The DFT study of thermoelectric properties of CuInS2: A first principle approach

The generalised gradient approximation (GGA) and ultrasoft pseudopotential (US PP) methods to the function of Perdew-Burke-Ernzerhof (PBE) approach are utilised for density functional computation of CuInS2. It enables the prediction of thermoelectric characteristics, including Seebeck coefficient, thermal conductivity, electrical conductivity, magnetic susceptibility, specific heat, power factor and figure of merit by semi-classical Boltzmann approach. At 800 K, the highest magnitude of Seebeck coefficient is estimated as 6.91× 10-5 V·K-1. The maximum figure of merit (zT) is predicted as 1.04 × 10-4 at 800 K. Findings from this study suggest that CuInS2 has prospective to be used in the thermoelectric power generating sector.


Introduction
Recent developments are focusing on to the expanding family of semiconducting materials and their wide variety of potential uses.It covers a wide range of fields, including thermoelectric effect [1,2], thermal study [3][4][5], superconductivity [6,7], photovoltaic devices [8,9], optical study [10,11], biological applications [12][13][14] and much more.Semiconducting materials with properties similar to chalcopyrite are of interest due to their potential use and low environmental impact.The high chemical stability and unique optoelectronic properties make the chalcopyrite CuInS2 (CIS) of the I-III-VI2 group to gain greater attention.The CIS is an excellent candidate for solar-energy conversion due to its significant absorption coefficient (~10 5 cm -1 ) and direct optical energy bandgap (1.36 eV to 1.54 eV) [15].Thermoelectric (TE) effect is a source of "green energy" since it uses thermal energy to vigour electrons in converting directly to energy.The TE effect offers a number of benefits for use in industry.The two most important TE effects are the Peltier and Seebeck phenomena.The TE device may chill substances by use of the Peltier effect.Alternatively, the Seebeck effect allows for heat conversion into electricity; this process is termed as TE power production.The zT value is used to characterise TE efficiency of materials.Hence, a high zT value is appreciated to enable effective energy conversion in a TE material.
In this work, looking into the relevance and benefit of TE materials, the authors decided to investigate TE features of CIS.Several aspects of CIS remain unclear, despite the fact that TE properties have been documented in a number of research articles [16,17].DFT analysis using first-principle approach is used to achieve this aim.TE features like the Seebeck coefficient, thermal conductivity, electrical conductivity, magnetic susceptibility, specific heat, power factor and figure of merit are estimated.

First principle computation
The DFT plane waves and pseudopotentials are computed in this investigation using Quantum ESPRESSO programme.Exchange-correlation term is studied using Perdew-Burke-Ernzerhof (PBE) function.Moreover, ultrasoft pseudopotentials (US PPs) and generalised gradient approximation (GGA) are employed.An upper limit of 50 Ry is placed on the energy at which the wave function may expand.Energy threshold value of 500 Ry is used to extrapolate the electronic wave function for charge density.The Monkhorst-Pack 8  8  8 meshes are used for the Brillouin zone integration.Adjustments are made to the lattice constant of CIS until the resulting energy level reaches 10 8 Ry or higher.The optimum structure is found through the implementation of variable-cell (vc-relax) simulations.For this simulation, four atoms are used because of the molecule's symmetry, which is discussed in further detail.To analyse the TE features of CIS, the BoltzTraP technique is used.The more compact k-mesh of 22  22  22 is used for predictions of TE properties like the Seebeck coefficient, thermal conductivity, electrical conductivity, magnetic susceptibility, specific heat, and figure of merit.In order to relate Seebeck coefficient (S) to the concentration of carriers, the Mott formula is used [18], where EF denotes Fermi energy, e denotes electronic charge, n denotes carrier concentration, μ denotes chemical potential, T is absolute temperature and kB is Boltzmann constant.
The relationship between carrier concentration (n) and electrical conductivity (σ) is as follows [19], σ = ne 2 τ m (2) where m denotes electronic mass, and τ denotes relaxation time.The relationship between carrier concentration, chemical potential, energy density (ε) and electronic-specific heat (c) is shown below [20], The Pauli magnetic susceptibility is shown to be related to carrier concentration and chemical potential by the equation below [21], ) where µ0 denotes the vacuum permeability, and µB denotes Bohr magneton.

