepts high realization potential. Because of these advantages, this work will deal with different concepts of photon management.
3.2.5.1 Spectrum splitting
The high efficiencies of tandem solar cells show that by utilizing different parts of the solar spectrum with different solar cells high efficiencies can be achieved. In tandem solar cells the transmission of the upper cells determines which spectrum is used by the lower solar cells. Using selective mirrors, filters, diffraction gratings, prism etc. the solar spectrum can be split and the different parts of the spectrum can be directed to different solar cells in a more active way. The advantage is that the stack configuration of tandem solar cells is avoided. This results into a greater freedom in the choice of material from which the solar cells are produced and a greater freedom in the way the solar cells are interconnected, and a series connection is no longer inevitable.
However, most of these concepts are very complex and use only direct radiation.
A special way to realize spectrum splitting is the concept of fluorescent concentrators [7], which will be discussed in detail in the following chapter 4. Fluorescent concentrators combine spectrum splitting with concentration and are able to utilize diffuse light as well. However, we will also see in this work that fluorescent concentrators are better suited to reduce cost via concentration and the use of cheap materials than to achieve high efficiencies.
3.2.5.2 Quantum cutting
We have seen before that the energy of the incident photons in excess of the conduction band edge is transformed into heat. These losses could be reduced significantly, if more than one free charge carrier was generated by a high-energy photon. The idea of quantum cutting, which is sometimes called down conversion as well, is to transform one high-energy photon into two lower energy photons, which still have sufficient energy to generate free carriers. A system of one single junction solar cell and a quantum cutting material with one intermediate level has a theoretical
the solar cell. Any parasitic absorption or reflection of this material affects the solar cells performance negatively.
3.2.5.3 Upconversion
Upconversion of photons with energies below the band-gap is a promising approach overcoming the losses due to the transmission of these photons. An upconverter generates one high-energy photon out of at least two low-energy photons. For most materials, this involves an intermediate energy level, which is excited by the absorption of the first photon. From this level, a higher excited state can be reached after the absorption of the second photon. If the electron returns directly to the ground state via radiative recombination, one high-energy photon is emitted. Depending on the energy levels involved, this high-energy photon can create a free charge carrier in the solar cell. An additional upconverter pushes the theoretical efficiency limit for a silicon solar cell with an upconverter illuminated by non-concentrated light up to 40.2% [10].
A big advantage of upconversion is that the upconverter can be placed at the back of the solar cell, as the sub-band-gap photons are transmitted through the solar cell. In this configuration, the upconverter does not interfere negatively with the solar cell performance. All improvements are real gain, since they come on top of the original performance of the solar cell. Upconversion can be used in conjunction with classical silicon solar cells. Therefore, upconversion addresses the fundamental problem of transmission losses, while still retaining the advantages of silicon photovoltaic devices.
The concept of upconversion will be investigated in detail in chapter 5 of this work.
4 Fluorescent Concentrators
This chapter deals with fluorescent concentrators. At the beginning, I will introduce the general working principle of fluorescent concentrators and review the results achieved so far. In the following, I will present the results from optical characterization of fluorescent concentrator materials and a method to characterize the light guiding behavior of fluorescent concentrators that I developed in the context of this work. Based on the optical characterization a Monte-Carlo simulation of the concentrator’s light guiding is developed. Finally, experimental results are presented of a complete system of fluorescent concentrators and solar cells. This includes systems with different collector materials and spectrally matched solar cells, as well as systems with photonic structures that increase light collection efficiency.
4.1 Introduction to fluorescent concentrators
4.1.1 The working principle of fluorescent concentrators
Fluorescent concentrators are a special type of light concentrating device. The underlying principle was first used in scintillation counters [27, 28] and then their application to concentrate solar radiation was proposed in the late 1970s [6, 7]. In a fluorescent collector, a luminescent material embedded in a transparent matrix absorbs sunlight and emits radiation with a different wavelength. Total internal reflection traps most of the emitted light and guides it to the edges of the collector (Fig. 4.1). Solar cells optically coupled to the edges convert this light into electricity.
Different configurations are possible as well: The luminescent material can be applied in a film on a transparent slab [29] and solar cells can also be coupled to the bottom of the collector [30]. The fluorescent concentrator has many different names, e.g.
luminescent collector or organic solar concentrator. All kinds of luminescent materials can be used in a fluorescent concentrator: fluorescent materials that show a Stokes shift of the emission to longer wavelengths; phosphorescent materials; upconverters that emit one high-energy photon after the absorption of at least two low-energy photons;
and quantum-cutting materials that emit two low-energy photons after the absorption of one high-energy photon.
Fig. 4.1: Principle of a fluorescent concentrator. A luminescent material in a matrix absorbs incoming sunlight (E1) and emits radiation with a different energy (E2). Total internal reflection traps most of the emitted light and guides it to solar cells optically coupled to the edges. Emitted light that impinges on the internal surface with an angle steeper than the critical angle șc is lost due to the escape cone of total internal reflection. A part of the emitted light is also reabsorbed, which can be followed by re-emission.
