University of LjubljanaFaculty of Mathematics and Physics

Seminar -1st year, 2nd cycle

Solar Cells

Author: Katja VozelAdvisor: izred. prof. dr. Denis Arcon

Ljubljana, May 2011

AbstractThis seminar is a short overview of current photovoltaics. Application of p-n junctions within solar cells isdiscussed. We give the upper limit to the solar cell efficiency. Three generations of solar cells, crystallinesilicon solar cells, thin-film solar cells and photoelectrochemical cells, are described by means of theiroperational principles and physics behind. We also compare efficiencies of current devices.

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Contents

1 Introduction 2

2 Timeline of solar cells 3

3 Analysis of p-n junction 43.1 Current-voltage characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Solar cell structure 6

5 Basic definitions 7

6 Efficiency: thermodynamic limit and detailed balance 8

7 Crystalline solar cells 9

8 Thin-film solar cells 108.1 Amorphous silicon solar cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

9 Novel solar cells 129.1 Operation principles of dye-sensitized solar cells . . . . . . . . . . . . . . . . . . . . . . . . . 129.2 Nanocrystaline junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139.3 Characteristics and practical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

10 Comparison of PV devices 14

11 Conclusion 14

1 Introduction

Photovoltaic effect is emergence of electric voltage in a system exposed to solar radiation. With absorbtionof photons, charge carriers are excited into conduction band. The mechanism of light induced electrontransition to a higher energy state is similar to that of photoelectric effect, where a photon carrying sufficientamount of energy frees an electron from the surface of a metal. The photoelectric effect was explained byAlbert Einstein in 1905. Converting solar radiation into electrical energy is called photovoltaics (PV).Devices exploiting PV effect are called solar cells, also photovoltaic cells or photovoltaic devices.

Global electricity consumption amounts to approximately 2·1014 kWh per year [1]. Could solar cellssatisfy the world’s hunger for energy and how much of the land would be needed? The Sun provides 1000W/m2 of power density for a surface perpendicular to the Sun’s rays at sea level on a clear day. The actualpower at specific area varies with seasons and depends on the geographic position of the area. It must betaken into account that the Sun shines only during the day and that the angle of Sun’s rays varies duringthe day, if the PV devices do not rotate. We also estimate, that there is 70% of sunny days in a year.With a little of calculation, we arrive at average power density of 120 W/m2 [2, 3, 4] coming from the Sun,which we multiply by PV device efficiency of 10% to get the power density obtained from PV. Dividing theconsumption by the power density obtained from solar cells, we get the area of solar cells needed, whichis approximately 1012 m2 or 0.7% of Earth’s land [5]. By making a similar calculation only for Europe, acontinent with relatively high population and little sun, we find that we should cover approximately 8%of Europe land to provide the whole Europe with electricity. That is quite a lot, but fortunately, Saharadessert, with area of 9.4·1012 m2 [6] is close enough to be exploited. After these estimates, we see thatsolar energy could be one of the most promising energy sources, alternative to the currently dominatingfossil fuels. The problem is, however, very high cost of PV, particularly crystalline silicon solar cells, whichcurrently have the highest known efficiency. Although there are cheaper alternatives to silicon, they lack ofeither efficiency or chemical stability, or can not be prepared by fast processing techniques [7]. In principle,efficiency of solar cells is limited by the band gap of the material used, because the band gap has to matcha part of solar frequency spectrum. It is also conected with impurities in the material. Cheaper materialsoften contain a lot of impurities, which can act as recombination centres for photogenerated charge carriers,

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thus lowering the efficiency and stability of a cell. Chemical instability refers to light induced degradationin amorphous silicon solar cells or to the limited number of redox cycles for electrolytes in novel solar cells.

PV is world’s fastest growing power generation technology. From 2008 until now, the global contributionof PV to electricity production raised from 0.06% to 0.5% [1, 8]. The rapid, we could say exponential growthof installed PV capacity from 2000 to 2010 was strongly influenced by national subsidies. Based on thecapacity installed and connected to the grid at the end of 2011, PV can provide roughly 2% of the electricitydemand in Europe, up from 1.15% at the end of 2010 [9]. In Slovenia, 0.44% of electricity demand wasprovided by solar cells in 2011 [9]. Currently, around 80% of solar cells is made of polycrystaline or singlecrystal silicon [10]. These are reffered to as first generation solar cells. Second generation solar cells compriseof thin films of materials like amorphous silicon, cadmium telluride and copper indium (gallium) diselenide.First and second generation solar cells use p-n monojunctions or heterojunctions to separate charge carriers.Third generation solar cells include photoelectrochemical or dye-sensitized cells, organic cells and nano-technology. Their working principles differ significantly from those of first and second generation cells. Theworking mechanisms of novel cells require much less material than is needed for production of the first andsecond generation solar cells. But these novel cells are not yet completely developed and their efficienciesremain low, cases up to 10%, in comparison to first generation devices with typical efficiencies around 20%and second generation devices with typical efficiencies between 10% and 19% [10, 11].

In this seminar we make a short glance at the history of PV in section 2. In section 3, we make a shortanalysis of p-n junction in connection with its use in solar cells. We present the structure of a solar cell insection 4. In the next section we explain basic physical principles of PV and we introduce some importantdefinitions considering PV. In section 6, the limiting efficiency of a single photovoltaic device is given. Inthe next three sections, 7, 8 and 9, we discuss specifics of structure, physics and properties of three typesof solar cells: single crystal silicon solar cell, amorphous silicon solar cell and dye sensitized solar cell. Wealso compare operation and efficiencies of devices in section 10.

