Evaluation of Vertical Integrated Nanogenerator Performances in Flexion

Piezoelectric nanowires have attracted great interest as new building blocks of mechanical energy harvesting systems. This paper presents the design improvements of mechanical energy harvesters integrating vertical ZnO piezoelectric nanowires onto a Silicon or plastic membrane. We have calculated the energy generation and conversion performance of ZnO nanowires based vertical integrated nanogenerators in flexion mode. We show that in flexion mode ZnO nanowires are superior to bulk ZnO layer. Both mechanical and electrical effects of matrix materials on the potential generation and energy conversion are discussed, in the aim of guiding further improvement of nanogenerator performance.


Introduction
Recently, piezoelectric nanowires (NWs) have attracted great interest as the fundamental building blocks for future electronic autonomous devices. Their unique electrical and mechanical properties can be exploited advantageously for applications such as sensors [1], piezoelectric diodes [2] and energy harvesting devices [3]. Among the latter, nanogenerators (NGs) have received much attention, where piezoelectricity is employed to convert mechanical energy to electrical energy for the operation of low-power electronics [4]. Given that the size-induced enhancement of electromechanical properties has been primarily reported for piezoelectric NWs [5], the development of new experimental, computational, and theoretical approaches is required to meet challenges at nanoscale. In this work, finite element method (FEM) simulations are used to calculate the energy generation and conversion performance of ZnO NWs based energy harvesters. The design of the devices is based on the Vertically Integrated NanoGenerator (VING) as proposed in [6].

Nanogenerator structure
The energy harvesting device (Figure 1) consists of a VING structure sandwiched between two aluminium electrodes on a substrate. The 1cm × 1cm substrate is made of silicon or plastic membrane: the former is compatible with current electric circuits and devices, while the latter is more flexible and adaptable to future independent self-powered nanosystems. As a continuation of previous work [7], Si membrane was used to calculate the strain distribution under given pressure. The functional core structure of the NG is the piezoelectric NWs integrated into a thin insulating PMMA layer. The NWs grow along their c-axis on a thin ZnO seed layer deposited using spattering. Si 3 N 4 insulating layers with no internal strain avoid the short circuit and increase NG robustness. We have previously evaluated NGs under compression [7]. Here we extend the study to a flexion mode using a thin membrane as a mechanical transducer. The hydrostatic pressure generates a force bending the membrane, compressing the NW from the sidewalls.

Nanogenerator operation and modelling assumptions
Under strain, the NW active layer of the VING structure generates a potential difference which can be used to power an external circuit by means of a capacitive displacement current.
The hypothesis of an applied hydrostatic pressure is applied over the membrane structure ( Figure  1). The main issue compared to previews studies [7] is how the constraint is transferred to the NW. For this reason, although the active part of the device is made of millions of NWs integrated into a polymer matrix, in this study only a single core cell of the device was considered (Figure 2c) with appropriate boundary conditions for fast and reliable FEM modeling.
When the device membrane is under flexion, the NG core cell is compressed laterally and extended along the c-axis ( Figure 2). In the core cell, the energy conversion mechanism has been divided into 3 steps [7]: mechanical energy transfer, mechanical to electrical energy conversion and, finally, electrical energy transfer to the output circuit. In the first step, the total input mechanical energy ξ is considered to be composed of two parts. One (ξ 1 ) is the energy stored in the Si 3 N 4 layers, and the other (ξ 2 ) is the energy stored in the NW/PMMA compound. The energy that reaches the core NW is used in the piezoelectric transfer process (ξ 3 ). Thus, the mechanical energy transfer efficiency is expressed as η m =ξ 3 /(ξ 1 +ξ 2 ), where ξ 1 is supposed to be a constant. Thus the major influencing factor is the ratio of ξ 3 and ξ 2 , whose reciprocal increases with (w 2 E NW )/(w 1 E PMMA ) where w 1 and w 2 are geometrical parameters (see Figure 2) and E is the Young Modulus. The energy conversion efficiency η p of the second step depends on the NW's electromechanical properties and is proportional to the square of piezoelectric strain constant e 33 2 [7]. The third step brings dielectric losses to our device with the efficiency (η p ) defined as 1/(1+d 1 ε 2eq /d 2 ε 1 ), where d is a geometrical parameter (see Figure 2), ε 2eq and ε 1 are the relative permittivity of the NW/matrix compound and the Si 3 N 4 layer respectively. Finally the total conversion efficiency is the product of the three individual step efficiencies.

