We present a theoretical investigation of the collective excitations in doped tunneling semiconductor superlattices by calculating the loss functions describing inelastic electron scattering and Raman scattering experiments. The dynamical response of this inhomogeneous electron system is treated within the random-phase approximation. Our calculations indicate that in addition to the conventional plasma modes associated with the in-phase motion of all electrons in the system, as well as the single-particle-like transitions with nonvanishing oscillator strength, there exist plasma modes related with the charge depletion in the surface layers of typical systems. A tunneling plasma mode corresponding to the electron motion along the superlattice growth direction is also shown to exist. The dispersion relations for the different plasma modes are obtained together with their effective oscillator strength for both inelastic electron and light scattering experiments. The strongest intraminiband plasmon behaves like that in two-dimensional electron systems in the small ${\mathit{q}}_{\mathrm{\parallel }}$ regime, while the surface plasma modes exhibit an acousticlike linear dispersion due to the screening of the electrons in the bulk subbands. The behavior of the tunneling plasma mode is intermediate to these two. We show explicitly that the two experimental probes emphasize different modes in the various wave-vector regimes, and are therefore rather complementary.

• Received 10 June 1993

DOI:https://doi.org/10.1103/PhysRevB.48.14407