Length and polarity dependent saturation of the electromechanical response of piezoelectric semiconducting nanowires

Abstract

The question of the length dependence of the electromechanical response of semiconducting piezoelectric NWs was explored. We identified a new physical mechanism of piezoresponse saturation, which originates from the combination of the influence of interface traps and piezoelectric polarization in the depleted NW. Our results are in better qualitative agreement with experimental observations than presently existing theories. To do so, we used the Finite Element Method to simulate the coupled set of equations describing mechanical, piezoelectric and semiconducting properties. In order to reduce the number of parameters, simulations focused on the case of uniform ZnO nanowires grown along the c-axis. Saturation was explained by the incapacity of surface traps to maintain depletion along the whole NW beyond a certain length, as a result of the electric potential shift induced by piezoelectric polarization. An analytical model was developed to support this analysis. It provided the dependence trends of saturation length and piezoresponse as a function of NW dimensions, doping level, surface traps density and crystal polarity, as well as with external pressure, in fair agreement with simulation results. Moreover, we discovered that one consequence of this mechanism was that crystal polarity had an impact on the smoothness of the radius-dependent transition between high and low piezoresponse under axial stress. These results have important implications for the optimization of electromechanical sensors and nanogenerators based on piezoelectric semiconducting NWs and related composite materials.

Piezo‐Semiconductor Coupled Model for the Simulation of Zinc Oxide 1–3 Piezo‐Composite

“…For the studies without surface traps, this model is close to previous ones [ 15,23 ] but when we add surface traps, this model differs from the others [ 17,24 ] because the recombination of free electrons assisted by surface traps is modeled without surface charges (see Section 3.2 for more details). In our model, it is also possible to specify the energy level of these traps in the SC gap.…”

“…This model differs from those previously published in the literature [ 12,17,23,24 ] that consider surface charge density as a consequence of the surface traps presence.…”

“…where C n is the average capture probability of an electron, f t the occupancy factor of the traps (in this study, equal to one-half), g D the degeneracy factor (in this study, equal to one),  F,n the ndoped Fermi energy level, k B the Boltzmann's constant and T the temperature. This model differs from those previously published in the literature [12,17,23,24] that consider surface charge density as a consequence of the surface traps presence.…”

Influence of the AZO Electrode on ZnO Nanowire Growth by PLI-MOCVD and Related Piezoelectric Performance: Implications for Mechanical Energy Transducers

“…The other factor that could also affect the results is the dimensions of NWs. For instance, the NWs grown on AZO thin films exhibit a slightly greater length (Table ), leading to a more effective impact of surface traps depleting the NW from its surface and thus enhancing the piezoelectric performance. − Conversely, the NWs on the AZO10 thin film are notably larger than others; in this case, the surface traps induced depletion is less effective, resulting in a decreased piezoelectric performance …”

ZnO nanowires-based piezoelectric energy transducers: the role of size and semiconducting properties

“…From a theoretical point of view, the role of the length and diameter of the NWs on the direct piezoelectric effect (i.e., induced voltage by the application of strain) were studied for vertically integrated nanogenerators (VINGs), in particular including the surface trap density and doping levels. [22][23][24] The converse piezoelectric effect is rarely studied including the PFM configuration, where the free charge carriers and surface traps are excluded. However, it is found that the surface traps greatly affect the piezoelectric properties.…”