Surface Charge: An Advantage for the Piezoelectric Properties of GaN Nanowires

: The optimization of the new generation of piezoelectric nanogenerators based on 1D nanostructures requires a fundamental understanding of the different physical mechanisms at play, especially those that become predominant at the nanoscale regime. One such phenomenon is the surface charge effect (SCE), which is very pronounced in GaN NWs with sub-100 nm diameters. With an advanced nano-characterization tool derived from AFM, the influence of SCE on the piezo generation capacity of GaN NWs is investigated by modifying their immediate environment. As-grown GaN NWs are analysed and compared to their post-treated counterparts featuring an Al 2 O 3 shell. We establish that the output voltages systematically decrease by the Al 2 O 3 shell. This phenomenon is directly related to the decrease of the surface trap density in the presence of Al 2 O 3 and the corresponding reduction of the surface Fermi level pinning. This leads to a stronger screening of the piezoelectric charges by the free carriers. These experimental results demonstrate and confirm that the piezo-conversion capacity of GaN NWs is favoured by the presence of the surface charges.


Introduction
The development of new ultracompact and highly efficient energy harvesting technologies is a key worldwide challenge, spurred by the constantly increasing use of portable smart objects both in our daily lives, as well as in high-tech applications.Among the available sources of renewable energies, mechanical deformations and vibrations originating from bodily or vehicular movements, acoustic waves, displacing fluids or friction present the advantage of being ubiquitous, available at all times and highly suitable for multiscale integration.These can be converted into an electrical output via piezoelectric systems.
In this context, nano-generators integrating piezoelectric nanowires (NWs) represent a very promising alternative compared to conventional piezo-generators based on 2D or bulk materials.In fact, thanks to their large aspect ratio and quasi-perfect crystalline quality, NWs are characterised by superior mechanical and piezoelectric properties [1][2][3].In addition, NWs characterised by sub-100 nm diameters exhibit nanometre-scale phenomena, opening up new possibilities for the modulation of their properties.
The first demonstration of direct piezoelectric conversion from 1D nanostructures was evidenced with ZnO NWs [4].Following the establishment of this new concept, other piezoelectric nanostructures have demonstrated their ability to convert a mechanical input into an electrical signal, such as PZT [5], CdS [6], CdSe [7], BaTiO 3 [8], KNBO 3 [9], GaAs [10], Nanoenergy Adv.2024, 4 134 Ga(In)N [11][12][13] and ZnO [4,14,15], the widely used semiconductor in NW-based piezo nanogenerators.Particularly, output signals up to 470 mV per nanowire [12] have been reported.Rapidly, nanogenerators integrating NWs have been demonstrated based on two main configurations: the lateral nanowire integrated nanogenerators (LINGs) and the vertical nanowire integrated nanogenerators (VINGs) [16].While these nanogenerators can deliver output power densities reaching up to a few tens of µW/cm 2 or a few mW/cm 3  under laboratory conditions [17][18][19][20][21][22][23][24], their piezoelectric response remains very sensitive to their measurement conditions and environment.This sensitivity is due to a number of physical phenomena that become predominant in the nanoscale regime.Therefore, the enhancement of the piezoelectric coefficients [25][26][27], or the formation of nanocontact at the NW/electrode interface leading to an enhanced energy harvesting [28], have been demonstrated.Only a deep understanding of all the phenomena in play can allow fine control of the piezoelectric response of these nanostructures and, more largely, a suitable device performance optimization.
The purpose of this paper is to address one important phenomenon particularly pronounced in sub-100 nm wide GaN [29][30][31][32]: the surface charge effect (SCE).This effect is associated with the abrupt interruption of the atomistic structure of a material at its surfaces, where the absence of neighbouring atoms results in a different electron density as compared to the bulk.This leads to the creation of new electronic states within the semiconductor bandgap, commonly known as surface charges (SCs) [33].
The presence of these surface charges creates an energetically unfavourable situation, where charge neutrality is required to achieve stabilization at the Fermi level [33].Consequently, a charge transfer occurs between the surface and the bulk of the material, resulting in the creation of a space charge region at the interface, commonly referred to as the depletion layer.The width of this layer is a function of the doping level of the material [34].Thus, a built-in electric field is created at the interface, and a strong band bending occurs associated with the alignment of the surface and bulk Fermi levels (also defined as surface Fermi level pinning (SFLP)) [34][35][36][37][38].
