Physics of the thermal behavior of photovoltaic cells O. Dupré *,2, Ph.D. candidate R. Vaillon, M. Green 2, advisors Université de Lyon, CNRS, INSA-Lyon, UCBL, CETHIL, UMR58, F-6962 Villeurbanne, France 2 Australian Centre for Advanced Photovoltaics, University of New South Wales, Sydney, 252, Australia * olivier.dupre@insa-lyon.fr, 449689 UNSW June 24, Sydney
Virtuani et al, 2 Introduction η PV T c P max b -.45%/K (for c-si)? Why are photovoltaic devices negatively affected by temperature? What are the parameters involved? T c 2 3 4 Fundamental losses in PV conversion Detailed balance principle (Shockley Queisser limit) Energy/Entropy balance (Thermodynamic limit) Dependences of these losses on temperature Additional losses in real PV cells External Radiative Efficiency Intrinsic temperature coefficient of silicon cells A thermal engineering view on PV performances 2
Detailed balance principle Condition for an equilibrium: ground state excited state = excited state ground state E c E g μ E fc Generation Recombination Load Current E fv E v 3
T s Detailed balance principle T a Condition for an equilibrium: ground state excited state = excited state ground state Ω abs Ω emit T c Shockley & Queisser assumptions: () photon excites only electron (2) All recombinations are radiative, i.e. generate a photon E g E c E v μ E fc () Absorption E fv P elec Emission (2) q( Nabs Nemit ) V Load Current = q (Photons absorbed Photons emitted) Generalized Planck s equation photon fluxes N ( E, T,, ) g 2 c h 2 3 E (3) μ is the chemical potential of the radiation (4) for the luminescent radiation from the cell: μ = qv (3) Single gap: absorbs every photons with E E g and none with E<E g (4) Assuming perfect charge transport 4 g E 2 E kt e de
Energy/Entropy balance + T s Thermodynamics enables to evaluate the theoretical limits of energy conversion processes S s + E s S c + E c T c Different energy forms do not contain the same amount of free energy (or exergy: energy that can be extracted to produce work) because they contain different amount of entropy Q /T c Q /T a + Q + S gen T a W Gibbs free energy We consider here the gas of excited electron-hole pairs : F N T S c E Electrochemical energy Number of e-h pairs Internal energy Entropy pv disordered energy ultimately converted into heat 5
(E s -μ N s )/T c Q /T c Q E s T c (E c -μ N c )/T c + S gen Energy/Entropy balance Irreversible thermodynamics entropy fluxes W... E N S T W E s E c Q Q E s N s E c N c S T T T c c c W ( N s N c) S T gen () photon creates excites only electron (2) All recombinations are radiative (3) Single gap: absorbs every photons with E E g and none with E<E g (4) Assuming perfect charge transport c gen T c Sgen and qv W q( NsNc) V 6
Analytical solution P E elec P elec q( Nabs Nemit ) V () f ( Eg, Ts, abs ) f ( Eg, Tc, V, emit ) (2) g P V elec V E g P max. N ( E, T,, ) 2 c h Boltzmann approximation g analytical solution of () Tc emit qvopt Eg ( ) ktc ln( ) T s Carnot efficiency abs 2 3 E Angle mismatch loss g E 2 E kt e de : relates the optimal operating voltage and E g (*) (*) only correct when E g =E g (max) but stays a good approximation for any E g P max.. J V q( Nabs Nemit ( V ))( E Carnot Angle mismatch ) opt opt opt g loss loss Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) 7
Fraction of the incident solar energy Losses = f(eg) Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission).9.8.7.6.5.4.3.2..4.4 2.4 3.4 E g (ev) Similarly to an heat engine, the work that can be extracted is ultimately limited by the temperature difference between the sun and the cell The radiation emitted by cell is lost + + A standard PV cell emits in more directions than it absorbs light coming directly from the sun + A single gap absorber can not efficiently use the broad solar spectrum = Shockley Queisser limit (numerical) Photons with insufficient energies Photons too energetic 8
Fraction of the incident solar energy 3 rd gen PV > Shockley-Queisser limit Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission).9.8.7.6 Hot carriers, Down conversion / Multiple Excitons Generation Solar TPV, Thermophotonics.5.4.3.2 Multi-junctions, Spectral splitting Impurity PV, Up conversion..4.4 2.4 3.4 E g (ev) Concentration, Limited angle emission Shockley Queisser limit 9
