Phonon engineering in graphene and van der Waals materials
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and phonon engineering in nanostructures Phonons, which are quanta of crystal lattice vibrations, affect the thermal, electrical, optical, and mechanical properties of solids.1 In semiconductors, acoustic and optical phonons limit electron mobility and influence their optical response. Acoustic phonons are the main heat carriers in electrical insulators and semiconductors. Long-wavelength acoustic phonons constitute the sound waves. Similar to electrons, phonons are characterized by their dispersion relation ω(q), where ω is angular frequency, and q is a wave vector of a phonon. In bulk semiconductors with α atoms per unit cell, there are 3α phonon dispersion branches for each value of q. Three types of vibrations describe the motion of the unit cell and form three acoustic phonon branches. The other 3(α–1) modes describe the relative motion of atoms inside the unit cell forming the optical phonon branches. Examples of the phonon dispersion branches are shown in Figure 1. Acoustic polarization branches are commonly referred to as longitudinal acoustic (LA) and transverse acoustic (TA) phonons. One can also distinguish between longitudinal optical (LO) and transverse optical (TO) phonons. In the case of
two-dimensional (2D) material systems such as graphene, the out-of-plane transverse vibrations are denoted as z-axis acoustic (ZA) phonons. In the long-wavelength limit, acoustic phonons in bulk crystals have nearly linear dispersion, which can be written, in the Debye approximation, as ω = VSq, where VS is the sound velocity, while the optical phonons are nearly dispersionless and have a small group velocity VG = dω/dq. Acoustic phonons usually carry most of the heat in semiconductors.2 Spatial confinement of acoustic phonons in nanostructures affects their energy dispersion3–6 and modifies acoustic phonon properties such as phonon group velocity, polarization, and density of states (DOS). As a result, spatial confinement changes the way acoustic phonons interact with other phonons, defects, and electrons.3–6 This creates opportunities for engineering the phonon spectrum in semiconductor nanostructures for improving their electrical, thermal, or mechanical properties. In order to understand when the structure size starts to affect phonon properties and phonon transport, one can recall that the average phonon mean free path (MFP) in semiconductors is ∼50–300 nm near room temperature (RT). At this length scale, the acoustic phonon transport is affected
Alexander A. Balandin, University of California–Riverside, USA; [email protected] DOI: 10.1557/mrs.2014.169
© 2014 Materials Research Society
MRS BULLETIN • VOLUME 39 • SEPTEMBER 2014 • www.mrs.org/bulletin
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PHONON ENGINEERING IN GRAPHENE AND VAN DER WAALS MATERIALS
The acoustic impedance is defined as ζ = ρVs, where ρ is the mass density. Engineering of the optical phonons in nanostructures via the boundary conditions requires different approaches than engineering of the acoustic phonons. In the long-wave limit, the optical phonons correspond to the motion of ato
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