#
Stability and Bandgap Engineering of In_{1−x}Ga_{x}Se Monolayer

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## Abstract

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## 1. Introduction

## 2. Methods

## 3. Results and Discussion

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Top and side views (

**a**) of the geometry of a pristine InSe (GaSe) monolayer. Selenium is represented in blue, while indium (gallium) is in orange. The monolayer is formed by four stacked atomic planes; therefore, two different levels in the In/Ga atoms arrangement can be distinguished (highlighted with the two horizontal dashed lines). This lattice arrangement is also shared by InGaSe compounds. (

**b**) InSe band structure (black lines) and GaSe band structure (dashed red lines) calculated at the DFT-PBE level. In both cases, the vacuum level (${\mathrm{E}}_{0}$) is set to 0 eV.

**Figure 2.**Phase diagram of the $\mathrm{I}{\mathrm{n}}_{1-x}\mathrm{G}{\mathrm{a}}_{x}\mathrm{S}\mathrm{e}$: gray crosses represent the energies of the structures predicted through the CE, blue dots indicate the energies found with DFT calculations performed on generated structures, black dots represent, instead, the energies of the two ground states associated with the two pure phases of InSe and GaSe, and the black dashed line marks the ground-state energy for all In/Ga fraction.

**Figure 3.**Representation of the less (

**a**) and the more (

**b**) stable pair figures obtained with the CE. ECIs related to red interactions (

**b**) are negative; therefore, these configurations lower the total energy of the structure. Blue figures (

**a**), instead, are associated with positive J coefficients, which implies that their formation is not energetically favored. Indium atoms are represented in black, selenium atoms in gray, and gallium atoms in blue (

**a**) and red (

**b**).

**Figure 4.**Panels (

**a**,

**c**) show the two initial KMC structures considered: a quantum dot and a stripe, respectively. Atoms belonging to the "bottom" plane are transparent, while their color represents the atomic species, gallium (red) and indium (light gray). Panels (

**b**,

**d**) report the equilibrium structures obtained from the two corresponding initial configurations shown in (

**a**,

**c**). It is apparent that in both cases the two pure phases tend to mix.

**Figure 5.**(

**a**) $\mathrm{I}{\mathrm{n}}_{1-x}\mathrm{G}{\mathrm{a}}_{x}\mathrm{S}\mathrm{e}$ bandgap (direct blue, indirect gray) at varying Ga concentrations. (

**b**) ${\mathrm{E}}_{\mathrm{G}}^{d}\left(x\right)$ alignment with respect to the vacuum level for some of the InGaSe structures.

**Figure 6.**Band diagrams and k-resolved projected density of states, for $\mathrm{I}{\mathrm{n}}_{0.83}\mathrm{G}{\mathrm{a}}_{0.17}\mathrm{S}\mathrm{e}$ (

**a**–

**c**) and $\mathrm{I}{\mathrm{n}}_{0.17}\mathrm{G}{\mathrm{a}}_{0.83}\mathrm{S}\mathrm{e}$ (

**d**). Selenium p orbitals provide a very similar contribution for both the considered compounds. S and p orbitals give a strong contribution both to conduction and valence bands, when the Ga percentage is low (panels

**b**,

**c**). When the Ga concentration is high, Ga s (not shown here) and p orbitals give a larger contribution.

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**MDPI and ACS Style**

Salomone, M.; Raffone, F.; Re Fiorentin, M.; Risplendi, F.; Cicero, G. Stability and Bandgap Engineering of In_{1−x}Ga_{x}Se Monolayer. *Nanomaterials* **2022**, *12*, 515.
https://doi.org/10.3390/nano12030515

**AMA Style**

Salomone M, Raffone F, Re Fiorentin M, Risplendi F, Cicero G. Stability and Bandgap Engineering of In_{1−x}Ga_{x}Se Monolayer. *Nanomaterials*. 2022; 12(3):515.
https://doi.org/10.3390/nano12030515

**Chicago/Turabian Style**

Salomone, Mattia, Federico Raffone, Michele Re Fiorentin, Francesca Risplendi, and Giancarlo Cicero. 2022. "Stability and Bandgap Engineering of In_{1−x}Ga_{x}Se Monolayer" *Nanomaterials* 12, no. 3: 515.
https://doi.org/10.3390/nano12030515