Improved Thermoelectric Properties of SrTiO3 via (La, Dy and N) Co-Doping: DFT Approach

This work considers the enhancement of the thermoelectric figure of merit, ZT, of SrTiO3 (STO) semiconductors by (La, Dy and N) co-doping. We have focused on SrTiO3 because it is a semiconductor with a high Seebeck coefficient compared to that of metals. It is expected that SrTiO3 can provide a high power factor, because the capability of converting heat into electricity is proportional to the Seebeck coefficient squared. This research aims to improve the thermoelectric performance of SrTiO3 by replacing host atoms by La, Dy and N atoms based on a theoretical approach performed with the Vienna Ab Initio Simulation Package (VASP) code. Here, undoped SrTiO3, Sr0.875La0.125TiO3, Sr0.875Dy0.125TiO3, SrTiO2.958N0.042, Sr0.750La0.125Dy0.125TiO3 and Sr0.875La0.125TiO2.958N0.042 are studied to investigate the influence of La, Dy and N doping on the thermoelectric properties of the SrTiO3 semiconductor. The undoped and La-, Dy- and N-doped STO structures are optimized. Next, the density of states (DOS), band structures, Seebeck coefficient, electrical conductivity per relaxation time, thermal conductivity per relaxation time and figure of merit (ZT) of all the doped systems are studied. From first-principles calculations, STO exhibits a high Seebeck coefficient and high figure of merit. However, metal and nonmetal doping, i.e., (La, N) co-doping, can generate a figure of merit higher than that of undoped STO. Interestingly, La, Dy and N doping can significantly shift the Fermi level and change the DOS of SrTiO3 around the Fermi level, leading to very different thermoelectric properties than those of undoped SrTiO3. All doped systems considered here show greater electrical conductivity per relaxation time than undoped STO. In particular, (La, N) co-doped STO exhibits the highest ZT of 0.79 at 300 K, and still a high value of 0.77 at 1000 K, as well as high electrical conductivity per relaxation time. This renders it a viable candidate for high-temperature applications.


Introduction
SrTiO 3 (STO), a semiconductor with a 3.2 eV [1] indirect bandgap (E g ) and a perovskite structure, has received much research attention. This is due to its outstanding properties. Researchers are presently trying to improve its properties, such as bandgap width, electrical conductivity, thermal conductivity, and effective mass, to enhance the performance of STO in applications such as dye-sensitized solar cells [2][3][4], photocatalysis [5][6][7], water splitting [8,9], hydrogen production [10] and thermoelectric devices [11][12][13]. There is growing interest in using STO as a catalyst for photocatalytic processes because of its semiconducting properties, thermal stability and photocorrosion resistance. However, the bandgap of this  The total density of states (TDOS) of the undoped SrTiO3 is illustrated in Figure 3a. Red dashed lines at x = 0 represent Fermi levels. The Fermi level (Ef) is 7.27 eV, and this is the conduction band minimum. Therefore, undoped SrTiO3 exhibits n-type behavior, in agreement with experimental measurements and other literature reports [34,35].
