In this paper, we have characterized the electrical properties related to gate leakage current in AlGaN/GaN MISHFETs with varying the thickness (0 to 10 nm) of $Al_2O_3$ gate insulator which also serves as a surface protection layer during high-temperature RTP. The sheet resistance of the unprotected TLM pattern after RTP was rapidly increased to $1323{Omega}/{square}$ from the value of $400{Omega}/{square}$ of the as-grown sample due to thermal damage during high temperature RTP. On the other hand, the sheet resistances of the TLM pattern protected with thin $Al_2O_3$ layer (when its thickness is larger than 5 nm) were slightly decreased after high-temperature RTP since the deposited $Al_2O_3$ layer effectively neutralizes the acceptor-like states on the surface of AlGaN layer which in turn increases the 2DEG density. AlGaN/GaN MISHFET with 8 nm-thick $Al_2O_3$ gate insulator exhibited extremely low gate leakage current of $10^{-9}A/mm$, which led to superior device performances such as a very low subthreshold swing (SS) of 80 mV/dec and high $I_{on}/I_{off}$ ratio of ${sim}10^{10}$. The PF emission and FN tunneling models were used to characterize the gate leakage currents of the devices. The device with 5 nm-thick $Al_2O_3$ layer exhibited both PF emission and FN tunneling at relatively lower gate voltages compared to that with 8 nm-thick $Al_2O_3$ layer due to thinner $Al_2O_3$ layer, as expected. The device with 10 nm-thick $Al_2O_3$ layer, however, showed very high gate leakage current of $5.5{ imes}10^{-4}A/mm$ due to poly-crystallization of the $Al_2O_3$ layer during the high-temperature RTP, which led to very poor performances.