Engineering semiconductor devices requires an understanding of charge carrier mobility. Typically mobilities are estimated using measurements of the Hall effect and electrical resistivity. Such measurements are routinely performed at room temperature and below in materials with mobilities greater than 1cm 2 /Vs. With the availability of combined Seebeck coefficient and electrical resistivity measurement systems, it is now easy to measure the weighted mobility (electron mobility weighted by the density of electronic states). Here we introduce a simple method to calculate the weighted mobility from combined Seebeck coefficient and electrical resistivity measurements that gives good results at room temperature and above, and for mobilities as low as 10 −3 cm 2 /Vs.
With significant recent advancements in thermal sciences—such as the development of new theoretical and experimental techniques, and the discovery of new transport mechanisms—it is helpful to revisit the fundamentals of vibrational heat conduction to formulate an updated and informed physical understanding. The increasing maturity of simulation and modeling methods sparks the desire to leverage these techniques to rapidly improve and develop technology through digital engineering and multi-scale, electro-thermal models. With that vision in mind, this review attempts to build a holistic understanding of thermal transport by focusing on the often unaddressed relationships between subfields, which can be critical for multi-scale modeling approaches. For example, we outline the relationship between mode-specific (computational) and spectral (analytical) models. We relate thermal boundary resistance models based on perturbation approaches and classic transmissivity based models. We discuss the relationship between lattice dynamics and molecular dynamics approaches along with two-channel transport frameworks that have emerged recently and that connect crystal-like and amorphous-like heat conduction. Throughout, we discuss best practices for modeling experimental data and outline how these models can guide material-level and system-level design.
Engineering semiconductor devices requires an understanding of the effective mass of electrons and holes. Effective masses have historically been determined in metals at cryogenic temperatures estimated using measurements of the electronic specific heat. Instead, by combining measurements of the Seebeck and Hall effects, a density of states effective mass can be determined in doped semiconductors at room temperature and above. Here, a simple method to calculate the electron effective mass using the Seebeck coefficient and an estimate of the free electron or hole concentration, such as that determined from the Hall effect, is introduced mS∗me=0.924(300KT)(nH1020cm−3)2/3[3(exp[|S|kB/e−2]−0.17)2/31+exp[−5(|S|kB/e−kB/e|S|)]+|S|kB/e1+exp[5(|S|kB/e−kB/e|S|)]] here mnormalS∗ is the Seebeck effective mass, nH is the charge carrier concentration measured by the Hall effect (nH = 1/eRH, RH is Hall resistance) in 1020 cm−3, T is the absolute temperature in K, S is the Seebeck coefficient, and kB/e = 86.3 μV K−1. This estimate of the effective mass can aid the understanding and engineering of the electronic structure as it is largely independent of scattering and the effects of microstructure (grain boundary resistance). It is particularly helpful in characterizing thermoelectric materials.
Point defects exist widely in engineering materials and are known to scatter vibrational modes to reduce thermal conductivity. The Klemens description of point defect scattering is the most prolific analytical model for this effect. This work reviews the essential physics of the model and compares its predictions to first principles results for isotope and alloy scattering, demonstrating the model as a useful materials design metric. A treatment of the scattering parameter (Γ) for a multiatomic lattice is recommended and compared to other treatments presented in literature, which have been at times misused to yield incomplete conclusions about the system's scattering mechanisms. Additionally, we demonstrate a reduced sensitivity of the model to the full phonon dispersion and discuss its origin. Finally, a simplified treatment of scattering in alloy systems with vacancies and interstitial defects is demonstrated to suitably describe the potent scattering strength of these off-stoichiometric defects.26. Carrete, J. et al. almaBTE: A solver of the space-time dependent Boltzmann transport equation for phonons in structured materials.
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