  In this work, we report the fabrication and characterizations of a
monocrystalline GaAs/$\beta$-Ga$_2$O$_3$ p-n heterojunction by employing
semiconductor grafting technology. The heterojunction was created by lifting
off and transfer printing a p-type GaAs single crystal nanomembrane to an
Al$_2$O$_3$-coated n-type$\beta$-Ga$_2$O$_3$ epitaxial substrate. The resultant
heterojunction diodes exhibit remarkable performance metrics, including an
ideality factor of 1.23, a high rectification ratio of 8.04E9 at +/- 4V, and a
turn on voltage of 2.35 V. Furthermore, at +5 V, the diode displays a large
current density of 2500 A/cm$^2$ along with a low ON resistance of 2
m$\Omega\cdot$cm$^2$.
