Figure 1a–c shows the FESEM images of the fabricated ZnO nanorod arrays grown on glass, PET and Si substrates, respectively. The nanorods were uniformly grown on all substrates with a hexagonal prism shape, suggesting growth along the (002) direction. Note that the density of nanorods per area decreases from PET to glass to Si substrates. The corresponding EDX analysis reveals the existence of Zn and O, which corresponds to the characteristic composition of ZnO, without the presence any impurities or substrate signal. The ratio between Zn and O was the same for all analyzed samples grown on PET, glass and Si substrates.

Figure 2a–c shows magnified FESEM images of the fabricated ZnO nanorods along with the corresponding cross-sectional views. The images reveal the formation of vertically oriented nanorods with various aspect ratios. For example, the nanorods grown on the glass substrates (Figure 2a) have an average length of 1200 nm and a diameter of 38 nm, while those grown on PET substrates (Figure 2b) have an average diameter of 51 nm and a length of 1180 nm. The nanorods grown on Si substrates (Figure 2c) were found to have an average length of 960 nm and a diameter of 92 nm. This implies that the aspect ratio of the single-crystal ZnO nanorods along the (002) direction is sensitive to the substrate type. This can be related to the different mismatch between each substrate and the ZnO seed layer.

Figure 3a–c shows a typical XRD pattern for the ZnO nanorod arrays grown on Si, PET and glass substrates, respectively. For all of the tested ZnO nanorods, a peak is observed at 2θ = 34.4 ± 0.03° corresponding to ZnO (002), revealing the preferentially oriented growth along the c-axis. All diffraction peaks are consistent with the wurtzite structure of ZnO [16], which can be indexed to a standard spectrum in the ICSD database (No. 01-079-0207). Additional broad and highly intense diffraction peaks were observed at a 2θ of 25.9° and 22.7° (and with less intensity at a 2θ of 46.5° and 55.1°) for the nanorods grown on a PET substrate, which can be related to the PET substrate itself.

The lattice constant c along the preferentially oriented growth direction for the hexagonal crystal structure can be calculated using Equation 1, where d is the distance between adjacent planes with Miller–Bravais indices (hkl), and a and c are the lattice constants [16].

[1]

The resulting values of c are listed in Table 1. The variation of these values can be attributed to the strain on the ZnO nanorods due to thermal and lattice mismatching between the substrates and ZnO. The Scherer equation (Equation 2) was used to evaluate the average crystallite size (D) of ZnO from the dominant (002) growth orientation, where β is the full width at half maximum (FWHM) intensity, k is a constant (0.90), and λ is the incident X-ray wavelength [16].

[2]

The obtained results reveal that the increase in the crystallite size is associated with the growth conditions and the type of substrate. For example, the crystallite sizes were 42.230, 42.227 and 33.813 nm for the ZnO nanorods grown on Si, PET and glass substrates, respectively. This variation in crystallite size can clearly be observed in the XRD pattern shown in Figure 3 as a decrease in the FWHM of the ZnO peaks. The dependence of the D values on the type of substrate can be attributed to both lattice and thermal mismatching between these substrates and ZnO. As reported in previous work [17], the lattice and thermal mismatches between ZnO and a Si substrate are 15 and 60%, respectively. PET and glass substrates are amorphous, and are thus expected to result in even larger lattice and thermal mismatching with ZnO than for the Si substrate [18]. In the current study, the lattice mismatch is more effective and can be considered as the main reason for the higher D values and minimized perpendicular strain along the a-axis (ε_a) as compared to that of Si. The perpendicular strain (ε_a) can be calculated using Equation 3 [19], where a is the calculated lattice parameter and a₀ is the corresponding unstrained values of the lattice parameter.

[3]

According to the ICSD diffraction data (No. 01-079-0207), a₀ = 5.2125 Å. The values of ε_a are positive for the tensile strain and negative for the compressive strain. The values of the obtained a, ε_a and D are listed in Table 1, indicating compressive strain.

Wurtzite ZnO belongs to the C_6v⁴ (P63mc) space group, having two formula units in the primitive cell with all atoms occupying C_3v. Also, wurtzite ZnO has eight sets of optical phonon modes at the Brillion zone center (q = 0). These include the Raman active Г = 2 × (A₁ + B₁ + E₁ + E₂) phonon modes, acoustic modes with A_acoustic = A₁ + E, and optical modes with O_optical = A₁ + (2 × B₁) + E₁ + (2 × E₁). The A and E modes are polar and split into transverse optical (TO) and longitudinal optical (LO) phonons while the B modes are silent modes. According to the selection rules, E₁, E₂ and LO are Raman active, while the E and TO are forbidden. Due to the long-range electrostatic forces, the phonons with A₁ and E symmetry are polar and hence exhibit different frequencies for the TO and LO phonons. Every mode corresponds to a band in the Raman spectrum, with the A₁ phonon vibration polarized parallel to the c-axis and the E phonon polarized perpendicular to the c-axis. The intensities of these bands depend on the scattering cross section of these modes [20].

Figure 4a–c shows the obtained Raman spectra of the single-crystal ZnO nanorod arrays grown on Si, PET and glass substrates, respectively. All samples exhibit the same peaks but with slightly different Raman shifts. The peak at ≈439 cm⁻¹ is attributed to the E₂ (high) mode, which is shifted by 2.6 cm⁻¹ compared to the standard E₂ (high) phonon mode in standard unstrained ZnO samples (437.0 cm⁻¹). This shift can be attributed to the compressive stress that exists in the ZnO nanorod samples, in good agreement with previous reports [21–22]. The peak at 576.45 cm⁻¹ in sample (b) (PET substrate) is an intrinsic LO mode of hexagonal wurtzite ZnO [23]. This peak is a result of the combination of resonance at the excitation wavelength and impurity-induced scattering [22]. Also, other highly intense peaks were detected in sample (b) in the region 600–890 cm⁻¹ characteristic of the PET substrate (sub), which also can be seen in sample (a) for glass substrate (sub), yet it was not detected for the Si substrate.