NOVEL SOLAR CELL CONCEPTS

Transcription

1 NOVEL SOLAR CELL CONCEPTS 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

2 Dissertation der Universität Konstanz Tag der mündlichen Prüfung: Referent/in: Prof. Gerhard Willeke Referent/in: Prof. Thomas Dekorsy

3 1 Table of contents 1 Table of contents... i 2 Motivation and Introduction Motivation Why it is essential to transform the global energy system? Why photovoltaics? Why new concepts for higher efficiencies? Photon management for full spectrum utilization Main objectives of this work Structure of this Work Efficiency limits of photovoltaic energy conversion and novel solar cell concepts A short theory of solar cells Thermodynamic efficiency limits Generating chemical energy Extracting useful energy The pn-structure Novel solar cell concepts Thermophotovoltaic Systems Hot carrier solar cells Tandem solar cells Intermediate band-gap solar cells Photon management Fluorescent Concentrators Introduction to fluorescent concentrators The working principle of fluorescent concentrators The factors that determine the efficiency of fluorescent concentrator systems Fluorescent concentrator system design i

4 1 Table of contents Materials for fluorescent collectors Fluorescence Theoretical description of fluorescent concentrators Maximum concentration and Stokes shift Thermodynamic model of the fluorescent concentrator Photonic structures Optical characterization of fluorescent concentrator materials Photoluminescence measurements Characterizing the light guiding of fluorescent concentrators Measuring the angular distribution of the guided light Short summary of the optical characterization Simulating fluorescent concentrators Monte Carlo simulation The used model Results of simple model Improvements of model Conclusions from simulation Fluorescent concentrator systems Solar cells for fluorescent concentrator systems Systems with different materials Systems with silicon bottom cells The effect of photonic structures The influence of system size on collection efficiency The future of fluorescent concentrators The Nano-Fluko concept ii

5 1 Table of contents 5 Upconversion Introduction to upconversion The potential of upconversion and ways to increase upconversion efficiency The potential of upconversion Definition of upconversion efficiency Upconversion efficiencies achieved so far Spectral concentration An advanced system design for spectral concentration Enhancing upconversion efficiency by plasmon resonances Upconversion mechanisms and their theoretical description Absorption and emission Migration of excitation energy Multi-phonon relaxation Intensity dependence of upconversion Suitable materials for upconversion Theoretical aspects of the energy spectrum of trivalent erbium Optical material characterization Absorption measurements The Kubelka-Munk theory Absorption coefficient and Einstein coefficients Time-resolved photoluminescence Intensity dependent upconversion photoluminescence Calibrated photoluminescence measurements Optical properties of luminescent nanocrystalline quantum dots (NQD) Simulating upconversion The rate equation model Input parameters iii

6 1 Table of contents Simulation results Upconversion systems Used solar cells and experimental setup Applying the upconverter to the solar cell External quantum efficiency with different upconverter samples Upconversion solar cell system under concentrated sunlight Conclusions and outlook on the application of upconverting materials to silicon solar cells Summary Fluorescent concentrators Upconversion Deutsche Zusammenfassung Fluoreszenzkonzentratoren Hochkonversion References Appendix Abbreviations Glossary Physical Constants Author s Publications Refereed journal papers Conference papers Oral presentations Patents Other publications Curriculum vitae Acknowledgements iv

7 2 Motivation and Introduction 2.1 Motivation 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 ecological and social criteria [1]. Such criteria are the mitigation of climate change, conservation 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 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 energy, water power, and biomass originate from solar energy, but their sustainably usable potential is not sufficient to meet the global energy demand [1]. The technology 1

8 2 Motivation and Introduction 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 Why new concepts for higher efficiencies? Crystalline silicon is the dominant material in the production of solar cells. It is nontoxic and abundant. At the moment the material costs for silicon in the required purity dominate the costs for solar cell production. Therefore, alternative production technologies, 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

9 2.1 Motivation 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 efficiencylimiting 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 can be used. This gives the concepts high realization potential. Because of these advantages, this work will deal with different concepts of photon management. 3

10 2 Motivation and Introduction 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 4

11 2.3 Structure of this Work generates one high-energy photon out of at least two low-energy photons. This highenergy 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 NaYF 4. 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, experimental investigations on systems with upconverting material attached to silicon solar cells will be presented. 5

