Density of States Effective Mass for p-Type Mg₂Si–Mg₂Sn Solid Solutions: Comparison between Experiments and First-Principles Calculations

Abstract

Tailoring and further optimization of thermoelectric materials requires detailed knowledge and understanding of the thermal and electrical transport in these materials. One crucial parameter is the density of states effective mass, which governs both the electrical conductivity as well as the Seebeck coefficient. We investigate the density of states effective mass for magnesium silicide, magnesium stannide and their solid solutions using experimental data as well as Density Functional Theory in a Generalized Gradient Approach; for the solid solutions, the Special Quasi-Random Structures approach is employed. Extracting the effective mass directly from the calculated densities of states we can show an approximatively linear decrease from Mg2Si to Mg2Sn and consistency with respect to the chosen cell size. The experimental data, obtained assuming a single parabolic band model, shows good agreement with the calculated data for Mg2Sn and Sn-rich solid solutions, but a clear difference at the Si-rich side. The lower effective mass for the Sn-rich solid solutions indicates that the electronic properties are expected to be superior to those of Si-rich solid solutions as long as minority carrier effects can be neglected.

Understanding the dopability of p-type Mg2(Si,Sn) by relating hybrid-density functional calculation results to experimental data

“…The trend of increasing carrier concentration with higher Sn content can be understood from the interplay between Fermi level and density of states or effective mass. Similar DOS shape and values for the VB have been reported [29,45,49,50], our results using hybrid-DFT, and with an exact-exchange mixing parameter of 25%, are shown in figures S1 and S2 of the SI. However, the VB-DOS close to the band edge differs between the two binaries, which determines the transport properties via the density of states effective mass (m * D ).…”

“…Figure 1 shows carrier concentration and dopant efficiency for the samples of Mg 2-y Li y Si 1-x Sn x discussed in [28,29]. It can be seen that the carrier concentration and dopant efficiency increase with higher Sn content by more than two orders of magnitude.…”

“…Li-doped Mg 2 Si 1-x Sn x samples were synthesized using a two-step synthesis method: high energy ball milling and current-assisted sintering, as described in our previous work [8,28], without providing Mg excess as is often done in a melting route. The chosen sintering temperature depends on the composition, varies between 873 K for Mg 2 Sn and 1073 K for Mg 2 Si, respectively [8,28], and is listed together with the measured carrier concentration in [29]. Note that all samples were found to be single phase and with similar microstructure, as discussed in [28,30].…”

“…For this reason, a possible influence of the microstructure is largely disregarded in the following. The room temperature Hall coefficient R H was determined using an in-house facility with a van der Pauw configuration under a magnetic field sweep up to a maximum of 0.5 T. The carrier concentration p was estimated using the experimental R H assuming a single carrier type; this is a reasonable estimation even for low doped Si-rich samples, as discussed in [29]. Note that the basic TE transport data of the samples was already published in [8,28,29].…”

Machine-learned model Hamiltonian and strength of spin-orbit interaction in strained Mg2X (X = Si, Ge, Sn, Pb)

“…For instance, one main approach followed to manipulate the electrical transport of these compounds was by intercalation with differing elements. [4,5,[7][8][9][10][11][12][13][14][15][16][17][18][19] It was found that the intercalation can result in nonlinearity in the band gap, enhanced spin-orbit interaction (SOI), and band splitting. The controllable and efficient thermoelectric materials are promising in designing micro-scale self-powered sensors, solar thermal elements, and waste heat recovery devices.…”