The Phys of Solar Cells

March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

Chapter 1 Introduction

1. Introduction 1.1. Photons In, Electrons Out: The Photovoltaic Eﬀect

1.1 PhSolarotons photoin, electronvoltaics ouenergyt: The Phconotovolversiontaic iseffecta one-step conversion process which generates electrical energy from light energy. The explanation relies on ideas Solar photovoltaic energy conversion is a one-step conversion process which generates electrical energy from quantum theory. Light is made up of packets of energy, called photons, from light energy. The explanation relies on ideas from quantum theory. Light is made up of packets of energy, whosecalled photenergyons, depwhosendse energonlyy depenupondsthe onlfrequencyy upon the ,forrequcolour,ency, orof coltheourligh, of t.theThe light. The energy energyof visibleof phvisibleotons isphotons sufficientis tosuﬃcien excite electront to excites, bounelectrons,d into solids,b oundup to hinigtohersolids, energy levels where thupey toare highermore freeenergy to movleve. Aelsn exwheretreme extheyampleare of morethis is thfreee phtootoelectricmove. Aneffect,extreme the celebrated experimexampleent which ofwathiss explisaithened photoby Einelectricstein in 1905,eﬀect, whtheere celebratedblue or ultravexpioleeriment light provt whicidesh enough energy fwoasr electronexplaineds to escapeby Einstein completelyin f1905,rom thewhere surfaceblue of a ormetal.ultra Normvioletally,ligh whent prolighvidest is absorbed by matter,enough photonenergys are givforen uelectronsp to excite electronto escaps toe hcompletelyigher energy fromstates wtheithinsurface the material,of a but the excited metal.electronNormallys quickly relax, when backligh tot thiseirabsorb grounded state.by matter,In a photovphotonsoltaic devareice,giv henowupever,to there is some buexciteilt-in asyelectronsmmetry wtohichhigher pulls energythe excitedstates electrowithinns awtheay bematerial,fore they canbut relax,the excitedand feeds them them to an external circuit. The extra energy of the excited electrons generates a potential difference, or electrons quickly relax back to their ground state. In a photovoltaic device, electro-motive force (e.m.f.). This force drives the electrons through a load in the external circuit to do electrical work. pn uv light light metal

Current e- e-

Load

Figure 1.1Fig. Co1.1.mparisoComparisonn of the photoeoflectrtheic ephotoffect (leelectricft), whereeffect uv ligh(left),t liberatewheres electruvons lighfromt thelib seratesurface oelectronsf a metal, with the photovoltfromaic effecthe t surfacein a solar cofell a(righmetal,t). The withphotovolttheaicphoto cell needvoltaics to haveeffect some inspaatialsolar asymmetcellry, (righsuch at).s coThentacts with photovoltaicdiffercellent elneedsectronicto prohapevrtiee ssome, to drivspatiale the exciteasymmetryd electrons, tosucwahrdsas thecon extetactsrnal cirwithcuit. different electronic properties, to drive the excited electrons through the external circuit. The effectiveness of a photovoltaic device depends upon the choice of light absorbing materials and the way in which they are connected to the external 1circuit. The following chapters will deal with the underlying physical ideas, the device physics of solar cells, the properties of photovoltaic materials and solar cell design. In this Chapter we will summarise the main characteristics of a photovoltaic cell without discussing its physical function in detail.

1.2 Brief history of the solar cell

The photovoltaic effect was first reported by Edmund Bequerel in 1839 when he observed that the action of light on a silver coated platinum electrode immersed in electrolyte produced an electric current. Forty years later the first solid state photovoltaic devices were constructed by workers investigating the recently discovered photoconductivity of selenium. In 1876 William Adams and Richard Day found that a photocurrent could be produced in a sample of selenium when contacted by two heated platinum contacts. The photovoltaic action of the selenium differed from its photoconductive action in that a current was produced spontaneously by the action of light. No external power supply was needed. In this early photovoltaic device a rectifying junction had been formed between the semiconductor and the metal contact. In 1894 Charles Fritts prepared what was probably the first large area solar cell by pressing a layer of selenium between gold and another metal. In the

1 March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

2 The Physics of Solar Cells

however, there is some built-in asymmetry which pulls the excited electrons away before they can relax, and feeds them to an external circuit. The extra energy of the excited electrons generates a potential diﬀerence, or electro- motive force (e.m.f.). This force drives the electrons through a load in the external circuit to do electrical work. The eﬀectiveness of a photovoltaic device depends upon the choice of light absorbing materials and the way in which they are connected to the external circuit. The following chapters will deal with the underlying physical ideas, the device physics of solar cells, the properties of photovoltaic materials and solar cell design. In this chapter we will summarise the main characteristics of a photovoltaic cell without discussing its physical function in detail.

1.2. Brief History of the Solar Cell

The photovoltaic effect was first reported by Edmund Bequerel in 1839 when he observed that the action of light on a silver coated platinum electrode immersed in electrolyte produced an electric current. Forty years later the first solid state photovoltaic devices were constructed by workers investigating the recently discovered photoconductivity of selenium. In 1876 William Adams and Richard Day found that a photocurrent could be produced in a sample of selenium when contacted by two heated platinum contacts. The photovoltaic action of the selenium differed from its photoconductive action in that a current was produced spontaneously by the action of light. No external power supply was needed. In this early photovoltaic device, a rectifying junction had been formed between the semiconductor and the metal contact. In 1894, Charles Fritts prepared what was probably the first large area solar cell by pressing a layer of selenium between gold and another metal. In the following years photovoltaic effects were observed in copper–copper oxide thin film structures, in lead sulphide and thallium sulphide. These early cells were thin film Schottky barrier devices, where a semitransparent layer of metal deposited on top of the semiconductor provided both the asymmetric electronic junction, which is necessary for photovoltaic action, and access to the junction for the incident light. The photovoltaic effect of structures like this was related to the existence of a barrier to current flow at one of the semiconductor–metal interfaces (i.e., rectifying action) by Goldman and Brodsky in 1914. Later, during the 1930s, the theory of metal–semiconductor barrier layers was developed by Walter Schottky, Neville Mott and others. March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

