Towards High-Efficiency Organic Solar Cells

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U

NIVERSITÀ DI

P

ISA

Dipartimento di Ingegneria Civile e Industriale

C

ORSO DI

L

AUREA

M

AGISTRALE IN

I

NGEGNERIA

M

ECCANICA

T

ESI DI

L

AUREA

Towards High-Efficiency Organic

Solar Cells

Relatori:

Candidato: Prof. Ing. Renzo Valentini

Alessio Cinopri Prof. Ing. Kee Moon

Prof. Ing. Khaled Morsi

Anno Accademico 2013/2014

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Abstract

In this research, we investigate the fundamental sciences and challenges that

need to be addressed in the production of flexible organic solar cell using

microfabri-cation techniques. The major focuses of the study are the determination of optimized

conditions and processes for depositing the photoactive layer, anodic layers, and

met-al cathodic layers. Along with, this research investigates and solves the engineering

and production problems associated with the prototyping system.

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List of Figures

1.1 U.S. energy consumption, 2012. . . 11 1.2 Projections on grid parity in the U.S. . . 12 1.3 Reported timeline of solar cell energy conversion eciencies. . . . 13 1.4 Theorical limits of solar cells depending on the band gap of

pho-toactive material. . . 14 2.1 Power spectrum of a black body sun at 5760K, and power

avail-able to the optimum band gap cell. . . 17 2.2 Band diagram of a silicon solar cell, under short circuit conditions. 18 2.3 Valence and conduction bands in conductor, semiconductor, and

insulator. . . 19 2.4 Drift. Carriers ow under an electric eld in order to reduce their

electrical potential energy. Electrons and holes drift in opposite directions. . . 22 2.5 Schematic energy diagram of a metal. . . 24 2.6 Schematic energy diagram of a n-type semiconductor. . . 25 2.7 (a) Band proles in isolation. (b) Band prole of a junction in

equilibrium. . . 26 2.8 Band prole of the semiconductor-metal junction under

illumina-tion at open circuit. The accumulaillumina-tion of photogenerated elec-trons in the n-type semiconductor raises electron Fermi level and generates a photovoltage, V. . . 28 2.9 Reverse and forward bias in a Schottky barrier junction in the

dark. . . 28 2.10 Schematic current-voltage characteristic of a Schottky barrier

junction in the dark. . . 28

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3.2 I-V curve of a solar cell. When there is no light present to gen-erate any current, the solar cell behaves like a diode. . . 36 3.3 Maximum-power point and other operating parameters. . . 38 3.4 Graphical interpretation of FF. . . 40 3.5 Resistances at ISC and at VOC. Typical parameters calculed by

the Solar Simulator. . . 41 3.6 Eect of shunt resistance on the currentvoltage characteristics

of a solar cell. . . 42 3.7 Eect of series resistance on the current-voltage characteristics of

a solar cell. . . 43 3.8 Eect of temperature on the current-voltage characteristic of a

solar cell. . . 45 3.9 I-V Curve of solar cell without light excitation. . . 46 3.10 Eect of reverse saturation current on the current-voltage

char-acteristics of a solar cell. . . 47 3.11 Eect of ideality factor on the current-voltage characteristics of

a solar cell. . . 47 3.12 Variation of the conversion eciency with the concentration of

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4.1 Energy-level diagram for an excitonic solar cell. Excitons created in the rst organic semiconductor (OSC1) and second organic semiconductor (OSC2) do not have enough energy to dissociate in bulk. But the band oset between OSC1 and OSC2 provides an exothermic pathway for dissociation of excitons in both phases. The band oset must be greater than the exciton binding energy for dissociation to occur. . . 52 4.2 Band diagram of a semiconductor showing the dierence between

electron anity (EEA) and work function (W ). . . 53

4.3 Schematic representation of inorganic Wannier excitons and or-ganic Frenkel excitons and relative diagram Coulombic potential vs size. . . 55 4.4 Sketch of a single layer organic photovoltaic cell. . . 60 4.5 Energy level schemes for photon-induced excitation (ex) and

emis-sion (em) of organic single layer type photovoltaic cell with a small work function electrode (SWFE) metal. . . 61 4.6 Sketch of a dispersed junction photovoltaic cell. . . 62 4.7 Schematic comparison of photocarrier generation processes of (a)

classic inorganic p-n junction bilayer solar cells with free holes and electrons and (b) organic D/A junction bilayer type solar cells with excitons as (+-). . . 63 4.8 Energy level schemes of (a) inorganic p-n bilayer and (b) organic

D/A bilayer type photovoltaic cells in open circuit voltage mode. 64 4.9 Sketch of a bulk heterojunction photovoltaic cell. . . 65 4.10 Energy level schemes of a bulk heterojunction photovoltaic cell in

(a) open-circuit voltage mode and (b) short-circuit current mode. 65 5.1 Typical device structures of single junction polymer solar cells. . 67 5.2 Schematic variation of VOC with the acceptor strength (VOC1)

and/or electrode work function (VOC2) in a BHJ solar cell device. 69

5.3 Schematic band diagram of a metalinsulatormetal (MIM) de-vice with (a) non-ohmic and (b) ohmic contacts for electrons and holes. Before (upper image) and after contact (lower image) un-der short-circuit conditions. ϕb and 4Vbare the injection barrier

height for electrons at a non-ohmic contact and the voltage loss at an ohmic contact, respectively. ϕM 1 and ϕM 2are work functions

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tions for metals. . . 73 5.8 Schematic pictures displaying the changes in the P3HT:PCBM

blend lm as a result of annealing. . . 75 5.9 Currentvoltage characteristic curves of P3HT:PCBM solar cells

with dierent treatments. Data is shown for three varying heat treatments of (i) no thermal annealing (opensquares), (ii) thermal annealing at 70 °C (opentriangles) and (iii) thermal annealing at 150 °C (lled squares). . . 75 5.10 Calculated zero-eld mobilities of electrons (lled circles) and

holes (open circles) for P3HT:PCBM devices as a function of annealing temperature. As a reference, the calculated zero-eld mobility of holes (opentriangles) in pristine P3HT is also displayed. 77 5.11 Power conversion eciency versus thermal annealing temperature

for P3HT:PCBM devices, with a constant annealing time of 15 min. . . 77 5.12 The combined eect of tuning the LUMO(A)-LUMO(D) oset to

0.5 eV and changing the polymer band gap. . . 79 5.13 Schematic representation of (a) generic morphology (b) vertical

phase separation in which it is possible to notice the absence of trapping sites. . . 81 5.14 Plots of (a) JSC and (b) P CE as a function of thickness of active

layer with dierent domain size. . . 82 5.15 Absorption spectra of glass and ITO glass. . . 84

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5.16 (a) (Left) JV characteristics of devices with non-annealed P3HT:PCBM layer (70 nm) and non-annealed PEDOT:PSS layer of which thick-ness is 0 (ITO only; black line), 60 (gray line), 65 (orange line), 70 (purple line), 85 (sky blue line), 100 (blue line), 110 (green line), and 165 nm (red line). (Right) Ideal at energy band diagram for the device with the PEDOT:PSS layer. . . 86 5.17 Optimized J V characteristics PEDOT : PSS HTL with a

com-parison to a control device without a HTL. . . 87 5.18 Electric eld intensity for ITO/HTL/PCPDTBT:PCBM/LiF/Al

devices where the HTL is (a) 41 nm PEDOT:PSS (b) 130 nm PEDOT:PSS. . . 89 5.19 Work function (WF, top panel) and conductivity (σ, bottom

panel) of PEDOT:PSS layers (70 nm thick) as a function of an-nealing temperature. . . 90 5.20 JSC, VOC, F F , and P CE as a function of PEDOT:PSS annealing

temperature. . . 90 5.21 Brightness vs current and brightness vs voltage (the inset) of

