We study tunneling through resonant tunneling diodes (RTD) with very long emitter drift regions (up to 2 microm). In such diodes, charge accumulation occurs near the double barrier on the emitter side, in a self-induced potential pocket. This leads to a substantial enhancement of the wave function overlap between states of the pocket and the RTD, and, consequently, to increased off-resonant current mediated by various scattering processes. For RTD with the longest drift region (2 microm), an additional strong current peak is observed between the first and the second resonant peaks. We attribute this pronounced feature to the intersubband transitions mediated by resonant emission of intersubband plasmons.