Ab initio calculations of conduction band effective mass parameters of thermoelectric $${\hbox {Mg}}_{2} {\hbox {X}}_{1{-}x} {\hbox {Y}}_x$$ (X, Y = Si, Ge, Sn) alloys

Abstract

Since there are still research interests in the physical properties of quasi-binary thermoelectric $${\hbox {Mg}}_{2} {\hbox {X}}_{1-x}{\hbox {Y}}_{x}$$ Mg 2 X 1 - x Y x alloys, with X, Y = Si, Ge, Sn, we present an ab initio analysis that yields the relative formation energy and effective masses of the conduction bands, in the whole compositional range x. We base our calculations on the full-relativistic Korringa, Kohn and Rostocker (KKR) Green’s functions formalism within the coherent potential approximation (CPA). Formation energies, measured relative to the end $${\hbox {Mg}}_{2} \hbox {X}$$ Mg 2 X compounds, show no excess energy for the $${\hbox {Mg}}_{2} \hbox {Si} {-} {\hbox {Mg}}_{2} \hbox {Ge}$$ Mg 2 Si - Mg 2 Ge substitution thus indicating a complete solubility. In contrast, concave and asymmetric formation energies for intermediate compositions in the $${\hbox {Mg}}_{2} \hbox {X} {-} {\hbox {Mg}}_{2} \hbox {Sn}$$ Mg 2 X - Mg 2 Sn alloys manifest a miscibility gap. With this basis, we compute and discuss the crossing of the conduction bands observed in n-type $${\hbox {Mg}}_{2} {\hbox {X}}_{1-x} {\hbox {Sn}}_x$$ Mg 2 X 1 - x Sn x materials. We present direction- and band-dependent effective masses using a generalized single parabolic band effective mass approximation to discuss anisotropic effects, to interpret available experimental and theoretical data, and to predict intermediate and not yet published transport parameters on these alloys.

Bridgman Growth of Mg2Sn1–xBixSingle Crystals and Anisotropic Thermoelectric Properties

“…Since the carrier concentrations are almost the same along these two directions based on the Hall measurement (Table ), the effective mass ( m *) is considered to be the key factor that determines the anisotropy of S deg . As it is known that the conducting effective mass of different orientations depends on the band structure of the crystal, ,, – it will be very helpful to carry out theoretical calculations to further understand experimental results. As is shown in Figure a, the conduction band edges along the [111] and [11̅0] directions within the first Brillouin zone along G-L and W-K are marked by navy and red curves, respectively.…”

Strain effects on electronic, optical properties and carriers mobility of Cs2SnI6 vacancy‐ordered double perovskite: A promising photovoltaic material

“…Moreover, we have calculated for the Cs 2 SnI 6 compound the effective mass of holes ( m h *) near the VBM and the electrons effective mass ( m e *) near the CBM using the following equation: where the continuous function E ( k ) was obtained by fitting the energies E at the band edge positions k to a parabolic function [51, 52], and is the reduced Planck constant.…”

“…where the continuous function E(k) was obtained by fitting the energies E at the band edge positions k to a parabolic function [51,52], and ℏ is the reduced Planck constant. From Figure 6, we observe that the electron effective mass is lower than hole effective mass for unstrained Cs 2 SnI 6 , which agrees reasonably with the previous findings [53].…”