thesis final

  • View
    30

  • Download
    1

Embed Size (px)

Text of thesis final

  • Passivating selective contacts for siliconphotovoltaics

    Solar cells designed by physics

    PROEFSCHRIFT

    ter verkrijging van de graad van doctor aan deTechnische Universiteit Eindhoven, op gezag van de

    rector magnificus prof.dr.ir. F.P.T. Baaijens, voor eencommissie aangewezen door het College voor

    Promoties, in het openbaar te verdedigenop dinsdag 14 juni 2016 om 16:00 uur

    door

    Sjoerd Smit

    geboren te Waalwijk

  • Dit proefschrift is goedgekeurd door de promotoren en de samenstellingvan de promotiecommissie is als volgt:

    voorzitter: prof.dr. H.J.H. Clercx1e promotor: prof.dr.ir. W.M.M. Kessels2e promotor: prof.dr. M. Zeman (TUD)leden: prof.dr.ir. P.P.A.M. van der Schoot

    prof.dr. J. Gomez RivasProf.Dr. K. Lips (Freie Universitat Berlin)Dr.rer.nat. P.P. Altermatt (Trina Solar Ltd.)

    adviseur: dr. P.C.P. Bronsveld (ECN Solar Energy)

    Het onderzoek dat in dit proefschrift wordt beschreven is uitgevoerd inovereenstemming met de TU/e Gedragscode Wetenschapsbeoefening.

  • Funding information

    This research is supported by the Dutch Technology Foundation STW,which is part of the Netherlands Organisation for Scientific Research(NWO) and partly funded by the Ministry of Economic Affairs (FLASHproject 1.4: Advanced Interface Engineering for Si Heterojunction SolarCells; STW project number 12167).

  • Contents

    1 Introduction 7

    2 The physics of solar cells: semiconductor physics enhanced bythermodynamics 23

    2.1 The theory of non-equilibrium thermodynamics . . . . . . . . . 27

    2.1.1 Literature discussion . . . . . . . . . . . . . . . . . . . . 29

    2.2 Overview of NETPV . . . . . . . . . . . . . . . . . . . . . . . . 29

    2.3 The thermodynamic formulation of solar cellphysics step 1: Equilibrium and thermodynamic variables . . . 31

    2.3.1 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

    2.3.2 Generalisation to non-equilibrium . . . . . . . . . . . . . 43

    2.4 The thermodynamic formulation of solar cellphysics step 2: Interaction with the environment . . . . . . . . 47

    2.5 The thermodynamic formulation of solar cellphysics step 3: Continuity equations . . . . . . . . . . . . . . . 50

    2.5.1 The entropy source term qs . . . . . . . . . . . . . . . . 53

    2.5.2 Loss processes in the bulk of a solar cell and the entropygeneration rate . . . . . . . . . . . . . . . . . . . . . . . 54

    2.6 The thermodynamic formulation of solar cellphysics step 4: Onsager theory . . . . . . . . . . . . . . . . . . 57

    2.7 The thermodynamic formulation of solar cellphysics step 5: Symmetry, the Onsager reciprocal relations andthe Curie principle . . . . . . . . . . . . . . . . . . . . . . . . . 64

    2.7.1 The Onsager reciprocal relations . . . . . . . . . . . . . 64

    2.7.2 The Curie principle . . . . . . . . . . . . . . . . . . . . 65

    2.8 Wrap up: what does thermodynamics tell us? . . . . . . . . . . 71

    3 The physics of solar cells: semiconductor physics enhanced bythermodynamics 77

    3.1 The thermodynamics of the selective membrane model . . . . . 77

    3.2 The selective membrane model . . . . . . . . . . . . . . . . . . 78

    3.2.1 What is selectivity? . . . . . . . . . . . . . . . . . . . . 89

    4

  • 3.3 The selectivity of Schottky-type junctions . . . . . . . . . . . . 92

    3.4 The selectivity of homojunctions . . . . . . . . . . . . . . . . . 97

    3.5 The selectivity of heterojunctions . . . . . . . . . . . . . . . . . 99

    3.6 Generation and recombination in selective membranes . . . . . 105

    3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

    4 Variational method for the minimisation of entropy generationin solar cells 115

    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

    4.2 Entropy production in solar cells . . . . . . . . . . . . . . . . . 117

    4.3 Variational solar cell optimisation . . . . . . . . . . . . . . . . . 123

    Appendices 127

    4.A Boundary conditions for the VEGM method . . . . . . . . . . . 127

    5 Metal-oxide-based hole-selective tunnelling contacts for crys-talline silicon solar cells 133

    5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

    5.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . 135

    5.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

    5.3.1 The ZnO/Al2O3/c-Si system as a selective contact . . . 138

    5.3.2 Modeling of the tunnelling currents . . . . . . . . . . . . 138

    5.3.3 Considerations for improving the contact resistance andsurface passivation . . . . . . . . . . . . . . . . . . . . . 140