Results and discussion
The TE characteristics are estimated by a semi-classical Boltzmann approach using BoltzTraP software in the constant relaxation time approximation.The computed characteristics are shown for wide temperatures considered from 25 K to 800 K.The Seebeck coefficient (S) quickly approaches zero as S drops when the temperature rises due to an increment in thermal energy.It suggests that CIS has excellent TE features.At 0 K, the minimum magnitude of S is 4.12 x 10 -6 V•K -1 .The value of S is significantly decreased from -4.12 x 10 -6 V•K -1 to -6.91 x 10 -5 V•K -1 at a higher temperature of 800 K.The CIS is predicted to have n-type semiconducting nature.
IOP Publishing doi:10.1088/1757-899X/1291/1/0120093 The S at various temperatures is greater for lower concentrations, according to equation (1).The Figure 1 depicts that as the temperature rises, S drops due to an increment of thermal energy, and hence CIS is predicted to have good TE performance.

Figure 2. Variation of electrical conductivity (σ) with T (K).
The Figure 3 illustrates electronic thermal conductivity (k) (W•m -1 •K -1 •s -1 ) related to temperature (K).Thermal conductivity rises with increasing temperature.To achieve a good TE property, materials should exhibit higher values of Seebeck coefficient and electrical conductivity, whilst low thermal conductivity value at an optimal temperature [22].According to the figure, as temperature rises, thermal conductivity increases linearly.

Figure 3. Variation of electronic thermal conductivity (k) with T (K).
The Figure 4 depicts electronic specific heat (c) related to absolute temperature (K).As temperature rises, the specific heat increases in a linear manner according to equation (3).The increasing positive values of the specific heat with increasing temperatures indicate that the carrier concentration is also increasing.

Figure 4. Variation of electronic specific heat (c) with T (K).
The Pauli magnetic susceptibility (χ) varying with temperature is illustrated in the Figure 5.A little variation in the value of χ is observed upto 200 K. Afterwards, the value of χ increases with increasing temperature.The highest recorded value of χ at exhibited Fermi temperature (~550 K) is found to be 1.795 x 10 -9 m 3 •mol -1 .A significant drop in χ occurs when the temperature crosses 550 K and reaches to 800 K.This variation in χ values is directly related to carrier concentration, as predicted by equation (4).To what extent may TE material functions efficiently is investigated.The Figure 6(a) shows that as temperatures rise, the power factors also rise accordingly.The maximum power factor is estimated as 9 10 11 μW•cm -1 •K -2 •s -1 with a negative chemical potential at 800 K.There has been a little decrement in the factor, which now stands at 2.5 10 11 μW•cm -1 •K -2 •s -1 .When comparing the positive and negative regions of the power factor, the former has a higher maxima value of 1 10 11 μW•cm -1 •K -2 •s -1 .The electronic thermal conductivity (σ/τ) is shown against chemical potential and carrier concentration in the Figure 6(b) for various temperatures.This graph shows how thermal conductivity increases with temperature.Therefore, 300 K is the optimum temperature for minimising electronic thermal conductivity (σ/τ).Heat conductivity increases with increasing chemical potential.In the E−EF range of +0.3 Ry to +0.65 Ry, the thermal conductivity is zero at 300 K.The chemical potential (μ) versus S from -0.1 Ry to +0.1 Ry is exhibited in the Figure 6(c).In the vicinity of the Fermi zone, the Seebeck coefficient has two peaks in the range of −300 Ry to +300 Ry; outside of this range, the Seebeck coefficient rapidly approaches zero.Due to an increment in thermal energy, S decreases as temperature rises.It points to the fact that CIS possesses superior TE characteristics.For temperatures between 300 K and 800 K, the maximum value of S is found as 300 μV•K -1 .A reduction in S to −300 μV•K -1 occurs at higher temperature of 800 K. Thus, CIS exhibits 350 μV•K -1 for the negative S peak and 750 μV•K -1 for the positive S peak at 300 K.
The figure of merit (zT) of a material quantifies its TE efficiency.The zT value is related to the absolute temperature as below [23], zT = S 2 σT k (5) The Figure 7 exhibits the variation of zT values with temperature (K).The zT values are found to increase with temperature.The maximum zT value is predicted as 1.04 10 -4 at 800 K, while it is 1.79 10 -5 at ambient temperature which agrees well with experimental findings of zT (~3.99 10 -4 at 423 K) [24].It affirms to the fact that CIS is a good TE material to be employed in various TE applications.

