# Electronic, Optical, and Thermoelectric Properties of Bulk and Monolayer Germanium Tellurides

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}Te

_{3}.

## 2. Computational Methods

#### 2.1. DFT Parameters

#### 2.2. Optical Coefficients

#### 2.3. Thermoelectric Transport Coefficients

## 3. Results and Discussion

#### 3.1. Electronic Band Structures

#### 3.2. Absorption Spectra

^{6}cm

^{−1}, which is better than most of low-dimensional solar-cell materials for the visible light [46]. However, it is clear that either puckered or buckled GeTe has stronger absorption coefficient peaks than their bulk counterparts. We notice that, within the same approximation, the monolayer GeTe has better absorption than the celebrated monolayer transition metal dichalcogenides [47] in the visible-light regime by almost one order of magnitude. The monolayer phases also exhibit moderate anisotropy in absorption coefficients for the in-plane polarization direction. Regardless, in the near-infrared to the ultraviolet regime, the absorption coefficients for all of the GeTe variants in all directions of the linearly polarized light stay within 1–2 × 10

^{6}cm

^{−1}. Comparing the joint DOS in Figure 3d with the absorption coefficients, it is interesting to see that only in buckled GeTe, the JDOS contributes strongly to the absorption coefficient in the visible-light regime. This feature can be traced back to the presence of stronger van Hove singularity in buckled GeTe than in the puckered GeTe, while the bulk GeTe phases do not possess any van Hove singularity.

#### 3.3. Thermoelectric Properties

## 4. Conclusions

^{6}cm

^{−1}, which is better than the absorption in most solar-cell materials. The absorption coefficients for the in-plane direction of the GeTe monolayers, in particular, have larger values than those of the bulk GeTe phases. As for thermoelectric properties, the GeTe monolayers also give better performance than their bulk counterparts with $ZT>1$ theoretically due to the survival of the band convergence, larger band gaps (for larger Seebeck coefficients), and quantum confinement effect, which gives a unique DOS for providing more available states of electronic conduction.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Lattice structures of (

**a**) bulk and (

**b**) monolayer GeTe. Bulk GeTe consists of cubic and rhombohedral lattices, while monolayer GeTe consists of puckered and buckled honeycomb lattices. The structural models are visualized by using VESTA [30].

**Figure 2.**Energy dispersion and density of states (DOS) of (

**a**) bulk cubic, (

**b**) bulk rhombohedral, (

**c**) puckered monolayer, and (

**d**) buckled monolayer GeTe. The DOS is expressed in arbitrary units for clarity since we do not need the details of the number of states per energy.

**Figure 3.**Optical properties of bulk and monolayer GeTe. Panels (

**a**–

**c**) give the absorption coefficients for light polarization along the x-, y-, and z-axes. Panel (

**d**) shows the joint density of states. Two vertical lines at $1.61$ eV and $3.10$ are the borders of the visible-light regime. Below $1.61$ eV (above $3.10$ eV) is the infrared (ultraviolet) regime.

**Figure 4.**Thermoelectric properties of bulk and monolayer GeTe calculated from band structure information: (

**a**) Seebeck coefficient, (

**b**) electrical conductivity, (

**c**) electronic thermal conductivity, and (

**d**) ideal figure of merit. Note that the electrical conductivity and electronic thermal conductivity are scaled by relaxation time constant $\tau $. Considering a possible phase transition at $T=700$ K, we set two different values of temperature: $T=900$ K for bulk cubic and monolayer buckled GeTe; and $T=500$ K for bulk rhombohedral and monolayer puckered GeTe.

**Table 1.**Lattice constants (in Å) of bulk and monolayer GeTe. The lattice constants (a, b, c) and angles ($\alpha $, $\beta $, $\gamma $) are in accordance to the illustrations in Figure 1.

GeTe Structure | This Work | Reference Data |
---|---|---|

cubic (bulk) | $a=b=c=4.370$, | $4.178$ [31], $4.228$ [5], $4.281$ [32] |

$\alpha =\beta =\gamma =60.{00}^{\circ}$ | ||

rhombohedral (bulk) | $a=b=c=4.249$, | $4.230$ [20], $4.260$ [31], $4.246$ [5] |

$\alpha =\beta =\gamma =57.{85}^{\circ}$ | ||

puckered (monolayer) | $(a=4.238,\phantom{\rule{3.33333pt}{0ex}}b=4.382$) | ($4.273$, $4.472$) [19] |

buckled (monolayer) | $a=b=3.961$ | $3.950$ [33], $3.955$ [34], $3.960$ [20,24] |

**Table 2.**Calculated band gaps of bulk (cubic and rhombohedral) and monolayer (puckered and buckled) GeTe using the ONCV-GGA and HSE methods.

Method | Cubic | Rhombohedral | Puckered | Buckled |
---|---|---|---|---|

ONCV-GGA | $0.38$ | $0.57$ | $0.90$ | $1.81$ |

HSE | $0.60$ | $1.08$ | $1.30$ | $2.60$ |

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**MDPI and ACS Style**

Sinambela, W.V.; Wella, S.A.; Arsyad, F.S.; Hung, N.T.; Nugraha, A.R.T. Electronic, Optical, and Thermoelectric Properties of Bulk and Monolayer Germanium Tellurides. *Crystals* **2021**, *11*, 1290.
https://doi.org/10.3390/cryst11111290

**AMA Style**

Sinambela WV, Wella SA, Arsyad FS, Hung NT, Nugraha ART. Electronic, Optical, and Thermoelectric Properties of Bulk and Monolayer Germanium Tellurides. *Crystals*. 2021; 11(11):1290.
https://doi.org/10.3390/cryst11111290

**Chicago/Turabian Style**

Sinambela, Wenny V., Sasfan A. Wella, Fitri S. Arsyad, Nguyen Tuan Hung, and Ahmad R. T. Nugraha. 2021. "Electronic, Optical, and Thermoelectric Properties of Bulk and Monolayer Germanium Tellurides" *Crystals* 11, no. 11: 1290.
https://doi.org/10.3390/cryst11111290