Due to the absence of p-type gallium oxide (Ga₂O₃), p-type nickel oxide (p-NiO_x) was commonly employed in Ga₂O₃ Schottky barrier diode (SBD), which typically utilized either junction termination extension (JTE) or hetero-junction barrier Schottky (HJBS) structure. However, the influence of the NiO_x on device performance has been insufficiently explored. In this work, the effects of NiO_x in JTE and HJBS were investigated by Sentaurus TCAD. In JTE structure, breakdown voltage (BV) presented positive correlation with NiO_x doping concentration and negative correlation with the NiO_x tilt angle. In HJBS structure, BV increased with the width and depth of the NiO_x field ring (FR), while decreased with the spacing between the FR and the anode edge. The optimal configuration was identified, consisting of 10° tilt angle and doping concentration of 3×10¹⁹ cm^-3 for the NiO_x JTE, as well as NiO_x rings of 5 μm width, 1.5 μm depth, and 1 μm spacing for NiO_x HJBS. This configuration achieved the BV of 4.52 kV, specific on-resistance (R_on,sp) of 5.68 mΩ·cm² and performance figure of merit (PFOM) value of 3.57 GW/cm², representing enhancements of 113% in BV and 132% in PFOM compared to experimental reports. This study contributed a design approach for vertical Ga₂O₃ SBD utilizing NiO_x JTE and HJBS structures, enhancing BV and PFOM in SBD.