OLEDs built on ITO treated in dierent ways. . . 92 5.22 Current density-voltage (J-V) characteristics of OPV devices

fab-ricated using four dierent ITO substrates: PET (Tg∼ 78°C )/ITO

(510 Ω/sq), PES (Tg ∼ 120 °C )/ITO (160 Ω/sq), PEN (Tg ∼

220°C )/ITO (21 Ω/sq), Glass (Tg> 500°C )/ITO (6 Ω/sq). . . 94

5.23 Current density-voltage (J-V) characteristics of OPV devices fab-ricated using four dierent ITO substrates. . . 95 5.24 Diagram of HOMO/LUMO for organic materials and work

func-tions for metals. . . 97 5.25 Reectivity spectra of dierent thicknesses of Ca on 150 nm Ag. 98 5.26 (a) I-V characteristics of typical MDMO-PPV/PCBM solar cells

with a LiF/Al electrode of various LiF thickness compared to the performance of a MDMO-PPV/PCBM solar cell with a pristine Al electrode; (b) Solar cell characteristics for various LiF thick-ness compared to a solar cell with a pristine Al electrode. . . 100 6.1 ITO glass slides purchased from Delta Technologies and Kapton

tape. . . 101 6.2 DI water, acetone, isopropyl and sonicator. . . 102 6.3 One of the hot plate used in Cleanroom. . . 103

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6.13 Cut-away view of an Oriel Solar Simulator. . . 108

6.14 Oriel® Sol1A Class ABB Solar Simulator in MEMS lab. . . 108

6.15 Typical I-V curve obtained from a photovoltaic device. . . 109

6.16 TM3000 Tabletop Microscope from Hitachi. . . 109

7.1 Details of a cell obtained with this process. . . 111

7.2 Resistance vs Thickness of Orgacon IJ-1005. . . 112

7.3 Details of a exible cell obtained with this process. . . 114

7.4 Details of a glass cell obtained with this process. . . 115

7.5 I-V curve of 10.79% eciency device. . . 116

7.6 Architecture of a 2D and a 3D organic PV cell. . . 116

7.7 Spray coated cells with SU-8 pillars (left), pressed PET pillars (bottom), 2D cell (right). . . 117

7.8 Deatail of SU-8 pillars (left) and pressed PET pillars (right). . . 118

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List of Tables

7.1 Anode comparison, ITO anode works better but not signicantly. 111 7.2 NREL-certied performance data of Plexcore® PV 1000 Ink

Sys-tem. . . 113 7.3 Characteristic results and peak eciency for our experiments. . . 113 7.4 Characteristic results and peak eciency for our experiments.

Cells are made on PET/ITO substrates. . . 114 7.5 Average results and peak eciency for our experiments. . . 115

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dard of living, however, are not without costs. The evidence for anthropogenic global warming, due primarily to the combustion of fossil fuels, is overwhelm-ing. Preventing an environmental catastrophe will require an end to the fossil fuel addiction. The Intergovernmental Panel on Climate Change produced an extensive report in 2007 outlining the threats brought by greenhouse gases. Ac-cording to this report, it is necessary to cap the atmospheric carbon dioxide concentration at a threshold beyond which drastic climatic change would likely be inevitable. According to some scientists is already past a safe threshold.

Since a return to a pre-industrial era is impossible, renewable energy (wind, solar, hydroelectric or geothermal) will have to supply a signicant portion of our power. Among these, solar energy conversion is perhaps the most appealing since the energy source is readily available and practically inexhaustible. The sun provides more than enough energy to meet global demands. Incoming solar radiation is roughly 10,000 times the global power consumption. In 2012 solar supplied a very small portion of the nation's energy, about 2% of the renew-able energy as shown in a report from U.S. Energy Information Administration (Figure 1.1). This small market share is a result of the high cost of manufac-turing and installing photovoltaics. Many costs are proportional to the panel area or land area involved. A higher eciency cell may reduce the required

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Figure 1.1: U.S. energy consumption, 2012.

space and so reduce the total plant cost, even if individual cells are more costly. Installation costs have reduced only slowly, because of its reliance on human labor. As total energy consumption continues to increase at a rate of 5% per year globally, there remains a large gap between the adoption of solar power and continued use of nonrenewable energy, such as that produced from fossil fuels. One of the main factors in sustaining this gap is the need for the cost to energy production ratio for solar devices to decrease over that for conventional sources. Grid parity occurs when an alternative energy source can generate electricity at a levelized cost that is less than or equal to the price of purchasing power from the electricity grid. Reaching grid parity is considered to be the point at which an energy source becomes a contender for widespread development without sub-sidies or government support. With help from government subsub-sidies, grid parity has been reached in some locations with on-shore wind power in 2000, and with solar power in 2013. Solar PV power should hit grid parity in the U.S. (on average) between 2014 and 2017 according to projections, as shown in Figure 1.2 by GBI Research.

The potential for organic solar cells has been recognized to greatly inuence solar power adoption by oering lower cost options as well as more design and

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Figure 1.2: Projections on grid parity in the U.S.

environmentally friendly options compared to what most conventional solar cell technologies oer today. The scale-up process is continuously being improved with a goal of producing commercial grade solar panels with a competitive eciency and price point. While the eciencies for conventional silicon cells are amongst the highest, the applications for these cells are limited by their rigidity and heaviness. Thin-lm solar cells are favorable alternatives to conventional silicon solar cells in terms of cost and design capabilities. In comparison to a bulk silicon solar cell, which is typically made by encapsulating wafers of rened silicon under rectangular sheets of glass, a thin-lm photovoltaic cell is made by depositing thin layers of photovoltaic material onto a substrate. The thickness range of the layers can vary from a few hundred nanometers to tens of micrometers. Because less material is used, thin-lm solar cells are also usually less expensive than conventional silicon solar cells. In addition, the manufacturing costs are often reduced due to dierent processing techniques that can be utilized and the versatility of the materials. However, inorganic thin-lm cells based on materials such as cadmium are highly toxic and supplies are very limited and costs results higher than that of organic think-lm photovoltaic cells. Figure 1.3, obtained from NREL, shows the research based conversion eciencies achieved worldwide from 1976 through 2014 for various photovoltaic technologies.

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Figure 1.4: Theorical limits of solar cells depending on the band gap of pho-toactive material.