2 Timeline of solar cells

French physicist Edmund Becquerel discovered photovoltaic effect in 1839 [12]. He noticed that by illu-minating silver coated platinum electrode in electrolite, he could produce electric current. Several yearslater, in 1876, William Adams and Richard Day observed light-induced photocurrent in selenium withtwo heated platinum contacts. Probably the first large area solar cell containing selenium and gold wasmade by Charles Fritts in 1894. It had efficiency of around 1%. In the following years the focus was oncoper-coper oxide thin film structures, which were Schottky barrier devices, where a semitransparent layerof metal was deposited on top of a semiconductor. Photovoltaic effect of such devices is related to a barrierto current flow at one of the metal-semiconductor interfaces. The teory of metal-semiconductor barrier wasdeveloped by Schottky, Neville Mott and others [12]. The disadvantage of Schottky contacts is that therequired unimpeded exchange of the minority carriers is unavoidably coupled with a high level of surfacerecombination at the metal contact [13].

In the middle of the 20th century, good quality silicon wafers were developed for applications in solidstate electronics. For the first time, considerable quantities of power were produced by photovoltaic cellsconsisting of crystalline silicon. These were p-n junction devices, which had some advantages over Schottkybarriers, for example much better rectifying action, which means that the charge carriers move only in thedesired direction. Devices with p-n junction could reach better efficiencies. First silicon cell was made byCapin, Fuller and Pearson in 1954 with 6% efficiency. The next few decades, efficiency was steadily rising,but the cost of photovoltaic systems was too high to compete with other energy sources. Photovoltaics weretherefore used mainly as space sattelite energy supply, as the importance of small weight and reliabilityouthweighted high costs.

At the same time, other materials were being researched. It was found out that cadmium sulphide,gallium arsenide, indium phosphide and cadmium telluride p-n junctions should have equal or betterefficiencies than silicon p-n junction. Despite that, silicon remained the most popular material, due toadvances of silicon technology for microelectronics industry [12]. Oil industry crisis followed in 1970s, whichled to several fundations in research of renewable energy sources. During that time, deep understanding ofphotovoltaics was gained. New strategies and materials were proposed to make photovoltaics cheaper, forinstance photoelectrochemical junctions, polycristalline silicon, amorphous silicon, organic conductors andso on. None of the mentioned technologies have taken over the market of photovoltaics so far.

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Since 1970s, interests in renewable energy sources as alternative to fossil fuels have been growing. In thelate 1990s, production of solar cells expanded 15-25% per year, which also reduced their cost. Solar cellshave become competitive at remote locations, in navigation systems, telecomunications and as additionalpower in grid connected loads at peak use [12].

3 Analysis of p-n junction

This section reveals the operational principle of most common solar cells and also serves as a basis forfurther discussion.

As we know, an electric field spontaneously occurs at the interface between p- and n-type semiconduc-tors, in so called space charge region (SCR). The built-in potential difference accross the p-n junction, Vbiis [12, 14]

Vbi =kBT

qln

(NdNa

n2i

), (1)

where Nd and Na stand for density of donor and acceptor atoms. q is the absolute value of the charge ofan electron. The width of the space charge region was also calculated before [12, 14] and is given by

wscr = | − wp|+ wn =

√2εsq

(1

Na+

1

Nd

)Vbi, (2)

where εs is the local permittivity of the semiconductor. We chose the origin of the longitudinal axis atthe interface between differently doped semiconductors. wp and wn are widths of charge regions on thep- and n-side. According to equations 1 and 2, the built-in potential difference increases with increasingdoping, while the width of the SCR decreases. In solar cells both high potential difference and wide SCRare needed for effective drift of charge carriers towards the right direction, so a compromise must be madewhen choosing the doping level. The SCR is highly resistant part of p-n junction, while the bulk of thejunction has very low resistance for electric current. Any applied bias would have the highest drop in theSCR.

A hole current flows from the n- to the p-side of the junction, known as hole generation current. It isminority carrier current, because it results from generation of holes when electrons are thermally excitedfrom valence to conduction band on the n-side. A hole must be generated within a diffusion lenght fromSCR and when it reaches the SCR, it is immediately driven to the p-side by strong electric field. Similarly,there flows an electron generation current from the p- to the n-side of the junction. Another hole currentflows from the p-side to the n-side of the junction, known as hole recombination current. It results fromthe holes, that reach the SCR with sufficient energy to surmount the potential barrier of the SCR. Thenumber of such holes is proportional to e−q∆V/kBT and thus depends strongly on the potential step ∆Vacross the junction. If a forward (positive) bias is applied, such that it raises the potential of the p-sidewith respect to the n-side, the potential barrier is lowered and the recombination current is stronger. Inthat case, the electric current flows with little resistance through the p-n junction, dominated by majoritycarrier current. On the contrary, if a negative bias is applied, the potential barrier is increased and onlylittle current flows through the device. This is known as the rectifying action of a diode.

