Scattering of plasmons in a quasi-two-dimensional electron gas containing a fixed-point charge

We study the scattering of two-dimensional (2D) plasmons by the carrier density nonuniformity created by a charged impurity. The plasmons are described by an integral equation obtained within the hydrodynamic model of the 2D plasma containing a fixed-point charge. We obtain the energy of the scattered plasmons, and evaluate the scattering cross section in the Born approximation. We find that at low energy it varies as the square of the frequency of the incident plasmon. This behavior is markedly different from the three-dimensional plasmon scattering where the scattering cross section goes to a nonzero value at zero momentum. In addition, we employ the random-phase approximation to treat both correlation and finite thickness effects in quantum wells. This allows us to extend these results for the 2D inhomogeneous hydrodynamic model to treat intrasubband plasmons in semiconductor quantum wells. © 1996 The American Physical Society.