Fraction of the incident solar energy 3 rd gen PV > Shockley-Queisser limit Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission).9.8.7.6 Hot carriers, Down conversion / Multiple Excitons Generation Solar TPV, Thermophotonics.5.4.3.2 Multi-junctions, Spectral splitting Impurity PV, Up conversion..4.4 2.4 3.4 E g (ev) E g (Si at 3K).2 ev Concentration, Limited angle emission Shockley Queisser limit
Band diagram of an ideal Si cell at MPP Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)
Current density (A.m -2 ) / Cumulated photon flux density *q (s -.m -2 ) IV curve of an ideal Silicon cell Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) 23% MPP % 3% IV curve 2% % 33% Photon energy (ev) / Cell voltage (V) 2
Virtuani et al, 2 Overview η PV T c P max b -.45%/K (for c-si)? Why are photovoltaic devices negatively affected by temperature? What are the parameters involved? T c 2 3 4 Fundamental losses in PV conversion Detailed balance principle (Shockley Queisser limit) Energy/Entropy balance (Thermodynamic limit) Dependences of these losses on temperature Additional losses in real PV cells External Radiative Efficiency Intrinsic temperature coefficient of silicon cells A thermal engineering view on PV performances 3
Fraction of the incident solar energy Some losses = f(t c ) G(T) - G(3K) Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission) T c T c T c.9.8.7.6 T c = 3K T c = 45K The emission rate increases with T c so the angle mismatch loss increases as well. Also, ΔT=T sun -T cell decreases with T c so the Carnot loss increases..5.4.3.2..4.4 2.4 3.4 E g (ev).4.4 2.4 3.4 E g (Si)=.2 ev.5.3. -. -.3 -.5 -.7 28 32 36 4 44 Temperature (K) 4
Fraction of the incident solar energy Temperature coefficient b βη_35k (ppm) Ratio Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission).9.8.7.6.5.4.3.2..4.4 2.4 3.4 E g (ev) Reducing certain losses also improves b b T c T T c T c T c b : temperature coefficient P max T 298.5K 298.5K T 298.5 Carnot + Angle mismatch + Emission b f( ) f ( E g ) Output power -.7 - -.37 -.57-2 -.77-3 -.97 -.7-4 -.37-5.4.4 2.4 E g (ev) -.57 5
Fraction of the incident solar energy βη_35k (ppm) Temperature coefficient = f(concentration) Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission).9.8.7.6.5.4.3.2 C C= () abs ( sun) abs C max C=C max 462 emit ( sun) abs - -2 Angle mismatch b f( Angle mismatch / Concent ration) (2) ( ) abs abs sun C emit emit C= Cmax..4.4 2.4 3.4 E g (ev).4.4 2.4 3.4 Minimizing the angle mismatch: -3.4.4 2.4 () Improves P max (2) AND improves E g (ev) b 6
Virtuani et al, 2 Overview η PV T c P max b -.45%/K (for c-si)? Why are photovoltaic devices negatively affected by temperature? What are the parameters involved? T c 2 3 4 Fundamental losses in PV conversion Detailed balance principle (Shockley Queisser limit) Energy/Entropy balance (Thermodynamic limit) Dependences of these losses on temperature Additional losses in real PV cells External Radiative Efficiency Intrinsic temperature coefficient of silicon cells A thermal engineering view on PV performances 7
βη_35k (ppm) Additional losses in real devices b fe ( g ) - -2 CdTe? -3 CIGS -4 Si -5.4.4 2.4 E g (ev) analytical numerical experimental measurements Virtuani et al, 2? Why do real PV devices have worse b than predicted before? 8
Additional losses in real devices 9
Current density (A.m -2 ) / Cumulated photon flux density *q (s -.m -2 ) IV curve of a commercial Silicon cell Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission + Non radiative recombination + Series + Shunt) Realistic IV curve Losses due to non radiative recombinations = Ideal IV curve - - Loss due to shunts - Loss due to series resistance Photon energy (ev) / Cell voltage (V) 2
External Radiative Efficiency: ERE J( V) J J ( V) light rec _ dark J q( Nabs Nemit ) ERE (superposition principle) photon emission Nemit q rec _ dark similar to EQE of a LED: how many electrons need to be excited to emit one photon? ERE Rrad total dark current recombination J different from IRE Using Boltzmann approximation analytical solution: Green, 22 R tot because of photon recycling Tc emit qvmpp Eg ( ) ktc ln( ) ktc ln( ) T ERE s abs MPP Carnot efficiency Angle mismatch loss Non radiative recombination loss Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission + Non radiative recombination) 2
