Using a transmission probability formalism, we perform theoretical calculations for the current‐noise characteristics of a finite semiconductor superlattice with correlated thickness randomness in which the thicknesses of barriers are regular but those of wells are partially random. The transmission probability is calculated by the use of an exact Airy‐function formalism combined with a transfer matrix technique. We show that the tunneling resonance, owing to the existence of reflectionless electron waves in the absence of electric field, is sensitively suppressed by the applied field, leading to a special region of negative differential resistivity at low bias voltages in theI‐Vcurve. The current fluctuations near the peak of theI‐Vcurve are decreased from the usual shot‐noise values due to the large transmission of the reflectionless waves. The results may shed light on the possibility of exploiting the structure in designing resonant‐tunneling systems that require optimum sensitivity to applied electric field. ©1995 American Institute of Physics.