After La doping, the highest state that the carriers occupy is the ground state or Fermi level (Ef), located at the bottom of the conduction band, at 8.00 eV, as seen in Figure 3c,d. Ef shifts to higher energy compared to undoped SrTiO3. This is caused by an increase of the number of electrons in the system when La is doped into SrTiO3. The electron configuration of Sr is Kr 5s 2 , while that of La is Kr 4d 10 5s 2 5p 6 5d 1 6s 2 . In other words, the oxidation number of La is +3, while it is +2 for Sr. Thus, La doping is electron doping. Likewise, Ef shifts to 7.79 eV with electron doping for Dy doping on the Sr site because Dy and La have the same oxidation number as previously mentioned. For N doping, the Fermi level shifts from the conduction band to the valence band and new states are found around the valence band maximum in the N mono-doped structures. The Fermi level of N-doped SrTiO3 is 4.48 eV. The Fermi energy shifts to a lower level because oxygen substituted by nitrogen is a p-type doping or hole doping and the number of electrons is reduced. The electron configurations of O and N are He 2s 2 2p 4 and He 2s 2 2p 3 , respectively. Notably, from the PDOS graphs, O and Ti atoms contribute the valence band maximum and conduction band minimum for all mono-doping systems.  For co-doped systems, the total DOS of (La, Dy) and (La, N) co-doped SrTiO3 structures is shown in Figure 4. Ef is shifted to a higher level compared to the STO. The Ef is at 8.22 and 7.78 eV for (La, Dy) and (La, N) co-doping, respectively. Comparing the DOS of the co-doped systems to those of undoped SrTiO3, it can be seen that (La, N) co-doping can induce a new state in the forbidden band, like the N doping. For the DOS of (La, Dy)- For co-doped systems, the total DOS of (La, Dy) and (La, N) co-doped SrTiO 3 structures is shown in Figure 4. E f is shifted to a higher level compared to the STO. The E f is at 8.22 and 7.78 eV for (La, Dy) and (La, N) co-doping, respectively. Comparing the DOS of the co-doped systems to those of undoped SrTiO 3 , it can be seen that (La, N) co-doping can induce a new state in the forbidden band, like the N doping. For the DOS of (La, Dy)-co-doping, not much difference is observed compared to the La and Dy mono-doping. A clear difference in electronic structures is seen for both mono-doping and co-doping, which affects the carrier behavior and is expected to be able to improve the thermoelectric properties of the STO.  The unfolding band structures of undoped and doped SrTiO3 were calculated, and the results are shown in Figures 5 and 6. For the undoped system, the VBM is at the R point, while the CBM is at the Г point. So, SrTiO3 is found to be an indirect bandgap material, in agreement with previous experimental and theoretical reports [36,37]. Similar to SrTiO3, La-doped SrTiO3 and Dy-doped SrTiO3 show an indirect bandgap. The results we obtain from the band structure calculations are similar to those obtained from the DOS. N-doped SrTiO3 has states above the valence band near Ef. New states above the valence band are found for N doping, leading to a narrower bandgap than undoped SrTiO3, in agreement with the previous theoretical and experimental studies [38,39]. This step above the valence band is also observed in (La, N)-co-doped systems, corresponding to the DOS.
From the study of electronic properties, we can conclude that the dopant atoms added into SrTiO3 can change the electronic behavior, as predicted from the DOS and band structure of SrTiO3. From the DOS we can group the systems for this study as STO and (La, N)-co-doped STO are the n-type semiconductors while N-STO is the p-type semiconductor. La-, Dy-, and (La, Dy)-doped STO are metallic materials. Due to the significant change in DOS after La, Dy and N atoms are added into the STO, it is possible that all systems, especially N-STO and (La, N)-co-doped STO, will show different thermoelectric properties because of the change in the number of carriers in the materials. The unfolding band structures of undoped and doped SrTiO 3 were calculated, and the results are shown in Figures 5 and 6. For the undoped system, the VBM is at the R point, while the CBM is at the Г point. So, SrTiO 3 is found to be an indirect bandgap material, in agreement with previous experimental and theoretical reports [36,37]. Similar to SrTiO 3 , La-doped SrTiO 3 and Dy-doped SrTiO 3 show an indirect bandgap. The results we obtain from the band structure calculations are similar to those obtained from the DOS. N-doped SrTiO 3 has states above the valence band near E f . New states above the valence band are found for N doping, leading to a narrower bandgap than undoped SrTiO 3 , in agreement with the previous theoretical and experimental studies [38,39]. This step above the valence band is also observed in (La, N)-co-doped systems, corresponding to the DOS.  