This work is based on fluorescent materials. Therefore, I will use the term fluorescent concentrator for the overall concept. For clarity, fluorescent collector will identify the collector plate without attached solar cells and fluorescent concentrator system will refer to a system constructed from a collector plate with solar cells attached. In graphs the abbreviation fluko will be used to describe collector or concentrator systems, whereas the meaning will be clear from the context.
Fluorescent concentrators are able to concentrate both direct and diffuse radiation. A geometric concentration is achieved, if the area of the solar cell at the edges is smaller than the illuminated front surface of the collector, i.e. when the area from which light is collected is larger than the solar cell area. If the solar cell is illuminated with a higher intensity than it would be in direct sunlight, a real concentration is achieved.
For real concentration, high geometric concentration, as well as high collection efficiency is necessary. The ability to concentrate diffuse radiation presents a great advantage for the application of fluorescent concentrators in temperate climates, such as in middle Europe, or in indoor applications with relatively high fractions of diffuse radiation. Additionally, fluorescent concentrators do not require tracking systems that follow the path of the sun, in contrast to concentrator systems that use lenses or mirrors. This facilitates, for instance, the integration of fluorescent concentrators in buildings.
4.1 Introduction to fluorescent concentrators Fluorescent concentrators were investigated intensively in the early 1980s [8, 9].
Research at that time aimed at cutting costs by using the concentrator to reduce the need for expensive solar cells. After 20 years of progress in the development of solar cells and luminescent materials, and with new concepts, several groups such as those of Refs. [20, 30-46] are currently reinvestigating the potential of fluorescent concentrators.
4.1.2 The factors that determine the efficiency of fluorescent concentrator systems
Several factors determine the efficiency of a fluorescent concentrator system. Most of these factors are wavelength dependent. By integrating over the respective relevant spectrum, a description of the overall system efficiency with a set of efficiencies for individual processes is possible [47, 48]. The important parameters are:
Ktrans,front Transmission of the front surface in respect to the solar spectrum
Kabs Absorption efficiency of the luminescent material due to its absorption spectrum with respect to the transmitted solar spectrum
QE Quantum efficiency of the luminescent material
Kstok “Stokes efficiency”; (1-Kstok) is the energy loss due to the Stokes shift Ktrap Fraction of the emitted light that is trapped by total internal reflection Kreabs Efficiency of light guiding limited by self-absorption of luminescent
material, (1-Kreabs) is the energy loss due to reabsorption
Kmat “Matrix efficiency”; (1-Kmat) is the loss caused by scattering or absorption in the matrix.
Ktref Efficiency of light guiding by total internal reflection
Kcoup Efficiency of the optical coupling of solar cell and fluorescent collector Kcell Efficiency of the solar cell under illumination with the edge emission of the
fluorescent collector
The overall system efficiency can be calculated from the single parameters via QEK K K K K K K
K K
K . (4.1)
The transmission of the front surface is determined by its reflection R(Oinc). This is usually the Fresnel reflection, which is
2
1 1¸¸¹
¨¨ ·
©
§
inc inc
n R n
O
O O
(4.2)for normal incidence and the surface between a medium with refractive index of one and a medium with refractive index n(Oinc). The reflection of typical materials is in the range of 4% for one surface. Special layers or structures applied to the front can reduce or increase reflection. Interestingly, an antireflection coating that reduces the Fresnel reflection does not affect the total internal reflection. This can be understood by considering that total internal reflection is an effect strongly linked to refraction. Total internal reflection occurs when the light from inside the high index material impinges on the surface with an angle sufficiently shallow that the light would be refracted back into the medium again. As the antireflection coating does not change the refraction, total internal reflection is not affected either.
The absorption spectrum Abs(Oinc) determines the absorption efficiency. A large fraction of the solar spectrum is lost, because many luminescent materials only absorb a narrow spectral region. The absorption range of typical fluorescent organic dyes is only about 200 nm in width.
The quantum efficiency QE of the luminescent material is defined as the ratio of emitted photons to the number of the absorbed photons. For organic dyes the fluorescent quantum efficiency can exceed 95%.
The energy of the emitted photons is usually different from the energy of the absorbed photons. For most luminescent materials, a Stokes shift to lower energy occurs. This means that the emitted photons possess less energy than the absorbed ones. Therefore the wavelength of the emitted photons Oemit is different from the wavelength of the incident photons Oinc. As we will see in section 4.2, this Stokes shift is of critical importance to the ability of the fluorescent concentrator to concentrate light.
The luminescent material emits light isotropically in a first approximation. All light that impinges on the internal surface with an angle smaller than the critical angle Tc(Oemit)leaves the collector and is lost (Fig. 4.1). The critical angle is given by
¸¸¹·
¨¨©
§
emit
c O nO
T arcsin 1 . (4.3)
4.1 Introduction to fluorescent concentrators This effect is also called the escape cone of total internal reflection. The light which impinges with greater angles is totally internally reflected. Integration gives a fraction
2
1
emittrap
O n O
K
(4.4)of the emitted photon flux that is trapped in the collector [49]. For PMMA (Polymethylmethacrylate) with n = 1.5, this results in a trapped fraction of around 74%, which means that a fraction of 26% is lost after every emission process. The 26%
account for the losses through both surfaces. An attached mirror does not change this number, as with a mirror the light leaves the collector through the front surface after being reflected.
