#
Over- and Undercoordinated Atoms as a Source of Electron and Hole Traps in Amorphous Silicon Nitride (a-Si_{3}N_{4})

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Computational Setup

#### 2.2. Structure Creation and Characterization

^{−3}, which is in the range of experimental values varying from 2.3 to 3.0 g cm

^{−3}[31].

#### 2.3. Charge Trapping Model

## 3. Results and Discussion

#### 3.1. Trapping Sites

#### 3.1.1. Hole Traps

#### 3.1.2. Electron Traps

#### 3.1.3. Defect States

#### 3.1.4. Inverse Participation Ratio

#### 3.2. Defect Characterization

#### 3.2.1. Charge Transition Level

#### 3.2.2. Relaxation Energy

#### 3.2.3. Energy Barriers

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Structural properties of amorphous Si${}_{3}$N${}_{4}$ model structures compared with experimental data [28,29]. (

**a**) Structure factor; (

**b**) radial distribution function; (

**c**) Si-N bond length distribution of all structures combined with a fitted normal distribution without stretched Si-N bonds > 1.85 Å. Fitting parameters are given in the plot and the green line denotes the mean bond length from experimental data. (

**d**) Energy gaps between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) as a function of the relative number of undercoordinated atoms in the respective structure. Only structures with band gaps above 3.8 eV, as denoted with a red horizontal line, were further investigated.

**Figure 2.**Schematics of potential energy curves as a function of the configuration coordinate for a Si${}_{3}$N${}_{4}$ system in two charge states in the context of a Si/Si${}_{3}$N${}_{4}$ band diagram to explain the charge transfer mechanism of electron traps (

**left**) and hole traps (

**right**). Applying a gate voltage shifts the trap level by $\delta $ as outlined with the dashed colored lines for positive (

**left**) and negative (

**right**) bias.

**Figure 3.**Hole trapping near intrinsic sites in a-Si${}_{3}$N${}_{4}$ with the localized wave functions (

**top**) and the projected density of states of the structure (

**bottom**). Silicon atoms are shown in yellow, nitrogen atoms in blue. (

**a**) Semi-localized HOMO around N adjacent to a five-fold coordinated Si (

**top left**). After trapping a hole, the state localizes at two of these N due to structural relaxations (

**top right**), shifting the now unoccupied state near the middle of the band gap. (

**b**) HOMO localized at twofold coordinated N (

**top left**), with an additional hole localized at this site (

**top right**). After trapping the hole, the amorphous network undergoes small structural relaxations and the state, now unoccupied, is shifted towards the middle of the band gap.

**Figure 4.**Electron trapping near intrinsic sites in a-Si${}_{3}$N${}_{4}$ with the localized wave functions (

**top**) and the according projected density of states (

**bottom**). Silicon atoms are shown in yellow, nitrogen in blue. (

**a**) LUMO localized at Si adjacent to a four-fold coordinated N. After trapping an electron, the Si relaxes away from the N, thereby shifting the state, now occupied, towards the middle of the band gap. (

**b**) LUMO hybridized between an undercoordinated and a fully coordinated Si (

**top left**). An additional electron localizes at this site, thereby moving the undercoordinated Si towards the other (

**top right**) and introducing one unoccupied and one occupied state in the band gap.

**Figure 5.**Energy levels of the electronic defect states introduced in the band gap after an electron (occupied state) or a hole (unoccupied state) is trapped in a-Si${}_{3}$N${}_{4}$.

**Figure 6.**Inverse participation ratio of two different a-Si${}_{3}$N${}_{4}$ structures with the HOMO and the LUMO shown at an isovalue of 0.05 e/Å${}^{3}$ for the respective structures as an inset. Silicon atoms are shown in yellow, nitrogen atoms in blue. The IPR is a measure of the localization of an orbital, showing that the band edge states are (semi)localized. (

**a**) States at the band edges introduced by overcoordinated atoms. (

**b**) States at the band edges introduced by undercoordinated atoms or dangling bonds.

**Figure 7.**Charge transition levels of intrinsic hole and electron traps of several a-Si${}_{3}$N${}_{4}$ structures. CTLs are given with respect to the VBM of the according a-Si${}_{3}$N${}_{4}$ structure and shown in the context of a Si/Si${}_{3}$N${}_{4}$ band diagram with valence band offsets from experimental data.

**Figure 8.**Relaxation energies according to the NMP model for different charge transfer processes with the fitting parameters of a normal distribution given in the plots. (

**a**) Hole capture, (

**b**) hole emission, (

**c**) electron capture, (

**d**) electron emission.

**Figure 9.**(

**a**) Energy barriers in logarithmic scale from minimum energy configurations to the crossing point of the PECs for electron emission vs. electron capture with the CBM of a Si substrate acting as an electron reservoir. Energy values are shown for initial conditions and after shifting the trap level by $\delta =-1$ eV after applying a positive voltage. (

**b**) Energy barriers in logarithmic scale from minimum energy configurations to the crossing point of the PECs for hole emission vs. hole capture with the VBM of a Si substrate acting as a hole reservoir. Energy values are plotted for initial conditions and after decreasing the Fermi level by $\delta =+1$ eV by applying a negative voltage.

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**MDPI and ACS Style**

Wilhelmer, C.; Waldhoer, D.; Cvitkovich, L.; Milardovich, D.; Waltl, M.; Grasser, T.
Over- and Undercoordinated Atoms as a Source of Electron and Hole Traps in Amorphous Silicon Nitride (a-Si_{3}N_{4}). *Nanomaterials* **2023**, *13*, 2286.
https://doi.org/10.3390/nano13162286

**AMA Style**

Wilhelmer C, Waldhoer D, Cvitkovich L, Milardovich D, Waltl M, Grasser T.
Over- and Undercoordinated Atoms as a Source of Electron and Hole Traps in Amorphous Silicon Nitride (a-Si_{3}N_{4}). *Nanomaterials*. 2023; 13(16):2286.
https://doi.org/10.3390/nano13162286

**Chicago/Turabian Style**

Wilhelmer, Christoph, Dominic Waldhoer, Lukas Cvitkovich, Diego Milardovich, Michael Waltl, and Tibor Grasser.
2023. "Over- and Undercoordinated Atoms as a Source of Electron and Hole Traps in Amorphous Silicon Nitride (a-Si_{3}N_{4})" *Nanomaterials* 13, no. 16: 2286.
https://doi.org/10.3390/nano13162286