Temperature and Size Effects on the Extremely Low Thermal Conductivity of Self-assembled Germanium Quantum-dot Supercrys
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Temperature and Size Effects on the Extremely Low Thermal Conductivity of Self-Assembled Germanium Quantum-Dot Supercrystals in Silicon Jean-Numa Gillet Université de Lille 1, Institut d’Electronique, de Microélectronique et de Nanotechnologie (CNRS UMR), Physics, Av. Poincaré, BP 60069, 59652 Villeneuve d’Ascq Cedex, France. Email: [email protected]
ABSTRACT Design of semiconducting nanomaterials with an indirect electronic bandgap is currently one of the major areas of research to obtain a high thermoelectric yield by lowering their lattice thermal conductivity. Intensive investigations on superlattices were performed to achieve this goal. However, like one-dimensional nanowires, they decrease heat transport in only one propagation direction of the phonons. Moreover, they often lead to dislocations since they are composed of layered materials with a lattice mismatch. Design of superlattices with a thermoelectric figure of merit ZT higher than unity is therefore hazardous. Self-assembly of epitaxial layers on silicon has been used for bottom-up synthesis of three-dimensional (3D) Ge quantum-dot (QD) arrays in Si for quantum-device and solar-energy applications. Using the atomic-scale 3D phononic crystal model, it is predicted that high-density 3D arrays of selfassembled Ge QDs in Si can as well show an extreme reduction of the thermal transport. 3D supercrystals of Ge QDs in Si present a thermal conductivity that can be as tiny as that of air. These extremely low values of the thermal conductivity are computed for a number of Ge filling ratios and size parameters of the 3D Si-Ge supercrystal. Owing to incoherent phonon scattering with predominant near-field effects, the same conclusion holds for supercrystals with moderate QD disordering. As a result, design of highly-efficient CMOS-compatible thermoelectric devices with ZT possibly much higher than unity might be possible. In this theoretical study, simultaneous evolution of both temperature and average distance between the Ge QDs is analyzed for a non-variable Ge filling ratio to obtain thermal-conductivity values as low as that of air (+/- 0.025 W/m/K).
INTRODUCTION The thermoelectric figure of merit ZT of a material is given by ZT = S2σT/λ where S, σ, T and λ denote the Seebeck coefficient, electrical conductivity, absolute temperature and thermal conductivity, respectively.[1,2] The thermoelectric yield is an increasing function of the nondimensional ZT that is inversely proportional to λ but directly proportional to the power factor S2σ. Discovery of a material with ZT ≥ 3 can produce a thermoelectric yield that is higher than 42 % of the Carnot efficiency for hot and cold junctions at 800 K and 300 K, respectively. This value is competitive with the yields obtained in traditional thermal engines. To achieve this dream, which could have a significant impact on energy conversion and clean energies, the design of semiconducting nanostructured materials with an indirect electronic bandgap showing a very low thermal conductivity is currently one
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