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7.5 Discussion 7.5.3 The Meaning of Multiple Trapping One approach to analyzing mobilities in polycrystalline materials is to invoke the effective masses, that would obtain for electrons and holes in the single crystal, and assume that the grain boundaries act as scatterers or barriers and as the locus for traps for the carriers [42]. It is instructive to use this approach crudely to calculate an ”effective-mass carrier mobility” for holes µ e.m. utilizing the expression µ e.m. = υ h h th l/(kT/e), where υ th is the ”thermal velocity” for holes (about 10 7 cm/s in c-Si near room-temperature) 2 and l is a scattering length. If the scattering length is identified with a typical crystallite size of 3 nm, one infers µ e.m. = 120 h cm 2 /Vs, which is about 100 times larger than the estimate in Table 7.2. The effects of traps and barriers do not seem to explain the discrepancy for the samples, since these were already (implicitly) incorporated in the analysis that led to the estimate µ 0 = 1cm 2 /Vs. It is therefore most likely that the existence of band-tail states strongly effects the charge carrier transport. The disorder within the investigated material is sufficient to strongly alter the band edge states from their crystalline counterparts. In particular, a mobility-edge has been formed within the band-tail 3 (i.e. states lying deeper in the energy gap are localized). The mobility-edge has been widely applied to amorphous semiconductors [97, 131], and has recently been applied to microcrystalline samples with a large fraction of amorphous ”tissue” [73]. Here the suggestion is that it also applies to samples that are predominantly crystalline. In the mobility-edge model, hole states with energy levels below the mobility-edge (E < E V ) are completely delocalized (by definition), although with very different wave functions than the effective-mass states of crystals. Hole states lying above the mobility-edge (E > E V ) are localized. Both analytical and computational studies of mobility-edges [164, 180] indicate that the localization radius for a hole state grows very rapidly, and may even diverge, as the energy state approaches the mobility-edge. It is not clear theoretically how particular atomic-scale features such as ”strained bonds” are incorporated into the band-tail states. The estimates of 31 meV and 32 meV (see table 7.2) for the microcrystalline material seem unremarkable in the context of work on holes in amorphous silicon, which yields values in the range 40 − 50 meV. It is worth noting, that disorder affects holes and electrons very differently. The conduction band-tail in amorphous silicon has a width around 22 meV [97, 131]. Electron properties in samples quite 2 The concept of a ”thermal velocity” υ th = (2k B T/me) 1/2 is based on effective-mass theory, and has no meaning in other transport models. 3 The multiple-trapping model invokes a ”transport edge” that most workers associate with Nevill Mott’s ”mobility-edge;” however, alternate views have been proposed, in particular ”hopping only” and ”potential fluctuation” models. 99
Chapter 7: Transient Photocurrent <strong>Measurements</strong> similar to the present ones have been studied using post-transit time-of-flight [73]. However the finding was that band-tail multiple-trapping did not apply for these transients. An interesting possibility is therefore that electron transport may be governed by effective masses in exactly the same material for which holes require a mobility-edge approach. The fact that the hole band-mobility µ 0 is about the same in the present microcrystalline samples and in amorphous silicon seems to support the mobility-edge interpretation, and more broadly suggests that a value near 1 cm 2 /Vs may be a universal property of a mobility edge. Such ”universality” is also suggested by the fact that electron band-mobilities in amorphous silicon are also around 1 cm 2 /Vs [97, 131]. Interestingly, a band mobility of 1 cm 2 /Vs is not an obvious implication of the existing theoretical treatments of mobility-edges. It is quite interesting, that the value of the attempt-to-escape frequency for microcrystalline silicon is substantially (about 100 times) smaller than the lower values reported for a-Si:H. However, even for a-Si:H, there is no well-accepted physical interpretation for this parameter. One often-mentioned interpretation is that ν be identified as a ”typical phonon frequency,” but this association fails to explain either the very low magnitudes or the enormous range of magnitudes that have been reported experimentally [181, 182]. Yelon and Movaghar have suggested that multi-phonon effects lead to the variations and this perspective has been applied by Chen et al. to drift mobility measurements [183]. Another possibility originating with high-field drift mobility measurements in a-Si:H has been that ν reflects the bandedge density-of-states g(E V ) [184], which suggests that the present measurements be interpreted as indicating a substantially lower value for g(E V ) in microcrystalline than in amorphous silicon. Plainly, one needs more clues from experiment about the meaning of this parameter, however it seems possible that its dramatic lowering in microcrystalline silicon could be providing it. 100
