Physics of the thermal behavior of photovoltaic cells O. Dupr 1*,2 , - - PowerPoint PPT Presentation

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Physics of the thermal behavior of photovoltaic cells O. Dupr 1*,2 , - - PowerPoint PPT Presentation

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Physics of the thermal behavior of photovoltaic cells O. Dupr 1*,2 , Ph.D. candidate R. Vaillon 1 , M. Green 2 , advisors 1 Universit de Lyon, CNRS, INSA-Lyon, UCBL, CETHIL, UMR5008, F-69621 Villeurbanne, France 2 Australian Centre for Advanced

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  • O. Dupré, June 2014, UNSW

Physics of the thermal behavior

  • f photovoltaic cells

UNSW June 2014, Sydney * olivier.dupre@insa-lyon.fr, 0449068191

  • O. Dupré1*,2, Ph.D. candidate
  • R. Vaillon1, M. Green2, advisors

1Université de Lyon, CNRS, INSA-Lyon, UCBL, CETHIL, UMR5008, F-69621 Villeurbanne, France 2Australian Centre for Advanced Photovoltaics, University of New South Wales, Sydney, 2052, Australia

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  • O. Dupré, June 2014, UNSW

Introduction

Virtuani et al, 2010

Pmax T

c

b ≈ -0.45%/K (for c-Si)

?

Why are photovoltaic devices negatively affected by temperature? What are the parameters involved? Fundamental losses in PV conversion

  • Detailed balance principle (Shockley Queisser limit)
  • Energy/Entropy balance (Thermodynamic limit)

1

Dependences of these losses on temperature

2

ηPV Tc ∝

Additional losses in real PV cells

  • External Radiative Efficiency
  • Intrinsic temperature coefficient of silicon cells

3

A thermal engineering view on PV performances

4

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  • O. Dupré, June 2014, UNSW

Detailed balance principle

Generation Recombination

Ev Ec Eg Efv Efc

Load

μ

Condition for an equilibrium: ground state  excited state = excited state  ground state

Current

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  • O. Dupré, June 2014, UNSW

Detailed balance principle

Ev Ec

Absorption Emission

Eg

Ts Ta Tc Ωemit Ωabs

Efv Efc

(3) (1) (2)

Condition for an equilibrium: ground state  excited state = excited state  ground state Shockley & Queisser assumptions: (1) 1 photon excites only 1 electron (2) All recombinations are radiative, i.e. generate a photon

Current = q (Photons absorbed – Photons emitted)

Generalized Planck’s equation  photon fluxes μ is the chemical potential of the radiation for the luminescent radiation from the cell: μ = qV

(3) Single gap: absorbs every photons with E≥Eg and none with E<Eg (4) Assuming perfect charge transport

(4)

Load

μ Pelec

2 2 3

2 ( , , , ) e 1

g

g E E kT

E N E T dE c h

 

   

( )

abs emit

q N N V  

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Energy/Entropy balance

Ts Tc Ta Ës Q ̇ Ëc Q ̇ /Tc Q ̇ /Ta Ẅ

  • Thermodynamics enables to evaluate the

theoretical limits of energy conversion processes

  • 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

  • f entropy

S̈s S̈c

     Tc F N S E pV

Gibbs free energy Number of e-h pairs Internal energy Entropy Electrochemical energy

“disordered energy” ultimately converted into heat We consider here the gas of excited electron-hole pairs :

+ + + + S̈gen +

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Energy/Entropy balance

Irreversible thermodynamics  entropy fluxes

. . . N E S T   

(1) 1 photon creates excites only 1 electron (2) All recombinations are radiative (3) Single gap: absorbs every photons with E≥Eg and none with E<Eg (4) Assuming perfect charge transport

Tc Ës Q ̇ /Tc

Ẅ

Q ̇ (Ës-μ N̈s)/Tc (Ëc-μ N̈c)/Tc

( )

s c

q N N V  

S̈gen + Ẅ

s c

W E E Q   

s s c c gen c

c c c

Q E N E N S T T T T        ( )

s c c

gen

W N N S T     0 and

gen

S qV   

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Analytical solution

Boltzmann approximation  analytical solution of (1)

(*) only correct when Eg=Eg(max) but stays a good approximation for any Eg

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

2 . 2 3

2 ( , , , ) e 1

g

g E E kT

E N E T dE c h

 

   

(1 ) ln( )

c emit

  • pt

g c s abs

T qV E kT T     

Pelec

( )

abs emit

q N N V  

elec g V

P E           

( , , , )

g c emit

f E T V  ( , , )

g s abs

f E T 

: relates the optimal operating voltage and Eg

(*) . .

