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Gong Chen, Pan-shuo Wang. Effect of Passivation on Piezoelectricity of ZnO Nanowire[J]. Chinese Journal of Chemical Physics , 2020, 33(4): 434-442. doi: 10.1063/1674-0068/cjcp1911208
Citation: Gong Chen, Pan-shuo Wang. Effect of Passivation on Piezoelectricity of ZnO Nanowire[J]. Chinese Journal of Chemical Physics , 2020, 33(4): 434-442. doi: 10.1063/1674-0068/cjcp1911208

Effect of Passivation on Piezoelectricity of ZnO Nanowire

doi: 10.1063/1674-0068/cjcp1911208
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  • Corresponding author: Gong Chen, E-mail: ustcchen@mail.ustc.edu.cn
  • Received Date: 2019-11-19
  • Accepted Date: 2020-03-03
  • Publish Date: 2020-08-27
  • Surface passivation is one valuable approach to tune the properties of nanomaterials. The piezoelectric properties of hexagonal [001] ZnO nanowires with four kinds of surface passivations were investigated using the first-principles calculations. It is found that in the 50% H(O) and 50% Cl(Zn), 50% H(O) and 50% F(Zn) passivations, the volume and surface effects both enhance the piezoelectric coefficient. This differs from the unpassivated cases where the surface effect was the sole source of piezoelectric enhancement. In the 100% H, 100% Cl passivations, the piezoelectric enhancement is not possible since the surface effect is screened by surface charge with weak polarization. The study reveals that the competition between the volume effect and surface effect influences the identification of the diameter-dependence phenomenon of piezoelectric coefficients for ZnO nanowires in experiments. Moreover, the results suggest that one effective means of improving piezoelectricity of ZnO nanowires is shrinking axial lattice or increasing surface polarization through passivation.
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Effect of Passivation on Piezoelectricity of ZnO Nanowire

doi: 10.1063/1674-0068/cjcp1911208

Abstract: Surface passivation is one valuable approach to tune the properties of nanomaterials. The piezoelectric properties of hexagonal [001] ZnO nanowires with four kinds of surface passivations were investigated using the first-principles calculations. It is found that in the 50% H(O) and 50% Cl(Zn), 50% H(O) and 50% F(Zn) passivations, the volume and surface effects both enhance the piezoelectric coefficient. This differs from the unpassivated cases where the surface effect was the sole source of piezoelectric enhancement. In the 100% H, 100% Cl passivations, the piezoelectric enhancement is not possible since the surface effect is screened by surface charge with weak polarization. The study reveals that the competition between the volume effect and surface effect influences the identification of the diameter-dependence phenomenon of piezoelectric coefficients for ZnO nanowires in experiments. Moreover, the results suggest that one effective means of improving piezoelectricity of ZnO nanowires is shrinking axial lattice or increasing surface polarization through passivation.

Gong Chen, Pan-shuo Wang. Effect of Passivation on Piezoelectricity of ZnO Nanowire[J]. Chinese Journal of Chemical Physics , 2020, 33(4): 434-442. doi: 10.1063/1674-0068/cjcp1911208
Citation: Gong Chen, Pan-shuo Wang. Effect of Passivation on Piezoelectricity of ZnO Nanowire[J]. Chinese Journal of Chemical Physics , 2020, 33(4): 434-442. doi: 10.1063/1674-0068/cjcp1911208
  • Wireless and portable devices are becoming more and more indispensable in modern lives. Miniaturization of these devices is recognized as an important technology trend. In pursuit of miniaturization, lots of efforts are devoted to designing self-powered systems and nanoscale control systems [1-9], among which, devices utilizing piezoelectric nanomaterials attract much attention due to their excellent capabilities in converting mechanical energy into electrical energy or vice versa. Nowadays, piezoelectric nanomaterials have been widely used in various micro-electro-mechanical systems (MEMS), such as nanogenerators [10-13], nanosensors [14, 15], piezotronics [16-18] and piezo-phototronics [19-22]. In the utilization of piezoelectric nanomaterials, it is observed that the nanomaterials show distinct piezoelectricity from their macroscale counterpart. For instance, the piezoelectric coefficient of ZnO nanowire can reach 26.7-45 pm/V, much larger than the bulk value (9.93 pm/V) [23-27].