Unlike bulk materials, the SFLP can partially or even fully deplete sub-100 NWs, inducing a local decrease in the diffusivity of the free charge carriers and, consequently, of their conductance [39,40].The origin of these surface charges might vary from one system to another.In GaN NWs, they originate mainly from covalent dangling bonds [29], bistable defects [41], nitrogen anti-sites or Ga vacancies [34,42,43].In contrast, in ZnO NWs, surface charges appear due to stabilization processes, including reconstruction, impurities and chemical adsorbates incorporation [44].The absorption of dioxygen atoms, which act as electron acceptors, is favoured [45,46].In GaN, Ga-O surface bonds seem to be at the origin of the strong surface trap density [45].
While the surface charges are detrimental for the optoelectronic device performance, they present an advantage for piezoelectric applications.In semiconductor materials presenting piezoelectric properties, free charge carriers are known to degrade the piezoelectric response by screening the generated piezo-charges [47][48][49].This phenomenon has been evidenced in ZnO [50][51][52] and GaN [48] NWs.The advantageous role of the SCE is clearly illustrated in chemically synthesised ZnO NWs.In fact, these 1D nanostructures grown by hydrothermal-based synthesis methods are generally characterised by a strong intrinsic doping [53,54] sufficiently high to screen the quasi-totality of the piezo-charges.However, a non-negligible piezo-response has been reported by several groups [14,[55][56][57].This unexpected response results from the presence of surface traps and, thus, the resulting SFLP, limiting free carrier diffusion and leading to lower piezo-charge screening.Consequently, the internal piezoelectric field within the ZnO NWs increases, allowing for a piezoelectric response to be harvested [49].
While nanogenerators integrating NWs have been investigated for almost two decades, only a few papers have considered the crucial role of the SCE.The first exploration of this effect dates back to 2018, with theoretical simulations reported by Tao et al. [49].In this study, the piezo-potential variation in the NWs was simulated as a function of the charge carrier concentration, NW morphology and pinning conditions.Considering the SFLP, an increase in the NW's piezo-potential by a factor of 10 to 16 times was observed as compared to NWs without SFLP.More recently, the relationship between the surface charge effect and the piezoelectric response of the NWs as a function of their diameter has been demonstrated.In ZnO NWs, the group of G. Ardila [57] observed variations in the piezoelectric coefficient d 33 as a function of the NW diameter.In GaN NWs, our group has demonstrated the enhancement of the piezoelectric coupling coefficient from 5% to 43% by taking advantage of the surface charges, with pronounced effects for a specific NW diameter window [58].In both these cases, the enhancement of the piezoelectric response is linked to the decrease in NW diameter, leading to its depletion and limiting the diffusion of surface-free carriers within the material, thus mitigating their screening impact.
Surface charges and trap densities have been reported to be of the order of 10 12 -10 13 cm −2 , as determined though electrical and optical characterization techniques [30][31][32].These characteristics are inherent to the material itself and the nanostructure growth mode [40].Notably, they exhibit strong sensitivity to the nanostructure environment.Consequently, a limited number of research groups have undertaken the functionalization of nanostructures to modulate the piezoelectric responses of the nanogenerators.Strategies such as gas adsorption or nanoparticles deposition onto the NW surface have been employed for this purpose, as demonstrated by X. Xue et al. [47] and S. Lu et al. [59].These approaches aim to modulate the depletion width within the NWs, thereby reducing the effective screening.
In the present study, we investigate the influence of SCE on the piezo generation capacity of GaN NWs by modifying their immediate environment.Both as-grown GaN NWs and post-treated NWs with an atomic layer deposition treatment to form an Al 2 O 3 shell surrounding the GaN NW core are considered.To ensure that the expression of the surface charge is solely influenced by the NW environment, the investigated GaN NWs maintain an approximately constant diameter.To assess the impact of the surface charges on the piezoelectric response, an advanced nano-characterization tool derived from atomic force microscopy (AFM) in employed.
Based on experimental measurements, we highlight that, for an equivalent deformation rate, the average output voltages are consistently lower for GaN/Al 2 O 3 core-shell NWs compared to bare GaN NWs.This observed behaviour aligns with the reduction in the surface trap density in presence of the Al 2 O 3 shell.As the surface Fermi level pinning decreases with a lower the trap density, the depletion of the NWs becomes less pronounced.Consequently, the screening of the piezo charges by the free carriers increases, resulting in a reduced output voltage.These results experimentally demonstrate and confirm that the piezo-conversion capacity of GaN NWs is favoured by the presence of surface charges.

