Resonant tunnelling in a double-barrier heterostructure (DBHS) designe
d in order to produce an intense coherent emission of phonons is studi
ed theoretically. This emission is achieved when the energy difference
between the first excited level and the ground state in the well is c
lose to the LO-ehonon energy. The LO phonons emitted during the electr
on transition decay into a pair of ((LO) over tilde and TA) phonons th
at leave the well in the [111] direction. These secondary TA phonons a
re coherent and form a beam that we call a SASER (by analogy with 'las
er'). The circulating current and the populations of phonons and elect
rons in the well are calculated by solving appropriate kinetic equatio
ns. Some possible applications of this system are discussed.