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2.3 Charge Carrier Transport function { t −(1−α 1 ) t < t I(t) ∝ τ t −(1+α 2) t > t τ . (2.2) The dispersion parameter α 1,2 is determined by the disorder of the material [97]. Note that Eq. 2.2 has no characteristic long time cut-off, in fact, even at times greater than 2t τ the magnitude of the current suggests that still a significant number of charge carriers remains within the specimen. Such a high degree of dispersion occurs when during transport the average charge carrier experiences a single localization event with a time that is comparable with the mean transit time defined by the applied voltage and the sample thickness [98]. A second phenomenon observed is the universality of the transient current pulse shape. Transient currents measured for a given sample at different applied fields exhibit the same degree of relative dispersion. This behavior also extends to variations in the sample thickness. To account for the high degree of dispersion, two mechanism have been proposed, namely hopping and trap-limited band transport. Hopping In a hopping system, developed by Scher and Montroll [99], the transport is based on hopping and tunneling of the charge carriers between states. The probability for a transition varies with the separation R of two sites as exp(−2R/R 0 ), where R 0 is the localization radius of the state (equal to the effective Bohr radius for localized carriers) [68]. If the mean intersite distance ¯R is large compared to R 0 , one will observe a wide spread of the probabilities to escape from a state and the broadening of the charge carrier packet is highly pronounced. The dispersion arises from the random distribution of the site separation. The immobilized carriers are trapped in centers more isolated from their neighbors than the average distance. With increasing time, the drifting carriers will be more and more accumulated in more isolated sites with longer release time constants. This results in the observed continuously decaying current even for very long times. Hopping in an exponential band-tail has been applied to describe the transport behavior of µc-Si:H in the low temperature region [46, 47] as well as the behavior found at elevated temperatures [46, 48]. Multiple Trapping in Band-Tails A number of studies in 1977 showed that dispersive transport can also arise from trap-limited band transport [100, 101, 98, 102, 103]. In a multiple trapping model, charge transport only takes place in the extended states of the band. Charge carriers trapped in localized states are immobile and must first be thermally excited 17
Chapter 2: Fundamentals above the mobility edge to contribute to transport. It has been shown by Schmidlin [98] that for anomalous dispersion to be generated, the concentration of the localized states must accomplish the following two criteria. First, a charge carrier is likely to be trapped in a localized state at least once during the transit and second, the release time of a carrier trapped in a localized state must be comparable to the transit time t τ [98]. As has been discussed above (see section 2.2.1), the band-tails in µc-Si:H are expected to decrease exponentially towards the gap. Provided that the localized states in the vicinity of the mobility edge all to have the same origin, e.g. potential fluctuations, the energy dependence of the capture cross section is probably weak [104], so that each localized state has the same probability to capture a charge carrier. However, the exponential dependence of the thermal reemission leads to a broad distribution of release times. The dispersion arises from the energy distribution of states and since thermal excitation is involved, both the mobility and the dispersion strongly depend on temperature. 18
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Page 8 and 9: Abstract The electronic properties
Page 10 and 11: Contents 1 Introduction 1 2 Fundame
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Page 14 and 15: Chapter 1 Introduction Solar cells
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6.1 Metastable Effects in µc-Si:H
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6.2 Irreversible Oxidation Effects
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6.3 On the Origin of Instability Ef
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6.3 On the Origin of Instability Ef
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Chapter 7 Transient Photocurrent Me
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7.2 Transient Photocurrent Measurem
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7.3 Temperature Dependent Drift Mob
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7.4 Multiple Trapping in Exponentia
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7.5 Discussion Table 7.2: Multiple
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7.5 Discussion 7.5.3 The Meaning of
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Chapter 8 Schematic Density of Stat
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silicon as shown in Fig. 8.1 b, whi
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Chapter 9 Summary In the present wo
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Appendix A Algebraic Description of
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Eq. A.7 then becomes L(t) F = sin(
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Appendix B List of Samples Table B.
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Table B.3: Parameters of n-type µc
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Appendix C Abbreviations, Physical
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µ d Drift mobility µ d,h Hole dri
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Bibliography [1] E. Becquerel. Mém
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BIBLIOGRAPHY [21] D. Will, C. Lerne
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BIBLIOGRAPHY [45] H. Overhof and M.
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BIBLIOGRAPHY [66] P.W. Anderson. Ab
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BIBLIOGRAPHY [93] J.W. Orton and M.
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BIBLIOGRAPHY [121] J.R. Haynes and
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BIBLIOGRAPHY [148] W. Luft and Y.S.
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BIBLIOGRAPHY [170] G.N. Advani, R.
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List of Publications 1. T. Dylla, R
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Acknowledgments At this point, I wa
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Schriften des Forschungszentrums J
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Forschungszentrum Jülich in der He
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Measurements

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