    5.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . 143

    5.4.1 Passivation of c-Si by Al2O3/ZnO stacks . . . . . . . . . 143

    5.4.2 Charge transport through Al2O3/ZnO stacks . . . . . . 147

    5.4.3 Improved c-Si passivation by a-Si:H/Al2O3/ZnO stacks 147

    5.5 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . 149

    6 Properties of graphene and its potential applications in siliconsolar cells 155

    6.1 The electrical and optical properties of graphene . . . . . . . . 156

    6.1.1 The graphene dispersion relation and density of states . 156

    6.1.2 Conduction and photon absorption in graphene . . . . . 162

    6.2 Junctions of graphene and silicon . . . . . . . . . . . . . . . . . 170

    6.2.1 Equilibrium conditions . . . . . . . . . . . . . . . . . . . 171

    6.2.2 Non-equilibrium conditions . . . . . . . . . . . . . . . . 173

    6.2.3 Graphene as a carrier selective contact . . . . . . . . . . 181

    6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

    Appendices 185

    6.A Approximate expressions for the graphene carrier densities . . . 185

    5

  • A Mathematical formulation of the charge transport in solarcells 195A.1 The drift-diffusion equations . . . . . . . . . . . . . . . . . . . . 195A.2 The Poisson-Boltzmann equation . . . . . . . . . . . . . . . . . 199

    Summary 205

    List of publications 207

    Acknowledgements 208

    CV 210

    6

  • Chapter 1

    Introduction

    As the title of this thesis makes abundantly clear, this work is about the physicsof solar cells. Our choice for this title deserves some extra clarification, since thephysics of solar cells is a very broad and developed field and one would probablyexpect to find such a title on a student handbook instead of a PhD thesis.There already exist sophisticated software packages that have implementeddetailed physical and mathematical models and that are capable of predictingthe efficiencies of complex cell designs, so the physics of solar cells might appearto be a closed chapter for the most part; a finished work. Then why do wedevote a PhD thesis to it? Our short answer to that question is, bluntly, thatwe still need to understand solar cells better than we currently do. Naturally,when we talk about understanding solar cells, we talk about improving them1

    since photovoltaics (PV) is not a purely academic subject that we study justfor the science of it. The question then rises what the role of physics is (orshould be) in the design of solar cells. The ideal we normally have of scienceand physics is that we study a subject to learn about it and then use thisknowledge improve what whatever it was that needed improvement. However,this ideal is not as straightforward to realise as we would often like and thestep from knowledge to improvement is not always trivial (as is often assumed,unfortunately). We can ask a computer to calculate the efficiency a certaincell design and we would get a very accurate answer, but what we would muchrather do is ask the computer to calculate a cell design that achieves, e.g., a26 % efficiency given certain practical constraints. The physics of solar cellsmay provide us with very accurate models, but in the end it seems that forsolar cell design we still need something else; something nebulous we usuallycall ingenuity, art or deeper understanding or something like that.

    1The term improvement can mean many different things in this context. Indeed, thereis a very fruitful discussion to be had about what we mean by improvement of solar cells.For the purposes of this work, we will mostly be talking about cell efficiency since that givesus a clear physical and thermodynamical measure of performance. For the argument in thisparagraph, though, any other metric of performance can be substituted if necessary.

    7

  • So let us try to analyse this limitation of current solar cell physics a bitfurther. The first thing to note is that physics in general is, in its roots, ascience based on an alternating loop of observation and prediction. A physicistobserves a system and based on his observations he makes predictions. Next,he tests his predictions by further observations. However, if we want to improvea solar cell, we are not primarily interested in continually making predictionsand then observing if the cell does indeed follow the mathematical model wemade of it. Instead, what we are effectively trying to achieve is to forcea particular observation we are interested in: the cell that performs best (seeFigure 1.1). So while physics is very good at making good models of solar cells,that does not immediately mean that these models are immediately useful formaking good cells. One could say that the problem of solar cell design is aninverse problem (i.e, one is trying to improve the observation rather than themodel that makes the predictions) compared to ordinary empirical science.2

    At the start of this research project in November 2011, we set out to gaina better understanding of the