Materials and Methods
Self-assembled GaN NWs were grown on a conductive Si(111) substrate (resistivity of about 0.007 Ω•cm) with a Plasma-Assisted Molecular Beam Epitaxy (PA-MBE) reactor equipped with a radio frequency N plasma source.Prior to the growth, the Si substrate was chemically cleaned and subsequently heated in situ at 850 • C to remove the organic pollutants and the native oxide, respectively.Then, a 2.5 nm thick AlN buffer layer was deposited at 620 • C on the clean Si surface, as describe in [60].The objective of this AlN buffer is to control the NW nucleation and density [61,62], reduce the NW twist [63], improve the NW verticality [64] and to ensure the conductivity between the GaN NWs and the conductive Si substrate [65].Indeed, the deposition of the AlN buffer layer involves two distinct steps.Firstly, the deoxidised Si(111) substrate is exposed at 620 • C to an Al flux, resulting in the formation of Al droplets dispersed on the surface in the form of an Al-Si eutectic [66].Subsequently, the surface is exclusively exposed to a nitrogen flux (by switching the Al/N shutters), leading to the formation of the AlN buffer layer over the surface due to the Al diffusion.During the nitridation phase, the Si atoms dissolved into the Al droplets are incorporated into the AlN layer, causing n-doping and thereby imparting a conductive behaviour to the buffer layer.Finally, GaN NWs are grown at 770 • C under nominally N-rich conditions (V/III = 1.36).During the growth, the Mg cell is maintained at 400 • C with a closed shutter to induce a p-type residual doping of the GaN NWs.
Under these growth conditions, vertically oriented GaN NWs crystallise in the wurtzite structure and present a hexagonal cross-section delimited by {10-10} planes [63].Figure 1a illustrates the GaN NW morphology, characterised by a density of 3.4 × 10 9 NW/cm 2 and a diameter of 36 nm ± 9 nm.This approximatively constant diameter ensures that the expression of the surface charges will not be dominated by diameter effects.Regarding the NW height, a trimodal dispersion is measured, resulting in three different NW aspect ratios, as we can see in Figure 1b.This distribution in terms of the aspect ratio allows spanning a significant range of deformation rates under the same mechanical external input.Thus, it provides the opportunity to experimentally establish the intrinsic relationship between the piezo generated output voltage (OV) and the expression of the surface charges as a function of the NW surrounding environment.
Nanoenergy Adv.2024, 4, FOR PEER REVIEW 4 switching the Al/N shutters), leading to the formation of the AlN buffer layer over the surface due to the Al diffusion.During the nitridation phase, the Si atoms dissolved into the Al droplets are incorporated into the AlN layer, causing n-doping and thereby imparting a conductive behaviour to the buffer layer.Finally, GaN NWs are grown at 770 °C under nominally N-rich conditions (V/III = 1.36).During the growth, the Mg cell is maintained at 400 °C with a closed shutter to induce a p-type residual doping of the GaN NWs.Under these growth conditions, vertically oriented GaN NWs crystallise in the wurtzite structure and present a hexagonal cross-section delimited by {10-10} planes [63].Figure 1a illustrates the GaN NW morphology, characterised by a density of 3.4 10 9 NW/cm 2 and a diameter of 36 nm ± 9 nm.This approximatively constant diameter ensures that the expression of the surface charges will not be dominated by diameter effects.Regarding the NW height, a trimodal dispersion is measured, resulting in three different NW aspect ratios, as we can see in Figure 1b.This distribution in terms of the aspect ratio allows spanning a significant range of deformation rates under the same mechanical external input.Thus, it provides the opportunity to experimentally establish the intrinsic relationship between the piezo generated output voltage (OV) and the expression of the surface charges as a function of the NW surrounding environment.To highlight the significance of the surface charge modulation as a function of the NW environment on the OV generation capacity, two portions of the same GaN NWs sample were prepared following different procedures, schematised in Figure 1c.The GaN NWs of the first portion were left unaltered, while those of the second portion were encapsulated by a 10 nm thick Al2O3 shell through an atomic layer deposition treatment.The Al2O3 shell is recognised for its ability to reduce the SCE [67][68][69].In presence of the Al2O3 shell, the GaN NW surfaces are passivated [70][71][72][73] through a limitation or even a suppression of the Ga-O bonds [45].As a consequence, the surface trap density is reduced by one to two orders of magnitude, resulting in a density of about 10 11 -10 12 cm −2 for GaN/Al2O3 core-shell NWs, while this density is about 10 13 cm −2 for as-grown GaN NWs [32].
The piezoelectric responses of the NWs were quantified using an atomic force microscope (AFM) operating in contact mode, equipped with a homemade modified Resiscope module [74] designed to measure the direct piezoelectric effect in the NWs [11].In this To highlight the significance of the surface charge modulation as a function of the NW environment on the OV generation capacity, two portions of the same GaN NWs sample were prepared following different procedures, schematised in Figure 1c.The GaN NWs of the first portion were left unaltered, while those of the second portion were encapsulated by a 10 nm thick Al 2 O 3 shell through an atomic layer deposition treatment.The Al 2 O 3 shell is recognised for its ability to reduce the SCE [67][68][69].In presence of the Al 2 O 3 shell, the GaN NW surfaces are passivated [70][71][72][73] through a limitation or even a suppression of the Ga-O bonds [45].As a consequence, the surface trap density is reduced by one to two orders of magnitude, resulting in a density of about 10 11 -10 12 cm −2 for GaN/Al 2 O 3 core-shell NWs, while this density is about 10 13 cm −2 for as-grown GaN NWs [32].
The piezoelectric responses of the NWs were quantified using an atomic force microscope (AFM) operating in contact mode, equipped with a homemade modified Resiscope module [74] designed to measure the direct piezoelectric effect in the NWs [11].In this experimental configuration, schematised in Figure 2a, the electrical module is connected to the substrate (forming an Ohmic contact with the GaN NWs [66]) and to the Cr/Pt AFM tip (with a work function around 5.2 eV), forming a Schottky barrier with the GaN NWs (electron affinity of the GaN is about 4.1 eV [75]), ensuring the harvesting of the piezo generated charges [50].No external voltage is applied, and the generated electrical signals are observed across a load resistance R L of 1 GΩ.
