  Infrared spectroscopic ellipsometry is applied to investigate the free-charge
carrier properties of Mg-doped InN films. Two representative sets of In-polar
InN grown by molecular beam epitaxy with Mg concentrations ranging from
$1.2\times10^{17}$ cm$^{-3}$ to $8\times10^{20}$ cm$^{-3}$ are compared. P-type
conductivity is indicated for the Mg concentration range of $1\times10^{18}$
cm$^{-3}$ to $9\times10^{19}$ cm$^{-3}$ from a systematic investigation of the
longitudinal optical phonon plasmon broadening and the mobility parameter in
dependence of the Mg concentration. A parameterized model that accounts for the
phonon-plasmon coupling is applied to determine the free-charge carrier
concentration and mobility parameters in the doped bulk InN layer as well as
the GaN template and undoped InN buffer layer for each sample. The free-charge
carrier properties in the second sample set are consistent with the results
determined in a comprehensive analysis of the first sample set reported earlier
[Sch\"oche et al., J. Appl. Phys. 113, 013502 (2013)]. In the second set, two
samples with Mg concentration of $2.3\times10^{20}$ cm$^{-3}$ are identified as
compensated n-type InN with very low electron concentrations which are suitable
for further investigation of intrinsic material properties that are typically
governed by high electron concentrations even in undoped InN. The compensated
n-type InN samples can be clearly distinguished from the p-type conductive
material of similar plasma frequencies by strongly reduced phonon plasmon
broadening.
