Heat Transfer in Low Temperature Micro- and Nanosystems

Abstract

The study of thermal and thermodynamic properties at the nanoscale requires the development of samples with well controlled small scale structure, but also ultrasensitive and innovative experimental techniques for handling such samples. The challenge is to measure very small amounts of energy, and to control the flow of these energies on very small length scales. Such measurements generally depend on very precise temperature control made possible by ultrasensitive thermometry. From this point of view, electrical measurements afford unique solutions, because they are easily adapted to small scales by exploiting experimental techniques developed to measure electrical resistances. With the help of technologies transferred from micro- and nanoelectronics, devices and sensors can be designed to measure the physical properties of small systems. In this chapter, we begin by calculating the thermodynamic properties expected for condensed matter at low temperatures. The temperature dependence of the specific heat and the thermal conductivity are calculated for each type of heat carrier, viz., phonons and electrons. Special attention is paid to the specificities of low-dimensional systems: quantum effects on the thermal conductance and the heat capacity. We then describe the experimental aspects (techniques and instrumentation), by reviewing the various solutions available in thermometry, and methods for measuring the specific heat and thermal conductivity, in either steady state or dynamical contexts. We will see how to apply each technique on the submicron scale, illustrating with different suspended systems in the case of membranes and nanowires.