  We demonstrate a tunnel field effect transistor based on a lateral
heterostructure patterned from an $\mathrm{LaAlO_3/SrTiO_3}$ electron gas.
Charge is injected by tunneling from the $\mathrm{LaAlO_3}$/$\mathrm{SrTiO_3}$
contacts and the current through a narrow channel of insulating
$\mathrm{SrTiO_3}$ is controlled via an electrostatic side gate. Drain-source
I/V-curves have been measured at low and elevated temperatures. The transistor
shows strong electric-field and temperature-dependent behaviour with a steep
sub-threshold slope %of up to as small as $10\:\mathrm{mV/decade}$ and a
transconductance as high as $g_m\approx 22 \: \mathrm{\mu A/V}$. A fully
consistent transport model for the drain-source tunneling reproduces the
measured steep sub-threshold slope.