Introduction 3

However, it was not the photovoltaic properties of materials like selenium which excited researchers, but the photoconductivity. The fact that the current produced was proportional to the intensity of the incident light, and related to the wavelength in a definite way meant that photoconductive materials were ideal for photographic light meters. The photovoltaic effect in barrier structures was an added benefit, meaning that the light meter could operate without a power supply. It was not until the 1950s, with the development of good quality silicon wafers for applications in the new solid state electronics, that potentially useful quantities of power were produced by photovoltaic devices in crystalline silicon. In the 1950s, the development of silicon electronics followed the discov- ery of a way to manufacture p–n junctions in silicon. Naturally n type silicon wafers developed a p type skin when exposed to the gas boron trichloride. Part of the skin could be etched away to give access to the n type layer beneath. These p–n junction structures produced much better rectifying action than Schottky barriers, and better photovoltaic behaviour. The first silicon solar cell was reported by Chapin, Fuller and Pearson in 1954 and converted sunlight with an efficiency of 6%, six times higher than the best previous attempt. That figure was to rise significantly over the following years and decades but, at an estimated production cost of some $200 per Watt, these cells were not seriously considered for power generation for sev- eral decades. Nevertheless, the early silicon solar cell did introduce the pos- sibility of power generation in remote locations where fuel could not easily be delivered. The obvious application was to satellites where the require- ment of reliability and low weight made the cost of the cells unimportant and during the 1950s and 60s, silicon solar cells were widely developed for applications in space. Also in 1954, a cadmium sulphide p–n junction was produced with an efficiency of 6%, and in the following years studies of p–n junction photovoltaic devices in gallium arsenide, indium phosphide and cadmium tel- luride were stimulated by theoretical work indicating that these materials would offer a higher efficiency. However, silicon remained and remains the foremost photovoltaic material, benefiting from the advances of silicon tech- nology for the microelectronics industry. Short histories of the solar cell are given elsewhere [Shive, 1959; Wolf, 1972; Green, 1990]. In the 1970s the crisis in energy supply experienced by the oil-dependent western world led to a sudden growth of interest in alternative sources of energy, and funding for research and development in those areas. Photo- voltaics was a subject of intense interest during this period, and a range of March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

4 The Physics of Solar Cells

strategies for producing photovoltaic devices and materials more cheaply and for improving device efficiency were explored. Routes to lower cost included photoelectrochemical junctions, and alternative materials such as polycrystalline silicon, amorphous silicon, other ‘thin film’ materials and organic conductors. Strategies for higher efficiency included tandem and other multiple band gap designs. Although none of these led to widespread commercial development, our understanding of the science of photovoltaics is mainly rooted in this period. During the 1990s, interest in photovoltaics expanded, along with growing awareness of the need to secure sources of electricity alternative to fossil fuels. The trend coincides with the widespread deregulation of the electricity markets and growing recognition of the viability of decentralised power. During this period, the economics of photovoltaics improved primarily through economies of scale. In the late 1990s the photovoltaic production expanded at a rate of 15–25% per annum, driving a reduction in cost. Photovoltaics first became competitive in contexts where conventional electricity supply is most expensive, for instance, for remote low power applications such as navigation, telecommunications, and rural electrification and for enhancement of supply in grid-connected loads at peak use [An- derson, 2001]. As prices fall, new markets are opened up. An important example is building integrated photovoltaic applications, where the cost of the photovoltaic system is offset by the savings in building materials.

1.3. Photovoltaic Cells and Power Generation

1.3.1. Photovoltaic cells, modules and systems

The solar cell is the basic building block of solar photovoltaics. The cell can be considered as a two terminal device which conducts like a diode in the dark and generates a photovoltage when charged by the sun. Usually it is a thin slice of semiconductor material of around 100 cm2 in area. The surface is treated to reﬂect as little visible light as possible and appears dark blue or black. A pattern of metal contacts is imprinted on the surface to make electrical contact (Fig. 1.2(a)). When charged by the sun, this basic unit generates a dc photovoltage of 0.5 to 1 volt and, in short circuit, a photocurrent of some tens of milliamps per cm2. Although the current is reasonable, the voltage is too small for most applications. To produce useful dc voltages, the cells are connected together in series and encapsulated into modules. A module typically contains supply is most expensive, for instance, for remote low power applications such as navigation, telecommunications, and rural electrification and for enhancement of supply in grid-connected situations at peak use (Anderson, 2001). As prices fall, new markets are opened up. An important example is building integrated photovoltaic applications, where the cost of the photovoltaic system is offset by the savings in building materials.