gy Adv.2024, 4, FOR PEER REVIEW experimental configuration, schematised in Figure 2a, the electrical module is connected to the substrate (forming an Ohmic contact with the GaN NWs [66]) and to the Cr/Pt AFM tip (with a work function around 5.2 eV), forming a Schottky barrier with the GaN NWs (electron affinity of the GaN is about 4.1 eV [75]), ensuring the harvesting of the piezo generated charges [50].No external voltage is applied, and the generated electrical signals are observed across a load resistance RL of 1 GΩ.The piezoelectric measurements on the GaN NWs were conducted under bending deformation.The conductive AFM tip is brought in contact with the surface and scans over the GaN NW array.The force applied by the tip, resulting from the convolution of the constant normal force (CNF) and the scanning force, induces a lateral bending of the NWs.In response to its elastic deformation, and owing to its piezoelectric properties, the NW generates an output voltage harvested through the Schottky diode (Figure 2a).
For N-polar GaN NWs under bending deformation, the piezoelectric potential is distributed from a negative value on the stretch side to a positive value on the compressed side [76].Depending on the majority charge carriers, the Schottky diode will be positively biased according to the NW doping: for n-doped GaN NWs, negative OVs are harvested when the conductive AFM tip is in contact with the negative piezo-potential, while for pdoped GaN NWs (as in the present study), positive OVs are harvested when the AFM tip is in contact with the positive piezo-potential (Figure 2b).
This modified Resiscope AFM technique combines the nanometre scale spatial resolution with real-time electrical measurements while scanning over large surfaces (several µm 2 ).Hence, it allows for the simultaneous recording of topographic and electrical signals.Thus, for each NW constituting the array, a direct correlation between its morphology and its electromechanical response can be established.
To perform reliable electrical measurements, and knowing that MBE-grown GaN NWs are very flexible [11], their bases were embedded into a soft polymer matrix (Figure 3a).PDMS was chosen at this scope due to its Young's modulus of about 0.9 MPa [77], which is lower than the one of the GaN NWs estimated at 1.8 GPa [78].This ensures mechanical consolidation of the nanostructures (preventing their fold up towards the neighbouring NWs or the substrate, leading to the leakage of the piezoelectric charges) while avoiding any strain effect on the NWs.The PDMS matrix was spin-coated and etched back The piezoelectric measurements on the GaN NWs were conducted under bending deformation.The conductive AFM tip is brought in contact with the surface and scans over the GaN NW array.The force applied by the tip, resulting from the convolution of the constant normal force (CNF) and the scanning force, induces a lateral bending of the NWs.In response to its elastic deformation, and owing to its piezoelectric properties, the NW generates an output voltage harvested through the Schottky diode (Figure 2a).
For N-polar GaN NWs under bending deformation, the piezoelectric potential is distributed from a negative value on the stretch side to a positive value on the compressed side [76].Depending on the majority charge carriers, the Schottky diode will be positively biased according to the NW doping: for n-doped GaN NWs, negative OVs are harvested when the conductive AFM tip is in contact with the negative piezo-potential, while for p-doped GaN NWs (as in the present study), positive OVs are harvested when the AFM tip is in contact with the positive piezo-potential (Figure 2b).
This modified Resiscope AFM technique combines the nanometre scale spatial resolution with real-time electrical measurements while scanning over large surfaces (several µm 2 ).Hence, it allows for the simultaneous recording of topographic and electrical signals.Thus, for each NW constituting the array, a direct correlation between its morphology and its electromechanical response can be established.
To perform reliable electrical measurements, and knowing that MBE-grown GaN NWs are very flexible [11], their bases were embedded into a soft polymer matrix (Figure 3a).PDMS was chosen at this scope due to its Young's modulus of about 0.9 MPa [77], which is lower than the one of the GaN NWs estimated at 1.8 GPa.This ensures mechanical consolidation of the nanostructures (preventing their fold up towards the neighbouring NWs or the substrate, leading to the leakage of the piezoelectric charges) while avoiding any strain effect on the NWs.The PDMS matrix was spin-coated and etched back by RIE using a O 2 /CF 4 plasma treatment to uncover the top portion of both sets of NWs.In the specific case of GaN/Al 2 O 3 core-shell NWs, two additional steps have been implemented in order to guaranty sample comparison.Before the matrix deposition, the GaN/Al 2 O 3 core-shell NWs were exposed to oxygen plasma to enhance the wettability of PDMS with the NW sidewalls and thus achieve a matrix distribution equivalent to that around the NWs.It is worth noting that this plasma treatment does not affect the surface trap density, since it is controlled by the GaN/Al 2 O 3 interface.Finally, the Al 2 O 3 capping the top facet of the NWs is removed by ion beam etching (IBE) to ensure the same GaN-Cr/Pt Schottky diode formed between the conductive AFM tip and the NWs.
Cr/Pt Schottky diode formed between the conductive AFM tip and the NWs.
It should be noted that the deposition of the Al2O3 shell increases the effective diameter of the NWs, which, in return, makes them stiffer.For the sake of comparing the piezoelectric responses of the NWs with the Al2O3 shell and as-grown NWs, an adjustment to the NW height emanating from the PDMS matrix was made.Thus, to probe the same deformation degree under an equivalent deformation force, the average aspect ratio of the NW emerging portion has been kept constant and equal to 5.5.This aspect ratio has been chosen to be able to access multiple degrees of deformation as a function of the applied force.Thus, for GaN NWs characterised by an average diameter of 36 ± 9 nm, the average NW top portion height has been fixed at 200 nm, while, for GaN/Al2O3 core-shell NWs with an average diameter of 56 ± 9 nm, the NW top portion height has been fixed at 310 nm (Figure 3b).

