Collective excitations of a multiple-quantum-well system with barrier of finite height

We present theoretical results for the effects of a finite barrier height on the electronic collective modes of a multiple-quantum-well structure. If the ratio of the barrier height to the miniband bandwidth is much smaller than unity, electrons can move almost freely along the superlattice axis. For nonzero value of $q_z$, the wave vector along the superlattice axis, the plasma frequency of the system is found to decrease from that of the corresponding three-dimensional free-electron gas by a small amount proportional to this ratio. On the other hand, if the ratio is much greater than unity, electrons are mostly confined within the quantum wells. Compared to the structures in which the electron wave functions in different layers have zero overlap, the weak tunneling of the present system is shown to change dramatically the intraminiband collective modes whose wave vectors along the layers, q, are small. The well-known acoustic plasma dispersion is replaced by ω=${\omega }_{\mathrm{pl}+\mathrm{\beta }{q}^2+{\beta }_z{q}_z^2}$, with the plasma frequency ${\omega }_{\mathrm{pl}}$ proportional to the miniband bandwidth.