Lecture Conference Ourzazate ennaoui

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  • There are three most used methods for producing thin films of CIGS. The first one is the coevaporation process. This method is named coevaporation because in the beginning all needed elements were evaporated in vacuum at the same time. The thin film is produced by evaporating Cu, In, Ga, Se from elemental sources. In order to achieve the favored film composition, a precise control of the particular evaporation rates is necessary. There an electron impact emission spectrometer and an atom absorption spectrometer or a mass spectrometer is used. But the process also requires a substrate temperature between 300 and 550°C for a certain time during film growth. There are several processes of coevaporation, but one of the most favored ones is the inverted three-stage process, which you can see on the right. At first In, Ga, and selenium are evaporated with different rates and deposited as (In,Ga) 2 Se 3 at 300°C on the substrate. Afterwards Cu and selenium are evaporated and deposited on the substrate at elevated temperatures. At last In, Ga, and selenium are evaporated again. The inverted three-stage process leads to smoother film morphology and to high efficiency solar cells.
  • Lecture Conference Ourzazate ennaoui

    1. 1. Solar Photovoltaic Technology from atoms to arraysAhmed EnnaouiHelmholtz-Zentrum Berlin für Materialien und EnergieScience Advisory Board Member of IRESEN - MoroccoE-mail: ennaoui@helmholtz-berlin.dehttps://www.helmholtz-berlin.deThe International Renewable and Sustainable Energy Conference(IRSEC13)March 7-9 2013, Ouarzazate, Moroccohttp://www.iresen.org/index.phpLecture 4 on Friday 09h30 10h15‐
    2. 2. Introduction: PV from atom to arrayArrays Absorbed photon creates 1 electron-hole pair. The electric field separates the electron-hole pair. The electrons are collected in the external load. Generation-Recombination.Enery levelsAtomModuleSolar cell
    3. 3. Prof. Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie Photo absorption and photo generation Direct and indirect band gap. External and Internal Quantum Efficiency (EQE and IQE). Absorption coefficient, absorption length, excess minority carrier. Recombination: Non Radiative, Radiative, Auger. Shockley-Read Hall Recombination. Continuity equation and Transport process. Basic J-V equation. Equivalent Circuit model. Silicon Technology versus. Thin Film technology. Basic building block for PV: cells in series, cells in parallel. Change in short circuit current and open-circuit with solar radiation. Change in short circuit current and open-circuit with the temperature Performance measurement standard conditionsWhat we have to learn
    4. 4. Task of Photovoltacis: Photo absorption and photo generationLight = wave λ, and particle with energy E = hνAlbert Einstein1879 - 1955Max Planck1858 - 1947)(1239)(hchEnmeVEλλν =⇒==)rkexp()rk,()rk,( ⋅= iunnψFunction withthe periodicityof the crystallatticePlane wave)rkexp()rk,()rk,( ⋅= iunnψFunction withthe periodicityof the crystallatticePlane wave Use of Bloch functionsBand structure of Si E(k)1000 nm  1.239 eV≅ 1.4 eV Solving Schrödingerequationψψψ ErVm=+∇− )(2202Particle in a box: wave functions and energiesn ; the quantum number (n= 1, 2, 3,....)L ; the length one dimensional) molecular boxm ; the mass of the particle (electron)h ; Plancks constant
