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Scaling rules of piezoelectric nanowires in view of sensor and energy harvester integration R. Hinchet1, J. Ferreira2, J. Keraudy1, G. Ardila1*, E. Pauliac-Vaujour2, M. Mouis1, L. Montès1. IMEP-LAHC, MINATEC, 3 rue Parvis Louis Neel, 38016 Grenoble, France. 2) CEA-Leti, Grenoble, France. * Email: [email protected], *Phone: +334 56 52 95 32. Student paper – Area: Modeling and simulation

Introduction In the context of SoC and SiP integration of new functions such as sensors and energy harvesters has been identified as mandatory for the development of autonomous smart systems (1), this paper aims at providing general scaling rules allowing the potential of the different solutions to be clearly evaluated. Up to now, few MEMS solutions to mechanical energy harvesting (2) and sensing (3) exist. But due to their high aspect ratio, fair elasticity, good resistance to fatigue and high strain sensitivity, piezoelectric nanowires (NWs) are promising candidates for mechanical energy harvesting and sensing (4). This paper aims to explore their performance scaling in three (pressure, displacement and force) sensing modes and two (flexion and compression) mechanical input harvesting modes. It also highlights and accounts for variability, which is playing an increasing role at nanoscale. Scaling of an individual NW To assess the benefits of using piezoelectric NWs in future technologies, we first measured the piezoelectric potential generated by GaN and ZnO NWs using an AFM (Fig.1). The generated potential depended on NW geometry and material properties, in agreement with a previous study (5). We measured a significant output voltage, in the range of 100mV, proportional to the applied force (Fig.2). To analyze NWs scaling properties, we started by exploiting extensively the linear model of a bent piezoelectric NW (6, 7) in order to relate the geometrical and material dependent characteristics (esp. their radius r, length L, piezoelectric coefficients dij) to the main figures of merit applicable to sensors and energy harvesters. We defined 3 working hypotheses: constant force (F), constant bending (δ) and constant pressure (P). By scaling down piezoelectric materials, smaller forces are needed to

Fig. 1: a) Schematics of the AFM experience setup, b) AFM and c) SEM image of a GaN NW measured with AFM. Piezoelectric potential (mV)

Abstract This paper presents for the first time the scaling rules of piezoelectric nanowires (NWs), as the active transducer element for sensors and mechanical energy harvesters. Moreover, to keep close to realistic structures, non-linear effects associated to large displacements were taken into account, as well as the influence of NW variability, based on experimental data. We demonstrate that well-above-state-of-the-art sensitivities and resolutions can be achieved for sensing applications, and that large energy conversion efficiencies can be obtained for mechanical energy harvesters (about 7 times larger than that of their bulk counterpart).

Force applied (nN)

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Time (s) Fig. 2: Piezoelectric potential generated by a GaN NW bended at the end due to the force applied by an AFM tip (100mv @ 1400nN).

Fig. 3: Effect of the size scaling down of a ZnO cantilever in terms of axial strain, axial deformation and stiffness under fixed lateral force (80nN). Stiffness, is linearly decreasing as size decreases, allowing much larger strains to be reached under fixed force. This means that a smaller force is sufficient to reach a high deformation and strain in a NW, producing a given voltage. The reference NW (α=1) features r=25nm and L=600nm).

bend the nano-cantilevers (Fig.3). Fig.4 displays the potential profile generated in a (r=25nm, L=600nm) ZnO NW under bending. It highlights the necessity of contacting NWs in a

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Fig. 4: (a) Simulation of the piezo-potential generated in a bent ZnO NW in the linear regime. L=600nm, r=25nm, c-axis=+z, bending verifies δ