The scattering due to intersubband transition via optical phonons is investigated for a Si-doped-thin-layer inserted ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum-well structure under an applied longitudinal electric field. The subband wave functions of electron states are determined by solving the Schr\"odinger and Poisson equations self-consistently, and the interface phonon modes are obtained by use of the transfer matrices method on the basis of the dielectric continuum model. The dependence of scattering rates on the position and Al content of inserted layer is clearly demonstrated. It is found that intersubband scattering can be modulated greatly by changing the applied field and adjusting the well structure parameters, which may be useful for some device applications. \textcopyright{} 1996 The American Physical Society.