## 3 Results and Discussion
### Effects on Ultraviolet (IV)-Visible Absorption  
Figure 6a shows the UV-visible absorption spectrum of the \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\) nanorod array. The absorption band is mainly located between 300 nm and 550 nm. Electron transition on the energy levels of \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\) can be divided into direct transition and indirect transition, corresponding to O\({}^{2-}\)\(\rightarrow\)Fe\({}^{3+}\) and Fe\({}^{3+}\) 3d\(\rightarrow\)3d, respectively [40]. The energy gaps of direct transition and indirect transition could be estimated by Equations (4) and (5), which were derived from Equations (2) and (3). The plots of (Ahv)\({}^{2}\) or (Ahv)\({}^{0.5}\) against hv (i.e., Tauc plots) of the undoped \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\) are displayed in Figure 6b.  
Figure 4: Photograph of the samples obtained from aqueous chemical growth before and after annealing.  
Figure 3: X-ray diffraction (XRD) profiles of the samples prepared by aqueous chemical growth: (**a**) before annealing; (**b**) after annealing, the (h k l) values of \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\) are marked.  
The intersection of the linear extension of the Tauc plots with x axis represents the energy gap of direct transition or indirect transition [41]. They are 2.24 eV and 1.85 eV, respectively, in the present work. The energy gap of the direct transition estimated by the Tauc plot is close to its theoretical value (2.1-2.2 eV). [PERSON] et al. [42] observed that the energy gap of \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\) nanorods increased by 0.3-0.6 eV compared with \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\) bulk due to the quantum confinement effect of nanorods. However, the quantum confinement effect was not observed in this study.  
\[\mathrm{Eg}=1240/\lambda \tag{1}\]  
\[\alpha\mathrm{h}\
u=\mathrm{B}(\mathrm{h}\
u-\mathrm{Eg})^{\mathrm{n}} \tag{2}\]  
\[\mathrm{A}=\alpha\mathrm{b}\mathrm{c} \tag{3}\]  
\[\left[(\mathrm{A}/\mathrm{Bbc})\mathrm{h}\
u\right]^{2}=\mathrm{h}\
u-\mathrm{ Eg} \tag{4}\]  
\[\left[(\mathrm{A}/\mathrm{Bbc})\mathrm{h}\
u\right]^{0.5}=\mathrm{h}\
u-\mathrm{Eg}\] for indirect transition (5)  
Eg: energy gap in eV between a conduction band and a valence band  
\(\lambda\): wavelength in nm  
\(\alpha\): absorption coefficient  
h\(\
u\): the energy of a photon  
B: a constant  
Figure 5: Scanning electron microscope (SEM) images of the samples: (**a**) precursor \(\beta\)-FeOOH; (**b**) undoped \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\); (**c**) Co -doped \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\); (**d**) Ni-doped \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\).  
The UV-visible absorption spectra of the doped samples are not displayed in Figure 6 as they overlap with the undoped one. As the UV-visible absorption spectra are almost the same this suggests that the Co or Ni doping has little influence on the optical absorption of \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\). Inducing a red shift of absorption onset is one of the reasons for an enhanced PEC performance [4; 36]. However, in this study, this reason was excluded. Similar to this study, other researchers [5; 43] also observed the doping of foreign elements did not change the energy gap of \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\).