1.3 Photovoltaic cells and power generation

1.3.1 Photovoltaic cells, modules and systems.

When charged by the sun, this basic unit generates a dc photovoltage of 0.5 to 1 volt and, in short circuit, a photocurrent of some tens of milliamps per cm2. Although the current is reasonable the voltage is too small for most applications. To produce useful dc voltages, the cells are connected together in series and encapsulated into modules. A module typically contains 28 to 36 cells in series, to generate a dc output voltage of 12V in standard illumination conditions (Fig. 1.2 (b)). The 12V modules can be used singly, or connected in parallel and series into an array with a larger current and voltage output, according to the power demanded by the application (Fig. 1.2(c)). Cells within a module are integrated with bypass and blocking diodes in order to avoid the complete loss of power which would result if one cell in the series fails. Modules within arrays are similarly protected. The array, which is also called a photovoltaic generator, is designed to generate power at a certain current and a voltage which is some multiple of 12V, under standard illumination. For almost all applications the illumination is too variable for efficient operation all the time and the photovoltaic generator must be integrated with a charge storage system (a battery) and with components for power regulation (Fig.1.2(d)). The battery is used to store charge generated during sunny periods and the power conditioning ensures that the power supply is regular and less sensitive to the solar irradiation. For ac electrical power, to power ac designed appliances and for integration with an electricity grid, the dc March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc current supplied by the photovoltaic modules is converted to ac power of appropriate frequency using an inverter.

The design and engineering of photovoltaic systems is beyond the scope of this book. A more detailed introduction is given by Markvart [Markvart, 2000] and Lorenzo [Lorenzo, 1994]. Photovoltaic systems Introduction 5 engineering essentially depends upon the electrical characteristics of the individual cells.

+12V

(a) (b)

+V 3

Power PV generator conditioning Load

Module Storage 0 (Battery (dc) or Grid (ac)) (c) (d) Figure 1.2 (a) Photovoltaic cell (b) In a module, cells are connected in series to give a standard dc voltage of 12V (c) For any appFig.licati1.2.on, mo(a)dulePhotos are covnnoltaicected incell serishoes andwing parasurfacellel into ancon artactray, wpatternshich produc(b)es sufInficiaemont curdule,rent andcells voltage to meet the aredemusuallyand. (d) Iconnectedn most cases intheseries photovoltotagivic aerraay standardshould be indctegrvaoltageted with ofcom12poVnen(c)ts forF orchaanrgey regappli-ulation and storage. cation, modules are connected in series into strings and then in parallel into an array, which produces suﬃcient current and voltage to meet the demand. (d) In most cases 1.3.2.the photo Somevoltaic imporarratanty defshouldinitionsbe integrated with components for charge regulation and storage.

solar cell battery 28 to 36 cells in series, to generate a dc output voltage of 12 V in standard illumination conditions (Fig. 1.2(b)). The 12 V modules can be used singly, or connected in parallel and series into an array with a larger current and voltage output, according to the power demanded by the application

(Fig. 1.2(c)).ABCells within loada module are integrated with bypass andloadblocking diodes in order to avoid the complete loss of power which would result if one

Figure 1.3 The solar cell may replace a battery in a simple circuit.

The solar cell can take the place of a battery in a simple electric circuit (Fig. 1.3). In the dark the cell in circuit A does nothing. When it is switched on by light it develops a voltage, or e.m.f., analogous to the e.m.f. of the battery in circuit B. The voltage developed when the terminals are isolated (infinite load

resistance) is called the open-circuit voltage Voc . The current drawn when the terminals are connected

together is the short-circuit current Isc. For any intermediate load resistance RL the cell develops a

voltage V between 0 and Voc and delivers a current I such that V = IRL and I(V) is determined by the current-voltage characteristic of the cell under that illumination. Thus both I and V are determined by the illumination as well as the load. Since the current is roughly proportional to the illuminated area, the

short circuit current density Jsc is the useful quantity for comparison. These quantities are defined for a simple, ideal diode model of a solar cell in section 1.4 below.

Box 1.1. Solar cell compared with conventional battery

The photovoltaic cell differs from a simple dc battery in these respects: the e.m.f. of the battery is due to the permanent electrochemical potential difference between two phases in the cell, while the solar cell derives its e.m.f. from a temporary change in electrochemical potential caused by light. The power delivered by the battery to a constant load resistance is relatively constant while the power delivered by the solar cell depends on the incident light intensity, and not primarily on the load. The battery is completely decharged when it reaches the end of its life while the solar cell, although its output varies with intensity, is in principle never exhausted since it can be continually recharged with light.

The battery is modelled electrically as a voltage generator and is characterised by its e.m.f. (which, in practice, depends upon the degree of discharge), its charge capacity, and by a polarisation curve which

4 March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

6 The Physics of Solar Cells

cell in the series failed. Modules within arrays are similarly protected. The array, which is also called a photovoltaic generator, is designed to generate power at a certain current and a voltage which is some multiple of 12 V, under standard illumination. For almost all applications, the illumination is too variable for eﬃcient operation all the time and the photovoltaic generator must be integrated with a charge storage system (a battery) and with components for power regulation (Fig. 1.2(d)). The battery is used to store charge generated during sunny periods and the power conditioning ensures that the power supply is regular and less sensitive to the solar irradiation. For ac electrical power, to power ac designed appliances and for integration with an electricity grid, the dc current supplied by the photovoltaic modules is conv+Verted to +Vac power of appropriate frequency using an inverter. The design and engineering of photovoltaic systems is beyond the scope of this book. A more detailed introduction is given by Markvart [Markvart, 2000] and Lorenzo [Lorenzo, 1994]. Photovoltaic systems engineering depends to a large degree upon the electrical characteristics of the individual Power Power cells. PV generatorPV generatorconditioning conditioning Load Load

1.3.2. Some important deﬁnitions Module Module The solar cell can take the place ofStoragea batteryStoragein a simple electric circuit (Fig. 1.3).0 In the0 dark the cell in circuit( BatteryA (dc)do( Batteryes nothing. (dc) When it is switched or Grid (ac)) or Grid (ac)) on by ligh t it develops a voltage, or e.m.f., analogous to the e.m.f. of the

