The scattering of a quasi two-dimensional electron gas by optical phon
ons in selectively doped AlxGa1-xAs/GaAs/AlxGa1-xAs quantum wells is s
ystematically studied in order to determine the effect of phonon confi
nement. The electron states are calculated solving self-consistently S
chrodinger and Poisson equations to obtain an accurate dependence upon
the structure parameters and the temperature. We study the way the sc
attering is affected by the form of the phonons calculating the mobili
ty using three models for the phonons. They are considered: (a) as thr
ee dimensional (3D), (b) as a set of confined and interface phonons, a
nd (c) as the normal modes of the heterostructure. The relaxation time
s for the electron energy subbands are calculated solving the system o
f Boltzmann equations. The effect of the temperature and the well widt
h variation is also investigated. The results are in a good agreement
with experimental measurements. The agreement is only slightly depende
nt on the model used for the phonons and becomes best when the effect
of the heterostructure on the phonon modes is taken into account.