Thermoelectric properties calculated using the BoltzTraP code are shown in Figures 7, 8 and S16-S19. As seen in Figure 7a, almost all materials, except N-doped STO, show a negative Seebeck coefficient, making them n-type semiconductors, in agreement with the DOS results and a previous experimental report [14]. N-doped STO is a p-type semiconductor with positive Seebeck coefficient. Undoped STO and (La, N)-co-doped STO exhibit Seebeck coefficients with large magnitudes of more than 200 µV/K and they remain almost constant along the temperature change from 300-1000 K, with about 3 and 30 µV/K changes when the temperature reaches 1000 K for STO and (La, N)-co-doped STO, respectively. At room temperature, Seebeck coefficients of undoped STO and (La, N)-co-doped STO are −245.07 and −253.86.23 µV/K, respectively, and are −243.61 and −222.23 µV/K at 1000 K. For La-, Dy-, N-, and (La, Dy)-doped STO, the magnitudes of the Seebeck coefficient are less than 100 µV/K at room temperature (300 K). These are 50.47, 44.45, 26.34 and 72.17 µV/K for La-, Dy-, N-, and (La, Dy)-doped STO, respectively. However, for the temperature increase to 1000 K, the magnitudes of the Seebeck coefficient increase for La-, Dy, and (La, Dy)-doped STO. These are 113.96, 113.78 and 87.56 µV/K, respectively. Opposite to N-doped STO, the magnitudes of the Seebeck coefficient decrease with an increase in temperature and drop to 26.34 µV/K at 1000 K. Therefore, STO and (La, N) co-doped STO are promising materials that exhibit the greatest capability to transform a temperature gradient into an electromotive force or voltage. Figure 7b shows the ratio of an electrical conductivity to relaxation time (σ/τ) for the STO and doped STO materials. STO and (La, N)-co-doped STO have the smallest σ/τ, opposite to the Seebeck coefficient. The highest σ/τ is for (La, Dy)-co-doped STO, followed by Dy-and La-doped STO. Although strange atom doping cannot improve the magnitude of the Seebeck coefficient of STO, La, Dy, and N can efficiently improve the electrical conductivity compared to undoped STO. This means that an increase in number of carriers for both hole and electron doping can improve carrier mobility and support the electrical conductivity when the relaxation time is fixed. The reason for the greater Seebeck coefficient but lower electrical conductivity per relaxation time in STO and (La, N)-co-doped STO compared to the other doping systems is that both STO and (La, N)-co-doped STO are semiconductors. Ef is at the bottom of CBM, while the La-, Dy-, N-and (La, Dy)-doped STO shows metallic behavior, as seen in the DOS. Normally, metals have high electrical conductivity but low Seebeck coefficients, while semiconductors have poorer electrical conductivity but higher Seebeck coefficients compared to metals. Since the Seebeck From the study of electronic properties, we can conclude that the dopant atoms added into SrTiO 3 can change the electronic behavior, as predicted from the DOS and band structure of SrTiO 3 . From the DOS we can group the systems for this study as STO and (La, N)-co-doped STO are the n-type semiconductors while N-STO is the p-type semiconductor. La-, Dy-, and (La, Dy)-doped STO are metallic materials. Due to the significant change in DOS after La, Dy and N atoms are added into the STO, it is possible that all systems, especially N-STO and (La, N)-co-doped STO, will show different thermoelectric properties because of the change in the number of carriers in the materials.
Thermoelectric properties calculated using the BoltzTraP code are shown in Figure 7, Figure 8 and Figures S16-S19. As seen in Figure 7a, almost all materials, except N-doped STO, show a negative Seebeck coefficient, making them n-type semiconductors, in agreement with the DOS results and a previous experimental report [14]. N-doped STO is a p-type semiconductor with positive Seebeck coefficient. Undoped STO and (La, N)-codoped STO exhibit Seebeck coefficients with large magnitudes of more than 200 µV/K and they remain almost constant along the temperature change from 300-1000 K, with about 3 and 30 µV/K changes when the temperature reaches 1000 K for STO and (La, N)-co-doped STO, respectively. At room temperature, Seebeck coefficients of undoped STO and (La, The ratio of electronic thermal conductivity to relaxation time (κe/τ) trends are the same as for σ/τ. This is because both κe/τ and σ/τ variations are effects that arise from electron motion. It was observed that STO, N-STO and (La, N)-co-doped STO show a small value of κe/τ while La-STO, Dy-STO and (La, Dy)-co-doped STO show larger values. Clearly, doping with N or (La, N) can reduce the electronic thermal conductivity. It therefore seems like N plays a more important role than La and Dy in changing the carrier mobility, including the electrical and thermal conductivity of STO. The