  Vertical $pn$ heterojunction diodes were prepared by plasma-assisted
molecular beam epitaxy of unintentionally-doped $p$-type SnO layers with hole
concentrations ranging from $p=10^{18}$ to $10^{19}$cm$^{-3}$ on
unintentionally-doped $n$-type $\beta$-Ga$_{2}$O$_{3}$(-201) substrates with an
electron concentration of $n=2.0\times10^{17}$cm$^{-3}$. The SnO layers consist
of (001)-oriented grains without in-plane expitaxial relation to the substrate.
After subsequent contact processing and mesa etching (which drastically reduced
the reverse current spreading in the SnO layer and associated high leakage)
electrical characterization by current-voltage and capacitance-voltage
measurement was performed. The results reveal a type-I band alignment and
junction transport by thermionic emission in forward bias. A rectification of
$2\times10^{8}$ at $\pm1$V, an ideality factor of 1.16, differential specific
on-resistance of 3.9m$\Omega\thinspace$cm$^{2}$, and built-in voltage of 0.96V
were determined. The $pn$-junction isolation prevented parallel conduction in
the highly-conductive Ga$_{2}$O$_{3}$ substrate (sheet resistance
$R_{S}\approx3\thinspace\Omega$) during van-der-Pauw Hall measurements of the
SnO layer on top ($R_{S}\approx150$k$\Omega$,
$p\approx2.5\times10^{18}$cm$^{-3}$, Hall mobility $\approx1$cm$^{2}$/Vs). The
measured maximum reverse breakdown voltage of the diodes was 66V, corresponding
to a peak breakdown field 2.2MV/cm in the Ga$_{2}$O$_{3}$-depletion region.
Higher breakdown voltages that are required in high-voltage devices could be
achieved by reducing the donor concentration in the $\beta$-Ga$_{2}$O$_{3}$ to
increase the depletion width as well as improving the contact geometry to
reduce field crowding.
