General model of the transverse dielectric constant of GaAs-AlAs superlattices

A general model of the transverse dielectric constant of GaAs-AlAs superlattices is presented. The model is based on treating separately the individual contributions from the Λ, X, and L valleys, enabling us to understand better the general trends of the overall dielectric constant. An accurate · band calculation is used to determine the bulk band structure around the three symmetry points and a realistic Kronig-Penney model is used to calculate the influence of the superlattice periodicity on the bulk band structure. The resulting dielectric constant shows a small polarization effect due to the anisotropy of the superstructure and a large amount of fine structure corresponding to different transitions between the quantized levels. The influence of the barrier and well thicknesses, L_B and L_Z, respectively, is also important and it is shown that for a constant value of =L_B/(L_B+L_Z), the real part of the zero frequency dielectric constant increases as a function of L_B. Finally, the real parts of the dielectric constants of a superlattice and the corresponding AlGaAs alloy, characterized by the same value of , are compared and it is found that at zero frequency the superlattice dielectric constant is slightly larger with the difference increasing for higher frequencies.