As the emerging organic solar cell data points can be seen in the bottom right of the gure, it is apparent that organic PV technology has signicant room for growth in terms of eciency. Single pn junction crystalline silicon devices are now approaching the theoretical limiting power eciency of 33.7%, noted as the ShockleyQueisser limit in 1961.1 _{In the extreme, with an innite}

number of layers, multijunction, the corresponding limit is 86% using concen-trated sunlight.2 _{In 2014, Panasonic broke the record of 25.6% for a silicon}

solar cell. In September 2013, a four-junction solar cell achieved a new labora-tory record with 44.7% eciency, as demonstrated by the German Fraunhofer Institute for Solar Energy Systems. However, bulk-silicon solar cells with high eciency are expensive for mass production. Multijunction cells were originally developed for special applications such as satellites and space exploration. That results in today's commercial solar cells to have typical eciency of around 14 ÷ 17%. Interest in OPVs began in the 1990s when Sariciftci et al. demon-strated photo-induced charge transfer between organic molecules in 1992.[39] Commercial success, however, requires that eciencies increase. The current

1_{Silicon has an energy band gap of 1.14 eV at 0}◦_C_.

2_{Each layers has a dierent band gap energy to allow it to absorb electromagnetic radiation}

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record PCE for an organic solar cell is 11.1% and is held by Mitsubishi Chem-ical Corporation (2013). Kirchartz et al. calculated the maximum theoretChem-ical eciency for OPVs of 23% for a bulk heterojunction organic solar cell according to ShockleyQueisser limit.[40]3_{Over the last two decades, OPVs have garnered}

serious attention because they have the potential to be an economically viable source of renewable energy. Polymers can be produced cheaply, and since plas-tics have a high optical absorption coecient, very little material is needed. In addition, polymers can be dissolved in solvents and deposited on substrates using wet-processing techniques such as spin coating or roll-to-roll printing. So-lution processing makes large-scale, low-cost production a possibility. Organic solar cells are also attractive because they lack a rigid crystalline lattice and can be deposited on exible substrates. Intensive research has focused on im-proving eciencies of solar cells, and PCEs have signicantly improved over the last decade. This has been made possible by the introduction of new materials, improved engineering methods for materials, and cheaper manufacturing pro-cedures (roll-to-roll). The organic solar cell industry has proted from the de-velopment of organic light emitting diodes based on similar technologies, which have been recently introduced into the market. Furthermore, the production of high eciency silicon cells requires many energy intensive processes at higher temperatures of 400 ÷ 1400 ◦_C_{, and high vacuum conditions with relatively}

costlier manufacturing process. In comparison, organic solar cells require sim-pler processing at much lower temperature of around 20 ÷ 200◦_C_{. These can}

be manufactured on exible substrates using simple and comparatively cheaper material deposition methods at room temperature.

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into internal energy for the purpose of either direct heating or indirect electrical power generation from heat. Solar thermal converters utilise the full range of solar wavelenghts, including the infrared, and are thermally insulated from the ambient to make the working temperature dierence as large as possible.

A photovoltaic converter is designed to convert the incident solar energy mainly into electrochemical potential energy. Absorption of a photon in mat-ter causes the promotion of an electron to a state of higher energy (an excited state). Unlike the solar thermal converter, the photovoltaic converter extracts solar energy only from those photons with energy sucient to bridge the band gap. These higher energy photons will be absorbed by the solar cell, but the dif-ference in energy between these photons and the material band gap is converted into heat (via lattice vibrations, called phonons) rather than into usable elec-trical energy. Since these photons mainly increase the electrochemical potential energy the increase in internal energy is much less. In addition the increase in temperature can decrease the eciency of photovoltaic conversion and so photovoltaic cells are usually designed to be in good thermal contact with the ambient. To complete the photovoltaic conversion process the excited electrons are extracted and collected (charge separation process) and then they travel to an external circuit and doing electrical work.

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Figure 2.1: Power spectrum of a black body sun at 5760K, and power available to the optimum band gap cell.

2.1 Requirements and limits for a photoconverter

The photovoltaic material needs an energy gap which separates states which are normally full from states which are normally empty. Semiconductors satisfy both the condition of the energy and the need of conductivity. With band gaps in the range 0.5 ÷ 3 eV semiconductors can absorb visible photons to excite electrons across the band gap, where they may be collected.

The most popular solar cell material, silicon, is not the best for its band gap (1.1 eV , maximum eciency 29%) but is cheap and abundant compared to other compund materials such as gallium arsenide (GaAs, 1.42 eV ) and indium phosphide (InP, 1.35 eV ) with band gaps close to the optimum and favoured for high eciency cells.[1]

The material should guarantee a spatial asymmetry to the promoted elec-trons in order to drive them away from the point of promotion (charge separation process). This can be an electric eld or a gradient in electron density. To con-duct the charge to the external circuit the material should be a good electrical conductor. Photogenerated carriers must not recombine giving up energy to the medium (non-radiative recombination) and there should be no resistive loss (no series resistance) or current leakage (parallel resistance).

By considering the principle of detailed balance it's possible to calculate ab-solute limiting eciency: any body which absorbs light must also emit light.

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Figure 2.2: Band diagram of a silicon solar cell, under short circuit conditions. A photovoltaic device will emit more light when optically excited on account of the extra electrochemical potential energy of the electrons. This radiative recombination is the mechanism which ultimately limits the eciency of a pho-tovoltaic cell. The current delivered by the ideal photoconverter is due to the dierence between the ux of photons absorbed from the sun and the ux of photons emitted by the excited device, while the voltage is due to the electro-chemical potential energy of the excited electrons. So a theoretically ideal solar cell will have around 33% eciency at a band gap of 1.4 eV for a standard solar spectrum.[2]

2.2 Electrons and holes in semiconductors

As we mentioned before, a suitable photovoltaic material should absorb visible light, possess a band gap between the initial occupied states and the nal, unoc-cupied states. The gap is necessary in order to make the extra potential energy which electrons gain from photon absorption available as electrical energy. All semiconducting and insulating solids possess an energy band gap but only semi-conductors are suitable for photovoltaics, because the band gap of insulators

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Figure 2.3: Valence and conduction bands in conductor, semiconductor, and insulator.

is too large to permit absorption of visible light. The band gap is important because it eneables excited electrons to remain in higher energy levels for long enough to be exploited. If electrons were simply promoted through a continuum of energy levels as in a metal, for example, they would very quickly decay back down to their ground state.

The electrons of a single isolated atom occupy atomic orbitals, which form a discrete set of energy levels. If multiple atoms are brought together into a molecule, their atomic orbitals will combine to form molecular orbitals each with a dierent energy, but in the same number. As more and more atoms are brought together, the molecular orbitals extend larger and larger, and the energy levels of the molecule will become increasingly dense, eventually, forming a solid. And in this case the energy levels are so close that they can be considered to form a continuum. Band gaps are essentially leftover ranges of energy not covered by any band, a result of the nite widths of the energy bands. Two adjacent bands may simply not be wide enough to fully cover the range of energy. The highest occupied band, which contains valence electrons, is called the valence band (VB). The lowest unoccupied band is called the conduction band (CB).