Figure 1.2 (a)F Phiguotreovolt 1battery.2 (aaic) Phcellot (bovoltin) Incircuita aic mod cell u(ble,B.) Icne llsThea mod are uvclooltagee,n nceecllsted a rideven csoenrielopnesec ttoed edgi iven whens ae ristesan tdoa thegirdve dc terminalsa volt stanadgeard of d 1c2 voltVare (ca)ge isolatedF oofr a1n2yV (c) For any application, mapplodulicatioes arn,(inﬁnitee comonnedulctees dar loadine cosennerieresistance)scte andd inpar sealrlieels intoandis anparcalled aralrlaeyl ,into wtheh ichan op arprroenaducey, wcirhs ichsufcuit fpricieoducenvoltaget curs sufrentfi cieandVno tcv cur.oltagTherente to and currenm eveot lthetagte to meet the demand. (d) Idne mamosntddra c. a(dses)wn I nth mosewhen phto ctaovoltsesthe tahiec paterminalshrraotyovolt shoualdic abrraeare inyt sehgraconnectedoutlded b we iitnht ecgraompttogetheredon weniths forcomp cishonargetheen tregus forshortla cthioanrge acirn regud cuitstoralatigoe.cur-n and storage. rent Isc. For any intermediate load resistance RL the cell develops a voltage V between 0 and Voc and delivers a current I such that V = IRL and 1.3.2. Some1.3.2. impor SomeIt(antV ) idefmisporindeterminedittiantons definitionsby the current–voltage characteristic of the cell under

solar cell solar cell battery battery

ABABload load load load

(a) (b) Figure 1.3 ThFei gsourlaer 1.3 cel lT mhea yso rleaplr acecell am batteay rerply acein a a sim battepler ycir inc uit.a simple circuit. Fig. 1.3. The solar cell may replace a battery in a simple circuit. The solar cellThe can solar tak celle th cane place take of th ae batteryplace of in a abattery simple in electric a simp lecircu electricit (Fig circu. 1.3).it (FigIn th. e1.3). dark In th the ecell dark in the cell in circuit A dcircuitoes no thing.A doe sW nohenthing. it is Wswhitcheden it is o swn bitchedy light o itn dbeyvelo lightp sit a d voeveloltage,ps oa rvo e.mltage,.f., analo or e.mgo.fu.,s analoto thegous to the e.m.f. of thee.m ba.fttery. of the in circuitbattery B in. Tcircuithe vo ltageB. T hdee velovoltageped dwehveloen theped term wheninals the areterm isoinalslated are (inf isoinitelated lo (infad inite load resistance)resistan is calledce) th ise open-cicalled thrceui open-cit voltagercui Vtoc vol . Ttagehe cu Vrrenoc . Tt hdrawe cunrren whten draw then term whenin alsthe areterm coninalsnected are connected together isto thegether shor t-iscircu the shit ocurt-rrencircut Iitsc .cu Forrren ant yI scin. termFor anediatey interm loadediate resistan loadce resistanRL the cellce RdLe velothe cellps a develops a voltage V betvoltaweenge V 0 betandw Veenoc an0 dan delivd Vocers an ad cudelivrrenerst I a su cuchrren thtat I V su =ch IR thL atan Vd I=( VIR) Lis an dedterm I(V)ined is d ebtermy theined by the current-volcurtagere ntchar-volacttageeri charstic oactf theeri scelltic oundf theer cellthat undillumeri natiothat illumn. Thusinatio bon.th TI husand bVo areth I determand V areined determ by ined by the illuminathetio illumn as winaelltio ans theas w loealld a. sSinc the elo thead. cSincurreent the is rcouughlyrrent ispr oportionroughly palr oportionto the illualm toin thatede illu area,min thatede area, the short circuishort curt cirerntcui denst curitrye Jntsc densis theit yusef Jsc ulis qtheuantity useful fo qr ucoantitympariso for nco. mThpeseariso qunantities. These arequantities defined are fo rd aefined for a simple, idealsim dpile,od eid mealod deilo odfe a m soolardel cellof a in so sectiolar celln 1in.4 sectio belown .1.4 below.

Box 1.1. SolBoxar 1.1. cell comparSolar celedl comparwith convented wiitonalh convent batteironaly battery

The photovTohltaice ph ocelltov odltaiciffers cell fro mdi faf esimrs fprolem d ac simbatteryple dinc thesebattery resp in ects:these the resp e.mects:.f. othef the e.m b.af.ttery of the is dbuaettery is due to the permtoan thene tperm electrochanentem electrochical potenemtialical difpotenferentialce difbetwfereneence tw betwo pheenases tw ino thpheases cell, in w thhilee cell, the solarwhile the solar cell derivecells its derive.m.fe.s f ritsom e.m a tem.f. fporaryrom a temchanporaryge in electrochchange inem electrochical potenemtialical cau potensedtial by caulighsedt. T byhe ligpowhter. The power delivered bdye liveredthe battery by the to ab acotterynstant to alo coadnstant resistance load resistanceis relatively is corelativelynstant w cohilenstant the pwohwileer thedelivered power bdyelivered by the solar cellthe sodelarpe ndcells o dne ptheend incids one ntthe light incid intensityent light, andintensity not ,p randimarily not opnrim thearily lo adon. Tthehe lobaadttery. T hise battery is completelyco dmecharpletelyged dwecharhen gedit reaches when theit reaches end of theits lifende wofh ileits thelife sowhlarile cell, the soaltholar ughcell, its altho outpughut varits ioesutput varies with intensitywith, is intensity in princip, isl ein never princip exhaustedle never exhaustedsince it can since be co itntinually can be co rechargedntinually rechargedwith light. with light.

