The electronic band structures are calculated using the full-potential linear augmented plane wave method (FP-LAPW), using the Tran-Blaha modified Becke-Johnson potential (TB-mBJ). We studied the variation in electronic and TE properties of the investigated compounds under varying pressures up to 10 GPa. It seems that for KZnAs and KZnSb.the.‘n’.type.doping.is.more.favorable.under.higher.pressure.
Research claims that in our world most of the energy is wasted in the form of heat, and here comes the role of thermoelectric materials. Where 𝑇𝐶 and 𝑇𝐻 refer to the temperature of the cold and warm part of the material. We investigated both the electronic and thermoelectric properties of the above-mentioned compounds at ambient temperature and at different pressures up to 10 GPa.
In a simple two-dimensional potential, or in the case of a hydrogen atom, we can solve the Schrödinger equation to obtain the wave function of the system. In equation (2.2), the first and second terms represent the kinetic energy of the electron and nucleus. The Hartree-Fock method involves the Hartree potential and implies exchange interactions by imposing the antisymmetric nature of the electron wave function.
The many-body electron wave function is a function of three variables N. The electron density is only a function of three variables (x,y,z).
Thomas- Fermi Equation
This functionality has only one adjustable parameter, β. The value of β = 0.0042 was determined from the best fit to the energies of six noble gas atoms using the sum of the LDA and GGA exchange terms. Here we calculated TE properties of KZnP, KZnAs and KZnSb for both the electron and hole concentrations at and 𝑐𝑚− as a function of temperature where the temperature varies from 100 to 900 K (Figure (5), (6) and ( 7)). The calculated TE properties for both electron and hole temperatures at 500 K and 900 K as a function of carrier concentration were concentrations ranging from to 𝑐𝑚− (Figure (7)).
It is found that in the case of hole doping, the power factor values are anisotropic along different 'x' and 'z' crystallographic directions. In general, we can say that the hole doping as well as the electron doping are favorable for TE properties for all the investigated compounds. Here, the changes in both electronic and TE properties of KZnX (X =P, As, Sb) were investigated upon the application of pressure.
Electronic properties such as density of states and band structure and TE properties such as Seebeck coefficient (μV/K), electrical conductivity/scattering time (Ωms− ) and power factor (W/mK S) were obtained under different pressures. The main objective in this section is to investigate the changes in TE properties of given ternary compounds under pressure ranging from 0 GPa to 10 GPa. For KZnAs, it was found that the anisotropy decreased slightly with increasing pressure and there is no large variation in thermoelectric properties in the case of 'p' type, but some variation in TE properties was observed in the case of 'n' type KZnAs.
The trend in variation of TE properties in the case of KZnSb is found to be almost the same for that of KZnAs. At 0 GPa, the TE properties are found to be the same for both 'n'-type and 'p'-type KZnAs. But at higher pressures, the improvement of TE properties is observed for ‘n’ type KZnAs compared to that of ‘p’ type.
The difference in thermopower between electrons and holes at higher pressure in the case of KZnAs is found to be of the order of 150μ/K which implies that at higher pressures electron doping may be more favorable for the TE properties of KZnAs. In the case of KZnSb, the TE properties are the same for 'n' and 'p' type. Figure.12: Changes in TE properties of KZnP using functionalized TB-mBJ with increasing pressure from 0GPa to 10 GPa.
Figure 13: Variations in TE properties of KZnAs using TB-mBJ, functional with increasing pressure from 0 GPa to 10 GPa. Figure 14: Variations in TE properties of KZnSb using TB-mBJ, functional with increasing pressure from 0 GPa to 10 GPa. Also, for the currently investigated compounds, the TE properties were calculated for both carrier concentrations and the variation as a function at different temperatures was studied.
We studied the changes in the electronic and TE properties of the investigated compounds at different pressures from 0 GPa to 10 GPa.
Khon-Sham Method
Electronic Properties
The band gap in electron volts was calculated for the optimized structures for each pressure using GGA, TB-mBJ potentials with the inclusion of spin orbit coupling, which is shown in figure (9) The band gap obtained using TB-mBJ is slightly higher than the obtained uses GGA. It is found that there is no large change in the band gap of KZnP by increasing the pressure from 0 GPa to 10 GPa. While for KZnAs, the band gap increases from 0GPa to 6GPa and then decreases.
In the case of KZnSb, the band gap was found to increase when the pressure was increased from 0 GPa to 10 GPa. Figure.9: Band gap obtained for KZnX when GGA, TB-mBJ functional was used including Spin-Orbit coupling from 0 GPa to 10 GPa. Figure.10: Calculated band structure using TB-mBJ functional of KZnP(a), KZnAs(b), KZnSb(c), under the pressure of 10GPa.
Figure.11: Calculated density of states using TB-mBJ functional of KZnP(a), KZnAs(b), KZnSb(c), under the pressure of 10GPa. We investigated the transport characteristics for the carrier concentration varying from − 9𝑐𝑚− and − 𝑐𝑚− along 'x' and 'z' axis of the compound. It is found that for KZnP there is no change in the thermal properties when the pressure is increased.
For KZnP, the Seebeck coefficient, electrical conductivity/relaxation time (σ/t) and power factor remain almost the same under different pressures. It is also seen that with the increase in pressure, the Seebeck coefficient of 'n' type KZnAs increases, which is shown in figure(13). Since the seebeck coefficient and power factor are found to be almost the same under all pressures for both 'n'.
The difference in the thermopower between electrons and holes at higher pressures in case of KZnSb was found to be of the order of 100-150μ/K showing that electron doping is more favorable for KZnSb at higher pressures.
Thermoelectric Properties
The electronic and transport properties of KZnX (X:P, As, Sb) are studied using calculations within DFT as a function of carrier concentration at different temperatures and solving the Boltzmann transport equation within the constant relaxation time approximation (CSTA) and the rigid band approximation (RBA). We found that under ambient conditions the thermopower is almost the same for both "n" and "p" type doping. For KZnAs and KZnSb, 'n'-type doping seems to be more favorable at higher pressure, which allowed us to predict that KZnAs.and.'n'.type.KZnSb.could.have.promising.applications. as.a.good.other.moelectric.material.under.high.pressure.
