Long-wavelength nonpolar optical modes in semiconductor heterostructures: Continuum phenomenological model

A continuum phenomenological model for long-wavelength nonpolar optical mod es in semiconductor heterostructures is proposed. Analytical expressions fo r the dispersion relation in quantum well and superlattice-type heterostruc tures are presented. These formulas allow us to compute the phonon modes at kappa=0 in both polar and nonpolar semiconductors. Numerical results for t he eigenfrequencies and squared eigenvectors in unstrained long phonon-band width Ge isotopic SLs and strained narrow phonon-bandwidth Si/Ge superlatti ces and quantum wells agree quite well with theoretical and experimental re sults recently reported elsewhere. A simple way to take into account the in terface modes originated by roughness is also developed.