We report a calculation of the electron-phonon interaction effects on
donor impurity binding energy in a semiconductor quantum wire of recta
ngular cross section and finite barrier potential. The results for the
binding energy are obtained as a function of the size of the wire for
different positions of the impurity and for several values of the pot
ential confining barrier height. It is found that the presence of phon
ons changes significantly the values of the impurity binding energies
of the system.