Generalized detailed balance theory of solar cells [Elektronische Ressource] / vorgelegt von Thomas Kirchartz

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Generalized detailed balance theory of solar cellsVon der Fakult¨at fu¨r Elektrotechnik und Informationstechnikder Rheinisch-Westf¨alischen Technischen Hochschule Aachenzur Erlangung des akademischen Grades eines Doktors derIngenieurwissenschaften genehmigte Dissertationvorgelegt vonDiplom-IngenieurThomas Kirchartzaus KarlsruheBerichter:Universit¨atsprofessor Dr. rer. nat. habil. Uwe RauUniversit¨atsprofessor Dr. phil. Heinrich KurzTag der mu¨ndlichen Pru¨fung:6. Februar 2009Diese Dissertation ist auf den Internetseiten der Hochschulbibliothekonline verfu¨gbar.ContentsAbstract 1Zusammenfassung 51 Introduction 92 Fundamentals 132.1 The principle of detailed balance . . . . . . . . . . . . . . . . . . . . 132.2 The Shockley-Queisser limit . . . . . . . . . . . . . . . . . . . . . . . 142.3 Combining transport with detailed balance . . . . . . . . . . . . . . . 182.3.1 A two state solar cell model . . . . . . . . . . . . . . . . . . . 182.3.2 The one sided pn-junction . . . . . . . . . . . . . . . . . . . . 212.3.3 Radiative limit for arbitrary mobilities . . . . . . . . . . . . . 232.4 Solar cell and light emitting diode . . . . . . . . . . . . . . . . . . . . 242.5 Properties of optoelectronic devices - a brief summary . . . . . . . . . 263 Detailed balance model for bipolar charge transport 313.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2 pn and pin type solar cells . . . . . . . . . . . . . . . . . . . .
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Generalized detailed balance theory of solar cells
Von der Fakult¨at fu¨r Elektrotechnik und Informationstechnik
der Rheinisch-Westf¨alischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines Doktors der
Ingenieurwissenschaften genehmigte Dissertation
vorgelegt von
Diplom-Ingenieur
Thomas Kirchartz
aus Karlsruhe
Berichter:
Universit¨atsprofessor Dr. rer. nat. habil. Uwe Rau
Universit¨atsprofessor Dr. phil. Heinrich Kurz
Tag der mu¨ndlichen Pru¨fung:
6. Februar 2009
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek
online verfu¨gbar.Contents
Abstract 1
Zusammenfassung 5
1 Introduction 9
2 Fundamentals 13
2.1 The principle of detailed balance . . . . . . . . . . . . . . . . . . . . 13
2.2 The Shockley-Queisser limit . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Combining transport with detailed balance . . . . . . . . . . . . . . . 18
2.3.1 A two state solar cell model . . . . . . . . . . . . . . . . . . . 18
2.3.2 The one sided pn-junction . . . . . . . . . . . . . . . . . . . . 21
2.3.3 Radiative limit for arbitrary mobilities . . . . . . . . . . . . . 23
2.4 Solar cell and light emitting diode . . . . . . . . . . . . . . . . . . . . 24
2.5 Properties of optoelectronic devices - a brief summary . . . . . . . . . 26
3 Detailed balance model for bipolar charge transport 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 pn and pin type solar cells . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Superposition, ideality and reciprocity in pin-type solar cells . . . . . 37
3.4 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Application to quantum well solar cells . . . . . . . . . . . . . . . . . 43
3.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5.2 Optical results. . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5.3 Results for finite mobilities . . . . . . . . . . . . . . . . . . . . 50
3.5.4 Results for non-radiative recombination . . . . . . . . . . . . . 54
iii CONTENTS
3.5.5 Tandem solar cells . . . . . . . . . . . . . . . . . . . . . . . . 58
3.5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4 Detailed balance model for excitonic and bipolar charge transport 63
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.1 Excitonic and bipolar solar cells . . . . . . . . . . . . . . . . . 64
4.2.2 pn-type and pin-type solar cells . . . . . . . . . . . . . . . . . 68
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.1 Excitonic and bipolar photocurrent . . . . . . . . . . . . . . . 69
4.3.2 Current/voltage curves . . . . . . . . . . . . . . . . . . . . . . 72
4.3.3 Electroluminescence and quantum efficiency . . . . . . . . . . 76
5 Detailed balance model for bulk heterojunction solar cells 81
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2.1 Charge separation scheme . . . . . . . . . . . . . . . . . . . . 83
5.2.2 Differential equations for free carriers . . . . . . . . . . . . . . 83
5.2.3 Balance equation for bound carriers . . . . . . . . . . . . . . . 84
5.2.4 Differential equation for excitons . . . . . . . . . . . . . . . . 87
5.2.5 Effective generation and recombination rates . . . . . . . . . . 89
5.2.6 Equilibrium concentration of excitons . . . . . . . . . . . . . . 90
5.2.7 Comparison with the model of Koster et al. . . . . . . . . . . 91
5.3 Fundamental aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.1 Influence of the carrier mobilities and the surface recombina-
