We show that epitaxial layers suitable for fabrication of AlGaAs/GaAs heterojunction bipolar transistors with a carbon base doping level of up to 10(20) cm(-3) can be grown by solid-source molecular beam epitaxy using CBr4 as a doping precursor. We have observed that the gain of devices fabricated from these layers is improved using an abrupt conduction-band discontinuity at the emitter-base heterointerface. The observed relationship between current gain and the base width Wb Of these devices deviates from the 1/W-b(2) dependence predicted by diffusive electron transport for base widths that are shorter than 60 nm. The relationship is better approximated by a 1/W-b dependence, which is in better agreement with the theories of ballistic or quasiballistic electron transport. Current gain of the devices drops rapidly as the base thickness exceeds 60 nm.