    In pioneering studies [28-35], the classical continuum electromechanical theories are employed to interpret the piezoelectricity at the nanoscale. Huang and Yu [28] proposed a surface piezoelectricity concept by assuming that the surface energy density depends on the electric field at the surface and the in-plane strains. Shen and Hu [29] introduced a core-shell model and established a theoretical framework of nanoscale dielectrics to represent the piezoelectric nanostructures. Based on this work, surface piezoelectric coefficients for various nanomaterials were calculated. For example, molecular statics and dynamics calculations were conducted by Dai et al. [36, 37] to demonstrate the surface piezoelectricity of $ \rm ZnO $, $ \rm GaN $, $ \rm BaTiO_3 $ and $ \rm SrTiO_3 $ nanocrystals. Also, Hoang et al. [38, 39] solved the equations of a continuum model using a finite element technique, providing the surface piezoelectric coefficients for wurtzite ZnO, AlN and GaN nanowires. The surface stress and surface polarization are generally regarded as the most important sources of the surface piezoelectricity [40-44]. In addition, it was reported that the surface high-order mechanical and electrical terms also contribute to the surface piezoelectricity [45].

    A number of subsequent atomistic simulations [8, 46-49] on nanomaterials reported that the piezoelectric coefficient monotonously depends on size due to surface-to-volume ratio. The role of surface effect in polarization and piezoelectricity at the nanoscale was widely investigated [50-52]. Xiang et al. [53] attributed the piezoelectric enhancement at the nanoscale to the increase of surface Poisson's ratio. Agrawal and Espinosa [46] pointed out surface contraction led to the piezoelectric enhancement in ZnO and GaN nanowires. Niu et al. [54] found surface relaxation enhanced spontaneous polarization using maximally localized Wannier functions analysis. Wu et al. [55] identified three different sources of surface effect through studying the free vibration behavior of a spherically isotropic piezoelectric nanosphere. Surface-induced shape effect in piezoelectric nanomaterials was also analyzed recently [56, 57]. These results demonstrated that the surface effect plays a crucial role in piezoelectricity at the nanoscale. Due to the notable influence of surface on piezoelectricity at the nanoscale, surface passivation [58-62] could become one effective means of improving piezoelectricity of nanomaterials. However, the influence of surface passivations on piezoelectricity at the nanoscale has not yet been well studied.

    In this work, we systematically investigate the piezoelectricity of hexagonal [001]-oriented ZnO passivated nanowires. To highlight the change of nanowire by passivating layer, the ZnO nanowire is passivated by H, Cl or F atom, so that the passivating layer itself has a relatively small volume and a wurtzite-like structure. The structural stability of ZnO nanoiwres with different passivations is first studied. The influence of the passivation on piezoelectric coefficients is then analyzed in detail from the aspects of volume change and surface change. Finally, the effect of passivation on piezoelectricity at different diameters is discussed.

  • Density functional theory (DFT) computations were performed using Vienna ab initio simulation package (VASP) [63, 64]. The projector augmented wave (PAW) method [63] was implemented in the local density approximation (LDA) [65, 66] for the exchange correlation energy functional. A converged plane-wave energy cutoff of 500 eV was used and atomic relaxation was carried out until the force on an individual atom was less than 0.01 eV/Å. To avoid interactions between adjacent nanowires, a vacuum space region greater than 10 Å was taken.

    The piezoelectric coefficient was computed using the Berry-phase approach [67] combined with the finite difference method. The supercell containing nanowires were strained along the polar [001] axial direction at fixed increments of 0.5% strain until up to 1% strain. Due to the freely relaxed lateral surface, the effective strain contains two parts, applied strain in the axial direction of lattice and relaxed strain in the radial direction. The polarization of supercell was computed using the Berry-phase approach in the modern theory of polarization. As noted by a number of authors, the Berry-phase approach can provide a satisfactory estimation to the polarization [68-70]. A polarization-strain curve was then obtained, and the slope of the polarization-strain curve yielded the piezoelectric coefficient for the supercell (shown in FIG. 1). The piezoelectric coefficient for a nanowire $ e_{33} $ was computed as

    Figure 1.  Polarization as a function of strain for supercells containing different nanowires.

    where $ e_{33}^{ \rm{cell}} $ is the piezoelectric coefficient for a supercell, $ V^{ \rm{cell}} $ is the volume of the supercell, and $ V^{ \rm{wire}} $ is the volume of the nanowire in the supercell, which is defined as the length of axial lattice of the supercell multiplied by the hexagon formed by connecting centers of the outermost Zn and O atoms (shown as the dashed lines in FIG. 2(b)).

