This paper establishes the design space of III-N hot electron transistors (HETs) for high current gain by designing and fabricating HETs with scaled base thickness. The device structure consists of GaN-based emitter, base and collector regions where emitter and collector barriers are implemented using AlN and InGaN layers, respectively, as polarization-dipoles. Electrons tunnel through the AlN layer to be injected into the base at a high energy where they travel in a quasi-ballistic manner before being collected. Current gain increases from 1 to 3.5 when base thickness is reduced from 7 to 4 nm. The extracted mean free path (λmfp) is 5.8 nm at estimated injection energy of 1.5 eV.