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2.3 Charge Carrier Transport influence on the transport properties and has to be considered in models used to explain transport features. The existence of band-tail states and deep defects may open new transport paths or they might act as traps for charge carriers or form barriers. In the past, various models have been proposed adopting and combining models successfully used to describe transport data from either poly-crystalline or pure amorphous material. As µc-Si:H consists of small crystals separated by grain boundaries, first attempts to explain the transport behavior were done adopting the model of ”grain boundary trapping” developed for polycrystalline silicon by Seto [41] and further extended by Baccarani et al. [92]. On the other hand, the existence of band-tail states suggests that transport might take place by direct tunneling between localized states (hopping) or by trap-limited band motion (multiple trapping). In the following section a phenomenological description of these ideas and their consequences will be given. 2.3.1 Barrier Limited Transport The model of barrier limited transport is based on the ideas of Seto [41] and got a further improvement by Baccarani [92] (see also [93]). It is successfully used to describe the transport behavior of poly-crystalline silicon. As microcrystalline silicon consists of crystallites separated by grain boundaries, the model proposes that the transport properties are mainly determined by defect states located at the grain boundaries. Charge carriers can be trapped and ionize these states leading to potential barriers. Charge carriers overcome these barriers by thermionic emission. Temperature dependent measurements done by Spear et al. [94] and Willeke [95] seemed to prove this model showing the characteristic temperature activated mobility expected for barrier limited transport, but have only been performed in a small temperature range. On the other hand, conductivity measurements over a wide range of temperatures showed that µc-Si:H does not exhibit a single activated transport behavior [44]. Lately this model has been further refined by including tunneling as a process to overcome the barriers [42] in order to explain Hall mobilities of n-type µc-Si:H. A detailed discussion of barrier-controlled transport in microcrystalline semiconductors can be found e.g. in Refs. [42, 96]. 2.3.2 Dispersive Transport in Disordered Semiconductors On the other hand, the existence of a broad tail of states extending into the gap (see section 2.2.1 for details), suggests that these states play an important role in the transport mechanism. As discussed above, band-tail states are a result of structural disorder. A typical transport feature found in disordered materials is that of 15
Chapter 2: Fundamentals τ τ τ Figure 2.4: Current pulse shapes obtained in a time-of-flight experiment. The different shapes are a result of different transport mechanism leading to different degrees of dispersion as described in the text. dispersive transport. In Fig. 2.4 transient photocurrents are shown. Experimentally, these currents can be measured by e.g. time-of-flight experiments (TOF), described in section 3.1.4. In a TOF experiment, the material of interest is usually packed between two contacts and the time required for a charge carrier packed to drift from one side of the sample to the other is measured. The left panel of Fig. 2.4 shows an idealized current following the generation of charge carriers. It describes a sheet of charge, photoinjected on the front side of the sample, moving across the specimen with a constant velocity. The current breaks down at the transit time t τ where the charge carriers reach the back contact. In practice, however, the initially discrete packet of charge carriers will broaden as it drifts across the specimen (middle panel of Fig. 2.4). The dispersion w is a consequence of statistical variations in scattering processes and carrier diffusion which is connected to the drift mobility through the Einstein relation (D = kT e µ d). When the first carriers arrive at the back contact, the current starts to drop, the width of the current decay is a measure of the dispersion at that time. In this case the transit time is defined as that time at which the mean position of the charge carrier packet traverses the back electrode. This is equal to the time, where half the charge has been collected. Because of the shape of the dispersion it is referred to as Gaussian transport in the literature. While transit pulses of the form shown above are observed in many crystalline and some amorphous solids, in some cases they differ significantly. A typical current transient shape for such a case is shown in the right panel of Fig. 2.4 (note the log-log scale). Quite surprisingly, the current appears to decrease over the whole time range of the measurement. Even at times prior to the transit time t τ the current does not show a constant value as observed for Gaussian transport. Perhaps the most outstanding feature is that as a function of time the current decays approximately linearly on a logarithmic scale, indicating a power-law behavior. The two linear regimes are separated by a time t τ and show the following time distribution 16
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Page 6 and 7: Kurzfassung In der vorliegenden Arb
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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