Recent Developments in Micro and Nanoscale Thermometry

Abstract

One of the key issues related to studies in microscale heat transfer is the ability to measure temperature at small scales. In the recent past, rapid and signi cant progress has enabled temperature measurements to be made with unprecedented high spatial and temporal resolutions. This has allowed heat transfer research to enter a new regime which was previously inaccessible. This article reviews recent developments and discusses future directions, indicating the variety of opportunities for research that are of scienti c and technological importance.A frequent question asked by researchers in microscale heat transfer is: What are the lowest limits of temperature measurement? The question is usually related to the limits of length and time scales. The answer to this question lies in the thermodynamic description of temperature. Temperature is a thermodynamic property that can only be de ned under equilibrium. Consider the fundamental energy carriers that we commonly encounter in heat transfer-molecules, electrons, photons, and phonons . For molecules, the equilibrium relates to the Maxwell-Boltzmann distribution, for electrons it is the Fermi-Dirac distribution, whereas for photons and phonons equilibrium is de ned by the Bose-Einstein distribution. The next question one may ask is: What are the length and time scales over which equilibrium distributions can be de ned? First, there must be suf cient number of particles within an ensemble for statistical mechanics to apply. But the distribution within that ensemble could be nonequilibrium, i.e., it may not follow the aforementioned distributions. In the event of a nonequilibrium distribution of energy carriers, equilibrium is restored by collisions or scattering. Hence, the length and time scales of scattering-the mean free path and the relaxation time-must be the fundamental quantities that decide the limits of temperature measurement. Typical values of these quantities under ambient conditions are listed in Table 1. It is interesting to note that in Table 1. Typical scattering length and time scales for energy carriers under ambient conditions Phonons in Molecules Molecules Electrons dielectric or in gas in liquid in metal semiconductor Mean free path, , [nm] 200 0.1-1 10 5-10 Relaxation time, s [s] (0.1-1)´10 2 9 (0.1-1)´10 2 12 (10-100)´10 2 15 (1-10)´10 2 12 Propagation speed, v [m/s] (0.2-2)´10 3(1-5)´10 3 » 10 6 (3-10)´10 3 solids the length scale limit is about 10 nm, whereas the time scale limit is in the 0.1-to 1-ps range. It is then natural to ask: Can we measure temperature at these length and time scales, and if so, what do we expect to observe? The development of femtosecond lasers has allowed researchers to study heat transfer phenomena at time scales below the relaxation times of electrons and phonons in solids. This has led to very interesting observations of nonequilibrium heat transfer. This article will not discuss the microtime scale temperature measurement, and the reader is referred to several other articles [1-3].Reaching the length scale lim...

Thermometry at the nanoscale

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Spatially and temporally resolved thermal imaging of cyclically heated interconnects by use of scanning thermal microscopy

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