Physics of the thermal behavior of photovoltaic cells O. Dupré 1*,2 , Ph.D. candidate R. Vaillon 1 , M. Green 2 , advisors 1 Université de Lyon, CNRS, INSA-Lyon, UCBL, CETHIL, UMR5008, F-69621 Villeurbanne, France 2 Australian Centre for Advanced Photovoltaics, University of New South Wales, Sydney, 2052, Australia UNSW * olivier.dupre@insa-lyon.fr, 0449068191 June 2014, Sydney 1 1 O. Dupré, June 2014, UNSW
Introduction Virtuani et al, 2010 η PV ∝ T c P max Why are photovoltaic devices b ≈ -0.45%/K (for c-Si) ? negatively affected by temperature? What are the parameters involved? T c Fundamental losses in PV conversion 1 • Detailed balance principle (Shockley Queisser limit) • Energy/Entropy balance (Thermodynamic limit) 2 Dependences of these losses on temperature Additional losses in real PV cells 3 • External Radiative Efficiency • Intrinsic temperature coefficient of silicon cells 4 A thermal engineering view on PV performances 2 2 O. Dupré, June 2014, UNSW
Detailed balance principle Condition for an equilibrium: ground state excited state = excited state ground state E c E fc Current Recombination μ Generation E g Load E fv E v 3 3 O. Dupré, June 2014, UNSW
T s Detailed balance principle T a Condition for an equilibrium: ground state excited state = excited state ground state Ω abs Shockley & Queisser assumptions: Ω emit T c (1) 1 photon excites only 1 electron (2) All recombinations are radiative, i.e. generate a photon E c E fc Current = q (Photons absorbed – Photons emitted) (2) (1) Emission μ Absorption E g Load Generalized Planck’s equation photon fluxes E fv 2 E v 2 E N E T ( , , , ) dE g E 2 3 c h E e kT 1 g (3) μ is the chemical potential of the radiation (4) q N ( N ) V P elec for the luminescent radiation from the cell: μ = qV abs emit (3) Single gap: absorbs every photons with E≥E g and none with E<E g (4) Assuming perfect charge transport 4 4 O. Dupré, June 2014, UNSW
Energy/Entropy balance • Thermodynamics enables to evaluate the T s theoretical limits of energy conversion + processes Ë c • Different energy forms do not contain the same amount of free energy (or exergy: + + energy that can be extracted to produce T c Ë s work ) because they contain different amount S̈ c S̈ s of entropy We consider here the gas of S̈ gen + excited electron-hole pairs : Ẅ Q ̇ /T c F N E Tc S pV + Q ̇ Electrochemical Gibbs Internal Entropy energy free energy Number of energy ̇ /T a Q T a e-h pairs “disordered energy” ultimately converted into heat 5 5 O. Dupré, June 2014, UNSW
Energy/Entropy balance Irreversible thermodynamics entropy fluxes . . . N E S T W E E Q s c T c Q E N E N s s c c Ë s S T gen c T T T ( Ë s - μ N̈ s )/T c ( Ë c - μ N̈ c )/T c c c c W ( N N ) S T gen S̈ gen s c c + Ẅ Q ̇ /T c (1) 1 photon creates excites only 1 electron (2) All recombinations are radiative (3) Single gap: absorbs every photons with E≥E g and none with E<E g Q ̇ (4) Assuming perfect charge transport S 0 and qV gen Ẅ q N ( N V ) s c 6 6 O. Dupré, June 2014, UNSW
Analytical solution P P elec q N ( N ) V elec 0 (1) abs emit E g V P max f E T P f E T V ( , , ) ( , , , ) elec 0 (2) g s abs g c emit V E g 2 . 2 E N E T ( , , , ) dE Boltzmann approximation analytical solution of (1) g 2 3 E c h E e kT 1 g T (*) c emit qV E (1 ) kT ln( ) : relates the optimal operating voltage and E g opt g c T s abs (*) only correct when E g =E g (max) but Angle mismatch loss Carnot efficiency stays a good approximation for any E g . . J V q N ( N ( V ))( E Carnot Anglemismatch ) P max abs emit opt opt opt g loss loss Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) 7 7 O. Dupré, June 2014, UNSW
