On the Origin of the Urbach Rule and the Urbach Focus
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ABSTRACTA 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.
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2008 ◽
Vol 39-40
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pp. 253-256
1985 ◽
Vol 77-78
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pp. 171-174
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1998 ◽
Vol 20
(3)
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pp. 139-142
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