The source of holes in p-type In$_{x}$Ga$_{1-x}$N films

InGaN is an important alloy for many optoelectronic applications due to its tunable bandgap, which can range from $\sim $1-3 eV, corresponding to wavelengths of $\sim $400-1200 nm. In$_{x}$Ga$_{1-x}$N films, with x between 0.02 and 0.11, are studied at 4 K using electron paramagnetic resonance (EPR) spectroscopy. The films were made p-type by doping with Mg to a concentration of 2-3$\times $10$^{19}$ cm$^{-3}$, and the thickness of each film was between 0.25 and 0.44 $\mu $m. Hall measurements show that the hole density of a film increases with increasing In mole fraction, as expected, but the measured EPR intensity of the Mg-related signal is found to decrease. This trend is opposite of what is observed in other nitrides. Because the Mg-related EPR signal intensity represents the amount of unionized Mg, the amount of EPR detected Mg at low temperatures ($\sim $4K) tracks the hole concentration at room temperature in p-type GaN films. Together, compensating defects and a lowering of the acceptor level may explain the decrease in EPR intensity and the increase in hole density observed as the In mole fraction is increased.