( ( ))( )

abs emit

  • pt
  • pt
  • pt

g loss loss

J V q N N V E Carnot Anglemismatch     

Carnot efficiency Angle mismatch loss

g

elec E

P V         

Pmax

(1) (2)

Pmax

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

Losses = f(Eg)

Shockley Queisser limit (numerical) Similarly to an heat engine, the work that can be extracted is ultimately limited by the temperature difference between the sun and the cell Photons with insufficient energies The radiation emitted by cell is lost A standard PV cell emits in more directions than it absorbs light coming directly from the sun Photons too energetic A single gap absorber can not efficiently use the broad solar spectrum Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

+ = + +

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3rd gen PV > Shockley-Queisser limit

Impurity PV, Up conversion Concentration, Limited angle emission Multi-junctions, Spectral splitting Solar TPV, Thermophotonics

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

Shockley Queisser limit

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

Hot carriers, Down conversion / Multiple Excitons Generation

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3rd gen PV > Shockley-Queisser limit

Hot carriers, Down conversion / Multiple Excitons Generation Impurity PV, Up conversion Concentration, Limited angle emission Multi-junctions, Spectral splitting

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

Eg (Si at 300K) ≈ 1.12 eV

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

Shockley Queisser limit Solar TPV, Thermophotonics

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Band diagram of an ideal Si cell at MPP

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

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Current density (A.m-2) / Cumulated photon flux density *q (s-1.m-2) Photon energy (eV) / Cell voltage (V)

IV curve of an ideal Silicon cell

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

IV curve MPP 33% 30% 23% 11% 2% 1%

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Overview

Virtuani et al, 2010

Pmax T

c

b ≈ -0.45%/K (for c-Si)

?

Why are photovoltaic devices negatively affected by temperature? What are the parameters involved? Fundamental losses in PV conversion

  • Detailed balance principle (Shockley Queisser limit)
  • Energy/Entropy balance (Thermodynamic limit)

1

Dependences of these losses on temperature

2

ηPV Tc ∝

Additional losses in real PV cells

  • External Radiative Efficiency
  • Intrinsic temperature coefficient of silicon cells

3

A thermal engineering view on PV performances

4

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  • 0.07
  • 0.05
  • 0.03
  • 0.01

0.01 0.03 0.05 280 320 360 400 440 G(T) - G(300K) Temperature (K)

0.4 1.4 2.4 3.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

= 300K = 450K T

c

T

c

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

Eg(Si)=1.12 eV

  • The emission rate increases with Tc

so the angle mismatch loss increases as well.

  • Also, ΔT=T

sun-T cell decreases with Tc so

the Carnot loss increases.

Some losses = f(Tc)

∝ Tc ∝ Tc ∝ Tc

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Temperature coefficient b

Reducing certain losses also improves

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

       

298.15K 1 298.15K 298.15 T T T   b    

b

Tc

Pmax : temperature coefficient b

( ) ( )

g

f f E  

b

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

∝ Tc ∝ Tc ∝ Tc

b

Carnot + Angle mismatch + Emission Output power

  • 1.57
  • 1.37
  • 1.17
  • 0.97
  • 0.77
  • 0.57
  • 0.37
  • 0.17
  • 5000
  • 4000
  • 3000
  • 2000
  • 1000

0.4 1.4 2.4

Ratio βη_350K (ppm) Eg (eV)

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  • 3000
  • 2000
  • 1000

0.4 1.4 2.4

βη_350K (ppm) Eg (eV) Cmax 10000 1000 100 10 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

C=Cmax≈46200

Temperature coefficient = f(Concentration)

0.4 1.4 2.4 3.4

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

(1) (2)

b ( / ) Angle mismatch Concent f ration 

(1 )

abs abs

C sun    (1 )

abs abs emit emit

Angle mismatch C sun      

(1) Improves (2) AND improves Pmax

b

Minimizing the angle mismatch:

max

(1 )

emit abs

C sun    C=1

C=

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Overview

Virtuani et al, 2010

Pmax T

c

b ≈ -0.45%/K (for c-Si)

?