In equilibrium, when no external bias is applied, the net electric current is zero. When a forward biasV is applied, the net charge current density, flowing in the direction of recombination currents, is given by[14]

J = (Jgenh + Jgene )(eqV /kBT − 1), (3)

where Jgenh and Jgene are hole and electron generation current densities. The situation is considerablyaltered, when a p-n junction within a photovoltaic material is illuminated. The generation currents, re-sulting from photogenerated minority charge carriers, are increased. The so called photocurrent becomesthe dominant electric current, flowing in the opposite direction as recombination current. We take thepotential drop accross the junction to be the difference between the built-in bias Vbi and the applied biasV , Vj = Vbi − V . We are trying to find solution for electric current density flowing through a photovoltaicdevice under illumination and applied bias. In general, problem consists of solving a set of coupled dif-ferential equations for the hole density, the electron density and the electrostatic potential, given specifiedforms for the photogeneration, the recombination and the hole and electron currents [12]. It is a complex

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problem, but analytic solutions can be found by using two approximations, which allow the hole and elec-tron currents to be decoupled. The first one is so called depletion approximation, which assumes thereare no free charge carriers in the space charge region around the junction. The electric field vanishes atfixed distances from the junction. Within the neutral regions away from the junction, majority carrierdensities have their equilibrium value and variations in minority carrier densities determine the current. Inneutral regions, there is no electric field and currents of minority carriers are only diffusive. The depletionapproximation allows the solutions in neutral p and n-regions to be decoupled.

In the second approximation we assume the recombination process to be linear in the minority carrierdensity. It is sometimes called superposition approximation [12], because the effect of bias and illuminationare decoupled, so the solution to the current is the sum of both.

We give some of the important steps in solving the problem of electric current density. When a deviceis illuminated with light with energy W , the rate of charge generation, g, is given by [12]

g(W,x) = (1−R(W ))α(W )bs(W )e−α(W )x, (4)

where R is the reflectance of the material, bs(W ) is the incident photon flux, which will be explained insection 5 and α(W ) is the absorption coefficient, which is given by the matrix element, calculated with useof the Fermi golden rule [12]. Integrating over photon energies, we obtain the integrated charge generationrate G. In the presence of both the electric field E and charge carrier density gradient, the carrier currentdensity can be written as the sum of a term proportional to the density gradient - diffusion current, and aterm proportional to the field - the drift current [12, 14]:

Jp(~r) = −qDp∇p+ qµpEp and Jn(~r) = qDn∇n+ qµnEn. (5)

Here, Jp denotes charge current density, as a consequence of motion of holes and Jn denotes charge currentdensity, as a consequence of motion of electrons. µp and µn are mobilities while Dp and Dn are thecorresponding diffusion constants of holes and electrons, respectively. If we combine equations 5 with thesteady state continuity equations, take the current generated by a spectrum containing a single wave lenghtand reduce the problem to one dimension, x, then the transport equations in the case of zero electric field- in the neutral p- and n- regions - simplify to [12]:

d2p

dx2− p− p0

L2p

+g(W,x)

Dp= 0, p0 =

n2i

Nd(6)

for holes in the n-region and

d2n

dx2− n− n0

L2n

+g(W,x)

Dn= 0, n0 =

n2i

Na(7)

for electrons in the p-region. Lp and Ln stand for diffusion lenghts of holes and electrons, depending onthe charge carrier lifetime τ ,

Lp =√τpDp, Ln =

√τnDn. (8)

At the boundary with the SCR, the condition for density of holes is given by [12]

p− p0 =n2i

Nd(eqV/kBT − 1), x = wn. (9)

The boundary condition at the outer surface is determined by the surface recombination rate Sp,

−Dpdp

dx= Sp(p− p0). (10)

It follows that the hole current in the n-region and the electron current in the p-region, which we obtainin a similar way, can be written as [12]

jp(W,x) = −qDpdp

dx, jn(W,x) = qDn

dn

dx. (11)

The current in the space charge region can be determined from carrier continuity. It can be writtenas integral of difference between charge recombination rate U and charge generation rate G over the SCR:[12]

Jscr = q

∫ wn

−wp

(U −G)dx. (12)

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This is equal for electrons and holes within the space charge region. The net current is given by the sum ofhole and electron currents at any point and is constant through the device in steady state. General solutionfor p can be obtained analitically by solving equation 6. From 11 and after intergrating over energy, weobtain general solution for Jp and similarly we obtain solution for Jn. We are not going to write downthe whole solutions, which can be found in [12]. There are two separate contributions to the net currentdensity. The first one is proportional to the incident spectral photon flux density and the second one isproportional to eqV/kBT − 1 as a consequence of applied bias.

With solutions for current densities, we can calculate the dark current Jdark, the case where there isno contribution from illumination, and the short-circuit current Jsc, the case where V = 0. The J isillustrated in Figure 1 as a function of applied bias V . By adding short circuit current and dark current,current-voltage characteristics of a solar cell, which will be discussed in section 5, is constructed:

J(V ) = Jsc − Jdark(V ) = Jsc − Jm,0(eqV/mkBT − 1). (13)

Jm,0 is material-dependent constant and m is ideality factor that describes deviation from ideal diodebehavior with m = 1. The last term in expression 13 is indeed the same one obtained by general analysisof p-n junctions [14]. The additional current density Jsc is a consequence of light illumination. The sign ofthe currents is chosen so that photocurrent is positive. With increasing V the flux emmited from a solarcell increases and the net current decreases. What is more, the latter expression provides the open-circuitvoltage - the voltage at which the current is zero,

Voc =mkBT

qln(

JscJm,0

+ 1). (14)

If the V is increased above the Voc, the cell begins to act like a light emmiting device. Voc must always beless than Eg/q, where Eg is the band gap of the semiconductor used.

