Theory of the Urbach Rule

Keil, Thomas

doi:10.1103/physrev.144.582

Cited by 87 publications

(42 citation statements)

References 15 publications

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“…(1), has been observed universally in crystals as well as glasses. Extensive research over many decades [2] has shown that it arises from transitions between localized electronic levels resulting from band-edge fluctuations and extended states [3,4]. In a pioneering work on amorphous Si, the fluctuations in the single-particle energies at the band edges obtained from ab initio molecular-dynamics (MD) simulations in the local density approximation were found to be in good agreement with experimentally measured band tail widths [5].…”

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confidence: 56%

First-Principles Calculations of the Urbach Tail in the Optical Absorption Spectra of Silica Glass

et al. 2011

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We present density-functional theory calculations of the optical absorption spectra of silica glass for temperatures up to 2400 K. The calculated spectra exhibit exponential tails near the fundamental absorption edge that follow the Urbach rule in good agreement with experiments. We discuss the accuracy of our results by comparing to hybrid exchange correlation functionals. We show that the Urbach rule holds in a frequency interval where optical absorption is Poisson distributed with very large statistical fluctuations. In this regime, a direct relation between the optical absorption coefficient and electronic density of states is derived, which provides a link between photoemission and absorption spectra and is used to determine the lower bound to the Urbach frequency regime.

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confidence: 56%

First-Principles Calculations of the Urbach Tail in the Optical Absorption Spectra of Silica Glass

et al. 2011

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“…2͑a͒. The optical absorption coefficient near the fundamental absorption band has an exponential dependency, which is given by the Urbach's rule as 36,37 It can be seen that when SiO 2 content increases, the band gap energy values increase, occurring at 4.6 and 5.2 eV for the LSCAS and AM39 ͑the glass with higher SiO 2 content͒ samples, respectively.…”

Section: Optical Absorption Coefficient and Band Gap Determinationmentioning

confidence: 98%

Relations among nonbridging oxygen, optical properties, optical basicity, and color center formation in CaO–MgO aluminosilicate glasses

Novatski

Steimacher

Medina

et al. 2008

Journal of Applied Physics

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In this study the relations among nonbridging oxygen ͑NBO͒, optical properties, optical basicity, and color center formation in CaO-MgO aluminosilicate glasses were studied. Samples containing ͑in mol %͒ 35.9-57.5 of CaO, 16-27.7 of Al 2 O 3 , 7.9-41.6 of SiO 2 , and 6.5-6.9 of MgO were measured by optical absorption and excitation, luminescence, and Raman spectroscopy. The results showed that when the SiO 2 content was increased, the absorption edge shifted toward lower wavelengths and the bonds between O 2− ions and cations became more covalent. These observations were confirmed by Raman results that showed a decrease in the number of NBO per silicon tetrahedron as a function of SiO 2 content. The results indicate that the effects of higher NBO concentration are the narrowing of the band gap energy and the delocalization of O 2− electrons, which facilitates the O 2− electrons to be trapped by anion vacancies and, consequently, forming color centers. The relationship between color center formation and SiO 2 content was confirmed by optical spectroscopic measurements under UV radiation.

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“…The second integral in the expression (3) which can be evaluated, say, by the stationary phase method 1191 is much smaller than the first one in the region IQ,v ( < A, and may be neglected.…”

Section: Shape Of the Emission Spectrum Due To Impurity Centresmentioning

confidence: 99%

Light Emission from Impurity Centres and Urbach's Rule

Lubchenko

Dudkin

1970

Physica Status Solidi (b)

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An investigation is made of the shape of the emission spectra due to impurity centres in a solid, taking into account the variation of its quasi-elastic constants during the phototransitions. A formula for the short-wavelength edge of the emission spectrum similar to the Urbach expression for absorption is obtained.Es wird die Linienform der Emissionsspektren von Fremddefektzentren in Festkorpern untersucht, wobei die Anderungen der quasielastischen Konstanten wiihrend des Photoiibergangs berucksichtigt werden. Es wird eine Pormel fur die kurzwellige Kante des Emissionsspektrums erhalten, die der Urbach-Formel fur die Absorption iihnlich ist.

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Theory of the Urbach Rule

Cited by 87 publications

References 15 publications

First-Principles Calculations of the Urbach Tail in the Optical Absorption Spectra of Silica Glass

First-Principles Calculations of the Urbach Tail in the Optical Absorption Spectra of Silica Glass

Relations among nonbridging oxygen, optical properties, optical basicity, and color center formation in CaO–MgO aluminosilicate glasses

Light Emission from Impurity Centres and Urbach's Rule

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