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A universal feature in the optical absorption spectrum associated with hydrogenated amorphous silicon: A dimensionless joint density of states analysis
R. A. Street, Hydrogenated Amorphous Silicon ( Cambridge University Press, New York, 1991).
Technology and Applications of Amorphous Silicon, edited by R. A. Street ( Springer-Verlag, Berlin, 2000).
L.-L. Tay, D. J. Lockwood, J.-M. Baribeau, M. Noël, J. C. Zwinkels, F. Orapunt, and S. K. O'Leary, Appl. Phys. Lett. 88, 121920 (2006).
Z. Remeš, Ph.D. thesis ( Charles University, Prague, 1999).
There have been considerable recent developments in the understanding of the network of atoms present within a-Si:H. These are amply discussed in the literature; see, for example, Refs. 35 and 36.
J. Melskens, M. Schouten, A. Mannheim, A. S. Vullers, Y. Mohammadian, S. W. H. Eijt, H. Schut, T. Matsui, M. Zeman, and A. H. M. Smets, IEEE J. Photovoltaics 4, 1331 (2014).
There is a prevailing consensus that suggests that the best forms of a-Si:H tend to exhibit the same properties, regardless of the exact means of deposition. In contrast, the most defective forms of a-Si:H are defective in so many different ways. We interpret this to imply that the distributions of band states and tail states are very similar in form for the case of a-Si:H, while the distribution of defect states is a strong function of the details of the deposition process; the exact form of the band states and the tail states are, of course, dependent upon the exact deposition details. Ample experimental evidence, available in the literature, bolsters this assertion.
This is not to say that the network of silicon atoms found within a-Si:H approaches the continuous random network ideality mentioned previously. Just that a universal feature corresponding to its spectral dependence, and the consequential scaling relationships, if they exist at all, are only applicable in regions II and III of the classification of Wood and Tauc.39
Analytical frameworks for the determination of the spectral dependence of the optical absorption coefficient associated with a-Si:H that take into account optical transitions involving defect states have, in fact, been devised; see, for example, Thevaril and O'Leary.15 Further details, pertaining to the treatment of the distributions of defect states in the determination of the spectral dependence of the optical absorption coefficient associated with a-Si:H, are amply provided for in the literature; see, for example, Güneş and Wronski,42 Niu,43 Wronski and Niu,44 and Melskens et al.45
X. Niu, Ph.D. thesis ( Pennsylvania State University, University Park, 2006).
J. Melskens, M. Schouten, R. Santbergen, M. Fischer, R. Vasudevan, D. J. van der Vlies, R. J. V. Quax, S. G. M. Heirman, K. Jäger, V. Demontis, M. Zeman, and A. H. M. Smets, Sol. Energy Mater. Sol. Cells 129, 70 (2014).
In an evaluation of the optical processes associated with a crystalline semiconductor, both energy conservation and conservation of the electron wave-vector, , must be taken into account in determining the probability of a given optical transition. In an amorphous semiconductor, however, the lack of periodicity in the atomic distribution leads to a relaxation in these -selection rules. Hence, the JDOS function associated with an amorphous semiconductor essentially reduces to an integration over the valence band and conduction band DOS functions, i.e., Eq. (3).
Given that the valence band and conduction band band energies, Ev and Ec, respectively, are relative quantities, the number of truly independent modeling parameters in the simplified empirical DOS model of O'Leary and Malik,31 i.e., Eqs. (4) and (5), is five.
In a recent paper, Thevaril and O'Leary55 demonstrate that the conduction band tail breadth plays a negligible role in shaping the optical absorption spectrum associated with a-Si:H. This justifies the use of the simplified empirical model of O'Leary and Malik31 for the DOS functions associated with a-Si:H.
For this further simplified empirical DOS model, i.e., Eqs. (4) and (5) with set to , the number of truly independent modeling parameters is four.