numerical results obtained in this study are in agreement with Chen et al. [17]. They reported theoretical results that La mono-doping provided a negative Seebeck coefficient, similar to undoped SrTiO3 as well as the small negative value (−50 µV/K) of the Seebeck coefficient being obtained from the calculations [17]. Comparing the Seebeck coefficients reported by Chen et al. [17] and those found in our work, the differences result from the methodology in the calculation. The energy cutoff of 600 eV, with GGA and k- points of 9 × 9 × 24, were employed in the calculation [17], while an energy cutoff of 500 eV, with GGA+U in PBE and k-points of 27 × 27 × 27, are treated in our work. Normally, the number of k-points is sensitive to the Fermi level, resulting in the change to transport properties of the carriers. The enhancement in electrical conductivity after La is doped into STO is also found in an experiment reported by Lv [41]. They revealed that the electrical conductivity of 20% La doping into STO is the highest value compared to 10%, 30% and 40% La doping. This results from an electric neutral imbalance of replacing Sr 2+ by La 3+ . It therefore affects the oxidation number of Ti and conductivity [41]. The thermal to electrical energy conversion is described by the figure of merit, ZT. By definition, ZT = S 2 σT/κ, where T is the temperature, S is the Seebeck coefficient, σ is the electrical conductivity, and κ is the thermal conductivity. The ZT values reported here are calculated for electronic thermal conductivity only, and do not include lattice thermal conductivity. Figure 8 shows the ZT of doped and undoped STO calculated using σ/τ and κe/τ. However, since the relaxation times for σ and κe are equal, the factors of τ cancel out, and the ZT is independent of this value. The maximum values of ZT for STO, La-STO, Dy-STO, N-STO, (La, Dy)-STO and (La, N)-STO are 0.77, 0.45, 0.40, 0.14, 0.33, and 0.79, respectively. The ZT of (La, N)-co-doped STO is better than for undoped STO. The huge ZT of undoped STO and (La, N)-co-doped STO results from the massive magnitude of Seebeck coefficients, as previously mentioned. Here, the most interesting material is (La, N)-codoped STO. It shows a ZT value in the range 0.77-0.79 in the temperature interval of 300-1000 K, which is always nigher than that of undoped STO at all temperatures. Interestingly, even though their ZT values are less than that of STO, the ZT values of La-and Dy-doped STO increase with temperatures up to 1000 K. Considering the previous experimental results, Lu et al. [42] experimentally studied the thermoelectric properties of STO and La-doped STO ceramics, Sr1−3x/2LaxTiO3−δ for x in the range 0.10-0.30. The magnitude of the Seebeck coefficient of undoped STO is 300-400 µV/K at temperatures of 450-1000 K, close to our theoretical results. After La is doped into the STO ceramic, the measured magnitude of the Seebeck coefficient is smaller than that  Figure 7b shows the ratio of an electrical conductivity to relaxation time (σ/τ) for the STO and doped STO materials. STO and (La, N)-co-doped STO have the smallest σ/τ, opposite to the Seebeck coefficient. The highest σ/τ is for (La, Dy)-co-doped STO, followed by Dy-and La-doped STO. Although strange atom doping cannot improve the magnitude of the Seebeck coefficient of STO, La, Dy, and N can efficiently improve the electrical conductivity compared to undoped STO. This means that an increase in number of carriers for both hole and electron doping can improve carrier mobility and support the electrical conductivity when the relaxation time is fixed. The reason for the greater Seebeck coefficient but lower electrical conductivity per relaxation time in STO and (La, N)-co-doped STO compared to the other doping systems is that both STO and (La, N)co-doped STO are semiconductors. E f is at the bottom of CBM, while the La-, Dy-, Nand (La, Dy)-doped STO shows metallic behavior, as seen in the DOS. Normally, metals have high electrical conductivity but low Seebeck coefficients, while semiconductors have poorer electrical conductivity but higher Seebeck coefficients compared to metals. Since the Seebeck coefficient is functional to mobility, semiconductors have better Seebeck coefficient than the metals [40].
The ratio of electronic thermal conductivity to relaxation time (κ e /τ) trends are the same as for σ/τ. This is because both κ e /τ and σ/τ variations are effects that arise from electron motion. It was observed that STO, N-STO and (La, N)-co-doped STO show a small value of κ e /τ while La-STO, Dy-STO and (La, Dy)-co-doped STO show larger values. Clearly, doping with N or (La, N) can reduce the electronic thermal conductivity. It therefore seems like N plays a more important role than La and Dy in changing the carrier mobility, including the electrical and thermal conductivity of STO.