Results and Discussions
In the first instance, the piezoelectric response of the 1D nanostructures depends on their deformation degree.However, the response is also affected by surface charge effects.It should be noted that the deposition of the Al 2 O 3 shell increases the effective diameter of the NWs, which, in return, makes them stiffer.For the sake of comparing the piezoelectric responses of the NWs with the Al 2 O 3 shell and as-grown NWs, an adjustment to the NW height emanating from the PDMS matrix was made.Thus, to probe the same deformation degree under an equivalent deformation force, the average aspect ratio of the NW emerging portion has been kept constant and equal to 5.5.This aspect ratio has been chosen to be able to access multiple degrees of deformation as a function of the applied force.Thus, for GaN NWs characterised by an average diameter of 36 ± 9 nm, the average NW top portion height has been fixed at 200 nm, while, for GaN/Al 2 O 3 core-shell NWs with an average diameter of 56 ± 9 nm, the NW top portion height has been fixed at 310 nm (Figure 3b).

Results and Discussions
In the first instance, the piezoelectric response of the 1D nanostructures depends on their deformation degree.However, the response is also affected by surface charge effects.For both sets of NWs, the topographic and output voltage mappings were simultaneously registered at constant normal forces (CNFs) ranging between 120 nN and 380 nN.The 3D electrical mappings are presented in Figure 4, and the corresponding statistical analyses are summarised in Table S1 (Supplementary Materials).
For both sets of NWs, the topographic and output voltage mappings were simultaneously registered at constant normal forces (CNFs) ranging between 120 nN and 380 nN.The 3D electrical mappings are presented in Figure 4, and the corresponding statistical analyses are summarised in Table S1 (Supplementary Materials).The average output voltages are plotted as a function of the applied force in Figure 5a,b for both samples.Similar behaviours can be observed.Firstly, positive output voltages are generated by the NWs independently from their stiffness and the applied CNF.This behaviour results from the intrinsic p-type doping of the GaN NWs achieved with our growth conditions [13,24].Secondly, the average output voltages follow Gaussian multimodal distributions, as shown in Figure 5c.This behaviour stems from the NW selfassembled growth paradigm, leading to a dispersion of morphologies [12,58]: while the The average output voltages are plotted as a function of the applied force in Figure 5a,b for both samples.Similar behaviours can be observed.Firstly, positive output voltages are generated by the NWs independently from their stiffness and the applied CNF.This behaviour results from the intrinsic p-type doping of the GaN NWs achieved with our growth conditions [13,24].Secondly, the average output voltages follow Gaussian multimodal distributions, as shown in Figure 5c.This behaviour stems from the NW self-assembled growth paradigm, leading to a dispersion of morphologies [12,58]: while the NW diameter is constant, the nanostructures are characterised by a multimodal dispersion of heights and, hence, of stiffnesses.In the present case, the first distribution corresponds to the shorter and most rigid set of NWs, while the second and third distributions refer to taller and more flexible NWs.Finally, we observe that the three distributions show an increase in the average OV when increasing the applied CNF due to the direct piezoelectric effect and the increased stability of the Schottky contact [28,78].
gy Adv.2024, 4, FOR PEER REVIEW 8 NW diameter is constant, the nanostructures are characterised by a multimodal dispersion of heights and, hence, of stiffnesses.In the present case, the first distribution corresponds to the shorter and most rigid set of NWs, while the second and third distributions refer to taller and more flexible NWs.Finally, we observe that the three distributions show an increase in the average OV when increasing the applied CNF due to the direct piezoelectric effect and the increased stability of the Schottky contact [28,79].At this stage, it is noteworthy that GaN NWs deliver average output voltages reaching up to 528 mV per NW, marking the highest recorded OV reported in the literature for this system, to the best of our knowledge.This piezoelectric response is higher than those generated by other piezoelectric 1D nanostructures, particularly ZnO NWs, which remain the most extensively investigated nanostructures for the development of a new generation of piezoelectric energy harvesters.
We now compare the OV generated by each set of samples.As a reminder, this comparison is possible, since the average aspect ratio of the emerging NW top portion has been maintained constant (AR = 5.5) for both samples.Consequently, the NWs present equivalent deformation rates under the same AFM scanning conditions.Referring to  S1 (Supplementary Materials), it is observed that, regardless of the applied CNF value and the specific NW distribution, the OVs generated by the GaN/Al2O3 core-shell NWs are systematically lower than the ones generated by the pure The OV variations are analysed for both sets of investigated samples.For the pure GaN NWs, the first distribution increases continuously with the applied CNF from ~58 ± 75 mV to ~250 ± 42 mV, while the second one saturates around 350 ± 62 mV for CNF ≥ 160 nN.The third distribution is characterised by approximatively constant OV values around 515 ± 25 mV in the whole CNF range.This means that these NWs are very flexible and attained their maxima of piezo-conversion at smaller forces.Concerning the GaN/Al 2 O 3 core-shell NWs, equivalent behaviours are observed.While the first distribution increases from 49 ± 33 mV to about 100 ± 70 mV, the second one achieves a saturation around 320 ± 60 mV for CNF ≥ 160 nN.Finally, the third distribution is characterised by approximatively constant OV values around 480 ± 60 mV.
At this stage, it is noteworthy that GaN NWs deliver average output voltages reaching up to 528 mV per NW, marking the highest recorded OV reported in the literature for this system, to the best of our knowledge.This piezoelectric response is higher than those generated by other piezoelectric 1D nanostructures, particularly ZnO NWs, which remain the most extensively investigated nanostructures for the development of a new generation of piezoelectric energy harvesters.
We now compare the OV generated by each set of samples.As a reminder, this comparison is possible, since the average aspect ratio of the emerging NW top portion has been maintained constant (AR = 5.5) for both samples.Consequently, the NWs present equivalent deformation rates under the same AFM scanning conditions.Referring to Figures 4 and 5, along with Table S1 (Supplementary Materials), it is observed that, regardless of the applied CNF value and the specific NW distribution, the OVs generated by the GaN/Al 2 O 3 core-shell NWs are systematically lower than the ones generated by the pure GaN NWs with reduction ranges from several tens of mV, representing a decrease ranging from 9 to 56%, depending on the specific NW considered.
To elucidate the variations in OVs observed among the sets of NWs, it is important to consider the different parameters influencing the NW ability to convert mechanical deformation into a direct electrical signal. - The piezo-conversion firstly depends on the deformation degree of the material.
According to the direct piezoelectric effect, as the deformation increases, the output signal rises accordingly.Consequently, under an equivalent mechanical input, two NWs presenting a different stiffness (directly related to the NW aspect ratio) will generate distinct internal piezoelectric fields and thus different output voltages.This mechanism is schematised in Figure 6.
Nanoenergy Adv.2024, 4, FOR PEER REVIEW 9 GaN NWs with reduction ranges from several tens of mV, representing a decrease ranging from 9 to 56%, depending on the specific NW considered.
To elucidate the variations in OVs observed among the sets of NWs, it is important to consider the different parameters influencing the NW ability to convert mechanical deformation into a direct electrical signal.

