Generation of Acoustic Phonons in Semiconductor Superlattice in the Case of an Intraband Absorption of Electromagnetic Wave

Abstract

We obtain the damping coefficient of an acoustic wave for the case of intraband multiphoton absorption of an electromagnetic wave in a superlattice. The ranges in which the acoustic damping coefficient reverses sign are determined for the sound-propagation directions which are transverse and parallel to the superlattice axis. Numerical summation of the series for the acoustic-wave gain is performed for typical parameters of the superlattice. The gain is estimated numerically. It is noted that multiphoton absorption affects the acoustic-wave gain in the superlattice if the field value is much smaller than that in a standard semiconductor.Generation of excess acoustic phonons in homogeneous semiconductors was considered in [1-3] for the case of intraband absorption of an electromagnetic wave. The instability region of such phonons, in whi9ch amplification of an acoustic wave can take place, is also determined in these works. A similar problem was solved for optical phonons in [4,5]. The influence of an electromagnetic wave on the sound damping in semiconductor superlattices was considered in [6], but the phonon instability region was not determined. We also note that in [7], the sign-reversal range for the sound damping coefficient in the superlattice in a constant electric field was found.In this paper, we obtain the damping coefficient of longitudinal acoustic phonons in a one-dimensional superlattice for the case of intraband absorption of an intense electromagnetic wave and determine the interval of the wave vectors q of phonons in which the damping coefficient reverses sign. To solve this problem, we assume that the effective Hamiltonian of the electron interaction with an electromagnetic wave in the nth conduction miniband has the formwhereis the electron energy in the nth miniband, z is the superlattice axis, ∆ n is the width of the nth miniband, µ is the effective electron mass, d is the superlattice constant,p = −i ∇, A(t) is the vector potential of the electromagnetic wave, is Plank's constant, e is the electron charge, and c is the speed of light. The Hamiltonian of the electron-phonon interaction for longitudinal acoustic phonons is written aŝwhere B q = /(2ρω q V ) qΞ for the case of the deformation potential of interaction, Ξ is the constant of the *

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