The scattering rates of electron–optical-phonon interaction in thin layered ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x{\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{1-y}{\mathrm{Al}}_y\mathrm{As}$ superlattices are presented, taking into account both electron and phonon confinement effects. Our approach is based on a macroscopical dielectric continuum model to describe phonon quantization, while a nonparabolic Krönig-Penney model is used to find electron eigenvalues and eigenstates. The presence of ternary alloy components is also considered in order to account for the detailed multimode phonon dispersion. We show numerical results for a ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}{\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ superlattice, with $W=60\mathrm{}\hspace{0.5em}\mathrm{\AA }\mathrm{}$ and $B=18\mathrm{}\hspace{0.5em}\mathrm{\AA }\mathrm{}$ which is the typical geometry of quantum cascade laser superlattices. AlAs-like interface phonons couple strongly with electrons and give the largest contribution to the total inter- and intraminiband transition rates. Carrier scatterings with confined phonons have smaller probabilities with respect to interface ones. Finally we show that a lot of care is necessary if effective bulklike InGaAs phonons are used in modeling superlattice structures.

• Received 2 May 2001

DOI:https://doi.org/10.1103/PhysRevB.65.125314