The batteryT hise mbatteryodelled is electricallymodelled electrically as a voltage as genera voltaagetor generand isa tchoraracterised and is characterised by its e.m .byf. (w itsh ie.mch, .fin. (which, in practice, depenpractice,ds u pondepen thde sdeg uponree thofe dischdegreearg ofe), disch its chargarge),e itscapacity charg,e an capacityd by a ,polarisation and by a polarisation curve which curve which

4 4 March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

Introduction 7

that illumination. Thus both I and V are determined by the illumination as well as the load. Since the current is roughly proportional to the illuminated area, the short circuit current density Jsc is the useful quantity for comparison. These quantities are deﬁned for a simple, ideal diode model of a solar cell in Sec. 1.4 below.

Box 1.1. Solar cell compared with conventional battery

The photovoltaic cell differs from a simple dc battery in these respects: the e.m.f. of the battery is due to the permanent electrochemical potential difference between two phases in the cell, while the solar cell derives its e.m.f. from a temporary change in electrochemical potential caused by light. The power delivered by the battery to a constant load resistance is relatively constant, while the power delivered by the solar cell depends on the incident light intensity, and not primarily on the load (Fig. 1.4). The battery is completely discharged when it reaches the end of its life, while the solar cell, although its output varies with intensity, is in principle never exhausted, since it can be continually recharged with light. The battery is modelled electrically as a voltage generator and is characterised by its e.m.f. (which, in practice, depends upon the degree of discharge), its charge capacity, and by a polarisation curve which describes how the e.m.f. varies with current [Vincent 1997]. The solar cell, in con- trast, is better modelled as a current generator, since for all but the largest loads the current drawn is independent of load. But its characteristics depend entirely on the nature of the illuminating source, and so Isc and Voc must be quoted for a known spectrum, usually for standard test conditions (defined below).

1.4. Characteristics of the Photovoltaic Cell: A Summary

1.4.1. Photocurrent and quantum eﬃciency

The photocurrent generated by a solar cell under illumination at short circuit is dependent on the incident light. To relate the photocurrent density, Jsc, to the incident spectrum we need the cell’s quantum eﬃciency, (QE). QE(E) is the probability that an incident photon of energy E will deliver one electron to the external circuit. Then

Jsc = q bs(E)QE(E)dE (1.1) Z March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

8 The Physics of Solar Cells

Voltage Solar cell

Battery e.m.f. Battery

Increasing light intensity

Current

Fig. 1.4. Voltage–current curves of a conventional battery (grey) and a solar cell under diﬀerent levFelsig 1.4of illumination. A battery normally delivers a constant e.m.f. at diﬀerent levels of current drain except for very low resistance loads, when the e.m.f. begins to fall. The battery e.m.f. will also deteriorate when the battery is heavily discharged. The solar cell delivers a constant current for any given illumination level while the voltage is determined largely by the resistance of the load. For photovoltaic cells it is usual to plot the data in the opposite sense, with current on the vertical axis and voltage on the horizontal axis. This is because the photovoltaic cell is essentially a current source, while the battery is a voltage source.

where bs(E) is the incident spectral photon flux density, the number of photons of energy in the range E to E +dE which are incident on unit area in unit time and q is the electronic charge. QE depends upon the absorption coefficient of the solar cell material, the efficiency of charge separation and the efficiency of charge collection in the device but does not depend on the incident spectrum. It is therefore a key quantity in describing solar cell performance under different conditions. Figure 1.5 shows a typical QE spectrum in comparison with the spectrum of solar photons. QE and spectrum can be given as functions of either photon energy or wavelength, λ. Energy is a more convenient parameter for the physics of solar cells and it will be used in this book. The relationship between E and λ is defined by hc E = (1.2) λ where h is Planck’s constant and c the speed of light in vacuum. A convenient rule for converting between photon energies, in electron-Volts, and wavelengths, in nm, is E/eV = 1240/(λ/nm). March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

Introduction 9

QE of gallium arsenide cell u. . Solar photon flux density a / y t i . s n u . de / a ux l QE f on ot Ph

200 400 600 800 1000 1200 1400 1600 1800 Wavelength / nm

Fig. 1.5. QuanFiguretum 1.5 efficiency of GaAs cell compared to the solar spectrum. The vertical scale is in arbitrary units, for comparison. The short circuit photocurrent is obtained by integrating the product of the photon flux density and QE over photon energy. It is desirable to have a high QE at wavelengths where the solar flux density is high.

1.4.2. Dark current and open circuit voltage

When a load is present, a potential difference develops between the terminals of the cell. This potential difference generates a current which acts in the opposite direction to the photocurrent, and the net current is reduced from its short circuit value. This reverse current is usually called the dark current in analogy with the current Idark(V ) which flows across the device under an applied voltage, or bias, V in the dark. Most solar cells behave like a diode in the dark, admitting a much larger current under forward bias (V > 0) than under reverse bias (V < 0). This rectifying behaviour is a feature of photovoltaic devices, since an asymmetric junction is needed to achieve charge separation. For an ideal diode the dark current density Jdark(V ) varies like

J (V ) = J (eqV/kBT 1) (1.3) dark o −

where Jo is a constant, kB is Boltzmann’s constant and T is temperature in degrees Kelvin. The overall current voltage response of the cell, its current–voltage characteristic, can be approximated as the sum of the short circuit photocurrent and the dark current (Fig. 1.6). This step is known as the superposition approximation. Although the reverse current which ﬂows in reponse to voltage in an illuminated cell is not formally equal to the current which ﬂows in the dark, the approximation is reasonable for many photovoltaic materials and March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

10 The Physics of Solar Cells

Jsc J , y t i Light current ns de

t n e

r Dark current r u

C Voc

Bias voltage, V

Fig. 1.6. Current–voltage characteristic of ideal diode in the light and the dark. To a ﬁrst approximation,Figure 1.6the net current is obtained by shifting the bias dependent dark current up by a constant amount, equal to the short circuit photocurrent. The sign convention is such that the short circuit photocurrent is positive.

