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Photovoltaic Solar Cells
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Solar Conversion Thermal – absorb suns energy to raise temp and use DT (relative to environment) to perform work. Photovoltaic – absorb photons that promote electrons to higher energy (excited state).
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How does a ideal crystalline semiconductor solar cell work
Assume there are no recombination events and we shine a pulse of light What is the potential energy we can now extract from this material? S0 S1 E Molecular picture Remember, we are going to attach electrodes that will interact with both excited and non excited electrons (equilibrium say there are back and forth reactions). Dm EFe EFh Eg Dm The fact that not all electrons (molecules) are excited is accounted for by the electrochemical potential (Dm)
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How does ideal crystalline or molecular semiconductor solar cell work
Now we shine a second pulse of light During the second light pulse we allow for radiative recombination During the second light pulse we open another recombination channel Dm Dm Dm The less recombination the better. Unfortunately, absorption is always accompanied by probability for emission and we can’t switch off the radiative recombination. We must minimize non-radiative channels
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How does ideal crystalline or molecular semiconductor solar cell work
Under steady state there are both excitation and emission events. The energy of an excited state (Eg) serves as an upper bound for VOC that due to the existence of radiative recombination is never reached. Dm Since absorption and emission are related through thermodynamic considerations it is possible to derive an upper bound that is more realistic Shockley’s paper
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Detailed balance Detailed balance and reciprocity in solar cells
Thomas Kirchartz and Uwe Rau phys. stat. sol. (a) 205, No. 12, 2737–2751 (2008)
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How does ideal semiconductor solar cell work
Shockley’s paper in simple terms Denote the density of electron-hole pairs as ne, the absorption rate of the sun light as I, and the excitation lifetime as t. Ideal: The lifetime is dictated by radiative emission only Eg Dm Denote the effective density of states for electron-hole pairs as ND and assume the semiconductor to be non degenerate (Boltzmann approximation holds): Ideal: Boltzmann approximation holds
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Max VOC of Solar Cell EEx Dm
In the ultimate case (only radiative loss): To find the maximum Dm we recall that we started with: We also recall that at any temperature there must be a finite black body radiation or a finite electron density. This requires that as T0 also (Eg - Dm) will approach zero or DmEg. EEx Loss Dm Excitation Energy. Here it is Eg In the ideal case the only voltage “loss” is due to: limited excitation (I) or recombination (t) Feel free to blame the temperature (T) too
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Losses t + Energy or Charge transfer to lower gap states
To define losses we first set the reference level or define the ideal case t I In the ultimate case the solar cell collects all photons emitted by the sun and all these photons are converted to free charges. In the ultimate case the only charge decay channel is due to radiative emission (this can not be avoided). Losses Not all the photons are being absorbed by the cell or Not all absorbed photons are converted to free charges Charge recombination that is different from the radiative rate of the absorbing material (this will always be on top of radiative). + Energy or Charge transfer to lower gap states
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Attributing VOC loss to Sun-Semiconductor not being a closed system I
We have seen that which means that there would be loss in Voc if either the sun intensity (I) is reduced or the radiation rate (t-1) is enhanced. The notion of a closed system means that the Sun and solar cell only emit towards each other. This is obviously not the case and we can say that this is because the sun is not filling the sky to surround the solar cell or that this is because the solar cell is emitting also outside the sun’s solid angle. If you want to be impressive you may call this “entropy loss” For isotropic emitter For ideal planar emitter (lambertian emission) qSun qSun Eg Dm
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VOC loss due to the Sun-Semiconductor not being a closed system - II
If the solar cell is partially transparent or some of the light is being reflected we effectively lose I and hence also Dm. Not all impinging light is absorbed by the active layer Eg Dm qSun If s is the fraction of impinging light that gets absorbed by the active layer the loss is:
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Loss due to shorter recombination time (non radiative loss)
Eg Dm Internal Luminescence Efficiency (h) below one reduces VOC by kT*ln(h-1) Generating charges through total luminescence quenching is not ideal
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The STRANGE Organics
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What might be different in organic semiconductor
Organics have two band gaps: Electronic band gap which is the difference between LUMO HOMO levels Optical band gap which is smaller than the electronic by the exciton binding energy Organics have vibronic structure Energy of luminescence is 1 to 2 vibration energy below the optical band gap. LUMO EEx Loss Dm Excitation Energy. Is ??? EL Ee Eg HOMO If you use the “standard” crystalline approach – which band gap will you choose? Relative to the optical gap or absorption gap – does the binding energy constitute a loss?
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Vibronic relaxation Mirror Image Absorption-Emission NO Stokes shift
2 2 1 1 Mirror Image Absorption-Emission NO Stokes shift 2 2 1 1 The spacing is due to: C—C, C—N, C—O à 800 – 1300cm^-1 C=C, C=N, C=O à 1500 – 1900cm^-1 C—H, N—H, O—H à 2850 – 3650cm^-1 A spacing of ~0.2eV. Eg ; ELum 0-0 1-0 0-1 0-2 Extinction coefficient Fluorescence Intensity 2-0 Which energy should we choose as the “excitation energy” Prior to recombination where are the electrons/holes
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Loss due to reorganization
2 2 1 Mirror Image Absorption-Emission With Stokes shift Eg Eg* 1 2 2 1 1 Eg-Eg* =~0.2eV Eg is the 0-0 transition Stokes shift or Marcus reorganization energy will affect the energy difference between electrons and holes prior to recombination 1-0 0-1 0-0 Extinction coefficient Fluorescence Intensity 2-0
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“Loss” due to broad density of state (or where is the band edge?)