    5. 5. Device fabrication1. Surface etch, Texturing2. Doping: p-n junction formation3. Edge etch: removes the junction at the edge4. Oxide Etch: removes oxides formed during diffusion5. Antireflection coating: Silicon nitride layer reduces reflectionCellsPurifying the silicon:STEP 1: Metallurgical Grade Silicon (MG-Silicon is produced from SiO2 meltedand taken through a complex series of reactions in a furnace at T = 1500 to2000°C.STEP 2: Trichlorosilane (TCS) is created by heating powdered MG-Si at around300°C in the reactor, Impurities such as Fe, Al and B are removed.Si + 3HCl SiHCl3 + H2STEP 3: TCS is distilled to obtain hyper-pure TCS (<1ppba) and then vaporized,diluted with high-purity hydrogen, and introduced into a deposition reactor to formpolysilicon: SiHCl3 + H2→Si + 3HCl Electronic grade (EG-Si), 1 ppb ImpuritiesSTEP 1STEPE 2 and 3ElectronicGrade ChunksSource: Wacker Chemie AG, Energieverbrauch: etwa 250kWh/kg im TCS-Process, Herstellungspreis von etwa 40-60 €/kg ReinstsiliziumIngot slicedto create wafersMaking singlecrystal siliconCzochralski (CZ) processcrucibleSeed crystal slowly growsMicroelectronic1G: Crystalline Si PV technology
    6. 6. P-N JunctionSi14Ge32Ga31As33Cd48Te52P15In49Al13Sb51Cu29Se34In4931IIB IIIB IVB VB VIBIBC6B5Zn30Sn50S16O8N7Periodic TableDoping Technology of Silicon: pn junction of SiliconSilicon (IV) Diamond StructureBoron doping Phosphorus dopingMartin Green, UNSW’s cell concepts PIP 2009; 17:183–189 / http://www.unsw.edu.au/
    7. 7. External Load +-Emitter Base Rear ContactFront ContactAntireflection coatingAbsorption of photon creates anelectron hole pair. If they arewithin a diffusion length of thedepletion region the electric fieldseparates them.The electron after passingthrough the load recombineswith the hole completing thecircuitn pFront contactTask of Photovoltacis: Photo absorption and photo generation1. Light absorption: Generation of free excess2. Charge separation:a) Photocurrent, I [A] (Ampere)b) Photovoltage, V [V] (Volt)3. Recombintion (defect  recombination centers)V[A] x I[V] = Power [Watt]Light fluxValence bandConduction band
    8. 8. ZnO,2500ÅCdS700ÅMo0.5-1µmGlass, Metal Foil, PlasticsGlassCd2SnO 4SnO 20.2-0.5 µmCdS600-2000ÅCdTe2-8µmCIGS1-2.5µmC-PastewithCu,CdTe based deviceQuelle: Noufi, NREL, Colorado, USA,*CIGS based deviceCdTe and CIGS Thin Film Solar cells (2G)
    9. 9. GlassMoly rearcontactCIGSBufferZnO FrontcontactTechnology: monolithic" interconnect from three scribes P1 to P3P1Step 1: Deposition of Cu, In,Ga (Se)(sputtering, codeposition, Electrodeposition)Step 2: Rapid Thermal Processing (RTP)Pulsed Picosecond LaserFront ZnO of one cell is connected to back Mo contatc of the next.dead-zone width can be up to 500 μm for mechanical scribing.Se CuGa InCu(In,Ga)Se2P3P2 P1P1 periodic scribes to defines the width of the cells.P2 scribe removes the CIGSdown to the Moly back contact.P3 scribe can also remove the whole layer stack downto the MolySiModuleVmodule= Vcell x Ncell  24 V for battery chargingQuelle: HZB / M. Lux-Steiner
    10. 10. RadiativerecombinationEVEC AugerrecombinationExcessenergygiventoanothercarrierinthesamebandECEVElectron thermalizesto band edgeAhmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie Recombination (r) is the opposite of generation, leading to voltage and current loss.Non-radiative recombination  phonons, lattice vibrations.Radiative recombination  photons (dominating in a direct bandgap materials )Auger recombination  charge carrier may give its energy to the other carrier.E(eV)Non-radiativerecombinationECEVPhonon Recombination processes are characterized by the minority carrier lifetime τ. Equilibrium: charge distributions np = ni2Out of equilibrium: The system tries to restore itself towards equilibrium through R-G Steady-state rates: deviation from equilibrium( )npnBgrRBnnB.pg.pnBr 2i2i00−=−====/scm102B(Si) 315−×=Generation vs. recombination processes