    Figure 2.  (a) Top views of relaxed ZnO nanowires with three different diameters of 9 Å for A, 15 Å for B, 26 Å for C. (b) Top views of relaxed passivated ZnO nanowires B. (c) Side views of relaxed passivated ZnO nanowires B. The volume of nanowire is indicated by dashed hexagons. The grey, red, white, green and cyan spheres stand for Zn, O, H, Cl and F atoms, respectively.

  • We start our calculation with wurtzite ZnO bulk and unpassivated nanowires. The calculated bulk structural constants are $ a $ = 3.195 Å, $ c $ = 5.163 Å and $ u $ = 0.379. ZnO unpassivated nanowires in three diameters (A: 9 Å, B: 15 Å, C: 26 Å) were constructed from relaxed ZnO bulk, as shown in FIG. 2(a). The computed piezoelectric coefficients for bulk and unpassivated nanowires are summarized in Table Ⅰ. A notable diameter dependence of the piezoelectric enhancement is observed in unpassivated nanowires. All the results agree well with the literature [71], which validate our chosen parameters.

    Table Ⅰ.  Calculated parameters for bulk and nanowires, including axial lattice $ c $, diameter $ d $, adsorption energies $ E_{ \rm{ads}} $ in eV/molecule and piezoelectric coefficient $ e_{33} $ in C/m$ ^2 $.

    Then four passivations were employed on nanowires A, B, and C: (1) 100% H passivation, (2) 100% Cl passivation, (3) 50% H(O) and 50% Cl(Zn) passivation, and (4) 50% H(O) and 50% F(Zn) passivation. Examples of the relaxed configurations of the passivated nanowires are drawn in FIG. 2(b). After passivation, two structural changes occur: volume change and surface reconstruction. In axial directions, the lattice is shrunk by relatively strong attractions among passivating atoms. In non-axial directions, the passivating atoms are of long distance, thus are weakly interacted, resulting in a slight increase in the nanowire diameter. At the surface, the outermost O atoms move inwards while the outermost Zn atoms shift outward in the passivated nanowires, which is contrary to the cases of unpassivated nanowires. The passivating atoms form atom pairs, similar to wurtzite structured ZnO bulk (shown in FIG. 2(c)). The contractions of the outermost Zn-O bonds in the passivated nanowires are smaller than those in the unpassivated nanowires. The distance between two nearest passivating atoms (i.e. H-H 1.72 Å, Cl-Cl 2.30 Å, H-Cl 1.93 Å and H-F 1.32 Å), is significantly larger than that in the corresponding molecules (i.e. H-H 0.74 Å, Cl-Cl 2.00 Å, H-Cl 1.30 Å and H-F 0.95 Å). In the full H passivation, the bond length of O-H is 1.00 Å and that of Zn-H is 1.56 Å, close to those in $ \rm H_2O $ (0.96 Å) and gas $ \rm ZnH $ (1.59 Å). In the full Cl passivation, the Zn-Cl bond length is 2.40 Å and the O-Cl bond length is 1.97 Å, larger than those in $ \rm ZnCl_2 $ (2.30 Å) and $ \rm HClO $ (1.69 Å), which indicates relatively weak interactions between the Cl atoms and the ZnO nanowire. In the 50% H and 50% Cl, 50% H and 50% F passivations, there are hydrogen bonds O-H$ \cdots $Cl/F, which elongate the Zn-Cl (2.17 Å), Zn-F (1.88 Å) and O-H (1.09 Å) bonds.

    To ensure the passivation is feasible, the dissociative adsorption energies of of $ \rm H_2 $, $ \rm Cl_2 $, $ \rm HCl $ and $ \rm HF $ were computed using the following expression:

    where $ E_{ \rm{ads}} $ is the dissociative adsorption energy per molecule; $ E_{ \rm{pass}} $ and $ E_{ \rm{unpass}} $ are the energies of passivated nanowire and unpassivated nanowire, respectively. $ E_{ \rm{molecule}} $ is the energy of the gas molecule; and $ n $ is the number of the gas molecules. Table Ⅰ shows the dissociative adsorption energies for passivations. All the energies are negative, indicating that the passivation stabilizes the nanowires at different diameters. The 50% H and 50% Cl, 50% H and 50% F passivations are energetically favorable compared to the 100% H, 100% Cl passivations, as a result of stronger bonding. The absolute value of the adsorption energy of the full Cl passivation is the smallest. The core of nanowire has the lowest energy at the axial lattice of the bulk value. The axial lattice in the 50% H and 50% Cl passivated nanowire is always close to the bulk value at all diameters, compared to other passivations. Therefore, the adsorption energy only decreases slightly as the axial lattice converges to the bulk value.