Bias voltage, V

Cu

rre

nt

de

ns

ity

, J

Current density

Voc

Jsc

Vm

Jm

Power

density

Maximum

power point

Figure 1: Current-voltage (black) and power-voltage (grey) characteristics of an ideal diode (ideal pho-tovoltaic device). Vm and Jm denote voltage and current density at maximum power point. Reproducedfrom [12].

3.1 Current-voltage characteristics

The voltage, which is a result of cell illumination when the sides of the cell are isolated, is called open-circuitvoltage Voc (denoted in Figure 1). The electric current, which emerges when the sides of the cell are shortcircued, is called short circuit current Isc. When a load with a resistance RL is added in the circuit, voltageV and current I developed by the cell under illumination are such that V = IRL. I(V) is determinedby current-voltage characteristics of the cell under given illumination [12]. The electric current is roughlyproportional to the illuminated area and that is why it will be useful to define short circuit current densityJsc.

4 Solar cell structure

We present the structure of a c-Si photovoltaic device. Crystalline silicon solar cell is composed of two basiclayers, the emitter, which is n-doped, and the base, which is p-doped semiconductor silicon(see Figure 2).

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The front contact has to be designed in a way that prevents shading of the front surface. Because the bulkof the electron-hole pairs is generated near the surface, the position of p-n junction is also near the surface.This prevents recombination of charge carriers before they reach the junction, where they are separated byelectric field.

Figure 2: Structure of crystalline silicon solar cell. Reproduced from [10].

5 Basic definitions

ModuleA single solar cell area is typically about 100 cm2, it generates a dc photovoltage of 0.5 -1 V and pho-tocurrent of several amperes [12]. Because of low voltage and electric current, cells are connected intomodules, which produce standard voltage of 12 V. Modules are further connected into strings. Due to thefluctuations in solar irradiation during the day, PV systems also include components for charge regulationand storage. Parts of PV system are illustrated in Figure 3.

0

+V

Module

PV generatorPower

Load

Storage

(Battery (dc)

or Grid (ac))

conditioning

(c) (d)(a) (b)

+12V

0V

Figure 3: (a) Solar cell with surface contacts. (b) Cells conected in a module. (c) Modules are connectedin series into strings and in parallel into an array, to produce sufficient current and voltage. (d) Integrationof charge regulation and storage. Reproduced from [12].

Quantum efficiencyQuantum efficiency ηQE of a solar cell is the probability that an incident photon will deliver one electronto the external circuit. The resulting short circuit photocurrent density depends upon quantum efficiency:

Jsc = q

∫bs(W )ηQE(W )dW. (15)

Here, q is unit charge, W denotes energy of photons and bs is the incident spectral photon flux density,that is number of photons with energy between W and W + dW falling on a cell per unit area and per unittime. The solar spectrum reaching surface of the Earth is presented in Figure 4.Quantum efficiency is a property of a solar cell, which means it is related to absorption coefficient and effi-ciency of charge separation but does not depend on incident spectrum. It is desirable to have a high ηQE atenergies where also solar photon flux density is high, that is somewhere between wavelenghts of 400 and 1300nm.

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Figure 4: Solar spectrum at the surface of theEarth. Reproduced from [15].

By combining cells that operate best at differ-ent wavelenghts, we can exploit larger part of so-lar spectrum. These are so called tandem cells.Although tandem originally referred to two cells,it is now also used for arrangements with morethan two cells. Each cell in the arangement con-verts a part of solar spectrum. The top cellconsists of a wide gap semiconductor. It con-verts the short wavelength part of the spectrumand transmits the other part to the cells below[10].

Fill factor and efficiencyCurrent-voltage characteristics of a solar cells has apoint of maximum power, as seen in Figure 1. At thepoint of maximum power density, we denote current density with Jm and voltage with Vm. The load, weattach to the solar cell circuit, has the optimum resistance given by Vm/Jm. Jm and Vm should be as nearto Jsc and Voc as possible. We define the fill factor:

FF =JmVmJscVoc

, (16)

which would be ideally one. For very good crystalline silicon solar cells, the fill factor is above 80% [10].General efficiency η of a PV device is the ratio of maximum output power density to incident radiation

power density,

η =JmVmPs

=JscVocFF

Ps. (17)

For most cells, the efficiency is temperature dependent. With increasing temperature, the energy of chargecarriers is increased, leading to higher difussion current densities. The cell emits more strongly. Accordingto equation 14, with higher diffusion current density Jm,0, the open-circuit voltage is lowered, which leadsto lower efficiency. Efficiencies are measured under Standard Test Conditions (STC), that is Air Mass 1.5spectrum (Air Mass is lenght of the light path to the Earth surface relative to the path at highest position ofthe sun), incident power density of 1000 W/m2 and temperature of 25◦C. The efficiencies of solar modulesare always somewhat lower than the laboratory efficiencies of single solar cells.

Parasitic resistancesEvery solar cell has two parasitic resistances, the series resistance Rs and the parallel or shunt resistanceRsh. The series resistance is the resistance of the material and contacts of the cell, through which electriccurrent flows. Parallel resistance results from current leakage because of imperfect rectifying action. Forhighly efficient cell Rs should be as low and Rsh as high as possible, otherwise the fill factor is considerablylowered.