    11. 11. Summary: Generation & RecombinationAhmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieShockley-Read HallrecombinationDirectrecombinationdirect bandAuger recombination(dominant effect at high carrier concentration)EVECEkinEkin= -qELscGenerationImpact ionization is ageneration mechanism.When the electron hits anatom, it may break acovalent bond to generatean electron-hole pair.The process continues with the newlygenerated electrons, leading to avalanchegeneration of electrons and holes.τ : average time it takes an excess minority carrier to recombine(1 ns to 1 ms) in Siτ : depends on the density of metallic impurities and the densityof crystalline defects.t/teffτ( )2DAugern,DTn .NcBNNcΔn ++=++∆=++=AugerDirectSRH111nτττRRRR AugerDirectSRH( ) 1eff−++=⇒ 2DAugern,DTn .NcBNNcτLoss to thermalvibrations
    12. 12. Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSunTask of Photovoltacis• 100 W light bulb is turning on for one hour• Energy consumed is 100 W·h = 0.1 kW.h.Production vs. consommation100 Wlight bulb
    13. 13. Controller, (charge regulator) regulates the voltage and currentcoming from the solar panels Determines whether this power isneeded for home use or whether it will charge a deep-cycle solarbattery to be drawn upon later on.All other current must passthrough a DC to AC inverter,transforming it into electricityusable by general householdappliances.DC-current from thecontroller can be used to runelectronic devices that dontrequire an AC-current.all surplus electricity not beingdrawn by your home can besent to your utility companyspower grid.PhotovoltaicP > CTraditional SystemPhotovoltaicP < CCopyrighted Material, from internetTask of Photovoltacis
    14. 14. Efficiencies beyond the Shockley-Queisser limit(1) Lattice thermalization loss (> 50%)(2) Transparency to hν < Band gap(3) Recombination Loss(4) Current flow(5) Contact voltage lossNot all the energy of absorbed photon can be capturedfor productive use (Th. Maxi efficiency ~32% ).R.R. King; Spectrolab Inc., AVS 54th International Symposium, Seattle 2007Reflection lossRecombinationlossResistive loss Top contactlossBack contact„Loss“ Good surface passivation. Antireflection coatings. Low metal coverage of the top surface. Light trapping or thick material(but not thicker than diffusion length). High diffusion length in the material. Junction depth optimized for absorptionin emitter and base. Low reflection by texturing
    15. 15. Route to high efficiency solar cellsTraditional cell design PERLPERCIBCPESCMINP(1) (2) (3)(1) PERL developed at UNSW (EFF. 25%) Passivated Emitter and Rear Locally diffused1(2) Localized Emitter Cell Using Semiconducting Fingers. (EFF. 18.6%, CZ n-type)(3) Laser-grooved, buried front contact (LGBC; EFF. 21.1%)1Martin Green, PIP 2009; 17:183–189, University of New South Wales, AustraliaCopyrighted Material, from internet
    16. 16. Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieWe need to use most of the solar spectrum: Tandem solar cellsPower [Watt/cm2] = Voltage [Volt ] x Current density [A/cm2]Materials with small Band gapBut low voltageExcess energy lost to heat Generating a large current (JSC)Materials with large band gapBut low currentSub-band gap light is lost Generating a large voltage (VOC)Solar cellversusSolar spectrum
    17. 17. = (in flow – out flow) + Rain -EvaporationrainIn flowOut flowEvaporationRate ofincrease ofwater levelin lake r-g.Jq1nnn +∇=dtdnnnnnnnnqDEqnμJr-g.Jq1tn∇+=+∇=∂∂Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieA little bit of Math: Continuity equation and Transport processtn0=∂∂
    18. 18. Voc0 La= 1/αLpWRecΕF,n=µeΕF,p=µhWLnLa= 1/αRecΕF,p=µhΕF,n=µe Generated closer to the junction Generated within a diffusion length of the junction Key issues:Minority carrier diffusionSurface recombinationCollection near front surface and also rearconditionsBondaryGτLxBexpLxAexpΔn(x) nnn←+++−=tn0=∂∂Differential equation is simple only when G = constant.n2n22Dx)G(λ(LΔndxΔnd−=p2p22Dx)G(λ(LΔpdxΔpd−=Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieBasic: Continuity equation and Transport process