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Forschungszentrum Jülich in der He
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Forschungszentrum Jülich GmbH Inst
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Kurzfassung In der vorliegenden Arb
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Abstract The electronic properties
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Contents 1 Introduction 1 2 Fundame
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CONTENTS C Abbreviations, Physical
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Chapter 1 Introduction Solar cells
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defect states provided that they ar
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Chapter 8: In this chapter, the inf
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Chapter 2 Fundamentals In this firs
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2.2 Electronic Density of States St
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2.2 Electronic Density of States ta
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2.2 Electronic Density of States Fi
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2.3 Charge Carrier Transport influe
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2.3 Charge Carrier Transport functi
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Chapter 3 Sample Preparation and Ch
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3.1 Characterization Methods Figure
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3.1 Characterization Methods Homoge
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3.1 Characterization Methods µ Fig
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3.1 Characterization Methods compar
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3.1 Characterization Methods bution
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3.1 Characterization Methods posite
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3.2 Deposition Technique admixture
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3.3 Sample Preparation 3.3.1 Sample
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3.3 Sample Preparation reverse bias
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Chapter 4 Intrinsic Microcrystallin
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4.2 Electrical Conductivity Figure
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4.3 ESR Signals and Paramagnetic St
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4.3 ESR Signals and Paramagnetic St
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4.4 Discussion - Relation between E
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Page 66 and 67: 5.2 Electrical Conductivity Figure
Page 68 and 69: 5.4 Dangling Bond Density Figure 5.
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Page 74 and 75: 5.7 Summary Figure 5.7: Schematic b
Page 76 and 77: Chapter 6 Reversible and Irreversib
Page 78 and 79: 6.1 Metastable Effects in µc-Si:H
Page 88 and 89: 6.2 Irreversible Oxidation Effects
Page 94 and 95: 6.3 On the Origin of Instability Ef
Page 96 and 97: 6.3 On the Origin of Instability Ef
Page 98 and 99: Chapter 7 Transient Photocurrent Me
Page 100 and 101: 7.2 Transient Photocurrent Measurem
Page 106 and 107: 7.3 Temperature Dependent Drift Mob
Page 108 and 109: 7.4 Multiple Trapping in Exponentia
Page 110 and 111: 7.5 Discussion Table 7.2: Multiple
Page 114 and 115: Chapter 8 Schematic Density of Stat
Page 116 and 117: silicon as shown in Fig. 8.1 b, whi
Page 118 and 119: Chapter 9 Summary In the present wo
Page 120 and 121: Appendix A Algebraic Description of
Page 122 and 123: Eq. A.7 then becomes L(t) F = sin(
Page 124 and 125: Appendix B List of Samples Table B.
Page 126 and 127: Table B.3: Parameters of n-type µc
Page 128 and 129: Appendix C Abbreviations, Physical
Page 130 and 131: µ d Drift mobility µ d,h Hole dri
Page 132 and 133: Bibliography [1] E. Becquerel. Mém
Page 134 and 135: BIBLIOGRAPHY [21] D. Will, C. Lerne
Page 136 and 137: BIBLIOGRAPHY [45] H. Overhof and M.
Page 138 and 139: BIBLIOGRAPHY [66] P.W. Anderson. Ab
Page 140 and 141: BIBLIOGRAPHY [93] J.W. Orton and M.
Page 142 and 143: BIBLIOGRAPHY [121] J.R. Haynes and
Page 144 and 145: BIBLIOGRAPHY [148] W. Luft and Y.S.
Page 146 and 147: BIBLIOGRAPHY [170] G.N. Advani, R.
Page 148 and 149: List of Publications 1. T. Dylla, R
Page 150 and 151: Acknowledgments At this point, I wa
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