Why are photovoltaic devices negatively affected by temperature? What are the parameters involved? Fundamental losses in PV conversion

  • Detailed balance principle (Shockley Queisser limit)
  • Energy/Entropy balance (Thermodynamic limit)

1

Dependences of these losses on temperature

2

ηPV Tc ∝

Additional losses in real PV cells

  • External Radiative Efficiency
  • Intrinsic temperature coefficient of silicon cells

3

A thermal engineering view on PV performances

4

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Additional losses in real devices

?

Why do real PV devices have worse than predicted before?

  • 5000
  • 4000
  • 3000
  • 2000
  • 1000

0.4 1.4 2.4 βη_350K (ppm) Eg (eV) analytical numerical

Si CdTe CIGS

?

experimental measurements

b

Virtuani et al, 2010

b

( )

g

f E 

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Additional losses in real devices

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Current density (A.m-2) / Cumulated photon flux density *q (s-1.m-2) Photon energy (eV) / Cell voltage (V)

IV curve of a commercial Silicon cell

Realistic IV curve

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission + Non radiative recombination + Series + Shunt)

Loss due to shunts Loss due to series resistance Losses due to non radiative recombinations =

  • Ideal IV curve
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  • similar to EQE of a LED:

how many electrons need to be excited to emit one photon?

  • different from

because of photon recycling

1 ( )

abs emit

J q N N ERE  

External Radiative Efficiency: ERE

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission + Non radiative recombination) (superposition principle)

1 (1 ) ln( ) ln( )

c emit MPP g c c s abs MPP

T qV E kT kT T ERE      

Carnot efficiency Angle mismatch loss

_

( ) ( )

light rec dark

J V J J V  

_ emit rec dark

photon emission N q ERE total dark current recombination J  

rad tot

R IRE R 

Non radiative recombination loss

Green, 2012

Using Boltzmann approximation  analytical solution:

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0.4 1.4 2.4 3.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

  • 5000
  • 4000
  • 3000
  • 2000
  • 1000

0.4 0.9 1.4 1.9 2.4 2.9

βη_350K (ppm) Eg (eV)

1 10-1 10-2 10-3 10-4 10-5

EREMPP=10-5

Temperature coefficient = f(ERE)

(1) (2)

b ( )

MPP

f ERE 

(1) Improves (2) AND improves Pmax

b

Minimizing the non radiative losses: EREMPP=1.5 10-3

State of the art Si cell Commercial Si cell

Si

  • 4450
  • 2870

ERE: 1 10-1 10-2 10-3 10-4 10-5 “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” Green et al, 1982 Voc=710 mV Voc=580 mV

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b ( )

MPP

f ERE  ( )

MPP c

ERE f T 

Radiative and non radiative recombination mechanisms have different temperature and voltage dependences (and VMPP=f(T

c))

BUT

Temperature coefficient = f(Tc)

Series and shunt losses = f(T

c)  impact on ?

b b ( )

c

f T 

Example: SRH recombination theory using 2 different trap energies Et:

  • - - - Ec-Et=0.26

—— Ec-Et=0.43

  • 5600
  • 5100
  • 4600
  • 4100
  • 3600
  • 3100

0.05 0.1 0.15 0.2 0.25 300 350 400 450

βη_350K (ppm) ηmax Tc (K)

ALSO

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Bandgap = f(Tc), influence of the spectrum