    19. 19. Basic Diode J-V equationNLnDNLnDqJDp2ipAn2in0+=+ JD)( 1TkqVexppLDqnLDqJBn,0ppp,0nn−+=0JLJcurrent,DarkTn.kqV0 J1expJJDB−−=  - JLW)LqG(L pn ++−LJntPhotocurreApplying boundary conditions (ideal diode case)Differentiating to find the currentEquating the currents on the n-type and p-type sidesJ0 : saturation currentkB : Boltzmann`s constant, 1.381 10-23J/Kelvinn : ideality factorni: carrier concentrationNA,ND. Doping concentrationdxpdqDJ npp∆=dxndqDJpnn∆=Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
    20. 20. One diode model / Equivalent CircuitRLoadJVDJD Ideal diode (dark current , ID)(Shockley diode equation)−= 1exp0nkTqVJJ DDSD RJVV .+= add a serie resistance RSjsh . RshCurrentlossRJ.RVJ-ShSL++−−= 1nkT)R.JV(qexpJJ S0 Add a shunt resistanceSshsh RJVRi .. +=JLLSJnkTRJVqJJ −−−= 1).(exp0 Under illuminationVOCJSC- JL4THQuadrantJ = I/AVReverseForward0 Solar cell in the dark−−= 1).(exp0nkTRJVqJJ SD+=DpipAninNLnDNLnDqJ220J. RS(Voltage drop)VDark characteristics being shifted down byphotocurrent which depend on lightintensity.PNSlope -1/RLoadPhotogenerated carriers can also flow through the crystalsurfaces or grain boundaries in polycrystalline devices
    21. 21. Two diodes model / Equivalent CircuitRJ.RVShS++−−+−−= 1).(exp1).(exp202101kTnRJVqJkTnRJVqJJ SSRLoadJ+-RSVJ01,n1J02,n2RshJLLJ-RJ.RVShS+−−−−−−−= 1).(exp1).(exp202101kTnRJVqJkTnRJVqJJJ SSL1stQuadrant4thQuadrant1stQuadrant4thQuadrantJVA. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
    22. 22. Photocurrent analysis: Quantum efficiency measurmentsAcceptorVocx = 0 La= 1/αx = Lnx = WEJ σ=dxdpDpDonorRecµhµeE→p∇→Load• How much light converted?• Limited information on the electronic properties• Information on the optical properties of the device)(R λ−=1EQEIQEλhceJΦEQE)()(1 λλ=This ratio can be measuredAhmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieΦ 0x R λΦ0[ ][ ]JoulehνWatt/cmΦN2photonsin =[ ][ ]CoulombeA/cmJN2electronsout =ElectronscollectedPhotonsabsorbedΦ 0x Rλh(c/λ) < EGx0 ).eR.(1ΦΦ αλ−−=Φ0
    23. 23. EQE and and absorption coefficientPhoton absorptiondirect band-gap( ) GG21E)E(hνvs..hν →−α2G )E(hhνB−= ναDirect Bandgap EgECEVPhotonConductionBandValenceBandE(k)GaAse.g.+k-kPhoton absorptionindirect band-gap( ) GG2E)E(hvs..h →−ννα21G )E(hhA−= νναPhoton+k-kEgECEVConductionBandValenceBandPhononEG+EpEpE(k)Sie.g.Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie and IRESENCut-off λ vs. EG[eV]E1.24m][μλGG =∫Φ=λλλλ dEQEqJsc )()(λhceJΦEQE)()(1 λλ=
    24. 24. hνBand Gap - absorption coefficient - absorption lengthTemperature changes:EG ↑ as T ↓Changing the absorption edgeAhmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieA(T)(0)E(T)E gG −=Si Ge GaAsEG (eV) 1.12 0.66 1.42λλλ ++= TAR100%)R.(1ΦΦln.d1αλ0 −−=λαx-o R).α).-(E).(1ΦdxdΦx)G(E, =−=Absorptionx0 ).eR.(1ΦΦ αλ−−=GenerationΦΦΦΦΦ TAR0 ++=
    25. 25. Quantum efficiency measurements2 – Cell Measurement2CELLCELLsc .Φq.EQEJ =2MONMON,2sc .aΦq.EQEJ =.a.EQEJJ.aEQE MONMON,2scCELLscCELL =3 – Final ResultREFREFscMON,1scMON,2scCELLscCELL EQEJJ.JJEQE =Monochromatorequipped with more gratings*ChopperBeam splitter*Gratings should have line density as high as possible for achieving high resolution and highpower throughput. (600 – 3000 lines/mm).EGEQE vs. λ1REFREFsc .Φq.EQEJ =1MONMON,1sc .aΦq.EQEJ =1MON,1scMONqΦJ.aEQE =1 - Reference measurementphoton1ofrgyphoton/eneofpowerTotalelectron1ofargecurrent/chEQE""EfficiencyQuantumExternal =Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
    26. 26. Design to high efficiency solar cellsLight trappingReflection Loss: ARCMaterial Parameter absorptionImportant cost factor €/kg+−−= −αWpeαL111R)(1ηλhce)J(Φ(λ)1 λη =Decisive Material ParameterThe band gap0.3 0.5 0.7 0.9 1.1200406080100012345NumberofSunlightPhotons(m-2s-1micron-1)E+19RExternalQuantumEfficiency,%µc-Si:H junctiona-Si:H junctionAM 1.5 global spectrumWavelength, micronsa-Si:H/µc-Si:H Cell Spectral ResponseTextured TCOa-SiTop cellBack ReflectorGlass substrateThin film mc-SiBottom cell[ ]∫ λ−=GEλ0λsc dλ.dα-exp.)().ΦR(1.η(λ).qJLight from the sunAhmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie and IRESEN
