Anharmonic Lifetime of Phonons in Nanophononic Semiconductors
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1172-T03-09
Anharmonic lifetime of phonons in nanophononic semiconductors
Steven P. Hepplestone and Gyaneshwar P. Srivastava School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK.
ABSTRACT We present a theory of three-phonon interactions in nanophononic semiconductors at 300 K. The intrinsic lifetime of phonon modes is estimated from the application of Fermi’s Golden Rule, based on realistic phonon dispersion relations and a quasi-continuum model for the cubic anharmonicity. We show that the lifetime of phonon modes in the Si(0.543 nm)/Ge(0.543 nm)[100] superlattice is shorter than the average of results for bulk Si and Ge. This is explained in terms of the availability of additional decay routes and an additional Dual Mass factor which arises due the different densities of Si and Ge. INTRODUCTION Phononic structures are the vibrational analogues of photonic crystals. These structures consist of two or more materials with contrasting vibrational properties, which result in one or more stop bands in the phonon dispersion relations. One-dimensional nanophononic semiconductors [1, 2] have recently been fabricated. Whilst a considerable amount of work has been performed for calculating and measuring the dispersion relations and stop bands [5, 6, 7, 8], relatively little progress has been made in calculating the consequential physical properties. These properties, such as phonon thermal conductivity [3, 4], require an understanding and calculation of the anharmonic lifetime of phonon modes in these structures. Previous calculations of the anharmonic lifetime of phonon modes have generally assumed one continuous medium [9] and do not take into account the effect of systems which consist of two different materials, such as superlattices. The effect of two materials is expected to modify phonon lifetime via three-phonon interactions [3, 4] as the interaction matrix is dependent on the masses and other properties of the two individual materials. In this work, we first calculate the phonon dispersion relations of the Si(0.543 nm)/Ge(0.543 nm)[100] superlattice by applying the Enhanced Adiabatic Bond Charge Model (EBCM) of lattice dynamics [10]. For the anharmonic lifetime of phonon modes, we describe an adaptation of the bulk relaxation rate equation, which uses a modification to the anharmonic potential similar to that suggested by Ren and Dow [11]. We compare, at 300 K, the lifetime of phonon modes in the superlattice with that for the two constituent bulk materials and their average. We also examine changes in the Normal and Umklapp processes due to the this modification to the anharmonic potential.
THEORY We applied an enhanced version of the adiabatic bond charge model [10] to calculate the phonon mode frequencies of the Si(0.543 nm)/Ge(0.543 nm)[100] superlattice. To calculate the relaxation rate of phonon modes due to three-phonon interactions in a A/B composite system, we apply a hybrid approach based upon the previously successful lifetime equation employed by Al-Shaikhi and Srivastava [12]
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