Losses = f(Eg) Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) Similarly to an heat engine, the work that can be 1 extracted is ultimately limited by the temperature Fraction of the incident solar energy 0.9 difference between the sun and the cell 0.8 + 0.7 The radiation emitted by cell is lost 0.6 + 0.5 A standard PV cell emits in more directions than it absorbs light coming directly from the sun 0.4 + 0.3 0.2 A single gap absorber can Photons with insufficient energies not efficiently use the broad 0.1 solar spectrum Photons too energetic 0 0.4 1.4 2.4 3.4 = E g (eV) Shockley Queisser limit (numerical) 8 8 O. Dupré, June 2014, UNSW
3 rd gen PV > Shockley-Queisser limit Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) 1 Solar TPV, Thermophotonics Fraction of the incident solar energy 0.9 0.8 Hot carriers, 0.7 Down conversion 0.6 / Multiple Excitons Generation 0.5 Impurity PV, 0.4 Up conversion Multi-junctions, 0.3 Spectral splitting 0.2 0.1 Concentration, Limited angle emission 0 0.4 1.4 2.4 3.4 E g (eV) Shockley Queisser limit 9 9 O. Dupré, June 2014, UNSW
3 rd gen PV > Shockley-Queisser limit Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) 1 Solar TPV, Thermophotonics Fraction of the incident solar energy 0.9 0.8 Hot carriers, 0.7 Down conversion 0.6 / Multiple Excitons Generation 0.5 Impurity PV, 0.4 Up conversion Multi-junctions, 0.3 Spectral splitting 0.2 0.1 Concentration, Limited angle emission 0 0.4 1.4 2.4 3.4 E g (eV) Shockley Queisser limit E g (Si at 300 K) ≈ 1.12 eV 10 10 O. Dupré, June 2014, UNSW
Band diagram of an ideal Si cell at MPP Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) 11 11 O. Dupré, June 2014, UNSW
IV curve of an ideal Silicon cell Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) / Cumulated photon flux density *q (s -1 .m -2 ) Current density (A.m -2 ) 23% MPP 1% 30% 11% IV curve 33% 2% Photon energy (eV) / Cell voltage (V) 12 12 O. Dupré, June 2014, UNSW
Overview Virtuani et al, 2010 η PV ∝ T c P max Why are photovoltaic devices b ≈ -0.45%/K (for c-Si) ? negatively affected by temperature? What are the parameters involved? T c Fundamental losses in PV conversion 1 • Detailed balance principle (Shockley Queisser limit) • Energy/Entropy balance (Thermodynamic limit) 2 Dependences of these losses on temperature Additional losses in real PV cells 3 • External Radiative Efficiency • Intrinsic temperature coefficient of silicon cells 4 A thermal engineering view on PV performances 13 13 O. Dupré, June 2014, UNSW
Some losses = f(T c ) Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) ∝ T c ∝ T c ∝ T c T T = 300K = 450K c c • The emission rate increases with T c 1 Fraction of the incident solar energy so the angle mismatch loss increases 0.9 as well. • Also, Δ T= T 0.8 sun -T cell decreases with T c so the Carnot loss increases. 0.7 0.6 0.5 0.05 0.4 0.03 0.3 G(T) - G(300K) 0.01 0.2 -0.01 0.1 -0.03 0 0.4 1.4 2.4 3.4 0.4 1.4 2.4 3.4 -0.05 E g (eV) E g (Si)=1.12 eV -0.07 280 320 360 400 440 Temperature (K) 14 14 O. Dupré, June 2014, UNSW
Temperature coefficient b b Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) ∝ T c ∝ T c ∝ T c 1 Fraction of the incident solar energy 0.9 b : temperature coefficient 0.8 T c P max 0.7 0.6 T 298.15K 1 b T 298.15K T 298.15 0.5 0.4 Carnot + Angle mismatch + Emission b f ( ) f E ( ) 0.3 g Output power 0.2 0 0.1 -0.17 -1000 βη _350K (ppm) -0.37 0 0.4 1.4 2.4 3.4 -0.57 -2000 Ratio E g (eV) -0.77 -3000 -0.97 Reducing certain losses -1.17 b -4000 also improves -1.37 -5000 -1.57 0.4 1.4 2.4 E g (eV) 15 15 O. Dupré, June 2014, UNSW
Temperature coefficient = f(Concentration) Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) (1 sun ) abs abs C abs emit Angle mismatch C C max (1 sun ) (1 sun ) abs abs emit emit C=C max ≈ 46200 C=1 1 Fraction of the incident solar energy b f ( Angle mismatch Concent / ration ) 0.9 0 0.8 C= 0.7 Cmax βη _350K (ppm) 10000 0.6 -1000 1000 0.5 (2) 100 0.4 (1) 10 -2000 0.3 1 0.2 0.1 -3000 0.4 1.4 2.4 0 E g (eV) 0.4 1.4 2.4 3.4 0.4 1.4 2.4 3.4 E g (eV) Minimizing the angle mismatch : b (1) Improves (2) AND improves P max 16 16 O. Dupré, June 2014, UNSW
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