(color online) Energy dispersions of the dilatational (SA) acoustic phonons in 2-nm thick free-standing Si slab (a), diamond/Si/diamond heterostructures with dimensions 1 nm/2 nm/1 nm (b) and 4 nm/2 nm/4 nm (c), and 2-nm thick Si slab with clamped boundaries (d). Reprinted with permission from Ref. [27] (copyright 2008 American Institute of Physics).