    27. 27. Power output characteristicsJsc VOCPmaxSunOCSCP.FF.VJEFF. =VmppPmpp= Impp x VmppOCSCmppmpp.VJ.VJInverse of slope Vmpp/Imppis characteristic resistanceJmpp mmpRmppVJmpp = Maximum Power PointP=I.VFill FactorOCSCmppmpp.VJVxJSunmppmppPV.JEFF =A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
    28. 28. Solar cell efficiency under simulated sun lightEarth´ s SurfaceAM1AM0AM1.5d=1.5 atmos d=1 atmosChallengesTo simulate a spectrum as similar as possible to the sun spectrum with excellenthomogeneity over relatively large areasA. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
    29. 29. Principle of a sun simulatorThe unit of the photon fluxA. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieReference cellsolar cellSources: Thomas FU-Berlin
    30. 30. ContactgridTotalAreaIncludinggridIluminatedArea (2)JSC is rather accurately determined by EQE measurements0.5 cm1 cmIluminatedArea (1)0.5 cm1 cm∫Φ=λλλλ dEQEq )()(J 0scFrommonochromatorPerformance measurement standard conditionsA. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie(1) effective area or(2) total area
    31. 31. A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergiePhotons to electrons, solar power to electrical powerYou need a computer for this exercisePhysical constants: elementary charge, e = 1.60 x 10-19CPlanck’s constant, = 6.63 × 10-34J sspeed of light, c = 3.00 x 108m s-1Exercice: An ideal solar cell has a band gap energy . The solar cell absorbs 100% of photons with energyand 0% of photons with energy . All absorbed photons are converted to current with 100% quantum efficiency.The solar cell has a fill factor of 70% and an active area of 1 cm2. The external quantum efficiency (EQE)spectrum and current-voltage (I-V) curves are sketched below:020406080100120EgCurrentVoltage VOCISCVmppEQE(%)a) The international standard AM1.5 solar spectrum is provided in the text file “Solar spectral irradiance.txt”(from NREL.gov). Use it to calculate the short circuit current, ISC, for the ideal solar cell made from:Crystalline silicon Si, EG = 1.1 eV; Germanium Ge, EG = 0.67 eV ; Gallium arsenide GaAs EG = 1.42 eVAmorphous Si, EG = 1.75 eV.b) If the open-circuit voltage is given by Voc = EG/e, what is the maximum power conversion efficiency ofeach of the four cells? (The total terrestrial irradiance is 1000 W m-2.).c) What is the optimum band gap for an ideal solar cell?00.511.522.50 500 1000 1500 2000Spectralirradiance(Wm-2nm-1)Solar spectral irradianceExtraterrestrialTerrestrial
    32. 32. From Cells to a Module The basic building block for PV applications is a module consisting of a numberof pre-wired cells in series. Typical module Silicon technolog/ 36 cells in series referred to as 12V. Large 72-cell modules are now quite common. Multiple modules can be wired in series to increase voltageand in parallel to increase current.Such combinations of modules are referred to as an arrayCells wired in series
    33. 33. From Cells to a Module0.6 V each cellN°1N° 364 cells4 x 0.6V36 x36 x 0.6V = 21.6 VAdding cells in seriesVmodule = n (Vd – I.RS)Series resistance RSCell 1 Cell 2 Cell 36. . . . .+ - + - + -
    34. 34. From Cells to a ModuleA parallel association of n cells is possible and enhances the output current of thegenerator created.In a group of identical cells connected in parallel, the cells are subjected to the samevoltage and the the resulting group is obtained by adding currentsVSC,nCell nn CellsCell 1n Cellsin parallelen x ISCISC,n
    35. 35. From Module to arrayFor modules in series, the I –V curves are simply added along the voltage axis at any givencurrent which flows through each of the modules), the total voltage is just the sum of theindividual module voltages.
