Plasmon-phonon-coupled modes and their lineshapes for a doped semiconductor superlattice

We studied the plasma oscillations of an electron gas and a hole gas in a GaAs doped superlattice. The doped superlattice is modelled to be a one-dimensional periodic sequence of electron and hole layers which are embedded alternately in a homogeneous polar dielectric host medium. The density-density correlation function has been calculated for a model structure in order to study the plasma-phonon-coupled modes. The strong charge carrier-impurity scattering which results from random doping impurities in the electron (hole) layers, has been taken into account by choosing appropriate polarizabilities for intrasubband-intersubband transitions and the harmonic oscillator wavefunctions as electron (hole) envelope functions. Our calculation demonstrates that the presence of random doping impurities in electron (hole) layers significantly affects both electron and hole plasmons. The well behaved plasma modes in a GaAs doped superlattice can be observed for restricted values of wavevector. In the 2D limiting case, the plasma frequency in a doped superlattice is approximately proportional to (q²-q_c²)¹2/, while for a modulation doped superlattice (such as Ga_xIn_1-xAs/GaAs_ySb_1-y) it is proportional to q, for small q-values. q_c is the critical value of the in-plane wavevector q. Our calculated lineshapes of coupled plasmon-phonon modes can be well separated from each other and could have reasonable half-widths and peak heights which could be observed experimentally for the right choice of values for the parameters of the doped superlattice.