Fraction of the incident solar energy βη_35k (ppm).9.8.7.6.5.4 Commercial Si cell V oc =58 mv ERE MPP = -5 Temperature coefficient = f(ere) State of the art Si cell V oc =7 mv ERE MPP =.5-3 - -2-3 -287 b ( ) f ERE MPP (2) ERE: - - -2-2 -3-3 -4-4.3.2. () -4 Si -445-5 -5.4.4 2.4 3.4.4.4 2.4 3.4 E g (ev) Minimizing the non radiative losses: () Improves P max (2) AND improves -5.4.9.4.9 2.4 2.9 b E g (ev) Green et al, 982 As the open-circuit voltage of silicon solar cells continues to improve, one resulting advantage, not widely appreciated, is reduced temperature sensitivity of device performance 22
Temperature coefficient = f(t c ) ηmax βη_35k (ppm) b ( ) f ERE MPP BUT Radiative and non radiative recombination mechanisms have different temperature and voltage dependences (and V MPP =f(t c )) ERE MPP f ( T ) c b ( ) ft c.25-3 Example: SRH recombination theory using 2 different trap energies E t : - - - - E c -E t =.26 E c -E t =.43.2.5..5-36 -4-46 -5-56 3 35 4 45 Tc (K) ALSO Series and shunt losses = f(t c ) impact on b? 23
Maximum efficiency Bandgap = f(t c ), influence of the spectrum.35 Si InP GaAs CdTe AM.5 spectrum.3 CsSnI3 T c.25 Ge E T g c 278K 298K.2 38K 338K.5 CdS 358K..5.5 2 2.5 E g (ev) Eg b f ( Eg,, incident spectrum) T c Perovskite compound (CsSnI3) Eg interesting ( Eg, ) T c 24
βη_45ºc (ppm) Bandgap = f(t c ), influence of the spectrum - -2-3 AM.5 spectrum -84 GaAs CsSnI3 CdTe Si InP -529 CdS deg/dt (GaAs) =-.52 mev/k deg/dt (CsSnI3) =+.36 mev/k deg/dt = -4 Ge -5.4.9.4.9 2.4 2.9 E g at 25ºC (ev) Eg b f ( Eg,, incident spectrum) T c Perovskite compound (CsSnI3) Eg interesting ( Eg, ) T c 25
Intrinsic b of silicon cells Using the state-of-the-art parameters* and considering carefully their temperature dependences, we derived the temperature coefficient of the limiting efficiency of crystalline silicon solar cells (SQ limit with AM.5) η(298.5k) = 29.6% < 33.4% Intrinsic b of crystalline silicon cells = -238 ppm/k < -582 ppm/k This is obviously not a minimum but as silicon cells improve towards their limiting efficiencies, their temperature sensitivity is expected to converge toward this value Differences with the SQ assumptions: Auger recombination Realistic absorbance of silicon with Free Carrier Absorption and assuming a Lambertian light trapping scheme bb() E Abb() E bb( E) FCA( E) 2 4nW r * Richter et al, 23 26
Virtuani et al, 2 Overview η PV T c P max b -.45%/K (for c-si)? Why are photovoltaic devices negatively affected by temperature? What are the parameters involved? T c 2 3 4 Fundamental losses in PV conversion Detailed balance principle (Shockley Queisser limit) Energy/Entropy balance (Thermodynamic limit) Dependences of these losses on temperature Additional losses in real PV cells External Radiative Efficiency Intrinsic temperature coefficient of silicon cells A thermal engineering view on PV performances 27
Fraction of the incident solar energy ηmax (%) Tc (K) A thermal engineering view on PV performances ERE MPP =.9.8.7.6.5.4.3.2..3.25.2.5 Si CdTe 5 η(3k) BIPV 48 η(tc) with h = W.m -2.K - - - - - ideal cell 46 44 42 4 38.4.4 2.4 3.4 E g (ev)..5 36 34 32 3.4.9.4.9 2.4 2.9 3.4 Eg (ev) 28
Fraction of the incident solar energy ηmax (%) Tc (K) A thermal engineering view on PV performances.9.8 ERE MPP = -5.7.6.5.4.3.3.25.2 Si CdTe BIPV 5 η(3k) 48 η(tc) with h = W.m -2.K - 46 - - - - ideal cell commercial cell 44 42.2.5 4. 38.4.4 2.4 3.4 E g (ev)..5 36 34 32 3.4.9.4.9 2.4 2.9 3.4 Eg (ev) 29
Conclusions and future work Reducing Angle mismatch or Non Radiative losses improves efficiencies AND temperature coefficients of PV cells At one sun, b is principally a function of the cell bandgap (Eg) and quality (ERE) b ERE Eg contact loss shunt loss f ( Eg, EREC,,,,incident spectrum,,...) T T T T c c c c Investigate the impact of these parameters to be able to predict b of different technologies Intrinsic b of crystalline silicon cells = -238 ppm/k Assess different PV strategies (TPV, BIPV, CPV, multi-junctions,...) with this thermal approach 3
Thank you for your attention 3
Fraction of the incident solar energy Temperature coefficient of multi-junctions Output power = Input power Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission).9.8.7.6.5.4 Carnot + Angle mismatch + Emission Output power b cst 26 ppm/k.3.2 Q cst T c cst. 2 3 4 Number of junctions 32