Formation of a Positive Fixed Charge at $c\text{\ensuremath{-}}\mathrm{Si}(111)/a\text{\ensuremath{-}}{\mathrm{Si}}_{3}{\mathrm{N}}_{3.5}:\mathrm{H}$ Interfaces

Formation of a Positive Fixed Charge at $c − Si (111) / a − {Si}_{3} N_{3.5} : H$ Interfaces

L. E. Hintzsche, C. M. Fang, M. Marsman, M. W. P. E. Lamers, A. W. Weeber, and G. Kresse

Phys. Rev. Applied 3, 064005 – Published 11 June 2015

Abstract

Modern electronic devices are unthinkable without the well-controlled formation of interfaces at heterostructures. These structures often involve at least one amorphous material. Modeling such interfaces poses a significant challenge, since a meaningful result can be expected only by using huge models or by drawing from many statistically independent samples. Here we report on the results of high-throughput calculations for interfaces between crystalline silicon ( $c − Si$ ) and amorphous silicon nitride ( $a − {Si}_{3} N_{3.5} : H$ ), which are omnipresent in commercially available solar cells. The findings reconcile only partly understood key features. At the interface, threefold-coordinated Si atoms are present. These are caused by the structural mismatch between the amorphous and crystalline parts. The local Fermi level of undoped $c − Si$ lies well below that of $a − Si N : H$ . To align the Fermi levels in the device, charge is transferred from the $a − Si N : H$ part to the $c − Si$ part resulting in an abundance of positively charged, threefold-coordinated Si atoms at the interface. This explains the existence of a positive, fixed charge at the interface that repels holes.

Received 16 January 2015

DOI:https://doi.org/10.1103/PhysRevApplied.3.064005

Authors & Affiliations

L. E. Hintzsche¹, C. M. Fang¹, M. Marsman¹, M. W. P. E. Lamers², A. W. Weeber², and G. Kresse¹

¹University of Vienna, Faculty of Physics and Center for Computational Materials Science, Sensengasse 8/12, A-1090 Vienna, Austria
²ECN Solar Energy, P.O. Box 1, 1755 ZG Petten, The Netherlands

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Vol. 3, Iss. 6 — June 2015

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Figure 1
(a) Number densities and (b) layer-resolved density of states (DOS) at the $c − Si / a − {Si}_{3} N_{3.5} : H$ interfaces with 1- and 11-at. % H (solid and dashed lines, respectively). (a) The $N$ number density shows a peak close to the interface integrating to 60% of the number density in the topmost Si layer. (b) The considered electronic states lie within $\pm 0.4 eV$ of the Fermi level. The states are found to be predominantly localized either at atoms with ideal coordination or undercoordination (red or black arrow). These states are related to the conduction band of $c − Si$ or to undercoordinated Si atoms in $a − {Si}_{3} N_{3.5} : H$ . In some microscopic models, a charge transfer from occupied coordination defects (red isosurface) to the Si conduction band (blue isosurface) occurs (green arrow).
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Figure 2
Typical band structure and DOS of a $c − Si / a − {Si}_{3} N_{3.5} : H$ interface sample in the presence of a single defect state. The color coding indicates the degree of localization and corresponds to the inverse participation ratio (IPR, red for localized states). Additionally, we show the DOS of a bulk undoped $c − Si$ and a defect-free bulk $a − {Si}_{3} N_{3.5} : H$ sample. In the band structure of the interface sample, the valance band (VB) and the conduction band (CB) can be determined by means of the IPR. For the bulk samples, the valance band maximum and the conduction band minimum are indicated. Note that $E_{F}$ refers to the average Fermi level of the interface models.
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Figure 3
Two examples for occupied K defects. In sample B, the defect level is close to the valence band, whereas, in sample C, it is close to the conduction band (CB). In sample C, a partial charge transfer into the conduction band is observed. Both defect states interact with the valence- or conduction-band states resulting in forbidden crossings.
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Figure 4
Local electronic density of states evaluated for the $c − Si$ part and for the $a − Si N : H$ part (red or black lines) of the $c − Si / a − {Si}_{3} N_{3.5} : H$ interfaces with 1- and 11-at. % H (solid and dashed lines, respectively). The midgap level of bulk $c − Si$ and the Fermi level of $a − {Si}_{3} N_{3.5} H_{0.8}$ are shown by vertical lines in the corresponding colors.
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Figure 5
Illustration of the predicted band bending at the $c − Si / a − Si N : H$ interface. Before bringing both subsystems in contact, the midgap level of $c − Si$ lies below the Fermi level of $a − Si N : H$ (offset between the red and blue lines at the interface). In $a − Si N : H$ , nearly all defect levels below and above the Fermi level are doubly occupied $K^{-}$ defects and unoccupied $K^{+}$ defects, respectively. Only a few singly occupied $K^{0}$ defects are located at the Fermi level. To align the Fermi levels, $K^{-}$ and $K^{0}$ defects donate charge to shallow acceptor levels in $c − Si$ (red area). They are thereby converted to $K^{0}$ and $K^{+}$ defects (blue area).
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Formation of a Positive Fixed Charge at c−Si(111)/a−Si3N3.5:H Interfaces

L. E. Hintzsche, C. M. Fang, M. Marsman, M. W. P. E. Lamers, A. W. Weeber, and G. Kresse

Phys. Rev. Applied 3, 064005 – Published 11 June 2015

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Formation of a Positive Fixed Charge at $c − Si (111) / a − {Si}_{3} N_{3.5} : H$ Interfaces