  We report a study on the electrical properties of 19 nm thick Yttrium Iron
Garnet (YIG) films grown by liquid phase epitaxy. The electrical conductivity
and Hall coefficient are measured in the high temperature range [300,400]~K
using a Van der Pauw four-point probe technique. We find that the electrical
resistivity decreases exponentially with increasing temperature following an
activated behavior corresponding to a band-gap of $E_g\approx 2$ eV, indicating
that epitaxial YIG ultra-thin films behave as large gap semiconductor, and not
as electrical insulator. The resistivity drops to about $5\times 10^3$~$\Omega
\cdot \text{cm}$ at $T=400$ K. We also infer the Hall mobility, which is found
to be positive ($p$-type) at 5 cm$^2$/(V$\cdot$sec) and about independent of
temperature. We discuss the consequence for non-local transport experiments
performed on YIG at room temperature. These electrical properties are
responsible for an offset voltage (independent of the in-plane field direction)
whose amplitude, odd in current, grows exponentially with current due to Joule
heating. These electrical properties also induce a sensitivity to the
perpendicular component of the magnetic field through the Hall effect. In our
lateral device, a thermoelectric offset voltage is produced by a temperature
gradient along the wire direction proportional to the perpendicular component
of the magnetic field (Righi-Leduc effects).
