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Understanding localized states in the band tails of amorphous semiconductors exemplified by a -Si:H from the perspective of excess delocalized charges

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Peer-reviewed

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Article

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Abstract

This work uses a perturbation strategy to show that the band tails in the density of states (DOS) distribution of amorphous semiconductors form due to the existence of excess delocalized charges. These charges satisfy a Gaussian distribution with a mean of zero and vary slowly in space due to the short- and medium-range order of amorphous materials. The charges exist due to the bond angle and bond length distortion. They induce an extra potential energy distribution that leads to energy band fluctuation in the energy−space diagram and con-sequently gives rise to localized states. A 150 nm×150 nm×7.5 nm large-scale finite-element excess charge model for hydrogenated amorphous silicon (a-Si:H) is developed through the use of a moving average smooth-ing that filters a Gaussian array of random charge values. Thanks to the analytical and computational simplici-ty of the theory in this work (compared to conventional approaches considering atomistic details and complex electron-electron interactions), this large-scale model is calculated in only 90 seconds and reproduces the typi-cal exponential and linear features found in the conduction band tail of a-Si:H and other amorphous semicon-ductors. Through a satisfactory fitting to experimental a-Si:H DOS data in the literature, model parameters are semi-quantitatively determined. Unlike previous analytical and computational efforts the authors are aware of, this large-scale model is physically unambiguous, computationally tractable and satisfactorily accurate.

The large-scale modelling capability allows reliable insights into the geometric features of localized and ex-tended states, which are visualized in a non-schematic manner for the first time. This further leads to re-investigations of several established concepts and conclusions. First, calculations of this work challenge the description that the wavefunction envelope of a localized state decays away from its center in an exponential manner and that the spread of this exponential decay varies with energy in a power-law manner. Second, im-purity states and/or extended states are critical to enable band tail hopping. Third, low-energy states are spa-tially included inside high-energy states, so the existing concept of “average spatial separation of localized states” is meaningless. Fourth, the mobility edge obtained from conductivity activation energy measurements turns out to be higher than the actual critical energy Ect that demarcates extended states from localized states; this judgement is supported by the electron mobility−energy relation that is inferred from the geometry of states, which validates a continuous increase of energy-specific mobility as electron energy increases from Ect.

Description

Keywords

51 Physical Sciences, 40 Engineering, 34 Chemical Sciences, 3406 Physical Chemistry

Journal Title

Physical Review B

Conference Name

Journal ISSN

2469-9950
2469-9969

Volume Title

Publisher

American Physical Society (APS)
Sponsorship
EPSRC (EP/W009757/1)
Cambridge Commonwealth, European & International Trust Ph.D. scholarship; Rank Prize Return to Research Grant.
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2024-04-29 12:59:19
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2024-02-15 00:31:01
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