Size Effects on the Thermal Properties of Self-assembled Ge Quantum Dots in Single-crystal Silicon
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1172-T06-02
Size Effects on the Thermal Properties of Self-assembled Ge Quantum Dots in Single-crystal Silicon Jean-Numa Gillet Dept. of Physics, Institut d’Electronique, de Microélectronique et de Nanotechnologie (CNRS UMR), Université de Lille 1, Av. Poincaré, BP 60069, 59652 Villeneuve d’Ascq Cedex, France. (Preceding affiliation: University of Colorado at Boulder) ABSTRACT Superlattices with an ultra-low thermal conductivity were extensively studied to design thermoelectric materials. However, since they are made up of superposed materials showing lattice mismatches, they often show cracks and dislocations. Therefore, it is challenging to fabricate superlattices with a thermoelectric figure of merit ZT higher than unity. Moreover, like nanowires, they decrease heat transport in only one main direction. Self-assembly from epitaxial layers on a Si substrate is a major bottom-up technology to fabricate 3D Ge quantum-dot (QD) arrays in Si, which have been used for 3D quantum-device applications. Using the model of the atomic-scale 3D phononic crystal, we showed that 3D high-density arrays of self-assembled Ge QDs in Si can also show an ultra-low thermal conductivity in 3D, which can be several orders of magnitude lower than that of bulk Si. As a result, they can be considered to design novel 3D thermoelectric devices showing CMOS compatibility. In an example QD crystal, the thermal conductivity can be decreased below only 0.2 W/m/K. The main objective of this paper is to show the size dependence of the thermal conductivity versus the supercell lattice parameter d. For a constant QD-crystal filling ratio x = 12.5 at%, a decrease of the thermal conductivity is observed for an increasing d. This analysis enables us to predict that the optimal d-value will be of the order of 11 nm for the given filling ratio. At this optimum, the thermal conductivity decreases to the global minimum value of 0.9 W/m/K. The presented results are a first step towards the optimal design of thermoelectric devices with a maximal ZT obtained by global optimization of the size parameters.
I.
INTRODUCTION
The energy-conversion efficiency of a thermoelectric material is an increasing function of its thermoelectric figure of merit ZT, which is inversely proportional to its thermal conductivity λ but directly proportional to its power factor (S2σ). Indeed, when S, σ and T denote its Seebeck coefficient, electrical conductivity and absolute temperature, respectively, the non-dimensional ZT is given by ZT = S2σT/λ [1]. Design of new semiconducting materials with an ultra-low thermal conductivity λ has therefore received a growing attention, and is now one of the major areas of research in solid state physics and chemistry [1-10]. Superlattices, which consist of periodic thin-film layers, were the first type of nanostructured materials (nanomaterials) to be studied to obtain ZT > 1. Indeed, the thermal conductivity of a superlattice can be several orders of magnitude lower than that of a bulk material owing to confinement effects of the phonons a
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