POLAR OPTICAL OSCILLATIONS OF LAYERED SEMICONDUCTOR STRUCTURES IN THE LONG-WAVELENGTH LIMIT

Polar optical oscillations coupled to unretarded electric fields are discussed for the long-wavelength limit with application to layered semiconductor structures (quantum wells, superlattices, etc.). A Lagrangian formalism is adopted for the deduction of the equations of both mechanical and electrical quantities. The obtained equations bear the form of second-order coupled differential equations for the fundamental quantities, displacement field a and electric potential phi. Matching boundary conditions are rigorously derived from the equations and interpreted physically. The particular case of materials belonging to the cubic symmetry is discussed with special application to the double heterostructure. Some comments are also made about the case of isotropic constituent materials. We have thus settled a theory for long-wavelength 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.