POLAR OPTICAL OSCILLATIONS OF LAYERED SEMICONDUCTOR STRUCTURES IN THELONG-WAVELENGTH LIMIT

Polar optical oscillations coupled to unretarded electric fields are d iscussed for the long-wavelength limit with application to layered sem iconductor structures (quantum wells, superlattices, etc.). A Lagrangi an formalism is adopted for the deduction of the equations of both mec hanical and electrical quantities. The obtained equations bear the for m of second-order coupled differential equations for the fundamental q uantities, displacement field a and electric potential phi. Matching b oundary conditions are rigorously derived from the equations and inter preted physically. The particular case of materials belonging to the c ubic symmetry is discussed with special application to the double hete rostructure. Some comments are also made about the case of isotropic c onstituent materials. We have thus settled a theory for long-wavelengt h oscillations taking into account dispersion up to quadratic terms in the wave vector (through the introduction of medium internal stresses ) with the aim of avoiding some problems which have been detected and discussed in earlier treatments of this subject.