The numerical results obtained in this study are in agreement with Chen et al. [17]. They reported theoretical results that La mono-doping provided a negative Seebeck coefficient, similar to undoped SrTiO 3 as well as the small negative value (−50 µV/K) of the Seebeck coefficient being obtained from the calculations [17]. Comparing the Seebeck coefficients reported by Chen et al. [17] and those found in our work, the differences result from the methodology in the calculation. The energy cutoff of 600 eV, with GGA and k-points of 9 × 9 × 24, were employed in the calculation [17], while an energy cutoff of 500 eV, with GGA+U in PBE and k-points of 27 × 27 × 27, are treated in our work. Normally, the number of k-points is sensitive to the Fermi level, resulting in the change to transport properties of the carriers. The enhancement in electrical conductivity after La is doped into STO is also found in an experiment reported by Lv [41]. They revealed that the electrical conductivity of 20% La doping into STO is the highest value compared to 10%, 30% and 40% La doping. This results from an electric neutral imbalance of replacing Sr 2+ by La 3+ . It therefore affects the oxidation number of Ti and conductivity [41].
The thermal to electrical energy conversion is described by the figure of merit, ZT. By definition, ZT = S 2 σT/κ, where T is the temperature, S is the Seebeck coefficient, σ is the electrical conductivity, and κ is the thermal conductivity. The ZT values reported here are calculated for electronic thermal conductivity only, and do not include lattice thermal conductivity. Figure 8 shows the ZT of doped and undoped STO calculated using σ/τ and κ e /τ. However, since the relaxation times for σ and κ e are equal, the factors of τ cancel out, and the ZT is independent of this value. The maximum values of ZT for STO, La-STO, Dy-STO, N-STO, (La, Dy)-STO and (La, N)-STO are 0.77, 0.45, 0.40, 0.14, 0.33, and 0.79, respectively. The ZT of (La, N)-co-doped STO is better than for undoped STO. The huge ZT of undoped STO and (La, N)-co-doped STO results from the massive magnitude of Seebeck coefficients, as previously mentioned. Here, the most interesting material is (La, N)-co-doped STO. It shows a ZT value in the range 0.77-0.79 in the temperature interval of 300-1000 K, which is always nigher than that of undoped STO at all temperatures. Interestingly, even though their ZT values are less than that of STO, the ZT values of Laand Dy-doped STO increase with temperatures up to 1000 K.
Considering the previous experimental results, Lu et al. [42] experimentally studied the thermoelectric properties of STO and La-doped STO ceramics, Sr 1−3x/2 La x TiO 3−δ for x in the range 0.10-0.30. The magnitude of the Seebeck coefficient of undoped STO is 300-400 µV/K at temperatures of 450-1000 K, close to our theoretical results. After La is doped into the STO ceramic, the measured magnitude of the Seebeck coefficient is smaller than that of the undoped STO, exhibiting the same trend as the theoretical results obtained in our work. For electrical conductivity, the smallest values are observed in the undoped STO compared to the La-doped STO for temperatures in the range 450-1000 K [42]. The electrical conductivity measured in the experiment also shows the same trend as the electrical conductivity per relaxation time obtained from the theoretical results of our work. In the case of thermal conductivity, the experiment revealed that the highest thermal conductivity is observed in undoped STO compared to La-doped STO, the opposite trend to that predicted by the theoretical calculations of our work. It is possible that only the electronic thermal conductivity is included in the calculation. Phonon or heat transfer caused by lattice vibrations is not included in our predictions, while it is included in the experiment.
The ZT of the STO observed from the experiment is less than 0.05 and this value is quite constant during an increase in temperatures [42]. The trends and values of the ZT obtained from experimental and theoretical approaches in our work are similar. Comparing the ZT of (La, Dy)-co-doping in experimental and theoretical studies, the experiment revealed that ZT values rise with an increase in the temperature from 300 to 900 K [20]. After that, it is almost constant when the temperature increases, and reaches of 0.22 at 1000 K [20]. These experimental results are quite close to the computational results found in our work. Specifically, here the ZT of (La, Dy)-co-doped STO is predicted to increase with an increase in temperature between 300-1000 K. The ZT starts from 0.21 at 300 K and it continually increases until reaching 0.33 at 1000 K. Because our theoretical results are corresponding to experiments, our theoretical approach is based on the VASP and BoltzTrap codes which can provide reliable results to guide experimentalists in improving the electronic and thermoelectric properties of semiconductors.
