# The Electronic and Optical Properties of InSe-GeTe Heterobilayer via Applying Biaxial Strain

^{1}

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## Abstract

**:**

## 1. Introduction

^{3}cm

^{2}·V

^{−1}·s

^{−1}), was successfully produced experimentally. Particularly, it is noted that the lattice mismatch between the ML GeTe and InSe is quite small, less than 1%, which could facilitate the formation of InSe-GeTe HBL by chemical or physical synthesis and growth. More importantly, it was easy to tune the electronic structures by exerting external electric field or strain upon their separate individuals [14]. Therefore, it is highly ideal and desirable to design proper InSe-GeTe heterostructure for potential applications.

## 2. Calculation Methods

^{−5}eV. The length of vacuum zone was set to no less than 20 Å along the c-direction, for the purpose of avoiding spurious interactions between the adjacent slabs. Table 1 summaries the first-principles calculation parameters of InSe-GeTe HBL.

## 3. Results and Discussion

#### 3.1. Geometric Structures of InSe-GeTe HBL

_{b}is defined as a criteria for the strength of interaction between HBL, and can be expressed as [25,26]:

_{b}= [E

_{InSe-GeTe}− (E

_{InSe}+ E

_{GeTe})]/A

_{InSe-GeTe}is the total energy of optimized InSe-GeTe HBL. E

_{InSe}and E

_{GeTe}denote the total energies of separate ML InSe and GeTe, respectively. A represents the interfacial area. It can be concluded from Table 1 that the type-IV HBL exhibits the best stability among the six stacking structures, which exhibits the minimum negative E

_{b}value and interfacial spacing. Therefore, it is convincingly to choose the type-IV HBL as an atomic construction to explore its electronic and optical properties.

#### 3.2. Electronic and Optical Properties of InSe-GeTe HBL

#### 3.3. Biaxial Strain Effect on InSe-GeTe HBL

_{a}) gradually increases with the enhancement of both compressive and tensile strains in the visible light range. Additionally, the absorption coefficients in the UV region from 250 (~5.0 eV) to 400 nm (~3.0 eV) are much larger that in the visible light region, indicating the strong UV absorption of the designed HBL. More specifically, a blue-shift of the absorption peak position for the HBL under compressive strain, and red-shift of the absorption peak position for the HBL under tensile strain with the increase of strain are obviously observed, which is consistent with the change of the band gap under different strains mentioned above. As a result, it is also demonstrated that the optical properties of the InSe-GeTe HBL could be modulated by employing biaxial strain.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Calculated band structures of monolayer (ML) GeTe and InSe along symmetry directions of the Brillouin zone (Γ-M-K-Γ). The Fermi energy (E

_{F}) is set as zero, in order to facilitate the negative meaning of valence band and positive meaning of conduction band.

**Figure 2.**(

**a**–

**f**) Top (upper) and side (lower) views of the six different stacking types for Indium selenide-Germanium telluride (InSe-GeTe) heterobilayer (HBL).

**Figure 3.**(

**a**) Band structure of the InSe-GeTe HBL. (

**b**) The density of states for the InSe-GeTe HBL (Fermi level is indicated by black dashed line).

**Figure 4.**(

**a**) Optical absorption coefficients of separate ML InSe (green line), GeTe (blue line), and InSe-GeTe HBL (red line), respectively. (

**b**) A schematic diagram with band alignment for InSe-GeTe HBL.

**Figure 5.**The band structures of the InSe-GeTe HBL under compressive strains of ε = (

**a**) −7%, (

**b**) −5%, (

**c**) −3%, (

**d**) −1%, and under tensile strains of ε = (

**e**) +1%, (

**f**) +3%, (

**g**) +5%, (

**h**) +7%. The bands drawn in red and black represent the bands dominated by GeTe and InSe monolayers, respectively. (Fermi level is set to 0 eV, and indicated by a dashed line). (

**i**) Band gap values of the InSe-GeTe HBL as a function of biaxial strain.

**Figure 6.**The calculated projected density of states (PDOS) of the InSe-GeTe HBL with biaxial strains of (

**a**) −1%, (

**b**) −3%, (

**c**) −5%, (

**d**) −7%, (

**e**) 1%, (

**f**) 3%, (

**g**) 5%, and (

**h**) 7%. The vertical black dashed line is the Fermi level.

**Figure 7.**(

**a**–

**h**) 3D plot and (

**j**,

**k**) plane-averaged electron density difference Δne(c) along the c direction perpendicular to the interface for the InSe-GeTe HBL under the compressive strains of ε= −7%, −5%, −3%, −1%, and the tensile strains of ε = +1%, +3%, +5%, +7%. The plot of electron density difference for the InSe-GeTe without strain (ε = 0) is considered as a reference. The purple and blue regions denote the electron accumulation and depletion, respectively.

**Figure 8.**Optical absorption spectra of the InSe-GeTe HBL under (

**a**) compressive and (

**b**) tensile strains.

**Table 1.**First-principles calculation parameters of the Indium selenide-Germanium telluride (InSe-GeTe) heterobilayer (HBL).

Parameter | InSe-GeTe HBL |
---|---|

Monkhorst−Pack k point mesh | 8 × 8 × 1 |

Mesh cutoff density (Hartree) | 100 |

Forces tolerance per atom (eV/Å) | ≤0.01 |

Stress error tolerance (eV) | ≤10^{−5} |

Length of vacuum zong (Å) | ≥20 |

**Table 2.**Calculated binding energies (E

_{b}), interlayer spacings (d), and band gaps (E

_{g}) of six different InSe-GeTe stacking structures.

Stacking Type | HBL Ⅰ | HBL Ⅱ | HBL Ⅲ | HBL Ⅳ | HBL Ⅴ | HBL Ⅵ |
---|---|---|---|---|---|---|

d (Å) | 3.19 | 3.81 | 3.09 | 2.80 | 2.98 | 3.54 |

E_{b} (meV) | −67 | −61 | −66 | −71 | –70 | −62 |

E_{g} (eV) | 1.28 | 1.27 | 1.26 | 0.78 | 0.87 | 0.93 |

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**MDPI and ACS Style**

Yang, G.; Sun, R.; Gu, Y.; Xie, F.; Ding, Y.; Zhang, X.; Wang, Y.; Hua, B.; Ni, X.; Fan, Q.; Gu, X. The Electronic and Optical Properties of InSe-GeTe Heterobilayer via Applying Biaxial Strain. *Nanomaterials* **2019**, *9*, 1705.
https://doi.org/10.3390/nano9121705

**AMA Style**

Yang G, Sun R, Gu Y, Xie F, Ding Y, Zhang X, Wang Y, Hua B, Ni X, Fan Q, Gu X. The Electronic and Optical Properties of InSe-GeTe Heterobilayer via Applying Biaxial Strain. *Nanomaterials*. 2019; 9(12):1705.
https://doi.org/10.3390/nano9121705

**Chicago/Turabian Style**

Yang, Guofeng, Rui Sun, Yan Gu, Feng Xie, Yu Ding, Xiumei Zhang, Yueke Wang, Bin Hua, Xianfeng Ni, Qian Fan, and Xing Gu. 2019. "The Electronic and Optical Properties of InSe-GeTe Heterobilayer via Applying Biaxial Strain" *Nanomaterials* 9, no. 12: 1705.
https://doi.org/10.3390/nano9121705