LUMO The higher the expectations The bigger the disappointment C B A=E0 HOMO
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Loss due to broad density of state (or where is the band edge?)
Grabitz, P. O.; Rau, U.; Werner, J. H, Phys. status solidi 2005, 202 (15), 2920–2927. J. C. Blakesley and N. C. Greenham, Journal of Applied Physics, vol. 106, p , 2009.
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What might be different in organic semiconductor
ELum Eg ELum Eg P3HT Since we are interested in the energy of excitations in organics it might be better to let ELum replace Eg as the upper bound that is never reached. Eg - ELum may be due to: coulomb binding , vibronic relaxation , stokes shift, Broad DOS
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Device structures
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PN Junction based Photo-Cell
(See BASICS OF SEMICONDUCTOR DEVICESׁ ) N P + - Depletion EC2 - Vbi=Vt EC1 EF EV2 + EV1 Relevant points: Plus on the left and minus on the right relative to the center: bands on the right go up (left down) Electron-hole pair may be broken in a region where EC(x) <> EC(x+Dx)
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If we continuously shine light what will happen (in open circuit)?
- Vbi=Vt EC1 EF EV2 + EV1 If we continuously shine light what will happen (in open circuit)? 1. Accumulation of negative Q on left and positive Q on right 2. Flattening of the bands 3. Reduced charge separation until band are flat! EC1 EF2 EC2 EV2 EV1 EF1 VOC=EF1-EF2
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EC2 EC1 EV2 EV1 V - + Maximum available potential energy = ?
Electron contribution = ? Hole contribution = ?
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Another way to create EC(x) <> EC(x+Dx)
Before physical contact between metals and organic Semiconductor M1 M2 After physical contact & equilibration: M2 M1 EF
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Yet another method (hetero-structure)
Operation of a simple plastic cell nm Light Absorption Separate the charges Transport / recombination I M T E O T A Glass L
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Thanks to J.J.M. Halls for the slide
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Self Assembly of Bulk Heterojunction
HOMO Glass ITO PEDOT:PSS Mg Ag Donor Acceptor Donor Acceptor
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Characteristic equations of ideal solar cell
Under applied voltage and illumination Current VOC Voltage JSC
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Characteristic equations of ideal solar cell
Under applied voltage and illumination The open circuit Voltage: And the Power conversion efficiency :
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The Fill Factor (non ideal diode)
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Equivalent circuit
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Equivalent circuit (of a diode type solar cell)
Ideal Current J V Jdark JSC VOC Voltage JSC
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Equivalent circuit (of a diode type solar cell)
Ideal V Jdark JSC RS RSH J V Jdark JSC
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Equivalent circuit (of a diode type solar cell)
Jdark JSC RS RSH Current Current VOC VOC Voltage Voltage JSC JSC RS RSH What about fill factor of 25%
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(Is this) The End בסוף הכל יהיה בסדר. אז אם הכל בסדר זה הסוף.
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The energy source
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Solar Spectrum at a point outside the Earth’s atmosphere (AM0)
It resembles radiation spectrum of a black body at 5760K.
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Solar radiation The surface of the sun, is at a temperature of about 6000K and closely approximates a blackbody. A blackbody absorbs all radiation incident on its surface and emits radiation based on its temperature. H=σT4 (where σ is the Stefan-Boltzmann constant) The spectral irradiance from a blackbody is given by Plank's radiation law, shown in the following equation:
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Solar radiation The solar radiation outside the earth's atmosphere is calculated using the radiant power density at the sun's surface Hsun =5.961 x 107 W/m2, the radius of the sun (Rsun), and the distance between the earth and the sun. The calculated solar irradiance at the Earth's atmosphere is about 1.36 kW/m2.
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Solar radiation Black 6000K AM0
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Solar Spectrum reaching Earth’s surface
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Black 6000K AM0 AM1.5
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Quantifying the attenuation by the atmosphere – Air Mass factor
datm X nAirMass datm gs AM1.5 angle of elevation is 42O Such atmospheric thickness would attenuate the irradiance to ~900Wm-2 but for convenience the AM1.5 is defined for irradiance of 1000Wm-2.
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Results For Ideal case Jsc:
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Results PCE:
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Loss of Voc If we assume that under short circuit conditions all the sun photons are converted to current and that the cell’s recombination is purely radiative so that we can use Plank’s formulas to calculate the loss of Voc as a function of band gap. Note: In practical cells J0 is only part of the leakage current and in the general case: Jsc/J0≠Jsc/Jleakage
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Max VOC of Solar Cell In the ultimate case (only radiative loss):
To find the maximum Dm we recall that we started with: We also recall that at any temperature there must be a finite black body radiation of a finite electron density. This requires that as T0 also (Eg - Dm) will approach zero or DmEg. If we now raise the temperature while keeping Dm close to Eg we find that the entire DOS is full of electrons (ne=ND) which is not physical. Namely as we raise the temperature we are losing in term of Dm. Since ne=It this implies that as T is raised t becomes shorter (for fixed sun intensity I). The above discussion can also be carried out with the aid of the current voltage characteristics that defines VOC as: Here J0 is dark. Spontaneous recombination, current.
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