−
The piezo-conversion firstly depends on the deformation degree of the material.
According to the direct piezoelectric effect, as the deformation increases, the output signal rises accordingly.Consequently, under an equivalent mechanical input, two NWs presenting a different stiffness (directly related to the NW aspect ratio) will generate distinct internal piezoelectric fields and thus different output voltages.This mechanism is schematised in Figure 6.

−
The piezo-conversion is directly related to the conductivity/resistivity of the NWs.
It is widely acknowledged that the free charge carriers play a crucial role in screening the generated piezo-charges, leading to a reduction in the internal piezoelectric field within the NW and consequent degradation of the output signal.As previously explained, the surface charges lead to a Fermi-level pinning in the depletion region along the NW sidewall surface formed by the M-plane facets.The extent of depletion, whether partial or complete, is contingent upon its diameter and the material's doping level [39,58].The surface barrier height, Φ , is of the order of the SFLP.For large NWs (NW diameters > two times the depletion width), a conduction channel exists surrounded by a SFLP at the NW surface (Figure 7a).In contrast, for thin NWs (NW diameters ≤ two times the depletion width), the NW is fully depleted (Figure 7b).- The piezo-conversion is directly related to the conductivity/resistivity of the NWs.
It is widely acknowledged that the free charge carriers play a crucial role in screening the generated piezo-charges, leading to a reduction in the internal piezoelectric field within the NW and consequent degradation of the output signal.As previously explained, the surface charges lead to a Fermi-level pinning in the depletion region along the NW sidewall surface formed by the M-plane facets.The extent of depletion, whether partial or complete, is contingent upon its diameter and the material's doping level [39,58].The surface barrier height, Φ Surface B , is of the order of the SFLP.For large NWs (NW diameters > two times the depletion width), a conduction channel exists surrounded by a SFLP at the NW surface (Figure 7a).In contrast, for thin NWs (NW diameters ≤ two times the depletion width), the NW is fully depleted (Figure 7b).
OVs collected for these nanostructures (Figures 4 and 5) and an estimated surface trap density of around 10 13 cm −2 for the pure GaN NWs [32], we infer a reduced band curvature.This results in a smaller barrier, noted as Φ GaN , and thus to a non-negligible ∆E, as illustrated in Figure 7b.This configuration is thus favourable for minimising the screening of the piezoelectric charges and for enhancing the internal piezo-potential and the generated Ovs.In the case of the same GaN NWs surrounded by the Al2O3 shell, the nanostructures are also considered fully depleted, since their core is defined by an unchanged doping level and diameter.However, due to their surface passivation, the surface trap density is reduced to around 10 11 -10 12 cm −2 , according to the literature [67][68][69].The OVs generated by these core-shell NWs are still significant but remain systematically lower than the ones generated by the pure GaN NWs.This combination of factors indicates that, for the GaN/Al2O3 core-shell NWs, the SFLP is less pronounced.The surface barrier Φ GaN Al ⁄ O and the corresponding ∆E(GaN/Al2O3) are, respectively, higher and smaller than the ones of the GaN NWs Φ GaN , ∆E GaN , as illustrated in Depending on the depletion degree, the band curvature and the corresponding barrier for surface electron-hole pair recombination are modulated.In other terms, a lower Φ Surface B results in a higher NW depletion and an increased difference between the Fermi level and the top of the valence band, denoted as ∆E.Consequently, the internal piezo-potential created in response to deformation will be more or less screened, leading to a corresponding decrease or increase in the generated OV.
In our intrinsically p-doped GaN NWs (doping level estimated to be around 5 × 10 16 cm −3 from SIMS measurements on 2D GaN films), the depletion width has been estimated to be less than 30 nm [58].With a diameter of 36 ± 9 nm, the investigated nanostructures are thus fully depleted, with the SFLP taking place across the entire NWs.Considering the OVs collected for these nanostructures (Figures 4 and 5) and an estimated surface trap density of around 10 13 cm −2 for the pure GaN NWs [32], we infer a reduced band curvature.This results in a smaller barrier, noted as Φ Surface B (GaN), and thus to a non-negligible ∆E, as illustrated in Figure 7b.This configuration is thus favourable for minimising the screening of the piezoelectric charges and for enhancing the internal piezo-potential and the generated Ovs.
In the case of the same GaN NWs surrounded by the Al 2 O 3 shell, the nanostructures are also considered fully depleted, since their core is defined by an unchanged doping level and diameter.However, due to their surface passivation, the surface trap density is reduced to around 10 11 -10 12 cm −2 , according to the literature [67][68][69].The OVs generated by these core-shell NWs are still significant but remain systematically lower than the ones generated by the pure GaN NWs.This combination of factors indicates that, for the GaN/Al 2 O 3 core-shell NWs, the SFLP is less pronounced.The surface barrier Φ Surface B (GaN/Al 2 O 3 ) and the corresponding ∆E(GaN/Al 2 O 3 ) are, respectively, higher and smaller than the ones of the GaN NWs Φ Surface B (GaN), ∆E(GaN) , as illustrated in Figure 7c.As a consequence, for an equivalent deformation degree, the screening of the piezo-charges is higher, leading to a reduction of the piezoelectric field and resulting OVs.
These experimental measurements thus demonstrate that the surface charge effect is favourable for enhancing the piezoelectric conversion efficiency in 1D-nanostructures.