Conclusion
Boltzmann computation via first principle approach using DFT reveals that the CIS material exhibits higher TE characteristics with the greatest magnitude of S found at 800 K.The material is found to be n-type with electrons as majority charge carriers.Electrical conductivity values decrease as temperature increases, while thermal conductivity values increase with increasing temperature.The highest value of χ at 550 K is estimated as 1.795 x 10 -9 m 3 •mol -1 .The maximum power factor is estimated as 9 x 10 11 μW•cm -1 •K -2 •s -1 having negative chemical potential at 800 K.The maximum zT value is predicted as 1.04 x 10 -4 at 800 K.This research indicates that CIS has a high potential to be applicable in the field of TE power generation.Although further studies are needed to enhance TE features of CIS by using suitable dopants.

Figure 5 .
Figure 5. Variation of Pauli magnetic susceptibility (χ) with T (K).The Figure6(a) displays power factor values (PF/τ) related to chemical potential with respect to Fermi level.To what extent may TE material functions efficiently is investigated.The Figure6(a) shows that as temperatures rise, the power factors also rise accordingly.The maximum power factor is estimated as 9 10 11 μW•cm -1 •K -2 •s -1 with a negative chemical potential at 800 K.There has been a little decrement in the factor, which now stands at 2.5 10 11 μW•cm -1 •K -2 •s -1 .When comparing the positive and negative regions of the power factor, the former has a higher maxima value of 1 10 11 μW•cm -1 •K -2 •s -1 .The electronic thermal conductivity (σ/τ) is shown against chemical potential and carrier concentration in the Figure6(b) for various temperatures.This graph shows how thermal conductivity increases with temperature.Therefore, 300 K is the optimum temperature for minimising electronic thermal conductivity (σ/τ).Heat conductivity increases with increasing chemical potential.In the E−EF range of +0.3 Ry to +0.65 Ry, the thermal conductivity is zero at 300 K.The chemical potential (μ) versus S from -0.1 Ry to +0.1 Ry is exhibited in the Figure6(c).In the vicinity of the Fermi zone, the Seebeck coefficient has two peaks in the range of −300 Ry to +300 Ry; outside of this range, the Seebeck coefficient rapidly approaches zero.Due to an increment in thermal energy, S decreases as temperature rises.It points to the fact that CIS possesses superior TE characteristics.For temperatures between 300 K and 800 K, the maximum value of S is found as 300 μV•K -1 .A reduction in S to −300 μV•K -1 occurs at higher temperature of 800 K. Thus, CIS exhibits 350 μV•K -1 for the negative S peak and 750 μV•K -1 for the positive S peak at 300 K.

6 Figure 6 .
Figure 6.The BoltzTraP plots of (a) power factor, (b) electrical conductivity, and (c) Seebeck coefficient as a function of E-EF (Ry).

Figure 7 .
Figure 7.The zT values of CIS as a function of T (K).