Electronic transport properties of electron- and hole-doped semiconducting $C{1}_b$ Heusler compounds: ${\text{NiTi}}_{1-x}{M}_x\text{Sn}$ $\left(M=\text{Sc},\text{V}\right)$

The substitutional series of Heusler compounds ${\text{NiTi}}_{1-x}{M}_x\text{Sn}$ (where $M=\text{Sc},\text{V}$ and $0<x\le 0.2$) were synthesized and investigated with respect to their electronic structure and transport properties. The results show the possibility to create $n$-type and $p$-type thermoelectrics within one Heusler compound. The electronic structure and transport properties were calculated by all-electron ab initio methods and compared to the measurements. Hard x-ray photoelectron spectroscopy was carried out and the results are compared to the calculated electronic structure. Pure NiTiSn exhibits massive “in gap” states containing about 0.1 electrons per cell. The comparison of calculations, x-ray diffraction, and photoemission reveals that Ti atoms swapped into the vacant site are responsible for these states. The carrier concentration and temperature dependence of electrical conductivity, Seebeck coefficient, and thermal conductivity were investigated in the range from 10 to 300 K. The experimentally determined electronic structure and transport measurements agree well with the calculations. The sign of the Seebeck coefficient changes from negative for V to positive for Sc substitution. The high $n$-type and low $p$-type power factors are explained by differences in the chemical-disorder scattering-induced electric resistivity. Major differences appear because $p$-type doping (Sc) creates holes in the triply degenerate valence band at $\Gamma$ whereas $n$-type doping (V) fills electrons in the single conduction band above the indirect gap at $X$ what is typical for all semiconducting transition-metal-based Heusler compounds with $C{1}_b$ structure.

Figure 1

Electronic structure of NiTiSn.

Figure 2

Calculated Seebeck and power coefficients of NiTiSn. The shift of the chemical potential is given with respect to the size of the gap. The valence and conduction band extrema are marked by dashed lines $\left(T=300\text{K}\right)$.

Figure 3

(Color online) Seebeck coefficient and chemical potential of NiTiSn. The shift of the chemical potential was calculated for pure as well as electron- and hole-doped NiTiSn ($e$ and $h$ assign electron and hole doping, respectively).

Figure 4

(Color online) Density of states of $M=\text{Sc}$- and V-substituted ${\text{NiTi}}_{1-x}{M}_x\text{Sn}$. For better comparison, the Fermi energy $\left({ϵ}_F\right)$ of the pure NiTiSn was set to the valence-band maximum in the case of Sc substitution and to the conduction-band minimum for V substitution.

Figure 5

(Color online) X-ray diffraction of polycrystalline NiTiSn. The data were taken at room temperature using $\text{Mo}K\alpha$ radiation. The inset shows the dependence of lattice parameter $a$ for ${\text{NiTi}}_{1-x}{\text{Sc}}_x\text{Sn}$ versus Sc content. The line is a result of a linear fit to Vegards law.

Figure 6

(Color online) Valence-band spectra of ${\text{NiTi}}_{1-x}{\text{Sc}}_x\text{Sn}$ ($x=0$, 0.01, 0.02, and 0.04). The measurements were performed at 20 K, the excitation energy was fixed to 7.939 keV.

Figure 7

(Color online) Valence-band spectra of ${\text{NiTi}}_{1-x}{\text{Sc}}_x\text{Sn}$ close to the Fermi edge ${ϵ}_F$ for an excitation energy of 7.939 keV and an improved, higher resolution $\left(\Delta E=150\text{meV}\right)$ compared to Fig. 6.

Figure 8

(Color online) Density of states of disordered NiTiSn. The left panels (a)–(c) show the density of states for 5% of the atoms swapped into the vacant site (Vc). The right panels $\left({\text{a}}^{\prime }\right)–\left({\text{c}}^{\prime }\right)$ compare the part around the Fermi energy for different amounts of disorder to the well-ordered compound. The Fermi energy $\left({ϵ}_F\right)$ of ordered NiTiSn was placed in the middle of the band gap for better comparison.

Figure 9

(Color online) Temperature dependence of thermal conductivity $\kappa \left(T\right)$, electrical conductivity $\sigma \left(T\right)$, and Seebeck coefficient $S\left(T\right)$ of NiTiSn and ${\text{NiTi}}_{0.97}{M}_{0.03}\text{Sn}$ $\left(M=\text{Sc},\text{V}\right)$.

Figure 10

(Color online) Dependence of the electric conductivity $\sigma \left(x\right)$, Seebeck coefficient $S\left(x\right)$, and power factor $PF\left(x\right)$ on the electron and hole doping of ${\text{NiTi}}_{1-x}{M}_x\text{Sn}$ $\left(M=\text{Sc},\text{V}\right)$.

Figure 11

(Color online) Calculated conductivity of $M=\text{Sc}$- and V-substituted ${\text{NiTi}}_{1-x}{M}_x\text{Sn}$. (a) shows the results of $\text{Sc}\leftrightarrow \text{Ti}$ and (b) of $\text{V}\leftrightarrow \text{Ti}$ substitution corresponding to hole or electron doping, respectively. The insets show the density of states $n\left({ϵ}_F,x\right)$ at the Fermi energy as function of the substitution. The density of states was broadened by a Lorentzian to reduce the numerical noise.