6 Efficiency: thermodynamic limit and detailed balance

Detailed balance is a way to determine maximum possible efficiency of a solar cell. It is based on balancingdifferent particle fluxes in the cell. The detailed treatment can be found for example in [16, 17]. A simpleform of detailed balance can be used to calculate the maximum efficiency of a two-band photoconverter,which has only two electronic levels with a bandgap Eg between them. It is an approximation for a basicc-Si or GaAs PV device containing p-n junction. In the calculation, the solar spectrum is fixed at AirMass 1.5 spectrum (see Figure 4). The short circuit current density Jsc, which is a result of excitation ofan electron to the upper band via photon absorption, as well as the dark current density Jdark, which is aresult of electron relaxation from upper to lower band, depend on the energy gap Eg. The power obtainedfrom the solar cell is a product of applied bias and net current density J = Jsc − Jdark, and is thereforealso Eg-dependent. From equation 17 we can anticipate that neither very small or very large band gapwould lead to maximum efficiency, because the Voc increases [13] and Jsc decreases with increasing bandgap (because less of the solar spectrum is absorbed). It can be shown, that the power of a cell has a

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maximum at energy gap of 1.4 eV [12]. Dividing the maximum power by the power coming from the sun,we obtain the maximum efficiency of 33% for a two-band photoconverter [12].

As can be seen from equation 15, the efficiency depends on the shape of solar spectrum bs(W ), whichvaries slightly with the composition of atmosphere at different places on earth at different times. Neverthe-less, the most important is the temperature of the light source - the Sun. If the Sun had lower temperature,the optimum band gap and the maximum efficiency would both be lower. Clearly, if the temperature of theSun was equal to the temperature of the cell, there would be no net photoconversion. On the other hand,if the temperature of the Sun would increase relative to the cell, so would the photoconversion efficiency.

The main limiting factor to efficiency of PV is that only part of the solar spectrum that matches theband gap can be converted into electricity. No photons with energy less than Eg contribute to the outputpower. Absorbed photons with energy W > Eg contribute only qV < Eg of electrical energy and the restof the energy is lost as heat. The efficiency of PV cells can be enhanced considerably by applying differenttechniques, for example multijunction cells [10, 12], multiple band gaps [18], multiple absorption, lightconcentration etc. Nevertheless, the efficiency is limited at least in the thermodynamic limit. Maximumobtainable conversion efficiency of solar radiation into electricity can be roughly estimated by using Carnotrelation [10]. For the temperature of the Sun of 5760 K and the temperature of surroundings of 300 K, themaximum efficiency would be 85% at cell temperature of 2470 K [10].

7 Crystalline solar cells

We move now to some specific examples of today’s solar cells, their properties and the physics behind.Most of present solar cells are manufactured from semiconductor Silicon [19], which can conduct electricitywhen electrons are excited from valence to conduction band via photon absorption. Silicon has a bandgapof ∼ 1.12 eV which corresponds to wavelength within infrared, λ ∼ 1.11 µm [10]. Theoretical limit tothe efficiency for such device is 30% [12]. Crystalline silicon (c-Si) is an indirect gap semiconductor, whichmeans that both a photon and a phonon are needed to raise the electron into the conduction band. Becauseof simultaneous involvement of both a photon and a phonon, indirect semiconductors have lower absorptionprobability than direct semiconductors. Thus, in order to absorb long wave part of solar spectrum, siliconlayers should be thick, and consequently large amounts of material must be used. The minimal thicknessof a crystalline silicon solar cell is 100 µm [20].

Another crystalline photovoltaic material is gallium arsenide (GaAs). It has a band gap of 1.42 eVat room temperature, almost the ideal one. It is a direct gap material which means it absorbs betterthan silicon which reduces the mass of devices significantly. Solar cells made of GaAs are only a few µmthick [20]. What is more, while silicon solar cell efficiency reduces with increasing temperature because ofmore recombination events, connected with more phonons, and reduced band gap, GaAs is not as muchtemperature sensitive. GaAs also has a better radiation hardness than silicon, so the extraterrestrialradiation does not affect its performance so much over cell’s lifetime. Its cost is significantly higher thanthat of silicon and it is primarily appropriate for space applications and light concentration systems.

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8 Thin-film solar cells

Figure 5: Schematic structures and band diagrams of three types of thin film devices: a-Si (top left), CIGS(top right) and CdTe (bottom). Reproduced from [10].

Because crystalline solar cells are expensive to produce, alternative photovoltaic materials are being re-searched that can be grown more cheaply. Various methods are used to deposit semiconductor layers asthin films directly onto useable substrates such as glass, metals, roofing sheets and plastics [19]. So far,amorphous silicon (a-Si) has been most widely used, for example in small consumer devices such as calcu-lators and in solar power plants. Apart from a-Si, polycristalline cadmium telluride (CdTe), polycristallinecopper indium disellenide (CuInSe2 and related compounds, often denoted by CIGS) and microcrystallinethin film silicon (p-Si) have also been well developed. These materials all have higher efficiencies (CdTehas efficiency above 16% [10] and the other two have efficiencies above 19% [10]) compared to a-Si (withefficiency below 10% [10]). However, high efficiencies of devices made of CIGS and CdTe were achieved inlaboratories and are connected with complicated deposition techniques, not really adapted for the indus-trial large-scale production. There are several technical problems making production of efficient modulesdifficult [10]. Some elements used, for example In, Ga and Te are rather rare and hence long term use maybe questionable. Schematic structures and band diagrams of a-Si, CIGS and CdTe solar cells are presentedin Figure 5. a-Si solar cell includes a p-i-n junction, junction of p-doped whereas the other two includevarious heterojunctions. The p-i-n junction is similar to p-n junction, the only difference is that there is aregion of intrinsic semiconductor between p-doped and n-doped regions.