If the valence band is partly full, or if it overlaps in energy with the lowest unoccupied band, the solid is a metal. In a metal, the availability of empty states at similar energies makes it easy for a valence electron to be excited, or scattered, into a neighbouring state. These electrons can act as transporters of heat or charge, and so the solid conducts heat and electric current. If the valence band is completely full and separated from the next band by an energy gap,

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Current conduction in these materials occurs through the movement of free elec-trons and holes, known as charge carriers. At absolute zero temperature, a pure semiconductor is unable to conduct heat or electricity since all of its electrons are involved in bonding. As the temperature is raised, the electrons gain some kinetic energy from vibrations of the lattice and some are able to break free (heating provides energy to promote some electrons across the band gap). The freed electrons have been excited into the conduction band and are able to travel and transport charge or energy. Meanwhile, the vacancies which they have left behind are able to move and can also conduct. The higher the temperature, the grater the number of electrons and holes which are mobilised, and the higher the conductivity. The electrons do not stay indenitely in the conduction band (due to the natural thermal recombination) but they can move around for some time. When an electron is removed from a bond between atoms, a positively charged vacancy remains. This vacancy can be lled by another electron, most easily by electrons which are involved in neighbouring bonds. If this happens, the vacancy moves to the neighbouring bond. The creation of holes in the valence band creates a means whereby charge can be transferred. In the presence of an electric els, a bonding, or valence, electron can respond to the eld by mov-ing into the hole. The vacancy which it leaves behind can be lled by another valence electron, and so on.

A semiconductor can be made to conduct in other ways: if the material is exposed to light of energy greater than the band gap, a photon can be absorbed by a valence electron to free it from the lattice and promote it into the con-duction band. This creates a vacancy in the valence band. The free electron and hole created in this ways are available to conduct electricity. This is called photoconductivity. Alternatively, impurities with dierent numbers of valence

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electrons or dierent bond strenghts can be added to the material. Electrons or holes may be freed more easily from these impurities than from the native atoms, thereby increasing the number of carriesrs normally available for con-duction compared to the pure semiconductor. Deliberate addition of impurities to increase conductivity in this way is called doping.

2.3 Doping

When a crystal is altered by introducing an impurity atom or a structural defect, the impurity or defect introduces bonds of dierent strength to those which make up the perfect crystal, and therefore changes the local distribution of electronic energy levels. The altered energy levels are localised unless the density of defect is very high.

The materials chosen as suitable dopants depend on the atomic properties of both the dopant and the material to be doped. In general, dopants that produce the desired controlled changes are classied as either electron accep-tors or donors. Semiconducaccep-tors doped with donor impurities are called n-type, while those doped with acceptor impurities are known as p-type. The n and p type designations indicate which charge carrier acts as the material's majority carrier. In n-type semiconductors they are electrons, while in p-type semicon-ductors they are holes. The opposite carrier is called the minority carrier, which exists due to thermal excitation at a much lower concentration compared to the majority carrier. If an intrinsic semiconductor is doped with a donor impurity then the majority carriers are electrons; if the semiconductor is doped with an acceptor impurity then the majority carriers are holes. For example, the pure semiconductor silicon has four valence electrons which bond each silicon atom to its neighbors. In silicon, the most common dopants are group III and group V elements. Group III elements all contain three valence electrons, causing them to function as acceptors when used to dope silicon. When an acceptor atom replaces a silicon atom in the crystal, a vacant state ( an electron "hole") is created, which can move around the lattice and functions as a charge carrier. Group V elements have ve valence electrons, which allows them to act as a donor; substitution of these atoms for silicon creates an extra free electron.

Doping with impurities of dierent valence increases the density of electrons or holes in the semiconductor at equilibrium. At equilibrium, electron and holes currents are always zero. The semiconductor can be disturbed from equilibrium

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Figure 2.4: Drift. Carriers ow under an electric eld in order to reduce their electrical potential energy. Electrons and holes drift in opposite directions. by the action of light or an applied electric bias. Application of bias produces electron and hole currents.

2.4 Charge carrier separation

There are two main modes for charge carrier separation in a semiconductor: drift of carriers and diusion of carriers.

Drift current is due to the applied electric eld that produces a ow of charge carriers. When an electric eld is applied across a semiconductor, the carriers start moving, producing a current.

Diusion current is caused by the diusion of charge carriers (holes and/or electrons). No external electric eld across the semiconductor is required for the diusion of current to take place. The carrier particles move from a place of higher concentration to a place of lower concentration. Hence, due to the ow of holes and electrons there is a current.

The drift current and the diusion current make up the total current in the conductor. The change in the concentration of the carrier particles develops a gradient. Due to this gradient, an electric eld is produced in the semiconductor.

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2.5 Generation and recombination

The essential function of a solar cell is the generation of photocurrent. The output is determined by a balance between light absorption, current generation and charge recombination. Generation is an electronic excitation event which increases the number of free carriers available to carry charge. Recombination is an electronic relaxation event which reduces the number of free carriers. The energy input can be provided by the vibrational energy of the lattice (phonons), light (photons) or kinetic energy of another carrier. The released energy is taken up by these same mechanisms. For every generation process there is an equivalent recombination process. Generation may be the promotion of an electron from valence to conduction band, which creates an electron-hole pair, or from valence band into a localised state in the band gap, or from a localised state into the conduction band, which generates only an electron. Recombination is the loss of an electron or hole through the decay of an electron to a lower energy state (as for generation). The energy can be given up as a photon (radiative recombination), as heat through phonon emission (non-radiative recombination) or as a kinetic energy to another free carrier (Auger recombination).

By photogeneration we mean the generation of mobile electrons and holes through the absorption of light in the semiconductor. As already mentioned, when higher energy photons are absorbed, they generate carriers with higher kinetic energy, but that energy is quickly lost and only the energy band gap remains to be collected. The photogenerated carriers lose any extra kinetic energy by thermalisation (simply, cooling). Microscopically, this means that they undergo repeated collisions with the lattice, giving up some of their kinetic energy to produce a phonon while they decay into a lower energy state, untill they are in thermal equilibrium with the ambient. Phonons are the means by which energy is carried away to the outside world.

By recombination we refer to the loss of mobile electrons or holes. We should distinguish two categories: unavoidable recombination process which are due to the essential physical processes in the intrinsic material, and avoidable processes which are largely due to imperfect material. Amongst the unavoidable recombi-nation process are the processes which result from optical generation (radiative recombination), spontaneous and stimulated emission. The other important un-avoidable process is the interaction of an electron or hole with a second similar carrier, resulting in the decay of one carrier across the band gap and the increase in the kinetic energy of the other carrier by an amount equal to the band gap.

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Figure 2.5: Schematic energy diagram of a metal.

This is called Auger recombination (non-radiative recombination). It is the re-verse of a rare generation process where a carrier with kinetic energy greater than the band gap is able to give up some of its kinetic energy to excite an electron across the gap. Avoidable recombination processes usually involve re-laxation by way of a localised trap state. These trap states are due to impurities in the crystal or defects in the crystal structure (non-radiative recombination). These are usually the dominant mechanisms. Trap recombination is a multiple step relaxation process. The energy lost by relaxation is given up as heat.[3]

2.6 Work function

The work function is the minimum thermodynamic work (energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. Here "immediately" means that the nal electron position is far from the surface on the atomic scale, but still too close to the solid to be inuenced by ambient electric elds in the vacuum.

In metals the valence bands are lled with electrons up to the Fermi energy (EF) and there is no band gap.

In semiconductors valence bands and conduction bands are separated by the band gap (Eg). The Fermi level is located within the band gap, it's somewhat

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Figure 2.6: Schematic energy diagram of a n-type semiconductor. theoretical construct since there are no allowed electronic states within the band gap. The Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time.

