  Beta-phase gallium oxide ($\beta$-Ga$_2$O$_3$) research has gained
accelerated pace due to its superiorly large bandgap and commercial
availability of large-diameter native substrates. However, the high acceptor
activation energy obstructs the development of homojunction bipolar devices
employing $\beta$-Ga$_2$O$_3$. The recently demonstrated semiconductor grafting
technique provides an alternative and viable approach towards
lattice-mismatched $\beta$-Ga$_2$O$_3$-based p-n heterojunctions with high
quality interfaces. Understanding and quantitatively characterizing the band
alignment of the grafted heterojunctions is crucial for future bipolar device
development employing the grafting method. In this work, we present a
systematic study of the band alignment in the grafted monocrystalline
Si/$\beta$-Ga$_2$O$_3$ heterostructure by employing X-ray photoelectron
spectroscopy (XPS). The core level peaks and valence band spectra of the Si,
$\beta$-Ga$_2$O$_3$, and the grafted heterojunction were carefully obtained and
analyzed. The band diagrams of the Si/$\beta$-Ga$_2$O$_3$ heterostructure were
constructed using two individual methods, the core level peak method and the
valence band spectrum method, by utilizing the different portions of the
measured data. The reconstructed band alignments of the Si/$\beta$-Ga$_2$O$_3$
heterostructure using the two different methods are identical within the error
range. The band alignment is also consistent with the prediction from the
electron affinity values of Si and $\beta$-Ga$_2$O$_3$. The study suggests that
the interface defect density in grafted Si/$\beta$-Ga$_2$O$_3$ heterostructure
is at a sufficiently low level such that Fermi level pinning at the interface
has been completely avoided and the universal electron affinity rule can be
safely employed to construct the band diagrams of grafted monocrystalline
Si/$\beta$-Ga$_2$O$_3$ heterostructures.
