On the mechanisms of heat transport across vacuum gaps

Heat exchange between closely positioned bodies has become an important issue for many areas of modern technology including, but not limited to, integrated circuits, atomic force microscopy, and high-density magnetic recording, which deal with bodies separated by gaps as narrow as a few nanometers. It is now recognized that heat transport across a gap of sub-micron width does not follow the Stefan–Boltzmann law, which is based on a conventional theory developed for sufficiently wide gaps. This paper describes the structure of thermally excited electromagnetic fields in arbitrarily narrow gaps, and it also shows that heat can be carried across narrow vacuum gaps by acoustic waves. The structure of the acoustic wave fields is also described, and it is shown that they become the dominant heat carriers in gaps narrower than a certain critical width, which is estimated to be a few nanometers. For example, consider a vacuum gap between silicon half-spaces. When the gap’s width is below a critical value, which is about 7.5 nm, the contribution of acoustic waves must be taken into account. Assuming that the wavelength of thermally excited acoustic waves is of order 1 nm, it may be possible to estimate the contribution of acoustic waves to heat transport across gaps with 4 nm < h < 7.5 nm by the kinetic theory, but for narrower gaps with h < 4 nm, this approximation is not valid, and then the full wave theory must be used. Also for gaps narrower than about 2.5 nm, there is no need to take into account electromagnetic radiation because its contribution is negligible compared to that of acoustic waves.