0.1 0.15 0.2 0.25 0.3 0.35 0.5 1 1.5 2 2.5 Maximum efficiency Eg (eV) 278K 298K 318K 338K 358K GaAs CsSnI3 Si Ge CdS CdTe InP

Tc

AM1.5 spectrum

b

( , , )

g c

E f Eg incident spectrum T   

g c

E T   

Perovskite compound (CsSnI3) interesting (

, )

g c

E Eg T  

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  • 5000
  • 4000
  • 3000
  • 2000
  • 1000

0.4 0.9 1.4 1.9 2.4 2.9 βη_45ºC (ppm) Eg at 25ºC (eV) dEg/dT (GaAs) =-0.52 meV/K dEg/dT (CsSnI3) =+0.36 meV/K dEg/dT = 0

Bandgap = f(Tc), influence of the spectrum

Ge CdS CdTe InP GaAs CsSnI3 Si

  • 1084
  • 1529

AM1.5 spectrum

b

( , , )

g c

E f Eg incident spectrum T   

Perovskite compound (CsSnI3) interesting (

, )

g c

E Eg T  

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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

Intrinsic of silicon cells

(SQ limit with AM1.5) < 33.4% < -1582 ppm/K Differences with the SQ assumptions:

  • Auger recombination
  • Realistic absorbance of silicon with Free

Carrier Absorption and assuming a Lambertian light trapping scheme

* Richter et al, 2013

Intrinsic of crystalline silicon cells = -2380 ppm/K

b

η(298.15K) = 29.6% 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

b

2

( ) ( ) 1 ( ) ( ) 4

bb bb bb FCA r

E A E E E n W      

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Overview

Virtuani et al, 2010

Pmax T

c

b ≈ -0.45%/K (for c-Si)

?

Why are photovoltaic devices negatively affected by temperature? What are the parameters involved? Fundamental losses in PV conversion

  • Detailed balance principle (Shockley Queisser limit)
  • Energy/Entropy balance (Thermodynamic limit)

1

Dependences of these losses on temperature

2

ηPV Tc ∝

Additional losses in real PV cells

  • External Radiative Efficiency
  • Intrinsic temperature coefficient of silicon cells

3

A thermal engineering view on PV performances

4

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300 320 340 360 380 400 420 440 460 480 500 0.05 0.1 0.15 0.2 0.25 0.3 0.4 0.9 1.4 1.9 2.4 2.9 3.4

Tc (K) ηmax (%) Eg (eV)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

CdTe Si

A thermal engineering view on PV performances

η(300K) η(Tc) with =10 W.m-2.K-1

  • - - - ideal cell

h

BIPV

EREMPP=1

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300 320 340 360 380 400 420 440 460 480 500 0.05 0.1 0.15 0.2 0.25 0.3 0.4 0.9 1.4 1.9 2.4 2.9 3.4

Tc (K) ηmax (%) Eg (eV)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 1.4 2.4 3.4

Fraction of the incident solar energy Eg (eV)

A thermal engineering view on PV performances

η(300K) η(Tc) with =10 W.m-2.K-1

  • - - - ideal cell

—— commercial cell h CdTe Si

BIPV

EREMPP=10-5

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Conclusions and future work

Reducing Angle mismatch or Non Radiative losses improves efficiencies AND temperature coefficients of PV cells Assess different PV strategies (TPV, BIPV, CPV, multi-junctions, ...) with this thermal approach Intrinsic of crystalline silicon cells = -2380 ppm/K At one sun, is principally a function of the cell bandgap (Eg) and quality (ERE)

b

Investigate the impact of these parameters to be able to predict of different technologies

b ( , , , , ,incident spect contact loss rum, , ...) loss

g g c c c c

E f E ER ERE shu E C T nt T T T          b b

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Thank you for your attention

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Temperature coefficient of multi-junctions

Output power = Input power – Losses (BelowEg + Thermalization + Carnot + Angle mismatch + Emission)

b ≈ cst ≈ 1260 ppm/K

Carnot + Angle mismatch + Emission Output power

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4

Fraction of the incident solar energy Number of junctions

Q ≈ cst  ≈ cst Tc