Modification of the lattice thermal conductivity in silicon quantum wires due to spatial confinement of acoustic phonons

Lattice thermal conductivity in silicon quantum wires is theoretically investigated. The bulk of heat in silicon structures is carried by acoustic phonons within a small region in the first Brillouin zone. Our formalism rigorously takes into account modification of these acoustic phonon modes and phonon group velocities in free- and clamped-surface wires due to spatial confinement. From our numerical results, we predict a significant decrease (more than an order of magnitude) of the lattice thermal conductivity in cylindrical quantum wires with diameter D = 200 angstrom. The decrease is about two times stronger in quantum wires than in quantum wells of corresponding dimensions. Our theoretical results are in qualitative agreement with experimentally observed drop of the lattice thermal conductivity in silicon low-dimensional structures.