    Table Ⅰ summarizes the piezoelectric coefficients for nanowires with four passivations in three diameters. It is interesting to notice that in passivations with two chemical species (2S passivation, i.e. 50% H and 50% Cl, 50% H and 50% F) as well as the unpassivated cases, the piezoelectric coefficients are increased compared to the bulk value. On the contrary, passivations with one chemical species (1S passivation, i.e. 100% H, 100% Cl) decrease the piezoelectric coefficients, which become even smaller than the bulk value. Capturing the physics of the different changes in piezoelectricity induced by passivation can be very useful in tuning the piezoelectricity of ZnO nanowire. For that, the effects of the volume change and the surface change on the piezoelectricity are investigated in detail.

    The volume effect can be easily quantified through comparing the piezoelectric coefficients of un-deformed and deformed passivated nanowires. Results of nanowire B is presented here as an example. Table Ⅱ lists the changes in axial lattice length and diameter for four passivated nanowires B, and the corresponding variations in piezoelectric coefficient. The axial lattice in the passivated nanowires is contracted by 0.2%-4.4%, leading to an increase in the piezoelectric coefficient (4%-39%). The piezoelectric coefficient, as a first-order electromechanical term, is regarded as a constant at small strains. At larger strains, the contraction of the axial lattice raises the piezoelectric coefficient due to considerable high-order terms. Meanwhile, the diameters of the nanowires are increased slightly by 0.6%-1.4%. According to Eq.(1), the increase of the diameter only slightly decreases the piezoelectric coefficient, by 4% at maximum. The volume change in passivated nanowires B makes a positive contribution to the piezoelectric coefficient (shown in Table Ⅱ), which is not responsible for the reduction of the piezoelectric coefficient in the 1S passivations. To sum up, there is no evident correlation between the volume effect and the different changes in piezoelectricity of the 2S and 1S passivations. Therefore, the finding suggests that a direction of improving piezoelectricity is shrinking the axial lattice via passivation.

    Table Ⅱ.  Volume effect ($ \Delta e_{33}^{ \rm{v}} $), lattice-induced volume effect ($ \Delta e_{33}^{ \rm{c}} $), diameter-induced volume effect ($ \Delta e_{33}^{ \rm{d}} $), surface effect ($ \Delta e_{33}^{ \rm{s}} $), piezoelectric coefficient only containing surface effect ($ e_{33}^{ \rm{s}} $), ion-displacement contribution ($ e_{33}^{ \rm{ion}} $) and lattice-deformation contribution ($ e_{33}^{ \rm{lat}} $) in nanowires B. All constants are in unit of C/m$ ^2 $.

    To solely compare the surface effects of the passivated nanowires B, the comparisons were conducted by fixing the axial lattice length and diameter as those of the unpassivated nanowires. The piezoelectric coefficient containing surface effect is decomposed into ion-displacement contribution $ e_{33}^{ \rm{ion}} $ and lattice-deformation contribution $ e_{33}^{ \rm{lat}} $ using the following expression [72].

    where i (i = $ x, y, z $) is the direction in the Cartesian coordinate, $ Z^*_{k, 3i} $ is the 3i component of the Born effective charge tensor of the kth ion, $ r_{k, i} $ is the Cartesian coordinate of the kth ion in a supercell in the i direction, $ V $ is the volume of the nanowire in a supercell, $ \epsilon_3 $ is the component of the strain tensor. The lattice-deformation contribution is the piezoelectric coefficient with clamped-ion (a homogeneous strain in which the ionic internal coordinates remain unchanged), the ion-displacement contribution is the residual part of the piezoelectric coefficient (an internal distortion of the ionic internal coordinates at zero strain), which arises from internal microscopic relaxation. The result in Table Ⅱ shows that the surface effect is the reason for different changes in piezoelectricity of the 2S and 1S passivations, where the ion-displacement contribution is much more important.

