A new expression is derived for the transmission coefficient of incide
nt electrons scattered by a varying potential with discontinuities. Th
e expression is applicable above, below, and near the potential peak.
As an example, electron transmission across the energy barrier in the
emitter of an InP/InGaAs heterojunction bipolar transistor is calculat
ed. Excellent agreement with a numerical calculation is obtained, even
for electron energies close to the potential peak, where other expres
sions fail. It is shown how this new approach reduces to other express
ions in limiting cases, and its validity in comparison to other approx
imations is discussed.