# Unveiling Influence of Dielectric Losses on the Localized Surface Plasmon Resonance in (Al,Ga)As:Sb Metamaterials

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## Abstract

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## 1. Introduction

## 2. Dielectric Functions of Al${}_{\mathit{x}}$Ga${}_{\mathbf{1}-\mathit{x}}$As and Sb

## 3. Modeling the Optical Properties of the Sb Nanoparticle Ensemble in Al${}_{\mathit{x}}$Ga${}_{\mathbf{1}-\mathit{x}}$As

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

LSPR | Localized surface plasmon resonance |

MBE | Molecular-beam epitaxy |

LT | Low-temperature |

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**Figure 1.**Atomic structures of the zincblende (Al,Ga)As (

**a**), A7 phase of Sb (

**b**), and schematic presentation of the (Al,Ga)As:Sb metamaterial (

**c**).

**Figure 2.**The real (${\epsilon}_{1}$) and imaginary (${\epsilon}_{2}$) parts of the dielectric permittivities for GaAs, AlAs, and Al${}_{x}$Ga${}_{1-x}$As solid solutions with aluminum content $x=0.3$ and $0.6$ according to Adachi [27] and Djurišić [28] models. Arrows indicate the energies of the major critical points.

**Figure 3.**The real (${\epsilon}_{1}$) and imaginary (${\epsilon}_{2}$) parts of the averaged Sb dielectric function calculated employing the ab initio data of Ref. [25].

**Figure 4.**The optical extinction spectra of the compositional metamaterial based on the systems of Sb nanoinclusions in GaAs and AlAs binary compounds and Al${}_{x}$Ga${}_{1-x}$As solid solutions with aluminum contents $x=0.3$ and $0.6$. The filling factor and nanoparticle radius used in calculations were $f=0.016$ and $3.1$ nm, respectively. Solid black and red lines represent optical extinction due to LSPR, calculated using the Adachi [27] and Djurišić [28] models. The dashed orange curves show absorption in the semiconductor matrix according to the Djurišić model in the absence of Sb nanoparticles. The solid blue curves are the cumulative optical extinction spectra of the metamaterial.

**Table 1.**Parameters describing the composition dependence of critical point energies (in eV) ${E}_{0}$, ${E}_{0}+{\Delta}_{0}$, ${E}_{1}$, and ${E}_{1}+{\Delta}_{1}$.

Parameter | $\mathit{E}\left(\mathbf{GaAs}\right)$ | $\mathit{E}\left(\mathbf{AlAs}\right)-\mathit{E}\left(\mathbf{GaAs}\right)$ | ${\mathit{c}}_{0}$ | ${\mathit{c}}_{1}$ |
---|---|---|---|---|

${E}_{0}$ [30] | 1.424 | 1.525 | −0.37 | 0 |

${E}_{0}+{\Delta}_{0}$ [30] | 1.764 | 1.485 | −0.37 | 0 |

${E}_{1}$ [29] | 2.926 | 0.962 | −0.2124 | −0.7850 |

${E}_{1}+{\Delta}_{1}$ [29] | 3.170 | 0.917 | −0.0734 | −0.9393 |

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**MDPI and ACS Style**

Ushanov, V.I.; Eremeev, S.V.; Silkin, V.M.; Chaldyshev, V.V.
Unveiling Influence of Dielectric Losses on the Localized Surface Plasmon Resonance in (Al,Ga)As:Sb Metamaterials. *Nanomaterials* **2024**, *14*, 167.
https://doi.org/10.3390/nano14020167

**AMA Style**

Ushanov VI, Eremeev SV, Silkin VM, Chaldyshev VV.
Unveiling Influence of Dielectric Losses on the Localized Surface Plasmon Resonance in (Al,Ga)As:Sb Metamaterials. *Nanomaterials*. 2024; 14(2):167.
https://doi.org/10.3390/nano14020167

**Chicago/Turabian Style**

Ushanov, Vitalii I., Sergey V. Eremeev, Vyacheslav M. Silkin, and Vladimir V. Chaldyshev.
2024. "Unveiling Influence of Dielectric Losses on the Localized Surface Plasmon Resonance in (Al,Ga)As:Sb Metamaterials" *Nanomaterials* 14, no. 2: 167.
https://doi.org/10.3390/nano14020167