will be used for the present discussion. The sign convention for current and voltage in photovoltaics is such that the photocurrent is positive. This is the opposite to the usual convention for electronic devices. With this sign convention the net current density in the cell is

J(V ) = J J (V ) , (1.4) sc − dark which becomes, for an ideal diode,

J = J J (eqV/kBT 1) . (1.5) sc − o − This result is derived in Chapter 6. When the contacts are isolated, the potential diﬀerence has its maximum value, the open circuit voltage Voc. This is equivalent to the condition when the dark current and short circuit photocurrent exactly cancel out. For the ideal diode, from Eq. 1.5, kT J V = ln sc + 1 . (1.6) oc q J 0 Equation 1.6 shows that Voc increases logarithmically with light intensity. Note that voltage is deﬁned so that the photovoltage occurs in forward bias, where V > 0. Figure 1.6 shows that the current–voltage product is positive, and the cell generates power, when the voltage is between 0 and Voc. At V < 0, the illuminated device acts as a photodetector, consuming power to generate a March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

difference between the cell terminals but a smaller current though the load. The diode thus provides the photovoltage. Without the diode, there is nothing to drive the photocurrent through the load. Introduction 11

+ V J Jsc dark -

Fig. 1.7. Equivalent circuit of ideal solar cell.

Figure 1.7. Equivalent circuit of ideal solar cell. photocurrent which is light dependent but bias independent. At V > Voc, the device again consumes power. This is the regime where light emitting diodes operate. We will see later that in some materials the dark current is 1.4.3 Efficienaccompaniedcy by the emission of light. Electrically, the solar cell is equivalent to a current generator in parallel The operating regime of the solar cell is the range of bias, from 0 to Voc, in which the cell delivers power. Twithhe cellan powasymmetric,er density is givenonn bylinear resistive element, i.e., a diode (Fig. 1.7). When illuminated, the ideal cell produces a photocurrent proportional to the light intensity. That PJphoto=Vcurrent is divided between the(1.7)variable resistance of the diode and the load, in a ratio which depends on the resistance P reachesof athe maxloadimumand at ththee cell’levsel operatinof illumination.g point or maxiFormumhigher powresistances,er point. Thismore occursof atthe some voltage Vphotom withcurren a correstponﬂodiwsngthrough current denthesitydio Jm,de, showresultingn in Fig. 1in.8. aThhighere optimumpoten loadtial thusdiﬀer- has sheet resistance given by VJ. The fill factor is defined as the ratio ence betweenmmthe cell terminals but a smaller current though the load. The diode thus provides the photovoltage. Without the diode, there is nothing JVmm to drive the photocurrenFFt=through the load. (1.8) JVsc oc

and describes1.4.3. the 'Eﬃciencysquareness' of thJ–e V curve.

The operating regime of the solar cell is the range of bias, from 0 to Voc, in which the cell delivers power. The cell power density is given by

P = JV . (1.7)

P reaches a maximum at the cell’s operating point or maximum power point. This occurs at some voltage Vm with a corresponding current density Jm, shown in Fig. 1.8. The optimum load thus has sheet resistance given by Vm/Jm. The ﬁll factor is deﬁned as the ratio

J V F F = m m (1.8) JscVoc and describes the ‘squareness’ of the J–V curve.

8 March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

12 The Physics of Solar Cells

Maximum power point Current density Jsc

Jm J , y t i s

den Power density ent r r u C

Vm Voc Bias voltage, V

Fig. 1.8. The current voltage (black) and power–voltage (grey) characteristics of an ideal cell. Power density reaches a maximum at a bias Vm, close to Voc. The maximum power density Jm Vm is given by the area of the inner rectangle. The outer rectangle Fig. 1.8 × has area Jsc Voc. If the ﬁll factor were equal to 1, the current voltage curve would × follow the outer rectangle.

The eﬃciency η of the cell is the power density delivered at operating point as a fraction of the incident light power density, Ps, J V η = m m . (1.9) Ps

Eﬃciency is related to Jsc and Voc using F F , J V F F η = sc oc . (1.10) Ps

These four quantities: Jsc, Voc, F F and η are the key performance characteristics of a solar cell. All of these should be deﬁned for particular illumination conditions. The Standard Test Condition (STC) for solar cells 2 is the Air Mass 1.5 spectrum, an incident power density of 1000 W m− , and a temperature of 25◦C. (Standard and other solar spectra are discussed in Chapter 2.) The performance characteristics for the most common solar cell materials are listed in Table 1.1. Table 1.1 shows that solar cell materials with higher Jsc tend to have lower Voc. This is a consequence of the material used, and particularly of March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc crystalline GaAs 3.9 1.022 28.2 87.1 25.1

poly-Si 1.1 0.654 38.1 79.5 19.8

a-Si 1.0 0.887 19.4 74.1 12.7 Introduction 13

CuInGaSe2 1.0 0.669 35.7 77.0 18.4 Table 1.1. Performance of some types of PV cell [Green et al., 2001]. Cd Te 1.1 0.848 25.9 74.5 16.4 2 2 Cell Type Area (cm ) Voc (V) Jsc (mA/cm ) FF Eﬃciency (%)

crystalline Si 4.0 0.706 42.2 82.8 24.7 Table 1.1 shows that solar cell materials with higher Jsc tend to have lower Voc. This is a consequence of crystalline GaAs 3.9 1.022 28.2 87.1 25.1 the material usedpoly-Si, and particularly1.1 of the ba0.654nd gap of the sem38.1iconducto79.5r. In Chapter19.8 2 we will see that there is a funa-Sidamental comp1.0romise betw0.887een photocu19.4rrent and v74.1oltage in 12.7photovoltaic energy conversion.CuInGaSe Figure 1.29 illustrates1.0 the correlatio0.669n between J35.7sc and Voc fo77.0r the cells in18.4 Table 1.1, together with the relatioCdTnshipe for a cell of1.1 maximum 0.848efficiency. 25.9 74.5 16.4