The work function is dened by

Φ = (Evac− EF) (2.1)

It is an experimentally obtained parameter and is most simply determined from the photoemission spectroscopy (PES).[4]

2.7 Junctions

For a light absorbing device to work as a solar cell, some kind of asymmetry needs to be built in to the system which drives electrons and holes in dierent directions. Spatial variation in electron anity, band gap, work function or density of states can drive charge separation (drift current and diusion cur-rent). Variation in work function can generate large electric elds and are most commonly used.

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equilibrium.

equal to the dierence in work function is established by exchange of charge carriers.

2.7.1 Metal-Semiconductor Junction

Suppose we have a uniform n type semiconductor of work function Φn and

a metal of work function Φm, such that Φm > Φn. When the two material

are isolated from each other, the Fermi levels will be independente. When they are brought into electronic contact the Fermi levels must line up, with the consequence that the vacuum level changes by (Φm − Φn) between the

semiconductor and the metal. Physically this is achieved by the exchange of charge carriers across the junction. Electrons ow from the semiconductor to the metal leaving a layer of positive xed charge behind, and a negative image charge on the metal until the charge gradient which builds up is sucient to prevent further ow (diusion current). At this point the two layers are in thermal equilibrium. The energy at the conduction band edge in the bulk of the semiconductor is lower than at the interface with the metal, and an electrostatic els exists close to the junction. The variation in electrostatic potential energy is represented by the change in Evac.

Because metals are much poorer at storing charge than semiconductors, vir-tually all of the potential dierence is dropped in the semiconductor. At some distance from the junction on either side, the potential dierence stops varying and the electric eld falls to zero. This distance is vanishingly short in the metal but is signicant, typically around a micron, in the semiconductor. Within these

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regions the materials carry a net charge. This region corresponds to the region where Evac is changing and because the electron anity and band gap are

in-variant in the semiconductor, the conduction and valence band energies must change in parallel with Evac. The space charge region is called depletion region.

Thus, by joining an n type semiconductor to a metal of larger work function, we set up an electric eld in a layer close to the interface. It is evident that this eld will drive electrons to the left and holes to the right, so eecting charge separation. The contact presents a lower resistance path for holes than electrons, from semiconductor to metal.[5]

Now suppose that the semiconductor is illuminated with photons of energy greater than Eg. The space charge layer will cause electron-hole pairs generated

in the semiconductor to be separated so that the electrons accumulate in the semiconductor and the holes in the metal (electrons removed from the metal). The semiconductor will become negatively charged and the potential dierence across the junction will be reduced. The electron quasi Fermi level far from the junction will be higher than it was in the dark, and higher that the Fermi level in the metal.1 _{The light has caused the Fermi levels to split. It has created}

a photovoltage, V, equal to the dierence in the Fermi levels of semiconductor and metal far from the junction. This ability to sustain a dierence in quasi Fermi levels under illumination is the key requirement for photovoltaic energy conversion.

The presence of the barrier also governs the current-voltage characteristic in the dark. Conduction in n type semiconductors is normally by electron ow. When a forward bias is appplied (the semiconductor is held at a more negative bias than a metal) the barrier height is reduced and electrons pass more easily over the barrier from semiconductor to metal. This forward current increases approximately exponentially as the barrier height is reduced. In reverse bias, the barrier height is increased, suppressing the activated current, and the only contribution is the small leakage current in the reverse direction, which is limited by the low density of mobile holes. This junction is also called Schottky barrier. A completely analogous situation applies to a p type semiconductor in con-tact with a metal of lower work function. The majority carriers are now holes. The forward current is provided by hole activation over the barrier, and the

1_{A quasi Fermi level is used for the Fermi level that describes the population of electrons}

separately when their populations are displaced from equilibrium. The displacement from equilibrium is such that the carrier populations can no longer be described by a single Fermi level, however it is possible to describe using separate quasi-Fermi levels for each band.

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Figure 2.8: Band prole of the semiconductor-metal junction under illumination at open circuit. The accumulation of photogenerated electrons in the n-type semiconductor raises electron Fermi level and generates a photovoltage, V.

Figure 2.9: Reverse and forward bias in a Schottky barrier junction in the dark.

Figure 2.10: Schematic current-voltage characteristic of a Schottky barrier junc-tion in the dark.

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Figure 2.11: (a) Band proles of p-type and n-type semiconductor in isolation. (b) Band prole of the p-n junction in equilibrium.

reverse current by electron leakage.

2.7.2 Semiconductor-Semiconductor Junction

The p-n junction is the classical model of a solar cell. This type of junction is created by doping dierent regions of the same semiconductor dierently, so we have an interface between p type and n type layers of the same material. Since the work function of the p type material is larger than the n type, the electrostatic potential must be smaller on the n side than the p side, and an electric eld is established at the junction which drives photogenerated electrons toward the n side and holes toward the p side. The junction region is depleted of both electrons and holes, and always presents a barrier to majority carriers, and a low resistance path to minority carriers.

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Figure 2.12: Schematic representation of crystal structure close to a p-n junc-tion. Close to the junction free carriers are removed, so that acceptor impurities on the p side become negatively charged, and donor impurities on the n side become positively charged.

Carriers diuse across the junction leaving behind a layer of xed charge. This space charge sets up an electrostatic eld which opposes further diusion across the junction. Equilibrium is established when diusion of majority carri-ers across the junction is balanced by the drift of minority carricarri-ers back across the junction in the built-in electrostatic eld. At this point the Fermi levels of the p and n type layers are equal, the dierence in the work functions is taken up by a step in the conduction and valence band edges, called the built-in bias, and the junction region is depleted of carriers. The built-in bias in equilibrium, Vbi,

is determined by the dierence in work functions of the n and p type materials, Φnand Φp.

The electric eld created by the space charge region opposes the diusion process for both electrons and holes. There are two concurrent phenomena: the diusion process that tends to generate more space charge, and the electric eld generated by the space charge that tends to counteract the diusion.

The space charge region is a zone with a net charge provided by the xed ions (donors or acceptors) that have been left uncovered by majority carrier diusion. When equilibrium is reached, the charge density is approximated by the displayed step function. In fact, the region is completely depleted of majority carriers (leaving a charge density equal to the net doping level), and the edge between the space charge region and the neutral region is quite sharp.

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Figure 2.13: A pn junction in thermal equilibrium with zero-bias voltage ap-plied. Under the junction, plots for the charge density, the electric eld, and the voltage are reported.

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carrier motion across the pn junction. The electrons that cross the pn junction into the p type material (or holes that cross into the n type material) will diuse in the near-neutral region. Therefore, the amount of minority diusion in the near-neutral zones determines the amount of current that may ow through the diode.

Only majority carriers (electrons in n type material or holes in p type) can ow through a semiconductor for a macroscopic length. With forward bias, the depletion region is narrow enough that electrons can cross the junction and inject into the p type material. However, they do not continue to ow through the p type material indenitely, because it is energetically favorable for them to recombine with holes. The average length an electron travels through the p type material before recombining is called the diusion length, and it is typically on the order of micrometers.

Although the electrons penetrate only a short distance into the p type ma-terial, the electric current continues uninterrupted, because holes (the majority carriers) begin to ow in the opposite direction. The total current (the sum of the electron and hole currents) is constant in space for the Kirchho's current law. The ow of holes from the p type region into the n type region is exactly analogous to the ow of electrons from n to p (electrons and holes swap roles and the signs of all currents and voltages are reversed).

