Mobility and homogeneity effects on the power conversion efficiency of solar cells [Elektronische Ressource] / vorgelegt von Julian Mattheis

Informations

• Publié par: universitat_stuttgart
• Publié le: 01 janvier 2008
• Nombre de lectures: 28
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Mobility and homogeneity efiects
on the power conversion e–ciency
of solar cells
Von der Fakult˜at Informatik, Elektrotechnik und Informationstechnik
der Universit˜at Stuttgart zur Erlangung der Wurde˜ eines
Doktor-Ingenieurs (Dr.-Ing.) genehmigte Abhandlung
Vorgelegt von
Julian Mattheis
geboren am 14.12.1975 in Hannover
Hauptberichter: Prof. Dr. rer. nat. habil. J. H. Werner
Mitberichter: Prof. Dr. rer. nat. habil. U. Rau
Prof. Dr. E. Kasper
Tag der Einreichung: 20.06.2007
Tag der mundlic˜ hen Prufung:˜ 08.01.2008
Institut fur˜ Physikalische Elektronik der Universit˜at Stuttgart
2008Contents
Abstract v
Zusammenfassung vii
1 Introduction 1
1.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 E–ciency limits of solar cells 4
2.1 Classiflcation of solar cell models . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Classiflcation scheme . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Current-voltage characteristic of solar cells . . . . . . . . . . . . . . . . 9
2.3 Radiative e–ciency limit . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Complete carrier collection . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Incomplete carrier . . . . . . . . . . . . . . . . . . . . 14
2.4 Classical diode theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 Incomplete carrier collection . . . . . . . . . . . . . . . . . . . . 15
2.4.2 Complete carrier . . . . . . . . . . . . . . . . . . . . . 16
3 Generalized e–ciency limit 18
3.1 Radiative recombination and photon recycling . . . . . . . . . . . . . . 19
3.2 Photon recycling in the literature . . . . . . . . . . . . . . . . . . . . . 20
3.3 Difiusion equation with reabsorption . . . . . . . . . . . . . . . . . . . 22
3.3.1 Parameter normalization . . . . . . . . . . . . . . . . . . . . . . 24
3.3.2 Free parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Results with constant absorption coe–cient . . . . . . . . . . . . . . . 27
3.4.1 Radiative e–ciency limit . . . . . . . . . . . . . . . . . . . . . . 28
iii CONTENTS
3.4.2 Non-radiative recombination . . . . . . . . . . . . . . . . . . . . 32
3.5 Photon recycling and detailed balance . . . . . . . . . . . . . . . . . . 35
3.5.1 Radiation balance in equilibrium . . . . . . . . . . . . . . . . . 35
3.5.2 Non-equilibrium concentration proflle . . . . . . . . . . . . . . . 40
3.5.3 Radiation balance in non-equilibrium . . . . . . . . . . . . . . . 42
3.5.4 Reciprocity between solar cell and light emitting diode . . . . . 47
3.6 Critical mobility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6.1 High mobility limit - absorptance . . . . . . . . . . . . . . . . . 50
3.6.2 Low mobility limit . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.6.3 Critical mobility in the radiative recombination limit . . . . . . 55
3.6.4 Critical mobility for non-radiative recom . . . . . . . . 57
3.7 Analytical approximation. . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.7.1 Analytical approximations in the literature . . . . . . . . . . . . 59
3.7.2 Two-layer model . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.7.3 Modifled-lifetime model . . . . . . . . . . . . . . . . . . . . . . 61
3.7.4 Evaluation of the approximation . . . . . . . . . . . . . . . . . . 64
3.8 Energy-dependent absorption coe–cient . . . . . . . . . . . . . . . . . 71
3.8.1 Thickness-dependent current enhancement . . . . . . . . . . . . 75
3.8.2 Thicendent e–ciencyt . . . . . . . . . . . 77
3.8.3 Maximum open circuit voltage . . . . . . . . . . . . . . . . . . . 79
3.9 Maximum e–ciencies of real materials . . . . . . . . . . . . . . . . . . 80
3.9.1 Analytical approximation . . . . . . . . . . . . . . . . . . . . . 82
3.9.2 Critical mobility . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.9.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.10 Limitations to the model . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4 Band gap uctuations 98
4.1 Disorder and band gap uctuations . . . . . . . . . . . . . . . . . . . . 101
4.2 Band gap uctuations model . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2.1 Light absorption . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.2 Light emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113CONTENTS iii