70 theoretical limit 60 -2 50 c-Si

40 poly-Si

/ mA cm GaAs CIGS CdTe sc 30 J a-Si 20

0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Voc /V

Fig. 1.9. Plot of Jsc against Voc for the cells listed in Table 1.1. Materials with high Figure 1V.9o.c Plottend of Jtosc aghaainstve loVwoc erforJ thesc. ceThislls listeisddue in Tatoblethe 1.1.band Materigapals wofith thehighsemiconductor Voc tend of have lmaterial.ower Jsc. This is due to theThe bandgrey gap lineof thesho semwsicothenductorelationshipr material. Thexpe grectedey line inshothews thetheoretical relationshiplimit. expected in the theoretical limit.

1.4.4 Parasitic resistances the band gap of the semiconductor. In Chapter 2 we will see that there is a In real fundamencells powetalr is compromisedissipated thrboetughw eenthe photoresistacurrennce of ttheand covntaoltagects anind thrphotooughv oltaicleakage currents around energythe sidescon of vtheersion. device.Figure These 1.9effectsillustrates are equivalentthe correlation electrically tobet twwoeen parasiticJsc and resistances in

series (RVso) candfor inthe parallelcells (Rinsh) Twableith the1.1, cell together(Fig. 1.9).with the relationship for a cell of maximum eﬃciency.

Rs 1.4.4. Parasitic resistances + In real cells power is dissipated through the resistance of the contacts and Rsh V through leakage currents around theJ sides of the device. These eﬀects are Jsc dark -

Fig 1.9. Equivalent circuit including series and shunt resistances.

10 crystalline GaAs 3.9 1.022 28.2 87.1 25.1

poly-Si 1.1 0.654 38.1 79.5 19.8

a-Si 1.0 0.887 19.4 74.1 12.7

CuInGaSe2 1.0 0.669 35.7 77.0 18.4

Cd Te 1.1 0.848 25.9 74.5 16.4

Table 1.1 shows that solar cell materials with higher Jsc tend to have lower Voc. This is a consequence of the material used, and particularly of the band gap of the semiconductor. In Chapter 2 we will see that there is a fundamental compromise between photocurrent and voltage in photovoltaic energy

conversion. Figure 1.9 illustrates the correlation between Jsc and Voc for the cells in Table 1.1, together with the relationship for a cell of maximum efficiency.

70 theoretical limit 60 -2 50 c-Si

40 poly-Si

/ mA cm GaAs CIGS CdTe sc 30 J a-Si 20

0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Voc /V

Figure 1.9. Plot of Jsc against Voc for the cells listed in Table 1.1. Materials with high Voc tend of have lower Jsc. This is due to the band gap of the semiconductor material. The grey line shows the relationship expected in the theoretical limit.

March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc 1.4.4 Parasitic resistances

In real cells power is dissipated through the resistance of the contacts and through leakage currents around the sides of the device. These effects are equivalent electrically to two parasitic resistances in 14 The Physics of Solar Cells series (Rs) and in parallel (Rsh) with the cell (Fig. 1.9).

Rs + The series resistance arises from the resistance of the cell material to current flow, particularly through The series resistance arises from the resistance of the cellR material to currenVt flow, particularly through the front surface to the contacts, and from resistive contacts. Seriessh resistance is a particular problem at the front surface to the contacts, and from resistive contacts. Series resistance is a particular problem at high current densities, for instance under concentrJated light. The parallel or shunt resistance arises from high current densities, for instaJscnce under concendarktrated light. The pa-rallel or shunt resistance arises from leakage of current through the cell, around the edges of the device and between contacts of different leakage of current through the cell, around the edges of the device and between contacts of different polarity. It is a problem in poorly rectifying devices. polarity. It is a problem in poorly rectifying devices. Fig. 1.10. Equivalent circuit including series and shunt resistances. Fig 1.9. Equivalent circuit including series and shunt resistances. Current

Current 10 R decreasing

Current shR decreasing

Current sh Rs incrRsea insicrneagsing

Bias Bias BiBiasas (a) (a) (b) (b) (a) (b) Figure 1.10: Effect of (a) increasing series and (b) reducing parallel resistances. In each case the outer curve has R = 0 Figure 1.10:Fig. 1.11. EffEﬀectect of (a)of incr(a)easingincreasing series and (seriesb) reducingand par(b)allelreducing resistances. parallelIn each caseresistances. the outer curvIne haseac Rsh =s 0 ∞ × and R and = ∞ R.sh I n= each. In case each the case ef ftheect e offfe thect o rf ethesistance resistances is tos isre toduce reduce the artheea ar oefa the of thema xmimaxuimu pom wpoewr reerctang rectangle lcoe compmarparede dto to J J sc× sh case the outer curve has Rs = 0 and Rsh = . In each case the eﬀect of the resistancessc V . Voc∞. is to reduce the area of the maximum poocwer rectangle compared to Jsc Voc. ×