From the ZT values calculated in our theoretical study, (La, N)-co-doped STO is the best potential candidate for thermoelectric applications. These results reveal that codoping with metal and nonmetal (La and N) can significantly improve the thermoelectric performance of STO. Notably, metal-nonmetal doping can improve the ZT of STO more than metal-metal (La and Dy) doping. These improved thermoelectric properties result from an increased number of carriers for both electrons and holes in the STO. A larger number of carriers means greater electron motion, resulting in higher thermal to electrical energy conversion. The reason that (La, N)-co-doped STO possesses a large value of the ZT is that it has a large Seebeck coefficient. Additionally, the high absolute value of the Seebeck coefficient results from a large difference in the number of carriers in the system. La and N co-doping of STO can improve the number of carriers because electrons and holes are the majority of carriers for La and N when they respectively replace Sr and O. Thus, when La and N are doped into STO, added carriers greatly affect the host material. However, lattice thermal conductivity should be included in further studies because it will make the results more reliable.

Conclusions
In this study, we aimed to improve the thermoelectric properties of STO via co-doping of La, Dy and N. We studied undoped and (La, Dy and N)-doped STO, using the firstprinciples approach to calculate the DOS, band structures and thermoelectric properties. To model the STO and doped STO supercells, the formation energy and the total energy for replacing the strange atoms by different host atoms were studied to examine the most stable structures and the possibility to synthesize these materials in the experiments. From the total DOS and band structure results, we found that appropriate atom doping can shift the Fermi level and change the electronic band structures, resulting in enhancement of the thermoelectric properties of STO due to a greater number of charge carriers in the system. Very large Seebeck coefficients and a very low ratio of thermal conductivity to relaxation time were investigated for (La, N)-co-doping into STO. The thermoelectric performance of the co-doped systems is better than that of the undoped STO. Thus, it can be concluded that our work successfully predicts the improved thermoelectric performance and figure of merit, ZT, as a result of (La and N) doping of STO. The best material is predicted to be (La, N)-co-doped STO. It has a ZT value of 0.79 which is greater than that of undoped STO and still exhibits a high ZT at 1000 K. The work demonstrates the successful synergy of La and N in improving the thermoelectric properties of the STO, which has not been reported before. This can help guide experimental and theoretical research to reach ultrahigh ZT and to produce efficient thermoelectric devices for applications in the modern world.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules27227923/s1, Figure S1: The optimized structures of La-doped SrTiO 3 after replacing La atoms in Sr, Ti, and O sites with formation energy (E form ) as the total energy as listed in Table S2. The pink spheres are the O atoms, yellow are Sr, light blue are Ti, and green are La. E min indicates the structure providing the lowest formation energy. Figure  S2: The optimized structures of Dy-doped SrTiO3 after replacing Dy atoms in Sr, Ti, and O sites with formation energy (E form ) as the total energy as listed in Table S2. The pink spheres are the O atoms, yellow are Sr, light blue are Ti, and grey are Dy. E min indicates the structure providing the lowest formation energy. Figure S3: The optimized structures of N-doped SrTiO3 after replacing N atoms in Sr, Ti, and O sites with formation energy (E form ) as the total energy as listed in Table S2. The pink spheres are the O atoms, yellow are Sr, light blue are Ti, and orange are N. E min indicates the structure providing the lowest formation energy. Figure S4: Three different La-N distances, with the total energy of the supercell configuration, for 3 different sites of La and N doping, in which both La and N atoms replace Sr and O sites, respectively. E min indicates the structure providing the lowest total energy, which is the most stable structure. Figure S5: Three different La-Dy distances, with the total energy of the supercell configuration, for 3 different sites of La and Dy doping, in which both La and Dy atoms replace Sr sites. E min indicates the structure providing the lowest total energy, which is the most stable structure. Figure Table S1: Amount of doping of La, Dy and N in SrTiO 3 . Table S2: Total energy (E tot ), total energy per atom (E atom ), and formation energy (E form ) of the host sites replaced by La, Dy and N atoms. The number in the parentheses gives the total number of atoms in the bulk structure. The bold numbers for E form representing the lowest values, indicating the most stable structures in experiments. Table S3: Lattice parameters of the most stable structures for undoped and doped SrTiO 3 [43,44].