A heterojunction bipolar transistor with an exponentially graded base doping is disclosed, in addition to a technique for fabricating the transistor. In accordance with the preferred embodiment, the transistor employs a base with an exponentially graded Beryllium doping which varies from 5.times.10.sup.19 cm.sup.-3 at the base-emitter junction to 5.times.10.sup.18 cm.sup.-3 at the base-collector junction. The built-in field due to the exponentially graded doping profile significantly reduces base transit time despite bandgap narrowing associated with high base doping. Compared to devices with the same base thickness and uniform base doping, the cut off frequency is increased and the maximum frequency of oscillation is also increased. Also, consistently higher common emitter current gain results even though the Gummel number is twice as high and the base resistance is reduced by 40%.