The principle of operation of a bipolar transistor with controlled multiplication of one type of carriers is outlined. The ideal device, with a few periods of a staircase superlattice in the base-collector depletion region, has high current outputs at extremely low bias voltages and high current gains. The principle is experimentally demonstrated in a GaAs/AlGaAs/InGaAs phototransistor where three periods of a periodic pseudormorphic structure, in which electrons should predominantly multiply, are included in the collector depletion region. Independent measurements of the electron and hole avalanche multiplication rates, Mn and Mp, in these structures confirm that Mn/Mp and α/β are ~2-4, depending on bias voltage. The observed photocurrent characteristics agree reasonably well with Monte Carlo calculations made to simulate the transport of electrons through the collector region. Measured optical gains are as high as 142 in an n-p-n phototransistor with a 2000-Å p-base region.