Electron-dependent thermoelectric properties in Si/Si1-xGex heterostructures and Si1-xGex alloys from first-principles

Abstract

Unlike phononic thermal conductivity (which is shown in the literature to be reduced due to alloying and has a nearly constant value over a range of compositional variations), electron-dependent thermoelectric properties are shown here, from first-principles, to vary nonlinearly with composition. Of the Si/Si 1 _xGex systems considered, the maximum thermopower observed, which is 10% higher than that of crystalline Si, is obtained for a Si 0 . 875 (J, Ke, K 1 are the Seebeck coefficient or thermopower, electrical conductivity, electron thermal conductivity, and lattice or phonon thermal conductivity, respectively, characterizes the efficiency of a thermoelectric material and involves transport of electrons as well as phonons. To enhance zr, phononic properties must be altered to reduce the thermal conductivity, and electronic properties must be altered to maximize the thermopower and electrical conductivity. However, due to the complexity of optimizing several interdependent phononic and electronic properties simultaneously, it remains a challenge to find a combination of the properties or to find mechanisms that would provide promising values of zr.Although both experimental 6 -9 and theoretical efforts 1 0-13 have focused on finding ways to enhance zr in different material/design conditions, accurate determination of electronic and phononic contributions and their dependence on alloy composition, strain, or nanostructuring, particularly on the nanoscale, continues to be a formidable task. While experimentally it is difficult to carry out transport measurements, particularly on the nanoscale, 5 • 13 theoretical studies, 1 3-16 mostly use a finite number of bands to estimate the electronic contribution. In these methods, using parabolic or non-parabolic dispersion relations for computing the effective mass of electrons, local strain-induced charge effects on band bending at the heterointerface are disregarded. Consequently, contradictory conclusions for the same system are reported. For example, unlike single band calculations, 14 · 15 multiple-miniband calculations13·16 show oscillatory behavior for the Seebeck coefficient and the Lorenz number (which is proportional to the ratio between Ke and (J).On the other hand, first-principles based transport calculation methods (which do not have any approximations and serve as the most accurate method, though with a high computational cost) incorporate a complete description of the •)E-mail: zubaer@caltech.edu. electronic bands and have been used to find electron dependent transport properties and mechanisms accurately, for a range of electronic materials. 17 -19 Using a combination of density functional theory (DFf) and the Boltzmann transport equation, we study the Si/Si 1 _xGex system (which holds particular importance in widely used Si-based technologies and offers high zr values, particularly at high temperatures 4 ) as a model for determining the role of alloying and heterostructuring on its electron dependent transport properties. We find that neither S nor ...

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