4.3 Numerical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3.1 Formulation of the problem . . . . . . . . . . . . . . . . . . . . 116
4.3.2 Correlated band gap sequence . . . . . . . . . . . . . . . . . . . 118
4.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.5.1 Length-scale of band gap uctuations . . . . . . . . . . . . . . . 124
4.5.2 Origin of band gap uctuations . . . . . . . . . . . . . . . . . . 128
4.5.3 Model reflnements . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.5.4 Implications for solar cell performance . . . . . . . . . . . . . . 133
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5 Outlook 136
A Radiative e–ciency limit with energy-dependent absorptance 138
A.1 Inhomogeneous band gap . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.2 Optimal absorptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
B Derivation and numerical implementation of the photon recycling
scheme 144
B.1 Exponential Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
B.2 Difiusion equation with reabsorption . . . . . . . . . . . . . . . . . . . 146
B.2.1 Linear matrix formalism . . . . . . . . . . . . . . . . . . . . . . 146
B.2.2 Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
B.2.3 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
B.2.4 Direct internal generation . . . . . . . . . . . . . . . . . . . . . 150
B.2.5 Internal generation after multiple re ections . . . . . . . . . . . 153
B.2.6 External . . . . . . . . . . . . . . . . . . . . . . . . . 160
B.3 Generation terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
B.3.1 Internal generation . . . . . . . . . . . . . . . . . . . . . . . . . 163
B.3.2 External . . . . . . . . . . . . . . . . . . . . . . . . . 166
B.4 Difiusion operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
B.5 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
B.5.1 Back contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169iv CONTENTS
B.5.2 Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
B.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
B.6.1 Reabsorption matrix . . . . . . . . . . . . . . . . . . . . . . . . 170
B.6.2 Energy superposition . . . . . . . . . . . . . . . . . . . . . . . . 171
B.7 Numerical error sources. . . . . . . . . . . . . . . . . . . . . . . . . . . 171
B.7.1 Optical limitations - absorption length . . . . . . . . . . . . . . 171
B.7.2 Electrical - difiusion length . . . . . . . . . . . . . . 173
C Derivation of the two-layer model 174
Nomenclature 179
Bibliography 184
Curriculum Vitae 194
List of Publications 195
Danksagung 197Abstract
The thesis on hand investigates the interplay between detailed radiation balances and
chargecarriertransport. Theflrstpartanalyzestheroleoflimitedcarriertransportfor
the e–ciency limits of pn-junction solar cells. The second part points out the in uence
oftransportontheabsorptionandemissionoflightininhomogeneoussemiconductors.
By incorporating an integral term that accounts for the repeated internal emission
andreabsorptionofphotons(theso-calledphotonrecycling)intothedifiusionequation
for the minority carriers, the flrst part of the thesis develops a self-consistent model
thatiscapableofdescribingthepowerconversione–cienciesofexistingdevicesaswell
as of devices in the radiative recombination limit. The model thus closes the gap be-
tween the classical diode theory and the Shockley Queisser detailed balance e–ciency
limit. While the model converges towards the Shockley Queisser limit when recombi-
nation is exclusively radiative and the minority carrier mobility is inflnity, it converges
towards the classical diode theory once the minority carrier lifetime is dominated by
non-radiative recombination. It is shown that the classical diode theory without the
inclusion of photon recycling produces accurate results only if the minority carrier life-
timeisatleasttentimessmallerthantheradiativelifetime. Thethesisshowsthateven
in the radiative recombination limit, charge carrier transport is extremely important.
The e–ciency is reduced drastically once the minority carrier mobility drops below a
critical mobility even under otherwise most ideal conditions. A closed-form expression
is derived for this critical mobility, which depends on the absorption coe–cient and
the doping concentration. The thesis thus presents a universal criterion that needs
to b