SeriesSeries and p andarallel parallel resistances resistances redu redce uthece ftheill factoill factor asr shoas shown winn Fig.in Fig. 1. 110.1. 0Fo. For anr an ef feficientficient cell cell w we ew wantant equivalent electrically to two parasitic resistances in series (Rs) and in par- Rs to be as small and Rsh to be as large as possible. Rs to be as small and Rsh to be as large as possible. allel (Rsh) with the cell (Fig. 1.10). When pThearasiticseries resistancesresistance are includarisesed the dfromiode eqtheuatioresistancen becomes of the cell material to When parasitic resistances are included the diode equation becomes current flow, particularly through the front surface to the contacts, and + VJ+AR qV()JARs /kT s from resistivJJe=−contacts.J()e+Series resistance−1VJ−+isARa particular. problem(1.11) at high =−sc qVo()JARs /kT −− s current JJdensities,sc Jofor()einstance under1concenRshtrated.light.(1.11)The parallel or Rsh shunt resistance arises from leakage of current through the cell, around 1.4.5 Non-ideal diode behaviour 1.4.5 Non-ithedealedges diodeof behavithe ourdevice and between contacts of different polarity. It is a Thprobleme ‘ideal’ diodein pbehoorlyaviourectifyingr of eqn. 1.5 devices.is seldom seen. It is common for the dark current to depend The ‘midealore ’w diSerieseakodely onbehand bias.aviouparallel Trh eof actu eqnaresistancesl. depen1.5 isd enseceldom onreduce Vseen is q. uItantifthe is iedcomfill bfactormy oann idfoealityras thesho fdarkactown rcu, minrren anFig.dt thtoe 1.11. depencurrendt– more voweakltaForgely canonha rbias.aefficiencter Tistiche tactugivecellnal b depenyw thee wnodenann-idcet eonRals dVito oisd eqb eueqantifuaastioiedn,small by anand idealityRsh factotor,b me anasd thlargee currenast– voltage cphossible.aracteristic given by the non-ideal diode equation, =− qV /mkBT − (1.12) When parasitic JJresistancessc Jo ()areeincluded,1the diode equation becomes =− qV /mkBT − JJsc Jo ()e 1 (1.12)

m typically lies between 1 and 2. Thq(V+JARe reasonss )f/okTr non-ideal bVehavio+ JuARr wills be discussed in later chapters. J = Jsc Jo(e 1) . (1.11) m typically lies between 1 and 2−. The reasons for non-id−eal b−ehavioRursh will be discussed in later chapters.

1.5 Summary of Chapter 1 1.5 Summary of Chapter 1 A photovoltaic cell consists of a light absorbing material which is connected to an external circuit in an asymmetric manner. Charge carriers are generated in the material by the absorption of photons of light, A photovoltaic cell consists of a light absorbing material which is connected to an external circuit in an and are driven towards one or other of the contacts by the built-in spatial asymmetry. This light driven asymmetric manner. Charge carriers are generated in the material by the absorption of photons of light, charge separation establishes a photovoltage at open circuit, and generates a photocurrent at short and are driven towards one or other of the contacts by the built-in spatial asymmetry. This light driven circuit. When a load is connected to the external circuit the cell produces both current and voltage and charge separation establishes a photovoltage at open circuit, and generates a photocurrent at short can do electrical work. circuit. When a load is connected to the external circuit the cell produces both current and voltage and can do electrical work.

11 11 March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

Introduction 15

1.4.5. Non-ideal diode behaviour

The ‘ideal’ diode behaviour of Eq. 1.5 is seldom seen. It is common for the dark current to depend more weakly on bias. The actual dependence on V is quantiﬁed by an ideality factor, m and the current–voltage characteristic given by the non-ideal diode equation,

J = J J (eqV/mkBT 1) (1.12) sc − o − m typically lies between 1 and 2. The reasons for non-ideal behaviour will be discussed in later chapters.

1.5. Summary

A photovoltaic cell consists of a light absorbing material which is connected to an external circuit in an asymmetric manner. Charge carriers are generated in the material by the absorption of photons of light, and are driven towards one or other of the contacts by the built-in spatial asymmetry. This light driven charge separation establishes a photovoltage at open circuit, and generates a photocurrent at short circuit. When a load is connected to the external circuit, the cell produces both current and voltage and can do electrical work. The size of the current generated by the cell in short circuit depends upon the intensity and the energy spectrum of the incident light. Photocur- rent is related to incident spectrum by the quantum efficiency of the cell, which is the probability of generating an electron per incident photon as a function of photon energy. When a load is present, a potential difference is created between the terminals of the cell and this drives a current, usually called the dark current, in the opposite direction to the photocurrent. As the load resistance is increased, the potential difference increases and the net current decreases until the photocurrent and dark current exactly cancel out. The potential difference at this point is called the open circuit voltage. At some point before Voc is reached, the current–voltage product is maximum. This is the maximum power point and the cell should be operated with a load resistance which corresponds to this point. The solar cell can be modelled as a current generator in parallel with an ideal diode, and the current–voltage characteristic given by the ideal diode equation, Eq. 1.5. In real cells, the behaviour is degraded by the presence of series and parallel resistances. March 12, 2003 15:18 WSPC/The Physics of Solar Cells psc

16 The Physics of Solar Cells

References

D. Anderson, Clean Electricity from Photovoltaics, eds. M.D. Archer and R.D. Hill (London: Imperial College Press, 2001). M.A. Green, “Photovoltaics: Coming of age”, Conf. Record 21st IEEE Photo- voltaic Specialists Conf., 1–7 (1990). E. Lorenzo, Solar Electricity: Engineering of Photovoltaic Systems (Progensa, 1994). T. Markvart, Solar Electricity (Wiley, 2000). J.N. Shive, Semiconductor Devices (Van Nostrand, 1959). C.A. Vincent, Modern Batteries (Arnold, 1997). M. Wolf, “Historical development of solar cells”, Proc. 25th Power Sources Sym- posium, 1972. In Solar Cells, ed. C.E. Backus (IEEE Press, 1976).