This nominal selection of modeling parameters is representative of the case of a-Si:H; see, for example, Jiao et al.52
Jiao et al.52 instead find that for a-Si:H (prepared without silane dilution); see Figure 2 of Jiao et al.52
The assumption that Å2 for a-Si:H follows from the analysis of Jackson et al.20 Others have performed their analysis of the optical response of a-Si:H within the framework of this assumption; see, for example, Jiao et al.,52 O'Leary and Malik,31 and others. It is interesting to note that , where 3.16 Å is a bit larger than the nearest-neighbor silicon atom separation distance within c-Si, i.e., 2.35 Å. We suspect that there might be a correlation between these values, the 3.16 Å value possibly corresponding to the length scale over which the phase associated with the atomic wave-functions within a-Si:H are coherent.68 Experimental evidence, buttressing this speculation, has yet to be acquired.
The HW70 sample of Remeš33 was prepared with a very high hydrogen content, i.e., 17 at. %. Remeš33 demonstrated that the hot-wire prepared forms of a-Si:H with high hydrogen contents (above 10 at. %) are structurally distinct from lower hydrogen content hot-wire prepared materials, lower hydrogen content hot-wire prepared materials having properties similar to those exhibited by conventionally prepared PECVD deposited a-Si:H. We suspect that that our inability to fit the optical absorption spectrum associated with the HW70 sample within the framework of our dimensionless JDOS formalism may be related to these structural differences.
A detailed analysis, the results of which are not presented here, shows that the optical properties of forms of a-Si:H prepared through conventional forms of UHV evaporation are quite distinct from those associated with forms of a-Si:H prepared through PECVD and hot-wire deposition. Thus, we might expect differences in the spectral dependencies exhibited by and to occur for the specific case of Viturro and Weiser32 from those found for more conventional forms of a-Si:H, i.e., such as those prepared by Cody et al.19 and Remeš.33
The relationship between the energy gap and the valence band tail breadth for the case of a-Si:H, a quantitative dependence that was suggested by Cody et al.,19 against which the role that intrinsic disorder plays in influencing the optical properties associated with a-Si:H may be benchmarked, may be probed within the framework of this JDOS formalism. The strain that is present within devices fabricated of a-Si:H, strain potentially further contributing to the amount of intrinsic disorder that is present, can probably also be probed within the framework of this approach. These possible applications of our JDOS function are beyond the scope of this particular paper.
Of course, there are a lot of details that must be taken into account in optimizing the performance of any given type of solar cell. We view this potential application of our dimensionless JDOS formalism as identifying general trends of interest, which could potentially stimulate further thought into this matter.
The atomic density of a-Si:H is known to vary from sample-to-sample, these variations arising as a product of the deposition conditions. For example, Melskens et al.,35 Remeš et al.,78 and Smets et al.,79 present experimental results which suggest that there are sample-to-sample variations in the mass density of a-Si:H; presumably these changes in the mass density are linked to those in the atomic density. We did not take into account these sample-to-sample variations as we did not have access to means whereby we could determine the atomic density corresponding to each sample. Moreover, it seems likely that taking into account such variations will lead to relatively minor corrections in the results. Melskens et al.,35 for example, find variations in the mass density of a-Si:H that range between 2.20 and 2.32 g/cm3. Remeš et al.78 find variations in the mass density of a-Si:H that range between 2.19 and 2.29 g/cm3. The mass density variations found by Smets et al.,79 however, are greater, but the lower density samples of Smets et al. (mass density values as low as 1.8 g/cm3 are reported by Smets et al.) are found to be in possession of unusually high hydrogen concentrations, i.e., as much as 26 at. % hydrogen, and thus, bear no similarity with the samples that we consider for the purposes of our analysis; our hydrogen contents are at most 10% for the purposes of this study. So the atomic density of a-Si:H might be expected to exhibit, at most, 10% sample-to-sample variations. In contrast, the JDOS function varies by many orders of magnitude. So by comparison, the atomic density variations are expected to make a relatively minor contribution.
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Using a dimensionless joint density of states formalism for the quantitative characterization of the optical response associated with hydrogenated amorphous silicon, a critical comparative analysis of a large number of different optical absorption
data sets is considered. When these data sets are cast into this dimensionless framework, we observe a trend that is almost completely coincident for all of the data sets considered. This suggests that there is a universal feature associated with the optical absorption
spectrum of hydrogenated amorphous silicon.
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