  The electronic structure of the magnetic semiconductor Ga$_{1-x}$Cr$_{x}$N
and the effect of Si doping on it have been investigated by photoemission and
soft x-ray absorption spectroscopy. We have confirmed that Cr in GaN is
predominantly trivalent substituting for Ga, and that Cr 3$d$ states appear
within the band gap of GaN just above the N 2$p$-derived valence-band maximum.
As a result of Si doping, downward shifts of the core levels (except for Cr
2$p$) and the formation of new states near the Fermi level were observed, which
we attribute to the upward chemical potential shift and the formation of a
small amount of Cr$^{2+}$ species caused by the electron doping. Possibility of
Cr-rich cluster growth by Si doping are discussed based on the spectroscopic
and magnetization data.
