Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems

Twenty years ago active experimental studies of plasma oscillations in two-dimensional electron systems (2DES’s) in Si metal-oxide-semiconductor field-effect transistors and ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures began. From the outset the idea of using the radiative decay of grating-coupled 2D plasmons for creation of tunable solid-state far-infrared sources has been discussed in the literature; however, numerous attempts to realize it in far-infrared 2D plasmon emission experiments (in which the plasmons are excited by a strong dc current flowing in the 2DES) have failed: the intensity of radiation turned out to be too small to be promising for device applications. We present a complete analytic theory of a grating-coupled 2DES with a flowing current. We show why the devices have not worked properly so far, and what should be done to increase the radiation, to get an amplification of light, and to reduce threshold currents of amplification down to experimentally achievable values. The main idea of the work—to replace the commonly employed metal grating by a quantum-wire one—allows one essentially to reduce threshold currents, and to increase the amplification of waves by several orders of magnitude. We show that tunable far-infrared emitters, amplifiers, and generators can be created at realistic parameters of modern semiconductor heterostructures. This work opens new ways to the practical implementation of plasma waves in low-dimensional electron systems.