Thin film cells are often multijunction devices - they include more than one junction between differentlydoped semiconductors. The use of heterojunctions increases efficiency of the devices in comparison tomonojunctions, because thin film materials often cannot be doped equally well n-type and p-type. In figure5 we see that CIGS solar cell includes heterojunctions between CIGS and CdS and between CdS and ZnO.The highly doped CdS layer with a band gap of 2.4 eV serves as a window, which reflects the electronsand therefore reduces losses due to surface recombination of charge carriers generated in CIGS by shortwavelenght light. The CdS also enables transport of electrons with minimum series resistance. However,heterojunctions have some disadvantages that lower the efficiency of a cell. The main problem is thatdefect states, encouraging the non-radiative recombination of charge carriers, appear at the heterojunctionbecause of differences between crystal structure or lattice constants of the two materials [12].

In comparison to single crystal materials, polycristalline and amorphous materials contain much moredefects which act as traps and recombination centres. Consequently, diffusion lenghts are shorter, dopingis more difficult, resistivity is increased and physical parameters like conductivity, minority carrier lifetime

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and diffusion constant become carrier density dependent. The latter makes transport equations as well astheir solutions rather complicated. Suitable thin film materials should be good absorbers so the cell can bethin, solving the problem of small diffusion length, therefore allowing less pure materials to be used. Here,we discuss some physics and properties of an a-Si solar cell.

8.1 Amorphous silicon solar cell

Figure 6: Top: Comparison between c-Siand a-Si density of electron states. Bot-tom: Position of chemical potential in pres-ence of defects.

The difference between single crystal and a-Si material is thata-Si lacks of long range crystal order. The neighbourhood ofan atom inside a lattice is very similar to that of crystallinesilicon atom, with a few degrees variation in the bond angles.The slightly altered local structure causes that momentum ofelectrons in valence and conduction band is largely undeter-mined, selection rules for photon absorption in crystalline sil-icon are no longer valid, so that a-Si behaves like a direct gapsemiconductor with high absorption coefficient (at energy 2.5eV, for example, absorption coefficient of c-Si is approximately104/cm, while absorption coefficient of a-Si is approximately105/cm). In Figure 6 (top), comparison between crystallineand amorphous silicon density of states is presented. Bandtails and dangling bond states occur in a-Si. Dangling bondstates are due to defects in the lattice, where an Si atom isbonded to only three of the neighbouring atoms, leaving thefourth valence band orbital unused. These dangling bondsmay be negatively charged, positively charged, or neutral. Thedangling bond states cause energy levels deep in the band gap.This kind of material can not be effectively doped, as the dan-gling states (with density more than 1016 cm−3 [12]) captureextra charge carriers. This so called background density of de-fects (also background doping) can be reduced by saturatingthe dangling bonds with atomic hydrogen. An atom of hy-drogen forms a bond with the unpaired electron in a neutraldangling defect, so that it can no longer trap a charge carrier.The density of dangling defects is then reduced by a factor of10. Still, the doping efficiency remains low in comparison tocrystalline silicon. The position of chemical potential is moved towards defect levels as shown in Figure 6(bottom), which enhances the activation energy of mayority carriers. In p-type a-Si this activation energyis around 0.4 eV [12]. These large activation energies limit the size of the built-in bias, increasing thedifference between the built-in bias and the band gap. Density of states as seen in Figure 6 leads to widedistribution of time constants for any transient process as well as strong dependence on the occupationof the states and hence carrier density. As we have mentioned before, mobility, lifetime and diffusionlenght are density dependent and difficult to determine. We shall mention some changes to be made whencalculating transport. Firstly, the tail density of states g is often modelled as

g(W ) =Nt

kBT0e

W−EckBT0 , (18)

where Nt is volume density of tail states, Ec is the energy of the lower boundary of conduction band andT0 describes the depth of the tail. And secondly, the dangling bond states can be modelled by two discretelevels in the band gap representing unoccupied and singly occupied defect state for which rate equations areconstructed for capture and emission of carriers. Typical values of parameters in undoped hydrogenateda-Si are: minority carrier lifetime of 10 to 20 µs, diffusion length of 0.1 µm and carrier mobility of 10−7

to 10−4 m2V−1s−1. By doping we increase the density of defects and so diffusion lenghts are furtherlyreduced. Because of small diffusion lengths, p-i-n junction is used in a-Si devices rather than p-n juction.

We should mention an important limitation to the a-Si cell efficiency, namely the light induced degra-dation. When illuminated, some of the Si-H bonds are broken, which increases the density of danglingbonds and reduces efficiency. This process can be reversed by annealing at a few hundred degrees Celsius

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and therefore a-Si may perform better in warmer enviroments. Typically, the efficiency is reduced by about30% in the first 6 months of operation and the fill factor falls by about 10%.

9 Novel solar cells

Novel technologies include dye-sensitized solar cells, organic materials and nanotechnology [19]. Thesenew material as well as operational concepts tend to lower the production cost further. The possibilityof depositing thin layers of photovoltaic materials onto light weight flexible substrates and wide range ofcolors makes them appropriate for placing onto buildings, clothing, mobile phones and so on. Apart fromreducing the cost, further development of third generation solar cells is focussing on improving efficiency,stability and durability. Here, we shortly represent operation of dye-sensitized solar cells.

