We prepared SOI(silicon-on-insulator) wafer pairs of Si II SiO$_2$/Si$_3$N$_4$ II Si using wafer direct bonding with an electric furnace annealing(EFA), a fast linear annealing(FLA), and a rapid thermal annealing(RTA), respectively, by varying the annealing temperatures at a given annealing process. We measured the bonding area and the bonding strength with processes. EFA and FLA showed almost identical bonding area and theoretical bonding strength at the elevated temperature. RTA was not bonded at all due to warpage, We report that FLA process was superior to other annealing processes in aspects of surface temperature, annealing time, and bonding strength.