  Aluminum nitride (AlN) plays a key role in modern power electronics and
deep-ultraviolet photonics, where an understanding of its thermal properties is
essential. Here we measure the thermal conductivity of crystalline AlN by the
3${\omega}$ method, finding it ranges from 674 ${\pm}$ 56 W/m/K at 100 K to 186
${\pm}$ 7 W/m/K at 400 K, with a value of 237 ${\pm}$ 6 W/m/K at room
temperature. We compare these data with analytical models and first principles
calculations, taking into account atomic-scale defects (O, Si, C impurities,
and Al vacancies). We find Al vacancies play the greatest role in reducing
thermal conductivity because of the largest mass-difference scattering.
Modeling also reveals that 10% of heat conduction is contributed by phonons
with long mean free paths, over ~7 ${\mu}$m at room temperature, and 50% by
phonons with MFPs over ~0.3 ${\mu}$m. Consequently, the effective thermal
conductivity of AlN is strongly reduced in sub-micron thin films or devices due
to phonon-boundary scattering.