9.1 Operation principles of dye-sensitized solar cells

Dye sensitized solar cells or also Gratzel solar cells [21] are photoelectrochemical cells. A basic type ofelectrochemical cell does not include a p-n or other junction between two solid inorganic semiconductors,but is composed of semiconductor electrode, an electrolyte layer and counter electrode, covered with Pt,as shown in Figure 7. The basis for both electrodes is the transparent TCO glass. TCO is short fortransparent conductive oxides. Photoelectrochemical cell converts light to electric power with no netchemical change behind [22]. At the interface between semiconductor and electrolyte, a space charge layeris formed, depending on type of both semiconductor and electrolyte. In equilibrium, the chemical potentialof electrons in the solid µn is equal to the redox potential of the electrolyte Eredox. Photons exceedingthe band gap energy produce electron hole pairs that are separated by electric field in the space chargelayer. The electrons diffuse to the end of electrode and are transported through the external circuit withresistance. The holes are driven to the electrolyte interface, where they oxidize a molecule of redox pair.The oxidized molecule is reduced again by an electron that re-enters the cell through the external circuit.

In a dye-sensitized solar cell, absorption of photons is enhanced by using an appropriate dye, absorbedon the semiconductor surface. Light causes transition of an electron in the dye to exited state S∗, as seenin Figure 7. Such an excited electron can tunnel to the semiconductor quicker than relaxation occurs -typical times of tunneling are of order 10−10 s and the lifetime of the excited state is of order 10−8 s [21].After the electron is transferred to the semiconductor, it again diffuses to the end of the electrode and flowsthrough the external circuit back to the cell. The oxidized dye molecule is reduced again in redox reactionwith electrolyte. The electrolyte is reduced, again, by the electron that re-enters the cell at the counterelectrode. The whole sequence of reactions can be written down as follows, where the semiconductor usedis TiO2 and the electrolyte is I−3 /I−. The latter reaction is catalyzed by Pt.

TiO2|S + hν → TiO2|S∗N (19)

TiO2|S∗ → TiO2|S+ + e- (20)

TiO2|2S+ + I− → TiO2|2S + I−3 (21)

I−3 + 2e− → I− (22)

The potential difference between electrodes is given by the difference between chemical potential ofsemiconductor and redox potential of electrolyte.

There are other processes within the dye-sensitized cell, that are undesired and decrease the efficiencyof the cell. These are: decay of excited state of the electron from the dye, recombination of the electronwith the dye and recombination of the electron with the electrolyte [21].

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Figure 7: Left: Structure and operation of a dye-sensitized solar cell. The TCO glass at the sides is notsketched. The incident light excites an electron in a dye molecule into a higher state. Such an excitedelectron tunnels onto a TiO2 molecule. The electron then diffuses to the end of the electrode, enters theexternal circuit and re-enters the cell through the opposite electrode. The oxidized dye molecule is reducedby the electrolyte and the electrolyte is reduced by the re-entering electron. Reproduced from [23]. Right:Surface of a mesoporous anatase film (scanned by SEM) prepared from a hydrothermally processed TiO2

colloid. Scale is 50 nm. Reproduced from [22].

9.2 Nanocrystaline junctions

It could be shown that only dye molecules directly attached to the semiconductor surface are able toefficiently inject charge carriers into the semiconductor with a quantum yield of more than 90% [10]. Inorder to absorb as much light as possible, minutely structured materials with an enourmous internal surfacearea were developed. Mesoporous oxide films, made up of arrays of tiny nano - crystals are used instead offlat semiconductor electrode. The pores are filled with semiconducting or conducting material. Throughsuch a junction of two interpenetrating networks charge carriers can move very easily. The structure istypically 10 µm thick and has a surface area available for dye absorption over a thousand times larger thanthat of a flat electrode [22]. Examples of oxides used are TiO2, ZnO, SnO2, Nb2O5, CdSe and other. Anexample of mesoscopic material used for dye-sensitized solar cell electrode is presented in Figure 7 (righthand side).

9.3 Characteristics and practical aspects

Today’s dye-sensitized solar cells reach the short-circuit photocurrent of more than 20 mA/cm2 [22], theopen-circuit voltage of 1 V and efficiency of more than 11% [24] in a laboratory under STC. These char-acteristics make dye-sensitized solar cells competitive with other solar cells, together with low productioncost. The main advantage of dye-sensitized solar cells is that the electric current results from majority,and not minority carrier transport. This means that no recombination events within the semiconductorcan happen. This allows use of less pure materials, simple processing and reduces cost. However, impurematerials can reduce the cell’s lifetime.

The problem is, however, that electrolyte used must sustain as much as 108 operating cycles, neededfor cell operation of 20 years [22], which is desired lifetime for a photovoltaic cell. Liquid electrolytes pre-pared in combination with some appropriate solvents provide a system able to pass the standard stabilityqualification tests for outdoor applications [22]. But, there is also a problem with leakage of liquid elec-trolyte, evaporation and possibility of destruction because of low temperatures during winter. Therefore,much effort has been made in order to replace the liquid electrolyte with either a gel electrolyte, solid-stateelectrolyte, or p-conducting polymer material [10]. No efficient solid state electrolytes, alternative to liquidelectrolytes have been discovered so far [25].

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10 Comparison of PV devices

Table 1 presents some efficiencies, illuminated areas, open-circuit voltages, short-circuit currents and fillfactors of different types of solar cells. Table 2 presents the same characteristics for some PV modules. Theexisting modules have somewhat lower efficiencies than single solar cell devices. The highest cell efficiency(over 30%) was achieved with multijunction devices, where one of the materials used is GaAs. This is notsurprising as we have already said that GaAs is a strong absorber with nearly ideal band gap.