12 2 Motivation and Introduction 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. 6

13 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 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 T S being the temperature of the sun and T 0 the ambient temperature, the Carnot efficiency is T 1 0. (3.1) T S With T S = 6000 K and T 0 = 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 processes that generate no extra entropy. Unfortunately, these processes are infinitely slow so the working power of a Carnot engine is infinitesimally small. 7

14 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts 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 T A equals T S the efficiency is zero, because the absorber would emit as much energy as it receives. When T A = T 0 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 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 s) 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

15 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 s the electrons and holes cool down to the ambient temperature. For the population of the energy levels dn e /de e and dn h /de h 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 E FC can be identified as the electrochemical potential e of the electrons [5], and the Fermi energy of the holes in the valence band E FV can be identified as minus one times the electrochemical potential h of the holes. Consequently, the difference of the Fermi energies equals the sum of the electrochemical potentials: E FC - E FV = e + h = e + h =: eh (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 excited state remains: the heat or thermal energy contained in the thermal solar radiation has been converted into chemical energy. 9

16 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts 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 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 pnjunction. 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 eh 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 j eh gives the extracted power density p ext : p ext = j eh. eh (3.3) The particle flux j eh that can be extracted from an illuminated semiconductor is given by the difference of the rates of generation g eh and recombination r eh (in this case the rates are defined per area): j eh = g eh - r eh. (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] B p, 2 2 n( ) c T,, 2 2 1, h exp 1 kbt (3.5) where is the frequency of the photons, T the temperature of the emitter, µ the chemical potential within the emitter (which has to be identified with eh in this case), n() is the refractive index into which the emission takes place, is the absorption coefficient, c the speed of light in vacuum, h the Planck constant and k B the Boltzmann 10

17 3.1 A short theory of solar cells constant. With this definition, B p, cos() da d d is the number of photons emitted from the surface element da in the frequency range of to +d into the solid angle d into the direction given by the polar angle and an azimuth angle. 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 j eh * eh 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 OC, 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 j eh g eh const eh kbt exp. (3.6) The structure of equation (3.6) is quite similar to that of the IV-characteristic of a pnjunction 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 characteristic is mainly determined by processes in the region close to the pn-junction. In this so-called space charge region, the recombination rate depends on the product of 11

18 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts 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 j eh and the extracted power depend on the sum of chemical potentials of the electrons and holes in the semiconductor eh [11]. At eh = OC all photons are emitted, so the extractable current is zero. Therefore the extracted power j eh * eh is zero as well. At eh = 0 the extracted current is at its maximum j SC, because the radiative recombination is at its minimum. Nevertheless, because of eh = 0 the extracted power is again zero. In between, a maximum power point (MPP) exists, at which the extracted power reaches its maximum j mpp * mpp (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 = T s and = 0, describes as well the absorbed photon flux 12

19 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 g eh. Because the concentration of electrons and holes rises, the chemical potential is also higher with concentration. In consequence, more power j eh * eh 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 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 electrochemical potential of the respective kind of charge carrier (considering the sign of its charge). Gradients in this electrochemical potential cause the charge carriers to flow in a certain direction. For instance, the particle flux density of the electrons is [11] 13

20 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts j eh = - n e /q m e grad(e FC ), (3.7) with n e being the electron concentration, q the elementary charge and m e 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 j e + q j h, (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 V cell 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 pnjunction. 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 14

21 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 E FC and E FV 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 J SC. 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 V OC 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 V cell 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. 15

22 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts Fig. 3.5: Illuminated pn-structure under open circuit conditions. At the open circuit voltage V OC the gradients of the electrochemical potentials across the pnjunction 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 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. 16

23 3.2 Novel solar cell concepts 3.2 Novel solar cell concepts 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 thermophotovoltaic 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 transmits 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 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 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 s 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 solar cell is a very demanding system design. Accordingly, no hot carrier solar cells have yet been successfully realized. 17

24 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts 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 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. 18

25 3.2 Novel solar cell concepts 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 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 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 efficiency limit of 39.6% [26]. The problem of this concept is that some kind of luminescent material that performs the down conversion has to be placed in front of 19

26 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts the solar cell. Any parasitic absorption or reflection of this material affects the solar cells performance negatively 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. 20