On the role of acoustic waves (phonons) in equilibrium heat exchange across a vacuum gap

Heat exchange between closely positioned bodies has become an important issue for such areas of modern technology as integrated circuits, atomic force microscopy, and high-density magnetic recording, which deal with bodies separated by gaps as narrow as a few nanometers. This paper shows that if the gap's width is below a certain value, estimated as about 10 nm for silicon at room temperature, then, in addition to electromagnetic radiation, significant heat is also carried by acoustic waves. Moreover, as the width of the gap decreases below about 5 nm, acoustic waves rapidly become the dominant heat carrier.