    The Born effective charge, the ion displacement and the corresponding ion-displacement contributions are plotted in FIG. 3. It is found that the Born effective charges $ Z^*_{3i} $ of atoms nearby surface dramatically change with respect to those at the core of the nanowire. The components $ Z^*_{33} $ of the passivating atoms are around one, and the components $ Z^*_{31} $ of the passivating atoms are raised compared to those of Zn and O atoms.

    Figure 3.  (a) Born effective charges (BEC), (b) ion displacements (ID), (c) ion-displacement contributions (IDC) for passivated nanowires. Note that "a" and "na" represent the axial and non-axial directions, respectively; "p", "n" and "pn" represent cation, anion, and atom pair composed of cation and anion, respectively.

    The charge density difference ($ \Delta Q $) before and after passivations at zero strain was computed to understand the change in Born effective charges due to charge rearrangement:

    where $ Q_{ \rm{pass}} $ and $ Q_{ \rm{unpass}} $ are charge densities for passivated and unpassivated nanowires, respectively; and $ Q_{ \rm{Ad}1} $ and $ Q_{ \rm{Ad2}} $ are charge densities for passivating atoms bonded to Zn and O atoms, respectively. Contour plots of the charge density difference nearby the passivated surfaces are drawn in FIG. 4. As can be seen, the H-O and Cl-O bonds are covalent bonds with electrons in the middle, while the H-Zn, Cl-Zn and F-Zn bonds have more ionic bond components with notable charge transfers. Bonding generally exists between ZnO nanowire and passivating atoms rather than between paired passivating atoms. Only one unpaired electron at a passivating atom leads to the components $ Z^*_{33} $ close to one. In addition, for the Cl passivation, a substantial amount of electrons lie between Cl-Cl paired atoms, which results in a relatively large component $ Z^*_{31} $. For other passivations, there are less electrons lying between paired passivating atoms compared to the Zn-O bond, leading to a smaller response in axial direction to ion displacement thus a reduced component $ Z^*_{31} $. Under a strain, the replacement of the axial ion displacement with the radial ion displacement is observed nearby surface due to the free boundary. For the H passivation, the H-H distance in atom pairs is significantly larger than that in $ \rm H_2 $ molecule, thus this replacement is minor. For the Cl passivation, a notable amount of the replacement occurs due to large repulsion among Cl atoms. And the 2S passivation shows an intermediate situation. In the 1S passivations, the change of the distance between paired passivating atoms is opposite to that of the length of the axial lattice under strain, because of weak interactions between passivating atoms and ZnO nanowires (shown in FIG. 3(b)). The result reflects that the atom pairs at the surface play a role in screening the change in polarization induced by the distortion at the core in the 1S passivations. Consequently, the surface ion-displacement contributions all decrease and those for the 1S passivation are even below 0. Our previous work [2] revealed that in unpassivated nanowires, the replacement of axial ion displacement with radial ion displacement at surface is the key reason for piezoelectric enhancement, since the extra component of piezoelectric coefficient $ e_{31} $ were taken into account. However, for the passivated nanowires in this study, the decrease of the component $ Z^*_{31} $ at the surface suppresses this piezoelectric enhancement. As an exception mentioned above, a large radial ion-displacement contribution exists in the Cl passivation but play a negative role; and therefore the piezoelectric enhancement is suppressed.

    Figure 4.  Contour plots of the charge difference nearby surface for (a) 100% H, (b) 100% Cl, (c) 50% H and 50% Cl, and (d) 50% H and 50% F. Increasing (decreasing) electron density is indicated by blue (red).

    Apart from the ion-displacement contribution, the lattice-deformation contribution also contributes to the different changes in piezoelectricity between the 2S and 1S passivations (list in Table Ⅱ). The polarization redistribution after reconstruction caused by passivation is studied. For that, Bader charge analysis was performed to determine the atomic charge (given in Table Ⅲ). In the bulk ZnO, the charges for Zn and O atoms are 1.162 and -1.162, respectively. In the unpassivated nanowires, the absolute charges of the outermost Zn (1.128) and O (-1.126) atoms are slightly decreased caused by the breakage of the surface bonds. In the passivated nanowires, the absolute charges of the outermost Zn and O atoms are increased by H-O and F-Zn bonds and decreased by H-Zn and Cl-O bonds. The absolute charges of the passivating atoms are different from each other due to different electronegativity. And they are generally smaller than Zn and O atoms because of the sole unpaired valence electron.

