  Ultra-thin (UT) oxide semiconductors are promising candidates for
back-end-of-line (BEOL) compatible transistors and monolithic three-dimensional
integration. Experimentally, UT indium oxide (In$_2$O$_3$) field-effect
transistors (FETs) with thicknesses down to 0.4 nm exhibits extremely high
drain current (10000 $\mu$A/$\mu$m) and transconductance (4000 $\mu$S/$\mu$m).
Here, we employ the ab initio quantum transport simulation to investigate the
performance limit of sub-5-nm gate length (Lg) UT In$_2$O$_3$ FET. Based on the
International Technology Roadmap for Semiconductors (ITRS) criteria for
high-performance (HP) devices, the scaling limit of UT In$_2$O$_3$ FETs can
reach 2 nm in terms of on-state current, delay time, and power dissipation. The
wide bandgap nature of UT In$_2$O$_3$ (3.15 eV) renders it a suitable candidate
for ITRS low-power (LP) electronics with Lg down to 3 nm. Both the HP and LP UT
In$_2$O$_3$ FETs exhibit superior energy-delay products as compared to other
common 2D semiconductors such as monolayer MoS2 and MoTe2. Our study unveils
the immense promise of UT In$_2$O$_3$ for both HP and LP device applications.