Simulation
FEM simulations of the device were performed. The coupling between the mechanical, electrical and piezoelectric equations was considered for a core NG cell. The input impact described by the strain in the cell was calculated from a 2D model of the membrane. Because the NW layer was far from neutral plane, the hydrostatic pressure generated constant strain at sidewalls of each cell along c-axis. We calculated that the NW/PMMA layer had a vertically homogeneous strain of -9.36×10 -4 (within linear deformation) when the device is bent by a hydrostatic pressure of 1.8 kPa, which is the limit of the linear deformation regime. The cell size was 100nm × 100nm × 850nm, with NW radius r=25nm and length L=600nm. Young's modulus, Poisson's ratio (υ) and relative permittivity of the matrix material were varied around parameters of PMMA in order to investigate optimization trends. Several real insulating compounds were used as the matrix material. Their functions on potential generation and energy conversion were compared with each other, as well as with a ZnO layer (the thickness is 118 nm) which has the same volume as ZnO NW. Analysis is focused on the displacement, the strain tensor S xx and the electric potential distributions. The hardness of the matrix material results in two different types of distribution of the displacement and the strain. When a soft matrix material (PMMA) was used, the matrix was more compressed than the NW as indicated by the displacement distribution (Figure 3a). The strain tensor S xx distribution (Figure 3b) shows that strain was concentrated in the matrix material instead of the NW. The opposite resulted when a hard matrix (Al 2 O 3 ) was used (Figure 3c) and strain is concentrated in the NW (Figure 3d). This is consistent with the mechanical energy transfer efficiency (η m ) defined in section 3. As the Young's modulus of the matrix material increases, the efficiency increases. More mechanical energy is transferred into the core NW, influencing the final potential and energy generation. Several insulating matrix materials were considered to improve the NG performances. In the simulations, the total volume of ZnO was kept constant. The potential (Figure 4) was calculated along the central axis of the NG cell. From simulations, the potential generation ability of bulk ZnO (yellow line) is weaker than that of NW based NG cells. Zones (1) and (4) correspond to the Si 3 N 4 insulating layers, where dielectric losses are unavoidable. Zone (2) corresponds to the thin seed ZnO layer, while zone (3) is corresponding to the NW layer. Globally, the NG cell with harder matrix materials (Al 2 O 3 , Si 3 N 4 ) generated higher potential.
To clarify the energy transfer process, Young's modulus, Poisson's ratio and relative permittivity of matrix materials were varied independently. The former two parameters mainly influence the mechanical energy transfer and slightly affect the piezoelectric energy transfer. The relative permittivity affects the electrical energy transfer to the output circuit. Mechanical and electrical parameters of real matrix materials are listed in Table 1. First, the effects of Young's modulus and Poisson's ratio on the potential generation were compared ( Figure 5). The curves were plotted against one parameter while the two others were kept equal to that of PMMA. As the value of Young's modulus spans from 3GPa (PMMA) to 400GPa (Al 2 O 3 ), the potential increases from 0.8V to 4.4V. In contrast, varying from 0.17 to 0.40, the change of Poisson's ratio only brings a potential difference of 1V. The relationship between the relative permittivity and the electric potential is more complex. In fact, the relative permittivity of the matrix material is not the direct factor that influences the electrical energy transfer process. Efficiency η e decreases with increasing ε eq of the matrix/NW compound. Here ε eq is not a linear combination of the permittivity of the NW and the matrix. As a result, the potential curve reaches a maximum value when the permittivity is close to 2.5 ( Figure 6). Considering that the relative permittivity of real matrix materials varies from 2.09 (SiO 2 ) to 9.7 (Si 3 N 4 ), the potential variation is less than 0.5V. In the simulation, the effect of Young's modulus is more significant than the effects of Poisson's ratio and relative permittivity.
Poisson's ratio Position along the central axis (m) Young's modulus (GPa)   The relationship between Young's modulus and the energy transfer process is discussed in Figure  7, 8 and 9. The solid line represents the simulation results of a material with fixed Poisson ratio (0.4) and relative permittivity (3.0) changing with increasing Young's Modulus, while the symbols represent simulation results for real matrix materials. At constant input strain, the strain energy is proportional to the equivalent Young's modulus of the matrix/NW compound, which means that more strain energy is needed to compress the NG cell with harder matrix material. With constant Poisson's ratio and relative permittivity, the total electric energy mainly benefits from the high mechanical energy transfer efficiency at high E. For hard materials, large relative permittivity reduces the electrical energy transfer to the output circuit. For PMMA, the low relative permittivity decreased the dielectric losses. The total energy conversion efficiency η is calculated by: Within the different materials investigated, SiO 2 achieved the highest conversion efficiency with low relative permittivity and medium hardness. The design has to be a compromise between mechanical energy transfer and electrical energy transfer. Low mechanical energy transfer obtained with soft materials can be translated into a low sensitivity of the device to external forces. On the other hand, low electrical energy transfer obtained with hard material (they usually have high relative permittivity) can increase the dielectric losses.

Conclusion
In this article, we have evaluated a VING structure working in flexion mode for the first time. The effect of matrix materials on NG cells was analyzed using FEM simulations, in order to improve the device performance. Comparing with PMMA, a NG cell using an aluminum oxide matrix improves the potential by two times and the electric energy by six times which is essential for energy harvesters.
On the other hand, silica glass will increase the energy conversion efficiency and could be better used in sensors applications.

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Relative permittivity Young's modulus of matrix material (GPa) Figure 6. Potential changing with the increasing relative permittivity of matrix materials

Acknowledgement
This work has been supported by CNRS INSIS Institute within the framework of Exploratory Projects on energy.