    Table Ⅲ.  Bader charges at different positions for passivated nanowires. "Ad1" and "Ad2" represent passivating atoms bonded to Zn and O atoms, respectively. "Bare" represents unpassivated nanowire. "ctr", "sub", "surf", "cnr" represent the position of center, subsurface, surface and corner respectively.

    The polarization of one atom pair with relaxed ions at zero strain is given as,

    where $ p $ is the polarization of an atom pair, $ V^{ \rm{wire}} $ is the volume of the nanowire in a supercell, $ q_{i} $ is the charge of the ith atoms in an atom pair from Bader charge analysis [73], and $ r_{i} $ is the axial displacement of the ith atoms in an atom pair with respect to reference position. The reference position is chosen to ensure that all atom pairs in one unit cell are located at the same side of the reference position. The polarization of atom pairs on the cross section of nanowires is shown as color maps in FIG. 5. Note that one atom pair composed of the nearest Zn-O atoms or the nearest two passivating atoms is labeled as one solid circle. Among all atom pairs of unpassivated and passivated nanowires, the polarization at the outermost layer drops most significantly. Benefit from a small reduction of charges, the outermost polarization in the unpassivated nanowire is decreased slightly. In contrast, the dramatic decrease of the outermost polarization in passivated nanowires is owing to much smaller charges of the passivating atoms compared to Zn and O atoms. As can be seen, the polarization nearby surface in the 2S passivations is generally greater than that in the 1S passivations mainly because of the gap of the atomic charges. The different surface polarization caused by the reconstruction leads to the different lattice-deformation contributions. The lattice-deformation contribution $ e_{33} $ is a measure of the degree to which the negative charges fail to follow a homogeneous deformation with ions at fixed internal coordinates [74]. The larger absolute values of the lattice-deformation contribution in the 1S passivations (shown in Table Ⅱ) indicate that the centers of the surface negative charges weakly follow a homogeneous deformation. In other words, surface negative charges screen the change in polarization induced by the homogeneous deformation.

    Figure 5.  Distribution of polarization of atom pairs on the cross section of passivated nanowires B.

    In essence, the decreases of the ion-displacement contribution and the lattice-deformation contribution in passivated nanowires originate from the lack of surface valence electron compared to Zn and O atoms. In particular, the surface charges are weakly polarized in the passivations with identical chemical species. Due to the screening of surface charge with weak polarization, the ion-displacement in the 1S passivation is largely reduced, even smaller than the unpassivated situation. The results demonstrate that increasing surface polarization is another route of improving piezoelectricity. Finally, the effects of passivation on piezoelectricity at different diameters are discussed. The volume and surface effects (relative to unpassivated counterpart) in nanowire A and C are drawn in FIG. 6. The different surface effects between the 2S and 1S passivations are also identified. However, there is no explicit diameter dependence of the overall effect of passivation due to the competition of the surface and volume effects. Therefore, the piezoelectric coefficient of passivated nanowires does not always converage monotonically to the bulk value with the decreasing surface-to-volume ratio, such as the full Cl passivation (show in Table Ⅰ). This illustrates why the diameter dependence of piezoelectric coefficients of ZnO nanowires was difficult to be identified in experiments [8].

    Figure 6.  Changes in piezoelectric coefficients $ \Delta e_{33} $ (C/m$ ^2 $) due to (a) volume effect and surface effect, (b) overall effect (sum of volume and surface effect) in passivated nanowires A, B and C.

  • In summary, the first-principles calculation was conducted on nanowires in different diameters with four kinds of surface passivations. The 50% H(O) and 50% Cl(Zn), 50% H(O) and 50% F(Zn), 100% H, 100% Cl passivations can all stabilize dangling bonds at the surface, where the 2S passivation is more energetically favorable due to relatively large electronegativity difference. The volume effect increases the piezoelectric coefficient as a result of the shrinkage of the axial lattice. At all diameters, the surface effect in the 2S passivation is slightly weaker than that in the unpassivated case as a result of a relatively small surface charge, but much stronger than that in the 1S passivation due to large polarization of the surface charge. The volume and surface effects compete with each other and influence the identification of the diameter-dependence phenomenon of piezoelectric coefficients for ZnO nanowires in experiments. Our finding sheds light on a strategy to improve piezoelectricity of ZnO nanowire through shrinking axial lattice or raising surface polarization by passivation.

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