tion velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.2 Influence of exciton diffusion on the photocurrent . . . . . . . 96
5.3.3 The role of band offsets. . . . . . . . . . . . . . . . . . . . . . 96
5.3.4 The role of the blend morphology . . . . . . . . . . . . . . . . 99
5.3.5 Optoelectronic reciprocity . . . . . . . . . . . . . . . . . . . . 101
5.4 Comparison to experimental results . . . . . . . . . . . . . . . . . . . 106CONTENTS iii
6 Detailed balance model for solar cells with multiple exciton gener-
ation 111
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.3 Generation of multiexcitons . . . . . . . . . . . . . . . . . . . . . . . 116
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7 Experimental applications of the reciprocity relation 123
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.2 Crystalline Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2.1 Spectrally resolved EL . . . . . . . . . . . . . . . . . . . . . . 125
7.2.2 Spatially resolved EL . . . . . . . . . . . . . . . . . . . . . . . 129
7.2.3 Interpretation of EL images taken with filters . . . . . . . . . 134
7.2.4 Absolute EL emission and the LED quantum efficiency . . . . 147
7.3 Cu(In,Ga)Se . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1492
7.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.3.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.3.3 Temperature dependent measurements . . . . . . . . . . . . . 151
7.3.4 Reciprocitybetweenelectroluminescenceandphotovoltaicquan-
tum efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.4 GaInP/GaInAs/Ge-multijunction solar cells . . . . . . . . . . . . . . 167
8 Conclusions and Outlook 173
A List of Publications 177
A.1 Publications in Journals . . . . . . . . . . . . . . . . . . . . . . . . . 177
A.2 Peer reviewed conference proceedings . . . . . . . . . . . . . . . . . . 178
A.3 Conference proceedings (not reviewed) . . . . . . . . . . . . . . . . . 179
B Curriculum vitae 181
Bibliography 182iv CONTENTS
Acknowledgements 197Abstract
The principle of detailed balance is the requirement that every microscopic process
inasystemmustbeinequilibriumwithitsinverseprocess, whenthesystemitselfis
in thermodynamic equilibrium. This detailed balance principle has been of special
importanceforphotovoltaics, sinceitallowsthecalculation ofthelimitingefficiency
of a given solar cell by defining the only fundamental loss process as the radiative
recombination of electron/hole pairs followed by the emission of a photon. In equi-
librium, i.e. in the dark and without applied voltage, the absorbed and emitted
photon flux must be equal due to detailed balance. This equality determines the
radiative recombination from absorption and vice versa. While the classical theory
ofphotovoltaicefficiencylimitsbyShockleyandQueisserconsidersonlyonedetailed
balancepair,namelyphotogenerationandradiativerecombination,thepresentwork
extends the detailed balance principle to any given process in the solar cell. Apply-
ing the detailed balance principle to the whole device leads to two major results,
namely(i)amodelthatiscompatiblewiththeShockley-Queisserefficiencylimitfor
efficientparticletransport,whilestillbeingabletodescribenon-idealandnon-linear
solar cells, and (ii) an analytical relation between electroluminescent emission and
photovoltaic action of a diode that is applied to a variety of different solar cells.
This thesis presents several variations of a detailed balance model that are
applicable to different types of solar cells. Any typical inorganic solar cell is a
mainly bipolar device, meaning that the current is carried by electrons and holes.
The detailed balance model for pn-type and pin-type bipolar solar cells is therefore
the most basic incorporation of a detailed balance model. The only addition com-
pared to the classical diode theory or compared to standard one-dimensional device
simulators is the incorporation of photon recycling, making the model compatible
with the Shockley-Queisser limit and the classical diode theory. For organic solar
12 CONTENTS
cells, exciton binding energies are sufficiently high, so that purely bipolar models
are no longer applicable. Instead, excitonic transport has to be included. Thus, the
inclusionofexcitontransportintothebipolardetailedbalancemodelleadstoagen-
eralizeddetailedbalancemodelthatsimulatessolarcellswithpredominantlybipolar
transport, with predominantly excitonic transport and with every combination of
both. Due to low exciton diffusion lengths, organic solar cells are usually combined
with a specific device geometry, the bulk heterojunction. In a bulk heterojunction
device, the whole bulk of the absorber is made up of distributed heterojunctions,
where the exciton is transferred to a bound pair at the interface, which is then split
into free electron and hole. The assumption that exciton transport is only relevant
towards the next heterointerface allows to develop also a version of the detailed
balance model that is applicable to bulk heterojunct

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