Submicron-scale thermics - Nanoscale heat conduction

Developed in 1956 to study certain aspects of phase change, the molecular dynamics (MD) technique was long considered a tool reserved for fluid and materials physicists. Today, with the exponential growth in computing power, it permeates many areas of upstream materials engineering, as well as mass and heat transfer. For example, at one of the first symposia devoted to heat transfer at micro and nano scales, topics such as heat transfer at interfaces, dynamic evaporation processes, condensation on a surface, thermal stresses during solidification and the estimation of conductive properties in micro or nanostructures were addressed using methods based on molecular dynamics techniques. Indeed, the thermal behavior of the elementary structures of many nanostructured materials, such as nanowires, particles, channels, pores or defects, can only be predicted by an atomic-level approach accessible to molecular dynamics. Molecular dynamics is still likely to be used in sectors where the accelerated integration of microsystems has made it essential to understand heat transfer at submicrometer scales, since nanometric systems such as superlattices (ultra-thin multilayers with thicknesses of less than 100 nm), nanotransistors, are now installed at the heart of electronic systems (chips, connections), optoelectronic systems (laser diodes, optical switches), thermal sensors (fluxmeters, thermopiles) and soon also in thermoelectric converters (Peltier pumps) and photovoltaic converters.

Molecular dynamics, which involves calculating the velocities and positions of each atom in the system over time, seems appropriate, but further work based on the results of statistical physics is needed to obtain the quantities useful to the thermic engineer.

This article develops the basis for explicit expressions of temperature, flux and thermal conductivity quantities as a function of microscopic quantities calculated by the molecular dynamics technique. These expressions are obtained in different formalisms and are accompanied by comments on the limits of validity of the underlying assumptions.

The principle behind the molecular dynamics technique is described in detail in the article [BE 8 290] "Thermal engineering on the submicron scale. Introduction to molecular dynamics", where the table of the main notations used in this article can be consulted.

Readers interested in the first applications of the molecular dynamics technique can consult references [1] [2]. References [3] [4] [5] [6] focus on thermal applications.