    36. 36. For modules in parallel, the same voltage is across each module and the totalcurrent is the sum of the currents at any given voltage, the I –V curve of theparallel combination is just the sum of the individual module currents at thatvoltage.From Module to array
    37. 37. Two ways to wire an array with three modules in series and two modules in parallel.The series modules may be wired asstrings, and the strings wired in parallel.The parallel modules may be wired togetherfirst and those units combined in seriesV VIf an entire string is removed from servicefor some reason, the array can stilldeliver whatever voltage is needed by theload, though the current is diminished,which is not the case when a parallelgroup of modules is removed.From Module to array
    38. 38. Two ways to wire an array with three modules in series and two modules in parallel.The series modules may be wired asstrings, and the strings wired in parallel.The parallel modules may be wired togetherfirst and those units combined in seriesV VIf an entire string is removed from servicefor some reason, the array can stilldeliver whatever voltage is needed by theload, though the current is diminished,which is not the case when a parallelgroup of modules is removed.From Module to array
    39. 39. Standard conditions of your PV moduleStandard Test Conditions:• 1 kW/m2, AM 1.5, 25°C Cell Temperature• Solar irradiance of 1 kW/m2(1 sun)• Air mass ratio of 1.5 (AM 1.5).• Key parameter: rated power PDC,STC• I –V curves at different insolation and cell temperature• NOCT: Nominal Operating Cell Temperature(T = 20°C,Solar Irradiation= 0.8 kW/m2, winds speed 1 m/s.).S0.8C20NOCTTT ambCell  °−+=cell temperature (°C)ambient temperature (°C)Insolation(1 kW/m2)VMPPMPPVMPPVMPP
    40. 40. Standard conditions of your PV module
    41. 41. A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieImpact of Cell Temperature on Power for a PV Module.Estimate cell temperature, open-circuit voltage, and maximum power output for the150-W BP2150S module under conditions of 1-sun insolation and ambienttemperature 30°C. The module has a NOCT of 47°C.C64.10.8C2043.S0.8C20NOCTTT ambCell °= °−+= °−+=70From The table for this module at the standard T = 25°C, VOC = 42.8VVOC drops by about 0.37% per °C , the new VOC = 42.8[1 − 0.0037(64 − 25)] = 36.7 Vwith decrease in maximum power available of about 0.5%/°C.With maximum power expected to drop about 0.5%/°C, this 150-W module atits maximum power point will deliver:Pmax = 150 W· [1 − 0.005(64 − 25)] = 121 WThis is a significant drop of 19% from its rated power.Standard conditions of your PV module
    42. 42. • Module with Power of 240 WC• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 %≈ 14.8 %Standard conditions of your PV module
    43. 43. • Module with Power of 240 WC• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 %≈ 14.8 %Siliken modules were awarded theNumber one test modules 2010 andNumber two test modules 2011.Standard conditions of your PV module
    44. 44. • Module with Power of 240 WC• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 %≈ 14.8 %• Module with Power of 240 WC• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 %≈ 14.8 %• KT(P) = -0.41 %/°C  Power decreases by (0.41% × 240W)= 0.984 W /°C• KT(Uco) = -0.356 %/°C Load voltage decreases by(0.356 × 37V) = 0.13 V / °C.• KT(Icc) = 0.062 %/°C  Isc enhanced by(0.062% × 8.61 = 0.0053 A / °C• NOCT = 49°C (±2°C).).S(kW/m0.8C20C249C)(TC)(T 2ambCell  °−°±+°=°NOCT terms:Level of illumination: 800 W / m²Outdoor temperature: 20 ° CWind speed: 1 m / sAir mass AM = 1.5Siliken modules were awarded theNumber one test modules 2010 andNumber two test modules 2011.Standard conditions of your PV module
    45. 45. Exercice: Electronic Structure of Semiconductors and DopingPhysical constants: Planck’s constant, h = 6.63 × 10-34J sBoltzmann’s constant, k = 1.38 × 10-23J K-1= 8.62 x 10-5eV K-1speed of light, c = 3.00 x 108m s-1Rest mass of an electron, m0 = 9.11 x 10−31kgElementary charge, e = 1.60 x 10-19C1) Germanium has an effective density of states (DOS) NC = 1019cm-3for the conduction band and a band gapEG = 0.66 eV. The intrinsic carrier density at 300 K is 1.8 x 1013cm-3.i) What is the effective DOS for the valence band, NV ?ii) If the material is n-doped to give an electron density of ne = 1018cm-3, what is the hole density?iii) What is the intrinsic carrier density at 100 K? You can assume that the effective DOS do not change with temperature.2) (Only attempt this question if you like calculus or use a program like Mathematica)The conduction-band DOS in a direct band gap semiconductor is given bywhere is the conduction band minimum and is the electron effective mass. Show that the conduction band electrondensity can be approximated by:where EF is the Fermi level and is the effective DOS.Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
    46. 46. Exercice: Electronic Structure of Semiconductors and Doping3) The effective electron mass in crystalline GaAs is .The effective hole mass is = 0.47 m0 , and the band gap is EG = 1.42 eV.i) Sketch the band structure (energy versus momentum) for GaAs.ii) Using the expression for the effective DOS given in question 2, determine the intrinsic carrier density at 300K.iii) A GaAs crystal is doped with 1016cm-3Si atoms, acting as electron donors by replacing Ga atoms in the lattice.What is the electron and hole density, assuming that all dopants are ionised?iv) What is the position of the Fermi-level relative to the conduction band onset? (Give your answer in electron volts.)4) Crystalline silicon has an effective DOS of NC = 3 x 1019cm-3for the conduction band and NV = 2 x 1019cm-3for valence band, and aband gap EG = 1.1 eV. A silicon crystal is doped with 1017cm-3boron (B) atoms. (Boron is a group III element.)i) What is the position of the Fermi-level relative to the valence band maximum, EV, and conduction band maximum, EC, at 300 K?ii) If the acceptor state energy, ED, is 0.05 eV above the valence band maximum (see diagram), use the Fermi-Diracdistribution and the Fermi level calculated in (i) to calculate the fraction of dopant atoms that are ionized.iii) Using the same approximations, calculate the Fermi-level and fraction of ionized dopants at 77 K. Is the assumption ofcomplete ionization still valid?iVI Roughly sketch the variation of hole density with temperature over a wide temperature range.energyEVEDEC0.05 eVAhmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
