Microelectronic Engineering 43–44 (1998) 471–479 A many body study of the SASER dynamics a a, a b * J. Weberszpil , S.S. Makler , E.V. Anda , M.I. Vasilevskiy a ´ Instituto de Fısica, Universidade Federal Fluminense, Campus Praia Vermelha, Av. Gal. Milton Tavares de Souza s / n, ´ 24210-340, Niteroi-RJ, Brazil b Faculty of Applied Physics, N. Novgorod University, Nizhni Novgorod 603600, Russia Abstract SASER is a device consisting of a double barrier heterostructure (DBH) tailored in such a way that the energy difference between the two lowest electronic resonant levels in the well is close to the LO-phonon energy. This LO-phonon decays in a pair of phonons producing an intense coherent beam of short wavelength TA phonons (a SASER beam). In previous works we studied an elementary model [1,2], its dynamics [3] and the polaronic effects on its static properties [4]. In this paper the system is described by a tight-binding Hamiltonian for the electrons, a single confined mode for the LO-phonon and the electron–phonon interaction. This interaction produces, near the condition for phonon emission, a pair of polaronic states through which the electron can tunnel. We have obtained for this model an analytical solution applied to the study of the dynamical properties. In a small region of the applied bias, depending on the relevant parameters of the system, an instability appears. By an adequate adjustment of these parameters it is possible to control the extension and characteristics of the instability region. The temporal behavior of the solutions is characterized applying the usual criteria for dynamical systems.  1998 Elsevier Science B.V. All rights reserved. Keywords: Polaronic; Dynamics; Chaotic 1. Introduction In recent works [1–5] we have proposed a device capable of generating ultra high-frequency coherent sound. It consists of a DBH under the effect of an external bias V, designed in such a way as to make the LO phonon field resonate with the two lowest electronic levels in the well. The short wavelength TA phonons produced by the decay of LO phonons form a beam that we called SASER by analogy with a laser. The SASER beam has potential applications to imaging (phonon optics [6], phonon microscopy [7,8]), nondestructive characterization at mesoscopic scale, phonoelectronics and phonolithography. To determine whether these applications are possible, a study of the stability of the device is required. It is essential to warrant a regular behavior of it at least for a wide region of the applied potential V. * Corresponding author. Fax: 155 21 6203881; e-mail: sergio@if.uff.br 0167-9317 / 98 / $19.00 Copyright  1998 Elsevier Science B.V. All rights reserved. PII: S0167-9317(98)00207-X