Therefore, the macroscopic picture of the current ow through the diode involves electrons owing through the n type region toward the junction, holes owing through the p type region in the opposite direction toward the junction, and the two species of carriers constantly recombining in the vicinity of the junction. The electrons and holes travel in opposite directions, but they also have opposite charges, so the overall current is in the same direction on both

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Figure 2.14: Typical diode characteristic. sides of the diode, as required.

Connecting the p type region to the negative terminal of the battery and the n type region to the positive terminal corresponds to reverse bias. If a diode is reverse-biased, the voltage at the cathode is higher than that at the anode. Therefore, no current will ow until the diode breaks down. Because the p type material is now connected to the negative terminal of the power supply, the holes in the p type material are pulled away from the junction, causing the width of the depletion zone to increase. Likewise, because the n type region is connected to the positive terminal, the electrons will also be pulled away from the junction. Therefore, the depletion region widens, and does so increasingly with increasing reverse-bias voltage. This increases the voltage barrier causing a high resistance to the ow of charge carriers, thus allowing minimal electric current to cross the pn junction. The increase in resistance of the pn junction results in the junction behaving as an insulator. The strength of the depletion zone electric eld increases as the reverse-bias voltage increases. Once the electric eld intensity increases beyond a critical level, the pn junction depletion zone breaks down and current begins to ow.

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at that bias[1]

J (V ) = Jsc− Jdark(V ) (2.2)

2_{This superposition of currents is valid when the bias chosen is much less than V}_oc_and

the current is dominated by the photocurrent and minority carrier recombination can be considered linear.

3_{If the dark current is dominated by diusion currents J}_{dif f,0}_{(identical to the ideal diode}

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Chapter 3 Equivalent Circuit

To understand the electronic behavior of a solar cell, it is useful to create a model which is electrically equivalent, and is based on discrete electrical components whose behavior is well known. An ideal solar cell may be modelled by a current source in parallel with a diode.

When a load is connected to an illuminated solar cell the current that ows is the net result of two counteracting components of internal current: the photo-generated current or simply photocurrent, IL, due to the generation of carriers

by the light, and the diode or dark current, ID, due to the recombination of

carriers driven by the external voltage. This voltage is needed to deliver power to the load.

Assume that the two currents can be superimposed linearly, as turns out to be true in many practical instances. Then the current in the external circuit can be calculated as the dierence between the two components.1 _{Taking the}

photocurrent as positive, we can write

I = IL− ID(V ) (3.1)

This is the fundamental characteristic equation of a solar cell. It is valide over all operating conditions, even when the device functions as a diode, dissipating rathen than generating electricity, in which case the recombination outweighs the photogeneration.

In practice no solar cell is ideal, so a shunt resistance and a series resistance

1_{This step is known as the superposition approximation. Although the reverse current}

which ows in response to voltage in an illuminated cell is not formally equal to the current which ows in the dark, the approximation is reasonable for many photovoltaic materials.

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Figure 3.1: The equivalent circuit of a solar cell.

Figure 3.2: I-V curve of a solar cell. When there is no light present to generate any current, the solar cell behaves like a diode.

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component are added to the model. From the equivalent circuit it is evident that the current produced by the solar cell is equal to that produced by the current source, minus that which ows through the diode, minus that which ows through the shunt resistor

I = IL− ID(V ) − ISH(V ) (3.2)

where I is the output current, ILis the photogenerated current, IDis the diode

current, ISH is the shunt current. The current through these elements is

gov-erned by the voltage across them

Vj= V + IRS (3.3)

where Vj is the voltage across both diode and resistor RSH, V is the voltage

across the output terminals, I is the output current, RS is the series resistance.

The current diverted through the diode can be expressed by the Shockley diode equation[1] ID= I0 n enkTqVj − 1 o (3.4) where I0is the reverse saturation current, n is the diode ideality factor (1 for an

ideal diode), q is the elementary charge (1.602 · 10−19_C_{), k is the Boltzmann's}

constant (1.38 · 10−23_{J K}−1_{), T is the absolute temperature. By Ohm's law, the}

current diverted through the shunt resistor is ISH=

Vj

RSH

(3.5) where RSH is the shunt resistance. Substituting these into the rst equation

produces the characteristic equation of a solar cell, which relates solar cell pa-rameters to the output current and voltage

I = IL− I0 n eq(V +IRS )nkT − 1 o −V + IRS RSH (3.6) In principle, given a particular operating voltage V the equation may be solved to determine the operating current I at that voltage. However, because the equation involves I on both sides in a transcendental function the equation has no general analytical solution. However, it is easily solved using numerical methods. Since the parameters I0, n, RS, RSH cannot be measured directly, the

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Figure 3.3: Maximum-power point and other operating parameters. to extract the values of these parameters on the basis of their combined eect on solar cell behavior.2

When the cell is operating at open circuit, I = 0 and the voltage across the output terminals is dened as the open-circuit voltage, the greatest voltage that can arise. Assuming the shunt resistance is high enough to neglect the nal term of the characteristic equation, the open-circuit voltage VOC is

VOC≈ nkT q ln IL I0 + 1 (3.7) Similarly, when the cell is operating at short circuit, V = 0 and the current I through the terminals is dened as the short-circuit current, the greatest current that can arise. For high-quality solar cell (low RS and I0, and high RSH) the

short-circuit ISC is

ISC ≈ IL (3.8)

As indicated above, the region of the curve between ISC and VOC

corre-2_{A solar simulator can plot the characteristic I-V curve by measuring voltage and current}

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sponds to operation of the cell as a generator. If the energy is supplied to a resistive load, the power supplied to the resistance is given by the product P = IV.3

It exists an operating point (IM; VM)at which the power dissipated in the

load is maximum. This is called the maximum-power point. The values of IM

and VM can be obtained from the usual condition for a maximum

dP

dV = 0 (3.9) This represent a completely general condition for a maximum. When it is ap-plied to a cell described by the equation (8), the result is[7]

IM =

IL+ I0

1 +_qVnkT

M

(3.10) The characteristic equation of the cell(8) should also be satised. From these two simultaneous equation, IM and VM may be calculated. Again, the system

has no explicit solution, it is necessary to solve a transcendental equation. A vey approximate analytic solution is[7]

IM IL = 1 − a−b (3.11) where a = 1 + lnIL I0 and b = a a + 1 VM VOC ' 1 −lna a (3.12) For the usual values applicable to practical solar cells, the formulas predict values of IM close to those of IL and values of VMclose to those of VOC.

Con-sequently, the maximum-power point is close to the elbow of the characteristic curve, as indicated in Figure.

3.1 Fill factor and energy conversion eciency

The Fill Factor (F F ) is essentially a measure of quality of the solar cell. It is calculated by comparing the maximum power to the theoretical power (PT)

3_{Note that it's not possible to extract any power from the device when operating at either}

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that would be output at both the open circuit voltage and short circuit current together. F F can also be interpreted graphically as the ratio of the rectangular areas depicted in Figure 3.4. The more pronounced the elbow of the character-istic curve, however, the closer the two products come to being equal.

