Piezo-Potential Generation in Capacitive Flexible Sensors Based on GaN Horizontal Wires
<p>(<b>a</b>) Scanning electron microscopy (SEM) image of metal organic vapour phase epitaxy (MOVPE) grown ultra-long wires (~300 µm) grown on sapphire substrate [<a href="#B23-nanomaterials-08-00426" class="html-bibr">23</a>]. (<b>b</b>) Schematics of the Boostream© process used for the wire assembly. (<b>c</b>) SEM image of about 300 µm long GaN wire encapsulated by a thin layer of Parylene-C after Boostream<sup>®</sup> assembly. (<b>d</b>) Schematics for the capacitive device structure using horizontally assembled GaN (in red) and parylene-C dielectric.</p> "> Figure 2
<p>(<b>a</b>) Stripes of GaN wires assembled with the Boostream<sup>®</sup> process. (<b>b</b>) Optical microscopy image of the wires. (<b>c</b>) Piezoelectric signal measured on three different regions of a flexible devices made of 104 µm long wires (see <a href="#nanomaterials-08-00426-f001" class="html-fig">Figure 1</a>d). The sensor is subjected to a cycled local compression load/release of 1 N/cm² on 1 cm-diameter disk at the speed of 900 mm/min.</p> "> Figure 3
<p>Schematics of the wire geometry (length <span class="html-italic">L</span> and conicity angle α) and definition of axes. The left inset gives a front view of the simulated structure consisting of a single conical wire embedded into a dielectric layer of height <span class="html-italic">h</span> and with <span class="html-italic">w</span>. The right inset is a front view of the conical wire showing its top and bottom diameter <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>b</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>.</p> "> Figure 4
<p>Maximum displacement and output voltage as function of the curvature radius <math display="inline"><semantics> <mi mathvariant="sans-serif">ρ</mi> </semantics></math> for a single wire embedded in a capacitive structure. The maximum displacement occurs at the wire extremities and the potential value is taken at the middle of the top facet of the wire (see point M in <a href="#nanomaterials-08-00426-f003" class="html-fig">Figure 3</a>).</p> "> Figure 5
<p>Calculated potential along the top dielectric facet with <span class="html-italic">L</span> = 120 and 200 µm long wires embedded in <span class="html-italic">h</span> = 2 µm dielectric layer with α = 1° conicity angle and <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">ρ</mi> <mo>=</mo> </mrow> </semantics></math> 10 cm curvature radius bending.</p> "> Figure 6
<p>(<b>a</b>) Piezo-potential calculated at center of the wire as a function of the wire length for α = 1° and <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">ρ</mi> <mo>=</mo> </mrow> </semantics></math> 10 cm curvature radius; (<b>b</b>) the related variation of the wire surface and volume.</p> "> Figure 7
<p>Two-dimensional finite element calculation of non-conical (α = 0°) and conical (α = 1°) embedded GaN wires bended under 10 cm radius curvature. (<b>a</b>) Piezoelectric charge density mappings (note the different scales along X and Y). (<b>b</b>) Piezo-potential taken at the top m-plane facet al.ong the length for (lines) and the corresponding cross-section mappings of the potential across the structure in insets.</p> "> Figure 8
<p>Time-dependent behaviour of the wire-based sensor obtained by finite element modelling simulation for a structure with a single cone-shaped wire of 120 µm length and 1° conicity angle under 10 cm curvature radius bending. The voltage is taken on the top electrode while the bottom is grounded. The inset shows the equivalent electrical circuit of the device. (<span class="html-italic">R</span><sub>1</sub>, <span class="html-italic">C</span><sub>1</sub>) correspond to the internal impedance of the sensor and (<span class="html-italic">R</span><sub>C</sub>, <span class="html-italic">C</span><sub>C</sub>) to the measurement setup.</p> "> Figure 9
<p>(<b>a</b>) Piezo-potential evolution as function of the conicity angle <math display="inline"><semantics> <mi mathvariant="sans-serif">α</mi> </semantics></math> for wires with <span class="html-italic">L</span> = 50, 120, 200 µm and and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>700</mn> <mo> </mo> <mi>nm</mi> </mrow> </semantics></math>. (<b>b</b>) The related variation of the surface over volume ratio.</p> "> Figure 10