Conclusions
While the piezoelectric response of materials is preliminarily regulated by the deformation rate, the role of the surface charges cannot be overlooked, especially in sub-100 nm wide NWs.The results presented in this study experimentally demonstrate that surface charges can play a favourable role by increasing the piezo-generation capacity of nonintentionally p-type doped GaN NWs.Consequently, by modifying the NW environment, it is possible to modulate the piezoelectric response of GaN NWs, known for their surface trap density on the order of 10 13 cm −2 .The passivation of the GaN core by an Al 2 O 3 shell leads to a noticeable reduction in the surface charge density, resulting in a significant decrease of the output voltages due to reduced surface Fermi level pinning and the resulting enhanced screening of the internal piezoelectric field.To support this conclusion, further investigations involving different shells and the quantification of the surface trap density are currently underway.
Leveraging the surface charge effect, the OVs generated by GaN NWs can reach an average value of 529 mV.This outcome stands as the highest reported in the literature for GaN NWs and exceeds the ones reported other piezoelectric 1D nanostructures.
In conclusion, surface engineering for the modulation and control of surface trap densities opens up new pathways to enhance the piezoelectric conversion efficiency of NWs and thus improve the performance of devices integrating these 1D nanostructures.

Supplementary Materials:
The following supplementary materials can be downloaded at https://www.mdpi.com/article/10.3390/nanoenergyadv4020008/s1:Table S1: Statistical analyses of the output voltage mappings registered at constant normal forces (CNFs) ranging between 120 nN and 380 nN for the three aspect ratio distributions.

Figure 1 .
Figure 1.(a) Top view and titled view SEM images of as-grown GaN NWs.(b) Histogram representing the aspect ratio (NW height/NW diameter) population of the as-grown GaN NWs.(c) The same as-grown GaN NW sample has been divided into two pieces: GaN and GaN/Al2O3 core-shell NWs for demonstrating the influence of the surface charge effect on the piezoelectric response of the nanostructures.

Figure 1 .
Figure 1.(a) Top view and titled view SEM images of as-grown GaN NWs.(b) Histogram representing the aspect ratio (NW height/NW diameter) population of the as-grown GaN NWs.(c) The same as-grown GaN NW sample has been divided into two pieces: GaN and GaN/Al 2 O 3 core-shell NWs for demonstrating the influence of the surface charge effect on the piezoelectric response of the nanostructures.

Figure 2 .
Figure 2. (a) Principle of the piezoelectric measurements performed by AFM equipped with a homemade modified Resiscope in the bending scanning configuration.(b) Distribution of the piezoelectric field in a N-polar GaN NW deformed by bending from the stretched side to the compressed one.

Figure 2 .
Figure 2. (a) Principle of the piezoelectric measurements performed by AFM equipped with a homemade modified Resiscope in the bending scanning configuration.(b) Distribution of the piezoelectric field in a N-polar GaN NW deformed by bending from the stretched side to the compressed one.

Figure 3 .
Figure 3. Schematic representation of the NW preparation.(a) The as-grown NW sample was divided into two portions to obtain GaN and GaN/Al2O3 core-shell NWs, respectively.(b) Nanostructures are mechanically consolidated by embedding their bases into a soft PDMS matrix.(c) The top portion of the consolidated NWs presents the same aspect ratio to ensure the equivalent deformation rate under applied force.

Figure 3 .
Figure 3. Schematic representation of the NW preparation.(a) The as-grown NW sample was divided into two portions to obtain GaN and GaN/Al 2 O 3 core-shell NWs, respectively.(b) Nanostructures are mechanically consolidated by embedding their bases into a soft PDMS matrix.(c) The top portion of the consolidated NWs presents the same aspect ratio to ensure the equivalent deformation rate under applied force.

Figure 4 .
Figure 4. Three-dimensional (10 µm × 5 µm) mappings of the OVs generated by GaN NWs (a-f) and GaN/Al2O3 core-shell NWs (g-l) under bending deformation.The increase in the OVs with the applied constant normal force is a direct demonstration of the direct piezoelectric effect taking place.

Figure 4 .
Figure 4. Three-dimensional (10 µm × 5 µm) mappings of the OVs generated by GaN NWs (a-f) and GaN/Al 2 O 3 core-shell NWs (g-l) under bending deformation.The increase in the OVs with the applied constant normal force is a direct demonstration of the direct piezoelectric effect taking place.