F F = IMVM ISCVOC

(3.13) It gives a quantitative measure of the form of the characteristic curve and de-scribe the 'squareness' It is nonethless always less than one. For many crystalline semiconductor cells it takes values in the range 0.7 to 0.8.

Eciency is the ratio of the electrical power output, Pout, compared to the

incident solar power input, Pin, into the solar cell. Pout can be taken to be PM

since the solar cell can be operated up to its maximum power output to get the maximum eciency. In this way the energy-conversion eciency of a solar cell is dened.

η ≡IMVM Pin

≡ F F ISCVOC

Pin (3.14)

All of these quantities should be dened for particular illumination conditions. The Standard Test Condition (STC) for solar cells in the Air Mass 1.5 spectrum, an incident power density of 1000 W m−2_{, and a temperature of 25C.[1]}

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Figure 3.5: Resistances at ISC and at VOC. Typical parameters calculed by the

Solar Simulator.

3.2 Parasitic resistances

In real cells power is dissipated trough the resistance of the contacts (particular problem at high current densitities) and through leakage currents (proportional to the voltage) around the sides of the device. These eects are distributed throughout the device and cannot always be represented by a resistance of constant value. However, from a practical and functional point of view, they are represented by two parasitic resistances in series (RS) and in parallel (RSH)

with the cell.

The parallel or shunt resistance arises from leakage of current through the cell, around the edges of the device and between contacts of dierent polarity (diusion paths along dislocations or grain boundaries and small metallic short circuits). It has its greatest eect when the voltage is lowest, when the current passing through the diode of the equivalent circuit is very small.

The series resistance arises from the resistance of the cell material to current ow, particularly through the front surface to the contacts, the resistance of the layers of the cell itself and from resistive contacts.

For an ideal cell, RSH would be innite and would not provide an alternate

path for current to ow, while RS would be zero, resulting in no further

volt-age drop before the load. It is possible to approximate the series and shunt resistances from the slopes of the I-V curve at VOC and ISC, respectively. The

resistance at VOC, however, is at best proportional to the series resistance but

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Figure 3.6: Eect of shunt resistance on the currentvoltage characteristics of a solar cell.

3.2.1 Shunt Resistance

As shunt resistance decreases, the current diverted through the shunt resistor increases for a given level of voltage. The result is that the voltage-controlled portion of the I-V curve begins to sag toward the origin, producing a signicant decrease in the terminal current I and a slight reduction in VOC. Very low

values of RSH will produce a signicant reduction in VOC. Much as in the case

of a high series resistance, a badly shunted solar cell will take on operating characteristics similar to those of a resistor. By studying the Figure 3.6 we can conrm that the eect of parallel resistance, when is suciently small, is to reduce the open-circuit voltage and the ll factor.

3.2.2 Series Resistance

As series resistance increases, the voltage drop between the junction voltage and the terminal voltage becomes greater for the same current. The result is that the current-controlled portion of the I-V curve begins to sag toward the origin, producing a signicant decrease in the terminal voltage V and a slight reduction in ISC, the short-circuit current. Very high values of RS will also produce a

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Figure 3.7: Eect of series resistance on the current-voltage characteristics of a solar cell.

signicant reduction in ISC; in these regimes, series resistance dominates and

the behavior of the solar cell resembles that of a resistor. Losses caused by series resistance are in a rst approximation given by Ploss= VRSI = I

2_R S and

increase quadratically with (photo-)current. Series resistance losses are therefore most important at high illumination intensities. A large series resistance reduces the ll factor and the short-circuit current, without aecting the open-circuit voltage. The eect on ISC is not, however, very marked in practical cells since

correct design should limit RS to a fairly low value. The situation is dierent,

though, as regards the eect on ll factor. This can be degraded signicantly, resulting in poor eciency, especially if the current is high as in cells working under optical concentrators.

3.3 The eect of temperature

Consider again the characteristic equation it is evident that temperature aects it in two ways: directly, via T in the exponential term, and indirectly via its

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VOC(T ) = EG0 q − kT q ln kT3 IL (3.17)

While increasing T reduces the magnitude of the exponent in the characteris-tic equation, the value of I0 increases exponentially with T . The net eect is

to reduce VOC linearly with increasing temperature. Cells with higher values

of VOC suer smaller reductions in voltage with increasing temperature. The

amount of photogenerated current IL increases slightly with increasing

temper-ature because of an increase in the number of thermally generated carriers in the cell. However, since the change in voltage is much stronger than the change in current, the overall eect on eciency tends to be similar to that on voltage.

3.4 Dark current

If incident light is prevented from exciting the solar cell, the I-V curve shown in Figure 3.9 can be obtained. This I-V curve is simply a reection of the No Light curve from Figure 3.2 about the V-axis (since in Figure 3.2 I has opposite bias). The slope of the linear region of the curve in the third quadrant (reverse-bias) is a continuation of the linear region in the rst quadrant, which is the same linear region used to calculate RSH. It follows that RSH can be

derived from the I-V plot obtained with or without providing light excitation,

4_{Temperature actually aects all of the terms, but these two far more signicantly than}

the others.

5_{The photocurrent I}_L_{increases slightly with temperature, in part because of greater}

dif-fusion lenghts of the minority carriers and in part because of the narrowing of the bandgap that displaces the absorption threshold towards photons of lower energy.

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Figure 3.8: Eect of temperature on the current-voltage characteristic of a solar cell.

even when power is sourced to the cell.6

In the dark, the system works as a normal diode: it has a forward bias after a given threshold and creates a large current, while a reverse bias gives negligible current.

3.5 Reverse saturation current

The reverse saturation current is that part of the reverse current in a diode caused by diusion of minority carriers from the neutral regions to the depletion region. This current is almost independent of the reverse voltage. It varies with temperature; this variance is the dominant term in the temperature coecient for a diode.7 _{If one assumes innite shunt resistance, the characteristic equation}

can be solved for VOC.

VOC= kT q ln ISC I0 + 1 (3.18)

6_{For real cells, these resistances are often a function of the light level, and can dier in}

value between the light and dark tests.

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Figure 3.9: I-V Curve of solar cell without light excitation.

Thus, an increase in I0produces a reduction in VOC proportional to the inverse

of the logarithm of the increase. Physically, reverse saturation current is a measure of the "leakage" of carriers across the junction in reverse bias. This leakage is a result of carrier recombination in the neutral regions on either side of the junction.

3.6 Ideality factor

The ideality factor n is a tting parameter that describes how closely the diode's behavior matches that predicted by theory, which assumes the junction of the diode is an innite plane and no recombination occurs within the space-charge region. A perfect match to theory is indicated when n = 1. When recombina-tion in the space-charge region dominate other recombinarecombina-tion, however, n = 2. Most solar cells, which are quite large compared to conventional diodes, well approximate an innite plane and will usually exhibit near-ideal behavior under Standard Test Condition (n ≈ 1). Under certain operating conditions, however, device operation may be dominated by recombination in the space-charge re-gion. This is characterized by a signicant increase in I0 as well as an increase

in ideality factor to n ≈ 2. The latter tends to increase solar cell output voltage while the former acts to erode it. Typically, I0is the more signicant factor and

the result is a reduction in voltage.8

8_{The ideality factor n typically varies from 1 to 2 (though can in some cases be higher).}

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Figure 3.10: Eect of reverse saturation current on the current-voltage charac-teristics of a solar cell.