<p>(<b>a</b>) Schematics of a regular horizontal assembly of wires. (<b>b</b>) Elementary cell structure composed of two wires illustrating the boundary condition calculation method.</p> "> Figure 11
<p>(<b>a</b>) Schematics of the wire relative crystallographic orientation: (<b>a</b>) parallel and (<b>b</b>) anti-parallel configurations of the <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>c</mi> <mo>¯</mo> </mover> </mrow> </semantics></math> growth axis. The m-planes of GaN are parallel to the bottom electrode. The black arrows in the center of the wires are the in-plane representations of the equivalent electric dipoles schematized in <a href="#nanomaterials-08-00426-f007" class="html-fig">Figure 7</a>. (<b>b</b>) Potential per surface area measured between metal electrodes as function of wire inter-distance d for parallel and anti-parallel configuration of the wire orientation. A bending deformation of 10 cm curvature radius is applied to the bottom part of the simulated structure.</p> "> Figure 12
<p>Surface potential as function of the parameter <span class="html-italic">h/d</span> for a two-wires in parallel and anti-parallel configurations under a bending with <math display="inline"><semantics> <mi mathvariant="sans-serif">ρ</mi> </semantics></math> = 10 cm curvature radius. The potential is taken at the top electrode while the bottom one is grounded (see <a href="#nanomaterials-08-00426-f008" class="html-fig">Figure 8</a>). The graph focuses on values of <span class="html-italic">h/d</span> lower than 1. The inset graph shows a zoom out for the whole range of values of <span class="html-italic">h/d</span> from 0.25 to 8.</p> "> Figure 13
<p>(<b>a</b>) Schematics of three in-plane arrays of two-dimensional wire assemblies. The black arrows sketch the equivalent electric dipoles shown in <a href="#nanomaterials-08-00426-f007" class="html-fig">Figure 7</a> and <a href="#nanomaterials-08-00426-f011" class="html-fig">Figure 11</a>. (<b>b</b>) Comparison of the evolution of the normalized potential by unit surface as function of <span class="html-italic">h/d</span> for configurations shown in (<b>a</b>). The value of <span class="html-italic">h</span> is fixed at 2 µm while d is varied between 2 and 10 µm.</p> ">
Abstract
:1. Introduction
2. Experiments: Piezoelectricity Measurements on Horizontal Capacitive GaN Wires Devices
- What is the physical nature of the piezoelectric signal measured in these capacitive flexible devices based on horizontal GaN wires? What is the role of the size and shape of the wires and the role of the bending amplitude?
- What is the role of the wire density, orientation and interaction?
- What are the best wire features in terms of geometry and configuration to be used in the flexible capacity devices?
3. Finite Element Modelling of Piezo-Potential Generation in Single GaN Wires
3.1. Method: Geometry and Physical Parameters
3.2. Method: Bending Deformation and Potential Generation
3.3. Potential Generation Dependence as a Function of Wire Length at Fixed Conicity
3.4. Potential Generation Dependence as a Function of Wire Conicity at Fixed Length
4. Finite-Element Modelling of the Complete Capacitive Stacking with Metallic Contacts and Wire Assemblies
4.1. Method: Simulated Structure and Calculation of Periodic Boundary Conditions
4.2. Screening of Electric Fields in a One-Dimensional Network
4.3. Screening of Piezoelectric Fields in a Two-Dimensional Network
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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El Kacimi, A.; Pauliac-Vaujour, E.; Delléa, O.; Eymery, J. Piezo-Potential Generation in Capacitive Flexible Sensors Based on GaN Horizontal Wires. Nanomaterials 2018, 8, 426. https://doi.org/10.3390/nano8060426
El Kacimi A, Pauliac-Vaujour E, Delléa O, Eymery J. Piezo-Potential Generation in Capacitive Flexible Sensors Based on GaN Horizontal Wires. Nanomaterials. 2018; 8(6):426. https://doi.org/10.3390/nano8060426
Chicago/Turabian StyleEl Kacimi, Amine, Emmanuelle Pauliac-Vaujour, Olivier Delléa, and Joël Eymery. 2018. "Piezo-Potential Generation in Capacitive Flexible Sensors Based on GaN Horizontal Wires" Nanomaterials 8, no. 6: 426. https://doi.org/10.3390/nano8060426