In general, devices with higher short-circuit current have lower open-circuit voltage. It is because Jscand Voc depend on the width of the band gap - the Jsc increases and the Voc decreases with increasing bandgap, as we have mentioned earlier.

Classification Efficiency

(%)

Area

(cm2)

Voc

(V)

Jsc

(mA/cm2)

FF

(%)

Test centre

(and date)

Silicon

Si (crystalline) 25.0 0.5 4.00 0.705 42.7 82.8 Sandia (3/99)

Si (multicrystalline) 20.4 0.5 1.002 0.664 38.0 80.9 NREL (5/04)

Si (thin film transfer) 16.7 0.4 4.017 0.645 33.0 78.2 FhG-ISE (7/01)III-V cells

GaAs (crystalline) 26.1 0.8 0.998 1.038 29.7 84.7 FhG-ISE (12/07)

GaAs (thin film) 26.1 0.8 1.001 1.045 29.5 84.6 FhG-ISE (07/08)

GaAs (multicrystalline) 18.4 0.5 4.011 0.994 23.2 79.7 NREL (11/95)

InP (crystalline) 22.1 0.7 4.02 0.878 29.5 85.4 NREL (4/90)

Thin film chalcogenide

CIGS (cell) 19.4 0.6 0.994 0.716 33.7 80.3 NREL (1/08)

CdTe (cell) 16.7 0.5 1.032 0.845 26.1 75.5 NREL (9/01)

Amorphous/nanocrystalline Si

Si (amorphous) 9.5 0.3 1.070 0.859 17.5 63.0 NREL (4/03)

Si (nanocrystalline) 10.1 0.2 1.199 0.539 24.4 76.6 JQA (12/97)

Photochemical

Dye sensitised 10.4 0.3 1.004 0.729 22.0 65.2 AIST (8/05)Organic

Organic polymer 5.15 0.3 1.021 0.876 9.39 62.5 NREL (12/06)

Multijunction devices

GaInP/GaAs/Ge 32.0 1.5 3.989 2.622 14.37 85.0 NREL (1/03)

GaInP/GaAs 30.3 4.0 2.488 14.22 85.6 JQA (4/96)

GaAs/CIS (thin film) 25.8 1.3 4.00 — — — NREL (11/89)

Table 1: Efficiencies and other characteristics of different solar cells. NREL = National renewable energylaboratory, FhG-ISE = Fraunhofer Institut fur Solare Energiesysteme; JQA = Japan Quality Assurance;AIST = Japanese National Institute of Advanced Industrial Science and Technology. Stability of organicand dye-sensitised solar cells was not investigated. Reproduced from [11].

Classification Efficiency

(%)

Area

(cm2)

Voc

(V)

Isc

(A)

FF

(%)

Test centre

(and date)

Si (crystalline) 22.9 0.6 778 5.60 3.97 80.3 Sandia (9/96)

Si (large crystalline) 20.3 0.6 16300 66.1 6.35 78.7 Sandia (8/07)

Si (multicrystalline) 15.5 0.4 1017 14.6 1.37 78.6 Sandia (10/94)

Si (thin-film polycrystalline) 8.2 0.2 661 25.0 0.320 68.0 Sandia (7/02)

CIGSS 13.5 0.7 3459 31.2 2.18 68.9 NREL (8/02)

CdTe 10.9 0.5 4874 26.21 3.24 62.3 NREL (4/00)

a-Si/a-SiGe/a-SiGe (tandem) 10.4 0.5 905 4.353 3.285 66.0 NREL (10/98)

Table 2: Efficiencies and other characteristics of different modules. Reproduced from [11].

11 Conclusion

Solar cells currently used contain p-n junctions. Theoretically, with no reflection of light, perfect absorptionand no losses inside the material or at the contacts, the efficiency of a solar cell containing a single junctioncould reach 33%. The actual maximum efficiencies are around 25% with use of the best materials, which arevery expensive. Various alternatives to the expensive devices are being reasearched. The main goal for thefuture is to further reduce the cost of PV modules, so the PV can be more widely used. Apart from reducingamount of material used, the price is also reduced indirectly by increasing the efficiency of PV devices.The efficiency is most effectively increased by using tandem cells in combination with light concentrationsystems, where mirrors are used to focus sunlight on to the surface of PV modules. Efficiencies above 30%are possible [10]. The limiting factor to the efficiency is heating of the system exposed to light irradiationwith power of several hundreds of suns.

In the past 10 years, the price of all known types of PV modules has fallen significantly. For example,the price of electricity produced by c-Si modules has fallen from ∼0.40 e/kWh to ∼0.30 e/kWh and for

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a-Si modules the price has fallen from ∼0.20 e/kWh to ∼0.15 e/kWh. The price of electricity producedby CIGS modules was ∼0.17 e/kWh in 2003 and has fallen to ∼0.09 e/kWh until 2010 [26]. All of thementioned modules have a lifetime of at least 20 years [10, 27]. During this time the efficiency falls forabout 20% (see, for example [27]).

There are many installation possibilities for PV modules, among the best known being installation onthe roofs of the houses. In urban areas, the modules may be connected to the grid system, while at remotelocations, they are independent systems and have to be combined with a good charge storage system. Thereare some ideas for the future, considering installation of PV, for example in large plain deserts, which areextremely sunny locations. The electric energy produced in deserts would have to be transported to otherparts of the world, which could be done by using power lines, or transport of liquified hydrogen. Water issplit into hydrogen and oxygen by electrolysis and hydrogen can then serve as the energy carrier [10].

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