Figure 3.11: Eect of ideality factor on the current-voltage characteristics of a solar cell.

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η (X) =

X PL1 (3.20)

If we assume that n and I0do not change appreciably as the level of illumination

is increased, no parasitic resistances and we ignore small variations in F F [7] η (X) = IL1VOC1F F (X) PL1 1 + nkT qVOC1 ln (X) (3.21) the above expressions predict an increase of eciency due to the increase in open-circuit voltage. This voltage varies logarithmically with the concentration level. The increase cannot continue indenitely due to physical limits not ap-parent in the analysis until now. In practice, however, these theoretical limits do not manifest themselves at low levels of illumination and we do observe a logarithmic increase in eency. But if the intensity of illumination, and hence the photogenerated current, is increased further, the ohmic losses due to the series resistance of the cell are no longer negligible and become responsible for a considerable deterioration in the eciency of the device. As a net result of all the factors mentioned, the variation in energy conversion eciency of a solar cell with the illumination intensity typically has the form shown in Figure.

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Figure 3.12: Variation of the conversion eciency with the concentration of the light.

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there is no net ow of charge across the junction, which is why the region between the two materials is termed the "depletion zone". Valence electrons in the silicon semiconductor absorb photons in the visible range. Photons with enough energy excite electrons across the semiconductor's band gap, a region of forbidden energies determined by the materials constructing the device, into the conduction band. The intrinsic electric eld separates the electron and its positively charged hole. Electrons ow toward the electrode on the n-type side and through an external load to produce power.

At a macroscopic level, organic solar cells operate like inorganic photovoltaics (solar energy is converted into electrical energy). There are signicant dierences, however, between the photoconversion mechanisms in inorganic and organic cells. The most obvious dierence is that photon absorption in an OPV device does not directly produce free charge carriers. Instead, light absorption in OPVs leads to the production of excitons (excited, tightly bound electron-hole pairs). The optical band gap (the energy of the exciton) is not as great as the electrical band gap (the energy needed to promote an electron from the valence band to the conduction band), as illustrated in Figure 4.1. The energy needed to separate the exciton into free charge carriers, known as the binding energy, is the dierence between the electrical and optical band gaps. The organic

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material's low dielectric constant relative to the dielectric constant of inorganic semiconductors prohibits the formation of free charge carriers following photon absorption.

Exciton dissociation occurs at the interface (heterojunction) of two materi-als. If the oset between the band gaps of the materials forming the hetero-junction is greater than the exciton's binding energy, it will be energetically favorable for the exciton to dissociate. The material that gives up the electron is the electron donor, and the material that accepts the electron is known as the electron acceptor (see Figure 4.1). Exciton dissociation highlights another dierence between organic and inorganic solar cells: charge carrier generation and separation are one and the same process in OPVs. After the exciton disso-ciates at the electron donor/acceptor interface, the electron and its hole diuse to opposite ends of the cell.

4.1 Denitions and physics

4.1.1 Electron anity and work function

An electron at the vacuum energy (Evac) is, by denition, completely free of

inuence from all external forces.

The electron anity, EEA, is the minimum energy needed to free an electron

from the bottom of the conduction band at a level energy Ec and take it to the

vacuum level.

EEA≡ Evac− Ec (4.1)

A molecule or atom that has the higher value of electron anity than another is often called an electron acceptor and the lower value an electron donor.

The work function, W , of a material is the energy required to remove an electron from the Fermi level (EF) at the surface to the vacuum level.

W ≡ Evac− EF (4.2)

While the work function of a semiconductor can be changed by doping, the electron anity ideally does not change with doping (EF can be changed) and

so it is closer to being a material constant. However, the electron anity does depend on the surface termination and it's strongly aected by temperature since it aects the number of electrons in the conduction band.

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Figure 4.1: Energy-level diagram for an excitonic solar cell. Excitons created in the rst organic semiconductor (OSC1) and second organic semiconductor (OSC2) do not have enough energy to dissociate in bulk. But the band oset between OSC1 and OSC2 provides an exothermic pathway for dissociation of excitons in both phases. The band oset must be greater than the exciton binding energy for dissociation to occur.

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Figure 4.2: Band diagram of a semiconductor showing the dierence between electron anity (EEA) and work function (W ).

4.1.2 Principal dierences

An important dierence to inorganic solid-state semiconductors lies in the gener-ally poor (order of magnitudes lower) charge-carrier mobility in these materials, which has a large eect on the design and eciency of organic semiconduc-tor devices. However, organic semiconducsemiconduc-tors have relatively strong absorption coecients (usually ≥ 105_cm−1_{), which partly balances low mobilities, giving}

high absorption in even < 100 nm thin devices. Another important dierence to crystalline, inorganic semiconductor is the relatively small diusion length of primary photoexcitation (excitons) in these rather amorphous and disordered organic materials.1 _{On photon absorption, an electron is excited from the}

high-est occupied molecular orbital (HOMO) to the lowhigh-est unoccupied molecular orbital (LUMO).2 _{This electron-hole pair then relaxes with a binding energy}

between 0.1 − 1.4 eV , and is known as exciton.

These excitons are an important intermediate in the solar energy

conver-1_{The diusion length is the average distance a carrier can move from point of generation}

until it recombines.

2_{Roughly, the HOMO level is to organic semiconductors what the valence band maximum}

is to inorganic semiconductors. The same analogy exists between the LUMO level and the conduction band minimum.

Towards High-Efficiency Organic Solar Cells

U

NIVERSITÀ DI

P

ISA

Dipartimento di Ingegneria Civile e Industriale

C

ORSO DI

L

AUREA

M

AGISTRALE IN

I

NGEGNERIA

M

ECCANICA

T

ESI DI

L

AUREA

Towards High-Efficiency Organic

Solar Cells

Relatori:

Candidato: Prof. Ing. Renzo Valentini

Alessio Cinopri Prof. Ing. Kee Moon

Prof. Ing. Khaled Morsi

Anno Accademico 2013/2014

Abstract

In this research, we investigate the fundamental sciences and challenges that

need to be addressed in the production of flexible organic solar cell using

microfabri-cation techniques. The major focuses of the study are the determination of optimized

conditions and processes for depositing the photoactive layer, anodic layers, and

met-al cathodic layers. Along with, this research investigates and solves the engineering

and production problems associated with the prototyping system.

Contents

List of Figures

List of Tables

2.1 Requirements and limits for a photoconverter

2.2 Electrons and holes in semiconductors

2.3 Doping

2.4 Charge carrier separation

2.5 Generation and recombination

2.6 Work function

2.7 Junctions

2.7.1 Metal-Semiconductor Junction

2.7.2 Semiconductor-Semiconductor Junction

Chapter 3

Equivalent Circuit

3.1 Fill factor and energy conversion eciency

3.2 Parasitic resistances

3.2.1 Shunt Resistance

3.2.2 Series Resistance

3.3 The eect of temperature

3.4 Dark current

3.5 Reverse saturation current

3.6 Ideality factor

4.1 Denitions and physics

4.1.1 Electron anity and work function

4.1.2 Principal dierences

3.1 Fill factor and energy conversion eciency

3.3 The eect of temperature

4.1 Denitions and physics

4.1.1 Electron anity and work function

4.1.2 Principal dierences