Figure 5 .
Figure 5. Statistical analysis of 3D electrical mappings for an applied force evolving in the 120-380 nN range for pure GaN NWs (a) and GaN/Al2O3 core-shell NWs (b).The saturation values of the different distributions are indicated for comparison.A trimodal distribution of the averaged OV is evidenced, as it is clearly visible in (c), showing examples of the OV distribution for two CNFs well described by Gaussian functions.The OV variations are analysed for both sets of investigated samples.For the pure GaN NWs, the first distribution increases continuously with the applied CNF from ∼58 ± 75 mV to ∼250 ± 42 mV, while the second one saturates around 350 ± 62 mV for CNF ≥ 160 nN.The third distribution is characterised by approximatively constant OV values around 515 ± 25 mV in the whole CNF range.This means that these NWs are very flexible and attained their maxima of piezo-conversion at smaller forces.Concerning the GaN/Al2O3 core-shell NWs, equivalent behaviours are observed.While the first distribution increases from 49 ± 33 mV to about 100 ± 70 mV, the second one achieves a saturation around 320 ± 60 mV for CNF ≥ 160 nN.Finally, the third distribution is characterised by approximatively constant OV values around 480 ± 60 mV.At this stage, it is noteworthy that GaN NWs deliver average output voltages reaching up to 528 mV per NW, marking the highest recorded OV reported in the literature for this system, to the best of our knowledge.This piezoelectric response is higher than those generated by other piezoelectric 1D nanostructures, particularly ZnO NWs, which remain the most extensively investigated nanostructures for the development of a new generation of piezoelectric energy harvesters.We now compare the OV generated by each set of samples.As a reminder, this comparison is possible, since the average aspect ratio of the emerging NW top portion has been maintained constant (AR = 5.5) for both samples.Consequently, the NWs present equivalent deformation rates under the same AFM scanning conditions.Referring to Figures 4 and 5, along with TableS1(Supplementary Materials), it is observed that, regardless of the applied CNF value and the specific NW distribution, the OVs generated by the GaN/Al2O3 core-shell NWs are systematically lower than the ones generated by the pure Figures 4 and 5, along with Table

Figure 5 .
Figure 5. Statistical analysis of 3D electrical mappings for an applied force evolving in the 120-380 nN range for pure GaN NWs (a) and GaN/Al 2 O 3 core-shell NWs (b).The saturation values of the different distributions are indicated for comparison.A trimodal distribution of the averaged OV is evidenced, as it is clearly visible in (c), showing examples of the OV distribution for two CNFs well described by Gaussian functions.

Figure 6 .
Figure 6.Schematic representation of the piezoelectric field distribution inside the NWs characterised by an equivalent diameter (D) but three different heights (H), resulting in three different aspect ratios, and the corresponding output voltage generated in response to an equivalent lateral force applied to the AFM tip.In the present experiments, the NWs being intrinsically p-doped, the OV is collected through the Schottky diode when the conductive AFM tip is in contact with the compressive NW side, where the piezo potential is positive[76].

Figure 6 .
Figure 6.Schematic representation of the piezoelectric field distribution inside the NWs characterised by an equivalent diameter (D) but three different heights (H), resulting in three different aspect ratios, and the corresponding output voltage generated in response to an equivalent lateral force applied to the AFM tip.In the present experiments, the NWs being intrinsically p-doped, the OV is collected through the Schottky diode when the conductive AFM tip is in contact with the compressive NW side, where the piezo potential is positive[76].

Figure 7 .
Figure 7. Schematic representation of the Fermi level pinning in p-doped NWs for (a) partially depleted GaN NWs.(b) Fully depleted GaN NWs.(c) Fully depleted GaN/Al2O3 core-shell NWs.Φ is the maximal surface barrier height, and ΔE is the energy difference between the Fermi level and the valence band maximum.For the fully depleted NWs, the Φ GaN Al ⁄ O is higher than the Φ GaN , and by consequence, the ∆E(GaN/Al2O3) is smaller than the ∆E GaN , due to the passivation of the GaN core by the Al2O3 shell inducing the reduction of the surface trap density.

Figure 7 .
Figure 7. Schematic representation of the Fermi level pinning in p-doped NWs for (a) partially depleted GaN NWs.(b) Fully depleted GaN NWs.(c) Fully depleted GaN/Al 2 O 3 core-shell NWs.Φ Surface B is the maximal surface barrier height, and ∆E is the energy difference between the Fermi level and the valence band maximum.For the fully depleted NWs, the Φ Surface B (GaN/Al 2 O 3 ) is higher than the Φ Surface B (GaN), and by consequence, the ∆E(GaN/Al 2 O 3 ) is smaller than the ∆E(GaN), due to the passivation of the GaN core by the Al 2 O 3 shell inducing the reduction of the surface trap density.

Author
Contributions: T.K.S.: conceptualisation, formal analysis, investigation and writing-original draft preparation; P.C.: conceptualisation, validation, formal analysis, investigation and supervision; Q.C.B.: formal analysis and technical support; A.C.: formal analysis and technical support; L.T.: technical support; M.M.: writing-original draft preparation; M.T.: project administration and funding acquisition; F.H.: validation, formal analysis and writing-original draft preparation; N.G.: conceptualisation, validation, formal analysis, writing-original draft preparation, supervision, project administration and funding acquisition.All authors have read and agreed to the published version of the manuscript.Funding: This work was financially supported by the French National Research Agency through the GANEX program (ANR-11-LABX-0014), the Project SCENIC (ANR-20-CE09-0005) and as part of the "Investissements d'Avenir" program (reference: ANR-10-LABX-0035, Labex NanoSaclay).Finally, this work was done within the C2N micro-nanotechnologies platforms and partly supported by the RENATECH network and the General Council of Essonn.