Coupling of intrinsic localized modes in doped polar semiconductors with plasmons

Abstract

We present a detailed analysis of the interaction between intrinsic localized modes andplasmons in a doped polar semiconductor. The investigation has been performed for ananharmonic one-dimensional diatomic lattice with alternating interactions couplingsuccessive neighbours. The system simulates a row of atoms in the direction of a III–V semiconductor. Specific calculations have been performed for GaN,because it has a large gap between the acoustic and optical phonon branches. Thecalculations of the intrinsic localized modes have been performed by using two-bodypotentials to describe the interactions. We have used the rotating wave approximation andwe have found the intrinsic localized modes in the phonon gap. The interaction with theplasmon has been studied by adding to the equations of motion the alternating electric fieldwhich is related to the electron density of the plasmons. We obtain an expression for theelectric dynamical polarization associated with the intrinsic localized modes and with theplasmons. We derive an expression for the dielectric function of the coupled system. Thezeros of the dielectric function give the frequency of the combined modes. We havefound two regimes in which combined modes are possible. One is related to smallanharmonicity of the potential. The combined mode has a frequency above the top ofthe optical branch and can be explained in terms of the theory of the harmonicdielectric response of polar lattice vibrations. The second regime is related to highanharmonicity. The combined modes exist only for a finite slab. We show that onincreasing the anharmonicity, i.e. the amplitude of the intrinsic localized mode,the width of the slab increases. The frequency of the combined mode is insidethe phonon gap. We have also studied the dynamical stability of these modes.