The absorption spectrum and the emission spectrum overlap. For principal reasons, absorption must be possible in the spectral region where emission occurs. Therefore, part of the emitted light is reabsorbed. Again, the energy loss due to a quantum efficiency smaller than one occurs, and again radiation is lost into the escape cone.
Realistic matrix materials are not perfectly transparent. They absorb light and they scatter light so it leaves the collector.
Total internal reflection is a loss-free process. However, the surface of the fluorescent collector is not perfect. Minor roughness at the surface causes light to leave the collector, because locally the light hits the uneven surface with a steep angle.
Fingerprints and scratches can seriously harm the efficiency of the light guiding.
The fluorescent collector and the solar cell have to be optically coupled. Otherwise, reflection losses occur at the interface between collector and air and again at the interface air to solar cell. However, the optical coupling can also cause losses: Light can be scattered away from the solar cell or parasitic absorption can occur.
Finally, the solar cell has to convert the radiation it receives from the collector into electricity. Again, a whole set of parameters determine this process, ranging from reflection and transparency losses, to thermalization and electrical losses.
This description is not very relevant for actually calculating the efficiency of fluorescent concentrator systems, because some of the involved efficiencies are neither easy to calculate nor directly accessible by measurement. Nevertheless, this description illustrates very well the effects that affect the efficiency of fluorescent concentrator systems.
4.1.3 Fluorescent concentrator system design
Many system designs have been proposed for efficient and economic fluorescent concentrator systems. Probably the most fundamental one was the concept to stack several collector plates [7]. With different dyes in each plate, different parts of the spectrum can be utilized (see Fig. 4.2). At each fluorescent collector, a solar cell can be attached, which is optimized for the spectrum emitted from the collector. With this spectrum splitting, high efficiencies can be achieved in principle. The stack design with the matched solar cells at the edges provides a high degree of freedom for cell interconnection. Therefore, there is no forced series connection like in tandem cell concepts, which causes current limitation problems. Additionally, no tunnel diodes are necessary.
Fig. 4.2: Concept of stacked fluorescent concentrators, as presented in [7]. (a) The different collectors C1-C3 are connected with different solar cells S1-S3. In each collector, a different dye is incorporated. The absorption and emission (shaded) spectra of the different dyes are shown in (b). With a proper alignment of the absorption and emission properties, the recycling of photons lost from one collector in another collector is possible. It is important that an air gap between the different collectors is maintained so that each spectral range of light is guided in one collector by total internal reflection and does not get lost in adjacent collectors.
The possibilities to realize systems in this configuration were limited during the first research campaign in the 1980s because the range of solar cell materials with different band-gaps was very limited. The situation has improved considerably in the interim, so in Chapter 4.5 a detailed investigation of stack systems with spectrally matched solar cells will be presented.
4.1 Introduction to fluorescent concentrators Fig. 4.2 shows mirrors at some of the edges of the collector plate as well. If some edges are not covered with solar cells, but with reflectors, the geometric concentration is increased. This can be beneficial for the costs of the fluorescent concentrator system, as solar cells are usually the most expensive component of the system. However, the reflection on mirrors is not free of losses. Therefore, it should be kept to a minimum and the emitted light should reach the solar cells with as few reflections on mirrors as possible. For this purpose, an isosceles and rectangular triangular shape of the fluorescent collector is beneficial [7]. With solar cells at the hypotenuse and the two other sides covered with mirrors, only two reflections are necessary at most until the emitted light hits a solar cell.
A reflector underneath the collector increases the collection efficiency as well. It reflects transmitted light back into the collector and creates a second chance for absorption. When a white reflector instead of a mirror is used, light can also be scattered and redirected towards the solar cells. Both for reflectors underneath the collector and for mirrors at the edges, it is beneficial to maintain an air gap between collector and reflector. In this configuration, the reflection of the reflector comes on top of total internal reflection. However, with an air gap the diffuse reflector does not change the direction of light emitted into the escape cone to directions that are subject to total internal reflection. The reason for this is that due to refraction, the light that leaves the collector is already distributed over a complete hemisphere, even before it hits the diffuse reflector. This is not changed by diffuse reflection. So consequently, when the light enters the collector again, it is refracted into exactly the angles of the escape cone.
Another idea to increase the geometric concentration was proposed in [50]. The angular range of the edge emission of the fluorescent concentrator is limited by the critical angle of total internal reflection. Therefore, a further concentration is possible until the divergence reaches the full hemisphere. Compound parabolic concentrators, which are attached to the edges, are one possibility for this purpose.
As mentioned before, no luminescent materials that are active in the infrared and show high quantum efficiency, high stability, and broad absorption have been developed so far. Therefore, a range of designs were proposed to utilize the infrared radiation. The infrared light transmitted through the collector could be used by a thermal collector. It was also suggested to use an upconverter to convert the transmitted radiation into light that could be collected by the fluorescent collector [48]. The transmitted light can also