    47. 47. At wavelength λ = 1050 nm, the refractive index of silicon is n = 3.6 and the absorptioncoefficient is α = 15 cm-1.i)A Si wafer of thickness d = 0.25 mm is illumined by light at wavelength λ = 1050 nm at normalincidence. What fraction of light is reflected and what fraction of light is absorbed?ii)A perfect reflective surface is added to the back side of the wafer. What is the absorptivitynow?iii)An estimate for the absorptivity of a wafer with a light-trapping surface is given by Würfel as:(P. Würfel, Physics of Solar Cells, p144) where R is the reflectivity of the surface. By whatfactor would you expect the external quantum efficiency at 1050 nm of the corresponding solarcell to be improved by a light-trapping surface?Use the absorption coefficient and refractive index for silicon as a function of wavelength andthe solar irradiance spectrum to calculate the reflectivity and absorptivity spectra for a 0.25 mm-thick Si solar cell with a reflective back side and no light trapping (assume normally incidentlight). Plot these spectra as functions of wavelength. Assuming that each absorbed photongenerates one electron in the external circuit (external quantum efficiency = absorptivity),calculate the short-circuit current for the cell under AM1.5 illumination.
    48. 48. Exercice: Charge transport and p-n diodesPhysical constants: Reduced Planck’s constant = 1.05 × 10-34J s = 6.58 × 10-16eV sBoltzmann’s constant, k = 1.38 × 10-23J K-1= 8.62 x 10-5eV K-1speed of light, c = 3.00 x 108m s-1elementary charge, e = 1.60 x 10-19C1. A crystalline silicon wafer, has a band gap EG = 1.1 eV and an intrinsic carrier density of ni = 1.3 x 1010cm-3at 300 K.The wafer is 200 µm thick and has an area of 1 cm-2. The electron mobility is µe = 1000 cm2V-1s-1, and the holemobility is µh = 100 cm2V-1s-1.i) What is the conductivity of the undoped wafer?ii) The wafer is doped with a donor density ND = 1018cm-3. Is the doped wafer n-type or ptype? Whichcarrier types (electron or hole) are the minority and majority carriers?iii) A voltage of 1.0 V is applied across the wafer. Sketch the energy band diagram (energy vs depth),indicating the direction of travel of holes and electrons. How large is the drift current?iv) The minority carrier lifetime is 1 µs. On average how far does a minority carrier travel (under 1.0 Vapplied bias) before recombining? How does this affect the photocurrent?v) Why is the n-type region made thin relative to the p-type region in typical crystalline silicon solar cells?
    49. 49. Exercise : Crystalline silicon solar cells2. A 250 micrometer-thick crystalline silicon wafer is doped with 5×1016acceptors per cubic centimetre. A 1 micrometer-thick emitter layer is formed at the surface of this wafer with a uniform concentration of 3×1019cm-3donors. Assume thatall doping atoms are ionized. The intrinsic carrier concentration in silicon at 300 K is ni = 1.3 x 1010cm-3. How large is (at300 K and thermal equilibrium):i)The electron and hole concentration in the p-type region and n-type region? Which charge carriers are the majoritycarriers in the p-type region and what is their concentration?ii)What is the position of the Fermi level (in eV) in respect to the conduction band in the ptype and n-type region,respectively?iii)The built-in voltage of the p-n junction? iv) Draw the corresponding band diagram of the p-n junction.iv)The width of the depletion region of the p-n junction. Compare it with the total thickness of the Si wafer.3. A 200 micrometer-thick multicrystalline silicon cell is doped with 5×1017acceptors per cubic centimetre. A 1 micrometer-thick n-type emitter layer is formed at the surface of this cell with a uniform concentration of 3×1019cm-3donors. Assumethat all doping atoms are ionized. The intrinsic carrier concentration in silicon at 300 K is ni = 1.3 x 1010cm-3, and thedielectric constant is ε = 11.7. At 300 K and thermal equilibrium:i) The electron mobility is µe= 500 cm2V-1s-1, and the hole mobility is µh= 50 cm2V-1s-1. The minoritycarrier lifetime for electrons is τe= 400 ns and τh= 100 ns for holes. The diffusion constant is givenby the Einstein relation, D
    50. 50. Exercice: Charge transport and p-n diodesiVI) Estimate the saturation current density for the cell, neglecting recombination in the depletion zone. How does thesaturation current affect the open-circuit voltage of the cell?iV) Minority carriers generated within one diffusion length of the depletion zone will be collected and will contribute to themeasured photocurrent. Those generated outside of this region will recombine and will not contribute to the current. Theabsorption coefficient for silicon at 950 nm is α(950nm) = 104m-1. Using the Beer-Lambert law for absorption, estimate thequantum efficiency for this cell at 950 nm. (The light has normal incidence and shines on the n-type side of the cell.)Vi) Sketch the energy band diagram for the cell, labelling all relevant distances. Explain whyreducing the doping in the p-type region might increase the short-circuit current of the cell. Howmight this affect the open-circuit voltage?
