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On the Origin of the Urbach Rule and the Urbach Focus

Published online by Cambridge University Press:  17 June 2013

J. A. Guerra ,
L. Montañez ,
F. De Zela ,
A. Winnacker  and
R. Weingärtner
J. A. Guerra
Affiliation:
Pontifical Catholic University of Peru, Sciences Department, Physics Section, Av. Universitaria 1801, Lima 32, Peru. University of Erlangen-Nurnberg, Institute of Material Science 6, Martensstr. 7, 91058 Erlangen, Germany
L. Montañez
Affiliation:
Pontifical Catholic University of Peru, Sciences Department, Physics Section, Av. Universitaria 1801, Lima 32, Peru.
F. De Zela
Affiliation:
Pontifical Catholic University of Peru, Sciences Department, Physics Section, Av. Universitaria 1801, Lima 32, Peru.
A. Winnacker
Affiliation:
University of Erlangen-Nurnberg, Institute of Material Science 6, Martensstr. 7, 91058 Erlangen, Germany
R. Weingärtner
Affiliation:
Pontifical Catholic University of Peru, Sciences Department, Physics Section, Av. Universitaria 1801, Lima 32, Peru. University of Erlangen-Nurnberg, Institute of Material Science 6, Martensstr. 7, 91058 Erlangen, Germany
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Abstract

A simple derivation of sub-bandgap exponential tails and fundamental absorption equations ruling the optical absorption of amorphous semiconductors are presented following the frozen phonon model. We use the Kubo-Greenwood formula to describe the average transition rate for the optical absorption process. Asymptotic analysis leads to the commonly observed exponential tail as well as the Tauc expression for the fundamental absorption. We test our theoretical results with experimental absorption coefficients of amorphous Si:H, SiC:H, AlN and SiN. The validity of the Urbach focus concept is evaluated.

Keywords

optical propertiesamorphoussputtering
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1536: Symposium A – Film Silicon Science and Technology , 2013 , pp. 139 - 145
Copyright
Copyright © Materials Research Society 2013 

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References

REFERENCES

Zhu, F., Hu, J., Matulionis, I., Deutsch, T., Gaillard, N., Miller, E., and Madan, A., Solar Energy Book, chapter 15, (Vukovar: Intech, 2010).Google Scholar
Gerhardt, R., Properties and Applications of Silicon Carbide, (Vienna: Intech, 2011).CrossRefGoogle Scholar
Richardson, H. H., Van Patten, P. G., Richardson, D. R., and Kordesch, M. E., Appl. Phys. Lett. 80, 2207 (2002).CrossRefGoogle Scholar
Adachi, D., Kitaike, R., Ota, J., Toyama, T., and Okamoto, H., J. Mater. Sci. Mater Electron. 18, S71 (2007).CrossRefGoogle Scholar
Wakahara, A., Takemoto, K., Oikawa, F., Okada, H., Ohshima, T., and Itoh, H., Phys. Stat. Sol. A 205, 56 (2008).CrossRefGoogle Scholar
Sumi, H., and Toyazawa, Y., J. Phys. Soc. Jpn. 31, 342 (1971).CrossRefGoogle Scholar
Abe, S., and Toyazawa, Y., J. Phys. Soc. Jpn. 50, 2185 (1981).CrossRefGoogle Scholar
Dunstan, D. J., J. Phys. C: Solid State Phys. 16, L567–L571 (1983).CrossRefGoogle Scholar
Soukoulis, C. M., Cohen, M. H., and Economou, E. N., Phys. Rev. Lett. 53, 616 (1984).CrossRefGoogle Scholar
Sajeev, J., Soukoulis, C. M., Cohen, M. H., and Economou, E. N., Phys. Rev Lett. 57, 1777 (1986).Google Scholar
O’Leary, S. K., Zukotynski, S., and Perz, J. M., Phys. Rev. B 51, 4143 (1995).CrossRefGoogle Scholar
O’Leary, S. K. and Lim, P. K., Solid State Communications 104, 17 (1997).CrossRefGoogle Scholar
O’Leary, S. K., Appl. Phys. Lett. 72, 1332 (1998).CrossRefGoogle Scholar
Nguyen, T. H., and O’Leary, S. K., J. Appl. Phys. 88, 3479 (2000).CrossRefGoogle Scholar
Cody, G. D., Tiedje, T., Abeles, B., Brooks, B., and Goldstein, Y., Phys. Rev. Lett. 47, 1480 (1981).CrossRefGoogle Scholar
Letz, M., Gottwald, A., Richter, M., Liberman, V., and Parthier, L., Phys. Rev. B 81, 155109 (2010).CrossRefGoogle Scholar
Mott, N. F., and Davis, E. A., Electronic processes in non-crystalline materials Second edition (Oxford University Press, 1979).Google Scholar
Moseley, L. L., and Lukes, T., Am. J. Phys. 46, 676 (1978).CrossRefGoogle Scholar
Tauc, J., Mat. Res. Bull. 3, 37 (1968).CrossRefGoogle Scholar
Orapunt, F., and O’Leary, S. K., Appl. Phys. Lett. 72, 1332 (2004).Google Scholar
Guerra, J. A., Montañez, L., Erlenbach, O., Galvez, G., De Zela, F., Winnacker, A., and Weingärtner, R., J. Phys. Conf. Ser. 274, 012113 (2011).CrossRefGoogle Scholar
Cody, G. D., Mater. Res. Soc. Symp. Proc. 862, A1.3.1 (2005).Google Scholar
Abay, B., Güder, H. S., Efeoglu, H, and Yogurtçu, Y. K., J. Phys. D: Appl. Phys. 32, 2941 (1999).CrossRefGoogle Scholar
Zhang, F., Xue, H., Song, Z., Guo, Y., and Chen, G., Phys. Rev. B 46, 4590 (1992).CrossRefGoogle Scholar
Weingärtner, R, Guerra, J. A., Erlenbach, O., Gálvez, G., De Zela, F., and Winnacker, A., Mat. Sci. and Eng. B 174, 114 (2010).CrossRefGoogle Scholar