Solar Photovoltaics & Energy Systems

Transcription

1 Solar Photovoltaics & Energy Systems Lecture 3. Solar energy conversion with band-gap materials ChE-600 Kevin Sivula, Spring 2014

2 The Müser Engine with a concentrator T s Q 1 = σσ CffT ss Cff T pp 4 T 3 4 Solar energy efficiency: T 1 T P Ω W = ηη ssssssssss CffσσT ss 4 Q 1 k 1 T 3 T =T 2 =T P T =T 3 W Solar energy conversion efficiency % maximum C = C max C = 100 C = 10 C = Q 2 T 2 Müser engine efficiency

3 The Müser Engine with a band gap A selective black body can be defined εε λλ = 0 ffffff EE < EE gg 1 ffffff EE > EE gg Recall that: QQ/AA = ππ λλ=0 2πππππ BBλ TT ddλλ = 2 λλ=0 1 λ 5 hcc ee λλkk BB TT 1 ddλλ = σσtt 4 Then: Q 1 = gg EE gg eeeeee EE 3 dddd EE 1 kk BB TT EE 1 gg eeeeee EE 3 dddd EE 1 kk BB TT 3 T 3 EE gg T 1 EE gg

4 The Müser Engine with with a band gap T s Solar energy efficiency: W = ηη ssssssssss CffσσT ss 4 T 1 T P Ω ηη ssssssssss Q 1 k 1 T 3 E g C = C max T =T 2 =T P T =T % E g = 0.90 ev C = 389 C = 1 Q 2 W T 2 Then: Q 1 = gg CCCC EE gg eeeeee EE 3 dddd 1 CCCC EE 1 kk BB TT ss EE gg eeeeee EE 3 dddd EE 1 kk BB TT EE pp gg eeeeee EE 3 dddd EE (1 ηη) 1 kk BB TT pp

5 Description of a semiconductor Si [Ne] 3s 2 3p 2 Model of a silicon crystal seen along the <100> direction.

6 Description of a semiconductor CB 3p 2 VB 3s 2 Si

7 Description of a semiconductor Empty states Distribution function for electrons: 1 ff EE ee = 1 + eeeeee (EE ee EE FF ) kk BB TT 100 K 300 K 1000 K Occupied states

8 Band structure and density of states Density of states Energy (ev)

9 Localized density of states as a function of energy EE CC Electron energy, E e Momentum, p e Number of states available for an electron in volume V: NN ee pp ee = 8ππ pp ee 3 VV 3h 3 Approximation of electron kinetic energy: EE ee,kkkkkk = EE ee EE CC = pp ee 2 2mm ee DD ee EE ee Density of states as a function of energy: = 1 VV ddnn ee ddee ee = 4ππ 2mm ee h 2 3/2 EE ee EE CC 1/2 EE VV The number of electrons in the conduction band: nn ee = EE CC DD ee EE ee ff ee EE ee NN CC = 2 dddd ee = NN CC eeeeee EE CC EE ff kk BB TT 2ππmm ee kk BB TT h 2 3/2

10 Deviations from global equilibrium EE CC ee EE ff h EE ff EE VV Electron energy, E e nn ee nn h Global equilibrium situations only: The number of electrons in the conduction band: nn ee = NN CC eeeeee EE CC EE ff kk BB TT Similarly for holes: nn h = NN VV eeeeee EE ff EE VV kk BB TT For non-equilibrium situations (globally) local equilibrium can be described: nn ee = NN CC eeeeee eeeeee EE CC EE ff ee kk BB TT Similarly for holes: nn h = NN VV eeeeee eeeeee EE ff h EE VV kk BB TT

11 Description of a semiconductor μμ = EE ff ee EE ff h Photon (hν< E g ) ee EE ff EEh EE ff ff Empty states e- h+ Occupied states Photon (hν > E g ) Photon (hν >> E g ),E g Thermalization of electron and hole to CB and VB edge when hν > E g

12 Description of a semiconductor μμ = EE ff ee EE ff h Empty states EE ff ee EE ff h e- h+ Occupied states,e g VV = μμ qq Metal V Metal

13 Emission from an ohmic diode BB EE = Emission spectrum from a semiconductor (at Temp T and with a chemical potential µ) 0 ffffff EE EE gg 2ππ EE 2 cc 2 h 3 ffffff EE > EE EE μμ gg eeeeee kk BB TT 1 T =300 K T =100 K Total Number of photons emitted per unit area: Φ(TT, μμ, EE gg ) = EE gg BB EE dddd Net electron flux through device: JJ = qqφ 10 B(E) E g E g 1.05E g 1.05E g T 2 µ 2 E g2 µ = 99.9 % E g µ = 99.0 % E g µ = 90.0 % E g V T 1 µ 1 E g1