    51. 51. PV module made up of 36 identical cells, all wired in series. With 1-sun insolation(1 kW/m2), each cell has short-circuit current ISC = 3.4 A and at 25°C its reverse saturationcurrent is I0 = 6 × 10−10A. Parallel resistance RP = 6.6 Ω and series resistance RS = 0.005Ω .a) Find the voltage, current, and power delivered when the junction voltage of each cell is0.50 V.b) Set up a spreadsheet for I and V and present a few lines of output to show how it works.Using Vd = 0.50 V along with the other dataThe voltage produced by the 36-cell module:Vmodule = n(Vd − I x RS ) = 36(0.50 − 3.16 x 0.005) = 17.43 VPower dilevred:P(watts) = Vmodule x I = 17.43 × 3.16 = 55.0 WRI.RV1n.k.T)I . Rq(Vexp.-IIIpSS0ph+−−−=[ ]pdV9.380phRV1e.-III d−−=[ ] A6.36.65.01e.10x6-4.3I 5.0x9.3810=−−= −Voltage and Current from a PV Module
    52. 52. A spreadsheet might look something like the following:From Cells to a Module
    53. 53. Gonçalves et al., Dye-sensitized solar cells, Energy Environ. Sci. 1, 655 (2008), is a very nicesummary of the current state of DSSCs. Use it as a reference to answer the following questions:(only brief answers required)What is the main reason for the lower efficiency of DSSCs compared to crystalline siliconcells?What is the main difference in the physical process of charge generation and transportcompared to silicon cells?After excitation, what prevents the dye from returning to its ground state viafluorescence?What are the main requirements when choosing a dye?What are the main requirements that the semiconductor (TiO2) layer must satisfy to inorder to make an efficient cell?What causes the lack of stability of DSSCs? How can this potentially be solved?
    54. 54. Exercise : Tandem Solar CellsA tandem cell is made from two sub-cells, A and B. The individual sub cells are ideal diodes, with current-voltage (J-V) characteristicsgiven by:Where J0 is the reverse saturation current density, and Jph is the photocurrent density.These have values of J0,A = 10-10mA/cm2, Jph,A= 25 mA/cm2and J0,B = 10-18mA/cm2, Jph,B= 20 mA/cm2for sub-cells A and Brespectively at temperature T = 300 K.Calculate the open-circuit voltage for each sub-cell. Which sub cell do you suppose has the highest band gap?The two sub-cells can be connected together in series or in parallel to make a tandem cell. Sketch the J-V characteristics of theindividual sub-cells as well as the two possible configurations of tandem cell.Write an expression for the J-V characteristic of the parallel-connected tandem cell. Calculate the short-circuit current and the open-circuit voltage.Calculate the short-circuit current and open-circuit voltage for the series-connected tandem cell.(optional) Using a computer or otherwise, calculate the fill-factor for each sub-cell and the two possible tandem-cell configurations. (Hint:it is simpler to calculate power as a function of current for the series-connected cell.) Assuming the J-V curves were generated withAM1.5 radiation (100 mW/cm2), what are the corresponding power conversion efficiencies?The series configuration is more efficient than the parallel configuration. Why?Light passes through sub-cell B before reaching sub-cell A. The band gaps of each sub-cell can be adjusted to optimise the overallefficiency. How are the J-V curves of sub-cells A and B affected by changing the band gaps of the two materials? What is an importantcriterion for optimising the efficiency of a series-connected stacked tandem cell?

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