Cerenkov generation of high-frequency confined acoustic phonons in quantum wells

Abstract

We analyze the Cerenkov emission of high-frequency confined acoustic phonons by drifting electrons in a quantum well. We find that the electron drift can cause strong phonon amplification (generation). A general formula for the gain coefficient α is obtained as a function of the phonon frequency and the structure parameters. The gain coefficient increases sharply in the short-wave region. For the example of a Si/SiGe/Si device it is shown that the amplification coefficients of the order of hundreds of cm −1 can be achieved in the sub-THz frequency range.PACS numbers 72.20, 68.65.+g, 63.20.Kr, 63.22. +m High-frequency lattice vibrations with a high degree of spatial and temporal coherence have been observed for a number of semiconductor materials and heterostructures. These include Si, Ge, GaAs as well as SiGe and AlGaAs superlattices. 1,2 These studies provide information on excitation mechanisms for the coherent phonons, their dynamics, electron-phonon interaction, and other important phenomena, including phonon control of the ionic motion. 3 Intense coherent phonon waves can be exploited for various applications: terahertz modulation of light, generation of high frequency electric oscillations, nondestructive testing of microstructures, etc. Usually, both optical and acoustic high-frequency coherent phonons are excited optically by ultrafast laser pulses. 1,2 The development of electrical methods of coherent phonon generation is an important problem. An electric current flowing though a semiconductor can produce high-frequency coherent acoustic phonons. Two distinct cases are possible. If the current results from transitions of carriers between bound electron states, coherent phonon generation can occur if there is a population inversion between these states. Hopping vertical transport in superlattices and three barrier structures provides examples of mechanisms for the establishment of a population inversion and for stimulated generation of terahertz phonons 4 and plasmons. 5 If the current is due to free electron motion in an electric field, phonon amplification (generation) can be achieved via the Cherenkov effect if the electron drift velocity exceeds the velocity of sound. This effect is well-known for bulk samples. 6 High drift velocities and large densities of electrons are necessary for practical use of the Cerenkov effect. Advanced technology of semiconductor heterostructures opens new possibilities to employ this effect for high-frequency phonon generation. Indeed, such phenomena as high electron mobility at large electron density and phonon confinement in a quantum well (QW) can greatly facilitate achieving phonon amplification and generation by electron drift. In this letter, we analyze the generation of high-frequency confined acoustic phonons under the electron drift in a QW layer.Consider a symmetric heterostructure shown in Fig. 1, (a) with electrons confined in the layer A of thickness 2d. Assuming isotropic elastic properties for both semiconductors A and B one can introduce the longitudin...

Confinement and amplification of acoustic waves in cubic heterostructures

“…The basic behavior of ␣ is similar to that found in the isotropic model calculations presented in Ref. 16. The maximum amplification is achieved at low temperatures: ␣ SSVϪ0 (364 GHz, 50 K) ϭ1200 cm Ϫ1 .…”

“…6͑a͒, these heterostructures are characterized by an overlap between the sectors S T B and S T A . It is important to emphasize that for such a case the isotropic elastic model 5, 16 cannot predict the existence of confined SV waves because in this model each sector S L,T M reduces to a line. Instead, criterion ͑23͒ resolves the confinement problem even for this case.…”

“…Such an analysis was made in Ref. 16. When the population of the mode becomes large and the phonon subsystem can be treated semiclassically, we can introduce the intensity of the corresponding acoustic wave and define the amplification ͑absorption͒ coefficient, ␣ q .…”

“…Recently, it was suggested that the confined high-frequency phonons can be amplified by the drift of two-dimensional electrons. 16 A realization of this effect in semiconductor heterostructures would open up interesting perspectives for the generation of coherent high-frequency confined phonons and for the study of confined electron-confined phonon interaction.…”

“…͑A general analysis of possible acoustical waves in layered systems can be found in Refs. [17][18][19].͒ Previously, confined waves 5 and their amplification 16 were studied based on a simple model of elastically isotropic media. In this paper, we develop a model of elastically anisotropic (cubic) media for layers constituting the heterostructure to make an analysis of the confined modes and their amplification ͑generation͒ more realistic.…”