14 Photon exchange between biased semiconductors Net photon Flux Φ = BB 1 EE dddd BB 2 EE dddd = kk EE ggg EE gg2 EE ggg EE 2 dddd eeeeee EE μμ 1 kk BB TT 1 1 EE ggg EE 2 dddd eeeeee EE μμ 2 kk BB TT 2 1 kk = 2ππ cc 2 h 3 Net electron flux through device: JJ = qqφ JJ VV 1, VV 2, TT 1, TT 2 = qqφ = qqqq EE ggg Recall that μμ = qqqq EE 2 dddd eeeeee EE qqqq 1 kk BB TT 1 1 EE ggg EE 2 dddd eeeeee EE qqqq 2 kk BB TT 2 1 T 2 µ 2 E g2 T 1 µ 1 E g1

15 Building a photovoltaic device T 1 T s Q 1 k 1 Ω T p, µ, E g T P W Q 2 T =T 2 =T P T =T p, µ, E g T p

16 Building a photovoltaic device JJ VV Net electron flux through device: JJ = qqφ Then: Recall that μμ = qqqq = qqqq CCCC EE gg eeeeee EE 2 dddd EE 1 kk BB TT ss T 1 Q 1 k 1 T p, µ, E g W Also the electrical power can be defined: Q 2 WW(VV) = VV JJ(VV) T p

17 Building a photovoltaic device JJ JJ VV = qqqq CCCC eeeeee EE gg EE 2 dddd EE 1 kk BB TT ss T 1 For dddd dddd = 0 Depends on T p TT ss, CCCC, EE gg Solar energy efficiency: Q 1 T p, µ, E g k 1 W W = VVVV VV = ηη ssssssssss CffσσT ss 4 ηη ssssssssss = VVJJ(VV) CffσσT ss 4 Q 2 ηη mmmmmm ssssssssss = VVJJ(VV) ddddjj(vv) dddd =0 CffσσT ss 4 T p

18 Building a photovoltaic device Maximum solar energy conversion efficiency for planet earth with a semiconductor of band gap E g T 1 mmmmmm ηη ssssssssss ηη mmmmmm ssssssssss = 40.8% wwwwwww EE gg = 1.15 eeee CC = CC mmmmmm CC = 400 CC = 1 Q 1 T p, µ, E g k 1 W ηη mmmmmm ssssssssss = 31.0% wwwwwww EE gg = 1.30 eeee Q 2 T p

19 Building a photovoltaic device Maximum solar energy conversion efficiency for planet earth with a semiconductor of band gap E g With the standard solar spectrum T 1 35% Q 1 k 1 CC = 1 T p, µ, E g mmmmmm ηη ssssssssss 25% 15% ηη mmmmmm ssssssssss = 33.0% wwwwwww EE gg = 1.15 eeee W 5% Q 2 T p

20 Losses in semiconductor solar cells qqqq < EE gg Radiative recombination Electron hole relaxation hνν < EE gg Useful photons

21 Single absorber conversion 6.0E+14 Terrestrial Spectra Photon Flux [photons/s/cm 2 /nm] 5.0E E E E+14 E g = 1.15 ev λ = 1078 nm 1.0E E Wavelength [nm]

22 Multi color conversion i = 1 E g = E g1 i = 2 E g = E g2 < E g1 i = 3 E g = E g3 < E g2... i = n E g = E gn < E gn-1

23 Multi color conversion mmmmmm ηη ssssssssss i = 1 E g = E g1 IV i = 2 E g = E g2 < E g1 IV nn 86.8 % i = 3 E g = E g3 < E g2 IV CC mmmmmm nn 68.2 %... CC = 1 i = n E g = E gn < E gn-1 IV

24 Multi color conversion A more practical way to connect devices: mmmmmm ηη ssssssssss i = 1 E g = E g % i = 2 E g = E g2 < E g1 Parallel Series i = 3 E g = E g3 < E g2 CC mmmmmm... i = n E g = E gn < E gn-1 IV

25 Individual cell characteristics Connection Independent Band gaps (ev) Independent Max. efficiency Series Band gaps (ev) n = n = n = n = Series Max. efficiency I. Tobias, A. Luque, Prog. Photovolt: Res. Appl. 2002; 10:

26 Summary of photovoltaic conversion limits Semiconductors are special because they can have local equilibriums (within bands) and global imbalance (between bands) This property leads to the concept of quasi Fermi levels and a chemical potential Creating a simple diode device and investigating in the framework of a photovoltaic device gives us the Shockley Queisser limit for solar energy conversion by a photovoltaic device Higher solar energy conversion can be achieved by using multicolor converters.