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 k·p 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 x=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 x, are compared and it is found that at zero frequency the superlattice dielectric constant is slightly larger with the difference increasing for higher frequencies.