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Atomistic configurations: (a) Si/Si1- x Ge x heterostructure configuration, (b) Si1− x Ge x alloy configuration. The lengths of crystalline Si and alloy Si1− x Ge x parts in (a) are denoted by “m” and “n,” respectively. The total length of the superlattice is (m + n). For studying the effect of alloying alone, the configuration (b) containing 64 atoms is used, and for the effect of nanostructuring alone, the configuration shown in (a) is used. To study the effect of compositional variation, Ge fraction is varied from x = 0 to 1.0 with an interval of 0.125 in (b), and for the lower figure in (a) x = 0, which gives a Si/Ge crystalline superlattice configuration; and for the upper figure in (a) x = 0.125, 0.25, 0.5, and 0.75.
(a) Variation of Lorenz number L and thermopower S as a function of the electron energy for a heterostructure configuration (Si/Ge) with Si:Ge = 3:3, under a constant relaxation time approximation. The compositional variation of the maximum thermopower Smax (x) is shown for alloy configuration (marked by SiGe), heterostructure configuration (marked by Si/Ge), and alloy-heterostructure configuration (marked by SiGe) are shown in (b). The straight line represents a linear prediction for the compositional variation of thermopower.
Effect of energy dependent relaxation time functions on thermopower in Si. The thermopower in crystalline Si is a maximum for an electron energy of ∼0.05 eV, which amounts to a doping level of 4 × 1019 (p-type), 2.5 × 1019 (Si n-type) cm−3. Compared to constant RTA, ionized impurity scattering results in higher thermopower and non-polar optical phonon scattering and acoustic phonon scattering results in lower thermopower.
Effect of temperature on the maximum thermopower Smax (x) and the electron energy ξ, where S(x) = Smax (x). Right (left) panels show temperature effects on the variation of the maximum thermopower, Smax (x) and the corresponding electron energy, for electron energies smaller (higher) than the Fermi energy, indicating asymmetric behavior of ξ on two sides of the Fermi energy.
Compositional variation of electrical conductivity and electron thermal conductivity in SiGe alloy and Si/Ge heterostructure. Layer thickness ratio does not show significant influence, particularly for lower electron energies. In the lower panel, the effect of temperature on conductivity is shown for x = 0.5 for the SiGe alloy configuration.
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