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3.1 Characterization Methods compared to CV, where C is the capacitance of the specimen and V the externally applied voltage [129]. Within this limit the photocurrent scales linearly with the density of injected charge. In principle the lower limit of a transit time t τ that can be measured is determined only by the RC time of the electronic circuit. The overall rise time of the system has to be shorter than the time scale of the experiment. On the other hand, the drift length µ d τ D F of the charge carriers has to be longer than the sample thickness L. In other words the transit time t τ has to be shorter than the deep trapping life time τ D , the time until the charge carriers are finally trapped in deep traps [99, 130]. Assuming that the charge induced by the laser is small compared to the CV the limitations of a reliable time-of-flight experiment can be expressed by RC ≪ t τ ≪ τ rel ,τ d (3.10) where the lower limit is the RC response time and the upper is determined by the dielectric relaxation τ rel and the deep trapping life time τ d . 3.1.4.3 Transit Time Evaluation In contrast to Gaussian transport, in the case of dispersion the excess charge carrier packet spreads out to a much higher degree in a non-symmetrical way (see section 2.3.2). In addition, the absence of a long time cut-off of the transient current makes it rather complicated to define a characteristic transit time t τ . A number of different methods have been used in the past to evaluate the transit time. This has led to different results for t τ depending on the particular method used and therefore has to be taken into account if one wants to compare mobility results obtained and published by different groups. This section will provide a short overview about the different methods. A more detailed review has been presented by Qi Wang et al. [131]. Transient Photocurrent Method The ”Transient Photocurrent Method” was used by a number of authors, e.g. Scharfe et al., Pai et al., Tiedje et al. and Serin et al. [76, 132, 133, 49]. Measuring the transient photocurrent as shown in Fig. 2.4, the characteristic transit time t τ is simply defined as the ”kink” in the power law. Method of Normalized Photocurrents For the determination of t τ using the ”Method of Normalized Photocurrents”, the photocurrent transients measured at different applied fields are normalized using 27
Chapter 3: Sample Preparation and Characterization Figure 3.3: Graphical evaluation of the transit time using the (a) method of normalized photocurrents, (b) the half-charge method, (c) the normalized photo charge technique as described in the text. Each panel shows 4 different curves taken on a µc-Si:H sample at different applied voltages V. I(t)d 2 /(Q 0 V), where d equals the specimen thickness, Q 0 is the total charge of the excess charge carrier package, and V the applied voltage. As shown in Fig. 3.3 (a) the pre-transients overlap establishing an ”envelope” curve µ(t). The ”envelope” curve µ(t) is used to determine the transit time. About the exact evaluation of the transit time there is still some controversy. While Marshall, Street, and Thompson defined the transit time as the crossing point of the measured transient with the curve 0.8 × µ(t) [134], Nebel et al. used 0.5 × µ(t) which gives somewhat larger values of t τ as can be seen in Fig. 3.3 [135, 136]. Half-Charge Method The evaluation of the transit time using the ”half-charge” method is based on the same principle as used for Gaussian transport. The procedure to determine t τ is illustrated in Fig. 3.3 (b), where the transient photocharge obtained by integrating the transient photocurrents is plotted versus the time. As the number of charge carriers in the packet is determined by the value where the charge transients show an asymptotic behavior, the transit time can be extracted by evaluating the time where half the charge has been collected. This method is typically applied to determine t τ for Gaussian transport behavior. However, Wang et al. have shown that this evaluation is also valid in the case where transport is dispersive [131]. This method has widely been used by the Schiff group [131, 137, 138]. Normalized Photo Charge Technique The ”half-charge method” described above is based on the fact that at times before the charge carriers have reached the collecting electrode, the photocharge Q(t) is proportional to the distance moved by the mean position of the photocarrier distri- 28
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Page 8 and 9: Abstract The electronic properties
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6.2 Irreversible Oxidation Effects
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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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