# Piezoelectric Potential in Single-Crystalline ZnO Nanohelices Based on Finite Element Analysis

^{1}

^{2}

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_{2}Based Nanostructures)

## Abstract

**:**

## 1. Introduction

## 2. Model and Method

#### 2.1. Model Configuration

#### 2.2. FEM Modeling of Nanowires and Nanohelices

^{®}. The bottom face of the nanowire and the nanohelix was fixed and electrically grounded in our model. A force was applied only to the top end, and the piezoelectric potential was numerically calculated. A nanowire and a nanohelix with the same side length and height were simulated to compare their piezoelectric potentials when exposed to the same force. A series of nanohelices with different numbers of coils and mean radii of the coil were calculated to reveal the change of piezoelectric potential in a helical structure. The effect of force direction was also investigated.

## 3. Simulation Results and Discussion

#### 3.1. Pizeoelectric Potential and Displacement of the ZnO Nanohelix and Nanowire

#### 3.2. Effect of the Number of Coils and the Mean Radius of the Coil on the Pizeoelectric Potential of a Nanohelix

#### 3.3. Effect of Acting Forces on the Pizeoelectric Potential and Displacement

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic illustration of (

**a**) ZnO nanowire and (

**b**) ZnO nanohelix. Both nanostructures have a hexagonal cross-section with the same side length D and height L. The nanohelix has a number of coils T and a mean radius of coil R.

**Figure 2.**The piezoelectric potential distribution in (

**a**) ZnO nanowire and (

**b**) nanohelix under a compressing force of 100 nN along the z-axis.

**Figure 3.**The change of the maximum piezoelectric potential and displacement with the number of coils in (

**a**) and the mean coils radius in (

**b**) of ZnO nanohelices with a constant length of 1900 nm.

Parameters | Value |
---|---|

Density (kg/m^{3}) | 5680 |

Elastic constants | |

c_{11} (GPa) | 209.7 |

c_{12} (GPa) | 121.1 |

c_{13} (GPa) | 105.1 |

c_{33} (GPa) | 211.3 |

c_{44} (GPa) | 42.3 |

c_{55} (GPa) | 43.6 |

Piezoelectric constants | |

e_{31} (C/m^{2}) | −0.57 |

e_{33} (C/m^{2}) | 1.32 |

e_{15} (C/m^{2}) | −0.48 |

Relative dielectric constants | |

${\kappa}_{\perp}^{r}$ | 8.54 |

${\kappa}_{\parallel}^{r}$ | 10.20 |

Applied Force Components (nN) | Piezoelectric Potential (V) | Displacement (nm) | ||
---|---|---|---|---|

x-Axis | y-Axis | z-Axis | ||

0 | 0 | 100 | 1.85 | 10.2 |

0 | 100 | 0 | 0.35 | 48.3 |

100 | 0 | 0 | 0.29 | 47.3 |

100 | 100 | 0 | 0.48 | 67.8 |

100 | 0 | 100 | 1.85 | 37.6 |

0 | 100 | 100 | 1.60 | 49.4 |

100 | 100 | 100 | 1.60 | 61.6 |

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## Share and Cite

**MDPI and ACS Style**

Hao, H.; Jenkins, K.; Huang, X.; Xu, Y.; Huang, J.; Yang, R.
Piezoelectric Potential in Single-Crystalline ZnO Nanohelices Based on Finite Element Analysis. *Nanomaterials* **2017**, *7*, 430.
https://doi.org/10.3390/nano7120430

**AMA Style**

Hao H, Jenkins K, Huang X, Xu Y, Huang J, Yang R.
Piezoelectric Potential in Single-Crystalline ZnO Nanohelices Based on Finite Element Analysis. *Nanomaterials*. 2017; 7(12):430.
https://doi.org/10.3390/nano7120430

**Chicago/Turabian Style**

Hao, Huimin, Kory Jenkins, Xiaowen Huang, Yiqian Xu, Jiahai Huang, and Rusen Yang.
2017. "Piezoelectric Potential in Single-Crystalline ZnO Nanohelices Based on Finite Element Analysis" *Nanomaterials* 7, no. 12: 430.
https://doi.org/10.3390/nano7120430